-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_179.17', 'a10': [-0.6881411722458688, -0.7255768236789827], 'a2': [0.9116210382765418, -0.41103172939762184], 'a3': [-0.19292606540949683, -0.9812132965291546], 'a4': [0.6621058348568004, -0.7494103438361251], 'a5': [-0.32908887327600994, -0.9442989534495557], 'a6': [-0.5791852582395334, -0.815195949841512], 'a7': [-0.9844653278615834, 0.17557909396732074], 'a8': [0.29555817896568404, -0.9553247420885155], 'a9': [-0.9255590665712211, 0.37860324125370337], 'algebraic': True, 'analytic_conductor': 0.8312725052572271, 'analytic_normalization': 0, 'bad_lfactors': [[179, [1]]], 'bad_primes': [179], 'central_character': '179.17', 'coeff_info': ['x^89 - 1', '0.997509025150764 + 0.0705389590423110*I', '\\\\zeta_{89}'], 'conductor': 179, 'conductor_radical': 179, 'conjugate': 'dirichlet_L_179.158', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^83', 'a^64', 'a^77', 'a^62', 'a^58', 'a^42', 'a^71', 'a^39', 'a^56', 'a^88', 'a^52', 'a^28', 'a^36', 'a^37', 'a^65', 'a^72', 'a^33', 'a^32', 'a^50', 'a^17', 'a^82', 'a^80', 'a^46', 'a^35', 'a^22', 'a^14', 'a^30', 'a^4', 'a^31', 'a^73', 'a^59', 'a^63', 'a^66', 'a^15', 'a^27', 'a^85', 'a^26', 'a^3', 'a^44', 'a^49', 'a^11', 'a^54', 'a^76', 'a^12', 'a^74', 'a^51', 'a^40', 'a^84', 'a^29', 'a^47', 'a^16', 'a^75', 'a^8', 'a^61', 'a^24', 'a^7', 'a^87', 'a^19', 'a^25', 'a^13', 'a^67', 'a^81', 'a^53', 'a^1', 'a^57', 'a^18', 'a^60', 'a^55', 'a^9', 'a^2', 'a^21', 'a^69', 'a^79', 'a^10', 'a^20', 'a^41', 'a^86', 'a^23', 'a^38', 'a^78', 'a^43', 'a^34', 'a^5', 'a^45', 'a^48', 'a^68', 'a^70', 'a^6', 'a^6', 'a^70', 'a^68', 'a^48', 'a^45', 'a^5', 'a^34', 'a^43', 'a^78', 'a^38', 'a^23'], 'euler_factors': [[1, 'a^83'], [1, 'a^64'], [1, 'a^62'], [1, 'a^42'], [1, 'a^88'], [1, 'a^28'], [1, 'a^72'], [1, 'a^32'], [1, 'a^80'], [1, 'a^4'], [1, 'a^73'], [1, 'a^85'], [1, 'a^49'], [1, 'a^54'], [1, 'a^51'], [1, 'a^75'], [1, 'a^19'], [1, 'a^13'], [1, 'a^18'], [1, 'a^2'], [1, 'a^69'], [1, 'a^23'], [1, 'a^34'], [1, 'a^6'], [1, 'a^43'], [1, 'a^86']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-179-179.17-r0-0-0', 'leading_term': '0.451282006261942875192454803782-1.43795452115668295424137413849*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/179/17', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.507106052701915, 1.16310331827801, 0.7495446261401756, 0.0706039550770033, -0.6837812790875246, -1.1806320980540963, -1.1447127342526897, -0.5178838263835297, 0.469658830308913, 1.3679323417938658, 1.7102728628145814, 1.265335667341276, 0.20065133189923504, -0.9580057874825603, -1.5857021697142775, -1.3151132041811318, -0.28358385643940803, 0.9051458507173629, 1.5245623658690368, 1.1943043362328645, 0.17853522563504476, -0.7160418727308083, -0.6349542153631188, 0.7180956103496459, 2.7691747444437085, 4.319638578554828, 4.262798129302974, 2.3431645060158997, -0.558242477625877, -2.863412383432422, -3.2373573037875647, -1.435955845748475, 1.515010458081294, 3.959628107493803, 4.657755412561774, 3.527026433049196, 1.5751073590491806, 0.09712380155714308, -0.2501245663832778, 0.19509877668604075, 0.5505446111586481, 0.2417223217162286, -0.4766140176079621, -0.7833876902219488, -0.12027201611696074, 1.1478208207791525, 1.8792649088082904, 1.0756346593165107, -1.1650492505181198, -3.5220852484064364, -4.3822407111712955, -3.1521261265866087, -0.8677350532656447, 0.49395034745318067, -0.4540751061236917, -3.342308570186922, -6.2305514637609765, -7.062070808212389, -5.242223435241309, -2.058208115705551, 0.40172397742465576, 0.9187385045994776, 0.0011398216427737473, -0.7615113643473729, -0.227999863321726, 1.2620956910464451, 2.2638854240280297, 