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lfunc_lfunctions • Show schema
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{'Lhash': '1277719796593067305852369473304', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [3.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-5.0, 0.0], 'a6': [0.0, 0.0], 'a7': [12.867962264113208, 0.0], 'a8': [0.0, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 56.64183360551102, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-3.0, 0]]], [5, [[1.0, 0], [5.0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '960.1', 'coefficient_field': 'CDF', 'conductor': 960, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [5.0, 0]], [[1.0, 0], [-12.867962264113208, 0], [343.0, 0]], [[1.0, 0], [-49.73592452822641, 0], [1331.0, 0]], [[1.0, 0], [-52.60388679233962, 0], [2197.0, 0]], [[1.0, 0], [-84.60388679233962, 0], [4913.0, 0]], [[1.0, 0], [26.603886792339623, 0], [6859.0, 0]], [[1.0, 0], [136.33981132056604, 0], [12167.0, 0]], 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[1295029.0, 0]], [[1.0, 0], [1557.8116603770188, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 22, 'label': '2-960-1.1-c3-0-22', 'leading_term': '3.14270151231276004084201154080', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/960/4/a/bn/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [3.14270151231276, 3.1283034779459795, 3.085263805881461, 3.01404619663385, 2.9154247336180243, 2.790485381456685, 2.6406273512849796, 2.4675636435339157, 2.2733199405908318, 2.060230924124549, 1.8309330399344552, 1.5883527303045173, 1.3356892015161126, 1.0763908920866854, 0.8141249534441481, 0.5527392455546231, 0.2962165805320644, 0.04862121126977082, -0.18596214765224803, -0.4034961713717347, -0.600064736033147, -0.7719514614451954, 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'5.24619901587105509511186047975290', '6.30992905251377243628461490649688', '7.20266819913761144000692791632966', '8.217707404741600505929734255393495', '8.570282874776049121251227720783592', '9.570700777087837403105439394016575'], 'prelabel': '2-960-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.526076906696543, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.00794319535921415067595237354', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.97286516672397735495687523576', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.60491304426032248986770349818', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 56.64183360551102, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 960, 'conductor_radical': 30, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/960/4/a/bn/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': '2-960-1.1-c3-0-22', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-960-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.526076906696543, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.00794319535921415067595237354', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1277719796593067305852369473304', 'Lhash_array': ['1277719796593067305852369473304'], 'label': '2-960-1.1-c3-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/960/4/a/bn/1/2'}