-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_185.107', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.3420201433256687, -0.9396926207859084], 'a3': [0.3420201433256687, 0.9396926207859084], 'a4': [-0.766044443118978, -0.6427876096865394], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, 0.0], 'a7': [0.984807753012208, 0.17364817766693036], 'a8': [-0.8660254037844386, 0.5], 'a9': [-0.766044443118978, 0.6427876096865394], 'algebraic': True, 'analytic_conductor': 19.88101108700563, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [37, [1]]], 'bad_primes': [5, 37], 'central_character': '185.107', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 185, 'conductor_radical': 185, 'conjugate': 'dirichlet_L_185.83', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^29', 'a^7', 'a^22', 0, 'a^0', 'a^1', 'a^15', 'a^14', 0, 'a^24', 'a^29', 'a^31', 'a^30', 0, 'a^8', 'a^5', 'a^7', 'a^34', 0, 'a^8', 'a^17', 'a^3', 'a^22', 0, 'a^24', 'a^21', 'a^23', 'a^6', 0, 'a^0', 'a^1', 'a^31', 'a^34', 0, 'a^0', 0, 'a^27', 'a^2', 0, 'a^4', 'a^1', 'a^27', 'a^10', 0, 'a^32', 'a^21', 'a^15', 'a^2', 0, 'a^12', 'a^17', 'a^35', 'a^14', 0, 'a^16', 'a^5', 'a^35', 'a^26', 0, 'a^4', 'a^29', 'a^15', 'a^30', 0, 'a^24', 'a^1', 'a^27', 'a^10', 0, 'a^16', 'a^29', 'a^27', 0, 0, 'a^20', 'a^25', 'a^31', 'a^10', 0, 'a^28', 'a^33', 'a^23', 'a^30', 0, 'a^20', 'a^13', 'a^3', 'a^26', 0, 'a^32', 'a^25', 'a^7', 'a^14', 0, 'a^8', 'a^21', 'a^31', 'a^2', 0], 'euler_factors': [[1, 'a^29'], [1, 'a^7'], [0], [1, 'a^1'], [1, 'a^24'], [1, 'a^31'], [1, 'a^5'], [1, 'a^34'], [1, 'a^3'], [1, 'a^6'], [1, 'a^0'], [0], [1, 'a^4'], [1, 'a^27'], [1, 'a^21'], [1, 'a^35'], [1, 'a^26'], [1, 'a^4'], [1, 'a^1'], [1, 'a^16'], [1, 'a^27'], [1, 'a^10'], [1, 'a^23'], [1, 'a^26'], [1, 'a^21'], [1, 'a^12']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-185-185.107-r1-0-0', 'leading_term': '2.46032610506600797969561814301-0.666810523887754632095692662733*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/185/107', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [2.549086271203219, 2.2658242508940623, 1.568680026922163, 0.5629001003883644, -0.5347229706142732, -1.4135605687484638, -1.781344410357959, -1.5165866440081228, -0.76864360591753, 0.07322197582193268, 0.5563433681311735, 0.4123750198838536, -0.26277017308224293, -1.0266911978032764, -1.3380643945137791, -0.9212602528141937, -0.02986087931774029, 0.5923049465112082, 0.09598646962995896, -1.9233950006166025, -5.041024714904741, -8.070099221407727, -9.620781938840143, -8.871430014098168, -6.090637208241059, -2.5516147155371947, 0.1603151824918822, 1.0464462546231301, 0.23338572399675123, -1.2040680129750116, -2.019145077783479, -1.6345897223064338, -0.461210432383431, 0.5222322917750506, 0.5971647500027075, -0.10373266891081032, -0.7137822656680342, -0.37568706420105996, 0.9849098948480841, 2.506873840042009, 3.0334532233996394, 2.060313186056262, 0.21104833701712655, -1.1990873477899393, -1.2082903998698509, -0.015415405460998961, 1.1597517459964273, 1.1120476175744356, -0.24967699948349456, -1.6983604448692815, -1.6435308767888053, 0.47727265679932707, 3.5384035698755922, 5.437706560000466, 4.697935590312429, 1.684196012699773, -1.5927406305783314, -2.9848941766488206, -1.8297536029272274, 0.6273264772598299, 2.332754012449727, 2.0959016648354596, 0.42631898376154875, -1.107647462937498, -1.339655450811254, -0.44364219435272156, 0.446811881055669, 0.4762222389812383, -0.09071546494965257, -0.2500712466344837, 0.5476865277570562, 1.6494019564599671, 1.7516132018903707, 0.2982749475096945, -1.678498350119529, -2.2663770439297033, -0.44744711647787727, 