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lfunc_lfunctions • Show schema
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{'Lhash': '1922018417831209780330849091834,3750727820340776706773006430702', 'a10': 48, 'a2': 2, 'a3': -6, 'a4': 1, 'a5': 24, 'a6': -12, 'a7': 0, 'a8': 12, 'a9': 27, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.294943809559112, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 6, 9]], [13, [1, 26, 169]]], 'bad_primes': [3, 13], 'central_character': '39.1', 'coefficient_field': '1.1.1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 4, 'euler_factors': [[1, -2, 3, -16, 64], [1, 6, 9], [1, -24, 338, -3000, 15625], [1, 0, 630, 0, 117649], [1, 44, 1130, 58564, 1771561], [1, 26, 169], [1, -164, 16326, -805732, 24137569], [1, -48, 14238, -329232, 47045881], [1, -8, -7906, -97336, 148035889], [1, -404, 81518, -9853156, 594823321], [1, -40, 50518, -1191640, 887503681], [1, 100, 92830, 5065300, 2565726409], [1, -200, 24138, -13784200, 4750104241], [1, 616, 216022, 48976312, 6321363049], [1, 324, 219554, 33638652, 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1.5169292963826246, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3e2-0', 'trace_hash': 1115466359071075655, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.51620518894178504511611455851', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.95880254359165764848938604180', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.99204993514547714957112126026', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 5.294943809559112, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 4, 'dirichlet_coefficients': [1, 2, -6, 1, 24, -12, 0, 12, 27, 48, -44, -6, -26, 0, -144, -11, 164, 54, 48, 24, 0, -88, 8, -72, 238, -52, -108, 0, 404, -288, 40, -170, 264, 328, 0, 27, -100, 96, 156, 288, 200, 0, -616, -44, 648, 16, -324, 66, -630, 476, -984, -26, -164, -216, -1056, 0, -288, 808, 140, -144, 628, 80, 0, -179, -624, 528, -472, 164, -48, 0, 428, 324, -900, -200, -1428, 48, 0, 312, -432, -264, 405, 400, -1388, 0, 3936, -1232, -2424, -528, 960, 1296, 0, 8, -240, -648, 1152, 1020, -532, -1260, -1188, 238], 'euler11': [1, 44, 1130, 58564, 1771561], 'euler13': [1, 26, 169, 0, 0], 'euler17': [1, -164, 16326, -805732, 24137569], 'euler19': [1, -48, 14238, -329232, 47045881], 'euler2': [1, -2, 3, -16, 64], 'euler23': [1, -8, -7906, -97336, 148035889], 'euler29': [1, -404, 81518, -9853156, 594823321], 'euler3': [1, 6, 9, 0, 0], 'euler31': [1, -40, 50518, -1191640, 887503681], 'euler37': [1, 100, 92830, 5065300, 2565726409], 'euler41': [1, -200, 24138, -13784200, 4750104241], 'euler43': [1, 616, 216022, 48976312, 6321363049], 'euler47': [1, 324, 219554, 33638652, 10779215329], 'euler5': [1, -24, 338, -3000, 15625], 'euler53': [1, 164, 102878, 24415828, 22164361129], 'euler59': [1, -140, 393258, -28753060, 42180533641], 'euler61': [1, -628, 293614, -142544068, 51520374361], 'euler67': [1, 472, 252622, 141960136, 90458382169], 'euler7': [1, 0, 630, 0, 117649], 'euler71': [1, -428, 662834, -153185908, 128100283921], 'euler73': [1, 900, 899670, 350115300, 151334226289], 'euler79': [1, 432, 924318, 212992848, 243087455521], 'euler83': [1, 1388, 1567866, 793640356, 326940373369], 'euler89': [1, -960, 1134938, -676770240, 496981290961], 'euler97': [1, 532, 1218502, 485542036, 832972004929], 'euler_factors': [[1, -2, 3, -16, 64], [1, 6, 9, 0, 0], [1, -24, 338, -3000, 15625], [1, 0, 630, 0, 117649], [1, 44, 1130, 58564, 1771561], [1, 26, 169, 0, 0], [1, -164, 16326, -805732, 24137569], [1, -48, 14238, -329232, 47045881], [1, -8, -7906, -97336, 148035889], [1, -404, 81518, -9853156, 594823321], [1, -40, 50518, -1191640, 887503681], [1, 100, 92830, 5065300, 2565726409], [1, -200, 24138, -13784200, 4750104241], [1, 616, 216022, 48976312, 6321363049], [1, 324, 219554, 33638652, 10779215329], [1, 164, 102878, 24415828, 22164361129], [1, -140, 393258, -28753060, 42180533641], [1, -628, 293614, -142544068, 51520374361], [1, 472, 252622, 141960136, 90458382169], [1, -428, 662834, -153185908, 128100283921], [1, 900, 899670, 350115300, 151334226289], [1, 432, 924318, 212992848, 243087455521], [1, 1388, 1567866, 793640356, 326940373369], [1, -960, 1134938, -676770240, 496981290961], [1, 532, 1218502, 485542036, 832972004929]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/39/4/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': '4-39e2-1.1-c3e2-0-2', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'prelabel': '4-39e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.5169292963826246, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1115466359071075655, 'z1': {'__RealLiteral__': 0, 'data': '1.51620518894178504511611455851', 'prec': 103}}
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{'Lhash': '1922018417831209780330849091834,3750727820340776706773006430702', 'Lhash_array': ['1922018417831209780330849091834', '3750727820340776706773006430702'], 'label': '4-39e2-1.1-c3e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/39/4/a/b'}