Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,2,Mod(109,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.g (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.52751779461\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.1767277521.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + x^{6} - 10x^{5} + 38x^{4} - 40x^{3} + 64x^{2} - 38x + 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.3 | ||
Root | \(0.0512865 + 1.21608i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 567.109 |
Dual form | 567.2.g.k.541.3 |
$q$-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 \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.768262 | − | 1.33067i | 0.543243 | − | 0.940925i | −0.455472 | − | 0.890250i | \(-0.650530\pi\) |
0.998715 | − | 0.0506745i | \(-0.0161371\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.180452 | − | 0.312552i | −0.0902259 | − | 0.156276i | ||||
\(5\) | −3.15761 | −1.41212 | −0.706062 | − | 0.708150i | \(-0.749530\pi\) | ||||
−0.706062 | + | 0.708150i | \(0.749530\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.00900690 | + | 2.64574i | −0.00340429 | + | 0.999994i | ||||
\(8\) | 2.51851 | 0.890428 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.42587 | + | 4.20173i | −0.767127 | + | 1.32870i | ||||
\(11\) | 5.74916 | 1.73344 | 0.866719 | − | 0.498797i | \(-0.166225\pi\) | ||||
0.866719 | + | 0.498797i | \(0.166225\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.180452 | − | 0.312552i | 0.0500484 | − | 0.0866863i | −0.839916 | − | 0.542717i | \(-0.817396\pi\) |
0.889964 | + | 0.456030i | \(0.150729\pi\) | |||||||
\(14\) | 3.51368 | + | 2.04460i | 0.939070 | + | 0.546443i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.29578 | − | 3.97640i | 0.573945 | − | 0.994101i | ||||
\(17\) | 1.38842 | − | 2.40481i | 0.336741 | − | 0.583253i | −0.647076 | − | 0.762425i | \(-0.724009\pi\) |
0.983818 | + | 0.179172i | \(0.0573419\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.61533 | + | 6.26193i | 0.829413 | + | 1.43658i | 0.898500 | + | 0.438974i | \(0.144658\pi\) |
−0.0690869 | + | 0.997611i | \(0.522009\pi\) | |||||||
\(20\) | 0.569796 | + | 0.986916i | 0.127410 | + | 0.220681i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.41686 | − | 7.65023i | 0.941678 | − | 1.63103i | ||||
\(23\) | 0.824381 | 0.171895 | 0.0859476 | − | 0.996300i | \(-0.472608\pi\) | ||||
0.0859476 | + | 0.996300i | \(0.472608\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.97047 | 0.994095 | ||||||||
\(26\) | −0.277269 | − | 0.480243i | −0.0543768 | − | 0.0941834i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.828555 | − | 0.474613i | 0.156582 | − | 0.0896934i | ||||
\(29\) | −2.13910 | − | 3.70502i | −0.397220 | − | 0.688006i | 0.596162 | − | 0.802864i | \(-0.296692\pi\) |
−0.993382 | + | 0.114859i | \(0.963358\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.49099 | + | 4.31453i | 0.447396 | + | 0.774912i | 0.998216 | − | 0.0597122i | \(-0.0190183\pi\) |
−0.550820 | + | 0.834624i | \(0.685685\pi\) | |||||||
\(32\) | −1.00901 | − | 1.74765i | −0.178369 | − | 0.308944i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.13334 | − | 3.69505i | −0.365865 | − | 0.633696i | ||||
\(35\) | 0.0284402 | − | 8.35419i | 0.00480728 | − | 1.41212i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.74542 | − | 6.48725i | −0.615743 | − | 1.06650i | −0.990254 | − | 0.139275i | \(-0.955523\pi\) |
0.374511 | − | 0.927222i | \(-0.377811\pi\) | |||||||
\(38\) | 11.1101 | 1.80229 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.95246 | −1.25739 | ||||||||
\(41\) | −1.66569 | + | 2.88506i | −0.260137 | + | 0.450570i | −0.966278 | − | 0.257501i | \(-0.917101\pi\) |
0.706141 | + | 0.708071i | \(0.250434\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.93487 | + | 6.81540i | 0.600063 | + | 1.03934i | 0.992811 | + | 0.119693i | \(0.0381910\pi\) |
−0.392748 | + | 0.919646i | \(0.628476\pi\) | |||||||
\(44\) | −1.03745 | − | 1.79691i | −0.156401 | − | 0.270895i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.633340 | − | 1.09698i | 0.0933809 | − | 0.161740i | ||||
\(47\) | −1.74075 | + | 3.01506i | −0.253914 | + | 0.439792i | −0.964600 | − | 0.263718i | \(-0.915051\pi\) |
0.710686 | + | 0.703509i | \(0.248385\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99984 | − | 0.0476598i | −0.999977 | − | 0.00680854i | ||||
\(50\) | 3.81862 | − | 6.61405i | 0.540035 | − | 0.935368i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.130252 | −0.0180626 | ||||||||
\(53\) | −1.45772 | + | 2.52485i | −0.200233 | + | 0.346814i | −0.948604 | − | 0.316467i | \(-0.897503\pi\) |
0.748370 | + | 0.663281i | \(0.230837\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.1536 | −2.44783 | ||||||||
\(56\) | −0.0226840 | + | 6.66331i | −0.00303127 | + | 0.890422i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.57354 | −0.863148 | ||||||||
\(59\) | 1.19939 | + | 2.07740i | 0.156147 | + | 0.270455i | 0.933476 | − | 0.358639i | \(-0.116759\pi\) |
−0.777329 | + | 0.629094i | \(0.783426\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.60056 | + | 2.77226i | −0.204931 | + | 0.354951i | −0.950111 | − | 0.311913i | \(-0.899030\pi\) |
0.745180 | + | 0.666864i | \(0.232364\pi\) | |||||||
\(62\) | 7.65494 | 0.972178 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.08239 | 0.760298 | ||||||||
\(65\) | −0.569796 | + | 0.986916i | −0.0706745 | + | 0.122412i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.949637 | − | 1.64482i | −0.116017 | − | 0.200947i | 0.802169 | − | 0.597097i | \(-0.203679\pi\) |
−0.918186 | + | 0.396150i | \(0.870346\pi\) | |||||||
\(68\) | −1.00217 | −0.121531 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −11.0948 | − | 6.45605i | −1.32608 | − | 0.771645i | ||||
\(71\) | −1.60957 | −0.191021 | −0.0955104 | − | 0.995428i | \(-0.530448\pi\) | ||||
−0.0955104 | + | 0.995428i | \(0.530448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.70688 | − | 13.3487i | 0.902022 | − | 1.56235i | 0.0771572 | − | 0.997019i | \(-0.475416\pi\) |
0.824865 | − | 0.565330i | \(-0.191251\pi\) | |||||||
\(74\) | −11.5098 | −1.33799 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.30478 | − | 2.25995i | 0.149669 | − | 0.259234i | ||||
\(77\) | −0.0517821 | + | 15.2108i | −0.00590112 | + | 1.73343i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.73641 | + | 4.73960i | −0.307870 | + | 0.533247i | −0.977896 | − | 0.209091i | \(-0.932950\pi\) |
0.670026 | + | 0.742337i | \(0.266283\pi\) | |||||||
\(80\) | −7.24916 | + | 12.5559i | −0.810481 | + | 1.40379i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.55937 | + | 4.43296i | 0.282635 | + | 0.489538i | ||||
\(83\) | −6.51742 | − | 11.2885i | −0.715380 | − | 1.23907i | −0.962813 | − | 0.270170i | \(-0.912920\pi\) |
0.247433 | − | 0.968905i | \(-0.420413\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.38408 | + | 7.59346i | −0.475521 | + | 0.823626i | ||||
\(86\) | 12.0921 | 1.30392 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 14.4793 | 1.54350 | ||||||||
\(89\) | −7.13384 | − | 12.3562i | −0.756185 | − | 1.30975i | −0.944783 | − | 0.327697i | \(-0.893728\pi\) |
0.188598 | − | 0.982054i | \(-0.439606\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.825304 | + | 0.480243i | 0.0865154 | + | 0.0503432i | ||||
\(92\) | −0.148761 | − | 0.257662i | −0.0155094 | − | 0.0268631i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.67470 | + | 4.63271i | 0.275874 | + | 0.477827i | ||||
\(95\) | −11.4158 | − | 19.7727i | −1.17123 | − | 2.02864i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.00266 | − | 13.8610i | −0.812547 | − | 1.40737i | −0.911076 | − | 0.412239i | \(-0.864747\pi\) |
0.0985289 | − | 0.995134i | \(-0.468586\pi\) | |||||||
\(98\) | −5.44113 | + | 9.27785i | −0.549637 | + | 0.937204i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.896931 | − | 1.55353i | −0.0896931 | − | 0.155353i | ||||
\(101\) | −3.00749 | −0.299257 | −0.149628 | − | 0.988742i | \(-0.547808\pi\) | ||||
−0.149628 | + | 0.988742i | \(0.547808\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.72063 | 0.957802 | 0.478901 | − | 0.877869i | \(-0.341035\pi\) | ||||
0.478901 | + | 0.877869i | \(0.341035\pi\) | |||||||
\(104\) | 0.454470 | − | 0.787165i | 0.0445644 | − | 0.0771879i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.23982 | + | 3.87948i | 0.217551 | + | 0.376809i | ||||
\(107\) | 5.21214 | + | 9.02770i | 0.503877 | + | 0.872740i | 0.999990 | + | 0.00448241i | \(0.00142680\pi\) |
−0.496113 | + | 0.868258i | \(0.665240\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.33713 | − | 4.04803i | 0.223857 | − | 0.387731i | −0.732119 | − | 0.681177i | \(-0.761469\pi\) |
