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lfunc_lfunctions • Show schema
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{'Lhash': '115382736382101398614584013633', 'a10': [2.5791818902418044, -4.467274075860341], 'a2': [0.7377180527501901, 1.2777651490241064], 'a3': [-0.5, 0.8660254037844386], 'a4': [-0.08845585070706462, 0.15321002765136332], 'a5': [-1.7480810457509437, -3.02776518698877], 'a6': [-1.4754361055003802, 0], 'a7': [-0.8398209603336728, -2.5089242225671597], 'a8': [2.6898502992488518, 0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.234951564394155, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.5, -0.8660254037844386]]], [7, [[1.0, 0], [0.8398209603336728, 2.5089242225671597]]], [67, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [3, 7, 67], 'central_character': '1407.403', 'coefficient_field': 'CDF', 'conductor': 1407, 'conductor_radical': 1407, 'conjugate': '1973449544525993593398364621474', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7377180527501901, 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-94.39676901250381]], [[1.0, 0], [19.63068361793479, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-1407-7.4-c1-0-1', 'leading_term': '0.271708561501487573815328654118656158212871779950687349', '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/1407/2/i/h/403/13', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.2717085615014876, 0.0971808890458169, -0.0787523449544914, -0.25624557687558763, -0.43536566152553685, -0.6160236035364013, -0.797918023311358, -0.9804928144192941, -1.1629102761230676, -1.3440399645178005, -1.522462703281353, -1.6964886582624907, -1.864188076976361, -2.0234331595156605, -2.171949489129158, -2.307375446923861, -2.4273280228739003, -2.5294733917194816, -2.6116005415922827, -2.671696131823855, 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'3.43157934723474484120666588157966', '4.85215428920899721360384554356264', '5.70330004272211334763555200659541', '6.74912799914885386872385957973788', '7.53079925752624297423262419584698', '8.003141979599279745363827900456161', '9.274039531792388571743524390928945'], 'prelabel': '2-1407-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.351857927238885, 'root_angle': 0.9173556240895906, 'root_number': '-0.9664837573457704790708733613826061916381368165636172555 + 0.2567277678530350318681323221423752485267643928240870459*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4586778120447953', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.091020929869261881994020259503', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.26645643219107483574088920213', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.90197440124866594064504191491', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.234951564394155, 'bad_primes': [3, 7, 67], 'central_character': '7.4', 'conductor': 1407, 'conductor_radical': 1407, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1407/2/i/h/403/13'], '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': '2-1407-7.4-c1-0-1', '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': '2-1407-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.351857927238885, 'root_angle': 0.4586778120447953, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.091020929869261881994020259503', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '115382736382101398614584013633', 'Lhash_array': ['115382736382101398614584013633'], 'label': '2-1407-7.4-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1407/2/i/h/403/13'}