-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1894776492537014258897502524079', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.9510565162951535, -0.30901699437494745], 'a4': [0.0, 0.0], 'a5': [1.333572487239016, 1.7948772719267312], 'a6': [0.0, 0.0], 'a7': [0.0, -2.61634388014236], 'a8': [0.0, 0.0], 'a9': [0.8090169943749475, -0.5877852522924731], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.791024121276825, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.9510565162951535, 0.30901699437494745]]], [5, [[1.0, 0], [-1.333572487239016, -1.7948772719267312]]]], 'bad_primes': [2, 3, 5], 'central_character': '600.409', 'coefficient_field': 'CDF', 'conductor': 600, 'conductor_radical': 30, 'conjugate': '1780670515177056993097446012859', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.9510565162951535, 0.30901699437494745]], [[1.0, 0], [-1.333572487239016, -1.7948772719267312]], [[1.0, 0], [0, 2.61634388014236], [-7.0, 0]], [[1.0, 0], [-0.7246288963348744, -0.5264737102088742], [3.3991869381244215, 10.46162167924669]], [[1.0, 0], [0.04636239487067185, 0.0638123620897382], [-4.017220926874317, 12.363734711836996]], [[1.0, 0], [-5.6915222508930645, -1.8492876808630019], [13.753288904374106, 9.992349288972044]], [[1.0, 0], [-1.2005570557574263, 3.6949346859442236], [-15.371322893124, -11.16791979355699]], [[1.0, 0], [-1.495053863089414, 2.0577651072868544], [-7.1073908706237905, -21.874299874788534]], [[1.0, 0], [0.5791111957832054, 1.7823209934558464], [-23.461492836873475, 17.04577231648172]], [[1.0, 0], [1.9171900785249638, -5.900504342312012], [-25.079526825623372, -18.221342821066667]], [[1.0, 0], [-0.20191292208035297, -0.27790929546090265], [-11.433628791873055, 35.189091102920685]], [[1.0, 0], [7.835144425920481, -5.6925656384953776], [12.669696769372845, -38.9933171681013]], [[1.0, 0], [0, -2.7986102138195523], [-43.0, 0]], [[1.0, 0], [-4.210123338653459, 1.3679519962983513], [38.02379873562253, -27.625906857746237]], [[1.0, 0], [-1.478382084744361, 0.4803554578913085], [42.877900701872214, -31.152618371501077]], [[1.0, 0], [-8.572711265530668, 6.228439314718688], [18.232002668121897, -56.11233446141406]], [[1.0, 0], [8.78255507705259, 6.380899768028106], [18.850036656871794, 58.014447494004365]], [[1.0, 0], [3.7540208476071966, 1.2197553134565278], [54.20413862312148, 39.3816119035957]], [[1.0, 0], [3.2260165213801506, 9.928657938507069], [-57.440206600621266, 41.73275291276559]], [[1.0, 0], [5.9296121464677976, -8.161410953804545], [-22.558240589371163, -69.42712568954622]], [[1.0, 0], [1.1599497135257923, 3.569958137269482], [-63.912342555620846, 46.43503493110538]], [[1.0, 0], [6.634775864595508, 2.1557693584977913], [67.14841053312064, 48.78617594027527]], [[1.0, 0], [-3.322226755737586, -2.413739025720634], [27.502512499370322, 84.64402995026867]], [[1.0, 0], [-2.139637767242457, 0.6952104533808732], [78.4746484543699, -57.01516947236989]], [[1.0, 0], [11.471409193024748, 0], [101.0, 0]], [[1.0, 0], [14.469878137468616, -4.701548408953475], [83.32875042061958, -60.54188098612473]], [[1.0, 0], [0, 5.930264079977151], [-107.0, 0]], [[1.0, 0], [14.755579655869223, -10.720556145359698], [33.68285238686927, -103.66516027617173]], [[1.0, 0], [-10.28012422175749, -14.149377119024802], [-34.91892036436906, 107.46938634135235]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-600-25.9-c1-0-8', '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/600/2/bc/c/409/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.0276941880856385, 2.036915577602939, 2.0366435133474523, 2.0208585080663894, 1.9805852791437841, 1.9054941211454988, 1.7856319616579999, 1.61306765351661, 1.3833452371023527, 1.096685183342471, 0.7588671930479813, 0.38170348606218096, -0.017003641349437874, -0.41411774047044164, -0.7824991254523874, -1.0930101518463908, -1.317112057317588, -1.429877497699103, -1.4131509387646846, -1.2585122411000305, -0.9696518760872802, -0.5637628088101699, -0.07160426320735061, 0.4639993977303614, 0.9912991451753592, 1.454271561612519, 1.7984252033556207, 1.9771941080525817, 1.9581768190380717, 1.7283827761074935, 1.2976558462489072, 0.699574440655775, -0.010619529937721075, -0.7611524614445914, -1.471575361536242, -2.062569713343817, -2.466542650440451, -2.6375877195766213, -2.559305565632112, -2.2491179376419588, -1.7580777615070617, -1.1657503230596775, -0.570450829607038, -0.07587439811565173, 0.22417195934340078, 0.26075038610474416, 0.002127359840259341, -0.5387031516205659, -1.3029048219830461, -2.1917952228343034, -3.079555573214424, -3.831115481400323, -4.322685983728766, -4.461766448196883, -4.203291249624502, -3.558986193033966, -2.5979539054106553, -1.4378818979022698, -0.22785664664737146, 0.8746985770769309, 1.7292512456674454, 2.2352383161382896, 2.348828428575704, 2.0901273280293955, 1.5391791956160985, 0.8211207516824744, 0.0829048718295912, -0.5342697762733392, -0.9216676304831379, -1.0236401475222705, -0.8479030753698805, -0.4630744623544458, 0.016459676318261233, 0.4556966683118471, 0.7293356093376522, 0.751092530289804, 0.4957283808554461, 0.008703144970023042, -0.5992881149925477, -1.1725745410293833, -1.5420555130753983, -1.5618941947012093, -1.1437455920162394, -0.28098230747964736, 