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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -3, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 5, 'A8': 0, 'A9': 3, 'Lhash': '1266467403797184741', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.030927835051546393, 0.0], 'a4': [0.0, 0.0], 'a5': [0.010309278350515464, 0.0], 'a6': [0.0, 0.0], 'a7': [0.05154639175257732, 0.0], 'a8': [0.0, 0.0], 'a9': [0.030927835051546393, 0.0], 'algebraic': True, 'analytic_conductor': 3.019714662521906, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[2, [1]], [5, [1, -1, 5, -5]], [37, [1, 5, 31, -37]]], 'bad_primes': [2, 5, 37], 'central_character': '47360.1', 'coefficient_field': '1.1.1.1', 'conductor': 47360, 'conductor_radical': 370, 'degree': 4, 'euler_factors': [[1], [1, 3, 6, 9, 9], [1, -1, 5, -5], [1, -5, 18, -35, 49], [1, 1, -14, 11, 121], [1, 4, 10, 52, 169], [1, 6, 30, 102, 289], [1, 2, -2, 38, 361], [1, 2, 38, 46, 529], [1, 6, 42, 174, 841], [1, 0, -2, 0, 961], [1, 5, 31, -37], [1, 11, 96, 451, 1681], [1, 2, 26, 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1.311340135606606, 3.867576833826171, 6.838790194626719, 9.23851616920349, 10.05589403137736, 8.753472012517468, 5.634226497401703, 1.814034836017828, -1.276832080453576, -2.636538179779448, -2.23086956204663, -0.9426253544000245, 0.08031089799488726, 0.2323486751593535, -0.2040483797927309, -0.4647592664327793, -0.1211252195009528, 0.4439317442835883, 0.4042180269227868, -0.5840600162466232, -1.82206084920054, -2.077305192973137, -0.8360123247839663, 0.9312186880911726, 1.467845429121167, -0.03627662744940204, -2.367678654387995, -3.205810605029337, -1.430813669438516, 1.464650710675661, 2.594106398119296, 0.6305980052439562, -2.511060643071159, -3.335725546820445, -0.4012881158930924, 3.853206475784185, 5.303178079042492, 2.316208439078344, -2.500220309896486, -4.954600858341919, -3.494349555939755, -0.413067097525693, 1.071106287456917, 0.2772689115272136, -0.8673473486432651, -0.7236552959878755, 0.1568568262555456, 0.36057311406022, -0.1160547438943193, -0.05231893239913741, 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[1.794921867805141, 2.290230937832692, 3.849546964626092, 4.665028806269777, 4.985100303802958, 5.475161142164494, 5.907936139635905, 6.646978822766084, 7.122005074902705, 7.777723023394645, 8.286689323543794, 8.829835764382183, 9.463432086234912, 10.1557270876446, 10.53736098114045, 11.02507600545791, 11.3909452920639, 11.64087919352157, 12.14423433776988, 12.52141434126046, 13.25106372292945, 13.65932458428748, 14.06869534660813, 14.72045030730105, 14.97381558778125, 15.5119117072901, 15.84090270571052, 16.69698257427801, 16.92369373560325, 17.30218168746843, 17.44356732814397, 17.90144588609901, 18.15899541228894, 18.65180047760378, 19.10602936079003, 19.85954508491641], 'prelabel': '4-47360-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.318230867915398, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 1266467403797184741, 'z1': {'__RealLiteral__': 0, 'data': '1.79492186781', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.29023093783', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.84954696463', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.019714662521906, 'bad_primes': [2, 5, 37], 'central_character': '1.1', 'conductor': 47360, 'conductor_radical': 370, 'degree': 4, 'dirichlet_coefficients': [1, 0, -3, 0, 1, 0, 5, 0, 3, 0, -1, 0, -4, 0, -3, 0, -6, 0, -2, 0, -15, 0, -2, 0, -4, 0, 0, 0, -6, 0, 0, 0, 3, 0, 5, 0, -5, 0, 12, 0, -11, 0, -2, 0, 3, 0, 9, 0, 7, 0, 18, 0, 5, 0, -1, 0, 6, 0, -6, 0, 8, 0, 15, 0, -4, 0, -8, 0, 6, 0, 11, 0, 9, 0, 12, 0, -5, 0, -4, 0, 0, 0, -3, 0, -6, 0, 18, 0, -4, 0, -20, 0, 0, 0, -2, 0, 8, 0, -3, 0], 'euler11': [1, 1, -14, 11, 121], 'euler13': [1, 4, 10, 52, 169], 'euler17': [1, 6, 30, 102, 289], 'euler19': [1, 2, -2, 38, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 2, 38, 46, 529], 'euler29': [1, 6, 42, 174, 841], 'euler3': [1, 3, 6, 9, 9], 'euler31': [1, 0, -2, 0, 961], 'euler37': [1, 5, 31, -37, 0], 'euler41': [1, 11, 96, 451, 1681], 'euler43': [1, 2, 26, 86, 1849], 'euler47': [1, -9, 90, -423, 2209], 'euler5': [1, -1, 5, -5, 0], 'euler53': [1, -5, 20, -265, 2809], 'euler59': [1, 6, 118, 354, 3481], 'euler61': [1, -8, 62, -488, 3721], 'euler67': [1, 8, 102, 536, 4489], 'euler7': [1, -5, 18, -35, 49], 'euler71': [1, -11, 70, -781, 5041], 'euler73': [1, -9, 136, -657, 5329], 'euler79': [1, 4, -82, 316, 6241], 'euler83': [1, 3, 134, 249, 6889], 'euler89': [1, 4, 102, 356, 7921], 'euler97': [1, -8, 50, -776, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 3, 6, 9, 9], [1, -1, 5, -5, 0], [1, -5, 18, -35, 49], [1, 1, -14, 11, 121], [1, 4, 10, 52, 169], [1, 6, 30, 102, 289], [1, 2, -2, 38, 361], [1, 2, 38, 46, 529], [1, 6, 42, 174, 841], [1, 0, -2, 0, 961], [1, 5, 31, -37, 0], [1, 11, 96, 451, 1681], [1, 2, 26, 86, 1849], [1, -9, 90, -423, 2209], [1, -5, 20, -265, 2809], [1, 6, 118, 354, 3481], [1, -8, 62, -488, 3721], [1, 8, 102, 536, 4489], [1, -11, 70, -781, 5041], [1, -9, 136, -657, 5329], [1, 4, -82, 316, 6241], [1, 3, 134, 249, 6889], [1, 4, 102, 356, 7921], [1, -8, 50, -776, 9409]], 'index': 8, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/47360/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-47360-1.1-c1e2-0-8', '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': 1, 'prelabel': '4-47360-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.318230867915398, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1266467403797184741, 'z1': {'__RealLiteral__': 0, 'data': '1.79492186781', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': '1266467403797184741', 'Lhash_array': ['1266467403797184741'], 'label': '4-47360-1.1-c1e2-0-8', 'type': 'G2Q', 'url': 'Genus2Curve/Q/47360/a'}