Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [490,2,Mod(97,490)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(490, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("490.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 490 = 2 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 490.g (of order \(4\), 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: | \(3.91266969904\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 97.5 | ||
Root | \(-0.144868 + 1.25092i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 490.97 |
Dual form | 490.2.g.c.293.5 |
$q$-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 \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | −1.42962 | − | 1.42962i | −0.825391 | − | 0.825391i | 0.161484 | − | 0.986875i | \(-0.448372\pi\) |
−0.986875 | + | 0.161484i | \(0.948372\pi\) | |||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −0.204875 | − | 2.22666i | −0.0916228 | − | 0.995794i | ||||
\(6\) | − | 2.02179i | − | 0.825391i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 1.08763i | 0.362542i | ||||||||
\(10\) | 1.42962 | − | 1.71936i | 0.452085 | − | 0.543708i | ||||
\(11\) | −4.03997 | −1.21810 | −0.609049 | − | 0.793133i | \(-0.708449\pi\) | ||||
−0.609049 | + | 0.793133i | \(0.708449\pi\) | |||||||
\(12\) | 1.42962 | − | 1.42962i | 0.412696 | − | 0.412696i | ||||
\(13\) | −0.204875 | − | 0.204875i | −0.0568221 | − | 0.0568221i | 0.678125 | − | 0.734947i | \(-0.262793\pi\) |
−0.734947 | + | 0.678125i | \(0.762793\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.89039 | + | 3.47617i | −0.746295 | + | 0.897544i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −1.44231 | + | 1.44231i | −0.349813 | + | 0.349813i | −0.860040 | − | 0.510227i | \(-0.829561\pi\) |
0.510227 | + | 0.860040i | \(0.329561\pi\) | |||||||
\(18\) | −0.769067 | + | 0.769067i | −0.181271 | + | 0.181271i | ||||
\(19\) | −6.20333 | −1.42314 | −0.711571 | − | 0.702615i | \(-0.752016\pi\) | ||||
−0.711571 | + | 0.702615i | \(0.752016\pi\) | |||||||
\(20\) | 2.22666 | − | 0.204875i | 0.497897 | − | 0.0458114i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.85669 | − | 2.85669i | −0.609049 | − | 0.609049i | ||||
\(23\) | 3.20895 | − | 3.20895i | 0.669111 | − | 0.669111i | −0.288399 | − | 0.957510i | \(-0.593123\pi\) |
0.957510 | + | 0.288399i | \(0.0931229\pi\) | |||||||
\(24\) | 2.02179 | 0.412696 | ||||||||
\(25\) | −4.91605 | + | 0.912375i | −0.983211 | + | 0.182475i | ||||
\(26\) | − | 0.289737i | − | 0.0568221i | ||||||
\(27\) | −2.73397 | + | 2.73397i | −0.526152 | + | 0.526152i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7.15869i | − | 1.32934i | −0.747139 | − | 0.664668i | \(-0.768573\pi\) | ||
0.747139 | − | 0.664668i | \(-0.231427\pi\) | |||||||
\(30\) | −4.50184 | + | 0.414214i | −0.821920 | + | 0.0756247i | ||||
\(31\) | − | 7.31256i | − | 1.31338i | −0.754163 | − | 0.656688i | \(-0.771957\pi\) | ||
0.754163 | − | 0.656688i | \(-0.228043\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 5.77563 | + | 5.77563i | 1.00541 | + | 1.00541i | ||||
\(34\) | −2.03974 | −0.349813 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.08763 | −0.181271 | ||||||||
\(37\) | 3.27091 | + | 3.27091i | 0.537734 | + | 0.537734i | 0.922863 | − | 0.385129i | \(-0.125843\pi\) |
−0.385129 | + | 0.922863i | \(0.625843\pi\) | |||||||
\(38\) | −4.38642 | − | 4.38642i | −0.711571 | − | 0.711571i | ||||
\(39\) | 0.585786i | 0.0938009i | ||||||||
\(40\) | 1.71936 | + | 1.42962i | 0.271854 | + | 0.226043i | ||||
\(41\) | − | 2.58745i | − | 0.404093i | −0.979376 | − | 0.202046i | \(-0.935241\pi\) | ||
0.979376 | − | 0.202046i | \(-0.0647591\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.97801 | + | 4.97801i | −0.759140 | + | 0.759140i | −0.976166 | − | 0.217026i | \(-0.930364\pi\) |
0.217026 | + | 0.976166i | \(0.430364\pi\) | |||||||
\(44\) | − | 4.03997i | − | 0.609049i | ||||||
\(45\) | 2.42177 | − | 0.222827i | 0.361017 | − | 0.0332171i | ||||
\(46\) | 4.53813 | 0.669111 | ||||||||
\(47\) | 0.222827 | − | 0.222827i | 0.0325027 | − | 0.0325027i | −0.690669 | − | 0.723171i | \(-0.742684\pi\) |
0.723171 | + | 0.690669i | \(0.242684\pi\) | |||||||
\(48\) | 1.42962 | + | 1.42962i | 0.206348 | + | 0.206348i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.12132 | − | 2.83103i | −0.582843 | − | 0.400368i | ||||
\(51\) | 4.12392 | 0.577464 | ||||||||
\(52\) | 0.204875 | − | 0.204875i | 0.0284110 | − | 0.0284110i | ||||
\(53\) | 5.85669 | − | 5.85669i | 0.804479 | − | 0.804479i | −0.179313 | − | 0.983792i | \(-0.557388\pi\) |
0.983792 | + | 0.179313i | \(0.0573876\pi\) | |||||||
\(54\) | −3.86642 | −0.526152 | ||||||||
\(55\) | 0.827689 | + | 8.99566i | 0.111606 | + | 1.21297i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.86840 | + | 8.86840i | 1.17465 | + | 1.17465i | ||||
\(58\) | 5.06196 | − | 5.06196i | 0.664668 | − | 0.664668i | ||||
\(59\) | 0.855404 | 0.111364 | 0.0556821 | − | 0.998449i | \(-0.482267\pi\) | ||||
0.0556821 | + | 0.998449i | \(0.482267\pi\) | |||||||
\(60\) | −3.47617 | − | 2.89039i | −0.448772 | − | 0.373147i | ||||
\(61\) | − | 6.92077i | − | 0.886113i | −0.896494 | − | 0.443057i | \(-0.853894\pi\) | ||
0.896494 | − | 0.443057i | \(-0.146106\pi\) | |||||||
\(62\) | 5.17076 | − | 5.17076i | 0.656688 | − | 0.656688i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −0.414214 | + | 0.498161i | −0.0513769 | + | 0.0617893i | ||||
\(66\) | 8.16797i | 1.00541i | ||||||||
\(67\) | −2.23353 | − | 2.23353i | −0.272870 | − | 0.272870i | 0.557385 | − | 0.830254i | \(-0.311805\pi\) |
−0.830254 | + | 0.557385i | \(0.811805\pi\) | |||||||
\(68\) | −1.44231 | − | 1.44231i | −0.174906 | − | 0.174906i | ||||
\(69\) | −9.17514 | −1.10456 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.12240 | 0.845273 | 0.422637 | − | 0.906299i | \(-0.361105\pi\) | ||||
0.422637 | + | 0.906299i | \(0.361105\pi\) | |||||||
\(72\) | −0.769067 | − | 0.769067i | −0.0906355 | − | 0.0906355i | ||||
\(73\) | 8.15002 | + | 8.15002i | 0.953887 | + | 0.953887i | 0.998983 | − | 0.0450954i | \(-0.0143592\pi\) |
−0.0450954 | + | 0.998983i | \(0.514359\pi\) | |||||||
\(74\) | 4.62576i | 0.537734i | ||||||||
\(75\) | 8.33243 | + | 5.72374i | 0.962147 | + | 0.660920i | ||||
\(76\) | − | 6.20333i | − | 0.711571i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.414214 | + | 0.414214i | −0.0469005 | + | 0.0469005i | ||||
\(79\) | 5.07627i | 0.571125i | 0.958360 | + | 0.285562i | \(0.0921804\pi\) | ||||
−0.958360 | + | 0.285562i | \(0.907820\pi\) | |||||||
\(80\) | 0.204875 | + | 2.22666i | 0.0229057 | + | 0.248948i | ||||
\(81\) | 11.0799 | 1.23111 | ||||||||
\(82\) | 1.82961 | − | 1.82961i | 0.202046 | − | 0.202046i | ||||
\(83\) | 3.85372 | + | 3.85372i | 0.423001 | + | 0.423001i | 0.886236 | − | 0.463235i | \(-0.153311\pi\) |
−0.463235 | + | 0.886236i | \(0.653311\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.50704 | + | 2.91605i | 0.380392 | + | 0.316290i | ||||
\(86\) | −7.03997 | −0.759140 | ||||||||
\(87\) | −10.2342 | + | 10.2342i | −1.09722 | + | 1.09722i | ||||
\(88\) | 2.85669 | − | 2.85669i | 0.304524 | − | 0.304524i | ||||
\(89\) | −3.07230 | −0.325664 | −0.162832 | − | 0.986654i | \(-0.552063\pi\) | ||||
−0.162832 | + | 0.986654i | \(0.552063\pi\) | |||||||
\(90\) | 1.87002 | + | 1.55489i | 0.197117 | + | 0.163900i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.20895 | + | 3.20895i | 0.334556 | + | 0.334556i | ||||
\(93\) | −10.4542 | + | 10.4542i | −1.08405 | + | 1.08405i | ||||
\(94\) | 0.315125 | 0.0325027 | ||||||||
\(95\) | 1.27091 | + | 13.8127i | 0.130392 | + | 1.41716i | ||||
\(96\) | 2.02179i | 0.206348i | ||||||||
\(97\) | 6.63103 | − | 6.63103i | 0.673279 | − | 0.673279i | −0.285191 | − | 0.958471i | \(-0.592057\pi\) |
0.958471 | + | 0.285191i | \(0.0920572\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 4.39398i | − | 0.441611i | ||||||
\(100\) | −0.912375 | − | 4.91605i | −0.0912375 | − | 0.491605i | ||||
\(101\) | 9.88844i | 0.983936i | 0.870613 | + | 0.491968i | \(0.163722\pi\) | ||||
−0.870613 | + | 0.491968i | \(0.836278\pi\) | |||||||
\(102\) | 2.91605 | + | 2.91605i | 0.288732 | + | 0.288732i | ||||
\(103\) | 3.02785 | + | 3.02785i | 0.298343 | + | 0.298343i | 0.840365 | − | 0.542022i | \(-0.182341\pi\) |
−0.542022 | + | 0.840365i | \(0.682341\pi\) | |||||||
\(104\) | 0.289737 | 0.0284110 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.28261 | 0.804479 | ||||||||
\(107\) | −10.5161 | − | 10.5161i | −1.01663 | − | 1.01663i | −0.999859 | − | 0.0167751i | \(-0.994660\pi\) |
−0.0167751 | − | 0.999859i | \(-0.505340\pi\) | |||||||
\(108\) | −2.73397 | − | 2.73397i | −0.263076 | − | 0.263076i | ||||
\(109\) | − | 13.2313i | − | 1.26733i | −0.773609 | − | 0.633664i | \(-0.781550\pi\) | ||
0.773609 | − | 0.633664i | \(-0.218450\pi\) | |||||||
\(110\) | −5.77563 | + | 6.94616i | −0.550684 | + | 0.662290i | ||||
\(111\) | − | 9.35230i | − | 0.887681i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.75336 | − | 9.75336i | 0.917519 | − | 0.917519i | −0.0793296 | − | 0.996848i | \(-0.525278\pi\) |
0.996848 | + | 0.0793296i | \(0.0252780\pi\) | |||||||
