Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [387,2,Mod(130,387)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(387, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("387.130");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 387 = 3^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 387.f (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: | \(3.09021055822\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Relative dimension: | \(19\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 259.14 | ||
Character | \(\chi\) | \(=\) | 387.259 |
Dual form | 387.2.f.c.130.14 |
$q$-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 \(\left(\mathbb{Z}/387\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(173\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.649321 | − | 1.12466i | 0.459139 | − | 0.795253i | −0.539776 | − | 0.841808i | \(-0.681491\pi\) |
0.998916 | + | 0.0465558i | \(0.0148245\pi\) | |||||||
\(3\) | −1.24030 | − | 1.20899i | −0.716086 | − | 0.698012i | ||||
\(4\) | 0.156764 | + | 0.271524i | 0.0783822 | + | 0.135762i | ||||
\(5\) | 1.38166 | + | 2.39311i | 0.617897 | + | 1.07023i | 0.989869 | + | 0.141985i | \(0.0453486\pi\) |
−0.371972 | + | 0.928244i | \(0.621318\pi\) | |||||||
\(6\) | −2.16505 | + | 0.609884i | −0.883879 | + | 0.248984i | ||||
\(7\) | −0.516159 | + | 0.894013i | −0.195090 | + | 0.337905i | −0.946930 | − | 0.321440i | \(-0.895833\pi\) |
0.751840 | + | 0.659345i | \(0.229166\pi\) | |||||||
\(8\) | 3.00445 | 1.06223 | ||||||||
\(9\) | 0.0766735 | + | 2.99902i | 0.0255578 | + | 0.999673i | ||||
\(10\) | 3.58856 | 1.13480 | ||||||||
\(11\) | −1.47222 | + | 2.54996i | −0.443890 | + | 0.768841i | −0.997974 | − | 0.0636203i | \(-0.979735\pi\) |
0.554084 | + | 0.832461i | \(0.313069\pi\) | |||||||
\(12\) | 0.133836 | − | 0.526297i | 0.0386351 | − | 0.151929i | ||||
\(13\) | 1.68562 | + | 2.91958i | 0.467507 | + | 0.809747i | 0.999311 | − | 0.0371213i | \(-0.0118188\pi\) |
−0.531803 | + | 0.846868i | \(0.678485\pi\) | |||||||
\(14\) | 0.670305 | + | 1.16100i | 0.179147 | + | 0.310291i | ||||
\(15\) | 1.17958 | − | 4.63858i | 0.304566 | − | 1.19768i | ||||
\(16\) | 1.63732 | − | 2.83592i | 0.409330 | − | 0.708981i | ||||
\(17\) | 1.55106 | 0.376188 | 0.188094 | − | 0.982151i | \(-0.439769\pi\) | ||||
0.188094 | + | 0.982151i | \(0.439769\pi\) | |||||||
\(18\) | 3.42265 | + | 1.86110i | 0.806727 | + | 0.438664i | ||||
\(19\) | 0.820840 | 0.188314 | 0.0941568 | − | 0.995557i | \(-0.469984\pi\) | ||||
0.0941568 | + | 0.995557i | \(0.469984\pi\) | |||||||
\(20\) | −0.433190 | + | 0.750307i | −0.0968643 | + | 0.167774i | ||||
\(21\) | 1.72105 | − | 0.484810i | 0.375563 | − | 0.105794i | ||||
\(22\) | 1.91188 | + | 3.31148i | 0.407615 | + | 0.706010i | ||||
\(23\) | −4.29584 | − | 7.44062i | −0.895745 | − | 1.55148i | −0.832880 | − | 0.553454i | \(-0.813309\pi\) |
−0.0628656 | − | 0.998022i | \(-0.520024\pi\) | |||||||
\(24\) | −3.72641 | − | 3.63235i | −0.760649 | − | 0.741451i | ||||
\(25\) | −1.31797 | + | 2.28279i | −0.263594 | + | 0.456558i | ||||
\(26\) | 4.37804 | 0.858604 | ||||||||
\(27\) | 3.53070 | − | 3.81237i | 0.679483 | − | 0.733692i | ||||
\(28\) | −0.323661 | −0.0611662 | ||||||||
\(29\) | 0.623396 | − | 1.07975i | 0.115762 | − | 0.200505i | −0.802322 | − | 0.596891i | \(-0.796402\pi\) |
0.918084 | + | 0.396386i | \(0.129736\pi\) | |||||||
\(30\) | −4.45089 | − | 4.33855i | −0.812617 | − | 0.792107i | ||||
\(31\) | 0.962734 | + | 1.66750i | 0.172912 | + | 0.299493i | 0.939437 | − | 0.342722i | \(-0.111349\pi\) |
−0.766525 | + | 0.642215i | \(0.778016\pi\) | |||||||
\(32\) | 0.878152 | + | 1.52100i | 0.155237 | + | 0.268878i | ||||
\(33\) | 4.90886 | − | 1.38280i | 0.854524 | − | 0.240715i | ||||
\(34\) | 1.00714 | − | 1.74442i | 0.172723 | − | 0.299165i | ||||
\(35\) | −2.85262 | −0.482181 | ||||||||
\(36\) | −0.802286 | + | 0.490958i | −0.133714 | + | 0.0818264i | ||||
\(37\) | −4.44739 | −0.731147 | −0.365574 | − | 0.930782i | \(-0.619127\pi\) | ||||
−0.365574 | + | 0.930782i | \(0.619127\pi\) | |||||||
\(38\) | 0.532989 | − | 0.923164i | 0.0864622 | − | 0.149757i | ||||
\(39\) | 1.43908 | − | 5.65905i | 0.230438 | − | 0.906174i | ||||
\(40\) | 4.15112 | + | 7.18996i | 0.656350 | + | 1.13683i | ||||
\(41\) | −3.13620 | − | 5.43205i | −0.489792 | − | 0.848344i | 0.510139 | − | 0.860092i | \(-0.329594\pi\) |
−0.999931 | + | 0.0117476i | \(0.996261\pi\) | |||||||
\(42\) | 0.572266 | − | 2.25038i | 0.0883026 | − | 0.347242i | ||||
\(43\) | −0.500000 | + | 0.866025i | −0.0762493 | + | 0.132068i | ||||
\(44\) | −0.923165 | −0.139172 | ||||||||
\(45\) | −7.07104 | + | 4.32711i | −1.05409 | + | 0.645048i | ||||
\(46\) | −11.1575 | −1.64509 | ||||||||
\(47\) | 5.05055 | − | 8.74780i | 0.736698 | − | 1.27600i | −0.217276 | − | 0.976110i | \(-0.569717\pi\) |
0.953974 | − | 0.299888i | \(-0.0969494\pi\) | |||||||
\(48\) | −5.45938 | + | 1.53788i | −0.787993 | + | 0.221974i | ||||
\(49\) | 2.96716 | + | 5.13927i | 0.423880 | + | 0.734182i | ||||
\(50\) | 1.71157 | + | 2.96453i | 0.242053 | + | 0.419248i | ||||
\(51\) | −1.92378 | − | 1.87523i | −0.269383 | − | 0.262584i | ||||
\(52\) | −0.528491 | + | 0.915373i | −0.0732885 | + | 0.126939i | ||||
\(53\) | 8.79973 | 1.20874 | 0.604368 | − | 0.796705i | \(-0.293426\pi\) | ||||
0.604368 | + | 0.796705i | \(0.293426\pi\) | |||||||
\(54\) | −1.99506 | − | 6.44628i | −0.271493 | − | 0.877227i | ||||
\(55\) | −8.13642 | −1.09711 | ||||||||
\(56\) | −1.55077 | + | 2.68601i | −0.207230 | + | 0.358934i | ||||
\(57\) | −1.01809 | − | 0.992390i | −0.134849 | − | 0.131445i | ||||
\(58\) | −0.809568 | − | 1.40221i | −0.106301 | − | 0.184120i | ||||
\(59\) | −3.31596 | − | 5.74341i | −0.431701 | − | 0.747728i | 0.565319 | − | 0.824872i | \(-0.308753\pi\) |
−0.997020 | + | 0.0771446i | \(0.975420\pi\) | |||||||
\(60\) | 1.44440 | − | 0.406880i | 0.186471 | − | 0.0525280i | ||||
\(61\) | 0.0348705 | − | 0.0603975i | 0.00446471 | − | 0.00773310i | −0.863784 | − | 0.503862i | \(-0.831912\pi\) |
0.868249 | + | 0.496128i | \(0.165246\pi\) | |||||||
\(62\) | 2.50049 | 0.317563 | ||||||||
\(63\) | −2.72074 | − | 1.47942i | −0.342781 | − | 0.186390i | ||||
\(64\) | 8.83009 | 1.10376 | ||||||||
\(65\) | −4.65791 | + | 8.06774i | −0.577743 | + | 1.00068i | ||||
\(66\) | 1.63225 | − | 6.41867i | 0.200916 | − | 0.790084i | ||||
\(67\) | 5.76481 | + | 9.98494i | 0.704283 | + | 1.21985i | 0.966950 | + | 0.254967i | \(0.0820647\pi\) |
−0.262667 | + | 0.964887i | \(0.584602\pi\) | |||||||
\(68\) | 0.243152 | + | 0.421151i | 0.0294865 | + | 0.0510720i | ||||
\(69\) | −3.66753 | + | 14.4222i | −0.441519 | + | 1.73623i | ||||
\(70\) | −1.85227 | + | 3.20822i | −0.221388 | + | 0.383456i | ||||
\(71\) | −5.88849 | −0.698835 | −0.349418 | − | 0.936967i | \(-0.613621\pi\) | ||||
−0.349418 | + | 0.936967i | \(0.613621\pi\) | |||||||
\(72\) | 0.230361 | + | 9.01039i | 0.0271483 | + | 1.06189i | ||||
\(73\) | 1.89767 | 0.222105 | 0.111053 | − | 0.993815i | \(-0.464578\pi\) | ||||
0.111053 | + | 0.993815i | \(0.464578\pi\) | |||||||
\(74\) | −2.88779 | + | 5.00179i | −0.335698 | + | 0.581447i | ||||
\(75\) | 4.39455 | − | 1.23792i | 0.507439 | − | 0.142943i | ||||
\(76\) | 0.128678 | + | 0.222878i | 0.0147604 | + | 0.0255658i | ||||
\(77\) | −1.51980 | − | 2.63236i | −0.173197 | − | 0.299986i | ||||
\(78\) | −5.43007 | − | 5.29302i | −0.614834 | − | 0.599316i | ||||
\(79\) | −3.49563 | + | 6.05462i | −0.393290 | + | 0.681198i | −0.992881 | − | 0.119109i | \(-0.961996\pi\) |
0.599592 | + | 0.800306i | \(0.295330\pi\) | |||||||
\(80\) | 9.04889 | 1.01170 | ||||||||
\(81\) | −8.98824 | + | 0.459891i | −0.998694 | + | 0.0510990i | ||||
\(82\) | −8.14560 | −0.899531 | ||||||||
\(83\) | −1.50913 | + | 2.61390i | −0.165649 | + | 0.286912i | −0.936886 | − | 0.349636i | \(-0.886305\pi\) |
0.771237 | + | 0.636549i | \(0.219639\pi\) | |||||||
\(84\) | 0.401436 | + | 0.391304i | 0.0438002 | + | 0.0426948i | ||||
\(85\) | 2.14304 | + | 3.71186i | 0.232446 | + | 0.402608i | ||||
\(86\) | 0.649321 | + | 1.12466i | 0.0700181 | + | 0.121275i | ||||
\(87\) | −2.07861 | + | 0.585534i | −0.222850 | + | 0.0627758i | ||||
\(88\) | −4.42320 | + | 7.66120i | −0.471514 | + | 0.816687i | ||||
\(89\) | −15.2655 | −1.61814 | −0.809071 | − | 0.587711i | \(-0.800029\pi\) | ||||
−0.809071 | + | 0.587711i | \(0.800029\pi\) | |||||||
\(90\) | 0.275148 | + | 10.7622i | 0.0290031 | + | 1.13443i | ||||
\(91\) | −3.48019 | −0.364823 | ||||||||
\(92\) | 1.34687 | − | 2.33285i | 0.140421 | − | 0.243216i | ||||
\(93\) | 0.821924 | − | 3.23214i | 0.0852296 | − | 0.335157i | ||||
\(94\) | −6.55885 | − | 11.3603i | −0.676494 | − | 1.17172i | ||||
\(95\) | 1.13412 | + | 1.96436i | 0.116359 | + | 0.201539i | ||||
\(96\) | 0.749713 | − | 2.94817i | 0.0765172 | − | 0.300897i | ||||
\(97\) | 1.93718 | − | 3.35530i | 0.196691 | − | 0.340679i | −0.750763 | − | 0.660572i | \(-0.770314\pi\) |
0.947454 | + | 0.319893i | \(0.103647\pi\) | |||||||
\(98\) | 7.70656 | 0.778480 | ||||||||
\(99\) | −7.76025 | − | 4.21970i | −0.779934 | − | 0.424095i | ||||
\(100\) | −0.826443 | −0.0826443 | ||||||||
\(101\) | 5.11490 | − | 8.85927i | 0.508952 | − | 0.881530i | −0.490994 | − | 0.871163i | \(-0.663366\pi\) |
0.999946 | − | 0.0103677i | \(-0.00330019\pi\) | |||||||
\(102\) | −3.35814 | + | 0.945970i | −0.332505 | + | 0.0936650i | ||||
\(103\) | −6.33977 | − | 10.9808i | −0.624676 | − | 1.08197i | −0.988603 | − | 0.150543i | \(-0.951898\pi\) |
0.363927 | − | 0.931427i | \(-0.381436\pi\) | |||||||
\(104\) | 5.06436 | + | 8.77173i | 0.496601 | + | 0.860139i | ||||
\(105\) | 3.53810 | + | 3.44880i | 0.345283 | + | 0.336568i | ||||
\(106\) | 5.71385 | − | 9.89668i | 0.554978 | − | 0.961251i | ||||
\(107\) | 10.2054 | 0.986597 | 0.493298 | − | 0.869860i | \(-0.335791\pi\) | ||||
0.493298 | + | 0.869860i | \(0.335791\pi\) | |||||||
\(108\) | 1.58864 | + | 0.361024i | 0.152867 | + | 0.0347395i | ||||
\(109\) | −4.68029 | −0.448290 | −0.224145 | − | 0.974556i | \(-0.571959\pi\) | ||||
