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lfunc_lfunctions • Show schema
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{'Lhash': '871533268423130526919088274060', 'a10': [0, 0], 'a2': [0, -1.0], 'a3': [0, 2.732050807568877], 'a4': [-1.0, 0], 'a5': [0, 0], 'a6': [2.732050807568877, 0], 'a7': [0, -1.2679491924311228], 'a8': [0, 1.0], 'a9': [-4.464101615137754, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.772324373936879, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0, 0]]], [37, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 5, 37], 'central_character': '1850.149', 'coefficient_field': 'CDF', 'conductor': 1850, 'conductor_radical': 370, 'conjugate': '1462928388313628091723705276469', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [0, -2.732050807568877], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.2679491924311228], [-7.0, 0]], [[1.0, 0], [-1.4641016151377546, 0], [11.0, 0]], [[1.0, 0], [0, 1.4641016151377546], [-13.0, 0]], [[1.0, 0], [0, 1.4641016151377546], [-17.0, 0]], 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[-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 18, 'label': '2-1850-5.4-c1-0-18', 'leading_term': '1.558390198358078603958271026495516967749072479838395181', '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/1850/2/b/l/149/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.5583901983580786, 1.4854279755357842, 1.4055137427873048, 1.3186812023629515, 1.2249029348387672, 1.1241265608706488, 1.0163136286807677, 0.9014792658096471, 0.7797307368880539, 0.6513032585482238, 0.5165916927369971, 0.37617702761821736, 0.2308468278232183, 0.0816090730645912, -0.07030100113250512, -0.22342129186591994, -0.37607055363421904, -0.5263634618253178, -0.6722329203524128, -0.8114594202560758, -0.9417071489617662, -1.060566430357106, -1.1656019428019082, 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'6.18629492953428028726422166610705', '6.80170566826505063176265144001019', '7.31124034696581311298476613016259', '8.400400058292028307658538958972338', '8.570400256540429979728589091937619'], 'prelabel': '2-1850-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8434781609808684, 'root_angle': -0.35241638234956674, 'root_number': '0.4472135954999579392818347337462552470881236719223051449 - 0.8944271909999158785636694674925104941762473438446102897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.17620819117478337', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68751852305849781152909956136', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.88321315829624607037759863753', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.93516964188152706749074709112', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.772324373936879, 'bad_primes': [2, 5, 37], 'central_character': '5.4', 'conductor': 1850, 'conductor_radical': 370, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1850/2/b/l/149/2'], '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': '2-1850-5.4-c1-0-18', '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': '2-1850-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8434781609808684, 'root_angle': -0.17620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.68751852305849781152909956136', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '871533268423130526919088274060', 'Lhash_array': ['871533268423130526919088274060'], 'label': '2-1850-5.4-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1850/2/b/l/149/2'}