\(114\) | 12.5418i | 1.17465i | ||||||||
\(115\) | −7.80267 | − | 6.48781i | −0.727603 | − | 0.604991i | ||||
\(116\) | 7.15869 | 0.664668 | ||||||||
\(117\) | 0.222827 | − | 0.222827i | 0.0206004 | − | 0.0206004i | ||||
\(118\) | 0.604862 | + | 0.604862i | 0.0556821 | + | 0.0556821i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.414214 | − | 4.50184i | −0.0378124 | − | 0.410960i | ||||
\(121\) | 5.32139 | 0.483762 | ||||||||
\(122\) | 4.89372 | − | 4.89372i | 0.443057 | − | 0.443057i | ||||
\(123\) | −3.69908 | + | 3.69908i | −0.333535 | + | 0.333535i | ||||
\(124\) | 7.31256 | 0.656688 | ||||||||
\(125\) | 3.03873 | + | 10.7595i | 0.271792 | + | 0.962356i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.19984 | − | 2.19984i | −0.195204 | − | 0.195204i | 0.602736 | − | 0.797940i | \(-0.294077\pi\) |
−0.797940 | + | 0.602736i | \(0.794077\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 14.2333 | 1.25317 | ||||||||
\(130\) | −0.645146 | + | 0.0593598i | −0.0565831 | + | 0.00520620i | ||||
\(131\) | − | 7.29876i | − | 0.637695i | −0.947806 | − | 0.318848i | \(-0.896704\pi\) | ||
0.947806 | − | 0.318848i | \(-0.103296\pi\) | |||||||
\(132\) | −5.77563 | + | 5.77563i | −0.502704 | + | 0.502704i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 3.15869i | − | 0.272870i | ||||||
\(135\) | 6.64775 | + | 5.52750i | 0.572147 | + | 0.475732i | ||||
\(136\) | − | 2.03974i | − | 0.174906i | ||||||
\(137\) | 5.07627 | + | 5.07627i | 0.433695 | + | 0.433695i | 0.889883 | − | 0.456188i | \(-0.150786\pi\) |
−0.456188 | + | 0.889883i | \(0.650786\pi\) | |||||||
\(138\) | −6.48781 | − | 6.48781i | −0.552279 | − | 0.552279i | ||||
\(139\) | −12.4172 | −1.05321 | −0.526605 | − | 0.850110i | \(-0.676535\pi\) | ||||
−0.526605 | + | 0.850110i | \(0.676535\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.637116 | −0.0536549 | ||||||||
\(142\) | 5.03630 | + | 5.03630i | 0.422637 | + | 0.422637i | ||||
\(143\) | 0.827689 | + | 0.827689i | 0.0692148 | + | 0.0692148i | ||||
\(144\) | − | 1.08763i | − | 0.0906355i | ||||||
\(145\) | −15.9400 | + | 1.46664i | −1.32374 | + | 0.121798i | ||||
\(146\) | 11.5259i | 0.953887i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.27091 | + | 3.27091i | −0.268867 | + | 0.268867i | ||||
\(149\) | − | 23.9483i | − | 1.96193i | −0.194197 | − | 0.980963i | \(-0.562210\pi\) | ||
0.194197 | − | 0.980963i | \(-0.437790\pi\) | |||||||
\(150\) | 1.84463 | + | 9.93921i | 0.150613 | + | 0.811533i | ||||
\(151\) | −3.54334 | −0.288353 | −0.144176 | − | 0.989552i | \(-0.546053\pi\) | ||||
−0.144176 | + | 0.989552i | \(0.546053\pi\) | |||||||
\(152\) | 4.38642 | − | 4.38642i | 0.355785 | − | 0.355785i | ||||
\(153\) | −1.56870 | − | 1.56870i | −0.126822 | − | 0.126822i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.2826 | + | 1.49816i | −1.30785 | + | 0.120335i | ||||
\(156\) | −0.585786 | −0.0469005 | ||||||||
\(157\) | −4.32927 | + | 4.32927i | −0.345513 | + | 0.345513i | −0.858435 | − | 0.512922i | \(-0.828563\pi\) |
0.512922 | + | 0.858435i | \(0.328563\pi\) | |||||||
\(158\) | −3.58946 | + | 3.58946i | −0.285562 | + | 0.285562i | ||||
\(159\) | −16.7457 | −1.32802 | ||||||||
\(160\) | −1.42962 | + | 1.71936i | −0.113021 | + | 0.135927i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 7.83471 | + | 7.83471i | 0.615553 | + | 0.615553i | ||||
\(163\) | −11.7082 | + | 11.7082i | −0.917056 | + | 0.917056i | −0.996814 | − | 0.0797585i | \(-0.974585\pi\) |
0.0797585 | + | 0.996814i | \(0.474585\pi\) | |||||||
\(164\) | 2.58745 | 0.202046 | ||||||||
\(165\) | 11.6771 | − | 14.0437i | 0.909060 | − | 1.09330i | ||||
\(166\) | 5.44998i | 0.423001i | ||||||||
\(167\) | 10.2873 | − | 10.2873i | 0.796056 | − | 0.796056i | −0.186415 | − | 0.982471i | \(-0.559687\pi\) |
0.982471 | + | 0.186415i | \(0.0596869\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.9161i | − | 0.993543i | ||||||
\(170\) | 0.417892 | + | 4.54181i | 0.0320508 | + | 0.348341i | ||||
\(171\) | − | 6.74690i | − | 0.515948i | ||||||
\(172\) | −4.97801 | − | 4.97801i | −0.379570 | − | 0.379570i | ||||
\(173\) | 5.49565 | + | 5.49565i | 0.417827 | + | 0.417827i | 0.884454 | − | 0.466627i | \(-0.154531\pi\) |
−0.466627 | + | 0.884454i | \(0.654531\pi\) | |||||||
\(174\) | −14.4734 | −1.09722 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.03997 | 0.304524 | ||||||||
\(177\) | −1.22290 | − | 1.22290i | −0.0919190 | − | 0.0919190i | ||||
\(178\) | −2.17245 | − | 2.17245i | −0.162832 | − | 0.162832i | ||||
\(179\) | 3.86472i | 0.288863i | 0.989515 | + | 0.144431i | \(0.0461353\pi\) | ||||
−0.989515 | + | 0.144431i | \(0.953865\pi\) | |||||||
\(180\) | 0.222827 | + | 2.42177i | 0.0166086 | + | 0.180508i | ||||
\(181\) | 6.99107i | 0.519642i | 0.965657 | + | 0.259821i | \(0.0836636\pi\) | ||||
−0.965657 | + | 0.259821i | \(0.916336\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.89407 | + | 9.89407i | −0.731390 | + | 0.731390i | ||||
\(184\) | 4.53813i | 0.334556i | ||||||||
\(185\) | 6.61308 | − | 7.95333i | 0.486203 | − | 0.584741i | ||||
\(186\) | −14.7845 | −1.08405 | ||||||||
\(187\) | 5.82691 | − | 5.82691i | 0.426106 | − | 0.426106i | ||||
\(188\) | 0.222827 | + | 0.222827i | 0.0162513 | + | 0.0162513i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.86840 | + | 10.6657i | −0.643381 | + | 0.773774i | ||||
\(191\) | 4.47442 | 0.323758 | 0.161879 | − | 0.986811i | \(-0.448245\pi\) | ||||
0.161879 | + | 0.986811i | \(0.448245\pi\) | |||||||
\(192\) | −1.42962 | + | 1.42962i | −0.103174 | + | 0.103174i | ||||
\(193\) | −14.1950 | + | 14.1950i | −1.02178 | + | 1.02178i | −0.0220201 | + | 0.999758i | \(0.507010\pi\) |
−0.999758 | + | 0.0220201i | \(0.992990\pi\) | |||||||
\(194\) | 9.37769 | 0.673279 | ||||||||
\(195\) | 1.30435 | − | 0.120013i | 0.0934064 | − | 0.00859431i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.84901 | − | 7.84901i | −0.559219 | − | 0.559219i | 0.369866 | − | 0.929085i | \(-0.379404\pi\) |
−0.929085 | + | 0.369866i | \(0.879404\pi\) | |||||||
\(198\) | 3.10701 | − | 3.10701i | 0.220806 | − | 0.220806i | ||||
\(199\) | −10.8021 | −0.765737 | −0.382869 | − | 0.923803i | \(-0.625064\pi\) | ||||
−0.382869 | + | 0.923803i | \(0.625064\pi\) | |||||||
\(200\) | 2.83103 | − | 4.12132i | 0.200184 | − | 0.291421i | ||||
\(201\) | 6.38621i | 0.450448i | ||||||||
\(202\) | −6.99218 | + | 6.99218i | −0.491968 | + | 0.491968i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.12392i | 0.288732i | ||||||||
\(205\) | −5.76139 | + | 0.530105i | −0.402393 | + | 0.0370241i | ||||
\(206\) | 4.28203i | 0.298343i | ||||||||
\(207\) | 3.49013 | + | 3.49013i | 0.242581 | + | 0.242581i | ||||
\(208\) | 0.204875 | + | 0.204875i | 0.0142055 | + | 0.0142055i | ||||
\(209\) | 25.0613 | 1.73353 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.56555 | 0.520834 | 0.260417 | − | 0.965496i | \(-0.416140\pi\) | ||||
0.260417 | + | 0.965496i | \(0.416140\pi\) | |||||||
\(212\) | 5.85669 | + | 5.85669i | 0.402239 | + | 0.402239i | ||||
\(213\) | −10.1823 | − | 10.1823i | −0.697681 | − | 0.697681i | ||||
\(214\) | − | 14.8721i | − | 1.01663i | ||||||
\(215\) | 12.1042 | + | 10.0645i | 0.825501 | + | 0.686392i | ||||
\(216\) | − | 3.86642i | − | 0.263076i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 9.35593 | − | 9.35593i | 0.633664 | − | 0.633664i | ||||
\(219\) | − | 23.3028i | − | 1.57466i | ||||||
\(220\) | −8.99566 | + | 0.827689i | −0.606487 | + | 0.0558028i | ||||
\(221\) | 0.590988 | 0.0397541 | ||||||||
\(222\) | 6.61308 | − | 6.61308i | 0.443841 | − | 0.443841i | ||||
\(223\) | −9.35230 | − | 9.35230i | −0.626277 | − | 0.626277i | 0.320853 | − | 0.947129i | \(-0.396031\pi\) |
−0.947129 | + | 0.320853i | \(0.896031\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.992322 | − | 5.34682i | −0.0661548 | − | 0.356455i | ||||
\(226\) | 13.7933 | 0.917519 | ||||||||
\(227\) | 11.4508 | − | 11.4508i | 0.760014 | − | 0.760014i | −0.216311 | − | 0.976325i | \(-0.569402\pi\) |
0.976325 | + | 0.216311i | \(0.0694024\pi\) | |||||||
\(228\) | −8.86840 | + | 8.86840i | −0.587324 | + | 0.587324i | ||||
\(229\) | 11.7764 | 0.778207 | 0.389103 | − | 0.921194i | \(-0.372785\pi\) | ||||
0.389103 | + | 0.921194i | \(0.372785\pi\) | |||||||
\(230\) | −0.929750 | − | 10.1049i | −0.0613059 | − | 0.666297i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.06196 | + | 5.06196i | 0.332334 | + | 0.332334i | ||||
\(233\) | −4.04765 | + | 4.04765i | −0.265170 | + | 0.265170i | −0.827151 | − | 0.561980i | \(-0.810040\pi\) |
0.561980 | + | 0.827151i | \(0.310040\pi\) | |||||||
\(234\) | 0.315125 | 0.0206004 | ||||||||
\(235\) | −0.541813 | − | 0.450509i | −0.0353440 | − | 0.0293880i | ||||
\(236\) | 0.855404i | 0.0556821i | ||||||||
\(237\) | 7.25713 | − | 7.25713i | 0.471402 | − | 0.471402i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.33794i | 0.539337i | 0.962953 | + | 0.269668i | \(0.0869141\pi\) | ||||
−0.962953 | + | 0.269668i | \(0.913086\pi\) | |||||||
\(240\) | 2.89039 | − | 3.47617i | 0.186574 | − | 0.224386i | ||||
\(241\) | − | 2.96438i | − | 0.190953i | −0.995432 | − | 0.0954763i | \(-0.969563\pi\) | ||