2.6933019962996494, 4.603337640861477, 3.3679023627392097, -0.5334051665246372, -4.459178774322204, -5.7272850122346295, -3.7901484759805886, -0.5442406184096855, 1.453974790600632, 1.1867955244032071, -0.2122935474093221, -0.8713430745548962, -0.12401101888702834, 0.9406134667705219, 0.7843919643322886, -0.8353580123299229, -2.5117073249992634, -2.593443790949288, -0.8893074175140352, 1.106225213761462, 1.711627841100514, 0.7285802171871694, -0.45403001191230197, -0.4139069951420393, 0.7647926626758702, 1.6373160267342974, 1.0907439793610612, -0.27691565542814994, -0.6983430737142325, 0.7486823273039798, 2.813431263977776, 3.0501808872546268, 0.3427009559454337, -3.5655828821543984, -5.294994107114647, -2.8577631621588404, 2.3774273211126005, 6.749288012525615, 7.445438265728699, 4.755364924676737, 1.3948462190186235, -0.22623964439735939, -0.0018260596442580103, 0.4200301754349032, -0.18799490534849075, -1.321263434713619, -1.602235746063018, -0.6084397769984794, 0.5536747734640277, 0.5973067777277101, -0.31339073839020665, -0.6742270052742043, 0.5083672353673259, 2.2655597940429497, 2.4704539741263023, 0.22717606991418027, -2.7950181748845337, -3.78479549268912, -1.6776860625044268, 1.560664433955003, 2.7898678889158077, 0.8775022847081893, -2.1310551106975177, -3.13926315434861, -1.1969285046650104, 1.616835429928921, 2.517631451785567, 0.9849703487597429, -0.8291312841578632, -0.6025012867655204, 1.576906168986961, 3.3849356896173406, 2.8945845631730025, 0.6610143394298964, -1.028495465239592, -0.7665507376333208, 0.5243904626997675, 0.8731439667801656, -0.3561976680648722, -1.806145656800529, -1.8747120569364624, -0.6562296207593561, 0.3163841848677603, 0.1642435590115184, -0.1145681785560373, 0.9984263531252681, 3.148704343872552, 3.793301429099329, 0.8437542813954608, -4.485342984883645, -8.081049053253562, -6.675055559620185, -1.179108299824617, 4.001905623404333, 5.113920768654218, 2.4000902515695843, -0.6973844341095621, -1.3362920791343813, 0.13099862249028651, 1.2966388631267953, 0.7973712569460863, -0.34662770647527846, -0.42979822838665016, 0.6316355097574081, 1.3254477065480958, 0.7295022864008562, -0.08845391409288975, 0.618557432943081, 2.8491147279909352, 4.4717630056894855, 3.604690344251721, 0.9597512232688614, -0.8087196217337692, -0.14049417150048082, 1.6266399077096172, 1.9550592792754973, 0.3347924888627699, -0.9315462841811593, 0.479341747749921, 3.8056585634362836, 5.644795814618976, 3.6906287450322903, -0.5155486156191166, -3.132616659190799, -2.2101038304887624, 0.2643814340129296, 0.7851145599771336, -1.6410970992491214, -4.497954352264119, -4.78382353312255, -2.3714834066807717, 0.1443075897895923, 0.6168264997259751, -0.4289985696373505, -0.9884536240537583, -0.3079479708878537, 0.41890864760492086, 0.05559746089494706, -0.6985695963527354, -0.2726325470941666, 1.3706502640254576, 2.32066142626885, 1.196417770860128, -0.6148744598708074, -0.22812372472727155, 3.028870269120597, 6.01449614987024, 4.765183016317203, -0.9518914908191292, -6.830152855096653, -8.21214316968921, -4.744666210257576, -0.3621191144917721, 1.1670491424138647, -0.07890729297270563, -1.2072584686855656, -0.4428327427869145, 1.0171739936306958, 1.1508253635727668, 0.05388069267437513, -0.2552159486112467, 1.2445052608905323, 2.9629917070425265, 2.6404999447395547, 0.33381369509203235, -1.51088449748519, -1.0721752273647185, 0.6352244205648117, 1.2238498507163003, 0.12717009920027847, -0.7161075219673614, 0.38665682031296544, 2.38980440902609, 2.7408477760663557, 0.8509089299758704, -0.8776061651771231, -0.1626429294479906, 1.751486266498688, 