Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [572,2,Mod(133,572)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(572, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("572.133");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 572 = 2^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 572.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.56744299562\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} + 9x^{8} + 6x^{7} + 59x^{6} + 2x^{5} + 47x^{4} - 26x^{3} + 38x^{2} - 12x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 529.2 | ||
Root | \(-0.542661 + 0.939916i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 572.529 |
Dual form | 572.2.i.c.133.2 |
$q$-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 \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(353\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.542661 | + | 0.939916i | −0.313305 | + | 0.542661i | −0.979076 | − | 0.203496i | \(-0.934770\pi\) |
0.665771 | + | 0.746157i | \(0.268103\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.28140 | −0.573060 | −0.286530 | − | 0.958071i | \(-0.592502\pi\) | ||||
−0.286530 | + | 0.958071i | \(0.592502\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.24710 | − | 2.16005i | −0.471361 | − | 0.816421i | 0.528102 | − | 0.849181i | \(-0.322904\pi\) |
−0.999463 | + | 0.0327594i | \(0.989570\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.911039 | + | 1.57797i | 0.303680 | + | 0.525989i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.63419 | − | 2.46191i | −0.730594 | − | 0.682812i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.695365 | − | 1.20441i | 0.179543 | − | 0.310977i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.07045 | − | 5.31818i | −0.744694 | − | 1.28985i | −0.950338 | − | 0.311221i | \(-0.899262\pi\) |
0.205644 | − | 0.978627i | \(-0.434071\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.187000 | + | 0.323894i | 0.0429008 | + | 0.0743064i | 0.886679 | − | 0.462386i | \(-0.153007\pi\) |
−0.843778 | + | 0.536693i | \(0.819673\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.70702 | 0.590720 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.919404 | − | 1.59245i | 0.191709 | − | 0.332050i | −0.754108 | − | 0.656751i | \(-0.771930\pi\) |
0.945817 | + | 0.324701i | \(0.105264\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.35801 | −0.671603 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.23350 | −1.00719 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.13056 | − | 7.15433i | 0.767025 | − | 1.32853i | −0.172145 | − | 0.985072i | \(-0.555070\pi\) |
0.939169 | − | 0.343454i | \(-0.111597\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.44774 | −1.15805 | −0.579024 | − | 0.815310i | \(-0.696566\pi\) | ||||
−0.579024 | + | 0.815310i | \(0.696566\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.542661 | − | 0.939916i | −0.0944651 | − | 0.163618i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.59804 | + | 2.76789i | 0.270118 | + | 0.467858i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.17428 | − | 2.03392i | 0.193051 | − | 0.334374i | −0.753209 | − | 0.657781i | \(-0.771495\pi\) |
0.946260 | + | 0.323408i | \(0.104828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.74346 | − | 1.13994i | 0.599434 | − | 0.182536i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.98513 | − | 3.43835i | 0.310025 | − | 0.536979i | −0.668342 | − | 0.743854i | \(-0.732996\pi\) |
0.978368 | + | 0.206874i | \(0.0663292\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.14070 | − | 3.70780i | −0.326454 | − | 0.565434i | 0.655352 | − | 0.755324i | \(-0.272520\pi\) |
−0.981805 | + | 0.189889i | \(0.939187\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.16741 | − | 2.02201i | −0.174027 | − | 0.301423i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.03014 | −1.31718 | −0.658591 | − | 0.752501i | \(-0.728847\pi\) | ||||
−0.658591 | + | 0.752501i | \(0.728847\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.389462 | − | 0.674568i | 0.0556374 | − | 0.0963668i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.66485 | 0.933266 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.6446 | 1.73686 | 0.868432 | − | 0.495808i | \(-0.165128\pi\) | ||||
0.868432 | + | 0.495808i | \(0.165128\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.640700 | − | 1.10972i | 0.0863920 | − | 0.149635i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.405911 | −0.0537642 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.07882 | + | 7.06472i | 0.531017 | + | 0.919748i | 0.999345 | + | 0.0361932i | \(0.0115232\pi\) |
−0.468328 | + | 0.883555i | \(0.655144\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.18336 | + | 5.51374i | 0.407588 | + | 0.705962i | 0.994619 | − | 0.103602i | \(-0.0330368\pi\) |
−0.587031 | + | 0.809564i | \(0.699703\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.27232 | − | 3.93578i | 0.286286 | − | 0.495861i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.37546 | + | 3.15470i | 0.418674 | + | 0.391292i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.93502 | + | 10.2798i | −0.725078 | + | 1.25587i | 0.233864 | + | 0.972269i | \(0.424863\pi\) |
−0.958942 | + | 0.283603i | \(0.908470\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.997848 | + | 1.72832i | 0.120127 | + | 0.208066i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.27291 | − | 5.66885i | −0.388423 | − | 0.672769i | 0.603814 | − | 0.797125i | \(-0.293647\pi\) |
−0.992238 | + | 0.124356i | \(0.960313\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.8984 | −1.74372 | −0.871860 | − | 0.489755i | \(-0.837086\pi\) | ||||
−0.871860 | + | 0.489755i | \(0.837086\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.82226 | − | 3.15625i | 0.210417 | − | 0.364452i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.49421 | 0.284241 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.17910 | −0.357677 | −0.178839 | − | 0.983878i | \(-0.557234\pi\) | ||||
−0.178839 | + | 0.983878i | \(0.557234\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.106898 | − | 0.185154i | 0.0118776 | − | 0.0205726i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −17.3167 | −1.90075 | −0.950377 | − | 0.311101i | \(-0.899302\pi\) | ||||
−0.950377 | + | 0.311101i | \(0.899302\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.93448 | + | 6.81471i | 0.426754 | + | 0.739159i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.48298 | + | 7.76475i | 0.480626 | + | 0.832468i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.905248 | + | 1.56793i | −0.0959561 | + | 0.166201i | −0.910007 | − | 0.414592i | \(-0.863924\pi\) |
0.814051 | + | 0.580793i | \(0.197257\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.03274 | + | 8.76025i | −0.213089 | + | 0.918324i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.49893 | − | 6.06033i | 0.362823 | − | 0.628427i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.239622 | − | 0.415038i | −0.0245847 | − | 0.0425820i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.68319 | + | 6.37947i | 0.373971 | + | 0.647738i | 0.990173 | − | 0.139851i | \(-0.0446625\pi\) |
−0.616201 | + | 0.787589i | \(0.711329\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.82208 | −0.183126 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.649779 | + | 1.12545i | −0.0646554 | + | 0.111986i | −0.896541 | − | 0.442961i | \(-0.853928\pi\) |
0.831886 | + | 0.554947i | \(0.187261\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.6572 | 1.54275 | 0.771376 | − | 0.636379i | \(-0.219569\pi\) | ||||
0.771376 | + | 0.636379i | \(0.219569\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.46877 | −0.338517 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.898540 | + | 1.55632i | −0.0868652 | + | 0.150455i | −0.906184 | − | 0.422883i | \(-0.861018\pi\) |
