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lfunc_lfunctions • Show schema
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{'Lhash': '1335445794442208595247766301473,2054558112697024300000920571494', 'a10': 0, 'a2': -2, 'a3': 0, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': 4, 'a8': 0, 'a9': 2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.82191556911358, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [11, [1, -2, 1]]], 'bad_primes': [5, 11], 'central_character': '275.1', 'coefficient_field': '1.1.1.1', 'conductor': 75625, 'conductor_radical': 55, 'degree': 4, 'euler_factors': [[1, 2, 3, 4, 4], [1, 0, -2, 0, 9], [1], [1, -4, 18, -28, 49], [1, -2, 1], [1, -8, 34, -104, 169], [1, 8, 42, 136, 289], [1, 0, 38, 0, 361], [1, 0, 38, 0, 529], [1, -4, 30, -116, 841], [1, 0, 62, 0, 961], [1, -4, 46, -148, 1369], [1, -12, 118, -492, 1681], [1, -12, 122, -516, 1849], [1, 0, 86, 0, 2209], [1, 12, 110, 636, 2809], [1, 8, 102, 472, 3481], [1, -4, -2, -244, 3721], [1, 8, 78, 536, 4489], [1, 0, 14, 0, 5041], [1, -8, 154, -584, 5329], [1, -8, 174, -632, 6241], [1, 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['1.05348097827727392870510429458934', '1.62076057261134817791620072556479', '2.68087087515998116401091200236278', '3.91275786896581322341708444462469', '4.32093856880512229575824594630970', '4.79496409631693048558279083329535', '5.78170041068762991597464841365290', '6.48170268766400170628637889021497', '6.55117649324971760946554101507899', '7.63373519091757555317365298931236', '8.079260243639446110251027998211047', '8.181288028444606161175625940355525', '9.030176806043449037762894238009714', '9.145660341697595489858477378965418', '9.364991687812248303675834307232496', '10.34216843190214001821092395944854', '10.76332109077944369674429873619164', '11.06226320084177966638189511931568', '11.34152724924583538335689542678810', '11.85078764068031628780781210826223'], 'prelabel': '4-275e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.4818522381078392, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1176208882623231927, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05348097827727392870510429459', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.62076057261134817791620072556', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.68087087515998116401091200236', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.82191556911358, 'bad_primes': [5, 11], 'central_character': '1.1', 'conductor': 75625, 'conductor_radical': 55, 'degree': 4, 'dirichlet_coefficients': [1, -2, 0, 1, 0, 0, 4, 0, 2, 0, 2, 0, 8, -8, 0, 1, -8, -4, 0, 0, 0, -4, 0, 0, 0, -16, 0, 4, 4, 0, 0, 2, 0, 16, 0, 2, 4, 0, 0, 0, 12, 0, 12, 2, 0, 0, 0, 0, -2, 0, 0, 8, -12, 0, 0, 0, 0, -8, -8, 0, 4, 0, 8, -11, 0, 0, -8, -8, 0, 0, 0, 0, 8, -8, 0, 0, 8, 0, 8, 0, -5, -24, 12, 0, 0, -24, 0, 0, -4, 0, 32, 0, 0, 0, 0, 0, 4, 4, 4, 0], 'euler11': [1, -2, 1, 0, 0], 'euler13': [1, -8, 34, -104, 169], 'euler17': [1, 8, 42, 136, 289], 'euler19': [1, 0, 38, 0, 361], 'euler2': [1, 2, 3, 4, 4], 'euler23': [1, 0, 38, 0, 529], 'euler29': [1, -4, 30, -116, 841], 'euler3': [1, 0, -2, 0, 9], 'euler31': [1, 0, 62, 0, 961], 'euler37': [1, -4, 46, -148, 1369], 'euler41': [1, -12, 118, -492, 1681], 'euler43': [1, -12, 122, -516, 1849], 'euler47': [1, 0, 86, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 12, 110, 636, 2809], 'euler59': [1, 8, 102, 472, 3481], 'euler61': [1, -4, -2, -244, 3721], 'euler67': [1, 8, 78, 536, 4489], 'euler7': [1, -4, 18, -28, 49], 'euler71': [1, 0, 14, 0, 5041], 'euler73': [1, -8, 154, -584, 5329], 'euler79': [1, -8, 174, -632, 6241], 'euler83': [1, -12, 202, -996, 6889], 'euler89': [1, 4, 54, 356, 7921], 'euler97': [1, -4, 166, -388, 9409], 'euler_factors': [[1, 2, 3, 4, 4], [1, 0, -2, 0, 9], [1, 0, 0, 0, 0], [1, -4, 18, -28, 49], [1, -2, 1, 0, 0], [1, -8, 34, -104, 169], [1, 8, 42, 136, 289], [1, 0, 38, 0, 361], [1, 0, 38, 0, 529], [1, -4, 30, -116, 841], [1, 0, 62, 0, 961], [1, -4, 46, -148, 1369], [1, -12, 118, -492, 1681], [1, -12, 122, -516, 1849], [1, 0, 86, 0, 2209], [1, 12, 110, 636, 2809], [1, 8, 102, 472, 3481], [1, -4, -2, -244, 3721], [1, 8, 78, 536, 4489], [1, 0, 14, 0, 5041], [1, -8, 154, -584, 5329], [1, -8, 174, -632, 6241], [1, -12, 202, -996, 6889], [1, 4, 54, 356, 7921], [1, -4, 166, -388, 9409]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/275/2/a/c'], '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': '4-275e2-1.1-c1e2-0-2', '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': '4-275e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.4818522381078392, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1176208882623231927, 'z1': {'__RealLiteral__': 0, 'data': '1.05348097827727392870510429459', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1335445794442208595247766301473,2054558112697024300000920571494', 'Lhash_array': ['1335445794442208595247766301473', '2054558112697024300000920571494'], 'label': '4-275e2-1.1-c1e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/275/2/a/c'}