Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,2,Mod(541,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1080.541");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.k (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.62384341830\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | 20.0.1780383353079852270621853183383699456.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{18} + 5x^{16} + 28x^{12} - 28x^{10} + 112x^{8} + 320x^{4} - 256x^{2} + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 541.17 | ||
Root | \(1.19357 + 0.758543i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.541 |
Dual form | 1080.2.k.d.541.18 |
$q$-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 \(\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times\).
\(n\) | \(217\) | \(271\) | \(541\) | \(1001\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.19357 | − | 0.758543i | 0.843982 | − | 0.536371i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.849224 | − | 1.81075i | 0.424612 | − | 0.905375i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.63236 | 1.75087 | 0.875434 | − | 0.483338i | \(-0.160576\pi\) | ||||
0.875434 | + | 0.483338i | \(0.160576\pi\) | |||||||
\(8\) | −0.359923 | − | 2.80543i | −0.127252 | − | 0.991870i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.758543 | − | 1.19357i | −0.239872 | − | 0.377440i | ||||
\(11\) | − | 2.39533i | − | 0.722220i | −0.932523 | − | 0.361110i | \(-0.882398\pi\) | ||
0.932523 | − | 0.361110i | \(-0.117602\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.95421i | 0.541999i | 0.962579 | + | 0.271000i | \(0.0873542\pi\) | ||||
−0.962579 | + | 0.271000i | \(0.912646\pi\) | |||||||
\(14\) | 5.52905 | − | 3.51385i | 1.47770 | − | 0.939115i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.55764 | − | 3.07547i | −0.639409 | − | 0.768867i | ||||
\(17\) | 4.76655 | 1.15606 | 0.578029 | − | 0.816016i | \(-0.303822\pi\) | ||||
0.578029 | + | 0.816016i | \(0.303822\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.29155i | 1.44338i | 0.692216 | + | 0.721691i | \(0.256635\pi\) | ||||
−0.692216 | + | 0.721691i | \(0.743365\pi\) | |||||||
\(20\) | −1.81075 | − | 0.849224i | −0.404896 | − | 0.189892i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.81696 | − | 2.85900i | −0.387378 | − | 0.609541i | ||||
\(23\) | −5.28106 | −1.10118 | −0.550589 | − | 0.834777i | \(-0.685597\pi\) | ||||
−0.550589 | + | 0.834777i | \(0.685597\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 1.48235 | + | 2.33248i | 0.290713 | + | 0.457438i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.93391 | − | 8.38805i | 0.743439 | − | 1.58519i | ||||
\(29\) | 0.201291i | 0.0373787i | 0.999825 | + | 0.0186894i | \(0.00594935\pi\) | ||||
−0.999825 | + | 0.0186894i | \(0.994051\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.26964 | −0.587244 | −0.293622 | − | 0.955922i | \(-0.594861\pi\) | ||||
−0.293622 | + | 0.955922i | \(0.594861\pi\) | |||||||
\(32\) | −5.38560 | − | 1.73071i | −0.952048 | − | 0.305949i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.68921 | − | 3.61563i | 0.975692 | − | 0.620076i | ||||
\(35\) | − | 4.63236i | − | 0.783012i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.43969i | − | 0.236684i | −0.992973 | − | 0.118342i | \(-0.962242\pi\) | ||
0.992973 | − | 0.118342i | \(-0.0377580\pi\) | |||||||
\(38\) | 4.77242 | + | 7.50942i | 0.774188 | + | 1.21819i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.80543 | + | 0.359923i | −0.443578 | + | 0.0569089i | ||||
\(41\) | −8.53808 | −1.33342 | −0.666712 | − | 0.745316i | \(-0.732299\pi\) | ||||
−0.666712 | + | 0.745316i | \(0.732299\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.10390i | − | 1.38833i | −0.719815 | − | 0.694166i | \(-0.755774\pi\) | ||
0.719815 | − | 0.694166i | \(-0.244226\pi\) | |||||||
\(44\) | −4.33735 | − | 2.03417i | −0.653880 | − | 0.306663i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.30332 | + | 4.00591i | −0.929374 | + | 0.590640i | ||||
\(47\) | 10.4923 | 1.53046 | 0.765228 | − | 0.643759i | \(-0.222626\pi\) | ||||
0.765228 | + | 0.643759i | \(0.222626\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.4588 | 2.06554 | ||||||||
\(50\) | −1.19357 | + | 0.758543i | −0.168796 | + | 0.107274i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.53858 | + | 1.65956i | 0.490713 | + | 0.230139i | ||||
\(53\) | − | 3.03261i | − | 0.416561i | −0.978069 | − | 0.208280i | \(-0.933213\pi\) | ||
0.978069 | − | 0.208280i | \(-0.0667867\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.39533 | −0.322986 | ||||||||
\(56\) | −1.66730 | − | 12.9958i | −0.222802 | − | 1.73663i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.152688 | + | 0.240255i | 0.0200489 | + | 0.0315470i | ||||
\(59\) | − | 2.75805i | − | 0.359068i | −0.983752 | − | 0.179534i | \(-0.942541\pi\) | ||
0.983752 | − | 0.179534i | \(-0.0574590\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.24576i | 1.05576i | 0.849319 | + | 0.527881i | \(0.177013\pi\) | ||||
−0.849319 | + | 0.527881i | \(0.822987\pi\) | |||||||
\(62\) | −3.90254 | + | 2.48016i | −0.495624 | + | 0.314981i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.74091 | + | 2.01948i | −0.967614 | + | 0.252435i | ||||
\(65\) | 1.95421 | 0.242389 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0173i | 1.46815i | 0.679071 | + | 0.734073i | \(0.262383\pi\) | ||||
−0.679071 | + | 0.734073i | \(0.737617\pi\) | |||||||
\(68\) | 4.04787 | − | 8.63103i | 0.490876 | − | 1.04667i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.51385 | − | 5.52905i | −0.419985 | − | 0.660848i | ||||
\(71\) | −0.514512 | −0.0610614 | −0.0305307 | − | 0.999534i | \(-0.509720\pi\) | ||||
−0.0305307 | + | 0.999534i | \(0.509720\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.03261 | −0.471981 | −0.235991 | − | 0.971755i | \(-0.575833\pi\) | ||||
−0.235991 | + | 0.971755i | \(0.575833\pi\) | |||||||
\(74\) | −1.09207 | − | 1.71838i | −0.126951 | − | 0.199757i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.3924 | + | 5.34294i | 1.30680 | + | 0.612877i | ||||
\(77\) | − | 11.0960i | − | 1.26451i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.43832 | −0.161824 | −0.0809118 | − | 0.996721i | \(-0.525783\pi\) | ||||
−0.0809118 | + | 0.996721i | \(0.525783\pi\) | |||||||
\(80\) | −3.07547 | + | 2.55764i | −0.343848 | + | 0.285952i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.1908 | + | 6.47650i | −1.12539 | + | 0.715210i | ||||
\(83\) | 7.66497i | 0.841340i | 0.907214 | + | 0.420670i | \(0.138205\pi\) | ||||
−0.907214 | + | 0.420670i | \(0.861795\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 4.76655i | − | 0.517005i | ||||||
\(86\) | −6.90570 | − | 10.8661i | −0.744661 | − | 1.17173i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.71994 | + | 0.862136i | −0.716348 | + | 0.0919040i | ||||
\(89\) | −9.10390 | −0.965011 | −0.482506 | − | 0.875893i | \(-0.660273\pi\) | ||||
−0.482506 | + | 0.875893i | \(0.660273\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.05259i | 0.948969i | ||||||||
\(92\) | −4.48480 | + | 9.56268i | −0.467573 | + | 0.996979i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.5233 | − | 7.95885i | 1.29168 | − | 0.820893i | ||||
\(95\) | 6.29155 | 0.645500 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.6927 | −1.18721 | −0.593605 | − | 0.804757i | \(-0.702296\pi\) | ||||
−0.593605 | + | 0.804757i | \(0.702296\pi\) | |||||||
\(98\) | 17.2576 | − | 10.9676i | 1.74328 | − | 1.10789i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.849224 | + | 1.81075i | −0.0849224 | + | 0.181075i | ||||
\(101\) | − | 17.6958i | − | 1.76080i | −0.474235 | − | 0.880398i | \(-0.657275\pi\) | ||
0.474235 | − | 0.880398i | \(-0.342725\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.4865 | 1.82152 | 0.910762 | − | 0.412931i | \(-0.135495\pi\) | ||||
0.910762 | + | 0.412931i | \(0.135495\pi\) | |||||||
\(104\) | 5.48240 | − | 0.703365i | 0.537593 | − | 0.0689706i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.30036 | − | 3.61963i | −0.223431 | − | 0.351570i | ||||
