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lfunc_lfunctions • Show schema
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{'Lhash': '5209988598976335385815655773106', 'a10': -124, 'a2': 4, 'a3': -29, 'a4': 16, 'a5': -31, 'a6': -116, 'a7': -230, 'a8': 64, 'a9': 598, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.528444035885575, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -4]], [11, [1, -121]]], 'bad_primes': [2, 11], 'central_character': '22.1', 'coefficient_field': '1.1.1.1', 'conductor': 22, 'conductor_radical': 22, 'degree': 2, 'euler_factors': [[1, -4], [1, 29, 243], [1, 31, 3125], [1, 230, 16807], [1, -121], [1, -112, 371293], [1, 1142, 1419857], [1, 612, 2476099], [1, 1941, 6436343], [1, -1192, 20511149], [1, 1037, 28629151], [1, -8083, 69343957], [1, 10444, 115856201], [1, -58, 147008443], [1, -8656, 229345007], [1, 20318, 418195493], [1, 21351, 714924299], [1, -47044, 844596301], [1, -48093, 1350125107], [1, 24967, 1804229351], [1, 42288, 2073071593], [1, 72410, 3077056399], [1, 15806, 3939040643], [1, 114761, 5584059449], [1, 5159, 8587340257], [1, 61426, 10510100501], [1, -185896, 11592740743], [1, 23970, 14025517307], [1, 56326, 15386239549], [1, 261903, 18424351793]], 'euler_factors_factorization': [[[[1, -4], 1]], [[[1, 29, 243], 1]], [[[1, 31, 3125], 1]], [[[1, 230, 16807], 1]], [[[1, -121], 1]], [[[1, -112, 371293], 1]], [[[1, 1142, 1419857], 1]], [[[1, 612, 2476099], 1]], [[[1, 1941, 6436343], 1]], [[[1, -1192, 20511149], 1]], [[[1, 1037, 28629151], 1]], [[[1, -8083, 69343957], 1]], [[[1, 10444, 115856201], 1]], [[[1, -58, 147008443], 1]], [[[1, -8656, 229345007], 1]], [[[1, 20318, 418195493], 1]], [[[1, 21351, 714924299], 1]], [[[1, -47044, 844596301], 1]], [[[1, -48093, 1350125107], 1]], [[[1, 24967, 1804229351], 1]], [[[1, 42288, 2073071593], 1]], [[[1, 72410, 3077056399], 1]], [[[1, 15806, 3939040643], 1]], [[[1, 114761, 5584059449], 1]], [[[1, 5159, 8587340257], 1]], [[[1, 61426, 10510100501], 1]], [[[1, -185896, 11592740743], 1]], [[[1, 23970, 14025517307], 1]], [[[1, 56326, 15386239549], 1]], [[[1, 261903, 18424351793], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-22-1.1-c5-0-4', '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/22/6/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [0.0, 0.25780983731563867, 0.5148137932220584, 0.7699922825628824, 1.02191067690021, 1.2685426370922595, 1.507130314192423, 1.734093418634213, 1.944998774851738, 2.1346012064324587, 2.2969651380252754, 2.4256738042493016, 2.514129088086365, 2.5559395313733164, 2.5453868974983087, 2.4779529832940805, 2.3508786123538368, 2.1637166322998866, 1.9188313102618677, 1.6217890463271636, 1.281581237449177, 0.9106208892853764, 0.5244615149525946, 0.14120095435683203, -0.21944560027446242, -0.5373902641075319, -0.7936870582518595, -0.9722306771928829, 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'15.61923593718955118297052990975410', '16.15595010129234074381616164300583'], 'prelabel': '2-22-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.878415299098039, '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': 1296477389105222849, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.10995632237962299247234454324', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.97424717232060262937512525245', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.84593743536970044315079720845', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.528444035885575, 'bad_primes': [2, 11], 'central_character': '1.1', 'conductor': 22, 'conductor_radical': 22, 'degree': 2, 'dirichlet_coefficients': [1, 4, -29, 16, -31, -116, -230, 64, 598, -124, 121, -464, 112, -920, 899, 256, -1142, 2392, -612, -496, 6670, 484, -1941, -1856, -2164, 448, -10295, -3680, 1192, 3596, -1037, 1024, -3509, -4568, 7130, 9568, 8083, -2448, -3248, -1984, -10444, 26680, 58, 1936, -18538, -7764, 8656, -7424, 36093, -8656, 33118, 1792, -20318, -41180, -3751, -14720, 17748, 4768, -21351, 14384, 47044, -4148, -137540, 4096, -3472, -14036, 48093, -18272, 56289, 28520, -24967, 38272, -42288, 32332, 62756, -9792, -27830, -12992, -72410, -7936, 153241, -41776, -15806, 106720, 35402, 232, -34568, 7744, -114761, -74152, -25760, -31056, 30073, 34624, 18972, -29696, -5159, 144372, 72358, -34624], 'euler11': [1, -121, 0], 'euler13': [1, -112, 371293], 'euler17': [1, 1142, 1419857], 'euler19': [1, 612, 2476099], 'euler2': [1, -4, 0], 'euler23': [1, 1941, 6436343], 'euler29': [1, -1192, 20511149], 'euler3': [1, 29, 243], 'euler31': [1, 1037, 28629151], 'euler37': [1, -8083, 69343957], 'euler41': [1, 10444, 115856201], 'euler43': [1, -58, 147008443], 'euler47': [1, -8656, 229345007], 'euler5': [1, 31, 3125], 'euler53': [1, 20318, 418195493], 'euler59': [1, 21351, 714924299], 'euler61': [1, -47044, 844596301], 'euler67': [1, -48093, 1350125107], 'euler7': [1, 230, 16807], 'euler71': [1, 24967, 1804229351], 'euler73': [1, 42288, 2073071593], 'euler79': [1, 72410, 3077056399], 'euler83': [1, 15806, 3939040643], 'euler89': [1, 114761, 5584059449], 'euler97': [1, 5159, 8587340257], 'euler_factors': [[1, -4, 0], [1, 29, 243], [1, 31, 3125], [1, 230, 16807], [1, -121, 0], [1, -112, 371293], [1, 1142, 1419857], [1, 612, 2476099], [1, 1941, 6436343], [1, -1192, 20511149], [1, 1037, 28629151], [1, -8083, 69343957], [1, 10444, 115856201], [1, -58, 147008443], [1, -8656, 229345007], [1, 20318, 418195493], [1, 21351, 714924299], [1, -47044, 844596301], [1, -48093, 1350125107], [1, 24967, 1804229351], [1, 42288, 2073071593], [1, 72410, 3077056399], [1, 15806, 3939040643], [1, 114761, 5584059449], [1, 5159, 8587340257]], 'index': 4, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/22/6/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/22/6/a/c'], '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': '2-22-1.1-c5-0-4', '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': '2-22-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.878415299098039, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 1296477389105222849, 'z1': {'__RealLiteral__': 0, 'data': '4.10995632237962299247234454324', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10028604
{'Lhash': '5209988598976335385815655773106', 'Lhash_array': ['5209988598976335385815655773106'], 'label': '2-22-1.1-c5-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/22/6/a/c'}
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id: 24549362
{'Lhash': '5209988598976335385815655773106', 'Lhash_array': ['5209988598976335385815655773106'], 'label': '2-22-1.1-c5-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/22/6/a/c/1/1'}