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{'Lhash': '1677123298705259505523141574466,1833888024658330083340393259252,2182648746821121464038524562637,2625555589770330919191614929553,2880496572783526172952878357485,3563991465670730007714906964767', 'a10': 18, 'a2': -6, 'a3': 0, 'a4': 18, 'a5': -3, 'a6': 0, 'a7': -9, 'a8': -36, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 38907.0060040338, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]]], 'bad_primes': [3], 'central_character': '729.1', 'coefficient_field': '1.1.1.1', 'conductor': 150094635296999121, 'conductor_radical': 3, 'degree': 12, 'euler_factors': [[1, 6, 18, 36, 54, 69, 91, 138, 216, 288, 288, 192, 64], [1], [1, 3, 18, 54, 189, 453, 1189, 2265, 4725, 6750, 11250, 9375, 15625], [1, 9, 45, 173, 594, 1782, 4881, 12474, 29106, 59339, 108045, 151263, 117649], [1, 15, 99, 333, 162, -4098, -21023, -45078, 19602, 443223, 1449459, 2415765, 1771561], [1, 9, 45, 191, 810, 2916, 10065, 37908, 136890, 419627, 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{'__RealLiteral__': 0, 'data': '1.44668256720594348858531417484', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.72180626619681689135093834528', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 38907.0060040338, 'bad_primes': [3], 'central_character': '1.1', 'conductor': 150094635296999121, 'conductor_radical': 3, 'degree': 12, 'dirichlet_coefficients': [1, -6, 0, 18, -3, 0, -9, -36, 0, 18, -15, 0, -9, 54, 0, 54, 9, 0, 3, -54, 0, 90, -12, 0, -9, 54, 0, -162, 3, 0, -9, -69, 0, -54, 27, 0, 3, -18, 0, 108, -21, 0, -9, -270, 0, 72, -15, 0, 36, 54, 0, -162, -36, 0, 45, 324, 0, -18, -3, 0, -27, 54, 0, 89, 27, 0, 27, 162, 0, -162, -9, 0, -6, -18, 0, 54, 135, 0, 18, -162, 0, 126, -15, 0, -27, 54, 0, 540, 0, 0, 81, -216, 0, 90, -9, 0, -36, -216, 0, -162], 'euler11': [1, 15, 99, 333, 162, -4098, -21023, -45078, 19602, 443223, 1449459, 2415765, 1771561], 'euler13': [1, 9, 45, 191, 810, 2916, 10065, 37908, 136890, 419627, 1285245, 3341637, 4826809], 'euler17': [1, -9, 3, -36, 1761, -4707, -6122, -80019, 508929, -176868, 250563, -12778713, 24137569], 'euler19': [1, -3, -24, 131, 117, -1116, 3003, -21204, 42237, 898529, -3127704, -7428297, 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'euler53': [1, 36, 804, 12618, 154644, 1513764, 12179707, 80229492, 434394996, 1878529986, 6343946724, 15055037748, 22164361129], 'euler59': [1, 3, -36, -972, -3402, 23781, 658585, 1403079, -11842362, -199628388, -436224996, 2144772897, 42180533641], 'euler61': [1, 27, 270, 794, -6183, -65691, -407355, -4007151, -23006943, 180222914, 3738377070, 22804100127, 51520374361], 'euler67': [1, -27, 324, -2320, 4941, 121797, -1636989, 8160399, 22180149, -697770160, 6528963204, -36453377889, 90458382169], 'euler7': [1, 9, 45, 173, 594, 1782, 4881, 12474, 29106, 59339, 108045, 151263, 117649], 'euler71': [1, 9, 30, -99, -3531, -5580, 200671, -396180, -17799771, -35433189, 762350430, 16238064159, 128100283921], 'euler73': [1, 6, -114, -58, 8676, -27576, -826869, -2013048, 46234404, -22562986, -3237399474, 12438429558, 151334226289], 'euler79': [1, -18, 153, -853, -5697, 179145, -1911282, 14152455, -35554977, -420562267, 5959362393, -55387015182, 243087455521], 'euler83': [1, 15, 72, -360, -3159, 68631, 989803, 5696373, -21762351, -205843320, 3416999112, 59085609645, 326940373369], 'euler89': [1, 0, -78, -1998, -858, 77922, 1866463, 6935058, -6796218, -1408528062, -4893894798, 0, 496981290961], 'euler97': [1, 36, 396, -610, -33480, 134136, 5366595, 13011192, -315013320, -556730530, 35057595276, 