Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [460,2,Mod(17,460)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(460, base_ring=CyclotomicField(44))
chi = DirichletCharacter(H, H._module([0, 11, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("460.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 460 = 2^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 460.x (of order \(44\), degree \(20\), 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: | \(3.67311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(240\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{44})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{44}]$ |
Embedding invariants
Embedding label | 17.11 | ||
Character | \(\chi\) | \(=\) | 460.17 |
Dual form | 460.2.x.a.433.11 |
$q$-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 \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(277\) | \(281\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{7}{22}\right)\) |
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 | 0 | ||||||||
\(3\) | 2.20798 | − | 1.20565i | 1.27478 | − | 0.696081i | 0.307923 | − | 0.951411i | \(-0.400366\pi\) |
0.966854 | + | 0.255331i | \(0.0821844\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.99649 | + | 1.00699i | 0.892857 | + | 0.450341i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.375619 | − | 0.501768i | −0.141970 | − | 0.189650i | 0.723920 | − | 0.689884i | \(-0.242338\pi\) |
−0.865891 | + | 0.500233i | \(0.833248\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.79966 | − | 2.80032i | 0.599886 | − | 0.933441i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.0603661 | + | 0.0275683i | −0.0182010 | + | 0.00831214i | −0.424495 | − | 0.905430i | \(-0.639548\pi\) |
0.406294 | + | 0.913743i | \(0.366821\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.355624 | + | 0.266217i | 0.0986325 | + | 0.0738353i | 0.647456 | − | 0.762103i | \(-0.275833\pi\) |
−0.548823 | + | 0.835938i | \(0.684924\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.62228 | − | 0.183642i | 1.45167 | − | 0.0474162i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.0449704 | + | 0.628768i | 0.0109069 | + | 0.152499i | 0.999987 | + | 0.00511887i | \(0.00162939\pi\) |
−0.989080 | + | 0.147380i | \(0.952916\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.607236 | − | 0.700788i | −0.139309 | − | 0.160772i | 0.681808 | − | 0.731532i | \(-0.261194\pi\) |
−0.821117 | + | 0.570760i | \(0.806649\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.43431 | − | 0.655028i | −0.312993 | − | 0.142939i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.74968 | − | 2.98996i | −0.781863 | − | 0.623450i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.97193 | + | 4.02090i | 0.594386 | + | 0.804180i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.0590001 | − | 0.824930i | 0.0113546 | − | 0.158758i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.43256 | + | 2.10783i | 0.451715 | + | 0.391414i | 0.850791 | − | 0.525505i | \(-0.176123\pi\) |
−0.399075 | + | 0.916918i | \(0.630669\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.49518 | + | 1.31991i | −0.807359 | + | 0.237062i | −0.659264 | − | 0.751911i | \(-0.729132\pi\) |
−0.148095 | + | 0.988973i | \(0.547314\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.100049 | + | 0.133650i | −0.0174163 | + | 0.0232655i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.244642 | − | 1.38002i | −0.0413520 | − | 0.233266i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.71439 | + | 1.46063i | −1.10384 | + | 0.240126i | −0.727330 | − | 0.686287i | \(-0.759239\pi\) |
−0.376509 | + | 0.926413i | \(0.622876\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.10617 | + | 0.159044i | 0.177130 | + | 0.0254674i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.16351 | − | 1.39041i | 0.337884 | − | 0.217145i | −0.360685 | − | 0.932688i | \(-0.617457\pi\) |
0.698569 | + | 0.715543i | \(0.253821\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.43629 | − | 9.95581i | −0.829026 | − | 1.51825i | −0.855026 | − | 0.518586i | \(-0.826459\pi\) |
0.0259998 | − | 0.999662i | \(-0.491723\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.41290 | − | 3.77857i | 0.955979 | − | 0.563276i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.75870 | + | 2.75870i | 0.402398 | + | 0.402398i | 0.879077 | − | 0.476679i | \(-0.158160\pi\) |
−0.476679 | + | 0.879077i | \(0.658160\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.86145 | − | 6.33950i | 0.265921 | − | 0.905643i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.857366 | + | 1.33409i | 0.120055 | + | 0.186810i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.18926 | + | 1.63886i | −0.300718 | + | 0.225114i | −0.738971 | − | 0.673737i | \(-0.764688\pi\) |
0.438254 | + | 0.898851i | \(0.355597\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.148281 | − | 0.00574849i | −0.0199942 | − | 0.000775127i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.18567 | − | 0.815211i | −0.289499 | − | 0.107977i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.540372 | + | 0.0776937i | −0.0703504 | + | 0.0101149i | −0.177400 | − | 0.984139i | \(-0.556769\pi\) |
0.107050 | + | 0.994254i | \(0.465860\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.64111 | + | 5.58909i | 0.210122 | + | 0.715610i | 0.995343 | + | 0.0963944i | \(0.0307310\pi\) |
−0.785221 | + | 0.619215i | \(0.787451\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.08110 | + | 0.148843i | −0.262194 | + | 0.0187525i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.441921 | + | 0.889611i | 0.0548136 | + | 0.110343i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.01402 | + | 5.39980i | 0.246052 | + | 0.659691i | 0.999996 | + | 0.00275241i | \(0.000876121\pi\) |
−0.753944 | + | 0.656938i | \(0.771851\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.8841 | − | 2.08098i | −1.43067 | − | 0.250520i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.22873 | + | 4.88024i | −0.264502 | + | 0.579178i | −0.994555 | − | 0.104212i | \(-0.966768\pi\) |
0.730053 | + | 0.683390i | \(0.239495\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.01580 | + | 0.430258i | 0.704096 | + | 0.0503579i | 0.418796 | − | 0.908080i | \(-0.362452\pi\) |
0.285300 | + | 0.958438i | \(0.407907\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11.4097 | + | 5.29496i | 1.31748 | + | 0.611409i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.0365075 | + | 0.0199346i | 0.00416041 | + | 0.00227176i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.20741 | + | 8.39774i | 0.135844 | + | 0.944819i | 0.937736 | + | 0.347349i | \(0.112918\pi\) |
−0.801891 | + | 0.597470i | \(0.796173\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.28414 | + | 7.19125i | 0.364904 | + | 0.799028i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.42936 | − | 15.7645i | −0.376422 | − | 1.73038i | −0.642370 | − | 0.766395i | \(-0.722049\pi\) |
0.265948 | − | 0.963987i | \(-0.414315\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.543382 | + | 1.30061i | −0.0589381 | + | 0.141071i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.91234 | + | 1.72122i | 0.848292 | + | 0.184535i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.87021 | − | 2.01727i | −0.728240 | − | 0.213831i | −0.103463 | − | 0.994633i | \(-0.532992\pi\) |
−0.624778 | + | 0.780803i | \(0.714810\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 0.278437i | − | 0.0291881i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.33393 | + | 8.33393i | −0.864188 | + | 0.864188i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.506651 | − | 2.01060i | −0.0519813 | − | 0.206283i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.64185 | + | 12.1444i | −0.268239 | + | 1.23308i | 0.623968 | + | 0.781450i | \(0.285520\pi\) |
−0.892207 | + | 0.451626i | \(0.850844\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.0314383 | + | 0.218658i | −0.00315966 | + | 0.0219759i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.30151 | − | 1.47909i | −0.229009 | − | 0.147175i | 0.421105 | − | 0.907012i | \(-0.361642\pi\) |
−0.650114 | + | 0.759837i | \(0.725279\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.327369 | + | 0.877710i | −0.0322566 | + | 0.0864833i | −0.952080 | − | 0.305850i | \(-0.901059\pi\) |
