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lfunc_lfunctions • Show schema
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{'Lhash': '2777563384356075239037164613579', 'a10': [-0.12591284424533725, -0.2653556979952507], 'a2': [-0.0988983986712, -0.4844363975984176], 'a3': [0.9870502626379128, 0.16041128085776024], 'a4': [1.615061157259244, -0.6881132517590937], 'a5': [0.5767848151746002, -0.14216468867352958], 'a6': [-0.019908627349995593, -0.4940274922865111], 'a7': [1.3264989694849152, -2.7955373579823277], 'a8': [-1.0548088395264192, -1.5281544252262664], 'a9': [0.9485364419471455, 0.3166679938014725], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.048415382478917, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.9870502626379128, -0.16041128085776024]]], [13, [[1.0, 0], [2.9338184402072813, 2.095879137712792]]]], 'bad_primes': [3, 13], 'central_character': '507.490', 'coefficient_field': 'CDF', 'conductor': 507, 'conductor_radical': 39, 'conjugate': '1689066557484429060180088901124', 'degree': 2, 'euler_factors': [[[1.0, 0], 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18.905937478717064]], [[1.0, 0], [-2.0611577319096677, 5.434826277058598], [-62.12639209820139, -55.039180633986]], [[1.0, 0], [2.8507614633910143, -4.937663694852641], [-44.5, -77.07626093681505]], [[1.0, 0], [-2.2507786831024585, -7.770589451720876], [-81.9834382977481, 51.843185134396705]], [[1.0, 0], [-0.22588355179352987, 5.605242525238814], [-100.6724881215552, -8.127123440389314]], [[1.0, 0], [-6.0333225617645265, -15.908564147717254], [-77.09660706162342, 68.3016337988019]], [[1.0, 0], [4.264871431431174, -14.724044263802984], [-90.43533915318604, -57.18784339567472]], [[1.0, 0], [-11.971925780768899, 6.2833513614717855], [61.91905739369598, -89.70524138240854]], [[1.0, 0], [4.8783739461875495, -0.7928129324637427], [107.18461794002745, -35.78348329956639]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 30, 'label': '2-507-169.152-c1-0-30', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 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'root_angle': 0.35545767342472173, 'root_number': '0.4386475104256698 + 0.8986592021435945*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.177728836712', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.19111116569187065353699614422', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.67553662132152456602292146699', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.40480505972086287663753000875', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.048415382478917, 'bad_primes': [3, 13], 'central_character': '169.152', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/2/q/b/490/7'], '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': '2-507-169.152-c1-0-30', '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': '2-507-169.152-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': 0.17772883671236087, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.19111116569187065353699614422', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2777563384356075239037164613579', 'Lhash_array': ['2777563384356075239037164613579'], 'label': '2-507-169.152-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/2/q/b/490/7'}