-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '530053183103811599424953426639', 'a10': [0.47318279289921894, -0.8195766385687889], 'a2': [-0.47318279289921894, 0.8195766385687889], 'a3': [0.0, 0.0], 'a4': [0.5521960890081898, 0.9564316819030108], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.7815289487007998, 1.353647846735676], 'a8': [-2.9378899220965593, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [3.463268804003968, -1.0028804471186605]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.451', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '2806266928672258268634548234645', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.47318279289921894, -0.8195766385687889], [-1.0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-0.7815289487007998, -1.353647846735676], [-3.5, 6.06217782649107]], [[1.0, 0], [0.7547117416000187, -1.3071990815200263], [-5.5, -9.526279441628825]], [[1.0, 0], [3.463268804003968, -1.0028804471186605]], [[1.0, 0], [1.6312093851171607, 2.82533753280611], [-8.5, 14.722431864335457]], [[1.0, 0], [-1.5521960890081898, -2.688482489471888], [-9.5, 16.454482671904334]], [[1.0, 0], [1.4689449610482797, -2.544287306057906], [-11.5, -19.91858428704209]], [[1.0, 0], [1.3026699987572694, -2.256290623343277], [-14.5, -25.11473670974872]], [[1.0, 0], [2.658974411716101, 0], [31.0, 0]], [[1.0, 0], [0.28576678055173904, -0.4949625830309977], [-18.5, -32.04293994002423]], [[1.0, 0], [2.8440042793720495, -4.925959908815701], [-20.5, -35.50704155516198]], [[1.0, 0], [0.632647710310533, 1.0957779775499599], [-21.5, 37.239092362730865]], [[1.0, 0], [5.134591458505078, 0], [47.0, 0]], [[1.0, 0], [-2.91733143877044, 0], [53.0, 0]], [[1.0, 0], [-6.407062176773649, -11.097357217424808], [-29.5, 51.09549882328188]], [[1.0, 0], [3.3294872058580505, 5.766841003696681], [-30.5, 52.827549630850754]], [[1.0, 0], [4.749035584555707, -8.225570919403047], [-33.5, -58.023702053557386]], [[1.0, 0], [-0.6100683350606912, -1.0566693524140707], [-35.5, 61.48780366869514]], [[1.0, 0], [12.878502207121509, 0], [73.0, 0]], [[1.0, 0], [-7.765634365403249, 0], [79.0, 0]], [[1.0, 0], [-11.231238478355197, 0], [83.0, 0]], [[1.0, 0], [-0.3984073286411873, 0.6900617353143275], [-44.5, -77.07626093681505]], [[1.0, 0], [-2.9002109066023687, -5.023312642900698], [-48.5, 84.00446416709055]], [[1.0, 0], [3.0200071622210847, -5.230805844188823], [-50.5, -87.4685657822283]], [[1.0, 0], [9.344106320073454, 0], [103.0, 0]], [[1.0, 0], [-5.505185651349098, 9.5352612532358], [-53.5, -92.66471820493493]], [[1.0, 0], [-18.567675899326307, 0], [109.0, 0]], [[1.0, 0], [-6.521506302824278, -11.295580258372315], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-585-13.9-c1-0-0', '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/585/2/j/i/451/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7146293548477589, 0.4984163115227504, 0.28601434375607265, 0.07364490858839966, -0.14019617683921956, -0.35379125237658426, -0.5618370630186177, -0.7556190549327917, -0.9236406596700752, -1.0526354223042074, -1.1289022020791244, -1.139894858936043, -1.0759673146656767, -0.9321324883229695, -0.7096516586015473, -0.4172408971865829, -0.071673212112992, 0.30242356501613, 0.6737180326917549, 1.0063316432908773, 1.2629386700586653, 1.4086120856419544, 1.4150790017137247, 1.2649275146355705, 0.9552234099568498, 0.4999706262109388, -0.0691004384839729, -0.7037999308047509, -1.3429718705603177, -1.9181093842835106, -2.360677787372648, -2.6104276783352227, -2.623729069900388, -2.3808063329711646, -1.8907425060141232, -1.193275475612385, -0.35673097344764354, 0.5280947229612597, 1.3577261412544455, 2.0285125291530495, 2.4503643693354107, 2.5598822480053864, 2.3309150267162257, 1.7807508035714408, 0.9706114876777835, -0.00014696660415342618, -1.0058175206231357, -1.910837355232537, -2.5888665643789364, -2.9417188401801395, -2.91519512301461, -2.509116708374969, -1.7795701949288891, -0.8324890227289281, 0.1909463490841304, 1.1352163054936508, 1.8546183827850993, 2.236857662834337, 2.2221048516711472, 1.8140847263853341, 1.0809293496546368, 0.14518477968696394, -0.835766429353997, -1.6958386237267065, -2.288579429756279, -2.5127505737205746, -2.330470575641601, -1.774400448172665, -0.9423400754522437, 0.020105186813078716, 0.9458504503934456, 1.6768946579301038, 2.093392306458866, 2.1356144182556864, 1.8144096085901293, 1.207936027943128, 0.44513186295814844, -0.3209021643146131, -0.9442817654495536, -1.3160306937943422, -1.3858316821360475, -1.1711181032773734, -0.7513951081127751, -0.2488438122046079, 0.20068254928101573, 0.4798966243097904, 0.5182447686650513, 0.3093806828735291, -0.08645939057736349, -0.5562505055594551, -0.9614706450543109, -1.172911092035316, -1.1049458629893298, -0.7409038595436257, -0.14284937504106154, 0.5575766509081086, 