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lfunc_lfunctions • Show schema
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{'Lhash': '1622582617056469399784964689100', 'a10': [0.0, 0.0], 'a2': [2.7925842604078706, 0.748270697372153], 'a3': [-5.184194694347295, -0.35231430726179175], 'a4': [0.3104145846564572, 0.17921794401179145], 'a5': [0.0, 0.0], 'a6': [-14.21367403393528, -4.863048368428048], 'a7': [-5.033744196984112, 18.786189095449707], 'a8': [-15.621753156920379, -15.621753156920379], 'a9': [26.751749257797286, 3.6529319248984473], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.275429751291645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [5.184194694347295, 0.35231430726179175]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '225.32', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '1008134475771191790885532802668', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.7925842604078706, -0.748270697372153], [6.928203230275509, 4.0]], [[1.0, 0], [5.184194694347295, 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'5.49320464577420818178027997598834', '6.48950201698515791034416326979547', '7.54329949238210053787147013202808', '9.173412282151890840809543158963708', '10.23732968266080090582627891888311', '11.10234528119388134039382501909101', '12.23474847860398105277568957156879'], 'prelabel': '2-15e2-45.32-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': 0.1638504567886122, 'root_number': '0.8704151438335941 + 0.49231847150512625*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0819252283943', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27999199208704480044451175198', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.65449662802699440441879699088', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.27051690150203315557181632738', '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': '45.32', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/4/p/b/32/12'], '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': '2-15e2-45.32-c3-0-30', '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': '2-15e2-45.32-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': 0.0819252283943061, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27999199208704480044451175198', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1622582617056469399784964689100', 'Lhash_array': ['1622582617056469399784964689100'], 'label': '2-15e2-45.32-c3-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/4/p/b/32/12'}