0.919823 | + | 0.392333i | \(0.128332\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.20398 | − | 2.75210i | −0.215086 | − | 0.268577i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.54004 | − | 15.6399i | 0.825597 | − | 1.51197i | −0.0330817 | − | 0.999453i | \(-0.510532\pi\) |
0.858678 | − | 0.512515i | \(-0.171286\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.8950 | + | 12.5735i | −1.04355 | + | 1.20432i | −0.0650903 | + | 0.997879i | \(0.520734\pi\) |
−0.978459 | + | 0.206441i | \(0.933812\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.0642 | + | 11.3202i | −1.24000 | + | 1.07447i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.2744 | + | 4.57810i | −1.15468 | + | 0.430672i | −0.852575 | − | 0.522604i | \(-0.824961\pi\) |
−0.302100 | + | 0.953276i | \(0.597688\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.47533 | − | 9.74533i | −0.417326 | − | 0.908757i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.38550 | − | 0.516763i | 0.128089 | − | 0.0477748i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.298604 | − | 0.258742i | 0.0273730 | − | 0.0237188i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.20058 | + | 8.30992i | −0.654599 | + | 0.755447i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.10065 | − | 5.67842i | 0.279576 | − | 0.512006i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.88441 | + | 11.0204i | 0.168547 | + | 0.985694i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.22789 | − | 11.3354i | 0.375165 | − | 1.00586i | −0.602948 | − | 0.797780i | \(-0.706007\pi\) |
0.978113 | − | 0.208075i | \(-0.0667198\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −24.0064 | − | 15.4280i | −2.11365 | − | 1.35836i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.82067 | − | 12.6630i | 0.159073 | − | 1.10637i | −0.741274 | − | 0.671202i | \(-0.765778\pi\) |
0.900347 | − | 0.435173i | \(-0.143313\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.123543 | + | 0.567920i | −0.0107126 | + | 0.0492449i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.948491 | − | 1.58755i | 0.0816331 | − | 0.136635i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.36585 | − | 4.36585i | 0.372999 | − | 0.372999i | −0.495569 | − | 0.868569i | \(-0.665040\pi\) |
0.868569 | + | 0.495569i | \(0.165040\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.5854i | 1.57639i | 0.615425 | + | 0.788196i | \(0.288984\pi\) | ||||
−0.615425 | + | 0.788196i | \(0.711016\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.41717 | + | 2.76513i | 0.793069 | + | 0.232866i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.0288068 | − | 0.00626653i | −0.00240894 | − | 0.000524034i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.73401 | + | 6.65782i | 0.227048 | + | 0.552902i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.53317 | − | 16.2417i | −0.291411 | − | 1.33960i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.26806 | − | 2.77667i | −0.103884 | − | 0.227474i | 0.850551 | − | 0.525892i | \(-0.176268\pi\) |
−0.954435 | + | 0.298418i | \(0.903541\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.58415 | + | 11.0180i | 0.128916 | + | 0.896633i | 0.946931 | + | 0.321436i | \(0.104165\pi\) |
−0.818015 | + | 0.575197i | \(0.804925\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.84168 | + | 1.00564i | 0.148891 | + | 0.0813008i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.3037 | − | 1.89144i | −0.827614 | − | 0.151924i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.01861 | + | 0.215895i | 0.240911 | + | 0.0172303i | 0.191273 | − | 0.981537i | \(-0.438739\pi\) |
0.0496386 | + | 0.998767i | \(0.484193\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.85795 | + | 6.25803i | −0.226650 | + | 0.496294i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.0918158 | + | 3.00456i | −0.00723610 | + | 0.236792i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.67174 | − | 9.84431i | −0.287593 | − | 0.771066i | −0.997751 | − | 0.0670242i | \(-0.978650\pi\) |
0.710159 | − | 0.704042i | \(-0.248623\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.334332 | + | 0.166082i | −0.0260277 | + | 0.0129295i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.4831 | − | 1.25042i | 1.35289 | − | 0.0967603i | 0.624015 | − | 0.781412i | \(-0.285500\pi\) |
0.728870 | + | 0.684652i | \(0.240046\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.60693 | − | 12.2841i | −0.277456 | − | 0.944928i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.05525 | + | 0.439278i | −0.233641 | + | 0.0335925i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.34127 | + | 2.73815i | 0.558147 | + | 0.208178i | 0.612676 | − | 0.790334i | \(-0.290093\pi\) |
−0.0545294 | + | 0.998512i | \(0.517366\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.901245 | − | 3.00154i | 0.0681277 | − | 0.226895i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.09946 | + | 0.823044i | −0.0826403 | + | 0.0618638i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.945877 | − | 1.47181i | −0.0706981 | − | 0.110008i | 0.804104 | − | 0.594488i | \(-0.202645\pi\) |
−0.874802 | + | 0.484480i | \(0.839009\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.53893 | + | 15.4582i | −0.337376 | + | 1.14900i | 0.599803 | + | 0.800148i | \(0.295246\pi\) |
−0.937179 | + | 0.348849i | \(0.886572\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.3620 | + | 10.3620i | 0.765981 | + | 0.765981i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.8760 | − | 3.84522i | −1.09371 | − | 0.282706i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.0200487 | − | 0.0367165i | −0.00146611 | − | 0.00268497i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.436085 | + | 0.280255i | −0.0317205 | + | 0.0203855i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.9585 | − | 2.43827i | −1.22708 | − | 0.176427i | −0.501861 | − | 0.864948i | \(-0.667351\pi\) |
−0.725216 | + | 0.688521i | \(0.758260\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.45234 | − | 0.533474i | 0.176523 | − | 0.0384003i | −0.123435 | − | 0.992353i | \(-0.539391\pi\) |
0.299958 | + | 0.953952i | \(0.403027\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.04831 | + | 1.43144i | 0.146682 | + | 0.102508i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.5755 | − | 18.1348i | 0.967216 | − | 1.29205i | 0.0108308 | − | 0.999941i | \(-0.496552\pi\) |
0.956385 | − | 0.292108i | \(-0.0943567\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.2813 | − | 3.89976i | 0.941490 | − | 0.276446i | 0.225250 | − | 0.974301i | \(-0.427680\pi\) |
0.716239 | + | 0.697855i | \(0.245862\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.9572 | + | 9.49444i | 0.772859 | + | 0.669686i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.143924 | − | 2.01232i | 0.0101015 | − | 0.141237i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.71956 | − | 0.597286i | 0.399471 | − | 0.0417163i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.1210 | + | 5.11941i | −1.05098 | + | 0.355824i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.0559759 | + | 0.0255633i | 0.00387194 | + | 0.00176825i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.5737 | + | 12.2027i | 0.727921 | + | 0.840065i | 0.992236 | − | 0.124371i | \(-0.0396913\pi\) |
−0.264315 | + | 0.964436i | \(0.585146\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.962859 | + | 13.4625i | 0.0659740 | + | 0.922437i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.828047 | − | 25.3510i | −0.0564723 | − | 1.72892i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.35076 | + | 1.75976i | 0.159580 | + | 0.119460i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.8015 | − | 6.30293i | 0.932618 | − | 0.425912i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.151396 | + | 0.235577i | −0.0101840 | + | 0.0158466i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.07424 | − | 5.44255i | −0.272832 | − | 0.364460i | 0.643109 | − | 0.765775i | \(-0.277644\pi\) |
−0.915940 | + | 0.401315i | \(0.868553\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 16.6083 | − | 1.08612i | 1.10722 | − | 0.0724081i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.18768 | + | 1.19456i | −0.145201 | + | 0.0792860i | −0.550207 | − | 0.835028i | \(-0.685451\pi\) |
0.405006 | + | 0.914314i | \(0.367269\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.4130 | 1.34893 | 0.674466 | − | 0.738306i | \(-0.264374\pi\) | ||||