0.955976 | + | 0.293445i | \(0.0948019\pi\) | |||||||
\(110\) | −13.9467 | + | 24.1564i | −1.32977 | + | 2.30322i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.4998 | + | 6.10984i | 0.992141 | + | 0.577325i | ||||
\(113\) | 2.34332 | − | 4.05875i | 0.220441 | − | 0.381815i | −0.734501 | − | 0.678608i | \(-0.762584\pi\) |
0.954942 | + | 0.296793i | \(0.0959171\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.60307 | −0.242737 | ||||||||
\(116\) | −0.772008 | + | 1.33716i | −0.0716791 | + | 0.124152i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.68578 | 0.339304 | ||||||||
\(119\) | 6.35000 | + | 3.69505i | 0.582103 | + | 0.338725i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.0529 | 2.00481 | ||||||||
\(122\) | 2.45930 | + | 4.25964i | 0.222655 | + | 0.385649i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.899009 | − | 1.55713i | 0.0807334 | − | 0.139834i | ||||
\(125\) | 0.0932326 | 0.00833898 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.15945 | −0.812770 | −0.406385 | − | 0.913702i | \(-0.633211\pi\) | ||||
−0.406385 | + | 0.913702i | \(0.633211\pi\) | |||||||
\(128\) | 6.69088 | − | 11.5889i | 0.591396 | − | 1.02433i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.875505 | + | 1.51642i | 0.0767868 | + | 0.132999i | ||||
\(131\) | −9.21165 | −0.804825 | −0.402413 | − | 0.915458i | \(-0.631828\pi\) | ||||
−0.402413 | + | 0.915458i | \(0.631828\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.6000 | + | 9.50880i | −1.43940 | + | 0.824517i | ||||
\(134\) | −2.91828 | −0.252101 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.49675 | − | 6.05655i | 0.299844 | − | 0.519345i | ||||
\(137\) | −6.82438 | −0.583046 | −0.291523 | − | 0.956564i | \(-0.594162\pi\) | ||||
−0.291523 | + | 0.956564i | \(0.594162\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.84332 | − | 4.92477i | 0.241167 | − | 0.417714i | −0.719880 | − | 0.694099i | \(-0.755803\pi\) |
0.961047 | + | 0.276385i | \(0.0891365\pi\) | |||||||
\(140\) | −2.61625 | + | 1.49864i | −0.221113 | + | 0.126658i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.23657 | + | 2.14180i | −0.103771 | + | 0.179736i | ||||
\(143\) | 1.03745 | − | 1.79691i | 0.0867557 | − | 0.150265i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.75442 | + | 11.6990i | 0.560924 | + | 0.971549i | ||||
\(146\) | −11.8418 | − | 20.5106i | −0.980035 | − | 1.69747i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.35173 | + | 2.34127i | −0.111112 | + | 0.192451i | ||||
\(149\) | −21.5885 | −1.76860 | −0.884301 | − | 0.466918i | \(-0.845364\pi\) | ||||
−0.884301 | + | 0.466918i | \(0.845364\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.55553 | −0.452102 | −0.226051 | − | 0.974115i | \(-0.572582\pi\) | ||||
−0.226051 | + | 0.974115i | \(0.572582\pi\) | |||||||
\(152\) | 9.10523 | + | 15.7707i | 0.738532 | + | 1.27917i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 20.2007 | + | 11.7548i | 1.62782 | + | 0.947225i | ||||
\(155\) | −7.86557 | − | 13.6236i | −0.631778 | − | 1.09427i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.03560 | − | 5.25781i | −0.242267 | − | 0.419619i | 0.719093 | − | 0.694914i | \(-0.244558\pi\) |
−0.961360 | + | 0.275295i | \(0.911224\pi\) | |||||||
\(158\) | 4.20456 | + | 7.28250i | 0.334496 | + | 0.579365i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.18605 | + | 5.51839i | 0.251879 | + | 0.436267i | ||||
\(161\) | −0.00742511 | + | 2.18109i | −0.000585181 | + | 0.171894i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.92630 | + | 3.33644i | 0.150879 | + | 0.261330i | 0.931551 | − | 0.363611i | \(-0.118456\pi\) |
−0.780672 | + | 0.624941i | \(0.785123\pi\) | |||||||
\(164\) | 1.20231 | 0.0938844 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −20.0283 | −1.55450 | ||||||||
\(167\) | −1.76919 | + | 3.06432i | −0.136904 | + | 0.237124i | −0.926323 | − | 0.376730i | \(-0.877048\pi\) |
0.789419 | + | 0.613854i | \(0.210382\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.43487 | + | 11.1455i | 0.494990 | + | 0.857348i | ||||
\(170\) | 6.73625 | + | 11.6675i | 0.516647 | + | 0.894858i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.42011 | − | 2.45970i | 0.108282 | − | 0.187551i | ||||
\(173\) | −4.92679 | + | 8.53345i | −0.374577 | + | 0.648786i | −0.990264 | − | 0.139205i | \(-0.955545\pi\) |
0.615687 | + | 0.787991i | \(0.288879\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.0447686 | + | 13.1506i | −0.00338419 | + | 0.994089i | ||||
\(176\) | 13.1988 | − | 22.8610i | 0.994897 | − | 1.72321i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −21.9226 | −1.64317 | ||||||||
\(179\) | −9.94855 | + | 17.2314i | −0.743590 | + | 1.28794i | 0.207261 | + | 0.978286i | \(0.433545\pi\) |
−0.950851 | + | 0.309649i | \(0.899788\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.0930 | 0.898869 | 0.449434 | − | 0.893313i | \(-0.351626\pi\) | ||||
0.449434 | + | 0.893313i | \(0.351626\pi\) | |||||||
\(182\) | 1.27309 | − | 0.729254i | 0.0943680 | − | 0.0540559i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.07621 | 0.153060 | ||||||||
\(185\) | 11.8265 | + | 20.4842i | 0.869505 | + | 1.50603i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.98225 | − | 13.8257i | 0.583720 | − | 1.01103i | ||||
\(188\) | 1.25648 | 0.0916385 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −35.0812 | −2.54506 | ||||||||
\(191\) | 4.85982 | − | 8.41745i | 0.351644 | − | 0.609065i | −0.634894 | − | 0.772600i | \(-0.718956\pi\) |
0.986538 | + | 0.163534i | \(0.0522894\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.15093 | + | 1.99346i | 0.0828454 | + | 0.143492i | 0.904471 | − | 0.426535i | \(-0.140266\pi\) |
−0.821626 | + | 0.570027i | \(0.806933\pi\) | |||||||
\(194\) | −24.5925 | −1.76564 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.24824 | + | 2.19641i | 0.0891598 | + | 0.156887i | ||||
\(197\) | −5.06470 | −0.360845 | −0.180422 | − | 0.983589i | \(-0.557746\pi\) | ||||
−0.180422 | + | 0.983589i | \(0.557746\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.97666 | − | 8.61982i | 0.352786 | − | 0.611043i | −0.633951 | − | 0.773374i | \(-0.718568\pi\) |
0.986736 | + | 0.162330i | \(0.0519011\pi\) | |||||||
\(200\) | 12.5182 | 0.885169 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.31054 | + | 4.00197i | −0.162569 | + | 0.281578i | ||||
\(203\) | 9.82178 | − | 5.62611i | 0.689354 | − | 0.394876i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.25959 | − | 9.10987i | 0.367346 | − | 0.636261i | ||||
\(206\) | 7.46798 | − | 12.9349i | 0.520319 | − | 0.901219i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.828555 | − | 1.43510i | −0.0574500 | − | 0.0995062i | ||||
\(209\) | 20.7851 | + | 36.0008i | 1.43774 | + | 2.49023i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.6503 | − | 20.1790i | 0.802042 | − | 1.38918i | −0.116228 | − | 0.993223i | \(-0.537080\pi\) |
0.918270 | − | 0.395955i | \(-0.129586\pi\) | |||||||
\(212\) | 1.05219 | 0.0722650 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 16.0172 | 1.09491 | ||||||||
\(215\) | −12.4248 | − | 21.5204i | −0.847363 | − | 1.46768i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.4375 | + | 6.55165i | −0.776430 | + | 0.444755i | ||||
\(218\) | −3.59106 | − | 6.21990i | −0.243217 | − | 0.421265i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.27585 | + | 5.67394i | 0.220858 | + | 0.382537i | ||||
\(221\) | −0.501086 | − | 0.867907i | −0.0337067 | − | 0.0583817i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.93770 | + | 10.2844i | 0.397618 | + | 0.688694i | 0.993431 | − | 0.114429i | \(-0.0365037\pi\) |
−0.595814 | + | 0.803123i | \(0.703170\pi\) | |||||||
\(224\) | 4.63291 | − | 2.65382i | 0.309549 | − | 0.177316i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.60056 | − | 6.23636i | −0.239506 | − | 0.414836i | ||||
\(227\) | −5.96081 | −0.395633 | −0.197816 | − | 0.980239i | \(-0.563385\pi\) | ||||
−0.197816 | + | 0.980239i | \(0.563385\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.7206 | −1.56750 | −0.783752 | − | 0.621074i | \(-0.786696\pi\) | ||||
−0.783752 | + | 0.621074i | \(0.786696\pi\) | |||||||
\(230\) | −1.99984 | + | 3.46382i | −0.131865 | + | 0.228398i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.38733 | − | 9.33114i | −0.353696 | − | 0.612619i | ||||
\(233\) | −6.92961 | − | 12.0024i | −0.453974 | − | 0.786306i | 0.544654 | − | 0.838661i | \(-0.316661\pi\) |
−0.998629 | + | 0.0523544i | \(0.983327\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.49659 | − | 9.52037i | 0.358558 | − | 0.621040i | ||||
