Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(209,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.209");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{11} + 4x^{10} - 8x^{8} + 26x^{7} - 50x^{6} + 78x^{5} - 72x^{4} + 324x^{2} - 486x + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.12 | ||
Root | \(-0.814390 + 1.52865i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.209 |
Dual form | 546.2.g.c.209.6 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.52865 | − | 0.814390i | 0.882566 | − | 0.470188i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.76081 | 0.787458 | 0.393729 | − | 0.919227i | \(-0.371185\pi\) | ||||
0.393729 | + | 0.919227i | \(0.371185\pi\) | |||||||
\(6\) | 0.814390 | + | 1.52865i | 0.332473 | + | 0.624068i | ||||
\(7\) | 2.58450 | + | 0.566014i | 0.976848 | + | 0.213933i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 1.67354 | − | 2.48983i | 0.557846 | − | 0.829945i | ||||
\(10\) | 1.76081i | 0.556817i | ||||||||
\(11\) | − | 3.38959i | − | 1.02200i | −0.859581 | − | 0.511000i | \(-0.829275\pi\) | ||
0.859581 | − | 0.511000i | \(-0.170725\pi\) | |||||||
\(12\) | −1.52865 | + | 0.814390i | −0.441283 | + | 0.235094i | ||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | −0.566014 | + | 2.58450i | −0.151274 | + | 0.690736i | ||||
\(15\) | 2.69166 | − | 1.43399i | 0.694984 | − | 0.370253i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.58785 | −1.35525 | −0.677627 | − | 0.735406i | \(-0.736992\pi\) | ||||
−0.677627 | + | 0.735406i | \(0.736992\pi\) | |||||||
\(18\) | 2.48983 | + | 1.67354i | 0.586859 | + | 0.394457i | ||||
\(19\) | − | 3.39471i | − | 0.778801i | −0.921069 | − | 0.389400i | \(-0.872682\pi\) | ||
0.921069 | − | 0.389400i | \(-0.127318\pi\) | |||||||
\(20\) | −1.76081 | −0.393729 | ||||||||
\(21\) | 4.41175 | − | 1.23955i | 0.962722 | − | 0.270492i | ||||
\(22\) | 3.38959 | 0.722663 | ||||||||
\(23\) | 3.58404i | 0.747324i | 0.927565 | + | 0.373662i | \(0.121898\pi\) | ||||
−0.927565 | + | 0.373662i | \(0.878102\pi\) | |||||||
\(24\) | −0.814390 | − | 1.52865i | −0.166237 | − | 0.312034i | ||||
\(25\) | −1.89955 | −0.379910 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 0.530556 | − | 5.16900i | 0.102105 | − | 0.994774i | ||||
\(28\) | −2.58450 | − | 0.566014i | −0.488424 | − | 0.106967i | ||||
\(29\) | 3.65877i | 0.679417i | 0.940531 | + | 0.339708i | \(0.110328\pi\) | ||||
−0.940531 | + | 0.339708i | \(0.889672\pi\) | |||||||
\(30\) | 1.43399 | + | 2.69166i | 0.261809 | + | 0.491428i | ||||
\(31\) | 9.08755i | 1.63217i | 0.577930 | + | 0.816086i | \(0.303861\pi\) | ||||
−0.577930 | + | 0.816086i | \(0.696139\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −2.76045 | − | 5.18149i | −0.480532 | − | 0.901982i | ||||
\(34\) | − | 5.58785i | − | 0.958309i | ||||||
\(35\) | 4.55081 | + | 0.996643i | 0.769227 | + | 0.168463i | ||||
\(36\) | −1.67354 | + | 2.48983i | −0.278923 | + | 0.414972i | ||||
\(37\) | 9.49548 | 1.56105 | 0.780523 | − | 0.625127i | \(-0.214953\pi\) | ||||
0.780523 | + | 0.625127i | \(0.214953\pi\) | |||||||
\(38\) | 3.39471 | 0.550695 | ||||||||
\(39\) | 0.814390 | + | 1.52865i | 0.130407 | + | 0.244780i | ||||
\(40\) | − | 1.76081i | − | 0.278408i | ||||||
\(41\) | −4.47910 | −0.699518 | −0.349759 | − | 0.936840i | \(-0.613737\pi\) | ||||
−0.349759 | + | 0.936840i | \(0.613737\pi\) | |||||||
\(42\) | 1.23955 | + | 4.41175i | 0.191267 | + | 0.680747i | ||||
\(43\) | 7.79778 | 1.18915 | 0.594575 | − | 0.804040i | \(-0.297320\pi\) | ||||
0.594575 | + | 0.804040i | \(0.297320\pi\) | |||||||
\(44\) | 3.38959i | 0.511000i | ||||||||
\(45\) | 2.94678 | − | 4.38412i | 0.439280 | − | 0.653546i | ||||
\(46\) | −3.58404 | −0.528438 | ||||||||
\(47\) | −6.44515 | −0.940122 | −0.470061 | − | 0.882634i | \(-0.655768\pi\) | ||||
−0.470061 | + | 0.882634i | \(0.655768\pi\) | |||||||
\(48\) | 1.52865 | − | 0.814390i | 0.220642 | − | 0.117547i | ||||
\(49\) | 6.35926 | + | 2.92573i | 0.908465 | + | 0.417961i | ||||
\(50\) | − | 1.89955i | − | 0.268637i | ||||||
\(51\) | −8.54187 | + | 4.55069i | −1.19610 | + | 0.637225i | ||||
\(52\) | − | 1.00000i | − | 0.138675i | ||||||
\(53\) | − | 4.99350i | − | 0.685910i | −0.939352 | − | 0.342955i | \(-0.888572\pi\) | ||
0.939352 | − | 0.342955i | \(-0.111428\pi\) | |||||||
\(54\) | 5.16900 | + | 0.530556i | 0.703411 | + | 0.0721995i | ||||
\(55\) | − | 5.96842i | − | 0.804782i | ||||||
\(56\) | 0.566014 | − | 2.58450i | 0.0756369 | − | 0.345368i | ||||
\(57\) | −2.76462 | − | 5.18933i | −0.366183 | − | 0.687343i | ||||
\(58\) | −3.65877 | −0.480420 | ||||||||
\(59\) | −0.204075 | −0.0265682 | −0.0132841 | − | 0.999912i | \(-0.504229\pi\) | ||||
−0.0132841 | + | 0.999912i | \(0.504229\pi\) | |||||||
\(60\) | −2.69166 | + | 1.43399i | −0.347492 | + | 0.185127i | ||||
\(61\) | 3.18551i | 0.407863i | 0.978985 | + | 0.203932i | \(0.0653720\pi\) | ||||
−0.978985 | + | 0.203932i | \(0.934628\pi\) | |||||||
\(62\) | −9.08755 | −1.15412 | ||||||||
\(63\) | 5.73454 | − | 5.48772i | 0.722484 | − | 0.691388i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.76081i | 0.218401i | ||||||||
\(66\) | 5.18149 | − | 2.76045i | 0.637798 | − | 0.339788i | ||||
\(67\) | −14.9381 | −1.82498 | −0.912489 | − | 0.409101i | \(-0.865842\pi\) | ||||
−0.912489 | + | 0.409101i | \(0.865842\pi\) | |||||||
\(68\) | 5.58785 | 0.677627 | ||||||||
\(69\) | 2.91881 | + | 5.47874i | 0.351383 | + | 0.659563i | ||||
\(70\) | −0.996643 | + | 4.55081i | −0.119122 | + | 0.543925i | ||||
\(71\) | 5.92908i | 0.703653i | 0.936065 | + | 0.351826i | \(0.114439\pi\) | ||||
−0.936065 | + | 0.351826i | \(0.885561\pi\) | |||||||
\(72\) | −2.48983 | − | 1.67354i | −0.293430 | − | 0.197228i | ||||
\(73\) | 8.84923i | 1.03572i | 0.855464 | + | 0.517862i | \(0.173272\pi\) | ||||
−0.855464 | + | 0.517862i | \(0.826728\pi\) | |||||||
\(74\) | 9.49548i | 1.10383i | ||||||||
\(75\) | −2.90375 | + | 1.54698i | −0.335296 | + | 0.178629i | ||||
\(76\) | 3.39471i | 0.389400i | ||||||||
\(77\) | 1.91856 | − | 8.76039i | 0.218640 | − | 0.998339i | ||||
\(78\) | −1.52865 | + | 0.814390i | −0.173085 | + | 0.0922115i | ||||
\(79\) | 1.31682 | 0.148154 | 0.0740770 | − | 0.997253i | \(-0.476399\pi\) | ||||
0.0740770 | + | 0.997253i | \(0.476399\pi\) | |||||||
\(80\) | 1.76081 | 0.196864 | ||||||||
\(81\) | −3.39855 | − | 8.33366i | −0.377616 | − | 0.925962i | ||||
\(82\) | − | 4.47910i | − | 0.494634i | ||||||
\(83\) | 0.878906 | 0.0964724 | 0.0482362 | − | 0.998836i | \(-0.484640\pi\) | ||||
0.0482362 | + | 0.998836i | \(0.484640\pi\) | |||||||
\(84\) | −4.41175 | + | 1.23955i | −0.481361 | + | 0.135246i | ||||
\(85\) | −9.83914 | −1.06721 | ||||||||
\(86\) | 7.79778i | 0.840856i | ||||||||
\(87\) | 2.97967 | + | 5.59298i | 0.319454 | + | 0.599630i | ||||
\(88\) | −3.38959 | −0.361331 | ||||||||
\(89\) | −13.3915 | −1.41949 | −0.709747 | − | 0.704457i | \(-0.751191\pi\) | ||||
−0.709747 | + | 0.704457i | \(0.751191\pi\) | |||||||
\(90\) | 4.38412 | + | 2.94678i | 0.462127 | + | 0.310618i | ||||
\(91\) | −0.566014 | + | 2.58450i | −0.0593344 | + | 0.270929i | ||||
\(92\) | − | 3.58404i | − | 0.373662i | ||||||
\(93\) | 7.40081 | + | 13.8917i | 0.767429 | + | 1.44050i | ||||
\(94\) | − | 6.44515i | − | 0.664767i | ||||||
\(95\) | − | 5.97744i | − | 0.613273i | ||||||
\(96\) | 0.814390 | + | 1.52865i | 0.0831183 | + | 0.156017i | ||||
\(97\) | − | 5.82999i | − | 0.591946i | −0.955196 | − | 0.295973i | \(-0.904356\pi\) | ||
0.955196 | − | 0.295973i | \(-0.0956438\pi\) | |||||||
\(98\) | −2.92573 | + | 6.35926i | −0.295543 | + | 0.642382i | ||||
\(99\) | −8.43951 | − | 5.67260i | −0.848203 | − | 0.570118i | ||||
\(100\) | 1.89955 | 0.189955 | ||||||||
\(101\) | −12.1410 | −1.20808 | −0.604039 | − | 0.796955i | \(-0.706443\pi\) | ||||
−0.604039 | + | 0.796955i | \(0.706443\pi\) | |||||||
\(102\) | −4.55069 | − | 8.54187i | −0.450586 | − | 0.845771i | ||||
\(103\) | 7.20411i | 0.709842i | 0.934896 | + | 0.354921i | \(0.115492\pi\) | ||||
−0.934896 | + | 0.354921i | \(0.884508\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 7.76824 | − | 2.18261i | 0.758103 | − | 0.213001i | ||||
\(106\) | 4.99350 | 0.485012 | ||||||||
\(107\) | 13.3798i | 1.29347i | 0.762714 | + | 0.646736i | \(0.223867\pi\) | ||||
−0.762714 | + | 0.646736i | \(0.776133\pi\) | |||||||
\(108\) | −0.530556 | + | 5.16900i | −0.0510527 | + | 0.497387i | ||||
\(109\) | −3.07251 | −0.294293 | −0.147146 | − | 0.989115i | \(-0.547009\pi\) | ||||
−0.147146 | + | 0.989115i | \(0.547009\pi\) | |||||||
\(110\) | 5.96842 | 0.569067 | ||||||||
\(111\) | 14.5153 | − | 7.73302i | 1.37773 | − | 0.733986i | ||||
\(112\) | 2.58450 | + | 0.566014i | 0.244212 | + | 0.0534833i | ||||
\(113\) | − | 19.8770i | − | 1.86987i | −0.354820 | − | 0.934934i | \(-0.615458\pi\) | ||
