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lfunc_lfunctions • Show schema
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{'Lhash': '803040542016805220231935961985,1630231038907822228163341495278', 'a10': 0, 'a2': 0, 'a3': 18, 'a4': 0, 'a5': -36, 'a6': 0, 'a7': -120, 'a8': 0, 'a9': 243, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 948.2515534652371, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -18, 81]]], 'bad_primes': [2, 3], 'central_character': '192.1', 'coefficient_field': '1.1.1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1, -18, 81], [1, 36, -1362, 112500, 9765625], [1, 120, 29278, 2016840, 282475249], [1, -200, 46406, -32210200, 25937424601], [1, 284, 477054, 105447212, 137858491849], [1, -2676, 4344262, -3799537332, 2015993900449], [1, 72, 4159894, 178279128, 6131066257801], [1, -3840, 9416686, -24715557120, 41426511213649], [1, 10212, 64228638, 209459853588, 420707233300201], [1, -10488, 84559438, -300262535688, 819628286980801], [1, 13148, 125908974, 911734346636, 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{'algebraic': True, 'analytic_conductor': 948.2515534652371, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 18, 0, -36, 0, -120, 0, 243, 0, 200, 0, -284, 0, -648, 0, 2676, 0, -72, 0, -2160, 0, 3840, 0, 2658, 0, 2916, 0, -10212, 0, 10488, 0, 3600, 0, 4320, 0, -13148, 0, -5112, 0, 4164, 0, 5832, 0, -8748, 0, 1520, 0, -14878, 0, 48168, 0, -9012, 0, -7200, 0, -1296, 0, 55096, 0, 63444, 0, -29160, 0, 10224, 0, -36792, 0, 69120, 0, 37664, 0, -37836, 0, 47844, 0, -24000, 0, 144888, 0, 32805, 0, 109272, 0, -96336, 0, -183816, 0, -32556, 0, 34080, 0, 188784, 0, 2592, 0, 69092, 0, 48600, 0], 'euler11': [1, -200, 46406, -32210200, 25937424601], 'euler13': [1, 284, 477054, 105447212, 137858491849], 'euler17': [1, -2676, 4344262, -3799537332, 2015993900449], 'euler19': [1, 72, 4159894, 178279128, 6131066257801], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -3840, 9416686, -24715557120, 41426511213649], 'euler29': [1, 10212, 64228638, 209459853588, 420707233300201], 'euler3': [1, -18, 81, 0, 0], 'euler31': [1, -10488, 84559438, -300262535688, 819628286980801], 'euler37': [1, 13148, 125908974, 911734346636, 4808584372417849], 'euler41': [1, -4164, 216207126, -482425220964, 13422659310152401], 'euler43': [1, -5832, 168401542, -857353239576, 21611482313284249], 'euler47': [1, -1520, 148144670, -348604410640, 52599132235830049], 'euler5': [1, 36, -1362, 112500, 9765625], 'euler53': [1, 9012, 816689646, 3768777782916, 174887470365513049], 'euler59': [1, -55096, 1818478886, -39389469177704, 511116753300641401], 'euler61': [1, -63444, 2677193342, -53584567720644, 713342911662882601], 'euler67': [1, 36792, 1148752246, 49673802936744, 1822837804551761449], 'euler7': [1, 120, 29278, 2016840, 282475249], 'euler71': [1, -37664, 2440628942, -67954494276064, 3255243551009881201], 'euler73': [1, 37836, 2085902966, 78436736792748, 4297625829703557649], 'euler79': [1, -144888, 10711615534, -445828547538312, 9468276082626847201], 'euler83': [1, -109272, 10472055958, -430426849141896, 15516041187205853449], 'euler89': [1, 32556, 8836559958, 181794639421644, 31181719929966183601], 'euler97': [1, -69092, 18339537030, -593316513036644, 73742412689492826049], 'euler_factors': [[1, 0, 0, 0, 0], [1, -18, 81, 0, 0], [1, 36, -1362, 112500, 9765625], [1, 120, 29278, 2016840, 282475249], [1, -200, 46406, -32210200, 25937424601], [1, 284, 477054, 105447212, 137858491849], [1, -2676, 4344262, -3799537332, 2015993900449], [1, 72, 4159894, 178279128, 6131066257801], [1, -3840, 9416686, -24715557120, 41426511213649], [1, 10212, 64228638, 209459853588, 420707233300201], [1, -10488, 84559438, -300262535688, 819628286980801], [1, 13148, 125908974, 911734346636, 4808584372417849], [1, -4164, 216207126, -482425220964, 13422659310152401], [1, -5832, 168401542, -857353239576, 21611482313284249], [1, -1520, 148144670, -348604410640, 52599132235830049], [1, 9012, 816689646, 3768777782916, 174887470365513049], [1, -55096, 1818478886, -39389469177704, 511116753300641401], [1, -63444, 2677193342, -53584567720644, 713342911662882601], [1, 36792, 1148752246, 49673802936744, 1822837804551761449], [1, -37664, 2440628942, -67954494276064, 3255243551009881201], [1, 37836, 2085902966, 78436736792748, 4297625829703557649], [1, -144888, 10711615534, -445828547538312, 9468276082626847201], [1, -109272, 10472055958, -430426849141896, 15516041187205853449], [1, 32556, 8836559958, 181794639421644, 31181719929966183601], [1, -69092, 18339537030, -593316513036644, 73742412689492826049]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/192/6/a/r'], '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': '4-192e2-1.1-c5e2-0-1', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5, 5], 'order_of_vanishing': 0, 'prelabel': '4-192e2-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.549206556264805, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e2-0', 'trace_hash': 908126276111426343, 'z1': {'__RealLiteral__': 0, 'data': '0.63348728890454893125083650516', 'prec': 103}}
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{'Lhash': '803040542016805220231935961985,1630231038907822228163341495278', 'Lhash_array': ['803040542016805220231935961985', '1630231038907822228163341495278'], 'factors': ['2-192-1.1-c5-0-1', '2-192-1.1-c5-0-9'], 'label': '4-192e2-1.1-c5e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/192/6/a/r'}