−0.224145 | + | 0.974556i | \(0.571959\pi\) | |||||||
\(110\) | −5.28315 | + | 9.15068i | −0.503728 | + | 0.872483i | ||||
\(111\) | 5.51609 | + | 5.37687i | 0.523564 | + | 0.510350i | ||||
\(112\) | 1.69023 | + | 2.92757i | 0.159712 | + | 0.276630i | ||||
\(113\) | 3.43891 | + | 5.95637i | 0.323505 | + | 0.560328i | 0.981209 | − | 0.192949i | \(-0.0618053\pi\) |
−0.657703 | + | 0.753277i | \(0.728472\pi\) | |||||||
\(114\) | −1.77716 | + | 0.500618i | −0.166447 | + | 0.0468871i | ||||
\(115\) | 11.8708 | − | 20.5608i | 1.10696 | − | 1.91731i | ||||
\(116\) | 0.390905 | 0.0362946 | ||||||||
\(117\) | −8.62664 | + | 5.27907i | −0.797534 | + | 0.488050i | ||||
\(118\) | −8.61248 | −0.792843 | ||||||||
\(119\) | −0.800595 | + | 1.38667i | −0.0733904 | + | 0.127116i | ||||
\(120\) | 3.54398 | − | 13.9364i | 0.323519 | − | 1.27221i | ||||
\(121\) | 1.16515 | + | 2.01810i | 0.105923 | + | 0.183464i | ||||
\(122\) | −0.0452843 | − | 0.0784347i | −0.00409985 | − | 0.00710114i | ||||
\(123\) | −2.67750 | + | 10.5290i | −0.241422 | + | 0.949368i | ||||
\(124\) | −0.301845 | + | 0.522811i | −0.0271065 | + | 0.0469498i | ||||
\(125\) | 6.53266 | 0.584299 | ||||||||
\(126\) | −3.43048 | + | 2.09928i | −0.305611 | + | 0.187018i | ||||
\(127\) | 6.24851 | 0.554466 | 0.277233 | − | 0.960803i | \(-0.410583\pi\) | ||||
0.277233 | + | 0.960803i | \(0.410583\pi\) | |||||||
\(128\) | 3.97726 | − | 6.88882i | 0.351544 | − | 0.608892i | ||||
\(129\) | 1.66717 | − | 0.469632i | 0.146786 | − | 0.0413488i | ||||
\(130\) | 6.04896 | + | 10.4771i | 0.530529 | + | 0.918903i | ||||
\(131\) | −5.77690 | − | 10.0059i | −0.504730 | − | 0.874219i | −0.999985 | − | 0.00547079i | \(-0.998259\pi\) |
0.495255 | − | 0.868748i | \(-0.335075\pi\) | |||||||
\(132\) | 1.14500 | + | 1.11610i | 0.0996593 | + | 0.0971440i | ||||
\(133\) | −0.423684 | + | 0.733842i | −0.0367380 | + | 0.0636322i | ||||
\(134\) | 14.9728 | 1.29346 | ||||||||
\(135\) | 14.0016 | + | 3.18192i | 1.20507 | + | 0.273856i | ||||
\(136\) | 4.66009 | 0.399599 | ||||||||
\(137\) | 10.4557 | − | 18.1097i | 0.893287 | − | 1.54722i | 0.0573759 | − | 0.998353i | \(-0.481727\pi\) |
0.835911 | − | 0.548865i | \(-0.184940\pi\) | |||||||
\(138\) | 13.8386 | + | 13.4894i | 1.17802 | + | 1.14829i | ||||
\(139\) | −11.1311 | − | 19.2797i | −0.944131 | − | 1.63528i | −0.757482 | − | 0.652855i | \(-0.773571\pi\) |
−0.186648 | − | 0.982427i | \(-0.559762\pi\) | |||||||
\(140\) | −0.447190 | − | 0.774555i | −0.0377944 | − | 0.0654619i | ||||
\(141\) | −16.8402 | + | 4.74380i | −1.41820 | + | 0.399500i | ||||
\(142\) | −3.82352 | + | 6.62253i | −0.320863 | + | 0.555750i | ||||
\(143\) | −9.92641 | −0.830088 | ||||||||
\(144\) | 8.63053 | + | 4.69292i | 0.719211 | + | 0.391077i | ||||
\(145\) | 3.44528 | 0.286115 | ||||||||
\(146\) | 1.23220 | − | 2.13423i | 0.101977 | − | 0.176630i | ||||
\(147\) | 2.53318 | − | 9.96150i | 0.208933 | − | 0.821611i | ||||
\(148\) | −0.697193 | − | 1.20757i | −0.0573089 | − | 0.0992619i | ||||
\(149\) | −6.32942 | − | 10.9629i | −0.518526 | − | 0.898114i | −0.999768 | − | 0.0215262i | \(-0.993147\pi\) |
0.481242 | − | 0.876588i | \(-0.340186\pi\) | |||||||
\(150\) | 1.46124 | − | 5.74617i | 0.119309 | − | 0.469173i | ||||
\(151\) | 1.88903 | − | 3.27189i | 0.153727 | − | 0.266262i | −0.778868 | − | 0.627188i | \(-0.784206\pi\) |
0.932595 | + | 0.360925i | \(0.117539\pi\) | |||||||
\(152\) | 2.46617 | 0.200033 | ||||||||
\(153\) | 0.118925 | + | 4.65167i | 0.00961456 | + | 0.376065i | ||||
\(154\) | −3.94734 | −0.318086 | ||||||||
\(155\) | −2.66034 | + | 4.60785i | −0.213684 | + | 0.370111i | ||||
\(156\) | 1.76216 | − | 0.496393i | 0.141086 | − | 0.0397432i | ||||
\(157\) | −1.63812 | − | 2.83730i | −0.130736 | − | 0.226441i | 0.793225 | − | 0.608929i | \(-0.208401\pi\) |
−0.923960 | + | 0.382488i | \(0.875067\pi\) | |||||||
\(158\) | 4.53958 | + | 7.86278i | 0.361149 | + | 0.625529i | ||||
\(159\) | −10.9143 | − | 10.6388i | −0.865559 | − | 0.843713i | ||||
\(160\) | −2.42661 | + | 4.20302i | −0.191841 | + | 0.332278i | ||||
\(161\) | 8.86935 | 0.699002 | ||||||||
\(162\) | −5.31904 | + | 10.4073i | −0.417903 | + | 0.817675i | ||||
\(163\) | −2.94951 | −0.231023 | −0.115512 | − | 0.993306i | \(-0.536851\pi\) | ||||
−0.115512 | + | 0.993306i | \(0.536851\pi\) | |||||||
\(164\) | 0.983288 | − | 1.70310i | 0.0767819 | − | 0.132990i | ||||
\(165\) | 10.0916 | + | 9.83687i | 0.785628 | + | 0.765799i | ||||
\(166\) | 1.95983 | + | 3.39452i | 0.152112 | + | 0.263466i | ||||
\(167\) | −11.9581 | − | 20.7120i | −0.925342 | − | 1.60274i | −0.791011 | − | 0.611803i | \(-0.790445\pi\) |
−0.134331 | − | 0.990936i | \(-0.542889\pi\) | |||||||
\(168\) | 5.17079 | − | 1.45658i | 0.398935 | − | 0.112378i | ||||
\(169\) | 0.817357 | − | 1.41570i | 0.0628736 | − | 0.108900i | ||||
\(170\) | 5.56609 | 0.426900 | ||||||||
\(171\) | 0.0629367 | + | 2.46172i | 0.00481289 | + | 0.188252i | ||||
\(172\) | −0.313529 | −0.0239063 | ||||||||
\(173\) | −10.9038 | + | 18.8860i | −0.829004 | + | 1.43588i | 0.0698168 | + | 0.997560i | \(0.477759\pi\) |
−0.898821 | + | 0.438317i | \(0.855575\pi\) | |||||||
\(174\) | −0.691160 | + | 2.71792i | −0.0523967 | + | 0.206045i | ||||
\(175\) | −1.36056 | − | 2.35656i | −0.102849 | − | 0.178139i | ||||
\(176\) | 4.82099 | + | 8.35019i | 0.363396 | + | 0.629419i | ||||
\(177\) | −2.83096 | + | 11.1325i | −0.212788 | + | 0.836770i | ||||
\(178\) | −9.91223 | + | 17.1685i | −0.742953 | + | 1.28683i | ||||
\(179\) | 6.92878 | 0.517882 | 0.258941 | − | 0.965893i | \(-0.416627\pi\) | ||||
0.258941 | + | 0.965893i | \(0.416627\pi\) | |||||||
\(180\) | −2.28340 | − | 1.24162i | −0.170195 | − | 0.0925447i | ||||
\(181\) | −11.0279 | −0.819698 | −0.409849 | − | 0.912153i | \(-0.634419\pi\) | ||||
−0.409849 | + | 0.912153i | \(0.634419\pi\) | |||||||
\(182\) | −2.25976 | + | 3.91402i | −0.167505 | + | 0.290127i | ||||
\(183\) | −0.116270 | + | 0.0327526i | −0.00859492 | + | 0.00242114i | ||||
\(184\) | −12.9066 | − | 22.3549i | −0.951489 | − | 1.64803i | ||||
\(185\) | −6.14479 | − | 10.6431i | −0.451774 | − | 0.782495i | ||||
\(186\) | −3.10136 | − | 3.02308i | −0.227402 | − | 0.221663i | ||||
\(187\) | −2.28350 | + | 3.95514i | −0.166986 | + | 0.289229i | ||||
\(188\) | 3.16698 | 0.230976 | ||||||||
\(189\) | 1.58591 | + | 5.12428i | 0.115358 | + | 0.372736i | ||||
\(190\) | 2.94564 | 0.213699 | ||||||||
\(191\) | −12.6528 | + | 21.9152i | −0.915522 | + | 1.58573i | −0.109386 | + | 0.993999i | \(0.534888\pi\) |
−0.806136 | + | 0.591731i | \(0.798445\pi\) | |||||||
\(192\) | −10.9519 | − | 10.6755i | −0.790388 | − | 0.770439i | ||||
\(193\) | 10.8578 | + | 18.8063i | 0.781563 | + | 1.35371i | 0.931031 | + | 0.364940i | \(0.118911\pi\) |
−0.149468 | + | 0.988767i | \(0.547756\pi\) | |||||||
\(194\) | −2.51570 | − | 4.35733i | −0.180617 | − | 0.312838i | ||||
\(195\) | 15.5310 | − | 4.37501i | 1.11220 | − | 0.313301i | ||||
\(196\) | −0.930290 | + | 1.61131i | −0.0664493 | + | 0.115094i | ||||
\(197\) | 6.79869 | 0.484386 | 0.242193 | − | 0.970228i | \(-0.422133\pi\) | ||||
0.242193 | + | 0.970228i | \(0.422133\pi\) | |||||||
\(198\) | −9.78460 | + | 5.98768i | −0.695361 | + | 0.425526i | ||||
\(199\) | 27.2806 | 1.93387 | 0.966935 | − | 0.255022i | \(-0.0820827\pi\) | ||||
0.966935 | + | 0.255022i | \(0.0820827\pi\) | |||||||
\(200\) | −3.95977 | + | 6.85852i | −0.279998 | + | 0.484971i | ||||
\(201\) | 4.92164 | − | 19.3539i | 0.347146 | − | 1.36512i | ||||
\(202\) | −6.64243 | − | 11.5050i | −0.467360 | − | 0.809491i | ||||
\(203\) | 0.643542 | + | 1.11465i | 0.0451678 | + | 0.0782329i | ||||
\(204\) | 0.207588 | − | 0.816321i | 0.0145341 | − | 0.0571539i | ||||
\(205\) | 8.66632 | − | 15.0105i | 0.605282 | − | 1.04838i | ||||
\(206\) | −16.4662 | −1.14725 | ||||||||
\(207\) | 21.9852 | − | 13.4538i | 1.52808 | − | 0.935105i | ||||
\(208\) | 11.0396 | 0.765460 | ||||||||
\(209\) | −1.20846 | + | 2.09311i | −0.0835906 | + | 0.144783i | ||||
\(210\) | 6.17608 | − | 1.73977i | 0.426190 | − | 0.120056i | ||||
\(211\) | −7.88503 | − | 13.6573i | −0.542828 | − | 0.940206i | −0.998740 | − | 0.0501808i | \(-0.984020\pi\) |
0.455912 | − | 0.890025i | \(-0.349313\pi\) | |||||||
\(212\) | 1.37948 | + | 2.38934i | 0.0947434 | + | 0.164100i | ||||
\(213\) | 7.30348 | + | 7.11914i | 0.500426 | + | 0.487795i | ||||
\(214\) | 6.62661 | − | 11.4776i | 0.452985 | − | 0.784594i | ||||
\(215\) | −2.76332 | −0.188457 | ||||||||
\(216\) | 10.6078 | − | 11.4541i | 0.721768 | − | 0.779351i | ||||
\(217\) | −1.98769 | −0.134933 | ||||||||
\(218\) | −3.03901 | + | 5.26372i | −0.205828 | + | 0.356504i | ||||
\(219\) | −2.35367 | − | 2.29427i | −0.159046 | − | 0.155032i | ||||
\(220\) | −1.27550 | − | 2.20923i | −0.0859942 | − | 0.148946i | ||||
\(221\) | 2.61451 | + | 4.52846i | 0.175871 | + | 0.304617i | ||||
\(222\) | 9.62885 | − | 2.71240i | 0.646246 | − | 0.182044i | ||||
\(223\) | −10.5956 | + | 18.3520i | −0.709531 | + | 1.22894i | 0.255500 | + | 0.966809i | \(0.417760\pi\) |
−0.965031 | + | 0.262135i | \(0.915574\pi\) | |||||||
\(224\) | −1.81306 | −0.121140 | ||||||||
\(225\) | −6.94719 | − | 3.77759i | −0.463146 | − | 0.251839i | ||||
\(226\) | 8.93183 | 0.594136 | ||||||||
\(227\) | −0.776999 | + | 1.34580i | −0.0515712 | + | 0.0893240i | −0.890659 | − | 0.454673i | \(-0.849756\pi\) |
0.839087 | + | 0.543997i | \(0.183090\pi\) | |||||||
\(228\) | 0.109858 | − | 0.432006i | 0.00727552 | − | 0.0286103i | ||||
\(229\) | −0.990433 | − | 1.71548i | −0.0654496 | − | 0.113362i | 0.831444 | − | 0.555609i | \(-0.187515\pi\) |
−0.896893 | + | 0.442247i | \(0.854181\pi\) | |||||||
\(230\) | −15.4159 | − | 26.7011i | −1.01649 | − | 1.76062i | ||||
\(231\) | −1.29751 | + | 5.10233i | −0.0853699 | + | 0.335709i | ||||
\(232\) | 1.87296 | − | 3.24406i | 0.122966 | − | 0.212983i | ||||
\(233\) | −25.5390 | −1.67311 | −0.836557 | − | 0.547880i | \(-0.815435\pi\) | ||||
−0.836557 | + | 0.547880i | \(0.815435\pi\) | |||||||