0.354820 | − | 0.934934i | \(-0.384542\pi\) | |||||||
\(114\) | 5.18933 | − | 2.76462i | 0.486025 | − | 0.258931i | ||||
\(115\) | 6.31081i | 0.588486i | ||||||||
\(116\) | − | 3.65877i | − | 0.339708i | ||||||
\(117\) | 2.48983 | + | 1.67354i | 0.230185 | + | 0.154719i | ||||
\(118\) | − | 0.204075i | − | 0.0187866i | ||||||
\(119\) | −14.4418 | − | 3.16281i | −1.32388 | − | 0.289934i | ||||
\(120\) | −1.43399 | − | 2.69166i | −0.130904 | − | 0.245714i | ||||
\(121\) | −0.489316 | −0.0444833 | ||||||||
\(122\) | −3.18551 | −0.288403 | ||||||||
\(123\) | −6.84698 | + | 3.64774i | −0.617371 | + | 0.328905i | ||||
\(124\) | − | 9.08755i | − | 0.816086i | ||||||
\(125\) | −12.1488 | −1.08662 | ||||||||
\(126\) | 5.48772 | + | 5.73454i | 0.488885 | + | 0.510873i | ||||
\(127\) | 1.58088 | 0.140280 | 0.0701402 | − | 0.997537i | \(-0.477655\pi\) | ||||
0.0701402 | + | 0.997537i | \(0.477655\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 11.9201 | − | 6.35043i | 1.04950 | − | 0.559124i | ||||
\(130\) | −1.76081 | −0.154433 | ||||||||
\(131\) | 18.2002 | 1.59015 | 0.795077 | − | 0.606508i | \(-0.207430\pi\) | ||||
0.795077 | + | 0.606508i | \(0.207430\pi\) | |||||||
\(132\) | 2.76045 | + | 5.18149i | 0.240266 | + | 0.450991i | ||||
\(133\) | 1.92146 | − | 8.77363i | 0.166611 | − | 0.760770i | ||||
\(134\) | − | 14.9381i | − | 1.29045i | ||||||
\(135\) | 0.934207 | − | 9.10161i | 0.0804038 | − | 0.783342i | ||||
\(136\) | 5.58785i | 0.479155i | ||||||||
\(137\) | − | 11.0958i | − | 0.947981i | −0.880530 | − | 0.473991i | \(-0.842813\pi\) | ||
0.880530 | − | 0.473991i | \(-0.157187\pi\) | |||||||
\(138\) | −5.47874 | + | 2.91881i | −0.466382 | + | 0.248465i | ||||
\(139\) | − | 13.5283i | − | 1.14746i | −0.819045 | − | 0.573729i | \(-0.805496\pi\) | ||
0.819045 | − | 0.573729i | \(-0.194504\pi\) | |||||||
\(140\) | −4.55081 | − | 0.996643i | −0.384613 | − | 0.0842317i | ||||
\(141\) | −9.85238 | + | 5.24887i | −0.829720 | + | 0.442034i | ||||
\(142\) | −5.92908 | −0.497558 | ||||||||
\(143\) | 3.38959 | 0.283452 | ||||||||
\(144\) | 1.67354 | − | 2.48983i | 0.139461 | − | 0.207486i | ||||
\(145\) | 6.44240i | 0.535012i | ||||||||
\(146\) | −8.84923 | −0.732367 | ||||||||
\(147\) | 12.1038 | − | 0.706506i | 0.998301 | − | 0.0582717i | ||||
\(148\) | −9.49548 | −0.780523 | ||||||||
\(149\) | − | 6.12739i | − | 0.501976i | −0.967990 | − | 0.250988i | \(-0.919245\pi\) | ||
0.967990 | − | 0.250988i | \(-0.0807554\pi\) | |||||||
\(150\) | −1.54698 | − | 2.90375i | −0.126310 | − | 0.237090i | ||||
\(151\) | −17.1388 | −1.39474 | −0.697368 | − | 0.716713i | \(-0.745646\pi\) | ||||
−0.697368 | + | 0.716713i | \(0.745646\pi\) | |||||||
\(152\) | −3.39471 | −0.275348 | ||||||||
\(153\) | −9.35148 | + | 13.9128i | −0.756023 | + | 1.12479i | ||||
\(154\) | 8.76039 | + | 1.91856i | 0.705932 | + | 0.154602i | ||||
\(155\) | 16.0014i | 1.28527i | ||||||||
\(156\) | −0.814390 | − | 1.52865i | −0.0652034 | − | 0.122390i | ||||
\(157\) | − | 4.50214i | − | 0.359310i | −0.983730 | − | 0.179655i | \(-0.942502\pi\) | ||
0.983730 | − | 0.179655i | \(-0.0574981\pi\) | |||||||
\(158\) | 1.31682i | 0.104761i | ||||||||
\(159\) | −4.06666 | − | 7.63331i | −0.322507 | − | 0.605361i | ||||
\(160\) | 1.76081i | 0.139204i | ||||||||
\(161\) | −2.02862 | + | 9.26295i | −0.159878 | + | 0.730022i | ||||
\(162\) | 8.33366 | − | 3.39855i | 0.654754 | − | 0.267015i | ||||
\(163\) | 1.40702 | 0.110206 | 0.0551032 | − | 0.998481i | \(-0.482451\pi\) | ||||
0.0551032 | + | 0.998481i | \(0.482451\pi\) | |||||||
\(164\) | 4.47910 | 0.349759 | ||||||||
\(165\) | −4.86062 | − | 9.12362i | −0.378399 | − | 0.710273i | ||||
\(166\) | 0.878906i | 0.0682163i | ||||||||
\(167\) | 2.93743 | 0.227305 | 0.113653 | − | 0.993521i | \(-0.463745\pi\) | ||||
0.113653 | + | 0.993521i | \(0.463745\pi\) | |||||||
\(168\) | −1.23955 | − | 4.41175i | −0.0956335 | − | 0.340374i | ||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | − | 9.83914i | − | 0.754628i | ||||||
\(171\) | −8.45227 | − | 5.68118i | −0.646362 | − | 0.434451i | ||||
\(172\) | −7.79778 | −0.594575 | ||||||||
\(173\) | 7.62715 | 0.579881 | 0.289941 | − | 0.957045i | \(-0.406364\pi\) | ||||
0.289941 | + | 0.957045i | \(0.406364\pi\) | |||||||
\(174\) | −5.59298 | + | 2.97967i | −0.424003 | + | 0.225888i | ||||
\(175\) | −4.90939 | − | 1.07517i | −0.371115 | − | 0.0812755i | ||||
\(176\) | − | 3.38959i | − | 0.255500i | ||||||
\(177\) | −0.311958 | + | 0.166196i | −0.0234482 | + | 0.0124921i | ||||
\(178\) | − | 13.3915i | − | 1.00373i | ||||||
\(179\) | 5.02398i | 0.375510i | 0.982216 | + | 0.187755i | \(0.0601211\pi\) | ||||
−0.982216 | + | 0.187755i | \(0.939879\pi\) | |||||||
\(180\) | −2.94678 | + | 4.38412i | −0.219640 | + | 0.326773i | ||||
\(181\) | 5.50980i | 0.409540i | 0.978810 | + | 0.204770i | \(0.0656447\pi\) | ||||
−0.978810 | + | 0.204770i | \(0.934355\pi\) | |||||||
\(182\) | −2.58450 | − | 0.566014i | −0.191576 | − | 0.0419558i | ||||
\(183\) | 2.59425 | + | 4.86953i | 0.191773 | + | 0.359966i | ||||
\(184\) | 3.58404 | 0.264219 | ||||||||
\(185\) | 16.7197 | 1.22926 | ||||||||
\(186\) | −13.8917 | + | 7.40081i | −1.01859 | + | 0.542654i | ||||
\(187\) | 18.9405i | 1.38507i | ||||||||
\(188\) | 6.44515 | 0.470061 | ||||||||
\(189\) | 4.29695 | − | 13.0590i | 0.312557 | − | 0.949899i | ||||
\(190\) | 5.97744 | 0.433649 | ||||||||
\(191\) | 4.76107i | 0.344499i | 0.985053 | + | 0.172249i | \(0.0551035\pi\) | ||||
−0.985053 | + | 0.172249i | \(0.944896\pi\) | |||||||
\(192\) | −1.52865 | + | 0.814390i | −0.110321 | + | 0.0587735i | ||||
\(193\) | 22.5891 | 1.62600 | 0.812998 | − | 0.582267i | \(-0.197834\pi\) | ||||
0.812998 | + | 0.582267i | \(0.197834\pi\) | |||||||
\(194\) | 5.82999 | 0.418569 | ||||||||
\(195\) | 1.43399 | + | 2.69166i | 0.102690 | + | 0.192754i | ||||
\(196\) | −6.35926 | − | 2.92573i | −0.454233 | − | 0.208980i | ||||
\(197\) | − | 18.3675i | − | 1.30863i | −0.756221 | − | 0.654316i | \(-0.772957\pi\) | ||
0.756221 | − | 0.654316i | \(-0.227043\pi\) | |||||||
\(198\) | 5.67260 | − | 8.43951i | 0.403134 | − | 0.599770i | ||||
\(199\) | − | 16.2052i | − | 1.14876i | −0.818589 | − | 0.574379i | \(-0.805243\pi\) | ||
0.818589 | − | 0.574379i | \(-0.194757\pi\) | |||||||
\(200\) | 1.89955i | 0.134319i | ||||||||
\(201\) | −22.8351 | + | 12.1654i | −1.61066 | + | 0.858084i | ||||
\(202\) | − | 12.1410i | − | 0.854240i | ||||||
\(203\) | −2.07092 | + | 9.45609i | −0.145350 | + | 0.663687i | ||||
\(204\) | 8.54187 | − | 4.55069i | 0.598050 | − | 0.318612i | ||||
\(205\) | −7.88685 | −0.550841 | ||||||||
\(206\) | −7.20411 | −0.501934 | ||||||||
\(207\) | 8.92367 | + | 5.99803i | 0.620238 | + | 0.416892i | ||||
\(208\) | 1.00000i | 0.0693375i | ||||||||
\(209\) | −11.5067 | −0.795934 | ||||||||
\(210\) | 2.18261 | + | 7.76824i | 0.150615 | + | 0.536060i | ||||
\(211\) | −16.9761 | −1.16868 | −0.584342 | − | 0.811508i | \(-0.698647\pi\) | ||||
−0.584342 | + | 0.811508i | \(0.698647\pi\) | |||||||
\(212\) | 4.99350i | 0.342955i | ||||||||
\(213\) | 4.82859 | + | 9.06349i | 0.330849 | + | 0.621020i | ||||
\(214\) | −13.3798 | −0.914623 | ||||||||
\(215\) | 13.7304 | 0.936405 | ||||||||
\(216\) | −5.16900 | − | 0.530556i | −0.351706 | − | 0.0360997i | ||||
\(217\) | −5.14369 | + | 23.4868i | −0.349176 | + | 1.59438i | ||||
\(218\) | − | 3.07251i | − | 0.208096i | ||||||
\(219\) | 7.20672 | + | 13.5274i | 0.486985 | + | 0.914095i | ||||
\(220\) | 5.96842i | 0.402391i | ||||||||
\(221\) | − | 5.58785i | − | 0.375880i | ||||||
\(222\) | 7.73302 | + | 14.5153i | 0.519006 | + | 0.974200i | ||||
\(223\) | 9.25112i | 0.619501i | 0.950818 | + | 0.309751i | \(0.100246\pi\) | ||||
−0.950818 | + | 0.309751i | \(0.899754\pi\) | |||||||
\(224\) | −0.566014 | + | 2.58450i | −0.0378184 | + | 0.172684i | ||||
\(225\) | −3.17897 | + | 4.72957i | −0.211931 | + | 0.315304i | ||||
\(226\) | 19.8770 | 1.32220 | ||||||||
\(227\) | −15.1216 | −1.00366 | −0.501828 | − | 0.864967i | \(-0.667339\pi\) | ||||
−0.501828 | + | 0.864967i | \(0.667339\pi\) | |||||||
\(228\) | 2.76462 | + | 5.18933i | 0.183092 | + | 0.343672i | ||||
\(229\) | − | 20.2697i | − | 1.33946i | −0.742605 | − | 0.669730i | \(-0.766410\pi\) | ||
0.742605 | − | 0.669730i | \(-0.233590\pi\) | |||||||
\(230\) | −6.31081 | −0.416123 | ||||||||
\(231\) | −4.20157 | − | 14.9540i | −0.276443 | − | 0.983902i | ||||
\(232\) | 3.65877 | 0.240210 | ||||||||
\(233\) | 5.58290i | 0.365748i | 0.983136 | + | 0.182874i | \(0.0585400\pi\) | ||||
−0.983136 | + | 0.182874i | \(0.941460\pi\) | |||||||
\(234\) | −1.67354 | + | 2.48983i | −0.109403 | + | 0.162766i | ||||
\(235\) | −11.3487 | −0.740306 | ||||||||
\(236\) | 0.204075 | 0.0132841 | ||||||||
\(237\) | 2.01296 | − | 1.07241i | 0.130756 | − | 0.0696603i | ||||
\(238\) | 3.16281 | − | 14.4418i | 0.205014 | − | 0.936123i | ||||
