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lfunc_lfunctions • Show schema
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{'Lhash': '1528052914547579535439351037284', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, -1.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 26.0], 'a8': [0.0, 0.0], 'a9': [26.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.900191000574064, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '100.49', 'coefficient_field': 'CDF', 'conductor': 100, 'conductor_radical': 10, 'conjugate': '2142793489888213296543912380688', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.0], [-27.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -26.0], [-343.0, 0]], [[1.0, 0], [-45.0, 0], [1331.0, 0]], [[1.0, 0], [0, 44.0], [-2197.0, 0]], [[1.0, 0], [0, -117.0], [-4913.0, 0]], [[1.0, 0], [-91.0, 0], [6859.0, 0]], [[1.0, 0], [0, -18.0], [-12167.0, 0]], [[1.0, 0], [144.0, 0], [24389.0, 0]], [[1.0, 0], [-26.0, 0], 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2.4290308768259954, 'root_angle': -0.14758361765043326, 'root_number': '0.894427190999916 - 0.44721359549995787*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0737918088252', 'prec': 54}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.20542120539560899129498037758', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.70804106047148059952631965846', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.74320459809182051351148795248', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.900191000574064, 'bad_primes': [2, 5], 'central_character': '5.4', 'conductor': 100, 'conductor_radical': 10, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/100/4/c/b/49/1'], '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': '2-10e2-5.4-c3-0-1', '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': '2-10e2-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4290308768259954, 'root_angle': -0.07379180882521663, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.20542120539560899129498037758', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1528052914547579535439351037284', 'Lhash_array': ['1528052914547579535439351037284'], 'label': '2-10e2-5.4-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/100/4/c/b/49/1'}