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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': 0, 'A8': 0, 'A9': 1, 'Lhash': '1483810997961004850', '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': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1841.6696722188117, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, -1]], [31, [1]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '230640.1', 'coefficient_field': '1.1.1.1', 'conductor': 230640, 'conductor_radical': 930, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, -1], [1, 0, 7], [1, 0, 11], [1, -2, 13], [1, 6, 17], [1, 4, 19], [1, -4, 23], [1, 2, 29], [1], [1, -2, 37], [1, 6, 41], [1, 4, 43], [1, 0, 47], [1, -10, 53], [1, 12, 59], [1, 10, 61], [1, 4, 67], [1, 0, 71], [1, 14, 73], [1, 8, 79], [1, -12, 83], [1, 10, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 11, 'label': '2-230640-1.1-c1-0-11', 'leading_term': '2.00274987635', '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/230640/db', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.002749876346518, 0.9306514288528988, -1.603181663831354, -3.758851370771031, -3.734023047707366, -1.666397138071223, 0.1279280362468337, -0.2479884975802662, -1.744212639752854, -1.738476196517868, 0.02333233469816161, 0.7983226008394594, -0.8272393819272006, -2.198659938355941, -0.5727971593769108, 2.018381750397997, 1.626199209110444, -0.9195031054271032, -1.130715288593871, 1.15886892907743, 0.9741903742661602, -2.851870036445228, -4.625895399306441, -1.261763276185833, 2.120584067329111, 1.131221394062676, -0.4612966860299799, 1.352594718215956, 2.854023297663138, 0.2968651515883472, -1.888133131708398, 0.7206595245962081, 3.72088173493205, 2.186100141253952, -0.3759872122822288, 0.01009452543715867, 0.2100397355930663, -1.649819490446393, -1.156103417266568, 2.139152004047171, 2.067937262428919, -1.484822790593491, -1.765956770834862, 0.6262108551701915, -0.7072651026680191, -3.083543726241314, 0.1224311493172414, 3.847109618796505, 0.284696617565519, -4.617465336080623, -2.493408873676405, 1.536765791587854, 0.825473968064226, -0.5463147809941594, 0.2150961849006831, -1.132278001748074, -3.253445948140048, -0.8153343307325005, 2.353918928530324, 0.8705805541509418, -0.597078677953485, 0.7722814190046127, -0.6908169559255835, -3.875239119042511, -1.578992031567163, 1.867108405655537, -1.205017327651843, -4.332694514599193, -1.346857072513597, 0.02221591852521492, -3.045519364170558, -2.011408023761848, 2.269276256642878, 1.698279325936554, 0.01632609543894283, 2.442960056629185, 2.382505031988158, -1.793503734376095, -1.883051315594328, 0.8202557326053704, -0.2775389380483404, -0.7772814238357517, 2.384107670664646, 2.434664712935323, -0.0448068237485913, 1.190497231766847, 1.83349671055464, -1.077141121636997, -0.1981970697198238, 2.672342896793773, -0.8074082477502108, -3.84682908182839, 0.5242651671561422, 2.209304935078559, -1.842877333057973, -0.6784484854866203, 3.592912977237387, 1.537755961286971, -1.05578191299467, 0.9484216875051231, 0.7215807534272383, -0.9602449289799136, 1.338422079931778, 2.24702914572824, -0.1502992481884395, 0.2889340851524443, 0.2708354310551474, -3.445879800245188, -2.693820086225475, 1.30018800687342, -0.5335864414305144, -1.800819997252581, 2.900159033784407, 2.664615745203046, -2.614969807365842, -1.652979499916373, 0.7711713972969582, -1.633640223972687, -0.6616867151728228, 2.442322860126477, -1.010366136857867], 'positive_zeros': ['0.3509013434806924', '1.467211785566502', '1.699027075610869', '2.496769323226594', '2.901941361194672', '3.548761384323406', '4.155478538310278', '4.627214233456157', '5.077188437449462', '5.819980301208583', '6.375757036912737', '6.613524040557751', '7.270695593572524', '7.705053513664234', '8.440111707716698', '8.747819763687371', '9.037429471410643', '9.590615971786105', '10.14415488628096', '10.66677794215777', '10.94134189840104', '11.49423874325870', '12.01129608951080', '12.62893076951266', '13.09752437405142', '13.42494075016833', '13.62030476635299', '14.29779213726626', '14.83510293080602', '15.12093698787617', '15.44774539349627', '16.08291462558817', '16.43944356696986', '17.10848188148752', '17.25295730230476', '17.85667098873626', '18.45346810736800', '18.49234777354405', '19.14122086667290', '19.65050992435273', '19.96922339316281'], 'prelabel': '2-230640-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 42.91467898305674, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1483810997961004850, 'z1': {'__RealLiteral__': 0, 'data': '0.3509013434806924', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.467211785566502', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.699027075610869', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1841.6696722188117, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 230640, 'conductor_radical': 930, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, -6, 0, -4, 0, 0, 0, 4, 0, 1, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, -6, 0, -4, 0, 1, 0, 0, 0, -7, 0, -6, 0, 10, 0, 0, 0, -4, 0, -12, 0, -10, 0, 0, 0, 2, 0, -4, 0, 4, 0, 0, 0, -14, 0, 1, 0, 0, 0, -8, 0, 1, 0, 12, 0, -6, 0, -2, 0, -10, 0, 0, 0, 0, 0, -4, 0, 10, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -2, 13], 'euler17': [1, 6, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, 2, 29], 'euler3': [1, -1, 0], 'euler31': [1, 0, 0], 'euler37': [1, -2, 37], 'euler41': [1, 6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 0, 47], 'euler5': [1, -1, 0], 'euler53': [1, -10, 53], 'euler59': [1, 12, 59], 'euler61': [1, 10, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, 14, 73], 'euler79': [1, 8, 79], 'euler83': [1, -12, 83], 'euler89': [1, 10, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, -1, 0], [1, 0, 7], [1, 0, 11], [1, -2, 13], [1, 6, 17], [1, 4, 19], [1, -4, 23], [1, 2, 29], [1, 0, 0], [1, -2, 37], [1, 6, 41], [1, 4, 43], [1, 0, 47], [1, -10, 53], [1, 12, 59], [1, 10, 61], [1, 4, 67], [1, 0, 71], [1, 14, 73], [1, 8, 79], [1, -12, 83], [1, 10, 89], [1, -10, 97]], 'index': 11, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/230640/db'], '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': '2-230640-1.1-c1-0-11', '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': '2-230640-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 42.91467898305674, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1483810997961004850, 'z1': {'__RealLiteral__': 0, 'data': '0.3509013434806924', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1483810997961004850', 'Lhash_array': ['1483810997961004850'], 'label': '2-230640-1.1-c1-0-11', 'type': 'ECQ', 'url': 'EllipticCurve/Q/230640/db'}