Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [729,2,Mod(28,729)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(729, base_ring=CyclotomicField(54))
chi = DirichletCharacter(H, H._module([44]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("729.28");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 729 = 3^{6} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 729.g (of order \(27\), degree \(18\), not 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: | \(5.82109430735\) |
Analytic rank: | \(0\) |
Dimension: | \(144\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{27})\) |
Twist minimal: | no (minimal twist has level 81) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{27}]$ |
Embedding invariants
Embedding label | 703.1 | ||
Character | \(\chi\) | \(=\) | 729.703 |
Dual form | 729.2.g.b.28.1 |
$q$-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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{5}{27}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.23053 | − | 1.46704i | −1.57722 | − | 1.03736i | −0.970087 | − | 0.242758i | \(-0.921948\pi\) |
−0.607136 | − | 0.794598i | \(-0.707682\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.03089 | + | 4.70814i | 1.01545 | + | 2.35407i | ||||
\(5\) | −1.73981 | − | 1.84410i | −0.778069 | − | 0.824705i | 0.210163 | − | 0.977666i | \(-0.432600\pi\) |
−0.988232 | + | 0.152962i | \(0.951119\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.507474 | + | 0.0593153i | −0.191807 | + | 0.0224191i | −0.211454 | − | 0.977388i | \(-0.567820\pi\) |
0.0196468 | + | 0.999807i | \(0.493746\pi\) | |||||||
\(8\) | 1.44988 | − | 8.22270i | 0.512611 | − | 2.90716i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.17534 | + | 6.66569i | 0.371676 | + | 2.10788i | ||||
\(11\) | 0.440769 | + | 1.47227i | 0.132897 | + | 0.443907i | 0.998372 | − | 0.0570461i | \(-0.0181682\pi\) |
−0.865475 | + | 0.500953i | \(0.832983\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.328014 | − | 5.63177i | −0.0909746 | − | 1.56197i | −0.667323 | − | 0.744769i | \(-0.732560\pi\) |
0.576348 | − | 0.817204i | \(-0.304477\pi\) | |||||||
\(14\) | 1.21896 | + | 0.612182i | 0.325779 | + | 0.163613i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.25967 | + | 8.75474i | −2.06492 | + | 2.18869i | ||||
\(17\) | 1.33086 | + | 0.484393i | 0.322781 | + | 0.117483i | 0.498328 | − | 0.866988i | \(-0.333947\pi\) |
−0.175548 | + | 0.984471i | \(0.556170\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.986977 | − | 0.359230i | 0.226428 | − | 0.0824131i | −0.226315 | − | 0.974054i | \(-0.572668\pi\) |
0.452743 | + | 0.891641i | \(0.350446\pi\) | |||||||
\(20\) | 5.14888 | − | 11.9364i | 1.15132 | − | 2.66907i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.17674 | − | 3.93058i | 0.250881 | − | 0.838001i | ||||
\(23\) | 0.258604 | + | 0.0302265i | 0.0539227 | + | 0.00630266i | 0.143011 | − | 0.989721i | \(-0.454321\pi\) |
−0.0890888 | + | 0.996024i | \(0.528395\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.0830100 | + | 1.42523i | −0.0166020 | + | 0.285045i | ||||
\(26\) | −7.53041 | + | 13.0431i | −1.47684 | + | 2.55795i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.30989 | − | 2.26880i | −0.247546 | − | 0.428762i | ||||
\(29\) | −1.58935 | + | 0.798201i | −0.295135 | + | 0.148222i | −0.590205 | − | 0.807253i | \(-0.700953\pi\) |
0.295070 | + | 0.955475i | \(0.404657\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.08537 | − | 4.14437i | 0.554148 | − | 0.744350i | −0.433480 | − | 0.901163i | \(-0.642715\pi\) |
0.987628 | + | 0.156813i | \(0.0501220\pi\) | |||||||
\(32\) | 15.0181 | − | 3.55935i | 2.65485 | − | 0.629210i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.25790 | − | 3.03288i | −0.387226 | − | 0.520135i | ||||
\(35\) | 0.992294 | + | 0.832634i | 0.167728 | + | 0.140741i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.04999 | + | 4.23745i | −0.830214 | + | 0.696632i | −0.955340 | − | 0.295509i | \(-0.904511\pi\) |
0.125126 | + | 0.992141i | \(0.460066\pi\) | |||||||
\(38\) | −2.72849 | − | 0.646664i | −0.442619 | − | 0.104903i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −17.6860 | + | 11.6322i | −2.79640 | + | 1.83922i | ||||
\(41\) | −5.64575 | + | 3.71327i | −0.881718 | + | 0.579915i | −0.907640 | − | 0.419749i | \(-0.862118\pi\) |
0.0259221 | + | 0.999664i | \(0.491748\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.94513 | − | 1.40902i | −0.906624 | − | 0.214874i | −0.249251 | − | 0.968439i | \(-0.580184\pi\) |
−0.657373 | + | 0.753565i | \(0.728333\pi\) | |||||||
\(44\) | −6.03650 | + | 5.06523i | −0.910037 | + | 0.763612i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.532481 | − | 0.446804i | −0.0785100 | − | 0.0658777i | ||||
\(47\) | −4.36612 | − | 5.86472i | −0.636864 | − | 0.855457i | 0.360132 | − | 0.932901i | \(-0.382732\pi\) |
−0.996997 | + | 0.0774440i | \(0.975324\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.55730 | + | 1.55411i | −0.936757 | + | 0.222016i | ||||
\(50\) | 2.27603 | − | 3.05723i | 0.321879 | − | 0.432358i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 25.8490 | − | 12.9819i | 3.58461 | − | 1.80026i | ||||
\(53\) | −4.74440 | − | 8.21755i | −0.651694 | − | 1.12877i | −0.982712 | − | 0.185142i | \(-0.940725\pi\) |
0.331018 | − | 0.943624i | \(-0.392608\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.94815 | − | 3.37430i | 0.262689 | − | 0.454991i | ||||
\(56\) | −0.248047 | + | 4.25881i | −0.0331467 | + | 0.569107i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.71609 | + | 0.551232i | 0.619253 | + | 0.0723802i | ||||
\(59\) | −1.42111 | + | 4.74684i | −0.185013 | + | 0.617986i | 0.814283 | + | 0.580468i | \(0.197130\pi\) |
−0.999296 | + | 0.0375182i | \(0.988055\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.10974 | + | 11.8457i | −0.654235 | + | 1.51669i | 0.190604 | + | 0.981667i | \(0.438955\pi\) |
−0.844839 | + | 0.535021i | \(0.820304\pi\) | |||||||
\(62\) | −12.9620 | + | 4.71777i | −1.64617 | + | 0.599157i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −16.0995 | − | 5.85975i | −2.01244 | − | 0.732468i | ||||
\(65\) | −9.81485 | + | 10.4031i | −1.21738 | + | 1.29035i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.73622 | + | 2.88084i | 0.700791 | + | 0.351951i | 0.763256 | − | 0.646097i | \(-0.223600\pi\) |
−0.0624643 | + | 0.998047i | \(0.519896\pi\) | |||||||
\(68\) | 0.422242 | + | 7.24961i | 0.0512044 | + | 0.879145i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.991833 | − | 3.31295i | −0.118547 | − | 0.395974i | ||||
\(71\) | 0.896716 | + | 5.08553i | 0.106421 | + | 0.603541i | 0.990643 | + | 0.136476i | \(0.0435776\pi\) |
−0.884223 | + | 0.467065i | \(0.845311\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.03528 | + | 5.87137i | −0.121171 | + | 0.687192i | 0.862338 | + | 0.506332i | \(0.168999\pi\) |
−0.983509 | + | 0.180860i | \(0.942112\pi\) | |||||||
\(74\) | 17.4807 | − | 2.04320i | 2.03209 | − | 0.237517i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.69575 | + | 3.91726i | 0.423931 | + | 0.449341i | ||||
\(77\) | −0.311007 | − | 0.720996i | −0.0354426 | − | 0.0821651i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.30647 | − | 5.46325i | −0.934551 | − | 0.614664i | −0.0117457 | − | 0.999931i | \(-0.503739\pi\) |
−0.922805 | + | 0.385267i | \(0.874109\pi\) | |||||||
\(80\) | 30.5149 | 3.41167 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 18.0405 | 1.99224 | ||||||||
\(83\) | 10.8213 | + | 7.11730i | 1.18779 | + | 0.781225i | 0.980397 | − | 0.197032i | \(-0.0631303\pi\) |
0.207397 | + | 0.978257i | \(0.433501\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.42218 | − | 3.29699i | −0.154257 | − | 0.357608i | ||||
\(86\) | 11.1937 | + | 11.8646i | 1.20705 | + | 1.27940i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 12.7451 | − | 1.48969i | 1.35863 | − | 0.158801i | ||||
\(89\) | 1.71260 | − | 9.71264i | 0.181535 | − | 1.02954i | −0.748791 | − | 0.662806i | \(-0.769366\pi\) |
0.930327 | − | 0.366732i | \(-0.119523\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.500509 | + | 2.83853i | 0.0524676 | + | 0.297558i | ||||
\(92\) | 0.382886 | + | 1.27893i | 0.0399187 | + | 0.133338i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.13497 | + | 19.4867i | 0.117063 | + | 2.00990i | ||||
\(95\) | −2.37961 | − | 1.19509i | −0.244143 | − | 0.122613i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.46841 | − | 2.61636i | 0.250629 | − | 0.265651i | −0.589829 | − | 0.807528i | \(-0.700805\pi\) |
0.840458 | + | 0.541877i | \(0.182286\pi\) | |||||||
\(98\) | 16.9062 | + | 6.15336i | 1.70778 | + | 0.621583i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.87874 | + | 2.50366i | −0.687874 | + | 0.250366i | ||||
\(101\) | −7.05948 | + | 16.3657i | −0.702444 | + | 1.62845i | 0.0732293 | + | 0.997315i | \(0.476669\pi\) |
−0.775674 | + | 0.631134i | \(0.782590\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.23827 | + | 4.13613i | −0.122011 | + | 0.407545i | −0.997072 | − | 0.0764677i | \(-0.975636\pi\) |
0.875061 | + | 0.484012i | \(0.160821\pi\) | |||||||
\(104\) | −46.7839 | − | 5.46826i | −4.58754 | − | 0.536207i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.47296 | + | 25.2897i | −0.143066 | + | 2.45636i | ||||
