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lfunc_lfunctions • Show schema
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{'Lhash': '6072853747384959779841591799056', 'a10': [5226781.041007272, 0.0], 'a2': [0.0, -225.68585268183566], 'a3': [1922.6724500404018, -1042.2569979883267], 'a4': [-34550.10410072723, 0.0], 'a5': [0.0, 23159.54225263651], 'a6': [-235222.6593046058, -433919.9713152422], 'a7': [478389.14510799956, 0.0], 'a8': [0.0, 4099832.693879617], 'a9': [2610369.7002887223, -4007837.6317879404], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.729869044557181, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '7.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1922.6724500404018, 1042.2569979883267]]]], 'bad_primes': [3], 'central_character': '3.2', 'coefficient_field': 'CDF', 'conductor': 3, 'conductor_radical': 3, 'conjugate': '1898821815960780135777508587263', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 225.68585268183566], [-16384.0, 0]], [[1.0, 0], [-1922.6724500404018, 1042.2569979883267]], [[1.0, 0], [0, -23159.54225263651], [-6103515625.0, 0]], [[1.0, 0], 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'24.43033538493855421497851368971050'], 'prelabel': '2-3-3.2-c14-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9312868882061984, 'root_angle': 0.8418801420043778, 'root_number': '-0.879136922743668 + 0.47656927205684807*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.420940071002', 'prec': 47}, 'spectral_label': 'c14-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.79063690443691312602537021462', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '7.56689236609126929954637885763', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '9.192216863625731928744722271051', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.729869044557181, 'bad_primes': [3], 'central_character': '3.2', 'conductor': 3, 'conductor_radical': 3, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3/15/b/a/2/1'], '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': '2-3-3.2-c14-0-3', 'motivic_weight': 14, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [14], 'order_of_vanishing': 0, 'prelabel': '2-3-3.2-c14-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9312868882061984, 'root_angle': 0.4209400710021889, 'self_dual': False, 'spectral_label': 'c14-0', 'z1': {'__RealLiteral__': 0, 'data': '4.79063690443691312602537021462', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '6072853747384959779841591799056', 'Lhash_array': ['6072853747384959779841591799056'], 'label': '2-3-3.2-c14-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3/15/b/a/2/1'}