0.995432 | − | 0.0954763i | \(-0.0304374\pi\) | |||||||
\(242\) | 3.76279 | + | 3.76279i | 0.241881 | + | 0.241881i | ||||
\(243\) | −7.63821 | − | 7.63821i | −0.489991 | − | 0.489991i | ||||
\(244\) | 6.92077 | 0.443057 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.23128 | −0.333535 | ||||||||
\(247\) | 1.27091 | + | 1.27091i | 0.0808658 | + | 0.0808658i | ||||
\(248\) | 5.17076 | + | 5.17076i | 0.328344 | + | 0.328344i | ||||
\(249\) | − | 11.0187i | − | 0.698283i | ||||||
\(250\) | −5.45939 | + | 9.75680i | −0.345282 | + | 0.617074i | ||||
\(251\) | − | 16.1800i | − | 1.02127i | −0.859796 | − | 0.510637i | \(-0.829410\pi\) | ||
0.859796 | − | 0.510637i | \(-0.170590\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.9641 | + | 12.9641i | −0.815043 | + | 0.815043i | ||||
\(254\) | − | 3.11104i | − | 0.195204i | ||||||
\(255\) | −0.844888 | − | 9.18258i | −0.0529089 | − | 0.575036i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.11867 | − | 4.11867i | 0.256916 | − | 0.256916i | −0.566883 | − | 0.823799i | \(-0.691851\pi\) |
0.823799 | + | 0.566883i | \(0.191851\pi\) | |||||||
\(258\) | 10.0645 | + | 10.0645i | 0.626587 | + | 0.626587i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.498161 | − | 0.414214i | −0.0308946 | − | 0.0256884i | ||||
\(261\) | 7.78598 | 0.481940 | ||||||||
\(262\) | 5.16100 | − | 5.16100i | 0.318848 | − | 0.318848i | ||||
\(263\) | 1.22833 | − | 1.22833i | 0.0757422 | − | 0.0757422i | −0.668221 | − | 0.743963i | \(-0.732944\pi\) |
0.743963 | + | 0.668221i | \(0.232944\pi\) | |||||||
\(264\) | −8.16797 | −0.502704 | ||||||||
\(265\) | −14.2408 | − | 11.8410i | −0.874803 | − | 0.727386i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.39223 | + | 4.39223i | 0.268800 | + | 0.268800i | ||||
\(268\) | 2.23353 | − | 2.23353i | 0.136435 | − | 0.136435i | ||||
\(269\) | −3.78337 | −0.230676 | −0.115338 | − | 0.993326i | \(-0.536795\pi\) | ||||
−0.115338 | + | 0.993326i | \(0.536795\pi\) | |||||||
\(270\) | 0.792131 | + | 8.60920i | 0.0482076 | + | 0.523939i | ||||
\(271\) | − | 21.2498i | − | 1.29083i | −0.763831 | − | 0.645416i | \(-0.776684\pi\) | ||
0.763831 | − | 0.645416i | \(-0.223316\pi\) | |||||||
\(272\) | 1.44231 | − | 1.44231i | 0.0874531 | − | 0.0874531i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.17893i | 0.433695i | ||||||||
\(275\) | 19.8607 | − | 3.68597i | 1.19765 | − | 0.222272i | ||||
\(276\) | − | 9.17514i | − | 0.552279i | ||||||
\(277\) | −3.45787 | − | 3.45787i | −0.207763 | − | 0.207763i | 0.595553 | − | 0.803316i | \(-0.296933\pi\) |
−0.803316 | + | 0.595553i | \(0.796933\pi\) | |||||||
\(278\) | −8.78027 | − | 8.78027i | −0.526605 | − | 0.526605i | ||||
\(279\) | 7.95333 | 0.476153 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.4776 | −1.75849 | −0.879243 | − | 0.476373i | \(-0.841951\pi\) | ||||
−0.879243 | + | 0.476373i | \(0.841951\pi\) | |||||||
\(282\) | −0.450509 | − | 0.450509i | −0.0268274 | − | 0.0268274i | ||||
\(283\) | 7.97872 | + | 7.97872i | 0.474286 | + | 0.474286i | 0.903298 | − | 0.429013i | \(-0.141138\pi\) |
−0.429013 | + | 0.903298i | \(0.641138\pi\) | |||||||
\(284\) | 7.12240i | 0.422637i | ||||||||
\(285\) | 17.9300 | − | 21.5638i | 1.06208 | − | 1.27733i | ||||
\(286\) | 1.17053i | 0.0692148i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.769067 | − | 0.769067i | 0.0453177 | − | 0.0453177i | ||||
\(289\) | 12.8395i | 0.755262i | ||||||||
\(290\) | −12.3083 | − | 10.2342i | −0.722771 | − | 0.600973i | ||||
\(291\) | −18.9597 | −1.11144 | ||||||||
\(292\) | −8.15002 | + | 8.15002i | −0.476944 | + | 0.476944i | ||||
\(293\) | 7.23407 | + | 7.23407i | 0.422619 | + | 0.422619i | 0.886105 | − | 0.463485i | \(-0.153401\pi\) |
−0.463485 | + | 0.886105i | \(0.653401\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.175251 | − | 1.90470i | −0.0102035 | − | 0.110896i | ||||
\(296\) | −4.62576 | −0.268867 | ||||||||
\(297\) | 11.0452 | − | 11.0452i | 0.640905 | − | 0.640905i | ||||
\(298\) | 16.9340 | − | 16.9340i | 0.980963 | − | 0.980963i | ||||
\(299\) | −1.31486 | −0.0760406 | ||||||||
\(300\) | −5.72374 | + | 8.33243i | −0.330460 | + | 0.481073i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.50552 | − | 2.50552i | −0.144176 | − | 0.144176i | ||||
\(303\) | 14.1367 | − | 14.1367i | 0.812133 | − | 0.812133i | ||||
\(304\) | 6.20333 | 0.355785 | ||||||||
\(305\) | −15.4102 | + | 1.41789i | −0.882386 | + | 0.0811882i | ||||
\(306\) | − | 2.21847i | − | 0.126822i | ||||||
\(307\) | 1.07859 | − | 1.07859i | 0.0615584 | − | 0.0615584i | −0.675657 | − | 0.737216i | \(-0.736140\pi\) |
0.737216 | + | 0.675657i | \(0.236140\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 8.65735i | − | 0.492500i | ||||||
\(310\) | −12.5729 | − | 10.4542i | −0.714093 | − | 0.593758i | ||||
\(311\) | 9.62824i | 0.545967i | 0.962019 | + | 0.272984i | \(0.0880105\pi\) | ||||
−0.962019 | + | 0.272984i | \(0.911990\pi\) | |||||||
\(312\) | −0.414214 | − | 0.414214i | −0.0234502 | − | 0.0234502i | ||||
\(313\) | 2.14023 | + | 2.14023i | 0.120973 | + | 0.120973i | 0.765001 | − | 0.644029i | \(-0.222738\pi\) |
−0.644029 | + | 0.765001i | \(0.722738\pi\) | |||||||
\(314\) | −6.12251 | −0.345513 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.07627 | −0.285562 | ||||||||
\(317\) | 1.37792 | + | 1.37792i | 0.0773916 | + | 0.0773916i | 0.744743 | − | 0.667351i | \(-0.232572\pi\) |
−0.667351 | + | 0.744743i | \(0.732572\pi\) | |||||||
\(318\) | −11.8410 | − | 11.8410i | −0.664010 | − | 0.664010i | ||||
\(319\) | 28.9209i | 1.61926i | ||||||||
\(320\) | −2.22666 | + | 0.204875i | −0.124474 | + | 0.0114529i | ||||
\(321\) | 30.0682i | 1.67824i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.94715 | − | 8.94715i | 0.497833 | − | 0.497833i | ||||
\(324\) | 11.0799i | 0.615553i | ||||||||
\(325\) | 1.19410 | + | 0.820253i | 0.0662367 | + | 0.0454995i | ||||
\(326\) | −16.5579 | −0.917056 | ||||||||
\(327\) | −18.9157 | + | 18.9157i | −1.04604 | + | 1.04604i | ||||
\(328\) | 1.82961 | + | 1.82961i | 0.101023 | + | 0.101023i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 18.1873 | − | 1.67341i | 1.00118 | − | 0.0921183i | ||||
\(331\) | −28.8935 | −1.58813 | −0.794066 | − | 0.607832i | \(-0.792039\pi\) | ||||
−0.794066 | + | 0.607832i | \(0.792039\pi\) | |||||||
\(332\) | −3.85372 | + | 3.85372i | −0.211500 | + | 0.211500i | ||||
\(333\) | −3.55752 | + | 3.55752i | −0.194951 | + | 0.194951i | ||||
\(334\) | 14.5485 | 0.796056 | ||||||||
\(335\) | −4.51573 | + | 5.43092i | −0.246721 | + | 0.296723i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.823226 | − | 0.823226i | −0.0448440 | − | 0.0448440i | 0.684329 | − | 0.729173i | \(-0.260095\pi\) |
−0.729173 | + | 0.684329i | \(0.760095\pi\) | |||||||
\(338\) | 9.13303 | − | 9.13303i | 0.496771 | − | 0.496771i | ||||
\(339\) | −27.8872 | −1.51462 | ||||||||
\(340\) | −2.91605 | + | 3.50704i | −0.158145 | + | 0.190196i | ||||
\(341\) | 29.5426i | 1.59982i | ||||||||
\(342\) | 4.77078 | − | 4.77078i | 0.257974 | − | 0.257974i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 7.03997i | − | 0.379570i | ||||||
\(345\) | 1.87976 | + | 20.4300i | 0.101203 | + | 1.09991i | ||||
\(346\) | 7.77203i | 0.417827i | ||||||||
\(347\) | −11.8116 | − | 11.8116i | −0.634082 | − | 0.634082i | 0.315007 | − | 0.949089i | \(-0.397993\pi\) |
−0.949089 | + | 0.315007i | \(0.897993\pi\) | |||||||
\(348\) | −10.2342 | − | 10.2342i | −0.548611 | − | 0.548611i | ||||
\(349\) | −36.7146 | −1.96529 | −0.982644 | − | 0.185503i | \(-0.940608\pi\) | ||||
−0.982644 | + | 0.185503i | \(0.940608\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.12024 | 0.0597942 | ||||||||
\(352\) | 2.85669 | + | 2.85669i | 0.152262 | + | 0.152262i | ||||
\(353\) | 10.0910 | + | 10.0910i | 0.537089 | + | 0.537089i | 0.922673 | − | 0.385584i | \(-0.126000\pi\) |
−0.385584 | + | 0.922673i | \(0.626000\pi\) | |||||||
\(354\) | − | 1.72945i | − | 0.0919190i | ||||||
\(355\) | −1.45920 | − | 15.8592i | −0.0774463 | − | 0.841718i | ||||
\(356\) | − | 3.07230i | − | 0.162832i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.73277 | + | 2.73277i | −0.144431 | + | 0.144431i | ||||
\(359\) | 27.0888i | 1.42969i | 0.699281 | + | 0.714847i | \(0.253504\pi\) | ||||
−0.699281 | + | 0.714847i | \(0.746496\pi\) | |||||||
\(360\) | −1.55489 | + | 1.87002i | −0.0819499 | + | 0.0985585i | ||||
\(361\) | 19.4813 | 1.02533 | ||||||||
\(362\) | −4.94343 | + | 4.94343i | −0.259821 | + | 0.259821i | ||||
\(363\) | −7.60756 | − | 7.60756i | −0.399293 | − | 0.399293i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.4776 | − | 19.8171i | 0.862477 | − | 1.03727i | ||||
\(366\) | −13.9923 | −0.731390 | ||||||||
\(367\) | 16.0312 | − | 16.0312i | 0.836821 | − | 0.836821i | −0.151618 | − | 0.988439i | \(-0.548448\pi\) |
0.988439 | + | 0.151618i | \(0.0484485\pi\) | |||||||
\(368\) | −3.20895 | + | 3.20895i | −0.167278 | + | 0.167278i | ||||
\(369\) | 2.81418 | 0.146500 | ||||||||
\(370\) | 10.3000 | − | 0.947702i | 0.535472 | − | 0.0492687i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −10.4542 | − | 10.4542i | −0.542024 | − | 0.542024i | ||||