\(107\) | −3.98940 | + | 6.90985i | −0.385670 | + | 0.668000i | −0.991862 | − | 0.127318i | \(-0.959363\pi\) |
0.606192 | + | 0.795319i | \(0.292696\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.106432 | + | 0.184345i | 0.0101943 | + | 0.0176571i | 0.871078 | − | 0.491145i | \(-0.163422\pi\) |
−0.860883 | + | 0.508803i | \(0.830088\pi\) | |||||||
\(110\) | −9.29566 | + | 4.66846i | −0.886306 | + | 0.445120i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.67228 | − | 4.93273i | 0.346998 | − | 0.466099i | ||||
\(113\) | −5.39679 | + | 1.27906i | −0.507687 | + | 0.120324i | −0.476474 | − | 0.879189i | \(-0.658085\pi\) |
−0.0312133 | + | 0.999513i | \(0.509937\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.394182 | − | 0.529479i | −0.0367577 | − | 0.0493742i | ||||
\(116\) | −6.98584 | − | 5.86181i | −0.648619 | − | 0.544256i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.1337 | − | 8.50315i | 0.932878 | − | 0.782778i | ||||
\(119\) | −0.704109 | − | 0.166877i | −0.0645455 | − | 0.0152976i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.21706 | − | 4.74673i | 0.656096 | − | 0.431521i | ||||
\(122\) | 28.7756 | − | 18.9260i | 2.60522 | − | 1.71348i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 25.7783 | + | 6.10956i | 2.31496 | + | 0.548655i | ||||
\(125\) | −6.93801 | + | 5.82168i | −0.620554 | + | 0.520707i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.9870 | − | 11.7365i | −1.24115 | − | 1.04145i | −0.997434 | − | 0.0715979i | \(-0.977190\pi\) |
−0.243713 | − | 0.969847i | \(-0.578365\pi\) | |||||||
\(128\) | 8.88076 | + | 11.9289i | 0.784956 | + | 1.05438i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 37.1542 | − | 8.80570i | 3.25863 | − | 0.772311i | ||||
\(131\) | −4.80136 | + | 6.44934i | −0.419497 | + | 0.563482i | −0.960763 | − | 0.277369i | \(-0.910537\pi\) |
0.541267 | + | 0.840851i | \(0.317945\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.479558 | + | 0.240843i | −0.0415829 | + | 0.0208837i | ||||
\(134\) | −8.56851 | − | 14.8411i | −0.740206 | − | 1.28207i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.91261 | − | 10.2409i | 0.507002 | − | 0.878153i | ||||
\(137\) | 0.496123 | − | 8.51811i | 0.0423867 | − | 0.727751i | −0.908438 | − | 0.418020i | \(-0.862724\pi\) |
0.950824 | − | 0.309731i | \(-0.100239\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.9612 | − | 1.51494i | −1.09935 | − | 0.128496i | −0.452981 | − | 0.891520i | \(-0.649640\pi\) |
−0.646370 | + | 0.763024i | \(0.723714\pi\) | |||||||
\(140\) | −1.90491 | + | 6.36285i | −0.160994 | + | 0.537759i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.46054 | − | 12.6589i | 0.458238 | − | 1.06232i | ||||
\(143\) | 8.14693 | − | 2.96524i | 0.681280 | − | 0.247966i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.23713 | + | 1.54219i | 0.351875 | + | 0.128072i | ||||
\(146\) | 10.9228 | − | 11.5775i | 0.903976 | − | 0.958159i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −30.2065 | − | 15.1703i | −2.48296 | − | 1.24699i | ||||
\(149\) | −0.948613 | − | 16.2871i | −0.0777134 | − | 1.33429i | −0.781513 | − | 0.623889i | \(-0.785552\pi\) |
0.703799 | − | 0.710399i | \(-0.251485\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.21112 | − | 20.7466i | −0.505454 | − | 1.68833i | −0.705636 | − | 0.708575i | \(-0.749339\pi\) |
0.200182 | − | 0.979759i | \(-0.435847\pi\) | |||||||
\(152\) | −1.52284 | − | 8.63645i | −0.123519 | − | 0.700509i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.364021 | + | 2.06446i | −0.0293336 | + | 0.166359i | ||||
\(155\) | −13.0106 | + | 1.52072i | −1.04503 | + | 0.122147i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.73207 | + | 1.83589i | 0.138234 | + | 0.146520i | 0.792792 | − | 0.609492i | \(-0.208627\pi\) |
−0.654558 | + | 0.756012i | \(0.727145\pi\) | |||||||
\(158\) | 10.5130 | + | 24.3719i | 0.836370 | + | 1.93892i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −32.6924 | − | 21.5022i | −2.58456 | − | 1.69989i | ||||
\(161\) | −0.133028 | −0.0104841 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.30888 | 0.572476 | 0.286238 | − | 0.958159i | \(-0.407595\pi\) | ||||
0.286238 | + | 0.958159i | \(0.407595\pi\) | |||||||
\(164\) | −28.9485 | − | 19.0397i | −2.26050 | − | 1.48675i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.6959 | − | 31.7507i | −1.06301 | − | 2.46433i | ||||
\(167\) | −4.40004 | − | 4.66377i | −0.340486 | − | 0.360894i | 0.534393 | − | 0.845236i | \(-0.320540\pi\) |
−0.874878 | + | 0.484343i | \(0.839059\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18.6972 | + | 2.18539i | −1.43825 | + | 0.168107i | ||||
\(170\) | −1.66460 | + | 9.44043i | −0.127669 | + | 0.724048i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.44005 | − | 30.8521i | −0.414800 | − | 2.35245i | ||||
\(173\) | −1.40205 | − | 4.68318i | −0.106596 | − | 0.356055i | 0.888004 | − | 0.459835i | \(-0.152091\pi\) |
−0.994600 | + | 0.103780i | \(0.966906\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.0424122 | − | 0.728190i | −0.00320606 | − | 0.0550460i | ||||
\(176\) | −16.5300 | − | 8.30166i | −1.24599 | − | 0.625762i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −18.0689 | + | 19.1519i | −1.35432 | + | 1.43549i | ||||
\(179\) | −0.481678 | − | 0.175316i | −0.0360023 | − | 0.0131038i | 0.323956 | − | 0.946072i | \(-0.394987\pi\) |
−0.359959 | + | 0.932968i | \(0.617209\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.55046 | − | 1.29226i | 0.263904 | − | 0.0960531i | −0.206680 | − | 0.978409i | \(-0.566266\pi\) |
0.470583 | + | 0.882356i | \(0.344044\pi\) | |||||||
\(182\) | 3.04784 | − | 7.06568i | 0.225921 | − | 0.523743i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.623489 | − | 2.08260i | 0.0459642 | − | 0.153531i | ||||
\(185\) | 16.6003 | + | 1.94030i | 1.22048 | + | 0.142654i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.126557 | + | 2.17289i | −0.00925473 | + | 0.158898i | ||||
\(188\) | 18.7448 | − | 32.4669i | 1.36710 | − | 2.36789i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.55455 | + | 6.15667i | 0.257874 | + | 0.446652i | ||||
\(191\) | 20.2508 | − | 10.1703i | 1.46530 | − | 0.735900i | 0.475678 | − | 0.879619i | \(-0.342203\pi\) |
0.989618 | + | 0.143719i | \(0.0459063\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.41785 | + | 4.59097i | −0.246022 | + | 0.330465i | −0.907931 | − | 0.419119i | \(-0.862339\pi\) |
0.661909 | + | 0.749584i | \(0.269746\pi\) | |||||||
\(194\) | −9.34418 | + | 2.21461i | −0.670873 | + | 0.159000i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −20.6341 | − | 27.7164i | −1.47387 | − | 1.97975i | ||||
\(197\) | 1.85381 | + | 1.55553i | 0.132078 | + | 0.110827i | 0.706434 | − | 0.707779i | \(-0.250303\pi\) |
−0.574356 | + | 0.818606i | \(0.694747\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.49610 | + | 6.28997i | −0.531384 | + | 0.445884i | −0.868579 | − | 0.495550i | \(-0.834966\pi\) |
0.337195 | + | 0.941435i | \(0.390522\pi\) | |||||||
\(200\) | 11.5988 | + | 2.74898i | 0.820163 | + | 0.194382i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 39.7556 | − | 26.1477i | 2.79719 | − | 1.83974i | ||||
\(203\) | 0.759209 | − | 0.499339i | 0.0532860 | − | 0.0350467i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.6702 | + | 3.95091i | 1.16430 | + | 0.275943i | ||||
\(206\) | 8.82988 | − | 7.40915i | 0.615207 | − | 0.516220i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 52.0140 | + | 43.6449i | 3.60652 | + | 3.02623i | ||||
\(209\) | 0.963914 | + | 1.29476i | 0.0666753 | + | 0.0895605i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.0832 | + | 4.52280i | −1.31374 | + | 0.311362i | −0.827009 | − | 0.562189i | \(-0.809959\pi\) |
−0.486732 | + | 0.873551i | \(0.661811\pi\) | |||||||
\(212\) | 29.0540 | − | 39.0262i | 1.99543 | − | 2.68033i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 19.0355 | − | 9.56000i | 1.30124 | − | 0.653508i | ||||
\(215\) | 7.74505 | + | 13.4148i | 0.528208 | + | 0.914884i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.31992 | + | 2.28617i | −0.0896020 | + | 0.155195i | ||||
\(218\) | 0.0330431 | − | 0.567328i | 0.00223796 | − | 0.0384243i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 19.8432 | + | 2.31933i | 1.33783 | + | 0.156369i | ||||
\(221\) | 2.29145 | − | 7.65399i | 0.154140 | − | 0.514863i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.03775 | − | 2.40578i | 0.0694930 | − | 0.161103i | −0.879930 | − | 0.475104i | \(-0.842410\pi\) |
0.949423 | + | 0.314001i | \(0.101670\pi\) | |||||||
\(224\) | −7.41017 | + | 2.69708i | −0.495113 | + | 0.180206i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.9141 | + | 5.06433i | 0.925555 | + | 0.336874i | ||||
\(227\) | 0.847597 | − | 0.898400i | 0.0562570 | − | 0.0596289i | −0.698634 | − | 0.715479i | \(-0.746208\pi\) |
0.754891 | + | 0.655850i | \(0.227690\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.37803 | + | 2.19873i | 0.289308 | + | 0.145296i | 0.587534 | − | 0.809199i | \(-0.300099\pi\) |
−0.298226 | + | 0.954495i | \(0.596395\pi\) | |||||||
\(230\) | 0.102468 | + | 1.75930i | 0.00675652 | + | 0.116005i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.25899 | + | 14.2260i | 0.279617 | + | 0.933985i | ||||