0.674466 | + | 0.738306i | \(0.264374\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.104642 | 0.00688492 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.9341 | − | 11.9769i | 1.43695 | − | 0.784634i | 0.443217 | − | 0.896415i | \(-0.353837\pi\) |
0.993733 | + | 0.111781i | \(0.0356554\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.72972 | + | 8.28571i | 0.178067 | + | 0.540500i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.7906 | + | 17.0863i | 0.830842 | + | 1.10987i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.54892 | − | 8.63428i | 0.358930 | − | 0.558505i | −0.614088 | − | 0.789238i | \(-0.710476\pi\) |
0.973017 | + | 0.230732i | \(0.0741122\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.2180 | − | 4.66642i | 0.658201 | − | 0.300590i | −0.0581732 | − | 0.998307i | \(-0.518528\pi\) |
0.716374 | + | 0.697716i | \(0.245800\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 17.9076 | + | 13.4055i | 1.14878 | + | 0.859963i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.1002 | − | 10.7823i | 0.645278 | − | 0.688855i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0293863 | − | 0.410874i | −0.00186980 | − | 0.0261433i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −26.5784 | − | 30.6731i | −1.68434 | − | 1.94383i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.9727 | + | 7.75119i | 1.07131 | + | 0.489251i | 0.871405 | − | 0.490565i | \(-0.163210\pi\) |
0.199905 | + | 0.979815i | \(0.435937\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.308782 | + | 0.0771200i | 0.0194129 | + | 0.00484849i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.368304 | + | 3.52685i | 0.0230641 | + | 0.220860i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.484145 | − | 6.76923i | 0.0302001 | − | 0.422253i | −0.959752 | − | 0.280849i | \(-0.909384\pi\) |
0.989952 | − | 0.141404i | \(-0.0451616\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.25495 | + | 2.82043i | 0.202253 | + | 0.175253i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.2804 | − | 3.01859i | 0.636339 | − | 0.186846i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.44180 | − | 11.2769i | 0.520544 | − | 0.695365i | −0.460827 | − | 0.887490i | \(-0.652447\pi\) |
0.981370 | + | 0.192125i | \(0.0615380\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.02115 | + | 1.06739i | −0.369876 | + | 0.0655695i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.6014 | + | 3.82895i | −1.07719 | + | 0.234328i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.8992 | + | 3.57996i | 1.51813 | + | 0.218274i | 0.850403 | − | 0.526132i | \(-0.176358\pi\) |
0.667727 | + | 0.744407i | \(0.267267\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.52309 | + | 1.62149i | −0.153267 | + | 0.0984986i | −0.615026 | − | 0.788507i | \(-0.710855\pi\) |
0.461760 | + | 0.887005i | \(0.347218\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.335697 | − | 0.614783i | −0.0203173 | − | 0.0372083i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.290253 | − | 0.160795i | −0.0175029 | − | 0.00969629i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.8274 | − | 14.8274i | −0.890894 | − | 0.890894i | 0.103714 | − | 0.994607i | \(-0.466927\pi\) |
−0.994607 | + | 0.103714i | \(0.966927\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.39363 | + | 14.9633i | −0.263040 | + | 0.895832i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.0016 | − | 20.2309i | −0.775611 | − | 1.20687i | −0.973955 | − | 0.226741i | \(-0.927193\pi\) |
0.198344 | − | 0.980132i | \(-0.436444\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.91550 | − | 7.42265i | 0.589415 | − | 0.441231i | −0.262484 | − | 0.964936i | \(-0.584542\pi\) |
0.851899 | + | 0.523706i | \(0.175451\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.54274 | − | 3.82851i | −0.209854 | − | 0.226781i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.51032 | − | 0.563319i | −0.0891512 | − | 0.0332517i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.4336 | − | 2.36280i | 0.966685 | − | 0.138988i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.80870 | + | 29.9997i | 0.516375 | + | 1.75861i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.9457 | + | 1.64111i | −1.34050 | + | 0.0958748i | −0.723085 | − | 0.690759i | \(-0.757276\pi\) |
−0.617420 | + | 0.786634i | \(0.711822\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.15708 | − | 0.389036i | −0.0673680 | − | 0.0226505i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.0191803 | + | 0.0514243i | 0.00111295 | + | 0.00298394i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.537500 | − | 2.06153i | −0.0310844 | − | 0.119222i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.95354 | + | 6.46734i | −0.170239 | + | 0.372771i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.86495 | − | 0.490991i | −0.394381 | − | 0.0282067i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.35173 | + | 12.8111i | −0.134660 | + | 0.733563i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.34440 | − | 2.91826i | −0.305021 | − | 0.166554i | 0.319448 | − | 0.947604i | \(-0.396503\pi\) |
−0.624469 | + | 0.781050i | \(0.714684\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.335385 | + | 2.33265i | 0.0190794 | + | 0.132700i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.1657 | − | 28.8289i | −0.746558 | − | 1.63473i | −0.772455 | − | 0.635070i | \(-0.780971\pi\) |
0.0258965 | − | 0.999665i | \(-0.491756\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.97651 | − | 9.08588i | −0.111719 | − | 0.513564i | −0.998663 | − | 0.0516878i | \(-0.983540\pi\) |
0.886944 | − | 0.461877i | \(-0.152824\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.30477 | − | 1.79849i | −0.242546 | − | 0.101333i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.8144 | + | 3.00514i | 0.775895 | + | 0.168786i | 0.583042 | − | 0.812442i | \(-0.301862\pi\) |
0.192853 | + | 0.981228i | \(0.438226\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.204953 | − | 0.0601797i | −0.0114752 | − | 0.00336942i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 44.8289i | − | 2.50210i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.413325 | − | 0.413325i | 0.0229980 | − | 0.0229980i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.0135409 | + | 2.22111i | −0.000751116 | + | 0.123205i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.89669 | + | 40.8974i | −0.491988 | + | 2.26163i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.348008 | − | 2.42045i | 0.0191863 | − | 0.133444i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.3702 | − | 16.3045i | −1.39447 | − | 0.896174i | −0.394730 | − | 0.918797i | \(-0.629162\pi\) |
−0.999744 | + | 0.0226235i | \(0.992798\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.99339 | + | 21.4311i | −0.438035 | + | 1.17442i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.41659 | + | 12.8087i | −0.0773966 | + | 0.699817i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.29950 | − | 17.0308i | 0.506576 | − | 0.927725i | −0.491797 | − | 0.870710i | \(-0.663660\pi\) |
0.998373 | − | 0.0570153i | \(-0.0181584\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −21.5820 | + | 24.9069i | −1.17217 | + | 1.35276i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.234969 | − | 0.203602i | 0.0127243 | − | 0.0110257i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.99102 | + | 2.98050i | −0.431474 | + | 0.160932i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −21.6309 | − | 16.1218i | −1.16457 | − | 0.867969i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.9819 | + | 4.09604i | −0.589539 | + | 0.219887i | −0.626489 | − | 0.779430i | \(-0.715509\pi\) |
0.0369497 | + | 0.999317i | \(0.488236\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.14419 | + | 2.72446i | −0.168305 | + | 0.145837i | −0.734941 | − | 0.678131i | \(-0.762790\pi\) |
0.566636 | + | 0.823968i | \(0.308245\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.240592 | − | 0.277658i | 0.0128419 | − | 0.0148203i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.5382 | + | 22.9620i | −0.667340 | + | 1.22214i | 0.296340 | + | 0.955082i | \(0.404234\pi\) |