\(239\) | 24.2290i | 1.56725i | 0.621237 | + | 0.783623i | \(0.286631\pi\) | ||||
−0.621237 | + | 0.783623i | \(0.713369\pi\) | |||||||
\(240\) | 2.69166 | − | 1.43399i | 0.173746 | − | 0.0925634i | ||||
\(241\) | − | 28.6978i | − | 1.84859i | −0.381678 | − | 0.924295i | \(-0.624654\pi\) | ||
0.381678 | − | 0.924295i | \(-0.375346\pi\) | |||||||
\(242\) | − | 0.489316i | − | 0.0314544i | ||||||
\(243\) | −11.9820 | − | 9.97150i | −0.768648 | − | 0.639672i | ||||
\(244\) | − | 3.18551i | − | 0.203932i | ||||||
\(245\) | 11.1974 | + | 5.15164i | 0.715378 | + | 0.329126i | ||||
\(246\) | −3.64774 | − | 6.84698i | −0.232571 | − | 0.436547i | ||||
\(247\) | 3.39471 | 0.216000 | ||||||||
\(248\) | 9.08755 | 0.577060 | ||||||||
\(249\) | 1.34354 | − | 0.715772i | 0.0851433 | − | 0.0453602i | ||||
\(250\) | − | 12.1488i | − | 0.768357i | ||||||
\(251\) | 22.5258 | 1.42181 | 0.710907 | − | 0.703286i | \(-0.248284\pi\) | ||||
0.710907 | + | 0.703286i | \(0.248284\pi\) | |||||||
\(252\) | −5.73454 | + | 5.48772i | −0.361242 | + | 0.345694i | ||||
\(253\) | 12.1484 | 0.763765 | ||||||||
\(254\) | 1.58088i | 0.0991932i | ||||||||
\(255\) | −15.0406 | + | 8.01290i | −0.941879 | + | 0.501787i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 27.5068 | 1.71582 | 0.857912 | − | 0.513796i | \(-0.171761\pi\) | ||||
0.857912 | + | 0.513796i | \(0.171761\pi\) | |||||||
\(258\) | 6.35043 | + | 11.9201i | 0.395361 | + | 0.742111i | ||||
\(259\) | 24.5410 | + | 5.37458i | 1.52491 | + | 0.333960i | ||||
\(260\) | − | 1.76081i | − | 0.109201i | ||||||
\(261\) | 9.10973 | + | 6.12309i | 0.563878 | + | 0.379010i | ||||
\(262\) | 18.2002i | 1.12441i | ||||||||
\(263\) | − | 7.57623i | − | 0.467171i | −0.972336 | − | 0.233585i | \(-0.924954\pi\) | ||
0.972336 | − | 0.233585i | \(-0.0750458\pi\) | |||||||
\(264\) | −5.18149 | + | 2.76045i | −0.318899 | + | 0.169894i | ||||
\(265\) | − | 8.79261i | − | 0.540125i | ||||||
\(266\) | 8.77363 | + | 1.92146i | 0.537946 | + | 0.117812i | ||||
\(267\) | −20.4709 | + | 10.9059i | −1.25280 | + | 0.667429i | ||||
\(268\) | 14.9381 | 0.912489 | ||||||||
\(269\) | 17.8846 | 1.09044 | 0.545222 | − | 0.838292i | \(-0.316445\pi\) | ||||
0.545222 | + | 0.838292i | \(0.316445\pi\) | |||||||
\(270\) | 9.10161 | + | 0.934207i | 0.553907 | + | 0.0568540i | ||||
\(271\) | 21.5689i | 1.31022i | 0.755533 | + | 0.655110i | \(0.227378\pi\) | ||||
−0.755533 | + | 0.655110i | \(0.772622\pi\) | |||||||
\(272\) | −5.58785 | −0.338813 | ||||||||
\(273\) | 1.23955 | + | 4.41175i | 0.0750211 | + | 0.267011i | ||||
\(274\) | 11.0958 | 0.670324 | ||||||||
\(275\) | 6.43870i | 0.388268i | ||||||||
\(276\) | −2.91881 | − | 5.47874i | −0.175692 | − | 0.329782i | ||||
\(277\) | −3.31754 | −0.199332 | −0.0996659 | − | 0.995021i | \(-0.531777\pi\) | ||||
−0.0996659 | + | 0.995021i | \(0.531777\pi\) | |||||||
\(278\) | 13.5283 | 0.811375 | ||||||||
\(279\) | 22.6265 | + | 15.2084i | 1.35461 | + | 0.910501i | ||||
\(280\) | 0.996643 | − | 4.55081i | 0.0595608 | − | 0.271963i | ||||
\(281\) | 31.8619i | 1.90072i | 0.311147 | + | 0.950362i | \(0.399287\pi\) | ||||
−0.311147 | + | 0.950362i | \(0.600713\pi\) | |||||||
\(282\) | −5.24887 | − | 9.85238i | −0.312566 | − | 0.586701i | ||||
\(283\) | 24.2711i | 1.44277i | 0.692536 | + | 0.721384i | \(0.256494\pi\) | ||||
−0.692536 | + | 0.721384i | \(0.743506\pi\) | |||||||
\(284\) | − | 5.92908i | − | 0.351826i | ||||||
\(285\) | −4.86797 | − | 9.13742i | −0.288354 | − | 0.541254i | ||||
\(286\) | 3.38959i | 0.200431i | ||||||||
\(287\) | −11.5762 | − | 2.53524i | −0.683323 | − | 0.149650i | ||||
\(288\) | 2.48983 | + | 1.67354i | 0.146715 | + | 0.0986141i | ||||
\(289\) | 14.2241 | 0.836713 | ||||||||
\(290\) | −6.44240 | −0.378311 | ||||||||
\(291\) | −4.74789 | − | 8.91201i | −0.278326 | − | 0.522431i | ||||
\(292\) | − | 8.84923i | − | 0.517862i | ||||||
\(293\) | 17.4689 | 1.02055 | 0.510273 | − | 0.860012i | \(-0.329544\pi\) | ||||
0.510273 | + | 0.860012i | \(0.329544\pi\) | |||||||
\(294\) | 0.706506 | + | 12.1038i | 0.0412043 | + | 0.705905i | ||||
\(295\) | −0.359336 | −0.0209214 | ||||||||
\(296\) | − | 9.49548i | − | 0.551913i | ||||||
\(297\) | −17.5208 | − | 1.79837i | −1.01666 | − | 0.104352i | ||||
\(298\) | 6.12739 | 0.354950 | ||||||||
\(299\) | −3.58404 | −0.207270 | ||||||||
\(300\) | 2.90375 | − | 1.54698i | 0.167648 | − | 0.0893147i | ||||
\(301\) | 20.1533 | + | 4.41365i | 1.16162 | + | 0.254399i | ||||
\(302\) | − | 17.1388i | − | 0.986228i | ||||||
\(303\) | −18.5594 | + | 9.88754i | −1.06621 | + | 0.568024i | ||||
\(304\) | − | 3.39471i | − | 0.194700i | ||||||
\(305\) | 5.60908i | 0.321175i | ||||||||
\(306\) | −13.9128 | − | 9.35148i | −0.795343 | − | 0.534589i | ||||
\(307\) | 10.6490i | 0.607773i | 0.952708 | + | 0.303886i | \(0.0982843\pi\) | ||||
−0.952708 | + | 0.303886i | \(0.901716\pi\) | |||||||
\(308\) | −1.91856 | + | 8.76039i | −0.109320 | + | 0.499169i | ||||
\(309\) | 5.86696 | + | 11.0126i | 0.333760 | + | 0.626483i | ||||
\(310\) | −16.0014 | −0.908821 | ||||||||
\(311\) | 12.6195 | 0.715584 | 0.357792 | − | 0.933801i | \(-0.383530\pi\) | ||||
0.357792 | + | 0.933801i | \(0.383530\pi\) | |||||||
\(312\) | 1.52865 | − | 0.814390i | 0.0865427 | − | 0.0461058i | ||||
\(313\) | − | 22.9015i | − | 1.29447i | −0.762292 | − | 0.647234i | \(-0.775926\pi\) | ||
0.762292 | − | 0.647234i | \(-0.224074\pi\) | |||||||
\(314\) | 4.50214 | 0.254070 | ||||||||
\(315\) | 10.0974 | − | 9.66283i | 0.568925 | − | 0.544439i | ||||
\(316\) | −1.31682 | −0.0740770 | ||||||||
\(317\) | − | 19.9238i | − | 1.11903i | −0.828820 | − | 0.559515i | \(-0.810988\pi\) | ||
0.828820 | − | 0.559515i | \(-0.189012\pi\) | |||||||
\(318\) | 7.63331 | − | 4.06666i | 0.428055 | − | 0.228047i | ||||
\(319\) | 12.4017 | 0.694364 | ||||||||
\(320\) | −1.76081 | −0.0984322 | ||||||||
\(321\) | 10.8964 | + | 20.4530i | 0.608176 | + | 1.14157i | ||||
\(322\) | −9.26295 | − | 2.02862i | −0.516204 | − | 0.113051i | ||||
\(323\) | 18.9692i | 1.05547i | ||||||||
\(324\) | 3.39855 | + | 8.33366i | 0.188808 | + | 0.462981i | ||||
\(325\) | − | 1.89955i | − | 0.105368i | ||||||
\(326\) | 1.40702i | 0.0779277i | ||||||||
\(327\) | −4.69678 | + | 2.50222i | −0.259733 | + | 0.138373i | ||||
\(328\) | 4.47910i | 0.247317i | ||||||||
\(329\) | −16.6575 | − | 3.64805i | −0.918357 | − | 0.201123i | ||||
\(330\) | 9.12362 | − | 4.86062i | 0.502239 | − | 0.267568i | ||||
\(331\) | 18.8267 | 1.03481 | 0.517404 | − | 0.855741i | \(-0.326899\pi\) | ||||
0.517404 | + | 0.855741i | \(0.326899\pi\) | |||||||
\(332\) | −0.878906 | −0.0482362 | ||||||||
\(333\) | 15.8910 | − | 23.6422i | 0.870823 | − | 1.29558i | ||||
\(334\) | 2.93743i | 0.160729i | ||||||||
\(335\) | −26.3031 | −1.43709 | ||||||||
\(336\) | 4.41175 | − | 1.23955i | 0.240681 | − | 0.0676231i | ||||
\(337\) | −30.0841 | −1.63879 | −0.819393 | − | 0.573231i | \(-0.805690\pi\) | ||||
−0.819393 | + | 0.573231i | \(0.805690\pi\) | |||||||
\(338\) | − | 1.00000i | − | 0.0543928i | ||||||
\(339\) | −16.1876 | − | 30.3849i | −0.879191 | − | 1.65028i | ||||
\(340\) | 9.83914 | 0.533603 | ||||||||
\(341\) | 30.8031 | 1.66808 | ||||||||
\(342\) | 5.68118 | − | 8.45227i | 0.307203 | − | 0.457047i | ||||
\(343\) | 14.7795 | + | 11.1610i | 0.798017 | + | 0.602635i | ||||
\(344\) | − | 7.79778i | − | 0.420428i | ||||||
\(345\) | 5.13946 | + | 9.64702i | 0.276699 | + | 0.519378i | ||||
\(346\) | 7.62715i | 0.410038i | ||||||||
\(347\) | 16.2862i | 0.874287i | 0.899392 | + | 0.437144i | \(0.144010\pi\) | ||||
−0.899392 | + | 0.437144i | \(0.855990\pi\) | |||||||
\(348\) | −2.97967 | − | 5.59298i | −0.159727 | − | 0.299815i | ||||
\(349\) | 24.0366i | 1.28665i | 0.765594 | + | 0.643324i | \(0.222445\pi\) | ||||
−0.765594 | + | 0.643324i | \(0.777555\pi\) | |||||||
\(350\) | 1.07517 | − | 4.90939i | 0.0574704 | − | 0.262418i | ||||
\(351\) | 5.16900 | + | 0.530556i | 0.275901 | + | 0.0283190i | ||||
\(352\) | 3.38959 | 0.180666 | ||||||||
\(353\) | −18.6483 | −0.992550 | −0.496275 | − | 0.868165i | \(-0.665299\pi\) | ||||
−0.496275 | + | 0.868165i | \(0.665299\pi\) | |||||||
\(354\) | −0.166196 | − | 0.311958i | −0.00883324 | − | 0.0165804i | ||||
\(355\) | 10.4400i | 0.554097i | ||||||||
\(356\) | 13.3915 | 0.709747 | ||||||||
\(357\) | −24.6522 | + | 6.92643i | −1.30473 | + | 0.366586i | ||||
\(358\) | −5.02398 | −0.265526 | ||||||||
\(359\) | − | 6.78798i | − | 0.358256i | −0.983826 | − | 0.179128i | \(-0.942672\pi\) | ||
0.983826 | − | 0.179128i | \(-0.0573276\pi\) | |||||||
\(360\) | −4.38412 | − | 2.94678i | −0.231064 | − | 0.155309i | ||||
\(361\) | 7.47592 | 0.393469 | ||||||||
\(362\) | −5.50980 | −0.289589 | ||||||||
\(363\) | −0.747993 | + | 0.398494i | −0.0392595 | + | 0.0209155i | ||||
\(364\) | 0.566014 | − | 2.58450i | 0.0296672 | − | 0.135464i | ||||