\(233\) | 0.664049 | + | 3.76601i | 0.0435033 | + | 0.246719i | 0.998803 | − | 0.0489208i | \(-0.0155782\pi\) |
−0.955299 | + | 0.295640i | \(0.904467\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.21886 | + | 18.2551i | −0.209975 | + | 1.19083i | ||||
\(236\) | −25.2349 | + | 2.94954i | −1.64265 | + | 0.191999i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.32572 | + | 1.40518i | 0.0859337 | + | 0.0910844i | ||||
\(239\) | 3.58337 | + | 8.30719i | 0.231789 | + | 0.537348i | 0.993924 | − | 0.110071i | \(-0.0351078\pi\) |
−0.762135 | + | 0.647419i | \(0.775849\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.5722 | + | 12.8728i | 1.26075 | + | 0.829211i | 0.991019 | − | 0.133724i | \(-0.0426936\pi\) |
0.269735 | + | 0.962935i | \(0.413064\pi\) | |||||||
\(242\) | −23.0615 | −1.48245 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −66.1485 | −4.23473 | ||||||||
\(245\) | 14.2744 | + | 9.38843i | 0.911959 | + | 0.599805i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.34685 | − | 5.44060i | −0.149326 | − | 0.346177i | ||||
\(248\) | −29.6044 | − | 31.3789i | −1.87988 | − | 1.99256i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 24.0161 | − | 2.80708i | 1.51891 | − | 0.177535i | ||||
\(251\) | 2.14133 | − | 12.1441i | 0.135160 | − | 0.766530i | −0.839588 | − | 0.543223i | \(-0.817204\pi\) |
0.974748 | − | 0.223307i | \(-0.0716851\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0694831 | + | 0.394058i | 0.00436837 | + | 0.0247742i | ||||
\(254\) | 13.9805 | + | 46.6981i | 0.877215 | + | 2.93010i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.316189 | − | 5.42876i | −0.0197618 | − | 0.339298i | ||||
\(257\) | −26.3443 | − | 13.2306i | −1.64331 | − | 0.825302i | −0.998121 | − | 0.0612816i | \(-0.980481\pi\) |
−0.645192 | − | 0.764021i | \(-0.723222\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.31140 | − | 2.44994i | 0.143623 | − | 0.152232i | ||||
\(260\) | −68.9122 | − | 25.0820i | −4.27376 | − | 1.55552i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 20.1710 | − | 7.34166i | 1.24617 | − | 0.453569i | ||||
\(263\) | 8.15499 | − | 18.9054i | 0.502858 | − | 1.16576i | −0.458060 | − | 0.888922i | \(-0.651455\pi\) |
0.960918 | − | 0.276834i | \(-0.0892854\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.89956 | + | 23.0461i | −0.423837 | + | 1.41571i | ||||
\(266\) | 1.42300 | + | 0.166324i | 0.0872494 | + | 0.0101980i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.91374 | + | 32.8576i | −0.116900 | + | 2.00710i | ||||
\(269\) | 6.08593 | − | 10.5411i | 0.371066 | − | 0.642705i | −0.618664 | − | 0.785656i | \(-0.712326\pi\) |
0.989730 | + | 0.142951i | \(0.0456591\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.5577 | − | 20.0185i | −0.702078 | − | 1.21603i | −0.967736 | − | 0.251967i | \(-0.918922\pi\) |
0.265658 | − | 0.964067i | \(-0.414411\pi\) | |||||||
\(272\) | −15.2332 | + | 7.65040i | −0.923648 | + | 0.463874i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.6030 | + | 18.2721i | −0.821790 | + | 1.10386i | ||||
\(275\) | −2.13491 | + | 0.505983i | −0.128740 | + | 0.0305119i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.817359 | + | 1.09790i | 0.0491104 | + | 0.0659667i | 0.826000 | − | 0.563670i | \(-0.190611\pi\) |
−0.776890 | + | 0.629637i | \(0.783204\pi\) | |||||||
\(278\) | 26.6878 | + | 22.3937i | 1.60063 | + | 1.34308i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.28520 | − | 6.95211i | 0.495136 | − | 0.415468i | ||||
\(281\) | 17.4219 | + | 4.12908i | 1.03931 | + | 0.246320i | 0.714628 | − | 0.699505i | \(-0.246596\pi\) |
0.324678 | + | 0.945825i | \(0.394744\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.15153 | + | 5.36135i | −0.484558 | + | 0.318699i | −0.768176 | − | 0.640238i | \(-0.778836\pi\) |
0.283618 | + | 0.958937i | \(0.408465\pi\) | |||||||
\(284\) | −22.1222 | + | 14.5500i | −1.31271 | + | 0.863385i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −22.5221 | − | 5.33784i | −1.33176 | − | 0.315633i | ||||
\(287\) | 2.64482 | − | 2.21927i | 0.156119 | − | 0.130999i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.4862 | − | 9.63807i | −0.675659 | − | 0.566945i | ||||
\(290\) | −7.18859 | − | 9.65596i | −0.422129 | − | 0.567017i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −29.7458 | + | 7.04988i | −1.74074 | + | 0.412563i | ||||
\(293\) | −1.83443 | + | 2.46406i | −0.107168 | + | 0.143952i | −0.852472 | − | 0.522774i | \(-0.824897\pi\) |
0.745303 | + | 0.666726i | \(0.232305\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.2261 | − | 5.63796i | 0.653609 | − | 0.328255i | ||||
\(296\) | 27.5213 | + | 47.6684i | 1.59965 | + | 2.77067i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −21.7779 | + | 37.7204i | −1.26156 | + | 2.18509i | ||||
\(299\) | 0.0854031 | − | 1.46631i | 0.00493899 | − | 0.0847991i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.10058 | + | 0.362406i | 0.178714 | + | 0.0208887i | ||||
\(302\) | −16.5820 | + | 55.3879i | −0.954189 | + | 3.18721i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.00714 | + | 11.6079i | −0.287179 | + | 0.665756i | ||||
\(305\) | 30.7346 | − | 11.1865i | 1.75986 | − | 0.640536i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.34825 | + | 1.94660i | 0.305241 | + | 0.111099i | 0.490099 | − | 0.871667i | \(-0.336960\pi\) |
−0.184859 | + | 0.982765i | \(0.559183\pi\) | |||||||
\(308\) | 2.76293 | − | 2.92853i | 0.157432 | − | 0.166868i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 31.2514 | + | 15.6951i | 1.77496 | + | 0.891419i | ||||
\(311\) | −0.189058 | − | 3.24600i | −0.0107205 | − | 0.184064i | −0.999417 | − | 0.0341346i | \(-0.989133\pi\) |
0.988697 | − | 0.149929i | \(-0.0479045\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.71298 | + | 9.06199i | 0.153347 | + | 0.512214i | 0.999795 | − | 0.0202573i | \(-0.00644855\pi\) |
−0.846448 | + | 0.532471i | \(0.821263\pi\) | |||||||
\(314\) | −1.17011 | − | 6.63603i | −0.0660332 | − | 0.374493i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.85219 | − | 50.2032i | 0.497974 | − | 2.82415i | ||||
\(317\) | 20.3710 | − | 2.38103i | 1.14415 | − | 0.133732i | 0.477172 | − | 0.878810i | \(-0.341662\pi\) |
0.666977 | + | 0.745078i | \(0.267588\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.87571 | − | 1.98813i | −0.105019 | − | 0.111314i | ||||
\(320\) | 17.2042 | + | 39.8839i | 0.961747 | + | 2.22958i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.296723 | + | 0.195158i | 0.0165357 | + | 0.0108757i | ||||
\(323\) | 1.48754 | 0.0827687 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.05378 | 0.446744 | ||||||||
\(326\) | −16.3027 | − | 10.7224i | −0.902922 | − | 0.593861i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 22.3474 | + | 51.8071i | 1.23393 | + | 2.86057i | ||||
\(329\) | 2.56356 | + | 2.71722i | 0.141334 | + | 0.149805i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.85491 | − | 0.801224i | 0.376780 | − | 0.0440393i | 0.0744045 | − | 0.997228i | \(-0.476294\pi\) |
0.302376 | + | 0.953189i | \(0.402220\pi\) | |||||||
\(332\) | −11.5323 | + | 65.4027i | −0.632915 | + | 3.58944i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.97247 | + | 16.8577i | 0.162647 | + | 0.922415i | ||||
\(335\) | −4.66742 | − | 15.5903i | −0.255008 | − | 0.851788i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.57688 | − | 27.0740i | −0.0858981 | − | 1.47481i | −0.715891 | − | 0.698212i | \(-0.753979\pi\) |
0.629993 | − | 0.776601i | \(-0.283058\pi\) | |||||||
\(338\) | 44.9107 | + | 22.5550i | 2.44282 | + | 1.22683i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12.6344 | − | 13.3916i | 0.685194 | − | 0.726264i | ||||
\(341\) | 7.46157 | + | 2.71579i | 0.404067 | + | 0.147068i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.59630 | − | 2.40086i | 0.356166 | − | 0.129634i | ||||
\(344\) | −20.2057 | + | 46.8421i | −1.08942 | + | 2.52556i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.74310 | + | 12.5028i | −0.201231 | + | 0.672157i | ||||
\(347\) | 23.0562 | + | 2.69489i | 1.23772 | + | 0.144669i | 0.709665 | − | 0.704539i | \(-0.248846\pi\) |
0.528058 | + | 0.849209i | \(0.322920\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.178494 | + | 3.06463i | −0.00955458 | + | 0.164046i | 0.990156 | + | 0.139971i | \(0.0447010\pi\) |
−0.999710 | + | 0.0240746i | \(0.992336\pi\) | |||||||
\(350\) | −0.973684 | + | 1.68647i | −0.0520456 | + | 0.0901456i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 11.8598 | + | 20.5418i | 0.632131 | + | 1.09488i | ||||
\(353\) | −9.38433 | + | 4.71299i | −0.499477 | + | 0.250847i | −0.680656 | − | 0.732603i | \(-0.738305\pi\) |
0.181179 | + | 0.983450i | \(0.442009\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.81808 | − | 10.5015i | 0.414941 | − | 0.557362i | ||||
\(356\) | 49.2065 | − | 11.6622i | 2.60794 | − | 0.618093i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.817201 | + | 1.09769i | 0.0431904 | + | 0.0580148i | ||||
\(359\) | −23.6540 | − | 19.8481i | −1.24841 | − | 1.04754i | −0.996818 | − | 0.0797090i | \(-0.974601\pi\) |
−0.251594 | − | 0.967833i | \(-0.580955\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.7098 | + | 11.5039i | −0.721567 | + | 0.605466i | ||||
