Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [156,3,Mod(103,156)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(156, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("156.103");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 156 = 2^{2} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 156.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.25069212402\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 103.9 | ||
Character | \(\chi\) | \(=\) | 156.103 |
Dual form | 156.3.e.c.103.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/156\mathbb{Z}\right)^\times\).
\(n\) | \(53\) | \(79\) | \(145\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.570481 | − | 1.91691i | −0.285241 | − | 0.958456i | ||||
\(3\) | − | 1.73205i | − | 0.577350i | ||||||
\(4\) | −3.34910 | + | 2.18712i | −0.837276 | + | 0.546781i | ||||
\(5\) | 7.79890i | 1.55978i | 0.625917 | + | 0.779890i | \(0.284725\pi\) | ||||
−0.625917 | + | 0.779890i | \(0.715275\pi\) | |||||||
\(6\) | −3.32019 | + | 0.988102i | −0.553365 | + | 0.164684i | ||||
\(7\) | 7.84779 | 1.12111 | 0.560557 | − | 0.828116i | \(-0.310587\pi\) | ||||
0.560557 | + | 0.828116i | \(0.310587\pi\) | |||||||
\(8\) | 6.10312 | + | 5.17222i | 0.762890 | + | 0.646528i | ||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 14.9498 | − | 4.44912i | 1.49498 | − | 0.444912i | ||||
\(11\) | 13.1778 | 1.19798 | 0.598990 | − | 0.800756i | \(-0.295569\pi\) | ||||
0.598990 | + | 0.800756i | \(0.295569\pi\) | |||||||
\(12\) | 3.78821 | + | 5.80082i | 0.315684 | + | 0.483401i | ||||
\(13\) | −10.3889 | + | 7.81476i | −0.799147 | + | 0.601136i | ||||
\(14\) | −4.47702 | − | 15.0435i | −0.319787 | − | 1.07454i | ||||
\(15\) | 13.5081 | 0.900539 | ||||||||
\(16\) | 6.43298 | − | 14.6498i | 0.402061 | − | 0.915613i | ||||
\(17\) | 22.5790 | 1.32818 | 0.664089 | − | 0.747654i | \(-0.268820\pi\) | ||||
0.664089 | + | 0.747654i | \(0.268820\pi\) | |||||||
\(18\) | 1.71144 | + | 5.75074i | 0.0950802 | + | 0.319485i | ||||
\(19\) | −26.2312 | −1.38059 | −0.690295 | − | 0.723528i | \(-0.742519\pi\) | ||||
−0.690295 | + | 0.723528i | \(0.742519\pi\) | |||||||
\(20\) | −17.0572 | − | 26.1193i | −0.852858 | − | 1.30597i | ||||
\(21\) | − | 13.5928i | − | 0.647275i | ||||||
\(22\) | −7.51768 | − | 25.2607i | −0.341713 | − | 1.14821i | ||||
\(23\) | 10.4194i | 0.453016i | 0.974009 | + | 0.226508i | \(0.0727309\pi\) | ||||
−0.974009 | + | 0.226508i | \(0.927269\pi\) | |||||||
\(24\) | 8.95855 | − | 10.5709i | 0.373273 | − | 0.440455i | ||||
\(25\) | −35.8228 | −1.43291 | ||||||||
\(26\) | 20.9069 | + | 15.4565i | 0.804111 | + | 0.594479i | ||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | −26.2831 | + | 17.1641i | −0.938681 | + | 0.613004i | ||||
\(29\) | 37.2030 | 1.28286 | 0.641432 | − | 0.767180i | \(-0.278341\pi\) | ||||
0.641432 | + | 0.767180i | \(0.278341\pi\) | |||||||
\(30\) | −7.70611 | − | 25.8938i | −0.256870 | − | 0.863127i | ||||
\(31\) | 49.6331 | 1.60107 | 0.800534 | − | 0.599287i | \(-0.204549\pi\) | ||||
0.800534 | + | 0.599287i | \(0.204549\pi\) | |||||||
\(32\) | −31.7523 | − | 3.97401i | −0.992259 | − | 0.124188i | ||||
\(33\) | − | 22.8246i | − | 0.691654i | ||||||
\(34\) | −12.8809 | − | 43.2820i | −0.378850 | − | 1.27300i | ||||
\(35\) | 61.2042i | 1.74869i | ||||||||
\(36\) | 10.0473 | − | 6.56137i | 0.279092 | − | 0.182260i | ||||
\(37\) | 38.6578i | 1.04481i | 0.852699 | + | 0.522403i | \(0.174964\pi\) | ||||
−0.852699 | + | 0.522403i | \(0.825036\pi\) | |||||||
\(38\) | 14.9644 | + | 50.2829i | 0.393800 | + | 1.32323i | ||||
\(39\) | 13.5356 | + | 17.9941i | 0.347066 | + | 0.461388i | ||||
\(40\) | −40.3376 | + | 47.5976i | −1.00844 | + | 1.18994i | ||||
\(41\) | 11.4818i | 0.280045i | 0.990148 | + | 0.140022i | \(0.0447175\pi\) | ||||
−0.990148 | + | 0.140022i | \(0.955283\pi\) | |||||||
\(42\) | −26.0562 | + | 7.75442i | −0.620385 | + | 0.184629i | ||||
\(43\) | − | 67.3590i | − | 1.56649i | −0.621714 | − | 0.783244i | \(-0.713564\pi\) | ||
0.621714 | − | 0.783244i | \(-0.286436\pi\) | |||||||
\(44\) | −44.1337 | + | 28.8214i | −1.00304 | + | 0.655033i | ||||
\(45\) | − | 23.3967i | − | 0.519927i | ||||||
\(46\) | 19.9730 | − | 5.94405i | 0.434196 | − | 0.129218i | ||||
\(47\) | 10.7509 | 0.228742 | 0.114371 | − | 0.993438i | \(-0.463515\pi\) | ||||
0.114371 | + | 0.993438i | \(0.463515\pi\) | |||||||
\(48\) | −25.3742 | − | 11.1422i | −0.528629 | − | 0.232130i | ||||
\(49\) | 12.5879 | 0.256895 | ||||||||
\(50\) | 20.4362 | + | 68.6692i | 0.408725 | + | 1.37338i | ||||
\(51\) | − | 39.1080i | − | 0.766824i | ||||||
\(52\) | 17.7017 | − | 48.8943i | 0.340417 | − | 0.940275i | ||||
\(53\) | −57.9959 | −1.09426 | −0.547131 | − | 0.837047i | \(-0.684280\pi\) | ||||
−0.547131 | + | 0.837047i | \(0.684280\pi\) | |||||||
\(54\) | 9.96057 | − | 2.96431i | 0.184455 | − | 0.0548946i | ||||
\(55\) | 102.772i | 1.86859i | ||||||||
\(56\) | 47.8961 | + | 40.5905i | 0.855287 | + | 0.724831i | ||||
\(57\) | 45.4338i | 0.797084i | ||||||||
\(58\) | −21.2236 | − | 71.3150i | −0.365925 | − | 1.22957i | ||||
\(59\) | −16.0034 | −0.271244 | −0.135622 | − | 0.990761i | \(-0.543303\pi\) | ||||
−0.135622 | + | 0.990761i | \(0.543303\pi\) | |||||||
\(60\) | −45.2400 | + | 29.5439i | −0.754000 | + | 0.492398i | ||||
\(61\) | −55.0061 | −0.901739 | −0.450870 | − | 0.892590i | \(-0.648886\pi\) | ||||
−0.450870 | + | 0.892590i | \(0.648886\pi\) | |||||||
\(62\) | −28.3148 | − | 95.1423i | −0.456690 | − | 1.53455i | ||||
\(63\) | −23.5434 | −0.373704 | ||||||||
\(64\) | 10.4962 | + | 63.1334i | 0.164004 | + | 0.986460i | ||||
\(65\) | −60.9466 | − | 81.0221i | −0.937639 | − | 1.24649i | ||||
\(66\) | −43.7527 | + | 13.0210i | −0.662920 | + | 0.197288i | ||||
\(67\) | −36.6889 | −0.547596 | −0.273798 | − | 0.961787i | \(-0.588280\pi\) | ||||
−0.273798 | + | 0.961787i | \(0.588280\pi\) | |||||||
\(68\) | −75.6194 | + | 49.3831i | −1.11205 | + | 0.726222i | ||||
\(69\) | 18.0469 | 0.261549 | ||||||||
\(70\) | 117.323 | − | 34.9158i | 1.67604 | − | 0.498797i | ||||
\(71\) | −56.5184 | −0.796033 | −0.398017 | − | 0.917378i | \(-0.630301\pi\) | ||||
−0.398017 | + | 0.917378i | \(0.630301\pi\) | |||||||
\(72\) | −18.3094 | − | 15.5167i | −0.254297 | − | 0.215509i | ||||
\(73\) | − | 37.3642i | − | 0.511839i | −0.966698 | − | 0.255919i | \(-0.917622\pi\) | ||
0.966698 | − | 0.255919i | \(-0.0823782\pi\) | |||||||
\(74\) | 74.1036 | − | 22.0535i | 1.00140 | − | 0.298021i | ||||
\(75\) | 62.0470i | 0.827293i | ||||||||
\(76\) | 87.8510 | − | 57.3709i | 1.15593 | − | 0.754880i | ||||
\(77\) | 103.417 | 1.34307 | ||||||||
\(78\) | 26.7714 | − | 36.2118i | 0.343223 | − | 0.464254i | ||||
\(79\) | − | 57.2222i | − | 0.724332i | −0.932114 | − | 0.362166i | \(-0.882037\pi\) | ||
0.932114 | − | 0.362166i | \(-0.117963\pi\) | |||||||
\(80\) | 114.252 | + | 50.1701i | 1.42815 | + | 0.627127i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 22.0097 | − | 6.55017i | 0.268411 | − | 0.0798801i | ||||
\(83\) | −14.2141 | −0.171255 | −0.0856273 | − | 0.996327i | \(-0.527289\pi\) | ||||
−0.0856273 | + | 0.996327i | \(0.527289\pi\) | |||||||
\(84\) | 29.7291 | + | 45.5236i | 0.353918 | + | 0.541948i | ||||
\(85\) | 176.091i | 2.07166i | ||||||||
\(86\) | −129.121 | + | 38.4270i | −1.50141 | + | 0.446826i | ||||
\(87\) | − | 64.4376i | − | 0.740662i | ||||||
\(88\) | 80.4256 | + | 68.1584i | 0.913928 | + | 0.774528i | ||||
\(89\) | 10.3684i | 0.116498i | 0.998302 | + | 0.0582492i | \(0.0185518\pi\) | ||||
−0.998302 | + | 0.0582492i | \(0.981448\pi\) | |||||||
\(90\) | −44.8494 | + | 13.3474i | −0.498327 | + | 0.148304i | ||||
\(91\) | −81.5300 | + | 61.3287i | −0.895934 | + | 0.673941i | ||||
\(92\) | −22.7884 | − | 34.8955i | −0.247700 | − | 0.379299i | ||||
\(93\) | − | 85.9671i | − | 0.924377i | ||||||
\(94\) | −6.13316 | − | 20.6085i | −0.0652464 | − | 0.219239i | ||||
\(95\) | − | 204.575i | − | 2.15342i | ||||||
\(96\) | −6.88320 | + | 54.9966i | −0.0717000 | + | 0.572881i | ||||
\(97\) | − | 30.8813i | − | 0.318364i | −0.987249 | − | 0.159182i | \(-0.949114\pi\) | ||
0.987249 | − | 0.159182i | \(-0.0508856\pi\) | |||||||
\(98\) | −7.18114 | − | 24.1298i | −0.0732770 | − | 0.246223i | ||||
\(99\) | −39.5334 | −0.399327 | ||||||||
\(100\) | 119.974 | − | 78.3490i | 1.19974 | − | 0.783490i | ||||
\(101\) | 136.133 | 1.34785 | 0.673925 | − | 0.738799i | \(-0.264607\pi\) | ||||
0.673925 | + | 0.738799i | \(0.264607\pi\) | |||||||
\(102\) | −74.9666 | + | 22.3104i | −0.734967 | + | 0.218729i | ||||
\(103\) | − | 124.738i | − | 1.21105i | −0.795825 | − | 0.605526i | \(-0.792963\pi\) | ||
0.795825 | − | 0.605526i | \(-0.207037\pi\) | |||||||
\(104\) | −103.825 | − | 6.03928i | −0.998313 | − | 0.0580700i | ||||
\(105\) | 106.009 | 1.00961 | ||||||||
\(106\) | 33.0856 | + | 111.173i | 0.312128 | + | 1.04880i | ||||
\(107\) | − | 53.3555i | − | 0.498650i | −0.968420 | − | 0.249325i | \(-0.919791\pi\) | ||
0.968420 | − | 0.249325i | \(-0.0802087\pi\) | |||||||
\(108\) | −11.3646 | − | 17.4024i | −0.105228 | − | 0.161134i | ||||
\(109\) | − | 50.9829i | − | 0.467733i | −0.972269 | − | 0.233867i | \(-0.924862\pi\) | ||
0.972269 | − | 0.233867i | \(-0.0751379\pi\) | |||||||