−0.963680 | + | 0.267059i | \(0.913948\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.36400 | + | 7.49903i | −0.496990 | + | 0.398007i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.347359 | − | 0.931306i | 0.0183842 | − | 0.0492900i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.36390 | + | 4.08983i | 0.335874 | + | 0.215853i | 0.697696 | − | 0.716394i | \(-0.254209\pi\) |
−0.361822 | + | 0.932247i | \(0.617845\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.58161 | − | 17.9555i | 0.135874 | − | 0.945027i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.87990 | + | 27.0295i | −0.308615 | + | 1.41868i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.5772 | + | 6.91687i | 0.605978 | + | 0.362045i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.7614 | + | 18.7614i | −0.979339 | + | 0.979339i | −0.999791 | − | 0.0204514i | \(-0.993490\pi\) |
0.0204514 | + | 0.999791i | \(0.493490\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 8.56079i | − | 0.445657i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.64465 | + | 0.482913i | 0.0853861 | + | 0.0250716i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.7344 | + | 2.55265i | 0.607582 | + | 0.132171i | 0.505823 | − | 0.862638i | \(-0.331189\pi\) |
0.101760 | + | 0.994809i | \(0.467553\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 17.4474 | + | 22.0608i | 0.900982 | + | 1.13922i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.303939 | + | 1.39718i | 0.0156536 | + | 0.0719586i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.74596 | + | 19.1510i | 0.449250 | + | 0.983720i | 0.989807 | + | 0.142413i | \(0.0454860\pi\) |
−0.540558 | + | 0.841307i | \(0.681787\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.33142 | − | 30.1257i | −0.221905 | − | 1.54339i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.7924 | − | 8.07728i | −0.755858 | − | 0.412730i | 0.0546135 | − | 0.998508i | \(-0.482607\pi\) |
−0.810472 | + | 0.585778i | \(0.800789\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0528127 | + | 0.0765619i | 0.00269159 | + | 0.00390196i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −37.6630 | − | 2.69371i | −1.91452 | − | 0.136929i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.66613 | + | 3.64832i | −0.0844762 | + | 0.184977i | −0.947156 | − | 0.320774i | \(-0.896057\pi\) |
0.862680 | + | 0.505751i | \(0.168784\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.71137 | − | 2.49214i | 0.0865476 | − | 0.126033i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.2472 | − | 30.1548i | −0.567344 | − | 1.52111i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.04588 | + | 17.9818i | −0.304201 | + | 0.904764i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.79219 | + | 0.414266i | −0.290702 | + | 0.0207914i | −0.215929 | − | 0.976409i | \(-0.569278\pi\) |
−0.0747732 | + | 0.997201i | \(0.523823\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.411930 | + | 1.40291i | 0.0206223 | + | 0.0702331i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.1757 | − | 3.61972i | 1.25722 | − | 0.180760i | 0.518676 | − | 0.854971i | \(-0.326425\pi\) |
0.738539 | + | 0.674210i | \(0.235516\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.94998 | − | 0.727304i | −0.0971353 | − | 0.0362296i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.684803 | + | 17.6644i | −0.0340281 | + | 0.877749i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.365054 | − | 0.273276i | 0.0180951 | − | 0.0135458i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.07719 | + | 11.0123i | 0.349944 | + | 0.544524i | 0.970950 | − | 0.239282i | \(-0.0769120\pi\) |
−0.621006 | + | 0.783806i | \(0.713276\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.37602 | − | 14.9034i | 0.215853 | − | 0.735129i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.241958 | + | 0.241958i | 0.0119060 | + | 0.0119060i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.02809 | − | 34.9271i | 0.443171 | − | 1.71450i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.4074 | + | 41.0361i | 1.09730 | + | 2.00955i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.82261 | + | 5.02729i | −0.382160 | + | 0.245599i | −0.717590 | − | 0.696466i | \(-0.754755\pi\) |
0.335430 | + | 0.942065i | \(0.391118\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.1246 | − | 2.60592i | −0.883338 | − | 0.127005i | −0.314308 | − | 0.949321i | \(-0.601772\pi\) |
−0.569031 | + | 0.822316i | \(0.692681\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.6900 | − | 2.76054i | 0.617008 | − | 0.134222i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.39456 | + | 2.04948i | −0.116153 | + | 0.0994142i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.18800 | − | 2.92282i | 0.105885 | − | 0.141445i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.0711600 | + | 0.0208945i | −0.00343564 | + | 0.00100879i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.96570 | + | 7.76882i | 0.431862 | + | 0.374211i | 0.843493 | − | 0.537140i | \(-0.180495\pi\) |
−0.411631 | + | 0.911351i | \(0.635041\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.73635 | − | 24.2774i | 0.0834438 | − | 1.16670i | −0.767361 | − | 0.641215i | \(-0.778431\pi\) |
0.850805 | − | 0.525482i | \(-0.176115\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.0636 | + | 11.4041i | 0.674299 | + | 0.546783i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.181614 | + | 4.44334i | 0.00868776 | + | 0.212554i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.292086 | + | 0.133391i | 0.0139405 | + | 0.00636641i | 0.422373 | − | 0.906422i | \(-0.361197\pi\) |
−0.408433 | + | 0.912788i | \(0.633924\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.4027 | − | 16.6216i | −0.685842 | − | 0.791504i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.618405 | − | 8.64643i | −0.0293813 | − | 0.410804i | −0.990765 | − | 0.135592i | \(-0.956706\pi\) |
0.961383 | − | 0.275212i | \(-0.0887481\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.6849 | − | 10.9457i | −0.553918 | − | 0.518877i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.14755 | − | 4.60200i | −0.290769 | − | 0.217667i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.3864 | − | 10.6802i | 1.10367 | − | 0.504031i | 0.221598 | − | 0.975138i | \(-0.428873\pi\) |
0.882076 | + | 0.471107i | \(0.156145\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.0922717 | + | 0.143578i | −0.00434490 | + | 0.00676080i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.7816 | + | 22.4176i | 0.788468 | + | 1.05327i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.280384 | − | 0.555896i | 0.0131446 | − | 0.0260608i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.0496 | + | 6.03353i | −0.516878 | + | 0.282237i | −0.716440 | − | 0.697648i | \(-0.754230\pi\) |
0.199562 | + | 0.979885i | \(0.436048\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.521343 | 0.0243342 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.5054 | 1.23448 | 0.617241 | − | 0.786774i | \(-0.288251\pi\) | ||||
0.617241 | + | 0.786774i | \(0.288251\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.1938 | + | 7.75038i | −0.659640 | + | 0.360191i | −0.773943 | − | 0.633255i | \(-0.781718\pi\) |
0.114303 | + | 0.993446i | \(0.463537\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −25.0308 | + | 8.24638i | −1.16078 | + | 0.382417i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.655124 | + | 0.875143i | 0.0303155 | + | 0.0404968i | 0.815443 | − | 0.578838i | \(-0.196493\pi\) |
−0.785127 | + | 0.619334i | \(0.787403\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.95294 | − | 3.03884i | 0.0901785 | − | 0.140320i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.92532 | − | 3.16269i | 0.319102 | − | 0.145729i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.602632 | + | 0.451124i | 0.0277090 | + | 0.0207427i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.01313 | − | 4.52433i | 0.0464857 | − | 0.207590i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.649415 | + | 9.08001i | 0.0297347 | + | 0.415745i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.6334 | − | 16.8878i | −0.668616 | − | 0.771624i | 0.315543 | − | 0.948911i | \(-0.397813\pi\) |
−0.984159 | + | 0.177287i | \(0.943268\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.77665 | − | 1.26805i | −0.126604 | − | 0.0578182i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.41971 | + | 6.74469i | 0.155602 | + | 0.306894i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.5037 | + | 21.5858i | −0.794804 | + | 0.980161i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.46915 | + | 34.5233i | −0.111888 | + | 1.56440i | 0.562986 | + | 0.826467i | \(0.309653\pi\) |