\(362\) | −9.81522 | − | 2.32625i | −0.515876 | − | 0.122265i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12.3477 | + | 8.12120i | −0.647194 | + | 0.425667i | ||||
\(365\) | 12.6286 | − | 8.30594i | 0.661010 | − | 0.434753i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.8135 | + | 3.51087i | 0.773260 | + | 0.183266i | 0.598259 | − | 0.801302i | \(-0.295859\pi\) |
0.175000 | + | 0.984568i | \(0.444007\pi\) | |||||||
\(368\) | −2.40061 | + | 2.01435i | −0.125140 | + | 0.105005i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −34.1810 | − | 28.6813i | −1.77699 | − | 1.49107i | ||||
\(371\) | 2.89509 | + | 3.88878i | 0.150306 | + | 0.201895i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.908175 | + | 0.215242i | −0.0470235 | + | 0.0111448i | −0.254060 | − | 0.967188i | \(-0.581766\pi\) |
0.207037 | + | 0.978333i | \(0.433618\pi\) | |||||||
\(374\) | 3.47001 | − | 4.66104i | 0.179430 | − | 0.241017i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −54.5542 | + | 27.3981i | −2.81342 | + | 1.41295i | ||||
\(377\) | 5.01662 | + | 8.68904i | 0.258369 | + | 0.447508i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.2328 | − | 33.3122i | 0.987924 | − | 1.71113i | 0.359781 | − | 0.933037i | \(-0.382851\pi\) |
0.628143 | − | 0.778098i | \(-0.283815\pi\) | |||||||
\(380\) | 0.793893 | − | 13.6306i | 0.0407259 | − | 0.699236i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −60.0904 | − | 7.02356i | −3.07449 | − | 0.359356i | ||||
\(383\) | 4.23110 | − | 14.1329i | 0.216199 | − | 0.722156i | −0.779237 | − | 0.626729i | \(-0.784393\pi\) |
0.995436 | − | 0.0954267i | \(-0.0304216\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.788491 | + | 1.82793i | −0.0401852 | + | 0.0931598i | ||||
\(386\) | 14.3588 | − | 5.22616i | 0.730841 | − | 0.266005i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 17.3313 | + | 6.30806i | 0.879862 | + | 0.320243i | ||||
\(389\) | −11.7270 | + | 12.4299i | −0.594583 | + | 0.630221i | −0.952866 | − | 0.303392i | \(-0.901881\pi\) |
0.358283 | + | 0.933613i | \(0.383362\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.329524 | + | 0.165493i | 0.0166647 | + | 0.00836935i | ||||
\(392\) | 3.27164 | + | 56.1720i | 0.165243 | + | 2.83711i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.85294 | − | 6.18926i | −0.0933500 | − | 0.311811i | ||||
\(395\) | 4.37696 | + | 24.8230i | 0.220229 | + | 1.24898i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.37414 | + | 24.8070i | −0.219532 | + | 1.24503i | 0.653335 | + | 0.757069i | \(0.273369\pi\) |
−0.872867 | + | 0.487958i | \(0.837742\pi\) | |||||||
\(398\) | 25.9479 | − | 3.03288i | 1.30065 | − | 0.152024i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −11.7919 | − | 12.4986i | −0.589593 | − | 0.624932i | ||||
\(401\) | 8.17128 | + | 18.9432i | 0.408054 | + | 0.945976i | 0.991049 | + | 0.133500i | \(0.0426216\pi\) |
−0.582995 | + | 0.812476i | \(0.698119\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.3522 | − | 16.0167i | −1.21307 | − | 0.797847i | ||||
\(404\) | −91.3890 | −4.54677 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.42599 | −0.120400 | ||||||||
\(407\) | −8.46456 | − | 5.56723i | −0.419573 | − | 0.275957i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.9343 | + | 32.3033i | 0.689006 | + | 1.59729i | 0.797585 | + | 0.603207i | \(0.206111\pi\) |
−0.108579 | + | 0.994088i | \(0.534630\pi\) | |||||||
\(410\) | −31.3872 | − | 33.2685i | −1.55010 | − | 1.64301i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −21.9882 | + | 2.57006i | −1.08328 | + | 0.126618i | ||||
\(413\) | 0.439618 | − | 2.49319i | 0.0216322 | − | 0.122682i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.70212 | − | 32.3383i | −0.279906 | − | 1.58743i | ||||
\(416\) | −24.9716 | − | 83.4109i | −1.22433 | − | 4.08956i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.250569 | − | 4.30211i | −0.0122557 | − | 0.210423i | ||||
\(419\) | 24.2225 | + | 12.1650i | 1.18335 | + | 0.594299i | 0.928011 | − | 0.372553i | \(-0.121518\pi\) |
0.255336 | + | 0.966852i | \(0.417814\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.8880 | − | 22.1400i | 1.01802 | − | 1.07904i | 0.0211670 | − | 0.999776i | \(-0.493262\pi\) |
0.996854 | − | 0.0792630i | \(-0.0252567\pi\) | |||||||
\(422\) | 49.2008 | + | 17.9076i | 2.39506 | + | 0.871729i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −74.4492 | + | 27.0973i | −3.61557 | + | 1.31596i | ||||
\(425\) | −0.800844 | + | 1.85657i | −0.0388467 | + | 0.0900567i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.89043 | − | 6.31448i | 0.0914844 | − | 0.305579i | ||||
\(428\) | −40.6346 | − | 4.74950i | −1.96415 | − | 0.229576i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.40455 | − | 41.2845i | 0.115958 | − | 1.99092i | ||||
\(431\) | 4.50933 | − | 7.81039i | 0.217207 | − | 0.376213i | −0.736746 | − | 0.676170i | \(-0.763639\pi\) |
0.953953 | + | 0.299956i | \(0.0969720\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.8523 | − | 20.5287i | −0.569584 | − | 0.986548i | −0.996607 | − | 0.0823075i | \(-0.973771\pi\) |
0.427023 | − | 0.904241i | \(-0.359562\pi\) | |||||||
\(434\) | 6.29803 | − | 3.16299i | 0.302315 | − | 0.151828i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.651772 | + | 0.875481i | −0.0312142 | + | 0.0419279i | ||||
\(437\) | 0.266094 | − | 0.0630655i | 0.0127290 | − | 0.00301683i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.40340 | + | 3.22832i | 0.114708 | + | 0.154080i | 0.855769 | − | 0.517358i | \(-0.173084\pi\) |
−0.741061 | + | 0.671438i | \(0.765677\pi\) | |||||||
\(440\) | −24.9213 | − | 20.9114i | −1.18807 | − | 0.996913i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −16.3399 | + | 13.7108i | −0.777209 | + | 0.652156i | ||||
\(443\) | −7.74314 | − | 1.83516i | −0.367888 | − | 0.0871909i | 0.0425140 | − | 0.999096i | \(-0.486463\pi\) |
−0.410402 | + | 0.911905i | \(0.634611\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.8906 | + | 13.7400i | −0.990311 | + | 0.651338i | ||||
\(446\) | −5.84412 | + | 3.84374i | −0.276727 | + | 0.182006i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.51767 | + | 2.01872i | 0.402422 | + | 0.0953758i | ||||
\(449\) | 11.2889 | − | 9.47253i | 0.532757 | − | 0.447037i | −0.336295 | − | 0.941757i | \(-0.609174\pi\) |
0.869052 | + | 0.494720i | \(0.164729\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.95542 | − | 6.67539i | −0.374606 | − | 0.314332i | ||||
\(452\) | −16.9823 | − | 22.8112i | −0.798780 | − | 1.07295i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.20858 | + | 0.760448i | −0.150586 | + | 0.0356896i | ||||
\(455\) | 4.36372 | − | 5.86149i | 0.204574 | − | 0.274791i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.02454 | + | 3.52786i | −0.328594 | + | 0.165026i | −0.605446 | − | 0.795886i | \(-0.707005\pi\) |
0.276852 | + | 0.960913i | \(0.410709\pi\) | |||||||
\(458\) | −6.53970 | − | 11.3271i | −0.305580 | − | 0.529280i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.69232 | − | 2.93118i | 0.0789047 | − | 0.136667i | ||||
\(461\) | 0.192100 | − | 3.29823i | 0.00894699 | − | 0.153614i | −0.990876 | − | 0.134779i | \(-0.956967\pi\) |
0.999823 | − | 0.0188344i | \(-0.00599554\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.5818 | + | 2.05502i | 0.817095 | + | 0.0955047i | 0.514365 | − | 0.857572i | \(-0.328028\pi\) |
0.302730 | + | 0.953076i | \(0.402102\pi\) | |||||||
\(464\) | 6.13946 | − | 20.5072i | 0.285017 | − | 0.952024i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.04371 | − | 9.37438i | 0.187321 | − | 0.434260i | ||||
\(467\) | −37.4545 | + | 13.6323i | −1.73319 | + | 0.630829i | −0.998849 | − | 0.0479555i | \(-0.984729\pi\) |
−0.734338 | + | 0.678784i | \(0.762507\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.08187 | − | 1.12171i | −0.142307 | − | 0.0517956i | ||||
\(470\) | 33.9607 | − | 35.9963i | 1.56649 | − | 1.66038i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 36.9714 | + | 18.5677i | 1.70175 | + | 0.854649i | ||||
\(473\) | −0.545968 | − | 9.37391i | −0.0251036 | − | 0.431013i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.430056 | + | 1.43649i | 0.0197323 | + | 0.0659105i | ||||
\(476\) | −0.644290 | − | 3.65395i | −0.0295310 | − | 0.167478i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.19419 | − | 23.7864i | 0.191838 | − | 1.08797i | ||||
\(479\) | −38.9258 | + | 4.54978i | −1.77857 | + | 0.207885i | −0.940990 | − | 0.338435i | \(-0.890102\pi\) |
−0.837577 | + | 0.546320i | \(0.816028\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.5208 | + | 27.0505i | 1.16365 | + | 1.23340i | ||||
\(482\) | −24.7713 | − | 57.4264i | −1.12830 | − | 2.61570i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 37.0053 | + | 24.3388i | 1.68206 | + | 1.10631i | ||||
\(485\) | −9.11940 | −0.414091 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.0579 | 1.58863 | 0.794313 | − | 0.607509i | \(-0.207831\pi\) | ||||
0.794313 | + | 0.607509i | \(0.207831\pi\) | |||||||
\(488\) | 89.9951 | + | 59.1907i | 4.07389 | + | 2.67944i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −18.0663 | − | 41.8824i | −0.816152 | − | 1.89205i | ||||