0.819319 | + | 0.573337i | \(0.194352\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.1064 | 0.968019 | 0.484010 | − | 0.875063i | \(-0.339180\pi\) | ||||
0.484010 | + | 0.875063i | \(0.339180\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.27447 | + | 2.20745i | 0.120968 | + | 0.209522i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.47499 | − | 4.28680i | −0.232827 | − | 0.403268i | 0.725812 | − | 0.687893i | \(-0.241464\pi\) |
−0.958639 | + | 0.284625i | \(0.908131\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.17812 | + | 2.04057i | −0.109861 | + | 0.190284i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.48496 | − | 6.39957i | 0.137285 | − | 0.591640i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.65835 | + | 13.2646i | −0.702039 | + | 1.21597i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.15450 | + | 3.73171i | 0.194265 | + | 0.336477i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.7100 | 0.957928 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.25186 | + | 16.0247i | −0.820970 | + | 1.42196i | 0.0839906 | + | 0.996467i | \(0.473233\pi\) |
−0.904961 | + | 0.425495i | \(0.860100\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.64669 | 0.409119 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.9833 | 0.959619 | 0.479809 | − | 0.877373i | \(-0.340706\pi\) | ||||
0.479809 | + | 0.877373i | \(0.340706\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.466418 | − | 0.807860i | 0.0404436 | − | 0.0700503i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.70621 | 0.577179 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.72644 | − | 8.18644i | −0.403807 | − | 0.699415i | 0.590375 | − | 0.807129i | \(-0.298980\pi\) |
−0.994182 | + | 0.107715i | \(0.965647\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.11547 | + | 14.0564i | 0.688345 | + | 1.19225i | 0.972373 | + | 0.233432i | \(0.0749957\pi\) |
−0.284028 | + | 0.958816i | \(0.591671\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.90030 | − | 8.48757i | 0.412680 | − | 0.714783i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.44918 | − | 1.05032i | 0.288435 | − | 0.0878324i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.29289 | + | 9.16756i | −0.439551 | + | 0.761324i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.422691 | + | 0.732122i | 0.0348630 | + | 0.0603844i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.44897 | − | 4.24175i | −0.200628 | − | 0.347498i | 0.748103 | − | 0.663583i | \(-0.230965\pi\) |
−0.948731 | + | 0.316085i | \(0.897632\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.97273 | −0.160539 | −0.0802693 | − | 0.996773i | \(-0.525578\pi\) | ||||
−0.0802693 | + | 0.996773i | \(0.525578\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.59460 | − | 9.69013i | 0.452297 | − | 0.783401i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.26213 | 0.663630 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.84504 | −0.785720 | −0.392860 | − | 0.919598i | \(-0.628514\pi\) | ||||
−0.392860 | + | 0.919598i | \(0.628514\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.86170 | + | 11.8848i | −0.544169 | + | 0.942528i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.58637 | −0.361457 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.61383 | + | 9.72343i | 0.439709 | + | 0.761598i | 0.997667 | − | 0.0682713i | \(-0.0217483\pi\) |
−0.557958 | + | 0.829869i | \(0.688415\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.695365 | + | 1.20441i | 0.0541341 | + | 0.0937630i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.55216 | − | 13.0807i | 0.584404 | − | 1.01222i | −0.410546 | − | 0.911840i | \(-0.634662\pi\) |
0.994949 | − | 0.100377i | \(-0.0320049\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.877966 | + | 12.9703i | 0.0675358 | + | 0.997717i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.340729 | + | 0.590161i | −0.0260562 | + | 0.0451307i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.40040 | + | 5.88967i | 0.258528 | + | 0.447783i | 0.965848 | − | 0.259110i | \(-0.0834294\pi\) |
−0.707320 | + | 0.706893i | \(0.750096\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.18779 | + | 7.25347i | 0.316567 | + | 0.548311i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.85365 | −0.665481 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.06209 | − | 12.2319i | 0.527845 | − | 0.914255i | −0.471628 | − | 0.881798i | \(-0.656333\pi\) |
0.999473 | − | 0.0324570i | \(-0.0103332\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.6671 | −1.68483 | −0.842416 | − | 0.538828i | \(-0.818867\pi\) | ||||
−0.842416 | + | 0.538828i | \(0.818867\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.90994 | −0.510797 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.50472 | + | 2.60626i | −0.110630 | + | 0.191616i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.14090 | 0.449067 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.52672 | + | 11.3046i | 0.474749 | + | 0.822290i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.20912 | − | 2.09426i | −0.0874890 | − | 0.151535i | 0.818960 | − | 0.573850i | \(-0.194551\pi\) |
−0.906449 | + | 0.422315i | \(0.861218\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.2279 | − | 19.4473i | 0.808203 | − | 1.39985i | −0.105904 | − | 0.994376i | \(-0.533774\pi\) |
0.914107 | − | 0.405473i | \(-0.132893\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.79688 | + | 1.46072i | −0.343511 | + | 0.104604i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0633 | − | 20.8943i | 0.859476 | − | 1.48866i | −0.0129525 | − | 0.999916i | \(-0.504123\pi\) |
0.872429 | − | 0.488741i | \(-0.162544\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.8229 | − | 20.4778i | −0.838101 | − | 1.45163i | −0.891480 | − | 0.453059i | \(-0.850333\pi\) |
0.0533792 | − | 0.998574i | \(-0.483001\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.44140 | − | 11.1568i | −0.454342 | − | 0.786943i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.6049 | −1.44618 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.54375 | + | 4.40590i | −0.177663 | + | 0.307721i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.35045 | 0.232872 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.374001 | −0.0258702 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.57916 | + | 4.46723i | −0.177557 | + | 0.307537i | −0.941043 | − | 0.338287i | \(-0.890153\pi\) |
0.763486 | + | 0.645824i | \(0.223486\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.10432 | 0.486780 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.74309 | + | 4.75118i | 0.187077 | + | 0.324028i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.04100 | + | 13.9274i | 0.545859 | + | 0.945455i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.08475 | − | 14.0032i | 0.546317 | − | 0.946248i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.00472 | + | 21.5683i | −0.336654 | + | 1.45084i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.58012 | − | 13.1292i | 0.507602 | − | 0.879193i | −0.492359 | − | 0.870392i | \(-0.663865\pi\) |
0.999961 | − | 0.00880089i | \(-0.00280145\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.05928 | − | 5.29883i | −0.203952 | − | 0.353255i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.15433 | + | 12.3917i | 0.474850 | + | 0.822464i | 0.999585 | − | 0.0288014i | \(-0.00916903\pi\) |
−0.524735 | + | 0.851265i | \(0.675836\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.2644 | −1.33911 | −0.669555 | − | 0.742762i | \(-0.733515\pi\) | ||||
−0.669555 | + | 0.742762i | \(0.733515\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.35351 | + | 2.34435i | −0.0890543 | + | 0.154247i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.72266 | 0.440416 | 0.220208 | − | 0.975453i | \(-0.429326\pi\) | ||||