\(373\) | −9.07627 | + | 9.07627i | −0.469951 | + | 0.469951i | −0.901899 | − | 0.431947i | \(-0.857827\pi\) |
0.431947 | + | 0.901899i | \(0.357827\pi\) | |||||||
\(374\) | 8.24050 | 0.426106 | ||||||||
\(375\) | 11.0377 | − | 19.7262i | 0.569986 | − | 1.01866i | ||||
\(376\) | 0.315125i | 0.0162513i | ||||||||
\(377\) | −1.46664 | + | 1.46664i | −0.0755356 | + | 0.0755356i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.4739i | 0.743476i | 0.928338 | + | 0.371738i | \(0.121238\pi\) | ||||
−0.928338 | + | 0.371738i | \(0.878762\pi\) | |||||||
\(380\) | −13.8127 | + | 1.27091i | −0.708578 | + | 0.0651961i | ||||
\(381\) | 6.28987i | 0.322240i | ||||||||
\(382\) | 3.16389 | + | 3.16389i | 0.161879 | + | 0.161879i | ||||
\(383\) | 1.23855 | + | 1.23855i | 0.0632870 | + | 0.0632870i | 0.738042 | − | 0.674755i | \(-0.235751\pi\) |
−0.674755 | + | 0.738042i | \(0.735751\pi\) | |||||||
\(384\) | −2.02179 | −0.103174 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −20.0747 | −1.02178 | ||||||||
\(387\) | −5.41421 | − | 5.41421i | −0.275220 | − | 0.275220i | ||||
\(388\) | 6.63103 | + | 6.63103i | 0.336640 | + | 0.336640i | ||||
\(389\) | − | 2.78230i | − | 0.141068i | −0.997509 | − | 0.0705341i | \(-0.977530\pi\) | ||
0.997509 | − | 0.0705341i | \(-0.0224704\pi\) | |||||||
\(390\) | 1.00718 | + | 0.837452i | 0.0510003 | + | 0.0424060i | ||||
\(391\) | 9.25661i | 0.468127i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.4344 | + | 10.4344i | −0.526348 | + | 0.526348i | ||||
\(394\) | − | 11.1002i | − | 0.559219i | ||||||
\(395\) | 11.3031 | − | 1.04000i | 0.568723 | − | 0.0523281i | ||||
\(396\) | 4.39398 | 0.220806 | ||||||||
\(397\) | −28.0495 | + | 28.0495i | −1.40776 | + | 1.40776i | −0.636421 | + | 0.771342i | \(0.719586\pi\) |
−0.771342 | + | 0.636421i | \(0.780414\pi\) | |||||||
\(398\) | −7.63821 | − | 7.63821i | −0.382869 | − | 0.382869i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.91605 | − | 0.912375i | 0.245803 | − | 0.0456187i | ||||
\(401\) | −19.9706 | −0.997282 | −0.498641 | − | 0.866809i | \(-0.666167\pi\) | ||||
−0.498641 | + | 0.866809i | \(0.666167\pi\) | |||||||
\(402\) | −4.51573 | + | 4.51573i | −0.225224 | + | 0.225224i | ||||
\(403\) | −1.49816 | + | 1.49816i | −0.0746287 | + | 0.0746287i | ||||
\(404\) | −9.88844 | −0.491968 | ||||||||
\(405\) | −2.27000 | − | 24.6713i | −0.112797 | − | 1.22593i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.2144 | − | 13.2144i | −0.655012 | − | 0.655012i | ||||
\(408\) | −2.91605 | + | 2.91605i | −0.144366 | + | 0.144366i | ||||
\(409\) | −15.3056 | −0.756813 | −0.378407 | − | 0.925639i | \(-0.623528\pi\) | ||||
−0.378407 | + | 0.925639i | \(0.623528\pi\) | |||||||
\(410\) | −4.44876 | − | 3.69908i | −0.219708 | − | 0.182684i | ||||
\(411\) | − | 14.5143i | − | 0.715936i | ||||||
\(412\) | −3.02785 | + | 3.02785i | −0.149172 | + | 0.149172i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.93579i | 0.242581i | ||||||||
\(415\) | 7.79141 | − | 9.37047i | 0.382465 | − | 0.459978i | ||||
\(416\) | 0.289737i | 0.0142055i | ||||||||
\(417\) | 17.7518 | + | 17.7518i | 0.869311 | + | 0.869311i | ||||
\(418\) | 17.7210 | + | 17.7210i | 0.866763 | + | 0.866763i | ||||
\(419\) | 27.7027 | 1.35337 | 0.676684 | − | 0.736274i | \(-0.263416\pi\) | ||||
0.676684 | + | 0.736274i | \(0.263416\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.0159 | 1.60910 | 0.804549 | − | 0.593887i | \(-0.202407\pi\) | ||||
0.804549 | + | 0.593887i | \(0.202407\pi\) | |||||||
\(422\) | 5.34965 | + | 5.34965i | 0.260417 | + | 0.260417i | ||||
\(423\) | 0.242352 | + | 0.242352i | 0.0117836 | + | 0.0117836i | ||||
\(424\) | 8.28261i | 0.402239i | ||||||||
\(425\) | 5.77456 | − | 8.40642i | 0.280107 | − | 0.407771i | ||||
\(426\) | − | 14.4000i | − | 0.697681i | ||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 10.5161 | − | 10.5161i | 0.508317 | − | 0.508317i | ||||
\(429\) | − | 2.36656i | − | 0.114259i | ||||||
\(430\) | 1.44231 | + | 15.6756i | 0.0695546 | + | 0.755947i | ||||
\(431\) | 23.9173 | 1.15205 | 0.576027 | − | 0.817431i | \(-0.304602\pi\) | ||||
0.576027 | + | 0.817431i | \(0.304602\pi\) | |||||||
\(432\) | 2.73397 | − | 2.73397i | 0.131538 | − | 0.131538i | ||||
\(433\) | 13.2515 | + | 13.2515i | 0.636829 | + | 0.636829i | 0.949772 | − | 0.312943i | \(-0.101315\pi\) |
−0.312943 | + | 0.949772i | \(0.601315\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 24.8849 | + | 20.6914i | 1.19314 | + | 0.992077i | ||||
\(436\) | 13.2313 | 0.633664 | ||||||||
\(437\) | −19.9061 | + | 19.9061i | −0.952240 | + | 0.952240i | ||||
\(438\) | 16.4776 | − | 16.4776i | 0.787330 | − | 0.787330i | ||||
\(439\) | −14.1077 | −0.673322 | −0.336661 | − | 0.941626i | \(-0.609298\pi\) | ||||
−0.336661 | + | 0.941626i | \(0.609298\pi\) | |||||||
\(440\) | −6.94616 | − | 5.77563i | −0.331145 | − | 0.275342i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.417892 | + | 0.417892i | 0.0198771 | + | 0.0198771i | ||||
\(443\) | 14.8941 | − | 14.8941i | 0.707638 | − | 0.707638i | −0.258400 | − | 0.966038i | \(-0.583195\pi\) |
0.966038 | + | 0.258400i | \(0.0831951\pi\) | |||||||
\(444\) | 9.35230 | 0.443841 | ||||||||
\(445\) | 0.629438 | + | 6.84098i | 0.0298382 | + | 0.324294i | ||||
\(446\) | − | 13.2262i | − | 0.626277i | ||||||
\(447\) | −34.2370 | + | 34.2370i | −1.61936 | + | 1.61936i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.3247i | 1.47831i | 0.673538 | + | 0.739153i | \(0.264774\pi\) | ||||
−0.673538 | + | 0.739153i | \(0.735226\pi\) | |||||||
\(450\) | 3.07910 | − | 4.48245i | 0.145150 | − | 0.211305i | ||||
\(451\) | 10.4532i | 0.492224i | ||||||||
\(452\) | 9.75336 | + | 9.75336i | 0.458759 | + | 0.458759i | ||||
\(453\) | 5.06562 | + | 5.06562i | 0.238004 | + | 0.238004i | ||||
\(454\) | 16.1938 | 0.760014 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.5418 | −0.587324 | ||||||||
\(457\) | −2.02342 | − | 2.02342i | −0.0946514 | − | 0.0946514i | 0.658196 | − | 0.752847i | \(-0.271320\pi\) |
−0.752847 | + | 0.658196i | \(0.771320\pi\) | |||||||
\(458\) | 8.32718 | + | 8.32718i | 0.389103 | + | 0.389103i | ||||
\(459\) | − | 7.88648i | − | 0.368109i | ||||||
\(460\) | 6.48781 | − | 7.80267i | 0.302496 | − | 0.363801i | ||||
\(461\) | 3.02674i | 0.140969i | 0.997513 | + | 0.0704846i | \(0.0224546\pi\) | ||||
−0.997513 | + | 0.0704846i | \(0.977545\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.2889 | − | 19.2889i | 0.896431 | − | 0.896431i | −0.0986876 | − | 0.995118i | \(-0.531464\pi\) |
0.995118 | + | 0.0986876i | \(0.0314644\pi\) | |||||||
\(464\) | 7.15869i | 0.332334i | ||||||||
\(465\) | 25.4197 | + | 21.1361i | 1.17881 | + | 0.980165i | ||||
\(466\) | −5.72424 | −0.265170 | ||||||||
\(467\) | 17.7688 | − | 17.7688i | 0.822244 | − | 0.822244i | −0.164185 | − | 0.986430i | \(-0.552500\pi\) |
0.986430 | + | 0.164185i | \(0.0524995\pi\) | |||||||
\(468\) | 0.222827 | + | 0.222827i | 0.0103002 | + | 0.0103002i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.0645612 | − | 0.701677i | −0.00297799 | − | 0.0323660i | ||||
\(471\) | 12.3784 | 0.570367 | ||||||||
\(472\) | −0.604862 | + | 0.604862i | −0.0278410 | + | 0.0278410i | ||||
\(473\) | 20.1110 | − | 20.1110i | 0.924707 | − | 0.924707i | ||||
\(474\) | 10.2631 | 0.471402 | ||||||||
\(475\) | 30.4959 | − | 5.65976i | 1.39925 | − | 0.259688i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.36989 | + | 6.36989i | 0.291657 | + | 0.291657i | ||||
\(478\) | −5.89582 | + | 5.89582i | −0.269668 | + | 0.269668i | ||||
\(479\) | −8.28692 | −0.378639 | −0.189319 | − | 0.981916i | \(-0.560628\pi\) | ||||
−0.189319 | + | 0.981916i | \(0.560628\pi\) | |||||||
\(480\) | 4.50184 | − | 0.414214i | 0.205480 | − | 0.0189062i | ||||
\(481\) | − | 1.34025i | − | 0.0611103i | ||||||
\(482\) | 2.09613 | − | 2.09613i | 0.0954763 | − | 0.0954763i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.32139i | 0.241881i | ||||||||
\(485\) | −16.1236 | − | 13.4065i | −0.732135 | − | 0.608759i | ||||
\(486\) | − | 10.8021i | − | 0.489991i | ||||||
\(487\) | 7.55069 | + | 7.55069i | 0.342155 | + | 0.342155i | 0.857177 | − | 0.515022i | \(-0.172216\pi\) |
−0.515022 | + | 0.857177i | \(0.672216\pi\) | |||||||
\(488\) | 4.89372 | + | 4.89372i | 0.221528 | + | 0.221528i | ||||
\(489\) | 33.4765 | 1.51386 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.7259 | 1.16100 | 0.580498 | − | 0.814262i | \(-0.302858\pi\) | ||||
0.580498 | + | 0.814262i | \(0.302858\pi\) | |||||||
\(492\) | −3.69908 | − | 3.69908i | −0.166767 | − | 0.166767i | ||||
\(493\) | 10.3251 | + | 10.3251i | 0.465018 | + | 0.465018i | ||||
\(494\) | 1.79733i | 0.0808658i | ||||||||
\(495\) | −9.78391 | + | 0.900216i | −0.439754 | + | 0.0404617i | ||||
\(496\) | 7.31256i | 0.328344i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.79141 | − | 7.79141i | 0.349141 | − | 0.349141i | ||||
\(499\) | 14.5988i | 0.653532i | 0.945105 | + | 0.326766i | \(0.105959\pi\) | ||||
−0.945105 | + | 0.326766i | \(0.894041\pi\) | |||||||
\(500\) | −10.7595 | + | 3.03873i | −0.481178 | + | 0.135896i | ||||
\(501\) | −29.4139 | −1.31412 | ||||||||
