-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2444218957949286410122466817850', 'a10': 2, 'a2': 1, 'a3': 1, 'a4': 1, 'a5': 2, 'a6': 1, 'a7': 4, 'a8': 1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.85116449342586, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1]], [11, [1, -1]], [13, [1, 1]]], 'bad_primes': [2, 3, 11, 13], 'central_character': '858.1', 'coefficient_field': '1.1.1.1', 'conductor': 858, 'conductor_radical': 858, 'degree': 2, 'euler_factors': [[1, -1], [1, -1], [1, -2, 5], [1, -4, 7], [1, -1], [1, 1], [1, 8, 17], [1, 6, 19], [1, 6, 23], [1, 2, 29], [1, 2, 31], [1, -4, 37], [1, -2, 41], [1, -4, 43], [1, -4, 47], [1, 8, 53], [1, -12, 59], [1, 2, 61], [1, -12, 67], [1, 16, 71], [1, 0, 73], [1, 8, 79], [1, -4, 83], [1, -10, 89], [1, -10, 97], [1, -14, 101], [1, -4, 103], [1, 18, 107], [1, -2, 109], [1, -6, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, -1], 1]], [[[1, -2, 5], 1]], [[[1, -4, 7], 1]], [[[1, -1], 1]], [[[1, 1], 1]], [[[1, 8, 17], 1]], [[[1, 6, 19], 1]], [[[1, 6, 23], 1]], [[[1, 2, 29], 1]], [[[1, 2, 31], 1]], [[[1, -4, 37], 1]], [[[1, -2, 41], 1]], [[[1, -4, 43], 1]], [[[1, -4, 47], 1]], [[[1, 8, 53], 1]], [[[1, -12, 59], 1]], [[[1, 2, 61], 1]], [[[1, -12, 67], 1]], [[[1, 16, 71], 1]], [[[1, 0, 73], 1]], [[[1, 8, 79], 1]], [[[1, -4, 83], 1]], [[[1, -10, 89], 1]], [[[1, -10, 97], 1]], [[[1, -14, 101], 1]], [[[1, -4, 103], 1]], [[[1, 18, 107], 1]], [[[1, -2, 109], 1]], [[[1, -6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-858-1.1-c1-0-17', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/858/2/a/l', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [3.60692373036912, 3.6065749874069533, 3.602170957656084, 3.5843633366921184, 3.5397490361712127, 3.4534596943593465, 3.311848201944827, 3.104908972510379, 2.828253738491603, 2.484548639323207, 2.084322514851101, 1.6460381590736757, 1.195320936896957, 0.7632813422700951, 0.38395075685013613, 0.09096326227343807, -0.08625521091417254, -0.12640616869051804, -0.019867135296790475, 0.2286542966698595, 0.5988607458396684, 1.0553955546186977, 1.5503753090886014, 2.0278846071195393, 2.4301011035497377, 2.7044249995660494, 2.810738821679162, 2.727769390861418, 2.457506587255024, 2.0267798258388297, 1.485406938268797, 0.9007870545283078, 0.3493555692666685, -0.09412309769354295, -0.3679741963898701, -0.43399423224796185, -0.2850047161799861, 0.051954117485187315, 0.5177648568302823, 1.0288864168471894, 1.4897656959290122, 1.8083411502874447, 1.9122460358582911, 1.7629368450552954, 1.3650487236587112, 0.7688580731246232, 0.06476716491934098, -0.6299228708217421, -1.190234137996504, -1.5057288110888192, -1.5018685878656295, -1.1564582888742738, -0.5076661324727169, 0.34860342905917846, 1.2723664960275498, 2.102533230431283, 2.6855274074483666, 2.90446622325669, 2.7032805634305133, 2.1006967968179073, 1.1906096107964768, 0.1278227370469469, -0.8990050706693336, -1.7026511509455953, -2.134296138830764, -2.114799252479556, -1.653572704697264, -0.8504530581913501, 0.12080784603311726, 1.0450652075046272, 1.7084460218224176, 1.9427933505839683, 1.662658178468866, 0.8866646894628413, -0.26203808461986466, -1.5773180727985043, -2.8099874224460453, -3.718344672386715, -4.118881145774128, -3.926189771561418, -3.1730123964614685, -2.005375103922932, -0.6530949105424304, 0.6185504136291814, 1.565766808649071, 2.019298317709098, 1.9215820956471035, 1.339275544647955, 