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lfunc_lfunctions • Show schema
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{'Lhash': '1940921342287284152551977775322', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-11.524174696260024, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [27.04834939252005, 0.0], 'a8': [0.0, 0.0], 'a9': [-110.1933975700802, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.07676396259613, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '200.1', 'coefficient_field': 'CDF', 'conductor': 200, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [11.524174696260024, 0], [243.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-27.04834939252005, 0], [16807.0, 0]], [[1.0, 0], [-226.0076686214605, 0], [161051.0, 0]], [[1.0, 0], [-511.2570842055212, 0], [371293.0, 0]], [[1.0, 0], [-387.38679514016036, 0], [1419857.0, 0]], [[1.0, 0], [1335.9263070793413, 0], [2476099.0, 0]], [[1.0, 0], 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'3.34106044768812835192819469994859', '4.73235305893953537125787853472819', '5.88859056451622014673679419598117', '6.69145796210014827263024826897137', '8.136392878723981349970843941112260', '9.030370538735780683620292940981460', '10.32597659820493160490778207020529', '11.21273078240248233241254584625049'], 'prelabel': '2-200-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.663635225064917, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.53111696703952827659537950607', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.34106044768812835192819469995', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.73235305893953537125787853473', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.07676396259613, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 200, 'conductor_radical': 10, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/200/6/a/f/1/1'], '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': '2-200-1.1-c5-0-16', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-200-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.663635225064917, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.53111696703952827659537950607', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1940921342287284152551977775322', 'Lhash_array': ['1940921342287284152551977775322'], 'label': '2-200-1.1-c5-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/200/6/a/f/1/1'}