\(502\) | 11.4410 | − | 11.4410i | 0.510637 | − | 0.510637i | ||||
\(503\) | −13.9891 | − | 13.9891i | −0.623744 | − | 0.623744i | 0.322743 | − | 0.946487i | \(-0.395395\pi\) |
−0.946487 | + | 0.322743i | \(0.895395\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.0182 | − | 2.02589i | 0.979798 | − | 0.0901510i | ||||
\(506\) | −18.3339 | −0.815043 | ||||||||
\(507\) | −18.4650 | + | 18.4650i | −0.820061 | + | 0.820061i | ||||
\(508\) | 2.19984 | − | 2.19984i | 0.0976020 | − | 0.0976020i | ||||
\(509\) | 2.85767 | 0.126664 | 0.0633319 | − | 0.997993i | \(-0.479827\pi\) | ||||
0.0633319 | + | 0.997993i | \(0.479827\pi\) | |||||||
\(510\) | 5.89564 | − | 7.09049i | 0.261063 | − | 0.313972i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 16.9597 | − | 16.9597i | 0.748789 | − | 0.748789i | ||||
\(514\) | 5.82469 | 0.256916 | ||||||||
\(515\) | 6.12167 | − | 7.36233i | 0.269753 | − | 0.324423i | ||||
\(516\) | 14.2333i | 0.626587i | ||||||||
\(517\) | −0.900216 | + | 0.900216i | −0.0395914 | + | 0.0395914i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 15.7134i | − | 0.689741i | ||||||
\(520\) | −0.0593598 | − | 0.645146i | −0.00260310 | − | 0.0282915i | ||||
\(521\) | − | 28.6269i | − | 1.25417i | −0.778951 | − | 0.627084i | \(-0.784248\pi\) | ||
0.778951 | − | 0.627084i | \(-0.215752\pi\) | |||||||
\(522\) | 5.50552 | + | 5.50552i | 0.240970 | + | 0.240970i | ||||
\(523\) | 22.3326 | + | 22.3326i | 0.976535 | + | 0.976535i | 0.999731 | − | 0.0231958i | \(-0.00738410\pi\) |
−0.0231958 | + | 0.999731i | \(0.507384\pi\) | |||||||
\(524\) | 7.29876 | 0.318848 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.73712 | 0.0757422 | ||||||||
\(527\) | 10.5470 | + | 10.5470i | 0.459435 | + | 0.459435i | ||||
\(528\) | −5.77563 | − | 5.77563i | −0.251352 | − | 0.251352i | ||||
\(529\) | 2.40533i | 0.104580i | ||||||||
\(530\) | −1.69690 | − | 18.4426i | −0.0737086 | − | 0.801095i | ||||
\(531\) | 0.930359i | 0.0403742i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.530105 | + | 0.530105i | −0.0229614 | + | 0.0229614i | ||||
\(534\) | 6.21155i | 0.268800i | ||||||||
\(535\) | −21.2614 | + | 25.5704i | −0.919211 | + | 1.10551i | ||||
\(536\) | 3.15869 | 0.136435 | ||||||||
\(537\) | 5.52508 | − | 5.52508i | 0.238425 | − | 0.238425i | ||||
\(538\) | −2.67525 | − | 2.67525i | −0.115338 | − | 0.115338i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.52750 | + | 6.64775i | −0.237866 | + | 0.286073i | ||||
\(541\) | 36.9989 | 1.59071 | 0.795353 | − | 0.606147i | \(-0.207286\pi\) | ||||
0.795353 | + | 0.606147i | \(0.207286\pi\) | |||||||
\(542\) | 15.0259 | − | 15.0259i | 0.645416 | − | 0.645416i | ||||
\(543\) | 9.99457 | − | 9.99457i | 0.428908 | − | 0.428908i | ||||
\(544\) | 2.03974 | 0.0874531 | ||||||||
\(545\) | −29.4616 | + | 2.71076i | −1.26200 | + | 0.116116i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.0765 | − | 20.0765i | −0.858409 | − | 0.858409i | 0.132742 | − | 0.991151i | \(-0.457622\pi\) |
−0.991151 | + | 0.132742i | \(0.957622\pi\) | |||||||
\(548\) | −5.07627 | + | 5.07627i | −0.216847 | + | 0.216847i | ||||
\(549\) | 7.52720 | 0.321253 | ||||||||
\(550\) | 16.6500 | + | 11.4373i | 0.709959 | + | 0.487687i | ||||
\(551\) | 44.4077i | 1.89183i | ||||||||
\(552\) | 6.48781 | − | 6.48781i | 0.276139 | − | 0.276139i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 4.89016i | − | 0.207763i | ||||||
\(555\) | −20.8244 | + | 1.91605i | −0.883948 | + | 0.0813319i | ||||
\(556\) | − | 12.4172i | − | 0.526605i | ||||||
\(557\) | −18.1818 | − | 18.1818i | −0.770386 | − | 0.770386i | 0.207788 | − | 0.978174i | \(-0.433374\pi\) |
−0.978174 | + | 0.207788i | \(0.933374\pi\) | |||||||
\(558\) | 5.62385 | + | 5.62385i | 0.238077 | + | 0.238077i | ||||
\(559\) | 2.03974 | 0.0862718 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.6605 | −0.703408 | ||||||||
\(562\) | −20.8438 | − | 20.8438i | −0.879243 | − | 0.879243i | ||||
\(563\) | −3.79500 | − | 3.79500i | −0.159940 | − | 0.159940i | 0.622600 | − | 0.782540i | \(-0.286076\pi\) |
−0.782540 | + | 0.622600i | \(0.786076\pi\) | |||||||
\(564\) | − | 0.637116i | − | 0.0268274i | ||||||
\(565\) | −23.7157 | − | 19.7192i | −0.997725 | − | 0.829594i | ||||
\(566\) | 11.2836i | 0.474286i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.03630 | + | 5.03630i | −0.211318 | + | 0.211318i | ||||
\(569\) | − | 25.5003i | − | 1.06903i | −0.845159 | − | 0.534514i | \(-0.820495\pi\) | ||
0.845159 | − | 0.534514i | \(-0.179505\pi\) | |||||||
\(570\) | 27.9264 | − | 2.56950i | 1.16971 | − | 0.107625i | ||||
\(571\) | 15.9047 | 0.665591 | 0.332795 | − | 0.942999i | \(-0.392008\pi\) | ||||
0.332795 | + | 0.942999i | \(0.392008\pi\) | |||||||
\(572\) | −0.827689 | + | 0.827689i | −0.0346074 | + | 0.0346074i | ||||
\(573\) | −6.39672 | − | 6.39672i | −0.267227 | − | 0.267227i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.8476 | + | 18.7031i | −0.535781 | + | 0.779973i | ||||
\(576\) | 1.08763 | 0.0453177 | ||||||||
\(577\) | −16.2985 | + | 16.2985i | −0.678514 | + | 0.678514i | −0.959664 | − | 0.281150i | \(-0.909284\pi\) |
0.281150 | + | 0.959664i | \(0.409284\pi\) | |||||||
\(578\) | −9.07887 | + | 9.07887i | −0.377631 | + | 0.377631i | ||||
\(579\) | 40.5869 | 1.68673 | ||||||||
\(580\) | −1.46664 | − | 15.9400i | −0.0608988 | − | 0.661872i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −13.4065 | − | 13.4065i | −0.555719 | − | 0.555719i | ||||
\(583\) | −23.6609 | + | 23.6609i | −0.979934 | + | 0.979934i | ||||
\(584\) | −11.5259 | −0.476944 | ||||||||
\(585\) | −0.541813 | − | 0.450509i | −0.0224012 | − | 0.0186263i | ||||
\(586\) | 10.2305i | 0.422619i | ||||||||
\(587\) | −28.2277 | + | 28.2277i | −1.16508 | + | 1.16508i | −0.181734 | + | 0.983348i | \(0.558171\pi\) |
−0.983348 | + | 0.181734i | \(0.941829\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 45.3622i | 1.86912i | ||||||||
\(590\) | 1.22290 | − | 1.47074i | 0.0503461 | − | 0.0605496i | ||||
\(591\) | 22.4422i | 0.923149i | ||||||||
\(592\) | −3.27091 | − | 3.27091i | −0.134433 | − | 0.134433i | ||||
\(593\) | −25.0523 | − | 25.0523i | −1.02877 | − | 1.02877i | −0.999574 | − | 0.0292000i | \(-0.990704\pi\) |
−0.0292000 | − | 0.999574i | \(-0.509296\pi\) | |||||||
\(594\) | 15.6202 | 0.640905 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 23.9483 | 0.980963 | ||||||||
\(597\) | 15.4428 | + | 15.4428i | 0.632033 | + | 0.632033i | ||||
\(598\) | −0.929750 | − | 0.929750i | −0.0380203 | − | 0.0380203i | ||||
\(599\) | 16.7823i | 0.685706i | 0.939389 | + | 0.342853i | \(0.111393\pi\) | ||||
−0.939389 | + | 0.342853i | \(0.888607\pi\) | |||||||
\(600\) | −9.93921 | + | 1.84463i | −0.405767 | + | 0.0753066i | ||||
\(601\) | 1.73528i | 0.0707833i | 0.999374 | + | 0.0353917i | \(0.0112679\pi\) | ||||
−0.999374 | + | 0.0353917i | \(0.988732\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.42925 | − | 2.42925i | 0.0989266 | − | 0.0989266i | ||||
\(604\) | − | 3.54334i | − | 0.144176i | ||||||
\(605\) | −1.09022 | − | 11.8489i | −0.0443237 | − | 0.481728i | ||||
\(606\) | 19.9923 | 0.812133 | ||||||||
\(607\) | −27.8860 | + | 27.8860i | −1.13186 | + | 1.13186i | −0.141989 | + | 0.989868i | \(0.545350\pi\) |
−0.989868 | + | 0.141989i | \(0.954650\pi\) | |||||||
\(608\) | 4.38642 | + | 4.38642i | 0.177893 | + | 0.177893i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11.8993 | − | 9.89407i | −0.481787 | − | 0.400599i | ||||
\(611\) | −0.0913034 | −0.00369374 | ||||||||
\(612\) | 1.56870 | − | 1.56870i | 0.0634108 | − | 0.0634108i | ||||
\(613\) | 0.241791 | − | 0.241791i | 0.00976586 | − | 0.00976586i | −0.702207 | − | 0.711973i | \(-0.747802\pi\) |
0.711973 | + | 0.702207i | \(0.247802\pi\) | |||||||
\(614\) | 1.52536 | 0.0615584 | ||||||||
\(615\) | 8.99444 | + | 7.47875i | 0.362691 | + | 0.301572i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.1876 | + | 11.1876i | 0.450397 | + | 0.450397i | 0.895486 | − | 0.445089i | \(-0.146828\pi\) |
−0.445089 | + | 0.895486i | \(0.646828\pi\) | |||||||
\(618\) | 6.12167 | − | 6.12167i | 0.246250 | − | 0.246250i | ||||
\(619\) | 36.5364 | 1.46852 | 0.734260 | − | 0.678868i | \(-0.237529\pi\) | ||||
0.734260 | + | 0.678868i | \(0.237529\pi\) | |||||||
\(620\) | −1.49816 | − | 16.2826i | −0.0601676 | − | 0.653926i | ||||
\(621\) | 17.5463i | 0.704109i | ||||||||
\(622\) | −6.80819 | + | 6.80819i | −0.272984 | + | 0.272984i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 0.585786i | − | 0.0234502i | ||||||
\(625\) | 23.3351 | − | 8.97056i | 0.933406 | − | 0.358823i | ||||
\(626\) | 3.02674i | 0.120973i | ||||||||
\(627\) | −35.8281 | − | 35.8281i | −1.43084 | − | 1.43084i | ||||
\(628\) | −4.32927 | − | 4.32927i | −0.172757 | − | 0.172757i | ||||
\(629\) | −9.43535 | −0.376212 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.8189 | −1.42593 | −0.712964 | − | 0.701201i | \(-0.752648\pi\) | ||||
−0.712964 | + | 0.701201i | \(0.752648\pi\) | |||||||
\(632\) | −3.58946 | − | 3.58946i | −0.142781 | − | 0.142781i | ||||
\(633\) | −10.8159 | − | 10.8159i | −0.429892 | − | 0.429892i | ||||
\(634\) | 1.94867i | 0.0773916i | ||||||||
