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lfunc_lfunctions • Show schema
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{'Lhash': '2398692587305671440663522007012,3645845177562555347899945125880', 'a10': 0, 'a2': 0, 'a3': 4, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 4, 'a8': 0, 'a9': 7, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.672837800770863, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -4, 9]], [5, [1, 0, 5]]], 'bad_primes': [2, 3, 5], 'central_character': '60.1', 'coefficient_field': '1.1.1.1', 'conductor': 3600, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1, -4, 9], [1, 0, 5], [1, -4, 102, -196, 2401], [1, 0, -62, 0, 14641], [1, -16, 402, -2704, 28561], [1, 0, -398, 0, 83521], [1, 68, 1878, 24548, 130321], [1, 0, 562, 0, 279841], [1, 0, -62, 0, 707281], [1, -28, 2118, -26908, 923521], [1, -112, 5874, -153328, 1874161], [1, 0, -2642, 0, 2825761], [1, -16, 3762, -29584, 3418801], [1, 0, -2798, 0, 4879681], [1, 0, -3998, 0, 7890481], [1, 0, -6782, 0, 12117361], [1, 92, 9558, 342332, 13845841], [1, -64, 10002, 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1.2786248809411545, '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': 39264146509825521, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.89223480576888286366263656030', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.87606472706765793080168502350', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.14352290029282797770081817173', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.672837800770863, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 3600, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 4, 0, 0, 0, 4, 0, 7, 0, 0, 0, 16, 0, 0, 0, 0, 0, -68, 0, 16, 0, 0, 0, -5, 0, -8, 0, 0, 0, 28, 0, 0, 0, 0, 0, 112, 0, 64, 0, 0, 0, 16, 0, 0, 0, 0, 0, -86, 0, 0, 0, 0, 0, 0, 0, -272, 0, 0, 0, -92, 0, 28, 0, 0, 0, 64, 0, 0, 0, 0, 0, -212, 0, -20, 0, 0, 0, -44, 0, -95, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 112, 0, 0, 0, 244, 0, 0, 0], 'euler11': [1, 0, -62, 0, 14641], 'euler13': [1, -16, 402, -2704, 28561], 'euler17': [1, 0, -398, 0, 83521], 'euler19': [1, 68, 1878, 24548, 130321], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 562, 0, 279841], 'euler29': [1, 0, -62, 0, 707281], 'euler3': [1, -4, 9, 0, 0], 'euler31': [1, -28, 2118, -26908, 923521], 'euler37': [1, -112, 5874, -153328, 1874161], 'euler41': [1, 0, -2642, 0, 2825761], 'euler43': [1, -16, 3762, -29584, 3418801], 'euler47': [1, 0, -2798, 0, 4879681], 'euler5': [1, 0, 5, 0, 0], 'euler53': [1, 0, -3998, 0, 7890481], 'euler59': [1, 0, -6782, 0, 12117361], 'euler61': [1, 92, 9558, 342332, 13845841], 'euler67': [1, -64, 10002, -287296, 20151121], 'euler7': [1, -4, 102, -196, 2401], 'euler71': [1, 0, -7202, 0, 25411681], 'euler73': [1, 212, 21894, 1129748, 28398241], 'euler79': [1, 44, 12966, 274604, 38950081], 'euler83': [1, 0, 802, 0, 47458321], 'euler89': [1, 0, -4322, 0, 62742241], 'euler97': [1, -244, 33702, -2295796, 88529281], 'euler_factors': [[1, 0, 0, 0, 0], [1, -4, 9, 0, 0], [1, 0, 5, 0, 0], [1, -4, 102, -196, 2401], [1, 0, -62, 0, 14641], [1, -16, 402, -2704, 28561], [1, 0, -398, 0, 83521], [1, 68, 1878, 24548, 130321], [1, 0, 562, 0, 279841], [1, 0, -62, 0, 707281], [1, -28, 2118, -26908, 923521], [1, -112, 5874, -153328, 1874161], [1, 0, -2642, 0, 2825761], [1, -16, 3762, -29584, 3418801], [1, 0, -2798, 0, 4879681], [1, 0, -3998, 0, 7890481], [1, 0, -6782, 0, 12117361], [1, 92, 9558, 342332, 13845841], [1, -64, 10002, -287296, 20151121], [1, 0, -7202, 0, 25411681], [1, 212, 21894, 1129748, 28398241], [1, 44, 12966, 274604, 38950081], [1, 0, 802, 0, 47458321], [1, 0, -4322, 0, 62742241], [1, -244, 33702, -2295796, 88529281]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/60/3/g/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': '4-60e2-1.1-c2e2-0-0', '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': '4-60e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2786248809411545, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e2-0', 'trace_hash': 39264146509825521, 'z1': {'__RealLiteral__': 0, 'data': '1.89223480576888286366263656030', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2398692587305671440663522007012,3645845177562555347899945125880', 'Lhash_array': ['2398692587305671440663522007012', '3645845177562555347899945125880'], 'label': '4-60e2-1.1-c2e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/60/3/g/a'}