\(234\) | 0.335680 | + | 13.1298i | 0.0219441 | + | 0.858324i | ||||
\(235\) | 27.9126 | 1.82081 | ||||||||
\(236\) | 1.03965 | − | 1.80072i | 0.0676753 | − | 0.117217i | ||||
\(237\) | 11.6556 | − | 3.28333i | 0.757113 | − | 0.213275i | ||||
\(238\) | 1.03969 | + | 1.80079i | 0.0673929 | + | 0.116728i | ||||
\(239\) | 7.98820 | + | 13.8360i | 0.516714 | + | 0.894975i | 0.999812 | + | 0.0194082i | \(0.00617822\pi\) |
−0.483098 | + | 0.875566i | \(0.660488\pi\) | |||||||
\(240\) | −11.2233 | − | 10.9400i | −0.724461 | − | 0.706176i | ||||
\(241\) | 4.85761 | − | 8.41363i | 0.312906 | − | 0.541969i | −0.666084 | − | 0.745877i | \(-0.732031\pi\) |
0.978990 | + | 0.203907i | \(0.0653641\pi\) | |||||||
\(242\) | 3.02623 | 0.194533 | ||||||||
\(243\) | 11.7041 | + | 10.2963i | 0.750818 | + | 0.660509i | ||||
\(244\) | 0.0218658 | 0.00139981 | ||||||||
\(245\) | −8.19922 | + | 14.2015i | −0.523829 | + | 0.907298i | ||||
\(246\) | 10.1030 | + | 9.84797i | 0.644141 | + | 0.627883i | ||||
\(247\) | 1.38363 | + | 2.39651i | 0.0880380 | + | 0.152486i | ||||
\(248\) | 2.89248 | + | 5.00993i | 0.183673 | + | 0.318131i | ||||
\(249\) | 5.03196 | − | 1.41748i | 0.318887 | − | 0.0898289i | ||||
\(250\) | 4.24179 | − | 7.34700i | 0.268274 | − | 0.464665i | ||||
\(251\) | 5.91101 | 0.373100 | 0.186550 | − | 0.982445i | \(-0.440269\pi\) | ||||
0.186550 | + | 0.982445i | \(0.440269\pi\) | |||||||
\(252\) | −0.0248162 | − | 0.970666i | −0.00156328 | − | 0.0611462i | ||||
\(253\) | 25.2977 | 1.59045 | ||||||||
\(254\) | 4.05729 | − | 7.02743i | 0.254577 | − | 0.440940i | ||||
\(255\) | 1.82960 | − | 7.19473i | 0.114574 | − | 0.450552i | ||||
\(256\) | 3.66505 | + | 6.34806i | 0.229066 | + | 0.396754i | ||||
\(257\) | −14.1947 | − | 24.5859i | −0.885439 | − | 1.53363i | −0.845210 | − | 0.534435i | \(-0.820525\pi\) |
−0.0402290 | − | 0.999190i | \(-0.512809\pi\) | |||||||
\(258\) | 0.554351 | − | 2.17993i | 0.0345124 | − | 0.135717i | ||||
\(259\) | 2.29556 | − | 3.97603i | 0.142639 | − | 0.247058i | ||||
\(260\) | −2.92078 | −0.181139 | ||||||||
\(261\) | 3.28600 | + | 1.78679i | 0.203398 | + | 0.110599i | ||||
\(262\) | −15.0043 | −0.926966 | ||||||||
\(263\) | −13.1146 | + | 22.7152i | −0.808683 | + | 1.40068i | 0.105094 | + | 0.994462i | \(0.466486\pi\) |
−0.913777 | + | 0.406217i | \(0.866848\pi\) | |||||||
\(264\) | 14.7484 | − | 4.15455i | 0.907702 | − | 0.255695i | ||||
\(265\) | 12.1582 | + | 21.0587i | 0.746875 | + | 1.29362i | ||||
\(266\) | 0.550214 | + | 0.952998i | 0.0337358 | + | 0.0584321i | ||||
\(267\) | 18.9338 | + | 18.4559i | 1.15873 | + | 1.12948i | ||||
\(268\) | −1.80743 | + | 3.13056i | −0.110406 | + | 0.191230i | ||||
\(269\) | 16.9061 | 1.03078 | 0.515392 | − | 0.856954i | \(-0.327646\pi\) | ||||
0.515392 | + | 0.856954i | \(0.327646\pi\) | |||||||
\(270\) | 12.6701 | − | 13.6809i | 0.771079 | − | 0.832596i | ||||
\(271\) | 14.9590 | 0.908693 | 0.454347 | − | 0.890825i | \(-0.349873\pi\) | ||||
0.454347 | + | 0.890825i | \(0.349873\pi\) | |||||||
\(272\) | 2.53959 | − | 4.39870i | 0.153985 | − | 0.266710i | ||||
\(273\) | 4.31647 | + | 4.20753i | 0.261245 | + | 0.254651i | ||||
\(274\) | −13.5782 | − | 23.5180i | −0.820286 | − | 1.42078i | ||||
\(275\) | −3.88068 | − | 6.72153i | −0.234014 | − | 0.405323i | ||||
\(276\) | −4.49091 | + | 1.26507i | −0.270321 | + | 0.0761481i | ||||
\(277\) | −0.464342 | + | 0.804265i | −0.0278996 | + | 0.0483236i | −0.879638 | − | 0.475644i | \(-0.842215\pi\) |
0.851738 | + | 0.523967i | \(0.175549\pi\) | |||||||
\(278\) | −28.9107 | −1.73395 | ||||||||
\(279\) | −4.92706 | + | 3.01511i | −0.294976 | + | 0.180510i | ||||
\(280\) | −8.57055 | −0.512188 | ||||||||
\(281\) | −8.89911 | + | 15.4137i | −0.530876 | + | 0.919505i | 0.468475 | + | 0.883477i | \(0.344804\pi\) |
−0.999351 | + | 0.0360276i | \(0.988530\pi\) | |||||||
\(282\) | −5.59955 | + | 22.0197i | −0.333449 | + | 1.31125i | ||||
\(283\) | −0.877006 | − | 1.51902i | −0.0521326 | − | 0.0902963i | 0.838781 | − | 0.544468i | \(-0.183269\pi\) |
−0.890914 | + | 0.454172i | \(0.849935\pi\) | |||||||
\(284\) | −0.923105 | − | 1.59886i | −0.0547762 | − | 0.0948752i | ||||
\(285\) | 0.968245 | − | 3.80753i | 0.0573539 | − | 0.225539i | ||||
\(286\) | −6.44543 | + | 11.1638i | −0.381126 | + | 0.660130i | ||||
\(287\) | 6.47510 | 0.382213 | ||||||||
\(288\) | −4.49419 | + | 2.75021i | −0.264823 | + | 0.162058i | ||||
\(289\) | −14.5942 | −0.858482 | ||||||||
\(290\) | 2.23710 | − | 3.87476i | 0.131367 | − | 0.227534i | ||||
\(291\) | −6.45921 | + | 1.81953i | −0.378645 | + | 0.106663i | ||||
\(292\) | 0.297487 | + | 0.515262i | 0.0174091 | + | 0.0301534i | ||||
\(293\) | 3.75036 | + | 6.49581i | 0.219098 | + | 0.379489i | 0.954533 | − | 0.298107i | \(-0.0963551\pi\) |
−0.735434 | + | 0.677596i | \(0.763022\pi\) | |||||||
\(294\) | −9.55842 | − | 9.31717i | −0.557459 | − | 0.543389i | ||||
\(295\) | 9.16305 | − | 15.8709i | 0.533493 | − | 0.924038i | ||||
\(296\) | −13.3620 | −0.776648 | ||||||||
\(297\) | 4.52343 | + | 14.6158i | 0.262476 | + | 0.848092i | ||||
\(298\) | −16.4393 | −0.952303 | ||||||||
\(299\) | 14.4823 | − | 25.0841i | 0.837535 | − | 1.45065i | ||||
\(300\) | 1.02503 | + | 0.999163i | 0.0591804 | + | 0.0576867i | ||||
\(301\) | −0.516159 | − | 0.894013i | −0.0297509 | − | 0.0515301i | ||||
\(302\) | −2.45317 | − | 4.24901i | −0.141164 | − | 0.244503i | ||||
\(303\) | −17.0548 | + | 4.80425i | −0.979772 | + | 0.275997i | ||||
\(304\) | 1.34398 | − | 2.32784i | 0.0770825 | − | 0.133511i | ||||
\(305\) | 0.192717 | 0.0110349 | ||||||||
\(306\) | 5.30876 | + | 2.88668i | 0.303481 | + | 0.165020i | ||||
\(307\) | 24.5577 | 1.40158 | 0.700792 | − | 0.713365i | \(-0.252830\pi\) | ||||
0.700792 | + | 0.713365i | \(0.252830\pi\) | |||||||
\(308\) | 0.476500 | − | 0.825321i | 0.0271511 | − | 0.0470271i | ||||
\(309\) | −5.41251 | + | 21.2842i | −0.307907 | + | 1.21082i | ||||
\(310\) | 3.45483 | + | 5.98395i | 0.196221 | + | 0.339865i | ||||
\(311\) | 9.36086 | + | 16.2135i | 0.530806 | + | 0.919382i | 0.999354 | + | 0.0359442i | \(0.0114439\pi\) |
−0.468548 | + | 0.883438i | \(0.655223\pi\) | |||||||
\(312\) | 4.32364 | − | 17.0023i | 0.244778 | − | 0.962567i | ||||
\(313\) | 0.549273 | − | 0.951369i | 0.0310468 | − | 0.0537746i | −0.850085 | − | 0.526646i | \(-0.823449\pi\) |
0.881131 | + | 0.472872i | \(0.156783\pi\) | |||||||
\(314\) | −4.25466 | −0.240104 | ||||||||
\(315\) | −0.218721 | − | 8.55507i | −0.0123235 | − | 0.482024i | ||||
\(316\) | −2.19196 | −0.123308 | ||||||||
\(317\) | −1.25859 | + | 2.17995i | −0.0706896 | + | 0.122438i | −0.899204 | − | 0.437530i | \(-0.855853\pi\) |
0.828514 | + | 0.559968i | \(0.189187\pi\) | |||||||
\(318\) | −19.0519 | + | 5.36682i | −1.06838 | + | 0.300956i | ||||
\(319\) | 1.83555 | + | 3.17926i | 0.102771 | + | 0.178005i | ||||
\(320\) | 12.2002 | + | 21.1313i | 0.682011 | + | 1.18128i | ||||
\(321\) | −12.6578 | − | 12.3383i | −0.706488 | − | 0.688657i | ||||
\(322\) | 5.75905 | − | 9.97497i | 0.320939 | − | 0.555883i | ||||
\(323\) | 1.27318 | 0.0708414 | ||||||||
\(324\) | −1.53391 | − | 2.36843i | −0.0852171 | − | 0.131579i | ||||
\(325\) | −8.88639 | −0.492928 | ||||||||
\(326\) | −1.91518 | + | 3.31718i | −0.106072 | + | 0.183722i | ||||
\(327\) | 5.80494 | + | 5.65843i | 0.321014 | + | 0.312912i | ||||
\(328\) | −9.42253 | − | 16.3203i | −0.520272 | − | 0.901138i | ||||
\(329\) | 5.21377 | + | 9.03051i | 0.287444 | + | 0.497868i | ||||
\(330\) | 17.6158 | − | 4.96227i | 0.969717 | − | 0.273164i | ||||
\(331\) | 6.76996 | − | 11.7259i | 0.372111 | − | 0.644515i | −0.617779 | − | 0.786352i | \(-0.711967\pi\) |
0.989890 | + | 0.141837i | \(0.0453008\pi\) | |||||||
\(332\) | −0.946314 | −0.0519357 | ||||||||
\(333\) | −0.340997 | − | 13.3378i | −0.0186865 | − | 0.730908i | ||||
\(334\) | −31.0585 | −1.69944 | ||||||||
\(335\) | −15.9300 | + | 27.5916i | −0.870349 | + | 1.50749i | ||||
\(336\) | 1.44302 | − | 5.67454i | 0.0787232 | − | 0.309572i | ||||
\(337\) | 1.22079 | + | 2.11448i | 0.0665009 | + | 0.115183i | 0.897359 | − | 0.441302i | \(-0.145483\pi\) |
−0.830858 | + | 0.556485i | \(0.812150\pi\) | |||||||
\(338\) | −1.06145 | − | 1.83849i | −0.0577355 | − | 0.100001i | ||||
\(339\) | 2.93593 | − | 11.5453i | 0.159458 | − | 0.627054i | ||||
\(340\) | −0.671906 | + | 1.16377i | −0.0364392 | + | 0.0631145i | ||||
\(341\) | −5.66942 | −0.307016 | ||||||||
\(342\) | 2.80945 | + | 1.52766i | 0.151918 | + | 0.0826065i | ||||
\(343\) | −13.3523 | −0.720958 | ||||||||
\(344\) | −1.50222 | + | 2.60193i | −0.0809944 | + | 0.140286i | ||||
\(345\) | −39.5812 | + | 11.1498i | −2.13098 | + | 0.600286i | ||||
\(346\) | 14.1602 | + | 24.5262i | 0.761256 | + | 1.31853i | ||||
\(347\) | −0.939688 | − | 1.62759i | −0.0504451 | − | 0.0873735i | 0.839700 | − | 0.543050i | \(-0.182731\pi\) |
−0.890145 | + | 0.455677i | \(0.849397\pi\) | |||||||
\(348\) | −0.484838 | − | 0.472601i | −0.0259901 | − | 0.0253341i | ||||
\(349\) | −12.0684 | + | 20.9031i | −0.646006 | + | 1.11892i | 0.338062 | + | 0.941124i | \(0.390229\pi\) |
−0.984068 | + | 0.177792i | \(0.943105\pi\) | |||||||
\(350\) | −3.53377 | −0.188888 | ||||||||
\(351\) | 17.0820 | + | 3.88194i | 0.911767 | + | 0.207202i | ||||
\(352\) | −5.17132 | −0.275632 | ||||||||
\(353\) | 6.77717 | − | 11.7384i | 0.360712 | − | 0.624772i | −0.627366 | − | 0.778724i | \(-0.715867\pi\) |
0.988078 | + | 0.153953i | \(0.0492003\pi\) | |||||||
\(354\) | 10.6820 | + | 10.4124i | 0.567744 | + | 0.553414i | ||||
\(355\) | −8.13589 | − | 14.0918i | −0.431808 | − | 0.747914i | ||||
\(356\) | −2.39309 | − | 4.14495i | −0.126834 | − | 0.219682i | ||||
\(357\) | 2.66945 | − | 0.751971i | 0.141282 | − | 0.0397985i | ||||
\(358\) | 4.49900 | − | 7.79250i | 0.237780 | − | 0.411847i | ||||
\(359\) | −3.49289 | −0.184348 | −0.0921739 | − | 0.995743i | \(-0.529382\pi\) | ||||
−0.0921739 | + | 0.995743i | \(0.529382\pi\) | |||||||
\(360\) | −21.2445 | + | 13.0006i | −1.11969 | + | 0.685191i | ||||