−0.674874 | + | 0.737933i | \(0.735802\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −19.9759 | − | 17.3092i | −0.903340 | − | 0.782749i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.5216 | + | 3.67666i | −0.565090 | + | 0.165925i | −0.551785 | − | 0.833986i | \(-0.686053\pi\) |
−0.0133046 | + | 0.999911i | \(0.504235\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.21594 | + | 1.62431i | −0.0547632 | + | 0.0731551i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.282953 | + | 0.404890i | −0.0127178 | + | 0.0181984i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.28590 | − | 0.714804i | 0.147393 | − | 0.0320633i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 40.5651 | + | 5.83238i | 1.81594 | + | 0.261093i | 0.964638 | − | 0.263579i | \(-0.0849030\pi\) |
0.851304 | + | 0.524672i | \(0.175812\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 37.0948 | − | 23.8394i | 1.65727 | − | 1.06507i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.70407 | − | 17.7717i | −0.432683 | − | 0.792400i | 0.566822 | − | 0.823840i | \(-0.308173\pi\) |
−0.999506 | + | 0.0314399i | \(0.989991\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.10551 | − | 5.27060i | −0.138193 | − | 0.234538i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −22.7743 | − | 22.7743i | −1.01144 | − | 1.01144i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.4509 | + | 42.4037i | −0.551874 | + | 1.87951i | −0.0823239 | + | 0.996606i | \(0.526234\pi\) |
−0.469550 | + | 0.882906i | \(0.655584\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.04376 | − | 3.18015i | −0.0904104 | − | 0.140681i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.613927 | + | 0.459580i | −0.0271056 | + | 0.0202910i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.53744 | + | 1.42268i | −0.0677475 | + | 0.0626907i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.242585 | − | 0.0904793i | −0.0106689 | − | 0.00397928i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.5106 | − | 2.80520i | 0.856421 | − | 0.123135i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.21246 | − | 10.9406i | −0.140740 | − | 0.479317i | 0.858710 | − | 0.512461i | \(-0.171266\pi\) |
−0.999451 | + | 0.0331439i | \(0.989448\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.9697 | − | 1.07066i | 0.654581 | − | 0.0468165i | 0.259901 | − | 0.965635i | \(-0.416310\pi\) |
0.394680 | + | 0.918819i | \(0.370856\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.62887 | − | 7.71392i | −0.0710899 | − | 0.336663i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.03206 | − | 2.76707i | −0.0449574 | − | 0.120535i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.12025 | + | 22.4228i | 0.222620 | + | 0.974905i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.754917 | + | 1.65304i | −0.0327606 | + | 0.0717357i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.13955 | + | 0.0815021i | 0.0493593 | + | 0.00353025i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.7994 | − | 22.6251i | 1.41804 | − | 0.978170i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.86296 | − | 2.10934i | −0.166699 | − | 0.0910246i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.0624009 | + | 0.434008i | 0.00268780 | + | 0.0186940i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.75542 | + | 6.03353i | 0.118465 | + | 0.259402i | 0.959570 | − | 0.281470i | \(-0.0908218\pi\) |
−0.841105 | + | 0.540871i | \(0.818095\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.61525 | + | 39.6037i | 0.369716 | + | 1.69956i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −34.4131 | + | 14.1316i | −1.47409 | + | 0.605332i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.89385 | + | 0.629519i | 0.123732 | + | 0.0269163i | 0.274005 | − | 0.961728i | \(-0.411652\pi\) |
−0.150273 | + | 0.988645i | \(0.548015\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 18.6047 | + | 5.46283i | 0.794029 | + | 0.233148i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.98466i | − | 0.127151i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.76019 | − | 3.76019i | 0.159899 | − | 0.159899i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −37.4820 | + | 9.44510i | −1.59102 | + | 0.400922i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.88830 | + | 27.0681i | −0.249495 | + | 1.14691i | 0.666432 | + | 0.745566i | \(0.267821\pi\) |
−0.915927 | + | 0.401345i | \(0.868543\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.717132 | − | 4.98776i | 0.0303315 | − | 0.210960i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.0885342 | − | 0.0568975i | −0.00373792 | − | 0.00240221i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.69270 | + | 15.2627i | −0.239919 | + | 0.643247i | −0.999978 | − | 0.00660664i | \(-0.997897\pi\) |
0.760060 | + | 0.649853i | \(0.225170\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −29.1158 | − | 3.22007i | −1.22491 | − | 0.135470i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.37476 | − | 4.34904i | 0.0997304 | − | 0.182643i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.3645 | − | 23.5018i | 0.853722 | − | 0.985248i | −0.146270 | − | 0.989245i | \(-0.546727\pi\) |
0.999992 | + | 0.00399652i | \(0.00127213\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.2033 | + | 20.9723i | −1.01288 | + | 0.877663i | −0.992514 | − | 0.122130i | \(-0.961027\pi\) |
−0.0203625 | + | 0.999793i | \(0.506482\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −40.3838 | + | 15.0624i | −1.68706 | + | 0.629240i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.878538 | − | 23.9631i | 0.0366376 | − | 0.999329i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.44290 | + | 2.77606i | −0.309852 | + | 0.115569i | −0.499580 | − | 0.866268i | \(-0.666512\pi\) |
0.189728 | + | 0.981837i | \(0.439239\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.77153 | − | 4.13455i | 0.198298 | − | 0.171826i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.62200 | + | 7.64220i | −0.274727 | + | 0.317052i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.0869764 | − | 0.159285i | 0.00360219 | − | 0.00659693i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.28650 | + | 0.363473i | 0.135880 | + | 0.0150278i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.85130 | − | 7.64463i | 0.117686 | − | 0.315528i | −0.864729 | − | 0.502238i | \(-0.832510\pi\) |
0.982415 | + | 0.186711i | \(0.0597827\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.65461 | + | 2.34868i | 0.150586 | + | 0.0967755i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.11031 | − | 56.4085i | 0.333614 | − | 2.32033i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.23157 | + | 10.2584i | −0.0916398 | + | 0.421261i | 0.908356 | + | 0.418199i | \(0.137338\pi\) |
−0.999995 | + | 0.00306243i | \(0.999025\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.856710 | − | 0.215883i | 0.0351217 | − | 0.00885033i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 24.6232 | − | 24.6232i | 1.00776 | − | 1.00776i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 11.0925i | − | 0.453227i | −0.973985 | − | 0.226614i | \(-0.927235\pi\) | ||
0.973985 | − | 0.226614i | \(-0.0727654\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.06702 | − | 1.78144i | −0.247479 | − | 0.0726664i | 0.155640 | − | 0.987814i | \(-0.450256\pi\) |
−0.403119 | + | 0.915147i | \(0.632074\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.7457 | + | 4.07789i | 0.763386 | + | 0.166064i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.7439 | + | 9.33971i | −0.924671 | + | 0.379713i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.87335 | − | 31.5963i | −0.278981 | − | 1.28245i | −0.876813 | − | 0.480832i | \(-0.840335\pi\) |
0.597832 | − | 0.801621i | \(-0.296029\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.10837 | − | 4.61668i | −0.0854353 | − | 0.187077i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.246648 | + | 1.71548i | 0.00997832 | + | 0.0694007i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.4827 | − | 18.2829i | −1.35235 | − | 0.738440i | −0.370633 | − | 0.928779i | \(-0.620859\pi\) |
