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lfunc_lfunctions • Show schema
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{'Lhash': '2705212214140924309092015413116', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -1.0], 'a6': [0, 0], 'a7': [0, -3.414213562373095], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.498457891064382, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1440.1151', 'coefficient_field': 'CDF', 'conductor': 1440, 'conductor_radical': 30, 'conjugate': '160256163956143712050489517037', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 3.414213562373095], [-7.0, 0]], [[1.0, 0], [2.585786437626905, 0], [11.0, 0]], [[1.0, 0], [3.414213562373095, 0], [13.0, 0]], [[1.0, 0], [0, -1.17157287525381], [-17.0, 0]], [[1.0, 0], [0, 0], [-19.0, 0]], [[1.0, 0], [4.82842712474619, 0], [23.0, 0]], [[1.0, 0], [0, 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'group': 'GL2', 'index': 15, 'label': '2-1440-12.11-c1-0-15', 'leading_term': '0.337972159011091242191575695193727548483430454506696857', '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/1440/2/h/a/1151/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.33797215901109123, 0.5096047174607953, 0.6844163719421001, 0.8624441672576392, 1.0435384512917747, 1.2272815105302497, 1.4129233583824394, 1.5993378775891254, 1.7850007985099836, 1.9679895749102858, 2.1460042139701745, 2.316407512221896, 2.476282844696082, 2.6225075221832155, 2.751839654994577, 2.8610163588851223, 2.946860966843167, 3.0063966598850707, 3.036963615751049, 3.0363364263811414, 3.0028381906185646, 2.935447387238289, 2.8338934132602276, 2.698736568084395, 2.531428304654398, 2.3343477777444686, 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'7.50986061553617405595987370587032', '8.433382451584547715549959545911437', '9.074238608412405889362099180842040', '10.07059232661073446077601059322540'], 'prelabel': '2-1440-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.390937612381623, 'root_angle': -0.9459132760153036, 'root_number': '-0.98559855965348878087536279295293935430859299804623856409 - 0.1691019787257627481429347680509755569866105044940151880*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.47295663800765186', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.13403615606214718347597235670', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.70807452517557273754609515357', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.94321465814082114241693158567', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.498457891064382, 'bad_primes': [2, 3, 5], 'central_character': '12.11', 'conductor': 1440, 'conductor_radical': 30, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1440/2/h/a/1151/1'], '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': '2-1440-12.11-c1-0-15', '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': '2-1440-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.390937612381623, 'root_angle': -0.4729566380076518, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.13403615606214718347597235670', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2705212214140924309092015413116', 'Lhash_array': ['2705212214140924309092015413116'], 'label': '2-1440-12.11-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1440/2/h/a/1151/1'}