0.220208 | + | 0.975453i | \(0.429326\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.5712 | 0.754824 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.72517 | − | 2.98809i | 0.112062 | − | 0.194097i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.53746 | 0.0994503 | 0.0497251 | − | 0.998763i | \(-0.484165\pi\) | ||||
0.0497251 | + | 0.998763i | \(0.484165\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.82985 | + | 4.90145i | 0.182287 | + | 0.315730i | 0.942659 | − | 0.333758i | \(-0.108317\pi\) |
−0.760372 | + | 0.649488i | \(0.774983\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.73424 | − | 13.3961i | −0.496151 | − | 0.859360i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.499056 | + | 0.864391i | −0.0318835 | + | 0.0552239i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.304804 | − | 1.31358i | 0.0193942 | − | 0.0835810i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.39709 | − | 16.2762i | 0.595516 | − | 1.03146i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.21899 | − | 14.2357i | −0.518778 | − | 0.898550i | −0.999762 | − | 0.0218208i | \(-0.993054\pi\) |
0.480984 | − | 0.876730i | \(-0.340280\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.919404 | + | 1.59245i | 0.0578024 | + | 0.100117i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.54034 | −0.534817 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.42122 | − | 7.65777i | 0.275788 | − | 0.477679i | −0.694546 | − | 0.719449i | \(-0.744395\pi\) |
0.970334 | + | 0.241770i | \(0.0777279\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.85781 | −0.363987 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.0524 | 0.931719 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.796659 | + | 1.37985i | −0.0491241 | + | 0.0850854i | −0.889542 | − | 0.456854i | \(-0.848976\pi\) |
0.840418 | + | 0.541939i | \(0.182310\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.2027 | −0.995326 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.982484 | − | 1.70171i | −0.0601271 | − | 0.104143i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.4317 | + | 21.5324i | 0.757976 | + | 1.31285i | 0.943881 | + | 0.330286i | \(0.107145\pi\) |
−0.185905 | + | 0.982568i | \(0.559522\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.984233 | + | 1.70474i | −0.0597879 | + | 0.103556i | −0.894370 | − | 0.447328i | \(-0.852376\pi\) |
0.834582 | + | 0.550883i | \(0.185709\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.13081 | − | 6.66444i | −0.431576 | − | 0.403350i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.67901 | − | 2.90813i | 0.101248 | − | 0.175367i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.63162 | − | 13.2184i | −0.458540 | − | 0.794214i | 0.540344 | − | 0.841444i | \(-0.318294\pi\) |
−0.998884 | + | 0.0472299i | \(0.984961\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.87414 | − | 10.1743i | −0.351676 | − | 0.609120i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −31.1697 | −1.85943 | −0.929713 | − | 0.368284i | \(-0.879945\pi\) | ||||
−0.929713 | + | 0.368284i | \(0.879945\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.9768 | − | 25.9406i | 0.890277 | − | 1.54201i | 0.0507346 | − | 0.998712i | \(-0.483844\pi\) |
0.839543 | − | 0.543294i | \(-0.182823\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.520134 | 0.0308101 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.90266 | −0.584535 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.3553 | + | 17.9360i | −0.609138 | + | 1.05506i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.99489 | −0.468669 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.57623 | − | 11.3904i | −0.384187 | − | 0.665432i | 0.607469 | − | 0.794343i | \(-0.292185\pi\) |
−0.991656 | + | 0.128912i | \(0.958852\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.22659 | − | 9.05273i | −0.304304 | − | 0.527070i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.61675 | − | 4.53235i | 0.151839 | − | 0.262993i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.34237 | + | 1.93134i | −0.366789 | + | 0.111692i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.33935 | + | 9.24803i | −0.307755 | + | 0.533048i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.705218 | − | 1.22147i | −0.0405137 | − | 0.0701718i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.07916 | − | 7.06531i | −0.233572 | − | 0.404558i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.28323 | 0.301530 | 0.150765 | − | 0.988570i | \(-0.451826\pi\) | ||||
0.150765 | + | 0.988570i | \(0.451826\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.49656 | + | 14.7165i | −0.483353 | + | 0.837191i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.149737 | 0.00849080 | 0.00424540 | − | 0.999991i | \(-0.498649\pi\) | ||||
0.00424540 | + | 0.999991i | \(0.498649\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.9562 | −1.63670 | −0.818350 | − | 0.574720i | \(-0.805111\pi\) | ||||
−0.818350 | + | 0.574720i | \(0.805111\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.91175 | + | 5.04330i | −0.164059 | + | 0.284158i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.1837 | 0.965134 | 0.482567 | − | 0.875859i | \(-0.339705\pi\) | ||||
0.482567 | + | 0.875859i | \(0.339705\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.13056 | + | 7.15433i | 0.231267 | + | 0.400566i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.975205 | − | 1.68910i | −0.0544306 | − | 0.0942766i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.14835 | − | 1.98900i | 0.0638960 | − | 0.110671i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.84566 | + | 8.26714i | 0.490669 | + | 0.458578i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.48436 | + | 9.49918i | −0.303286 | + | 0.525306i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.2615 | + | 19.5055i | 0.620868 | + | 1.07538i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.06900 | − | 13.9759i | −0.443512 | − | 0.768186i | 0.554435 | − | 0.832227i | \(-0.312934\pi\) |
−0.997947 | + | 0.0640414i | \(0.979601\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.27927 | 0.234502 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.60514 | − | 13.1725i | 0.415513 | − | 0.719690i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.46802 | 0.188915 | 0.0944576 | − | 0.995529i | \(-0.469888\pi\) | ||||
0.0944576 | + | 0.995529i | \(0.469888\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.37231 | 0.291784 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.22387 | − | 5.58391i | 0.174582 | − | 0.302385i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.4023 | −1.04762 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.27864 | − | 2.21467i | −0.0688398 | − | 0.119234i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.90904 | − | 8.50271i | −0.263531 | − | 0.456450i | 0.703647 | − | 0.710550i | \(-0.251554\pi\) |
−0.967178 | + | 0.254101i | \(0.918221\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.30899 | − | 5.73134i | 0.177126 | − | 0.306791i | −0.763769 | − | 0.645490i | \(-0.776653\pi\) |
0.940895 | + | 0.338698i | \(0.109987\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.7861 | + | 12.8844i | 0.735846 | + | 0.687720i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.4955 | − | 19.9108i | 0.611844 | − | 1.05975i | −0.379085 | − | 0.925362i | \(-0.623761\pi\) |
0.990929 | − | 0.134384i | \(-0.0429055\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.19391 | + | 7.26407i | 0.222590 | + | 0.385537i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.31176 | − | 14.3964i | −0.439905 | − | 0.761938i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.32235 | 0.122569 | 0.0612845 | − | 0.998120i | \(-0.480480\pi\) | ||||