\(361\) | −18.3262 | −0.964538 | ||||||||
\(362\) | −7.16065 | + | 12.4026i | −0.376355 | + | 0.651867i | ||||
\(363\) | 0.994735 | − | 3.91170i | 0.0522101 | − | 0.205311i | ||||
\(364\) | −0.545570 | − | 0.944955i | −0.0285957 | − | 0.0495291i | ||||
\(365\) | 2.62193 | + | 4.54132i | 0.137238 | + | 0.237704i | ||||
\(366\) | −0.0386610 | + | 0.152031i | −0.00202084 | + | 0.00794677i | ||||
\(367\) | −14.5976 | + | 25.2838i | −0.761989 | + | 1.31980i | 0.179834 | + | 0.983697i | \(0.442444\pi\) |
−0.941824 | + | 0.336107i | \(0.890890\pi\) | |||||||
\(368\) | −28.1347 | −1.46662 | ||||||||
\(369\) | 16.0504 | − | 9.82201i | 0.835549 | − | 0.511314i | ||||
\(370\) | −15.9598 | −0.829708 | ||||||||
\(371\) | −4.54206 | + | 7.86707i | −0.235812 | + | 0.408438i | ||||
\(372\) | 1.00645 | − | 0.283512i | 0.0521821 | − | 0.0146994i | ||||
\(373\) | 2.95796 | + | 5.12334i | 0.153157 | + | 0.265276i | 0.932387 | − | 0.361463i | \(-0.117723\pi\) |
−0.779229 | + | 0.626739i | \(0.784389\pi\) | |||||||
\(374\) | 2.96545 | + | 5.13632i | 0.153340 | + | 0.265593i | ||||
\(375\) | −8.10243 | − | 7.89793i | −0.418408 | − | 0.407848i | ||||
\(376\) | 15.1741 | − | 26.2823i | 0.782544 | − | 1.35541i | ||||
\(377\) | 4.20324 | 0.216478 | ||||||||
\(378\) | 6.79282 | + | 1.54369i | 0.349385 | + | 0.0793990i | ||||
\(379\) | 8.06235 | 0.414135 | 0.207067 | − | 0.978327i | \(-0.433608\pi\) | ||||
0.207067 | + | 0.978327i | \(0.433608\pi\) | |||||||
\(380\) | −0.355580 | + | 0.615882i | −0.0182409 | + | 0.0315941i | ||||
\(381\) | −7.75001 | − | 7.55441i | −0.397045 | − | 0.387024i | ||||
\(382\) | 16.4314 | + | 28.4600i | 0.840704 | + | 1.45614i | ||||
\(383\) | −2.31912 | − | 4.01683i | −0.118501 | − | 0.205250i | 0.800673 | − | 0.599102i | \(-0.204476\pi\) |
−0.919174 | + | 0.393852i | \(0.871142\pi\) | |||||||
\(384\) | −13.2615 | + | 3.73570i | −0.676749 | + | 0.190637i | ||||
\(385\) | 4.19968 | − | 7.27406i | 0.214036 | − | 0.370721i | ||||
\(386\) | 28.2008 | 1.43539 | ||||||||
\(387\) | −2.63556 | − | 1.43311i | −0.133973 | − | 0.0728490i | ||||
\(388\) | 1.21472 | 0.0616683 | ||||||||
\(389\) | 9.06993 | − | 15.7096i | 0.459864 | − | 0.796507i | −0.539090 | − | 0.842248i | \(-0.681232\pi\) |
0.998953 | + | 0.0457413i | \(0.0145650\pi\) | |||||||
\(390\) | 5.16424 | − | 20.3079i | 0.261501 | − | 1.02833i | ||||
\(391\) | −6.66313 | − | 11.5409i | −0.336969 | − | 0.583647i | ||||
\(392\) | 8.91467 | + | 15.4407i | 0.450259 | + | 0.779871i | ||||
\(393\) | −4.93197 | + | 19.3945i | −0.248785 | + | 0.978324i | ||||
\(394\) | 4.41453 | − | 7.64619i | 0.222401 | − | 0.385210i | ||||
\(395\) | −19.3191 | −0.972050 | ||||||||
\(396\) | −0.0707823 | − | 2.76859i | −0.00355694 | − | 0.139127i | ||||
\(397\) | 32.4912 | 1.63069 | 0.815343 | − | 0.578979i | \(-0.196549\pi\) | ||||
0.815343 | + | 0.578979i | \(0.196549\pi\) | |||||||
\(398\) | 17.7139 | − | 30.6813i | 0.887916 | − | 1.53792i | ||||
\(399\) | 1.41270 | − | 0.397951i | 0.0707236 | − | 0.0199225i | ||||
\(400\) | 4.31588 | + | 7.47532i | 0.215794 | + | 0.373766i | ||||
\(401\) | −2.47708 | − | 4.29042i | −0.123699 | − | 0.214254i | 0.797524 | − | 0.603287i | \(-0.206143\pi\) |
−0.921224 | + | 0.389033i | \(0.872809\pi\) | |||||||
\(402\) | −18.5708 | − | 18.1021i | −0.926226 | − | 0.902848i | ||||
\(403\) | −3.24561 | + | 5.62156i | −0.161675 | + | 0.280030i | ||||
\(404\) | 3.20734 | 0.159571 | ||||||||
\(405\) | −13.5193 | − | 20.8744i | −0.671778 | − | 1.03726i | ||||
\(406\) | 1.67146 | 0.0829533 | ||||||||
\(407\) | 6.54753 | − | 11.3407i | 0.324549 | − | 0.562136i | ||||
\(408\) | −5.77989 | − | 5.63401i | −0.286147 | − | 0.278925i | ||||
\(409\) | −13.5836 | − | 23.5274i | −0.671664 | − | 1.16336i | −0.977432 | − | 0.211250i | \(-0.932247\pi\) |
0.305768 | − | 0.952106i | \(-0.401087\pi\) | |||||||
\(410\) | −11.2544 | − | 19.4933i | −0.555817 | − | 0.962704i | ||||
\(411\) | −34.8626 | + | 9.82063i | −1.71965 | + | 0.484416i | ||||
\(412\) | 1.98770 | − | 3.44280i | 0.0979269 | − | 0.169614i | ||||
\(413\) | 6.84624 | 0.336881 | ||||||||
\(414\) | −0.855486 | − | 33.4616i | −0.0420449 | − | 1.64455i | ||||
\(415\) | −8.34044 | −0.409416 | ||||||||
\(416\) | −2.96046 | + | 5.12767i | −0.145149 | + | 0.251405i | ||||
\(417\) | −9.50309 | + | 37.3700i | −0.465368 | + | 1.83002i | ||||
\(418\) | 1.56935 | + | 2.71820i | 0.0767595 | + | 0.132951i | ||||
\(419\) | −0.591184 | − | 1.02396i | −0.0288812 | − | 0.0500238i | 0.851224 | − | 0.524803i | \(-0.175861\pi\) |
−0.880105 | + | 0.474780i | \(0.842528\pi\) | |||||||
\(420\) | −0.381784 | + | 1.50133i | −0.0186291 | + | 0.0732573i | ||||
\(421\) | −12.8870 | + | 22.3209i | −0.628072 | + | 1.08785i | 0.359867 | + | 0.933004i | \(0.382822\pi\) |
−0.987938 | + | 0.154848i | \(0.950511\pi\) | |||||||
\(422\) | −20.4797 | −0.996935 | ||||||||
\(423\) | 26.6221 | + | 14.4760i | 1.29441 | + | 0.703846i | ||||
\(424\) | 26.4383 | 1.28396 | ||||||||
\(425\) | −2.04426 | + | 3.54075i | −0.0991610 | + | 0.171752i | ||||
\(426\) | 12.7489 | − | 3.59130i | 0.617686 | − | 0.173999i | ||||
\(427\) | 0.0359974 | + | 0.0623493i | 0.00174204 | + | 0.00301730i | ||||
\(428\) | 1.59985 | + | 2.77102i | 0.0773316 | + | 0.133942i | ||||
\(429\) | 12.3117 | + | 12.0010i | 0.594414 | + | 0.579412i | ||||
\(430\) | −1.79428 | + | 3.10779i | −0.0865280 | + | 0.149871i | ||||
\(431\) | −9.39722 | −0.452648 | −0.226324 | − | 0.974052i | \(-0.572671\pi\) | ||||
−0.226324 | + | 0.974052i | \(0.572671\pi\) | |||||||
\(432\) | −5.03072 | − | 16.2549i | −0.242040 | − | 0.782062i | ||||
\(433\) | −21.5740 | −1.03678 | −0.518391 | − | 0.855144i | \(-0.673469\pi\) | ||||
−0.518391 | + | 0.855144i | \(0.673469\pi\) | |||||||
\(434\) | −1.29065 | + | 2.23547i | −0.0619533 | + | 0.107306i | ||||
\(435\) | −4.27318 | − | 4.16532i | −0.204883 | − | 0.199712i | ||||
\(436\) | −0.733702 | − | 1.27081i | −0.0351380 | − | 0.0608607i | ||||
\(437\) | −3.52620 | − | 6.10756i | −0.168681 | − | 0.292164i | ||||
\(438\) | −4.10855 | + | 1.15736i | −0.196314 | + | 0.0553007i | ||||
\(439\) | −1.04927 | + | 1.81739i | −0.0500790 | + | 0.0867395i | −0.889978 | − | 0.456003i | \(-0.849281\pi\) |
0.839899 | + | 0.542742i | \(0.182614\pi\) | |||||||
\(440\) | −24.4454 | −1.16539 | ||||||||
\(441\) | −15.1853 | + | 9.29262i | −0.723109 | + | 0.442506i | ||||
\(442\) | 6.79062 | 0.322997 | ||||||||
\(443\) | −18.2063 | + | 31.5342i | −0.865007 | + | 1.49824i | 0.00203309 | + | 0.999998i | \(0.499353\pi\) |
−0.867040 | + | 0.498238i | \(0.833980\pi\) | |||||||
\(444\) | −0.595221 | + | 2.34065i | −0.0282480 | + | 0.111082i | ||||
\(445\) | −21.0918 | − | 36.5320i | −0.999846 | − | 1.73178i | ||||
\(446\) | 13.7598 | + | 23.8327i | 0.651547 | + | 1.12851i | ||||
\(447\) | −5.40368 | + | 21.2494i | −0.255585 | + | 1.00506i | ||||
\(448\) | −4.55773 | + | 7.89422i | −0.215332 | + | 0.372967i | ||||
\(449\) | 7.78784 | 0.367531 | 0.183765 | − | 0.982970i | \(-0.441171\pi\) | ||||
0.183765 | + | 0.982970i | \(0.441171\pi\) | |||||||
\(450\) | −8.75945 | + | 5.36034i | −0.412924 | + | 0.252689i | ||||
\(451\) | 18.4687 | 0.869655 | ||||||||
\(452\) | −1.07820 | + | 1.86749i | −0.0507141 | + | 0.0878394i | ||||
\(453\) | −6.29864 | + | 1.77430i | −0.295936 | + | 0.0833637i | ||||
\(454\) | 1.00904 | + | 1.74771i | 0.0473567 | + | 0.0820243i | ||||
\(455\) | −4.80844 | − | 8.32847i | −0.225423 | − | 0.390445i | ||||
\(456\) | −3.05878 | − | 2.98158i | −0.143241 | − | 0.139625i | ||||
\(457\) | 11.8008 | − | 20.4395i | 0.552016 | − | 0.956120i | −0.446113 | − | 0.894977i | \(-0.647192\pi\) |
0.998129 | − | 0.0611431i | \(-0.0194746\pi\) | |||||||
\(458\) | −2.57243 | −0.120202 | ||||||||
\(459\) | 5.47633 | − | 5.91324i | 0.255613 | − | 0.276006i | ||||
\(460\) | 7.44367 | 0.347063 | ||||||||
\(461\) | −0.177184 | + | 0.306891i | −0.00825227 | + | 0.0142933i | −0.870122 | − | 0.492836i | \(-0.835960\pi\) |
0.861870 | + | 0.507130i | \(0.169293\pi\) | |||||||
\(462\) | 4.89588 | + | 4.77231i | 0.227777 | + | 0.222028i | ||||
\(463\) | 5.49903 | + | 9.52459i | 0.255561 | + | 0.442645i | 0.965048 | − | 0.262074i | \(-0.0844064\pi\) |
−0.709486 | + | 0.704719i | \(0.751073\pi\) | |||||||
\(464\) | −2.04140 | − | 3.53581i | −0.0947695 | − | 0.164146i | ||||
\(465\) | 8.87047 | − | 2.49877i | 0.411358 | − | 0.115878i | ||||
\(466\) | −16.5830 | + | 28.7226i | −0.768192 | + | 1.33055i | ||||
\(467\) | 0.429641 | 0.0198814 | 0.00994072 | − | 0.999951i | \(-0.496836\pi\) | ||||
0.00994072 | + | 0.999951i | \(0.496836\pi\) | |||||||
\(468\) | −2.78574 | − | 1.51477i | −0.128771 | − | 0.0700203i | ||||
\(469\) | −11.9022 | −0.549593 | ||||||||
\(470\) | 18.1242 | − | 31.3921i | 0.836008 | − | 1.44801i | ||||
\(471\) | −1.39853 | + | 5.49957i | −0.0644407 | + | 0.253407i | ||||
\(472\) | −9.96261 | − | 17.2557i | −0.458566 | − | 0.794260i | ||||
\(473\) | −1.47222 | − | 2.54996i | −0.0676926 | − | 0.117247i | ||||
\(474\) | 3.87562 | − | 15.2405i | 0.178013 | − | 0.700019i | ||||
\(475\) | −1.08184 | + | 1.87381i | −0.0496383 | + | 0.0859761i | ||||
\(476\) | −0.502019 | −0.0230100 | ||||||||
\(477\) | 0.674706 | + | 26.3906i | 0.0308927 | + | 1.20834i | ||||
\(478\) | 20.7476 | 0.948975 | ||||||||
\(479\) | 0.666231 | − | 1.15395i | 0.0304409 | − | 0.0527252i | −0.850404 | − | 0.526131i | \(-0.823642\pi\) |
0.880845 | + | 0.473406i | \(0.156976\pi\) | |||||||
\(480\) | 8.09114 | − | 2.27923i | 0.369308 | − | 0.104032i | ||||
\(481\) | −7.49663 | − | 12.9845i | −0.341817 | − | 0.592044i | ||||
\(482\) | −6.30830 | − | 10.9263i | −0.287335 | − | 0.497679i | ||||
\(483\) | −11.0006 | − | 10.7230i | −0.500546 | − | 0.487912i | ||||
\(484\) | −0.365308 | + | 0.632732i | −0.0166049 | + | 0.0287606i | ||||
\(485\) | 10.7061 | 0.486139 | ||||||||
\(486\) | 19.1795 | − | 6.47748i | 0.870002 | − | 0.293824i | ||||
\(487\) | −17.8776 | −0.810113 | −0.405057 | − | 0.914292i | \(-0.632748\pi\) | ||||
−0.405057 | + | 0.914292i | \(0.632748\pi\) | |||||||
