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lfunc_lfunctions • Show schema
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{'Lhash': '1128762998865726926833380050773', 'a10': [3841.214872033927, 9787.255875464145], 'a2': [-6.818176145925813, 6.326342942420469], 'a3': [-100.92994780037134, 15.212741903118536], 'a4': [-31.79689698449072, 424.3001030748495], 'a5': [412.98577387555736, -1052.2705905557461], 'a6': [591.9171401283712, -742.2406169037143], 'a7': [5120.083273278775, 3760.100301147684], 'a8': [-5436.625812666622, -6817.313139797208], 'a9': [-8853.112689513826, 2730.823605565277], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.23675597202979, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-5120.083273278775, -3760.100301147684]]]], 'bad_primes': [7], 'central_character': '49.11', 'coefficient_field': 'CDF', 'conductor': 49, 'conductor_radical': 7, 'conjugate': '802617141075435008687484260367', 'degree': 2, 'euler_factors': [[[1.0, 0], [6.818176145925813, -6.326342942420469], [38.26180791624922, -510.5683441567642]], [[1.0, 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'root_number': '0.992533366836545 - 0.12197342217103052*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.01946113359960606', 'prec': 67}, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.890437001065201265245920201865564', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '2.38132589136299558917849307295819', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.74828069581515638686336119415829', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.23675597202979, 'bad_primes': [7], 'central_character': '49.11', 'conductor': 49, 'conductor_radical': 7, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/49/10/g/a/11/17'], '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': '2-7e2-49.11-c9-0-21', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-7e2-49.11-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.023619807671535, 'root_angle': -0.019461133599606058, 'self_dual': False, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '0.890437001065201265245920201865564', 'prec': 117}}
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lfunc_instances • Show schema
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{'Lhash': '1128762998865726926833380050773', 'Lhash_array': ['1128762998865726926833380050773'], 'factors': ['2-7e2-49.11-c9-0-21'], 'label': '2-7e2-49.11-c9-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/49/10/g/a/11/17'}