0.0612845 | + | 0.998120i | \(0.480480\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.43006 | − | 16.3333i | 0.496319 | − | 0.859650i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.08532 | 0.0569646 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.0908 | 0.999256 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.25524 | − | 3.90619i | 0.117723 | − | 0.203901i | −0.801142 | − | 0.598474i | \(-0.795774\pi\) |
0.918865 | + | 0.394573i | \(0.129107\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.23412 | 0.376593 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15.7691 | − | 27.3129i | −0.818690 | − | 1.41801i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.7495 | + | 20.3507i | 0.608366 | + | 1.05372i | 0.991510 | + | 0.130032i | \(0.0415079\pi\) |
−0.383144 | + | 0.923689i | \(0.625159\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.81187 | + | 10.0665i | −0.300124 | + | 0.519830i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −28.4940 | + | 8.67683i | −1.46752 | + | 0.446880i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.1362 | + | 19.2885i | −0.572028 | + | 0.990782i | 0.424330 | + | 0.905508i | \(0.360510\pi\) |
−0.996358 | + | 0.0852737i | \(0.972824\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.0412 | − | 17.3919i | −0.514428 | − | 0.891016i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.79725 | − | 3.11292i | −0.0918350 | − | 0.159063i | 0.816448 | − | 0.577419i | \(-0.195940\pi\) |
−0.908283 | + | 0.418356i | \(0.862607\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.19608 | −0.162887 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.90052 | − | 6.75590i | 0.198275 | − | 0.343422i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 36.5723 | 1.85429 | 0.927144 | − | 0.374706i | \(-0.122256\pi\) | ||||
0.927144 | + | 0.374706i | \(0.122256\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.2919 | −0.571058 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.96022 | + | 10.3234i | −0.300654 | + | 0.520747i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.07370 | 0.204970 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.21753 | − | 2.10883i | −0.0611063 | − | 0.105839i | 0.833854 | − | 0.551985i | \(-0.186130\pi\) |
−0.894960 | + | 0.446146i | \(0.852796\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.506213 | + | 0.876787i | 0.0253424 | + | 0.0438943i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.54048 | + | 7.86434i | −0.226741 | + | 0.392727i | −0.956840 | − | 0.290614i | \(-0.906140\pi\) |
0.730099 | + | 0.683341i | \(0.239474\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.9846 | + | 15.8738i | 0.846063 | + | 0.790729i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.136980 | + | 0.237256i | −0.00680657 | + | 0.0117893i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.17428 | + | 2.03392i | 0.0582070 | + | 0.100817i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.203111 | + | 0.351799i | 0.0100432 | + | 0.0173953i | 0.871003 | − | 0.491277i | \(-0.163470\pi\) |
−0.860960 | + | 0.508672i | \(0.830136\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.2594 | 0.506060 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.1734 | − | 17.6209i | 0.500601 | − | 0.867067i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.1896 | 1.08925 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.6158 | −0.862648 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.27288 | + | 7.40084i | −0.208744 | + | 0.361555i | −0.951319 | − | 0.308208i | \(-0.900271\pi\) |
0.742575 | + | 0.669763i | \(0.233604\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.68530 | −0.374559 | −0.187279 | − | 0.982307i | \(-0.559967\pi\) | ||||
−0.187279 | + | 0.982307i | \(0.559967\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.22681 | − | 14.2493i | −0.400001 | − | 0.692823i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.3106 | + | 17.8585i | 0.500138 | + | 0.866265i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.93997 | − | 13.7524i | 0.384242 | − | 0.665526i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.884517 | + | 3.81190i | −0.0427049 | + | 0.184040i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.6713 | − | 25.4114i | 0.706690 | − | 1.22402i | −0.259389 | − | 0.965773i | \(-0.583521\pi\) |
0.966078 | − | 0.258249i | \(-0.0831456\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.27709 | − | 7.40814i | −0.205544 | − | 0.356013i | 0.744762 | − | 0.667330i | \(-0.232563\pi\) |
−0.950306 | + | 0.311318i | \(0.899230\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.74449 | − | 9.94975i | −0.275427 | − | 0.477054i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.687716 | 0.0328979 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.89662 | − | 5.01709i | 0.138248 | − | 0.239453i | −0.788586 | − | 0.614925i | \(-0.789186\pi\) |
0.926834 | + | 0.375473i | \(0.122520\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.41926 | 0.0675838 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.3714 | −1.01539 | −0.507693 | − | 0.861538i | \(-0.669501\pi\) | ||||
−0.507693 | + | 0.861538i | \(0.669501\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.15998 | − | 2.00915i | 0.0549885 | − | 0.0952429i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.31585 | 0.251431 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.2570 | + | 17.7657i | 0.484058 | + | 0.838413i | 0.999832 | − | 0.0183112i | \(-0.00582896\pi\) |
−0.515774 | + | 0.856725i | \(0.672496\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.98513 | + | 3.43835i | 0.0934761 | + | 0.161905i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.07052 | − | 1.85420i | 0.0502976 | − | 0.0871180i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.60475 | − | 11.2254i | 0.122112 | − | 0.526254i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.3951 | + | 26.6651i | −0.720154 | + | 1.24734i | 0.240784 | + | 0.970579i | \(0.422595\pi\) |
−0.960938 | + | 0.276764i | \(0.910738\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 16.0692 | + | 27.8327i | 0.750047 | + | 1.29912i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.8077 | − | 20.4516i | −0.549942 | − | 0.952527i | −0.998278 | − | 0.0586619i | \(-0.981317\pi\) |
0.448336 | − | 0.893865i | \(-0.352017\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.25379 | −0.197691 | −0.0988453 | − | 0.995103i | \(-0.531515\pi\) | ||||
−0.0988453 | + | 0.995103i | \(0.531515\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.48353 | + | 7.76571i | −0.207919 | + | 0.360126i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 40.9716 | 1.89594 | 0.947970 | − | 0.318361i | \(-0.103132\pi\) | ||||
0.947970 | + | 0.318361i | \(0.103132\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29.6064 | 1.36709 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.34252 | − | 9.25351i | 0.246170 | − | 0.426379i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.28140 | 0.196859 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.627950 | − | 1.08764i | −0.0288123 | − | 0.0499044i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.5197 | + | 19.9527i | 0.527450 | + | 0.913571i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.47023 | + | 16.4029i | −0.432706 | + | 0.749469i | −0.997105 | − | 0.0760332i | \(-0.975775\pi\) |
0.564399 | + | 0.825502i | \(0.309108\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.10061 | + | 2.46675i | −0.369356 | + | 0.112474i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.48884 | − | 4.31080i | 0.113246 | − | 0.196148i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.71964 | − | 8.17466i | −0.214308 | − | 0.371192i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.10920 | + | 7.11734i | 0.186206 | + | 0.322517i | 0.943982 | − | 0.329997i | \(-0.107048\pi\) |