\(488\) | 0.104767 | − | 0.181461i | 0.00474256 | − | 0.00821435i | ||||
\(489\) | 3.65826 | + | 3.56593i | 0.165432 | + | 0.161257i | ||||
\(490\) | 10.6478 | + | 18.4426i | 0.481021 | + | 0.833152i | ||||
\(491\) | 11.4781 | + | 19.8806i | 0.517998 | + | 0.897199i | 0.999781 | + | 0.0209087i | \(0.00665593\pi\) |
−0.481783 | + | 0.876290i | \(0.660011\pi\) | |||||||
\(492\) | −3.27861 | + | 0.923568i | −0.147811 | + | 0.0416376i | ||||
\(493\) | 0.966927 | − | 1.67477i | 0.0435482 | − | 0.0754277i | ||||
\(494\) | 3.59367 | 0.161687 | ||||||||
\(495\) | −0.623848 | − | 24.4013i | −0.0280399 | − | 1.09676i | ||||
\(496\) | 6.30522 | 0.283113 | ||||||||
\(497\) | 3.03939 | − | 5.26439i | 0.136335 | − | 0.236140i | ||||
\(498\) | 1.67318 | − | 6.57962i | 0.0749770 | − | 0.294840i | ||||
\(499\) | −4.72216 | − | 8.17902i | −0.211393 | − | 0.366143i | 0.740758 | − | 0.671772i | \(-0.234467\pi\) |
−0.952151 | + | 0.305629i | \(0.901133\pi\) | |||||||
\(500\) | 1.02409 | + | 1.77377i | 0.0457986 | + | 0.0793255i | ||||
\(501\) | −10.2091 | + | 40.1462i | −0.456107 | + | 1.79360i | ||||
\(502\) | 3.83815 | − | 6.64786i | 0.171305 | − | 0.296709i | ||||
\(503\) | 44.4176 | 1.98048 | 0.990241 | − | 0.139366i | \(-0.0445066\pi\) | ||||
0.990241 | + | 0.139366i | \(0.0445066\pi\) | |||||||
\(504\) | −8.17431 | − | 4.44485i | −0.364113 | − | 0.197989i | ||||
\(505\) | 28.2682 | 1.25792 | ||||||||
\(506\) | 16.4263 | − | 28.4512i | 0.730238 | − | 1.26481i | ||||
\(507\) | −2.72534 | + | 0.767715i | −0.121037 | + | 0.0340954i | ||||
\(508\) | 0.979544 | + | 1.69662i | 0.0434602 | + | 0.0752753i | ||||
\(509\) | −21.3394 | − | 36.9609i | −0.945852 | − | 1.63826i | −0.754037 | − | 0.656832i | \(-0.771896\pi\) |
−0.191815 | − | 0.981431i | \(-0.561437\pi\) | |||||||
\(510\) | −6.90361 | − | 6.72937i | −0.305697 | − | 0.297981i | ||||
\(511\) | −0.979498 | + | 1.69654i | −0.0433304 | + | 0.0750505i | ||||
\(512\) | 25.4282 | 1.12378 | ||||||||
\(513\) | 2.89814 | − | 3.12935i | 0.127956 | − | 0.138164i | ||||
\(514\) | −36.8676 | −1.62616 | ||||||||
\(515\) | 17.5188 | − | 30.3435i | 0.771971 | − | 1.33709i | ||||
\(516\) | 0.388869 | + | 0.379054i | 0.0171190 | + | 0.0166869i | ||||
\(517\) | 14.8710 | + | 25.7573i | 0.654026 | + | 1.13281i | ||||
\(518\) | −2.98111 | − | 5.16344i | −0.130983 | − | 0.226868i | ||||
\(519\) | 36.3570 | − | 10.2416i | 1.59590 | − | 0.449556i | ||||
\(520\) | −13.9944 | + | 24.2391i | −0.613697 | + | 1.06295i | ||||
\(521\) | −30.0291 | −1.31560 | −0.657799 | − | 0.753194i | \(-0.728512\pi\) | ||||
−0.657799 | + | 0.753194i | \(0.728512\pi\) | |||||||
\(522\) | 4.14319 | − | 2.53542i | 0.181343 | − | 0.110972i | ||||
\(523\) | −20.0700 | −0.877599 | −0.438799 | − | 0.898585i | \(-0.644596\pi\) | ||||
−0.438799 | + | 0.898585i | \(0.644596\pi\) | |||||||
\(524\) | 1.81122 | − | 3.13713i | 0.0791237 | − | 0.137046i | ||||
\(525\) | −1.16157 | + | 4.56775i | −0.0506949 | + | 0.199353i | ||||
\(526\) | 17.0312 | + | 29.4989i | 0.742596 | + | 1.28621i | ||||
\(527\) | 1.49326 | + | 2.58641i | 0.0650475 | + | 0.112666i | ||||
\(528\) | 4.11587 | − | 16.1853i | 0.179120 | − | 0.704373i | ||||
\(529\) | −25.4085 | + | 44.0089i | −1.10472 | + | 1.91343i | ||||
\(530\) | 31.5784 | 1.37168 | ||||||||
\(531\) | 16.9703 | − | 10.3850i | 0.736450 | − | 0.450670i | ||||
\(532\) | −0.265674 | −0.0115184 | ||||||||
\(533\) | 10.5729 | − | 18.3128i | 0.457963 | − | 0.793214i | ||||
\(534\) | 33.0507 | − | 9.31021i | 1.43024 | − | 0.402892i | ||||
\(535\) | 14.1004 | + | 24.4227i | 0.609615 | + | 1.05588i | ||||
\(536\) | 17.3200 | + | 29.9992i | 0.748112 | + | 1.29577i | ||||
\(537\) | −8.59375 | − | 8.37685i | −0.370848 | − | 0.361488i | ||||
\(538\) | 10.9775 | − | 19.0136i | 0.473274 | − | 0.819734i | ||||
\(539\) | −17.4732 | −0.752625 | ||||||||
\(540\) | 1.33099 | + | 4.30059i | 0.0572767 | + | 0.185068i | ||||
\(541\) | 25.4769 | 1.09534 | 0.547669 | − | 0.836695i | \(-0.315515\pi\) | ||||
0.547669 | + | 0.836695i | \(0.315515\pi\) | |||||||
\(542\) | 9.71318 | − | 16.8237i | 0.417217 | − | 0.722641i | ||||
\(543\) | 13.6779 | + | 13.3327i | 0.586974 | + | 0.572159i | ||||
\(544\) | 1.36207 | + | 2.35917i | 0.0583982 | + | 0.101149i | ||||
\(545\) | −6.46656 | − | 11.2004i | −0.276997 | − | 0.479773i | ||||
\(546\) | 7.53480 | − | 2.12252i | 0.322460 | − | 0.0908353i | ||||
\(547\) | 12.7230 | − | 22.0368i | 0.543994 | − | 0.942226i | −0.454675 | − | 0.890657i | \(-0.650245\pi\) |
0.998669 | − | 0.0515683i | \(-0.0164220\pi\) | |||||||
\(548\) | 6.55629 | 0.280071 | ||||||||
\(549\) | 0.183807 | + | 0.0999464i | 0.00784469 | + | 0.00426561i | ||||
\(550\) | −10.0792 | −0.429779 | ||||||||
\(551\) | 0.511708 | − | 0.886305i | 0.0217995 | − | 0.0377579i | ||||
\(552\) | −11.0189 | + | 43.3308i | −0.468996 | + | 1.84428i | ||||
\(553\) | −3.60860 | − | 6.25028i | −0.153453 | − | 0.265789i | ||||
\(554\) | 0.603015 | + | 1.04445i | 0.0256196 | + | 0.0443745i | ||||
\(555\) | −5.24605 | + | 20.6296i | −0.222682 | + | 0.875677i | ||||
\(556\) | 3.48993 | − | 6.04474i | 0.148006 | − | 0.256354i | ||||
\(557\) | 43.3451 | 1.83659 | 0.918295 | − | 0.395898i | \(-0.129567\pi\) | ||||
0.918295 | + | 0.395898i | \(0.129567\pi\) | |||||||
\(558\) | 0.191722 | + | 7.49903i | 0.00811622 | + | 0.317459i | ||||
\(559\) | −3.37124 | −0.142588 | ||||||||
\(560\) | −4.67066 | + | 8.08982i | −0.197371 | + | 0.341857i | ||||
\(561\) | 7.61396 | − | 2.14481i | 0.321462 | − | 0.0905542i | ||||
\(562\) | 11.5568 | + | 20.0169i | 0.487492 | + | 0.844361i | ||||
\(563\) | 19.1697 | + | 33.2028i | 0.807905 | + | 1.39933i | 0.914312 | + | 0.405010i | \(0.132732\pi\) |
−0.106407 | + | 0.994323i | \(0.533935\pi\) | |||||||
\(564\) | −3.92800 | − | 3.82886i | −0.165399 | − | 0.161224i | ||||
\(565\) | −9.50281 | + | 16.4593i | −0.399786 | + | 0.692450i | ||||
\(566\) | −2.27783 | −0.0957445 | ||||||||
\(567\) | 4.22821 | − | 8.27298i | 0.177568 | − | 0.347433i | ||||
\(568\) | −17.6916 | −0.742325 | ||||||||
\(569\) | 2.85151 | − | 4.93897i | 0.119542 | − | 0.207052i | −0.800044 | − | 0.599941i | \(-0.795191\pi\) |
0.919586 | + | 0.392888i | \(0.128524\pi\) | |||||||
\(570\) | −3.65347 | − | 3.56125i | −0.153027 | − | 0.149165i | ||||
\(571\) | −21.5962 | − | 37.4056i | −0.903771 | − | 1.56538i | −0.822559 | − | 0.568680i | \(-0.807454\pi\) |
−0.0812121 | − | 0.996697i | \(-0.525879\pi\) | |||||||
\(572\) | −1.55611 | − | 2.69526i | −0.0650641 | − | 0.112694i | ||||
\(573\) | 42.1885 | − | 11.8843i | 1.76245 | − | 0.496473i | ||||
\(574\) | 4.20442 | − | 7.28227i | 0.175489 | − | 0.303956i | ||||
\(575\) | 22.6472 | 0.944452 | ||||||||
\(576\) | 0.677034 | + | 26.4816i | 0.0282098 | + | 1.10340i | ||||
\(577\) | 1.62734 | 0.0677469 | 0.0338735 | − | 0.999426i | \(-0.489216\pi\) | ||||
0.0338735 | + | 0.999426i | \(0.489216\pi\) | |||||||
\(578\) | −9.47632 | + | 16.4135i | −0.394163 | + | 0.682710i | ||||
\(579\) | 9.26975 | − | 36.4524i | 0.385238 | − | 1.51491i | ||||
\(580\) | 0.540098 | + | 0.935477i | 0.0224263 | + | 0.0388436i | ||||
\(581\) | −1.55791 | − | 2.69837i | −0.0646328 | − | 0.111947i | ||||
\(582\) | −2.14776 | + | 8.44585i | −0.0890274 | + | 0.350092i | ||||
\(583\) | −12.9551 | + | 22.4389i | −0.536546 | + | 0.929325i | ||||
\(584\) | 5.70144 | 0.235927 | ||||||||
\(585\) | −24.5525 | − | 13.3506i | −1.01512 | − | 0.551979i | ||||
\(586\) | 9.74075 | 0.402387 | ||||||||
\(587\) | 22.8904 | − | 39.6473i | 0.944786 | − | 1.63642i | 0.188607 | − | 0.982053i | \(-0.439603\pi\) |
0.756179 | − | 0.654365i | \(-0.227064\pi\) | |||||||
\(588\) | 3.10190 | − | 0.873789i | 0.127920 | − | 0.0360344i | ||||
\(589\) | 0.790251 | + | 1.36876i | 0.0325617 | + | 0.0563986i | ||||
\(590\) | −11.8995 | − | 20.6106i | −0.489896 | − | 0.848524i | ||||
\(591\) | −8.43239 | − | 8.21956i | −0.346862 | − | 0.338108i | ||||
\(592\) | −7.28181 | + | 12.6125i | −0.299281 | + | 0.518369i | ||||
\(593\) | 22.1612 | 0.910051 | 0.455026 | − | 0.890478i | \(-0.349630\pi\) | ||||
0.455026 | + | 0.890478i | \(0.349630\pi\) | |||||||
\(594\) | 19.3749 | + | 4.40301i | 0.794961 | + | 0.180658i | ||||
\(595\) | −4.42460 | −0.181391 | ||||||||
\(596\) | 1.98446 | − | 3.43718i | 0.0812865 | − | 0.140792i | ||||
\(597\) | −33.8360 | − | 32.9820i | −1.38482 | − | 1.34987i | ||||
\(598\) | −18.8074 | − | 32.5753i | −0.769091 | − | 1.33210i | ||||
\(599\) | 16.3016 | + | 28.2351i | 0.666063 | + | 1.15366i | 0.978996 | + | 0.203880i | \(0.0653554\pi\) |
−0.312932 | + | 0.949775i | \(0.601311\pi\) | |||||||
\(600\) | 13.2032 | − | 3.71927i | 0.539018 | − | 0.151839i | ||||
\(601\) | −0.818207 | + | 1.41718i | −0.0333753 | + | 0.0578078i | −0.882231 | − | 0.470818i | \(-0.843959\pi\) |
0.848855 | + | 0.528625i | \(0.177292\pi\) | |||||||
\(602\) | −1.34061 | −0.0546392 | ||||||||
\(603\) | −29.5030 | + | 18.0543i | −1.20146 | + | 0.735230i | ||||
\(604\) | 1.18453 | 0.0481977 | ||||||||
\(605\) | −3.21968 | + | 5.57666i | −0.130899 | + | 0.226723i | ||||
\(606\) | −5.67090 | + | 22.3003i | −0.230365 | + | 0.905887i | ||||
\(607\) | −4.95802 | − | 8.58754i | −0.201240 | − | 0.348557i | 0.747688 | − | 0.664050i | \(-0.231164\pi\) |
−0.948928 | + | 0.315492i | \(0.897830\pi\) | |||||||
\(608\) | 0.720822 | + | 1.24850i | 0.0292332 | + | 0.0506334i | ||||
\(609\) | 0.549418 | − | 2.16053i | 0.0222635 | − | 0.0875492i | ||||
\(610\) | 0.125135 | − | 0.216740i | 0.00506657 | − | 0.00877555i | ||||
\(611\) | 34.0533 | 1.37765 | ||||||||
\(612\) | −1.24440 | + | 0.761507i | −0.0503017 | + | 0.0307821i | ||||
\(613\) | 26.3963 | 1.06614 | 0.533068 | − | 0.846072i | \(-0.321039\pi\) | ||||
0.533068 | + | 0.846072i | \(0.321039\pi\) | |||||||
\(614\) | 15.9459 | − | 27.6190i | 0.643523 | − | 1.11461i | ||||
\(615\) | −28.8964 | + | 8.13997i | −1.16522 | + | 0.328235i | ||||
\(616\) | −4.56614 | − | 7.90879i | −0.183975 | − | 0.318654i | ||||
\(617\) | 9.98736 | + | 17.2986i | 0.402076 | + | 0.696416i | 0.993976 | − | 0.109595i | \(-0.0349555\pi\) |