1.6346714023533195, -0.3430878336411367, -2.169913268643087, -2.473711918995391, -1.231071365833723, 0.2780009675562301, 0.7226923661746294, -0.03352801755072443, -0.9016001903051805, -0.7639206256668303, 0.3198322775555773, 1.1652243326909006, 0.7963794212521346, -0.2695867910786762, -0.20596416021309316, 2.422482260850939, 6.959766391006506, 10.686002778219157, 10.810616766856507, 6.806509134147725, 1.000612272044201, -3.1892249881933936, -3.8779012865924316, -1.9318691351398964, 0.17910124304494626, 0.7004422699822468, -0.09076714326200719, -0.644552335239693, 0.005940980194331342, 1.2458372614545392, 1.676503481710659, 0.7373030168115016, -0.6472341436009799, -1.096647230047279, -0.34004059049653806, 0.4390478999461197, -0.06536545516872345, -1.679140008375556, -2.689488531007136, -1.568656198921166, 1.2441534298794539, 3.4594695703638068, 3.0360895932800944, 0.2335263267235567, -2.5157508135167053, -2.910180911583289, -1.0022239604384078, 0.922485245232747, 0.7290948365177874, -1.3339178667990494, -2.858111892046028, -1.7573343877387975, 1.5256172802738086, 4.360785751902098, 4.4798463583057355, 2.1321814523026523, -0.30705752404400577, -0.7738156058237489, 0.5699347744112815, 1.8348897951074026, 1.5883100911885086, 0.27789303362231144, -0.5559709272340663, -0.20805112974806808, 0.4124837728655753, 0.018644191334904747, -1.3375847813889046, -2.2035506847744943, -1.509097332612603, -0.10279454410015977, -0.0381850528252356, -2.1395384515284093, -4.554096430429865, -4.216169140308533, -0.026295369026512225, 5.5536050850713465, 8.406498473981532, 6.490346455445446, 1.704100909702523, -1.9855228782368257, -2.2335800160748756, -0.12614564124077926, 1.4875880933846835, 1.0868880493431436, -0.32446793032122717, -0.8884932679585937, -0.19749837131616757, 0.47360079962989304, 0.0807470252602282, -0.6307436580493611, 0.06682997188779485, 2.6247211436608167, 5.275420810098909, 5.707504330216837, 3.549613990943374, 0.7919166767300819, -0.4004936746093729, 0.023050102233031073, 0.27057923527028543, -0.8110048479325905, -2.0785556076247365, -1.399885330941055, 1.4883771344625105, 4.0417361262700116, 3.3354957623543995, -0.6302332947344155, -4.523612783388813, -4.8992137831321125, -1.6991511294698864, 1.7538736201543814, 2.268990222044187, -0.018137947449949284, -2.1487622305752727, -1.7629640550094217, 0.47229227930470985, 1.9725985846624525, 1.3048647802213111, -0.4145976290279084, -1.1780440418851987, -0.5156405739376495, 0.27681786514215834, 0.14117180630930215, -0.28224583984832363, 0.31773009474789293, 1.8131140397632977, 2.4108869099490913, 0.9296534469681783, -1.206073175755331, -1.0959084648016277, 2.238760180047626, 6.1244217457435415, 6.591575738011433, 2.563984305886219, -2.7595699842437886, -5.044475172533701, -3.137857428521195, 0.12317304712794426, 1.316861454897667, 0.05125365452548279, -1.2103224506899677, -0.5301227940016414, 1.1551528415209482, 1.4335716907505813, -0.38951228235877294, -2.3480909071195715, -2.2359571673492713, -0.30402820540874315, 1.1202641180789172, 0.540496340039637, -0.9611178243267836, -1.2798423656799467, -0.07489476277167267, 0.8179408962902807, -0.1386503145706086, -2.061872127569488, -2.7003478714235847, -1.3576428631419843, 0.14721329708781794, -0.12162494942762045, -1.495674253405458, -1.3828509862225695, 1.153192496067249, 3.388556966315843, 1.4902871683893493, -4.900679328353188, -11.436021933948739, -13.01074147949561, -8.759800367182148, -2.6556730778886926, 0.7618387215105453, 0.6116414533150483, -0.5773366111813293, -0.5529827343709787, 0.2845673008997669, 0.2979169328180993, -0.6682950386236675, -1.0567820210812133, 0.041672825797232124, 1.4051999478581312, 