−0.981718 | + | 0.190339i | \(0.939041\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.9085 | − | 8.21456i | 0.480199 | − | 0.331243i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.0077 | − | 1.07337i | −0.604188 | − | 0.0432124i | −0.234105 | − | 0.972211i | \(-0.575216\pi\) |
−0.370083 | + | 0.928999i | \(0.620671\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.577910 | + | 1.26545i | −0.0232282 | + | 0.0508626i | −0.920891 | − | 0.389821i | \(-0.872537\pi\) |
0.897662 | + | 0.440684i | \(0.145264\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.68774 | + | 2.91682i | −0.107855 | + | 0.117048i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.56837 | + | 4.20497i | 0.0628356 | + | 0.168469i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.33526 | + | 23.8997i | −0.293410 | + | 0.955987i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.154414 | − | 0.0110439i | 0.00616670 | − | 0.000441051i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.22034 | − | 4.15611i | −0.0486583 | − | 0.165715i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.4216 | + | 5.81176i | −1.60916 | + | 0.231362i | −0.887474 | − | 0.460858i | \(-0.847542\pi\) |
−0.721686 | + | 0.692220i | \(0.756633\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 38.0585 | + | 14.1951i | 1.51269 | + | 0.564204i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.8556 | − | 18.3736i | 0.787946 | − | 0.729133i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.34966 | − | 1.75893i | 0.0930969 | − | 0.0696915i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.65529 | + | 15.0239i | 0.381958 | + | 0.594338i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.59468 | + | 32.6765i | −0.378967 | + | 1.29064i | 0.520577 | + | 0.853815i | \(0.325717\pi\) |
−0.899544 | + | 0.436829i | \(0.856101\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.4585 | + | 23.4585i | 0.925112 | + | 0.925112i | 0.997385 | − | 0.0722733i | \(-0.0230254\pi\) |
−0.0722733 | + | 0.997385i | \(0.523025\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −32.3926 | − | 54.9760i | −1.27546 | − | 2.16468i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.45768 | + | 11.8264i | 0.253878 | + | 0.464942i | 0.973271 | − | 0.229661i | \(-0.0737618\pi\) |
−0.719393 | + | 0.694603i | \(0.755580\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.0304782 | − | 0.0195872i | 0.00119638 | − | 0.000768864i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.31207 | + | 1.05132i | 0.286583 | + | 0.0412044i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 37.1674 | − | 8.08527i | 1.45447 | − | 0.316401i | 0.585262 | − | 0.810844i | \(-0.300992\pi\) |
0.869210 | + | 0.494443i | \(0.164628\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.3865 | − | 23.4482i | 0.640275 | − | 0.916197i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.0312 | − | 16.0719i | 0.469383 | − | 0.627023i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.8366 | + | 8.17355i | −1.08436 | + | 0.318396i | −0.774621 | − | 0.632426i | \(-0.782059\pi\) |
−0.309738 | + | 0.950822i | \(0.600241\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.6495 | + | 11.8273i | 0.530902 | + | 0.460030i | 0.878587 | − | 0.477582i | \(-0.158487\pi\) |
−0.347685 | + | 0.937611i | \(0.613032\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.0502566 | + | 0.702679i | −0.00195181 | + | 0.0272898i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.818545 | + | 1.00944i | −0.0317418 | + | 0.0391444i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.81901 | − | 15.1769i | −0.109153 | − | 0.587654i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.5576 | − | 7.10493i | −0.601493 | − | 0.274693i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.253149 | − | 0.292149i | −0.00977269 | − | 0.0112783i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.21307 | − | 44.9246i | −0.123855 | − | 1.73171i | −0.557106 | − | 0.830442i | \(-0.688088\pi\) |
0.433251 | − | 0.901273i | \(-0.357366\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.49230 | − | 2.21440i | 0.134419 | − | 0.0852323i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.2096 | + | 17.3745i | 0.892018 | + | 0.667756i | 0.943663 | − | 0.330909i | \(-0.107355\pi\) |
−0.0516449 | + | 0.998666i | \(0.516446\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.08599 | − | 3.23606i | 0.271935 | − | 0.124189i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.39013 | + | 5.27514i | −0.129910 | + | 0.202144i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.6171 | + | 35.5563i | 1.01848 | + | 1.36053i | 0.931268 | + | 0.364336i | \(0.118704\pi\) |
0.0872093 | + | 0.996190i | \(0.472205\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.1127 | − | 4.31999i | 0.501012 | − | 0.165058i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 45.0715 | − | 24.6109i | 1.71959 | − | 0.938965i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.21485 | −0.0462819 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 49.5944 | 1.88666 | 0.943330 | − | 0.331856i | \(-0.107675\pi\) | ||||
0.943330 | + | 0.331856i | \(0.107675\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.121524 | − | 0.0663573i | 0.00461632 | − | 0.00252070i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.7153 | + | 37.1055i | −0.709913 | + | 1.40749i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.971536 | + | 1.29782i | 0.0367996 | + | 0.0491585i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 33.9900 | − | 52.8895i | 1.28562 | − | 2.00047i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.3225 | − | 16.1312i | 1.33411 | − | 0.609268i | 0.384624 | − | 0.923073i | \(-0.374331\pi\) |
0.949487 | + | 0.313805i | \(0.101604\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.10081 | + | 3.81842i | 0.192381 | + | 0.144014i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.0168 | + | 15.0036i | 0.603228 | + | 0.565067i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.122330 | + | 1.71040i | 0.00460070 | + | 0.0643262i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.20810 | − | 10.6267i | −0.345817 | − | 0.399094i | 0.556021 | − | 0.831168i | \(-0.312327\pi\) |
−0.901838 | + | 0.432074i | \(0.857782\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.6893 | + | 11.7319i | 0.963424 | + | 0.439981i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.8020 | + | 8.49120i | 0.779040 | + | 0.317998i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.0512021 | − | 0.0415193i | −0.00191485 | − | 0.00155273i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.84199 | − | 25.7543i | 0.0687903 | − | 0.961813i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32.6514 | − | 28.2926i | −1.21769 | − | 1.05514i | −0.996808 | − | 0.0798375i | \(-0.974560\pi\) |
−0.220885 | − | 0.975300i | \(-0.570895\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.563372 | − | 0.165421i | 0.0209811 | − | 0.00616060i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.9351 | − | 22.6227i | 0.629824 | − | 0.841347i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.24595 | + | 16.0454i | −0.0462735 | + | 0.595911i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.04338 | + | 1.09712i | −0.187049 | + | 0.0406900i | −0.305114 | − | 0.952316i | \(-0.598695\pi\) |
0.118065 | + | 0.993006i | \(0.462331\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 32.2264 | + | 4.63345i | 1.19357 | + | 0.171609i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.01542 | − | 3.86588i | 0.222489 | − | 0.142985i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.7627 | + | 19.7104i | 0.397529 | + | 0.728019i | 0.997399 | − | 0.0720780i | \(-0.0229631\pi\) |
−0.599870 | + | 0.800097i | \(0.704781\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.30137 | − | 35.9843i | 0.343086 | − | 1.32730i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.270442 | − | 0.270442i | −0.00996185 | − | 0.00996185i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.2377 | + | 41.6776i | −0.450170 | + | 1.53314i | 0.351977 | + | 0.936009i | \(0.385510\pi\) |
−0.802146 | + | 0.597128i | \(0.796308\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.560253 | − | 0.871771i | −0.0205814 | − | 0.0320253i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.4131 | − | 9.29232i | 0.455392 | − | 0.340902i | −0.346830 | − | 0.937928i | \(-0.612742\pi\) |