\(107\) | 8.66810i | 0.837977i | 0.907992 | + | 0.418988i | \(0.137615\pi\) | ||||
−0.907992 | + | 0.418988i | \(0.862385\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.37816i | − | 0.323569i | −0.986826 | − | 0.161785i | \(-0.948275\pi\) | ||
0.986826 | − | 0.161785i | \(-0.0517250\pi\) | |||||||
\(110\) | −2.85900 | + | 1.81696i | −0.272595 | + | 0.173241i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −11.8479 | − | 14.2467i | −1.11952 | − | 1.34618i | ||||
\(113\) | −11.0736 | −1.04171 | −0.520857 | − | 0.853644i | \(-0.674388\pi\) | ||||
−0.520857 | + | 0.853644i | \(0.674388\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.28106i | 0.492461i | ||||||||
\(116\) | 0.364487 | + | 0.170941i | 0.0338418 | + | 0.0158715i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.09210 | − | 3.29193i | −0.192594 | − | 0.303047i | ||||
\(119\) | 22.0804 | 2.02410 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.26239 | 0.478399 | ||||||||
\(122\) | 6.25477 | + | 9.84190i | 0.566280 | + | 0.891044i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.77665 | + | 5.92050i | −0.249351 | + | 0.531676i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.4865 | −1.81788 | −0.908939 | − | 0.416928i | \(-0.863107\pi\) | ||||
−0.908939 | + | 0.416928i | \(0.863107\pi\) | |||||||
\(128\) | −7.70746 | + | 8.28221i | −0.681250 | + | 0.732051i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.33248 | − | 1.48235i | 0.204572 | − | 0.130011i | ||||
\(131\) | 13.2901i | 1.16116i | 0.814203 | + | 0.580580i | \(0.197174\pi\) | ||||
−0.814203 | + | 0.580580i | \(0.802826\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 29.1447i | 2.52717i | ||||||||
\(134\) | 9.11563 | + | 14.3435i | 0.787471 | + | 1.23909i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.71559 | − | 13.3722i | −0.147111 | − | 1.14666i | ||||
\(137\) | −5.26253 | −0.449608 | −0.224804 | − | 0.974404i | \(-0.572174\pi\) | ||||
−0.224804 | + | 0.974404i | \(0.572174\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.9901i | 1.94999i | 0.222220 | + | 0.974996i | \(0.428670\pi\) | ||||
−0.222220 | + | 0.974996i | \(0.571330\pi\) | |||||||
\(140\) | −8.38805 | − | 3.93391i | −0.708920 | − | 0.332476i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.614107 | + | 0.390280i | −0.0515347 | + | 0.0327516i | ||||
\(143\) | 4.68097 | 0.391443 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.201291 | 0.0167163 | ||||||||
\(146\) | −4.81320 | + | 3.05891i | −0.398344 | + | 0.253157i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.60693 | − | 1.22262i | −0.214288 | − | 0.100499i | ||||
\(149\) | − | 5.79871i | − | 0.475049i | −0.971382 | − | 0.237524i | \(-0.923664\pi\) | ||
0.971382 | − | 0.237524i | \(-0.0763360\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.2924 | 1.48862 | 0.744308 | − | 0.667837i | \(-0.232780\pi\) | ||||
0.744308 | + | 0.667837i | \(0.232780\pi\) | |||||||
\(152\) | 17.6505 | − | 2.26448i | 1.43165 | − | 0.183673i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.41683 | − | 13.2439i | −0.678247 | − | 1.06722i | ||||
\(155\) | 3.26964i | 0.262624i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.5163i | 0.998912i | 0.866339 | + | 0.499456i | \(0.166467\pi\) | ||||
−0.866339 | + | 0.499456i | \(0.833533\pi\) | |||||||
\(158\) | −1.71674 | + | 1.09103i | −0.136576 | + | 0.0867975i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.73071 | + | 5.38560i | −0.136825 | + | 0.425769i | ||||
\(161\) | −24.4638 | −1.92802 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 7.07985i | − | 0.554537i | −0.960793 | − | 0.277268i | \(-0.910571\pi\) | ||
0.960793 | − | 0.277268i | \(-0.0894291\pi\) | |||||||
\(164\) | −7.25074 | + | 15.4603i | −0.566188 | + | 1.20725i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.81421 | + | 9.14869i | 0.451270 | + | 0.710076i | ||||
\(167\) | 23.4190 | 1.81222 | 0.906109 | − | 0.423045i | \(-0.139039\pi\) | ||||
0.906109 | + | 0.423045i | \(0.139039\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.18108 | 0.706237 | ||||||||
\(170\) | −3.61563 | − | 5.68921i | −0.277306 | − | 0.436343i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −16.4849 | − | 7.73125i | −1.25696 | − | 0.589502i | ||||
\(173\) | 5.99508i | 0.455798i | 0.973685 | + | 0.227899i | \(0.0731856\pi\) | ||||
−0.973685 | + | 0.227899i | \(0.926814\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.63236 | −0.350174 | ||||||||
\(176\) | −7.36676 | + | 6.12639i | −0.555291 | + | 0.461794i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10.8661 | + | 6.90570i | −0.814452 | + | 0.517604i | ||||
\(179\) | 18.0554i | 1.34952i | 0.738036 | + | 0.674761i | \(0.235753\pi\) | ||||
−0.738036 | + | 0.674761i | \(0.764247\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.28106i | 0.392538i | 0.980550 | + | 0.196269i | \(0.0628826\pi\) | ||||
−0.980550 | + | 0.196269i | \(0.937117\pi\) | |||||||
\(182\) | 6.86678 | + | 10.8049i | 0.509000 | + | 0.800913i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.90078 | + | 14.8157i | 0.140127 | + | 1.09223i | ||||
\(185\) | −1.43969 | −0.105848 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 11.4175i | − | 0.834928i | ||||||
\(188\) | 8.91030 | − | 18.9989i | 0.649850 | − | 1.38564i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.50942 | − | 4.77242i | 0.544790 | − | 0.346227i | ||||
\(191\) | 4.48971 | 0.324864 | 0.162432 | − | 0.986720i | \(-0.448066\pi\) | ||||
0.162432 | + | 0.986720i | \(0.448066\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.869389 | −0.0625800 | −0.0312900 | − | 0.999510i | \(-0.509962\pi\) | ||||
−0.0312900 | + | 0.999510i | \(0.509962\pi\) | |||||||
\(194\) | −13.9560 | + | 8.86939i | −1.00198 | + | 0.636785i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.2787 | − | 26.1812i | 0.877052 | − | 1.87009i | ||||
\(197\) | 15.8134i | 1.12666i | 0.826232 | + | 0.563330i | \(0.190480\pi\) | ||||
−0.826232 | + | 0.563330i | \(0.809520\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.2679 | 0.798757 | 0.399378 | − | 0.916786i | \(-0.369226\pi\) | ||||
0.399378 | + | 0.916786i | \(0.369226\pi\) | |||||||
\(200\) | 0.359923 | + | 2.80543i | 0.0254504 | + | 0.198374i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −13.4230 | − | 21.1212i | −0.944441 | − | 1.48608i | ||||
\(203\) | 0.932450i | 0.0654452i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.53808i | 0.596325i | ||||||||
\(206\) | 22.0649 | − | 14.0228i | 1.53733 | − | 0.977013i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.01010 | − | 4.99815i | 0.416725 | − | 0.346559i | ||||
\(209\) | 15.0704 | 1.04244 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 5.78010i | − | 0.397919i | −0.980008 | − | 0.198959i | \(-0.936244\pi\) | ||
0.980008 | − | 0.198959i | \(-0.0637561\pi\) | |||||||
\(212\) | −5.49130 | − | 2.57536i | −0.377144 | − | 0.176877i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.57513 | + | 10.3460i | 0.449466 | + | 0.707237i | ||||
\(215\) | −9.10390 | −0.620881 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.1461 | −1.02819 | ||||||||
\(218\) | −2.56248 | − | 4.03208i | −0.173553 | − | 0.273087i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.03417 | + | 4.33735i | −0.137144 | + | 0.292424i | ||||
\(221\) | 9.31482i | 0.626583i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.30304 | 0.622978 | 0.311489 | − | 0.950250i | \(-0.399172\pi\) | ||||
0.311489 | + | 0.950250i | \(0.399172\pi\) | |||||||
\(224\) | −24.9480 | − | 8.01727i | −1.66691 | − | 0.535676i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.2171 | + | 8.39979i | −0.879188 | + | 0.558745i | ||||
\(227\) | 2.59429i | 0.172189i | 0.996287 | + | 0.0860945i | \(0.0274387\pi\) | ||||
−0.996287 | + | 0.0860945i | \(0.972561\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 25.4072i | − | 1.67896i | −0.543393 | − | 0.839478i | \(-0.682861\pi\) | ||
0.543393 | − | 0.839478i | \(-0.317139\pi\) | |||||||
\(230\) | 4.00591 | + | 6.30332i | 0.264142 | + | 0.415629i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.564707 | − | 0.0724492i | 0.0370748 | − | 0.00475652i | ||||
