-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1622323271424834156843272952527', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -20.0], 'a4': [0, 0], 'a5': [0, 74.0], 'a6': [0, 0], 'a7': [-24.0, 0], 'a8': [0, 0], 'a9': [-157.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.05825787212305, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]]], 'bad_primes': [2], 'central_character': '256.129', 'coefficient_field': 'CDF', 'conductor': 256, 'conductor_radical': 2, 'conjugate': '401496112458575463501763856404', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 20.0], [-243.0, 0]], [[1.0, 0], [0, -74.0], [-3125.0, 0]], [[1.0, 0], [24.0, 0], [16807.0, 0]], [[1.0, 0], [0, -124.0], [-161051.0, 0]], [[1.0, 0], [0, -478.0], [-371293.0, 0]], [[1.0, 0], [1198.0, 0], [1419857.0, 0]], [[1.0, 0], [0, 3044.0], [-2476099.0, 0]], [[1.0, 0], [-184.0, 0], [6436343.0, 0]], [[1.0, 0], [0, 3282.0], [-20511149.0, 0]], [[1.0, 0], [-5728.0, 0], [28629151.0, 0]], [[1.0, 0], [0, 10326.0], [-69343957.0, 0]], [[1.0, 0], [-8886.0, 0], [115856201.0, 0]], [[1.0, 0], [0, 9188.0], [-147008443.0, 0]], [[1.0, 0], [23664.0, 0], [229345007.0, 0]], [[1.0, 0], [0, 11686.0], [-418195493.0, 0]], [[1.0, 0], [0, -16876.0], [-714924299.0, 0]], [[1.0, 0], [0, 18482.0], [-844596301.0, 0]], [[1.0, 0], [0, -15532.0], [-1350125107.0, 0]], [[1.0, 0], [31960.0, 0], [1804229351.0, 0]], [[1.0, 0], [-4886.0, 0], [2073071593.0, 0]], [[1.0, 0], [44560.0, 0], [3077056399.0, 0]], [[1.0, 0], [0, 67364.0], [-3939040643.0, 0]], [[1.0, 0], [71994.0, 0], [5584059449.0, 0]], [[1.0, 0], [-48866.0, 0], [8587340257.0, 0]], [[1.0, 0], [0, 51606.0], [-10510100501.0, 0]], [[1.0, 0], [-180424.0, 0], [11592740743.0, 0]], [[1.0, 0], [0, 65700.0], [-14025517307.0, 0]], [[1.0, 0], [0, 112706.0], [-15386239549.0, 0]], [[1.0, 0], [23502.0, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 26, 'label': '2-2e8-8.5-c5-0-26', 'leading_term': '1.092727895649994814795076133943474655431016158082271184', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/256/6/b/d/129/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [1.0927278956499948, 1.3022042388548785, 1.490999199334979, 1.6555280962185632, 1.792510813356689, 1.8990207875944995, 1.9725318012473665, 2.0109622003688674, 2.012716043086318, 1.9767205603975169, 1.9024591928613903, 1.7899993583313447, 1.6400140160275773, 1.4537960283059226, 1.2332642903988404, 0.9809606063210293, 0.7000363411402758, 0.39422797972395673, 0.06782087220038481, -0.2743993526383936, -0.6272079741102, -0.9850149375218631, -1.3419508155095734, -1.6919642324165625, -2.028929613464507, -2.346763708659226, -2.6395489282998916, -2.90166112681349, -3.1278990996947376, -3.3136127305672254, -3.454826457968006, -3.548354540219249, -3.591904496556509, -3.584165106805602, -3.5248754713537247, -3.4148718760480548, -3.256109577546279, -3.0516571240134707, -2.805661449820267, -2.5232827220476683, -2.2105987570325203, -1.8744797476496766, -1.5224350223183232, -1.162434566068163, -0.8027090396764577, -0.4515329990393636, -0.11699690565180042, 0.19322570840047, 0.47210893933110276, 0.7134956649581699, 0.9123015376942625, 1.0646942467049443, 1.1682407923111455, 1.2220161101539242, 1.2266672597038244, 1.1844285424546899, 1.099084319312416, 0.9758779223856627, 0.8213668603183821, 0.6432264444780894, 0.4500059522391791, 0.25084342201545407, 0.055147065778422905, -0.1277469911816509, -0.2889294561525341, -0.4202727590000183, -0.5147729825033845, -0.5668654183227753, -0.5727005196195768, -0.5303677324273522, -0.44005593371225, -0.30414097282709024, -0.12719307043413394, 0.08410048219558287, 0.32109883965132513, 0.573455557609218, 0.8294457822161303, 1.076364038956107, 1.3009806952593217, 1.490042164676748, 1.630797342340446, 1.7115307470207488, 1.7220815148378599, 1.6543268427515916, 1.5026087882885688, 1.2640845351688237, 0.9389823357602807, 0.5307483047288992, 0.04607298779104359, -0.5052089504670003, -1.110347637698502, -1.75403195086655, -2.418859573718865, -3.0859089245125304, -3.7353937858055946, -4.347377113811241, -4.90251695883727, -5.382814891644891, -5.772335969552521, -6.057869212731722, -6.2294988644626805, -6.281059388880568, -6.21045116236914, -6.019799022135732, -5.715442066853699, -5.307750121156283, -4.810769790280264, -4.241710716932032, -3.6202901583367257, -2.9679609671797307, -2.3070541334674926, -1.6598718985717966, -1.047770804305777, -0.49027566460232513, -0.004265194618529964, 0.3967321638009974, 0.7030977934760472, 0.9095093086369903, 1.0151327767604874, 1.0236084660073426, 0.9428274659900006, 