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lfunc_lfunctions • Show schema
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{'Lhash': '1597487423620087974696472041595', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.585786437626905, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [4.82842712474619, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.65685424949238, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.137261107234623, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 19], 'central_character': '1520.1', 'coefficient_field': 'CDF', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.585786437626905, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-4.82842712474619, 0], [7.0, 0]], [[1.0, 0], [-2.0, 0], [11.0, 0]], [[1.0, 0], [-2.242640687119285, 0], [13.0, 0]], [[1.0, 0], [4.82842712474619, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-6.0, 0], [23.0, 0]], [[1.0, 0], 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[[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-1520-1.1-c1-0-15', 'leading_term': '2.53638750020562992017414095833', '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/1520/2/a/o/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.5363875002056298, 2.5325970397253412, 2.5210831984985123, 2.5014289102162146, 2.472972613314738, 2.4348558147915194, 2.3860846164181377, 2.3256010726443894, 2.252360116209874, 2.1654080597129144, 2.0639592021777404, 1.9474676802417867, 1.815692281440819, 1.6687524118243382, 1.5071737606697115, 1.331922446090693, 1.1444265913428293, 0.9465844132820299, 0.7407580394040177, 0.529752437956001, 0.3167790669116706, 0.10540413282432681, -0.10051829795888861, -0.2969276802049923, -0.4796517430675073, -0.6445129953989193, 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'7.04007419226724166778727163224210', '8.181895377243302681506538839003621', '8.631701213045925488478188799566041', '9.126219677021526773619159829210289'], 'prelabel': '2-1520-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26019537507612455551548251757', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.22346747470726762631896537131', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.35359836181160138157132269303', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.137261107234623, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1520/2/a/o/1/1'], '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': '2-1520-1.1-c1-0-15', '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': '2-1520-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.26019537507612455551548251757', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1597487423620087974696472041595', 'Lhash_array': ['1597487423620087974696472041595'], 'label': '2-1520-1.1-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1520/2/a/o/1/1'}