\(233\) | −27.9430 | −1.83061 | −0.915303 | − | 0.402766i | \(-0.868049\pi\) | ||||
−0.915303 | + | 0.402766i | \(0.868049\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 10.4923i | − | 0.684441i | ||||||
\(236\) | −4.99415 | − | 2.34221i | −0.325091 | − | 0.152465i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 26.3545 | − | 16.7489i | 1.70831 | − | 1.08567i | ||||
\(239\) | 11.4515 | 0.740734 | 0.370367 | − | 0.928886i | \(-0.379232\pi\) | ||||
0.370367 | + | 0.928886i | \(0.379232\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0707 | 0.906372 | 0.453186 | − | 0.891416i | \(-0.350287\pi\) | ||||
0.453186 | + | 0.891416i | \(0.350287\pi\) | |||||||
\(242\) | 6.28103 | − | 3.99175i | 0.403760 | − | 0.256599i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 14.9310 | + | 7.00250i | 0.955860 | + | 0.448289i | ||||
\(245\) | − | 14.4588i | − | 0.923736i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.2950 | −0.782312 | ||||||||
\(248\) | 1.17682 | + | 9.17275i | 0.0747281 | + | 0.582470i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.758543 | + | 1.19357i | 0.0479745 | + | 0.0754881i | ||||
\(251\) | − | 0.402581i | − | 0.0254107i | −0.999919 | − | 0.0127053i | \(-0.995956\pi\) | ||
0.999919 | − | 0.0127053i | \(-0.00404435\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.6499i | 0.795292i | ||||||||
\(254\) | −24.4520 | + | 15.5399i | −1.53426 | + | 0.975058i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.91699 | + | 15.7319i | −0.182312 | + | 0.983241i | ||||
\(257\) | −26.4022 | −1.64693 | −0.823463 | − | 0.567369i | \(-0.807961\pi\) | ||||
−0.823463 | + | 0.567369i | \(0.807961\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 6.66918i | − | 0.414403i | ||||||
\(260\) | 1.65956 | − | 3.53858i | 0.102921 | − | 0.219453i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.0811 | + | 15.8627i | 0.622812 | + | 0.979998i | ||||
\(263\) | −2.96470 | −0.182811 | −0.0914056 | − | 0.995814i | \(-0.529136\pi\) | ||||
−0.0914056 | + | 0.995814i | \(0.529136\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.03261 | −0.186292 | ||||||||
\(266\) | 22.1076 | + | 34.7863i | 1.35550 | + | 2.13289i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 21.7603 | + | 10.2054i | 1.32922 | + | 0.623392i | ||||
\(269\) | − | 12.5294i | − | 0.763933i | −0.924176 | − | 0.381967i | \(-0.875247\pi\) | ||
0.924176 | − | 0.381967i | \(-0.124753\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0634 | −0.975784 | −0.487892 | − | 0.872904i | \(-0.662234\pi\) | ||||
−0.487892 | + | 0.872904i | \(0.662234\pi\) | |||||||
\(272\) | −12.1911 | − | 14.6594i | −0.739194 | − | 0.888854i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.28120 | + | 3.99186i | −0.379461 | + | 0.241157i | ||||
\(275\) | 2.39533i | 0.144444i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 19.5807i | − | 1.17649i | −0.808683 | − | 0.588245i | \(-0.799819\pi\) | ||
0.808683 | − | 0.588245i | \(-0.200181\pi\) | |||||||
\(278\) | 17.4390 | + | 27.4403i | 1.04592 | + | 1.64576i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −12.9958 | + | 1.66730i | −0.776646 | + | 0.0996400i | ||||
\(281\) | 4.33761 | 0.258760 | 0.129380 | − | 0.991595i | \(-0.458701\pi\) | ||||
0.129380 | + | 0.991595i | \(0.458701\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 13.4755i | − | 0.801036i | −0.916289 | − | 0.400518i | \(-0.868830\pi\) | ||
0.916289 | − | 0.400518i | \(-0.131170\pi\) | |||||||
\(284\) | −0.436936 | + | 0.931654i | −0.0259274 | + | 0.0552835i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.58707 | − | 3.55072i | 0.330371 | − | 0.209958i | ||||
\(287\) | −39.5514 | −2.33465 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.71998 | 0.336470 | ||||||||
\(290\) | 0.240255 | − | 0.152688i | 0.0141082 | − | 0.00896613i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.42459 | + | 7.30205i | −0.200409 | + | 0.427320i | ||||
\(293\) | 17.8134i | 1.04067i | 0.853962 | + | 0.520336i | \(0.174193\pi\) | ||||
−0.853962 | + | 0.520336i | \(0.825807\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.75805 | −0.160580 | ||||||||
\(296\) | −4.03897 | + | 0.518180i | −0.234760 | + | 0.0301186i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.39857 | − | 6.92117i | −0.254802 | − | 0.400933i | ||||
\(299\) | − | 10.3203i | − | 0.596837i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 42.1725i | − | 2.43078i | ||||||
\(302\) | 21.8333 | − | 13.8756i | 1.25636 | − | 0.798450i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 19.3495 | − | 16.0915i | 1.10977 | − | 0.922911i | ||||
\(305\) | 8.24576 | 0.472151 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 20.3999i | − | 1.16429i | −0.813087 | − | 0.582143i | \(-0.802214\pi\) | ||
0.813087 | − | 0.582143i | \(-0.197786\pi\) | |||||||
\(308\) | −20.0922 | − | 9.42302i | −1.14486 | − | 0.536927i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.48016 | + | 3.90254i | 0.140864 | + | 0.221650i | ||||
\(311\) | −19.8854 | −1.12760 | −0.563799 | − | 0.825912i | \(-0.690661\pi\) | ||||
−0.563799 | + | 0.825912i | \(0.690661\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.6108 | −1.39108 | −0.695541 | − | 0.718486i | \(-0.744835\pi\) | ||||
−0.695541 | + | 0.718486i | \(0.744835\pi\) | |||||||
\(314\) | 9.49418 | + | 14.9391i | 0.535787 | + | 0.843064i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.22146 | + | 2.60444i | −0.0687122 | + | 0.146511i | ||||
\(317\) | 19.3250i | 1.08540i | 0.839926 | + | 0.542701i | \(0.182598\pi\) | ||||
−0.839926 | + | 0.542701i | \(0.817402\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.482158 | 0.0269956 | ||||||||
\(320\) | 2.01948 | + | 7.74091i | 0.112893 | + | 0.432730i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −29.1993 | + | 18.5568i | −1.62721 | + | 1.03413i | ||||
\(323\) | 29.9890i | 1.66863i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1.95421i | − | 0.108400i | ||||||
\(326\) | −5.37037 | − | 8.45031i | −0.297437 | − | 0.468019i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.07305 | + | 23.9530i | 0.169681 | + | 1.32258i | ||||
\(329\) | 48.6040 | 2.67963 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.91393i | 0.325059i | 0.986704 | + | 0.162529i | \(0.0519652\pi\) | ||||
−0.986704 | + | 0.162529i | \(0.948035\pi\) | |||||||
\(332\) | 13.8793 | + | 6.50928i | 0.761728 | + | 0.357243i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 27.9523 | − | 17.7643i | 1.52948 | − | 0.972021i | ||||
\(335\) | 12.0173 | 0.656575 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 31.9081 | 1.73814 | 0.869072 | − | 0.494686i | \(-0.164717\pi\) | ||||
0.869072 | + | 0.494686i | \(0.164717\pi\) | |||||||
\(338\) | 10.9583 | − | 6.96425i | 0.596051 | − | 0.378805i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.63103 | − | 4.04787i | −0.468083 | − | 0.219526i | ||||
\(341\) | 7.83186i | 0.424119i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 34.5517 | 1.86561 | ||||||||
\(344\) | −25.5404 | + | 3.27671i | −1.37704 | + | 0.176668i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.54753 | + | 7.15556i | 0.244477 | + | 0.384685i | ||||
\(347\) | 25.0004i | 1.34209i | 0.741417 | + | 0.671045i | \(0.234154\pi\) | ||||
−0.741417 | + | 0.671045i | \(0.765846\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 6.22477i | − | 0.333204i | −0.986024 | − | 0.166602i | \(-0.946720\pi\) | ||
0.986024 | − | 0.166602i | \(-0.0532796\pi\) | |||||||
\(350\) | −5.52905 | + | 3.51385i | −0.295540 | + | 0.187823i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.14562 | + | 12.9003i | −0.220962 | + | 0.687588i | ||||
\(353\) | 5.92940 | 0.315590 | 0.157795 | − | 0.987472i | \(-0.449561\pi\) | ||||
0.157795 | + | 0.987472i | \(0.449561\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.514512i | 0.0273075i | ||||||||
\(356\) | −7.73125 | + | 16.4849i | −0.409755 | + | 0.873697i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.6958 | + | 21.5504i | 0.723845 | + | 1.13897i | ||||
\(359\) | 28.4933 | 1.50382 | 0.751910 | − | 0.659265i | \(-0.229133\pi\) | ||||
