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lfunc_lfunctions • Show schema
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{'Lhash': '1658107279007443454717071906038', 'a10': [0.0, 0.0], 'a2': [-2.6089236478659714, 0.0], 'a3': [9.0, 0.0], 'a4': [-25.193517399605714, 0.0], 'a5': [0.0, 0.0], 'a6': [-23.480312830793743, 0.0], 'a7': [174.96891968399984, 0.0], 'a8': [149.21352004846526, 0.0], 'a9': [81.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 132.31665134570906, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-9.0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-121.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '825.1', 'coefficient_field': 'CDF', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.6089236478659714, 0], [32.0, 0]], [[1.0, 0], [-9.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-174.96891968399984, 0], [16807.0, 0]], [[1.0, 0], [-121.0, 0]], [[1.0, 0], [815.526840045178, 0], [371293.0, 0]], [[1.0, 0], [-462.99066615831936, 0], [1419857.0, 0]], [[1.0, 0], 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'positive_zeros': ['1.30801600907136062872419968018035', '2.19342892276920978944989755982494', '3.60905552699983414160064663086291', '4.76019867506817493026901997372346', '5.04475317920928906263383441447920', '6.72512598825535730022664541834116', '7.67029717082913828509095295465582', '8.340891973979042317580053135979039', '8.856451858854642394372428771085534'], 'prelabel': '2-825-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.502897519569105, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30801600907136062872419968018', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.19342892276920978944989755982', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.60905552699983414160064663086', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 132.31665134570906, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'index': 132, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/6/a/m/1/4'], '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': '2-825-1.1-c5-0-132', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-825-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.502897519569105, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30801600907136062872419968018', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1658107279007443454717071906038', 'Lhash_array': ['1658107279007443454717071906038'], 'label': '2-825-1.1-c5-0-132', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/6/a/m/1/4'}