\(110\) | 197.005 | − | 58.6296i | 1.79096 | − | 0.532996i | ||||
\(111\) | 66.9573 | 0.603219 | ||||||||
\(112\) | 50.4847 | − | 114.969i | 0.450756 | − | 1.02651i | ||||
\(113\) | −33.1089 | −0.293000 | −0.146500 | − | 0.989211i | \(-0.546801\pi\) | ||||
−0.146500 | + | 0.989211i | \(0.546801\pi\) | |||||||
\(114\) | 87.0926 | − | 25.9191i | 0.763970 | − | 0.227361i | ||||
\(115\) | −81.2595 | −0.706605 | ||||||||
\(116\) | −124.597 | + | 81.3677i | −1.07411 | + | 0.701446i | ||||
\(117\) | 31.1667 | − | 23.4443i | 0.266382 | − | 0.200379i | ||||
\(118\) | 9.12964 | + | 30.6771i | 0.0773698 | + | 0.259976i | ||||
\(119\) | 177.195 | 1.48904 | ||||||||
\(120\) | 82.4415 | + | 69.8668i | 0.687013 | + | 0.582224i | ||||
\(121\) | 52.6540 | 0.435157 | ||||||||
\(122\) | 31.3799 | + | 105.442i | 0.257213 | + | 0.864277i | ||||
\(123\) | 19.8871 | 0.161684 | ||||||||
\(124\) | −166.226 | + | 108.554i | −1.34054 | + | 0.875434i | ||||
\(125\) | − | 84.4062i | − | 0.675250i | ||||||
\(126\) | 13.4311 | + | 45.1306i | 0.106596 | + | 0.358179i | ||||
\(127\) | − | 184.395i | − | 1.45193i | −0.687733 | − | 0.725963i | \(-0.741394\pi\) | ||
0.687733 | − | 0.725963i | \(-0.258606\pi\) | |||||||
\(128\) | 115.033 | − | 56.1368i | 0.898698 | − | 0.438569i | ||||
\(129\) | −116.669 | −0.904412 | ||||||||
\(130\) | −120.543 | + | 163.051i | −0.927256 | + | 1.25424i | ||||
\(131\) | − | 9.22179i | − | 0.0703953i | −0.999380 | − | 0.0351977i | \(-0.988794\pi\) | ||
0.999380 | − | 0.0351977i | \(-0.0112061\pi\) | |||||||
\(132\) | 49.9202 | + | 76.4419i | 0.378183 | + | 0.579105i | ||||
\(133\) | −205.857 | −1.54780 | ||||||||
\(134\) | 20.9303 | + | 70.3295i | 0.156197 | + | 0.524847i | ||||
\(135\) | −40.5243 | −0.300180 | ||||||||
\(136\) | 137.803 | + | 116.784i | 1.01325 | + | 0.858704i | ||||
\(137\) | − | 25.1044i | − | 0.183244i | −0.995794 | − | 0.0916218i | \(-0.970795\pi\) | ||
0.995794 | − | 0.0916218i | \(-0.0292051\pi\) | |||||||
\(138\) | −10.2954 | − | 34.5942i | −0.0746043 | − | 0.250683i | ||||
\(139\) | 122.678i | 0.882578i | 0.897365 | + | 0.441289i | \(0.145479\pi\) | ||||
−0.897365 | + | 0.441289i | \(0.854521\pi\) | |||||||
\(140\) | −133.861 | − | 204.979i | −0.956151 | − | 1.46414i | ||||
\(141\) | − | 18.6210i | − | 0.132064i | ||||||
\(142\) | 32.2427 | + | 108.341i | 0.227061 | + | 0.762963i | ||||
\(143\) | −136.903 | + | 102.981i | −0.957362 | + | 0.720149i | ||||
\(144\) | −19.2989 | + | 43.9494i | −0.134020 | + | 0.305204i | ||||
\(145\) | 290.143i | 2.00099i | ||||||||
\(146\) | −71.6239 | + | 21.3156i | −0.490575 | + | 0.145997i | ||||
\(147\) | − | 21.8028i | − | 0.148319i | ||||||
\(148\) | −84.5494 | − | 129.469i | −0.571280 | − | 0.874790i | ||||
\(149\) | − | 24.4303i | − | 0.163962i | −0.996634 | − | 0.0819809i | \(-0.973875\pi\) | ||
0.996634 | − | 0.0819809i | \(-0.0261246\pi\) | |||||||
\(150\) | 118.939 | − | 35.3966i | 0.792924 | − | 0.235977i | ||||
\(151\) | 163.895 | 1.08540 | 0.542700 | − | 0.839927i | \(-0.317402\pi\) | ||||
0.542700 | + | 0.839927i | \(0.317402\pi\) | |||||||
\(152\) | −160.092 | − | 135.674i | −1.05324 | − | 0.892590i | ||||
\(153\) | −67.7371 | −0.442726 | ||||||||
\(154\) | −58.9972 | − | 198.240i | −0.383099 | − | 1.28728i | ||||
\(155\) | 387.084i | 2.49731i | ||||||||
\(156\) | −84.6874 | − | 30.6602i | −0.542868 | − | 0.196540i | ||||
\(157\) | 148.220 | 0.944077 | 0.472039 | − | 0.881578i | \(-0.343518\pi\) | ||||
0.472039 | + | 0.881578i | \(0.343518\pi\) | |||||||
\(158\) | −109.690 | + | 32.6442i | −0.694240 | + | 0.206609i | ||||
\(159\) | 100.452i | 0.631773i | ||||||||
\(160\) | 30.9929 | − | 247.633i | 0.193706 | − | 1.54771i | ||||
\(161\) | 81.7690i | 0.507882i | ||||||||
\(162\) | −5.13433 | − | 17.2522i | −0.0316934 | − | 0.106495i | ||||
\(163\) | −67.4230 | −0.413638 | −0.206819 | − | 0.978379i | \(-0.566311\pi\) | ||||
−0.206819 | + | 0.978379i | \(0.566311\pi\) | |||||||
\(164\) | −25.1122 | − | 38.4539i | −0.153123 | − | 0.234475i | ||||
\(165\) | 178.007 | 1.07883 | ||||||||
\(166\) | 8.10889 | + | 27.2472i | 0.0488487 | + | 0.164140i | ||||
\(167\) | −148.240 | −0.887668 | −0.443834 | − | 0.896109i | \(-0.646382\pi\) | ||||
−0.443834 | + | 0.896109i | \(0.646382\pi\) | |||||||
\(168\) | 70.3049 | − | 82.9584i | 0.418481 | − | 0.493800i | ||||
\(169\) | 46.8589 | − | 162.374i | 0.277272 | − | 0.960792i | ||||
\(170\) | 337.552 | − | 100.457i | 1.98560 | − | 0.590923i | ||||
\(171\) | 78.6936 | 0.460197 | ||||||||
\(172\) | 147.322 | + | 225.592i | 0.856526 | + | 1.31158i | ||||
\(173\) | 23.5907 | 0.136362 | 0.0681811 | − | 0.997673i | \(-0.478280\pi\) | ||||
0.0681811 | + | 0.997673i | \(0.478280\pi\) | |||||||
\(174\) | −123.521 | + | 36.7604i | −0.709892 | + | 0.211267i | ||||
\(175\) | −281.130 | −1.60646 | ||||||||
\(176\) | 84.7724 | − | 193.052i | 0.481661 | − | 1.09689i | ||||
\(177\) | 27.7187i | 0.156603i | ||||||||
\(178\) | 19.8752 | − | 5.91496i | 0.111659 | − | 0.0332301i | ||||
\(179\) | − | 87.8770i | − | 0.490933i | −0.969405 | − | 0.245466i | \(-0.921059\pi\) | ||
0.969405 | − | 0.245466i | \(-0.0789411\pi\) | |||||||
\(180\) | 51.1715 | + | 78.3579i | 0.284286 | + | 0.435322i | ||||
\(181\) | −156.626 | −0.865338 | −0.432669 | − | 0.901553i | \(-0.642428\pi\) | ||||
−0.432669 | + | 0.901553i | \(0.642428\pi\) | |||||||
\(182\) | 164.073 | + | 121.299i | 0.901500 | + | 0.666478i | ||||
\(183\) | 95.2734i | 0.520619i | ||||||||
\(184\) | −53.8912 | + | 63.5906i | −0.292887 | + | 0.345601i | ||||
\(185\) | −301.488 | −1.62967 | ||||||||
\(186\) | −164.791 | + | 49.0426i | −0.885975 | + | 0.263670i | ||||
\(187\) | 297.541 | 1.59113 | ||||||||
\(188\) | −36.0057 | + | 23.5135i | −0.191520 | + | 0.125072i | ||||
\(189\) | 40.7783i | 0.215758i | ||||||||
\(190\) | −392.151 | + | 116.706i | −2.06395 | + | 0.614242i | ||||
\(191\) | − | 365.952i | − | 1.91598i | −0.286800 | − | 0.957990i | \(-0.592591\pi\) | ||
0.286800 | − | 0.957990i | \(-0.407409\pi\) | |||||||
\(192\) | 109.350 | − | 18.1800i | 0.569533 | − | 0.0946876i | ||||
\(193\) | − | 28.6209i | − | 0.148295i | −0.997247 | − | 0.0741473i | \(-0.976377\pi\) | ||
0.997247 | − | 0.0741473i | \(-0.0236235\pi\) | |||||||
\(194\) | −59.1967 | + | 17.6172i | −0.305138 | + | 0.0908103i | ||||
\(195\) | −140.334 | + | 105.563i | −0.719663 | + | 0.541346i | ||||
\(196\) | −42.1581 | + | 27.5312i | −0.215092 | + | 0.140465i | ||||
\(197\) | − | 312.113i | − | 1.58433i | −0.610307 | − | 0.792165i | \(-0.708954\pi\) | ||
0.610307 | − | 0.792165i | \(-0.291046\pi\) | |||||||
\(198\) | 22.5530 | + | 75.7820i | 0.113904 | + | 0.382737i | ||||
\(199\) | 155.166i | 0.779729i | 0.920872 | + | 0.389865i | \(0.127478\pi\) | ||||
−0.920872 | + | 0.389865i | \(0.872522\pi\) | |||||||
\(200\) | −218.631 | − | 185.284i | −1.09316 | − | 0.926418i | ||||
\(201\) | 63.5471i | 0.316155i | ||||||||
\(202\) | −77.6613 | − | 260.955i | −0.384462 | − | 1.29186i | ||||
\(203\) | 291.962 | 1.43824 | ||||||||
\(204\) | 85.5341 | + | 130.977i | 0.419285 | + | 0.642043i | ||||
\(205\) | −89.5457 | −0.436808 | ||||||||
\(206\) | −239.113 | + | 71.1609i | −1.16074 | + | 0.345441i | ||||
\(207\) | − | 31.2581i | − | 0.151005i | ||||||
\(208\) | 47.6531 | + | 202.468i | 0.229102 | + | 0.973403i | ||||
\(209\) | −345.669 | −1.65392 | ||||||||
\(210\) | −60.4760 | − | 203.209i | −0.287981 | − | 0.967664i | ||||
\(211\) | 294.581i | 1.39612i | 0.716040 | + | 0.698059i | \(0.245953\pi\) | ||||
−0.716040 | + | 0.698059i | \(0.754047\pi\) | |||||||
\(212\) | 194.234 | − | 126.844i | 0.916200 | − | 0.598322i | ||||
\(213\) | 97.8927i | 0.459590i | ||||||||
\(214\) | −102.278 | + | 30.4383i | −0.477934 | + | 0.142235i | ||||
\(215\) | 525.326 | 2.44338 | ||||||||
\(216\) | −26.8757 | + | 31.7128i | −0.124424 | + | 0.146818i | ||||
\(217\) | 389.511 | 1.79498 | ||||||||
\(218\) | −97.7297 | + | 29.0848i | −0.448301 | + | 0.133416i | ||||
\(219\) | −64.7167 | −0.295510 | ||||||||
\(220\) | −224.776 | − | 344.195i | −1.02171 | − | 1.56452i | ||||
\(221\) | −234.571 | + | 176.450i | −1.06141 | + | 0.798415i | ||||
\(222\) | −38.1979 | − | 128.351i | −0.172062 | − | 0.578159i | ||||
\(223\) | −130.127 | −0.583529 | −0.291765 | − | 0.956490i | \(-0.594242\pi\) | ||||
−0.291765 | + | 0.956490i | \(0.594242\pi\) | |||||||
\(224\) | −249.185 | − | 31.1873i | −1.11243 | − | 0.139229i | ||||
\(225\) | 107.469 | 0.477638 | ||||||||
\(226\) | 18.8880 | + | 63.4669i | 0.0835753 | + | 0.280827i | ||||
\(227\) | −129.292 | −0.569567 | −0.284783 | − | 0.958592i | \(-0.591922\pi\) | ||||
−0.284783 | + | 0.958592i | \(0.591922\pi\) | |||||||
\(228\) | −99.3693 | − | 152.162i | −0.435830 | − | 0.667379i | ||||
\(229\) | 163.279i | 0.713007i | 0.934294 | + | 0.356504i | \(0.116031\pi\) | ||||
−0.934294 | + | 0.356504i | \(0.883969\pi\) | |||||||
\(230\) | 46.3570 | + | 155.767i | 0.201552 | + | 0.677250i | ||||
\(231\) | − | 179.123i | − | 0.775423i | ||||||
\(232\) | 227.055 | + | 192.422i | 0.978685 | + | 0.829407i | ||||
\(233\) | 419.074 | 1.79860 | 0.899301 | − | 0.437330i | \(-0.144076\pi\) | ||||
0.899301 | + | 0.437330i | \(0.144076\pi\) | |||||||
\(234\) | −62.7207 | − | 46.3694i | −0.268037 | − | 0.198160i | ||||
\(235\) | 83.8449i | 0.356787i | ||||||||