0.7845066083330761, 0.5635791470486132, 0.2974281415818873, 0.004997918266398612, -0.29417409789729093, -0.5809578982377552, -0.8376137296403972, -1.04870697006582, -1.201907064413305, -1.2886274066200476, -1.3044703028151787, -1.2494504909605362, -1.1279817064539486, -0.9486229464816429, -0.7235937919173882, -0.46808073443677334, -0.19936824857063268, 0.06416131972569089, 0.30410671492268754, 0.5031475811923412, 0.6461044374766137, 0.7208987003845907, 0.719356524992043, 0.6378073474148106, 0.47743807117572123, 0.24437638573460654, -0.05050887250367228, -0.3920868499497689, -0.7617039717659055, -1.138148801855796, -1.4987940498344285, -1.8208557881285719, -2.082701451131129, -2.265133313777312, -2.352573292284727, -2.334078262861317, -2.2041226077603997, -1.9630960834529492, -1.617479839894723, -1.1796807668217368, -0.6675233881914275, -0.10341822287420982, 0.4867552435900106, 1.074995209633386, 1.6326831284187184, 2.132166208092737, 2.548327990448281, 2.8600562708092316, 3.051520981556044, 3.1131832369337733, 3.0424701869191892, 2.844068010786986, 2.5298063806563147, 2.118130897327523, 1.6331840332084868, 1.1035386039975876, 0.5606493136527145, 0.03710613098405226, -0.4352130264635234, -0.8269845568478542, -1.1131684730862594, -1.2745210526463966, -1.2987977018799999, -1.1815692947747825, -0.9265966492234753, -0.5457330416232672, -0.05835229101714588, 0.5096716626257473, 1.1273803268581786, 1.7604632463787742, 2.3732089793115163, 2.9305609402438733, 3.400156378827053, 3.754225884991808, 3.971237483245932, 4.0371833446805745, 3.9464276848799007, 3.7020603737881217, 3.315730632922624, 2.8069671255284656, 2.2020227708548976, 1.5323126977773536, 0.8325399375658518, 0.1386239908580297, -0.5144391327700815, -1.0946514070438682, -1.5748909763769348, -1.934474857842569, -2.160306512877947, -2.247534910129125, -2.1996830803177567, -2.0282386672777113, -1.751734368591223, -1.394380092163448, -0.9843388393148371, -0.5517626738395685, -0.1267219146557378, 0.2628313609020379, 0.5929259794371846, 0.8451321016234545, 1.0077111075835998, 1.0762744398797297, 1.0539046636580147, 0.9507294682032654, 0.7829779679232547, 0.5715857899886175, 0.34044843427506544, 0.11444886414773431, -0.08259675637567877, -0.22992325917947737, -0.31158139930033774, -0.31784777783747237, -0.24616751510182686, -0.10154948344039331, 0.10362756937930322, 0.3503972958011536, 0.614532421274098, 0.8683306920869339, 1.0827390309050873, 1.2296667709173117, 1.2843208730753006, 1.2273897040344792, 1.0469080137095563, 0.7396540794738036, 0.3119595736032756, -0.22014827857129243, -0.8315068146008758, -1.4890652880340343, -2.1537545570819394, -2.7828676571982878, -3.3327999997873405, -3.7619679060898297, -4.0337063252347365, -4.118942480188253, -3.9984524633101954, -3.664532070573249], 'positive_zeros': ['1.27978740445730790762136059629068', '3.26016466579534332080095697164907', '4.37991032047716966787286406760236', '5.10600479756497898249165081884755', '6.19369643979329962808526480952900', '8.016298864661784869699502929620450', '8.719924864879738623924814177993073', '9.685606024860844524266183740563938', '10.32474364038249819197637538674710', '11.40307937028845557837432240109247'], 'prelabel': '2-2e8-8.5-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.407671798096642, 'root_angle': 0.75, 'root_number': '-0.7071067811865475244008443621048490392848359376884740366 + 0.7071067811865475244008443621048490392848359376884740366*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.375', 'prec': 17}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27978740445730790762136059629', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.26016466579534332080095697165', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.37991032047716966787286406760', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 41.05825787212305, 'bad_primes': [2], 'central_character': '8.5', 'conductor': 256, 'conductor_radical': 2, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/256/6/b/d/129/1'], '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': '2-2e8-8.5-c5-0-26', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-2e8-8.5-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.407671798096642, 'root_angle': 0.375, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27978740445730790762136059629', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1622323271424834156843272952527', 'Lhash_array': ['1622323271424834156843272952527'], 'label': '2-2e8-8.5-c5-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/256/6/b/d/129/1'}