\(365\) | 15.5818i | 0.815589i | ||||||||
\(366\) | −4.86953 | + | 2.59425i | −0.254535 | + | 0.135604i | ||||
\(367\) | − | 21.2093i | − | 1.10711i | −0.832811 | − | 0.553557i | \(-0.813270\pi\) | ||
0.832811 | − | 0.553557i | \(-0.186730\pi\) | |||||||
\(368\) | 3.58404i | 0.186831i | ||||||||
\(369\) | −7.49595 | + | 11.1522i | −0.390223 | + | 0.580562i | ||||
\(370\) | 16.7197i | 0.869217i | ||||||||
\(371\) | 2.82639 | − | 12.9057i | 0.146739 | − | 0.670030i | ||||
\(372\) | −7.40081 | − | 13.8917i | −0.383714 | − | 0.720250i | ||||
\(373\) | −3.41020 | −0.176573 | −0.0882867 | − | 0.996095i | \(-0.528139\pi\) | ||||
−0.0882867 | + | 0.996095i | \(0.528139\pi\) | |||||||
\(374\) | −18.9405 | −0.979392 | ||||||||
\(375\) | −18.5712 | + | 9.89386i | −0.959015 | + | 0.510917i | ||||
\(376\) | 6.44515i | 0.332383i | ||||||||
\(377\) | −3.65877 | −0.188436 | ||||||||
\(378\) | 13.0590 | + | 4.29695i | 0.671680 | + | 0.221011i | ||||
\(379\) | −13.7818 | −0.707921 | −0.353960 | − | 0.935260i | \(-0.615165\pi\) | ||||
−0.353960 | + | 0.935260i | \(0.615165\pi\) | |||||||
\(380\) | 5.97744i | 0.306636i | ||||||||
\(381\) | 2.41661 | − | 1.28745i | 0.123807 | − | 0.0659582i | ||||
\(382\) | −4.76107 | −0.243598 | ||||||||
\(383\) | −20.6937 | −1.05740 | −0.528699 | − | 0.848809i | \(-0.677320\pi\) | ||||
−0.528699 | + | 0.848809i | \(0.677320\pi\) | |||||||
\(384\) | −0.814390 | − | 1.52865i | −0.0415592 | − | 0.0780086i | ||||
\(385\) | 3.37821 | − | 15.4254i | 0.172170 | − | 0.786149i | ||||
\(386\) | 22.5891i | 1.14975i | ||||||||
\(387\) | 13.0499 | − | 19.4152i | 0.663362 | − | 0.986928i | ||||
\(388\) | 5.82999i | 0.295973i | ||||||||
\(389\) | − | 13.7432i | − | 0.696807i | −0.937345 | − | 0.348404i | \(-0.886724\pi\) | ||
0.937345 | − | 0.348404i | \(-0.113276\pi\) | |||||||
\(390\) | −2.69166 | + | 1.43399i | −0.136297 | + | 0.0726127i | ||||
\(391\) | − | 20.0271i | − | 1.01281i | ||||||
\(392\) | 2.92573 | − | 6.35926i | 0.147771 | − | 0.321191i | ||||
\(393\) | 27.8216 | − | 14.8220i | 1.40342 | − | 0.747672i | ||||
\(394\) | 18.3675 | 0.925342 | ||||||||
\(395\) | 2.31867 | 0.116665 | ||||||||
\(396\) | 8.43951 | + | 5.67260i | 0.424102 | + | 0.285059i | ||||
\(397\) | − | 9.96913i | − | 0.500336i | −0.968202 | − | 0.250168i | \(-0.919514\pi\) | ||
0.968202 | − | 0.250168i | \(-0.0804859\pi\) | |||||||
\(398\) | 16.2052 | 0.812295 | ||||||||
\(399\) | −4.20792 | − | 14.9766i | −0.210660 | − | 0.749769i | ||||
\(400\) | −1.89955 | −0.0949776 | ||||||||
\(401\) | 3.80987i | 0.190256i | 0.995465 | + | 0.0951280i | \(0.0303261\pi\) | ||||
−0.995465 | + | 0.0951280i | \(0.969674\pi\) | |||||||
\(402\) | −12.1654 | − | 22.8351i | −0.606757 | − | 1.13891i | ||||
\(403\) | −9.08755 | −0.452683 | ||||||||
\(404\) | 12.1410 | 0.604039 | ||||||||
\(405\) | −5.98419 | − | 14.6740i | −0.297357 | − | 0.729156i | ||||
\(406\) | −9.45609 | − | 2.07092i | −0.469298 | − | 0.102778i | ||||
\(407\) | − | 32.1858i | − | 1.59539i | ||||||
\(408\) | 4.55069 | + | 8.54187i | 0.225293 | + | 0.422886i | ||||
\(409\) | 6.06247i | 0.299770i | 0.988703 | + | 0.149885i | \(0.0478903\pi\) | ||||
−0.988703 | + | 0.149885i | \(0.952110\pi\) | |||||||
\(410\) | − | 7.88685i | − | 0.389504i | ||||||
\(411\) | −9.03634 | − | 16.9616i | −0.445730 | − | 0.836656i | ||||
\(412\) | − | 7.20411i | − | 0.354921i | ||||||
\(413\) | −0.527430 | − | 0.115509i | −0.0259531 | − | 0.00568383i | ||||
\(414\) | −5.99803 | + | 8.92367i | −0.294787 | + | 0.438574i | ||||
\(415\) | 1.54759 | 0.0759680 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −11.0173 | − | 20.6801i | −0.539521 | − | 1.01271i | ||||
\(418\) | − | 11.5067i | − | 0.562810i | ||||||
\(419\) | −2.46363 | −0.120356 | −0.0601782 | − | 0.998188i | \(-0.519167\pi\) | ||||
−0.0601782 | + | 0.998188i | \(0.519167\pi\) | |||||||
\(420\) | −7.76824 | + | 2.18261i | −0.379052 | + | 0.106501i | ||||
\(421\) | 2.44268 | 0.119049 | 0.0595244 | − | 0.998227i | \(-0.481042\pi\) | ||||
0.0595244 | + | 0.998227i | \(0.481042\pi\) | |||||||
\(422\) | − | 16.9761i | − | 0.826384i | ||||||
\(423\) | −10.7862 | + | 16.0474i | −0.524443 | + | 0.780249i | ||||
\(424\) | −4.99350 | −0.242506 | ||||||||
\(425\) | 10.6144 | 0.514875 | ||||||||
\(426\) | −9.06349 | + | 4.82859i | −0.439127 | + | 0.233946i | ||||
\(427\) | −1.80305 | + | 8.23296i | −0.0872556 | + | 0.398421i | ||||
\(428\) | − | 13.3798i | − | 0.646736i | ||||||
\(429\) | 5.18149 | − | 2.76045i | 0.250165 | − | 0.133276i | ||||
\(430\) | 13.7304i | 0.662138i | ||||||||
\(431\) | − | 28.7881i | − | 1.38667i | −0.720614 | − | 0.693337i | \(-0.756140\pi\) | ||
0.720614 | − | 0.693337i | \(-0.243860\pi\) | |||||||
\(432\) | 0.530556 | − | 5.16900i | 0.0255264 | − | 0.248693i | ||||
\(433\) | − | 32.1412i | − | 1.54461i | −0.635255 | − | 0.772303i | \(-0.719105\pi\) | ||
0.635255 | − | 0.772303i | \(-0.280895\pi\) | |||||||
\(434\) | −23.4868 | − | 5.14369i | −1.12740 | − | 0.246905i | ||||
\(435\) | 5.24663 | + | 9.84817i | 0.251556 | + | 0.472184i | ||||
\(436\) | 3.07251 | 0.147146 | ||||||||
\(437\) | 12.1668 | 0.582017 | ||||||||
\(438\) | −13.5274 | + | 7.20672i | −0.646363 | + | 0.344351i | ||||
\(439\) | 9.12045i | 0.435295i | 0.976027 | + | 0.217648i | \(0.0698384\pi\) | ||||
−0.976027 | + | 0.217648i | \(0.930162\pi\) | |||||||
\(440\) | −5.96842 | −0.284533 | ||||||||
\(441\) | 17.9270 | − | 10.9372i | 0.853668 | − | 0.520818i | ||||
\(442\) | 5.58785 | 0.265787 | ||||||||
\(443\) | − | 3.69881i | − | 0.175736i | −0.996132 | − | 0.0878680i | \(-0.971995\pi\) | ||
0.996132 | − | 0.0878680i | \(-0.0280054\pi\) | |||||||
\(444\) | −14.5153 | + | 7.73302i | −0.688863 | + | 0.366993i | ||||
\(445\) | −23.5798 | −1.11779 | ||||||||
\(446\) | −9.25112 | −0.438053 | ||||||||
\(447\) | −4.99009 | − | 9.36663i | −0.236023 | − | 0.443027i | ||||
\(448\) | −2.58450 | − | 0.566014i | −0.122106 | − | 0.0267417i | ||||
\(449\) | 16.5731i | 0.782133i | 0.920363 | + | 0.391066i | \(0.127894\pi\) | ||||
−0.920363 | + | 0.391066i | \(0.872106\pi\) | |||||||
\(450\) | −4.72957 | − | 3.17897i | −0.222954 | − | 0.149858i | ||||
\(451\) | 15.1823i | 0.714908i | ||||||||
\(452\) | 19.8770i | 0.934934i | ||||||||
\(453\) | −26.1992 | + | 13.9577i | −1.23095 | + | 0.655789i | ||||
\(454\) | − | 15.1216i | − | 0.709693i | ||||||
\(455\) | −0.996643 | + | 4.55081i | −0.0467234 | + | 0.213345i | ||||
\(456\) | −5.18933 | + | 2.76462i | −0.243013 | + | 0.129465i | ||||
\(457\) | −27.3619 | −1.27994 | −0.639968 | − | 0.768402i | \(-0.721052\pi\) | ||||
−0.639968 | + | 0.768402i | \(0.721052\pi\) | |||||||
\(458\) | 20.2697 | 0.947141 | ||||||||
\(459\) | −2.96467 | + | 28.8836i | −0.138379 | + | 1.34817i | ||||
\(460\) | − | 6.31081i | − | 0.294243i | ||||||
\(461\) | −21.5496 | −1.00367 | −0.501833 | − | 0.864964i | \(-0.667341\pi\) | ||||
−0.501833 | + | 0.864964i | \(0.667341\pi\) | |||||||
\(462\) | 14.9540 | − | 4.20157i | 0.695724 | − | 0.195475i | ||||
\(463\) | 23.3617 | 1.08571 | 0.542856 | − | 0.839826i | \(-0.317343\pi\) | ||||
0.542856 | + | 0.839826i | \(0.317343\pi\) | |||||||
\(464\) | 3.65877i | 0.169854i | ||||||||
\(465\) | 13.0314 | + | 24.4606i | 0.604318 | + | 1.13433i | ||||
\(466\) | −5.58290 | −0.258623 | ||||||||
\(467\) | 1.04693 | 0.0484461 | 0.0242230 | − | 0.999707i | \(-0.492289\pi\) | ||||
0.0242230 | + | 0.999707i | \(0.492289\pi\) | |||||||
\(468\) | −2.48983 | − | 1.67354i | −0.115093 | − | 0.0773593i | ||||
\(469\) | −38.6075 | − | 8.45517i | −1.78273 | − | 0.390424i | ||||
\(470\) | − | 11.3487i | − | 0.523476i | ||||||
\(471\) | −3.66650 | − | 6.88219i | −0.168943 | − | 0.317115i | ||||
\(472\) | 0.204075i | 0.00939329i | ||||||||
\(473\) | − | 26.4313i | − | 1.21531i | ||||||
\(474\) | 1.07241 | + | 2.01296i | 0.0492573 | + | 0.0924583i | ||||
\(475\) | 6.44843i | 0.295874i | ||||||||
\(476\) | 14.4418 | + | 3.16281i | 0.661939 | + | 0.144967i | ||||
\(477\) | −12.4330 | − | 8.35681i | −0.569268 | − | 0.382632i | ||||
\(478\) | −24.2290 | −1.10821 | ||||||||
\(479\) | 1.19995 | 0.0548271 | 0.0274135 | − | 0.999624i | \(-0.491273\pi\) | ||||
0.0274135 | + | 0.999624i | \(0.491273\pi\) | |||||||
\(480\) | 1.43399 | + | 2.69166i | 0.0654522 | + | 0.122857i | ||||
\(481\) | 9.49548i | 0.432956i | ||||||||
\(482\) | 28.6978 | 1.30715 | ||||||||
\(483\) | 4.44261 | + | 15.8119i | 0.202146 | + | 0.719466i | ||||
\(484\) | 0.489316 | 0.0222416 | ||||||||
\(485\) | − | 10.2655i | − | 0.466132i | ||||||
\(486\) | 9.97150 | − | 11.9820i | 0.452317 | − | 0.543516i | ||||
\(487\) | 13.6246 | 0.617389 | 0.308695 | − | 0.951161i | \(-0.400108\pi\) | ||||
0.308695 | + | 0.951161i | \(0.400108\pi\) | |||||||
\(488\) | 3.18551 | 0.144201 | ||||||||
\(489\) | 2.15084 | − | 1.14586i | 0.0972644 | − | 0.0518178i | ||||