\(491\) | 14.1243 | + | 14.9709i | 0.637421 | + | 0.675627i | 0.962880 | − | 0.269929i | \(-0.0870003\pi\) |
−0.325459 | + | 0.945556i | \(0.605519\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.50184 | + | 0.292423i | −0.112677 | + | 0.0131701i | ||||
\(494\) | −2.74688 | + | 15.5783i | −0.123588 | + | 0.700903i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.7987 | + | 61.2427i | 0.484878 | + | 2.74988i | ||||
\(497\) | −0.756710 | − | 2.52759i | −0.0339431 | − | 0.113378i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.479420 | − | 8.23132i | −0.0214618 | − | 0.368484i | −0.991890 | − | 0.127096i | \(-0.959434\pi\) |
0.970429 | − | 0.241388i | \(-0.0776027\pi\) | |||||||
\(500\) | −41.4996 | − | 20.8419i | −1.85592 | − | 0.932077i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −22.5922 | + | 23.9464i | −1.00834 | + | 1.06878i | ||||
\(503\) | −15.9904 | − | 5.82003i | −0.712977 | − | 0.259503i | −0.0400358 | − | 0.999198i | \(-0.512747\pi\) |
−0.672941 | + | 0.739696i | \(0.734969\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 42.4621 | − | 15.4549i | 1.88954 | − | 0.687736i | ||||
\(506\) | 0.423116 | − | 0.980894i | 0.0188098 | − | 0.0436061i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 26.8509 | − | 89.6883i | 1.19132 | − | 3.97927i | ||||
\(509\) | −16.2943 | − | 1.90453i | −0.722232 | − | 0.0844168i | −0.252968 | − | 0.967475i | \(-0.581407\pi\) |
−0.469264 | + | 0.883058i | \(0.655481\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.177117 | − | 3.04098i | 0.00783519 | − | 0.134525i | ||||
\(512\) | 7.61274 | − | 13.1856i | 0.336439 | − | 0.582729i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 39.3519 | + | 68.1595i | 1.73574 | + | 3.00639i | ||||
\(515\) | 9.78178 | − | 4.91259i | 0.431037 | − | 0.216475i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.71001 | − | 9.01311i | 0.295106 | − | 0.396396i | ||||
\(518\) | −8.74981 | + | 2.07374i | −0.384444 | + | 0.0911150i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 71.3114 | + | 95.7878i | 3.12721 | + | 4.20057i | ||||
\(521\) | 9.25237 | + | 7.76366i | 0.405354 | + | 0.340132i | 0.822559 | − | 0.568680i | \(-0.192546\pi\) |
−0.417205 | + | 0.908812i | \(0.636990\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.53110 | + | 4.64114i | −0.241858 | + | 0.202943i | −0.755657 | − | 0.654968i | \(-0.772682\pi\) |
0.513799 | + | 0.857911i | \(0.328238\pi\) | |||||||
\(524\) | −40.1154 | − | 9.50753i | −1.75245 | − | 0.415338i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −45.9250 | + | 30.2053i | −2.00242 | + | 1.31701i | ||||
\(527\) | 6.11369 | − | 4.02104i | 0.266316 | − | 0.175159i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3141 | − | 5.28853i | −0.970177 | − | 0.229936i | ||||
\(530\) | 49.1993 | − | 41.2832i | 2.13708 | − | 1.79323i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.10785 | − | 1.76870i | −0.0913869 | − | 0.0766827i | ||||
\(533\) | 22.7642 | + | 30.5776i | 0.986026 | + | 1.32446i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.6832 | − | 4.66501i | 0.850981 | − | 0.201686i | ||||
\(536\) | 32.0051 | − | 42.9903i | 1.38241 | − | 1.85690i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −29.0392 | + | 14.5840i | −1.25197 | + | 0.628762i | ||||
\(539\) | −5.17833 | − | 8.96913i | −0.223046 | − | 0.386328i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.0806 | + | 33.0486i | −0.820339 | + | 1.42087i | 0.0850910 | + | 0.996373i | \(0.472882\pi\) |
−0.905430 | + | 0.424496i | \(0.860451\pi\) | |||||||
\(542\) | −3.58822 | + | 61.6074i | −0.154127 | + | 2.64626i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 21.7111 | + | 2.53766i | 0.930854 | + | 0.108801i | ||||
\(545\) | 0.154779 | − | 0.516997i | 0.00663000 | − | 0.0221457i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.7275 | + | 34.1421i | −0.629702 | + | 1.45981i | 0.242247 | + | 0.970215i | \(0.422116\pi\) |
−0.871949 | + | 0.489598i | \(0.837144\pi\) | |||||||
\(548\) | 41.1120 | − | 14.9635i | 1.75622 | − | 0.639211i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.50428 | + | 2.00339i | 0.234703 | + | 0.0854250i | ||||
\(551\) | −1.28191 | + | 1.35875i | −0.0546113 | + | 0.0578846i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.53937 | + | 2.27976i | 0.193034 | + | 0.0969452i | ||||
\(554\) | −0.212472 | − | 3.64801i | −0.00902709 | − | 0.154989i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −19.1901 | − | 64.0996i | −0.813844 | − | 2.71843i | ||||
\(557\) | −4.26215 | − | 24.1719i | −0.180593 | − | 1.02420i | −0.931488 | − | 0.363773i | \(-0.881488\pi\) |
0.750894 | − | 0.660422i | \(-0.229623\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.98521 | + | 33.9438i | −0.253147 | + | 1.43567i | ||||
\(560\) | −15.4855 | + | 1.81000i | −0.654383 | + | 0.0764864i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −32.8026 | − | 34.7688i | −1.38370 | − | 1.46663i | ||||
\(563\) | −2.79634 | − | 6.48265i | −0.117852 | − | 0.273211i | 0.849072 | − | 0.528278i | \(-0.177162\pi\) |
−0.966924 | + | 0.255066i | \(0.917903\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.7481 | + | 7.72686i | 0.494247 | + | 0.325071i | ||||
\(566\) | 26.0476 | 1.09486 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 43.1169 | 1.80914 | ||||||||
\(569\) | −7.06923 | − | 4.64950i | −0.296357 | − | 0.194917i | 0.392619 | − | 0.919701i | \(-0.371569\pi\) |
−0.688976 | + | 0.724784i | \(0.741940\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.175018 | − | 0.405738i | −0.00732428 | − | 0.0169796i | 0.914515 | − | 0.404553i | \(-0.132573\pi\) |
−0.921839 | + | 0.387573i | \(0.873313\pi\) | |||||||
\(572\) | 30.5063 | + | 32.3348i | 1.27553 | + | 1.35198i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.15512 | + | 1.07008i | −0.382127 | + | 0.0446643i | ||||
\(575\) | −0.0645463 | + | 0.366060i | −0.00269177 | + | 0.0152658i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.80812 | + | 10.2544i | 0.0752730 | + | 0.426894i | 0.999035 | + | 0.0439266i | \(0.0139868\pi\) |
−0.923762 | + | 0.382968i | \(0.874902\pi\) | |||||||
\(578\) | 11.4809 | + | 38.3488i | 0.477541 | + | 1.59510i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.34432 | + | 23.0810i | 0.0558197 | + | 0.958387i | ||||
\(581\) | −5.91371 | − | 2.96998i | −0.245342 | − | 0.123215i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.0073 | − | 10.6071i | 0.414459 | − | 0.439301i | ||||
\(584\) | 46.7775 | + | 17.0256i | 1.93567 | + | 0.704525i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.70663 | − | 2.80498i | 0.318358 | − | 0.115873i | ||||
\(587\) | 14.6266 | − | 33.9083i | 0.603705 | − | 1.39955i | −0.292655 | − | 0.956218i | \(-0.594539\pi\) |
0.896360 | − | 0.443327i | \(-0.146202\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.55640 | − | 5.19875i | 0.0641305 | − | 0.214211i | ||||
\(590\) | −33.3113 | − | 3.89353i | −1.37140 | − | 0.160294i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.61353 | − | 79.2113i | 0.189615 | − | 3.25557i | ||||
\(593\) | −1.15692 | + | 2.00385i | −0.0475091 | + | 0.0822881i | −0.888802 | − | 0.458291i | \(-0.848462\pi\) |
0.841293 | + | 0.540579i | \(0.181795\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.917282 | + | 1.58878i | 0.0376049 | + | 0.0651336i | ||||
\(596\) | 74.7552 | − | 37.5435i | 3.06209 | − | 1.53784i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.34164 | + | 3.14537i | −0.0957568 | + | 0.128624i | ||||
\(599\) | −7.85260 | + | 1.86110i | −0.320848 | + | 0.0760425i | −0.387884 | − | 0.921708i | \(-0.626794\pi\) |
0.0670358 | + | 0.997751i | \(0.478646\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.09918 | + | 12.2223i | 0.371163 | + | 0.498559i | 0.947987 | − | 0.318310i | \(-0.103115\pi\) |
−0.576823 | + | 0.816869i | \(0.695708\pi\) | |||||||
\(602\) | −6.38427 | − | 5.35704i | −0.260203 | − | 0.218337i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 85.0636 | − | 71.3769i | 3.46119 | − | 2.90428i | ||||
\(605\) | −21.3098 | − | 5.05051i | −0.866365 | − | 0.205332i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.4698 | − | 16.0940i | 0.993198 | − | 0.653237i | 0.0546933 | − | 0.998503i | \(-0.482582\pi\) |
0.938505 | + | 0.345267i | \(0.112212\pi\) | |||||||
\(608\) | 13.5439 | − | 8.90794i | 0.549276 | − | 0.361265i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −84.9656 | − | 20.1372i | −3.44015 | − | 0.815332i | ||||
\(611\) | −31.5966 | + | 26.5127i | −1.27826 | + | 1.07259i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.16392 | + | 4.33305i | 0.208569 | + | 0.175010i | 0.741088 | − | 0.671408i | \(-0.234310\pi\) |
−0.532519 | + | 0.846418i | \(0.678755\pi\) | |||||||
\(614\) | −9.07368 | − | 12.1881i | −0.366184 | − | 0.491871i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.37946 | + | 1.51196i | −0.257036 | + | 0.0609186i | ||||
\(617\) | −7.19212 | + | 9.66070i | −0.289544 | + | 0.388925i | −0.922966 | − | 0.384881i | \(-0.874242\pi\) |
0.633422 | + | 0.773807i | \(0.281650\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.0062 | + | 6.02974i | −0.482570 | + | 0.242356i | −0.673415 | − | 0.739264i | \(-0.735173\pi\) |
0.190845 | + | 0.981620i | \(0.438877\pi\) | |||||||