−0.591900 | + | 0.806011i | \(0.701622\pi\) | |||||||
\(618\) | 20.4230 | + | 19.9075i | 0.821532 | + | 0.800797i | ||||
\(619\) | −18.0421 | + | 31.2499i | −0.725174 | + | 1.25604i | 0.233728 | + | 0.972302i | \(0.424907\pi\) |
−0.958902 | + | 0.283737i | \(0.908426\pi\) | |||||||
\(620\) | −1.66819 | −0.0669960 | ||||||||
\(621\) | −43.5337 | − | 9.89320i | −1.74695 | − | 0.397000i | ||||
\(622\) | 24.3128 | 0.974855 | ||||||||
\(623\) | 7.87943 | − | 13.6476i | 0.315683 | − | 0.546779i | ||||
\(624\) | −13.6924 | − | 13.3468i | −0.548135 | − | 0.534300i | ||||
\(625\) | 15.6158 | + | 27.0473i | 0.624630 | + | 1.08189i | ||||
\(626\) | −0.713309 | − | 1.23549i | −0.0285096 | − | 0.0493800i | ||||
\(627\) | 4.02939 | − | 1.13506i | 0.160919 | − | 0.0453299i | ||||
\(628\) | 0.513597 | − | 0.889576i | 0.0204947 | − | 0.0354979i | ||||
\(629\) | −6.89819 | −0.275049 | ||||||||
\(630\) | −9.76354 | − | 5.30900i | −0.388989 | − | 0.211516i | ||||
\(631\) | −46.6716 | −1.85797 | −0.928984 | − | 0.370120i | \(-0.879317\pi\) | ||||
−0.928984 | + | 0.370120i | \(0.879317\pi\) | |||||||
\(632\) | −10.5024 | + | 18.1908i | −0.417765 | + | 0.723590i | ||||
\(633\) | −6.73176 | + | 26.4720i | −0.267564 | + | 1.05217i | ||||
\(634\) | 1.63446 | + | 2.83097i | 0.0649128 | + | 0.112432i | ||||
\(635\) | 8.63332 | + | 14.9534i | 0.342603 | + | 0.593406i | ||||
\(636\) | 1.17772 | − | 4.63127i | 0.0466997 | − | 0.183642i | ||||
\(637\) | −10.0030 | + | 17.3257i | −0.396334 | + | 0.686471i | ||||
\(638\) | 4.76744 | 0.188745 | ||||||||
\(639\) | −0.451491 | − | 17.6597i | −0.0178607 | − | 0.698607i | ||||
\(640\) | 21.9809 | 0.868871 | ||||||||
\(641\) | 0.383789 | − | 0.664742i | 0.0151588 | − | 0.0262557i | −0.858347 | − | 0.513070i | \(-0.828508\pi\) |
0.873505 | + | 0.486815i | \(0.161841\pi\) | |||||||
\(642\) | −22.0953 | + | 6.22414i | −0.872033 | + | 0.245647i | ||||
\(643\) | −14.4053 | − | 24.9507i | −0.568090 | − | 0.983960i | −0.996755 | − | 0.0804966i | \(-0.974349\pi\) |
0.428665 | − | 0.903463i | \(-0.358984\pi\) | |||||||
\(644\) | 1.39040 | + | 2.40824i | 0.0547893 | + | 0.0948979i | ||||
\(645\) | 3.42734 | + | 3.34083i | 0.134951 | + | 0.131545i | ||||
\(646\) | 0.826700 | − | 1.43189i | 0.0325261 | − | 0.0563368i | ||||
\(647\) | −5.46805 | −0.214971 | −0.107486 | − | 0.994207i | \(-0.534280\pi\) | ||||
−0.107486 | + | 0.994207i | \(0.534280\pi\) | |||||||
\(648\) | −27.0047 | + | 1.38172i | −1.06084 | + | 0.0542789i | ||||
\(649\) | 19.5272 | 0.766511 | ||||||||
\(650\) | −5.77012 | + | 9.99415i | −0.226323 | + | 0.392003i | ||||
\(651\) | 2.46533 | + | 2.40311i | 0.0966240 | + | 0.0941852i | ||||
\(652\) | −0.462378 | − | 0.800861i | −0.0181081 | − | 0.0313642i | ||||
\(653\) | −2.85758 | − | 4.94948i | −0.111826 | − | 0.193688i | 0.804681 | − | 0.593708i | \(-0.202337\pi\) |
−0.916506 | + | 0.400020i | \(0.869003\pi\) | |||||||
\(654\) | 10.1331 | − | 2.85443i | 0.396234 | − | 0.111617i | ||||
\(655\) | 15.9634 | − | 27.6495i | 0.623743 | − | 1.08035i | ||||
\(656\) | −20.5398 | −0.801946 | ||||||||
\(657\) | 0.145501 | + | 5.69115i | 0.00567653 | + | 0.222033i | ||||
\(658\) | 13.5416 | 0.527908 | ||||||||
\(659\) | −18.2149 | + | 31.5491i | −0.709552 | + | 1.22898i | 0.255471 | + | 0.966817i | \(0.417769\pi\) |
−0.965023 | + | 0.262163i | \(0.915564\pi\) | |||||||
\(660\) | −1.08895 | + | 4.28217i | −0.0423871 | + | 0.166683i | ||||
\(661\) | 9.85404 | + | 17.0677i | 0.383278 | + | 0.663856i | 0.991529 | − | 0.129888i | \(-0.0414619\pi\) |
−0.608251 | + | 0.793745i | \(0.708129\pi\) | |||||||
\(662\) | −8.79176 | − | 15.2278i | −0.341701 | − | 0.591844i | ||||
\(663\) | 2.23211 | − | 8.77756i | 0.0866879 | − | 0.340892i | ||||
\(664\) | −4.53411 | + | 7.85331i | −0.175958 | + | 0.304768i | ||||
\(665\) | −2.34155 | −0.0908013 | ||||||||
\(666\) | −15.2219 | − | 8.27703i | −0.589836 | − | 0.320728i | ||||
\(667\) | −10.7120 | −0.414772 | ||||||||
\(668\) | 3.74919 | − | 6.49379i | 0.145061 | − | 0.251252i | ||||
\(669\) | 35.3291 | − | 9.95203i | 1.36590 | − | 0.384768i | ||||
\(670\) | 20.6874 | + | 35.8316i | 0.799223 | + | 1.38429i | ||||
\(671\) | 0.102674 | + | 0.177836i | 0.00396368 | + | 0.00686530i | ||||
\(672\) | 2.24874 | + | 2.19198i | 0.0867469 | + | 0.0845574i | ||||
\(673\) | 1.68997 | − | 2.92712i | 0.0651437 | − | 0.112832i | −0.831614 | − | 0.555354i | \(-0.812583\pi\) |
0.896758 | + | 0.442522i | \(0.145916\pi\) | |||||||
\(674\) | 3.17075 | 0.122133 | ||||||||
\(675\) | 4.04950 | + | 13.0844i | 0.155865 | + | 0.503620i | ||||
\(676\) | 0.512530 | 0.0197127 | ||||||||
\(677\) | 8.48897 | − | 14.7033i | 0.326258 | − | 0.565095i | −0.655508 | − | 0.755188i | \(-0.727546\pi\) |
0.981766 | + | 0.190093i | \(0.0608790\pi\) | |||||||
\(678\) | −11.0781 | − | 10.7985i | −0.425453 | − | 0.414714i | ||||
\(679\) | 1.99979 | + | 3.46373i | 0.0767447 | + | 0.132926i | ||||
\(680\) | 6.43866 | + | 11.1521i | 0.246911 | + | 0.427663i | ||||
\(681\) | 2.59077 | − | 0.729808i | 0.0992786 | − | 0.0279663i | ||||
\(682\) | −3.68127 | + | 6.37615i | −0.140963 | + | 0.244155i | ||||
\(683\) | −10.3202 | −0.394890 | −0.197445 | − | 0.980314i | \(-0.563264\pi\) | ||||
−0.197445 | + | 0.980314i | \(0.563264\pi\) | |||||||
\(684\) | −0.658548 | + | 0.402998i | −0.0251802 | + | 0.0154090i | ||||
\(685\) | 57.7846 | 2.20784 | ||||||||
\(686\) | −8.66994 | + | 15.0168i | −0.331020 | + | 0.573343i | ||||
\(687\) | −0.845572 | + | 3.32513i | −0.0322606 | + | 0.126862i | ||||
\(688\) | 1.63732 | + | 2.83592i | 0.0624223 | + | 0.108119i | ||||
\(689\) | 14.8330 | + | 25.6915i | 0.565093 | + | 0.978770i | ||||
\(690\) | −13.1612 | + | 51.7551i | −0.501037 | + | 1.97028i | ||||
\(691\) | −2.11921 | + | 3.67057i | −0.0806184 | + | 0.139635i | −0.903516 | − | 0.428555i | \(-0.859023\pi\) |
0.822897 | + | 0.568190i | \(0.192356\pi\) | |||||||
\(692\) | −6.83733 | −0.259916 | ||||||||
\(693\) | 7.77798 | − | 4.75973i | 0.295461 | − | 0.180807i | ||||
\(694\) | −2.44064 | −0.0926453 | ||||||||
\(695\) | 30.7589 | − | 53.2760i | 1.16675 | − | 2.02087i | ||||
\(696\) | −6.24507 | + | 1.75920i | −0.236719 | + | 0.0666825i | ||||
\(697\) | −4.86444 | − | 8.42546i | −0.184254 | − | 0.319137i | ||||
\(698\) | 15.6725 | + | 27.1456i | 0.593214 | + | 1.02748i | ||||
\(699\) | 31.6759 | + | 30.8764i | 1.19809 | + | 1.16785i | ||||
\(700\) | 0.426576 | − | 0.738850i | 0.0161230 | − | 0.0279259i | ||||
\(701\) | −4.89904 | −0.185034 | −0.0925171 | − | 0.995711i | \(-0.529491\pi\) | ||||
−0.0925171 | + | 0.995711i | \(0.529491\pi\) | |||||||
\(702\) | 15.4575 | − | 16.6907i | 0.583407 | − | 0.629951i | ||||
\(703\) | −3.65060 | −0.137685 | ||||||||
\(704\) | −12.9998 | + | 22.5163i | −0.489949 | + | 0.848617i | ||||
\(705\) | −34.6199 | − | 33.7461i | −1.30386 | − | 1.27095i | ||||
\(706\) | −8.80111 | − | 15.2440i | −0.331234 | − | 0.573715i | ||||
\(707\) | 5.28020 | + | 9.14558i | 0.198582 | + | 0.343955i | ||||
\(708\) | −3.46653 | + | 0.976504i | −0.130280 | + | 0.0366993i | ||||
\(709\) | 17.1625 | − | 29.7264i | 0.644552 | − | 1.11640i | −0.339853 | − | 0.940479i | \(-0.610377\pi\) |
0.984405 | − | 0.175918i | \(-0.0562894\pi\) | |||||||
\(710\) | −21.1312 | −0.793041 | ||||||||
\(711\) | −18.4259 | − | 10.0192i | −0.691027 | − | 0.375751i | ||||
\(712\) | −45.8644 | −1.71884 | ||||||||
\(713\) | 8.27151 | − | 14.3267i | 0.309770 | − | 0.536538i | ||||
\(714\) | 0.887622 | − | 3.49049i | 0.0332184 | − | 0.130628i | ||||
\(715\) | −13.7149 | − | 23.7549i | −0.512909 | − | 0.888385i | ||||
\(716\) | 1.08619 | + | 1.88133i | 0.0405927 | + | 0.0703086i | ||||
\(717\) | 6.81985 | − | 26.8184i | 0.254692 | − | 1.00155i | ||||
\(718\) | −2.26801 | + | 3.92831i | −0.0846413 | + | 0.146603i | ||||
\(719\) | −13.6554 | −0.509260 | −0.254630 | − | 0.967039i | \(-0.581954\pi\) | ||||
−0.254630 | + | 0.967039i | \(0.581954\pi\) | |||||||
\(720\) | 0.693810 | + | 27.1378i | 0.0258568 | + | 1.01137i | ||||
\(721\) | 13.0893 | 0.487471 | ||||||||
\(722\) | −11.8996 | + | 20.6107i | −0.442857 | + | 0.767051i | ||||
\(723\) | −16.1969 | + | 4.56258i | −0.602369 | + | 0.169684i | ||||
\(724\) | −1.72878 | − | 2.99434i | −0.0642497 | − | 0.111284i | ||||
\(725\) | 1.64323 | + | 2.84616i | 0.0610282 | + | 0.105704i | ||||
\(726\) | −3.75342 | − | 3.65869i | −0.139303 | − | 0.135787i | ||||
\(727\) | −19.1619 | + | 33.1895i | −0.710677 | + | 1.23093i | 0.253926 | + | 0.967224i | \(0.418278\pi\) |
−0.964603 | + | 0.263705i | \(0.915055\pi\) | |||||||
\(728\) | −10.4561 | −0.387527 | ||||||||
\(729\) | −2.06838 | − | 26.9207i | −0.0766067 | − | 0.997061i | ||||
\(730\) | 6.80990 | 0.252046 | ||||||||
\(731\) | −0.775532 | + | 1.34326i | −0.0286841 | + | 0.0496823i | ||||
\(732\) | −0.0271201 | − | 0.0264356i | −0.00100239 | − | 0.000977088i | ||||
\(733\) | −2.13197 | − | 3.69269i | −0.0787463 | − | 0.136393i | 0.823963 | − | 0.566644i | \(-0.191758\pi\) |
−0.902709 | + | 0.430251i | \(0.858425\pi\) | |||||||
\(734\) | 18.9571 | + | 32.8346i | 0.699718 | + | 1.21195i | ||||
\(735\) | 27.3389 | − | 7.70123i | 1.00841 | − | 0.284064i | ||||
\(736\) | 7.54480 | − | 13.0680i | 0.278105 | − | 0.481692i | ||||
\(737\) | −33.9482 | −1.25050 | ||||||||
\(738\) | −0.624551 | − | 24.4288i | −0.0229900 | − | 0.899237i | ||||
\(739\) | −33.6314 | −1.23715 | −0.618576 | − | 0.785725i | \(-0.712290\pi\) | ||||
−0.618576 | + | 0.785725i | \(0.712290\pi\) | |||||||
\(740\) | 1.92657 | − | 3.33691i | 0.0708220 | − | 0.122667i | ||||
\(741\) | 1.18126 | − | 4.64518i | 0.0433946 | − | 0.170645i | ||||
\(742\) | 5.89851 | + | 10.2165i | 0.216541 | + | 0.375060i | ||||
\(743\) | −8.45867 | − | 14.6508i | −0.310318 | − | 0.537487i | 0.668113 | − | 0.744060i | \(-0.267102\pi\) |
−0.978431 | + | 0.206573i | \(0.933769\pi\) | |||||||
\(744\) | 2.46943 | − | 9.71079i | 0.0905336 | − | 0.356015i | ||||
\(745\) | 17.4902 | − | 30.2939i | 0.640792 | − | 1.10988i | ||||
\(746\) | 7.68266 | 0.281282 | ||||||||
