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lfunc_lfunctions • Show schema
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{'Lhash': '1193948092015173036854963471585', 'a10': [-0.7728655578293103, 0.0], 'a2': [-0.7728655578293103, 0.0], 'a3': [1.0, 0.0], 'a4': [-1.402678829521189, 0.0], 'a5': [1.0, 0.0], 'a6': [-0.7728655578293103, 0.0], 'a7': [1.6298132716918785, 0.0], 'a8': [2.6298132716918787, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.492847966862398, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '1815.1', 'coefficient_field': 'CDF', 'conductor': 1815, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7728655578293103, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.6298132716918785, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.805357659042378, 0], [13.0, 0]], [[1.0, 0], [2.175544387350499, 0], [17.0, 0]], [[1.0, 0], 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[8.786259705435254, 0], [109.0, 0]], [[1.0, 0], [-12.526633162051498, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 23, 'label': '2-1815-1.1-c1-0-23', 'leading_term': '1.551098460356402993756583237708', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1815/2/a/l/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.551098460356403, 1.5459331087585286, 1.5303359427485839, 1.5040134717441023, 1.466508567504201, 1.4172458651776232, 1.3555904667042122, 1.2809159254760383, 1.1926772885728227, 1.0904851470056518, 0.9741770608368011, 0.8438832472916867, 0.7000839389420342, 0.5436562733787568, 0.3759089458993286, 0.19860315429962502, 0.01395861891479774, -0.17535629406845496, -0.36625105096307903, -0.5552564225617503, -0.7385849684131188, 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'4.60313745511980984402685975464336', '4.86364877590769821777102640764651', '6.05649699975906286599709467032452', '7.40452439086391821040392787310371', '7.64567541403390110697011726259180', '8.613617086914132581731130873397754', '9.385057483733456711529088363270495'], 'prelabel': '2-1815-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.80694732914213, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.941858972653989298969166853147', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.14942376985784947632609425073', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.19192704479617888795970635275', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.492847966862398, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 1815, 'conductor_radical': 165, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1815/2/a/l/1/2'], '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': '2-1815-1.1-c1-0-23', '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': '2-1815-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.80694732914213, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.941858972653989298969166853147', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1193948092015173036854963471585', 'Lhash_array': ['1193948092015173036854963471585'], 'label': '2-1815-1.1-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1815/2/a/l/1/2'}