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lfunc_lfunctions • Show schema
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{'Lhash': '178434756590032081118124576008,2840799689297802002604854145997', 'a10': 0, 'a2': -2, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 8, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 66.82094501927158, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 4]], [3, [1, 0, 3]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '300.1', 'coefficient_field': '1.1.1.1', 'conductor': 90000, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, 2, 4], [1, 0, 3], [1], [1, 0, 10, 0, 2401], [1, 0, -134, 0, 14641], [1, 36, 662, 6084, 28561], [1, 20, 678, 5780, 83521], [1, 0, -530, 0, 130321], [1, 0, -1010, 0, 279841], [1, 72, 2978, 60552, 707281], [1, 0, -1874, 0, 923521], [1, 108, 5654, 147852, 1874161], [1, -36, 3686, -60516, 2825761], [1, 0, -3266, 0, 3418801], [1, 0, -4418, 0, 4879681], [1, -52, 6294, -146068, 7890481], [1, 0, -5990, 0, 12117361], [1, 148, 12918, 550708, 13845841], [1, 0, -7250, 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'10.80710478036473586456040153738475', '11.06376711814805310732006231697317', '11.72429673964229557739502510916768'], 'prelabel': '4-300e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.8590921515069967, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c2e2-0', 'trace_hash': 1276290743143530127, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.14076020360650360919204248652', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.82788240727114936257363018312', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.24099581445103317043046238246', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 66.82094501927158, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 90000, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, -2, 0, 0, 0, 0, 0, 8, -3, 0, 0, 0, -36, 0, 0, -16, -20, 6, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, -72, 0, 0, 0, 0, 40, 0, 0, -108, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 52, 0, 0, 0, 0, 144, 0, 0, -148, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, -24, -72, 216, 0, 0, 0, 0, 0, 0, 9, -72, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 144, 20, 0, 0], 'euler11': [1, 0, -134, 0, 14641], 'euler13': [1, 36, 662, 6084, 28561], 'euler17': [1, 20, 678, 5780, 83521], 'euler19': [1, 0, -530, 0, 130321], 'euler2': [1, 2, 4, 0, 0], 'euler23': [1, 0, -1010, 0, 279841], 'euler29': [1, 72, 2978, 60552, 707281], 'euler3': [1, 0, 3, 0, 0], 'euler31': [1, 0, -1874, 0, 923521], 'euler37': [1, 108, 5654, 147852, 1874161], 'euler41': [1, -36, 3686, -60516, 2825761], 'euler43': [1, 0, -3266, 0, 3418801], 'euler47': [1, 0, -4418, 0, 4879681], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, -52, 6294, -146068, 7890481], 'euler59': [1, 0, -5990, 0, 12117361], 'euler61': [1, 148, 12918, 550708, 13845841], 'euler67': [1, 0, -7250, 0, 20151121], 'euler7': [1, 0, 10, 0, 2401], 'euler71': [1, 0, 718, 0, 25411681], 'euler73': [1, 72, 11954, 383688, 28398241], 'euler79': [1, 0, -4370, 0, 38950081], 'euler83': [1, 0, -5666, 0, 47458321], 'euler89': [1, 36, 16166, 285156, 62742241], 'euler97': [1, -144, 24002, -1354896, 88529281], 'euler_factors': [[1, 2, 4, 0, 0], [1, 0, 3, 0, 0], [1, 0, 0, 0, 0], [1, 0, 10, 0, 2401], [1, 0, -134, 0, 14641], [1, 36, 662, 6084, 28561], [1, 20, 678, 5780, 83521], [1, 0, -530, 0, 130321], [1, 0, -1010, 0, 279841], [1, 72, 2978, 60552, 707281], [1, 0, -1874, 0, 923521], [1, 108, 5654, 147852, 1874161], [1, -36, 3686, -60516, 2825761], [1, 0, -3266, 0, 3418801], [1, 0, -4418, 0, 4879681], [1, -52, 6294, -146068, 7890481], [1, 0, -5990, 0, 12117361], [1, 148, 12918, 550708, 13845841], [1, 0, -7250, 0, 20151121], [1, 0, 718, 0, 25411681], [1, 72, 11954, 383688, 28398241], [1, 0, -4370, 0, 38950081], [1, 0, -5666, 0, 47458321], [1, 36, 16166, 285156, 62742241], [1, -144, 24002, -1354896, 88529281]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/300/3/c/a'], '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': '4-300e2-1.1-c2e2-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'prelabel': '4-300e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.8590921515069967, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e2-0', 'trace_hash': 1276290743143530127, 'z1': {'__RealLiteral__': 0, 'data': '0.14076020360650360919204248652', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '178434756590032081118124576008,2840799689297802002604854145997', 'Lhash_array': ['178434756590032081118124576008', '2840799689297802002604854145997'], 'label': '4-300e2-1.1-c2e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/300/3/c/a'}