309144249252, 832972004929], 'euler_factors': [[1, 6, 18, 36, 54, 69, 91, 138, 216, 288, 288, 192, 64], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 3, 18, 54, 189, 453, 1189, 2265, 4725, 6750, 11250, 9375, 15625], [1, 9, 45, 173, 594, 1782, 4881, 12474, 29106, 59339, 108045, 151263, 117649], [1, 15, 99, 333, 162, -4098, -21023, -45078, 19602, 443223, 1449459, 2415765, 1771561], [1, 9, 45, 191, 810, 2916, 10065, 37908, 136890, 419627, 1285245, 3341637, 4826809], [1, -9, 3, -36, 1761, -4707, -6122, -80019, 508929, -176868, 250563, -12778713, 24137569], [1, -3, -24, 131, 117, -1116, 3003, -21204, 42237, 898529, -3127704, -7428297, 47045881], [1, 12, 99, 675, 4455, 24051, 121258, 553173, 2356695, 8212725, 27704259, 77236116, 148035889], [1, -3, -36, 270, -945, -5637, 70993, -163473, -794745, 6585030, -25462116, -61533447, 594823321], [1, 9, 72, 650, 4293, 24921, 159267, 772551, 4125573, 19364150, 66493512, 257662359, 887503681], [1, -3, -78, 185, 3681, -4194, -141339, -155178, 5039289, 9370805, -146184558, -208031871, 2565726409], [1, 21, 207, 1089, 378, -52980, -510623, -2172180, 635418, 75054969, 584932527, 2432980221, 4750104241], [1, 9, 72, 794, 5697, 34965, 270831, 1503495, 10533753, 63128558, 246153672, 1323075987, 6321363049], [1, 15, 180, 1476, 10665, 64275, 398503, 3020925, 23558985, 153242748, 878342580, 3440175105, 10779215329], [1, 36, 804, 12618, 154644, 1513764, 12179707, 80229492, 434394996, 1878529986, 6343946724, 15055037748, 22164361129], [1, 3, -36, -972, -3402, 23781, 658585, 1403079, -11842362, -199628388, -436224996, 2144772897, 42180533641], [1, 27, 270, 794, -6183, -65691, -407355, -4007151, -23006943, 180222914, 3738377070, 22804100127, 51520374361], [1, -27, 324, -2320, 4941, 121797, -1636989, 8160399, 22180149, -697770160, 6528963204, -36453377889, 90458382169], [1, 9, 30, -99, -3531, -5580, 200671, -396180, -17799771, -35433189, 762350430, 16238064159, 128100283921], [1, 6, -114, -58, 8676, -27576, -826869, -2013048, 46234404, -22562986, -3237399474, 12438429558, 151334226289], [1, -18, 153, -853, -5697, 179145, -1911282, 14152455, -35554977, -420562267, 5959362393, -55387015182, 243087455521], [1, 15, 72, -360, -3159, 68631, 989803, 5696373, -21762351, -205843320, 3416999112, 59085609645, 326940373369], [1, 0, -78, -1998, -858, 77922, 1866463, 6935058, -6796218, -1408528062, -4893894798, 0, 496981290961], [1, 36, 396, -610, -33480, 134136, 5366595, 13011192, -315013320, -556730530, 35057595276, 309144249252, 832972004929]], 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/e/a'], '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': '12-3e36-1.1-c1e6-0-11', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 6, 'prelabel': '12-3e36-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.4126944081982993, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e6-0', 'trace_hash': 2100431176345818781, 'z1': {'__RealLiteral__': 0, 'data': '1.32301700358388038993176109676', 'prec': 103}}
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{'Lhash': '1677123298705259505523141574466,1833888024658330083340393259252,2182648746821121464038524562637,2625555589770330919191614929553,2880496572783526172952878357485,3563991465670730007714906964767', 'Lhash_array': ['1677123298705259505523141574466', '1833888024658330083340393259252', '2182648746821121464038524562637', '2625555589770330919191614929553', '2880496572783526172952878357485', '3563991465670730007714906964767'], 'label': '12-3e36-1.1-c1e6-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/e/a'}