\(490\) | −5.15164 | + | 11.1974i | −0.232728 | + | 0.505849i | ||||
\(491\) | − | 6.31588i | − | 0.285032i | −0.989793 | − | 0.142516i | \(-0.954481\pi\) | ||
0.989793 | − | 0.142516i | \(-0.0455192\pi\) | |||||||
\(492\) | 6.84698 | − | 3.64774i | 0.308686 | − | 0.164453i | ||||
\(493\) | − | 20.4447i | − | 0.920782i | ||||||
\(494\) | 3.39471i | 0.152735i | ||||||||
\(495\) | −14.8604 | − | 9.98837i | −0.667924 | − | 0.448944i | ||||
\(496\) | 9.08755i | 0.408043i | ||||||||
\(497\) | −3.35595 | + | 15.3237i | −0.150535 | + | 0.687362i | ||||
\(498\) | 0.715772 | + | 1.34354i | 0.0320745 | + | 0.0602054i | ||||
\(499\) | 7.28573 | 0.326154 | 0.163077 | − | 0.986613i | \(-0.447858\pi\) | ||||
0.163077 | + | 0.986613i | \(0.447858\pi\) | |||||||
\(500\) | 12.1488 | 0.543311 | ||||||||
\(501\) | 4.49030 | − | 2.39221i | 0.200612 | − | 0.106876i | ||||
\(502\) | 22.5258i | 1.00537i | ||||||||
\(503\) | 15.4358 | 0.688250 | 0.344125 | − | 0.938924i | \(-0.388176\pi\) | ||||
0.344125 | + | 0.938924i | \(0.388176\pi\) | |||||||
\(504\) | −5.48772 | − | 5.73454i | −0.244443 | − | 0.255436i | ||||
\(505\) | −21.3780 | −0.951311 | ||||||||
\(506\) | 12.1484i | 0.540064i | ||||||||
\(507\) | −1.52865 | + | 0.814390i | −0.0678897 | + | 0.0361683i | ||||
\(508\) | −1.58088 | −0.0701402 | ||||||||
\(509\) | 8.02621 | 0.355756 | 0.177878 | − | 0.984053i | \(-0.443077\pi\) | ||||
0.177878 | + | 0.984053i | \(0.443077\pi\) | |||||||
\(510\) | −8.01290 | − | 15.0406i | −0.354817 | − | 0.666009i | ||||
\(511\) | −5.00879 | + | 22.8708i | −0.221576 | + | 1.01174i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −17.5473 | − | 1.80108i | −0.774730 | − | 0.0795198i | ||||
\(514\) | 27.5068i | 1.21327i | ||||||||
\(515\) | 12.6851i | 0.558971i | ||||||||
\(516\) | −11.9201 | + | 6.35043i | −0.524752 | + | 0.279562i | ||||
\(517\) | 21.8464i | 0.960804i | ||||||||
\(518\) | −5.37458 | + | 24.5410i | −0.236145 | + | 1.07827i | ||||
\(519\) | 11.6592 | − | 6.21147i | 0.511783 | − | 0.272653i | ||||
\(520\) | 1.76081 | 0.0772166 | ||||||||
\(521\) | 20.7278 | 0.908102 | 0.454051 | − | 0.890976i | \(-0.349978\pi\) | ||||
0.454051 | + | 0.890976i | \(0.349978\pi\) | |||||||
\(522\) | −6.12309 | + | 9.10973i | −0.268000 | + | 0.398722i | ||||
\(523\) | 1.29750i | 0.0567359i | 0.999598 | + | 0.0283679i | \(0.00903100\pi\) | ||||
−0.999598 | + | 0.0283679i | \(0.990969\pi\) | |||||||
\(524\) | −18.2002 | −0.795077 | ||||||||
\(525\) | −8.38034 | + | 2.35459i | −0.365748 | + | 0.102763i | ||||
\(526\) | 7.57623 | 0.330339 | ||||||||
\(527\) | − | 50.7799i | − | 2.21201i | ||||||
\(528\) | −2.76045 | − | 5.18149i | −0.120133 | − | 0.225496i | ||||
\(529\) | 10.1546 | 0.441506 | ||||||||
\(530\) | 8.79261 | 0.381926 | ||||||||
\(531\) | −0.341526 | + | 0.508112i | −0.0148210 | + | 0.0220502i | ||||
\(532\) | −1.92146 | + | 8.77363i | −0.0833057 | + | 0.380385i | ||||
\(533\) | − | 4.47910i | − | 0.194012i | ||||||
\(534\) | −10.9059 | − | 20.4709i | −0.471944 | − | 0.885861i | ||||
\(535\) | 23.5592i | 1.01855i | ||||||||
\(536\) | 14.9381i | 0.645227i | ||||||||
\(537\) | 4.09148 | + | 7.67991i | 0.176560 | + | 0.331412i | ||||
\(538\) | 17.8846i | 0.771060i | ||||||||
\(539\) | 9.91701 | − | 21.5553i | 0.427156 | − | 0.928451i | ||||
\(540\) | −0.934207 | + | 9.10161i | −0.0402019 | + | 0.391671i | ||||
\(541\) | 8.41510 | 0.361793 | 0.180897 | − | 0.983502i | \(-0.442100\pi\) | ||||
0.180897 | + | 0.983502i | \(0.442100\pi\) | |||||||
\(542\) | −21.5689 | −0.926466 | ||||||||
\(543\) | 4.48713 | + | 8.42255i | 0.192561 | + | 0.361446i | ||||
\(544\) | − | 5.58785i | − | 0.239577i | ||||||
\(545\) | −5.41010 | −0.231743 | ||||||||
\(546\) | −4.41175 | + | 1.23955i | −0.188805 | + | 0.0530479i | ||||
\(547\) | −26.0661 | −1.11451 | −0.557254 | − | 0.830342i | \(-0.688145\pi\) | ||||
−0.557254 | + | 0.830342i | \(0.688145\pi\) | |||||||
\(548\) | 11.0958i | 0.473991i | ||||||||
\(549\) | 7.93140 | + | 5.33108i | 0.338504 | + | 0.227525i | ||||
\(550\) | −6.43870 | −0.274547 | ||||||||
\(551\) | 12.4205 | 0.529130 | ||||||||
\(552\) | 5.47874 | − | 2.91881i | 0.233191 | − | 0.124233i | ||||
\(553\) | 3.40332 | + | 0.745340i | 0.144724 | + | 0.0316951i | ||||
\(554\) | − | 3.31754i | − | 0.140949i | ||||||
\(555\) | 25.5586 | − | 13.6164i | 1.08490 | − | 0.577983i | ||||
\(556\) | 13.5283i | 0.573729i | ||||||||
\(557\) | − | 14.7515i | − | 0.625043i | −0.949911 | − | 0.312522i | \(-0.898826\pi\) | ||
0.949911 | − | 0.312522i | \(-0.101174\pi\) | |||||||
\(558\) | −15.2084 | + | 22.6265i | −0.643821 | + | 0.957856i | ||||
\(559\) | 7.79778i | 0.329811i | ||||||||
\(560\) | 4.55081 | + | 0.996643i | 0.192307 | + | 0.0421159i | ||||
\(561\) | 15.4250 | + | 28.9534i | 0.651243 | + | 1.22241i | ||||
\(562\) | −31.8619 | −1.34401 | ||||||||
\(563\) | 43.4063 | 1.82936 | 0.914679 | − | 0.404182i | \(-0.132444\pi\) | ||||
0.914679 | + | 0.404182i | \(0.132444\pi\) | |||||||
\(564\) | 9.85238 | − | 5.24887i | 0.414860 | − | 0.221017i | ||||
\(565\) | − | 34.9996i | − | 1.47244i | ||||||
\(566\) | −24.2711 | −1.02019 | ||||||||
\(567\) | −4.06656 | − | 23.4619i | −0.170779 | − | 0.985309i | ||||
\(568\) | 5.92908 | 0.248779 | ||||||||
\(569\) | 19.1247i | 0.801748i | 0.916133 | + | 0.400874i | \(0.131294\pi\) | ||||
−0.916133 | + | 0.400874i | \(0.868706\pi\) | |||||||
\(570\) | 9.13742 | − | 4.86797i | 0.382724 | − | 0.203897i | ||||
\(571\) | 20.0263 | 0.838073 | 0.419036 | − | 0.907969i | \(-0.362368\pi\) | ||||
0.419036 | + | 0.907969i | \(0.362368\pi\) | |||||||
\(572\) | −3.38959 | −0.141726 | ||||||||
\(573\) | 3.87737 | + | 7.27801i | 0.161979 | + | 0.304043i | ||||
\(574\) | 2.53524 | − | 11.5762i | 0.105819 | − | 0.483183i | ||||
\(575\) | − | 6.80807i | − | 0.283916i | ||||||
\(576\) | −1.67354 | + | 2.48983i | −0.0697307 | + | 0.103743i | ||||
\(577\) | − | 27.0600i | − | 1.12652i | −0.826279 | − | 0.563261i | \(-0.809546\pi\) | ||
0.826279 | − | 0.563261i | \(-0.190454\pi\) | |||||||
\(578\) | 14.2241i | 0.591645i | ||||||||
\(579\) | 34.5307 | − | 18.3963i | 1.43505 | − | 0.764524i | ||||
\(580\) | − | 6.44240i | − | 0.267506i | ||||||
\(581\) | 2.27153 | + | 0.497473i | 0.0942389 | + | 0.0206387i | ||||
\(582\) | 8.91201 | − | 4.74789i | 0.369415 | − | 0.196806i | ||||
\(583\) | −16.9259 | −0.701000 | ||||||||
\(584\) | 8.84923 | 0.366184 | ||||||||
\(585\) | 4.38412 | + | 2.94678i | 0.181261 | + | 0.121834i | ||||
\(586\) | 17.4689i | 0.721635i | ||||||||
\(587\) | −11.1995 | −0.462252 | −0.231126 | − | 0.972924i | \(-0.574241\pi\) | ||||
−0.231126 | + | 0.972924i | \(0.574241\pi\) | |||||||
\(588\) | −12.1038 | + | 0.706506i | −0.499150 | + | 0.0291358i | ||||
\(589\) | 30.8496 | 1.27114 | ||||||||
\(590\) | − | 0.359336i | − | 0.0147936i | ||||||
\(591\) | −14.9583 | − | 28.0775i | −0.615303 | − | 1.15495i | ||||
\(592\) | 9.49548 | 0.390262 | ||||||||
\(593\) | 5.03154 | 0.206621 | 0.103310 | − | 0.994649i | \(-0.467057\pi\) | ||||
0.103310 | + | 0.994649i | \(0.467057\pi\) | |||||||
\(594\) | 1.79837 | − | 17.5208i | 0.0737878 | − | 0.718886i | ||||
\(595\) | −25.4292 | − | 5.56910i | −1.04250 | − | 0.228311i | ||||
\(596\) | 6.12739i | 0.250988i | ||||||||
\(597\) | −13.1974 | − | 24.7721i | −0.540133 | − | 1.01386i | ||||
\(598\) | − | 3.58404i | − | 0.146562i | ||||||
\(599\) | 36.7468i | 1.50143i | 0.660625 | + | 0.750716i | \(0.270291\pi\) | ||||
−0.660625 | + | 0.750716i | \(0.729709\pi\) | |||||||
\(600\) | 1.54698 | + | 2.90375i | 0.0631550 | + | 0.118545i | ||||
\(601\) | − | 4.32636i | − | 0.176476i | −0.996099 | − | 0.0882380i | \(-0.971876\pi\) | ||
0.996099 | − | 0.0882380i | \(-0.0281236\pi\) | |||||||
\(602\) | −4.41365 | + | 20.1533i | −0.179887 | + | 0.821388i | ||||
\(603\) | −24.9995 | + | 37.1934i | −1.01806 | + | 1.51463i | ||||
\(604\) | 17.1388 | 0.697368 | ||||||||
\(605\) | −0.861593 | −0.0350287 | ||||||||
\(606\) | −9.88754 | − | 18.5594i | −0.401654 | − | 0.753924i | ||||
\(607\) | 11.0662i | 0.449163i | 0.974455 | + | 0.224582i | \(0.0721015\pi\) | ||||
−0.974455 | + | 0.224582i | \(0.927898\pi\) | |||||||
\(608\) | 3.39471 | 0.137674 | ||||||||
\(609\) | 4.53524 | + | 16.1416i | 0.183777 | + | 0.654090i | ||||
\(610\) | −5.60908 | −0.227105 | ||||||||
\(611\) | − | 6.44515i | − | 0.260743i | ||||||
\(612\) | 9.35148 | − | 13.9128i | 0.378011 | − | 0.562393i | ||||
\(613\) | 7.04915 | 0.284712 | 0.142356 | − | 0.989815i | \(-0.454532\pi\) | ||||
0.142356 | + | 0.989815i | \(0.454532\pi\) | |||||||
\(614\) | −10.6490 | −0.429760 | ||||||||
\(615\) | −12.0562 | + | 6.42297i | −0.486154 | + | 0.258999i | ||||
\(616\) | −8.76039 | − | 1.91856i | −0.352966 | − | 0.0773008i | ||||
\(617\) | − | 31.6993i | − | 1.27617i | −0.769967 | − | 0.638083i | \(-0.779727\pi\) | ||
0.769967 | − | 0.638083i | \(-0.220273\pi\) | |||||||
