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lfunc_lfunctions • Show schema
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{'Lhash': '185536061667432379801498658231,2445957659310159632700346317323', 'a10': -4, 'a2': 1, 'a3': 0, 'a4': 0, 'a5': -4, 'a6': 0, 'a7': 0, 'a8': -1, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 74.09548340122691, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 1]], [7, [1]], [11, [1, -1, 1]]], 'bad_primes': [2, 7, 11], 'central_character': '1078.1', 'coefficient_field': '1.1.1.1', 'conductor': 1162084, 'conductor_radical': 154, 'degree': 4, 'euler_factors': [[1, -1, 1], [1, 0, -3, 0, 9], [1, 4, 11, 20, 25], [1], [1, -1, 1], [1, 4, 30, 52, 169], [1, 4, -1, 68, 289], [1, 6, 17, 114, 361], [1, 4, -7, 92, 529], [1, 4, 62, 116, 841], [1, 2, -27, 62, 961], [1, 10, 63, 370, 1369], [1, 8, 98, 328, 1681], [1, 16, 150, 688, 1849], [1, -2, -43, -94, 2209], [1, 6, -17, 318, 2809], [1, 12, 85, 708, 3481], [1, 14, 135, 854, 3721], [1, -12, 77, -804, 4489], [1, 16, 206, 1136, 5041], [1, -4, -57, -292, 5329], [1, 0, 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'6.11054143141054975237765970774966', '6.11518121962573745494109512909496', '6.85635868816809327932155916650900', '7.22680704622501398107131237885159', '7.48860344856437729135364096388284', '7.905878418643774710519691748611832', '8.559011360012276137600174435808435', '8.675465696989419823372271681782063', '9.133009965674375628519104596176322', '9.875038947519482512342610663379406', '10.08000033787343492297607970988598'], 'prelabel': '4-1078e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1359277739367903621, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.14636214555811217611461498834', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.92525314806828388113684110865', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.92952037325567972179124686277', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 74.09548340122691, 'bad_primes': [2, 7, 11], 'central_character': '1.1', 'conductor': 1162084, 'conductor_radical': 154, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 0, -4, 0, 0, -1, 3, -4, 1, 0, -4, 0, 0, -1, -4, 3, -6, 0, 0, 1, -4, 0, 5, -4, 0, 0, -4, 0, -2, 0, 0, -4, 0, 0, -10, -6, 0, 4, -8, 0, -16, 0, -12, -4, 2, 0, 0, 5, 0, 0, -6, 0, -4, 0, 0, -4, -12, 0, -14, -2, 0, 1, 16, 0, 12, 0, 0, 0, -16, -3, 4, -10, 0, 0, 0, 0, 0, 4, 0, -8, 12, 0, 16, -16, 0, -1, -6, -12, 0, 0, 0, 2, 24, 0, 28, 0, 3, 0], 'euler11': [1, -1, 1, 0, 0], 'euler13': [1, 4, 30, 52, 169], 'euler17': [1, 4, -1, 68, 289], 'euler19': [1, 6, 17, 114, 361], 'euler2': [1, -1, 1, 0, 0], 'euler23': [1, 4, -7, 92, 529], 'euler29': [1, 4, 62, 116, 841], 'euler3': [1, 0, -3, 0, 9], 'euler31': [1, 2, -27, 62, 961], 'euler37': [1, 10, 63, 370, 1369], 'euler41': [1, 8, 98, 328, 1681], 'euler43': [1, 16, 150, 688, 1849], 'euler47': [1, -2, -43, -94, 2209], 'euler5': [1, 4, 11, 20, 25], 'euler53': [1, 6, -17, 318, 2809], 'euler59': [1, 12, 85, 708, 3481], 'euler61': [1, 14, 135, 854, 3721], 'euler67': [1, -12, 77, -804, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 16, 206, 1136, 5041], 'euler73': [1, -4, -57, -292, 5329], 'euler79': [1, 0, -79, 0, 6241], 'euler83': [1, -12, 202, -996, 6889], 'euler89': [1, 6, -53, 534, 7921], 'euler97': [1, -28, 390, -2716, 9409], 'euler_factors': [[1, -1, 1, 0, 0], [1, 0, -3, 0, 9], [1, 4, 11, 20, 25], [1, 0, 0, 0, 0], [1, -1, 1, 0, 0], [1, 4, 30, 52, 169], [1, 4, -1, 68, 289], [1, 6, 17, 114, 361], [1, 4, -7, 92, 529], [1, 4, 62, 116, 841], [1, 2, -27, 62, 961], [1, 10, 63, 370, 1369], [1, 8, 98, 328, 1681], [1, 16, 150, 688, 1849], [1, -2, -43, -94, 2209], [1, 6, -17, 318, 2809], [1, 12, 85, 708, 3481], [1, 14, 135, 854, 3721], [1, -12, 77, -804, 4489], [1, 16, 206, 1136, 5041], [1, -4, -57, -292, 5329], [1, 0, -79, 0, 6241], [1, -12, 202, -996, 6889], [1, 6, -53, 534, 7921], [1, -28, 390, -2716, 9409]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1078/2/e/i'], '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': '4-1078e2-1.1-c1e2-0-0', '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': '4-1078e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1359277739367903621, 'z1': {'__RealLiteral__': 0, 'data': '0.14636214555811217611461498834', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '185536061667432379801498658231,2445957659310159632700346317323', 'Lhash_array': ['185536061667432379801498658231', '2445957659310159632700346317323'], 'label': '4-1078e2-1.1-c1e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1078/2/e/i'}