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lfunc_lfunctions • Show schema
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{'Lhash': '4280978492374332742107731481744', 'a10': [-5.346158348092683, 9.259817884205026], 'a2': [-0.3472963553338607, -1.969615506024416], 'a3': [1.0928493451853294, -6.1978566229306775], 'a4': [-3.7587704831436337, 1.3680805733026749], 'a5': [-4.095394894590535, -3.4364443455762332], 'a6': [-12.586937103152247, 1.1852701601112585e-60], 'a7': [-9.537184374033462, -8.002647890721196], 'a8': [4.0, 6.928203230275509], 'a9': [-11.84740626591413, -4.31210323405164], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.366141340424807, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.3472963553338607, 1.969615506024416]]], [37, [[1.0, 0], [-200.46542895098355, 102.30646018457564]]]], 'bad_primes': [2, 37], 'central_character': '74.9', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '891426218113141929243182848759', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.3472963553338607, 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'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.37709656872609851123866781186', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.74264596332475282078439823756', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.21999372928893429963743859083', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.366141340424807, 'bad_primes': [2, 37], 'central_character': '37.9', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/4/f/a/9/4'], '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': '2-74-37.9-c3-0-8', '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': '2-74-37.9-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0895313686146966, 'root_angle': -0.49745375110602535, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '3.37709656872609851123866781186', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4280978492374332742107731481744', 'Lhash_array': ['4280978492374332742107731481744'], 'label': '2-74-37.9-c3-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/4/f/a/9/4'}