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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 4, 'A8': 0, 'A9': 1, 'Lhash': '95794283550296294', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 647.7464611966268, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, 1]], [13, [1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '81120.1', 'coefficient_field': '1.1.1.1', 'conductor': 81120, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 1], [1, -4, 7], [1, 0, 11], [1], [1, -2, 17], [1, -8, 19], [1, 4, 23], [1, -6, 29], [1, 8, 31], [1, 6, 37], [1, -6, 41], [1, -4, 43], [1, -4, 47], [1, -6, 53], [1, -8, 59], [1, 10, 61], [1, -4, 67], [1, -8, 71], [1, -14, 73], [1, 0, 79], [1, -12, 83], [1, -6, 89], [1, -6, 97]], 'gamma_factors': [[], [0]], 'index': 27, 'label': '2-81120-1.1-c1-0-27', 'leading_term': '4.5835592095', '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': 0, 'origin': 'EllipticCurve/Q/81120/bo', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [4.583559209503426, 3.852223977748601, 1.967080177372918, -0.08853999173890723, -0.9941933953280793, -0.1781491523923493, 1.349776023959096, 1.754052372656252, 0.3960734486845955, -1.14314031948179, -0.7278289218416591, 1.562599109991446, 3.175080315356215, 2.227799001576129, 0.1519645851689125, -0.1204349996402427, 1.64215532177729, 2.466675978246996, 0.6048446037793598, -1.570660125621687, -1.123963427776547, 0.5122181533362224, -0.5324411330912773, -3.91284257492067, -4.407412278217294, 0.4180612355818982, 5.687802038743529, 5.651473590127652, 1.695520179306458, -0.4677586709955529, 0.4765555094016082, 0.9907205299622945, 0.001545416514298595, 0.3282417574462245, 2.220130961138754, 2.093986768730679, -0.4030950814251848, -0.7701823836115312, 2.056025497828455, 2.754170269681459, -1.094952595923217, -3.995834465216806, -1.944006181335644, 0.4921634462000225, -1.242194652732234, -3.407273710836336, -1.570658763587163, 0.904144439597546, 0.09565287917491394, -0.2919546415914926, 3.133983311073257, 5.090402520468535, 0.7910289260311689, -4.27920376760576, -3.529762677736568, -0.238354856360819, 0.0283153332924432, -0.7434386847865825, 0.3413886641793217, 0.1898643882739547, -2.434812733727801, -2.66310342839735, 0.3509285855928427, 0.9350752345440273, -0.9732986492057043, 0.862588547777481, 4.942329864608055, 3.301619527040331, -2.226006971507943, -2.339925908050693, 2.136595951890036, 2.790995338006614, 0.1818487405159135, 0.2208321140513703, 0.4783377683665794, -3.100688662353663, -5.158286298177999, -1.458283356461112, 1.675339197074861, 0.1042683714616381, -0.771369103094644, 1.028824413435479, 0.6697808803479111, -1.120403814187366, 0.08543203064059744, 1.044131971398743, -1.662263788536757, -1.993937257027271, 2.484734050685265, 3.278032331585913, -1.226913829665646, -1.120954270161747, 4.191182805013871, 4.377803340771381, -0.4236654000658854, -1.257866154078618, 0.7816533998277666, -0.04619456881399351, -0.6879588067649861, 0.8886395910664374, -0.7467890707554389, -4.328677429809589, -2.411874950518849, 1.746867550835614, 0.5302953957339479, -1.627491391572587, 0.9004660629026847, 2.530376168852699, 0.4029968631714613, 0.1600120404193101, 1.266337958062755, -0.3559895652545251, 0.2754957027099542, 5.218664098342343, 5.102963326029195, -0.5393361062217765, 0.04327502424005853, 5.485730091764935, 3.789123735735583, -1.909523118717585, -1.337090132877856], 'positive_zeros': ['0.7370765834934863', '1.279506454130694', '2.053146621891313', '2.591963965893027', '3.526326670593522', '3.775485462880403', '4.556397607126668', '5.151689694604651', '5.446896403125793', '6.233334465515831', '7.141189135048139', '7.414412218927116', '8.000472662307790', '8.184521478029343', '8.958127707850947', '9.333047904094248', '9.941514197333107', '10.65814978360349', '10.88612101669202', '11.62676244665418', '12.01437200642815', '12.28611880477285', '13.03140391587681', '13.78158116475816', '14.00634034850278', '14.43734951129146', '14.77361781692567', '15.46948636440009', '15.86299674625236', '16.19399380495725', '16.89130892916309', '17.38011050043473', '18.02896656951467', '18.20420374962342', '18.55297896106204', '19.32870392104180', '19.76110609905434'], 'prelabel': '2-81120-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 25.450863663078838, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 95794283550296294, 'z1': {'__RealLiteral__': 0, 'data': '0.7370765834934863', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.279506454130694', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.053146621891313', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 647.7464611966268, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 81120, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -1, 0, 4, 0, 1, 0, 0, 0, 0, 0, -1, 0, 2, 0, 8, 0, 4, 0, -4, 0, 1, 0, 1, 0, 6, 0, -8, 0, 0, 0, -4, 0, -6, 0, 0, 0, 6, 0, 4, 0, -1, 0, 4, 0, 9, 0, 2, 0, 6, 0, 0, 0, 8, 0, 8, 0, -10, 0, 4, 0, 0, 0, 4, 0, -4, 0, 8, 0, 14, 0, 1, 0, 0, 0, 0, 0, 1, 0, 12, 0, -2, 0, 6, 0, 6, 0, 0, 0, -8, 0, -8, 0, 6, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 0, 0], 'euler17': [1, -2, 17], 'euler19': [1, -8, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 8, 31], 'euler37': [1, 6, 37], 'euler41': [1, -6, 41], 'euler43': [1, -4, 43], 'euler47': [1, -4, 47], 'euler5': [1, 1, 0], 'euler53': [1, -6, 53], 'euler59': [1, -8, 59], 'euler61': [1, 10, 61], 'euler67': [1, -4, 67], 'euler7': [1, -4, 7], 'euler71': [1, -8, 71], 'euler73': [1, -14, 73], 'euler79': [1, 0, 79], 'euler83': [1, -12, 83], 'euler89': [1, -6, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 1, 0], [1, -4, 7], [1, 0, 11], [1, 0, 0], [1, -2, 17], [1, -8, 19], [1, 4, 23], [1, -6, 29], [1, 8, 31], [1, 6, 37], [1, -6, 41], [1, -4, 43], [1, -4, 47], [1, -6, 53], [1, -8, 59], [1, 10, 61], [1, -4, 67], [1, -8, 71], [1, -14, 73], [1, 0, 79], [1, -12, 83], [1, -6, 89], [1, -6, 97]], 'index': 27, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/81120/bo'], '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': '2-81120-1.1-c1-0-27', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-81120-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 25.450863663078838, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 95794283550296294, 'z1': {'__RealLiteral__': 0, 'data': '0.7370765834934863', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '95794283550296294', 'Lhash_array': ['95794283550296294'], 'label': '2-81120-1.1-c1-0-27', 'type': 'ECQ', 'url': 'EllipticCurve/Q/81120/bo'}