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lfunc_lfunctions • Show schema
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{'Lhash': '1848132030273122122588419122461', 'a10': [-1.3027756377319946, 0.0], 'a2': [1.0, 0.0], 'a3': [0.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.3027756377319946, 0.0], 'a6': [0.0, 0.0], 'a7': [4.60555127546399, 0.0], 'a8': [1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.318036774617276, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [37, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 37], 'central_character': '666.1', 'coefficient_field': 'CDF', 'conductor': 666, 'conductor_radical': 222, 'conjugate': '1848132030273122122588419122461', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.3027756377319946, 0], [5.0, 0]], [[1.0, 0], [-4.60555127546399, 0], [7.0, 0]], [[1.0, 0], [1.3027756377319946, 0], [11.0, 0]], [[1.0, 0], [2.302775637731995, 0], [13.0, 0]], [[1.0, 0], [-6.0, 0], [17.0, 0]], [[1.0, 0], [-2.0, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-666-1.1-c1-0-5', '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/666/2/a/j/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.4753170261823083, 2.471004407160845, 2.4553603977626235, 2.4208106201479063, 2.3563708976839934, 2.249617251858286, 2.088767901668905, 1.8646211992587052, 1.5722278564805536, 1.2122322654143562, 0.7918114773009285, 0.3251141678850262, -0.16691144316768375, -0.6573964905864625, -1.1151856382935645, -1.5071994344825683, -1.8014023948808815, -1.9701512023037249, -1.9936012250351378, -1.8627767179501755, -1.5818767194922791, -1.169408326047515, -0.6578200007392618, -0.09145043881650318, 0.47719564701657635, 0.9926036805418709, 1.4023607019226696, 1.6635391533246993, 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'7.66593324608740923429045774346493', '8.522826508070270413003441427636415', '9.816211648176531494013209199008164', '10.80173622629491757159567795677421'], 'prelabel': '2-666-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3060868965885213, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.45791910636920151145052736404', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.89482296470876112563179558494', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.12270267488747912083793452666', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.318036774617276, 'bad_primes': [2, 3, 37], 'central_character': '1.1', 'conductor': 666, 'conductor_radical': 222, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/666/2/a/j/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': '2-666-1.1-c1-0-5', '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': '2-666-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3060868965885213, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.45791910636920151145052736404', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1848132030273122122588419122461', 'Lhash_array': ['1848132030273122122588419122461'], 'label': '2-666-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/666/2/a/j/1/1'}