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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 1, 'Lhash': '664016220871429878', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [7, [1, 1]], [11, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '369600.1', 'coefficient_field': '1.1.1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, 1], [1, 1], [1, 6, 13], [1, -7, 17], [1, -5, 19], [1, 3, 23], [1, 5, 29], [1, 4, 31], [1, 4, 37], [1, -2, 41], [1, 5, 43], [1, 6, 47], [1, 11, 53], [1, 1, 59], [1, 3, 61], [1, 16, 67], [1, -8, 71], [1, -10, 73], [1, -16, 79], [1, 9, 83], [1, -9, 89], [1, -11, 97]], 'gamma_factors': [[], [0]], 'index': 1, 'label': '2-369600-1.1-c1-0-1', 'leading_term': '0.208447789836', '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/369600/l', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.2084477898359662, -0.5149645606457954, -1.93993894841581, -2.341024032918374, -0.7376215409059778, 1.415712658593725, 1.395375594071953, -1.073096429454369, -2.622884673267127, -0.5735517313716555, 2.702170037667798, 2.714802031852889, -0.271464316293529, -1.476425350925161, 0.4396545749224408, 0.8282525162817007, -2.843410023126861, -5.890850320440055, -3.991147358720833, -0.4793965946154513, -0.1420668000588932, -1.107668108243333, 0.04163183994874067, 0.8002259665334681, -1.543151760938865, -2.947830263789001, -0.1190829202182839, 2.144096041511568, -0.04573877548749596, -2.028076151181417, -0.508354710519515, 0.02231430069607832, -1.237898139991134, 2.384274749959491, 9.991299710721597, 11.00265372128874, 4.069314724642196, -0.3823372413320237, 0.5264756841362209, 0.134938707032019, -1.590938048258055, -0.232569793563466, 0.5288782549377228, -2.781358374895659, -3.715058657949551, 0.5575540933677497, 2.449319713716455, 0.02889077705599104, -0.365674440387753, 0.664271796662776, -0.8430328526512402, -0.6805547521742438, 2.438433498320558, 0.8043816812657617, -4.347338441631308, -3.084914782978972, 1.530646658188557, 0.3106711846985218, -1.640423416053552, 1.472222795502827, 1.876112703785515, -2.195692618404463, -1.199937966582038, 3.197739808930182, 2.044501259619649, -0.7249182869145931, 0.361645368283489, 0.329878602991708, -0.806118455826481, 1.8996936311059, 3.293714066135979, -0.006832131036751501, -0.1867249788855943, 2.539069571997416, 0.6397644481766251, -1.175433535849673, 1.661636909874539, 1.15755766840528, -2.154718816676751, 0.4744643123851926, 3.058058304870685, -0.6246402372976074, -0.6138306197702212, 4.159948991466106, 2.390181249309052, -1.919465551235677, -0.09087563149877428, 0.7336462703642675, -2.285066196479592, -1.544562773257285, 0.4242465843814075, -0.171239804237787, 2.27726947121207, 4.726506566508428, 0.8259577072541033, -1.738738322777912, 0.1457572029635071, -0.8677216822185821, -0.7790322365100726, 4.045235893188946, 3.500288235959152, -0.7089400190806282, 1.711675129573183, 2.887264732841322, -2.375701465196814, -2.308025071100369, 1.568632727747692, -0.5313910966700248, -1.657860659823171, 0.9522157812654196, -1.22215524339082, -3.176805778168882, 0.4473794992712865, 1.07647890068163, -0.170368211218623, 2.885396421534958, 3.122089566868646, -0.1521458304873325, 0.420568522975117, 0.6863757964262305, 0.2149413845480855], 'positive_zeros': ['0.1299432269639483', '1.077120722142449', '1.654108280438769', '2.290180678987324', '2.977232589312946', '3.450932144875462', '3.829371025956181', '4.822304632478343', '4.965031567515492', '5.494180477123048', '5.865347642557068', '6.507904566237792', '6.996505169588769', '7.575987518941466', '7.754677249599150', '8.146254063764897', '9.194377121229101', '9.410999960122283', '9.766628285420874', '10.27584104143693', '10.55955184530452', '11.22007974390167', '11.75319034411827', '12.06323021388504', '12.39321831648827', '12.80767645242103', '13.28767627890500', '13.89604802783265', '14.27211275613023', '14.65358105805705', '15.11484575078741', '15.56173910903107', '16.14653791081008', '16.44706441976023', '16.79702547516633', '17.11325482374625', '17.74945072925264', '18.01655924008975', '18.54515805731212', '18.87252584978136', '19.32299793964777', '19.72524082970597'], 'prelabel': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 664016220871429878, 'z1': {'__RealLiteral__': 0, 'data': '0.1299432269639483', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.077120722142449', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.654108280438769', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, -1, 0, 1, 0, -1, 0, -6, 0, 0, 0, 7, 0, 5, 0, 1, 0, -3, 0, 0, 0, -1, 0, -5, 0, -4, 0, 1, 0, 0, 0, -4, 0, 6, 0, 2, 0, -5, 0, 0, 0, -6, 0, 1, 0, -7, 0, -11, 0, 0, 0, -5, 0, -1, 0, -3, 0, -1, 0, 0, 0, -16, 0, 3, 0, 8, 0, 10, 0, 0, 0, 1, 0, 16, 0, 1, 0, -9, 0, 0, 0, 5, 0, 9, 0, 6, 0, 4, 0, 0, 0, 11, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, 6, 13], 'euler17': [1, -7, 17], 'euler19': [1, -5, 19], 'euler2': [1, 0, 0], 'euler23': [1, 3, 23], 'euler29': [1, 5, 29], 'euler3': [1, 1, 0], 'euler31': [1, 4, 31], 'euler37': [1, 4, 37], 'euler41': [1, -2, 41], 'euler43': [1, 5, 43], 'euler47': [1, 6, 47], 'euler5': [1, 0, 0], 'euler53': [1, 11, 53], 'euler59': [1, 1, 59], 'euler61': [1, 3, 61], 'euler67': [1, 16, 67], 'euler7': [1, 1, 0], 'euler71': [1, -8, 71], 'euler73': [1, -10, 73], 'euler79': [1, -16, 79], 'euler83': [1, 9, 83], 'euler89': [1, -9, 89], 'euler97': [1, -11, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 1, 0], [1, 1, 0], [1, 6, 13], [1, -7, 17], [1, -5, 19], [1, 3, 23], [1, 5, 29], [1, 4, 31], [1, 4, 37], [1, -2, 41], [1, 5, 43], [1, 6, 47], [1, 11, 53], [1, 1, 59], [1, 3, 61], [1, 16, 67], [1, -8, 71], [1, -10, 73], [1, -16, 79], [1, 9, 83], [1, -9, 89], [1, -11, 97]], 'index': 1, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/369600/l'], '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': '2-369600-1.1-c1-0-1', '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': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 664016220871429878, 'z1': {'__RealLiteral__': 0, 'data': '0.1299432269639483', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '664016220871429878', 'Lhash_array': ['664016220871429878'], 'label': '2-369600-1.1-c1-0-1', 'type': 'ECQ', 'url': 'EllipticCurve/Q/369600/l'}