0.802222 | + | 0.597026i | \(0.203651\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.264415 | − | 6.82053i | 0.00968742 | − | 0.249885i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −50.3175 | − | 18.7674i | −1.84102 | − | 0.686665i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.0554 | + | 1.58953i | −0.403956 | + | 0.0580800i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.01304 | + | 23.8842i | 0.255909 | + | 0.871547i | 0.982781 | + | 0.184774i | \(0.0591553\pi\) |
−0.726872 | + | 0.686773i | \(0.759026\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 46.8206 | − | 3.34868i | 1.70624 | − | 0.122033i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.93232 | + | 23.5925i | −0.288687 | + | 0.858621i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.46470 | − | 17.3325i | −0.234964 | − | 0.629962i | 0.764936 | − | 0.644106i | \(-0.222770\pi\) |
−0.999900 | + | 0.0141442i | \(0.995498\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.774762 | − | 0.202002i | 0.0281221 | − | 0.00733222i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.8886 | + | 41.3602i | −0.684710 | + | 1.49930i | 0.172865 | + | 0.984945i | \(0.444697\pi\) |
−0.857575 | + | 0.514359i | \(0.828030\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.4013 | + | 0.743917i | 0.376553 | + | 0.0269316i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.66423 | + | 3.86230i | 0.0963256 | + | 0.139642i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.212853 | − | 0.116226i | −0.00768567 | − | 0.00419669i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.29776 | + | 22.9364i | 0.118920 | + | 0.827109i | 0.958748 | + | 0.284256i | \(0.0917467\pi\) |
−0.839828 | + | 0.542853i | \(0.817344\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.09232 | − | 15.5300i | −0.255424 | − | 0.559300i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.57341 | + | 30.2175i | 0.236429 | + | 1.08685i | 0.930315 | + | 0.366762i | \(0.119534\pi\) |
−0.693885 | + | 0.720085i | \(0.744103\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.6666 | − | 14.1520i | −0.670523 | − | 0.508355i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.5873 | + | 2.30312i | 0.379817 | + | 0.0826241i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.28814 | − | 0.671859i | −0.0819812 | − | 0.0240719i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 0.356043i | − | 0.0127402i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.88233 | − | 1.88233i | 0.0672690 | − | 0.0672690i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.80922 | + | 3.47075i | 0.207340 | + | 0.123876i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.601648 | − | 2.76573i | 0.0214464 | − | 0.0985877i | −0.965179 | − | 0.261589i | \(-0.915754\pi\) |
0.986626 | + | 0.163001i | \(0.0521173\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.04332 | − | 35.0770i | 0.179547 | − | 1.24878i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.90763 | + | 4.43926i | 0.245607 | + | 0.157842i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.904295 | + | 2.42451i | −0.0321124 | + | 0.0860968i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.0077 | + | 9.61616i | −0.425868 | + | 0.341050i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.6727 | − | 37.8593i | 0.732265 | − | 1.34104i | −0.200190 | − | 0.979757i | \(-0.564156\pi\) |
0.932455 | − | 0.361286i | \(-0.117662\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.61052 | + | 1.85864i | −0.0569762 | + | 0.0657541i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.0130 | + | 15.6084i | −0.636460 | + | 0.551495i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.375011 | + | 0.139872i | −0.0132339 | + | 0.00493598i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.20888 | + | 5.90610i | −0.113098 | + | 0.208163i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 59.2930 | − | 22.1151i | 2.08721 | − | 0.778490i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.6523 | + | 23.0943i | −0.937043 | + | 0.811953i | −0.982356 | − | 0.187020i | \(-0.940117\pi\) |
0.0453128 | + | 0.998973i | \(0.485572\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.30963 | − | 6.12764i | 0.186446 | − | 0.215170i | −0.654830 | − | 0.755777i | \(-0.727260\pi\) |
0.841276 | + | 0.540606i | \(0.181805\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.61598 | + | 6.62218i | −0.126818 | + | 0.232250i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.58257 | − | 23.3515i | 0.0904634 | − | 0.817966i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.67580 | + | 9.85521i | −0.128600 | + | 0.344790i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.779713 | − | 0.501091i | −0.0272454 | − | 0.0175095i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.05382 | + | 14.2846i | −0.0716788 | + | 0.498537i | 0.922081 | + | 0.386997i | \(0.126487\pi\) |
−0.993760 | + | 0.111540i | \(0.964422\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.69710 | + | 35.3830i | −0.268304 | + | 1.23337i | 0.623815 | + | 0.781572i | \(0.285582\pi\) |
−0.892119 | + | 0.451801i | \(0.850782\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.834734 | − | 0.00508894i | −0.0290617 | − | 0.000177174i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.2641 | + | 25.2641i | −0.878519 | + | 0.878519i | −0.993381 | − | 0.114862i | \(-0.963357\pi\) |
0.114862 | + | 0.993381i | \(0.463357\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 5.69858i | − | 0.197920i | −0.995091 | − | 0.0989600i | \(-0.968448\pi\) | ||
0.995091 | − | 0.0989600i | \(-0.0315516\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −50.6153 | − | 14.8620i | −1.75582 | − | 0.515556i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.06979 | + | 0.885328i | 0.141010 | + | 0.0306748i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 36.1640 | + | 15.1089i | 1.25151 | + | 0.522867i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.823612 | + | 3.78608i | 0.0284682 | + | 0.130866i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.85614 | − | 8.44376i | −0.133129 | − | 0.291511i | 0.831314 | − | 0.555803i | \(-0.187589\pi\) |
−0.964443 | + | 0.264292i | \(0.914862\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.65271 | − | 18.4500i | −0.0914727 | − | 0.636206i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −53.0986 | − | 28.9940i | −1.82881 | − | 0.998607i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.16878 | − | 28.1571i | 0.177811 | − | 0.968635i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.87432 | + | 0.491661i | 0.236204 | + | 0.0168937i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.9441 | − | 28.3436i | 0.444240 | − | 0.972751i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29.5441 | + | 14.5989i | 1.01276 | + | 0.500444i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.8462 | − | 47.8474i | −0.611041 | − | 1.63826i | −0.760380 | − | 0.649478i | \(-0.774987\pi\) |
0.149339 | − | 0.988786i | \(-0.452285\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.54212 | − | 2.19960i | −0.223736 | − | 0.0752247i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.57022 | + | 0.326869i | −0.156116 | + | 0.0111656i | −0.149178 | − | 0.988810i | \(-0.547663\pi\) |
−0.00693755 | + | 0.999976i | \(0.502208\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.7831 | + | 43.5352i | 0.436153 | + | 1.48540i | 0.825549 | + | 0.564331i | \(0.190866\pi\) |
−0.389396 | + | 0.921071i | \(0.627316\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.01391 | + | 0.577113i | −0.136794 | + | 0.0196680i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.2387 | − | 12.0244i | −1.09742 | − | 0.409316i | −0.265442 | − | 0.964127i | \(-0.585518\pi\) |
−0.831977 | + | 0.554811i | \(0.812791\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.8995 | + | 12.8593i | 0.404594 | + | 0.437229i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 33.4364 | − | 25.0302i | 1.13556 | − | 0.850069i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.304398 | − | 0.473652i | −0.0103260 | − | 0.0160675i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.721284 | + | 2.45647i | −0.0244398 | + | 0.0832343i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 29.2538 | + | 29.2538i | 0.990091 | + | 0.990091i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.82186 | − | 5.08500i | 0.163009 | − | 0.171904i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.0748 | + | 40.4271i | 0.745414 | + | 1.36512i | 0.924458 | + | 0.381283i | \(0.124518\pi\) |