\(236\) | 53.5971 | − | 35.0014i | 0.227106 | − | 0.148311i | ||||
\(237\) | −99.1118 | −0.418193 | ||||||||
\(238\) | −101.087 | − | 339.668i | −0.424734 | − | 1.42718i | ||||
\(239\) | 11.5936 | 0.0485089 | 0.0242545 | − | 0.999706i | \(-0.492279\pi\) | ||||
0.0242545 | + | 0.999706i | \(0.492279\pi\) | |||||||
\(240\) | 86.8972 | − | 197.891i | 0.362072 | − | 0.824545i | ||||
\(241\) | − | 183.134i | − | 0.759892i | −0.925009 | − | 0.379946i | \(-0.875943\pi\) | ||
0.925009 | − | 0.379946i | \(-0.124057\pi\) | |||||||
\(242\) | −30.0381 | − | 100.933i | −0.124124 | − | 0.417079i | ||||
\(243\) | − | 15.5885i | − | 0.0641500i | ||||||
\(244\) | 184.221 | − | 120.305i | 0.755004 | − | 0.493054i | ||||
\(245\) | 98.1715i | 0.400700i | ||||||||
\(246\) | −11.3452 | − | 38.1219i | −0.0461188 | − | 0.154967i | ||||
\(247\) | 272.514 | − | 204.991i | 1.10329 | − | 0.829922i | ||||
\(248\) | 302.917 | + | 256.714i | 1.22144 | + | 1.03514i | ||||
\(249\) | 24.6196i | 0.0988738i | ||||||||
\(250\) | −161.799 | + | 48.1521i | −0.647197 | + | 0.192609i | ||||
\(251\) | 192.907i | 0.768555i | 0.923218 | + | 0.384278i | \(0.125549\pi\) | ||||
−0.923218 | + | 0.384278i | \(0.874451\pi\) | |||||||
\(252\) | 78.8492 | − | 51.4923i | 0.312894 | − | 0.204335i | ||||
\(253\) | 137.304i | 0.542704i | ||||||||
\(254\) | −353.468 | + | 105.194i | −1.39161 | + | 0.414148i | ||||
\(255\) | 304.999 | 1.19608 | ||||||||
\(256\) | −173.234 | − | 188.484i | −0.676694 | − | 0.736265i | ||||
\(257\) | 192.474 | 0.748925 | 0.374462 | − | 0.927242i | \(-0.377827\pi\) | ||||
0.374462 | + | 0.927242i | \(0.377827\pi\) | |||||||
\(258\) | 66.5576 | + | 223.645i | 0.257975 | + | 0.866839i | ||||
\(259\) | 303.378i | 1.17135i | ||||||||
\(260\) | 381.322 | + | 138.054i | 1.46662 | + | 0.530975i | ||||
\(261\) | −111.609 | −0.427621 | ||||||||
\(262\) | −17.6774 | + | 5.26086i | −0.0674708 | + | 0.0200796i | ||||
\(263\) | 38.1415i | 0.145025i | 0.997368 | + | 0.0725124i | \(0.0231017\pi\) | ||||
−0.997368 | + | 0.0725124i | \(0.976898\pi\) | |||||||
\(264\) | 118.054 | − | 139.301i | 0.447174 | − | 0.527656i | ||||
\(265\) | − | 452.304i | − | 1.70681i | ||||||
\(266\) | 117.438 | + | 394.610i | 0.441495 | + | 1.48350i | ||||
\(267\) | 17.9585 | 0.0672604 | ||||||||
\(268\) | 122.875 | − | 80.2433i | 0.458489 | − | 0.299415i | ||||
\(269\) | −80.2898 | −0.298475 | −0.149238 | − | 0.988801i | \(-0.547682\pi\) | ||||
−0.149238 | + | 0.988801i | \(0.547682\pi\) | |||||||
\(270\) | 23.1183 | + | 77.6815i | 0.0856234 | + | 0.287709i | ||||
\(271\) | 241.183 | 0.889975 | 0.444987 | − | 0.895537i | \(-0.353208\pi\) | ||||
0.444987 | + | 0.895537i | \(0.353208\pi\) | |||||||
\(272\) | 145.250 | − | 330.778i | 0.534009 | − | 1.21610i | ||||
\(273\) | 106.224 | + | 141.214i | 0.389100 | + | 0.517268i | ||||
\(274\) | −48.1229 | + | 14.3216i | −0.175631 | + | 0.0522685i | ||||
\(275\) | −472.066 | −1.71660 | ||||||||
\(276\) | −60.4408 | + | 39.4707i | −0.218988 | + | 0.143010i | ||||
\(277\) | 115.454 | 0.416800 | 0.208400 | − | 0.978044i | \(-0.433174\pi\) | ||||
0.208400 | + | 0.978044i | \(0.433174\pi\) | |||||||
\(278\) | 235.164 | − | 69.9857i | 0.845912 | − | 0.251747i | ||||
\(279\) | −148.899 | −0.533690 | ||||||||
\(280\) | −316.561 | + | 373.537i | −1.13058 | + | 1.33406i | ||||
\(281\) | 362.576i | 1.29031i | 0.764053 | + | 0.645153i | \(0.223206\pi\) | ||||
−0.764053 | + | 0.645153i | \(0.776794\pi\) | |||||||
\(282\) | −35.6949 | + | 10.6229i | −0.126578 | + | 0.0376700i | ||||
\(283\) | − | 239.084i | − | 0.844820i | −0.906405 | − | 0.422410i | \(-0.861184\pi\) | ||
0.906405 | − | 0.422410i | \(-0.138816\pi\) | |||||||
\(284\) | 189.286 | − | 123.613i | 0.666499 | − | 0.435256i | ||||
\(285\) | −354.333 | −1.24328 | ||||||||
\(286\) | 275.506 | + | 203.682i | 0.963309 | + | 0.712174i | ||||
\(287\) | 90.1071i | 0.313962i | ||||||||
\(288\) | 95.2568 | + | 11.9220i | 0.330753 | + | 0.0413960i | ||||
\(289\) | 220.812 | 0.764056 | ||||||||
\(290\) | 556.178 | − | 165.521i | 1.91786 | − | 0.570762i | ||||
\(291\) | −53.4880 | −0.183807 | ||||||||
\(292\) | 81.7202 | + | 125.137i | 0.279864 | + | 0.428550i | ||||
\(293\) | 439.949i | 1.50153i | 0.660569 | + | 0.750766i | \(0.270315\pi\) | ||||
−0.660569 | + | 0.750766i | \(0.729685\pi\) | |||||||
\(294\) | −41.7941 | + | 12.4381i | −0.142157 | + | 0.0423065i | ||||
\(295\) | − | 124.809i | − | 0.423081i | ||||||
\(296\) | −199.947 | + | 235.933i | −0.675496 | + | 0.797072i | ||||
\(297\) | 68.4738i | 0.230551i | ||||||||
\(298\) | −46.8307 | + | 13.9370i | −0.157150 | + | 0.0467685i | ||||
\(299\) | −81.4248 | − | 108.246i | −0.272324 | − | 0.362026i | ||||
\(300\) | −135.704 | − | 207.802i | −0.452348 | − | 0.692672i | ||||
\(301\) | − | 528.619i | − | 1.75621i | ||||||
\(302\) | −93.4992 | − | 314.173i | −0.309600 | − | 1.04031i | ||||
\(303\) | − | 235.789i | − | 0.778182i | ||||||
\(304\) | −168.745 | + | 384.282i | −0.555081 | + | 1.26409i | ||||
\(305\) | − | 428.987i | − | 1.40651i | ||||||
\(306\) | 38.6427 | + | 129.846i | 0.126283 | + | 0.424333i | ||||
\(307\) | 409.415 | 1.33360 | 0.666800 | − | 0.745237i | \(-0.267664\pi\) | ||||
0.666800 | + | 0.745237i | \(0.267664\pi\) | |||||||
\(308\) | −346.353 | + | 226.185i | −1.12452 | + | 0.734366i | ||||
\(309\) | −216.053 | −0.699202 | ||||||||
\(310\) | 742.006 | − | 220.824i | 2.39357 | − | 0.712335i | ||||
\(311\) | 298.658i | 0.960315i | 0.877182 | + | 0.480157i | \(0.159420\pi\) | ||||
−0.877182 | + | 0.480157i | \(0.840580\pi\) | |||||||
\(312\) | −10.4603 | + | 179.829i | −0.0335267 | + | 0.576376i | ||||
\(313\) | 20.3892 | 0.0651412 | 0.0325706 | − | 0.999469i | \(-0.489631\pi\) | ||||
0.0325706 | + | 0.999469i | \(0.489631\pi\) | |||||||
\(314\) | −84.5568 | − | 284.125i | −0.269289 | − | 0.904856i | ||||
\(315\) | − | 183.612i | − | 0.582897i | ||||||
\(316\) | 125.152 | + | 191.643i | 0.396051 | + | 0.606465i | ||||
\(317\) | 514.348i | 1.62255i | 0.584665 | + | 0.811275i | \(0.301226\pi\) | ||||
−0.584665 | + | 0.811275i | \(0.698774\pi\) | |||||||
\(318\) | 192.557 | − | 57.3059i | 0.605526 | − | 0.180207i | ||||
\(319\) | 490.254 | 1.53685 | ||||||||
\(320\) | −492.371 | + | 81.8591i | −1.53866 | + | 0.255810i | ||||
\(321\) | −92.4145 | −0.287896 | ||||||||
\(322\) | 156.744 | − | 46.6477i | 0.486782 | − | 0.144869i | ||||
\(323\) | −592.275 | −1.83367 | ||||||||
\(324\) | −30.1419 | + | 19.6841i | −0.0930306 | + | 0.0607534i | ||||
\(325\) | 372.160 | − | 279.947i | 1.14511 | − | 0.861375i | ||||
\(326\) | 38.4635 | + | 129.244i | 0.117986 | + | 0.396454i | ||||
\(327\) | −88.3050 | −0.270046 | ||||||||
\(328\) | −59.3866 | + | 70.0751i | −0.181057 | + | 0.213644i | ||||
\(329\) | 84.3705 | 0.256445 | ||||||||
\(330\) | −101.549 | − | 341.223i | −0.307726 | − | 1.03401i | ||||
\(331\) | −456.718 | −1.37981 | −0.689906 | − | 0.723899i | \(-0.742348\pi\) | ||||
−0.689906 | + | 0.723899i | \(0.742348\pi\) | |||||||
\(332\) | 47.6046 | − | 31.0881i | 0.143387 | − | 0.0936387i | ||||
\(333\) | − | 115.973i | − | 0.348269i | ||||||
\(334\) | 84.5684 | + | 284.164i | 0.253199 | + | 0.850790i | ||||
\(335\) | − | 286.133i | − | 0.854130i | ||||||
\(336\) | −199.132 | − | 87.4420i | −0.592653 | − | 0.260244i | ||||
\(337\) | −597.668 | −1.77349 | −0.886747 | − | 0.462254i | \(-0.847041\pi\) | ||||
−0.886747 | + | 0.462254i | \(0.847041\pi\) | |||||||
\(338\) | −337.988 | + | 2.80672i | −0.999966 | + | 0.00830391i | ||||
\(339\) | 57.3464i | 0.169163i | ||||||||
\(340\) | −385.134 | − | 589.748i | −1.13275 | − | 1.73455i | ||||
\(341\) | 654.055 | 1.91805 | ||||||||
\(342\) | −44.8932 | − | 150.849i | −0.131267 | − | 0.441078i | ||||
\(343\) | −285.755 | −0.833105 | ||||||||
\(344\) | 348.396 | − | 411.100i | 1.01278 | − | 1.19506i | ||||
\(345\) | 140.746i | 0.407958i | ||||||||
\(346\) | −13.4580 | − | 45.2212i | −0.0388960 | − | 0.130697i | ||||
\(347\) | − | 354.809i | − | 1.02251i | −0.859430 | − | 0.511253i | \(-0.829182\pi\) | ||
0.859430 | − | 0.511253i | \(-0.170818\pi\) | |||||||
\(348\) | 140.933 | + | 215.808i | 0.404980 | + | 0.620138i | ||||
\(349\) | − | 443.875i | − | 1.27185i | −0.771752 | − | 0.635923i | \(-0.780619\pi\) | ||
0.771752 | − | 0.635923i | \(-0.219381\pi\) | |||||||
\(350\) | 160.379 | + | 538.902i | 0.458227 | + | 1.53972i | ||||
\(351\) | −40.6067 | − | 53.9824i | −0.115689 | − | 0.153796i | ||||
\(352\) | −418.425 | − | 52.3687i | −1.18871 | − | 0.148775i | ||||
\(353\) | 138.241i | 0.391617i | 0.980642 | + | 0.195808i | \(0.0627331\pi\) | ||||
−0.980642 | + | 0.195808i | \(0.937267\pi\) | |||||||
\(354\) | 53.1343 | − | 15.8130i | 0.150097 | − | 0.0446695i | ||||
\(355\) | − | 440.781i | − | 1.24164i | ||||||
\(356\) | −22.6769 | − | 34.7247i | −0.0636992 | − | 0.0975414i | ||||
\(357\) | − | 306.912i | − | 0.859696i | ||||||
\(358\) | −168.452 | + | 50.1322i | −0.470538 | + | 0.140034i | ||||
\(359\) | 245.747 | 0.684533 | 0.342266 | − | 0.939603i | \(-0.388806\pi\) | ||||
0.342266 | + | 0.939603i | \(0.388806\pi\) | |||||||
\(360\) | 121.013 | − | 142.793i | 0.336147 | − | 0.396647i | ||||
\(361\) | 327.076 | 0.906028 | ||||||||
\(362\) | 89.3523 | + | 300.239i | 0.246829 | + | 0.829388i | ||||