0.4478461166988438, -0.5087145507101231, -1.2741361147616108, -1.639232525427093, -1.4905512145239341, -0.8367636986886503, 0.1936310069270221, 1.382930827931924, 2.4759781398234884, 3.240609969729567, 3.5221440640319095, 3.2785944582531674, 2.5880227379437586, 1.6263780266369203, 0.6216336076689568, -0.20391901831317222, -0.6883084334563473, -0.7673579075787355, -0.4854411317802569, 0.02290274690650762, 0.5750549002793616, 0.9941905311793342, 1.159746523803944, 1.040182370383747, 0.6986600377679508, 0.26995600944935755, -0.08472604480250381, -0.2317128126517459, -0.11126859706859073, 0.23818153462332545, 0.6865732006950498, 1.049140884047253, 1.1442061133629071, 0.8553521931265946, 0.17912109097941953, -0.7575765801459627, -1.718214433986872, -2.4126676739441266, -2.574966545594969, -2.0418911238231336, -0.8097618017627242, 0.9485018477488791, 2.9137740493353057, 4.693226407048211, 5.917300215877129, 6.3355631129144605, 5.884811383035589, 4.709280633981505, 3.125395966088483, 1.5388055548041737, 0.33521863661962503, -0.2252253944489213, -0.08029698522538423, 0.6165537978516439, 1.5394022850696683, 2.283228674309831, 2.4820337795722294, 1.9185076933428233, 0.5936760035093083, -1.264286882733754, -3.2558522730286525, -4.915819314410333, -5.839579061938617, -5.794329805065444, -4.783557016065262, -3.0463120902702396, -0.9915534678466683, 0.9134227228643399, 2.268204921271751, 2.842165694923719, 2.626014160023255, 1.8185342472371917, 0.7545074688903985, -0.20273136855151222, -0.7705584783223864, -0.8249343884465125, -0.42429079386159935, 0.22564648849285507, 0.8523206729111341, 1.2141300109779232, 1.1825922344108226, 0.7817556070308037, 0.172428656227324, -0.4124226652639848, -0.7581110912227885, -0.7525373403018183, -0.43422383474020704, 0.013956195883798168, 0.32487787877942836, 0.24186778414726792, -0.38384903232894935, -1.5269027221186129, -2.9772295296281874, -4.391628263944568, -5.392996066289278, -5.686217615921224, -5.153054620091965, -3.8942421005854158, -2.2036952913090504, -0.4818984171454361, 0.8841775989568545, 1.6358004333141496, 1.7144077913166555, 1.2673553978970846, 0.5862476991605527, -0.0005486002833161503, -0.24392535177941094, -0.05831055060518076, 0.4551146741196812, 1.0542176581264475, 1.4542047585253672, 1.4428049771409435, 0.9699757569066633, 0.178003411613157, -0.6413715229819672, -1.1499205789257112, -1.0905570138025957, -0.3935697385545262, 0.7790495539778186, 2.071302575097549, 3.0444463571181766, 3.3264514072487525, 2.7486885960249867, 1.4206296139934582, -0.28740722549789405, -1.8527210395092402, -2.7672906589781876, -2.708927917840392, -1.6581440615779257, 0.08145240110006234, 1.9700410181174326, 3.4003856504226118, 3.8945210889635096, 3.263306168542972, 1.6747228350429337, -0.3936144262530911, -2.303776845934048, -3.460347132087853, -3.500062598742522, -2.4056948517241645, -0.50695794235295, 1.6307270294847294, 3.3911396652596264, 4.303094272263536, 4.181884694689097, 3.1709040273805726, 1.6731997990401044, 0.20075346061231364, -0.8032617901194011, -1.1066104685770504, -0.7468338731511212, 0.009375289003379828, 0.7860742045156625, 1.249131913947147, 1.230874348508118, 0.7828358346791262, 0.13987707929653684, -0.3867665099406206, -0.5431049017867347, -0.2389973562310322, 0.41433539154212473, 1.1501302973006595, 1.6562914627155598, 1.705453847848275, 1.2523572648541792, 0.45875332182397677, -0.3653020524519035, -0.881592728579396, -0.8582524987295768], 