1.066379921260008, -3.9007898811994908, -9.97375623739672, -11.998291357276505, -8.309880688996412, -2.4736855656958614, 0.6765348383664046, -0.011452127672451493, -1.6606343028642798, -1.4284621027558806, 0.31062367203510377, 1.2356201436724341, 0.4965324397466217, -0.3858428703080761, 0.032402658373753494, 1.0429628575407752, 0.9896991063379341, -0.12560491400659154, -0.5269491641469796, 0.6512591373804666, 1.744987291484834, 0.663669656799608, -1.854417783991064, -2.487282773284767, 0.6101667501220602, 4.937231076563496, 6.022286190760587, 2.5774517580828222, -1.8499264484798361, -2.9372601092320214, -0.49981875403312265, 1.6897760452591855, 0.7592895061643792, -1.8956882110751092, -2.774224914521253, -0.8788979416850023, 1.215583159878136, 0.9499682529176234, -0.9227614635147753, -1.6239959382470317, -0.2641996482490879, 0.9761548646212105, -0.09124050820882713, -2.601667894013609, -3.718058973910337, -2.317206927252284, -0.28619317952596557, 0.17722021210791528, -0.6014898776338542, -0.6747456795632981, 0.392637598550411, 0.8308932467167562, -0.4703245441571345, -1.7699410178812611, -0.6016723357850386, 2.2549493372863605, 2.675210428859324, -1.975634275312276, -8.842835729856828, -11.913453982861235, -8.485667514019001, -2.150638285877997, 1.3178543014274888, 0.1849417307542987, -2.2131782547056025, -2.2253589056555128, -0.07522848566996262, 1.3825462003615727, 0.8444886647339154, -0.13900014007040903, 0.053256881670932614, 0.7128036710455398, 0.21495033597391777, -1.14104269125414, -1.3364607502934713, 0.23799706924946587, 1.3961377342704506, -0.06496752918575839, -3.060261824264851, -4.205280089025924, -2.1441515923893593, 0.6012629935021813, 0.9994612022457319, -0.32097336945059846, 0.11135986222987983, 3.6682579601986673, 7.217766880395343, 6.780943340434794, 2.6405926497988217, -0.8669600443261627, -0.7184588592320451, 1.2628606880133935, 1.2455690469598437, -1.3284413189058561, -3.0698488437839786, -1.3134216706735462, 2.2454980539189253, 3.72845337826899, 1.954305233522152, -0.47079635908369943, -0.9142975443402469, 0.08012007260447293, 0.27136836133379766, -0.7655001311075993, -1.2816395492313264, -0.3582669838150923, 0.5136392111845925, -0.23305249683342438, -1.5955722441078695, -1.3609575939262242, 0.2241855494737678, 0.13863484368790582, -3.1136477864560974, -6.344976117223155, -4.790157226584158, 1.7082320880044346, 7.48527560534132, 7.059485504544597, 1.287089299765237, -3.8720892598965615, -4.264516455594112, -1.520074490093006, 0.2070855291527463, -0.34486070196182417, -1.0223288778720987, -0.3150170866216573, 0.3658242950968597, -0.7680638967841784, -2.751376269868679, -3.0298584483414484, -1.2132103178919973, 0.24332386174292733, -0.41566839823950763, -1.6365240781456247, -0.8225517379358723, 1.7086934589993203, 2.897777042626235, 1.185654923637792, -1.2327007687399334, -1.4920908694989987, -0.09971368431903448, -0.005464941818116143, -1.9222319600023188, -2.8063116127032597, -0.1446130019462526, 3.8174347282088017, 4.294063630205774, 0.23236078652391726, -3.7810625271274967, -2.948272948614173, 1.8360150356673688, 5.238134337389375, 4.101109166940149, 0.782960214360424, -0.6164940886046211, 0.5093494996561423, 1.4467017462825362, 0.6029693968900537, -0.48593920766643284, -0.0013052802667223935, 1.2515032951117242, 1.2547199975362968, 0.020640374681214487, -0.5392599634278246, 0.12134940008417983, 0.1356884589351603, -1.5611048406307204, -2.6439980086762107, -0.10215361296011996, 4.924865766528467, 7.383734489736364, 4.348165367383374, -0.876576117995219, -2.4909724435166942, 0.6954454593706165, 4.039184336701752, 3.240701341189401, -0.3591454251683983, -2.148268166522471, -0.5360734371624661, 