-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '615560041729511755', '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': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 469.52036388512886, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '58800.1', 'coefficient_field': '1.1.1.1', 'conductor': 58800, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1], [1, -1], [1], [1], [1, 2, 11], [1, 3, 13], [1, -8, 17], [1, 1, 19], [1, -8, 23], [1, -4, 29], [1, -3, 31], [1, -1, 37], [1, 6, 41], [1, -11, 43], [1, 6, 47], [1, -12, 53], [1, -4, 59], [1, -6, 61], [1, -13, 67], [1, -10, 71], [1, 11, 73], [1, -3, 79], [1, 2, 83], [1, 0, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 87, 'label': '2-58800-1.1-c1-0-87', 'leading_term': '3.59286170696', '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/58800/gk', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.592861706960476, 2.972737141779063, 1.367730277212581, -0.3794970542743994, -1.05626174038867, 0.01202877906313595, 2.078204207334978, 3.320270506124577, 2.530695794900552, 0.5138825375434817, -0.6387838977050229, 0.03815671990870222, 1.117485710087717, 0.5910926827522232, -1.236019759169944, -1.773468527392865, 0.3712077031100728, 3.010305772270045, 2.914298878875646, 0.29654952497136, -1.267838136301633, -0.001778344333177677, 1.1938807471334, -1.027888112210657, -4.944492876341862, -5.626222286533617, -2.070495742350501, 1.136775981929594, 0.5176707952121581, -1.48059852860956, -1.013848885691366, 0.8932019943251494, 0.7005949416436781, -1.042919920697738, -0.6159327170992173, 1.918030448056607, 2.32486113094891, -0.3915237048092707, -1.986759479872427, -0.4061610444749072, 0.7027288373898466, -0.8590019968255705, -1.249853013720242, 2.104885138527807, 4.46485921424336, 1.3437842119672, -3.026284397078652, -2.290213172218707, 1.378597596033259, 1.641055530073965, -0.766977181483413, -0.503213838506429, 1.68091316924423, 0.7593806699223437, -2.228068465266311, -1.930780578355651, 0.9395619517502628, 1.218992238726246, -0.5951469807669916, -0.1578719870600195, 1.222788934325757, -0.4336224047436611, -2.428395720890618, -0.1165066341721321, 2.980631004282185, 1.298188666146358, -1.604144885676069, 0.06018794373151893, 2.596516160117362, 0.4991029739080301, -1.754461454692843, 1.512144588592187, 5.158001080566701, 2.782139967916618, -1.182126575536641, -0.810830567722372, 0.5703455161307008, -0.569622747823237, -0.3182925394853251, 2.61699053204245, 2.562167718095771, -1.121120089777951, -1.995403523792583, 0.3782468635640467, 0.4482808212807207, -0.8833858498408904, 0.4273272480058263, 0.4432764643784218, -4.623404268439966, -7.661655299790868, -3.283461576812647, 0.9878232670387638, -0.4930444043212859, -1.338533386456286, 1.524488168198056, 1.186187386880372, -3.094466857697073, -3.416986092816537, -0.03985438042075822, -0.224265215441343, -2.472336330008176, -1.21343213206209, 0.3659429661377493, -1.250258089959265, -1.258713260616059, 1.564251726142349, 1.051683434100796, -2.030995248682143, -1.179657755509552, 1.129721524368881, -0.1330182486419767, 0.1285999103817025, 4.819754234188916, 5.29976329467962, -0.6567938470660678, -2.78514495738046, 0.7445652271692085, 1.100731314981233, -1.096838587582192, 0.840585400420026, 2.747726900853466], 'positive_zeros': ['0.6881227333801396', '1.248345531066765', '2.323299250607315', '2.742457992386439', '3.336148371978817', '3.968648291907307', '4.777873492520047', '5.250223254551096', '5.675963467391551', '6.631080327716618', '7.057706316892495', '7.623562433960880', '8.097122232801872', '8.566357333053405', '9.217995548207968', '9.799045315401731', '10.14127099548226', '10.61723406050728', '11.31474732435570', '11.89792392995244', '12.41274357874342', '12.80509042894707', '13.31131077239865', '13.91236199255518', '14.40717296193690', '14.77214751149100', '15.21144000056711', '15.75730107997332', '16.33771030948213', '16.74563385614702', '17.28429405816006', '17.67138124631542', '18.40234332708020', '18.85219234321165', '19.15672314693120', '19.53291946674633'], 'prelabel': '2-58800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 21.668418582931448, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 615560041729511755, 'z1': {'__RealLiteral__': 0, 'data': '0.6881227333801396', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.248345531066765', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.323299250607315', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 469.52036388512886, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 58800, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, -2, 0, -3, 0, 0, 0, 8, 0, -1, 0, 0, 0, 8, 0, 0, 0, 1, 0, 4, 0, 3, 0, -2, 0, 0, 0, 1, 0, -3, 0, -6, 0, 11, 0, 0, 0, -6, 0, 0, 0, 8, 0, 12, 0, 0, 0, -1, 0, 4, 0, 6, 0, 0, 0, 0, 0, 13, 0, 8, 0, 10, 0, -11, 0, 0, 0, 0, 0, 3, 0, 1, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 3, 0, 0, 0, 10, 0, -2, 0], 'euler11': [1, 2, 11], 'euler13': [1, 3, 13], 'euler17': [1, -8, 17], 'euler19': [1, 1, 19], 'euler2': [1, 0, 0], 'euler23': [1, -8, 23], 'euler29': [1, -4, 29], 'euler3': [1, -1, 0], 'euler31': [1, -3, 31], 'euler37': [1, -1, 37], 'euler41': [1, 6, 41], 'euler43': [1, -11, 43], 'euler47': [1, 6, 47], 'euler5': [1, 0, 0], 'euler53': [1, -12, 53], 'euler59': [1, -4, 59], 'euler61': [1, -6, 61], 'euler67': [1, -13, 67], 'euler7': [1, 0, 0], 'euler71': [1, -10, 71], 'euler73': [1, 11, 73], 'euler79': [1, -3, 79], 'euler83': [1, 2, 83], 'euler89': [1, 0, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 0], [1, 0, 0], [1, 2, 11], [1, 3, 13], [1, -8, 17], [1, 1, 19], [1, -8, 23], [1, -4, 29], [1, -3, 31], [1, -1, 37], [1, 6, 41], [1, -11, 43], [1, 6, 47], [1, -12, 53], [1, -4, 59], [1, -6, 61], [1, -13, 67], [1, -10, 71], [1, 11, 73], [1, -3, 79], [1, 2, 83], [1, 0, 89], [1, -10, 97]], 'index': 87, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/58800/gk'], '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': '2-58800-1.1-c1-0-87', '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': '2-58800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 21.668418582931448, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 615560041729511755, 'z1': {'__RealLiteral__': 0, 'data': '0.6881227333801396', 'prec': 60}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '615560041729511755', 'Lhash_array': ['615560041729511755'], 'label': '2-58800-1.1-c1-0-87', 'type': 'ECQ', 'url': 'EllipticCurve/Q/58800/gk'}