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lfunc_lfunctions • Show schema
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{'Lhash': '1348354686267609280106049129095,1753889881868999105578130591273', 'a10': 0, 'a2': 0, 'a3': 4, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 4, 'a8': 0, 'a9': 8, '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, -4, 8, -12, 9], [1], [1, -4, 10, -28, 49], [1, 4, 26, 44, 121], [1, -4, 12, -52, 169], [1, -4, 30, -68, 289], [1, 2, 1], [1, -12, 82, -276, 529], [1, -4, -10, -116, 841], [1, 8, 70, 248, 961], [1, -12, 92, -444, 1369], [1, 4, 54, 164, 1681], [1, 4, 82, 172, 1849], [1, -4, 90, -188, 2209], [1, 4, 60, 212, 2809], [1, -16, 150, -944, 3481], [1, 16, 154, 976, 3721], [1, -4, 136, -268, 4489], [1, -16, 198, -1136, 5041], [1, 12, 110, 876, 5329], [1, 8, 142, 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[0, 0]], 'group': 'GL2', 'index': 3, 'label': '4-1900e2-1.1-c1e2-0-3', 'leading_term': '8.5035306242124229646359246587857584440091894044830927825880000000000000000000000000000000', '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/a/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.029296875', 'prec': 37}, 'plot_values': [8.503530624212424, 8.493845495882162, 8.473546742006747, 8.435744507537448, 8.381714463996202, 8.312501619149705, 8.22728499866091, 8.125476863750425, 8.006801443873657, 7.870904363718737, 7.717399436795645, 7.545976266885554, 7.356411259732403, 7.148586424799933, 6.92252146720477, 6.678392748095595, 6.416572130601204, 6.1376336774989255, 5.842387699120174, 5.531885771615837, 5.207438223238342, 4.8706189230910715, 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'5.09402850330044237063682818957960', '5.80048231792358514132792270165200', '6.22801289309547539997526798333139', '7.07776387859571917303056921611054', '7.12570631103319291875353444802950', '7.82274375813984079578170040733324', '7.895962890627497027233527050110328', '8.286866276828365740360376758947380', '8.518153926659759368142620055655405', '8.991426195530261133363842420588272', '9.105350401243179652686633724661043'], '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': 1499864221308240992, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06366429836805963243822559245', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.38357515986915209515578547703', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.33385823526127338015047033583', '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, 4, 0, 0, 0, 4, 0, 8, 0, -4, 0, 4, 0, 0, 0, 4, 0, -2, 0, 16, 0, 12, 0, 0, 0, 12, 0, 4, 0, -8, 0, -16, 0, 0, 0, 12, 0, 16, 0, -4, 0, -4, 0, 0, 0, 4, 0, 6, 0, 16, 0, -4, 0, 0, 0, -8, 0, 16, 0, -16, 0, 32, 0, 0, 0, 4, 0, 48, 0, 16, 0, -12, 0, 0, 0, -16, 0, -8, 0, 23, 0, 4, 0, 0, 0, 16, 0, 4, 0, 16, 0, -32, 0, 0, 0, 12, 0, -32, 0], 'euler11': [1, 4, 26, 44, 121], 'euler13': [1, -4, 12, -52, 169], 'euler17': [1, -4, 30, -68, 289], 'euler19': [1, 2, 1, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -12, 82, -276, 529], 'euler29': [1, -4, -10, -116, 841], 'euler3': [1, -4, 8, -12, 9], 'euler31': [1, 8, 70, 248, 961], 'euler37': [1, -12, 92, -444, 1369], 'euler41': [1, 4, 54, 164, 1681], 'euler43': [1, 4, 82, 172, 1849], 'euler47': [1, -4, 90, -188, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 4, 60, 212, 2809], 'euler59': [1, -16, 150, -944, 3481], 'euler61': [1, 16, 154, 976, 3721], 'euler67': [1, -4, 136, -268, 4489], 'euler7': [1, -4, 10, -28, 49], 'euler71': [1, -16, 198, -1136, 5041], 'euler73': [1, 12, 110, 876, 5329], 'euler79': [1, 8, 142, 632, 6241], 'euler83': [1, -4, 42, -332, 6889], 'euler89': [1, -4, 110, -356, 7921], 'euler97': [1, -12, 212, -1164, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -4, 8, -12, 9], [1, 0, 0, 0, 0], [1, -4, 10, -28, 49], [1, 4, 26, 44, 121], [1, -4, 12, -52, 169], [1, -4, 30, -68, 289], [1, 2, 1, 0, 0], [1, -12, 82, -276, 529], [1, -4, -10, -116, 841], [1, 8, 70, 248, 961], [1, -12, 92, -444, 1369], [1, 4, 54, 164, 1681], [1, 4, 82, 172, 1849], [1, -4, 90, -188, 2209], [1, 4, 60, 212, 2809], [1, -16, 150, -944, 3481], [1, 16, 154, 976, 3721], [1, -4, 136, -268, 4489], [1, -16, 198, -1136, 5041], [1, 12, 110, 876, 5329], [1, 8, 142, 632, 6241], [1, -4, 42, -332, 6889], [1, -4, 110, -356, 7921], [1, -12, 212, -1164, 9409]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1900/2/a/e'], '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-c1e2-0-3', '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': 1499864221308240992, 'z1': {'__RealLiteral__': 0, 'data': '1.06366429836805963243822559245', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1348354686267609280106049129095,1753889881868999105578130591273', 'Lhash_array': ['1348354686267609280106049129095', '1753889881868999105578130591273'], 'label': '4-1900e2-1.1-c1e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1900/2/a/e'}