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lfunc_lfunctions • Show schema
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{'Lhash': '767721502176217226893524258706,1713160173732309416953093808622', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 230.1767299768598, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [19, [1, -2, 1]]], 'bad_primes': [2, 5, 19], 'central_character': '1900.1', 'coefficient_field': '1.1.1.1', 'conductor': 3610000, 'conductor_radical': 190, 'degree': 4, 'euler_factors': [[1], [1, 0, -2, 0, 9], [1], [1, 0, -10, 0, 49], [1, 0, 22, 0, 121], [1, 0, 10, 0, 169], [1, 0, -30, 0, 289], [1, -2, 1], [1, 0, -42, 0, 529], [1, -4, 62, -116, 841], [1, -8, 78, -248, 961], [1, 0, 26, 0, 1369], [1, 20, 182, 820, 1681], [1, 0, -50, 0, 1849], [1, 0, -58, 0, 2209], [1, 0, -70, 0, 2809], [1, -8, 134, -472, 3481], [1, -4, 126, -244, 3721], [1, 0, -130, 0, 4489], [1, -24, 286, -1704, 5041], [1, 0, -110, 0, 5329], [1, 16, 222, 1264, 6241], [1, 0, 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'group': 'GL2', 'index': 1, 'label': '4-1900e2-1.1-c1e2-0-1', 'leading_term': '2.42587738322963989446369939797382573747302905987784285137529991257751305804118868977882655', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1900/2/c/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.029296875', 'prec': 37}, 'plot_values': [2.42587738322964, 2.419002543343779, 2.4012599896235876, 2.370488395157981, 2.3270957612682324, 2.2715449863072927, 2.203717645287605, 2.123590098463802, 2.031289578849916, 1.9269837067324875, 1.8108839320458991, 1.6833011158274522, 1.544649044205842, 1.395460274291458, 1.2364029965364662, 1.068289237907551, 0.8920929087310255, 0.7089522386240018, 0.5201766447560418, 0.3272518904577069, 0.13182747747685425, -0.06427675183501129, 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'5.08425147123881701964406324837307', '5.25878705003116847708138839490815', '5.73408840322144802552398059788603', '6.45540485107953424439008618878489', '6.68623316230868009385269762014734', '6.95102633656829355135763511277715', '7.38085164086044896113199831655322', '8.006229235820168198037045670735954', '8.215003478037161535612588454734177', '8.604157004218894647066953018031874', '8.902395607164004577111770790657094', '9.589794720351627286948179479459140'], 'prelabel': '4-1900e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.8950707803637257, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 2188534990411836478, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.60562547916436570633318595538', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.35144508543905545735368819591', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.85608172423703575011480547082', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 230.1767299768598, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 3610000, 'conductor_radical': 190, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, -16, 0, -5, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, 0, 10, 0, 169], 'euler17': [1, 0, -30, 0, 289], 'euler19': [1, -2, 1, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -42, 0, 529], 'euler29': [1, -4, 62, -116, 841], 'euler3': [1, 0, -2, 0, 9], 'euler31': [1, -8, 78, -248, 961], 'euler37': [1, 0, 26, 0, 1369], 'euler41': [1, 20, 182, 820, 1681], 'euler43': [1, 0, -50, 0, 1849], 'euler47': [1, 0, -58, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -70, 0, 2809], 'euler59': [1, -8, 134, -472, 3481], 'euler61': [1, -4, 126, -244, 3721], 'euler67': [1, 0, -130, 0, 4489], 'euler7': [1, 0, -10, 0, 49], 'euler71': [1, -24, 286, -1704, 5041], 'euler73': [1, 0, -110, 0, 5329], 'euler79': [1, 16, 222, 1264, 6241], 'euler83': [1, 0, -162, 0, 6889], 'euler89': [1, 4, 182, 356, 7921], 'euler97': [1, 0, 130, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -2, 0, 9], [1, 0, 0, 0, 0], [1, 0, -10, 0, 49], [1, 0, 22, 0, 121], [1, 0, 10, 0, 169], [1, 0, -30, 0, 289], [1, -2, 1, 0, 0], [1, 0, -42, 0, 529], [1, -4, 62, -116, 841], [1, -8, 78, -248, 961], [1, 0, 26, 0, 1369], [1, 20, 182, 820, 1681], [1, 0, -50, 0, 1849], [1, 0, -58, 0, 2209], [1, 0, -70, 0, 2809], [1, -8, 134, -472, 3481], [1, -4, 126, -244, 3721], [1, 0, -130, 0, 4489], [1, -24, 286, -1704, 5041], [1, 0, -110, 0, 5329], [1, 16, 222, 1264, 6241], [1, 0, -162, 0, 6889], [1, 4, 182, 356, 7921], [1, 0, 130, 0, 9409]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1900/2/c/a'], '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': '4-1900e2-1.1-c1e2-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-1900e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.8950707803637257, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2188534990411836478, 'z1': {'__RealLiteral__': 0, 'data': '0.60562547916436570633318595538', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '767721502176217226893524258706,1713160173732309416953093808622', 'Lhash_array': ['767721502176217226893524258706', '1713160173732309416953093808622'], 'label': '4-1900e2-1.1-c1e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1900/2/c/a'}