\(747\) | −7.95484 | − | 4.32551i | −0.291052 | − | 0.158262i | ||||
\(748\) | −1.43189 | −0.0523550 | ||||||||
\(749\) | −5.26762 | + | 9.12379i | −0.192475 | + | 0.333376i | ||||
\(750\) | −14.1435 | + | 3.98417i | −0.516449 | + | 0.145481i | ||||
\(751\) | 4.64235 | + | 8.04079i | 0.169402 | + | 0.293412i | 0.938210 | − | 0.346067i | \(-0.112483\pi\) |
−0.768808 | + | 0.639480i | \(0.779150\pi\) | |||||||
\(752\) | −16.5387 | − | 28.6459i | −0.603106 | − | 1.04461i | ||||
\(753\) | −7.33141 | − | 7.14637i | −0.267172 | − | 0.260428i | ||||
\(754\) | 2.72925 | − | 4.72720i | 0.0993935 | − | 0.172155i | ||||
\(755\) | 10.4400 | 0.379949 | ||||||||
\(756\) | −1.14275 | + | 1.23392i | −0.0415614 | + | 0.0448771i | ||||
\(757\) | −34.5024 | −1.25401 | −0.627005 | − | 0.779015i | \(-0.715719\pi\) | ||||
−0.627005 | + | 0.779015i | \(0.715719\pi\) | |||||||
\(758\) | 5.23505 | − | 9.06737i | 0.190146 | − | 0.329342i | ||||
\(759\) | −31.3766 | − | 30.5847i | −1.13890 | − | 1.11015i | ||||
\(760\) | 3.40741 | + | 5.90181i | 0.123600 | + | 0.214081i | ||||
\(761\) | 7.97924 | + | 13.8204i | 0.289247 | + | 0.500991i | 0.973630 | − | 0.228132i | \(-0.0732617\pi\) |
−0.684383 | + | 0.729123i | \(0.739928\pi\) | |||||||
\(762\) | −13.5284 | + | 3.81087i | −0.490081 | + | 0.138053i | ||||
\(763\) | 2.41577 | − | 4.18424i | 0.0874567 | − | 0.151480i | ||||
\(764\) | −7.93401 | −0.287042 | ||||||||
\(765\) | −10.9676 | + | 6.71163i | −0.396535 | + | 0.242660i | ||||
\(766\) | −6.02341 | −0.217635 | ||||||||
\(767\) | 11.1789 | − | 19.3624i | 0.403647 | − | 0.699136i | ||||
\(768\) | 3.12900 | − | 12.3045i | 0.112908 | − | 0.444000i | ||||
\(769\) | 7.85906 | + | 13.6123i | 0.283405 | + | 0.490872i | 0.972221 | − | 0.234064i | \(-0.0752026\pi\) |
−0.688816 | + | 0.724936i | \(0.741869\pi\) | |||||||
\(770\) | −5.45388 | − | 9.44640i | −0.196544 | − | 0.340425i | ||||
\(771\) | −12.1185 | + | 47.6550i | −0.436439 | + | 1.71625i | ||||
\(772\) | −3.40424 | + | 5.89631i | −0.122521 | + | 0.212213i | ||||
\(773\) | 0.818514 | 0.0294399 | 0.0147200 | − | 0.999892i | \(-0.495314\pi\) | ||||
0.0147200 | + | 0.999892i | \(0.495314\pi\) | |||||||
\(774\) | −3.32308 | + | 2.03356i | −0.119446 | + | 0.0730947i | ||||
\(775\) | −5.07542 | −0.182314 | ||||||||
\(776\) | 5.82016 | − | 10.0808i | 0.208931 | − | 0.361880i | ||||
\(777\) | −7.65417 | + | 2.15614i | −0.274592 | + | 0.0773511i | ||||
\(778\) | −11.7786 | − | 20.4011i | −0.422283 | − | 0.731415i | ||||
\(779\) | −2.57432 | − | 4.45885i | −0.0922345 | − | 0.159755i | ||||
\(780\) | 3.62263 | + | 3.53120i | 0.129711 | + | 0.126437i | ||||
\(781\) | 8.66914 | − | 15.0154i | 0.310206 | − | 0.537293i | ||||
\(782\) | −17.3060 | −0.618863 | ||||||||
\(783\) | −1.91540 | − | 6.18890i | −0.0684509 | − | 0.221173i | ||||
\(784\) | 19.4328 | 0.694028 | ||||||||
\(785\) | 4.52664 | − | 7.84037i | 0.161563 | − | 0.279835i | ||||
\(786\) | 18.6097 | + | 18.1400i | 0.663787 | + | 0.647034i | ||||
\(787\) | −18.3210 | − | 31.7329i | −0.653074 | − | 1.13116i | −0.982373 | − | 0.186932i | \(-0.940146\pi\) |
0.329299 | − | 0.944226i | \(-0.393188\pi\) | |||||||
\(788\) | 1.06579 | + | 1.84601i | 0.0379673 | + | 0.0657612i | ||||
\(789\) | 43.7285 | − | 12.3181i | 1.55678 | − | 0.438536i | ||||
\(790\) | −12.5443 | + | 21.7274i | −0.446306 | + | 0.773025i | ||||
\(791\) | −7.10009 | −0.252450 | ||||||||
\(792\) | −23.3152 | − | 12.6778i | −0.828471 | − | 0.450488i | ||||
\(793\) | 0.235114 | 0.00834914 | ||||||||
\(794\) | 21.0972 | − | 36.5414i | 0.748712 | − | 1.29681i | ||||
\(795\) | 10.3800 | − | 40.8183i | 0.368140 | − | 1.44767i | ||||
\(796\) | 4.27663 | + | 7.40733i | 0.151581 | + | 0.262546i | ||||
\(797\) | −6.01770 | − | 10.4230i | −0.213158 | − | 0.369200i | 0.739543 | − | 0.673109i | \(-0.235042\pi\) |
−0.952701 | + | 0.303909i | \(0.901708\pi\) | |||||||
\(798\) | 0.469739 | − | 1.84720i | 0.0166286 | − | 0.0653903i | ||||
\(799\) | 7.83372 | − | 13.5684i | 0.277137 | − | 0.480016i | ||||
\(800\) | −4.62951 | −0.163678 | ||||||||
\(801\) | −1.17046 | − | 45.7816i | −0.0413562 | − | 1.61761i | ||||
\(802\) | −6.43367 | −0.227181 | ||||||||
\(803\) | −2.79378 | + | 4.83897i | −0.0985904 | + | 0.170764i | ||||
\(804\) | 6.02658 | − | 1.69766i | 0.212541 | − | 0.0598718i | ||||
\(805\) | 12.2544 | + | 21.2253i | 0.431912 | + | 0.748093i | ||||
\(806\) | 4.21489 | + | 7.30040i | 0.148463 | + | 0.257146i | ||||
\(807\) | −20.9686 | − | 20.4394i | −0.738130 | − | 0.719500i | ||||
\(808\) | 15.3674 | − | 26.6172i | 0.540625 | − | 0.936390i | ||||
\(809\) | −8.87248 | −0.311940 | −0.155970 | − | 0.987762i | \(-0.549850\pi\) | ||||
−0.155970 | + | 0.987762i | \(0.549850\pi\) | |||||||
\(810\) | −32.2549 | + | 1.65035i | −1.13332 | + | 0.0579873i | ||||
\(811\) | 9.69230 | 0.340343 | 0.170171 | − | 0.985414i | \(-0.445568\pi\) | ||||
0.170171 | + | 0.985414i | \(0.445568\pi\) | |||||||
\(812\) | −0.201769 | + | 0.349474i | −0.00708070 | + | 0.0122641i | ||||
\(813\) | −18.5536 | − | 18.0853i | −0.650702 | − | 0.634279i | ||||
\(814\) | −8.50290 | − | 14.7275i | −0.298027 | − | 0.516197i | ||||
\(815\) | −4.07522 | − | 7.05848i | −0.142749 | − | 0.247248i | ||||
\(816\) | −8.46784 | + | 2.38535i | −0.296434 | + | 0.0835039i | ||||
\(817\) | −0.410420 | + | 0.710869i | −0.0143588 | + | 0.0248701i | ||||
\(818\) | −35.2804 | −1.23355 | ||||||||
\(819\) | −0.266839 | − | 10.4372i | −0.00932409 | − | 0.364704i | ||||
\(820\) | 5.43428 | 0.189773 | ||||||||
\(821\) | −5.13985 | + | 8.90248i | −0.179382 | + | 0.310699i | −0.941669 | − | 0.336540i | \(-0.890743\pi\) |
0.762287 | + | 0.647239i | \(0.224076\pi\) | |||||||
\(822\) | −11.5922 | + | 45.5852i | −0.404325 | + | 1.58997i | ||||
\(823\) | −20.9587 | − | 36.3015i | −0.730573 | − | 1.26539i | −0.956639 | − | 0.291277i | \(-0.905920\pi\) |
0.226066 | − | 0.974112i | \(-0.427413\pi\) | |||||||
\(824\) | −19.0475 | − | 32.9912i | −0.663551 | − | 1.14930i | ||||
\(825\) | −3.31309 | + | 13.0284i | −0.115347 | + | 0.453591i | ||||
\(826\) | 4.44541 | − | 7.69967i | 0.154675 | − | 0.267906i | ||||
\(827\) | 27.5477 | 0.957927 | 0.478963 | − | 0.877835i | \(-0.341013\pi\) | ||||
0.478963 | + | 0.877835i | \(0.341013\pi\) | |||||||
\(828\) | 7.09953 | + | 3.86042i | 0.246726 | + | 0.134159i | ||||
\(829\) | −23.3262 | −0.810154 | −0.405077 | − | 0.914283i | \(-0.632755\pi\) | ||||
−0.405077 | + | 0.914283i | \(0.632755\pi\) | |||||||
\(830\) | −5.41562 | + | 9.38014i | −0.187979 | + | 0.325589i | ||||
\(831\) | 1.54827 | − | 0.436140i | 0.0537090 | − | 0.0151295i | ||||
\(832\) | 14.8842 | + | 25.7802i | 0.516017 | + | 0.893767i | ||||
\(833\) | 4.60226 | + | 7.97134i | 0.159459 | + | 0.276191i | ||||
\(834\) | 35.8579 | + | 34.9529i | 1.24166 | + | 1.21032i | ||||
\(835\) | 33.0439 | − | 57.2338i | 1.14353 | − | 1.98066i | ||||
\(836\) | −0.757771 | −0.0262081 | ||||||||
\(837\) | 9.75627 | + | 2.21715i | 0.337226 | + | 0.0766359i | ||||
\(838\) | −1.53547 | −0.0530421 | ||||||||
\(839\) | −4.31079 | + | 7.46651i | −0.148825 | + | 0.257773i | −0.930793 | − | 0.365545i | \(-0.880882\pi\) |
0.781968 | + | 0.623318i | \(0.214216\pi\) | |||||||
\(840\) | 10.6300 | + | 10.3617i | 0.366771 | + | 0.357514i | ||||
\(841\) | 13.7228 | + | 23.7685i | 0.473198 | + | 0.819604i | ||||
\(842\) | 16.7355 | + | 28.9868i | 0.576745 | + | 0.998951i | ||||
\(843\) | 29.6726 | − | 8.35862i | 1.02198 | − | 0.287886i | ||||
\(844\) | 2.47218 | − | 4.28195i | 0.0850961 | − | 0.147391i | ||||
\(845\) | 4.51724 | 0.155398 | ||||||||
\(846\) | 33.5668 | − | 20.5412i | 1.15405 | − | 0.706220i | ||||
\(847\) | −2.40561 | −0.0826577 | ||||||||
\(848\) | 14.4080 | − | 24.9554i | 0.494772 | − | 0.856971i | ||||
\(849\) | −0.748735 | + | 2.94433i | −0.0256965 | + | 0.101049i | ||||
\(850\) | 2.65476 | + | 4.59817i | 0.0910574 | + | 0.157716i | ||||
\(851\) | 19.1053 | + | 33.0914i | 0.654922 | + | 1.13436i | ||||
\(852\) | −0.788091 | + | 3.09909i | −0.0269996 | + | 0.106173i | ||||
\(853\) | −21.3858 | + | 37.0412i | −0.732235 | + | 1.26827i | 0.223691 | + | 0.974660i | \(0.428189\pi\) |
−0.955926 | + | 0.293608i | \(0.905144\pi\) | |||||||
\(854\) | 0.0934955 | 0.00319935 | ||||||||
\(855\) | −5.80419 | + | 3.55187i | −0.198499 | + | 0.121471i | ||||
\(856\) | 30.6617 | 1.04799 | ||||||||
\(857\) | −22.2710 | + | 38.5744i | −0.760762 | + | 1.31768i | 0.181697 | + | 0.983355i | \(0.441841\pi\) |
−0.942458 | + | 0.334323i | \(0.891492\pi\) | |||||||
\(858\) | 21.4912 | − | 6.05396i | 0.733698 | − | 0.206679i | ||||
\(859\) | 15.9851 | + | 27.6871i | 0.545406 | + | 0.944671i | 0.998581 | + | 0.0532497i | \(0.0169579\pi\) |
−0.453175 | + | 0.891422i | \(0.649709\pi\) | |||||||
\(860\) | −0.433190 | − | 0.750307i | −0.0147717 | − | 0.0255853i | ||||
\(861\) | −8.03105 | − | 7.82835i | −0.273697 | − | 0.266789i | ||||
\(862\) | −6.10181 | + | 10.5687i | −0.207829 | + | 0.359970i | ||||
\(863\) | −39.0037 | −1.32770 | −0.663851 | − | 0.747865i | \(-0.731079\pi\) | ||||
−0.663851 | + | 0.747865i | \(0.731079\pi\) | |||||||
\(864\) | 8.89912 | + | 2.02236i | 0.302754 | + | 0.0688020i | ||||
\(865\) | −60.2616 | −2.04896 | ||||||||
\(866\) | −14.0085 | + | 24.2634i | −0.476028 | + | 0.824504i | ||||
\(867\) | 18.1011 | + | 17.6443i | 0.614747 | + | 0.599231i | ||||
\(868\) | −0.311600 | − | 0.539706i | −0.0105764 | − | 0.0183188i | ||||
\(869\) | −10.2927 | − | 17.8274i | −0.349155 | − | 0.604754i | ||||
\(870\) | −7.45922 | + | 2.10123i | −0.252891 | + | 0.0712382i | ||||
\(871\) | −19.4346 | + | 33.6617i | −0.658515 | + | 1.14058i | ||||
\(872\) | −14.0617 | −0.476188 | ||||||||
\(873\) | 10.2111 | + | 5.55238i | 0.345594 | + | 0.187920i | ||||
\(874\) | −9.15855 | −0.309792 | ||||||||
\(875\) | −3.37189 | + | 5.84028i | −0.113991 | + | 0.197437i | ||||
\(876\) | 0.253976 | − | 0.998737i | 0.00858106 | − | 0.0337442i | ||||
\(877\) | 25.0560 | + | 43.3983i | 0.846082 | + | 1.46546i | 0.884678 | + | 0.466202i | \(0.154378\pi\) |