\(635\) | −4.44761 | + | 5.34899i | −0.176498 | + | 0.212268i | ||||
\(636\) | − | 16.7457i | − | 0.664010i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −20.4502 | + | 20.4502i | −0.809631 | + | 0.809631i | ||||
\(639\) | 7.74650i | 0.306447i | ||||||||
\(640\) | −1.71936 | − | 1.42962i | −0.0679635 | − | 0.0565107i | ||||
\(641\) | −14.3315 | −0.566059 | −0.283029 | − | 0.959111i | \(-0.591339\pi\) | ||||
−0.283029 | + | 0.959111i | \(0.591339\pi\) | |||||||
\(642\) | −21.2614 | + | 21.2614i | −0.839121 | + | 0.839121i | ||||
\(643\) | −7.65201 | − | 7.65201i | −0.301766 | − | 0.301766i | 0.539939 | − | 0.841704i | \(-0.318447\pi\) |
−0.841704 | + | 0.539939i | \(0.818447\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.91605 | − | 31.6928i | −0.114819 | − | 1.24790i | ||||
\(646\) | 12.6532 | 0.497833 | ||||||||
\(647\) | 22.8742 | − | 22.8742i | 0.899278 | − | 0.899278i | −0.0960943 | − | 0.995372i | \(-0.530635\pi\) |
0.995372 | + | 0.0960943i | \(0.0306350\pi\) | |||||||
\(648\) | −7.83471 | + | 7.83471i | −0.307776 | + | 0.307776i | ||||
\(649\) | −3.45581 | −0.135652 | ||||||||
\(650\) | 0.264349 | + | 1.42436i | 0.0103686 | + | 0.0558681i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.7082 | − | 11.7082i | −0.458528 | − | 0.458528i | ||||
\(653\) | −0.362210 | + | 0.362210i | −0.0141744 | + | 0.0141744i | −0.714158 | − | 0.699984i | \(-0.753190\pi\) |
0.699984 | + | 0.714158i | \(0.253190\pi\) | |||||||
\(654\) | −26.7508 | −1.04604 | ||||||||
\(655\) | −16.2519 | + | 1.49533i | −0.635013 | + | 0.0584275i | ||||
\(656\) | 2.58745i | 0.101023i | ||||||||
\(657\) | −8.86417 | + | 8.86417i | −0.345824 | + | 0.345824i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.5542i | 0.761723i | 0.924632 | + | 0.380862i | \(0.124373\pi\) | ||||
−0.924632 | + | 0.380862i | \(0.875627\pi\) | |||||||
\(660\) | 14.0437 | + | 11.6771i | 0.546648 | + | 0.454530i | ||||
\(661\) | − | 39.2972i | − | 1.52848i | −0.644930 | − | 0.764242i | \(-0.723113\pi\) | ||
0.644930 | − | 0.764242i | \(-0.276887\pi\) | |||||||
\(662\) | −20.4308 | − | 20.4308i | −0.794066 | − | 0.794066i | ||||
\(663\) | −0.844888 | − | 0.844888i | −0.0328127 | − | 0.0328127i | ||||
\(664\) | −5.44998 | −0.211500 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.03109 | −0.194951 | ||||||||
\(667\) | −22.9719 | − | 22.9719i | −0.889474 | − | 0.889474i | ||||
\(668\) | 10.2873 | + | 10.2873i | 0.398028 | + | 0.398028i | ||||
\(669\) | 26.7405i | 1.03385i | ||||||||
\(670\) | −7.03334 | + | 0.647137i | −0.271722 | + | 0.0250011i | ||||
\(671\) | 27.9597i | 1.07937i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.4813 | − | 18.4813i | 0.712401 | − | 0.712401i | −0.254636 | − | 0.967037i | \(-0.581956\pi\) |
0.967037 | + | 0.254636i | \(0.0819556\pi\) | |||||||
\(674\) | − | 1.16422i | − | 0.0448440i | ||||||
\(675\) | 10.9459 | − | 15.9347i | 0.421309 | − | 0.613328i | ||||
\(676\) | 12.9161 | 0.496771 | ||||||||
\(677\) | 29.1321 | − | 29.1321i | 1.11964 | − | 1.11964i | 0.127842 | − | 0.991795i | \(-0.459195\pi\) |
0.991795 | − | 0.127842i | \(-0.0408049\pi\) | |||||||
\(678\) | −19.7192 | − | 19.7192i | −0.757312 | − | 0.757312i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4.54181 | + | 0.417892i | −0.174171 | + | 0.0160254i | ||||
\(681\) | −32.7405 | −1.25462 | ||||||||
\(682\) | −20.8898 | + | 20.8898i | −0.799910 | + | 0.799910i | ||||
\(683\) | −6.45442 | + | 6.45442i | −0.246971 | + | 0.246971i | −0.819726 | − | 0.572755i | \(-0.805875\pi\) |
0.572755 | + | 0.819726i | \(0.305875\pi\) | |||||||
\(684\) | 6.74690 | 0.257974 | ||||||||
\(685\) | 10.2631 | − | 12.3431i | 0.392134 | − | 0.471607i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.8358 | − | 16.8358i | −0.642325 | − | 0.642325i | ||||
\(688\) | 4.97801 | − | 4.97801i | 0.189785 | − | 0.189785i | ||||
\(689\) | −2.39978 | −0.0914243 | ||||||||
\(690\) | −13.1170 | + | 15.7753i | −0.499354 | + | 0.600557i | ||||
\(691\) | − | 48.4941i | − | 1.84480i | −0.386234 | − | 0.922401i | \(-0.626224\pi\) | ||
0.386234 | − | 0.922401i | \(-0.373776\pi\) | |||||||
\(692\) | −5.49565 | + | 5.49565i | −0.208913 | + | 0.208913i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 16.7042i | − | 0.634082i | ||||||
\(695\) | 2.54397 | + | 27.6489i | 0.0964982 | + | 1.04878i | ||||
\(696\) | − | 14.4734i | − | 0.548611i | ||||||
\(697\) | 3.73192 | + | 3.73192i | 0.141357 | + | 0.141357i | ||||
\(698\) | −25.9611 | − | 25.9611i | −0.982644 | − | 0.982644i | ||||
\(699\) | 11.5732 | 0.437739 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.8898 | −1.16669 | −0.583347 | − | 0.812223i | \(-0.698257\pi\) | ||||
−0.583347 | + | 0.812223i | \(0.698257\pi\) | |||||||
\(702\) | 0.792131 | + | 0.792131i | 0.0298971 | + | 0.0298971i | ||||
\(703\) | −20.2905 | − | 20.2905i | −0.765271 | − | 0.765271i | ||||
\(704\) | 4.03997i | 0.152262i | ||||||||
\(705\) | 0.130529 | + | 1.41864i | 0.00491601 | + | 0.0534292i | ||||
\(706\) | 14.2708i | 0.537089i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.22290 | − | 1.22290i | 0.0459595 | − | 0.0459595i | ||||
\(709\) | 14.7055i | 0.552278i | 0.961118 | + | 0.276139i | \(0.0890550\pi\) | ||||
−0.961118 | + | 0.276139i | \(0.910945\pi\) | |||||||
\(710\) | 10.1823 | − | 12.2459i | 0.382136 | − | 0.459582i | ||||
\(711\) | −5.52108 | −0.207057 | ||||||||
\(712\) | 2.17245 | − | 2.17245i | 0.0814159 | − | 0.0814159i | ||||
\(713\) | −23.4656 | − | 23.4656i | −0.878795 | − | 0.878795i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.67341 | − | 2.01256i | 0.0625821 | − | 0.0752654i | ||||
\(716\) | −3.86472 | −0.144431 | ||||||||
\(717\) | 11.9201 | − | 11.9201i | 0.445164 | − | 0.445164i | ||||
\(718\) | −19.1547 | + | 19.1547i | −0.714847 | + | 0.714847i | ||||
\(719\) | 23.4720 | 0.875358 | 0.437679 | − | 0.899131i | \(-0.355801\pi\) | ||||
0.437679 | + | 0.899131i | \(0.355801\pi\) | |||||||
\(720\) | −2.42177 | + | 0.222827i | −0.0902542 | + | 0.00830428i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13.7753 | + | 13.7753i | 0.512665 | + | 0.512665i | ||||
\(723\) | −4.23794 | + | 4.23794i | −0.157611 | + | 0.157611i | ||||
\(724\) | −6.99107 | −0.259821 | ||||||||
\(725\) | 6.53141 | + | 35.1925i | 0.242570 | + | 1.30702i | ||||
\(726\) | − | 10.7587i | − | 0.399293i | ||||||
\(727\) | 14.1380 | − | 14.1380i | 0.524349 | − | 0.524349i | −0.394533 | − | 0.918882i | \(-0.629093\pi\) |
0.918882 | + | 0.394533i | \(0.129093\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 11.4004i | − | 0.422236i | ||||||
\(730\) | 25.6642 | − | 2.36136i | 0.949875 | − | 0.0873979i | ||||
\(731\) | − | 14.3597i | − | 0.531113i | ||||||
\(732\) | −9.89407 | − | 9.89407i | −0.365695 | − | 0.365695i | ||||
\(733\) | −19.6123 | − | 19.6123i | −0.724395 | − | 0.724395i | 0.245102 | − | 0.969497i | \(-0.421179\pi\) |
−0.969497 | + | 0.245102i | \(0.921179\pi\) | |||||||
\(734\) | 22.6715 | 0.836821 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.53813 | −0.167278 | ||||||||
\(737\) | 9.02342 | + | 9.02342i | 0.332382 | + | 0.332382i | ||||
\(738\) | 1.98993 | + | 1.98993i | 0.0732502 | + | 0.0732502i | ||||
\(739\) | − | 13.5620i | − | 0.498888i | −0.968389 | − | 0.249444i | \(-0.919752\pi\) | ||
0.968389 | − | 0.249444i | \(-0.0802479\pi\) | |||||||
\(740\) | 7.95333 | + | 6.61308i | 0.292370 | + | 0.243102i | ||||
\(741\) | − | 3.63383i | − | 0.133492i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.5961 | − | 13.5961i | 0.498791 | − | 0.498791i | −0.412270 | − | 0.911062i | \(-0.635264\pi\) |
0.911062 | + | 0.412270i | \(0.135264\pi\) | |||||||
\(744\) | − | 14.7845i | − | 0.542024i | ||||||
\(745\) | −53.3249 | + | 4.90642i | −1.95367 | + | 0.179757i | ||||
\(746\) | −12.8358 | −0.469951 | ||||||||
\(747\) | −4.19141 | + | 4.19141i | −0.153355 | + | 0.153355i | ||||
\(748\) | 5.82691 | + | 5.82691i | 0.213053 | + | 0.213053i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 21.7534 | − | 6.14366i | 0.794320 | − | 0.224335i | ||||
\(751\) | 43.6619 | 1.59324 | 0.796622 | − | 0.604478i | \(-0.206618\pi\) | ||||
0.796622 | + | 0.604478i | \(0.206618\pi\) | |||||||
\(752\) | −0.222827 | + | 0.222827i | −0.00812567 | + | 0.00812567i | ||||
\(753\) | −23.1313 | + | 23.1313i | −0.842951 | + | 0.842951i | ||||
\(754\) | −2.07414 | −0.0755356 | ||||||||
\(755\) | 0.725941 | + | 7.88981i | 0.0264197 | + | 0.287140i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.88896 | + | 7.88896i | 0.286729 | + | 0.286729i | 0.835785 | − | 0.549056i | \(-0.185013\pi\) |
−0.549056 | + | 0.835785i | \(0.685013\pi\) | |||||||
\(758\) | −10.2346 | + | 10.2346i | −0.371738 | + | 0.371738i | ||||
\(759\) | 37.0673 | 1.34546 | ||||||||
\(760\) | −10.6657 | − | 8.86840i | −0.386887 | − | 0.321691i | ||||
\(761\) | − | 1.97365i | − | 0.0715447i | −0.999360 | − | 0.0357724i | \(-0.988611\pi\) | ||
0.999360 | − | 0.0357724i | \(-0.0113891\pi\) | |||||||
\(762\) | −4.44761 | + | 4.44761i | −0.161120 | + | 0.161120i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4.47442i | 0.161879i | ||||||||
\(765\) | −3.17157 | + | 3.81435i | −0.114668 | + | 0.137908i | ||||