1.2661458235191634, -0.15599994366040482, -0.7593639805825365, 0.5956233564642031, 2.257400148406173, 1.6704237908590611, -1.1883246909226515, -3.336657828617577, -2.258886682168478, 0.8425102314341556, 2.254224570000444, 0.22159759583996314, -2.7537589702987058, -2.763259675582198, 0.8437986926157399, 4.627637036114578, 5.050531721750857, 2.407441565375215, 0.014225101588926602, -0.0690175750383697, 0.6763921493822797, -0.37658800328951025, -3.2537044948843667, -5.180070653910022, -4.099318384870782, -1.293013786354415, 0.2288083633160804, -0.6225361746254491, -2.00890361380135, -1.8508234285816805, -0.4513434770709236, 0.32185308402229995, -0.1615437992434327, -0.597615473527877, -0.09925818210365864, -0.014748082608074125, -2.1561833789123477, -5.516776982847994, -6.285319068853416, -2.0778100934279067, 4.521121783984563, 7.945950063769279, 5.471555419563514, 0.1787079670875722, -2.532410536655388, -0.8271089762209414, 2.1127251111964407, 2.3908134279325175, -0.0864777734098177, -2.1683982087207667, -1.7465683854569352, -0.054248176834659934, 0.561998695713126, -0.12154713737909978, -0.3715901626762916, 0.5690909008264107, 1.2252701951936444, 0.1638996468455512, -1.5432156764895066, -1.4421165353115815, 0.8682832443075285, 2.77018753931762, 1.7974755009363896, -1.0914482626662056, -2.604613489814697, -1.308905353839758, 0.6166750556756965, 0.48341150122011955, -1.0861550901110284, -0.8970802804666405, 2.301308533249228, 5.582075023376496, 5.2029100638509185, 1.4640788014905521, -1.3115707641430951, 0.06381824561683856, 3.754529399695358, 5.1729051355808835, 2.5093916423142413, -1.3678281750220131, -2.6930590282942344, -1.1549602926365152, 0.5132919311342238, 0.4995850198709468, -0.12599183363592667, 0.32194080483703374, 1.3830793877205072, 1.234778084960988, -0.34594424506405497, -1.4078489051746412, -0.6333207952764986, 0.5985427383667961, 0.14616627392236758, -1.570801672253623, -1.8931265590121635, 0.01204913413312551, 0.9587163322305943, -2.790198753380666, -10.21479608093699, -15.426309551742412, -13.692900183018654, -6.642171291401043, -0.3589641021207655, 1.2365577476640255, -0.24059177968248924, -0.9660837345413809, 0.08027860402006004, 0.8088112976900801, -0.0859267302809968, -1.0183268247530957, -0.05303925608194437, 1.899678658097331, 2.0800221944237145, -0.22843045642898022, -2.468217807308525, -2.1095230102112414, 0.04665071494435072, 1.1215108719792186, 0.1289431330482045, -0.9371931102724029, -0.29710727454675756, 0.9027566948469694, 0.39103960697151957, -1.5362061363320292, -2.0399097152567807, 0.15922705291823538, 2.4273664664683006, 1.4822746335194756, -1.7522224492486942, -2.574552038570689, 1.6472188152695983, 7.618926853932884, 9.571563771553729, 5.953525726210006, 1.005432908362103, -0.5675948532996872, 1.1225269938154083, 2.313760156015225, 0.936201961287754, -1.1447548248155301, -1.3462090342891406, 0.04332124801664661, 0.7788970340775538, 0.11873629215454963, -0.47405478055972233, -0.08287773741141496, 0.079818756887758, -1.0839393731465936, -2.0322682131370633, -0.21616298437358575, 3.8829501304405527, 6.315777111810952, 4.325800624788645, 0.17794653207696182, -1.368495376011965, 0.9490199831049952, 3.3421369896925683, 2.063056328742191, -1.6081848572343227, -3.163576339616047, -0.964612001795488, 1.630552565413652, 0.8729971994010797, -2.421185847863233, -4.190584994772451, -2.6055463397804988, -0.11237474556583742, 0.3911806416534842, -0.50394587974538, -0.14445717651485995, 1.8429544337038837, 2.7944263186990623, 0.8981476520605917, -2.017301963711139, -2.863460467092029, -1.3685643611134761, -0.03418087158048376, -0.30315180526606805, -0.7405631498837354, 