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lfunc_lfunctions • Show schema
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{'Lhash': '1901548128389395730322744544977', 'a10': [1.1209954597689475, 1.9347788450304613], 'a2': [-0.8660254037844386, 0.5], 'a3': [-0.9659258262890683, -0.25881904510252074], 'a4': [0.5, -0.8660254037844386], 'a5': [-0.003421123171694694, -2.236065360385569], 'a6': [0.9659258262890683, -0.25881904510252074], 'a7': [-1.8805672546084804, 3.257238032032205], 'a8': [0.0, 1.0], 'a9': [0.8660254037844386, 0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, -0.5]]], [3, [[1.0, 0], [0.9659258262890683, 0.25881904510252074]]], [5, [[1.0, 0], [0.003421123171694694, 2.236065360385569]]], [13, [[1.0, 0], [0.44022443280769064, 3.578575477583105]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '390.37', 'coefficient_field': 'CDF', 'conductor': 390, 'conductor_radical': 390, 'conjugate': '839833209901506981981467506630', 'degree': 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[-92.66471820493493, -53.5]], [[1.0, 0], [-4.691572752852352, 4.691572752852352], [0, -109.0]], [[1.0, 0], [5.278309837936905, 19.698920493271174], [-97.86087062764156, 56.5]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-390-65.37-c1-0-4', '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/390/2/bd/b/37/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7111365358052243, 0.7967925516915919, 0.8735512744847526, 0.9397446617877062, 0.9910803149741232, 1.0210670051720574, 1.0217090178163555, 0.9843552580447894, 0.9006364832304379, 0.7634552336795077, 0.5679956027870127, 0.31270240515186093, 0.00015459234843937406, -0.3622638917841322, -0.7620046689537723, -1.181414108991342, -1.5983006299506535, -1.987064945343682, -2.32039738174099, 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'4.07507847559208165149452158935276', '6.24438888967346761978428153756614', '6.67174001394155436365267124998760', '7.59032329166771871375464540751357', '9.003190821047877794294532708040919', '9.864029654973386906104943234912069', '10.58671441542891930733189733406938', '11.24298022563686024567516477638005'], 'prelabel': '2-390-65.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': 0.35538532589535643, 'root_number': '0.4388517521687112 + 0.8985594802896757*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.177692662948', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.50005697788257949315816997977', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.52446381431592051465974289861', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.07507847559208165149452158935', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'bad_primes': [2, 3, 5, 13], 'central_character': '65.37', 'conductor': 390, 'conductor_radical': 390, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/bd/b/37/2'], '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': '2-390-65.37-c1-0-4', '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': '2-390-65.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': 0.17769266294767821, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.50005697788257949315816997977', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1901548128389395730322744544977', 'Lhash_array': ['1901548128389395730322744544977'], 'label': '2-390-65.37-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/bd/b/37/2'}