\(363\) | − | 91.1994i | − | 0.251238i | ||||||
\(364\) | 138.919 | − | 383.712i | 0.381646 | − | 1.05415i | ||||
\(365\) | 291.400 | 0.798356 | ||||||||
\(366\) | 182.631 | − | 54.3516i | 0.498991 | − | 0.148502i | ||||
\(367\) | − | 458.704i | − | 1.24988i | −0.780674 | − | 0.624938i | \(-0.785124\pi\) | ||
0.780674 | − | 0.624938i | \(-0.214876\pi\) | |||||||
\(368\) | 152.642 | + | 67.0275i | 0.414787 | + | 0.182140i | ||||
\(369\) | − | 34.4455i | − | 0.0933483i | ||||||
\(370\) | 171.993 | + | 577.927i | 0.464847 | + | 1.56196i | ||||
\(371\) | −455.140 | −1.22679 | ||||||||
\(372\) | 188.021 | + | 287.913i | 0.505432 | + | 0.773959i | ||||
\(373\) | −269.970 | −0.723780 | −0.361890 | − | 0.932221i | \(-0.617868\pi\) | ||||
−0.361890 | + | 0.932221i | \(0.617868\pi\) | |||||||
\(374\) | −169.742 | − | 570.361i | −0.453855 | − | 1.52503i | ||||
\(375\) | −146.196 | −0.389856 | ||||||||
\(376\) | 65.6138 | + | 55.6058i | 0.174505 | + | 0.147888i | ||||
\(377\) | −386.499 | + | 290.733i | −1.02520 | + | 0.771175i | ||||
\(378\) | 78.1685 | − | 23.2633i | 0.206795 | − | 0.0615430i | ||||
\(379\) | −474.173 | −1.25112 | −0.625559 | − | 0.780177i | \(-0.715129\pi\) | ||||
−0.625559 | + | 0.780177i | \(0.715129\pi\) | |||||||
\(380\) | 447.430 | + | 685.141i | 1.17745 | + | 1.80300i | ||||
\(381\) | −319.381 | −0.838270 | ||||||||
\(382\) | −701.498 | + | 208.769i | −1.83638 | + | 0.546515i | ||||
\(383\) | −237.625 | −0.620431 | −0.310215 | − | 0.950666i | \(-0.600401\pi\) | ||||
−0.310215 | + | 0.950666i | \(0.600401\pi\) | |||||||
\(384\) | −97.2318 | − | 199.244i | −0.253208 | − | 0.518863i | ||||
\(385\) | 806.535i | 2.09490i | ||||||||
\(386\) | −54.8637 | + | 16.3277i | −0.142134 | + | 0.0422996i | ||||
\(387\) | 202.077i | 0.522163i | ||||||||
\(388\) | 67.5412 | + | 103.425i | 0.174075 | + | 0.266558i | ||||
\(389\) | 94.1823 | 0.242114 | 0.121057 | − | 0.992646i | \(-0.461372\pi\) | ||||
0.121057 | + | 0.992646i | \(0.461372\pi\) | |||||||
\(390\) | 282.412 | + | 208.787i | 0.724134 | + | 0.535352i | ||||
\(391\) | 235.259i | 0.601685i | ||||||||
\(392\) | 76.8253 | + | 65.1073i | 0.195983 | + | 0.166090i | ||||
\(393\) | −15.9726 | −0.0406428 | ||||||||
\(394\) | −598.293 | + | 178.054i | −1.51851 | + | 0.451915i | ||||
\(395\) | 446.270 | 1.12980 | ||||||||
\(396\) | 132.401 | − | 86.4643i | 0.334347 | − | 0.218344i | ||||
\(397\) | − | 418.475i | − | 1.05409i | −0.849836 | − | 0.527047i | \(-0.823299\pi\) | ||
0.849836 | − | 0.527047i | \(-0.176701\pi\) | |||||||
\(398\) | 297.440 | − | 88.5193i | 0.747336 | − | 0.222410i | ||||
\(399\) | 356.555i | 0.893621i | ||||||||
\(400\) | −230.447 | + | 524.798i | −0.576119 | + | 1.31199i | ||||
\(401\) | − | 673.251i | − | 1.67893i | −0.543413 | − | 0.839465i | \(-0.682868\pi\) | ||
0.543413 | − | 0.839465i | \(-0.317132\pi\) | |||||||
\(402\) | 121.814 | − | 36.2524i | 0.303020 | − | 0.0901802i | ||||
\(403\) | −515.634 | + | 387.871i | −1.27949 | + | 0.962460i | ||||
\(404\) | −455.923 | + | 297.740i | −1.12852 | + | 0.736979i | ||||
\(405\) | 70.1901i | 0.173309i | ||||||||
\(406\) | −166.559 | − | 559.665i | −0.410243 | − | 1.37849i | ||||
\(407\) | 509.424i | 1.25166i | ||||||||
\(408\) | 202.275 | − | 238.681i | 0.495773 | − | 0.585002i | ||||
\(409\) | 159.073i | 0.388932i | 0.980909 | + | 0.194466i | \(0.0622973\pi\) | ||||
−0.980909 | + | 0.194466i | \(0.937703\pi\) | |||||||
\(410\) | 51.0841 | + | 171.651i | 0.124595 | + | 0.418662i | ||||
\(411\) | −43.4821 | −0.105796 | ||||||||
\(412\) | 272.818 | + | 417.762i | 0.662181 | + | 1.01398i | ||||
\(413\) | −125.591 | −0.304095 | ||||||||
\(414\) | −59.9190 | + | 17.8321i | −0.144732 | + | 0.0430728i | ||||
\(415\) | − | 110.855i | − | 0.267119i | ||||||
\(416\) | 360.928 | − | 206.851i | 0.867614 | − | 0.497238i | ||||
\(417\) | 212.485 | 0.509557 | ||||||||
\(418\) | 197.198 | + | 662.617i | 0.471765 | + | 1.58521i | ||||
\(419\) | 706.798i | 1.68687i | 0.537232 | + | 0.843435i | \(0.319470\pi\) | ||||
−0.537232 | + | 0.843435i | \(0.680530\pi\) | |||||||
\(420\) | −355.034 | + | 231.854i | −0.845319 | + | 0.552034i | ||||
\(421\) | − | 181.323i | − | 0.430696i | −0.976537 | − | 0.215348i | \(-0.930911\pi\) | ||
0.976537 | − | 0.215348i | \(-0.0690885\pi\) | |||||||
\(422\) | 564.686 | − | 168.053i | 1.33812 | − | 0.398229i | ||||
\(423\) | −32.2526 | −0.0762472 | ||||||||
\(424\) | −353.956 | − | 299.968i | −0.834803 | − | 0.707471i | ||||
\(425\) | −808.844 | −1.90316 | ||||||||
\(426\) | 187.652 | − | 55.8459i | 0.440497 | − | 0.131094i | ||||
\(427\) | −431.676 | −1.01095 | ||||||||
\(428\) | 116.695 | + | 178.693i | 0.272652 | + | 0.417507i | ||||
\(429\) | 178.369 | + | 237.123i | 0.415778 | + | 0.552733i | ||||
\(430\) | −299.689 | − | 1007.00i | −0.696950 | − | 2.34187i | ||||
\(431\) | 430.786 | 0.999505 | 0.499752 | − | 0.866168i | \(-0.333424\pi\) | ||||
0.499752 | + | 0.866168i | \(0.333424\pi\) | |||||||
\(432\) | 76.1226 | + | 33.4267i | 0.176210 | + | 0.0773767i | ||||
\(433\) | 12.3174 | 0.0284467 | 0.0142233 | − | 0.999899i | \(-0.495472\pi\) | ||||
0.0142233 | + | 0.999899i | \(0.495472\pi\) | |||||||
\(434\) | −222.208 | − | 746.658i | −0.512001 | − | 1.72041i | ||||
\(435\) | 502.542 | 1.15527 | ||||||||
\(436\) | 111.506 | + | 170.747i | 0.255748 | + | 0.391621i | ||||
\(437\) | − | 273.312i | − | 0.625429i | ||||||
\(438\) | 36.9197 | + | 124.056i | 0.0842915 | + | 0.283234i | ||||
\(439\) | 499.229i | 1.13719i | 0.822616 | + | 0.568597i | \(0.192514\pi\) | ||||
−0.822616 | + | 0.568597i | \(0.807486\pi\) | |||||||
\(440\) | −531.561 | + | 627.231i | −1.20809 | + | 1.42553i | ||||
\(441\) | −37.7636 | −0.0856318 | ||||||||
\(442\) | 472.057 | + | 348.992i | 1.06800 | + | 0.789574i | ||||
\(443\) | − | 417.285i | − | 0.941953i | −0.882146 | − | 0.470976i | \(-0.843902\pi\) | ||
0.882146 | − | 0.470976i | \(-0.156098\pi\) | |||||||
\(444\) | −224.247 | + | 146.444i | −0.505060 | + | 0.329829i | ||||
\(445\) | −80.8618 | −0.181712 | ||||||||
\(446\) | 74.2350 | + | 249.442i | 0.166446 | + | 0.559287i | ||||
\(447\) | −42.3145 | −0.0946634 | ||||||||
\(448\) | 82.3723 | + | 495.458i | 0.183867 | + | 1.10593i | ||||
\(449\) | − | 290.199i | − | 0.646323i | −0.946344 | − | 0.323161i | \(-0.895254\pi\) | ||
0.946344 | − | 0.323161i | \(-0.104746\pi\) | |||||||
\(450\) | −61.3087 | − | 206.008i | −0.136242 | − | 0.457795i | ||||
\(451\) | 151.305i | 0.335488i | ||||||||
\(452\) | 110.885 | − | 72.4134i | 0.245321 | − | 0.160207i | ||||
\(453\) | − | 283.875i | − | 0.626656i | ||||||
\(454\) | 73.7584 | + | 247.841i | 0.162464 | + | 0.545905i | ||||
\(455\) | −478.296 | − | 635.845i | −1.05120 | − | 1.39746i | ||||
\(456\) | −234.994 | + | 277.288i | −0.515337 | + | 0.608088i | ||||
\(457\) | 561.395i | 1.22844i | 0.789137 | + | 0.614218i | \(0.210528\pi\) | ||||
−0.789137 | + | 0.614218i | \(0.789472\pi\) | |||||||
\(458\) | 312.991 | − | 93.1474i | 0.683386 | − | 0.203379i | ||||
\(459\) | 117.324i | 0.255608i | ||||||||
\(460\) | 272.147 | − | 177.725i | 0.591623 | − | 0.386358i | ||||
\(461\) | 381.251i | 0.827009i | 0.910502 | + | 0.413505i | \(0.135695\pi\) | ||||
−0.910502 | + | 0.413505i | \(0.864305\pi\) | |||||||
\(462\) | −343.362 | + | 102.186i | −0.743209 | + | 0.221182i | ||||
\(463\) | −24.2335 | −0.0523401 | −0.0261700 | − | 0.999658i | \(-0.508331\pi\) | ||||
−0.0261700 | + | 0.999658i | \(0.508331\pi\) | |||||||
\(464\) | 239.326 | − | 545.017i | 0.515790 | − | 1.17461i | ||||
\(465\) | 670.449 | 1.44183 | ||||||||
\(466\) | −239.074 | − | 803.329i | −0.513034 | − | 1.72388i | ||||
\(467\) | − | 813.014i | − | 1.74093i | −0.492230 | − | 0.870465i | \(-0.663818\pi\) | ||
0.492230 | − | 0.870465i | \(-0.336182\pi\) | |||||||
\(468\) | −53.1050 | + | 146.683i | −0.113472 | + | 0.313425i | ||||
\(469\) | −287.927 | −0.613917 | ||||||||
\(470\) | 160.723 | − | 47.8319i | 0.341964 | − | 0.101770i | ||||
\(471\) | − | 256.725i | − | 0.545063i | ||||||
\(472\) | −97.6708 | − | 82.7732i | −0.206930 | − | 0.175367i | ||||
\(473\) | − | 887.642i | − | 1.87662i | ||||||
\(474\) | 56.5414 | + | 189.989i | 0.119286 | + | 0.400820i | ||||
\(475\) | 939.676 | 1.97827 | ||||||||
\(476\) | −593.446 | + | 387.548i | −1.24673 | + | 0.814177i | ||||
\(477\) | 173.988 | 0.364754 | ||||||||
\(478\) | −6.61395 | − | 22.2240i | −0.0138367 | − | 0.0464936i | ||||
\(479\) | 10.7399 | 0.0224214 | 0.0112107 | − | 0.999937i | \(-0.496431\pi\) | ||||
0.0112107 | + | 0.999937i | \(0.496431\pi\) | |||||||
\(480\) | −428.913 | − | 53.6814i | −0.893568 | − | 0.111836i | ||||
\(481\) | −302.102 | − | 401.612i | −0.628070 | − | 0.834953i | ||||
\(482\) | −351.052 | + | 104.474i | −0.728323 | + | 0.216752i | ||||
\(483\) | 141.628 | 0.293226 | ||||||||
\(484\) | −176.344 | + | 115.161i | −0.364346 | + | 0.237935i | ||||
\(485\) | 240.840 | 0.496577 | ||||||||
\(486\) | −29.8817 | + | 8.89292i | −0.0614850 | + | 0.0182982i | ||||
\(487\) | −561.520 | −1.15302 | −0.576509 | − | 0.817091i | \(-0.695586\pi\) | ||||
−0.576509 | + | 0.817091i | \(0.695586\pi\) | |||||||
\(488\) | −335.709 | − | 284.504i | −0.687928 | − | 0.582999i | ||||
\(489\) | 116.780i | 0.238814i | ||||||||