\(236\) | 0.432864 | − | 0.749743i | 0.0281771 | − | 0.0488041i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.79535 | − | 5.61097i | 0.634938 | − | 0.363705i | ||||
\(239\) | 11.1713 | − | 19.3492i | 0.722610 | − | 1.25160i | −0.237340 | − | 0.971427i | \(-0.576276\pi\) |
0.959950 | − | 0.280171i | \(-0.0903911\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.72063 | 0.626161 | 0.313080 | − | 0.949727i | \(-0.398639\pi\) | ||||
0.313080 | + | 0.949727i | \(0.398639\pi\) | |||||||
\(242\) | 16.9424 | − | 29.3450i | 1.08910 | − | 1.88637i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.15530 | 0.0739604 | ||||||||
\(245\) | 22.1027 | + | 0.150491i | 1.41209 | + | 0.00961450i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.60957 | 0.166043 | ||||||||
\(248\) | 6.27359 | + | 10.8662i | 0.398373 | + | 0.690003i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.0716270 | − | 0.124062i | 0.00453009 | − | 0.00784635i | ||||
\(251\) | 6.51950 | 0.411507 | 0.205754 | − | 0.978604i | \(-0.434035\pi\) | ||||
0.205754 | + | 0.978604i | \(0.434035\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.73950 | 0.297970 | ||||||||
\(254\) | −7.03686 | + | 12.1882i | −0.441532 | + | 0.764755i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.19830 | − | 7.27167i | −0.262394 | − | 0.454480i | ||||
\(257\) | −5.53002 | −0.344953 | −0.172477 | − | 0.985014i | \(-0.555177\pi\) | ||||
−0.172477 | + | 0.985014i | \(0.555177\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 17.1973 | − | 9.85095i | 1.06859 | − | 0.612108i | ||||
\(260\) | 0.411283 | 0.0255067 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.07696 | + | 12.2576i | −0.437216 | + | 0.757280i | ||||
\(263\) | −8.69499 | −0.536156 | −0.268078 | − | 0.963397i | \(-0.586388\pi\) | ||||
−0.268078 | + | 0.963397i | \(0.586388\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.60291 | − | 7.97247i | 0.282754 | − | 0.489745i | ||||
\(266\) | −0.100067 | + | 29.3943i | −0.00613552 | + | 1.80228i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.342728 | + | 0.593622i | −0.0209354 | + | 0.0362612i | ||||
\(269\) | −1.88951 | + | 3.27272i | −0.115205 | + | 0.199541i | −0.917862 | − | 0.396900i | \(-0.870086\pi\) |
0.802657 | + | 0.596442i | \(0.203419\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.30995 | − | 5.73300i | −0.201065 | − | 0.348255i | 0.747807 | − | 0.663916i | \(-0.231107\pi\) |
−0.948872 | + | 0.315661i | \(0.897774\pi\) | |||||||
\(272\) | −6.37501 | − | 11.0418i | −0.386542 | − | 0.669510i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.24291 | + | 9.08099i | −0.316736 | + | 0.548602i | ||||
\(275\) | 28.5761 | 1.72320 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.2658 | −1.51808 | −0.759038 | − | 0.651046i | \(-0.774330\pi\) | ||||
−0.759038 | + | 0.651046i | \(0.774330\pi\) | |||||||
\(278\) | −4.36882 | − | 7.56703i | −0.262025 | − | 0.453840i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.0716270 | − | 21.0401i | 0.00428053 | − | 1.25739i | ||||
\(281\) | 3.71221 | + | 6.42974i | 0.221452 | + | 0.383566i | 0.955249 | − | 0.295803i | \(-0.0955871\pi\) |
−0.733797 | + | 0.679369i | \(0.762254\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.71013 | − | 13.3543i | −0.458320 | − | 0.793833i | 0.540553 | − | 0.841310i | \(-0.318215\pi\) |
−0.998872 | + | 0.0474771i | \(0.984882\pi\) | |||||||
\(284\) | 0.290450 | + | 0.503074i | 0.0172350 | + | 0.0298520i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.59406 | − | 2.76100i | −0.0942588 | − | 0.163261i | ||||
\(287\) | −7.61810 | − | 4.43296i | −0.449682 | − | 0.261669i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.64458 | + | 8.04465i | 0.273211 | + | 0.473215i | ||||
\(290\) | 20.7567 | 1.21887 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.56289 | −0.325543 | ||||||||
\(293\) | 15.2899 | − | 26.4828i | 0.893243 | − | 1.54714i | 0.0572791 | − | 0.998358i | \(-0.481758\pi\) |
0.835964 | − | 0.548784i | \(-0.184909\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.78720 | − | 6.55962i | −0.220499 | − | 0.381916i | ||||
\(296\) | −9.43286 | − | 16.3382i | −0.548274 | − | 0.949639i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −16.5856 | + | 28.7272i | −0.960780 | + | 1.66412i | ||||
\(299\) | 0.148761 | − | 0.257662i | 0.00860307 | − | 0.0149010i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.0672 | + | 10.3493i | −1.04138 | + | 0.596521i | ||||
\(302\) | −4.26810 | + | 7.39256i | −0.245602 | + | 0.425394i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 33.1999 | 1.90415 | ||||||||
\(305\) | 5.05395 | − | 8.75369i | 0.289388 | − | 0.501235i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.7794 | −1.64252 | −0.821262 | − | 0.570551i | \(-0.806730\pi\) | ||||
−0.821262 | + | 0.570551i | \(0.806730\pi\) | |||||||
\(308\) | 4.76350 | − | 2.72863i | 0.271425 | − | 0.155478i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −24.1713 | −1.37284 | ||||||||
\(311\) | −1.28628 | − | 2.22789i | −0.0729380 | − | 0.126332i | 0.827250 | − | 0.561834i | \(-0.189904\pi\) |
−0.900188 | + | 0.435502i | \(0.856571\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.25724 | − | 16.0340i | 0.523250 | − | 0.906296i | −0.476383 | − | 0.879238i | \(-0.658053\pi\) |
0.999634 | − | 0.0270587i | \(-0.00861409\pi\) | |||||||
\(314\) | −9.32854 | −0.526440 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.97516 | 0.111111 | ||||||||
\(317\) | 7.75909 | − | 13.4391i | 0.435794 | − | 0.754817i | −0.561566 | − | 0.827432i | \(-0.689801\pi\) |
0.997360 | + | 0.0726145i | \(0.0231343\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.2980 | − | 21.3008i | −0.688556 | − | 1.19261i | ||||
\(320\) | −19.2058 | −1.07364 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.89661 | + | 1.68553i | 0.161422 | + | 0.0939309i | ||||
\(323\) | 20.0784 | 1.11719 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.896931 | − | 1.55353i | 0.0497528 | − | 0.0861744i | ||||
\(326\) | 5.91960 | 0.327856 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.19505 | + | 7.26604i | −0.231633 | + | 0.401200i | ||||
\(329\) | −7.96137 | − | 4.63271i | −0.438925 | − | 0.255409i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.7952 | + | 27.3581i | −0.868182 | + | 1.50374i | −0.00432948 | + | 0.999991i | \(0.501378\pi\) |
−0.863853 | + | 0.503745i | \(0.831955\pi\) | |||||||
\(332\) | −2.35216 | + | 4.07407i | −0.129092 | + | 0.223593i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.71839 | + | 4.70840i | 0.148744 | + | 0.257632i | ||||
\(335\) | 2.99858 | + | 5.19369i | 0.163830 | + | 0.283762i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.70406 | − | 9.87972i | 0.310720 | − | 0.538183i | −0.667798 | − | 0.744342i | \(-0.732763\pi\) |
0.978518 | + | 0.206159i | \(0.0660965\pi\) | |||||||
\(338\) | 19.7747 | 1.07560 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.16446 | 0.171617 | ||||||||
\(341\) | 14.3211 | + | 24.8049i | 0.775532 | + | 1.34326i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.189142 | − | 18.5193i | 0.0102127 | − | 0.999948i | ||||
\(344\) | 9.91002 | + | 17.1647i | 0.534312 | + | 0.925456i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.57013 | + | 13.1118i | 0.406973 | + | 0.704897i | ||||
\(347\) | −2.04070 | − | 3.53459i | −0.109550 | − | 0.189747i | 0.806038 | − | 0.591864i | \(-0.201608\pi\) |
−0.915588 | + | 0.402117i | \(0.868274\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.1389 | + | 21.0253i | 0.649782 | + | 1.12546i | 0.983175 | + | 0.182668i | \(0.0584733\pi\) |
−0.333392 | + | 0.942788i | \(0.608193\pi\) | |||||||
\(350\) | 17.4646 | + | 10.1626i | 0.933524 | + | 0.543216i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.80094 | − | 10.0475i | −0.309191 | − | 0.535535i | ||||
\(353\) | 34.0790 | 1.81384 | 0.906922 | − | 0.421299i | \(-0.138426\pi\) | ||||
0.906922 | + | 0.421299i | \(0.138426\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.08239 | 0.269745 | ||||||||
\(356\) | −2.57463 | + | 4.45939i | −0.136455 | + | 0.236347i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.2862 | + | 26.4764i | 0.807900 | + | 1.39932i | ||||
\(359\) | 2.74465 | + | 4.75388i | 0.144857 | + | 0.250900i | 0.929320 | − | 0.369276i | \(-0.120394\pi\) |
−0.784462 | + | 0.620176i | \(0.787061\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.6412 | + | 28.8233i | −0.875851 | + | 1.51702i | ||||
\(362\) | 9.29062 | − | 16.0918i | 0.488304 | − | 0.845768i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.00117316 | − | 0.344611i | 6.14904e−5 | − | 0.0180625i | ||||
