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lfunc_lfunctions • Show schema
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{'Lhash': '2188376404786792920243765982176', 'a10': [0, 0], 'a2': [0, -1.0], 'a3': [0, -1.0], 'a4': [-1.0, 0], 'a5': [0, 0], 'a6': [-1.0, 0], 'a7': [0, -1.0], 'a8': [0, 1.0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.36185251542651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 3, 5, 17], 'central_character': '2550.2449', 'coefficient_field': 'CDF', 'conductor': 2550, 'conductor_radical': 510, 'conjugate': '220413198053223684663228023587', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.0], [-7.0, 0]], [[1.0, 0], [3.0, 0], [11.0, 0]], [[1.0, 0], [0, 2.0], [-13.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [-7.0, 0], [19.0, 0]], [[1.0, 0], [0, 6.0], [-23.0, 0]], [[1.0, 0], [6.0, 0], [29.0, 0]], [[1.0, 0], [7.0, 0], [31.0, 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2.4225904988084004, 2.652864794199716, 2.7536323605575044, 2.713290226959012, 2.531375474969707, 2.2183432380936066, 1.794519363425046, 1.28831937400936, 0.7338808828571968, 0.1683005460007295, -0.37130441006906445, -0.8506783529728396, -1.241027842487004, -1.5211395546535422, -1.6788543608085313, -1.7117889648746936, -1.6272575507023308, -1.4414105541009812, -1.1776707779766256, -0.8646035370508477, -0.5334027792703191], 'positive_zeros': ['1.72632459164441281525344687421344', '3.13277066085658569817202219749249', '3.82056319352285405482983521167694', '5.07838740298404740682706793086516', '5.34506079162002874048220604550790', '6.21514010011937852838357450133779', '7.34587201565838584997364620744254', '7.69990400716311455162435486875955', '8.756441586066739600777039885811297', '9.279353336671326402025373360324316'], 'prelabel': '2-2550-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.512410942658759, 'root_angle': -0.6475836176504333, 'root_number': '-0.4472135954999579392818347337462552470881236719223051449 - 0.8944271909999158785636694674925104941762473438446102897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.32379180882521663', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.72632459164441281525344687421', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.13277066085658569817202219749', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.82056319352285405482983521168', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 20.36185251542651, 'bad_primes': [2, 3, 5, 17], 'central_character': '5.4', 'conductor': 2550, 'conductor_radical': 510, 'degree': 2, 'index': 44, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2550/2/d/c/2449/1'], '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': '2-2550-5.4-c1-0-44', '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': '2-2550-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.512410942658759, 'root_angle': -0.32379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72632459164441281525344687421', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2188376404786792920243765982176', 'Lhash_array': ['2188376404786792920243765982176'], 'label': '2-2550-5.4-c1-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2550/2/d/c/2449/1'}