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lfunc_lfunctions • Show schema
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{'Lhash': '5206602409007376064277390719156', 'a10': -24, 'a2': 2, 'a3': -2, 'a4': 4, 'a5': -12, 'a6': -4, 'a7': 7, 'a8': 8, 'a9': -23, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.826026740080369, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2]], [7, [1, -7]]], 'bad_primes': [2, 7], 'central_character': '14.1', 'coefficient_field': '1.1.1.1', 'conductor': 14, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[1, -2], [1, 2, 27], [1, 12, 125], [1, -7], [1, -48, 1331], [1, -56, 2197], [1, 114, 4913], [1, -2, 6859], [1, 120, 12167], [1, 54, 24389], [1, -236, 29791], [1, -146, 50653], [1, -126, 68921], [1, 376, 79507], [1, 12, 103823], [1, -174, 148877], [1, -138, 205379], [1, -380, 226981], [1, 484, 300763], [1, -576, 357911], [1, 1150, 389017], [1, -776, 493039], [1, -378, 571787], [1, 390, 704969], [1, 1330, 912673], [1, 1500, 1030301], [1, -380, 1092727], [1, -636, 1225043], [1, -146, 1295029], [1, -198, 1442897]], 'euler_factors_factorization': [[[[1, -2], 1]], [[[1, 2, 27], 1]], [[[1, 12, 125], 1]], [[[1, -7], 1]], [[[1, -48, 1331], 1]], [[[1, -56, 2197], 1]], [[[1, 114, 4913], 1]], [[[1, -2, 6859], 1]], [[[1, 120, 12167], 1]], [[[1, 54, 24389], 1]], [[[1, -236, 29791], 1]], [[[1, -146, 50653], 1]], [[[1, -126, 68921], 1]], [[[1, 376, 79507], 1]], [[[1, 12, 103823], 1]], [[[1, -174, 148877], 1]], [[[1, -138, 205379], 1]], [[[1, -380, 226981], 1]], [[[1, 484, 300763], 1]], [[[1, -576, 357911], 1]], [[[1, 1150, 389017], 1]], [[[1, -776, 493039], 1]], [[[1, -378, 571787], 1]], [[[1, 390, 704969], 1]], [[[1, 1330, 912673], 1]], [[[1, 1500, 1030301], 1]], [[[1, -380, 1092727], 1]], [[[1, -636, 1225043], 1]], [[[1, -146, 1295029], 1]], [[[1, -198, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-14-1.1-c3-0-1', '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/14/4/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [1.136203385719111, 1.1409092407905517, 1.1548472487477086, 1.1774801897670266, 1.207916457750093, 1.2449126653216744, 1.2868733982434164, 1.3318479162760959, 1.3775263568039793, 1.4212405432233572, 1.4599762137909955, 1.4904042025371966, 1.5089379199629311, 1.5118235490874807, 1.495267785373267, 1.4556057279403387, 1.3895086593955706, 1.2942279313190048, 1.1678670573108216, 1.009669548256877, 0.8203052538315576, 0.6021333614405259, 0.3594162163897651, 0.098455318705562, -0.1723801734437171, -0.44276074450065805, -0.7006636607814084, -0.9328164056104853, -1.1253218419761366, -1.2644562310147287, -1.3376142156126656, -1.3343561428240838, -1.2474940910217847, -1.0741355351904065, -0.8165898754670521, -0.4830353552017716, -0.08784440138009778, 0.3485240356476505, 0.8001348180829403, 1.236726152644115, 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2.805610616630899, 3.2802941327911195, 3.1977228757118277, 2.569600850949851, 1.570545762497503, 0.4860263342762074, -0.377669720447882, -0.7933353921339193, -0.6902489030640697, -0.1828031939982787, 0.4610818521361724, 0.9040852082105851, 0.8510808428113953, 0.15316089415194253, -1.1300214838446596, -2.7317400310261717, -4.246124880964727, -5.244026322436931, -5.402331895195385, -4.606724283791636, -2.99489151174837, -0.9249235405511671], 