1.186258889523596, 1.5662856356084602, 1.561471337057896, 1.1135020552612422, 0.263339284537693, -0.8493338579118822, -2.010007844033271, -2.9725020429268585, -3.512470678041128, -3.479355453231834, -2.834549262064189, -1.6661041318378396, -0.17533609012469817, 1.3629198122058073, 2.6583365242202137, 3.468637082148743, 3.654021679684957, 3.2094169839370887, 2.266268961584412, 1.0625872226570867, -0.11246811031809566, -0.9868185503734281, -1.3703810619968029, -1.2008565318183826, -0.5588171741533434, 0.3522495855462888, 1.2567369756733866, 1.8765802534315486, 2.002791911084956, 1.5509731265036686, 0.5864766636742318, -0.6878112039830107, -1.9788263702175988, -2.9746223029431107, -3.4220742299976226, -3.1914490831469062, -2.3112430563964286, -0.963959892723194, 0.5566741933289658, 1.9166793797430652, 2.8232238933153897, 3.095826446042477, 2.709178024477423, 1.796632296501059, 0.613590477629495, -0.529528863020847, -1.3470775040074965, -1.6497583161264258, -1.3893253453678382, -0.665047550811694, 0.30902771623583775, 1.266335788064693, 1.9619490778335893, 2.237944741565134, 2.0620401372574158, 1.529326781789303, 0.8275705412246226, 0.17701842451290353, -0.23705797918633773, -0.3188865155020975, -0.08757153541996786, 0.334070344053251, 0.7635073614586142, 1.0215126495148197, 0.9943545246444498, 0.6752349385469265, 0.1711235759160786, -0.3283425595387887, -0.6113389115781513, -0.5155163108549855, 0.011695810368541797, 0.8841954502406624, 1.8909261279581258, 2.750661947743439, 3.1934159653594967, 3.044937992414371, 2.2884544569320804, 1.0832947874848462, -0.26796331231798604, -1.3970633070266654, -1.9717651839855548, -1.7928215547221023, -0.8574448868906125, 0.6308192978351269, 2.3108194801850312, 3.7589773880021475, 4.604636434544172, 4.632549561113431, 3.842401937162016, 2.447287492877503, 0.8108224133802586, -0.6591278758762037, -1.6288418100117121, -1.9338717655391942, -1.6220691250829908, -0.9311223923859467, -0.20708230537989458, 0.21139427846619063, 0.10734559064547726, -0.5375773581118274, -1.5285832483613544, -2.51170598118841, -3.081163011089477, -2.908030957544749, -1.8507743684036169, -0.012852790833418865, 2.2718202997150843, 4.5230127905681545, 6.24399328595736, 7.058829600577858, 6.816262686792265, 5.629120437361505, 3.8377178642113727, 1.9087861926819063, 0.3009954623619499, -0.6620279630296666, -0.8732183495095498, -0.4548957624067494, 0.29848249261238197, 1.0270648702903493, 1.4261996482134707, 1.3418464169869484, 0.8110353862515356, 0.036377233454682925, -0.6943435045962486, -1.1144721450455486, -1.0736600830551577, -0.5894570888923008, 0.1616258605595174, 0.9093967070572364, 1.3878972322788439, 1.4310299272460696, 1.0319388458201477, 0.3450280223287868, -0.37019685764570703, -0.843566060688873, -0.8932184692262817, -0.4933528053674595, 0.2142871354536987, 0.9703792180450382, 1.492502688432491, 1.580635690661909, 1.1952383233506505, 0.478254233850279, -0.29289766799268335, -0.8042719360311211, -0.8234011049104877, -0.29407245625514783, 0.627965781105841, 1.6146589189302423, 2.270730715620663, 2.2704266182857182, 1.4792230039309582, 0.016816557344366566, -1.7637831273971893, -3.3781202918616784, -4.361949358447684, -4.423028634943134, -3.5414632840648412, -1.982860290330749, -0.21726466446540235], 'positive_zeros': ['0.41813823383855153823387318029304', '2.02439802509190014260273124543070', '3.23577558499124725871142205989556', '4.55041612934241816305549533796797', '5.62498182177589126322734301153147', '6.72651609181756424780771332989611', '7.64334972849307288634220556422920', '8.622416044080007475510203032871830', '9.571085743284041791780027471077881', '10.44006969736153160824163506075028'], 'prelabel': '2-585-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.9956533864556082, 'root_number': '-0.9999067679874556 + 0.013654864806387067*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.497826693228', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.41813823383855153823387318029', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.02439802509190014260273124543', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.23577558499124725871142205990', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '13.9', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/j/i/451/2'], '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': '2-585-13.9-c1-0-0', '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': '2-585-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.4978266932278041, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.41813823383855153823387318029', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '530053183103811599424953426639', 'Lhash_array': ['530053183103811599424953426639'], 'label': '2-585-13.9-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/j/i/451/2'}