-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '335338223122751794711554442822', 'a10': [0, 0], 'a2': [0, 0], 'a3': [2.449489742783178, -4.58257569495584], 'a4': [0, 0], 'a5': [-2.3146441975848298, 0], 'a6': [0, 0], 'a7': [0, 29.663568003794833], 'a8': [0, 0], 'a9': [-15.0, -22.44994432064365], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.656733442204406, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-2.449489742783178, 4.58257569495584]]]], 'bad_primes': [2, 3], 'central_character': '384.191', 'coefficient_field': 'CDF', 'conductor': 384, 'conductor_radical': 6, 'conjugate': '2188358106618421795541950776855', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.449489742783178, 4.58257569495584]], [[1.0, 0], [2.3146441975848298, 0], [125.0, 0]], [[1.0, 0], [0, -29.663568003794833], [-343.0, 0]], [[1.0, 0], [0, 22.83484861008832], [-1331.0, 0]], [[1.0, 0], [0, -8.66060555964672], [-2197.0, 0]], [[1.0, 0], [0, -93.35030131615747], [-4913.0, 0]], [[1.0, 0], [85.44017997780163, 0], [6859.0, 0]], [[1.0, 0], [116.66060555964673, 0], [12167.0, 0]], [[1.0, 0], [103.53052699367231, 0], [24389.0, 0]], [[1.0, 0], [0, 10.607032242322804], [-29791.0, 0]], [[1.0, 0], [0, -380.62423891752707], [-50653.0, 0]], [[1.0, 0], [0, -257.9832263342109], [-68921.0, 0]], [[1.0, 0], [-359.7830311695176, 0], [79507.0, 0]], [[1.0, 0], [-293.28484447717375, 0], [103823.0, 0]], [[1.0, 0], [-679.6777287992996, 0], [148877.0, 0]], [[1.0, 0], [0, 45.8257569495584], [-205379.0, 0]], [[1.0, 0], [0, -595.2302945139943], [-226981.0, 0]], [[1.0, 0], [206.34106043300616, 0], [300763.0, 0]], [[1.0, 0], [996.515138991168, 0], [357911.0, 0]], [[1.0, 0], [593.9272667157607, 0], [389017.0, 0]], [[1.0, 0], [0, 910.9404932249456], [-493039.0, 0]], [[1.0, 0], [0, 332.88939857326784], [-571787.0, 0]], [[1.0, 0], [0, 821.6355582647385], [-704969.0, 0]], [[1.0, 0], [-420.71515552282625, 0], [912673.0, 0]], [[1.0, 0], [923.1446280503566, 0], [1030301.0, 0]], [[1.0, 0], [0, -1426.1894042788706], [-1092727.0, 0]], [[1.0, 0], [0, 1581.8257569495584], [-1225043.0, 0]], [[1.0, 0], [0, -766.0909166052992], [-1295029.0, 0]], [[1.0, 0], [0, -1047.6640682967036], [-1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-384-24.11-c3-0-5', 'leading_term': '0.885380313972398725793667341744769138781254364831281363', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/384/4/f/g/191/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.8853803139723987, 0.689794180050291, 0.48473548986690423, 0.2716049096489014, 0.05188030650706778, -0.17287778079190624, -0.4010211178451006, -0.6308099159142495, -0.860410841946454, -1.0878975608896846, -1.3112544108036464, -1.5283837271453982, -1.7371172299856412, -1.9352317695496906, -2.120469594236983, -2.290563164035627, -2.443264383888113, -2.5763779789611645, -2.6877985798544266, -2.7755509335790385, -2.837832508833494, -2.873057625080756, -2.879902107777142, -2.8573473606035265, -2.804722653630262, -2.721744357996731, -2.6085508168382385, -2.465731532585611, -2.2943493757784235, -2.0959545830218484, -1.8725894138185286, -1.6267824789690593, -1.3615319372481332, -1.0802769811111472, -0.7868572939213133, -0.4854604568448084, -0.18055760791059958, 0.12317199792334993, 0.42092651862237873, 0.7078757710589721, 0.9792624606948805, 1.23050832139802, 1.4573227802890298, 1.655811492915668, 1.8225818786567272, 1.954842636791943, 2.050494150897372, 2.1082067024562816, 2.1274835212339056, 2.1087059051289256, 2.053157948216399, 1.9630288217702219, 1.8413910550599144, 1.6921538529628921, 1.5199911545958094, 1.330244866340756, 1.1288044755158255, 0.9219650461243801, 0.7162663916020892, 0.5183169852333774, 0.33460687960562324, 0.17131453433916224, 0.03411296909404236, -0.07201895927127511, -0.14297413376854076, -0.17567754299181249, -0.168223519769433, -0.11998429031788779, -0.031684831329344264, 0.09456020484534623, 0.25525078230993, 0.4455491490031716, 0.6593717631945365, 0.8895249755665104, 1.1278825026933623, 1.3656012393172794, 1.5933704905316441, 1.8016883134954418, 1.9811573954001624, 2.1227918130473933, 2.218325169675617, 2.2605100317704245, 2.243398330691351, 2.162592480315075, 2.015457411125956, 1.8012845397500008, 1.5213998740683619, 1.179209977108684, 0.7801813431775919, 0.3317508287449219, -0.1568329327719895, -0.6747347914124527, -1.2098202201534254, -1.7489971270734115, -2.278602860461783, -2.784824883067965, -3.254141865952994, -3.6737706270934587, -4.0321034864327086, -4.31912028478834, -4.5267595589570195, -4.649234199653005, -4.683278340817683, -4.628314213450739, -4.486530196046974, -4.262864235664663, -3.9648901059298858, -3.6026074994026636, -3.1881405948511867, -2.7353533572256965, -2.259393275626337, -1.7761783780439382, -1.3018450423650842, -0.8521762238801417, -0.4420311305824628, -0.08479801212033244, 