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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 3, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '1198149309201877374', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [1.3416407864998738, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1295.8762043229558, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1]], [23, [1, -1]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '162288.1', 'coefficient_field': '1.1.1.1', 'conductor': 162288, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[1], [1], [1, -3, 5], [1], [1, -4, 11], [1, -3, 13], [1, 4, 17], [1, 0, 19], [1, -1], [1, 3, 29], [1, 6, 31], [1, 9, 37], [1, -9, 41], [1, -3, 43], [1, -7, 47], [1, -4, 53], [1, 6, 59], [1, 10, 61], [1, 4, 67], [1, 6, 71], [1, -8, 73], [1, 8, 79], [1, 4, 83], [1, 14, 89], [1, -7, 97]], 'gamma_factors': [[], [0]], 'index': 158, 'label': '2-162288-1.1-c1-0-158', 'leading_term': '10.750609432', '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/162288/gj', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 2.447163676559416, 3.55640582231712, 2.672234572831907, 0.5925062511009264, -0.7829487125862089, -0.3670245935474299, 0.6823347086934644, 0.3305166763295062, -1.355821259053309, -1.816063659687646, 0.4332003737003473, 2.983825472691856, 2.329944167859723, -0.9148136456967684, -2.398975812556996, -0.4283126519017415, 1.20668486919048, -0.8890284511709783, -4.00080737774164, -3.375121950845854, 0.1378585887974052, 1.634875361920352, 0.2924521746716812, -0.08844242797954908, 1.29657664816109, 0.9698843877916824, -1.259341902541369, -1.055512293196708, 1.622525669437313, 0.7350943210440255, -4.95880086820329, 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2.624222039642948, 0.3487407670933411, -1.226162434829444, 0.7322175956490118, -0.007697874400756761, -2.21083976684395, -0.5168366798691484, 0.7190146353492154, -0.9981224043431312, 0.452070416114107, 2.34279812165371, -3.180661399738387, -8.445148180474748, -4.175146731295323, 0.5850185669628247, -1.478387345738899, -2.390772947063889, 0.02384470114647108, -0.5535846536055622, -1.32536379927784, 1.198229791094202, 1.287733539566471, -0.5481959275737361, 1.093248801959035, 0.4114768921746418, -5.519993866354709, -5.760330742670354, 0.4376769346064573, 1.307006274347795, -0.8879637497654794, 1.963359197144105, 3.318229567401203, -0.324949390314876, -0.3949435189325401, 2.14619136697261, 0.6296912647195749, -0.2131883989787216, 1.69026695304423, 0.3431981086587604], 'positive_zeros': ['1.077917672493038', '1.578311719423415', '2.056291758261890', '2.714357572333653', '3.431131753472653', '4.040509457126481', '4.432433806187555', '5.239453067529919', '5.805240356865835', '6.022072172291713', '6.609090124647291', '7.099374446938770', '7.541148142512070', '8.431877287850043', '8.896972295314024', '9.227653598142821', '9.444281212287832', '10.24923441331726', '10.63215538917462', '11.11150438145898', '11.45983497185818', '12.23973558253352', '12.55359209207653', '13.12944461338540', '13.56496156497440', '13.94968879573520', '14.25147711575252', '14.80421446793989', '15.32262049381335', '15.78302702535426', '16.31098585251725', '16.84127684941565', '17.17930815512444', '17.54548252199458', '17.97263178869766', '18.44232676056240', '18.76445208610605', '19.51529354686285', '19.76022747697309'], 'prelabel': '2-162288-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 35.998280574535165, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1198149309201877374, 'z1': {'__RealLiteral__': 0, 'data': '1.077917672493038', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.578311719423415', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.056291758261890', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1295.8762043229558, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 162288, 'conductor_radical': 966, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 3, 0, 0, 0, -4, 0, 0, 0, 0, 0, 1, 0, 4, 0, 0, 0, -3, 0, -6, 0, 0, 0, 0, 0, -9, 0, 0, 0, 9, 0, 3, 0, 0, 0, 7, 0, 0, 0, 0, 0, 4, 0, 12, 0, 0, 0, -6, 0, -10, 0, 0, 0, 9, 0, -4, 0, 0, 0, -6, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, 0, -4, 0, -12, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0], 'euler11': [1, -4, 11], 'euler13': [1, -3, 13], 'euler17': [1, 4, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 0], 'euler29': [1, 3, 29], 'euler3': [1, 0, 0], 'euler31': [1, 6, 31], 'euler37': [1, 9, 37], 'euler41': [1, -9, 41], 'euler43': [1, -3, 43], 'euler47': [1, -7, 47], 'euler5': [1, -3, 5], 'euler53': [1, -4, 53], 'euler59': [1, 6, 59], 'euler61': [1, 10, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 0], 'euler71': [1, 6, 71], 'euler73': [1, -8, 73], 'euler79': [1, 8, 79], 'euler83': [1, 4, 83], 'euler89': [1, 14, 89], 'euler97': [1, -7, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -3, 5], [1, 0, 0], [1, -4, 11], [1, -3, 13], [1, 4, 17], [1, 0, 19], [1, -1, 0], [1, 3, 29], [1, 6, 31], [1, 9, 37], [1, -9, 41], [1, -3, 43], [1, -7, 47], [1, -4, 53], [1, 6, 59], [1, 10, 61], [1, 4, 67], [1, 6, 71], [1, -8, 73], [1, 8, 79], [1, 4, 83], [1, 14, 89], [1, -7, 97]], 'index': 158, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/162288/gj'], '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': '2-162288-1.1-c1-0-158', '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': '2-162288-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 35.998280574535165, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1198149309201877374, 'z1': {'__RealLiteral__': 0, 'data': '1.077917672493038', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1198149309201877374', 'Lhash_array': ['1198149309201877374'], 'label': '2-162288-1.1-c1-0-158', 'type': 'ECQ', 'url': 'EllipticCurve/Q/162288/gj'}