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increase tolerance of doctests in modular/modform/numerical.py #33353

@mwageringel

Description

@mwageringel

Part of #32544.

sage -t --long --random-seed=274324363002908225943176410710152162058 src/sage/modular/modform/numerical.py
**********************************************************************
File "src/sage/modular/modform/numerical.py", line 447, in sage.modular.modform.numerical.NumericalEigenforms.systems_of_eigenvalues
Failed example:
    numerical_eigenforms(61).systems_of_eigenvalues(10)  # rel tol 1e-11
Expected:
    [
    [-1.4811943040920152, 0.8060634335253695, 3.1563251746586642, 0.6751308705666477],
    [-1.0, -2.0000000000000027, -3.000000000000003, 1.0000000000000044],
    [0.3111078174659775, 2.903211925911551, -2.525427560843529, -3.214319743377552],
    [2.170086486626034, -1.7092753594369208, -1.63089761381512, -0.46081112718908984],
    [3.0, 4.0, 6.0, 8.0]
    ]
Got:
    [
    [-1.4811943039966973, 0.8060634334597021, 3.1563251745336816, 0.6751308705369921],
    [-1.0, -2.0, -3.0, 1.0],
    [0.31110781746598, 2.903211925911552, -2.525427560843522, -3.214319743377545],
    [2.170086486660904, -1.709275359460946, -1.6308976138608664, -0.46081112719995876],
    [3.0, 4.0, 6.0, 8.0]
    ]
Tolerance exceeded in 8 of 20:
    -1.4811943040920152 vs -1.4811943039966973, tolerance 7e-11 > 1e-11
    0.8060634335253695 vs 0.8060634334597021, tolerance 9e-11 > 1e-11
    3.1563251746586642 vs 3.1563251745336816, tolerance 4e-11 > 1e-11
    0.6751308705666477 vs 0.6751308705369921, tolerance 5e-11 > 1e-11
    2.170086486626034 vs 2.170086486660904, tolerance 2e-11 > 1e-11
    -1.7092753594369208 vs -1.709275359460946, tolerance 2e-11 > 1e-11
    -1.63089761381512 vs -1.6308976138608664, tolerance 3e-11 > 1e-11
    -0.46081112718908984 vs -0.46081112719995876, tolerance 3e-11 > 1e-11
**********************************************************************
File "src/sage/modular/modform/numerical.py", line 474, in sage.modular.modform.numerical.NumericalEigenforms.systems_of_abs
Failed example:
    numerical_eigenforms(61).systems_of_abs(10)  # rel tol 1e-11
Expected:
    [
    [0.3111078174659775, 2.903211925911551, 2.525427560843529, 3.214319743377552],
    [1.0, 2.0000000000000027, 3.000000000000003, 1.0000000000000044],
    [1.4811943040920152, 0.8060634335253695, 3.1563251746586642, 0.6751308705666477],
    [2.170086486626034, 1.7092753594369208, 1.63089761381512, 0.46081112718908984],
    [3.0, 4.0, 6.0, 8.0]
    ]
Got:
    [
    [0.31110781746598, 2.903211925911552, 2.525427560843522, 3.214319743377545],
    [1.0, 2.0, 3.0, 1.0],
    [1.4811943039966973, 0.8060634334597021, 3.1563251745336816, 0.6751308705369921],
    [2.170086486660904, 1.709275359460946, 1.6308976138608664, 0.46081112719995876],
    [3.0, 4.0, 6.0, 8.0]
    ]
Tolerance exceeded in 8 of 20:
    1.4811943040920152 vs 1.4811943039966973, tolerance 7e-11 > 1e-11
    0.8060634335253695 vs 0.8060634334597021, tolerance 9e-11 > 1e-11
    3.1563251746586642 vs 3.1563251745336816, tolerance 4e-11 > 1e-11
    0.6751308705666477 vs 0.6751308705369921, tolerance 5e-11 > 1e-11
    2.170086486626034 vs 2.170086486660904, tolerance 2e-11 > 1e-11
    1.7092753594369208 vs 1.709275359460946, tolerance 2e-11 > 1e-11
    1.63089761381512 vs 1.6308976138608664, tolerance 3e-11 > 1e-11
    0.46081112718908984 vs 0.46081112719995876, tolerance 3e-11 > 1e-11
**********************************************************************

Component: numerical

Author: Markus Wageringel

Branch/Commit: 1882e1c

Reviewer: Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/33353

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