\(490\) | 188.186 | − | 56.0050i | 0.384053 | − | 0.114296i | ||||
\(491\) | 573.500i | 1.16803i | 0.811745 | + | 0.584013i | \(0.198518\pi\) | ||||
−0.811745 | + | 0.584013i | \(0.801482\pi\) | |||||||
\(492\) | −66.6040 | + | 43.4956i | −0.135374 | + | 0.0884057i | ||||
\(493\) | 840.008 | 1.70387 | ||||||||
\(494\) | −548.413 | − | 405.441i | −1.11015 | − | 0.820731i | ||||
\(495\) | − | 308.317i | − | 0.622862i | ||||||
\(496\) | 319.289 | − | 727.116i | 0.643727 | − | 1.46596i | ||||
\(497\) | −443.545 | −0.892444 | ||||||||
\(498\) | 47.1936 | − | 14.0450i | 0.0947662 | − | 0.0282028i | ||||
\(499\) | 700.846 | 1.40450 | 0.702250 | − | 0.711930i | \(-0.252179\pi\) | ||||
0.702250 | + | 0.711930i | \(0.252179\pi\) | |||||||
\(500\) | 184.607 | + | 282.685i | 0.369214 | + | 0.565370i | ||||
\(501\) | 256.760i | 0.512495i | ||||||||
\(502\) | 369.786 | − | 110.050i | 0.736626 | − | 0.219223i | ||||
\(503\) | 220.983i | 0.439330i | 0.975575 | + | 0.219665i | \(0.0704964\pi\) | ||||
−0.975575 | + | 0.219665i | \(0.929504\pi\) | |||||||
\(504\) | −143.688 | − | 121.772i | −0.285096 | − | 0.241610i | ||||
\(505\) | 1061.69i | 2.10235i | ||||||||
\(506\) | 263.200 | − | 78.3294i | 0.520158 | − | 0.154801i | ||||
\(507\) | −281.240 | − | 81.1620i | −0.554713 | − | 0.160083i | ||||
\(508\) | 403.294 | + | 617.557i | 0.793886 | + | 1.21566i | ||||
\(509\) | 686.143i | 1.34802i | 0.738721 | + | 0.674011i | \(0.235430\pi\) | ||||
−0.738721 | + | 0.674011i | \(0.764570\pi\) | |||||||
\(510\) | −173.996 | − | 584.657i | −0.341169 | − | 1.14639i | ||||
\(511\) | − | 293.227i | − | 0.573829i | ||||||
\(512\) | −262.480 | + | 439.600i | −0.512657 | + | 0.858594i | ||||
\(513\) | − | 136.301i | − | 0.265695i | ||||||
\(514\) | −109.803 | − | 368.955i | −0.213624 | − | 0.717811i | ||||
\(515\) | 972.823 | 1.88898 | ||||||||
\(516\) | 390.737 | − | 255.170i | 0.757242 | − | 0.494515i | ||||
\(517\) | 141.673 | 0.274028 | ||||||||
\(518\) | 581.550 | − | 173.072i | 1.12268 | − | 0.334115i | ||||
\(519\) | − | 40.8602i | − | 0.0787288i | ||||||
\(520\) | 47.0998 | − | 809.717i | 0.0905765 | − | 1.55715i | ||||
\(521\) | 384.581 | 0.738160 | 0.369080 | − | 0.929398i | \(-0.379673\pi\) | ||||
0.369080 | + | 0.929398i | \(0.379673\pi\) | |||||||
\(522\) | 63.6709 | + | 213.945i | 0.121975 | + | 0.409856i | ||||
\(523\) | − | 367.884i | − | 0.703411i | −0.936111 | − | 0.351706i | \(-0.885602\pi\) | ||
0.936111 | − | 0.351706i | \(-0.114398\pi\) | |||||||
\(524\) | 20.1692 | + | 30.8847i | 0.0384908 | + | 0.0589403i | ||||
\(525\) | 486.932i | 0.927489i | ||||||||
\(526\) | 73.1139 | − | 21.7590i | 0.139000 | − | 0.0413670i | ||||
\(527\) | 1120.67 | 2.12650 | ||||||||
\(528\) | −334.376 | − | 146.830i | −0.633288 | − | 0.278087i | ||||
\(529\) | 420.437 | 0.794777 | ||||||||
\(530\) | −867.028 | + | 258.031i | −1.63590 | + | 0.486851i | ||||
\(531\) | 48.0102 | 0.0904147 | ||||||||
\(532\) | 689.437 | − | 450.235i | 1.29593 | − | 0.846306i | ||||
\(533\) | −89.7279 | − | 119.284i | −0.168345 | − | 0.223797i | ||||
\(534\) | −10.2450 | − | 34.4249i | −0.0191854 | − | 0.0644662i | ||||
\(535\) | 416.114 | 0.777784 | ||||||||
\(536\) | −223.917 | − | 189.763i | −0.417756 | − | 0.354036i | ||||
\(537\) | −152.207 | −0.283440 | ||||||||
\(538\) | 45.8038 | + | 153.909i | 0.0851372 | + | 0.286075i | ||||
\(539\) | 165.880 | 0.307756 | ||||||||
\(540\) | 135.720 | − | 88.6316i | 0.251333 | − | 0.164133i | ||||
\(541\) | 235.088i | 0.434544i | 0.976111 | + | 0.217272i | \(0.0697158\pi\) | ||||
−0.976111 | + | 0.217272i | \(0.930284\pi\) | |||||||
\(542\) | −137.590 | − | 462.327i | −0.253857 | − | 0.853001i | ||||
\(543\) | 271.285i | 0.499603i | ||||||||
\(544\) | −716.935 | − | 89.7294i | −1.31790 | − | 0.164944i | ||||
\(545\) | 397.610 | 0.729561 | ||||||||
\(546\) | 210.096 | − | 284.183i | 0.384791 | − | 0.520481i | ||||
\(547\) | − | 230.496i | − | 0.421382i | −0.977553 | − | 0.210691i | \(-0.932429\pi\) | ||
0.977553 | − | 0.210691i | \(-0.0675714\pi\) | |||||||
\(548\) | 54.9064 | + | 84.0771i | 0.100194 | + | 0.153425i | ||||
\(549\) | 165.018 | 0.300580 | ||||||||
\(550\) | 269.304 | + | 904.908i | 0.489644 | + | 1.64529i | ||||
\(551\) | −975.881 | −1.77111 | ||||||||
\(552\) | 110.142 | + | 93.3424i | 0.199533 | + | 0.169099i | ||||
\(553\) | − | 449.068i | − | 0.812058i | ||||||
\(554\) | −65.8641 | − | 221.315i | −0.118888 | − | 0.399485i | ||||
\(555\) | 522.193i | 0.940888i | ||||||||
\(556\) | −268.313 | − | 410.862i | −0.482577 | − | 0.738961i | ||||
\(557\) | − | 497.920i | − | 0.893933i | −0.894551 | − | 0.446966i | \(-0.852504\pi\) | ||
0.894551 | − | 0.446966i | \(-0.147496\pi\) | |||||||
\(558\) | 84.9443 | + | 285.427i | 0.152230 | + | 0.511518i | ||||
\(559\) | 526.395 | + | 699.787i | 0.941672 | + | 1.25185i | ||||
\(560\) | 896.629 | + | 393.725i | 1.60112 | + | 0.703080i | ||||
\(561\) | − | 515.357i | − | 0.918640i | ||||||
\(562\) | 695.026 | − | 206.843i | 1.23670 | − | 0.368048i | ||||
\(563\) | − | 10.9662i | − | 0.0194782i | −0.999953 | − | 0.00973912i | \(-0.996900\pi\) | ||
0.999953 | − | 0.00973912i | \(-0.00310011\pi\) | |||||||
\(564\) | 40.7265 | + | 62.3638i | 0.0722101 | + | 0.110574i | ||||
\(565\) | − | 258.213i | − | 0.457015i | ||||||
\(566\) | −458.303 | + | 136.393i | −0.809723 | + | 0.240977i | ||||
\(567\) | 70.6301 | 0.124568 | ||||||||
\(568\) | −344.939 | − | 292.326i | −0.607286 | − | 0.514658i | ||||
\(569\) | −1049.19 | −1.84393 | −0.921964 | − | 0.387276i | \(-0.873416\pi\) | ||||
−0.921964 | + | 0.387276i | \(0.873416\pi\) | |||||||
\(570\) | 202.141 | + | 679.226i | 0.354633 | + | 1.19162i | ||||
\(571\) | − | 1062.00i | − | 1.85989i | −0.367703 | − | 0.929943i | \(-0.619856\pi\) | ||
0.367703 | − | 0.929943i | \(-0.380144\pi\) | |||||||
\(572\) | 233.269 | − | 644.318i | 0.407813 | − | 1.12643i | ||||
\(573\) | −633.848 | −1.10619 | ||||||||
\(574\) | 172.727 | − | 51.4044i | 0.300919 | − | 0.0895547i | ||||
\(575\) | − | 373.251i | − | 0.649132i | ||||||
\(576\) | −31.4887 | − | 189.400i | −0.0546679 | − | 0.328820i | ||||
\(577\) | 634.074i | 1.09892i | 0.835521 | + | 0.549458i | \(0.185166\pi\) | ||||
−0.835521 | + | 0.549458i | \(0.814834\pi\) | |||||||
\(578\) | −125.969 | − | 423.277i | −0.217940 | − | 0.732314i | ||||
\(579\) | −49.5728 | −0.0856179 | ||||||||
\(580\) | −634.578 | − | 971.718i | −1.09410 | − | 1.67538i | ||||
\(581\) | −111.550 | −0.191996 | ||||||||
\(582\) | 30.5139 | + | 102.532i | 0.0524293 | + | 0.176171i | ||||
\(583\) | −764.258 | −1.31091 | ||||||||
\(584\) | 193.256 | − | 228.038i | 0.330918 | − | 0.390477i | ||||
\(585\) | 182.840 | + | 243.066i | 0.312546 | + | 0.415498i | ||||
\(586\) | 843.343 | − | 250.982i | 1.43915 | − | 0.428298i | ||||
\(587\) | −64.5958 | −0.110044 | −0.0550220 | − | 0.998485i | \(-0.517523\pi\) | ||||
−0.0550220 | + | 0.998485i | \(0.517523\pi\) | |||||||
\(588\) | 47.6855 | + | 73.0199i | 0.0810978 | + | 0.124184i | ||||
\(589\) | −1301.94 | −2.21042 | ||||||||
\(590\) | −239.248 | + | 71.2011i | −0.405505 | + | 0.120680i | ||||
\(591\) | −540.595 | −0.914713 | ||||||||
\(592\) | 566.329 | + | 248.685i | 0.956637 | + | 0.420076i | ||||
\(593\) | − | 146.523i | − | 0.247087i | −0.992339 | − | 0.123544i | \(-0.960574\pi\) | ||
0.992339 | − | 0.123544i | \(-0.0394259\pi\) | |||||||
\(594\) | 131.258 | − | 39.0630i | 0.220973 | − | 0.0657626i | ||||
\(595\) | 1381.93i | 2.32257i | ||||||||
\(596\) | 53.4321 | + | 81.8196i | 0.0896512 | + | 0.137281i | ||||
\(597\) | 268.756 | 0.450177 | ||||||||
\(598\) | −161.046 | + | 217.836i | −0.269308 | + | 0.364275i | ||||
\(599\) | 469.062i | 0.783074i | 0.920162 | + | 0.391537i | \(0.128057\pi\) | ||||
−0.920162 | + | 0.391537i | \(0.871943\pi\) | |||||||
\(600\) | −320.921 | + | 378.680i | −0.534868 | + | 0.631134i | ||||
\(601\) | 287.117 | 0.477732 | 0.238866 | − | 0.971052i | \(-0.423224\pi\) | ||||
0.238866 | + | 0.971052i | \(0.423224\pi\) | |||||||
\(602\) | −1013.32 | + | 301.567i | −1.68325 | + | 0.500943i | ||||
\(603\) | 110.067 | 0.182532 | ||||||||
\(604\) | −548.902 | + | 358.459i | −0.908778 | + | 0.593476i | ||||
\(605\) | 410.643i | 0.678749i | ||||||||
\(606\) | −451.987 | + | 134.513i | −0.745853 | + | 0.221969i | ||||
\(607\) | 534.181i | 0.880035i | 0.897989 | + | 0.440017i | \(0.145028\pi\) | ||||
−0.897989 | + | 0.440017i | \(0.854972\pi\) | |||||||
\(608\) | 832.901 | + | 104.243i | 1.36990 | + | 0.171453i | ||||
\(609\) | − | 505.693i | − | 0.830366i | ||||||
\(610\) | −822.330 | + | 244.729i | −1.34808 | + | 0.401195i | ||||
\(611\) | −111.690 | + | 84.0154i | −0.182798 | + | 0.137505i | ||||
\(612\) | 226.858 | − | 148.149i | 0.370684 | − | 0.242074i | ||||
\(613\) | 845.316i | 1.37898i | 0.724294 | + | 0.689491i | \(0.242166\pi\) | ||||
−0.724294 | + | 0.689491i | \(0.757834\pi\) | |||||||
\(614\) | −233.564 | − | 784.813i | −0.380397 | − | 1.27820i | ||||
\(615\) | 155.098i | 0.252191i | ||||||||
\(616\) | 631.164 | + | 534.893i | 1.02462 | + | 0.868333i | ||||
\(617\) | 30.9449i | 0.0501538i | 0.999686 | + | 0.0250769i | \(0.00798305\pi\) | ||||
−0.999686 | + | 0.0250769i | \(0.992017\pi\) | |||||||
\(618\) | 123.254 | + | 414.155i | 0.199441 | + | 0.670154i | ||||