0.9429097569040282, 2.364519580343031, 3.7681834761234203, 4.92620478150813, 5.643706030249857, 5.798787647939069, 5.369224776075226, 4.439447079423221, 3.1855627018929797, 1.8408892548233136, 0.6488224711554199, -0.1870934094475937, -0.5450807258482507, -0.40966464757791976, 0.12691103738329002, 0.8870704056565359, 1.6493861087814778, 2.1999635941522, 2.382044745633808, 2.132305007768229, 1.4951906660186687, 0.6116483314887549, -0.3153814289350946, -1.0707104571253783, -1.4800394084378217, -1.4535497080211004, -1.0090640718119446, -0.26867416175407255, 0.570830191153139, 1.286851955852272, 1.6872997243186572, 1.6602423505681916, 1.2041333977587552, 0.43042404538527895, -0.4627948449684223, -1.240091520262572, -1.6888233442838378, -1.674833390327969, -1.179142131597818, -0.30556543680477094, 0.7435307135605632, 1.7178735366926872, 2.3837586100128174, 2.5857553100365607, 2.2892500521369286, 1.5919905757196344, 0.7006485124157453, -0.12239885222453165, -0.6287550066162727, -0.6520155268861573, -0.155825776574551, 0.7515276403386317, 1.8409460150230512, 2.8195478713809092, 3.4065821983538527, 3.4083934275003798, 2.7722872642666587, 1.6042811559274763, 0.14508509348253235, -1.2901790143992757, -2.3930499102618095, -2.9421302591725347, -2.861096440148589, -2.2382837345914024, -1.302045402361845, -0.3581269898922904, 0.29415245724692685, 0.4440401986516981, 0.027127836864013977, -0.857377932702472, -1.9748675495780195, -3.0212687169803156, -3.7082557498123814, -3.843682958441005, -3.384416739029084, -2.446530800177256, -1.2700445861289145, -0.14854934346399298, 0.6556491878936573, 0.9859037443883834, 0.8331339018157676, 0.3328456189668952, -0.2817649924090549, -0.756349843810005, -0.8981145034692842, -0.6389862626006503, -0.0591189329299068, 0.6375059716408069, 1.1888931710531703, 1.362632209285434, 1.0381757219961334, 0.25736076368280963, -0.7743903798010439, -1.7391264385811243, -2.296533031875293, -2.1874086519932403, -1.3194327027415171, 0.19172024626947684, 2.0404310140295663, 3.8055842304057617, 5.0616392716888505, 5.494994398944654, 4.991881083933975, 3.671687422687131, 1.8552771850296008, -0.02304788130724567, -1.5345411387478887, -2.371274224445789, -2.424109182463105, -1.8011266257695493, -0.7823689635826028, 0.27386727952605866, 1.0433233598769, 1.331488441261818, 1.1233016606006352, 0.5724323933188313, -0.06472097665185333, -0.5273111647135497, -0.6471890518189232, -0.4119771408168818, 0.027571768269930883, 0.4090210123508944, 0.4517905728001701, -0.03845900330199035, -1.0902264577980905, -2.539546348829208, -4.0675085978456265, -5.291908560172343, -5.884622778601987, -5.676877251830201, -4.717462179170467, -3.2634944234418084, -1.7049930089606753, -0.4462960310665283, 0.21800967146029743, 0.19247343251223772, -0.39395533230160834, -1.2355336724913504, -1.9549978782261872, -2.2319966735806887, -1.9120641128995028, -1.0595095749955996, 0.06403365180834762, 1.0888681517595284, 1.6647724329421254, 1.583880995591799, 0.8568443103927808, -0.2846465255434501, -1.4613337852015023, -2.272414298405742, -2.432313977853456, -1.8719216843728297, -0.769118902477655, 0.5032918605619279, 1.4964450027617027, 1.8324255171838026, 1.3307215363256724, 0.07165971748146967, -1.6249322764367482, -3.2993221393559313, -4.496924866791774, -4.910684094763985, -4.47361783838718, -3.371375633316004, -1.9719452881393502, -0.6978460023099021, 0.11450148689388431, 0.3197619962797166, -0.0023027189541770707, -0.593687876323901, -1.1269643654716273, -1.3352311052263268, -1.11513903535372], 'positive_zeros': ['1.49471509909424278773909630085823', '2.76705646354898624632714771356978', '3.99821353289162458031588342423982', '5.39920809821517255130696453724081', '5.75065410356757723439608951324827', '7.27433574534945734624816844532511', '8.264983931881148523698633788435650', '8.995738415374952258607480903997253', '9.626903409149234008348091219266034', '10.40665023068279164204613124161577'], 'prelabel': '2-600-25.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.188840816797061, 'root_angle': 0.03320099670167404, 'root_number': '0.9945652668949221 + 0.104114983965961*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0166004983508', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.49471509909424278773909630086', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.76705646354898624632714771357', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.99821353289162458031588342424', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.791024121276825, 'bad_primes': [2, 3, 5], 'central_character': '25.9', 'conductor': 600, 'conductor_radical': 30, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/600/2/bc/c/409/6'], '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': '2-600-25.9-c1-0-8', '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': '2-600-25.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.188840816797061, 'root_angle': 0.01660049835083702, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.49471509909424278773909630086', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1894776492537014258897502524079', 'Lhash_array': ['1894776492537014258897502524079'], 'label': '2-600-25.9-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/600/2/bc/c/409/6'}