−0.757777 | + | 0.652514i | \(0.773714\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.1856 | −0.551052 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.75967 | + | 11.7081i | −0.305060 | + | 0.528379i | −0.977275 | − | 0.211977i | \(-0.932010\pi\) |
0.672215 | + | 0.740356i | \(0.265343\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −50.7307 | −2.28479 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.33481 | 0.104942 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.16333 | + | 14.1393i | −0.366175 | + | 0.634234i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.63251 | −0.296912 | −0.148456 | − | 0.988919i | \(-0.547430\pi\) | ||||
−0.148456 | + | 0.988919i | \(0.547430\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.19652 | + | 14.1968i | 0.366193 | + | 0.634266i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.634098 | − | 1.09829i | −0.0282730 | − | 0.0489703i | 0.851543 | − | 0.524285i | \(-0.175667\pi\) |
−0.879816 | + | 0.475315i | \(0.842334\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.832626 | − | 1.44215i | 0.0370514 | − | 0.0641749i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.6674 | − | 6.21327i | −0.562581 | − | 0.275941i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.0229687 | − | 0.0397830i | 0.00101807 | − | 0.00176335i | −0.865516 | − | 0.500881i | \(-0.833009\pi\) |
0.866534 | + | 0.499118i | \(0.166343\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.5798 | + | 32.1812i | 0.821922 | + | 1.42361i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.978667 | − | 1.69510i | −0.0432092 | − | 0.0748405i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −20.0632 | −0.884089 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.51507 | − | 7.82033i | 0.198573 | − | 0.343938i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.38105 | −0.323992 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.07130 | −0.265989 | −0.132994 | − | 0.991117i | \(-0.542459\pi\) | ||||
−0.132994 | + | 0.991117i | \(0.542459\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.51895 | − | 16.4873i | 0.416235 | − | 0.720940i | −0.579322 | − | 0.815099i | \(-0.696683\pi\) |
0.995557 | + | 0.0941587i | \(0.0300161\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.09020 | −0.396729 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.7975 | + | 34.2902i | 0.862391 | + | 1.49371i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.80939 | + | 16.9904i | 0.426495 | + | 0.738712i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.43192 | + | 12.8725i | −0.322518 | + | 0.558617i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.6941 | + | 4.17006i | −0.593159 | + | 0.180625i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.15139 | − | 1.99427i | 0.0497789 | − | 0.0862196i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.66463 | + | 13.2755i | 0.330753 | + | 0.572881i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.389462 | + | 0.674568i | 0.0167753 | + | 0.0290557i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.7778 | 1.36623 | 0.683116 | − | 0.730310i | \(-0.260624\pi\) | ||||
0.683116 | + | 0.730310i | \(0.260624\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.3005 | − | 21.3051i | 0.527866 | − | 0.914291i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.9504 | −0.554733 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.38974 | −0.102178 | −0.0510890 | − | 0.998694i | \(-0.516269\pi\) | ||||
−0.0510890 | + | 0.998694i | \(0.516269\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.80033 | + | 10.0465i | −0.247552 | + | 0.428773i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.08966 | 0.131624 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.96467 | + | 6.86702i | 0.168595 | + | 0.292015i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.63311 | − | 2.82863i | −0.0693216 | − | 0.120069i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.0775645 | + | 0.134346i | −0.00328651 | + | 0.00569241i | −0.867664 | − | 0.497151i | \(-0.834379\pi\) |
0.864377 | + | 0.502844i | \(0.167713\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.48926 | + | 15.0373i | −0.147580 | + | 0.636010i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.33243 | + | 5.77193i | −0.140695 | + | 0.243691i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.6644 | − | 37.5238i | −0.913044 | − | 1.58144i | −0.809740 | − | 0.586789i | \(-0.800392\pi\) |
−0.103304 | − | 0.994650i | \(-0.532941\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.17145 | + | 5.49311i | 0.133424 | + | 0.231097i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.533254 | −0.0223946 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.53399 | + | 13.0492i | −0.315841 | + | 0.547053i | −0.979616 | − | 0.200880i | \(-0.935620\pi\) |
0.663775 | + | 0.747933i | \(0.268953\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.5521 | 1.11117 | 0.555586 | − | 0.831459i | \(-0.312494\pi\) | ||||
0.555586 | + | 0.831459i | \(0.312494\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.62457 | 0.109643 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.08737 | + | 5.34748i | −0.128752 | + | 0.223005i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.43141 | −0.101221 | −0.0506105 | − | 0.998718i | \(-0.516117\pi\) | ||||
−0.0506105 | + | 0.998718i | \(0.516117\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.1859 | + | 21.1066i | 0.506429 | + | 0.877160i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 21.5957 | + | 37.4049i | 0.895941 | + | 1.55182i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.32228 | + | 10.9505i | −0.261842 | + | 0.453524i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.90283 | + | 8.20041i | −0.0786723 | + | 0.339045i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.50352 | + | 9.53237i | −0.227154 | + | 0.393443i | −0.956964 | − | 0.290208i | \(-0.906276\pi\) |
0.729809 | + | 0.683651i | \(0.239609\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.20573 | − | 2.08839i | −0.0496812 | − | 0.0860504i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.0926 | + | 22.6770i | 0.538557 | + | 0.932808i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 43.1297 | 1.77113 | 0.885563 | − | 0.464520i | \(-0.153773\pi\) | ||||
0.885563 | + | 0.464520i | \(0.153773\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.81340 | − | 16.9973i | 0.402310 | − | 0.696822i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 25.6632 | 1.05033 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.1586 | 0.619363 | 0.309682 | − | 0.950840i | \(-0.399778\pi\) | ||||
0.309682 | + | 0.950840i | \(0.399778\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.09213 | + | 7.08778i | −0.166922 | + | 0.289117i | −0.937336 | − | 0.348427i | \(-0.886716\pi\) |
0.770414 | + | 0.637543i | \(0.220049\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −21.6281 | −0.880766 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.640700 | + | 1.10972i | 0.0260482 | + | 0.0451167i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.1054 | + | 20.9671i | 0.491341 | + | 0.851028i | 0.999950 | − | 0.00996936i | \(-0.00317340\pi\) |
−0.508609 | + | 0.860998i | \(0.669840\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.1815 | − | 19.3669i | 0.453097 | − | 0.784786i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.7872 | + | 22.2314i | 0.962326 | + | 0.899388i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.03140 | + | 3.51848i | −0.0820474 | + | 0.142110i | −0.904129 | − | 0.427259i | \(-0.859479\pi\) |