\(618\) | −11.0126 | + | 5.86696i | −0.442990 | + | 0.236004i | ||||
\(619\) | 29.9020i | 1.20186i | 0.799301 | + | 0.600931i | \(0.205203\pi\) | ||||
−0.799301 | + | 0.600931i | \(0.794797\pi\) | |||||||
\(620\) | − | 16.0014i | − | 0.642633i | ||||||
\(621\) | 18.5259 | + | 1.90153i | 0.743419 | + | 0.0763059i | ||||
\(622\) | 12.6195i | 0.505995i | ||||||||
\(623\) | −34.6102 | − | 7.57977i | −1.38663 | − | 0.303677i | ||||
\(624\) | 0.814390 | + | 1.52865i | 0.0326017 | + | 0.0611949i | ||||
\(625\) | −11.8939 | −0.475758 | ||||||||
\(626\) | 22.9015 | 0.915327 | ||||||||
\(627\) | −17.5897 | + | 9.37093i | −0.702465 | + | 0.374239i | ||||
\(628\) | 4.50214i | 0.179655i | ||||||||
\(629\) | −53.0593 | −2.11561 | ||||||||
\(630\) | 9.66283 | + | 10.0974i | 0.384976 | + | 0.402291i | ||||
\(631\) | −39.2320 | −1.56180 | −0.780900 | − | 0.624655i | \(-0.785239\pi\) | ||||
−0.780900 | + | 0.624655i | \(0.785239\pi\) | |||||||
\(632\) | − | 1.31682i | − | 0.0523804i | ||||||
\(633\) | −25.9505 | + | 13.8252i | −1.03144 | + | 0.549501i | ||||
\(634\) | 19.9238 | 0.791273 | ||||||||
\(635\) | 2.78363 | 0.110465 | ||||||||
\(636\) | 4.06666 | + | 7.63331i | 0.161254 | + | 0.302681i | ||||
\(637\) | −2.92573 | + | 6.35926i | −0.115921 | + | 0.251963i | ||||
\(638\) | 12.4017i | 0.490989i | ||||||||
\(639\) | 14.7624 | + | 9.92254i | 0.583993 | + | 0.392530i | ||||
\(640\) | − | 1.76081i | − | 0.0696021i | ||||||
\(641\) | − | 4.48351i | − | 0.177088i | −0.996072 | − | 0.0885439i | \(-0.971779\pi\) | ||
0.996072 | − | 0.0885439i | \(-0.0282214\pi\) | |||||||
\(642\) | −20.4530 | + | 10.8964i | −0.807215 | + | 0.430045i | ||||
\(643\) | − | 27.5681i | − | 1.08718i | −0.839351 | − | 0.543590i | \(-0.817065\pi\) | ||
0.839351 | − | 0.543590i | \(-0.182935\pi\) | |||||||
\(644\) | 2.02862 | − | 9.26295i | 0.0799388 | − | 0.365011i | ||||
\(645\) | 20.9890 | − | 11.1819i | 0.826439 | − | 0.440287i | ||||
\(646\) | −18.9692 | −0.746332 | ||||||||
\(647\) | 20.4352 | 0.803389 | 0.401695 | − | 0.915774i | \(-0.368421\pi\) | ||||
0.401695 | + | 0.915774i | \(0.368421\pi\) | |||||||
\(648\) | −8.33366 | + | 3.39855i | −0.327377 | + | 0.133507i | ||||
\(649\) | 0.691729i | 0.0271527i | ||||||||
\(650\) | 1.89955 | 0.0745065 | ||||||||
\(651\) | 11.2645 | + | 40.0920i | 0.441490 | + | 1.57133i | ||||
\(652\) | −1.40702 | −0.0551032 | ||||||||
\(653\) | 7.32638i | 0.286703i | 0.989672 | + | 0.143352i | \(0.0457880\pi\) | ||||
−0.989672 | + | 0.143352i | \(0.954212\pi\) | |||||||
\(654\) | −2.50222 | − | 4.69678i | −0.0978445 | − | 0.183659i | ||||
\(655\) | 32.0470 | 1.25218 | ||||||||
\(656\) | −4.47910 | −0.174880 | ||||||||
\(657\) | 22.0331 | + | 14.8095i | 0.859593 | + | 0.577774i | ||||
\(658\) | 3.64805 | − | 16.6575i | 0.142216 | − | 0.649376i | ||||
\(659\) | 46.0263i | 1.79293i | 0.443116 | + | 0.896464i | \(0.353873\pi\) | ||||
−0.443116 | + | 0.896464i | \(0.646127\pi\) | |||||||
\(660\) | 4.86062 | + | 9.12362i | 0.189199 | + | 0.355136i | ||||
\(661\) | − | 38.8111i | − | 1.50958i | −0.655969 | − | 0.754788i | \(-0.727740\pi\) | ||
0.655969 | − | 0.754788i | \(-0.272260\pi\) | |||||||
\(662\) | 18.8267i | 0.731719i | ||||||||
\(663\) | −4.55069 | − | 8.54187i | −0.176734 | − | 0.331739i | ||||
\(664\) | − | 0.878906i | − | 0.0341082i | ||||||
\(665\) | 3.38332 | − | 15.4487i | 0.131199 | − | 0.599074i | ||||
\(666\) | 23.6422 | + | 15.8910i | 0.916115 | + | 0.615765i | ||||
\(667\) | −13.1132 | −0.507745 | ||||||||
\(668\) | −2.93743 | −0.113653 | ||||||||
\(669\) | 7.53402 | + | 14.1417i | 0.291282 | + | 0.546751i | ||||
\(670\) | − | 26.3031i | − | 1.01618i | ||||||
\(671\) | 10.7976 | 0.416836 | ||||||||
\(672\) | 1.23955 | + | 4.41175i | 0.0478167 | + | 0.170187i | ||||
\(673\) | −4.35748 | −0.167969 | −0.0839843 | − | 0.996467i | \(-0.526765\pi\) | ||||
−0.0839843 | + | 0.996467i | \(0.526765\pi\) | |||||||
\(674\) | − | 30.0841i | − | 1.15880i | ||||||
\(675\) | −1.00782 | + | 9.81877i | −0.0387909 | + | 0.377925i | ||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −19.1334 | −0.735355 | −0.367677 | − | 0.929953i | \(-0.619847\pi\) | ||||
−0.367677 | + | 0.929953i | \(0.619847\pi\) | |||||||
\(678\) | 30.3849 | − | 16.1876i | 1.16693 | − | 0.621682i | ||||
\(679\) | 3.29986 | − | 15.0676i | 0.126637 | − | 0.578241i | ||||
\(680\) | 9.83914i | 0.377314i | ||||||||
\(681\) | −23.1156 | + | 12.3149i | −0.885794 | + | 0.471908i | ||||
\(682\) | 30.8031i | 1.17951i | ||||||||
\(683\) | − | 28.9373i | − | 1.10726i | −0.832764 | − | 0.553628i | \(-0.813243\pi\) | ||
0.832764 | − | 0.553628i | \(-0.186757\pi\) | |||||||
\(684\) | 8.45227 | + | 5.68118i | 0.323181 | + | 0.217225i | ||||
\(685\) | − | 19.5377i | − | 0.746495i | ||||||
\(686\) | −11.1610 | + | 14.7795i | −0.426127 | + | 0.564283i | ||||
\(687\) | −16.5074 | − | 30.9853i | −0.629798 | − | 1.18216i | ||||
\(688\) | 7.79778 | 0.297287 | ||||||||
\(689\) | 4.99350 | 0.190237 | ||||||||
\(690\) | −9.64702 | + | 5.13946i | −0.367256 | + | 0.195656i | ||||
\(691\) | − | 42.5806i | − | 1.61984i | −0.586539 | − | 0.809921i | \(-0.699510\pi\) | ||
0.586539 | − | 0.809921i | \(-0.300490\pi\) | |||||||
\(692\) | −7.62715 | −0.289941 | ||||||||
\(693\) | −18.6011 | − | 19.4377i | −0.706598 | − | 0.738378i | ||||
\(694\) | −16.2862 | −0.618214 | ||||||||
\(695\) | − | 23.8208i | − | 0.903575i | ||||||
\(696\) | 5.59298 | − | 2.97967i | 0.212001 | − | 0.112944i | ||||
\(697\) | 25.0286 | 0.948025 | ||||||||
\(698\) | −24.0366 | −0.909798 | ||||||||
\(699\) | 4.54666 | + | 8.53429i | 0.171970 | + | 0.322797i | ||||
\(700\) | 4.90939 | + | 1.07517i | 0.185557 | + | 0.0406377i | ||||
\(701\) | 20.7064i | 0.782069i | 0.920376 | + | 0.391034i | \(0.127883\pi\) | ||||
−0.920376 | + | 0.391034i | \(0.872117\pi\) | |||||||
\(702\) | −0.530556 | + | 5.16900i | −0.0200245 | + | 0.195091i | ||||
\(703\) | − | 32.2344i | − | 1.21574i | ||||||
\(704\) | 3.38959i | 0.127750i | ||||||||
\(705\) | −17.3482 | + | 9.24226i | −0.653369 | + | 0.348083i | ||||
\(706\) | − | 18.6483i | − | 0.701839i | ||||||
\(707\) | −31.3785 | − | 6.87200i | −1.18011 | − | 0.258448i | ||||
\(708\) | 0.311958 | − | 0.166196i | 0.0117241 | − | 0.00624604i | ||||
\(709\) | −12.1165 | −0.455046 | −0.227523 | − | 0.973773i | \(-0.573063\pi\) | ||||
−0.227523 | + | 0.973773i | \(0.573063\pi\) | |||||||
\(710\) | −10.4400 | −0.391806 | ||||||||
\(711\) | 2.20375 | − | 3.27867i | 0.0826471 | − | 0.122960i | ||||
\(712\) | 13.3915i | 0.501867i | ||||||||
\(713\) | −32.5702 | −1.21976 | ||||||||
\(714\) | −6.92643 | − | 24.6522i | −0.259215 | − | 0.922585i | ||||
\(715\) | 5.96842 | 0.223206 | ||||||||
\(716\) | − | 5.02398i | − | 0.187755i | ||||||
\(717\) | 19.7319 | + | 37.0377i | 0.736901 | + | 1.38320i | ||||
\(718\) | 6.78798 | 0.253325 | ||||||||
\(719\) | 43.1786 | 1.61029 | 0.805144 | − | 0.593079i | \(-0.202088\pi\) | ||||
0.805144 | + | 0.593079i | \(0.202088\pi\) | |||||||
\(720\) | 2.94678 | − | 4.38412i | 0.109820 | − | 0.163387i | ||||
\(721\) | −4.07763 | + | 18.6190i | −0.151859 | + | 0.693408i | ||||
\(722\) | 7.47592i | 0.278225i | ||||||||
\(723\) | −23.3712 | − | 43.8689i | −0.869186 | − | 1.63150i | ||||
\(724\) | − | 5.50980i | − | 0.204770i | ||||||
\(725\) | − | 6.95002i | − | 0.258117i | ||||||
\(726\) | −0.398494 | − | 0.747993i | −0.0147895 | − | 0.0277606i | ||||
\(727\) | − | 38.9882i | − | 1.44599i | −0.690852 | − | 0.722996i | \(-0.742764\pi\) | ||
0.690852 | − | 0.722996i | \(-0.257236\pi\) | |||||||
\(728\) | 2.58450 | + | 0.566014i | 0.0957879 | + | 0.0209779i | ||||
\(729\) | −26.4370 | − | 5.48488i | −0.979149 | − | 0.203144i | ||||
\(730\) | −15.5818 | −0.576708 | ||||||||
\(731\) | −43.5728 | −1.61160 | ||||||||
\(732\) | −2.59425 | − | 4.86953i | −0.0958863 | − | 0.179983i | ||||
\(733\) | 44.4475i | 1.64171i | 0.571139 | + | 0.820853i | \(0.306502\pi\) | ||||
−0.571139 | + | 0.820853i | \(0.693498\pi\) | |||||||
\(734\) | 21.2093 | 0.782848 | ||||||||
\(735\) | 21.3124 | − | 1.24402i | 0.786120 | − | 0.0458865i | ||||
\(736\) | −3.58404 | −0.132110 | ||||||||
\(737\) | 50.6340i | 1.86513i | ||||||||
\(738\) | −11.1522 | − | 7.49595i | −0.410519 | − | 0.275930i | ||||
\(739\) | 43.9802 | 1.61784 | 0.808920 | − | 0.587919i | \(-0.200053\pi\) | ||||
0.808920 | + | 0.587919i | \(0.200053\pi\) | |||||||
\(740\) | −16.7197 | −0.614629 | ||||||||
\(741\) | 5.18933 | − | 2.76462i | 0.190635 | − | 0.101561i | ||||
\(742\) | 12.9057 | + | 2.82639i | 0.473783 | + | 0.103760i | ||||
\(743\) | 7.77737i | 0.285324i | 0.989771 | + | 0.142662i | \(0.0455662\pi\) | ||||
−0.989771 | + | 0.142662i | \(0.954434\pi\) | |||||||
\(744\) | 13.8917 | − | 7.40081i | 0.509294 | − | 0.271327i | ||||
\(745\) | − | 10.7892i | − | 0.395285i | ||||||
\(746\) | − | 3.41020i | − | 0.124856i | ||||||