\(619\) | 637.250 | 1.02948 | 0.514741 | − | 0.857346i | \(-0.327888\pi\) | ||||
0.514741 | + | 0.857346i | \(0.327888\pi\) | |||||||
\(620\) | −846.600 | − | 1296.38i | −1.36548 | − | 2.09094i | ||||
\(621\) | −54.1406 | −0.0871829 | ||||||||
\(622\) | 572.501 | − | 170.379i | 0.920419 | − | 0.273921i | ||||
\(623\) | 81.3688i | 0.130608i | ||||||||
\(624\) | 350.684 | − | 82.5377i | 0.561994 | − | 0.132272i | ||||
\(625\) | −237.295 | −0.379673 | ||||||||
\(626\) | −11.6316 | − | 39.0843i | −0.0185809 | − | 0.0624349i | ||||
\(627\) | 598.716i | 0.954891i | ||||||||
\(628\) | −496.404 | + | 324.176i | −0.790453 | + | 0.516203i | ||||
\(629\) | 872.855i | 1.38769i | ||||||||
\(630\) | −351.969 | + | 104.747i | −0.558681 | + | 0.166266i | ||||
\(631\) | −440.047 | −0.697380 | −0.348690 | − | 0.937238i | \(-0.613373\pi\) | ||||
−0.348690 | + | 0.937238i | \(0.613373\pi\) | |||||||
\(632\) | 295.966 | − | 349.234i | 0.468301 | − | 0.552586i | ||||
\(633\) | 510.229 | 0.806049 | ||||||||
\(634\) | 985.960 | − | 293.426i | 1.55514 | − | 0.462817i | ||||
\(635\) | 1438.08 | 2.26469 | ||||||||
\(636\) | −219.701 | − | 336.424i | −0.345441 | − | 0.528968i | ||||
\(637\) | −130.774 | + | 98.3712i | −0.205297 | + | 0.154429i | ||||
\(638\) | −279.680 | − | 939.773i | −0.438371 | − | 1.47300i | ||||
\(639\) | 169.555 | 0.265344 | ||||||||
\(640\) | 437.805 | + | 897.133i | 0.684071 | + | 1.40177i | ||||
\(641\) | 203.080 | 0.316817 | 0.158408 | − | 0.987374i | \(-0.449364\pi\) | ||||
0.158408 | + | 0.987374i | \(0.449364\pi\) | |||||||
\(642\) | 52.7207 | + | 177.150i | 0.0821195 | + | 0.275935i | ||||
\(643\) | 130.355 | 0.202729 | 0.101365 | − | 0.994849i | \(-0.467679\pi\) | ||||
0.101365 | + | 0.994849i | \(0.467679\pi\) | |||||||
\(644\) | −178.839 | − | 273.853i | −0.277700 | − | 0.425237i | ||||
\(645\) | − | 909.891i | − | 1.41068i | ||||||
\(646\) | 337.882 | + | 1135.34i | 0.523036 | + | 1.75749i | ||||
\(647\) | − | 423.596i | − | 0.654709i | −0.944902 | − | 0.327354i | \(-0.893843\pi\) | ||
0.944902 | − | 0.327354i | \(-0.106157\pi\) | |||||||
\(648\) | 54.9281 | + | 46.5500i | 0.0847656 | + | 0.0718364i | ||||
\(649\) | −210.889 | −0.324945 | ||||||||
\(650\) | −748.944 | − | 553.694i | −1.15222 | − | 0.851837i | ||||
\(651\) | − | 674.652i | − | 1.03633i | ||||||
\(652\) | 225.807 | − | 147.462i | 0.346329 | − | 0.226169i | ||||
\(653\) | 149.879 | 0.229524 | 0.114762 | − | 0.993393i | \(-0.463389\pi\) | ||||
0.114762 | + | 0.993393i | \(0.463389\pi\) | |||||||
\(654\) | 50.3763 | + | 169.273i | 0.0770280 | + | 0.258827i | ||||
\(655\) | 71.9198 | 0.109801 | ||||||||
\(656\) | 168.207 | + | 73.8624i | 0.256413 | + | 0.112595i | ||||
\(657\) | 112.093i | 0.170613i | ||||||||
\(658\) | −48.1318 | − | 161.731i | −0.0731486 | − | 0.245792i | ||||
\(659\) | 590.762i | 0.896452i | 0.893920 | + | 0.448226i | \(0.147944\pi\) | ||||
−0.893920 | + | 0.448226i | \(0.852056\pi\) | |||||||
\(660\) | −596.163 | + | 389.323i | −0.903277 | + | 0.589883i | ||||
\(661\) | 668.639i | 1.01156i | 0.862664 | + | 0.505778i | \(0.168795\pi\) | ||||
−0.862664 | + | 0.505778i | \(0.831205\pi\) | |||||||
\(662\) | 260.549 | + | 875.487i | 0.393578 | + | 1.32249i | ||||
\(663\) | 305.620 | + | 406.290i | 0.460965 | + | 0.612805i | ||||
\(664\) | −86.7506 | − | 73.5186i | −0.130648 | − | 0.110721i | ||||
\(665\) | − | 1605.46i | − | 2.41422i | ||||||
\(666\) | −222.311 | + | 66.1606i | −0.333800 | + | 0.0993403i | ||||
\(667\) | 387.632i | 0.581157i | ||||||||
\(668\) | 496.473 | − | 324.220i | 0.743223 | − | 0.485360i | ||||
\(669\) | 225.387i | 0.336901i | ||||||||
\(670\) | −548.493 | + | 163.234i | −0.818646 | + | 0.243632i | ||||
\(671\) | −724.858 | −1.08027 | ||||||||
\(672\) | −54.0179 | + | 431.602i | −0.0803838 | + | 0.642264i | ||||
\(673\) | −1223.15 | −1.81746 | −0.908729 | − | 0.417388i | \(-0.862946\pi\) | ||||
−0.908729 | + | 0.417388i | \(0.862946\pi\) | |||||||
\(674\) | 340.958 | + | 1145.68i | 0.505873 | + | 1.69982i | ||||
\(675\) | − | 186.141i | − | 0.275764i | ||||||
\(676\) | 198.196 | + | 646.293i | 0.293190 | + | 0.956054i | ||||
\(677\) | 1157.62 | 1.70992 | 0.854961 | − | 0.518692i | \(-0.173581\pi\) | ||||
0.854961 | + | 0.518692i | \(0.173581\pi\) | |||||||
\(678\) | 109.928 | − | 32.7150i | 0.162136 | − | 0.0482522i | ||||
\(679\) | − | 242.350i | − | 0.356922i | ||||||
\(680\) | −910.784 | + | 1074.71i | −1.33939 | + | 1.58045i | ||||
\(681\) | 223.940i | 0.328839i | ||||||||
\(682\) | −373.126 | − | 1253.77i | −0.547105 | − | 1.83837i | ||||
\(683\) | −1000.21 | −1.46443 | −0.732217 | − | 0.681072i | \(-0.761514\pi\) | ||||
−0.732217 | + | 0.681072i | \(0.761514\pi\) | |||||||
\(684\) | −263.553 | + | 172.113i | −0.385311 | + | 0.251627i | ||||
\(685\) | 195.787 | 0.285820 | ||||||||
\(686\) | 163.018 | + | 547.767i | 0.237635 | + | 0.798494i | ||||
\(687\) | 282.807 | 0.411655 | ||||||||
\(688\) | −986.796 | − | 433.319i | −1.43430 | − | 0.629824i | ||||
\(689\) | 602.514 | − | 453.224i | 0.874477 | − | 0.657800i | ||||
\(690\) | 269.797 | − | 80.2927i | 0.391010 | − | 0.116366i | ||||
\(691\) | −120.026 | −0.173699 | −0.0868496 | − | 0.996221i | \(-0.527680\pi\) | ||||
−0.0868496 | + | 0.996221i | \(0.527680\pi\) | |||||||
\(692\) | −79.0076 | + | 51.5957i | −0.114173 | + | 0.0745603i | ||||
\(693\) | −310.250 | −0.447691 | ||||||||
\(694\) | −680.138 | + | 202.412i | −0.980027 | + | 0.291660i | ||||
\(695\) | −956.756 | −1.37663 | ||||||||
\(696\) | 333.285 | − | 393.270i | 0.478858 | − | 0.565044i | ||||
\(697\) | 259.249i | 0.371949i | ||||||||
\(698\) | −850.868 | + | 253.222i | −1.21901 | + | 0.362782i | ||||
\(699\) | − | 725.858i | − | 1.03842i | ||||||
\(700\) | 941.534 | − | 614.867i | 1.34505 | − | 0.878381i | ||||
\(701\) | 882.073 | 1.25831 | 0.629153 | − | 0.777281i | \(-0.283402\pi\) | ||||
0.629153 | + | 0.777281i | \(0.283402\pi\) | |||||||
\(702\) | −80.3141 | + | 108.635i | −0.114408 | + | 0.154751i | ||||
\(703\) | − | 1014.04i | − | 1.44245i | ||||||
\(704\) | 138.317 | + | 831.959i | 0.196473 | + | 1.18176i | ||||
\(705\) | 145.224 | 0.205991 | ||||||||
\(706\) | 264.995 | − | 78.8637i | 0.375348 | − | 0.111705i | ||||
\(707\) | 1068.34 | 1.51109 | ||||||||
\(708\) | −60.6243 | − | 92.8328i | −0.0856275 | − | 0.131120i | ||||
\(709\) | 285.806i | 0.403112i | 0.979477 | + | 0.201556i | \(0.0645998\pi\) | ||||
−0.979477 | + | 0.201556i | \(0.935400\pi\) | |||||||
\(710\) | −844.939 | + | 251.457i | −1.19005 | + | 0.354165i | ||||
\(711\) | 171.667i | 0.241444i | ||||||||
\(712\) | −53.6275 | + | 63.2794i | −0.0753195 | + | 0.0888756i | ||||
\(713\) | 517.146i | 0.725309i | ||||||||
\(714\) | −588.322 | + | 175.087i | −0.823981 | + | 0.245220i | ||||
\(715\) | −803.141 | − | 1067.69i | −1.12327 | − | 1.49327i | ||||
\(716\) | 192.198 | + | 294.309i | 0.268433 | + | 0.411046i | ||||
\(717\) | − | 20.0808i | − | 0.0280066i | ||||||
\(718\) | −140.194 | − | 471.076i | −0.195256 | − | 0.656094i | ||||
\(719\) | 984.643i | 1.36946i | 0.728796 | + | 0.684731i | \(0.240080\pi\) | ||||
−0.728796 | + | 0.684731i | \(0.759920\pi\) | |||||||
\(720\) | −342.757 | − | 150.510i | −0.476052 | − | 0.209042i | ||||
\(721\) | − | 978.922i | − | 1.35773i | ||||||
\(722\) | −186.591 | − | 626.976i | −0.258436 | − | 0.868388i | ||||
\(723\) | −317.197 | −0.438724 | ||||||||
\(724\) | 524.557 | − | 342.561i | 0.724526 | − | 0.473150i | ||||
\(725\) | −1332.72 | −1.83823 | ||||||||
\(726\) | −174.821 | + | 52.0275i | −0.240800 | + | 0.0716632i | ||||
\(727\) | 566.297i | 0.778950i | 0.921037 | + | 0.389475i | \(0.127344\pi\) | ||||
−0.921037 | + | 0.389475i | \(0.872656\pi\) | |||||||
\(728\) | −814.793 | − | 47.3950i | −1.11922 | − | 0.0651031i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | −166.238 | − | 558.588i | −0.227723 | − | 0.765189i | ||||
\(731\) | − | 1520.90i | − | 2.08057i | ||||||
\(732\) | −208.375 | − | 319.080i | −0.284665 | − | 0.435902i | ||||
\(733\) | − | 1398.80i | − | 1.90832i | −0.299303 | − | 0.954158i | \(-0.596754\pi\) | ||
0.299303 | − | 0.954158i | \(-0.403246\pi\) | |||||||
\(734\) | −879.296 | + | 261.682i | −1.19795 | + | 0.356515i | ||||
\(735\) | 170.038 | 0.231344 | ||||||||
\(736\) | 41.4067 | − | 330.838i | 0.0562591 | − | 0.449509i | ||||
\(737\) | −483.479 | −0.656009 | ||||||||
\(738\) | −66.0290 | + | 19.6505i | −0.0894702 | + | 0.0266267i | ||||
\(739\) | −500.468 | −0.677223 | −0.338611 | − | 0.940926i | \(-0.609957\pi\) | ||||
−0.338611 | + | 0.940926i | \(0.609957\pi\) | |||||||
\(740\) | 1009.72 | − | 659.392i | 1.36448 | − | 0.891071i | ||||
\(741\) | −355.054 | − | 472.007i | −0.479156 | − | 0.636987i | ||||
\(742\) | 259.649 | + | 872.463i | 0.349931 | + | 1.17583i | ||||
\(743\) | −349.050 | −0.469784 | −0.234892 | − | 0.972021i | \(-0.575474\pi\) | ||||
−0.234892 | + | 0.972021i | \(0.575474\pi\) | |||||||
\(744\) | 444.641 | − | 524.668i | 0.597636 | − | 0.705199i | ||||
\(745\) | 190.529 | 0.255744 | ||||||||
\(746\) | 154.013 | + | 517.509i | 0.206451 | + | 0.693711i | ||||
\(747\) | 42.6424 | 0.0570848 | ||||||||
\(748\) | −996.497 | + | 650.760i | −1.33221 | + | 0.870000i | ||||
\(749\) | − | 418.723i | − | 0.559043i | ||||||
\(750\) | 83.4019 | + | 280.245i | 0.111203 | + | 0.373659i | ||||