'positive_zeros': ['4.10728508949545943221697599589025', '6.36455880219347397070988808395488', '8.454298897419624859030526746703424', '11.22780708054999787555304036772966', '11.83139263343001526257239926146492', '13.72439967177253770172734555098472', '15.09686444946375758885149736495655', '16.28749175378899646413987168835567', '17.72055148312217158731195318477454', '19.55131588676090196951499634616827'], 'prelabel': '2-14-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.9088601322977969, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 459051724693685361, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.10728508949545943221697599589', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.36455880219347397070988808395', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.454298897419624859030526746703', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.826026740080369, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 14, 'conductor_radical': 14, 'degree': 2, 'dirichlet_coefficients': [1, 2, -2, 4, -12, -4, 7, 8, -23, -24, 48, -8, 56, 14, 24, 16, -114, -46, 2, -48, -14, 96, -120, -16, 19, 112, 100, 28, -54, 48, 236, 32, -96, -228, -84, -92, 146, 4, -112, -96, 126, -28, -376, 192, 276, -240, -12, -32, 49, 38, 228, 224, 174, 200, -576, 56, -4, -108, 138, 96, 380, 472, -161, 64, -672, -192, -484, -456, 240, -168, 576, -184, -1150, 292, -38, 8, 336, -224, 776, -192, 421, 252, 378, -56, 1368, -752, 108, 384, -390, 552, 392, -480, -472, -24, -24, -64, -1330, 98, -1104, 76], 'euler11': [1, -48, 1331], 'euler13': [1, -56, 2197], 'euler17': [1, 114, 4913], 'euler19': [1, -2, 6859], 'euler2': [1, -2, 0], 'euler23': [1, 120, 12167], 'euler29': [1, 54, 24389], 'euler3': [1, 2, 27], 'euler31': [1, -236, 29791], 'euler37': [1, -146, 50653], 'euler41': [1, -126, 68921], 'euler43': [1, 376, 79507], 'euler47': [1, 12, 103823], 'euler5': [1, 12, 125], 'euler53': [1, -174, 148877], 'euler59': [1, -138, 205379], 'euler61': [1, -380, 226981], 'euler67': [1, 484, 300763], 'euler7': [1, -7, 0], 'euler71': [1, -576, 357911], 'euler73': [1, 1150, 389017], 'euler79': [1, -776, 493039], 'euler83': [1, -378, 571787], 'euler89': [1, 390, 704969], 'euler97': [1, 1330, 912673], 'euler_factors': [[1, -2, 0], [1, 2, 27], [1, 12, 125], [1, -7, 0], [1, -48, 1331], [1, -56, 2197], [1, 114, 4913], [1, -2, 6859], [1, 120, 12167], [1, 54, 24389], [1, -236, 29791], [1, -146, 50653], [1, -126, 68921], [1, 376, 79507], [1, 12, 103823], [1, -174, 148877], [1, -138, 205379], [1, -380, 226981], [1, 484, 300763], [1, -576, 357911], [1, 1150, 389017], [1, -776, 493039], [1, -378, 571787], [1, 390, 704969], [1, 1330, 912673]], 'index': 1, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/14/4/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/14/4/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': '2-14-1.1-c3-0-1', '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': '2-14-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.9088601322977969, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 459051724693685361, 'z1': {'__RealLiteral__': 0, 'data': '4.10728508949545943221697599589', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9956910
{'Lhash': '5206602409007376064277390719156', 'Lhash_array': ['5206602409007376064277390719156'], 'factors': ['2-14-1.1-c3-0-1'], 'label': '2-14-1.1-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/14/4/a/b'}
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id: 24546723
{'Lhash': '5206602409007376064277390719156', 'Lhash_array': ['5206602409007376064277390719156'], 'factors': ['2-14-1.1-c3-0-1'], 'label': '2-14-1.1-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/14/4/a/b/1/1'}