\(620\) | −33.5828 | − | 58.1671i | −1.34872 | − | 2.33605i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.34032 | + | 7.51765i | −0.174031 | + | 0.301430i | ||||
\(623\) | −0.292993 | + | 5.03050i | −0.0117385 | + | 0.201543i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 29.8965 | + | 3.49440i | 1.19586 | + | 0.139776i | ||||
\(626\) | 7.24294 | − | 24.1931i | 0.289486 | − | 0.966951i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.12597 | + | 11.8833i | −0.204548 | + | 0.474196i | ||||
\(629\) | −8.77342 | + | 3.19326i | −0.349819 | + | 0.127324i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.571023 | − | 0.207835i | −0.0227321 | − | 0.00827379i | 0.330629 | − | 0.943761i | \(-0.392739\pi\) |
−0.353361 | + | 0.935487i | \(0.614961\pi\) | |||||||
\(632\) | −56.9660 | + | 60.3805i | −2.26599 | + | 2.40181i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −48.9312 | − | 24.5742i | −1.94331 | − | 0.975965i | ||||
\(635\) | 2.69158 | + | 46.2127i | 0.106812 | + | 1.83390i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.9033 | + | 36.4195i | 0.432004 | + | 1.44299i | ||||
\(638\) | 1.26714 | + | 7.18633i | 0.0501667 | + | 0.284510i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.54721 | − | 37.1311i | 0.258801 | − | 1.46774i | ||||
\(641\) | −22.5001 | + | 2.62988i | −0.888700 | + | 0.103874i | −0.548177 | − | 0.836362i | \(-0.684678\pi\) |
−0.340523 | + | 0.940236i | \(0.610604\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.4459 | − | 35.4506i | −1.31898 | − | 1.39803i | −0.860604 | − | 0.509275i | \(-0.829913\pi\) |
−0.458374 | − | 0.888759i | \(-0.651568\pi\) | |||||||
\(644\) | −0.270165 | − | 0.626313i | −0.0106460 | − | 0.0246802i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.31799 | − | 2.18228i | −0.130545 | − | 0.0858606i | ||||
\(647\) | 20.1953 | 0.793960 | 0.396980 | − | 0.917827i | \(-0.370058\pi\) | ||||
0.396980 | + | 0.917827i | \(0.370058\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.61503 | −0.298916 | ||||||||
\(650\) | −17.9642 | − | 11.8152i | −0.704614 | − | 0.463432i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.8435 | + | 34.4112i | 0.581318 | + | 1.34765i | ||||
\(653\) | 13.1374 | + | 13.9248i | 0.514107 | + | 0.544921i | 0.931470 | − | 0.363819i | \(-0.118527\pi\) |
−0.417363 | + | 0.908740i | \(0.637046\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.2467 | − | 2.36650i | 0.791103 | − | 0.0924667i | ||||
\(656\) | 14.1233 | − | 80.0975i | 0.551424 | − | 3.12728i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.73183 | − | 9.82169i | −0.0675137 | − | 0.382889i | ||||
\(659\) | −11.8035 | − | 39.4263i | −0.459798 | − | 1.53583i | −0.802655 | − | 0.596444i | \(-0.796580\pi\) |
0.342857 | − | 0.939388i | \(-0.388605\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.65588 | + | 28.4304i | 0.0644065 | + | 1.10582i | 0.863414 | + | 0.504496i | \(0.168322\pi\) |
−0.799008 | + | 0.601321i | \(0.794641\pi\) | |||||||
\(662\) | −16.4655 | − | 8.26930i | −0.639951 | − | 0.321395i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 74.2130 | − | 78.6612i | 2.88002 | − | 3.05265i | ||||
\(665\) | 1.27848 | + | 0.465328i | 0.0495773 | + | 0.0180447i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.435139 | + | 0.158378i | −0.0168486 | + | 0.00613241i | ||||
\(668\) | 13.0217 | − | 30.1876i | 0.503824 | − | 1.16799i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −12.4608 | + | 41.6219i | −0.481402 | + | 1.60799i | ||||
\(671\) | −19.6923 | − | 2.30170i | −0.760214 | − | 0.0888562i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.12301 | − | 36.4506i | 0.0818359 | − | 1.40507i | −0.668353 | − | 0.743844i | \(-0.733001\pi\) |
0.750189 | − | 0.661223i | \(-0.229962\pi\) | |||||||
\(674\) | −36.2014 | + | 62.7027i | −1.39443 | + | 2.41522i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −48.2611 | − | 83.5906i | −1.85620 | − | 3.21502i | ||||
\(677\) | −1.58178 | + | 0.794398i | −0.0607926 | + | 0.0305312i | −0.478936 | − | 0.877850i | \(-0.658977\pi\) |
0.418143 | + | 0.908381i | \(0.362681\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.09747 | + | 1.47415i | −0.0421168 | + | 0.0565727i | ||||
\(680\) | −29.1721 | + | 6.91391i | −1.11870 | + | 0.265137i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.6591 | − | 17.0041i | −0.484741 | − | 0.651120i | ||||
\(683\) | −17.5030 | − | 14.6868i | −0.669734 | − | 0.561973i | 0.243253 | − | 0.969963i | \(-0.421786\pi\) |
−0.912987 | + | 0.407989i | \(0.866230\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.5714 | + | 13.9050i | −0.633159 | + | 0.531284i | ||||
\(686\) | −18.2354 | − | 4.32187i | −0.696231 | − | 0.165010i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 61.4405 | − | 40.4100i | 2.34240 | − | 1.54062i | ||||
\(689\) | −44.7231 | + | 29.4149i | −1.70382 | + | 1.12062i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.50438 | + | 1.30456i | 0.209396 | + | 0.0496279i | 0.333975 | − | 0.942582i | \(-0.391610\pi\) |
−0.124579 | + | 0.992210i | \(0.539758\pi\) | |||||||
\(692\) | 19.2016 | − | 16.1121i | 0.729936 | − | 0.612489i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −47.4741 | − | 39.8355i | −1.80209 | − | 1.51213i | ||||
\(695\) | 19.7563 | + | 26.5373i | 0.749399 | + | 1.00662i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.31238 | + | 2.20707i | −0.352732 | + | 0.0835989i | ||||
\(698\) | 4.89408 | − | 6.57389i | 0.185244 | − | 0.248825i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.34228 | − | 1.67856i | 0.126326 | − | 0.0634435i | ||||
\(701\) | 12.8656 | + | 22.2838i | 0.485926 | + | 0.841648i | 0.999869 | − | 0.0161763i | \(-0.00514928\pi\) |
−0.513944 | + | 0.857824i | \(0.671816\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.46201 | + | 5.99637i | −0.130572 | + | 0.226157i | ||||
\(704\) | 1.53097 | − | 26.2857i | 0.0577005 | − | 0.990679i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 27.8462 | + | 3.25475i | 1.04800 | + | 0.122494i | ||||
\(707\) | 2.61177 | − | 8.72392i | 0.0982257 | − | 0.328097i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.2718 | − | 30.7675i | 0.498433 | − | 1.15550i | −0.464455 | − | 0.885597i | \(-0.653750\pi\) |
0.962888 | − | 0.269901i | \(-0.0869908\pi\) | |||||||
\(710\) | −32.8446 | + | 11.9545i | −1.23264 | + | 0.448643i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −77.3810 | − | 28.1644i | −2.89997 | − | 1.05550i | ||||
\(713\) | 0.923158 | − | 0.978490i | 0.0345725 | − | 0.0366447i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.6423 | − | 9.86474i | −0.734581 | − | 0.368921i | ||||
\(716\) | −0.152822 | − | 2.62385i | −0.00571123 | − | 0.0980580i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 23.6430 | + | 78.9732i | 0.882350 | + | 2.94726i | ||||
\(719\) | 0.373099 | + | 2.11595i | 0.0139143 | + | 0.0789116i | 0.990974 | − | 0.134053i | \(-0.0427992\pi\) |
−0.977060 | + | 0.212965i | \(0.931688\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.383057 | − | 2.17243i | 0.0142658 | − | 0.0809054i | ||||
\(722\) | 47.4567 | − | 5.54689i | 1.76616 | − | 0.206434i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.2948 | + | 14.0916i | 0.494096 | + | 0.523711i | ||||
\(725\) | −1.00569 | − | 2.33144i | −0.0373502 | − | 0.0865876i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.24322 | − | 6.07936i | −0.342812 | − | 0.225471i | 0.366415 | − | 0.930452i | \(-0.380585\pi\) |
−0.709226 | + | 0.704981i | \(0.750956\pi\) | |||||||
\(728\) | 24.0660 | 0.891946 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −40.3536 | −1.49355 | ||||||||
\(731\) | −7.22961 | − | 4.75499i | −0.267397 | − | 0.175870i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.73459 | − | 15.6125i | −0.248748 | − | 0.576662i | 0.747398 | − | 0.664377i | \(-0.231303\pi\) |
−0.996146 | + | 0.0877145i | \(0.972044\pi\) | |||||||
\(734\) | −27.8914 | − | 29.5632i | −1.02949 | − | 1.09120i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.99132 | − | 0.466519i | 0.147122 | − | 0.0171961i | ||||
\(737\) | −1.71303 | + | 9.71507i | −0.0631002 | + | 0.357859i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.23694 | − | 24.0289i | −0.155858 | − | 0.883917i | −0.957997 | − | 0.286779i | \(-0.907416\pi\) |
0.802138 | − | 0.597138i | \(-0.203696\pi\) | |||||||
\(740\) | 24.5782 | + | 82.0970i | 0.903514 | + | 3.01795i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.752578 | − | 12.9213i | −0.0276280 | − | 0.474354i | ||||
\(743\) | 5.27562 | + | 2.64951i | 0.193544 | + | 0.0972012i | 0.542932 | − | 0.839777i | \(-0.317314\pi\) |
−0.349388 | + | 0.936978i | \(0.613611\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28.3845 | + | 30.0858i | −1.03993 | + | 1.10226i | ||||
\(746\) | 2.34148 | + | 0.852230i | 0.0857277 | + | 0.0312023i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −10.4873 | + | 3.81706i | −0.383453 | + | 0.139566i | ||||
\(749\) | 1.61466 | − | 3.74320i | 0.0589984 | − | 0.136774i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.90970 | − | 33.1007i | 0.361610 | − | 1.20786i | −0.562842 | − | 0.826564i | \(-0.690292\pi\) |
0.924452 | − | 0.381298i | \(-0.124523\pi\) | |||||||
\(752\) | 87.4068 | + | 10.2164i | 3.18740 | + | 0.372554i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.55747 | − | 26.7408i | 0.0567198 | − | 0.973841i | ||||