1.4835688820223942, 1.038446827546569, -0.7702349881659721, -1.1105767202634953, 0.09601953766601543, 0.24154333920404, -1.6693757113836596, -3.155215196358019, -1.7549111014627232, 1.2699353479863844, 2.5468843639945087, 1.1969782113030707, -0.25057993715455235, 0.22704425739363415, 1.3667661750695812, 1.0028585553255982, -0.3208883090928052, -0.30012680155635907, 1.0226589190781616, 0.6900471335939602, -2.591841486678123, -5.397945658383032, -3.4412921350307637, 2.1940906991579827, 5.331463328916176, 2.0521231365957893, -4.249906470759989, -6.908675502514677, -3.9411644499811507, 0.2880784154931909, 1.216396494763122, -0.5953280953907658, -1.517990199688505, -0.30633888846403634, 0.8958611485812766, 0.46875854963884905, -0.38522353628013184, -0.13830620893805806, 0.3261837308499746, -0.6500089025285233, -2.215173462255787, -1.7410759456827225, 1.0604637840824762, 3.056713764803791, 1.9185864610952739, -0.342458890256621, -0.13183385766223882, 2.275597908870871, 2.6876882277227603, -1.0368546335765882, -5.395392631993017, -5.519391470540578, -1.6589818335140585, 1.191839277812035, 0.0466447832650921, -2.3806845029504724, -1.9924903881891334, 0.8196021233076911, 2.1026411902736655, 0.3528963609953184, -1.3318350242766281, 0.05252960569027044, 2.9478991182410854, 3.490569286490874, 0.9974693495061958, -1.3123664765565148, -1.0488897524898673, 0.35023963151641857, 0.42199881532730316, -0.509606774581157, -0.35915515144818166, 0.9193395017787186, 1.1185454086141489, -0.4541080897191707, -1.4939024587880243, -0.31388436055135743, 1.0764581366030939, -0.05714378719504527, -2.044501770478089, 0.15935754854466336, 7.858873249254064, 15.135547841187641, 14.87458182980168, 7.195784940838228, -0.685061948396578, -2.946016892019226, -0.9240960487458024, 0.5327367770060035, -0.08213755753561686, -0.2882975416916752, 1.345132587453391, 2.810127989720083, 2.091919345251367, 0.3984556020519061, 0.029950341328633657, 0.5755013577391165, -0.2644240665223143, -2.517746652573217, -3.3147035720903273, -1.2056989188088825, 1.2271494609366704, 0.8973803697706089, -1.1779155564098835, -1.3104876701533883, 1.2906966920174099, 3.2310574753009003, 2.0519454426341466, 0.029922634773537272, 0.6590170183597613, 2.9733315547332455, 2.5649397988326075, -1.7065428861053862, -5.23408254914429, -3.6089839748619754, 1.1889507806879127, 3.2760035002946584, 0.6488463758936451, -2.5890195364174753, -2.290819067168181, 0.32162196778318086, 1.2174448161071725, -0.42755646831025357, -1.643534353893593, -0.5959101987159799, 0.8935832413443272, 0.6531502773724245, -0.4641435881432692, -0.3946134720420299, 0.5713468500670821, 0.5550424685529121, -0.23393635717530648, 0.4972608033227076, 2.846164533477498, 3.2935999708503614, -0.38136832165657963, -4.70109028689389, -4.107557838093124, 1.3902552783068365, 5.420117971977065, 3.23840151367689, -2.14517425833045, -4.1347398131874975, -1.1424536623490211, 2.1313805436378956, 1.7263405567510048, -0.6833389388674416, -1.3348967351026362, -0.06334444005187245, 0.3598275024088986, -0.7462332941638676, -0.9757214062278241, 0.7959266882445593, 2.1044757474698996, 0.6479284134568711, -1.8084105631317415, -1.7686920914317392, 0.8093283845138636, 2.4749669959519385, 1.4391677322851069, -0.06814968512189762, 0.29515313495532064, 1.2678171689300026, 0.45832836613249983, -1.1732671671774577, -0.5536443652527347, 2.024289900226405, 2.1924010389059774, -2.2033582052222367, -6.941291638788552, -6.465088120955452, -1.6755933959068292, 0.8417147309716676, -2.3997074076306903, -7.151223762286811, -7.3014696086545685, -2.811690308416532, 1.0653618748641942, 