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lfunc_lfunctions • Show schema
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{'Lhash': '1408838158885282797040599101306,1989825712532700610629769950195', 'a10': 0, 'a2': 0, 'a3': -6, 'a4': 0, 'a5': -8, 'a6': 0, 'a7': -16, 'a8': 0, 'a9': 27, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2053.3102810844143, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 6, 9]]], 'bad_primes': [2, 3], 'central_character': '768.1', 'coefficient_field': '1.1.1.1', 'conductor': 589824, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1, 6, 9], [1, 8, 58, 1000, 15625], [1, 16, 542, 5488, 117649], [1, 8, -650, 10648, 1771561], [1, -72, 4858, -158184, 4826809], [1, 36, 6822, 176868, 24137569], [1, -136, 15014, -932824, 47045881], [1, 256, 39886, 3114752, 148035889], [1, -152, 37706, -3707128, 594823321], [1, -80, 26030, -2383280, 887503681], [1, -136, 102602, -6888808, 2565726409], [1, 436, 102166, 30049556, 4750104241], [1, 712, 282422, 56608984, 6321363049], [1, -224, 179422, -23256352, 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'4.11710082384153050518921276683589', '4.86525960549443810643976406669489', '5.19381106996727299346845073070460', '5.89567119012448387212568069366182', '6.15167787167665318345459511193069', '6.62579326908117151843684088880450', '6.87231718350630663830168543731998', '7.62784892959693206614881267296641', '7.912192020414814435349601215298253', '8.534866204890713709838693015677596', '8.636709630530718719726098333068315', '9.582836305606770944345708164943389', '9.759808236985410230177181781194794'], 'prelabel': '4-768e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.731527826905926, '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': 1052365112146728088, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.11137734532814784348255038158', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.56969571282059101897698431212', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.60043023523854513975889096301', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 2053.3102810844143, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 589824, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, -6, 0, -8, 0, -16, 0, 27, 0, -8, 0, 72, 0, 48, 0, -36, 0, 136, 0, 96, 0, -256, 0, 6, 0, -108, 0, 152, 0, 80, 0, 48, 0, 128, 0, 136, 0, -432, 0, -436, 0, -712, 0, -216, 0, 224, 0, -286, 0, 216, 0, 344, 0, 64, 0, -816, 0, -648, 0, 648, 0, -432, 0, -576, 0, 456, 0, 1536, 0, -2048, 0, 660, 0, -36, 0, 128, 0, -496, 0, 405, 0, 776, 0, 288, 0, -912, 0, 532, 0, -1152, 0, -480, 0, -1088, 0, -1220, 0, -216, 0], 'euler11': [1, 8, -650, 10648, 1771561], 'euler13': [1, -72, 4858, -158184, 4826809], 'euler17': [1, 36, 6822, 176868, 24137569], 'euler19': [1, -136, 15014, -932824, 47045881], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 256, 39886, 3114752, 148035889], 'euler29': [1, -152, 37706, -3707128, 594823321], 'euler3': [1, 6, 9, 0, 0], 'euler31': [1, -80, 26030, -2383280, 887503681], 'euler37': [1, -136, 102602, -6888808, 2565726409], 'euler41': [1, 436, 102166, 30049556, 4750104241], 'euler43': [1, 712, 282422, 56608984, 6321363049], 'euler47': [1, -224, 179422, -23256352, 10779215329], 'euler5': [1, 8, 58, 1000, 15625], 'euler53': [1, -344, 280538, -51213688, 22164361129], 'euler59': [1, 648, 515734, 133085592, 42180533641], 'euler61': [1, -648, 558938, -147083688, 51520374361], 'euler67': [1, -456, 174278, -137147928, 90458382169], 'euler7': [1, 16, 542, 5488, 117649], 'euler71': [1, 2048, 1763566, 733001728, 128100283921], 'euler73': [1, -660, 407702, -256751220, 151334226289], 'euler79': [1, 496, 323534, 244547344, 243087455521], 'euler83': [1, -776, 1131046, -443706712, 326940373369], 'euler89': [1, -532, 1467382, -375043508, 496981290961], 'euler97': [1, 1220, 586694, 1113461060, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0], [1, 6, 9, 0, 0], [1, 8, 58, 1000, 15625], [1, 16, 542, 5488, 117649], [1, 8, -650, 10648, 1771561], [1, -72, 4858, -158184, 4826809], [1, 36, 6822, 176868, 24137569], [1, -136, 15014, -932824, 47045881], [1, 256, 39886, 3114752, 148035889], [1, -152, 37706, -3707128, 594823321], [1, -80, 26030, -2383280, 887503681], [1, -136, 102602, -6888808, 2565726409], [1, 436, 102166, 30049556, 4750104241], [1, 712, 282422, 56608984, 6321363049], [1, -224, 179422, -23256352, 10779215329], [1, -344, 280538, -51213688, 22164361129], [1, 648, 515734, 133085592, 42180533641], [1, -648, 558938, -147083688, 51520374361], [1, -456, 174278, -137147928, 90458382169], [1, 2048, 1763566, 733001728, 128100283921], [1, -660, 407702, -256751220, 151334226289], [1, 496, 323534, 244547344, 243087455521], [1, -776, 1131046, -443706712, 326940373369], [1, -532, 1467382, -375043508, 496981290961], [1, 1220, 586694, 1113461060, 832972004929]], 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/768/4/a/e'], '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': '4-768e2-1.1-c3e2-0-30', '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': 2, 'prelabel': '4-768e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.731527826905926, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1052365112146728088, 'z1': {'__RealLiteral__': 0, 'data': '1.11137734532814784348255038158', 'prec': 103}}
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{'Lhash': '1408838158885282797040599101306,1989825712532700610629769950195', 'Lhash_array': ['1408838158885282797040599101306', '1989825712532700610629769950195'], 'label': '4-768e2-1.1-c3e2-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/768/4/a/e'}