-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1808307469785534751845292373838', 'a10': [0, 0], 'a2': [-1.4142135623730951, 0], 'a3': [0, -1.7320508075688772], 'a4': [2.0, 0], 'a5': [0, 0], 'a6': [0, 2.449489742783178], 'a7': [-0.8532176147806924, 6.947806826749571], 'a8': [-2.8284271247461903, 0], 'a9': [-3.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.61042775783118, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.4142135623730951, 0]]], [3, [[1.0, 0], [0, 1.7320508075688772]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.8532176147806924, -6.947806826749571]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.601', 'coefficient_field': 'CDF', 'conductor': 1050, 'conductor_radical': 210, 'conjugate': '30891874557966011664233072246', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.4142135623730951, 0]], [[1.0, 0], [0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.8532176147806924, -6.947806826749571]], [[1.0, 0], [-2.8809673616381035, 0], [121.0, 0]], [[1.0, 0], [0, 13.814525194775243], [-169.0, 0]], [[1.0, 0], [0, -24.17539928106395], [-289.0, 0]], [[1.0, 0], [0, 6.534031093158327], [-361.0, 0]], [[1.0, 0], [28.84199213807291, 0], [529.0, 0]], [[1.0, 0], [-32.95889287403637, 0], [841.0, 0]], [[1.0, 0], [0, 2.4327636089584557], [-961.0, 0]], [[1.0, 0], [50.97987938371908, 0], [1369.0, 0]], [[1.0, 0], [0, 21.52253877658128], [-1681.0, 0]], [[1.0, 0], [13.555444219521327, 0], [1849.0, 0]], [[1.0, 0], [0, 40.73045568075666], [-2209.0, 0]], [[1.0, 0], [-17.275826080267667, 0], [2809.0, 0]], [[1.0, 0], [0, -1.4748849127720787], [-3481.0, 0]], [[1.0, 0], [0, 111.56777958696246], [-3721.0, 0]], [[1.0, 0], [120.29295093720324, 0], [4489.0, 0]], [[1.0, 0], [90.3854892647539, 0], [5041.0, 0]], [[1.0, 0], [0, -21.48899634876161], [-5329.0, 0]], [[1.0, 0], [-66.13236518412246, 0], [6241.0, 0]], [[1.0, 0], [0, -78.5171995460118], [-6889.0, 0]], [[1.0, 0], [0, -90.97240845806675], [-7921.0, 0]], [[1.0, 0], [0, 44.19723136872207], [-9409.0, 0]], [[1.0, 0], [0, -180.0516483494671], [-10201.0, 0]], [[1.0, 0], [0, 107.20813844853475], [-10609.0, 0]], [[1.0, 0], [33.15214581527373, 0], [11449.0, 0]], [[1.0, 0], [108.81885405533617, 0], [11881.0, 0]], [[1.0, 0], [157.65754726019878, 0], [12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 39, 'label': '2-1050-7.6-c2-0-39', 'leading_term': '0.062192650095210459931077212097953885509112267562908598', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1050/3/f/e/601/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.06219265009521046, 0.22133842722797478, 0.37850672737098745, 0.5318312842083185, 0.6793947692513727, 0.819218996951902, 0.9492615375588227, 1.0674203644816476, 1.1715477378145223, 1.2594740466916508, 1.3290418271960578, 1.3781496631414165, 1.4048051829817398, 1.407185901329863, 1.3837062280150683, 1.333088588526901, 1.2544362730660596, 1.1473053631993957, 1.0117728819842913, 0.8484981831241085, 0.6587745458678285, 0.4445679839668449, 0.2085404176311715, -0.0459453956650935, -0.31484141753683825, -0.593452147083618, -0.8764958943801574, -1.1581900165184849, -1.4323598463696314, -1.692570192671987, -1.9322773869682541, -2.1449989260843885, -2.324496840517178, -2.4649700451365977, -2.5612501373878187, -2.6089944392223337, -2.604869571413681, -2.5467185396965295, -2.433704234312432, -2.266422425217206, -2.046977793912485, -1.7790172897754033, -1.4677161332445465, -1.119713097708944, -0.7429932612008211, -0.3467181898549948, 0.05899455320588597, 0.4633386498635414, 0.8551270404939586, 1.2231327290130634, 1.5564525402180494, 1.8448823603382793, 2.079291078096209, 2.2519795274220877, 2.357010285945381, 2.3904942635616764, 2.35082066336432, 2.2388181328175576, 2.0578367424191173, 1.8137428029100808, 1.5148214045213357, 1.171584850702301, 0.7964887573073821, 0.40356136721409774, 0.007955442525448674, -0.3745642184435745, -0.7281812013996668, -1.0376164658523197, -1.2887242271801944, -1.4690715073794023, -1.5684774673340975, -1.5794889412572215, -1.4977699242859992, -1.3223851256467551, -1.0559610547254996, -0.7047123703966905, -0.2783262624158013, 0.21029672949081496, 0.7454410342600426, 1.3091029281650035, 1.8816293786449476, 2.4424466579513555, 2.9708516264410565, 3.446834639606158, 3.851900280617207, 4.169850753301952, 4.387496926812423, 4.495263776054695, 4.487660312580335, 4.363588973903549, 4.126475682539435, 3.784209172367688, 3.348886414448494, 2.836369705410723, 2.265669814529709, 1.6581781007275653, 1.036778282314411, 0.42487516005939396, -0.15461731519753, -0.6802829911514094, -1.1331586725783012, -1.4975917426341652, -1.7619578245135157, -1.9192015781644378, -1.9671712478438632, -1.9087268022507078, -1.751612039975107, -1.5080923845786318, -1.1943717180475524, -0.8298129135567077, -0.43599713524448297, -0.03566590387548491, 