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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': -2, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '2112463989315092871', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1756.006160930382, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [7, [1]], [11, [1, 1]], [17, [1, 1]]], 'bad_primes': [2, 3, 7, 11, 17], 'central_character': '219912.1', 'coefficient_field': '1.1.1.1', 'conductor': 219912, 'conductor_radical': 7854, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 2, 5], [1], [1, 1], [1, 2, 13], [1, 1], [1, 4, 19], [1, 4, 23], [1, -6, 29], [1, -8, 31], [1, 2, 37], [1, -6, 41], [1, -4, 43], [1, 4, 47], [1, -2, 53], [1, -4, 59], [1, 10, 61], [1, -12, 67], [1, 4, 71], [1, -14, 73], [1, 4, 79], [1, -4, 83], [1, -6, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 7, 'label': '2-219912-1.1-c1-0-7', 'leading_term': '1.66492035123', '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/219912/bm', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.664920351232569, 0.8567990259792034, -0.9137930206624821, -1.945908498702751, -0.7426893535719575, 2.151108695662045, 4.071875660001303, 3.013598373938155, 0.2924470678572963, -0.8642344866188507, 0.3694439045595539, 1.244105121573357, -0.3357076922992497, -2.348530763072631, -1.788943444849447, 0.272741310460243, 0.372823568935126, -1.291007344939043, -1.216773546574144, 0.4806848272835211, -0.7099499748331513, -5.29790881128753, -6.978759461076447, -2.467295115043726, 2.191646276202966, 1.076882969648524, -2.020049223694467, -0.8971800316375167, 2.139590241621623, 1.477549734911533, -1.220333562841075, -1.173655196914953, 0.1664384269501093, -0.4990651666920164, -0.654992961179476, 1.896479178858885, 2.657090434578182, -0.682989985906999, -2.188281641327432, 0.9421424724442709, 2.377434178086416, -0.3050746863924973, -0.5179118046542651, 2.946196579832115, 2.654273029707774, -1.664199948864888, -1.966945657853879, 1.543593172266808, 1.576111929713815, -0.475336394516272, 1.050967086551409, 2.365361964789803, -0.9921857568509725, -2.830689192142223, 0.7233673160212968, 2.586273958153735, 0.2058012289698173, 0.3456990926139738, 3.018511862462747, 1.904592734976065, -0.6535752859856899, 0.5006420879528549, 1.512690593931962, -0.06267477163499618, 0.6051141188643469, 1.662246027876121, -3.007317711882683, -7.219793297308759, -3.386229141938129, 0.3191410756214549, -2.647832568141541, -3.202476176349631, 1.77507230456803, 2.096323365983422, -2.349009717450397, -1.958241697767747, 1.212168579319698, 0.5501157919002824, -0.4296505548640329, 0.2498458847321213, -1.281848499159267, -1.668991967521513, 2.467519664324696, 3.784902773911917, 0.498168060302829, 0.6201099308508135, 1.881216539463003, -2.119463964656455, -3.578463605931655, 1.977433672831905, 3.365802417467458, -1.318282587175989, -1.691244308897169, 0.03135098185513866, -2.807065159117407, -3.607827263300777, -0.06014158685492786, -0.1488399926411524, -1.541664966996196, 1.186067972461571, 0.9009960119899035, -3.681183159491435, -2.972450115074519, 0.4569645340347193, -1.051736498852931, -1.864295775838683, 0.561712048060942, -0.5345329727999337, -2.201940231298842, 0.1785887807141957, 0.1865537339950753, -1.54859834132451, 1.393264021637192, 1.759967337069514, -3.614250792987491, -2.357948832446016, 3.931017511378431, 2.383289785864599, -0.6599258451756028, 3.019703078394984, 3.617213022169794], 'positive_zeros': ['0.3752496529681827', '1.071166884239452', '2.031910543432882', '2.444586564566619', '2.964642446032231', '3.709751557082633', '4.061763586441183', '4.666729525421891', '4.941005864188228', '5.855736515572210', '6.323892841274827', '6.815802121131535', '7.375569057484695', '7.944467852372006', '8.142344924698656', '8.582746046662281', '9.205540542693775', '9.687302206263791', '10.22290420857809', '10.54447178627378', '11.15117526057179', '11.63684455659126', '12.16227757486519', '12.39698821610341', '12.94183480726151', '13.45817891944442', '14.02537802826037', '14.21045507816491', '14.90487368854291', '15.19292969449316', '15.73758636052875', '15.91850023123456', '16.37494424865119', '17.17978033677944', '17.31697328545025', '17.91237868607122', '18.36479188240563', '18.88372108975592', '19.32587555226169', '19.63142706259725', '19.84000235951024'], 'prelabel': '2-219912-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 41.90472719074045, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2112463989315092871, 'z1': {'__RealLiteral__': 0, 'data': '0.3752496529681827', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.071166884239452', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.031910543432882', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1756.006160930382, 'bad_primes': [2, 3, 7, 11, 17], 'central_character': '1.1', 'conductor': 219912, 'conductor_radical': 7854, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -2, 0, 0, 0, 1, 0, -1, 0, -2, 0, -2, 0, -1, 0, -4, 0, 0, 0, -4, 0, -1, 0, 1, 0, 6, 0, 8, 0, -1, 0, 0, 0, -2, 0, -2, 0, 6, 0, 4, 0, -2, 0, -4, 0, 0, 0, -1, 0, 2, 0, 2, 0, -4, 0, 4, 0, -10, 0, 0, 0, 4, 0, 12, 0, -4, 0, -4, 0, 14, 0, -1, 0, 0, 0, -4, 0, 1, 0, 4, 0, 2, 0, 6, 0, 6, 0, 0, 0, 8, 0, 8, 0, -2, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, 2, 13], 'euler17': [1, 1, 0], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, -8, 31], 'euler37': [1, 2, 37], 'euler41': [1, -6, 41], 'euler43': [1, -4, 43], 'euler47': [1, 4, 47], 'euler5': [1, 2, 5], 'euler53': [1, -2, 53], 'euler59': [1, -4, 59], 'euler61': [1, 10, 61], 'euler67': [1, -12, 67], 'euler7': [1, 0, 0], 'euler71': [1, 4, 71], 'euler73': [1, -14, 73], 'euler79': [1, 4, 79], 'euler83': [1, -4, 83], 'euler89': [1, -6, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 2, 5], [1, 0, 0], [1, 1, 0], [1, 2, 13], [1, 1, 0], [1, 4, 19], [1, 4, 23], [1, -6, 29], [1, -8, 31], [1, 2, 37], [1, -6, 41], [1, -4, 43], [1, 4, 47], [1, -2, 53], [1, -4, 59], [1, 10, 61], [1, -12, 67], [1, 4, 71], [1, -14, 73], [1, 4, 79], [1, -4, 83], [1, -6, 89], [1, 2, 97]], 'index': 7, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/219912/bm'], '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': '2-219912-1.1-c1-0-7', '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': '2-219912-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 41.90472719074045, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2112463989315092871, 'z1': {'__RealLiteral__': 0, 'data': '0.3752496529681827', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2112463989315092871', 'Lhash_array': ['2112463989315092871'], 'label': '2-219912-1.1-c1-0-7', 'type': 'ECQ', 'url': 'EllipticCurve/Q/219912/bm'}