\(755\) | −27.4525 | + | 47.5491i | −0.999099 | + | 1.73049i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.4091 | + | 33.6176i | 0.705437 | + | 1.22185i | 0.966534 | + | 0.256540i | \(0.0825824\pi\) |
−0.261097 | + | 0.965313i | \(0.584084\pi\) | |||||||
\(758\) | −91.7699 | + | 46.0886i | −3.33323 | + | 1.67401i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −13.2770 | + | 17.8341i | −0.481607 | + | 0.646910i | ||||
\(761\) | 39.7704 | − | 9.42575i | 1.44167 | − | 0.341683i | 0.565928 | − | 0.824455i | \(-0.308518\pi\) |
0.875746 | + | 0.482771i | \(0.160370\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.0649459 | − | 0.0872375i | −0.00235120 | − | 0.00315821i | ||||
\(764\) | 89.0105 | + | 74.6887i | 3.22029 | + | 2.70214i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −30.1711 | + | 25.3166i | −1.09013 | + | 0.914725i | ||||
\(767\) | 27.1993 | + | 6.44635i | 0.982109 | + | 0.232764i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.8208 | − | 16.9826i | 0.931122 | − | 0.612409i | 0.00927263 | − | 0.999957i | \(-0.497048\pi\) |
0.921849 | + | 0.387548i | \(0.126678\pi\) | |||||||
\(770\) | 4.44040 | − | 2.92050i | 0.160021 | − | 0.105247i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −28.5562 | − | 6.76794i | −1.02776 | − | 0.243583i | ||||
\(773\) | −22.5762 | + | 18.9437i | −0.812009 | + | 0.681356i | −0.951086 | − | 0.308925i | \(-0.900031\pi\) |
0.139077 | + | 0.990282i | \(0.455586\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.65054 | + | 4.74137i | 0.202974 | + | 0.170315i | ||||
\(776\) | −17.9346 | − | 24.0904i | −0.643816 | − | 0.864795i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 44.3927 | − | 10.5213i | 1.59155 | − | 0.377205i | ||||
\(779\) | −4.23831 | + | 5.69304i | −0.151853 | + | 0.203974i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.09204 | + | 3.56175i | −0.253773 | + | 0.127450i | ||||
\(782\) | −0.492228 | − | 0.852563i | −0.0176020 | − | 0.0304876i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 40.5553 | − | 70.2439i | 1.44841 | − | 2.50871i | ||||
\(785\) | 0.372071 | − | 6.38821i | 0.0132798 | − | 0.228005i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.3206 | − | 1.90760i | −0.581765 | − | 0.0679986i | −0.179880 | − | 0.983689i | \(-0.557571\pi\) |
−0.401885 | + | 0.915690i | \(0.631645\pi\) | |||||||
\(788\) | −3.55876 | + | 11.8871i | −0.126775 | + | 0.423460i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 26.6534 | − | 61.7896i | 0.948286 | − | 2.19837i | ||||
\(791\) | 2.66286 | − | 0.969203i | 0.0946805 | − | 0.0344609i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 68.3884 | + | 24.8914i | 2.42854 | + | 0.883918i | ||||
\(794\) | 46.1496 | − | 48.9157i | 1.63779 | − | 1.73595i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −44.8378 | − | 22.5184i | −1.58923 | − | 0.798143i | ||||
\(797\) | −0.488972 | − | 8.39532i | −0.0173203 | − | 0.297378i | −0.995833 | − | 0.0911925i | \(-0.970932\pi\) |
0.978513 | − | 0.206185i | \(-0.0661049\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.96986 | − | 9.92003i | −0.105066 | − | 0.350946i | ||||
\(800\) | 3.82623 | + | 21.6996i | 0.135278 | + | 0.767198i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.56414 | − | 54.2409i | 0.337721 | − | 1.91531i | ||||
\(803\) | −9.10058 | + | 1.06371i | −0.321152 | + | 0.0375373i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.231444 | + | 0.245316i | 0.00815732 | + | 0.00864625i | ||||
\(806\) | 30.8211 | + | 71.4514i | 1.08563 | + | 2.51677i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 124.335 | + | 81.7763i | 4.37408 | + | 2.87688i | ||||
\(809\) | 1.83823 | 0.0646289 | 0.0323144 | − | 0.999478i | \(-0.489712\pi\) | ||||
0.0323144 | + | 0.999478i | \(0.489712\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.25761 | −0.289964 | −0.144982 | − | 0.989434i | \(-0.546312\pi\) | ||||
−0.144982 | + | 0.989434i | \(0.546312\pi\) | |||||||
\(812\) | 3.89283 | + | 2.56035i | 0.136611 | + | 0.0898508i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10.7131 | + | 24.8357i | 0.375494 | + | 0.870492i | ||||
\(815\) | −12.7161 | − | 13.4783i | −0.445425 | − | 0.472123i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.37387 | + | 0.744999i | −0.222994 | + | 0.0260642i | ||||
\(818\) | 16.3095 | − | 92.4956i | 0.570248 | − | 3.23403i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 15.2539 | + | 86.5093i | 0.532690 | + | 3.02104i | ||||
\(821\) | −7.32243 | − | 24.4586i | −0.255554 | − | 0.853611i | −0.985437 | − | 0.170039i | \(-0.945611\pi\) |
0.729883 | − | 0.683572i | \(-0.239575\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.204192 | + | 3.50585i | 0.00711770 | + | 0.122206i | 0.999995 | + | 0.00306726i | \(0.000976340\pi\) |
−0.992878 | + | 0.119139i | \(0.961987\pi\) | |||||||
\(824\) | 32.2147 | + | 16.1789i | 1.12225 | + | 0.563617i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.63820 | + | 4.91621i | −0.161384 | + | 0.171057i | ||||
\(827\) | −29.3726 | − | 10.6908i | −1.02139 | − | 0.371754i | −0.223591 | − | 0.974683i | \(-0.571778\pi\) |
−0.797795 | + | 0.602929i | \(0.794000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.5589 | − | 16.2181i | 1.54759 | − | 0.563278i | 0.579743 | − | 0.814800i | \(-0.303153\pi\) |
0.967852 | + | 0.251521i | \(0.0809308\pi\) | |||||||
\(830\) | −34.7230 | + | 80.4969i | −1.20525 | + | 2.79409i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −27.7199 | + | 92.5910i | −0.961015 | + | 3.21001i | ||||
\(833\) | −9.47964 | − | 1.10801i | −0.328450 | − | 0.0383903i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.945185 | + | 16.2282i | −0.0327095 | + | 0.561600i | ||||
\(836\) | −4.13831 | + | 7.16776i | −0.143126 | + | 0.247902i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −36.1825 | − | 62.6699i | −1.24990 | − | 2.16489i | ||||
\(839\) | −26.5599 | + | 13.3389i | −0.916950 | + | 0.460509i | −0.843707 | − | 0.536805i | \(-0.819631\pi\) |
−0.0732431 | + | 0.997314i | \(0.523335\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.4287 | + | 20.7243i | −0.532024 | + | 0.714632i | ||||
\(842\) | −79.0718 | + | 18.7404i | −2.72499 | + | 0.645835i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −60.0498 | − | 80.6609i | −2.06700 | − | 2.77646i | ||||
\(845\) | 36.5597 | + | 30.6772i | 1.25769 | + | 1.05533i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.38092 | + | 2.83693i | −0.116170 | + | 0.0974780i | ||||
\(848\) | 111.130 | + | 26.3382i | 3.81621 | + | 0.904458i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.50997 | − | 2.96625i | 0.154691 | − | 0.101742i | ||||
\(851\) | −1.43403 | + | 0.943177i | −0.0491580 | + | 0.0323317i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.2598 | + | 2.43161i | 0.351287 | + | 0.0832566i | 0.402471 | − | 0.915433i | \(-0.368151\pi\) |
−0.0511840 | + | 0.998689i | \(0.516300\pi\) | |||||||
\(854\) | −13.4803 | + | 11.3113i | −0.461286 | + | 0.387065i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 51.0334 | + | 42.8221i | 1.74429 | + | 1.46363i | ||||
\(857\) | −8.85593 | − | 11.8956i | −0.302513 | − | 0.406345i | 0.624709 | − | 0.780858i | \(-0.285218\pi\) |
−0.927222 | + | 0.374512i | \(0.877810\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.7582 | − | 7.28983i | 1.04946 | − | 0.248726i | 0.330518 | − | 0.943800i | \(-0.392777\pi\) |
0.718938 | + | 0.695074i | \(0.244628\pi\) | |||||||
\(860\) | −47.4295 | + | 63.7088i | −1.61733 | + | 2.17245i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −21.5164 | + | 10.8059i | −0.732851 | + | 0.368052i | ||||
\(863\) | −1.64562 | − | 2.85030i | −0.0560177 | − | 0.0970255i | 0.836657 | − | 0.547728i | \(-0.184507\pi\) |
−0.892674 | + | 0.450702i | \(0.851174\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.19692 | + | 10.7334i | −0.210701 | + | 0.364946i | ||||
\(866\) | −3.67969 | + | 63.1778i | −0.125041 | + | 2.14687i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −13.4442 | − | 1.57140i | −0.456326 | − | 0.0533369i | ||||
\(869\) | 4.38215 | − | 14.6374i | 0.148654 | − | 0.496540i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.3427 | − | 33.2501i | 0.485983 | − | 1.12664i | ||||
\(872\) | 1.67013 | − | 0.607878i | 0.0565577 | − | 0.0205853i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.686052 | − | 0.249702i | −0.0232060 | − | 0.00844631i | ||||
\(875\) | 3.17555 | − | 3.36588i | 0.107353 | − | 0.113788i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.0068 | − | 16.5766i | −1.11456 | − | 0.559753i | −0.206439 | − | 0.978459i | \(-0.566187\pi\) |
−0.908122 | + | 0.418706i | \(0.862484\pi\) | |||||||
\(878\) | −0.624763 | − | 10.7268i | −0.0210847 | − | 0.362011i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 13.4500 | + | 44.9262i | 0.453400 | + | 1.51446i | ||||
\(881\) | −5.05857 | − | 28.6886i | −0.170427 | − | 0.966542i | −0.943290 | − | 0.331969i | \(-0.892287\pi\) |
0.772863 | − | 0.634573i | \(-0.218824\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.27904 | + | 18.5963i | −0.110348 | + | 0.625817i | 0.878600 | + | 0.477558i | \(0.158478\pi\) |
−0.988949 | + | 0.148259i | \(0.952633\pi\) | |||||||