−0.0385964 | + | 0.999255i | \(0.512289\pi\) | |||||||
\(878\) | 1.36263 | + | 2.36014i | 0.0459865 | + | 0.0796510i | ||||
\(879\) | 3.20183 | − | 12.5909i | 0.107995 | − | 0.424680i | ||||
\(880\) | −13.3219 | + | 23.0743i | −0.449082 | + | 0.777833i | ||||
\(881\) | −30.9354 | −1.04224 | −0.521120 | − | 0.853483i | \(-0.674486\pi\) | ||||
−0.521120 | + | 0.853483i | \(0.674486\pi\) | |||||||
\(882\) | 0.590889 | + | 23.1121i | 0.0198963 | + | 0.778226i | ||||
\(883\) | 35.3840 | 1.19077 | 0.595383 | − | 0.803442i | \(-0.297000\pi\) | ||||
0.595383 | + | 0.803442i | \(0.297000\pi\) | |||||||
\(884\) | −0.819723 | + | 1.41980i | −0.0275703 | + | 0.0477531i | ||||
\(885\) | −30.5527 | + | 8.60653i | −1.02702 | + | 0.289305i | ||||
\(886\) | 23.6435 | + | 40.9517i | 0.794318 | + | 1.37580i | ||||
\(887\) | −24.4733 | − | 42.3890i | −0.821733 | − | 1.42328i | −0.904391 | − | 0.426705i | \(-0.859674\pi\) |
0.0826579 | − | 0.996578i | \(-0.473659\pi\) | |||||||
\(888\) | 16.5728 | + | 16.1545i | 0.556147 | + | 0.542110i | ||||
\(889\) | −3.22522 | + | 5.58625i | −0.108171 | + | 0.187357i | ||||
\(890\) | −54.7813 | −1.83627 | ||||||||
\(891\) | 12.0599 | − | 23.5967i | 0.404023 | − | 0.790518i | ||||
\(892\) | −6.64402 | −0.222458 | ||||||||
\(893\) | 4.14569 | − | 7.18055i | 0.138730 | − | 0.240288i | ||||
\(894\) | 20.3896 | + | 19.8750i | 0.681931 | + | 0.664719i | ||||
\(895\) | 9.57322 | + | 16.5813i | 0.319998 | + | 0.554252i | ||||
\(896\) | 4.10580 | + | 7.11145i | 0.137165 | + | 0.237577i | ||||
\(897\) | −48.2889 | + | 13.6027i | −1.61232 | + | 0.454183i | ||||
\(898\) | 5.05681 | − | 8.75865i | 0.168748 | − | 0.292280i | ||||
\(899\) | 2.40066 | 0.0800664 | ||||||||
\(900\) | −0.0633662 | − | 2.47852i | −0.00211221 | − | 0.0826173i | ||||
\(901\) | 13.6489 | 0.454712 | ||||||||
\(902\) | 11.9921 | − | 20.7709i | 0.399293 | − | 0.691596i | ||||
\(903\) | −0.440665 | + | 1.73287i | −0.0146644 | + | 0.0576664i | ||||
\(904\) | 10.3320 | + | 17.8956i | 0.343638 | + | 0.595198i | ||||
\(905\) | −15.2368 | − | 26.3909i | −0.506489 | − | 0.877265i | ||||
\(906\) | −2.09437 | + | 8.23590i | −0.0695807 | + | 0.273619i | ||||
\(907\) | −14.1919 | + | 24.5811i | −0.471234 | + | 0.816202i | −0.999459 | − | 0.0329029i | \(-0.989525\pi\) |
0.528224 | + | 0.849105i | \(0.322858\pi\) | |||||||
\(908\) | −0.487223 | −0.0161691 | ||||||||
\(909\) | 26.9613 | + | 14.6604i | 0.894250 | + | 0.486256i | ||||
\(910\) | −12.4889 | −0.414003 | ||||||||
\(911\) | −2.89932 | + | 5.02177i | −0.0960588 | + | 0.166379i | −0.910050 | − | 0.414499i | \(-0.863957\pi\) |
0.813991 | + | 0.580877i | \(0.197290\pi\) | |||||||
\(912\) | −4.48128 | + | 1.26235i | −0.148390 | + | 0.0418007i | ||||
\(913\) | −4.44355 | − | 7.69645i | −0.147060 | − | 0.254715i | ||||
\(914\) | −15.3250 | − | 26.5436i | −0.506905 | − | 0.877984i | ||||
\(915\) | −0.239026 | − | 0.232993i | −0.00790195 | − | 0.00770251i | ||||
\(916\) | 0.310529 | − | 0.537852i | 0.0102602 | − | 0.0177711i | ||||
\(917\) | 11.9272 | 0.393871 | ||||||||
\(918\) | −3.09446 | − | 9.99859i | −0.102132 | − | 0.330003i | ||||
\(919\) | −46.2912 | −1.52701 | −0.763503 | − | 0.645804i | \(-0.776522\pi\) | ||||
−0.763503 | + | 0.645804i | \(0.776522\pi\) | |||||||
\(920\) | 35.6651 | − | 61.7738i | 1.17585 | − | 2.03662i | ||||
\(921\) | −30.4589 | − | 29.6901i | −1.00365 | − | 0.978323i | ||||
\(922\) | 0.230098 | + | 0.398542i | 0.00757788 | + | 0.0131253i | ||||
\(923\) | −9.92577 | − | 17.1919i | −0.326711 | − | 0.565879i | ||||
\(924\) | −1.58881 | + | 0.447559i | −0.0522680 | + | 0.0147236i | ||||
\(925\) | 5.86153 | − | 10.1525i | 0.192726 | − | 0.333811i | ||||
\(926\) | 14.2825 | 0.469353 | ||||||||
\(927\) | 32.4456 | − | 19.8550i | 1.06565 | − | 0.652125i | ||||
\(928\) | 2.18974 | 0.0718819 | ||||||||
\(929\) | −21.1201 | + | 36.5811i | −0.692928 | + | 1.20019i | 0.277947 | + | 0.960596i | \(0.410346\pi\) |
−0.970874 | + | 0.239589i | \(0.922987\pi\) | |||||||
\(930\) | 2.94953 | − | 11.5987i | 0.0967188 | − | 0.380338i | ||||
\(931\) | 2.43557 | + | 4.21852i | 0.0798224 | + | 0.138256i | ||||
\(932\) | −4.00360 | − | 6.93444i | −0.131142 | − | 0.227145i | ||||
\(933\) | 7.99174 | − | 31.4267i | 0.261638 | − | 1.02887i | ||||
\(934\) | 0.278975 | − | 0.483199i | 0.00912835 | − | 0.0158108i | ||||
\(935\) | −12.6201 | −0.412722 | ||||||||
\(936\) | −25.9183 | + | 15.8607i | −0.847166 | + | 0.518422i | ||||
\(937\) | 34.2767 | 1.11977 | 0.559886 | − | 0.828570i | \(-0.310845\pi\) | ||||
0.559886 | + | 0.828570i | \(0.310845\pi\) | |||||||
\(938\) | −7.72836 | + | 13.3859i | −0.252340 | + | 0.437066i | ||||
\(939\) | −1.83146 | + | 0.515913i | −0.0597674 | + | 0.0168362i | ||||
\(940\) | 4.37569 | + | 7.57892i | 0.142719 | + | 0.247197i | ||||
\(941\) | 15.2021 | + | 26.3309i | 0.495576 | + | 0.858362i | 0.999987 | − | 0.00510142i | \(-0.00162384\pi\) |
−0.504411 | + | 0.863463i | \(0.668291\pi\) | |||||||
\(942\) | 5.27704 | + | 5.14385i | 0.171935 | + | 0.167596i | ||||
\(943\) | −26.9452 | + | 46.6705i | −0.877457 | + | 1.51980i | ||||
\(944\) | −21.7171 | −0.706833 | ||||||||
\(945\) | −10.0717 | + | 10.8753i | −0.327634 | + | 0.353772i | ||||
\(946\) | −3.82377 | −0.124321 | ||||||||
\(947\) | −18.1345 | + | 31.4099i | −0.589293 | + | 1.02068i | 0.405033 | + | 0.914302i | \(0.367260\pi\) |
−0.994325 | + | 0.106383i | \(0.966073\pi\) | |||||||
\(948\) | 2.71869 | + | 2.65007i | 0.0882988 | + | 0.0860702i | ||||
\(949\) | 3.19875 | + | 5.54040i | 0.103836 | + | 0.179849i | ||||
\(950\) | 1.40493 | + | 2.43340i | 0.0455818 | + | 0.0789501i | ||||
\(951\) | 4.19657 | − | 1.18215i | 0.136083 | − | 0.0383339i | ||||
\(952\) | −2.40534 | + | 4.16618i | −0.0779577 | + | 0.135027i | ||||
\(953\) | −21.1687 | −0.685722 | −0.342861 | − | 0.939386i | \(-0.611396\pi\) | ||||
−0.342861 | + | 0.939386i | \(0.611396\pi\) | |||||||
\(954\) | 30.1184 | + | 16.3771i | 0.975121 | + | 0.530230i | ||||
\(955\) | −69.9273 | −2.26279 | ||||||||
\(956\) | −2.50453 | + | 4.33797i | −0.0810023 | + | 0.140300i | ||||
\(957\) | 1.56708 | − | 6.16240i | 0.0506565 | − | 0.199202i | ||||
\(958\) | −0.865196 | − | 1.49856i | −0.0279532 | − | 0.0484164i | ||||
\(959\) | 10.7936 | + | 18.6950i | 0.348542 | + | 0.603692i | ||||
\(960\) | 10.4158 | − | 40.9591i | 0.336168 | − | 1.32195i | ||||
\(961\) | 13.6463 | − | 23.6361i | 0.440203 | − | 0.762454i | ||||
\(962\) | −19.4709 | −0.627766 | ||||||||
\(963\) | 0.782486 | + | 30.6063i | 0.0252153 | + | 0.986275i | ||||
\(964\) | 3.04600 | 0.0981051 | ||||||||
\(965\) | −30.0036 | + | 51.9678i | −0.965851 | + | 1.67290i | ||||
\(966\) | −19.2026 | + | 5.40928i | −0.617834 | + | 0.174041i | ||||
\(967\) | 1.59049 | + | 2.75482i | 0.0511468 | + | 0.0885889i | 0.890465 | − | 0.455051i | \(-0.150379\pi\) |
−0.839318 | + | 0.543640i | \(0.817046\pi\) | |||||||
\(968\) | 3.50063 | + | 6.06327i | 0.112515 | + | 0.194881i | ||||
\(969\) | −1.57912 | − | 1.53926i | −0.0507285 | − | 0.0494482i | ||||
\(970\) | 6.95170 | − | 12.0407i | 0.223206 | − | 0.386603i | ||||
\(971\) | −23.4998 | −0.754145 | −0.377072 | − | 0.926184i | \(-0.623069\pi\) | ||||
−0.377072 | + | 0.926184i | \(0.623069\pi\) | |||||||
\(972\) | −0.960911 | + | 4.79204i | −0.0308212 | + | 0.153705i | ||||
\(973\) | 22.9817 | 0.736760 | ||||||||
\(974\) | −11.6083 | + | 20.1062i | −0.371955 | + | 0.644245i | ||||
\(975\) | 11.0218 | + | 10.7436i | 0.352979 | + | 0.344070i | ||||
\(976\) | −0.114188 | − | 0.197780i | −0.00365508 | − | 0.00633079i | ||||
\(977\) | −20.2314 | − | 35.0418i | −0.647260 | − | 1.12109i | −0.983775 | − | 0.179409i | \(-0.942582\pi\) |
0.336515 | − | 0.941678i | \(-0.390752\pi\) | |||||||
\(978\) | 6.38584 | − | 1.79886i | 0.204197 | − | 0.0575211i | ||||
\(979\) | 22.4742 | − | 38.9264i | 0.718278 | − | 1.24409i | ||||
\(980\) | −5.14138 | −0.164235 | ||||||||
\(981\) | −0.358854 | − | 14.0363i | −0.0114573 | − | 0.448144i | ||||
\(982\) | 29.8118 | 0.951333 | ||||||||
\(983\) | −20.9320 | + | 36.2552i | −0.667626 | + | 1.15636i | 0.310940 | + | 0.950430i | \(0.399356\pi\) |
−0.978566 | + | 0.205933i | \(0.933977\pi\) | |||||||
\(984\) | −8.04439 | + | 31.6338i | −0.256446 | + | 1.00845i | ||||
\(985\) | 9.39348 | + | 16.2700i | 0.299301 | + | 0.518405i | ||||
\(986\) | −1.25569 | − | 2.17492i | −0.0399894 | − | 0.0692636i | ||||
\(987\) | 4.45120 | − | 17.5039i | 0.141683 | − | 0.557156i | ||||
\(988\) | −0.433807 | + | 0.751375i | −0.0138012 | + | 0.0239044i | ||||
\(989\) | 8.59169 | 0.273200 | ||||||||
\(990\) | −27.8481 | − | 15.1427i | −0.885072 | − | 0.481265i | ||||
\(991\) | −18.0897 | −0.574638 | −0.287319 | − | 0.957835i | \(-0.592764\pi\) | ||||
−0.287319 | + | 0.957835i | \(0.592764\pi\) | |||||||
\(992\) | −1.69085 | + | 2.92864i | −0.0536846 | + | 0.0929845i | ||||
\(993\) | −22.5733 | + | 6.35879i | −0.716343 | + | 0.201790i | ||||
\(994\) | −3.94709 | − | 6.83655i | −0.125194 | − | 0.216842i | ||||
\(995\) | 37.6925 | + | 65.2854i | 1.19493 | + | 2.06968i | ||||
\(996\) | 1.17371 | + | 1.14409i | 0.0371904 | + | 0.0362518i | ||||
\(997\) | 18.6698 | − | 32.3370i | 0.591278 | − | 1.02412i | −0.402783 | − | 0.915296i | \(-0.631957\pi\) |
0.994061 | − | 0.108828i | \(-0.0347096\pi\) | |||||||
\(998\) | −12.2648 | −0.388235 | ||||||||
\(999\) | −15.7024 | + | 16.9551i | −0.496802 | + | 0.536437i |
(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 | 387.2.f.c.259.14 | yes | 38 | |
3.2 | odd | 2 | 1161.2.f.c.775.6 | 38 | |||
9.2 | odd | 6 | 3483.2.a.r.1.14 | 19 | |||
9.4 | even | 3 | inner | 387.2.f.c.130.14 | ✓ | 38 | |
9.5 | odd | 6 | 1161.2.f.c.388.6 | 38 | |||
9.7 | even | 3 | 3483.2.a.s.1.6 | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
387.2.f.c.130.14 | ✓ | 38 | 9.4 | even | 3 | inner | |
387.2.f.c.259.14 | yes | 38 | 1.1 | even | 1 | trivial | |
1161.2.f.c.388.6 | 38 | 9.5 | odd | 6 | |||
1161.2.f.c.775.6 | 38 | 3.2 | odd | 2 | |||
3483.2.a.r.1.14 | 19 | 9.2 | odd | 6 | |||
3483.2.a.s.1.6 | 19 | 9.7 | even | 3 |