0.751910 | + | 0.659265i | \(0.229133\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −20.5837 | −1.08335 | ||||||||
\(362\) | 4.00591 | + | 6.30332i | 0.210546 | + | 0.331295i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 16.3920 | + | 7.68768i | 0.859173 | + | 0.402944i | ||||
\(365\) | 4.03261i | 0.211076i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.8541 | −0.931976 | −0.465988 | − | 0.884791i | \(-0.654301\pi\) | ||||
−0.465988 | + | 0.884791i | \(0.654301\pi\) | |||||||
\(368\) | 13.5070 | + | 16.2417i | 0.704103 | + | 0.846658i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.71838 | + | 1.09207i | −0.0893342 | + | 0.0567740i | ||||
\(371\) | − | 14.0481i | − | 0.729343i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.06438i | 0.365780i | 0.983133 | + | 0.182890i | \(0.0585452\pi\) | ||||
−0.983133 | + | 0.182890i | \(0.941455\pi\) | |||||||
\(374\) | −8.66064 | − | 13.6276i | −0.447831 | − | 0.704664i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.77642 | − | 29.4354i | −0.194754 | − | 1.51801i | ||||
\(377\) | −0.393363 | −0.0202592 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 4.76655i | − | 0.244841i | −0.992478 | − | 0.122421i | \(-0.960934\pi\) | ||
0.992478 | − | 0.122421i | \(-0.0390657\pi\) | |||||||
\(380\) | 5.34294 | − | 11.3924i | 0.274087 | − | 0.584420i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.35878 | − | 3.40564i | 0.274179 | − | 0.174248i | ||||
\(383\) | −5.36637 | −0.274209 | −0.137104 | − | 0.990557i | \(-0.543780\pi\) | ||||
−0.137104 | + | 0.990557i | \(0.543780\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.0960 | −0.565506 | ||||||||
\(386\) | −1.03768 | + | 0.659469i | −0.0528164 | + | 0.0335661i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.92969 | + | 21.1725i | −0.504104 | + | 1.07487i | ||||
\(389\) | − | 31.9686i | − | 1.62087i | −0.585828 | − | 0.810435i | \(-0.699231\pi\) | ||
0.585828 | − | 0.810435i | \(-0.300769\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.1724 | −1.27302 | ||||||||
\(392\) | −5.20405 | − | 40.5631i | −0.262844 | − | 2.04875i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.9952 | + | 18.8745i | 0.604308 | + | 0.950882i | ||||
\(395\) | 1.43832i | 0.0723697i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 18.9244i | − | 0.949789i | −0.880043 | − | 0.474894i | \(-0.842486\pi\) | ||
0.880043 | − | 0.474894i | \(-0.157514\pi\) | |||||||
\(398\) | 13.4490 | − | 8.54715i | 0.674137 | − | 0.428430i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.55764 | + | 3.07547i | 0.127882 | + | 0.153773i | ||||
\(401\) | 2.17947 | 0.108838 | 0.0544189 | − | 0.998518i | \(-0.482669\pi\) | ||||
0.0544189 | + | 0.998518i | \(0.482669\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 6.38955i | − | 0.318286i | ||||||
\(404\) | −32.0427 | − | 15.0277i | −1.59418 | − | 0.747656i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.707304 | + | 1.11295i | 0.0351029 | + | 0.0552346i | ||||
\(407\) | −3.44854 | −0.170938 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.78279 | −0.187047 | −0.0935236 | − | 0.995617i | \(-0.529813\pi\) | ||||
−0.0935236 | + | 0.995617i | \(0.529813\pi\) | |||||||
\(410\) | 6.47650 | + | 10.1908i | 0.319852 | + | 0.503288i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 15.6991 | − | 33.4744i | 0.773441 | − | 1.64916i | ||||
\(413\) | − | 12.7763i | − | 0.628681i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.66497 | 0.376259 | ||||||||
\(416\) | 3.38216 | − | 10.5246i | 0.165824 | − | 0.516009i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 17.9875 | − | 11.4315i | 0.879800 | − | 0.559134i | ||||
\(419\) | − | 28.0481i | − | 1.37024i | −0.728430 | − | 0.685120i | \(-0.759750\pi\) | ||
0.728430 | − | 0.685120i | \(-0.240250\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 28.3719i | − | 1.38276i | −0.722490 | − | 0.691381i | \(-0.757002\pi\) | ||
0.722490 | − | 0.691381i | \(-0.242998\pi\) | |||||||
\(422\) | −4.38446 | − | 6.89896i | −0.213432 | − | 0.335836i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.50778 | + | 1.09151i | −0.413174 | + | 0.0530083i | ||||
\(425\) | −4.76655 | −0.231212 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 38.1973i | 1.84850i | ||||||||
\(428\) | 15.6958 | + | 7.36116i | 0.758683 | + | 0.355815i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −10.8661 | + | 6.90570i | −0.524012 | + | 0.333022i | ||||
\(431\) | 15.2246 | 0.733341 | 0.366671 | − | 0.930351i | \(-0.380498\pi\) | ||||
0.366671 | + | 0.930351i | \(0.380498\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.1508 | 1.01644 | 0.508221 | − | 0.861226i | \(-0.330303\pi\) | ||||
0.508221 | + | 0.861226i | \(0.330303\pi\) | |||||||
\(434\) | −18.0780 | + | 11.4890i | −0.867771 | + | 0.551490i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.11701 | − | 2.86882i | −0.292952 | − | 0.137391i | ||||
\(437\) | − | 33.2261i | − | 1.58942i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.54732 | 0.312487 | 0.156243 | − | 0.987719i | \(-0.450062\pi\) | ||||
0.156243 | + | 0.987719i | \(0.450062\pi\) | |||||||
\(440\) | 0.862136 | + | 6.71994i | 0.0411007 | + | 0.320361i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.06569 | + | 11.1179i | 0.336081 | + | 0.528825i | ||||
\(443\) | − | 24.2042i | − | 1.14998i | −0.818161 | − | 0.574989i | \(-0.805006\pi\) | ||
0.818161 | − | 0.574989i | \(-0.194994\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.10390i | 0.431566i | ||||||||
\(446\) | 11.1038 | − | 7.05676i | 0.525782 | − | 0.334147i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −35.8587 | + | 9.35497i | −1.69416 | + | 0.441981i | ||||
\(449\) | −1.56084 | −0.0736607 | −0.0368304 | − | 0.999322i | \(-0.511726\pi\) | ||||
−0.0368304 | + | 0.999322i | \(0.511726\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.4515i | 0.963024i | ||||||||
\(452\) | −9.40395 | + | 20.0515i | −0.442324 | + | 0.943143i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.96788 | + | 3.09647i | 0.0923572 | + | 0.145324i | ||||
\(455\) | 9.05259 | 0.424392 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.16948 | −0.428930 | −0.214465 | − | 0.976732i | \(-0.568801\pi\) | ||||
−0.214465 | + | 0.976732i | \(0.568801\pi\) | |||||||
\(458\) | −19.2725 | − | 30.3253i | −0.900544 | − | 1.41701i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9.56268 | + | 4.48480i | 0.445862 | + | 0.209105i | ||||
\(461\) | 11.0563i | 0.514944i | 0.966286 | + | 0.257472i | \(0.0828895\pi\) | ||||
−0.966286 | + | 0.257472i | \(0.917110\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.4988 | −1.60330 | −0.801649 | − | 0.597795i | \(-0.796044\pi\) | ||||
−0.801649 | + | 0.597795i | \(0.796044\pi\) | |||||||
\(464\) | 0.619062 | − | 0.514828i | 0.0287393 | − | 0.0239003i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −33.3519 | + | 21.1960i | −1.54500 | + | 0.981884i | ||||
\(467\) | − | 38.8495i | − | 1.79774i | −0.438213 | − | 0.898871i | \(-0.644388\pi\) | ||
0.438213 | − | 0.898871i | \(-0.355612\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 55.6684i | 2.57053i | ||||||||
\(470\) | −7.95885 | − | 12.5233i | −0.367114 | − | 0.577656i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.73754 | + | 0.992689i | −0.356149 | + | 0.0456922i | ||||
\(473\) | −21.8068 | −1.00268 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 6.29155i | − | 0.288676i | ||||||
\(476\) | 18.7512 | − | 39.9820i | 0.859459 | − | 1.83257i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 13.6681 | − | 8.68643i | 0.625166 | − | 0.397308i | ||||
\(479\) | 28.4575 | 1.30026 | 0.650128 | − | 0.759825i | \(-0.274715\pi\) | ||||
0.650128 | + | 0.759825i | \(0.274715\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.81346 | 0.128283 | ||||||||
\(482\) | 16.7944 | − | 10.6732i | 0.764962 | − | 0.486152i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.46895 | − | 9.52887i | 0.203134 | − | 0.433131i | ||||
\(485\) | 11.6927i | 0.530936i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.9552 | −0.496429 | −0.248214 | − | 0.968705i | \(-0.579844\pi\) | ||||
−0.248214 | + | 0.968705i | \(0.579844\pi\) | |||||||
