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lfunc_lfunctions • Show schema
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{'Lhash': '2566540356190789394104334482259', 'a10': [-0.5824329102078061, 3.3031411748085646], 'a2': [-0.9396926207859084, -0.3420201433256687], 'a3': [-1.7147342600337758, 0.24430803807165147], 'a4': [0.766044443118978, 0.6427876096865394], 'a5': [-0.5824329102078061, -3.3031411748085646], 'a6': [1.6948814009594033, 0.35689919680757287], 'a7': [1.4334567872166248, 2.4828199859136437], 'a8': [-0.5, -0.8660254037844386], 'a9': [2.880627165067161, -0.8378467257661936], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.7308837491277904, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9396926207859084, 0.3420201433256687]]], [3, [[1.0, 0], [1.7147342600337758, -0.24430803807165147]]], [19, [[1.0, 0], [4.26775261205342, -0.8867286181866523]]]], 'bad_primes': [2, 3, 19], 'central_character': '342.313', 'coefficient_field': 'CDF', 'conductor': 342, 'conductor_radical': 114, 'conjugate': '301257675171668389331495399208', 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[15.4546878123568, 87.64789001808651]], [[1.0, 0], [3.720531080778144, 1.3541625690655081], [74.30631098254086, 62.35039813959431]], [[1.0, 0], [0.41895808324877465, -0.15248827170777562], [77.37048875501678, -64.92154857834048]], [[1.0, 0], [-3.615001322529393, 6.261365960049594], [-51.5, -89.20061658979718]], [[1.0, 0], [-4.68164328407325, 8.108844030928482], [-53.5, -92.66471820493493]], [[1.0, 0], [14.30442618244039, 5.206385348666427], [83.49884429996861, 70.06384945583278]], [[1.0, 0], [2.9497488814023263, 5.109114932158292], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-342-171.142-c1-0-15', '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/342/2/v/b/313/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': 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'0.475387373314', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.02464334867092419188133423106', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.88737998787247521558158081347', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.27721125373893957416276338236', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.7308837491277904, 'bad_primes': [2, 3, 19], 'central_character': '171.142', 'conductor': 342, 'conductor_radical': 114, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/342/2/v/b/313/2'], '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': '2-342-171.142-c1-0-15', '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': '2-342-171.142-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6525385771980605, 'root_angle': 0.4753873733135286, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.02464334867092419188133423106', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2566540356190789394104334482259', 'Lhash_array': ['2566540356190789394104334482259'], 'label': '2-342-171.142-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/342/2/v/b/313/2'}