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lfunc_lfunctions • Show schema
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{'Lhash': '876202001248612736716603234361', 'a10': [0.0, 0.0], 'a2': [-0.7040301030613592, -0.2562460015417015], 'a3': [0.29452401294294617, 1.6703286800441817], 'a4': [-0.3360480704084997, -0.28197781193760874], 'a5': [0.0, 0.0], 'a6': [0.2206612743354821, -1.2514322734324956], 'a7': [-0.9975640502598242, 1.7278316188542087], 'a8': [0.5389388642266889, 0.9334694950140899], 'a9': [-1.763560884392213, 0.6418836682349448], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3559596393238675, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-0.5, -0.8660254037844386]]], [13, [[1.0, 0], [0.17364817766693036, -0.984807753012208]]], [19, [[1.0, 0], [-0.882947592858927, -0.46947156278589075]]]], 'bad_primes': [11, 13, 19], 'central_character': '2717.1429', 'coefficient_field': 'CDF', 'conductor': 2717, 'conductor_radical': 2717, 'conjugate': '2444638339420776151202783142520', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[0.17364817766693036, -0.984807753012208]], [[1.0, 0], [-1.9805361374831407, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-2717-2717.1429-c0-0-1', 'leading_term': '0.69257445143745362264292973793680', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2717/1/db/c/1429/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.6925744514374537, 0.630967318187611, 0.5749774287258027, 0.522905000567602, 0.4731522770090062, 0.42435909565563273, 0.3754984211691913, 0.3259289727535156, 0.27541148333244797, 0.2240989528706555, 0.17251074195318855, 0.12149777786730485, 0.07220328885976657, 0.026021214976839544, -0.015447026299887616, -0.05043752669660401, -0.07707103335286876, -0.09340265767935346, -0.09747437280825058, -0.08737026102535045, 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'3.36460270635726673860180272118853', '4.66780534965741679341029785539607', '6.01857622370776221329259858026839', '6.88156721066162718496196831450386', '7.11852452913230438063685442418193', '7.75881881663070393191640549874175', '8.460908566100001911613754732679029'], 'prelabel': '2-2717-2717.1429-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1644568001106212, 'root_angle': -0.9987056166863829, 'root_number': '-0.99999173210480953308054909092378 - 0.0040664139020570641310723896363947*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.49935280834319146', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.69120150386144275968211190354', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.08227980969358040978710317496', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.06548581307168029416230445041', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3559596393238675, 'bad_primes': [11, 13, 19], 'central_character': '2717.1429', 'conductor': 2717, 'conductor_radical': 2717, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2717/1/db/c/1429/2'], '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': '2-2717-2717.1429-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-2717-2717.1429-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1644568001106212, 'root_angle': -0.49935280834319146, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.69120150386144275968211190354', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '876202001248612736716603234361', 'Lhash_array': ['876202001248612736716603234361'], 'label': '2-2717-2717.1429-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2717/1/db/c/1429/2'}