0.34840313276398105, 0.6945312681254253, 0.9832274110396932, 1.198174284059076, 1.3270601786571923, 1.3622112554718084, 1.3009888943312213, 1.1459282468482832, 0.904607362438798, 0.5892503789851303, 0.21608255077853905, -0.19553144752131496, -0.6241222207540843, -1.0472694589202616, -1.4428135020098214, -1.7900590916033159, -2.0709050620575407, -2.2708367379587675, -2.3797244391817785, -2.392381473079092, -2.3088478366574625, -2.134380900914862, -1.8791507966756824, -1.5576551510548833, -1.1878842637223088, -0.7902827882177028, -0.3865665773125628, 0.0015372430814874155, 0.35355333101253894, 0.6514493622097035, 0.8806836242818249, 1.0310446735778638, 1.097230316098331, 1.0791281789023366, 0.9817777659221333, 0.8150131326378905, 0.5928050280603092, 0.33234033584242667, 0.05289370292246998, -0.22543973973749812, -0.4830716427343782, -0.7022234890892197, -0.8681211514993817, -0.9700019516472566, -1.0018656613068575, -0.9629159817746143, -0.8576579580574865, -0.6956384267184073, -0.4908396505229363, -0.2607593145906939, -0.025231557551976858, 0.19493775408433262, 0.3794340272745119, 0.5098987923655977, 0.5712971099630948, 0.5530918442940269, 0.4501391546251584, 0.2632355919104103, -0.0007316386223112512, -0.3290545998142296, -0.7038906009893532, -1.1033319675210032, -1.5028003841530864, -1.876682653136177, -2.2001054713067254, -2.450733740968455, -2.6104710754733618, -2.666943188782077, -2.61465491626817, -2.4557293209299247, -2.2001617922786005, -1.8655518607163062, -1.4763088379817833, -1.0623622621264066, -0.6574422081538426, -0.297025529378887, -0.016069850254905, 0.153324257019976, 0.18417249812495298, 0.056636680304158, -0.24031611394279942, -0.7077470458164743, -1.3361658708861723, -2.1055972225241772, -2.986311848612982, -3.9401991959640013, -4.922715312732691, -5.8853006378796024, -6.778128575213011, -7.553020214149399, -8.166345094156334, -8.58172383145338, -8.77235632610073, -8.722818949107635, -8.430204579561027, -7.904518875088236, -7.168292313573749, -6.255417427493516, -5.209271025473188, -4.080228705066191, -2.9227203638830903, -1.7920078064400204, -0.7408865580351541, 0.1834780099913752, 0.9423759624677435, 1.5078547195530307, 1.8643449746628817, 2.00950077657328, 1.954194695995852, 1.721664385144141, 1.345863162092738, 0.869120680706439, 0.3392665853464719, -0.1935930049126968, -0.6804319549633804, -1.0765693054688192, -1.344624268311531, -1.4569624463749304, -1.3974688666473698, -1.162529161837102, -0.7611544737502425, -0.2142446557781678, 0.4469559878485052, 1.183100077478173, 1.949516739203616, 2.699332978834947, 3.386716738583254, 3.970013421759935, 4.414555836969745, 4.694951456857713, 4.796688963274707, 4.71695557140735, 4.464614039829972, 4.059349421478655, 3.530056022062207, 2.9125902546843934, 2.2470610082585107, 1.5748623369501364, 0.9356712063633618, 0.3646343007734049, -0.11004765313756142, -0.46896084746367056, -0.7026120990427043, -0.8117774783768574, -0.807048683930171], 'positive_zeros': ['1.42650306753293439888644360053594', '2.86593908604901864543173488933573', '4.00126976685593565538081729647071', '4.78644694695130524402931260379094', '6.10783962869203855712609823630290', '6.94314085782451910912803853648801', '7.65833481848891307093292186756575', '8.687242682159363597856495345996958', '9.386722274455433754666880445885393', '10.13184331326161985727743673335178'], 'prelabel': '2-1050-7.6-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': -0.9611050539476599, 'root_number': '-0.9925438323927958861363566191044588575160545444350126995 - 0.1218882306829560464535922949977411425342738916850589299*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.48055252697382994', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.42650306753293439888644360054', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.86593908604901864543173488934', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.00126976685593565538081729647', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 28.61042775783118, 'bad_primes': [2, 3, 5, 7], 'central_character': '7.6', 'conductor': 1050, 'conductor_radical': 210, 'degree': 2, 'index': 39, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1050/3/f/e/601/2'], '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': '2-1050-7.6-c2-0-39', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-1050-7.6-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': -0.48055252697382994, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.42650306753293439888644360054', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1808307469785534751845292373838', 'Lhash_array': ['1808307469785534751845292373838'], 'label': '2-1050-7.6-c2-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/3/f/e/601/2'}