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lfunc_lfunctions • Show schema
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{'Lhash': '1790421660603282650243554067055', 'a10': [0.0, 0.0], 'a2': [-0.6234898018587335, 0.7818314824680298], 'a3': [0.0, 0.0], 'a4': [-0.2225209339563144, -0.9749279121818236], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.2225209339563144, -0.9749279121818236], 'a8': [0.9009688679024191, 0.4338837391175581], 'a9': [0.6234898018587335, 0.7818314824680298], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.2716176521888902, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.6234898018587335, -0.7818314824680298]]], [7, [[1.0, 0], [-0.2225209339563144, 0.9749279121818236]]], [13, [[1.0, 0], [-0.6234898018587335, 0.7818314824680298]]]], 'bad_primes': [2, 7, 13], 'central_character': '2548.1611', 'coefficient_field': 'CDF', 'conductor': 2548, 'conductor_radical': 182, 'conjugate': '1157199442386980766971432088527', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6234898018587335, -0.7818314824680298]], [[1.0, 0], [0, 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[0.2774790660436856, 0.3479477433504717], [-0.2225209339563144, 0.9749279121818236]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-2548-2548.1611-c0-0-1', 'leading_term': '0.97266747752467929938678637561830', '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/2548/1/co/b/1611/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.9726674775246793, 0.9988360313198282, 1.0319171345277438, 1.07116750907759, 1.1149611550327099, 1.161027747280297, 1.2067070785910887, 1.2491716635648042, 1.285599816725327, 1.3133027627398415, 1.3298181028008995, 1.332982237460437, 1.3209909933454633, 1.2924537688103894, 1.2464432745255054, 1.1825406688270659, 1.1008744504440655, 1.0021506655825958, 0.887671635139761, 0.7593403868565808, 0.6196482064790627, 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'4.73445706412136860626948757395593', '6.35674388255373662121523280368704', '6.84044724117511008089653924366527', '7.61905587609909426986840796107077', '8.907936083124650340922509049795950', '9.056524198829664815906161117751182'], 'prelabel': '2-2548-2548.1611-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1276602556572126, 'root_angle': 0.04081632653061225, 'root_number': '0.99179001382324610895744277721886 + 0.12787716168450601059056272223114*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.02040816326530612', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.41239365191081272110012516078', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.13710632925934534562561376081', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.27091258126448816161472248267', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.2716176521888902, 'bad_primes': [2, 7, 13], 'central_character': '2548.1611', 'conductor': 2548, 'conductor_radical': 182, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2548/1/co/b/1611/1'], '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': '2-2548-2548.1611-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': '2-2548-2548.1611-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1276602556572126, 'root_angle': 0.020408163265306124, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.41239365191081272110012516078', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1790421660603282650243554067055', 'Lhash_array': ['1790421660603282650243554067055'], 'label': '2-2548-2548.1611-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2548/1/co/b/1611/1'}