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lfunc_lfunctions • Show schema
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{'Lhash': '1030265886692078971486198300589,1140595537531586114039710286961', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 694.3558419523555, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, 1]], [5, [1]], [11, [1, -2, 1]]], 'bad_primes': [2, 3, 5, 11], 'central_character': '3300.1', 'coefficient_field': '1.1.1.1', 'conductor': 10890000, 'conductor_radical': 330, 'degree': 4, 'euler_factors': [[1], [1, 0, 1], [1], [1, 0, -10, 0, 49], [1, -2, 1], [1, 0, -22, 0, 169], [1, 0, -18, 0, 289], [1, -12, 74, -228, 361], [1, 0, -46, 0, 529], [1, -16, 122, -464, 841], [1, 16, 126, 496, 961], [1, 0, 26, 0, 1369], [1, -16, 146, -656, 1681], [1, 0, -82, 0, 1849], [1, 0, -30, 0, 2209], [1, 0, -102, 0, 2809], [1, 24, 262, 1416, 3481], [1, -20, 222, -1220, 3721], [1, 0, 10, 0, 4489], [1, -16, 206, -1136, 5041], [1, 0, -110, 0, 5329], [1, -4, 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['0.812736479994241797450003334490336', '0.899771228228213567001215918722545', '1.76478075288825487983398612163533', '2.33464781868136450376704728862469', '3.00077528210424142678170074749776', '3.10548905861548274337659435618136', '3.84946862447953932051315066287430', '3.97145991633301667778086157478264', '4.69739602723093305136970329638758', '5.04860348054364907420789976853785', '5.47415499105600653095977112258726', '5.66579187298214255086375364133164', '6.31495171883503283910924525880296', '6.47138926975835557601854511766211', '7.09959620284081841832896129480134', '7.33282486254383327967625189607868', '7.74605146323033103501731218108470', '7.918483050373540834725268828864632', '8.494913972075969112483859501834973', '8.964543476441895619854935788781060'], 'prelabel': '4-3300e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.133286731424862, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 694.3558419523555, 'bad_primes': [2, 3, 5, 11], 'central_character': '1.1', 'conductor': 10890000, 'conductor_radical': 330, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0], 'euler11': [1, -2, 1, 0, 0], 'euler13': [1, 0, -22, 0, 169], 'euler17': [1, 0, -18, 0, 289], 'euler19': [1, -12, 74, -228, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -46, 0, 529], 'euler29': [1, -16, 122, -464, 841], 'euler3': [1, 0, 1, 0, 0], 'euler31': [1, 16, 126, 496, 961], 'euler37': [1, 0, 26, 0, 1369], 'euler41': [1, -16, 146, -656, 1681], 'euler43': [1, 0, -82, 0, 1849], 'euler47': [1, 0, -30, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -102, 0, 2809], 'euler59': [1, 24, 262, 1416, 3481], 'euler61': [1, -20, 222, -1220, 3721], 'euler67': [1, 0, 10, 0, 4489], 'euler7': [1, 0, -10, 0, 49], 'euler71': [1, -16, 206, -1136, 5041], 'euler73': [1, 0, -110, 0, 5329], 'euler79': [1, -4, 162, -316, 6241], 'euler83': [1, 0, 90, 0, 6889], 'euler89': [1, -28, 374, -2492, 7921], 'euler97': [1, 0, -190, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 1, 0, 0], [1, 0, 0, 0, 0], [1, 0, -10, 0, 49], [1, -2, 1, 0, 0], [1, 0, -22, 0, 169], [1, 0, -18, 0, 289], [1, -12, 74, -228, 361], [1, 0, -46, 0, 529], [1, -16, 122, -464, 841], [1, 16, 126, 496, 961], [1, 0, 26, 0, 1369], [1, -16, 146, -656, 1681], [1, 0, -82, 0, 1849], [1, 0, -30, 0, 2209], [1, 0, -102, 0, 2809], [1, 24, 262, 1416, 3481], [1, -20, 222, -1220, 3721], [1, 0, 10, 0, 4489], [1, -16, 206, -1136, 5041], [1, 0, -110, 0, 5329], [1, -4, 162, -316, 6241], [1, 0, 90, 0, 6889], [1, -28, 374, -2492, 7921], [1, 0, -190, 0, 9409]], 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3300/2/c/j'], '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': '4-3300e2-1.1-c1e2-0-12', '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': '4-3300e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.133286731424862, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 628760522575717338, 'z1': {'__RealLiteral__': 0, 'data': '0.812736479994241797450003334490', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1030265886692078971486198300589,1140595537531586114039710286961', 'Lhash_array': ['1030265886692078971486198300589', '1140595537531586114039710286961'], 'factors': ['2-3300-5.4-c1-0-15', '2-3300-5.4-c1-0-17'], 'label': '4-3300e2-1.1-c1e2-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3300/2/c/j'}