\(884\) | 40.6897 | − | 4.75594i | 1.36854 | − | 0.159960i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.5790 | + | 15.4529i | 0.489793 | + | 0.519150i | ||||
\(887\) | −9.62067 | − | 22.3032i | −0.323031 | − | 0.748869i | −0.999918 | − | 0.0127828i | \(-0.995931\pi\) |
0.676888 | − | 0.736086i | \(-0.263328\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.79420 | + | 5.12633i | 0.261409 | + | 0.171932i | ||||
\(890\) | 66.7543 | 2.23761 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.4343 | 0.449814 | ||||||||
\(893\) | −6.41605 | − | 4.21990i | −0.214705 | − | 0.141214i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.514730 | + | 1.19328i | 0.0172055 | + | 0.0398869i | ||||
\(896\) | −5.21433 | − | 5.52686i | −0.174198 | − | 0.184640i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −39.0769 | + | 4.56744i | −1.30401 | + | 0.152417i | ||||
\(899\) | −1.59569 | + | 9.04959i | −0.0532191 | + | 0.301821i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.33361 | − | 13.2346i | −0.0777438 | − | 0.440907i | ||||
\(902\) | 7.95172 | + | 26.5606i | 0.264763 | + | 0.884371i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.69263 | + | 46.2306i | 0.0895555 | + | 1.53761i | ||||
\(905\) | −8.56020 | − | 4.29909i | −0.284551 | − | 0.142907i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.0555 | + | 28.6772i | −0.898364 | + | 0.952211i | −0.999088 | − | 0.0427038i | \(-0.986403\pi\) |
0.100723 | + | 0.994914i | \(0.467884\pi\) | |||||||
\(908\) | 5.95117 | + | 2.16605i | 0.197496 | + | 0.0718828i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −18.3325 | + | 6.67247i | −0.607715 | + | 0.221190i | ||||
\(911\) | −16.3902 | + | 37.9968i | −0.543032 | + | 1.25889i | 0.397004 | + | 0.917817i | \(0.370050\pi\) |
−0.940037 | + | 0.341073i | \(0.889210\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.70889 | + | 19.0690i | −0.188937 | + | 0.631092i | ||||
\(914\) | 20.8440 | + | 2.43631i | 0.689457 | + | 0.0805860i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.46061 | + | 25.0777i | −0.0482600 | + | 0.828592i | ||||
\(917\) | 2.05402 | − | 3.55767i | 0.0678298 | − | 0.117485i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.677038 | + | 1.17266i | 0.0223334 | + | 0.0386826i | 0.876976 | − | 0.480534i | \(-0.159557\pi\) |
−0.854643 | + | 0.519217i | \(0.826224\pi\) | |||||||
\(920\) | −4.92526 | + | 2.47356i | −0.162381 | + | 0.0815509i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.26713 | + | 7.07498i | −0.173464 | + | 0.233002i | ||||
\(923\) | 28.3464 | − | 6.71822i | 0.933034 | − | 0.221133i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.62012 | − | 7.54913i | −0.184788 | − | 0.248214i | ||||
\(926\) | −36.2019 | − | 30.3770i | −1.18967 | − | 0.998250i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −21.0279 | + | 17.6445i | −0.690274 | + | 0.579209i | ||||
\(929\) | 25.9999 | + | 6.16209i | 0.853029 | + | 0.202172i | 0.633796 | − | 0.773501i | \(-0.281496\pi\) |
0.219234 | + | 0.975672i | \(0.429644\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.91362 | + | 3.88945i | −0.193811 | + | 0.127472i | ||||
\(932\) | −16.3823 | + | 10.7748i | −0.536619 | + | 0.352940i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 103.543 | + | 24.5400i | 3.38802 | + | 0.802975i | ||||
\(935\) | 4.22721 | − | 3.54705i | 0.138244 | − | 0.116001i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.08507 | − | 1.74958i | −0.0681162 | − | 0.0571563i | 0.608094 | − | 0.793865i | \(-0.291934\pi\) |
−0.676210 | + | 0.736709i | \(0.736379\pi\) | |||||||
\(938\) | 5.22860 | + | 7.02323i | 0.170720 | + | 0.229317i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −92.4845 | + | 21.9192i | −3.01651 | + | 0.714926i | ||||
\(941\) | −13.6172 | + | 18.2911i | −0.443908 | + | 0.596272i | −0.966613 | − | 0.256242i | \(-0.917516\pi\) |
0.522705 | + | 0.852514i | \(0.324923\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.57225 | + | 0.789615i | −0.0511996 | + | 0.0257134i | ||||
\(944\) | −29.8195 | − | 51.6488i | −0.970541 | − | 1.68103i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.5341 | + | 21.7097i | −0.407520 | + | 0.705845i | ||||
\(947\) | 0.952785 | − | 16.3587i | 0.0309613 | − | 0.531586i | −0.946794 | − | 0.321839i | \(-0.895699\pi\) |
0.977756 | − | 0.209747i | \(-0.0672639\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33.4058 | + | 3.90458i | 1.08440 | + | 0.126748i | ||||
\(950\) | 1.14813 | − | 3.83503i | 0.0372504 | − | 0.124425i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.39305 | + | 5.54772i | −0.0775593 | + | 0.179803i | ||||
\(953\) | −33.5144 | + | 12.1982i | −1.08564 | + | 0.395140i | −0.822003 | − | 0.569483i | \(-0.807143\pi\) |
−0.263634 | + | 0.964623i | \(0.584921\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −53.9877 | − | 19.6499i | −1.74700 | − | 0.635857i | ||||
\(956\) | −31.8340 | + | 33.7420i | −1.02958 | + | 1.09129i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 93.5000 | + | 46.9574i | 3.02085 | + | 1.51713i | ||||
\(959\) | 0.253484 | + | 4.35215i | 0.00818542 | + | 0.140538i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.23462 | + | 4.12391i | 0.0398263 | + | 0.133029i | ||||
\(962\) | −17.2407 | − | 97.7770i | −0.555863 | − | 3.15246i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −20.8580 | + | 118.292i | −0.671791 | + | 3.80992i | ||||
\(965\) | 14.4126 | − | 1.68459i | 0.463958 | − | 0.0542289i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.52220 | + | 5.85319i | 0.177582 | + | 0.188226i | 0.810050 | − | 0.586360i | \(-0.199440\pi\) |
−0.632469 | + | 0.774586i | \(0.717958\pi\) | |||||||
\(968\) | −28.5671 | − | 66.2259i | −0.918180 | − | 2.12858i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 20.3411 | + | 13.3785i | 0.653113 | + | 0.429559i | ||||
\(971\) | 44.9410 | 1.44223 | 0.721113 | − | 0.692818i | \(-0.243631\pi\) | ||||
0.721113 | + | 0.692818i | \(0.243631\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.66731 | 0.213744 | ||||||||
\(974\) | −78.1977 | − | 51.4314i | −2.50562 | − | 1.64797i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −61.5013 | − | 142.576i | −1.96861 | − | 4.56375i | ||||
\(977\) | −19.0563 | − | 20.1985i | −0.609664 | − | 0.646206i | 0.346840 | − | 0.937924i | \(-0.387255\pi\) |
−0.956504 | + | 0.291718i | \(0.905773\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.0545 | − | 1.75962i | 0.481144 | − | 0.0562377i | ||||
\(980\) | −15.2122 | + | 86.2728i | −0.485936 | + | 2.75588i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.54176 | − | 54.1140i | −0.304490 | − | 1.72685i | ||||
\(983\) | −2.00822 | − | 6.70794i | −0.0640524 | − | 0.213950i | 0.919972 | − | 0.391984i | \(-0.128211\pi\) |
−0.984024 | + | 0.178035i | \(0.943026\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.356736 | − | 6.12492i | −0.0113666 | − | 0.195156i | ||||
\(986\) | 6.00943 | + | 3.01805i | 0.191379 | + | 0.0961143i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 20.8489 | − | 22.0985i | 0.663292 | − | 0.703048i | ||||
\(989\) | −1.49485 | − | 0.544079i | −0.0475333 | − | 0.0173007i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55.0238 | − | 20.0270i | 1.74789 | − | 0.636179i | 0.748259 | − | 0.663407i | \(-0.230890\pi\) |
0.999629 | + | 0.0272280i | \(0.00866800\pi\) | |||||||
\(992\) | 31.5850 | − | 73.2223i | 1.00283 | − | 2.32481i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.02021 | + | 6.74799i | −0.0640773 | + | 0.214033i | ||||
\(995\) | 24.6411 | + | 2.88014i | 0.781176 | + | 0.0913064i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.23842 | − | 38.4322i | 0.0708916 | − | 1.21716i | −0.755913 | − | 0.654672i | \(-0.772807\pi\) |
0.826805 | − | 0.562489i | \(-0.190156\pi\) | |||||||
\(998\) | −11.0063 | + | 19.0635i | −0.348400 | + | 0.603446i | ||||
\(999\) | 0 | 0 |
(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 | 729.2.g.b.703.1 | 144 | ||
3.2 | odd | 2 | 729.2.g.c.703.8 | 144 | |||
9.2 | odd | 6 | 729.2.g.d.217.8 | 144 | |||
9.4 | even | 3 | 243.2.g.a.73.8 | 144 | |||
9.5 | odd | 6 | 81.2.g.a.25.1 | yes | 144 | ||
9.7 | even | 3 | 729.2.g.a.217.1 | 144 | |||
81.13 | even | 27 | 729.2.g.a.514.1 | 144 | |||
81.14 | odd | 54 | 729.2.g.c.28.8 | 144 | |||
81.38 | odd | 54 | 6561.2.a.c.1.2 | 72 | |||
81.40 | even | 27 | 243.2.g.a.10.8 | 144 | |||
81.41 | odd | 54 | 81.2.g.a.13.1 | ✓ | 144 | ||
81.43 | even | 27 | 6561.2.a.d.1.71 | 72 | |||
81.67 | even | 27 | inner | 729.2.g.b.28.1 | 144 | ||
81.68 | odd | 54 | 729.2.g.d.514.8 | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
81.2.g.a.13.1 | ✓ | 144 | 81.41 | odd | 54 | ||
81.2.g.a.25.1 | yes | 144 | 9.5 | odd | 6 | ||
243.2.g.a.10.8 | 144 | 81.40 | even | 27 | |||
243.2.g.a.73.8 | 144 | 9.4 | even | 3 | |||
729.2.g.a.217.1 | 144 | 9.7 | even | 3 | |||
729.2.g.a.514.1 | 144 | 81.13 | even | 27 | |||
729.2.g.b.28.1 | 144 | 81.67 | even | 27 | inner | ||
729.2.g.b.703.1 | 144 | 1.1 | even | 1 | trivial | ||
729.2.g.c.28.8 | 144 | 81.14 | odd | 54 | |||
729.2.g.c.703.8 | 144 | 3.2 | odd | 2 | |||
729.2.g.d.217.8 | 144 | 9.2 | odd | 6 | |||
729.2.g.d.514.8 | 144 | 81.68 | odd | 54 | |||
6561.2.a.c.1.2 | 72 | 81.38 | odd | 54 | |||
6561.2.a.d.1.71 | 72 | 81.43 | even | 27 |