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lfunc_lfunctions • Show schema
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{'Lhash': '762145084480979886936769175450', 'a10': [-1.2592801267497653, 0.0], 'a2': [-1.2592801267497653, 0.0], 'a3': [-1.7808910340764283, 0.0], 'a4': [-0.41421356237309503, 0.0], 'a5': [1.0, 0.0], 'a6': [2.242640687119285, 0.0], 'a7': [-0.8284271247461901, 0.0], 'a8': [3.0401711608261937, 0.0], 'a9': [0.1715728752538099, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.412997564841117, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 19], 'central_character': '1805.1', 'coefficient_field': 'CDF', 'conductor': 1805, 'conductor_radical': 95, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.2592801267497653, 0], [2.0, 0]], [[1.0, 0], [1.7808910340764283, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.8284271247461901, 0], [7.0, 0]], [[1.0, 0], [-2.0, 0], [11.0, 0]], [[1.0, 0], [4.299451287575959, 0], [13.0, 0]], [[1.0, 0], [-7.656854249492381, 0], 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'5.44551906650689574645642644387476', '5.89697178596742466041060977825909', '7.13641516447116453110366122203077', '7.56659948305816631947221108637672', '8.703020067506486367481499145146074', '9.369491778227454632504485444292119'], 'prelabel': '2-1805-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7964453854679796, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.60122646125341031000255316467', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.80536949849057093925698171919', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.32461300071538811162404986123', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.412997564841117, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 1805, 'conductor_radical': 95, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1805/2/a/m/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': '2-1805-1.1-c1-0-13', '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': '2-1805-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7964453854679796, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.60122646125341031000255316467', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '762145084480979886936769175450', 'Lhash_array': ['762145084480979886936769175450'], 'label': '2-1805-1.1-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1805/2/a/m/1/2'}