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lfunc_lfunctions • Show schema
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{'Lhash': '1645710835494753208243813828682', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [1.8090233941192602, 1.0444401435650852], 'a6': [0, 0], 'a7': [-0.7814517207857921, -1.3535140840631201], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.084589681459306, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1728.449', 'coefficient_field': 'CDF', 'conductor': 1728, 'conductor_radical': 6, 'conjugate': '33777984953509351063186277724', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.8090233941192602, -1.0444401435650852], [12.5, 21.650635094610966]], [[1.0, 0], [0.7814517207857921, 1.3535140840631201], [-24.5, 42.4352447854375]], [[1.0, 0], [10.830163733916294, -6.252797947144295], [60.5, -104.78907385791707]], [[1.0, 0], [11.044078923680388, 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[[1.0, 0], [0, -18.35987321443477], [-5041.0, 0]], [[1.0, 0], [68.57773733844283, 0], [5329.0, 0]], [[1.0, 0], [-13.312960137484053, -23.058723357261524], [-3120.5, 5404.864545018681]], [[1.0, 0], [-21.037598049404103, 12.146062896926605], [3444.5, -5966.049006670998]], [[1.0, 0], [0, -111.72970589459678], [-7921.0, 0]], [[1.0, 0], [2.511824620156955, 4.350607861814242], [-4704.5, 8148.433024207783]], [[1.0, 0], [86.10524660632964, -49.71288730680353], [5100.5, -8834.325144005059]], [[1.0, 0], [-13.616021680784984, 23.583641348078974], [-5304.5, -9187.66350874911]], [[1.0, 0], [0, -127.2418456183337], [-11449.0, 0]], [[1.0, 0], [55.31001906216571, 0], [11881.0, 0]], [[1.0, 0], [102.84479739030611, 59.377471458045754], [6384.5, 11058.278380923497]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 36, 'label': '2-12e3-9.5-c2-0-36', 'leading_term': '0.103869323481727839078352232788643420229790869573993757', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': 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'primitive': True, 'rational': False, 'root_analytic_conductor': 6.861821163616792, 'root_angle': 0.8516815346028881, 'root_number': '-0.89339237459403220829104110510681774191381207489131191607 + 0.4492772696422960969336176984849672871149954369171388908*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.42584076730144405', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.29823693942041866154520807330', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.75232082987585170758711505074', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.26684246145157382369430499570', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 47.084589681459306, 'bad_primes': [2, 3], 'central_character': '9.5', 'conductor': 1728, 'conductor_radical': 6, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1728/3/q/j/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': '2-12e3-9.5-c2-0-36', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-12e3-9.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.861821163616792, 'root_angle': 0.42584076730144405, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29823693942041866154520807330', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1645710835494753208243813828682', 'Lhash_array': ['1645710835494753208243813828682'], 'label': '2-12e3-9.5-c2-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1728/3/q/j/449/3'}