-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1963573387512672222901103153522', 'a10': [3.1173428509845835, 0.5312001029887964], 'a2': [0.8359486113924353, -1.1406971197960742], 'a3': [1.1023798382221184, 1.3359486113924353], 'a4': [-0.6023798382221184, -1.9071283466257571], 'a5': [1.0, 2.0], 'a6': [2.445445628199713, -0.14069711979607416], 'a7': [1.0, 0.0], 'a8': [-2.67901440137003, -0.9071283466257573], 'a9': [-0.5695173845627522, 2.945445628199713], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.3537168848937777, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8359486113924353, 1.1406971197960742]]], [3, [[1.0, 0], [-1.1023798382221184, -1.3359486113924353]]], [5, [[1.0, 0], [-1.0, -2.0]]], [7, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '420.239', 'coefficient_field': 'CDF', 'conductor': 420, 'conductor_radical': 210, 'conjugate': '2553224547206076867661056728372', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8359486113924353, 1.1406971197960742]], [[1.0, 0], [-1.1023798382221184, -1.3359486113924353]], [[1.0, 0], [-1.0, -2.0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.2047596764442368, 0], [11.0, 0]], [[1.0, 0], [0, -1.890891256399426], [-13.0, 0]], [[1.0, 0], [-1.1390347691255045, 0], [17.0, 0]], [[1.0, 0], [0, 8.562788479184297], [-19.0, 0]], [[1.0, 0], [0, -3.2189940336145555], [-23.0, 0]], [[1.0, 0], [0, 1.890891256399426], [-29.0, 0]], [[1.0, 0], [0, 5.906582924754038], [-31.0, 0]], [[1.0, 0], [0, 0.4095193528884735], [-37.0, 0]], [[1.0, 0], [0, 4.4095193528884735], [-41.0, 0]], [[1.0, 0], [0.9342750926812677, 0], [43.0, 0]], [[1.0, 0], [0, 2.6718972227848705], [-47.0, 0]], [[1.0, 0], [6.819038705776947, 0], [53.0, 0]], [[1.0, 0], [13.535096311257067, 0], [59.0, 0]], [[1.0, 0], [-12.469371403938334, 0], [61.0, 0]], [[1.0, 0], [10.847507420117584, 0], [67.0, 0]], [[1.0, 0], [8.0, 0], [71.0, 0]], [[1.0, 0], [0, 8.0], [-73.0, 0]], [[1.0, 0], [0, -3.7660908444442405], [-79.0, 0]], [[1.0, 0], [0, -6.8408580174353055], [-83.0, 0]], [[1.0, 0], [0, 16.191301865687326], [-89.0, 0]], [[1.0, 0], [0, -18.491712474975227], [-97.0, 0]], [[1.0, 0], [0, -14.878890756826808], [-101.0, 0]], [[1.0, 0], [-14.920817281924357, 0], [103.0, 0]], [[1.0, 0], [0, -0.371486613496971], [-107.0, 0]], [[1.0, 0], [-2.8609652308744957, 0], [109.0, 0]], [[1.0, 0], [-14.191301865687326, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 40, 'label': '2-420-60.59-c1-0-40', '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/420/2/l/f/239/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.3790605744889475, 2.3552816688011795, 2.334165308367609, 2.308028577373069, 2.266254914084502, 2.1966762473996573, 2.087002367720214, 1.9261558397869345, 1.7054783307154102, 1.4198124394609988, 1.0684469058512336, 0.655876174944043, 0.19229241982635392, -0.3062888391230873, -0.8183655356614186, -1.3178214280781764, -1.775365903520678, -2.1605164984618157, -2.444032369132917, -2.6006361390791826, -2.6117953993423555, -2.4682831830198046, -2.1722086805917087, -1.738213879750785, -1.193574701532476, -0.5770285673319414, 0.06372897150364627, 0.6757868020930852, 1.2057453758367858, 1.605016399656227, 1.8351534834718384, 1.872592573454339, 1.7121706868333109, 1.3688630283759544, 0.877334998884528, 0.2891380763187146, -0.33233431332943203, -0.9187058404554832, -1.4045764985138902, -1.7356415583578466, -1.8759096090795044, -1.812976098792252, -1.5604783678674696, -1.1571742197996306, -0.6625189953710146, -0.14911403481423524, 0.30710663988101783, 0.6376719003525673, 0.7918145049978478, 0.7445770243700682, 0.5014029240418086, 0.0982723783923534, -0.4029255372449705, -0.9233513273823992, -1.3793323624120863, -1.6958546328932875, -1.8192752212831385, -1.7270633063103547, -1.432710421003574, -0.9846349101617373, -0.4588570684039087, 0.05370022678147631, 0.46340380369822387, 0.6989269959592191, 0.7220410089700275, 0.5372642435083076, 0.19412863364848634, -0.2190287514274167, -0.589380821183922, -0.8001310162504226, -0.7540063513538573, -0.3956256055124275, 0.27154626803607584, 1.1773647001846903, 2.1886793180103425, 3.125017116962926, 3.7846278953653343, 3.9772064155800275, 3.5580672023391506, 2.457838616547887, 0.7020640847372902, -1.5835267445708048, -4.184060348235028, -6.822081389866364, -9.19602223338833, -11.024633241850266, -12.090046412759971, -12.272035785260936, -11.5672940959659, -10.090001603509762, -8.053212458044603, -5.734041991835798, -3.428649120729422, -1.4049719357655226, 0.13832831901497278, 1.0993747425433937, 1.4822482915663557, 1.3865657312439823, 0.9800085543404152, 0.4596752883254445, 0.010282392424336765, -0.23224770119010418, -0.20453261894099276, 0.07767608120208827, 0.5307884321442466, 1.0293916932737748, 1.440606605448221, 1.658612262165937, 1.6312157836193621, 