0.2281199603297337, 1.500401261489423, 1.0242942978677085, -0.4534419613689461, 0.19562291404351775, 3.608518419177925, 5.55960338838754, 1.5588401163150865, -6.820412228412141, -12.516119792750485, -10.601480530322531, -3.722664086622658, 1.3413468753992226, 1.401272136515225, -0.733901641520955, -1.181963190703302, 0.12945833570870624, 0.715250326092525, -0.10383687991882683, -0.4669135508929492, 0.6165109625430018, 1.4678274525444648, 0.4320454703111993, -1.2521460063900043, -1.1028722350366515, 0.7507645501015809, 1.4811591436005553, -0.3036364848111857, -2.3058015411150645, -1.7876339730392947, 0.27598102579056394, 0.4713280755311623, -1.8452273196915323, -3.0286146113058376, -0.03072779460300374, 4.931091260487206, 6.744049415993774, 3.906102396209519, 0.288896753299649, -0.2419981180730696, 1.189267005536974, 0.7310430477709275, -2.169203038944379, -3.708714273984753, -1.1519134943020313, 3.029390657019982, 4.180057004261007, 1.4017878855282435, -1.7063155687497071, -2.0569685890478575, -0.5769987399500679, 0.16635444306226974, -0.08255567875766559, 0.36276703179764946, 1.7072239962722515, 2.061089266957281, 0.6586642736934715, -0.4858446333351032, 0.4120649671621311, 1.7690660827802533, 0.7756548514301661, -1.7783032128843101, -1.524997814759316, 3.518792412707583, 9.110530392796505, 9.2260943315314, 3.636604284830066, -1.481903164303999, -1.0314919792912975, 3.1334965782224766, 5.3285288699729545, 3.4058270580855607, 0.5216191154670856, -0.08468531893489184, 0.7532109987625732, 0.4492742665193856, -0.9704240516695162, -1.2386137257631424, 0.13683062155989326, 0.8921209160195726, -0.31276760111853025, -1.4704585322933257, -0.171170568083351, 2.408303205109429, 2.772557328469508, 0.10576845108756398, -2.3768181806613087, -1.8755067739976514, 0.24483686381768893, 0.8695352283774532, -0.14099460484123205, -0.26510609204495883, 0.8366257468121251, -0.17153114124523636, -5.290923097516899, -10.784068582625691, -10.674532057880317, -4.347483187367385, 2.0961554518719945, 3.041702808421065, -0.2544624410028016, -2.28097994006752, -0.7311923849319483, 1.397737718293613, 1.007484535396584, -0.762102303150332, -0.9273048671017927, 0.63198644005317, 1.3580172418461571, 0.24150028611876675, -0.775903447728613, -0.15248254976551714, 0.8096631438157682, 0.340934691534712, -0.7151858220491835, -0.4882625536818944, 0.07567807180707119, -2.125589099795468, -7.163897940525813, -10.241582103631568, -7.23105697780337, -0.6145520537715261, 2.90605501327625, 0.646772571803826, -2.9577242434136446, -2.5560860645132077, 1.2359426248701522, 3.4758202110844514, 2.039446562586365, -0.04870636222796907, 0.28133876794169366, 1.7752658087291882, 1.5018273836030351, -0.1515107684506622, -0.05169947387441834, 2.555130935935018, 4.464411588259767, 3.0437405679777774, 0.027792832644901736, -1.0916017332006511, 0.01530240314470768, 0.6556232318278129, -0.34737084716739824, -1.0393905268632049, 0.01018001550344791, 0.9930309604764744, -0.2334985488258998, -2.2224977617613613, -1.7297314573568359, 1.0101174012651881, 1.9442274111330728, -0.7909066702166179, -3.2994173126565594, -0.9390534059601352, 4.571921791547701, 6.429596752271082, 1.4498784978941812, -5.523779061444686, -7.593173530373702, -4.027833604936071, -0.005559521555409492, 0.6919595951070638, -0.4685142087789607, -0.5574488553806721, 0.32054838517990625, 0.3025451192781164, -0.49072180875064975, -0.3456896387802286, 0.5280966494509045, -0.1623662471478638, -2.7963383678238656, -4.299693999672002, -2.30549816332952, 1.0417877205607726, 1.8924607701411063, 0.3146998746466387, 0.11471605705236913, 2.7880988986363735, 4.799441919780228, 2.760744922061285, -1.021821588311776, -1.2792023760449138, 