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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 2, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 1, 'Lhash': '756521969133558728', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [1.1547005383792517, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1520.3516544851793, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1, -1]], [17, [1, 1]]], 'bad_primes': [2, 5, 7, 17], 'central_character': '190400.1', 'coefficient_field': '1.1.1.1', 'conductor': 190400, 'conductor_radical': 1190, 'degree': 2, 'euler_factors': [[1], [1, -2, 3], [1], [1, -1], [1, 2, 11], [1, 1, 13], [1, 1], [1, 6, 19], [1, 9, 23], [1, 6, 29], [1, -5, 31], [1, 7, 37], [1, 5, 41], [1, 8, 43], [1, 9, 47], [1, -2, 53], [1, 14, 59], [1, 13, 61], [1, -2, 67], [1, 8, 71], [1, -8, 73], [1, -16, 79], [1, -1, 83], [1, 6, 89], [1, -16, 97]], 'gamma_factors': [[], [0]], 'index': 125, 'label': '2-190400-1.1-c1-0-125', 'leading_term': '18.8047814171', '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': 2, 'origin': 'EllipticCurve/Q/190400/eg', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, -1.120065065382095, -3.809392683228819, -6.196939276595429, -6.260817878548738, -3.741958546603779, -0.7767416595894693, 0.2500055197299825, -0.5149032817936935, -0.7689119380929126, 0.5066110345853126, 1.438769392737262, 0.2916939675189417, -1.357326557980796, -0.8570461376080326, 0.9035078695486428, 0.5213271978755137, -1.994562695367921, -2.528363046829931, 0.1284890175308317, 1.246901543169636, -2.194673014916151, -5.422417664797499, -3.065410318701572, 1.477518791441203, 1.297965056902864, -2.259429273971329, -2.014805311755367, 2.395548586860151, 4.173590261481897, 1.425275274314242, -0.6415244735705956, -0.0162307587817054, -0.07383662515160282, -1.078187638796473, 0.05074186222244549, 1.759419371757943, 0.2842544198155115, -1.668509618507442, 0.286407589633434, 2.562184768075057, 0.5190753247166768, -1.282493114384356, 1.587899588394591, 2.839491514288088, -2.36399593492371, -6.20062446496963, -2.731383660193465, 0.4088136415449831, -2.365595768328387, -3.747971992649038, 0.5321886575066221, 3.137886922129234, 0.7891973311288846, -0.4096162115049276, 0.7538042520208197, -0.2810283452388722, -1.823571840420544, -0.1924107536243596, 1.040655949521763, -0.3182279570132677, 0.02073592126880018, 1.200082675021455, -1.651438072981269, -3.597222237241379, 1.540764477074536, 5.811855805549385, 2.225255841765123, -0.328232221870035, 3.324405227176186, 3.439838876158505, -2.160894629222798, -2.938533778981528, 1.089287516155059, 0.8589612750752124, -1.039310965812956, 1.566688477260815, 3.387831578334156, 0.8812224983003553, -0.1811024297915816, 0.4841815801341666, -1.3315255082301, -2.113721440496503, 0.2311893357429571, 0.2379234027457738, -0.9769555143124501, 1.338426503571171, 1.214726552348022, -4.156804234377775, -4.222701280697439, 1.285463173273615, -0.3785025254574797, -6.057656339704526, -3.321745450462444, 1.624747636329597, -0.6505885778076809, -2.278012836034891, 1.02865510771213, 1.404641265790514, 0.02644676835879916, 2.683981612219906, 3.82721227848378, 0.6725930462162805, -0.1457281304212228, 0.8090129321571004, -0.2010813614014595, 0.4849122488571634, 1.19120373805313, -3.255772693813472, -5.352453670104553, -0.4509081621542342, 1.135190816443634, -1.358166832908821, 0.9483396797083743, 