0.20810847263601812, 0.4276849081238729, 0.5676933127092936, 0.6249161172132144, 0.5992996465436958, 0.4939779053200809, 0.3151730299179837, 0.07197363583630628, -0.2240027306610728, -0.5590519385335091, -0.9179147286425638, -1.2843775110581035, -1.6419193478248257, -1.9743794490990685, -2.266618001345133, -2.5051427461071367, -2.6786744937091687, -2.7786266961525476, -2.7994772741261005, -2.7390149993384263, -2.5984477305117557, -2.3823654991864682, -2.0985576111143533, -1.7576893116403711, -1.3728498808070764, -0.9589899901246797, -0.5322714874225548, -0.10935721667563744, 0.29332820486796496, 0.6603337274078143, 0.9778798468896426, 1.2344867043949563, 1.4215022772652781, 1.5335045763532331, 1.5685570268908011, 1.528302588797908, 1.4178894019055117, 1.2457285090229002, 1.0230921649454907, 0.7635690110284671, 0.4823996072320413, 0.19572210460799952, -0.08023711929542582, -0.32998953320841784, -0.5395871480541549, -0.6973618850026664, -0.7945637417327926, -0.8258638630476944, -0.7896943706873493, -0.6884040988685383, -0.5282179076443919, -0.31899662523396055, -0.07380446763575901, 0.19169947166708146, 0.4600198612718225, 0.7126999024129691, 0.931271483776678, 1.0982350557798601, 1.1980207740825253, 1.2178820145040274, 1.1486743462112905, 0.9854774420846809, 0.7280240573033241, 0.38090885316309087, -0.046439892859106165, -0.54003123765651, -1.0818187134342208, -1.6504251578211384, -2.222055297230797, -2.7715559077424037, -3.2735748886244633, -3.7037643279664745, -4.039969000280649, -4.263340971625385, -4.35932321731714, -4.318450347858654, -4.136922503216821, -3.816918877614518, -3.366629703868544, -2.7999992697267206, -2.1361869822189425, -1.3987679082284128, -0.6147078507132014, 0.1868398582700263, 0.9758587225897917, 1.722850284350529, 2.400203835460603, 2.983485773601074, 3.452582776148497, 3.792639496278066, 3.9947412370601487, 4.056304581732662, 3.981153642168101, 3.7792756931964875, 3.466266654675338, 3.0624932821929365, 2.5920141435678308, 2.081314649170753, 1.5579218189603337, 1.0489714930400718, 0.5798038833838547, 0.17266248142599588, -0.15443364169823956, -0.3885829736087359, -0.5226113030199472, -0.5553644050156283, -0.4916672257742092, -0.3419514579792303, -0.12157184309110154, 0.15015094085152667, 0.4511073476012522, 0.757729762801503, 1.0464016457397558, 1.2948646340001804, 1.4835427692561214, 1.596707161099053, 1.6234130183595208, 1.5581536162892702, 1.4011917650208336, 1.1585478245723122, 0.8416432383282925, 0.46661879069534096, 0.05336615647380179, -0.3756713506906383, -0.7968586585849671, -1.1868089751543585, -1.523817858424176, -1.7892045869522868, -1.968478670631079, -2.052258900823848, -2.036886400275636, -1.9246909319129861, -1.7238902574858852, -1.448124413946451, -1.1156490927786362, -0.748233519785258, -0.3698270342688927, -0.005073770637283463, 0.3222345404143287, 0.5906723441260315, 0.7825657602322161], 'positive_zeros': ['0.26453521424781961298245148792833', '2.28706216497373339454775517234957', '3.89308984050703027655006004631997', '4.26751901753234692874637441823375', '5.60541030640563978862970585864743', '7.20416299965730794464161393533513', '7.70365701269539751484029201156376', '8.954065228250439074366999597428067', '9.856360266927136774095488504033176', '10.51768646166640746086758425238689'], 'prelabel': '2-384-24.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.759908974151124, 'root_angle': -0.593747190544135, 'root_number': '-0.290276231128990230930624788719424883626003301296454491 - 0.956942897795656897597291455386091550292669967963121158*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2968735952720675', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.26453521424781961298245148793', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.28706216497373339454775517235', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.89308984050703027655006004632', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 22.656733442204406, 'bad_primes': [2, 3], 'central_character': '24.11', 'conductor': 384, 'conductor_radical': 6, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/384/4/f/g/191/6'], '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': '2-384-24.11-c3-0-5', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-384-24.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.759908974151124, 'root_angle': -0.2968735952720675, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.26453521424781961298245148793', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '335338223122751794711554442822', 'Lhash_array': ['335338223122751794711554442822'], 'label': '2-384-24.11-c3-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/384/4/f/g/191/6'}