2.744210084750465, 5.985675188018853, 4.532977314065348, 0.8408167123164912, -0.19569367531312454, 1.7430350091940894, 2.5517603367386283, 0.2755417099390296, -2.023010016753167, -1.1425127110904205, 1.3981014082189653, 1.8456390879541809, -0.08605506838877479, -1.0676394104331062, 0.563068613759927, 2.4279078818713784, 2.007760496497336, 0.35437316759201587, -0.04965577511604152, 0.6596695589357927, 0.4738481848476628, -0.5429713586370444, -0.2047687427242946, 1.4999227773720354, 1.3319559018121634, -1.9604568780778329, -3.8418599623163328, 1.0803217070953508, 10.957770319060339, 17.194160367053094, 14.183899914156829, 5.761712795650008, -0.05155202660061843, -0.5137260477504726], 'positive_zeros': ['0.96611517036954088524444927977', '2.3574710257804776176213254277', '3.801201648739725047782438670122', '5.07095988340524771233857528909', '6.30067198773021443689979179451', '7.05370770693503274673913522362', '8.69044279149536005080273919404', '9.84411183137594110053555923334', '11.59745949175464351375647743607', '12.0767962111154301659717276765', '12.921790163735681162416452216408', '13.78279240301449107904542043241', '14.85380591608991018873491713009', '16.396026496087191245724252997634', '16.79945520496964291611127490143', '18.67964740274450108631145296557', '19.375317883039863319287905516698', '20.05542387438952600486558406352', '21.20127587743345568105225856966', '22.43044297230729574349646776205', '23.11497749972617888747227610721', '23.980372097849878888683259179843', '24.91375402394614691670023613757', '25.35710056127202275155767603240', '27.24611667780315265343648342690', '28.40139136193223362284651303494', '29.03278792961360607259266965393', '29.685905902437875823478280593445', '30.78224670208088538147350160340', '31.66742151825329661838432308413', '32.17070543710641785546747101668', '33.30834156405211869204077989237', '34.39737318476805555452906218679', '35.44920622985541205000521077211', '36.06570034742936467174768788890', '37.05405305252034608991788651188', '38.38475158856695326153932343379', '38.95359143813609132925804278419', '40.06980191691045613404243295783', '40.710962840246652204431614080672', '41.25556051937970599514692828237', '42.53270656474339977746723299593', '42.80120252378828506101879048515', '44.06397911960176609769191916633', '45.42939514050898129737162226360', '46.26715810397739561416702323354', '47.111639203512834853769922927367', '47.87839716348179744757129110150', '48.467374485119514409650853830638', '49.05029404757454600792726699279', '50.76491568797131729665287553899', '51.239389361891335000893805329055', '51.68290603177208459971505797221', '52.66906273411797014994980563632', '53.70746548077923674991545886765', '54.82252182011097826528225713641', '55.622961958718854915855249886680', '56.50016100481892835396888291114', '57.42047067309156522024030499201', '58.29492586465275424641979777609', '58.83093971566222800925647611649', '59.28289666348566325715065283225', '60.43629325442263054519910247599', '61.06974688285978014681220991390', '62.33033798008157512972037956403', '63.423096617688431032633624647710', '64.07160860299792587548907789368', '64.78465638623752754421223924391', '65.57272826710045384719474194514', '66.60885726316999732415655164719', '67.29743098117677028055920425834', '68.141401753319110011032632088973', '68.725193908587393756078357238074', '69.950577413342409408432506363667', '70.27832275194469285357912983481', '71.13062098004978018065634721422', '71.96449273780035421946104766547', '73.637975024235108880301051747882', '74.207725491635142104862202808766', '74.88694885219612943487839276223', '75.425060871815420372689834804364', '76.24172353977778