\(488\) | 23.1329 | − | 2.96784i | 1.04718 | − | 0.134348i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −10.9676 | − | 17.2576i | −0.495466 | − | 0.779617i | ||||
\(491\) | 25.9440i | 1.17084i | 0.810731 | + | 0.585419i | \(0.199070\pi\) | ||||
−0.810731 | + | 0.585419i | \(0.800930\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.959461i | 0.0432120i | ||||||||
\(494\) | −14.6750 | + | 9.32629i | −0.660257 | + | 0.419609i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.36254 | + | 10.0557i | 0.375489 | + | 0.451512i | ||||
\(497\) | −2.38341 | −0.106910 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 20.5554i | − | 0.920184i | −0.887871 | − | 0.460092i | \(-0.847816\pi\) | ||
0.887871 | − | 0.460092i | \(-0.152184\pi\) | |||||||
\(500\) | 1.81075 | + | 0.849224i | 0.0809792 | + | 0.0379785i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.305375 | − | 0.480509i | −0.0136296 | − | 0.0214462i | ||||
\(503\) | 3.22301 | 0.143707 | 0.0718535 | − | 0.997415i | \(-0.477109\pi\) | ||||
0.0718535 | + | 0.997415i | \(0.477109\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.6958 | −0.787452 | ||||||||
\(506\) | 9.59549 | + | 15.0985i | 0.426572 | + | 0.671212i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −17.3976 | + | 37.0959i | −0.771893 | + | 1.64586i | ||||
\(509\) | 2.88647i | 0.127941i | 0.997952 | + | 0.0639703i | \(0.0203763\pi\) | ||||
−0.997952 | + | 0.0639703i | \(0.979624\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.6805 | −0.826376 | ||||||||
\(512\) | 8.45166 | + | 20.9897i | 0.373514 | + | 0.927625i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −31.5130 | + | 20.0272i | −1.38998 | + | 0.883364i | ||||
\(515\) | − | 18.4865i | − | 0.814610i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 25.1325i | − | 1.10533i | ||||||
\(518\) | −5.05886 | − | 7.96014i | −0.222274 | − | 0.349749i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.703365 | − | 5.48240i | −0.0308446 | − | 0.240419i | ||||
\(521\) | 13.3049 | 0.582898 | 0.291449 | − | 0.956586i | \(-0.405863\pi\) | ||||
0.291449 | + | 0.956586i | \(0.405863\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 34.2889i | − | 1.49935i | −0.661806 | − | 0.749675i | \(-0.730210\pi\) | ||
0.661806 | − | 0.749675i | \(-0.269790\pi\) | |||||||
\(524\) | 24.0650 | + | 11.2863i | 1.05129 | + | 0.493042i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.53858 | + | 2.24885i | −0.154289 | + | 0.0980547i | ||||
\(527\) | −15.5849 | −0.678888 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.88960 | 0.212591 | ||||||||
\(530\) | −3.61963 | + | 2.30036i | −0.157227 | + | 0.0999215i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 52.7739 | + | 24.7504i | 2.28804 | + | 1.07307i | ||||
\(533\) | − | 16.6852i | − | 0.722715i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.66810 | 0.374755 | ||||||||
\(536\) | 33.7137 | − | 4.32530i | 1.45621 | − | 0.186825i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9.50412 | − | 14.9548i | −0.409752 | − | 0.644746i | ||||
\(539\) | − | 34.6335i | − | 1.49177i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 15.5478i | − | 0.668453i | −0.942493 | − | 0.334226i | \(-0.891525\pi\) | ||
0.942493 | − | 0.334226i | \(-0.108475\pi\) | |||||||
\(542\) | −19.1728 | + | 12.1848i | −0.823544 | + | 0.523382i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −25.6707 | − | 8.24951i | −1.10062 | − | 0.353695i | ||||
\(545\) | −3.37816 | −0.144705 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 5.65869i | − | 0.241948i | −0.992656 | − | 0.120974i | \(-0.961398\pi\) | ||
0.992656 | − | 0.120974i | \(-0.0386018\pi\) | |||||||
\(548\) | −4.46907 | + | 9.52913i | −0.190909 | + | 0.407064i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.81696 | + | 2.85900i | 0.0774755 | + | 0.121908i | ||||
\(551\) | −1.26643 | −0.0539518 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.66281 | −0.283332 | ||||||||
\(554\) | −14.8528 | − | 23.3710i | −0.631036 | − | 0.992937i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 41.6293 | + | 19.5237i | 1.76548 | + | 0.827991i | ||||
\(557\) | − | 5.26159i | − | 0.222941i | −0.993768 | − | 0.111470i | \(-0.964444\pi\) | ||
0.993768 | − | 0.111470i | \(-0.0355560\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.7909 | 0.752475 | ||||||||
\(560\) | −14.2467 | + | 11.8479i | −0.602032 | + | 0.500665i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.17725 | − | 3.29027i | 0.218389 | − | 0.138792i | ||||
\(563\) | − | 0.523609i | − | 0.0220675i | −0.999939 | − | 0.0110337i | \(-0.996488\pi\) | ||
0.999939 | − | 0.0110337i | \(-0.00351222\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.0736i | 0.465869i | ||||||||
\(566\) | −10.2218 | − | 16.0840i | −0.429653 | − | 0.676060i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.185185 | + | 1.44343i | 0.00777019 | + | 0.0605650i | ||||
\(569\) | −10.8202 | −0.453605 | −0.226803 | − | 0.973941i | \(-0.572827\pi\) | ||||
−0.226803 | + | 0.973941i | \(0.572827\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 45.7061i | 1.91274i | 0.292156 | + | 0.956371i | \(0.405628\pi\) | ||||
−0.292156 | + | 0.956371i | \(0.594372\pi\) | |||||||
\(572\) | 3.97519 | − | 8.47607i | 0.166211 | − | 0.354402i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −47.2075 | + | 30.0015i | −1.97040 | + | 1.25224i | ||||
\(575\) | 5.28106 | 0.220235 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.5983 | −0.774259 | −0.387129 | − | 0.922025i | \(-0.626533\pi\) | ||||
−0.387129 | + | 0.922025i | \(0.626533\pi\) | |||||||
\(578\) | 6.82721 | − | 4.33886i | 0.283974 | − | 0.180473i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.170941 | − | 0.364487i | 0.00709793 | − | 0.0151345i | ||||
\(581\) | 35.5069i | 1.47307i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.26410 | −0.300848 | ||||||||
\(584\) | 1.45143 | + | 11.3132i | 0.0600606 | + | 0.468144i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.5123 | + | 21.2616i | 0.558186 | + | 0.878309i | ||||
\(587\) | 32.9752i | 1.36103i | 0.732732 | + | 0.680517i | \(0.238245\pi\) | ||||
−0.732732 | + | 0.680517i | \(0.761755\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 20.5711i | − | 0.847617i | ||||||
\(590\) | −3.29193 | + | 2.09210i | −0.135527 | + | 0.0861306i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.42773 | + | 3.68221i | −0.181979 | + | 0.151338i | ||||
\(593\) | −42.6200 | −1.75019 | −0.875097 | − | 0.483948i | \(-0.839202\pi\) | ||||
−0.875097 | + | 0.483948i | \(0.839202\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 22.0804i | − | 0.905207i | ||||||
\(596\) | −10.5000 | − | 4.92440i | −0.430097 | − | 0.201711i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.82838 | − | 12.3180i | −0.320126 | − | 0.503720i | ||||
\(599\) | −26.0947 | −1.06620 | −0.533101 | − | 0.846052i | \(-0.678973\pi\) | ||||
−0.533101 | + | 0.846052i | \(0.678973\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.04009 | 0.327962 | 0.163981 | − | 0.986463i | \(-0.447566\pi\) | ||||
0.163981 | + | 0.986463i | \(0.447566\pi\) | |||||||
\(602\) | −31.9897 | − | 50.3359i | −1.30380 | − | 2.05154i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 15.5344 | − | 33.1230i | 0.632084 | − | 1.34776i | ||||
\(605\) | − | 5.26239i | − | 0.213946i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.65218 | 0.310593 | 0.155296 | − | 0.987868i | \(-0.450367\pi\) | ||||
0.155296 | + | 0.987868i | \(0.450367\pi\) | |||||||
\(608\) | 10.8889 | − | 33.8838i | 0.441601 | − | 1.37417i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.84190 | − | 6.25477i | 0.398487 | − | 0.253248i | ||||
\(611\) | 20.5041i | 0.829506i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 18.3475i | − | 0.741047i | −0.928823 | − | 0.370524i | \(-0.879178\pi\) | ||
0.928823 | − | 0.370524i | \(-0.120822\pi\) | |||||||
\(614\) | −15.4742 | − | 24.3488i | −0.624489 | − | 0.982636i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −31.1292 | + | 3.99372i | −1.25423 | + | 0.160912i | ||||
\(617\) | −8.16298 | −0.328629 | −0.164315 | − | 0.986408i | \(-0.552541\pi\) | ||||
