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lfunc_lfunctions • Show schema
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{'Lhash': '214753866669907624198277762310', 'a10': [1.111446944155215, 5.54935886325888e-61], 'a2': [-1.194296639313865, 0.6895274862001254], 'a3': [-2.8812030140671023, 0.0], 'a4': [-0.04910369154907175, 0.08505008860218279], 'a5': [-0.6979716602027064, -0.40297412590476256], 'a6': [3.441011076881319, -1.9866686715219137], 'a7': [0.0, 0.0], 'a8': [0.0, -2.893543324788413], 'a9': [5.3013308082693555, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-2.365805103344664, -2.720839247913839]]]], 'bad_primes': [7, 13], 'central_character': '637.30', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '1882056457538371211840977264276', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.194296639313865, -0.6895274862001254], [1.0, -1.7320508075688772]], [[1.0, 0], [2.8812030140671023, 0], [3.0, 0]], 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'7.48238386518554884044393973081219', '8.471398001335411889194880443041351', '9.363532218998560009259016612041382', '10.43817994843934870094093200814941'], 'prelabel': '2-637-91.30-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.808445207243818, 'root_number': '-0.8243252081309781 + 0.5661165526990177*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.404222603622', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.16941092966093580448331921964', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.17185208351360676201559859086', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.15668939565791682070067643918', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '91.30', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/u/g/30/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-637-91.30-c1-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-637-91.30-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.404222603621909, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.16941092966093580448331921964', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '214753866669907624198277762310', 'Lhash_array': ['214753866669907624198277762310'], 'label': '2-637-91.30-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/u/g/30/2'}