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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': -1, 'A3': -1, 'A4': 1, 'A5': -1, 'A6': 1, 'A7': -2, 'A8': -1, 'A9': 1, 'Lhash': '1170241088723489954', 'a10': [0.31622776601683794, 0], 'a2': [-0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.4082482904638631, 0], 'a7': [-0.7559289460184544, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1315.3756724965524, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [5, [1, 1]], [17, [1]], [19, [1, 1]]], 'bad_primes': [2, 3, 5, 17, 19], 'central_character': '164730.1', 'coefficient_field': '1.1.1.1', 'conductor': 164730, 'conductor_radical': 9690, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1, 1], [1, 2, 7], [1, -5, 11], [1, 2, 13], [1], [1, 1], [1, 3, 23], [1, 6, 29], [1, 4, 31], [1, 4, 37], [1, -5, 41], [1, -4, 43], [1, -11, 47], [1, -5, 53], [1, 4, 59], [1, 11, 61], [1, 3, 67], [1, -10, 71], [1, 3, 73], [1, 1, 79], [1, -7, 83], [1, -6, 89], [1, 18, 97]], 'gamma_factors': [[], [0]], 'index': 34, 'label': '2-164730-1.1-c1-0-34', 'leading_term': '3.16563418327', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/164730/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.6403479722340235, 0.5003303423705, -0.5369747665991005, -1.50818923510597, -1.097656021972744, 0.6300500480995453, 1.63597309623522, 0.09609440611880785, -2.71689661462532, -3.154111951517927, 0.1808490308070844, 3.815439848785578, 3.469003777370308, 0.04421160444840761, -1.473925663900398, 0.4275715202813896, 1.178948607110544, -2.516284043182193, -6.462888354014327, -4.705118836636916, 1.007750725322539, 3.522939979084741, 1.148006987826319, -0.6613903194683403, 0.924764619606039, 2.139342554944449, 0.6156197087000476, -0.3106794717431789, 1.168394792618453, 1.399726899665743, -1.038436443110158, -1.418280445038111, 2.327302915889452, 4.796137019591025, 2.503085523536614, -0.2144938086017319, -0.01143412144350923, -0.1922498952408457, -2.379525019255039, -2.471136785731558, 0.2867170111243592, 0.8491607755140177, -1.35633135523937, -1.259353235628611, 0.9268060861325313, 0.2527481022410193, -1.948385379747235, -1.055973934698351, 0.3881223866368332, -0.7960436582346462, 0.7789176883492689, 7.108864571945908, 8.053396349410415, -0.1956878171692028, -4.657104601174422, 1.409164709657723, 5.711299457556988, 0.8761114960531748, -2.726178072220145, 0.5269876416162417, 1.800812769361969, -1.773539540150997, -2.322147726787314, 0.6979260618872747, 0.8242679489444809, -0.7608122105125269, -0.05775168723821272, 0.1312955816627539, -1.26616164895597, -0.1978977615464305, 1.496630280755572, -0.831043842480916, -2.989502433948212, -0.62865592491056, 0.9496758698277739, -0.8738599719702662, -0.9016196879967469, 0.4482541071585001, -0.9258396375521393, -1.177619774340737, 1.275684179822442, -1.027872174989332, -6.083113567801495, -2.499902836736622, 5.370264763580195, 4.189941455865788, -1.361751956987622, -0.7309319356718491, 0.6375424191667773, -1.933893883259083, -1.385004349533354, 0.8040524293383764, -3.186554968937489, -6.524250273022689, -1.724034668022005, 1.88472385796437, -0.5736382036928342, -0.5230727527307162, 1.297600132432415, -2.035200257040271, -4.146088171736207, 0.02063589947505079, 1.771477908693985, -0.4611741833137024, 1.151797259110996, 3.410560650480385, 0.5271100767800022, -1.366191416711499, 0.5060067790354469, 0.5015456242419511, -0.3291636775127277, 