1.3722505405261194, 0.9569492566661645, 0.5015058493940768, 0.13187692371762638, -0.05042983883901293, 0.003051456337749181, 0.27221148225775843, 0.6702874569538013, 1.063412765638047, 1.303552202389205, 1.2670471355356632, 0.8892467355951327, 0.18624523657111947, -0.7424520876454609, -1.7320409322178156, -2.5879070713885506, -3.130585654352535, -3.2395294110547783, -2.88479358308613, -2.1382198016781953, -1.1603966788675433, -0.16552738270240205, 0.6280643080687497, 1.0501251427761227, 1.0205021258535705, 0.5701317761825753, -0.16507979335682335, -0.9769892490272766, -1.6373181030722457, -1.9566551156550838, -1.8355825851889178, -1.2944906458430996, -0.4734676977444037, 0.399098013685465, 1.0626324236490974, 1.2919957221744043, 0.9598217273096407, 0.0773302550668915, -1.1979220409992661, -2.5910172452148683, -3.7698859399783013, -4.42309962387196, -4.336562389471637, -3.4499309996355145, -1.8779563350902986, 0.10977556970874273, 2.1469948935238063, 3.853462346670374, 4.922391830088811, 5.191070974478588, 4.676952560777256, 3.5698887478782395, 2.182145559600524, 0.8685911610405703, -0.06279803154421383, -0.4273046211596745, -0.2071178562868433, 0.4489710077774644, 1.2696637125409393, 1.9374068986395614, 2.1766527118015437, 1.83072197583596, 0.906795347585135, -0.42303437263952387, -1.8650293961260505, -3.07992246444472, -3.7715890758848123, -3.7646045514966624, -3.0500242602214174, -1.7873354989807342, -0.262404525749532, 1.1868694590712148, 2.256853842562671, 2.753111307588554, 2.6341064393291194, 2.0127748269859653, 1.116901117052492, 0.22067271961964674, -0.4324861420231992, -0.6938208010835887, -0.5423875570375923, -0.07938511958634144, 0.5127428029758627, 1.0325184220847516, 1.323069931135221, 1.317480863592314, 1.05234649843042, 0.6463807184217863, 0.25218349926369915, -0.0020580223635021126, -0.06086498278851993, 0.037115938126325666, 0.1726588693887903, 0.1908664210566486, -0.037051132663367306, -0.5561330215598472, -1.2950110402645683, -2.071988626161277, -2.6415134215422698, -2.7692580782311125, -2.3134971598707845, -1.2864278140039607, 0.12675797150553245, 1.6016622800456162, 2.756110016887427, 3.2585952531619156, 2.932987911899275, 1.8273590719473556, 0.22313504115105645, -1.4230704809613268, -2.5931075381878115, -2.8474389575299197, -1.9532709074274532, 0.03653481614646394, 2.778681814500813, 5.713613359291938, 8.201168229262468, 9.68222999382003, 9.822555757311212, 8.599036790683803, 6.304203325961123, 3.4675167582354645, 0.7153658634615112, -1.3911228156332922, -2.4954106725073117, -2.524050376934614, -1.6844375872770116, -0.38548292415312585, 0.89298736891347, 1.7422002075126801, 1.935937258393161, 1.4803507002559506, 0.5906035414734857, -0.39451719040290184, -1.1303446266426793, -1.3780115189918676, -1.0751759532288874, -0.3453317659252432, 0.5542628314812595, 1.3261376439713086, 1.7349030938699874, 1.6837675006776287, 1.2404335442626697, 0.6052604401103765, 0.0343565569180557, -0.25455975022642946, -0.1602001410957539, 0.2676946215753514], 'positive_zeros': ['1.54898627994113520815872536121051', '3.23749000233078838930528540860442', '4.43315845006297842323589090966862', '5.66325777951156073206922414393348', '6.40091357015312444951906726911502', '7.61103738340364389575417072896709', '8.309390418075724492866591321168622', '8.955216836775243830040107474914313', '10.04110852281352022947695730872556', '11.73661535659481206275624809490465'], 'prelabel': '2-420-60.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8313156158602968, 'root_angle': 0.035430891166592995, 'root_number': '0.9938114991643336 + 0.11107971970049062*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0177154455833', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.54898627994113520815872536121', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.23749000233078838930528540860', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.43315845006297842323589090967', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.3537168848937777, 'bad_primes': [2, 3, 5, 7], 'central_character': '60.59', 'conductor': 420, 'conductor_radical': 210, 'degree': 2, 'index': 40, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/420/2/l/f/239/5'], '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': '2-420-60.59-c1-0-40', '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': '2-420-60.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8313156158602968, 'root_angle': 0.017715445583296498, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.54898627994113520815872536121', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1963573387512672222901103153522', 'Lhash_array': ['1963573387512672222901103153522'], 'label': '2-420-60.59-c1-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/420/2/l/f/239/5'}