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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': '865762862288946052', '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': 375.6162911081031, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, 1]], [7, [1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '47040.1', 'coefficient_field': '1.1.1.1', 'conductor': 47040, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 1], [1], [1, -6, 11], [1, -3, 13], [1, 4, 17], [1, 1, 19], [1, 4, 23], [1, -8, 29], [1, -1, 31], [1, 7, 37], [1, 6, 41], [1, 1, 43], [1, -2, 47], [1, 4, 53], [1, -8, 59], [1, -14, 61], [1, 7, 67], [1, -6, 71], [1, -1, 73], [1, 1, 79], [1, 2, 83], [1, 12, 89], [1, 6, 97]], 'gamma_factors': [[], [0]], 'index': 139, 'label': '2-47040-1.1-c1-0-139', 'leading_term': '5.19334213724', '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/47040/bv', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.187724249414361, 1.7367819136928, 1.242324173832001, -0.02165868485968476, -0.9677033586317926, -0.460000302885207, 1.411897828185508, 2.914088614301791, 2.047546443023008, -1.247444030538835, -4.492743777531488, -4.891755312259046, -2.326193303986158, 0.4073909363755952, 0.7982169169993947, -0.4595651076963789, -0.663674447227449, 0.9626663425962813, 1.989183974599969, 0.2545628137399237, -2.64012241551014, -3.137443351214588, -0.6581766689319836, 1.530014711200157, 1.053563579008136, -0.3033865464097957, 0.03416766470782996, 0.7711545866771463, -1.292713715696095, -5.338975318918747, -6.59783888126961, -3.338383377022572, 0.1472619111460295, -0.005607486691347361, -1.362303642725164, 0.3320442696963056, 3.571003153451771, 3.350113022176051, -0.1962266039398988, -1.56880012016258, 1.122173041541699, 3.18622731717858, 1.425833952889745, -0.8382344830767398, -0.1705981022288584, 1.199161159042327, 0.4308520859400048, -0.3531050036727028, 1.075195250826303, 1.553617908915588, -1.753815596020507, -4.694738235465365, -2.48483600616029, 1.408158497488787, 0.9366125118617257, -1.775624446118576, -0.6316015178613639, 2.759373585819477, 1.968179179077448, -2.049071577739515, -2.593086779064452, 0.5017179312486642, 1.373920269960676, -0.3103299491221345, 0.3851006282705502, 2.978218293460466, 2.510236430291817, -0.1097557113340886, 0.06082063545519057, 1.830819393401166, 0.8029812704199014, -0.6746728776821488, 1.893029336535009, 4.839901917263221, 2.558667674367705, -1.332794207808839, -0.9668715424299825, 0.4864221897158542, -1.627793058350947, -3.172443392814926, -0.334342066508272, 1.128021957019295, -2.709891472747874, -4.868294294989002, -0.599206830026889, 3.255540247978047, 1.544441556443808, -0.4871589901846772, 0.6507665746407881, 0.6674885230386657, -1.245083893610877, -0.4305152757985338, 1.893243155324074, 0.5984628076423812, -1.786478569905009, -0.4195695169257975, 0.8615663676908829, -1.876478755753407, -3.107678344604439, 0.3008689272404136, 1.57214810588174, -1.079032677378896, 0.5097440500733981, 6.698733003028935, 7.426346653939125, 1.848072898530716, -0.5723510276847403, 1.090792147628707, 0.2214387132437264, -1.824028073311212, -0.4057460834548156, 1.003662110637423, -0.3936292171344317, 0.1735967108765755, 2.800532661068714, 1.051327516519305, -3.08647549446841, -2.018071424691456, 1.467353194316371, 0.7559129171558188], 'positive_zeros': ['0.9959416674135029', '1.573534160270856', '2.417093542860978', '3.449483654325270', '3.912124435330891', '4.372082520223618', '5.021502757519502', '5.806255832318278', '6.423522227462599', '6.742248491834562', '7.145127009967053', '8.231457698835370', '8.499137667831511', '8.973931248680771', '9.735834282783745', '10.16736818053562', '10.87791339293702', '11.27394767080686', '11.82802198961007', '12.09694601190197', '12.64364302835582', '13.39109697231123', '13.82770079314085', '14.29418693798345', '14.87071330901794', '15.45869902736565', '15.94633782139670', '16.20637800725202', '16.98529701215858', '17.24156201072706', '17.83895766756483', '18.11421856628018', '18.89341847487474', '19.36421875756620', '19.60327869951597'], 'prelabel': '2-47040-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.38082276654175, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 865762862288946052, 'z1': {'__RealLiteral__': 0, 'data': '0.9959416674135029', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.573534160270856', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.417093542860978', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 375.6162911081031, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 47040, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 6, 0, 3, 0, 1, 0, -4, 0, -1, 0, 0, 0, -4, 0, 1, 0, -1, 0, 8, 0, 1, 0, -6, 0, 0, 0, -7, 0, -3, 0, -6, 0, -1, 0, -1, 0, 2, 0, 0, 0, 4, 0, -4, 0, -6, 0, 1, 0, 8, 0, 14, 0, 0, 0, -3, 0, -7, 0, 4, 0, 6, 0, 1, 0, -1, 0, 0, 0, -1, 0, 1, 0, -2, 0, 4, 0, -8, 0, -12, 0, 0, 0, -1, 0, 1, 0, -6, 0, 6, 0], 'euler11': [1, -6, 11], 'euler13': [1, -3, 13], 'euler17': [1, 4, 17], 'euler19': [1, 1, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, -8, 29], 'euler3': [1, 1, 0], 'euler31': [1, -1, 31], 'euler37': [1, 7, 37], 'euler41': [1, 6, 41], 'euler43': [1, 1, 43], 'euler47': [1, -2, 47], 'euler5': [1, 1, 0], 'euler53': [1, 4, 53], 'euler59': [1, -8, 59], 'euler61': [1, -14, 61], 'euler67': [1, 7, 67], 'euler7': [1, 0, 0], 'euler71': [1, -6, 71], 'euler73': [1, -1, 73], 'euler79': [1, 1, 79], 'euler83': [1, 2, 83], 'euler89': [1, 12, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 1, 0], [1, 0, 0], [1, -6, 11], [1, -3, 13], [1, 4, 17], [1, 1, 19], [1, 4, 23], [1, -8, 29], [1, -1, 31], [1, 7, 37], [1, 6, 41], [1, 1, 43], [1, -2, 47], [1, 4, 53], [1, -8, 59], [1, -14, 61], [1, 7, 67], [1, -6, 71], [1, -1, 73], [1, 1, 79], [1, 2, 83], [1, 12, 89], [1, 6, 97]], 'index': 139, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/47040/bv'], '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': '2-47040-1.1-c1-0-139', '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': '2-47040-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.38082276654175, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 865762862288946052, 'z1': {'__RealLiteral__': 0, 'data': '0.9959416674135029', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '865762862288946052', 'Lhash_array': ['865762862288946052'], 'label': '2-47040-1.1-c1-0-139', 'type': 'ECQ', 'url': 'EllipticCurve/Q/47040/bv'}