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lfunc_lfunctions • Show schema
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{'Lhash': '1763588577968026768193267564734', 'a10': [-2.145799997193362, -0.6289215945131542], 'a2': [0, -1.0], 'a3': [0, 0], 'a4': [-1.0, 0], 'a5': [0.6289215945131542, -2.145799997193362], 'a6': [0, 0], 'a7': [5.151923654818663, 0], 'a8': [0, 1.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.34249703648981, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.6289215945131542, 2.145799997193362]]], [13, [[1.0, 0], [-0.7916971982684795, -3.517558179512293]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1170.307', 'coefficient_field': 'CDF', 'conductor': 1170, 'conductor_radical': 390, 'conjugate': '1637157103830151443528032549278', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.6289215945131542, 2.145799997193362]], [[1.0, 0], [-5.151923654818663, 0], [7.0, 0]], [[1.0, 0], [-2.4568374284119057, 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'sign_arg': {'__RealLiteral__': 0, 'data': '0.21883030283212326', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.39122608205329455304138288931', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.66610089860499550761859359650', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.10700979888117467239628246135', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.34249703648981, 'bad_primes': [2, 3, 5, 13], 'central_character': '65.47', 'conductor': 1170, 'conductor_radical': 390, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1170/2/w/i/307/5'], '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': '2-1170-65.47-c1-0-23', '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': '2-1170-65.47-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0565498583353437, 'root_angle': 0.21883030283212326, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.39122608205329455304138288931', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1763588577968026768193267564734', 'Lhash_array': ['1763588577968026768193267564734'], 'label': '2-1170-65.47-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1170/2/w/i/307/5'}