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lfunc_lfunctions • Show schema
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{'Lhash': '850976310090830603269297082650', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 67.07433769787555, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [7, [1, -1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '8400.1', 'coefficient_field': '1.1.1.1', 'conductor': 8400, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, -1], [1, 4, 11], [1, -2, 13], [1, -6, 17], [1, 4, 19], [1, -8, 23], [1, 2, 29], [1, 0, 31], [1, -2, 37], [1, -10, 41], [1, -4, 43], [1, 0, 47], [1, 14, 53], [1, 12, 59], [1, 2, 61], [1, 4, 67], [1, 0, 71], [1, 2, 73], [1, -8, 79], [1, 4, 83], [1, 6, 89], [1, -6, 97], [1, -6, 101], [1, 8, 103], [1, -20, 107], [1, -14, 109], [1, -14, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [1], [[[1, -1], 1]], [[[1, 4, 11], 1]], [[[1, -2, 13], 1]], [[[1, -6, 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0.0870602599411262, 0.5524559860941691, 1.0582503119454827, 1.5816110949579105, 2.097856580042453, 2.581869365690955, 3.0095572300178133, 3.359274202366436, 3.6131165039139463, 3.758014320199328, 3.7865515084580545, 3.6974606917185775, 3.49575989847996], 'positive_zeros': ['0.67130194229988907255249909615426', '1.61064772967630764736206760825975', '2.72231481779507610874042185304323', '3.42380871091229607902765303858923', '4.51145005984982096793873626454478', '4.97840844284651408143896241075129', '5.81064883104820539331654621605547', '6.18139128581516128362302547225052', '7.29257861220060160446555454097895', '7.66534995900909120234577858350373'], 'prelabel': '2-8400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.189892410641031, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 279443355569306238, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.67130194229988907255249909615', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.61064772967630764736206760826', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.72231481779507610874042185304', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 67.07433769787555, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 8400, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 1, 0, 1, 0, -4, 0, 2, 0, 0, 0, 6, 0, -4, 0, -1, 0, 8, 0, 0, 0, -1, 0, -2, 0, 0, 0, 4, 0, 0, 0, 2, 0, -2, 0, 10, 0, 4, 0, 0, 0, 0, 0, 1, 0, -6, 0, -14, 0, 0, 0, 4, 0, -12, 0, -2, 0, 1, 0, 0, 0, -4, 0, -8, 0, 0, 0, -2, 0, 0, 0, -4, 0, 8, 0, 1, 0, -4, 0, 0, 0, 2, 0, -6, 0, 2, 0, 0, 0, 0, 0, 6, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, -2, 13], 'euler17': [1, -6, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -8, 23], 'euler29': [1, 2, 29], 'euler3': [1, 1, 0], 'euler31': [1, 0, 31], 'euler37': [1, -2, 37], 'euler41': [1, -10, 41], 'euler43': [1, -4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 14, 53], 'euler59': [1, 12, 59], 'euler61': [1, 2, 61], 'euler67': [1, 4, 67], 'euler7': [1, -1, 0], 'euler71': [1, 0, 71], 'euler73': [1, 2, 73], 'euler79': [1, -8, 79], 'euler83': [1, 4, 83], 'euler89': [1, 6, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, -1, 0], [1, 4, 11], [1, -2, 13], [1, -6, 17], [1, 4, 19], [1, -8, 23], [1, 2, 29], [1, 0, 31], [1, -2, 37], [1, -10, 41], [1, -4, 43], [1, 0, 47], [1, 14, 53], [1, 12, 59], [1, 2, 61], [1, 4, 67], [1, 0, 71], [1, 2, 73], [1, -8, 79], [1, 4, 83], [1, 6, 89], [1, -6, 97]], 'index': 21, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/8400/q', 'ModularForm/GL2/Q/holomorphic/8400/2/a/q/1/1', 'ModularForm/GL2/Q/holomorphic/8400/2/a/q'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-8400-1.1-c1-0-21', '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': '2-8400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.189892410641031, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 279443355569306238, 'z1': {'__RealLiteral__': 0, 'data': '0.67130194229988907255249909615', 'prec': 103}}
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lfunc_instances • Show schema
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id: 22305816
{'Lhash': '850976310090830603269297082650', 'Lhash_array': ['850976310090830603269297082650'], 'label': '2-8400-1.1-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8400/2/a/q'}
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id: 24583856
{'Lhash': '850976310090830603269297082650', 'Lhash_array': ['850976310090830603269297082650'], 'label': '2-8400-1.1-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8400/2/a/q/1/1'}
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id: 103655
{'Lhash': '279443355569306238', 'Lhash_array': ['279443355569306238'], 'label': '2-8400-1.1-c1-0-21', 'type': 'ECQ', 'url': 'EllipticCurve/Q/8400/q'}