1.102769163885295, -7.032030392780058, -9.434974612224392, -2.235620235581839, -0.09540087669981649, -2.851904998893129, -0.7061734680667353], 'positive_zeros': ['1.614134396634640', '1.864484412534808', '2.419187961550552', '3.037225350792723', '3.613874965142329', '4.058786341165222', '4.739066987195823', '5.122290005145143', '5.903902395073888', '6.341557896123274', '6.871886310376154', '7.624400756817606', '8.004764287214387', '8.230966278378925', '8.744232428782512', '9.275628426863607', '9.728308492983214', '10.29013167343956', '10.64390910636757', '11.15844186990668', '11.91298857938117', '12.08064044785136', '12.72381413230889', '13.33008612384248', '13.59170778359681', '13.96756219192021', '14.52010919268556', '14.94462636192329', '15.24701217781443', '15.64458409929334', '16.19420269748238', '16.88143018739383', '17.04203891764388', '17.65449025625416', '18.17414442501562', '18.57739048942756', '18.89120134129273', '19.60073160622242', '19.80205917841154'], 'prelabel': '2-190400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 38.99168699203946, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 756521969133558728, 'z1': {'__RealLiteral__': 0, 'data': '1.614134396634640', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.864484412534808', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.419187961550552', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1520.3516544851793, 'bad_primes': [2, 5, 7, 17], 'central_character': '1.1', 'conductor': 190400, 'conductor_radical': 1190, 'degree': 2, 'dirichlet_coefficients': [1, 0, 2, 0, 0, 0, 1, 0, 1, 0, -2, 0, -1, 0, 0, 0, -1, 0, -6, 0, 2, 0, -9, 0, 0, 0, -4, 0, -6, 0, 5, 0, -4, 0, 0, 0, -7, 0, -2, 0, -5, 0, -8, 0, 0, 0, -9, 0, 1, 0, -2, 0, 2, 0, 0, 0, -12, 0, -14, 0, -13, 0, 1, 0, 0, 0, 2, 0, -18, 0, -8, 0, 8, 0, 0, 0, -2, 0, 16, 0, -11, 0, 1, 0, 0, 0, -12, 0, -6, 0, -1, 0, 10, 0, 0, 0, 16, 0, -2, 0], 'euler11': [1, 2, 11], 'euler13': [1, 1, 13], 'euler17': [1, 1, 0], 'euler19': [1, 6, 19], 'euler2': [1, 0, 0], 'euler23': [1, 9, 23], 'euler29': [1, 6, 29], 'euler3': [1, -2, 3], 'euler31': [1, -5, 31], 'euler37': [1, 7, 37], 'euler41': [1, 5, 41], 'euler43': [1, 8, 43], 'euler47': [1, 9, 47], 'euler5': [1, 0, 0], 'euler53': [1, -2, 53], 'euler59': [1, 14, 59], 'euler61': [1, 13, 61], 'euler67': [1, -2, 67], 'euler7': [1, -1, 0], 'euler71': [1, 8, 71], 'euler73': [1, -8, 73], 'euler79': [1, -16, 79], 'euler83': [1, -1, 83], 'euler89': [1, 6, 89], 'euler97': [1, -16, 97], 'euler_factors': [[1, 0, 0], [1, -2, 3], [1, 0, 0], [1, -1, 0], [1, 2, 11], [1, 1, 13], [1, 1, 0], [1, 6, 19], [1, 9, 23], [1, 6, 29], [1, -5, 31], [1, 7, 37], [1, 5, 41], [1, 8, 43], [1, 9, 47], [1, -2, 53], [1, 14, 59], [1, 13, 61], [1, -2, 67], [1, 8, 71], [1, -8, 73], [1, -16, 79], [1, -1, 83], [1, 6, 89], [1, -16, 97]], 'index': 125, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/190400/eg'], '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': '2-190400-1.1-c1-0-125', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 2, 'prelabel': '2-190400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 38.99168699203946, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 756521969133558728, 'z1': {'__RealLiteral__': 0, 'data': '1.614134396634640', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '756521969133558728', 'Lhash_array': ['756521969133558728'], 'factors': ['2-190400-1.1-c1-0-125'], 'label': '2-190400-1.1-c1-0-125', 'type': 'ECQ', 'url': 'EllipticCurve/Q/190400/eg'}