0.822082 | + | 0.569369i | \(0.192813\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.76078 | − | 4.78181i | −0.111325 | − | 0.192821i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.8534 | + | 20.5307i | 0.477200 | + | 0.826534i | 0.999659 | − | 0.0261305i | \(-0.00831855\pi\) |
−0.522459 | + | 0.852664i | \(0.674985\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.94190 | −0.158438 | −0.0792192 | − | 0.996857i | \(-0.525243\pi\) | ||||
−0.0792192 | + | 0.996857i | \(0.525243\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.81170 | + | 8.33411i | −0.193087 | + | 0.334436i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.51575 | 0.180920 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.06633 | 0.122653 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.202955 | − | 0.351529i | 0.00810526 | − | 0.0140387i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.4223 | −0.575055 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.2159 | − | 38.4790i | −0.884400 | − | 1.53183i | −0.846400 | − | 0.532547i | \(-0.821235\pi\) |
−0.0379993 | − | 0.999278i | \(-0.512098\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.79921 | − | 4.84838i | −0.111259 | − | 0.192706i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.8553 | − | 20.5340i | 0.470465 | − | 0.814869i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.68664 | + | 0.818121i | −0.106449 | + | 0.0324151i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.96350 | − | 10.3291i | 0.235913 | − | 0.408612i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.28566 | − | 10.8871i | −0.248269 | − | 0.430014i | 0.714777 | − | 0.699353i | \(-0.246528\pi\) |
−0.963046 | + | 0.269338i | \(0.913195\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.03031 | + | 15.6410i | 0.356121 | + | 0.616819i | 0.987309 | − | 0.158810i | \(-0.0507658\pi\) |
−0.631188 | + | 0.775630i | \(0.717432\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.95427 | −0.234449 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.4321 | − | 21.5330i | 0.488755 | − | 0.846549i | −0.511161 | − | 0.859485i | \(-0.670784\pi\) |
0.999916 | + | 0.0129361i | \(0.00411780\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.15763 | −0.320215 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.4541 | −0.684082 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.3196 | + | 26.5343i | −0.599502 | + | 1.03837i | 0.393392 | + | 0.919371i | \(0.371301\pi\) |
−0.992895 | + | 0.118998i | \(0.962032\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.0740 | −0.549919 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13.5730 | − | 23.5091i | −0.529532 | − | 0.917177i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.14839 | − | 14.1134i | −0.317416 | − | 0.549781i | 0.662532 | − | 0.749034i | \(-0.269482\pi\) |
−0.979948 | + | 0.199253i | \(0.936149\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.22990 | − | 7.32640i | 0.164524 | − | 0.284964i | −0.771962 | − | 0.635669i | \(-0.780725\pi\) |
0.936486 | + | 0.350705i | \(0.114058\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.5565 | − | 16.4083i | −0.681839 | − | 0.637245i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.597668 | + | 1.03519i | −0.0231766 | + | 0.0401430i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.59530 | − | 13.1554i | −0.294091 | − | 0.509381i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.22686 | + | 14.2493i | 0.318069 | + | 0.550912i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.36672 | −0.245785 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.1282 | + | 33.1310i | −0.737337 | + | 1.27711i | 0.216353 | + | 0.976315i | \(0.430584\pi\) |
−0.953690 | + | 0.300790i | \(0.902750\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17.5742 | 0.676430 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.74820 | 0.0671886 | 0.0335943 | − | 0.999436i | \(-0.489305\pi\) | ||||
0.0335943 | + | 0.999436i | \(0.489305\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.18665 | − | 15.9117i | 0.352551 | − | 0.610637i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.5295 | −0.595092 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.62994 | + | 9.75134i | 0.215424 | + | 0.373125i | 0.953404 | − | 0.301698i | \(-0.0975534\pi\) |
−0.737980 | + | 0.674823i | \(0.764220\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.05646 | + | 10.4901i | 0.231406 | + | 0.400806i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.9967 | − | 19.0468i | 0.419550 | − | 0.726683i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −33.3082 | − | 31.1298i | −1.26894 | − | 1.18595i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.5134 | − | 26.8699i | 0.590156 | − | 1.02218i | −0.404055 | − | 0.914735i | \(-0.632400\pi\) |
0.994211 | − | 0.107445i | \(-0.0342671\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.27232 | + | 3.93578i | 0.0863184 | + | 0.149508i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.3992 | − | 18.0119i | −0.394463 | − | 0.683229i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.3810 | −0.923495 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.64812 | + | 6.31873i | −0.137985 | + | 0.238996i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.2113 | 0.498984 | 0.249492 | − | 0.968377i | \(-0.419736\pi\) | ||||
0.249492 | + | 0.968377i | \(0.419736\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.878365 | 0.0331282 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.27925 | + | 10.8760i | −0.236490 | + | 0.409613i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.24137 | 0.121904 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.8890 | − | 22.3245i | −0.484058 | − | 0.838413i | 0.515774 | − | 0.856725i | \(-0.327504\pi\) |
−0.999832 | + | 0.0183111i | \(0.994171\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.89629 | − | 5.01652i | −0.108619 | − | 0.188134i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.92808 | + | 10.2677i | −0.222008 | + | 0.384529i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.41978 | + | 1.34588i | −0.165290 | + | 0.0503332i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.834321 | + | 1.44509i | −0.0311583 | + | 0.0539677i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.7004 | + | 34.1220i | 0.734700 | + | 1.27254i | 0.954855 | + | 0.297072i | \(0.0960102\pi\) |
−0.220156 | + | 0.975465i | \(0.570656\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.5262 | − | 33.8204i | −0.727194 | − | 1.25954i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.14260 | −0.228446 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.8705 | + | 24.0243i | −0.515136 | + | 0.892242i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.86872 | 0.254747 | 0.127373 | − | 0.991855i | \(-0.459345\pi\) | ||||
0.127373 | + | 0.991855i | \(0.459345\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.4296 | 0.645543 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.1458 | + | 22.7692i | −0.486216 | + | 0.842151i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.7310 | −0.396359 | −0.198180 | − | 0.980166i | \(-0.563503\pi\) | ||||
−0.198180 | + | 0.980166i | \(0.563503\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.541636 | − | 0.938142i | −0.0199786 | − | 0.0346039i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.93502 | − | 10.2798i | −0.218619 | − | 0.378660i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.506275 | − | 0.876894i | 0.0186236 | − | 0.0322571i | −0.856563 | − | 0.516042i | \(-0.827405\pi\) |
0.875187 | + | 0.483785i | \(0.160738\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.06925 | + | 0.999318i | 0.0392798 | + | 0.0367108i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.31579 | − | 4.01106i | 0.0849580 | − | 0.147152i | −0.820415 | − | 0.571768i | \(-0.806258\pi\) |