\(365\) | −24.3353 | + | 42.1500i | −1.27377 | + | 2.20623i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.6391 | −0.711955 | −0.355978 | − | 0.934495i | \(-0.615852\pi\) | ||||
−0.355978 | + | 0.934495i | \(0.615852\pi\) | |||||||
\(368\) | 1.89259 | − | 3.27807i | 0.0986583 | − | 0.170881i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 36.3435 | 1.88941 | ||||||||
\(371\) | −6.66695 | − | 3.87948i | −0.346131 | − | 0.201413i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.92379 | 0.462056 | 0.231028 | − | 0.972947i | \(-0.425791\pi\) | ||||
0.231028 | + | 0.972947i | \(0.425791\pi\) | |||||||
\(374\) | −12.2649 | − | 21.2435i | −0.634204 | − | 1.09847i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.38408 | + | 7.59346i | −0.226092 | + | 0.391603i | ||||
\(377\) | −1.54402 | −0.0795209 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.7035 | 1.52576 | 0.762882 | − | 0.646537i | \(-0.223784\pi\) | ||||
0.762882 | + | 0.646537i | \(0.223784\pi\) | |||||||
\(380\) | −4.12000 | + | 7.13604i | −0.211351 | + | 0.366071i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.46722 | − | 12.9336i | −0.382056 | − | 0.661741i | ||||
\(383\) | 17.7101 | 0.904944 | 0.452472 | − | 0.891779i | \(-0.350542\pi\) | ||||
0.452472 | + | 0.891779i | \(0.350542\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.163508 | − | 48.0296i | 0.00833312 | − | 2.44781i | ||||
\(386\) | 3.53685 | 0.180021 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.88819 | + | 5.00249i | −0.146626 | + | 0.253963i | ||||
\(389\) | −21.3255 | −1.08125 | −0.540624 | − | 0.841264i | \(-0.681812\pi\) | ||||
−0.540624 | + | 0.841264i | \(0.681812\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.14459 | − | 1.98248i | 0.0578842 | − | 0.100258i | ||||
\(392\) | −17.6292 | − | 0.120032i | −0.890407 | − | 0.00606251i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.89101 | + | 6.73943i | −0.196026 | + | 0.339528i | ||||
\(395\) | 8.64050 | − | 14.9658i | 0.434751 | − | 0.753010i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.11783 | + | 1.93614i | 0.0561024 | + | 0.0971722i | 0.892713 | − | 0.450626i | \(-0.148799\pi\) |
−0.836610 | + | 0.547799i | \(0.815466\pi\) | |||||||
\(398\) | −7.64675 | − | 13.2446i | −0.383297 | − | 0.663890i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.4111 | − | 19.7646i | 0.570555 | − | 0.988231i | ||||
\(401\) | −8.73702 | −0.436306 | −0.218153 | − | 0.975915i | \(-0.570003\pi\) | ||||
−0.218153 | + | 0.975915i | \(0.570003\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.79802 | 0.0895656 | ||||||||
\(404\) | 0.542708 | + | 0.939997i | 0.0270007 | + | 0.0467666i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.0592072 | − | 17.3919i | 0.00293841 | − | 0.863143i | ||||
\(407\) | −21.5330 | − | 37.2962i | −1.06735 | − | 1.84871i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.3460 | + | 24.8480i | 0.709363 | + | 1.22865i | 0.965094 | + | 0.261905i | \(0.0843506\pi\) |
−0.255731 | + | 0.966748i | \(0.582316\pi\) | |||||||
\(410\) | −8.08148 | − | 13.9975i | −0.399116 | − | 0.691289i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.75411 | − | 3.03820i | −0.0864186 | − | 0.149681i | ||||
\(413\) | −5.50706 | + | 3.15456i | −0.270985 | + | 0.155226i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.5795 | + | 35.6447i | 1.01021 | + | 1.74973i | ||||
\(416\) | −0.728309 | −0.0357083 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 63.8736 | 3.12416 | ||||||||
\(419\) | 4.32221 | − | 7.48628i | 0.211154 | − | 0.365729i | −0.740922 | − | 0.671591i | \(-0.765611\pi\) |
0.952076 | + | 0.305862i | \(0.0989446\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.23347 | − | 15.9928i | −0.450012 | − | 0.779444i | 0.548374 | − | 0.836233i | \(-0.315247\pi\) |
−0.998386 | + | 0.0567894i | \(0.981914\pi\) | |||||||
\(422\) | −17.9010 | − | 31.0055i | −0.871408 | − | 1.50932i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.67128 | + | 6.35885i | −0.178293 | + | 0.308813i | ||||
\(425\) | 6.90111 | − | 11.9531i | 0.334753 | − | 0.579809i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.32024 | − | 4.25964i | −0.354251 | − | 0.206138i | ||||
\(428\) | 1.88108 | − | 3.25813i | 0.0909255 | − | 0.157488i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −38.1819 | −1.84130 | ||||||||
\(431\) | −2.90368 | + | 5.02932i | −0.139865 | + | 0.242254i | −0.927445 | − | 0.373958i | \(-0.878000\pi\) |
0.787580 | + | 0.616212i | \(0.211334\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.63877 | 0.174868 | 0.0874341 | − | 0.996170i | \(-0.472133\pi\) | ||||
0.0874341 | + | 0.996170i | \(0.472133\pi\) | |||||||
\(434\) | −0.0689473 | + | 20.2529i | −0.00330958 | + | 0.972172i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.68696 | −0.0807908 | ||||||||
\(437\) | 2.98040 | + | 5.16221i | 0.142572 | + | 0.246942i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.33095 | − | 16.1617i | 0.445342 | − | 0.771355i | −0.552734 | − | 0.833358i | \(-0.686415\pi\) |
0.998076 | + | 0.0620029i | \(0.0197488\pi\) | |||||||
\(440\) | −45.7200 | −2.17961 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.53986 | −0.0732437 | ||||||||
\(443\) | −13.0455 | + | 22.5955i | −0.619812 | + | 1.07355i | 0.369708 | + | 0.929148i | \(0.379458\pi\) |
−0.989520 | + | 0.144398i | \(0.953876\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.5258 | + | 39.0159i | 1.06783 | + | 1.84953i | ||||
\(446\) | 18.2468 | 0.864012 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.0547835 | + | 16.0924i | −0.00258828 | + | 0.760294i | ||||
\(449\) | 5.63824 | 0.266085 | 0.133042 | − | 0.991110i | \(-0.457525\pi\) | ||||
0.133042 | + | 0.991110i | \(0.457525\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.57631 | + | 16.5867i | −0.450931 | + | 0.781035i | ||||
\(452\) | −1.69142 | −0.0795579 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.57946 | + | 7.93186i | −0.214925 | + | 0.372261i | ||||
\(455\) | −2.60599 | − | 1.51642i | −0.122170 | − | 0.0710908i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.99616 | − | 17.3139i | 0.467601 | − | 0.809908i | −0.531714 | − | 0.846924i | \(-0.678452\pi\) |
0.999315 | + | 0.0370159i | \(0.0117852\pi\) | |||||||
\(458\) | −18.2236 | + | 31.5643i | −0.851535 | + | 1.47490i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.469729 | + | 0.813594i | 0.0219012 | + | 0.0379340i | ||||
\(461\) | 18.7247 | + | 32.4322i | 0.872098 | + | 1.51052i | 0.859823 | + | 0.510593i | \(0.170574\pi\) |
0.0122753 | + | 0.999925i | \(0.496093\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.22756 | + | 2.12620i | −0.0570497 | + | 0.0988130i | −0.893140 | − | 0.449779i | \(-0.851503\pi\) |
0.836090 | + | 0.548592i | \(0.184836\pi\) | |||||||
\(464\) | −19.6436 | −0.911929 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.2950 | −0.986473 | ||||||||
\(467\) | 16.7054 | + | 28.9345i | 0.773032 | + | 1.33893i | 0.935894 | + | 0.352282i | \(0.114594\pi\) |
−0.162862 | + | 0.986649i | \(0.552072\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.36031 | − | 2.49768i | 0.201341 | − | 0.115332i | ||||
\(470\) | −8.44563 | − | 14.6283i | −0.389568 | − | 0.674752i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.02067 | + | 5.23196i | 0.139038 | + | 0.240821i | ||||
\(473\) | 22.6222 | + | 39.1828i | 1.04017 | + | 1.80163i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17.9699 | + | 31.1248i | 0.824515 | + | 1.42810i | ||||
\(476\) | 0.00902647 | − | 2.65148i | 0.000413727 | − | 0.121531i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −17.1649 | − | 29.7305i | −0.785106 | − | 1.35984i | ||||
\(479\) | −34.6936 | −1.58519 | −0.792595 | − | 0.609748i | \(-0.791271\pi\) | ||||
−0.792595 | + | 0.609748i | \(0.791271\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.70347 | −0.123268 | ||||||||
\(482\) | 7.46798 | − | 12.9349i | 0.340157 | − | 0.589170i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.97948 | − | 6.89266i | −0.180885 | − | 0.313303i | ||||
\(485\) | 25.2692 | + | 43.7676i | 1.14742 | + | 1.98739i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.479909 | + | 0.831226i | −0.0217467 | + | 0.0376665i | −0.876694 | − | 0.481049i | \(-0.840256\pi\) |
0.854947 | + | 0.518715i | \(0.173589\pi\) | |||||||
\(488\) | −4.03103 | + | 6.98195i | −0.182476 | + | 0.316058i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 17.1809 | − | 29.2958i | 0.776155 | − | 1.32345i | ||||
\(491\) | 7.88691 | − | 13.6605i | 0.355931 | − | 0.616491i | −0.631346 | − | 0.775501i | \(-0.717497\pi\) |