1.1815926850866698, -0.33600781718160283, -0.5368742195714266, 0.09568055712426787, -0.34660814760615305, -1.3463892156732038, -0.9309916489495338, 0.5685901757971975, 0.7579979657099599, -0.7367547775596075, -1.3632671341543923, 0.06348733713393027, 0.8386397081443112, -1.5692833293683988, -4.796702250288309, -4.208651540406219, 0.1749738018182596, 2.942414754422798, 0.6768494859576066, -2.9992779353791814, -2.3605169918943023, 2.399998290869724, 5.578171453847337, 3.9517576413334234, 0.634229789989584, -0.2615575996037579, 0.49663617237679925, -0.48373230066827694, -3.0939089008538954], 'positive_zeros': ['1.09584137482545198114888876525', '2.78192838926539079503707284911', '3.64552743687174386099100035480', '5.01033684996259965624694393765', '5.64787459993405800463780930957', '8.099402962230463474029440397856', '8.80219562692880015885221595157', '10.12212053763246949703620479151', '10.89856965832477291516552823854', '11.66896314232889303884263983046', '13.161103229941794493408093039699', '14.06587018474188240005534629522', '14.95332430676551457130149565062', '15.88440556952594917564356200704', '17.336860564743060238996729444476', '18.35863652231004651909627426984', '19.44726273119207582070633656551', '20.443481045548341718574469885987', '21.19992176263328212457992015370', '21.70264289520853781457971037664', '22.857992083807308266965648370353', '23.797548498583415137919906551218', '24.962422571710968230059433361094', '26.31009089807919864768086890939', '27.13848004903082126849325166526', '27.844631013500337566276279869938', '28.61165667793073111029256040337', '29.81455621582242825562550453422', '30.794064481127375588500112348384', '31.378804759453191555024084593550', '32.43277970195352738395072340520', '33.004333632082188564255589125136', '34.09010961035558958517910923378', '35.17816644998074262198660501580', '36.787202405763090495341858360893', '37.18839315094429770245399673749', '37.75519602361311927302364756937', '38.89322223847765738126632382338', '39.58777728421791075677602124618', '40.21679357512782925970314190535', '41.27269456179600835508908683634', '42.34300041559742122284027231614', '43.21272454180230288509127554859', '44.18731654600099165508621345508', '45.14547564546797894162648233600', '45.729863597371054056280429461830', '46.96765182666997773574233111673', '47.683562579840481777044125349948', '48.36908073911110533855892146384', '49.544806166672674022703292644392', '50.10145556152828357969357687543', '50.390231659328122805690426499971', '51.61650626378641373915561609031', '52.87280856261954183969334832813', '53.97432365047157122269470787514', '54.66399594699935815485614545071', '55.516480595630060961033937388239', '56.08380332165423822209035497548', '57.123382277199822775876094169356', '57.33785775755542758350759797792', '58.87518076937002255002951743393', '59.40084256423418564864602174349', '60.36714795879826328453117694026', '60.87966846673132928161890771227', '62.14851887741107995556291973640', '63.08590063384134890096887307799', '63.574068802207047350779510838887', '64.97413197713750094286388858399', '65.511076015852494469996610217917', '66.34988507019310871222228636919', '66.895613803289448790602115601300', '67.56228273938713749992655052376', '68.62488679462610433978519656225', '69.094656650764886349246647003306', '70.26813393667161831538144318169', '71.59871630225044762105753550882', '72.17308619464031919139088978186', '72.90030040026769663632353947794', '73.76619525558147667106511096090', '74.14844350612001380756058902412', '75.35408173764912840563267548273', '76.13153906710412127492051567137', '76.9038033456375842954741263619', '77.434028702333888214036377401362', '78.556448