\(747\) | 1.47088 | − | 2.18833i | 0.0538167 | − | 0.0800668i | ||||
\(748\) | − | 18.9405i | − | 0.692534i | ||||||
\(749\) | −7.57315 | + | 34.5800i | −0.276717 | + | 1.26353i | ||||
\(750\) | −9.89386 | − | 18.5712i | −0.361273 | − | 0.678126i | ||||
\(751\) | 10.8242 | 0.394979 | 0.197490 | − | 0.980305i | \(-0.436721\pi\) | ||||
0.197490 | + | 0.980305i | \(0.436721\pi\) | |||||||
\(752\) | −6.44515 | −0.235031 | ||||||||
\(753\) | 34.4340 | − | 18.3448i | 1.25485 | − | 0.668521i | ||||
\(754\) | − | 3.65877i | − | 0.133245i | ||||||
\(755\) | −30.1782 | −1.09830 | ||||||||
\(756\) | −4.29695 | + | 13.0590i | −0.156278 | + | 0.474950i | ||||
\(757\) | 49.3460 | 1.79351 | 0.896756 | − | 0.442525i | \(-0.145917\pi\) | ||||
0.896756 | + | 0.442525i | \(0.145917\pi\) | |||||||
\(758\) | − | 13.7818i | − | 0.500576i | ||||||
\(759\) | 18.5707 | − | 9.89356i | 0.674073 | − | 0.359114i | ||||
\(760\) | −5.97744 | −0.216825 | ||||||||
\(761\) | 1.65026 | 0.0598219 | 0.0299109 | − | 0.999553i | \(-0.490478\pi\) | ||||
0.0299109 | + | 0.999553i | \(0.490478\pi\) | |||||||
\(762\) | 1.28745 | + | 2.41661i | 0.0466395 | + | 0.0875446i | ||||
\(763\) | −7.94088 | − | 1.73908i | −0.287479 | − | 0.0629590i | ||||
\(764\) | − | 4.76107i | − | 0.172249i | ||||||
\(765\) | −16.4662 | + | 24.4978i | −0.595336 | + | 0.885721i | ||||
\(766\) | − | 20.6937i | − | 0.747693i | ||||||
\(767\) | − | 0.204075i | − | 0.00736871i | ||||||
\(768\) | 1.52865 | − | 0.814390i | 0.0551604 | − | 0.0293868i | ||||
\(769\) | − | 5.66416i | − | 0.204255i | −0.994771 | − | 0.102127i | \(-0.967435\pi\) | ||
0.994771 | − | 0.102127i | \(-0.0325649\pi\) | |||||||
\(770\) | 15.4254 | + | 3.37821i | 0.555892 | + | 0.121742i | ||||
\(771\) | 42.0482 | − | 22.4012i | 1.51433 | − | 0.806761i | ||||
\(772\) | −22.5891 | −0.812998 | ||||||||
\(773\) | −16.2379 | −0.584037 | −0.292019 | − | 0.956413i | \(-0.594327\pi\) | ||||
−0.292019 | + | 0.956413i | \(0.594327\pi\) | |||||||
\(774\) | 19.4152 | + | 13.0499i | 0.697864 | + | 0.469068i | ||||
\(775\) | − | 17.2623i | − | 0.620079i | ||||||
\(776\) | −5.82999 | −0.209284 | ||||||||
\(777\) | 41.8916 | − | 11.7701i | 1.50285 | − | 0.422251i | ||||
\(778\) | 13.7432 | 0.492717 | ||||||||
\(779\) | 15.2053i | 0.544786i | ||||||||
\(780\) | −1.43399 | − | 2.69166i | −0.0513449 | − | 0.0963769i | ||||
\(781\) | 20.0972 | 0.719133 | ||||||||
\(782\) | 20.0271 | 0.716168 | ||||||||
\(783\) | 18.9122 | + | 1.94118i | 0.675866 | + | 0.0693722i | ||||
\(784\) | 6.35926 | + | 2.92573i | 0.227116 | + | 0.104490i | ||||
\(785\) | − | 7.92741i | − | 0.282941i | ||||||
\(786\) | 14.8220 | + | 27.8216i | 0.528684 | + | 0.992365i | ||||
\(787\) | 21.0932i | 0.751893i | 0.926641 | + | 0.375946i | \(0.122682\pi\) | ||||
−0.926641 | + | 0.375946i | \(0.877318\pi\) | |||||||
\(788\) | 18.3675i | 0.654316i | ||||||||
\(789\) | −6.17001 | − | 11.5814i | −0.219658 | − | 0.412309i | ||||
\(790\) | 2.31867i | 0.0824946i | ||||||||
\(791\) | 11.2507 | − | 51.3720i | 0.400027 | − | 1.82658i | ||||
\(792\) | −5.67260 | + | 8.43951i | −0.201567 | + | 0.299885i | ||||
\(793\) | −3.18551 | −0.113121 | ||||||||
\(794\) | 9.96913 | 0.353791 | ||||||||
\(795\) | −7.16061 | − | 13.4408i | −0.253961 | − | 0.476696i | ||||
\(796\) | 16.2052i | 0.574379i | ||||||||
\(797\) | −55.1246 | −1.95261 | −0.976307 | − | 0.216392i | \(-0.930571\pi\) | ||||
−0.976307 | + | 0.216392i | \(0.930571\pi\) | |||||||
\(798\) | 14.9766 | − | 4.20792i | 0.530167 | − | 0.148959i | ||||
\(799\) | 36.0146 | 1.27410 | ||||||||
\(800\) | − | 1.89955i | − | 0.0671593i | ||||||
\(801\) | −22.4111 | + | 33.3426i | −0.791859 | + | 1.17810i | ||||
\(802\) | −3.80987 | −0.134531 | ||||||||
\(803\) | 29.9952 | 1.05851 | ||||||||
\(804\) | 22.8351 | − | 12.1654i | 0.805332 | − | 0.429042i | ||||
\(805\) | −3.57201 | + | 16.3103i | −0.125897 | + | 0.574862i | ||||
\(806\) | − | 9.08755i | − | 0.320095i | ||||||
\(807\) | 27.3393 | − | 14.5650i | 0.962389 | − | 0.512714i | ||||
\(808\) | 12.1410i | 0.427120i | ||||||||
\(809\) | 26.5257i | 0.932594i | 0.884628 | + | 0.466297i | \(0.154412\pi\) | ||||
−0.884628 | + | 0.466297i | \(0.845588\pi\) | |||||||
\(810\) | 14.6740 | − | 5.98419i | 0.515591 | − | 0.210263i | ||||
\(811\) | − | 50.5615i | − | 1.77545i | −0.460370 | − | 0.887727i | \(-0.652283\pi\) | ||
0.460370 | − | 0.887727i | \(-0.347717\pi\) | |||||||
\(812\) | 2.07092 | − | 9.45609i | 0.0726750 | − | 0.331844i | ||||
\(813\) | 17.5655 | + | 32.9714i | 0.616050 | + | 1.15636i | ||||
\(814\) | 32.1858 | 1.12811 | ||||||||
\(815\) | 2.47750 | 0.0867829 | ||||||||
\(816\) | −8.54187 | + | 4.55069i | −0.299025 | + | 0.159306i | ||||
\(817\) | − | 26.4712i | − | 0.926111i | ||||||
\(818\) | −6.06247 | −0.211969 | ||||||||
\(819\) | 5.48772 | + | 5.73454i | 0.191757 | + | 0.200381i | ||||
\(820\) | 7.88685 | 0.275421 | ||||||||
\(821\) | 27.9672i | 0.976062i | 0.872826 | + | 0.488031i | \(0.162285\pi\) | ||||
−0.872826 | + | 0.488031i | \(0.837715\pi\) | |||||||
\(822\) | 16.9616 | − | 9.03634i | 0.591605 | − | 0.315179i | ||||
\(823\) | 14.9297 | 0.520416 | 0.260208 | − | 0.965553i | \(-0.416209\pi\) | ||||
0.260208 | + | 0.965553i | \(0.416209\pi\) | |||||||
\(824\) | 7.20411 | 0.250967 | ||||||||
\(825\) | 5.24361 | + | 9.84251i | 0.182559 | + | 0.342672i | ||||
\(826\) | 0.115509 | − | 0.527430i | 0.00401908 | − | 0.0183516i | ||||
\(827\) | 8.32248i | 0.289401i | 0.989476 | + | 0.144700i | \(0.0462219\pi\) | ||||
−0.989476 | + | 0.144700i | \(0.953778\pi\) | |||||||
\(828\) | −8.92367 | − | 5.99803i | −0.310119 | − | 0.208446i | ||||
\(829\) | 34.0881i | 1.18393i | 0.805964 | + | 0.591965i | \(0.201648\pi\) | ||||
−0.805964 | + | 0.591965i | \(0.798352\pi\) | |||||||
\(830\) | 1.54759i | 0.0537175i | ||||||||
\(831\) | −5.07136 | + | 2.70177i | −0.175924 | + | 0.0937235i | ||||
\(832\) | − | 1.00000i | − | 0.0346688i | ||||||
\(833\) | −35.5346 | − | 16.3485i | −1.23120 | − | 0.566443i | ||||
\(834\) | 20.6801 | − | 11.0173i | 0.716092 | − | 0.381499i | ||||
\(835\) | 5.17225 | 0.178993 | ||||||||
\(836\) | 11.5067 | 0.397967 | ||||||||
\(837\) | 46.9735 | + | 4.82145i | 1.62364 | + | 0.166654i | ||||
\(838\) | − | 2.46363i | − | 0.0851048i | ||||||
\(839\) | 19.0851 | 0.658889 | 0.329445 | − | 0.944175i | \(-0.393138\pi\) | ||||
0.329445 | + | 0.944175i | \(0.393138\pi\) | |||||||
\(840\) | −2.18261 | − | 7.76824i | −0.0753073 | − | 0.268030i | ||||
\(841\) | 15.6134 | 0.538393 | ||||||||
\(842\) | 2.44268i | 0.0841802i | ||||||||
\(843\) | 25.9480 | + | 48.7057i | 0.893698 | + | 1.67751i | ||||
\(844\) | 16.9761 | 0.584342 | ||||||||
\(845\) | −1.76081 | −0.0605737 | ||||||||
\(846\) | −16.0474 | − | 10.7862i | −0.551720 | − | 0.370837i | ||||
\(847\) | −1.26464 | − | 0.276960i | −0.0434534 | − | 0.00951646i | ||||
\(848\) | − | 4.99350i | − | 0.171478i | ||||||
\(849\) | 19.7661 | + | 37.1020i | 0.678372 | + | 1.27334i | ||||
\(850\) | 10.6144i | 0.364071i | ||||||||
\(851\) | 34.0322i | 1.16661i | ||||||||
\(852\) | −4.82859 | − | 9.06349i | −0.165425 | − | 0.310510i | ||||
\(853\) | 29.6954i | 1.01675i | 0.861135 | + | 0.508376i | \(0.169754\pi\) | ||||
−0.861135 | + | 0.508376i | \(0.830246\pi\) | |||||||
\(854\) | −8.23296 | − | 1.80305i | −0.281726 | − | 0.0616990i | ||||
\(855\) | −14.8828 | − | 10.0035i | −0.508982 | − | 0.342112i | ||||
\(856\) | 13.3798 | 0.457312 | ||||||||
\(857\) | 9.71299 | 0.331790 | 0.165895 | − | 0.986143i | \(-0.446949\pi\) | ||||
0.165895 | + | 0.986143i | \(0.446949\pi\) | |||||||
\(858\) | 2.76045 | + | 5.18149i | 0.0942401 | + | 0.176893i | ||||
\(859\) | 48.7424i | 1.66307i | 0.555473 | + | 0.831535i | \(0.312537\pi\) | ||||
−0.555473 | + | 0.831535i | \(0.687463\pi\) | |||||||
\(860\) | −13.7304 | −0.468203 | ||||||||
\(861\) | −19.7607 | + | 5.55208i | −0.673442 | + | 0.189214i | ||||
\(862\) | 28.7881 | 0.980526 | ||||||||
\(863\) | − | 9.46910i | − | 0.322332i | −0.986927 | − | 0.161166i | \(-0.948475\pi\) | ||
0.986927 | − | 0.161166i | \(-0.0515254\pi\) | |||||||
\(864\) | 5.16900 | + | 0.530556i | 0.175853 | + | 0.0180499i | ||||
\(865\) | 13.4299 | 0.456632 | ||||||||
\(866\) | 32.1412 | 1.09220 | ||||||||
\(867\) | 21.7437 | − | 11.5840i | 0.738454 | − | 0.393413i | ||||
\(868\) | 5.14369 | − | 23.4868i | 0.174588 | − | 0.797192i | ||||
\(869\) | − | 4.46349i | − | 0.151413i | ||||||
\(870\) | −9.84817 | + | 5.24663i | −0.333884 | + | 0.177877i | ||||
\(871\) | − | 14.9381i | − | 0.506158i | ||||||
\(872\) | 3.07251i | 0.104048i | ||||||||
\(873\) | −14.5157 | − | 9.75671i | −0.491282 | − | 0.330215i | ||||
\(874\) | 12.1668i | 0.411548i | ||||||||
\(875\) | −31.3985 | − | 6.87639i | −1.06146 | − | 0.232464i | ||||
\(876\) | −7.20672 | − | 13.5274i | −0.243493 | − | 0.457047i | ||||