'positive_zeros': ['1.92814877972623226631135598751820', '2.26326736979752848209934129716397', '4.09464619000295058481802737652575', '4.60896546773282466465581973181442', '5.76124847444114544900893975199342', '6.57651112815013131067556299489549', '7.63986618398519576100110925604881', '8.484705470801542137562478640846655', '9.223837190946646176988675459038457', '10.31160160089939555137362853113777'], 'prelabel': '2-858-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.6174729212402292, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 441598452406580695, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.92814877972623226631135598752', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.26326736979752848209934129716', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.09464619000295058481802737653', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.85116449342586, 'bad_primes': [2, 3, 11, 13], 'central_character': '1.1', 'conductor': 858, 'conductor_radical': 858, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, 1, 2, 1, 4, 1, 1, 2, 1, 1, -1, 4, 2, 1, -8, 1, -6, 2, 4, 1, -6, 1, -1, -1, 1, 4, -2, 2, -2, 1, 1, -8, 8, 1, 4, -6, -1, 2, 2, 4, 4, 1, 2, -6, 4, 1, 9, -1, -8, -1, -8, 1, 2, 4, -6, -2, 12, 2, -2, -2, 4, 1, -2, 1, 12, -8, -6, 8, -16, 1, 0, 4, -1, -6, 4, -1, -8, 2, 1, 2, 4, 4, -16, 4, -2, 1, 10, 2, -4, -6, -2, 4, -12, 1, 10, 9, 1, -1], 'euler11': [1, -1, 0], 'euler13': [1, 1, 0], 'euler17': [1, 8, 17], 'euler19': [1, 6, 19], 'euler2': [1, -1, 0], 'euler23': [1, 6, 23], 'euler29': [1, 2, 29], 'euler3': [1, -1, 0], 'euler31': [1, 2, 31], 'euler37': [1, -4, 37], 'euler41': [1, -2, 41], 'euler43': [1, -4, 43], 'euler47': [1, -4, 47], 'euler5': [1, -2, 5], 'euler53': [1, 8, 53], 'euler59': [1, -12, 59], 'euler61': [1, 2, 61], 'euler67': [1, -12, 67], 'euler7': [1, -4, 7], 'euler71': [1, 16, 71], 'euler73': [1, 0, 73], 'euler79': [1, 8, 79], 'euler83': [1, -4, 83], 'euler89': [1, -10, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, -1, 0], [1, -1, 0], [1, -2, 5], [1, -4, 7], [1, -1, 0], [1, 1, 0], [1, 8, 17], [1, 6, 19], [1, 6, 23], [1, 2, 29], [1, 2, 31], [1, -4, 37], [1, -2, 41], [1, -4, 43], [1, -4, 47], [1, 8, 53], [1, -12, 59], [1, 2, 61], [1, -12, 67], [1, 16, 71], [1, 0, 73], [1, 8, 79], [1, -4, 83], [1, -10, 89], [1, -10, 97]], 'index': 17, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/858/l', 'ModularForm/GL2/Q/holomorphic/858/2/a/l/1/1', 'ModularForm/GL2/Q/holomorphic/858/2/a/l'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-858-1.1-c1-0-17', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-858-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.6174729212402292, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 441598452406580695, 'z1': {'__RealLiteral__': 0, 'data': '1.92814877972623226631135598752', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 16161340
{'Lhash': '2444218957949286410122466817850', 'Lhash_array': ['2444218957949286410122466817850'], 'factors': ['2-858-1.1-c1-0-17'], 'label': '2-858-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/858/2/a/l'}
-
id: 24550802
{'Lhash': '2444218957949286410122466817850', 'Lhash_array': ['2444218957949286410122466817850'], 'factors': ['2-858-1.1-c1-0-17'], 'label': '2-858-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/858/2/a/l/1/1'}
-
id: 27964
{'Lhash': '441598452406580695', 'Lhash_array': ['441598452406580695'], 'factors': ['2-858-1.1-c1-0-17'], 'label': '2-858-1.1-c1-0-17', 'type': 'ECQ', 'url': 'EllipticCurve/Q/858/l'}