0.5028344553281549, -1.190111116849946, -3.552965186758494, -1.331286691212933, 0.3472896648061313, -1.397318121680566, -0.2634086801696207, 1.632163856853272, -0.6298064745734576], 'positive_zeros': ['0.6382265422607918', '1.415921961268619', '2.008811482478244', '2.739628978658621', '3.503390623389885', '3.955610409493926', '4.361482914433429', '5.204072073695128', '5.852957803250816', '6.145093161236062', '6.837901273303404', '7.079303145962665', '7.652453804005541', '8.114735363738617', '8.962843403183340', '9.253531459587258', '9.464299721889610', '10.22276534231547', '10.60323653232382', '11.13363551653928', '11.52561486656646', '12.12938033589645', '12.36612012024917', '12.70400674219403', '13.49463337576218', '13.95614049048494', '14.53445670639399', '14.96838100335656', '15.38587232879969', '15.93628190825576', '16.35731883037816', '16.76184920326169', '17.02627541641450', '17.52002283532102', '17.94105494286209', '18.55121931727405', '18.89560364371947', '19.37933733144490', '19.63176789949180'], 'prelabel': '2-164730-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 36.26810820123587, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1170241088723489954, 'z1': {'__RealLiteral__': 0, 'data': '0.6382265422607918', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.415921961268619', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.008811482478244', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1315.3756724965524, 'bad_primes': [2, 3, 5, 17, 19], 'central_character': '1.1', 'conductor': 164730, 'conductor_radical': 9690, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, -1, 1, -2, -1, 1, 1, 5, -1, -2, 2, 1, 1, 0, -1, -1, -1, 2, -5, -3, 1, 1, 2, -1, -2, -6, -1, -4, -1, -5, 0, 2, 1, -4, 1, 2, 1, 5, -2, 4, 5, -1, 3, 11, -1, -3, -1, 0, -2, 5, 1, -5, 2, 1, 6, -4, 1, -11, 4, -2, 1, 2, 5, -3, 0, 3, -2, 10, -1, -3, 4, -1, -1, -10, -2, -1, -1, 1, -5, 7, 2, 0, -4, 6, -5, 6, 1, 4, -3, 4, -11, 1, 1, -18, 3, 5, 1], 'euler11': [1, -5, 11], 'euler13': [1, 2, 13], 'euler17': [1, 0, 0], 'euler19': [1, 1, 0], 'euler2': [1, 1, 0], 'euler23': [1, 3, 23], 'euler29': [1, 6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 4, 31], 'euler37': [1, 4, 37], 'euler41': [1, -5, 41], 'euler43': [1, -4, 43], 'euler47': [1, -11, 47], 'euler5': [1, 1, 0], 'euler53': [1, -5, 53], 'euler59': [1, 4, 59], 'euler61': [1, 11, 61], 'euler67': [1, 3, 67], 'euler7': [1, 2, 7], 'euler71': [1, -10, 71], 'euler73': [1, 3, 73], 'euler79': [1, 1, 79], 'euler83': [1, -7, 83], 'euler89': [1, -6, 89], 'euler97': [1, 18, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, 1, 0], [1, 2, 7], [1, -5, 11], [1, 2, 13], [1, 0, 0], [1, 1, 0], [1, 3, 23], [1, 6, 29], [1, 4, 31], [1, 4, 37], [1, -5, 41], [1, -4, 43], [1, -11, 47], [1, -5, 53], [1, 4, 59], [1, 11, 61], [1, 3, 67], [1, -10, 71], [1, 3, 73], [1, 1, 79], [1, -7, 83], [1, -6, 89], [1, 18, 97]], 'index': 34, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/164730/g'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-164730-1.1-c1-0-34', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-164730-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 36.26810820123587, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1170241088723489954, 'z1': {'__RealLiteral__': 0, 'data': '0.6382265422607918', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1170241088723489954', 'Lhash_array': ['1170241088723489954'], 'label': '2-164730-1.1-c1-0-34', 'type': 'ECQ', 'url': 'EllipticCurve/Q/164730/g'}