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lfunc_lfunctions • Show schema
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{'Lhash': '737722461832892291724403701184', 'a10': [0, 0], 'a2': [0, -2.5615528128088303], 'a3': [0, -3.0], 'a4': [1.4384471871911697, 0], 'a5': [0, 0], 'a6': [-7.68465843842649, 0], 'a7': [0, 6.246211251235321], 'a8': [0, -24.177080940897135], 'a9': [-9.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.67657575473603, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 3.0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [11.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '825.199', 'coefficient_field': 'CDF', 'conductor': 825, 'conductor_radical': 165, 'conjugate': '1491790130229031512122176549476', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.5615528128088303], [-8.0, 0]], [[1.0, 0], [0, 3.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -6.246211251235321], [-343.0, 0]], [[1.0, 0], [11.0, 0]], [[1.0, 0], [0, -49.12310562561766], [-2197.0, 0]], [[1.0, 0], [0, -82.70832376358854], [-4913.0, 0]], [[1.0, 0], 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'positive_zeros': ['0.58196040904336874519970965885330', '2.49037797879548003224072618428983', '3.43155501171034160453977048250512', '5.00997838876306786949897323656992', '5.29828134623063684670295875589916', '6.54128650735784058590856815824106', '7.26409122590379874320780763424562', '8.109004567893520568525678062616677', '8.821563197584928950875157829730696', '10.05054208086214427461482657548419'], 'prelabel': '2-825-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.976860021151064, 'root_angle': 0.14758361765043326, 'root_number': '0.8944271909999158785636694674925104941762473438446102897 + 0.447213595499957939281834733746255247088123671922305145*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.07379180882521663', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58196040904336874519970965885', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.49037797879548003224072618429', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43155501171034160453977048251', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 48.67657575473603, 'bad_primes': [3, 5, 11], 'central_character': '5.4', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/4/c/j/199/1'], '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': '2-825-5.4-c3-0-29', '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': '2-825-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.976860021151064, 'root_angle': 0.07379180882521663, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.58196040904336874519970965885', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '737722461832892291724403701184', 'Lhash_array': ['737722461832892291724403701184'], 'label': '2-825-5.4-c3-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/4/c/j/199/1'}