−0.164315 | + | 0.986408i | \(0.552541\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 40.3555i | − | 1.62202i | −0.585030 | − | 0.811012i | \(-0.698917\pi\) | ||
0.585030 | − | 0.811012i | \(-0.301083\pi\) | |||||||
\(620\) | 5.92050 | + | 2.77665i | 0.237773 | + | 0.111513i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −23.7347 | + | 15.0840i | −0.951673 | + | 0.604811i | ||||
\(623\) | −42.1725 | −1.68961 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −29.3747 | + | 18.6683i | −1.17405 | + | 0.746136i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 22.6640 | + | 10.6292i | 0.904390 | + | 0.424150i | ||||
\(629\) | − | 6.86237i | − | 0.273621i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.21565 | 0.207632 | 0.103816 | − | 0.994597i | \(-0.466895\pi\) | ||||
0.103816 | + | 0.994597i | \(0.466895\pi\) | |||||||
\(632\) | 0.517685 | + | 4.03511i | 0.0205924 | + | 0.160508i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14.6589 | + | 23.0658i | 0.582178 | + | 0.916059i | ||||
\(635\) | 20.4865i | 0.812980i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.2554i | 1.11952i | ||||||||
\(638\) | 0.575489 | − | 0.365737i | 0.0227838 | − | 0.0144797i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 8.28221 | + | 7.70746i | 0.327383 | + | 0.304664i | ||||
\(641\) | 14.1597 | 0.559275 | 0.279637 | − | 0.960106i | \(-0.409786\pi\) | ||||
0.279637 | + | 0.960106i | \(0.409786\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 11.7095i | − | 0.461778i | −0.972980 | − | 0.230889i | \(-0.925837\pi\) | ||
0.972980 | − | 0.230889i | \(-0.0741634\pi\) | |||||||
\(644\) | −20.7752 | + | 44.2978i | −0.818659 | + | 1.74558i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 22.7480 | + | 35.7940i | 0.895006 | + | 1.40830i | ||||
\(647\) | −2.33183 | −0.0916738 | −0.0458369 | − | 0.998949i | \(-0.514595\pi\) | ||||
−0.0458369 | + | 0.998949i | \(0.514595\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.60646 | −0.259326 | ||||||||
\(650\) | −1.48235 | − | 2.33248i | −0.0581426 | − | 0.0914876i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.8198 | − | 6.01238i | −0.502064 | − | 0.235463i | ||||
\(653\) | − | 16.7826i | − | 0.656755i | −0.944547 | − | 0.328377i | \(-0.893498\pi\) | ||
0.944547 | − | 0.328377i | \(-0.106502\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.2901 | 0.519286 | ||||||||
\(656\) | 21.8373 | + | 26.2586i | 0.852603 | + | 1.02522i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 58.0124 | − | 36.8683i | 2.26156 | − | 1.43727i | ||||
\(659\) | 47.5355i | 1.85172i | 0.377865 | + | 0.925861i | \(0.376658\pi\) | ||||
−0.377865 | + | 0.925861i | \(0.623342\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 15.1189i | − | 0.588057i | −0.955797 | − | 0.294028i | \(-0.905004\pi\) | ||
0.955797 | − | 0.294028i | \(-0.0949960\pi\) | |||||||
\(662\) | 4.48597 | + | 7.05869i | 0.174352 | + | 0.274344i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 21.5036 | − | 2.75880i | 0.834500 | − | 0.107062i | ||||
\(665\) | 29.1447 | 1.13018 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1.06303i | − | 0.0411606i | ||||||
\(668\) | 19.8880 | − | 42.4060i | 0.769489 | − | 1.64074i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 14.3435 | − | 9.11563i | 0.554137 | − | 0.352168i | ||||
\(671\) | 19.7513 | 0.762492 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.0868 | −1.12121 | −0.560607 | − | 0.828082i | \(-0.689432\pi\) | ||||
−0.560607 | + | 0.828082i | \(0.689432\pi\) | |||||||
\(674\) | 38.0846 | − | 24.2037i | 1.46696 | − | 0.932290i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.79679 | − | 16.6246i | 0.299877 | − | 0.639409i | ||||
\(677\) | − | 25.6431i | − | 0.985545i | −0.870158 | − | 0.492772i | \(-0.835984\pi\) | ||
0.870158 | − | 0.492772i | \(-0.164016\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −54.1646 | −2.07865 | ||||||||
\(680\) | −13.3722 | + | 1.71559i | −0.512802 | + | 0.0657900i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.94081 | + | 9.34789i | 0.227485 | + | 0.357949i | ||||
\(683\) | 21.0523i | 0.805542i | 0.915301 | + | 0.402771i | \(0.131953\pi\) | ||||
−0.915301 | + | 0.402771i | \(0.868047\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.26253i | 0.201071i | ||||||||
\(686\) | 41.2399 | − | 26.2089i | 1.57455 | − | 1.00066i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −27.9987 | + | 23.2845i | −1.06744 | + | 0.887712i | ||||
\(689\) | 5.92634 | 0.225776 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 22.9903i | − | 0.874594i | −0.899317 | − | 0.437297i | \(-0.855936\pi\) | ||
0.899317 | − | 0.437297i | \(-0.144064\pi\) | |||||||
\(692\) | 10.8556 | + | 5.09117i | 0.412668 | + | 0.193537i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.9639 | + | 29.8397i | 0.719858 | + | 1.13270i | ||||
\(695\) | 22.9901 | 0.872063 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −40.6971 | −1.54151 | ||||||||
\(698\) | −4.72176 | − | 7.42971i | −0.178721 | − | 0.281219i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.93391 | + | 8.38805i | −0.148688 | + | 0.317038i | ||||
\(701\) | − | 42.7645i | − | 1.61519i | −0.589735 | − | 0.807597i | \(-0.700768\pi\) | ||
0.589735 | − | 0.807597i | \(-0.299232\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.05791 | 0.341626 | ||||||||
\(704\) | 4.83733 | + | 18.5420i | 0.182314 | + | 0.698830i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.07716 | − | 4.49771i | 0.266352 | − | 0.169273i | ||||
\(707\) | − | 81.9733i | − | 3.08292i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.5449i | 1.07203i | 0.844209 | + | 0.536014i | \(0.180070\pi\) | ||||
−0.844209 | + | 0.536014i | \(0.819930\pi\) | |||||||
\(710\) | 0.390280 | + | 0.614107i | 0.0146469 | + | 0.0230470i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.27671 | + | 25.5404i | 0.122800 | + | 0.957166i | ||||
\(713\) | 17.2672 | 0.646660 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 4.68097i | − | 0.175058i | ||||||
\(716\) | 32.6938 | + | 15.3331i | 1.22182 | + | 0.573024i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 34.0088 | − | 21.6134i | 1.26920 | − | 0.806606i | ||||
\(719\) | −9.39342 | −0.350315 | −0.175158 | − | 0.984540i | \(-0.556044\pi\) | ||||
−0.175158 | + | 0.984540i | \(0.556044\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 85.6359 | 3.18925 | ||||||||
\(722\) | −24.5681 | + | 15.6136i | −0.914329 | + | 0.581078i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.56268 | + | 4.48480i | 0.355394 | + | 0.166676i | ||||
\(725\) | − | 0.201291i | − | 0.00747574i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.5974 | 0.578476 | 0.289238 | − | 0.957257i | \(-0.406598\pi\) | ||||
0.289238 | + | 0.957257i | \(0.406598\pi\) | |||||||
\(728\) | 25.3964 | − | 3.25824i | 0.941254 | − | 0.120758i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.05891 | + | 4.81320i | 0.113215 | + | 0.178145i | ||||
\(731\) | − | 43.3942i | − | 1.60499i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 38.0264i | − | 1.40454i | −0.711912 | − | 0.702269i | \(-0.752170\pi\) | ||
0.711912 | − | 0.702269i | \(-0.247830\pi\) | |||||||
\(734\) | −21.3101 | + | 13.5431i | −0.786571 | + | 0.499885i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 28.4417 | + | 9.13998i | 1.04837 | + | 0.336904i | ||||
\(737\) | 28.7854 | 1.06032 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.5308i | 0.571309i | 0.958333 | + | 0.285654i | \(0.0922109\pi\) | ||||
−0.958333 | + | 0.285654i | \(0.907789\pi\) | |||||||
\(740\) | −1.22262 | + | 2.60693i | −0.0449445 | + | 0.0958325i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.6561 | − | 16.7674i | −0.391198 | − | 0.615552i | ||||
\(743\) | −28.8169 | −1.05719 | −0.528594 | − | 0.848875i | \(-0.677281\pi\) | ||||
−0.528594 | + | 0.848875i | \(0.677281\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.79871 | −0.212448 | ||||||||
\(746\) | 5.35864 | + | 8.43184i | 0.196194 | + | 0.308712i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −20.6742 | − | 9.69599i | −0.755923 | − | 0.354520i | ||||
