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lfunc_lfunctions • Show schema
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{'Lhash': '619171817552761895292522571309', 'a10': [20.75458089458499, -46.06140617176392], 'a2': [-0.9395042787861912, -4.420020117961355], 'a3': [-1.0300881497949228, 5.093026448355837], 'a4': [-11.345545892184742, 5.051362481685076], 'a5': [9.015676836767499, 6.611926434479892], 'a6': [23.47905158730135, -0.23190979483439966], 'a7': [13.185551268733574, -7.612681574416941], 'a8': [11.737800611611759, 16.15569654791791], 'a9': [-24.877836807304146, -10.492532382086942], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.275429751291645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0300881497949228, -5.093026448355837]]], [5, [[1.0, 0], [-9.015676836767499, -6.611926434479892]]]], 'bad_primes': [3, 5], 'central_character': '225.4', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '2102240050989969654547738295746', 'degree': 2, 'euler_factors': [[[1.0, 0], 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-0.23900327200142352, 'root_number': '0.7311085816046922 - 0.6822611244266927*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.119501636001', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.48844044048201091522737190865', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.28596645110730923125225633690', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.17708970106190552196981602399', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.275429751291645, 'bad_primes': [3, 5], 'central_character': '225.4', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/4/u/a/4/11'], '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': '2-15e2-225.4-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': '2-15e2-225.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': -0.11950163600071176, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.48844044048201091522737190865', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '619171817552761895292522571309', 'Lhash_array': ['619171817552761895292522571309'], 'label': '2-15e2-225.4-c3-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/4/u/a/4/11'}