\(751\) | − | 25.5035i | − | 0.0339594i | −0.999856 | − | 0.0169797i | \(-0.994595\pi\) | ||
0.999856 | − | 0.0169797i | \(-0.00540507\pi\) | |||||||
\(752\) | 69.1601 | − | 157.498i | 0.0919682 | − | 0.209439i | ||||
\(753\) | 334.125 | 0.443725 | ||||||||
\(754\) | 777.800 | + | 575.027i | 1.03157 | + | 0.762635i | ||||
\(755\) | 1278.20i | 1.69298i | ||||||||
\(756\) | −89.1873 | − | 136.571i | −0.117973 | − | 0.180649i | ||||
\(757\) | 371.325 | 0.490522 | 0.245261 | − | 0.969457i | \(-0.421126\pi\) | ||||
0.245261 | + | 0.969457i | \(0.421126\pi\) | |||||||
\(758\) | 270.507 | + | 908.949i | 0.356869 | + | 1.19914i | ||||
\(759\) | 237.818 | 0.313330 | ||||||||
\(760\) | 1058.10 | − | 1248.54i | 1.39224 | − | 1.64282i | ||||
\(761\) | 30.6207i | 0.0402374i | 0.999798 | + | 0.0201187i | \(0.00640441\pi\) | ||||
−0.999798 | + | 0.0201187i | \(0.993596\pi\) | |||||||
\(762\) | 182.201 | + | 612.225i | 0.239109 | + | 0.803445i | ||||
\(763\) | − | 400.103i | − | 0.524382i | ||||||
\(764\) | 800.383 | + | 1225.61i | 1.04762 | + | 1.60420i | ||||
\(765\) | − | 528.274i | − | 0.690555i | ||||||
\(766\) | 135.561 | + | 455.506i | 0.176972 | + | 0.594655i | ||||
\(767\) | 166.258 | − | 125.063i | 0.216764 | − | 0.163055i | ||||
\(768\) | −326.463 | + | 300.049i | −0.425083 | + | 0.390689i | ||||
\(769\) | 563.426i | 0.732674i | 0.930482 | + | 0.366337i | \(0.119388\pi\) | ||||
−0.930482 | + | 0.366337i | \(0.880612\pi\) | |||||||
\(770\) | 1546.06 | − | 460.113i | 2.00787 | − | 0.597549i | ||||
\(771\) | − | 333.374i | − | 0.432392i | ||||||
\(772\) | 62.5974 | + | 95.8542i | 0.0810847 | + | 0.124163i | ||||
\(773\) | − | 1408.83i | − | 1.82255i | −0.411800 | − | 0.911274i | \(-0.635100\pi\) | ||
0.411800 | − | 0.911274i | \(-0.364900\pi\) | |||||||
\(774\) | 387.364 | − | 115.281i | 0.500470 | − | 0.148942i | ||||
\(775\) | −1778.00 | −2.29419 | ||||||||
\(776\) | 159.725 | − | 188.472i | 0.205831 | − | 0.242877i | ||||
\(777\) | 525.467 | 0.676277 | ||||||||
\(778\) | −53.7292 | − | 180.539i | −0.0690607 | − | 0.232055i | ||||
\(779\) | − | 301.182i | − | 0.386627i | ||||||
\(780\) | 239.116 | − | 660.468i | 0.306559 | − | 0.846754i | ||||
\(781\) | −744.787 | −0.953632 | ||||||||
\(782\) | 450.971 | − | 134.211i | 0.576689 | − | 0.171625i | ||||
\(783\) | 193.313i | 0.246887i | ||||||||
\(784\) | 80.9775 | − | 184.410i | 0.103288 | − | 0.235217i | ||||
\(785\) | 1155.95i | 1.47255i | ||||||||
\(786\) | 9.11207 | + | 30.6181i | 0.0115930 | + | 0.0389543i | ||||
\(787\) | −740.379 | −0.940761 | −0.470381 | − | 0.882464i | \(-0.655883\pi\) | ||||
−0.470381 | + | 0.882464i | \(0.655883\pi\) | |||||||
\(788\) | 682.630 | + | 1045.30i | 0.866281 | + | 1.32652i | ||||
\(789\) | 66.0631 | 0.0837301 | ||||||||
\(790\) | −254.589 | − | 855.461i | −0.322264 | − | 1.08286i | ||||
\(791\) | −259.832 | −0.328486 | ||||||||
\(792\) | −241.277 | − | 204.475i | −0.304643 | − | 0.258176i | ||||
\(793\) | 571.453 | − | 429.860i | 0.720622 | − | 0.542068i | ||||
\(794\) | −802.180 | + | 238.732i | −1.01030 | + | 0.300670i | ||||
\(795\) | −783.414 | −0.985427 | ||||||||
\(796\) | −339.367 | − | 519.667i | −0.426341 | − | 0.652848i | ||||
\(797\) | 1439.36 | 1.80597 | 0.902985 | − | 0.429673i | \(-0.141371\pi\) | ||||
0.902985 | + | 0.429673i | \(0.141371\pi\) | |||||||
\(798\) | 683.484 | − | 203.408i | 0.856497 | − | 0.254897i | ||||
\(799\) | 242.744 | 0.303810 | ||||||||
\(800\) | 1137.46 | + | 142.360i | 1.42182 | + | 0.177951i | ||||
\(801\) | − | 31.1051i | − | 0.0388328i | ||||||
\(802\) | −1290.56 | + | 384.077i | −1.60918 | + | 0.478899i | ||||
\(803\) | − | 492.378i | − | 0.613173i | ||||||
\(804\) | −138.985 | − | 212.826i | −0.172867 | − | 0.264709i | ||||
\(805\) | −637.708 | −0.792184 | ||||||||
\(806\) | 1037.67 | + | 767.152i | 1.28744 | + | 0.951802i | ||||
\(807\) | 139.066i | 0.172325i | ||||||||
\(808\) | 830.836 | + | 704.110i | 1.02826 | + | 0.871423i | ||||
\(809\) | −676.465 | −0.836174 | −0.418087 | − | 0.908407i | \(-0.637299\pi\) | ||||
−0.418087 | + | 0.908407i | \(0.637299\pi\) | |||||||
\(810\) | 134.548 | − | 40.0421i | 0.166109 | − | 0.0494347i | ||||
\(811\) | 839.069 | 1.03461 | 0.517305 | − | 0.855801i | \(-0.326935\pi\) | ||||
0.517305 | + | 0.855801i | \(0.326935\pi\) | |||||||
\(812\) | −977.810 | + | 638.557i | −1.20420 | + | 0.786400i | ||||
\(813\) | − | 417.741i | − | 0.513827i | ||||||
\(814\) | 976.521 | − | 290.617i | 1.19966 | − | 0.357023i | ||||
\(815\) | − | 525.825i | − | 0.645184i | ||||||
\(816\) | −572.925 | − | 251.581i | −0.702114 | − | 0.308310i | ||||
\(817\) | 1766.91i | 2.16268i | ||||||||
\(818\) | 304.929 | − | 90.7481i | 0.372774 | − | 0.110939i | ||||
\(819\) | 244.590 | − | 183.986i | 0.298645 | − | 0.224647i | ||||
\(820\) | 299.898 | − | 195.848i | 0.365729 | − | 0.238838i | ||||
\(821\) | 1228.30i | 1.49611i | 0.663638 | + | 0.748054i | \(0.269012\pi\) | ||||
−0.663638 | + | 0.748054i | \(0.730988\pi\) | |||||||
\(822\) | 24.8057 | + | 83.3513i | 0.0301772 | + | 0.101401i | ||||
\(823\) | 1171.99i | 1.42405i | 0.702154 | + | 0.712025i | \(0.252222\pi\) | ||||
−0.702154 | + | 0.712025i | \(0.747778\pi\) | |||||||
\(824\) | 645.175 | − | 761.294i | 0.782979 | − | 0.923901i | ||||
\(825\) | 817.642i | 0.991081i | ||||||||
\(826\) | 71.6475 | + | 240.748i | 0.0867404 | + | 0.291462i | ||||
\(827\) | −750.467 | −0.907457 | −0.453729 | − | 0.891140i | \(-0.649906\pi\) | ||||
−0.453729 | + | 0.891140i | \(0.649906\pi\) | |||||||
\(828\) | 68.3653 | + | 104.687i | 0.0825668 | + | 0.126433i | ||||
\(829\) | 766.089 | 0.924113 | 0.462056 | − | 0.886851i | \(-0.347112\pi\) | ||||
0.462056 | + | 0.886851i | \(0.347112\pi\) | |||||||
\(830\) | −212.498 | + | 63.2404i | −0.256022 | + | 0.0761933i | ||||
\(831\) | − | 199.972i | − | 0.240640i | ||||||
\(832\) | −602.417 | − | 573.862i | −0.724059 | − | 0.689738i | ||||
\(833\) | 284.222 | 0.341203 | ||||||||
\(834\) | −121.219 | − | 407.315i | −0.145346 | − | 0.488388i | ||||
\(835\) | − | 1156.11i | − | 1.38457i | ||||||
\(836\) | 1157.68 | − | 756.021i | 1.38479 | − | 0.904332i | ||||
\(837\) | 257.901i | 0.308126i | ||||||||
\(838\) | 1354.87 | − | 403.215i | 1.61679 | − | 0.481163i | ||||
\(839\) | 180.988 | 0.215719 | 0.107859 | − | 0.994166i | \(-0.465600\pi\) | ||||
0.107859 | + | 0.994166i | \(0.465600\pi\) | |||||||
\(840\) | 646.984 | + | 548.301i | 0.770219 | + | 0.652739i | ||||
\(841\) | 543.067 | 0.645739 | ||||||||
\(842\) | −347.580 | + | 103.441i | −0.412803 | + | 0.122852i | ||||
\(843\) | 628.000 | 0.744959 | ||||||||
\(844\) | −644.285 | − | 986.581i | −0.763371 | − | 1.16894i | ||||
\(845\) | 1266.34 | + | 365.448i | 1.49862 | + | 0.432483i | ||||
\(846\) | 18.3995 | + | 61.8254i | 0.0217488 | + | 0.0730796i | ||||
\(847\) | 413.218 | 0.487860 | ||||||||
\(848\) | −373.086 | + | 849.629i | −0.439960 | + | 1.00192i | ||||
\(849\) | −414.106 | −0.487757 | ||||||||
\(850\) | 461.430 | + | 1550.48i | 0.542859 | + | 1.82410i | ||||
\(851\) | −402.790 | −0.473313 | ||||||||
\(852\) | −214.103 | − | 327.853i | −0.251295 | − | 0.384804i | ||||
\(853\) | 984.643i | 1.15433i | 0.816628 | + | 0.577165i | \(0.195841\pi\) | ||||
−0.816628 | + | 0.577165i | \(0.804159\pi\) | |||||||
\(854\) | 246.263 | + | 827.486i | 0.288364 | + | 0.968953i | ||||
\(855\) | 613.724i | 0.717805i | ||||||||
\(856\) | 275.967 | − | 325.635i | 0.322391 | − | 0.380415i | ||||
\(857\) | −1513.36 | −1.76588 | −0.882939 | − | 0.469488i | \(-0.844439\pi\) | ||||
−0.882939 | + | 0.469488i | \(0.844439\pi\) | |||||||
\(858\) | 352.787 | − | 477.191i | 0.411174 | − | 0.556167i | ||||
\(859\) | 107.816i | 0.125513i | 0.998029 | + | 0.0627564i | \(0.0199891\pi\) | ||||
−0.998029 | + | 0.0627564i | \(0.980011\pi\) | |||||||
\(860\) | −1759.37 | + | 1148.95i | −2.04578 | + | 1.33599i | ||||
\(861\) | 156.070 | 0.181266 | ||||||||
\(862\) | −245.756 | − | 825.780i | −0.285099 | − | 0.957981i | ||||
\(863\) | −642.697 | −0.744725 | −0.372362 | − | 0.928087i | \(-0.621452\pi\) | ||||
−0.372362 | + | 0.928087i | \(0.621452\pi\) | |||||||
\(864\) | 20.6496 | − | 164.990i | 0.0239000 | − | 0.190960i | ||||
\(865\) | 183.981i | 0.212695i | ||||||||
\(866\) | −7.02685 | − | 23.6114i | −0.00811414 | − | 0.0272649i | ||||
\(867\) | − | 382.458i | − | 0.441128i | ||||||
\(868\) | −1304.51 | + | 851.908i | −1.50289 | + | 0.981461i | ||||
\(869\) | − | 754.062i | − | 0.867735i | ||||||
\(870\) | −286.691 | − | 963.329i | −0.329530 | − | 1.10727i | ||||
\(871\) | 381.158 | − | 286.715i | 0.437610 | − | 0.329180i | ||||
\(872\) | 263.695 | − | 311.155i | 0.302402 | − | 0.356829i | ||||
\(873\) | 92.6439i | 0.106121i | ||||||||
\(874\) | −523.916 | + | 155.920i | −0.599446 | + | 0.178398i | ||||
\(875\) | − | 662.402i | − | 0.757031i | ||||||
\(876\) | 216.743 | − | 141.544i | 0.247424 | − | 0.161579i | ||||
\(877\) | 235.180i | 0.268164i | 0.990970 | + | 0.134082i | \(0.0428085\pi\) | ||||
−0.990970 | + | 0.134082i | \(0.957191\pi\) | |||||||
\(878\) | 956.977 | − | 284.800i | 1.08995 | − | 0.324374i | ||||
\(879\) | 762.013 | 0.866909 | ||||||||
\(880\) | 1505.59 | + | 661.131i | 1.71090 | + | 0.751286i | ||||
