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lfunc_lfunctions • Show schema
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{'Lhash': '3705968432664443542885780887329', 'a10': [-41.19765433126005, 71.35643045440241], 'a2': [-0.3954024763395444, -0.6848571784586418], 'a3': [0.0, 0.0], 'a4': [15.687313763409112, -27.171224472499116], 'a5': [-52.09584764446738, -90.23265498358492], 'a6': [0.0, 0.0], 'a7': [-7.129797810743692, 129.44561013482812], 'a8': [-50.116969322400365, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.104180648217781, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [7.129797810743692, -129.44561013482812]]]], 'bad_primes': [3, 7], 'central_character': '63.46', 'coefficient_field': 'CDF', 'conductor': 63, 'conductor_radical': 21, 'conjugate': '360024624663023314514488159508', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.3954024763395444, 0.6848571784586418], [-16.0, 27.712812921102035]], [[1.0, 0], [0, 0]], [[1.0, 0], [52.09584764446738, 90.23265498358492], [-1562.5, 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'8.180321088817603791552714983957725', '10.43706585978135634408303443706615', '11.04413882974535540259722188143646', '12.09424435501793983936283550860717', '13.55202788767945386986015260961684', '14.61797927900795289993661054231904'], 'prelabel': '2-63-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.178707386378586, 'root_angle': -0.9623123990641872, 'root_number': '-0.9929990119737211 - 0.11812265751841926*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.481156199532', 'prec': 50}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.92349361251216726866432611491', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.83149634142669973452798908691', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.45217917745580103600456006529', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.104180648217781, 'bad_primes': [3, 7], 'central_character': '7.4', 'conductor': 63, 'conductor_radical': 21, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/63/6/e/e/46/2'], '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': '2-63-7.4-c5-0-15', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-63-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.178707386378586, 'root_angle': -0.4811561995320936, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '2.92349361251216726866432611491', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3705968432664443542885780887329', 'Lhash_array': ['3705968432664443542885780887329'], 'label': '2-63-7.4-c5-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/63/6/e/e/46/2'}