506023932611446730637763', '79.08901129508099503858102818902', '79.77926196398362236645805458003', '81.445863310141577887610482828739', '81.873019354122416862896851367353', '82.75761480493080811948892726163', '83.57576347658043584433886996504', '84.05230963561614137423339879108', '84.96510395564904786460199334053', '85.48887793077558020215650665742', '86.33540002121348826229798946652', '87.14362306063178164030476213585', '88.29229182455711254488110046851', '89.11447974814896701256856226613', '89.779178107404035075634047871361', '90.73301893465861088901550399650', '91.41272896352514502776836081966', '92.23366321174254860976274725158', '92.7993931820397478982353374456', '94.13559815067656665825106222463', '94.46427795038709353774626233978', '95.20924632902912891158959053411', '95.85325519011233052222371601260', '96.63164276397818384440043949831', '97.40031483070933086839893361156', '98.88974819588167437881037663921', '99.39727533271161253241555322733', '100.32289203487434627721568860658', '101.18226753242371648862610643818', '101.53888886798049855968881103133', '102.239991195378416801845313470332', '103.08573704105524676694511937168', '103.742485927083999746017495823574', '104.914572232110672849020222219875', '105.54369439634212437019308796955', '105.920688869063285957289373259136', '107.3912435918774365722133003736', '107.92493940978430361987170404597', '108.60714972272860126026965100125', '109.49013239577924851200656179240', '110.54807775208032703432887874223', '111.22357435580145561680107776262', '111.66615893405190527192991488692', '112.59046654401705855916707261736', '113.07179492965643009196078064327', '114.013635441927133422883870163189', '114.397480832313415323519004012798', '115.55245740574197690373349725157', '116.62506871639288027313165026665', '117.72932325514757209306373457496', '118.01796504965520383792029187058', '118.84229666856330817881397342831', '119.22943252391077858285638270571', '120.52932416413815783271438087501', '120.83535191000733200522543575546', '121.67174119915888560355229193909', '122.636969921186056031402071127566', '123.46503527196021247067435414628', '123.74852967993517399471756134476', '124.698466567856790418752666059338', '125.639294936339762860431682456559', '126.45185052547068583182648970847', '127.59989162337988825785578983463', '128.02130268566454364715855863387', '128.88859702496800033878048551170', '129.37533309813844706531167911857', '130.31784042581413315820085724006', '130.88862673828896035121384173630', '131.28972362574894898086238481510', '132.19463822983999378936728632691', '133.37737690935796524637323440673', '134.01124587227730441474010926551', '134.96789519145082537186536465191', '135.69149748317119193065981646753', '136.423340946247933973424940818847', '137.16201693127251019301970121876', '137.55947901469834364355088145916', '138.61608003653463192657449376069', '139.59768853212361477648587882834', '139.93856542547146435717319458547', '140.85072891690639709597646125401', '141.32867457637416660145864770464', '141.96285195351222208690759231048', '143.007836574226400019737328262675', '143.85145787745970572468561919593', '144.97141238902158361615316991632', '145.5336982575801709842528280981', '146.30795899323824933556484237155', '147.01773671708179953461606888291', '147.560733069745465942751019999', '147.98162074651166538420907971210', '148.95606318101699770271985232698', '149.937376146330335563004698713', '150.33410016733504027016809884975', '151.18342076875869921971380918788', '152.3227748249428026953947393899', '152.81807510252339698978170382776', '153.66153231044890541821069378610', '154.42040946517700153801632106998', '154.99