0.987277 | + | 0.159011i | \(0.0508305\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.8799 | −0.535042 | ||||||||
\(494\) | 2.00483 | − | 3.47247i | 0.0902017 | − | 0.156234i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 22.8751 | 1.02712 | ||||||||
\(497\) | 0.0144972 | − | 4.25850i | 0.000650290 | − | 0.191020i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.1287 | −0.856320 | −0.428160 | − | 0.903703i | \(-0.640838\pi\) | ||||
−0.428160 | + | 0.903703i | \(0.640838\pi\) | |||||||
\(500\) | −0.0168240 | − | 0.0291400i | −0.000752392 | − | 0.00130318i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.00868 | − | 8.67529i | 0.223548 | − | 0.387197i | ||||
\(503\) | 33.3898 | 1.48878 | 0.744388 | − | 0.667747i | \(-0.232741\pi\) | ||||
0.744388 | + | 0.667747i | \(0.232741\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.49648 | 0.422588 | ||||||||
\(506\) | 3.64117 | − | 6.30670i | 0.161870 | − | 0.280367i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.65284 | + | 2.86280i | 0.0733330 | + | 0.127016i | ||||
\(509\) | −33.5176 | −1.48564 | −0.742822 | − | 0.669489i | \(-0.766513\pi\) | ||||
−0.742822 | + | 0.669489i | \(0.766513\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 35.2478 | + | 20.5106i | 1.55927 | + | 0.907336i | ||||
\(512\) | 13.8619 | 0.612617 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.24850 | + | 7.35862i | −0.187393 | + | 0.324575i | ||||
\(515\) | −30.6939 | −1.35254 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.0078 | + | 17.3341i | −0.440144 | + | 0.762351i | ||||
\(518\) | 0.103668 | − | 30.4520i | 0.00455491 | − | 1.33798i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.43504 | + | 2.48556i | −0.0629305 | + | 0.108999i | ||||
\(521\) | −13.3622 | + | 23.1439i | −0.585407 | + | 1.01395i | 0.409418 | + | 0.912347i | \(0.365732\pi\) |
−0.994825 | + | 0.101607i | \(0.967601\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.53219 | − | 14.7782i | −0.373086 | − | 0.646205i | 0.616952 | − | 0.787001i | \(-0.288367\pi\) |
−0.990039 | + | 0.140796i | \(0.955034\pi\) | |||||||
\(524\) | 1.66226 | + | 2.87912i | 0.0726161 | + | 0.125775i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.68002 | + | 11.5701i | −0.291263 | + | 0.504482i | ||||
\(527\) | 13.8342 | 0.602626 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3204 | −0.970452 | ||||||||
\(530\) | −7.07247 | − | 12.2499i | −0.307209 | − | 0.532101i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.96749 | + | 3.47247i | 0.258723 | + | 0.150551i | ||||
\(533\) | 0.601153 | + | 1.04123i | 0.0260388 | + | 0.0451006i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.4579 | − | 28.5059i | −0.711537 | − | 1.23242i | ||||
\(536\) | −2.39167 | − | 4.14250i | −0.103304 | − | 0.178929i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.90327 | + | 5.02861i | 0.125169 | + | 0.216799i | ||||
\(539\) | −40.2432 | − | 0.274004i | −1.73340 | − | 0.0118022i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.17128 | − | 10.6890i | −0.265324 | − | 0.459555i | 0.702324 | − | 0.711857i | \(-0.252146\pi\) |
−0.967648 | + | 0.252302i | \(0.918812\pi\) | |||||||
\(542\) | −10.1716 | −0.436909 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.60370 | −0.240257 | ||||||||
\(545\) | −7.37975 | + | 12.7821i | −0.316114 | + | 0.547525i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.7212 | − | 20.3017i | −0.501163 | − | 0.868040i | −0.999999 | − | 0.00134350i | \(-0.999572\pi\) |
0.498836 | − | 0.866696i | \(-0.333761\pi\) | |||||||
\(548\) | 1.23147 | + | 2.13297i | 0.0526059 | + | 0.0911161i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 21.9539 | − | 38.0252i | 0.936117 | − | 1.62140i | ||||
\(551\) | 15.4671 | − | 26.7897i | 0.658919 | − | 1.14128i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.5151 | − | 7.28250i | −0.532195 | − | 0.309684i | ||||
\(554\) | −19.4108 | + | 33.6204i | −0.824684 | + | 1.42840i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.05233 | −0.0870381 | ||||||||
\(557\) | −12.2557 | + | 21.2275i | −0.519292 | + | 0.899440i | 0.480457 | + | 0.877018i | \(0.340471\pi\) |
−0.999749 | + | 0.0224216i | \(0.992862\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.84022 | 0.120129 | ||||||||
\(560\) | −33.1543 | − | 19.2925i | −1.40103 | − | 0.815255i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.4078 | 0.481209 | ||||||||
\(563\) | −6.68571 | − | 11.5800i | −0.281769 | − | 0.488039i | 0.690051 | − | 0.723760i | \(-0.257588\pi\) |
−0.971821 | + | 0.235722i | \(0.924255\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.39927 | + | 12.8159i | −0.311290 | + | 0.539170i | ||||
\(566\) | −23.6936 | −0.995916 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.05372 | −0.170090 | ||||||||
\(569\) | −7.12440 | + | 12.3398i | −0.298670 | + | 0.517312i | −0.975832 | − | 0.218522i | \(-0.929876\pi\) |
0.677162 | + | 0.735834i | \(0.263210\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.6618 | + | 25.3951i | 0.613579 | + | 1.06275i | 0.990632 | + | 0.136559i | \(0.0436042\pi\) |
−0.377053 | + | 0.926192i | \(0.623062\pi\) | |||||||
\(572\) | −0.748837 | −0.0313105 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −11.7515 | + | 6.73149i | −0.490498 | + | 0.280967i | ||||
\(575\) | 4.09756 | 0.170880 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.05004 | − | 15.6751i | 0.376758 | − | 0.652564i | −0.613830 | − | 0.789438i | \(-0.710372\pi\) |
0.990588 | + | 0.136874i | \(0.0437055\pi\) | |||||||
\(578\) | 14.2730 | 0.593679 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.43770 | − | 4.22221i | 0.101220 | − | 0.175318i | ||||
\(581\) | 29.9251 | − | 17.1417i | 1.24150 | − | 0.711158i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.38067 | + | 14.5157i | −0.347092 | + | 0.601181i | ||||
\(584\) | 19.4099 | − | 33.6189i | 0.803186 | − | 1.39116i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −23.4932 | − | 40.6915i | −0.970496 | − | 1.68095i | ||||
\(587\) | 3.26402 | + | 5.65345i | 0.134721 | + | 0.233343i | 0.925491 | − | 0.378770i | \(-0.123653\pi\) |
−0.790770 | + | 0.612113i | \(0.790320\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.0115 | + | 31.1968i | −0.742151 | + | 1.28544i | ||||
\(590\) | −11.6382 | −0.479139 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −34.3946 | −1.41361 | ||||||||
\(593\) | −12.7202 | − | 22.0321i | −0.522357 | − | 0.904749i | −0.999662 | − | 0.0260111i | \(-0.991719\pi\) |
0.477305 | − | 0.878738i | \(-0.341614\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.0508 | − | 11.6675i | −0.822002 | − | 0.478322i | ||||
\(596\) | 3.89569 | + | 6.74753i | 0.159574 | + | 0.276390i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.228575 | − | 0.395903i | −0.00934712 | − | 0.0161897i | ||||
\(599\) | 3.08966 | + | 5.35144i | 0.126240 | + | 0.218654i | 0.922217 | − | 0.386673i | \(-0.126376\pi\) |
−0.795977 | + | 0.605327i | \(0.793042\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.46722 | + | 11.2016i | 0.263804 | + | 0.456921i | 0.967249 | − | 0.253828i | \(-0.0816896\pi\) |
−0.703446 | + | 0.710749i | \(0.748356\pi\) | |||||||
\(602\) | −0.108912 | + | 31.9924i | −0.00443892 | + | 1.30391i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.00251 | + | 1.73639i | 0.0407914 | + | 0.0706527i | ||||
\(605\) | −69.6342 | −2.83103 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.0756 | −0.936608 | −0.468304 | − | 0.883567i | \(-0.655135\pi\) | ||||
−0.468304 | + | 0.883567i | \(0.655135\pi\) | |||||||
\(608\) | 7.29578 | − | 12.6367i | 0.295883 | − | 0.512484i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.76551 | − | 13.4503i | −0.314416 | − | 0.544585i | ||||
\(611\) | 0.628242 | + | 1.08815i | 0.0254159 | + | 0.0440217i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.81363 | − | 15.2657i | 0.355979 | − | 0.616574i | −0.631306 | − | 0.775534i | \(-0.717481\pi\) |
0.987285 | + | 0.158960i | \(0.0508141\pi\) | |||||||
\(614\) | −22.1101 | + | 38.2958i | −0.892290 | + | 1.54549i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.130414 | + | 38.3085i | −0.00525452 | + | 1.54349i | ||||
\(617\) | 10.8220 | − | 18.7443i | 0.435679 | − | 0.754618i | −0.561672 | − | 0.827360i | \(-0.689842\pi\) |
0.997351 | + | 0.0727418i | \(0.0231749\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.57941 | −0.385029 | −0.192514 | − | 0.981294i | \(-0.561664\pi\) | ||||
−0.192514 | + | 0.981294i | \(0.561664\pi\) | |||||||
\(620\) | −2.83872 | + | 4.91680i | −0.114006 | + | 0.197463i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.95278 | −0.158492 | ||||||||