\(766\) | 1.75158i | 0.0632870i | ||||||||
\(767\) | −0.175251 | − | 0.175251i | −0.00632794 | − | 0.00632794i | ||||
\(768\) | −1.42962 | − | 1.42962i | −0.0515870 | − | 0.0515870i | ||||
\(769\) | 17.4914 | 0.630756 | 0.315378 | − | 0.948966i | \(-0.397869\pi\) | ||||
0.315378 | + | 0.948966i | \(0.397869\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.7763 | −0.424112 | ||||||||
\(772\) | −14.1950 | − | 14.1950i | −0.510889 | − | 0.510889i | ||||
\(773\) | −31.6197 | − | 31.6197i | −1.13728 | − | 1.13728i | −0.988936 | − | 0.148345i | \(-0.952605\pi\) |
−0.148345 | − | 0.988936i | \(-0.547395\pi\) | |||||||
\(774\) | − | 7.65685i | − | 0.275220i | ||||||
\(775\) | 6.67180 | + | 35.9490i | 0.239658 | + | 1.29132i | ||||
\(776\) | 9.37769i | 0.336640i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.96738 | − | 1.96738i | 0.0705341 | − | 0.0705341i | ||||
\(779\) | 16.0508i | 0.575081i | ||||||||
\(780\) | 0.120013 | + | 1.30435i | 0.00429715 | + | 0.0467032i | ||||
\(781\) | −28.7743 | −1.02963 | ||||||||
\(782\) | −6.54541 | + | 6.54541i | −0.234064 | + | 0.234064i | ||||
\(783\) | 19.5716 | + | 19.5716i | 0.699433 | + | 0.699433i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.5268 | + | 8.75286i | 0.375717 | + | 0.312403i | ||||
\(786\) | −14.7565 | −0.526348 | ||||||||
\(787\) | 18.3483 | − | 18.3483i | 0.654047 | − | 0.654047i | −0.299918 | − | 0.953965i | \(-0.596959\pi\) |
0.953965 | + | 0.299918i | \(0.0969593\pi\) | |||||||
\(788\) | 7.84901 | − | 7.84901i | 0.279610 | − | 0.279610i | ||||
\(789\) | −3.51210 | −0.125034 | ||||||||
\(790\) | 8.72792 | + | 7.25713i | 0.310525 | + | 0.258197i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.10701 | + | 3.10701i | 0.110403 | + | 0.110403i | ||||
\(793\) | −1.41789 | + | 1.41789i | −0.0503508 | + | 0.0503508i | ||||
\(794\) | −39.6680 | −1.40776 | ||||||||
\(795\) | 3.43077 | + | 37.2870i | 0.121677 | + | 1.32243i | ||||
\(796\) | − | 10.8021i | − | 0.382869i | ||||||
\(797\) | 37.3374 | − | 37.3374i | 1.32256 | − | 1.32256i | 0.410861 | − | 0.911698i | \(-0.365228\pi\) |
0.911698 | − | 0.410861i | \(-0.134772\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.642773i | 0.0227397i | ||||||||
\(800\) | 4.12132 | + | 2.83103i | 0.145711 | + | 0.100092i | ||||
\(801\) | − | 3.34152i | − | 0.118067i | ||||||
\(802\) | −14.1213 | − | 14.1213i | −0.498641 | − | 0.498641i | ||||
\(803\) | −32.9259 | − | 32.9259i | −1.16193 | − | 1.16193i | ||||
\(804\) | −6.38621 | −0.225224 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.11872 | −0.0746287 | ||||||||
\(807\) | 5.40878 | + | 5.40878i | 0.190398 | + | 0.190398i | ||||
\(808\) | −6.99218 | − | 6.99218i | −0.245984 | − | 0.245984i | ||||
\(809\) | − | 16.0505i | − | 0.564306i | −0.959369 | − | 0.282153i | \(-0.908951\pi\) | ||
0.959369 | − | 0.282153i | \(-0.0910486\pi\) | |||||||
\(810\) | 15.8401 | − | 19.0504i | 0.556565 | − | 0.669362i | ||||
\(811\) | − | 35.4040i | − | 1.24320i | −0.783334 | − | 0.621602i | \(-0.786482\pi\) | ||
0.783334 | − | 0.621602i | \(-0.213518\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −30.3791 | + | 30.3791i | −1.06544 | + | 1.06544i | ||||
\(814\) | − | 18.6879i | − | 0.655012i | ||||||
\(815\) | 28.4689 | + | 23.6715i | 0.997222 | + | 0.829175i | ||||
\(816\) | −4.12392 | −0.144366 | ||||||||
\(817\) | 30.8802 | − | 30.8802i | 1.08036 | − | 1.08036i | ||||
\(818\) | −10.8227 | − | 10.8227i | −0.378407 | − | 0.378407i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.530105 | − | 5.76139i | −0.0185121 | − | 0.201196i | ||||
\(821\) | 26.8462 | 0.936938 | 0.468469 | − | 0.883480i | \(-0.344806\pi\) | ||||
0.468469 | + | 0.883480i | \(0.344806\pi\) | |||||||
\(822\) | 10.2631 | − | 10.2631i | 0.357968 | − | 0.357968i | ||||
\(823\) | 19.7862 | − | 19.7862i | 0.689704 | − | 0.689704i | −0.272463 | − | 0.962166i | \(-0.587838\pi\) |
0.962166 | + | 0.272463i | \(0.0878381\pi\) | |||||||
\(824\) | −4.28203 | −0.149172 | ||||||||
\(825\) | −33.6628 | − | 23.1237i | −1.17199 | − | 0.805066i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.8901 | + | 16.8901i | 0.587325 | + | 0.587325i | 0.936906 | − | 0.349581i | \(-0.113676\pi\) |
−0.349581 | + | 0.936906i | \(0.613676\pi\) | |||||||
\(828\) | −3.49013 | + | 3.49013i | −0.121290 | + | 0.121290i | ||||
\(829\) | 14.1682 | 0.492083 | 0.246042 | − | 0.969259i | \(-0.420870\pi\) | ||||
0.246042 | + | 0.969259i | \(0.420870\pi\) | |||||||
\(830\) | 12.1353 | − | 1.11657i | 0.421222 | − | 0.0387565i | ||||
\(831\) | 9.88686i | 0.342972i | ||||||||
\(832\) | −0.204875 | + | 0.204875i | −0.00710276 | + | 0.00710276i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 25.1049i | 0.869311i | ||||||||
\(835\) | −25.0140 | − | 20.7988i | −0.865645 | − | 0.719771i | ||||
\(836\) | 25.0613i | 0.866763i | ||||||||
\(837\) | 19.9923 | + | 19.9923i | 0.691036 | + | 0.691036i | ||||
\(838\) | 19.5888 | + | 19.5888i | 0.676684 | + | 0.676684i | ||||
\(839\) | −18.1874 | −0.627900 | −0.313950 | − | 0.949439i | \(-0.601652\pi\) | ||||
−0.313950 | + | 0.949439i | \(0.601652\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.2469 | −0.767134 | ||||||||
\(842\) | 23.3458 | + | 23.3458i | 0.804549 | + | 0.804549i | ||||
\(843\) | 42.1418 | + | 42.1418i | 1.45144 | + | 1.45144i | ||||
\(844\) | 7.56555i | 0.260417i | ||||||||
\(845\) | −28.7597 | + | 2.64618i | −0.989363 | + | 0.0910312i | ||||
\(846\) | 0.342738i | 0.0117836i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.85669 | + | 5.85669i | −0.201120 | + | 0.201120i | ||||
\(849\) | − | 22.8131i | − | 0.782943i | ||||||
\(850\) | 10.0275 | − | 1.86101i | 0.343939 | − | 0.0638320i | ||||
\(851\) | 20.9923 | 0.719608 | ||||||||
\(852\) | 10.1823 | − | 10.1823i | 0.348841 | − | 0.348841i | ||||
\(853\) | 17.4820 | + | 17.4820i | 0.598574 | + | 0.598574i | 0.939933 | − | 0.341359i | \(-0.110887\pi\) |
−0.341359 | + | 0.939933i | \(0.610887\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −15.0231 | + | 1.38227i | −0.513778 | + | 0.0472726i | ||||
\(856\) | 14.8721 | 0.508317 | ||||||||
\(857\) | −18.4941 | + | 18.4941i | −0.631747 | + | 0.631747i | −0.948506 | − | 0.316759i | \(-0.897405\pi\) |
0.316759 | + | 0.948506i | \(0.397405\pi\) | |||||||
\(858\) | 1.67341 | − | 1.67341i | 0.0571293 | − | 0.0571293i | ||||
\(859\) | 48.8251 | 1.66589 | 0.832946 | − | 0.553354i | \(-0.186652\pi\) | ||||
0.832946 | + | 0.553354i | \(0.186652\pi\) | |||||||
\(860\) | −10.0645 | + | 12.1042i | −0.343196 | + | 0.412751i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.9121 | + | 16.9121i | 0.576027 | + | 0.576027i | ||||
\(863\) | 10.8532 | − | 10.8532i | 0.369449 | − | 0.369449i | −0.497827 | − | 0.867276i | \(-0.665869\pi\) |
0.867276 | + | 0.497827i | \(0.165869\pi\) | |||||||
\(864\) | 3.86642 | 0.131538 | ||||||||
\(865\) | 11.1110 | − | 13.3629i | 0.377787 | − | 0.454352i | ||||
\(866\) | 18.7405i | 0.636829i | ||||||||
\(867\) | 18.3555 | − | 18.3555i | 0.623387 | − | 0.623387i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 20.5080i | − | 0.695686i | ||||||
\(870\) | 2.96523 | + | 32.2273i | 0.100531 | + | 1.09261i | ||||
\(871\) | 0.915190i | 0.0310100i | ||||||||
\(872\) | 9.35593 | + | 9.35593i | 0.316832 | + | 0.316832i | ||||
\(873\) | 7.21208 | + | 7.21208i | 0.244092 | + | 0.244092i | ||||
\(874\) | −28.1515 | −0.952240 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 23.3028 | 0.787330 | ||||||||
\(877\) | −27.9035 | − | 27.9035i | −0.942235 | − | 0.942235i | 0.0561853 | − | 0.998420i | \(-0.482106\pi\) |
−0.998420 | + | 0.0561853i | \(0.982106\pi\) | |||||||
\(878\) | −9.97563 | − | 9.97563i | −0.336661 | − | 0.336661i | ||||
\(879\) | − | 20.6839i | − | 0.697652i | ||||||
\(880\) | −0.827689 | − | 8.99566i | −0.0279014 | − | 0.303244i | ||||
\(881\) | − | 52.5926i | − | 1.77189i | −0.463791 | − | 0.885945i | \(-0.653511\pi\) | ||
0.463791 | − | 0.885945i | \(-0.346489\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.0940 | − | 13.0940i | 0.440649 | − | 0.440649i | −0.451581 | − | 0.892230i | \(-0.649140\pi\) |
0.892230 | + | 0.451581i | \(0.149140\pi\) | |||||||
\(884\) | 0.590988i | 0.0198771i | ||||||||
\(885\) | −2.47245 | + | 2.97353i | −0.0831105 | + | 0.0999542i | ||||
\(886\) | 21.0634 | 0.707638 | ||||||||
\(887\) | −26.1335 | + | 26.1335i | −0.877477 | + | 0.877477i | −0.993273 | − | 0.115796i | \(-0.963058\pi\) |
0.115796 | + | 0.993273i | \(0.463058\pi\) | |||||||
\(888\) | 6.61308 | + | 6.61308i | 0.221920 | + | 0.221920i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −4.39223 | + | 5.28239i | −0.147228 | + | 0.177066i | ||||
\(891\) | −44.7627 | −1.49961 | ||||||||
\(892\) | 9.35230 | − | 9.35230i | 0.313138 | − | 0.313138i | ||||
\(893\) | −1.38227 | + | 1.38227i | −0.0462559 | + | 0.0462559i | ||||
\(894\) | −48.4185 | −1.61936 | ||||||||
\(895\) | 8.60543 | − | 0.791785i | 0.287648 | − | 0.0264664i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.87976 | + | 1.87976i | 0.0627633 | + | 0.0627633i | ||||
\(898\) | −22.1499 | + | 22.1499i | −0.739153 | + | 0.739153i | ||||
\(899\) | −52.3484 | −1.74592 | ||||||||
