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lfunc_lfunctions • Show schema
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{'Lhash': '1376665669427996028345556746441', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': 16, 'a6': 0, 'a7': 7, 'a8': 0, 'a9': -23, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.43285568257181, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, -7]]], 'bad_primes': [2, 7], 'central_character': '448.1', 'coefficient_field': '1.1.1.1', 'conductor': 448, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[1], [1, 2, 27], [1, -16, 125], [1, -7], [1, -24, 1331], [1, -68, 2197], [1, -54, 4913], [1, 46, 6859], [1, 176, 12167], [1, -174, 24389], [1, -116, 29791], [1, 74, 50653], [1, 10, 68921], [1, 480, 79507], [1, -572, 103823], [1, -162, 148877], [1, 86, 205379], [1, -904, 226981], [1, -660, 300763], [1, 1024, 357911], [1, -770, 389017], [1, -904, 493039], [1, -682, 571787], [1, 102, 704969], [1, 218, 912673], [1, -80, 1030301], [1, 108, 1092727], [1, -1492, 1225043], [1, -1510, 1295029], [1, 2138, 1442897]], 'euler_factors_factorization': [[1], [[[1, 2, 27], 1]], [[[1, -16, 125], 1]], [[[1, -7], 1]], [[[1, -24, 1331], 1]], [[[1, -68, 2197], 1]], [[[1, -54, 4913], 1]], [[[1, 46, 6859], 1]], [[[1, 176, 12167], 1]], [[[1, -174, 24389], 1]], [[[1, -116, 29791], 1]], [[[1, 74, 50653], 1]], [[[1, 10, 68921], 1]], [[[1, 480, 79507], 1]], [[[1, -572, 103823], 1]], [[[1, -162, 148877], 1]], [[[1, 86, 205379], 1]], [[[1, -904, 226981], 1]], [[[1, -660, 300763], 1]], [[[1, 1024, 357911], 1]], [[[1, -770, 389017], 1]], [[[1, -904, 493039], 1]], [[[1, -682, 571787], 1]], [[[1, 102, 704969], 1]], [[[1, 218, 912673], 1]], [[[1, -80, 1030301], 1]], [[[1, 108, 1092727], 1]], [[[1, -1492, 1225043], 1]], [[[1, -1510, 1295029], 1]], [[[1, 2138, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-448-1.1-c3-0-11', 'leading_term': '2.40419495277982540413333455518000000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/448/4/a/h', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [2.404194952779825, 2.394261523806847, 2.364530460982531, 2.3152107741562262, 2.2466551868811893, 2.1593664036709486, 2.0540053084898173, 1.9314005444361548, 1.7925588026053423, 1.6386750502084024, 1.4711418572424662, 1.2915569394351887, 1.1017280239619218, 0.9036741638910923, 0.6996226770946449, 0.4920009645525435, 0.2834225702089722, 0.07666697802943684, -0.12534720049137546, -0.31959581596367825, -0.5029895177537268, -0.6724205947508145, -0.8248158535805556, -0.957194837513314, -1.0667324582341484, -1.1508248864892976, -1.2071573329009324, -1.23377215390888, -1.22913554713796, -1.192200962917826, -1.1224672615198374, -1.0200295958900762, -0.8856210035793228, -0.7206427545935882, -0.5271816281678287, 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0.5030770892899981, 0.10404736417422995, -0.3897549774552825, -0.9596223402860494, -1.581300752293552, -2.2262447699653234, -2.863151769397241, -3.4596901413947125, -3.9843229655351715, -4.408121447445331, -4.706461307524091, -4.860500586481945, -4.858348779348639, -4.695854242674468, -4.376958506304114, -3.913591226905608, -3.325106579071487, -2.6372892782781068, -1.8809845048313523, -1.0904291367280279, -0.30138044137776954, 0.4508484942686498, 1.1333306887118766, 1.7173290184572194, 2.1798537325107126], 'positive_zeros': ['1.08599772617165914430570884843144', '2.26641089135339627238958984134712', '3.75046211898536870871056101513583', '5.20110970311538089375129196469333', '6.05012059571621196865816067981944', '6.49918233833926407681722809875607', '8.216718257510508179639488871985158', '8.813979355129286989845266630099742', '9.945878943104851608220139975777385', '10.56480593280988231971019898374678'], 'prelabel': '2-448-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.141289301583, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 244354660081156938, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.08599772617165914430570884843', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.26641089135339627238958984135', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.75046211898536870871056101514', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.43285568257181, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 448, 'conductor_radical': 14, 'degree': 2, 'dirichlet_coefficients': [1, 0, -2, 0, 16, 0, 7, 0, -23, 0, 24, 0, 68, 0, -32, 0, 54, 0, -46, 0, -14, 0, -176, 0, 131, 0, 100, 0, 174, 0, 116, 0, -48, 0, 112, 0, -74, 0, -136, 0, -10, 0, -480, 0, -368, 0, 572, 0, 49, 0, -108, 0, 162, 0, 384, 0, 92, 0, -86, 0, 904, 0, -161, 0, 1088, 0, 660, 0, 352, 0, -1024, 0, 770, 0, -262, 0, 168, 0, 904, 0, 421, 0, 682, 0, 864, 0, -348, 0, -102, 0, 476, 0, -232, 0, -736, 0, -218, 0, -552, 0], 'euler11': [1, -24, 1331], 'euler13': [1, -68, 2197], 'euler17': [1, -54, 4913], 'euler19': [1, 46, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 176, 12167], 'euler29': [1, -174, 24389], 'euler3': [1, 2, 27], 'euler31': [1, -116, 29791], 'euler37': [1, 74, 50653], 'euler41': [1, 10, 68921], 'euler43': [1, 480, 79507], 'euler47': [1, -572, 103823], 'euler5': [1, -16, 125], 'euler53': [1, -162, 148877], 'euler59': [1, 86, 205379], 'euler61': [1, -904, 226981], 'euler67': [1, -660, 300763], 'euler7': [1, -7, 0], 'euler71': [1, 1024, 357911], 'euler73': [1, -770, 389017], 'euler79': [1, -904, 493039], 'euler83': [1, -682, 571787], 'euler89': [1, 102, 704969], 'euler97': [1, 218, 912673], 'euler_factors': [[1, 0, 0], [1, 2, 27], [1, -16, 125], [1, -7, 0], [1, -24, 1331], [1, -68, 2197], [1, -54, 4913], [1, 46, 6859], [1, 176, 12167], [1, -174, 24389], [1, -116, 29791], [1, 74, 50653], [1, 10, 68921], [1, 480, 79507], [1, -572, 103823], [1, -162, 148877], [1, 86, 205379], [1, -904, 226981], [1, -660, 300763], [1, 1024, 357911], [1, -770, 389017], [1, -904, 493039], [1, -682, 571787], [1, 102, 704969], [1, 218, 912673]], 'index': 11, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/448/4/a/h/1/1', 'ModularForm/GL2/Q/holomorphic/448/4/a/h'], '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': '2-448-1.1-c3-0-11', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-448-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.141289301583, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 244354660081156938, 'z1': {'__RealLiteral__': 0, 'data': '1.08599772617165914430570884843', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20587687
{'Lhash': '1376665669427996028345556746441', 'Lhash_array': ['1376665669427996028345556746441'], 'label': '2-448-1.1-c3-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/448/4/a/h'}
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id: 24561003
{'Lhash': '1376665669427996028345556746441', 'Lhash_array': ['1376665669427996028345556746441'], 'label': '2-448-1.1-c3-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/448/4/a/h/1/1'}