\(877\) | −30.6530 | −1.03508 | −0.517538 | − | 0.855660i | \(-0.673152\pi\) | ||||
−0.517538 | + | 0.855660i | \(0.673152\pi\) | |||||||
\(878\) | −9.12045 | −0.307800 | ||||||||
\(879\) | 26.7039 | − | 14.2265i | 0.900700 | − | 0.479849i | ||||
\(880\) | − | 5.96842i | − | 0.201195i | ||||||
\(881\) | 9.61977 | 0.324098 | 0.162049 | − | 0.986783i | \(-0.448190\pi\) | ||||
0.162049 | + | 0.986783i | \(0.448190\pi\) | |||||||
\(882\) | 10.9372 | + | 17.9270i | 0.368274 | + | 0.603634i | ||||
\(883\) | −16.5344 | −0.556427 | −0.278214 | − | 0.960519i | \(-0.589742\pi\) | ||||
−0.278214 | + | 0.960519i | \(0.589742\pi\) | |||||||
\(884\) | 5.58785i | 0.187940i | ||||||||
\(885\) | −0.549299 | + | 0.292640i | −0.0184645 | + | 0.00983699i | ||||
\(886\) | 3.69881 | 0.124264 | ||||||||
\(887\) | −6.47491 | −0.217406 | −0.108703 | − | 0.994074i | \(-0.534670\pi\) | ||||
−0.108703 | + | 0.994074i | \(0.534670\pi\) | |||||||
\(888\) | −7.73302 | − | 14.5153i | −0.259503 | − | 0.487100i | ||||
\(889\) | 4.08578 | + | 0.894801i | 0.137033 | + | 0.0300106i | ||||
\(890\) | − | 23.5798i | − | 0.790398i | ||||||
\(891\) | −28.2477 | + | 11.5197i | −0.946333 | + | 0.385924i | ||||
\(892\) | − | 9.25112i | − | 0.309751i | ||||||
\(893\) | 21.8794i | 0.732168i | ||||||||
\(894\) | 9.36663 | − | 4.99009i | 0.313267 | − | 0.166894i | ||||
\(895\) | 8.84627i | 0.295698i | ||||||||
\(896\) | 0.566014 | − | 2.58450i | 0.0189092 | − | 0.0863420i | ||||
\(897\) | −5.47874 | + | 2.91881i | −0.182930 | + | 0.0974562i | ||||
\(898\) | −16.5731 | −0.553051 | ||||||||
\(899\) | −33.2493 | −1.10893 | ||||||||
\(900\) | 3.17897 | − | 4.72957i | 0.105966 | − | 0.157652i | ||||
\(901\) | 27.9030i | 0.929583i | ||||||||
\(902\) | −15.1823 | −0.505516 | ||||||||
\(903\) | 34.4018 | − | 9.66575i | 1.14482 | − | 0.321656i | ||||
\(904\) | −19.8770 | −0.661099 | ||||||||
\(905\) | 9.70171i | 0.322496i | ||||||||
\(906\) | −13.9577 | − | 26.1992i | −0.463713 | − | 0.870411i | ||||
\(907\) | −41.8043 | −1.38809 | −0.694045 | − | 0.719931i | \(-0.744173\pi\) | ||||
−0.694045 | + | 0.719931i | \(0.744173\pi\) | |||||||
\(908\) | 15.1216 | 0.501828 | ||||||||
\(909\) | −20.3185 | + | 30.2292i | −0.673921 | + | 1.00264i | ||||
\(910\) | −4.55081 | − | 0.996643i | −0.150858 | − | 0.0330384i | ||||
\(911\) | − | 24.1762i | − | 0.800995i | −0.916298 | − | 0.400497i | \(-0.868837\pi\) | ||
0.916298 | − | 0.400497i | \(-0.131163\pi\) | |||||||
\(912\) | −2.76462 | − | 5.18933i | −0.0915458 | − | 0.171836i | ||||
\(913\) | − | 2.97913i | − | 0.0985948i | ||||||
\(914\) | − | 27.3619i | − | 0.905051i | ||||||
\(915\) | 4.56798 | + | 8.57432i | 0.151013 | + | 0.283458i | ||||
\(916\) | 20.2697i | 0.669730i | ||||||||
\(917\) | 47.0382 | + | 10.3015i | 1.55334 | + | 0.340187i | ||||
\(918\) | −28.8836 | − | 2.96467i | −0.953301 | − | 0.0978486i | ||||
\(919\) | 0.658058 | 0.0217073 | 0.0108537 | − | 0.999941i | \(-0.496545\pi\) | ||||
0.0108537 | + | 0.999941i | \(0.496545\pi\) | |||||||
\(920\) | 6.31081 | 0.208061 | ||||||||
\(921\) | 8.67247 | + | 16.2786i | 0.285768 | + | 0.536400i | ||||
\(922\) | − | 21.5496i | − | 0.709699i | ||||||
\(923\) | −5.92908 | −0.195158 | ||||||||
\(924\) | 4.20157 | + | 14.9540i | 0.138222 | + | 0.491951i | ||||
\(925\) | −18.0371 | −0.593058 | ||||||||
\(926\) | 23.3617i | 0.767715i | ||||||||
\(927\) | 17.9370 | + | 12.0563i | 0.589130 | + | 0.395982i | ||||
\(928\) | −3.65877 | −0.120105 | ||||||||
\(929\) | −3.26561 | −0.107141 | −0.0535707 | − | 0.998564i | \(-0.517060\pi\) | ||||
−0.0535707 | + | 0.998564i | \(0.517060\pi\) | |||||||
\(930\) | −24.4606 | + | 13.0314i | −0.802095 | + | 0.427317i | ||||
\(931\) | 9.93200 | − | 21.5879i | 0.325508 | − | 0.707513i | ||||
\(932\) | − | 5.58290i | − | 0.182874i | ||||||
\(933\) | 19.2907 | − | 10.2772i | 0.631551 | − | 0.336459i | ||||
\(934\) | 1.04693i | 0.0342565i | ||||||||
\(935\) | 33.3507i | 1.09068i | ||||||||
\(936\) | 1.67354 | − | 2.48983i | 0.0547013 | − | 0.0813828i | ||||
\(937\) | 16.9455i | 0.553586i | 0.960930 | + | 0.276793i | \(0.0892716\pi\) | ||||
−0.960930 | + | 0.276793i | \(0.910728\pi\) | |||||||
\(938\) | 8.45517 | − | 38.6075i | 0.276071 | − | 1.26058i | ||||
\(939\) | −18.6507 | − | 35.0083i | −0.608644 | − | 1.14245i | ||||
\(940\) | 11.3487 | 0.370153 | ||||||||
\(941\) | 29.5843 | 0.964421 | 0.482210 | − | 0.876055i | \(-0.339834\pi\) | ||||
0.482210 | + | 0.876055i | \(0.339834\pi\) | |||||||
\(942\) | 6.88219 | − | 3.66650i | 0.224234 | − | 0.119461i | ||||
\(943\) | − | 16.0533i | − | 0.522767i | ||||||
\(944\) | −0.204075 | −0.00664206 | ||||||||
\(945\) | 7.56610 | − | 22.9943i | 0.246125 | − | 0.748005i | ||||
\(946\) | 26.4313 | 0.859354 | ||||||||
\(947\) | 19.8609i | 0.645391i | 0.946503 | + | 0.322696i | \(0.104589\pi\) | ||||
−0.946503 | + | 0.322696i | \(0.895411\pi\) | |||||||
\(948\) | −2.01296 | + | 1.07241i | −0.0653779 | + | 0.0348302i | ||||
\(949\) | −8.84923 | −0.287258 | ||||||||
\(950\) | −6.44843 | −0.209215 | ||||||||
\(951\) | −16.2257 | − | 30.4564i | −0.526155 | − | 0.987617i | ||||
\(952\) | −3.16281 | + | 14.4418i | −0.102507 | + | 0.468061i | ||||
\(953\) | 3.71754i | 0.120423i | 0.998186 | + | 0.0602114i | \(0.0191775\pi\) | ||||
−0.998186 | + | 0.0602114i | \(0.980823\pi\) | |||||||
\(954\) | 8.35681 | − | 12.4330i | 0.270562 | − | 0.402533i | ||||
\(955\) | 8.38334i | 0.271278i | ||||||||
\(956\) | − | 24.2290i | − | 0.783623i | ||||||
\(957\) | 18.9579 | − | 10.0999i | 0.612822 | − | 0.326482i | ||||
\(958\) | 1.19995i | 0.0387686i | ||||||||
\(959\) | 6.28040 | − | 28.6772i | 0.202805 | − | 0.926034i | ||||
\(960\) | −2.69166 | + | 1.43399i | −0.0868729 | + | 0.0462817i | ||||
\(961\) | −51.5836 | −1.66399 | ||||||||
\(962\) | −9.49548 | −0.306146 | ||||||||
\(963\) | 33.3134 | + | 22.3916i | 1.07351 | + | 0.721558i | ||||
\(964\) | 28.6978i | 0.924295i | ||||||||
\(965\) | 39.7750 | 1.28040 | ||||||||
\(966\) | −15.8119 | + | 4.44261i | −0.508739 | + | 0.142938i | ||||
\(967\) | 19.3495 | 0.622239 | 0.311120 | − | 0.950371i | \(-0.399296\pi\) | ||||
0.311120 | + | 0.950371i | \(0.399296\pi\) | |||||||
\(968\) | 0.489316i | 0.0157272i | ||||||||
\(969\) | 15.4483 | + | 28.9972i | 0.496271 | + | 0.931524i | ||||
\(970\) | 10.2655 | 0.329605 | ||||||||
\(971\) | −16.4867 | −0.529083 | −0.264542 | − | 0.964374i | \(-0.585221\pi\) | ||||
−0.264542 | + | 0.964374i | \(0.585221\pi\) | |||||||
\(972\) | 11.9820 | + | 9.97150i | 0.384324 | + | 0.319836i | ||||
\(973\) | 7.65723 | − | 34.9639i | 0.245480 | − | 1.12089i | ||||
\(974\) | 13.6246i | 0.436560i | ||||||||
\(975\) | −1.54698 | − | 2.90375i | −0.0495429 | − | 0.0929944i | ||||
\(976\) | 3.18551i | 0.101966i | ||||||||
\(977\) | 43.6047i | 1.39504i | 0.716566 | + | 0.697519i | \(0.245713\pi\) | ||||
−0.716566 | + | 0.697519i | \(0.754287\pi\) | |||||||
\(978\) | 1.14586 | + | 2.15084i | 0.0366407 | + | 0.0687763i | ||||
\(979\) | 45.3916i | 1.45072i | ||||||||
\(980\) | −11.1974 | − | 5.15164i | −0.357689 | − | 0.164563i | ||||
\(981\) | −5.14195 | + | 7.65003i | −0.164170 | + | 0.244247i | ||||
\(982\) | 6.31588 | 0.201548 | ||||||||
\(983\) | −27.8266 | −0.887532 | −0.443766 | − | 0.896143i | \(-0.646358\pi\) | ||||
−0.443766 | + | 0.896143i | \(0.646358\pi\) | |||||||
\(984\) | 3.64774 | + | 6.84698i | 0.116286 | + | 0.218274i | ||||
\(985\) | − | 32.3417i | − | 1.03049i | ||||||
\(986\) | 20.4447 | 0.651091 | ||||||||
\(987\) | −28.4344 | + | 7.98910i | −0.905076 | + | 0.254296i | ||||
\(988\) | −3.39471 | −0.108000 | ||||||||
\(989\) | 27.9476i | 0.888680i | ||||||||
\(990\) | 9.98837 | − | 14.8604i | 0.317451 | − | 0.472294i | ||||
\(991\) | 13.6266 | 0.432863 | 0.216431 | − | 0.976298i | \(-0.430558\pi\) | ||||
0.216431 | + | 0.976298i | \(0.430558\pi\) | |||||||
\(992\) | −9.08755 | −0.288530 | ||||||||
\(993\) | 28.7794 | − | 15.3323i | 0.913286 | − | 0.486554i | ||||
\(994\) | −15.3237 | − | 3.35595i | −0.486038 | − | 0.106444i | ||||
\(995\) | − | 28.5343i | − | 0.904599i | ||||||
\(996\) | −1.34354 | + | 0.715772i | −0.0425716 | + | 0.0226801i | ||||
\(997\) | − | 53.7319i | − | 1.70171i | −0.525403 | − | 0.850854i | \(-0.676085\pi\) | ||
0.525403 | − | 0.850854i | \(-0.323915\pi\) | |||||||
\(998\) | 7.28573i | 0.230626i | ||||||||
\(999\) | 5.03788 | − | 49.0821i | 0.159391 | − | 1.55289i |
(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 | 546.2.g.c.209.12 | yes | 12 | |
3.2 | odd | 2 | 546.2.g.d.209.1 | yes | 12 | ||
7.6 | odd | 2 | 546.2.g.d.209.7 | yes | 12 | ||
21.20 | even | 2 | inner | 546.2.g.c.209.6 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.g.c.209.6 | ✓ | 12 | 21.20 | even | 2 | inner | |
546.2.g.c.209.12 | yes | 12 | 1.1 | even | 1 | trivial | |
546.2.g.d.209.1 | yes | 12 | 3.2 | odd | 2 | ||
546.2.g.d.209.7 | yes | 12 | 7.6 | odd | 2 |