\(881\) | 370.037 | 0.420019 | 0.210010 | − | 0.977699i | \(-0.432650\pi\) | ||||
0.210010 | + | 0.977699i | \(0.432650\pi\) | |||||||
\(882\) | 21.5434 | + | 72.3895i | 0.0244257 | + | 0.0820743i | ||||
\(883\) | − | 1004.78i | − | 1.13792i | −0.822367 | − | 0.568958i | \(-0.807347\pi\) | ||
0.822367 | − | 0.568958i | \(-0.192653\pi\) | |||||||
\(884\) | 399.686 | − | 1103.98i | 0.452134 | − | 1.24885i | ||||
\(885\) | −216.175 | −0.244266 | ||||||||
\(886\) | −799.899 | + | 238.053i | −0.902820 | + | 0.268683i | ||||
\(887\) | 301.209i | 0.339582i | 0.985480 | + | 0.169791i | \(0.0543093\pi\) | ||||
−0.985480 | + | 0.169791i | \(0.945691\pi\) | |||||||
\(888\) | 408.649 | + | 346.318i | 0.460190 | + | 0.389998i | ||||
\(889\) | − | 1447.09i | − | 1.62777i | ||||||
\(890\) | 46.1302 | + | 155.005i | 0.0518316 | + | 0.174163i | ||||
\(891\) | 118.600 | 0.133109 | ||||||||
\(892\) | 435.809 | − | 284.604i | 0.488575 | − | 0.319063i | ||||
\(893\) | −282.008 | −0.315798 | ||||||||
\(894\) | 24.1396 | + | 81.1132i | 0.0270018 | + | 0.0907307i | ||||
\(895\) | 685.344 | 0.765747 | ||||||||
\(896\) | 902.758 | − | 440.550i | 1.00754 | − | 0.491685i | ||||
\(897\) | −187.487 | + | 141.032i | −0.209016 | + | 0.157226i | ||||
\(898\) | −556.286 | + | 165.553i | −0.619472 | + | 0.184357i | ||||
\(899\) | 1846.50 | 2.05395 | ||||||||
\(900\) | −359.923 | + | 235.047i | −0.399914 | + | 0.261163i | ||||
\(901\) | −1309.49 | −1.45338 | ||||||||
\(902\) | 290.039 | − | 86.3167i | 0.321551 | − | 0.0956948i | ||||
\(903\) | −915.596 | −1.01395 | ||||||||
\(904\) | −202.068 | − | 171.247i | −0.223527 | − | 0.189432i | ||||
\(905\) | − | 1221.51i | − | 1.34974i | ||||||
\(906\) | −544.163 | + | 161.945i | −0.600622 | + | 0.178748i | ||||
\(907\) | − | 446.087i | − | 0.491827i | −0.969292 | − | 0.245914i | \(-0.920912\pi\) | ||
0.969292 | − | 0.245914i | \(-0.0790879\pi\) | |||||||
\(908\) | 433.011 | − | 282.777i | 0.476884 | − | 0.311428i | ||||
\(909\) | −408.399 | −0.449284 | ||||||||
\(910\) | −945.999 | + | 1279.59i | −1.03956 | + | 1.40614i | ||||
\(911\) | − | 12.3523i | − | 0.0135591i | −0.999977 | − | 0.00677954i | \(-0.997842\pi\) | ||
0.999977 | − | 0.00677954i | \(-0.00215801\pi\) | |||||||
\(912\) | 665.596 | + | 292.274i | 0.729820 | + | 0.320476i | ||||
\(913\) | −187.311 | −0.205160 | ||||||||
\(914\) | 1076.14 | − | 320.265i | 1.17740 | − | 0.350399i | ||||
\(915\) | −743.027 | −0.812052 | ||||||||
\(916\) | −357.111 | − | 546.837i | −0.389859 | − | 0.596984i | ||||
\(917\) | − | 72.3707i | − | 0.0789212i | ||||||
\(918\) | 224.900 | − | 66.9311i | 0.244989 | − | 0.0729097i | ||||
\(919\) | − | 1314.71i | − | 1.43059i | −0.698822 | − | 0.715295i | \(-0.746292\pi\) | ||
0.698822 | − | 0.715295i | \(-0.253708\pi\) | |||||||
\(920\) | −495.937 | − | 420.292i | −0.539062 | − | 0.456840i | ||||
\(921\) | − | 709.128i | − | 0.769954i | ||||||
\(922\) | 730.825 | − | 217.497i | 0.792652 | − | 0.235897i | ||||
\(923\) | 587.164 | − | 441.678i | 0.636148 | − | 0.478524i | ||||
\(924\) | 391.764 | + | 599.900i | 0.423986 | + | 0.649243i | ||||
\(925\) | − | 1384.83i | − | 1.49712i | ||||||
\(926\) | 13.8247 | + | 46.4534i | 0.0149295 | + | 0.0501657i | ||||
\(927\) | 374.215i | 0.403684i | ||||||||
\(928\) | −1181.28 | − | 147.845i | −1.27293 | − | 0.159316i | ||||
\(929\) | 1683.34i | 1.81199i | 0.423292 | + | 0.905993i | \(0.360874\pi\) | ||||
−0.423292 | + | 0.905993i | \(0.639126\pi\) | |||||||
\(930\) | −382.478 | − | 1285.19i | −0.411267 | − | 1.38193i | ||||
\(931\) | −330.195 | −0.354667 | ||||||||
\(932\) | −1403.52 | + | 916.568i | −1.50593 | + | 0.983442i | ||||
\(933\) | 517.291 | 0.554438 | ||||||||
\(934\) | −1558.48 | + | 463.809i | −1.66860 | + | 0.496584i | ||||
\(935\) | 2320.50i | 2.48181i | ||||||||
\(936\) | 311.474 | + | 18.1178i | 0.332771 | + | 0.0193567i | ||||
\(937\) | −652.570 | −0.696447 | −0.348223 | − | 0.937412i | \(-0.613215\pi\) | ||||
−0.348223 | + | 0.937412i | \(0.613215\pi\) | |||||||
\(938\) | 164.257 | + | 551.931i | 0.175114 | + | 0.588413i | ||||
\(939\) | − | 35.3151i | − | 0.0376093i | ||||||
\(940\) | −183.379 | − | 280.805i | −0.195084 | − | 0.298729i | ||||
\(941\) | 857.642i | 0.911416i | 0.890129 | + | 0.455708i | \(0.150614\pi\) | ||||
−0.890129 | + | 0.455708i | \(0.849386\pi\) | |||||||
\(942\) | −492.119 | + | 146.457i | −0.522419 | + | 0.155474i | ||||
\(943\) | −119.633 | −0.126865 | ||||||||
\(944\) | −102.950 | + | 234.447i | −0.109057 | + | 0.248355i | ||||
\(945\) | −318.026 | −0.336536 | ||||||||
\(946\) | −1701.53 | + | 506.383i | −1.79866 | + | 0.535289i | ||||
\(947\) | −1477.66 | −1.56036 | −0.780181 | − | 0.625554i | \(-0.784873\pi\) | ||||
−0.780181 | + | 0.625554i | \(0.784873\pi\) | |||||||
\(948\) | 331.936 | − | 216.770i | 0.350143 | − | 0.228660i | ||||
\(949\) | 291.993 | + | 388.174i | 0.307685 | + | 0.409034i | ||||
\(950\) | −536.067 | − | 1801.28i | −0.564281 | − | 1.89608i | ||||
\(951\) | 890.877 | 0.936780 | ||||||||
\(952\) | 1081.45 | + | 916.494i | 1.13597 | + | 0.962704i | ||||
\(953\) | 589.275 | 0.618337 | 0.309169 | − | 0.951007i | \(-0.399949\pi\) | ||||
0.309169 | + | 0.951007i | \(0.399949\pi\) | |||||||
\(954\) | −99.2567 | − | 333.519i | −0.104043 | − | 0.349601i | ||||
\(955\) | 2854.03 | 2.98851 | ||||||||
\(956\) | −38.8282 | + | 25.3567i | −0.0406153 | + | 0.0265237i | ||||
\(957\) | − | 849.144i | − | 0.887298i | ||||||
\(958\) | −6.12688 | − | 20.5874i | −0.00639549 | − | 0.0214899i | ||||
\(959\) | − | 197.014i | − | 0.205437i | ||||||
\(960\) | 141.784 | + | 852.812i | 0.147692 | + | 0.888346i | ||||
\(961\) | 1502.45 | 1.56342 | ||||||||
\(962\) | −597.512 | + | 808.215i | −0.621115 | + | 0.840140i | ||||
\(963\) | 160.067i | 0.166217i | ||||||||
\(964\) | 400.537 | + | 613.334i | 0.415494 | + | 0.636239i | ||||
\(965\) | 223.211 | 0.231307 | ||||||||
\(966\) | −80.7961 | − | 271.489i | −0.0836399 | − | 0.281044i | ||||
\(967\) | −834.227 | −0.862696 | −0.431348 | − | 0.902186i | \(-0.641962\pi\) | ||||
−0.431348 | + | 0.902186i | \(0.641962\pi\) | |||||||
\(968\) | 321.354 | + | 272.338i | 0.331977 | + | 0.281341i | ||||
\(969\) | 1025.85i | 1.05867i | ||||||||
\(970\) | −137.395 | − | 461.669i | −0.141644 | − | 0.475948i | ||||
\(971\) | − | 489.291i | − | 0.503905i | −0.967740 | − | 0.251952i | \(-0.918927\pi\) | ||
0.967740 | − | 0.251952i | \(-0.0810726\pi\) | |||||||
\(972\) | 34.0939 | + | 52.2073i | 0.0350760 | + | 0.0537113i | ||||
\(973\) | 962.754i | 0.989470i | ||||||||
\(974\) | 320.337 | + | 1076.38i | 0.328888 | + | 1.10512i | ||||
\(975\) | −484.882 | − | 644.600i | −0.497315 | − | 0.661129i | ||||
\(976\) | −353.853 | + | 805.829i | −0.362554 | + | 0.825644i | ||||
\(977\) | − | 665.403i | − | 0.681068i | −0.940232 | − | 0.340534i | \(-0.889392\pi\) | ||
0.940232 | − | 0.340534i | \(-0.110608\pi\) | |||||||
\(978\) | 223.857 | − | 66.6208i | 0.228893 | − | 0.0681194i | ||||
\(979\) | 136.632i | 0.139563i | ||||||||
\(980\) | −214.713 | − | 328.787i | −0.219095 | − | 0.335496i | ||||
\(981\) | 152.949i | 0.155911i | ||||||||
\(982\) | 1099.35 | − | 327.171i | 1.11950 | − | 0.333168i | ||||
\(983\) | 1117.01 | 1.13633 | 0.568164 | − | 0.822915i | \(-0.307654\pi\) | ||||
0.568164 | + | 0.822915i | \(0.307654\pi\) | |||||||
\(984\) | 121.374 | + | 102.861i | 0.123347 | + | 0.104533i | ||||
\(985\) | 2434.14 | 2.47121 | ||||||||
\(986\) | −479.209 | − | 1610.22i | −0.486013 | − | 1.63309i | ||||
\(987\) | − | 146.134i | − | 0.148059i | ||||||
\(988\) | −464.336 | + | 1282.56i | −0.469976 | + | 1.29813i | ||||
\(989\) | 701.838 | 0.709644 | ||||||||
\(990\) | −591.016 | + | 175.889i | −0.596986 | + | 0.177665i | ||||
\(991\) | 1643.98i | 1.65891i | 0.558575 | + | 0.829454i | \(0.311348\pi\) | ||||
−0.558575 | + | 0.829454i | \(0.688652\pi\) | |||||||
\(992\) | −1575.97 | − | 197.243i | −1.58867 | − | 0.198833i | ||||
\(993\) | 791.058i | 0.796635i | ||||||||
\(994\) | 253.034 | + | 850.236i | 0.254561 | + | 0.855368i | ||||
\(995\) | −1210.12 | −1.21621 | ||||||||
\(996\) | −53.8461 | − | 82.4535i | −0.0540623 | − | 0.0827847i | ||||
\(997\) | −1794.73 | −1.80013 | −0.900066 | − | 0.435754i | \(-0.856482\pi\) | ||||
−0.900066 | + | 0.435754i | \(0.856482\pi\) | |||||||
\(998\) | −399.819 | − | 1343.46i | −0.400621 | − | 1.34615i | ||||
\(999\) | −200.872 | −0.201073 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 156.3.e.c.103.9 | ✓ | 24 | |
3.2 | odd | 2 | 468.3.e.m.415.16 | 24 | |||
4.3 | odd | 2 | inner | 156.3.e.c.103.15 | yes | 24 | |
12.11 | even | 2 | 468.3.e.m.415.10 | 24 | |||
13.12 | even | 2 | inner | 156.3.e.c.103.16 | yes | 24 | |
39.38 | odd | 2 | 468.3.e.m.415.9 | 24 | |||
52.51 | odd | 2 | inner | 156.3.e.c.103.10 | yes | 24 | |
156.155 | even | 2 | 468.3.e.m.415.15 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
156.3.e.c.103.9 | ✓ | 24 | 1.1 | even | 1 | trivial | |
156.3.e.c.103.10 | yes | 24 | 52.51 | odd | 2 | inner | |
156.3.e.c.103.15 | yes | 24 | 4.3 | odd | 2 | inner | |
156.3.e.c.103.16 | yes | 24 | 13.12 | even | 2 | inner | |
468.3.e.m.415.9 | 24 | 39.38 | odd | 2 | |||
468.3.e.m.415.10 | 24 | 12.11 | even | 2 | |||
468.3.e.m.415.15 | 24 | 156.155 | even | 2 | |||
468.3.e.m.415.16 | 24 | 3.2 | odd | 2 |