406501784678964274503956230', '156.04385340427654247163604460375', '156.783263290467111649484513969014', '157.32716413771337230354830464839', '157.90872686245917856996861748947', '158.67332365962583200801936061268', '159.42696859801115065570268752516', '159.99219822411472095258329020113', '160.61558271555578325812430395932', '162.150876957039691663515460348341', '162.949525777044654830194762324568', '163.41021720655788092974699741170', '163.83328097169968710280302234749', '165.14774476401039046162497370500', '165.28900809086467391429063242720', '165.88982966870759516546115863225', '167.005047733950272322901218980941', '167.634822559063646174331855039644', '168.30301811860068177631852163721', '169.384537155166399303723817442630', '169.5561816374569707481649609044', '170.51705555738080807018898874922', '171.48292028341182266665733995481', '172.239240789005038889318416106994', '173.08381835984985063989714729826', '173.684717500636516421266246025105', '174.478977162947710534057368205566', '175.16940029315114357425894742901', '175.75146196440186578885176055660', '176.44878704219649706592867536267', '176.77415931368194883308385830218', '177.78854553665773444261116869326', '178.67923862921880615866260268368', '179.55911820203619703314361266503', '180.39991402064980043040274115584', '181.15518292108104893002927398834', '181.89070728192073362189110562948', '182.3127421358686931808536303342', '183.00832812740318154920700191358', '183.82540472305088605471280785437', '184.598617735585281181099469812406', '185.598041554774141862362098312177', '185.84542399920108736875025543483', '186.64109287794706428868312707480', '187.26070941726046891760866159700', '187.997347461713097191480838819511', '189.19064126445715994655714214222', '189.51545957906069112925793204855', '190.81971493005017583217484751665', '191.482092604204966628790001143758', '192.117019418615224880573372353876', '192.373844590671826269762613677403', '193.31432767013761881954479199494', '193.92416979054831810707630712877', '194.67629835561505547460543912757', '195.15780964336732077675795718215', '196.23823699902847940351971404160', '196.92578539074414705049170404233', '197.66770818298297440691212456651', '198.85111622972172221255515429836', '199.17134072504989125991803555956', '199.61158254710953784421460050981'], 'prelabel': '1-185-185.107-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.88101108700563, 'root_angle': -0.16849236323207636, 'root_number': '0.863143377248258078788256848696-0.504958919430552526558438984159*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.084246181616', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.47084657774843991913675474258-0.339407286675341655175641453916*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.09584137483', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.78192838927', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.64552743687', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 19.88101108700563, 'bad_primes': [5, 37], 'central_character': '185.107', 'conductor': 185, 'conductor_radical': 185, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/185/107'], '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': '1-185-185.107-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-185-185.107-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.88101108700563, 'root_angle': -0.08424618161603818, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09584137483', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_185.107', 'Lhash_array': ['dirichlet_L_185.107'], 'label': '1-185-185.107-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/185/107'}