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lfunc_lfunctions • Show schema
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{'Lhash': '1158369475529570334455485709985,2283237824088650384611344993678', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 84, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -27, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 393.9047154139059, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, 27]]], 'bad_primes': [2, 3], 'central_character': '192.1', 'coefficient_field': '1.1.1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1, 0, 27], [1, -84, 3014, -52500, 390625], [1, 0, 1006, 0, 5764801], [1, 0, -28850, 0, 214358881], [1, -364, 90246, -10396204, 815730721], [1, 492, 227558, 41092332, 6975757441], [1, 0, -246770, 0, 16983563041], [1, 0, 190, 0, 78310985281], [1, 156, 1420646, 110335836, 500246412961], [1, 0, 330670, 0, 852891037441], [1, 1060, 4029222, 1986610660, 3512479453921], [1, 1836, 6494246, 5188097196, 7984925229121], [1, 0, -6111410, 0, 11688200277601], [1, 0, 4550206, 0, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 393.9047154139059, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 84, 0, 0, 0, -27, 0, 0, 0, 364, 0, 0, 0, -492, 0, 0, 0, 0, 0, 0, 0, 4042, 0, 0, 0, -156, 0, 0, 0, 0, 0, 0, 0, -1060, 0, 0, 0, -1836, 0, 0, 0, -2268, 0, 0, 0, -1006, 0, 0, 0, 9252, 0, 0, 0, 0, 0, 0, 0, -2692, 0, 0, 0, 30576, 0, 0, 0, 0, 0, 0, 0, -1852, 0, 0, 0, 0, 0, 0, 0, 729, 0, 0, 0, -41328, 0, 0, 0, 23172, 0, 0, 0, 0, 0, 0, 0, -26236, 0, 0, 0], 'euler11': [1, 0, -28850, 0, 214358881], 'euler13': [1, -364, 90246, -10396204, 815730721], 'euler17': [1, 492, 227558, 41092332, 6975757441], 'euler19': [1, 0, -246770, 0, 16983563041], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 190, 0, 78310985281], 'euler29': [1, 156, 1420646, 110335836, 500246412961], 'euler3': [1, 0, 27, 0, 0], 'euler31': [1, 0, 330670, 0, 852891037441], 'euler37': [1, 1060, 4029222, 1986610660, 3512479453921], 'euler41': [1, 1836, 6494246, 5188097196, 7984925229121], 'euler43': [1, 0, -6111410, 0, 11688200277601], 'euler47': [1, 0, 4550206, 0, 23811286661761], 'euler5': [1, -84, 3014, -52500, 390625], 'euler53': [1, -9252, 37180838, -73002730212, 62259690411361], 'euler59': [1, 0, -24182450, 0, 146830437604321], 'euler61': [1, 2692, 29503398, 37273003972, 191707312997281], 'euler67': [1, 0, -39119090, 0, 406067677556641], 'euler7': [1, 0, 1006, 0, 5764801], 'euler71': [1, 0, -47477954, 0, 645753531245761], 'euler73': [1, 1852, 57653958, 52593542332, 806460091894081], 'euler79': [1, 0, -58545362, 0, 1517108809906561], 'euler83': [1, 0, 48908686, 0, 2252292232139041], 'euler89': [1, -23172, 259719878, -1453863208452, 3936588805702081], 'euler97': [1, 26236, 349140486, 2322654216316, 7837433594376961], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 27, 0, 0], [1, -84, 3014, -52500, 390625], [1, 0, 1006, 0, 5764801], [1, 0, -28850, 0, 214358881], [1, -364, 90246, -10396204, 815730721], [1, 492, 227558, 41092332, 6975757441], [1, 0, -246770, 0, 16983563041], [1, 0, 190, 0, 78310985281], [1, 156, 1420646, 110335836, 500246412961], [1, 0, 330670, 0, 852891037441], [1, 1060, 4029222, 1986610660, 3512479453921], [1, 1836, 6494246, 5188097196, 7984925229121], [1, 0, -6111410, 0, 11688200277601], [1, 0, 4550206, 0, 23811286661761], [1, -9252, 37180838, -73002730212, 62259690411361], [1, 0, -24182450, 0, 146830437604321], [1, 2692, 29503398, 37273003972, 191707312997281], [1, 0, -39119090, 0, 406067677556641], [1, 0, -47477954, 0, 645753531245761], [1, 1852, 57653958, 52593542332, 806460091894081], [1, 0, -58545362, 0, 1517108809906561], [1, 0, 48908686, 0, 2252292232139041], [1, -23172, 259719878, -1453863208452, 3936588805702081], [1, 26236, 349140486, 2322654216316, 7837433594376961]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/192/5/g/b'], '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': '4-192e2-1.1-c4e2-0-3', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4, 4], 'order_of_vanishing': 0, 'prelabel': '4-192e2-1.1-c4e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.455000888001945, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c4e2-0', 'trace_hash': 2235206874918625138, 'z1': {'__RealLiteral__': 0, 'data': '0.913792393046645537420334612113', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1158369475529570334455485709985,2283237824088650384611344993678', 'Lhash_array': ['1158369475529570334455485709985', '2283237824088650384611344993678'], 'label': '4-192e2-1.1-c4e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/192/5/g/b'}