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lfunc_lfunctions • Show schema
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{'Lhash': '1270754781861034594958960232416', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 1.5615528128088303], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 1.0], 'a8': [0, 0], 'a9': [0.5615528128088303, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.358112565958518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 5, 7], 'central_character': '2800.449', 'coefficient_field': 'CDF', 'conductor': 2800, 'conductor_radical': 70, 'conjugate': '1410660565501323614058588770497', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.5615528128088303], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [-6.123105625617661, 0], [11.0, 0]], [[1.0, 0], [0, -2.0], [-13.0, 0]], [[1.0, 0], [0, 1.5615528128088303], [-17.0, 0]], [[1.0, 0], [-3.5615528128088303, 0], [19.0, 0]], [[1.0, 0], [0, 1.4384471871911697], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 26, 'label': '2-2800-5.4-c1-0-26', 'leading_term': '2.3077672003604404133445740857711535100309663424757912061', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2800/2/g/v/449/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.3077672003604404, 2.2490280991117544, 2.181539463983559, 2.105531951246339, 2.0211556957846453, 1.9285212815611326, 1.8277453365915513, 1.718997996069099, 1.6025495454273455, 1.4788137945305473, 1.3483860865006774, 1.2120742505599649, 1.070921218498611, 0.9262184058718343, 0.7795092955266879, 0.6325829502388951, 0.4874574301144649, 0.3463533105884399, 0.21165770067089623, 0.085879358987329, -0.02840429575161616, -0.1286072796431772, -0.21220103596581696, -0.2767849089378221, 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'5.84390331609604569277444602572280', '6.57603444304151916800840967957474', '7.01194564757859043766357645120441', '7.910914727899275087312089858127123', '8.442004490897878620438887965390434'], 'prelabel': '2-2800-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.728436587917672, 'root_angle': -0.35241638234956674, 'root_number': '0.4472135954999579392818347337462552470881236719223051449 - 0.89442719099991587856366946749251049417624734384461028971*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.17620819117478337', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.00244876753282514339032836496', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.54546765895884468657678162668', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.92609117601338841310720152516', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.358112565958518, 'bad_primes': [2, 5, 7], 'central_character': '5.4', 'conductor': 2800, 'conductor_radical': 70, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2800/2/g/v/449/3'], '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': '2-2800-5.4-c1-0-26', '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': '2-2800-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.728436587917672, 'root_angle': -0.17620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.00244876753282514339032836496', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1270754781861034594958960232416', 'Lhash_array': ['1270754781861034594958960232416'], 'label': '2-2800-5.4-c1-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2800/2/g/v/449/3'}