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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': '2067929099814821400', '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, -6, 17], [1, -2, 19], [1, 0, 23], [1, 8, 29], [1, 0, 31], [1, -10, 37], [1, -8, 41], [1, 0, 43], [1, 6, 47], [1, 2, 53], [1, 8, 59], [1, -14, 61], [1, 14, 67], [1, 8, 71], [1, -10, 73], [1, -14, 79], [1, 4, 83], [1, -2, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 116, 'label': '2-369600-1.1-c1-0-116', 'leading_term': '1.62667426451', '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/k', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.626674264505147, 0.9372922291644732, -0.4002415028438532, -0.7001082932899477, 0.9623466444450717, 3.070043099054004, 2.844714434240236, -0.01301534190989444, -2.106483360824318, -0.6542268495461006, 2.136141638281176, 1.963564859188339, -0.7666602369372162, -1.257756098838265, 1.676091413437485, 3.083067463383953, 0.0769761709286982, -2.913635321294585, -1.594322190109317, 0.938479168230661, 0.3167798785664589, -1.17422580215245, 0.1003522711301733, 1.559463804590899, 0.1772151194250606, -0.391764848082177, 2.868442314671798, 5.073237160160549, 2.404454663681783, -0.3561415425494359, 0.1900272527328759, -0.3454620360009239, -2.603371400401441, 0.3178451838204208, 7.722464388027196, 9.066506621659292, 2.818049173011981, -0.8881105217689103, 0.6347719427918465, 0.7570814764338358, -0.3967711241444396, 1.625099061841661, 2.884413563769276, -0.5079180966759742, -2.294697505262798, 0.6851588831449412, 1.578446329434903, -0.9497424037774979, -0.6453160200359088, 1.098386651037345, -0.5620202666604694, -1.586292286602419, 0.135715786303836, -1.877931528947131, -5.78941685498358, -2.290654274677552, 4.102236039265527, 3.023219805360815, -0.4245101604155352, 0.6601659886996678, -0.2219413190657657, -4.35937808071135, -2.698430683405845, 2.289946867083691, 1.299296881265888, -1.474009027234743, -0.1601031621120972, 0.2792109930024477, -0.5211161187670057, 2.059707158148735, 2.944839699747783, -0.9021211003940359, -1.457778537151297, 0.9655978955170328, -1.300305502878974, -3.395207777682822, -0.396772351021245, -0.2136557972486599, -2.795710145394967, -0.1113603633518186, 1.624830350073181, -3.176699016789253, -3.517180264290179, 2.224752188097756, 2.326616678976532, -0.2119480525181573, 2.513809683423725, 3.269866910224226, -0.4312982678219042, -0.6773984489140549, 0.147218064973561, -1.486518446983786, 0.552666994136239, 3.618131624761948, 1.044383656911509, -0.5540549431351837, 0.8814643945806384, -2.06305783135306, -4.248321673352339, -0.530051714421735, -0.3129232626604637, -2.496245533712823, 1.881836571200966, 3.953624783445757, -1.48918978359864, -1.922623923929634, 1.935050798505939, 0.5582079065849207, 0.5234919716649831, 3.925139057425757, 1.740944694811691, -1.0499436491537, 1.366375612374836, 1.048902921184113, -0.4988234420362808, 2.79087922134822, 3.331805239315426, 0.0382018720736868, 0.2893380082597763, 0.3447513987901856, 0.2342659410669164], 'positive_zeros': ['0.4202370213291917', '0.8866091231586141', '1.748984882863145', '2.303965530761623', '2.928827110655332', '3.374288261036591', '4.004661667341116', '4.633684213372473', '5.039742236903528', '5.488734337333729', '6.022927321853355', '6.299267307539577', '7.187229910536928', '7.454526861960376', '7.706195410831208', '8.237615832795162', '9.132795556998821', '9.421872396609724', '9.867423147073493', '10.09512640243385', '10.71943511032922', '11.20013989591070', '11.65410847329011', '12.06962305309919', '12.44506440807369', '12.97026172001964', '13.10711467631067', '13.82664782477864', '14.44101089212677', '14.66153975004151', '14.98463466132689', '15.61894949371643', '16.08743732486584', '16.52122865345156', '16.80359974956704', '17.08440354781119', '17.69332612243794', '18.12551264147253', '18.41374117265144', '19.03560845591848', '19.22914305750647', '19.75636559892942'], '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': 2067929099814821400, 'z1': {'__RealLiteral__': 0, 'data': '0.4202370213291917', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.8866091231586141', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '1.748984882863145', '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, 6, 0, 2, 0, 1, 0, 0, 0, 0, 0, -1, 0, -8, 0, 0, 0, 1, 0, 0, 0, 10, 0, 6, 0, 8, 0, 0, 0, 0, 0, -6, 0, 1, 0, -6, 0, -2, 0, 0, 0, -2, 0, -8, 0, 14, 0, -1, 0, 0, 0, -14, 0, 0, 0, -8, 0, 10, 0, 0, 0, 1, 0, 14, 0, 1, 0, -4, 0, 0, 0, 8, 0, 2, 0, 6, 0, 0, 0, 0, 0, 10, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, 6, 13], 'euler17': [1, -6, 17], 'euler19': [1, -2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 8, 29], 'euler3': [1, 1, 0], 'euler31': [1, 0, 31], 'euler37': [1, -10, 37], 'euler41': [1, -8, 41], 'euler43': [1, 0, 43], 'euler47': [1, 6, 47], 'euler5': [1, 0, 0], 'euler53': [1, 2, 53], 'euler59': [1, 8, 59], 'euler61': [1, -14, 61], 'euler67': [1, 14, 67], 'euler7': [1, 1, 0], 'euler71': [1, 8, 71], 'euler73': [1, -10, 73], 'euler79': [1, -14, 79], 'euler83': [1, 4, 83], 'euler89': [1, -2, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 1, 0], [1, 1, 0], [1, 6, 13], [1, -6, 17], [1, -2, 19], [1, 0, 23], [1, 8, 29], [1, 0, 31], [1, -10, 37], [1, -8, 41], [1, 0, 43], [1, 6, 47], [1, 2, 53], [1, 8, 59], [1, -14, 61], [1, 14, 67], [1, 8, 71], [1, -10, 73], [1, -14, 79], [1, 4, 83], [1, -2, 89], [1, -10, 97]], 'index': 116, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/369600/k'], '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-c1-0-116', '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': 2067929099814821400, 'z1': {'__RealLiteral__': 0, 'data': '0.4202370213291917', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2067929099814821400', 'Lhash_array': ['2067929099814821400'], 'label': '2-369600-1.1-c1-0-116', 'type': 'ECQ', 'url': 'EllipticCurve/Q/369600/k'}