0.905373 | + | 0.424616i | \(0.139591\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.13812 | + | 5.43538i | 0.114972 | + | 0.199137i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.7762 | − | 27.3251i | −0.577220 | − | 0.999775i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.48229 | 0.163779 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.3718 | − | 37.0171i | 0.779869 | − | 1.35077i | −0.152147 | − | 0.988358i | \(-0.548619\pi\) |
0.932017 | − | 0.362415i | \(-0.118048\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.8405 | 0.650144 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.52786 | 0.0919982 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.8352 | − | 37.8198i | 0.793616 | − | 1.37458i | −0.130099 | − | 0.991501i | \(-0.541530\pi\) |
0.923715 | − | 0.383081i | \(-0.125137\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.99570 | −0.0724392 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.3833 | − | 24.9126i | −0.521395 | − | 0.903082i | −0.999690 | − | 0.0248833i | \(-0.992079\pi\) |
0.478296 | − | 0.878199i | \(-0.341255\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.6038 | − | 21.8304i | −0.456287 | − | 0.790312i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.16892 | + | 12.4169i | −0.259193 | + | 0.448935i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.64832 | − | 28.6515i | 0.240057 | − | 1.03455i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.1419 | − | 27.9585i | 0.582091 | − | 1.00821i | −0.413141 | − | 0.910667i | \(-0.635568\pi\) |
0.995231 | − | 0.0975432i | \(-0.0310984\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.79844 | + | 8.31114i | 0.172812 | + | 0.299318i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.3216 | − | 19.6096i | −0.407210 | − | 0.705308i | 0.587366 | − | 0.809321i | \(-0.300165\pi\) |
−0.994576 | + | 0.104013i | \(0.966831\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.6516 | 0.777748 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.17880 | − | 5.50585i | 0.114039 | − | 0.197521i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.48488 | 0.0532014 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.54582 | 0.234228 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21.6173 | + | 37.4422i | −0.772538 | + | 1.33808i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.6154 | 0.450264 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.0984 | + | 40.0075i | 0.823368 | + | 1.42611i | 0.903161 | + | 0.429303i | \(0.141241\pi\) |
−0.0797930 | + | 0.996811i | \(0.525426\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.864630 | − | 1.49758i | −0.0307817 | − | 0.0533154i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.17313 | + | 10.6922i | −0.219491 | + | 0.380170i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.18876 | − | 22.3614i | 0.184258 | − | 0.794078i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.79259 | − | 15.2292i | 0.311841 | − | 0.540124i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.95967 | − | 15.5186i | −0.317368 | − | 0.549697i | 0.662570 | − | 0.749000i | \(-0.269466\pi\) |
−0.979938 | + | 0.199303i | \(0.936132\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.7266 | + | 48.0239i | 0.980897 | + | 1.69896i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.29886 | −0.116560 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.44918 | − | 12.9024i | 0.262876 | − | 0.455314i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.87697 | 0.207136 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.9848 | −0.949912 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.2511 | − | 29.8797i | 0.606515 | − | 1.05052i | −0.385295 | − | 0.922794i | \(-0.625900\pi\) |
0.991810 | − | 0.127722i | \(-0.0407665\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.99615 | −0.280783 | −0.140391 | − | 0.990096i | \(-0.544836\pi\) | ||||
−0.140391 | + | 0.990096i | \(0.544836\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.06821 | − | 1.85019i | −0.0374637 | − | 0.0648891i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.19356 | − | 12.4596i | −0.251979 | − | 0.436441i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.800623 | − | 1.38672i | 0.0280103 | − | 0.0485152i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −15.6753 | + | 4.77334i | −0.547739 | + | 0.166794i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.9602 | + | 20.7156i | −0.417413 | + | 0.722980i | −0.995678 | − | 0.0928684i | \(-0.970396\pi\) |
0.578266 | + | 0.815849i | \(0.303730\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.28214 | + | 9.14894i | 0.184124 | + | 0.318912i | 0.943281 | − | 0.331996i | \(-0.107722\pi\) |
−0.759157 | + | 0.650907i | \(0.774389\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.82226 | + | 3.15625i | 0.0634430 | + | 0.109887i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.4854 | −0.468934 | −0.234467 | − | 0.972124i | \(-0.575334\pi\) | ||||
−0.234467 | + | 0.972124i | \(0.575334\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.6692 | + | 47.9244i | −0.960990 | + | 1.66448i | −0.240966 | + | 0.970534i | \(0.577464\pi\) |
−0.720024 | + | 0.693949i | \(0.755869\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.5655 | 0.574652 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.78329 | −0.165731 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.67734 | + | 16.7616i | −0.334898 | + | 0.580061i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 33.7443 | 1.16637 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.6189 | − | 35.7129i | −0.711843 | − | 1.23295i | −0.964165 | − | 0.265304i | \(-0.914528\pi\) |
0.252322 | − | 0.967643i | \(-0.418806\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.6230 | − | 33.9880i | −0.676654 | − | 1.17200i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.9145 | − | 29.2969i | 0.582568 | − | 1.00904i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.12503 | − | 16.6202i | −0.0387020 | − | 0.571751i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.24710 | + | 2.16005i | −0.0428510 | + | 0.0742201i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.2546 | + | 28.1538i | 0.557857 | + | 0.966237i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.15928 | − | 3.73998i | −0.0740191 | − | 0.128205i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.00722 | −0.171444 | −0.0857220 | − | 0.996319i | \(-0.527320\pi\) | ||||
−0.0857220 | + | 0.996319i | \(0.527320\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.436611 | − | 0.756232i | 0.0149318 | − | 0.0258626i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −42.2505 | −1.44325 | −0.721626 | − | 0.692284i | \(-0.756605\pi\) | ||||
−0.721626 | + | 0.692284i | \(0.756605\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.2658 | −0.691461 | −0.345731 | − | 0.938334i | \(-0.612369\pi\) | ||||
−0.345731 | + | 0.938334i | \(0.612369\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.37378 | − | 9.30766i | 0.183138 | − | 0.317204i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.74439 | 0.331703 | 0.165851 | − | 0.986151i | \(-0.446963\pi\) | ||||
0.165851 | + | 0.986151i | \(0.446963\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.35727 | − | 7.54702i | −0.148152 | − | 0.256606i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.2389 | − | 19.4663i | −0.381692 | − | 0.661110i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.58955 | − | 2.75318i | 0.0539219 | − | 0.0933954i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40.9419 | − | 12.4674i | 1.38726 | − | 0.422441i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.71106 | + | 11.6239i | −0.227135 | + | 0.393409i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.3564 | − | 23.1340i | −0.451530 | − | 0.782073i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.22766 | − | 5.59047i | −0.108990 | − | 0.188777i | 0.806371 | − | 0.591410i | \(-0.201428\pi\) |
