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lfunc_lfunctions • Show schema
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{'Lhash': '2214910338266127626641022426571', 'a10': [0.0, 0.0], 'a2': [1.0, 0.0], 'a3': [2.618033988749895, 0.0], 'a4': [1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [2.618033988749895, 0.0], 'a7': [3.0, 0.0], 'a8': [1.0, 0.0], 'a9': [3.8541019662496847, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.981300252660052, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '1250.1', 'coefficient_field': 'CDF', 'conductor': 1250, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.618033988749895, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.0, 0], [7.0, 0]], [[1.0, 0], [0.2360679774997897, 0], [11.0, 0]], [[1.0, 0], [1.0, 0], [13.0, 0]], [[1.0, 0], [7.854101966249685, 0], [17.0, 0]], [[1.0, 0], [0.8541019662496846, 0], [19.0, 0]], [[1.0, 0], [-6.23606797749979, 0], [23.0, 0]], [[1.0, 0], 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'7.26434383423211810310183374058541', '8.236297554710082162191599007390694', '8.658534591711380554171487687337012', '9.497794991451045244494878291033178'], 'prelabel': '2-1250-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1593195869775585, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.74725617442799490308283835448', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.50001226606509840114794003456', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.49741567533310055207531403313', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.981300252660052, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 1250, 'conductor_radical': 10, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1250/2/a/d/1/2'], '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': '2-1250-1.1-c1-0-30', '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': '2-1250-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1593195869775585, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.74725617442799490308283835448', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2214910338266127626641022426571', 'Lhash_array': ['2214910338266127626641022426571'], 'label': '2-1250-1.1-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1250/2/a/d/1/2'}