013437324282158', '77.153606600028279538748830583975', '77.71278908196606389650489919890', '78.63263039835896823700397908923', '79.60184691414585587270992745389', '80.33386527398387118195876633209', '81.19019464508031928424235270282', '82.50351163710160297063215458245', '82.83781370569303272771609184647', '83.38065779520513793877710839995', '84.89547246218828902822515282152', '85.167197696765120352089823937203', '86.36808130019961417272765444413', '86.80688842938701449041801902269', '87.54876194597681626060027658868', '87.80710893628541840505087539089', '89.16111628197491671736656775426', '90.32435693051554358145736857737', '91.017687765387831783539475236969', '91.86560338320783772012001275710', '92.82449815726690670564370929164', '93.39059382979099007466538207403', '93.90534788044588934415091026554', '94.71568382033216862026582563360', '95.52390828896179911387077146987', '96.44655940741281693416124372831', '97.37679360905103084534051670819', '97.91245501669876479690012501518', '98.55187270569369734682770429805', '99.80952571632521838793740696457', '100.30630977904455550057472927069', '101.44085787924096690878441212350', '102.37276765502355045922639687120', '103.03049580146231582785591648299', '103.320122352061159369456200899275', '104.313392201089881561791313985', '105.13622109133192109644683752435', '105.65523474069999122379366047441', '106.56079292620389809919049301032', '107.0103069154746958715500992860', '108.77891988068531506466084055077', '109.330401186137591980837926448714', '109.98109401758159581082595681098', '110.60503684605745752179384268449', '111.25873008937196736713677690431', '112.16249178344154043910471568278', '113.117966690654200492244812038523', '113.77709521687166173838228164028', '114.44174677098041503322422132096', '115.07001232238737025713280470514', '115.92040953528184962152386020589', '116.708824349486086297682213890911', '117.40986423176252533132819489980', '118.85303726958680360768321309790', '119.20529358578578490529315404393', '120.12586367236084288356662244000', '120.92799700316901381009311813372', '121.6027031422910701565363215605', '122.23310270259793228296125726322', '122.54080726590575475162072574785', '123.45681001518976242705272809274', '124.70362297137041976230999450749', '125.21756326539883643716909138463', '126.11378694209738720814561915656', '126.96917337915870508416923510051', '127.592125141089571398889521038904', '128.77106732164028526649702501845', '129.20273512268624180967798171152', '129.71698414566964594298468553718', '130.7159296921758920053130138873', '131.89971602663632728811219305889', '132.02622760054526828461608619857', '132.76429950522743231012070485848', '133.6375268524926902888845880614', '134.03498512035045776180126833688', '135.06445904305399672281068695947', '136.44500740281022445056381437917', '137.0734393577534230673782534223', '137.78307373825060351773129201295', '138.40462844362039084122389225855', '138.91928630895283253220140086598', '139.759680577043783953743239347043', '140.50534737237333776736206438459', '141.211557946982935620562763746685', '142.1392530520743140733507330202', '142.58394958579549634522666372572', '143.439497648556825535313621152534', '144.73021321347781812747800976858', '145.060149695336702341493322346170', '145.718373762304518929123609614619', '146.64507997486882749550835872537', '147.62048871783186265854134271417', '148.60221181659871100877474615717', '148.966002041116244928676580120144', '149.23658752608650683807092690448', '150.440719015615212294924171775885', '150.8540009512809504895962348020', '151.656777966063451659505081041431', '152.31092992494042315713808420350', '153.62845059688630386490004209327', '154.15004