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lfunc_lfunctions • Show schema
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{'Lhash': '1999244420217033808434845033040,2213541654490737585289375701890', 'a10': -4, 'a2': -4, 'a3': 6, 'a4': 12, 'a5': 1, 'a6': -24, 'a7': -14, 'a8': -32, 'a9': 27, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1037.808986673586, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 4, 4]], [3, [1, -6, 9]], [7, [1, 14, 49]], [13, [1, 26, 169]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.1', 'coefficient_field': '1.1.1.1', 'conductor': 298116, 'conductor_radical': 546, 'degree': 4, 'euler_factors': [[1, 4, 4], [1, -6, 9], [1, -1, 218, -125, 15625], [1, 14, 49], [1, 16, 2210, 21296, 1771561], [1, 26, 169], [1, -18, 3586, -88434, 24137569], [1, -63, 5390, -432117, 47045881], [1, 95, 9530, 1155865, 148035889], [1, 419, 91088, 10218991, 594823321], [1, 73, 60882, 2174743, 887503681], [1, -90, 35090, -4558770, 2565726409], [1, -186, 38002, -12819306, 4750104241], [1, 67, 136626, 5326969, 6321363049], [1, 421, 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'1.74617647330597940306195420218126', '2.71370216544147130421061147039551', '2.93969727675367858733959102683997', '3.90701783051876407669587130152151', '3.95680359232056079770773355993535', '5.30256366122942019045428068996485', '5.53060053218149427209970626958090', '6.31235716596756363088837624644654', '6.66814066786533764008775580892183', '7.37289794031841749582743307471563', '7.70787908719662167531816966641306', '7.967042510896100582807416408608306', '8.206422999833152166964222667454618', '9.231213262047884386489035705173594', '9.307657521557175911444393825177799', '9.605284750774727919276580183024020', '9.790123134128536799088259468064981'], 'prelabel': '4-546e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.675829707023846, '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': 2241696644686165843, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.57712576309046620530899965683', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.74617647330597940306195420218', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.71370216544147130421061147040', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 1037.808986673586, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 298116, 'conductor_radical': 546, 'degree': 4, 'dirichlet_coefficients': [1, -4, 6, 12, 1, -24, -14, -32, 27, -4, -16, 72, -26, 56, 6, 80, 18, -108, 63, 12, -84, 64, -95, -192, -217, 104, 108, -168, -419, -24, -73, -192, -96, -72, -14, 324, 90, -252, -156, -32, 186, 336, -67, -192, 27, 380, -421, 480, 147, 868, 108, -312, -819, -432, -16, 448, 378, 1676, -698, 72, 68, 292, -378, 448, -26, 384, 638, 216, -570, 56, -538, -864, 541, -360, -1302, 756, 224, 624, -815, 80, 405, -744, 291, -1008, 18, 268, -2514, 512, -945, -108, 364, -1140, -438, 1684, 63, -1152, -23, -588, -432, -2604], 'euler11': [1, 16, 2210, 21296, 1771561], 'euler13': [1, 26, 169, 0, 0], 'euler17': [1, -18, 3586, -88434, 24137569], 'euler19': [1, -63, 5390, -432117, 47045881], 'euler2': [1, 4, 4, 0, 0], 'euler23': [1, 95, 9530, 1155865, 148035889], 'euler29': [1, 419, 91088, 10218991, 594823321], 'euler3': [1, -6, 9, 0, 0], 'euler31': [1, 73, 60882, 2174743, 887503681], 'euler37': [1, -90, 35090, -4558770, 2565726409], 'euler41': [1, -186, 38002, -12819306, 4750104241], 'euler43': [1, 67, 136626, 5326969, 6321363049], 'euler47': [1, 421, 251924, 43709483, 10779215329], 'euler5': [1, -1, 218, -125, 15625], 'euler53': [1, 819, 394204, 121930263, 22164361129], 'euler59': [1, 698, 531398, 143354542, 42180533641], 'euler61': [1, -68, 157902, -15434708, 51520374361], 'euler67': [1, -638, 700062, -191886794, 90458382169], 'euler7': [1, 14, 49, 0, 0], 'euler71': [1, 538, 766382, 192556118, 128100283921], 'euler73': [1, -541, 191724, -210458197, 151334226289], 'euler79': [1, 815, 1080894, 401826785, 243087455521], 'euler83': [1, -291, 1157488, -166390017, 326940373369], 'euler89': [1, 945, 356062, 666195705, 496981290961], 'euler97': [1, 23, 1634268, 20991479, 832972004929], 'euler_factors': [[1, 4, 4, 0, 0], [1, -6, 9, 0, 0], [1, -1, 218, -125, 15625], [1, 14, 49, 0, 0], [1, 16, 2210, 21296, 1771561], [1, 26, 169, 0, 0], [1, -18, 3586, -88434, 24137569], [1, -63, 5390, -432117, 47045881], [1, 95, 9530, 1155865, 148035889], [1, 419, 91088, 10218991, 594823321], [1, 73, 60882, 2174743, 887503681], [1, -90, 35090, -4558770, 2565726409], [1, -186, 38002, -12819306, 4750104241], [1, 67, 136626, 5326969, 6321363049], [1, 421, 251924, 43709483, 10779215329], [1, 819, 394204, 121930263, 22164361129], [1, 698, 531398, 143354542, 42180533641], [1, -68, 157902, -15434708, 51520374361], [1, -638, 700062, -191886794, 90458382169], [1, 538, 766382, 192556118, 128100283921], [1, -541, 191724, -210458197, 151334226289], [1, 815, 1080894, 401826785, 243087455521], [1, -291, 1157488, -166390017, 326940373369], [1, 945, 356062, 666195705, 496981290961], [1, 23, 1634268, 20991479, 832972004929]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/4/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': '4-546e2-1.1-c3e2-0-6', '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': '4-546e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.675829707023846, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 2241696644686165843, 'z1': {'__RealLiteral__': 0, 'data': '1.57712576309046620530899965683', 'prec': 103}}
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{'Lhash': '1999244420217033808434845033040,2213541654490737585289375701890', 'Lhash_array': ['1999244420217033808434845033040', '2213541654490737585289375701890'], 'factors': ['2-546-1.1-c3-0-28', '2-546-1.1-c3-0-31'], 'label': '4-546e2-1.1-c3e2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/4/a/h'}