\(900\) | 5.34682 | − | 0.992322i | 0.178227 | − | 0.0330774i | ||||
\(901\) | 16.8944i | 0.562833i | ||||||||
\(902\) | −7.39156 | + | 7.39156i | −0.246112 | + | 0.246112i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.7933i | 0.458759i | ||||||||
\(905\) | 15.5668 | − | 1.43229i | 0.517456 | − | 0.0476111i | ||||
\(906\) | 7.16387i | 0.238004i | ||||||||
\(907\) | −11.7173 | − | 11.7173i | −0.389066 | − | 0.389066i | 0.485288 | − | 0.874354i | \(-0.338715\pi\) |
−0.874354 | + | 0.485288i | \(0.838715\pi\) | |||||||
\(908\) | 11.4508 | + | 11.4508i | 0.380007 | + | 0.380007i | ||||
\(909\) | −10.7549 | −0.356718 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.46770 | −0.0486270 | −0.0243135 | − | 0.999704i | \(-0.507740\pi\) | ||||
−0.0243135 | + | 0.999704i | \(0.507740\pi\) | |||||||
\(912\) | −8.86840 | − | 8.86840i | −0.293662 | − | 0.293662i | ||||
\(913\) | −15.5689 | − | 15.5689i | −0.515256 | − | 0.515256i | ||||
\(914\) | − | 2.86154i | − | 0.0946514i | ||||||
\(915\) | 24.0578 | + | 20.0037i | 0.795326 | + | 0.661302i | ||||
\(916\) | 11.7764i | 0.389103i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.57658 | − | 5.57658i | 0.184055 | − | 0.184055i | ||||
\(919\) | − | 27.8886i | − | 0.919961i | −0.887929 | − | 0.459981i | \(-0.847856\pi\) | ||
0.887929 | − | 0.459981i | \(-0.152144\pi\) | |||||||
\(920\) | 10.1049 | − | 0.929750i | 0.333149 | − | 0.0306529i | ||||
\(921\) | −3.08395 | −0.101620 | ||||||||
\(922\) | −2.14023 | + | 2.14023i | −0.0704846 | + | 0.0704846i | ||||
\(923\) | −1.45920 | − | 1.45920i | −0.0480302 | − | 0.0480302i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.0642 | − | 13.0957i | −0.626828 | − | 0.430582i | ||||
\(926\) | 27.2786 | 0.896431 | ||||||||
\(927\) | −3.29317 | + | 3.29317i | −0.108162 | + | 0.108162i | ||||
\(928\) | −5.06196 | + | 5.06196i | −0.166167 | + | 0.166167i | ||||
\(929\) | −33.2936 | −1.09233 | −0.546164 | − | 0.837678i | \(-0.683913\pi\) | ||||
−0.546164 | + | 0.837678i | \(0.683913\pi\) | |||||||
\(930\) | 3.02896 | + | 32.9200i | 0.0993236 | + | 1.07949i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −4.04765 | − | 4.04765i | −0.132585 | − | 0.132585i | ||||
\(933\) | 13.7647 | − | 13.7647i | 0.450637 | − | 0.450637i | ||||
\(934\) | 25.1289 | 0.822244 | ||||||||
\(935\) | −14.1684 | − | 11.7808i | −0.463355 | − | 0.385273i | ||||
\(936\) | 0.315125i | 0.0103002i | ||||||||
\(937\) | −25.6651 | + | 25.6651i | −0.838442 | + | 0.838442i | −0.988654 | − | 0.150212i | \(-0.952004\pi\) |
0.150212 | + | 0.988654i | \(0.452004\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 6.11942i | − | 0.199700i | ||||||
\(940\) | 0.450509 | − | 0.541813i | 0.0146940 | − | 0.0176720i | ||||
\(941\) | 24.3333i | 0.793242i | 0.917983 | + | 0.396621i | \(0.129817\pi\) | ||||
−0.917983 | + | 0.396621i | \(0.870183\pi\) | |||||||
\(942\) | 8.75286 | + | 8.75286i | 0.285184 | + | 0.285184i | ||||
\(943\) | −8.30300 | − | 8.30300i | −0.270383 | − | 0.270383i | ||||
\(944\) | −0.855404 | −0.0278410 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 28.4413 | 0.924707 | ||||||||
\(947\) | −1.52032 | − | 1.52032i | −0.0494039 | − | 0.0494039i | 0.681973 | − | 0.731377i | \(-0.261122\pi\) |
−0.731377 | + | 0.681973i | \(0.761122\pi\) | |||||||
\(948\) | 7.25713 | + | 7.25713i | 0.235701 | + | 0.235701i | ||||
\(949\) | − | 3.33947i | − | 0.108404i | ||||||
\(950\) | 25.5659 | + | 17.5618i | 0.829467 | + | 0.569780i | ||||
\(951\) | − | 3.93980i | − | 0.127757i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.1863 | + | 13.1863i | −0.427146 | + | 0.427146i | −0.887655 | − | 0.460509i | \(-0.847667\pi\) |
0.460509 | + | 0.887655i | \(0.347667\pi\) | |||||||
\(954\) | 9.00838i | 0.291657i | ||||||||
\(955\) | −0.916697 | − | 9.96303i | −0.0296636 | − | 0.322396i | ||||
\(956\) | −8.33794 | −0.269668 | ||||||||
\(957\) | 41.3459 | − | 41.3459i | 1.33652 | − | 1.33652i | ||||
\(958\) | −5.85973 | − | 5.85973i | −0.189319 | − | 0.189319i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3.47617 | + | 2.89039i | 0.112193 | + | 0.0932869i | ||||
\(961\) | −22.4736 | −0.724955 | ||||||||
\(962\) | 0.947702 | − | 0.947702i | 0.0305551 | − | 0.0305551i | ||||
\(963\) | 11.4376 | − | 11.4376i | 0.368572 | − | 0.368572i | ||||
\(964\) | 2.96438 | 0.0954763 | ||||||||
\(965\) | 34.5156 | + | 28.6993i | 1.11110 | + | 0.923862i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.7931 | − | 27.7931i | −0.893766 | − | 0.893766i | 0.101109 | − | 0.994875i | \(-0.467761\pi\) |
−0.994875 | + | 0.101109i | \(0.967761\pi\) | |||||||
\(968\) | −3.76279 | + | 3.76279i | −0.120941 | + | 0.120941i | ||||
\(969\) | −25.5820 | −0.821813 | ||||||||
\(970\) | −1.92125 | − | 20.8810i | −0.0616877 | − | 0.670447i | ||||
\(971\) | 13.9752i | 0.448486i | 0.974533 | + | 0.224243i | \(0.0719909\pi\) | ||||
−0.974533 | + | 0.224243i | \(0.928009\pi\) | |||||||
\(972\) | 7.63821 | − | 7.63821i | 0.244996 | − | 0.244996i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 10.6783i | 0.342155i | ||||||||
\(975\) | −0.534457 | − | 2.87976i | −0.0171163 | − | 0.0922260i | ||||
\(976\) | 6.92077i | 0.221528i | ||||||||
\(977\) | 5.90367 | + | 5.90367i | 0.188875 | + | 0.188875i | 0.795210 | − | 0.606335i | \(-0.207361\pi\) |
−0.606335 | + | 0.795210i | \(0.707361\pi\) | |||||||
\(978\) | 23.6715 | + | 23.6715i | 0.756930 | + | 0.756930i | ||||
\(979\) | 12.4120 | 0.396690 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.3907 | 0.459459 | ||||||||
\(982\) | 18.1910 | + | 18.1910i | 0.580498 | + | 0.580498i | ||||
\(983\) | 17.2224 | + | 17.2224i | 0.549309 | + | 0.549309i | 0.926241 | − | 0.376932i | \(-0.123021\pi\) |
−0.376932 | + | 0.926241i | \(0.623021\pi\) | |||||||
\(984\) | − | 5.23128i | − | 0.166767i | ||||||
\(985\) | −15.8690 | + | 19.0852i | −0.505630 | + | 0.608104i | ||||
\(986\) | 14.6019i | 0.465018i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.27091 | + | 1.27091i | −0.0404329 | + | 0.0404329i | ||||
\(989\) | 31.9483i | 1.01590i | ||||||||
\(990\) | −7.55482 | − | 6.28172i | −0.240108 | − | 0.199646i | ||||
\(991\) | 17.4400 | 0.554001 | 0.277000 | − | 0.960870i | \(-0.410660\pi\) | ||||
0.277000 | + | 0.960870i | \(0.410660\pi\) | |||||||
\(992\) | −5.17076 | + | 5.17076i | −0.164172 | + | 0.164172i | ||||
\(993\) | 41.3067 | + | 41.3067i | 1.31083 | + | 1.31083i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.21307 | + | 24.0525i | 0.0701590 | + | 0.762516i | ||||
\(996\) | 11.0187 | 0.349141 | ||||||||
\(997\) | 18.5048 | − | 18.5048i | 0.586054 | − | 0.586054i | −0.350506 | − | 0.936560i | \(-0.613990\pi\) |
0.936560 | + | 0.350506i | \(0.113990\pi\) | |||||||
\(998\) | −10.3229 | + | 10.3229i | −0.326766 | + | 0.326766i | ||||
\(999\) | −17.8851 | −0.565860 |
(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 | 490.2.g.c.97.5 | 16 | ||
5.3 | odd | 4 | inner | 490.2.g.c.293.8 | 16 | ||
7.2 | even | 3 | 70.2.k.a.17.4 | yes | 16 | ||
7.3 | odd | 6 | 70.2.k.a.47.2 | yes | 16 | ||
7.4 | even | 3 | 490.2.l.c.117.1 | 16 | |||
7.5 | odd | 6 | 490.2.l.c.227.3 | 16 | |||
7.6 | odd | 2 | inner | 490.2.g.c.97.8 | 16 | ||
21.2 | odd | 6 | 630.2.bv.c.577.2 | 16 | |||
21.17 | even | 6 | 630.2.bv.c.397.4 | 16 | |||
28.3 | even | 6 | 560.2.ci.c.257.1 | 16 | |||
28.23 | odd | 6 | 560.2.ci.c.17.1 | 16 | |||
35.2 | odd | 12 | 350.2.o.c.143.3 | 16 | |||
35.3 | even | 12 | 70.2.k.a.33.4 | yes | 16 | ||
35.9 | even | 6 | 350.2.o.c.157.1 | 16 | |||
35.13 | even | 4 | inner | 490.2.g.c.293.5 | 16 | ||
35.17 | even | 12 | 350.2.o.c.243.1 | 16 | |||
35.18 | odd | 12 | 490.2.l.c.313.3 | 16 | |||
35.23 | odd | 12 | 70.2.k.a.3.2 | ✓ | 16 | ||
35.24 | odd | 6 | 350.2.o.c.257.3 | 16 | |||
35.33 | even | 12 | 490.2.l.c.423.1 | 16 | |||
105.23 | even | 12 | 630.2.bv.c.73.4 | 16 | |||
105.38 | odd | 12 | 630.2.bv.c.523.2 | 16 | |||
140.3 | odd | 12 | 560.2.ci.c.33.1 | 16 | |||
140.23 | even | 12 | 560.2.ci.c.353.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.k.a.3.2 | ✓ | 16 | 35.23 | odd | 12 | ||
70.2.k.a.17.4 | yes | 16 | 7.2 | even | 3 | ||
70.2.k.a.33.4 | yes | 16 | 35.3 | even | 12 | ||
70.2.k.a.47.2 | yes | 16 | 7.3 | odd | 6 | ||
350.2.o.c.143.3 | 16 | 35.2 | odd | 12 | |||
350.2.o.c.157.1 | 16 | 35.9 | even | 6 | |||
350.2.o.c.243.1 | 16 | 35.17 | even | 12 | |||
350.2.o.c.257.3 | 16 | 35.24 | odd | 6 | |||
490.2.g.c.97.5 | 16 | 1.1 | even | 1 | trivial | ||
490.2.g.c.97.8 | 16 | 7.6 | odd | 2 | inner | ||
490.2.g.c.293.5 | 16 | 35.13 | even | 4 | inner | ||
490.2.g.c.293.8 | 16 | 5.3 | odd | 4 | inner | ||
490.2.l.c.117.1 | 16 | 7.4 | even | 3 | |||
490.2.l.c.227.3 | 16 | 7.5 | odd | 6 | |||
490.2.l.c.313.3 | 16 | 35.18 | odd | 12 | |||
490.2.l.c.423.1 | 16 | 35.33 | even | 12 | |||
560.2.ci.c.17.1 | 16 | 28.23 | odd | 6 | |||
560.2.ci.c.33.1 | 16 | 140.3 | odd | 12 | |||
560.2.ci.c.257.1 | 16 | 28.3 | even | 6 | |||
560.2.ci.c.353.1 | 16 | 140.23 | even | 12 | |||
630.2.bv.c.73.4 | 16 | 105.23 | even | 12 | |||
630.2.bv.c.397.4 | 16 | 21.17 | even | 6 | |||
630.2.bv.c.523.2 | 16 | 105.38 | odd | 12 | |||
630.2.bv.c.577.2 | 16 | 21.2 | odd | 6 |