763710574917338361076243', '155.4225481624204624741447517156', '155.664614192496828833948578871731', '156.35376485659836645596927112537', '157.159921951683937397577386057716', '157.755097090196916815764109867304', '158.4586449555647376359605383995', '159.38509987894867652567788937122', '160.2715157726544121669520403205', '160.895109228053395262770950736136', '161.33257713137521656012923934044', '161.857363576744359680824822525300', '163.31333904149431526567660615396', '164.040330667831418765857664200', '164.77546189010691915556613610966', '165.48274002514481306329343907669', '166.13372037282544947753902165510', '166.925896153889854400424422889214', '167.53935579802344066419391627845', '168.214067834872587516947852608657', '168.92988594051335975851608202262', '169.10330559324100155118553120952', '170.65741013474032828436186517575', '171.29881185819762516657906205686', '172.09162967191749295982200094631', '173.11150555876199983120427354262', '173.368969289390679613366150647141', '174.34054865203076456983404289057', '174.6971436612723608872991559069', '175.94098899150485574410114474703', '176.558972319631683215969122079672', '177.104656770667581912509523649310', '177.81041036011212038608949767448', '178.40296743662286292285621577008', '179.263269664207686599820773177566', '179.93109305982549480922867979537', '180.6816864428539816197205908522', '181.62331600707427932946893397204', '182.813186500771098342758553658447', '183.31024035305639797138185965818', '183.94236177450244862454839734022', '184.49297671685429627000001119682', '185.114810796940954392128307680596', '185.59741654204886244382512437921', '186.76616550375707933468142678531', '187.57451450151251643583822294643', '187.7851590495621446434381461363', '188.96508382915493037166931179411', '189.49834303714455350088926373263', '190.7381207668016962993362922790', '190.98833665119284448968972102294', '191.90324387891637286445558589642', '192.63588454054919005907979963134', '193.42461118286486941228031143112', '193.985343295110235370187617515253', '195.11009939165894840375670510592', '195.34238021034145892875660894093', '196.076835686351076994691788837519', '196.60536779460366752706872531727', '197.33617094971752668577534273684', '198.08334278490759343289884121046', '199.68203313953255026341192232450'], 'prelabel': '1-179-179.17-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8312725052572271, 'root_angle': -0.8064028996118004, 'root_number': '-0.820676006240537422873615583144-0.571393815840774899917612476045*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.403201449806', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(89)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.998145761492564691813164690991-0.993579185819021186941933942462*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.96611517037', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.35747102578', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.80120164874', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.8312725052572271, 'bad_primes': [179], 'central_character': '179.17', 'conductor': 179, 'conductor_radical': 179, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/179/17'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-179-179.17-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-179-179.17-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8312725052572271, 'root_angle': -0.4032014498059002, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.96611517037', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_179.17', 'Lhash_array': ['dirichlet_L_179.17'], 'label': '1-179-179.17-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/179/17'}