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lfunc_lfunctions • Show schema
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{'Lhash': '2244212951987490059701500679987', 'a10': 112, 'a2': 4, 'a3': 9, 'a4': 16, 'a5': 28, 'a6': 36, 'a7': 49, 'a8': 64, 'a9': 81, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 154.9307699393393, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -4]], [3, [1, -9]], [7, [1, -49]], [23, [1, -529]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '966.1', 'coefficient_field': '1.1.1.1', 'conductor': 966, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[1, -4], [1, -9], [1, -28, 3125], [1, -49], [1, 15, 161051], [1, 1066, 371293], [1, 80, 1419857], [1, 1319, 2476099], [1, -529], [1, 3586, 20511149], [1, 7850, 28629151], [1, -5074, 69343957], [1, 17627, 115856201], [1, -10392, 147008443], [1, 11805, 229345007], [1, 345, 418195493], [1, 31347, 714924299], [1, 5019, 844596301], [1, 26552, 1350125107], [1, 23492, 1804229351], [1, 5356, 2073071593], [1, -99870, 3077056399], [1, -47482, 3939040643], [1, 58182, 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15386239549], 1]], [[[1, -31666, 18424351793], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 106, 'label': '2-966-1.1-c5-0-106', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/966/6/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-3.852921568519496e-60, 0.47924562386443803, 0.9532005575454312, 1.4166413409734733, 1.8644782643934303, 2.291820469457399, 2.694038923738332, 3.066826564473359, 3.406254912987963, 3.7088264702736007, 3.971522217779685, 4.191843566941567, 4.367848127663511, 4.498178701268343, 4.582084948599712, 4.619437240164264, 4.61073226336745, 4.557090042695111, 4.460242122460804, 4.322510768433399, 4.14677916381604, 3.9364527057486094, 3.695411649362364, 3.4279554955616742, 3.138739673810465, 2.832705229483027, 2.515002383618878, 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'7.25926427979336317174411803351926', '7.79663162520243274166295578797386', '8.954889792762959753404528229900408'], 'prelabel': '2-966-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.447118941318884, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'trace_hash': 751951207741635916, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.77037186081357051342176995070', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.33375619470170670960788654688', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.44600011807659256509426801215', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 154.9307699393393, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 966, 'conductor_radical': 966, 'degree': 2, 'dirichlet_coefficients': [1, 4, 9, 16, 28, 36, 49, 64, 81, 112, -15, 144, -1066, 196, 252, 256, -80, 324, -1319, 448, 441, -60, 529, 576, -2341, -4264, 729, 784, -3586, 1008, -7850, 1024, -135, -320, 1372, 1296, 5074, -5276, -9594, 1792, -17627, 1764, 10392, -240, 2268, 2116, -11805, 2304, 2401, -9364, -720, -17056, -345, 2916, -420, 3136, -11871, -14344, -31347, 4032, -5019, -31400, 3969, 4096, -29848, -540, -26552, -1280, 4761, 5488, -23492, 5184, -5356, 20296, -21069, -21104, -735, -38376, 99870, 7168, 6561, -70508, 47482, 7056, -2240, 41568, -32274, -960, -58182, 9072, -52234, 8464, -70650, -47220, -36932, 9216, 72722, 9604, -1215, -37456], 'euler11': [1, 15, 161051], 'euler13': [1, 1066, 371293], 'euler17': [1, 80, 1419857], 'euler19': [1, 1319, 2476099], 'euler2': [1, -4, 0], 'euler23': [1, -529, 0], 'euler29': [1, 3586, 20511149], 'euler3': [1, -9, 0], 'euler31': [1, 7850, 28629151], 'euler37': [1, -5074, 69343957], 'euler41': [1, 17627, 115856201], 'euler43': [1, -10392, 147008443], 'euler47': [1, 11805, 229345007], 'euler5': [1, -28, 3125], 'euler53': [1, 345, 418195493], 'euler59': [1, 31347, 714924299], 'euler61': [1, 5019, 844596301], 'euler67': [1, 26552, 1350125107], 'euler7': [1, -49, 0], 'euler71': [1, 23492, 1804229351], 'euler73': [1, 5356, 2073071593], 'euler79': [1, -99870, 3077056399], 'euler83': [1, -47482, 3939040643], 'euler89': [1, 58182, 5584059449], 'euler97': [1, -72722, 8587340257], 'euler_factors': [[1, -4, 0], [1, -9, 0], [1, -28, 3125], [1, -49, 0], [1, 15, 161051], [1, 1066, 371293], [1, 80, 1419857], [1, 1319, 2476099], [1, -529, 0], [1, 3586, 20511149], [1, 7850, 28629151], [1, -5074, 69343957], [1, 17627, 115856201], [1, -10392, 147008443], [1, 11805, 229345007], [1, 345, 418195493], [1, 31347, 714924299], [1, 5019, 844596301], [1, 26552, 1350125107], [1, 23492, 1804229351], [1, 5356, 2073071593], [1, -99870, 3077056399], [1, -47482, 3939040643], [1, 58182, 5584059449], [1, -72722, 8587340257]], 'index': 106, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/966/6/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/966/6/a/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-966-1.1-c5-0-106', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-966-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.447118941318884, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 751951207741635916, 'z1': {'__RealLiteral__': 0, 'data': '1.77037186081357051342176995070', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20829308
{'Lhash': '2244212951987490059701500679987', 'Lhash_array': ['2244212951987490059701500679987'], 'label': '2-966-1.1-c5-0-106', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/966/6/a/b'}
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id: 24593856
{'Lhash': '2244212951987490059701500679987', 'Lhash_array': ['2244212951987490059701500679987'], 'label': '2-966-1.1-c5-0-106', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/966/6/a/b/1/1'}