\(749\) | 40.1538i | 1.46719i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.22432 | −0.0811664 | −0.0405832 | − | 0.999176i | \(-0.512922\pi\) | ||||
−0.0405832 | + | 0.999176i | \(0.512922\pi\) | |||||||
\(752\) | −26.8354 | − | 32.2687i | −0.978588 | − | 1.17672i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.469507 | + | 0.298383i | −0.0170984 | + | 0.0108665i | ||||
\(755\) | − | 18.2924i | − | 0.665729i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 43.7191i | − | 1.58900i | −0.607265 | − | 0.794499i | \(-0.707733\pi\) | ||
0.607265 | − | 0.794499i | \(-0.292267\pi\) | |||||||
\(758\) | −3.61563 | − | 5.68921i | −0.131326 | − | 0.206642i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.26448 | − | 17.6505i | −0.0821413 | − | 0.640252i | ||||
\(761\) | −4.33761 | −0.157238 | −0.0786192 | − | 0.996905i | \(-0.525051\pi\) | ||||
−0.0786192 | + | 0.996905i | \(0.525051\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 15.6489i | − | 0.566527i | ||||||
\(764\) | 3.81277 | − | 8.12974i | 0.137941 | − | 0.294124i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.40515 | + | 4.07063i | −0.231427 | + | 0.147078i | ||||
\(767\) | 5.38981 | 0.194615 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.7789 | −0.496879 | −0.248439 | − | 0.968647i | \(-0.579918\pi\) | ||||
−0.248439 | + | 0.968647i | \(0.579918\pi\) | |||||||
\(770\) | −13.2439 | + | 8.41683i | −0.477277 | + | 0.303321i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.738306 | + | 1.57425i | −0.0265722 | + | 0.0566584i | ||||
\(773\) | 42.9986i | 1.54655i | 0.634070 | + | 0.773276i | \(0.281383\pi\) | ||||
−0.634070 | + | 0.773276i | \(0.718617\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.26964 | 0.117449 | ||||||||
\(776\) | 4.20846 | + | 32.8030i | 0.151075 | + | 1.17756i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.2495 | − | 38.1567i | −0.869388 | − | 1.36799i | ||||
\(779\) | − | 53.7178i | − | 1.92464i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.23243i | 0.0440997i | ||||||||
\(782\) | −30.0451 | + | 19.0944i | −1.07441 | + | 0.682814i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −36.9803 | − | 44.4674i | −1.32072 | − | 1.58812i | ||||
\(785\) | 12.5163 | 0.446727 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.6437i | 1.34185i | 0.741525 | + | 0.670926i | \(0.234103\pi\) | ||||
−0.741525 | + | 0.670926i | \(0.765897\pi\) | |||||||
\(788\) | 28.6342 | + | 13.4292i | 1.02005 | + | 0.478394i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.09103 | + | 1.71674i | 0.0388170 | + | 0.0610787i | ||||
\(791\) | −51.2968 | −1.82390 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.1139 | −0.572222 | ||||||||
\(794\) | −14.3550 | − | 22.5876i | −0.509439 | − | 0.801605i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.56893 | − | 20.4033i | 0.339162 | − | 0.723175i | ||||
\(797\) | 2.69524i | 0.0954704i | 0.998860 | + | 0.0477352i | \(0.0152004\pi\) | ||||
−0.998860 | + | 0.0477352i | \(0.984800\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 50.0120 | 1.76930 | ||||||||
\(800\) | 5.38560 | + | 1.73071i | 0.190410 | + | 0.0611898i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.60136 | − | 1.65323i | 0.0918571 | − | 0.0583774i | ||||
\(803\) | 9.65943i | 0.340874i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.4638i | 0.862235i | ||||||||
\(806\) | −4.84675 | − | 7.62638i | −0.170719 | − | 0.268628i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −49.6444 | + | 6.36913i | −1.74648 | + | 0.224065i | ||||
\(809\) | 29.8268 | 1.04866 | 0.524328 | − | 0.851517i | \(-0.324317\pi\) | ||||
0.524328 | + | 0.851517i | \(0.324317\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.7273i | 0.622489i | 0.950330 | + | 0.311245i | \(0.100746\pi\) | ||||
−0.950330 | + | 0.311245i | \(0.899254\pi\) | |||||||
\(812\) | 1.68844 | + | 0.791859i | 0.0592525 | + | 0.0277888i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.11608 | + | 2.61587i | −0.144269 | + | 0.0916862i | ||||
\(815\) | −7.07985 | −0.247996 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 57.2777 | 2.00389 | ||||||||
\(818\) | −4.51503 | + | 2.86941i | −0.157864 | + | 0.100327i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 15.4603 | + | 7.25074i | 0.539898 | + | 0.253207i | ||||
\(821\) | 17.2808i | 0.603105i | 0.953450 | + | 0.301552i | \(0.0975048\pi\) | ||||
−0.953450 | + | 0.301552i | \(0.902495\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.83186 | −0.133570 | −0.0667852 | − | 0.997767i | \(-0.521274\pi\) | ||||
−0.0667852 | + | 0.997767i | \(0.521274\pi\) | |||||||
\(824\) | −6.65371 | − | 51.8625i | −0.231793 | − | 1.80672i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.69138 | − | 15.2494i | −0.337206 | − | 0.530595i | ||||
\(827\) | 11.8492i | 0.412036i | 0.978548 | + | 0.206018i | \(0.0660506\pi\) | ||||
−0.978548 | + | 0.206018i | \(0.933949\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 0.601935i | − | 0.0209061i | −0.999945 | − | 0.0104530i | \(-0.996673\pi\) | ||
0.999945 | − | 0.0104530i | \(-0.00332736\pi\) | |||||||
\(830\) | 9.14869 | − | 5.81421i | 0.317555 | − | 0.201814i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.94649 | − | 15.1273i | −0.136820 | − | 0.524446i | ||||
\(833\) | 68.9184 | 2.38788 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 23.4190i | − | 0.810448i | ||||||
\(836\) | 12.7981 | − | 27.2887i | 0.442632 | − | 0.943798i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −21.2757 | − | 33.4774i | −0.734958 | − | 1.15646i | ||||
\(839\) | −1.99004 | −0.0687039 | −0.0343520 | − | 0.999410i | \(-0.510937\pi\) | ||||
−0.0343520 | + | 0.999410i | \(0.510937\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9595 | 0.998603 | ||||||||
\(842\) | −21.5213 | − | 33.8639i | −0.741674 | − | 1.16703i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.4663 | − | 4.90860i | −0.360266 | − | 0.168961i | ||||
\(845\) | − | 9.18108i | − | 0.315839i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.3773 | 0.837613 | ||||||||
\(848\) | −9.32668 | + | 7.75631i | −0.320280 | + | 0.266353i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.68921 | + | 3.61563i | −0.195138 | + | 0.124015i | ||||
\(851\) | 7.60311i | 0.260631i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47.3134i | 1.61998i | 0.586444 | + | 0.809989i | \(0.300527\pi\) | ||||
−0.586444 | + | 0.809989i | \(0.699473\pi\) | |||||||
\(854\) | 28.9743 | + | 45.5912i | 0.991481 | + | 1.56010i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 24.3178 | − | 3.11985i | 0.831164 | − | 0.106634i | ||||
\(857\) | 40.3552 | 1.37851 | 0.689254 | − | 0.724520i | \(-0.257938\pi\) | ||||
0.689254 | + | 0.724520i | \(0.257938\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 41.0795i | − | 1.40162i | −0.713350 | − | 0.700808i | \(-0.752823\pi\) | ||
0.713350 | − | 0.700808i | \(-0.247177\pi\) | |||||||
\(860\) | −7.73125 | + | 16.4849i | −0.263633 | + | 0.562130i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.1716 | − | 11.5485i | 0.618927 | − | 0.393343i | ||||
\(863\) | −23.4889 | −0.799570 | −0.399785 | − | 0.916609i | \(-0.630915\pi\) | ||||
−0.399785 | + | 0.916609i | \(0.630915\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.99508 | 0.203839 | ||||||||
\(866\) | 25.2450 | − | 16.0438i | 0.857860 | − | 0.545191i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12.8625 | + | 27.4259i | −0.436580 | + | 0.930895i | ||||
\(869\) | 3.44525i | 0.116872i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.4843 | −0.795734 | ||||||||
\(872\) | −9.47721 | + | 1.21588i | −0.320939 | + | 0.0411749i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −25.2034 | − | 39.6577i | −0.852518 | − | 1.34144i | ||||
\(875\) | 4.63236i | 0.156602i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 13.7849i | − | 0.465482i | −0.972539 | − | 0.232741i | \(-0.925231\pi\) | ||
0.972539 | − | 0.232741i | \(-0.0747694\pi\) | |||||||
\(878\) | 7.81469 | − | 4.96643i | 0.263733 | − | 0.167609i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.12639 | + | 7.36676i | 0.206520 | + | 0.248333i | ||||