\(623\) | 32.7554 | − | 18.7630i | 1.31232 | − | 0.751722i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.1468 | −1.00587 | ||||||||
\(626\) | −14.2240 | − | 24.6366i | −0.568504 | − | 0.984678i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.09556 | + | 1.89756i | −0.0437176 | + | 0.0757211i | ||||
\(629\) | −20.8008 | −0.829384 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.1742 | −1.24103 | −0.620514 | − | 0.784196i | \(-0.713076\pi\) | ||||
−0.620514 | + | 0.784196i | \(0.713076\pi\) | |||||||
\(632\) | −6.89167 | + | 11.9367i | −0.274136 | + | 0.474817i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11.9220 | − | 20.6496i | −0.473484 | − | 0.820099i | ||||
\(635\) | 28.9219 | 1.14773 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.27803 | + | 2.17921i | −0.0506374 | + | 0.0863435i | ||||
\(638\) | −37.7924 | −1.49621 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −21.1272 | + | 36.5933i | −0.835124 | + | 1.44648i | ||||
\(641\) | 8.25214 | 0.325940 | 0.162970 | − | 0.986631i | \(-0.447893\pi\) | ||||
0.162970 | + | 0.986631i | \(0.447893\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.2159 | + | 21.1585i | −0.481748 | + | 0.834411i | −0.999781 | − | 0.0209493i | \(-0.993331\pi\) |
0.518033 | + | 0.855361i | \(0.326664\pi\) | |||||||
\(644\) | 0.683045 | − | 0.391262i | 0.0269157 | − | 0.0154179i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 15.4254 | − | 26.7176i | 0.606906 | − | 1.05119i | ||||
\(647\) | 19.3432 | − | 33.5034i | 0.760461 | − | 1.31716i | −0.182153 | − | 0.983270i | \(-0.558307\pi\) |
0.942613 | − | 0.333886i | \(-0.108360\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.89548 | + | 11.9433i | 0.270671 | + | 0.468817i | ||||
\(650\) | −1.37816 | − | 2.38704i | −0.0540557 | − | 0.0936273i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.695207 | − | 1.20413i | 0.0272264 | − | 0.0471575i | ||||
\(653\) | −7.65430 | −0.299536 | −0.149768 | − | 0.988721i | \(-0.547853\pi\) | ||||
−0.149768 | + | 0.988721i | \(0.547853\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29.0867 | 1.13651 | ||||||||
\(656\) | 7.64810 | + | 13.2469i | 0.298608 | + | 0.517205i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.2810 | + | 7.03481i | −0.478764 | + | 0.274246i | ||||
\(659\) | 19.2572 | + | 33.3545i | 0.750156 | + | 1.29931i | 0.947747 | + | 0.319023i | \(0.103355\pi\) |
−0.197591 | + | 0.980285i | \(0.563312\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.1066 | − | 27.8974i | −0.626474 | − | 1.08508i | −0.988254 | − | 0.152821i | \(-0.951164\pi\) |
0.361780 | − | 0.932263i | \(-0.382169\pi\) | |||||||
\(662\) | 24.2697 | + | 42.0363i | 0.943268 | + | 1.63379i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16.4142 | − | 28.4302i | −0.636994 | − | 1.10331i | ||||
\(665\) | 52.4162 | − | 30.0250i | 2.03261 | − | 1.16432i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.76343 | − | 3.05435i | −0.0682803 | − | 0.118265i | ||||
\(668\) | 1.27701 | 0.0494091 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.21478 | 0.355998 | ||||||||
\(671\) | −9.20190 | + | 15.9382i | −0.355235 | + | 0.615285i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.630680 | − | 1.09237i | −0.0243109 | − | 0.0421077i | 0.853614 | − | 0.520906i | \(-0.174406\pi\) |
−0.877925 | + | 0.478798i | \(0.841073\pi\) | |||||||
\(674\) | −8.76442 | − | 15.1804i | −0.337593 | − | 0.584728i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.32237 | − | 4.02246i | 0.0893219 | − | 0.154710i | ||||
\(677\) | 7.41589 | − | 12.8447i | 0.285016 | − | 0.493662i | −0.687597 | − | 0.726092i | \(-0.741335\pi\) |
0.972613 | + | 0.232431i | \(0.0746679\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36.7447 | − | 21.0481i | 1.41013 | − | 0.807751i | ||||
\(680\) | −11.0414 | + | 19.1242i | −0.423417 | + | 0.733379i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 44.0095 | 1.68521 | ||||||||
\(683\) | −2.76560 | + | 4.79016i | −0.105823 | + | 0.183290i | −0.914074 | − | 0.405547i | \(-0.867081\pi\) |
0.808251 | + | 0.588838i | \(0.200414\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.5487 | 0.823334 | ||||||||
\(686\) | −24.4977 | − | 14.4793i | −0.935327 | − | 0.552824i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 36.1344 | 1.37761 | ||||||||
\(689\) | 0.526097 | + | 0.911226i | 0.0200427 | + | 0.0347150i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.31896 | + | 7.48065i | −0.164301 | + | 0.284577i | −0.936407 | − | 0.350916i | \(-0.885870\pi\) |
0.772106 | + | 0.635494i | \(0.219203\pi\) | |||||||
\(692\) | 3.55620 | 0.135186 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.27116 | −0.238050 | ||||||||
\(695\) | −8.97808 | + | 15.5505i | −0.340558 | + | 0.589864i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.62535 | + | 8.01134i | 0.175198 | + | 0.303451i | ||||
\(698\) | 37.3035 | 1.41196 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.11831 | − | 2.35905i | 0.155658 | − | 0.0891638i | ||||
\(701\) | −26.5897 | −1.00428 | −0.502140 | − | 0.864786i | \(-0.667454\pi\) | ||||
−0.502140 | + | 0.864786i | \(0.667454\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27.0818 | − | 46.9070i | 1.02141 | − | 1.76913i | ||||
\(704\) | 34.9686 | 1.31793 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 26.1816 | − | 45.3479i | 0.985358 | − | 1.70669i | ||||
\(707\) | 0.0270882 | − | 7.95703i | 0.00101876 | − | 0.299255i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.06305 | + | 8.76946i | −0.190147 | + | 0.329344i | −0.945299 | − | 0.326206i | \(-0.894230\pi\) |
0.755152 | + | 0.655550i | \(0.227563\pi\) | |||||||
\(710\) | 3.90460 | − | 6.76297i | 0.146537 | − | 0.253810i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −17.9666 | − | 31.1191i | −0.673328 | − | 1.16624i | ||||
\(713\) | 2.05353 | + | 3.55681i | 0.0769052 | + | 0.133204i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.27585 | + | 5.67394i | −0.122510 | + | 0.212193i | ||||
\(716\) | 7.18094 | 0.268364 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.43445 | 0.314771 | ||||||||
\(719\) | 16.1938 | + | 28.0485i | 0.603927 | + | 1.04603i | 0.992220 | + | 0.124496i | \(0.0397315\pi\) |
−0.388293 | + | 0.921536i | \(0.626935\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.0875527 | + | 25.7182i | −0.00326063 | + | 0.957796i | ||||
\(722\) | 25.5695 | + | 44.2877i | 0.951600 | + | 1.64822i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.18221 | − | 3.77970i | −0.0811013 | − | 0.140472i | ||||
\(725\) | −10.6323 | − | 18.4157i | −0.394874 | − | 0.683943i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.6174 | − | 21.8540i | −0.467953 | − | 0.810519i | 0.531376 | − | 0.847136i | \(-0.321675\pi\) |
−0.999329 | + | 0.0366171i | \(0.988342\pi\) | |||||||
\(728\) | 2.07854 | + | 1.20950i | 0.0770357 | + | 0.0448269i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 37.3917 | + | 64.7644i | 1.38393 | + | 2.39704i | ||||
\(731\) | 21.8530 | 0.808264 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.84672 | 0.105146 | 0.0525731 | − | 0.998617i | \(-0.483258\pi\) | ||||
0.0525731 | + | 0.998617i | \(0.483258\pi\) | |||||||
\(734\) | −10.4784 | + | 18.1491i | −0.386765 | + | 0.669896i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.831806 | − | 1.44073i | −0.0306608 | − | 0.0531060i | ||||
\(737\) | −5.45962 | − | 9.45634i | −0.201108 | − | 0.348329i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.2708 | + | 21.2537i | −0.451390 | + | 0.781830i | −0.998473 | − | 0.0552485i | \(-0.982405\pi\) |
0.547083 | + | 0.837078i | \(0.315738\pi\) | |||||||
\(740\) | 4.26824 | − | 7.39282i | 0.156904 | − | 0.271765i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.2843 | + | 5.89103i | −0.377547 | + | 0.216267i | ||||
\(743\) | 2.29535 | − | 3.97566i | 0.0842082 | − | 0.145853i | −0.820845 | − | 0.571151i | \(-0.806497\pi\) |
0.905054 | + | 0.425298i | \(0.139831\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 68.1681 | 2.49748 | ||||||||
\(746\) | 6.85581 | − | 11.8746i | 0.251009 | − | 0.434760i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.76165 | −0.210667 | ||||||||
\(749\) | −23.9318 | + | 13.7086i | −0.874451 | + | 0.500903i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.4356 | 1.14710 | 0.573551 | − | 0.819170i | \(-0.305566\pi\) | ||||
0.573551 | + | 0.819170i | \(0.305566\pi\) | |||||||
\(752\) | 7.99273 | + | 13.8438i | 0.291465 | + | 0.504832i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.18621 | + | 2.05457i | −0.0431992 | + | 0.0748231i | ||||
\(755\) | 17.5422 | 0.638425 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.5432 | 1.07376 | 0.536882 | − | 0.843657i | \(-0.319602\pi\) | ||||
