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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 0, 'Lhash': '18935499604166969', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1063.6073549234552, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [37, [1, -1]]], 'bad_primes': [2, 3, 5, 37], 'central_character': '133200.1', 'coefficient_field': '1.1.1.1', 'conductor': 133200, 'conductor_radical': 1110, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, 4, 7], [1, 4, 11], [1, -2, 13], [1, -6, 17], [1, -6, 19], [1, -8, 23], [1, -6, 29], [1, 2, 31], [1, -1], [1, 0, 41], [1, 10, 43], [1, 12, 47], [1, 4, 53], [1, -4, 59], [1, -10, 61], [1, 4, 67], [1, -12, 71], [1, -10, 73], [1, 10, 79], [1, 0, 83], [1, 2, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 116, 'label': '2-133200-1.1-c1-0-116', 'leading_term': '6.25247649964', '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/133200/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.372125300773742, 1.711197332110364, 0.6579551450362864, -0.8128078230513363, -0.816294443488177, 1.537140880299253, 4.609566299280774, 5.440736316899386, 3.041405635356883, -0.1783641925370885, -1.227105501280279, -0.2667700536871806, 0.07410427679947192, -0.8426327856251602, -0.2640399564158484, 3.409621279486275, 6.909010322572989, 5.953637432007043, 1.667564552064754, -0.75216524446464, 0.2387044161529654, 0.6917663821765505, -1.629238135647439, -3.259318154143327, -1.340700944493326, 0.9614519614369151, 0.04663020438110215, -1.466396213473158, 0.3427759418019207, 2.945422252559344, 1.754037021478384, -0.9507695010676747, 0.1445127945628386, 3.173517766781745, 2.077106575290369, -2.092425263571599, -2.936296406982366, -0.2735309627338667, 0.6491495085857758, -0.118345111695479, 1.466206352318469, 3.45990462778208, 1.240873892032905, -1.860011337924617, 0.1989052271600213, 3.927015052019839, 2.369725606945147, -1.495037261978609, -0.8339264567678814, 1.903118562430893, 1.121774040350505, -0.6715208715576598, -0.01394914639642494, -0.6521896371209641, -3.885188343568135, -3.536921597086909, 0.8104543292241652, 0.945020452257025, -3.606109197915224, -3.942500570874872, 0.5647930093759125, 1.902028401284125, -0.09922457931773969, 0.259119322620335, 1.294369692203046, -0.07064617574202676, 0.6524932650645902, 4.213264201958432, 2.781680494961246, -3.413199913611391, -4.260868073579873, 0.475661384492886, 1.678168891374429, -0.2305923674765097, 0.7961586153007074, 1.713291212219954, -0.7091545604621952, -0.7563462373394886, 2.33960597960076, 1.315283727985026, -2.079979761727013, -0.251705428055235, 2.885828021165905, 1.024363286000307, -0.2548037808841689, 2.186160614128101, 0.8044555664353054, -4.180793517745815, -3.642096759618356, 0.5560519822076762, 0.6652730541561228, -0.3735412082412491, 0.7382706264197262, -0.6642848000439634, -2.44992754212475, 1.811329183868905, 5.215151087538047, 0.07378118180913541, -4.588104599538409, -1.832848399957686, 0.3741439947443821, -0.8499409944014735, 0.2295240432077686, 1.043305310707892, -1.804705436727004, -1.941678898791742, 0.8437584578007111, -0.5887039924063107, -1.445492043502042, 4.720565435840571, 8.137464553233311, 2.83845837238194, -0.7629696341673915, 0.6762560025544764, -0.03128970641749056, -1.227611382017395, 0.06160047851969321, -1.538848264175337, -3.677159005497689, 0.4878462245982417], 'positive_zeros': ['0.8529938363147937', '1.363815273018851', '2.482407192109412', '3.072636264639358', '3.279596889342851', '3.776985243330643', '4.871364393289666', '5.212038994556284', '5.600043121895201', '6.365439979972248', '6.755491862090029', '7.222381299408995', '7.890691768345138', '8.238206761801786', '8.872517680840263', '9.528984862579101', '9.925631999544562', '10.06661473799618', '10.82749474401543', '11.23839361832293', '11.88562642742184', '12.31636207105901', '12.87227747751057', '13.25375732767287', '13.41436606501903', '14.19924588954076', '14.55908452505798', '15.21709971298066', '15.73332485451312', '15.95811813378685', '16.48746956136832', '16.68447955667669', '17.36235990614548', '17.97292666433786', '18.45318714179005', '18.64820943619362', '19.18422079176700', '19.56346931327442'], 'prelabel': '2-133200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 32.61299365166368, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 18935499604166969, 'z1': {'__RealLiteral__': 0, 'data': '0.8529938363147937', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.363815273018851', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.482407192109412', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1063.6073549234552, 'bad_primes': [2, 3, 5, 37], 'central_character': '1.1', 'conductor': 133200, 'conductor_radical': 1110, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 2, 0, 0, 0, 6, 0, 6, 0, 0, 0, 8, 0, 0, 0, 0, 0, 6, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -10, 0, 0, 0, -12, 0, 9, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 10, 0, 0, 0, 0, 0, -4, 0, 0, 0, 12, 0, 10, 0, 0, 0, 16, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -8, 0, 0, 0, 0, 0, 2, 0, 0, 0], 'euler11': [1, 4, 11], 'euler13': [1, -2, 13], 'euler17': [1, -6, 17], 'euler19': [1, -6, 19], 'euler2': [1, 0, 0], 'euler23': [1, -8, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 2, 31], 'euler37': [1, -1, 0], 'euler41': [1, 0, 41], 'euler43': [1, 10, 43], 'euler47': [1, 12, 47], 'euler5': [1, 0, 0], 'euler53': [1, 4, 53], 'euler59': [1, -4, 59], 'euler61': [1, -10, 61], 'euler67': [1, 4, 67], 'euler7': [1, 4, 7], 'euler71': [1, -12, 71], 'euler73': [1, -10, 73], 'euler79': [1, 10, 79], 'euler83': [1, 0, 83], 'euler89': [1, 2, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 4, 7], [1, 4, 11], [1, -2, 13], [1, -6, 17], [1, -6, 19], [1, -8, 23], [1, -6, 29], [1, 2, 31], [1, -1, 0], [1, 0, 41], [1, 10, 43], [1, 12, 47], [1, 4, 53], [1, -4, 59], [1, -10, 61], [1, 4, 67], [1, -12, 71], [1, -10, 73], [1, 10, 79], [1, 0, 83], [1, 2, 89], [1, -2, 97]], 'index': 116, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/133200/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': '2-133200-1.1-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': 1, 'prelabel': '2-133200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 32.61299365166368, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 18935499604166969, 'z1': {'__RealLiteral__': 0, 'data': '0.8529938363147937', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '18935499604166969', 'Lhash_array': ['18935499604166969'], 'label': '2-133200-1.1-c1-0-116', 'type': 'ECQ', 'url': 'EllipticCurve/Q/133200/g'}