\(881\) | −5.93246 | −0.199870 | −0.0999348 | − | 0.994994i | \(-0.531863\pi\) | ||||
−0.0999348 | + | 0.994994i | \(0.531863\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.1403i | 0.812384i | 0.913788 | + | 0.406192i | \(0.133144\pi\) | ||||
−0.913788 | + | 0.406192i | \(0.866856\pi\) | |||||||
\(884\) | 16.8668 | + | 7.91037i | 0.567292 | + | 0.266054i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18.3600 | − | 28.8895i | −0.616815 | − | 0.970561i | ||||
\(887\) | 19.5964 | 0.657984 | 0.328992 | − | 0.944333i | \(-0.393291\pi\) | ||||
0.328992 | + | 0.944333i | \(0.393291\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −94.9006 | −3.18286 | ||||||||
\(890\) | 6.90570 | + | 10.8661i | 0.231480 | + | 0.364234i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.90037 | − | 16.8455i | 0.264524 | − | 0.564029i | ||||
\(893\) | 66.0128i | 2.20903i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.0554 | 0.603525 | ||||||||
\(896\) | −35.7037 | + | 38.3662i | −1.19278 | + | 1.28172i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.86298 | + | 1.18397i | −0.0621684 | + | 0.0395095i | ||||
\(899\) | − | 0.658147i | − | 0.0219504i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 14.4551i | − | 0.481568i | ||||||
\(902\) | 15.5134 | + | 24.4103i | 0.516539 | + | 0.812776i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.98564 | + | 31.0662i | 0.132560 | + | 1.03325i | ||||
\(905\) | 5.28106 | 0.175548 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.3272i | 0.807770i | 0.914810 | + | 0.403885i | \(0.132340\pi\) | ||||
−0.914810 | + | 0.403885i | \(0.867660\pi\) | |||||||
\(908\) | 4.69761 | + | 2.20313i | 0.155896 | + | 0.0731135i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 10.8049 | − | 6.86678i | 0.358179 | − | 0.227632i | ||||
\(911\) | −39.2591 | −1.30071 | −0.650357 | − | 0.759629i | \(-0.725381\pi\) | ||||
−0.650357 | + | 0.759629i | \(0.725381\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.3601 | 0.607632 | ||||||||
\(914\) | −10.9444 | + | 6.95545i | −0.362009 | + | 0.230066i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −46.0061 | − | 21.5764i | −1.52009 | − | 0.712905i | ||||
\(917\) | 61.5644i | 2.03304i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.58169 | −0.217110 | −0.108555 | − | 0.994090i | \(-0.534622\pi\) | ||||
−0.108555 | + | 0.994090i | \(0.534622\pi\) | |||||||
\(920\) | 14.8157 | − | 1.90078i | 0.488458 | − | 0.0626668i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.38670 | + | 13.1965i | 0.276201 | + | 0.434604i | ||||
\(923\) | − | 1.00546i | − | 0.0330952i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.43969i | 0.0473368i | ||||||||
\(926\) | −41.1768 | + | 26.1689i | −1.35315 | + | 0.859962i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.348376 | − | 1.08407i | 0.0114360 | − | 0.0355863i | ||||
\(929\) | −15.0642 | −0.494242 | −0.247121 | − | 0.968985i | \(-0.579484\pi\) | ||||
−0.247121 | + | 0.968985i | \(0.579484\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 90.9681i | 2.98136i | ||||||||
\(932\) | −23.7299 | + | 50.5978i | −0.777297 | + | 1.65739i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −29.4691 | − | 46.3697i | −0.964257 | − | 1.51726i | ||||
\(935\) | −11.4175 | −0.373391 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 54.0670 | 1.76629 | 0.883146 | − | 0.469099i | \(-0.155421\pi\) | ||||
0.883146 | + | 0.469099i | \(0.155421\pi\) | |||||||
\(938\) | 42.2269 | + | 66.4442i | 1.37876 | + | 2.16948i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −18.9989 | − | 8.91030i | −0.619676 | − | 0.290622i | ||||
\(941\) | 16.2573i | 0.529973i | 0.964252 | + | 0.264986i | \(0.0853674\pi\) | ||||
−0.964252 | + | 0.264986i | \(0.914633\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 45.0901 | 1.46834 | ||||||||
\(944\) | −8.48230 | + | 7.05410i | −0.276076 | + | 0.229591i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −26.0280 | + | 16.5414i | −0.846244 | + | 0.537809i | ||||
\(947\) | − | 7.94302i | − | 0.258113i | −0.991637 | − | 0.129057i | \(-0.958805\pi\) | ||
0.991637 | − | 0.129057i | \(-0.0411949\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 7.88055i | − | 0.255813i | ||||||
\(950\) | −4.77242 | − | 7.50942i | −0.154838 | − | 0.243638i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.94724 | − | 61.9450i | −0.257572 | − | 2.00765i | ||||
\(953\) | −10.5096 | −0.340439 | −0.170219 | − | 0.985406i | \(-0.554448\pi\) | ||||
−0.170219 | + | 0.985406i | \(0.554448\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 4.48971i | − | 0.145283i | ||||||
\(956\) | 9.72486 | − | 20.7358i | 0.314524 | − | 0.670642i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 33.9661 | − | 21.5862i | 1.09739 | − | 0.697420i | ||||
\(959\) | −24.3779 | −0.787205 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.3095 | −0.655144 | ||||||||
\(962\) | 3.35806 | − | 2.13413i | 0.108268 | − | 0.0688071i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.9492 | − | 25.4785i | 0.384857 | − | 0.820607i | ||||
\(965\) | 0.869389i | 0.0279866i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.4035 | −0.559659 | −0.279830 | − | 0.960050i | \(-0.590278\pi\) | ||||
−0.279830 | + | 0.960050i | \(0.590278\pi\) | |||||||
\(968\) | −1.89406 | − | 14.7633i | −0.0608773 | − | 0.474510i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.86939 | + | 13.9560i | 0.284779 | + | 0.448101i | ||||
\(971\) | 12.4994i | 0.401125i | 0.979681 | + | 0.200563i | \(0.0642770\pi\) | ||||
−0.979681 | + | 0.200563i | \(0.935723\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 106.498i | 3.41418i | ||||||||
\(974\) | −13.0758 | + | 8.31001i | −0.418977 | + | 0.266270i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 25.3596 | − | 21.0897i | 0.811740 | − | 0.675064i | ||||
\(977\) | 14.2994 | 0.457478 | 0.228739 | − | 0.973488i | \(-0.426540\pi\) | ||||
0.228739 | + | 0.973488i | \(0.426540\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.8068i | 0.696950i | ||||||||
\(980\) | −26.1812 | − | 12.2787i | −0.836328 | − | 0.392230i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 19.6797 | + | 30.9661i | 0.628004 | + | 0.988167i | ||||
\(983\) | −43.3572 | −1.38288 | −0.691441 | − | 0.722433i | \(-0.743024\pi\) | ||||
−0.691441 | + | 0.722433i | \(0.743024\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.8134 | 0.503858 | ||||||||
\(986\) | 0.727793 | + | 1.14519i | 0.0231776 | + | 0.0364701i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.4412 | + | 22.2632i | −0.332179 | + | 0.708286i | ||||
\(989\) | 48.0782i | 1.52880i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.0947 | −0.415967 | −0.207983 | − | 0.978132i | \(-0.566690\pi\) | ||||
−0.207983 | + | 0.978132i | \(0.566690\pi\) | |||||||
\(992\) | 17.6089 | + | 5.65879i | 0.559085 | + | 0.179667i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.84477 | + | 1.80792i | −0.0902305 | + | 0.0573436i | ||||
\(995\) | − | 11.2679i | − | 0.357215i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 53.5961i | 1.69741i | 0.528870 | + | 0.848703i | \(0.322616\pi\) | ||||
−0.528870 | + | 0.848703i | \(0.677384\pi\) | |||||||
\(998\) | −15.5921 | − | 24.5343i | −0.493560 | − | 0.776619i | ||||
\(999\) | 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 | 1080.2.k.d.541.17 | yes | 20 | |
3.2 | odd | 2 | inner | 1080.2.k.d.541.4 | yes | 20 | |
4.3 | odd | 2 | 4320.2.k.d.2161.2 | 20 | |||
8.3 | odd | 2 | 4320.2.k.d.2161.11 | 20 | |||
8.5 | even | 2 | inner | 1080.2.k.d.541.18 | yes | 20 | |
12.11 | even | 2 | 4320.2.k.d.2161.12 | 20 | |||
24.5 | odd | 2 | inner | 1080.2.k.d.541.3 | ✓ | 20 | |
24.11 | even | 2 | 4320.2.k.d.2161.1 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.2.k.d.541.3 | ✓ | 20 | 24.5 | odd | 2 | inner | |
1080.2.k.d.541.4 | yes | 20 | 3.2 | odd | 2 | inner | |
1080.2.k.d.541.17 | yes | 20 | 1.1 | even | 1 | trivial | |
1080.2.k.d.541.18 | yes | 20 | 8.5 | even | 2 | inner | |
4320.2.k.d.2161.1 | 20 | 24.11 | even | 2 | |||
4320.2.k.d.2161.2 | 20 | 4.3 | odd | 2 | |||
4320.2.k.d.2161.11 | 20 | 8.3 | odd | 2 | |||
4320.2.k.d.2161.12 | 20 | 12.11 | even | 2 |