0.536882 | + | 0.843657i | \(0.319602\pi\) | |||||||
\(758\) | 22.8200 | − | 39.5255i | 0.828861 | − | 1.43563i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −28.7507 | − | 49.7977i | −1.04290 | − | 1.80635i | ||||
\(761\) | 46.4873 | 1.68516 | 0.842582 | − | 0.538567i | \(-0.181034\pi\) | ||||
0.842582 | + | 0.538567i | \(0.181034\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.6890 | + | 6.21990i | 0.386967 | + | 0.225175i | ||||
\(764\) | −3.50785 | −0.126910 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.6060 | − | 23.5663i | 0.491605 | − | 0.851484i | ||||
\(767\) | 0.865728 | 0.0312596 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.08532 | + | 12.2721i | −0.255503 | + | 0.442545i | −0.965032 | − | 0.262132i | \(-0.915574\pi\) |
0.709529 | + | 0.704676i | \(0.248908\pi\) | |||||||
\(770\) | −63.7858 | − | 37.1169i | −2.29868 | − | 1.33760i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.415373 | − | 0.719448i | 0.0149496 | − | 0.0258935i | ||||
\(773\) | −17.0042 | + | 29.4522i | −0.611600 | + | 1.05932i | 0.379371 | + | 0.925245i | \(0.376140\pi\) |
−0.990971 | + | 0.134078i | \(0.957193\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.3814 | + | 21.4452i | 0.444754 | + | 0.770336i | ||||
\(776\) | −20.1548 | − | 34.9091i | −0.723514 | − | 1.25316i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −16.3836 | + | 28.3772i | −0.587380 | + | 1.01737i | ||||
\(779\) | −24.0880 | −0.863043 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.25368 | −0.331123 | ||||||||
\(782\) | −1.75868 | − | 3.04613i | −0.0628904 | − | 0.108929i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −16.2596 | + | 27.7248i | −0.580700 | + | 0.990170i | ||||
\(785\) | 9.58523 | + | 16.6021i | 0.342111 | + | 0.592554i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.5530 | + | 25.2065i | 0.518757 | + | 0.898514i | 0.999762 | + | 0.0217964i | \(0.00693855\pi\) |
−0.481005 | + | 0.876718i | \(0.659728\pi\) | |||||||
\(788\) | 0.913934 | + | 1.58298i | 0.0325576 | + | 0.0563914i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −13.2763 | − | 22.9953i | −0.472351 | − | 0.818135i | ||||
\(791\) | 10.7173 | + | 6.23636i | 0.381062 | + | 0.221739i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.577649 | + | 1.00052i | 0.0205129 | + | 0.0355294i | ||||
\(794\) | 3.43515 | 0.121909 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.59219 | −0.127322 | ||||||||
\(797\) | −9.25192 | + | 16.0248i | −0.327720 | + | 0.567627i | −0.982059 | − | 0.188574i | \(-0.939613\pi\) |
0.654339 | + | 0.756201i | \(0.272947\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.83377 | + | 8.37234i | 0.171007 | + | 0.296192i | ||||
\(800\) | −5.01524 | − | 8.68665i | −0.177316 | − | 0.307120i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.71231 | + | 11.6261i | −0.237020 | + | 0.410531i | ||||
\(803\) | 44.3081 | − | 76.7439i | 1.56360 | − | 2.70823i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0234456 | − | 6.88703i | 0.000826348 | − | 0.242736i | ||||
\(806\) | 1.38135 | − | 2.39257i | 0.0486559 | − | 0.0842745i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.57440 | −0.266466 | ||||||||
\(809\) | 20.5407 | − | 35.5775i | 0.722172 | − | 1.25084i | −0.237956 | − | 0.971276i | \(-0.576477\pi\) |
0.960128 | − | 0.279562i | \(-0.0901892\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43.1361 | −1.51471 | −0.757357 | − | 0.653001i | \(-0.773510\pi\) | ||||
−0.757357 | + | 0.653001i | \(0.773510\pi\) | |||||||
\(812\) | −3.53081 | − | 2.05457i | −0.123907 | − | 0.0721014i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −66.1719 | −2.31932 | ||||||||
\(815\) | −6.08248 | − | 10.5352i | −0.213060 | − | 0.369031i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28.4517 | + | 49.2798i | −0.995399 | + | 1.72408i | ||||
\(818\) | 44.0859 | 1.54143 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.79641 | −0.132576 | ||||||||
\(821\) | 6.58738 | − | 11.4097i | 0.229901 | − | 0.398201i | −0.727877 | − | 0.685707i | \(-0.759493\pi\) |
0.957779 | + | 0.287507i | \(0.0928264\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.99083 | + | 10.3764i | 0.208827 | + | 0.361699i | 0.951345 | − | 0.308127i | \(-0.0997020\pi\) |
−0.742518 | + | 0.669826i | \(0.766369\pi\) | |||||||
\(824\) | 24.4815 | 0.852853 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.0331975 | + | 9.75160i | −0.00115509 | + | 0.339302i | ||||
\(827\) | −29.9879 | −1.04278 | −0.521391 | − | 0.853318i | \(-0.674587\pi\) | ||||
−0.521391 | + | 0.853318i | \(0.674587\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.4619 | + | 23.3167i | −0.467551 | + | 0.809822i | −0.999313 | − | 0.0370721i | \(-0.988197\pi\) |
0.531762 | + | 0.846894i | \(0.321530\pi\) | |||||||
\(830\) | 63.2416 | 2.19515 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.09758 | − | 1.90106i | 0.0380517 | − | 0.0659074i | ||||
\(833\) | −9.83333 | + | 16.7671i | −0.340705 | + | 0.580947i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.58639 | − | 9.67591i | 0.193325 | − | 0.334849i | ||||
\(836\) | 7.50142 | − | 12.9928i | 0.259442 | − | 0.449367i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.64117 | − | 11.5029i | −0.229416 | − | 0.397359i | ||||
\(839\) | −5.61191 | − | 9.72012i | −0.193745 | − | 0.335576i | 0.752744 | − | 0.658314i | \(-0.228730\pi\) |
−0.946488 | + | 0.322738i | \(0.895397\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.34853 | − | 9.26393i | 0.184432 | − | 0.319446i | ||||
\(842\) | −28.3749 | −0.977864 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8.40930 | −0.289460 | ||||||||
\(845\) | −20.3188 | − | 35.1932i | −0.698988 | − | 1.21068i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.198628 | + | 58.3460i | −0.00682494 | + | 2.00479i | ||||
\(848\) | 6.69321 | + | 11.5930i | 0.229846 | + | 0.398104i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −10.6037 | − | 18.3662i | −0.363704 | − | 0.629954i | ||||
\(851\) | −3.08765 | − | 5.34796i | −0.105843 | − | 0.183326i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.09672 | + | 10.5598i | 0.208748 | + | 0.361562i | 0.951320 | − | 0.308204i | \(-0.0997279\pi\) |
−0.742573 | + | 0.669766i | \(0.766395\pi\) | |||||||
\(854\) | −11.2920 | + | 6.46830i | −0.386405 | + | 0.221341i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.1268 | + | 22.7363i | 0.448666 | + | 0.777112i | ||||
\(857\) | 37.4382 | 1.27887 | 0.639433 | − | 0.768847i | \(-0.279169\pi\) | ||||
0.639433 | + | 0.768847i | \(0.279169\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.757734 | 0.0258535 | 0.0129268 | − | 0.999916i | \(-0.495885\pi\) | ||||
0.0129268 | + | 0.999916i | \(0.495885\pi\) | |||||||
\(860\) | −4.48415 | + | 7.76678i | −0.152908 | + | 0.264845i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.46157 | + | 7.72767i | 0.151962 | + | 0.263205i | ||||
\(863\) | 11.7796 | + | 20.4029i | 0.400983 | + | 0.694522i | 0.993845 | − | 0.110782i | \(-0.0353354\pi\) |
−0.592862 | + | 0.805304i | \(0.702002\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.5569 | − | 26.9453i | 0.528949 | − | 0.916167i | ||||
\(866\) | 2.79553 | − | 4.84200i | 0.0949959 | − | 0.164538i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.11166 | + | 2.39257i | 0.139559 | + | 0.0812089i | ||||
\(869\) | −15.7321 | + | 27.2487i | −0.533673 | + | 0.924349i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.685455 | −0.0232258 | ||||||||
\(872\) | 5.88609 | − | 10.1950i | 0.199328 | − | 0.345247i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.15892 | 0.309805 | ||||||||
\(875\) | −0.000839737 | 0.246669i | −2.83883e−5 | 0.00833893i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.6739 | 1.23839 | 0.619196 | − | 0.785237i | \(-0.287459\pi\) | ||||
0.619196 | + | 0.785237i | \(0.287459\pi\) | |||||||
\(878\) | −14.3372 | − | 24.8328i | −0.483858 | − | 0.838066i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −41.6766 | + | 72.1860i | −1.40492 | + | 2.43339i | ||||
\(881\) | 39.4357 | 1.32862 | 0.664311 | − | 0.747456i | \(-0.268725\pi\) | ||||
0.664311 | + | 0.747456i | \(0.268725\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.76912 | −0.295105 | −0.147552 | − | 0.989054i | \(-0.547139\pi\) | ||||
−0.147552 | + | 0.989054i | \(0.547139\pi\) | |||||||
\(884\) | −0.180844 | + | 0.313231i | −0.00608244 | + | 0.0105351i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 20.0448 | + | 34.7185i | 0.673417 | + | 1.16639i | ||||
\(887\) | −7.82601 | −0.262772 | −0.131386 | − | 0.991331i | \(-0.541943\pi\) | ||||
