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lfunc_lfunctions • Show schema
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{'Lhash': '1822343584983772106329025254169,1882552478303733207808326769054', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': 5, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5586.064056116536, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -2, 1]], [13, [1, 2, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '9360.1', 'coefficient_field': '1.1.1.1', 'conductor': 87609600, 'conductor_radical': 390, 'degree': 4, 'euler_factors': [[1], [1], [1, -2, 1], [1, -5, 16, -35, 49], [1, 1, 18, 11, 121], [1, 2, 1], [1, 1, 30, 17, 289], [1, -2, 22, -38, 361], [1, 9, 62, 207, 529], [1, 6, 50, 174, 841], [1, 12, 98, 372, 961], [1, 9, 56, 333, 1369], [1, -3, 80, -123, 1681], [1, -2, 70, -86, 1849], [1, 14, 126, 658, 2209], [1, -3, 70, -159, 2809], [1, 24, 262, 1416, 3481], [1, 1, 84, 61, 3721], [1, 2, -18, 134, 4489], [1, 25, 294, 1775, 5041], [1, 12, 182, 876, 5329], [1, -3, 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'1.48507205216074216520246176702937', '1.97255672866968911267077175713063', '2.07720068936321360482182710077723', '2.79710430694435538976692478721037', '3.22703814353017751886902231326108', '3.61881409878745915715574603079964', '4.16076445854621581259954130650531', '4.49960807842746904731067276607653', '4.77639799981178319614907430537642', '5.25177300777133945870242579393604', '5.37785113468469007359117471042399', '5.79986410952386088974612850144369', '6.00866554670626865042079744713807', '6.63264688609698015462378773701508', '6.70668270789967633890177593550700', '7.53118532001094719175023556089596', '7.63745624210096357171202597080446'], 'prelabel': '4-9360e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.645228527454812, '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': 1712121994908182696, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.43757561007400231991021636840', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.48507205216074216520246176703', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.97255672866968911267077175713', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5586.064056116536, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 87609600, 'conductor_radical': 390, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, 5, 0, 0, 0, -1, 0, -2, 0, 0, 0, -1, 0, 2, 0, 0, 0, -9, 0, 3, 0, 0, 0, -6, 0, -12, 0, 0, 0, 10, 0, -9, 0, 0, 0, 3, 0, 2, 0, 0, 0, -14, 0, 9, 0, 0, 0, 3, 0, -2, 0, 0, 0, -24, 0, -1, 0, 0, 0, -4, 0, -2, 0, 0, 0, -25, 0, -12, 0, 0, 0, -5, 0, 3, 0, 0, 0, 0, 0, -2, 0, 0, 0, 9, 0, -10, 0, 0, 0, 4, 0, 5, 0, 0, 0], 'euler11': [1, 1, 18, 11, 121], 'euler13': [1, 2, 1, 0, 0], 'euler17': [1, 1, 30, 17, 289], 'euler19': [1, -2, 22, -38, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 9, 62, 207, 529], 'euler29': [1, 6, 50, 174, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 12, 98, 372, 961], 'euler37': [1, 9, 56, 333, 1369], 'euler41': [1, -3, 80, -123, 1681], 'euler43': [1, -2, 70, -86, 1849], 'euler47': [1, 14, 126, 658, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, -3, 70, -159, 2809], 'euler59': [1, 24, 262, 1416, 3481], 'euler61': [1, 1, 84, 61, 3721], 'euler67': [1, 2, -18, 134, 4489], 'euler7': [1, -5, 16, -35, 49], 'euler71': [1, 25, 294, 1775, 5041], 'euler73': [1, 12, 182, 876, 5329], 'euler79': [1, -3, 122, -237, 6241], 'euler83': [1, 0, -106, 0, 6889], 'euler89': [1, -9, 160, -801, 7921], 'euler97': [1, -5, -8, -485, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -2, 1, 0, 0], [1, -5, 16, -35, 49], [1, 1, 18, 11, 121], [1, 2, 1, 0, 0], [1, 1, 30, 17, 289], [1, -2, 22, -38, 361], [1, 9, 62, 207, 529], [1, 6, 50, 174, 841], [1, 12, 98, 372, 961], [1, 9, 56, 333, 1369], [1, -3, 80, -123, 1681], [1, -2, 70, -86, 1849], [1, 14, 126, 658, 2209], [1, -3, 70, -159, 2809], [1, 24, 262, 1416, 3481], [1, 1, 84, 61, 3721], [1, 2, -18, 134, 4489], [1, 25, 294, 1775, 5041], [1, 12, 182, 876, 5329], [1, -3, 122, -237, 6241], [1, 0, -106, 0, 6889], [1, -9, 160, -801, 7921], [1, -5, -8, -485, 9409]], 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9360/2/a/cw'], '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': '4-9360e2-1.1-c1e2-0-20', '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': 2, 'prelabel': '4-9360e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.645228527454812, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1712121994908182696, 'z1': {'__RealLiteral__': 0, 'data': '1.43757561007400231991021636840', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1822343584983772106329025254169,1882552478303733207808326769054', 'Lhash_array': ['1822343584983772106329025254169', '1882552478303733207808326769054'], 'label': '4-9360e2-1.1-c1e2-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9360/2/a/cw'}