−0.915362 | + | 0.402633i | \(0.868095\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.2746 | 0.481471 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.1154 | + | 19.2524i | −0.374487 | + | 0.648631i | −0.990250 | − | 0.139301i | \(-0.955515\pi\) |
0.615763 | + | 0.787931i | \(0.288848\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43.5781 | −1.46652 | −0.733260 | − | 0.679949i | \(-0.762002\pi\) | ||||
−0.733260 | + | 0.679949i | \(0.762002\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.3451 | 0.381360 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.53851 | + | 14.7891i | −0.286695 | + | 0.496570i | −0.973019 | − | 0.230726i | \(-0.925890\pi\) |
0.686324 | + | 0.727296i | \(0.259223\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 46.1521 | 1.54789 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.106898 | + | 0.185154i | 0.00358123 | + | 0.00620288i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.68864 | − | 2.92481i | −0.0565082 | − | 0.0978751i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.04936 | + | 15.6739i | −0.302487 | + | 0.523922i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.62646 | − | 7.00936i | 0.0543058 | − | 0.234036i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −26.6327 | + | 46.1293i | −0.888252 | + | 1.53850i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −38.8245 | − | 67.2460i | −1.29343 | − | 2.24029i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.79491 | − | 10.0371i | −0.192843 | − | 0.334013i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 29.0456 | 0.965509 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.83633 | − | 15.3050i | 0.293405 | − | 0.508193i | −0.681207 | − | 0.732091i | \(-0.738545\pi\) |
0.974613 | + | 0.223897i | \(0.0718781\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.36789 | −0.0785381 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.7970 | −0.821560 | −0.410780 | − | 0.911734i | \(-0.634744\pi\) | ||||
−0.410780 | + | 0.911734i | \(0.634744\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.65835 | − | 14.9967i | 0.286549 | − | 0.496318i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.85439 | 0.292717 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.6974 | − | 23.7245i | −0.452327 | − | 0.783453i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.58343 | + | 4.47464i | 0.0852196 | + | 0.147605i | 0.905485 | − | 0.424379i | \(-0.139507\pi\) |
−0.820265 | + | 0.571983i | \(0.806174\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.86700 | + | 4.96579i | −0.0944709 | + | 0.163628i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.33473 | + | 22.9905i | −0.175595 | + | 0.756741i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.94326 | + | 6.82992i | −0.129653 | + | 0.224566i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.2644 | + | 24.7066i | 0.468503 | + | 0.811471i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.98518 | + | 6.90254i | 0.130750 | + | 0.226465i | 0.923966 | − | 0.382475i | \(-0.124928\pi\) |
−0.793216 | + | 0.608940i | \(0.791595\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.291318 | 0.00954756 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.0812563 | + | 0.140740i | −0.00266021 | + | 0.00460762i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.86895 | −0.257342 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.34395 | −0.0439049 | −0.0219525 | − | 0.999759i | \(-0.506988\pi\) | ||||
−0.0219525 | + | 0.999759i | \(0.506988\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.7134 | − | 27.2164i | 0.512787 | − | 0.888172i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.2405 | 0.496827 | 0.248414 | − | 0.968654i | \(-0.420091\pi\) | ||||
0.248414 | + | 0.968654i | \(0.420091\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.65027 | − | 6.32246i | −0.118869 | − | 0.205888i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.36334 | − | 14.4857i | −0.272060 | − | 0.471221i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.62129 | + | 16.6646i | −0.312650 | + | 0.541526i | −0.978935 | − | 0.204171i | \(-0.934550\pi\) |
0.666285 | + | 0.745697i | \(0.267883\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 39.2452 | + | 36.6785i | 1.27395 | + | 1.19063i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.32493 | + | 16.1512i | −0.302381 | + | 0.523740i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.6391 | − | 18.4275i | −0.344634 | − | 0.596924i | 0.640653 | − | 0.767830i | \(-0.278664\pi\) |
−0.985287 | + | 0.170907i | \(0.945330\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.54937 | + | 2.68359i | 0.0501364 | + | 0.0868388i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.96596 | −0.289828 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.7887 | + | 20.4187i | −0.380678 | + | 0.659354i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.5733 | 0.341075 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.27442 | −0.105517 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14.3875 | + | 24.9198i | −0.463148 | + | 0.802197i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.6914 | −0.633232 | −0.316616 | − | 0.948554i | \(-0.602547\pi\) | ||||
−0.316616 | + | 0.948554i | \(0.602547\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.24633 | + | 2.15871i | 0.0400379 | + | 0.0693476i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.39292 | + | 4.14465i | 0.0767923 | + | 0.133008i | 0.901864 | − | 0.432019i | \(-0.142199\pi\) |
−0.825072 | + | 0.565028i | \(0.808865\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.2417 | − | 35.0596i | 0.648918 | − | 1.12396i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.5706 | + | 3.82793i | −0.402582 | + | 0.122592i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.0951 | + | 29.6096i | −0.546920 | + | 0.947294i | 0.451563 | + | 0.892239i | \(0.350867\pi\) |
−0.998483 | + | 0.0550545i | \(0.982467\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.905248 | − | 1.56793i | −0.0289318 | − | 0.0501114i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.20734 | + | 15.9476i | 0.293968 | + | 0.509167i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.2798 | −1.25283 | −0.626416 | − | 0.779489i | \(-0.715479\pi\) | ||||
−0.626416 | + | 0.779489i | \(0.715479\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.4579 | + | 26.7740i | −0.492531 | + | 0.853089i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −24.4448 | −0.778085 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.87267 | −0.250336 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.3037 | − | 49.0235i | 0.899098 | − | 1.55728i | 0.0704485 | − | 0.997515i | \(-0.477557\pi\) |
0.828649 | − | 0.559768i | \(-0.189110\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.5149 | 0.555819 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.1498 | + | 26.2403i | 0.480282 | + | 0.831873i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.1683 | − | 45.3248i | −0.828758 | − | 1.43545i | −0.899013 | − | 0.437922i | \(-0.855715\pi\) |
0.0702553 | − | 0.997529i | \(-0.477619\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.14561 | + | 10.6445i | −0.194438 | + | 0.336777i |
(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 | 572.2.i.c.529.2 | yes | 10 | |
13.3 | even | 3 | inner | 572.2.i.c.133.2 | ✓ | 10 | |
13.4 | even | 6 | 7436.2.a.q.1.4 | 5 | |||
13.9 | even | 3 | 7436.2.a.r.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
572.2.i.c.133.2 | ✓ | 10 | 13.3 | even | 3 | inner | |
572.2.i.c.529.2 | yes | 10 | 1.1 | even | 1 | trivial | |
7436.2.a.q.1.4 | 5 | 13.4 | even | 6 | |||
7436.2.a.r.1.4 | 5 | 13.9 | even | 3 |