−0.131386 | + | 0.991331i | \(0.541943\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.0824983 | − | 24.2335i | 0.00276690 | − | 0.812765i | ||||
\(890\) | 69.2230 | 2.32036 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.14294 | − | 3.71168i | 0.0717508 | − | 0.124276i | ||||
\(893\) | −25.1734 | −0.842397 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31.4136 | − | 54.4100i | 1.05004 | − | 1.81872i | ||||
\(896\) | 30.6010 | + | 17.8067i | 1.02231 | + | 0.594879i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.33164 | − | 7.50263i | 0.144549 | − | 0.250366i | ||||
\(899\) | 10.6569 | − | 18.4584i | 0.355429 | − | 0.615621i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.04786 | + | 7.01109i | 0.134854 | + | 0.233573i | ||||
\(902\) | 14.7142 | + | 25.4858i | 0.489930 | + | 0.848584i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.90167 | − | 10.2220i | 0.196287 | − | 0.339978i | ||||
\(905\) | −38.1851 | −1.26931 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51.9332 | 1.72442 | 0.862208 | − | 0.506555i | \(-0.169081\pi\) | ||||
0.862208 | + | 0.506555i | \(0.169081\pi\) | |||||||
\(908\) | 1.07564 | + | 1.86306i | 0.0356963 | + | 0.0618279i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.01993 | + | 2.30270i | −0.133259 | + | 0.0763336i | ||||
\(911\) | 18.0762 | + | 31.3089i | 0.598891 | + | 1.03731i | 0.992985 | + | 0.118240i | \(0.0377252\pi\) |
−0.394094 | + | 0.919070i | \(0.628941\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −37.4697 | − | 64.8995i | −1.24007 | − | 2.14786i | ||||
\(914\) | −15.3593 | − | 26.6031i | −0.508042 | − | 0.879954i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.28043 | + | 7.41393i | 0.141429 | + | 0.244963i | ||||
\(917\) | 0.0829684 | − | 24.3716i | 0.00273986 | − | 0.804821i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.58842 | + | 9.67942i | 0.184345 | + | 0.319295i | 0.943356 | − | 0.331783i | \(-0.107650\pi\) |
−0.759011 | + | 0.651078i | \(0.774317\pi\) | |||||||
\(920\) | −6.55585 | −0.216140 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 57.5420 | 1.89504 | ||||||||
\(923\) | −0.290450 | + | 0.503074i | −0.00956028 | + | 0.0165589i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.6165 | − | 32.2447i | −0.612106 | − | 1.06020i | ||||
\(926\) | 1.88618 | + | 3.26696i | 0.0619837 | + | 0.107359i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.31673 | + | 7.47679i | −0.141703 | + | 0.245438i | ||||
\(929\) | 16.4192 | − | 28.4389i | 0.538696 | − | 0.933049i | −0.460279 | − | 0.887775i | \(-0.652250\pi\) |
0.998975 | − | 0.0452744i | \(-0.0144162\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25.0083 | − | 44.0048i | −0.819612 | − | 1.44220i | ||||
\(932\) | −2.50092 | + | 4.33173i | −0.0819205 | + | 0.141890i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 51.3364 | 1.67978 | ||||||||
\(935\) | −25.2048 | + | 43.6560i | −0.824285 | + | 1.42770i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.9566 | −0.847965 | −0.423983 | − | 0.905670i | \(-0.639368\pi\) | ||||
−0.423983 | + | 0.905670i | \(0.639368\pi\) | |||||||
\(938\) | 0.0262847 | − | 7.72100i | 0.000858225 | − | 0.252100i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.96748 | −0.129405 | ||||||||
\(941\) | 14.7340 | + | 25.5200i | 0.480314 | + | 0.831928i | 0.999745 | − | 0.0225845i | \(-0.00718949\pi\) |
−0.519431 | + | 0.854512i | \(0.673856\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.37316 | + | 2.37839i | −0.0447163 | + | 0.0774509i | ||||
\(944\) | 11.0141 | 0.358479 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 69.5192 | 2.26026 | ||||||||
\(947\) | −5.76137 | + | 9.97898i | −0.187219 | + | 0.324273i | −0.944322 | − | 0.329022i | \(-0.893281\pi\) |
0.757103 | + | 0.653296i | \(0.226614\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.78144 | − | 4.81760i | −0.0902895 | − | 0.156386i | ||||
\(950\) | 55.2223 | 1.79165 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 15.9925 | + | 9.30603i | 0.518321 | + | 0.301610i | ||||
\(953\) | −29.2912 | −0.948835 | −0.474417 | − | 0.880300i | \(-0.657341\pi\) | ||||
−0.474417 | + | 0.880300i | \(0.657341\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.3454 | + | 26.5790i | −0.496565 | + | 0.860076i | ||||
\(956\) | −8.06352 | −0.260793 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −26.6537 | + | 46.1656i | −0.861144 | + | 1.49154i | ||||
\(959\) | 0.0614665 | − | 18.0555i | 0.00198486 | − | 0.583043i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.08991 | − | 5.35188i | 0.0996744 | − | 0.172641i | ||||
\(962\) | −2.07697 | + | 3.59742i | −0.0669643 | + | 0.115985i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.75411 | − | 3.03820i | −0.0564959 | − | 0.0978538i | ||||
\(965\) | −3.63417 | − | 6.29457i | −0.116988 | − | 0.202629i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.0402 | + | 36.4427i | −0.676606 | + | 1.17192i | 0.299390 | + | 0.954131i | \(0.403217\pi\) |
−0.975997 | + | 0.217786i | \(0.930117\pi\) | |||||||
\(968\) | 55.5403 | 1.78513 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 77.6536 | 2.49331 | ||||||||
\(971\) | −17.5774 | − | 30.4450i | −0.564087 | − | 0.977027i | −0.997134 | − | 0.0756560i | \(-0.975895\pi\) |
0.433047 | − | 0.901371i | \(-0.357438\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.0040 | + | 7.56703i | 0.416890 | + | 0.242588i | ||||
\(974\) | 0.737391 | + | 1.27720i | 0.0236275 | + | 0.0409241i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.34907 | + | 12.7290i | 0.235238 | + | 0.407444i | ||||
\(977\) | −2.21513 | − | 3.83671i | −0.0708682 | − | 0.122747i | 0.828414 | − | 0.560117i | \(-0.189244\pi\) |
−0.899282 | + | 0.437369i | \(0.855910\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −41.0136 | − | 71.0376i | −1.31080 | − | 2.27037i | ||||
\(980\) | −3.94144 | − | 6.93540i | −0.125905 | − | 0.221543i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12.1184 | − | 20.9897i | −0.386714 | − | 0.669809i | ||||
\(983\) | −22.1601 | −0.706798 | −0.353399 | − | 0.935473i | \(-0.614974\pi\) | ||||
−0.353399 | + | 0.935473i | \(0.614974\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.9923 | 0.509558 | ||||||||
\(986\) | −9.12684 | + | 15.8081i | −0.290658 | + | 0.503434i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.470902 | − | 0.815626i | −0.0149814 | − | 0.0259485i | ||||
\(989\) | 3.24383 | + | 5.61848i | 0.103148 | + | 0.178657i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.3602 | − | 31.8007i | 0.583229 | − | 1.01018i | −0.411864 | − | 0.911245i | \(-0.635122\pi\) |
0.995094 | − | 0.0989378i | \(-0.0315445\pi\) | |||||||
\(992\) | 5.02686 | − | 8.70677i | 0.159603 | − | 0.276440i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.65551 | − | 3.29093i | −0.179382 | − | 0.104382i | ||||
\(995\) | −15.7143 | + | 27.2180i | −0.498178 | + | 0.862869i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.9031 | −1.26374 | −0.631872 | − | 0.775073i | \(-0.717713\pi\) | ||||
−0.631872 | + | 0.775073i | \(0.717713\pi\) | |||||||
\(998\) | −14.6959 | + | 25.4540i | −0.465190 | + | 0.805733i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 567.2.g.k.109.3 | 8 | ||
3.2 | odd | 2 | 567.2.g.j.109.2 | 8 | |||
7.2 | even | 3 | 567.2.h.j.352.2 | 8 | |||
9.2 | odd | 6 | 567.2.h.k.298.3 | 8 | |||
9.4 | even | 3 | 567.2.e.d.487.3 | yes | 8 | ||
9.5 | odd | 6 | 567.2.e.c.487.2 | yes | 8 | ||
9.7 | even | 3 | 567.2.h.j.298.2 | 8 | |||
21.2 | odd | 6 | 567.2.h.k.352.3 | 8 | |||
63.2 | odd | 6 | 567.2.g.j.541.2 | 8 | |||
63.4 | even | 3 | 3969.2.a.s.1.2 | 4 | |||
63.16 | even | 3 | inner | 567.2.g.k.541.3 | 8 | ||
63.23 | odd | 6 | 567.2.e.c.163.2 | ✓ | 8 | ||
63.31 | odd | 6 | 3969.2.a.t.1.2 | 4 | |||
63.32 | odd | 6 | 3969.2.a.x.1.3 | 4 | |||
63.58 | even | 3 | 567.2.e.d.163.3 | yes | 8 | ||
63.59 | even | 6 | 3969.2.a.w.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
567.2.e.c.163.2 | ✓ | 8 | 63.23 | odd | 6 | ||
567.2.e.c.487.2 | yes | 8 | 9.5 | odd | 6 | ||
567.2.e.d.163.3 | yes | 8 | 63.58 | even | 3 | ||
567.2.e.d.487.3 | yes | 8 | 9.4 | even | 3 | ||
567.2.g.j.109.2 | 8 | 3.2 | odd | 2 | |||
567.2.g.j.541.2 | 8 | 63.2 | odd | 6 | |||
567.2.g.k.109.3 | 8 | 1.1 | even | 1 | trivial | ||
567.2.g.k.541.3 | 8 | 63.16 | even | 3 | inner | ||
567.2.h.j.298.2 | 8 | 9.7 | even | 3 | |||
567.2.h.j.352.2 | 8 | 7.2 | even | 3 | |||
567.2.h.k.298.3 | 8 | 9.2 | odd | 6 | |||
567.2.h.k.352.3 | 8 | 21.2 | odd | 6 | |||
3969.2.a.s.1.2 | 4 | 63.4 | even | 3 | |||
3969.2.a.t.1.2 | 4 | 63.31 | odd | 6 | |||
3969.2.a.w.1.3 | 4 | 63.59 | even | 6 | |||
3969.2.a.x.1.3 | 4 | 63.32 | odd | 6 |