−0.179044 | + | 0.983841i | \(0.557300\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −48.6851 | + | 31.2880i | −1.64211 | + | 1.05532i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.4715 | − | 5.38759i | −1.26245 | − | 0.181512i | −0.521602 | − | 0.853189i | \(-0.674665\pi\) |
−0.740844 | + | 0.671677i | \(0.765574\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.3370 | + | 6.16433i | −0.953615 | + | 0.207446i | −0.662349 | − | 0.749196i | \(-0.730440\pi\) |
−0.291266 | + | 0.956642i | \(0.594077\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.02385 | + | 0.536051i | −0.101646 | + | 0.0180192i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31.9121 | + | 42.6295i | −1.07150 | + | 1.43136i | −0.177046 | + | 0.984203i | \(0.556654\pi\) |
−0.894456 | + | 0.447157i | \(0.852437\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.27582 | + | 2.13637i | −0.244023 | + | 0.0716517i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.396501 | − | 0.343570i | −0.0132833 | − | 0.0115100i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.258081 | − | 3.60845i | 0.00863636 | − | 0.120752i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.406327 | − | 3.89095i | −0.0135820 | − | 0.130060i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.67227 | − | 3.90379i | −0.122614 | − | 0.130344i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.7169 | − | 6.26432i | −0.457486 | − | 0.208927i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.12891 | − | 1.30283i | −0.0376095 | − | 0.0434037i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.27599 | + | 17.8407i | 0.0424623 | + | 0.593700i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24.6282 | + | 26.2914i | −0.818669 | + | 0.873956i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.48982 | − | 1.11527i | −0.0494688 | − | 0.0370319i | 0.574257 | − | 0.818675i | \(-0.305291\pi\) |
−0.623726 | + | 0.781643i | \(0.714382\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.28387 | + | 3.78312i | −0.274759 | + | 0.125478i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.8084 | + | 21.4863i | −0.457492 | + | 0.711871i | −0.990991 | − | 0.133929i | \(-0.957240\pi\) |
0.533499 | + | 0.845801i | \(0.320877\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.641618 | + | 0.857101i | 0.0212345 | + | 0.0283659i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.2531 | + | 31.1221i | 0.338959 | + | 1.02886i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.03778 | + | 3.84292i | −0.232408 | + | 0.126904i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.6605 | 0.384644 | 0.192322 | − | 0.981332i | \(-0.438398\pi\) | ||||
0.192322 | + | 0.981332i | \(0.438398\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.3187 | −0.504769 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.09179 | + | 1.14221i | −0.0688523 | + | 0.0375962i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.8277 | − | 22.6570i | −0.849211 | − | 0.744958i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.86872 | + | 2.49632i | 0.0613768 | + | 0.0819898i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.14718 | − | 8.00916i | 0.168873 | − | 0.262772i | −0.746494 | − | 0.665393i | \(-0.768264\pi\) |
0.915367 | + | 0.402620i | \(0.131901\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.57298 | + | 2.54510i | −0.182647 | + | 0.0834122i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −63.8270 | − | 47.7803i | −2.08960 | − | 1.56426i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.00305379 | − | 0.0934929i | −9.98696e−5 | − | 0.00305755i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.18848 | − | 16.6172i | −0.0388260 | − | 0.542859i | −0.979224 | − | 0.202782i | \(-0.935002\pi\) |
0.940398 | − | 0.340076i | \(-0.110453\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.3185 | − | 17.6785i | −0.499899 | − | 0.576914i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.4588 | + | 17.1069i | 1.22112 | + | 0.557668i | 0.918492 | − | 0.395439i | \(-0.129408\pi\) |
0.302631 | + | 0.953108i | \(0.402135\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.2698 | − | 1.25524i | −0.399558 | − | 0.0408763i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.15285 | + | 0.120391i | −0.0375023 | + | 0.00391631i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.80278 | + | 25.2061i | −0.0585824 | + | 0.819090i | 0.880205 | + | 0.474593i | \(0.157405\pi\) |
−0.938788 | + | 0.344496i | \(0.888050\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.02482 | + | 1.75452i | 0.0657285 | + | 0.0569541i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 34.1251 | − | 10.0200i | 1.10658 | − | 0.324922i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.508094 | + | 0.678733i | −0.0164588 | + | 0.0219863i | −0.808695 | − | 0.588228i | \(-0.799826\pi\) |
0.792236 | + | 0.610214i | \(0.208917\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −31.4022 | − | 21.9451i | −1.01615 | − | 0.710127i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.525088 | + | 0.114226i | −0.0169737 | + | 0.00369240i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.83053 | − | 0.550748i | −0.123694 | − | 0.0177846i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.61433 | + | 4.89343i | −0.245624 | + | 0.157853i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −28.4277 | − | 52.0614i | −0.916068 | − | 1.67765i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.43327 | + | 1.40441i | 0.174903 | + | 0.0452097i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.19326 | − | 5.19326i | −0.167004 | − | 0.167004i | 0.618657 | − | 0.785661i | \(-0.287677\pi\) |
−0.785661 | + | 0.618657i | \(0.787677\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.414288 | − | 1.41094i | 0.0133089 | − | 0.0453258i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.5163 | − | 38.1481i | −0.786765 | − | 1.22423i | −0.970464 | − | 0.241247i | \(-0.922444\pi\) |
0.183699 | − | 0.982983i | \(-0.441193\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.32554 | − | 6.98101i | 0.298963 | − | 0.223801i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.64798 | + | 4.92048i | 0.0848031 | + | 0.157582i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.9432 | + | 8.93037i | 0.766012 | + | 0.285708i | 0.701939 | − | 0.712237i | \(-0.252318\pi\) |
0.0640736 | + | 0.997945i | \(0.479591\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.470340 | − | 0.0676247i | 0.0150321 | − | 0.00216129i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.6025 | + | 53.1374i | 0.498151 | + | 1.69655i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.65470 | + | 0.547475i | −0.244147 | + | 0.0174617i | −0.192876 | − | 0.981223i | \(-0.561782\pi\) |
−0.0512706 | + | 0.998685i | \(0.516327\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 45.3650 | − | 22.5354i | 1.44545 | − | 0.718038i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.14981 | − | 5.76387i | −0.0684293 | − | 0.183466i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.38316 | + | 53.5854i | −0.298367 | + | 1.70392i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.2360 | + | 24.6034i | −0.356923 | + | 0.781551i | 0.642955 | + | 0.765904i | \(0.277708\pi\) |
−0.999878 | + | 0.0156474i | \(0.995019\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −75.6743 | − | 5.41233i | −2.40145 | − | 0.171755i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30.4431 | + | 5.58841i | 0.965111 | + | 0.177164i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −45.4417 | − | 24.8131i | −1.43915 | − | 0.785837i | −0.445178 | − | 0.895442i | \(-0.646860\pi\) |
−0.993975 | + | 0.109605i | \(0.965042\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.808764 | + | 5.62508i | 0.0255882 | + | 0.177970i |
(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 | 460.2.x.a.17.11 | ✓ | 240 | |
5.3 | odd | 4 | inner | 460.2.x.a.293.11 | yes | 240 | |
23.19 | odd | 22 | inner | 460.2.x.a.157.11 | yes | 240 | |
115.88 | even | 44 | inner | 460.2.x.a.433.11 | yes | 240 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.x.a.17.11 | ✓ | 240 | 1.1 | even | 1 | trivial | |
460.2.x.a.157.11 | yes | 240 | 23.19 | odd | 22 | inner | |
460.2.x.a.293.11 | yes | 240 | 5.3 | odd | 4 | inner | |
460.2.x.a.433.11 | yes | 240 | 115.88 | even | 44 | inner |