Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [294,3,Mod(263,294)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(294, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("294.263");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 294 = 2 \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 294.h (of order \(6\), 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: | \(8.01091977219\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 275.3 | ||
Root | \(0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 294.275 |
Dual form | 294.3.h.e.263.3 |
$q$-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 \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(199\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22474 | + | 0.707107i | 0.612372 | + | 0.353553i | ||||
\(3\) | −2.28024 | − | 1.94949i | −0.760080 | − | 0.649830i | ||||
\(4\) | 1.00000 | + | 1.73205i | 0.250000 | + | 0.433013i | ||||
\(5\) | −3.46410 | − | 2.00000i | −0.692820 | − | 0.400000i | 0.111847 | − | 0.993725i | \(-0.464323\pi\) |
−0.804668 | + | 0.593725i | \(0.797657\pi\) | |||||||
\(6\) | −1.41421 | − | 4.00000i | −0.235702 | − | 0.666667i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 1.39898 | + | 8.89060i | 0.155442 | + | 0.987845i | ||||
\(10\) | −2.82843 | − | 4.89898i | −0.282843 | − | 0.489898i | ||||
\(11\) | −8.57321 | + | 4.94975i | −0.779383 | + | 0.449977i | −0.836212 | − | 0.548407i | \(-0.815235\pi\) |
0.0568285 | + | 0.998384i | \(0.481901\pi\) | |||||||
\(12\) | 1.09638 | − | 5.89898i | 0.0913647 | − | 0.491582i | ||||
\(13\) | 12.7279 | 0.979071 | 0.489535 | − | 0.871983i | \(-0.337166\pi\) | ||||
0.489535 | + | 0.871983i | \(0.337166\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.00000 | + | 11.3137i | 0.266667 | + | 0.754247i | ||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | −27.7128 | + | 16.0000i | −1.63017 | + | 0.941176i | −0.646125 | + | 0.763232i | \(0.723612\pi\) |
−0.984040 | + | 0.177945i | \(0.943055\pi\) | |||||||
\(18\) | −4.57321 | + | 11.8780i | −0.254067 | + | 0.659886i | ||||
\(19\) | −14.1421 | + | 24.4949i | −0.744323 | + | 1.28921i | 0.206188 | + | 0.978512i | \(0.433894\pi\) |
−0.950510 | + | 0.310693i | \(0.899439\pi\) | |||||||
\(20\) | − | 8.00000i | − | 0.400000i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −14.0000 | −0.636364 | ||||||||
\(23\) | −1.22474 | − | 0.707107i | −0.0532498 | − | 0.0307438i | 0.473139 | − | 0.880988i | \(-0.343121\pi\) |
−0.526389 | + | 0.850244i | \(0.676454\pi\) | |||||||
\(24\) | 5.51399 | − | 6.44949i | 0.229750 | − | 0.268729i | ||||
\(25\) | −4.50000 | − | 7.79423i | −0.180000 | − | 0.311769i | ||||
\(26\) | 15.5885 | + | 9.00000i | 0.599556 | + | 0.346154i | ||||
\(27\) | 14.1421 | − | 23.0000i | 0.523783 | − | 0.851852i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 56.5685i | 1.95064i | 0.220797 | + | 0.975320i | \(0.429134\pi\) | ||||
−0.220797 | + | 0.975320i | \(0.570866\pi\) | |||||||
\(30\) | −3.10102 | + | 16.6848i | −0.103367 | + | 0.556161i | ||||
\(31\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(32\) | −4.89898 | + | 2.82843i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 29.1985 | + | 5.42679i | 0.884802 | + | 0.164448i | ||||
\(34\) | −45.2548 | −1.33102 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −14.0000 | + | 11.3137i | −0.388889 | + | 0.314270i | ||||
\(37\) | 25.0000 | − | 43.3013i | 0.675676 | − | 1.17030i | −0.300595 | − | 0.953752i | \(-0.597185\pi\) |
0.976271 | − | 0.216553i | \(-0.0694813\pi\) | |||||||
\(38\) | −34.6410 | + | 20.0000i | −0.911606 | + | 0.526316i | ||||
\(39\) | −29.0227 | − | 24.8130i | −0.744172 | − | 0.636230i | ||||
\(40\) | 5.65685 | − | 9.79796i | 0.141421 | − | 0.244949i | ||||
\(41\) | 16.0000i | 0.390244i | 0.980779 | + | 0.195122i | \(0.0625103\pi\) | ||||
−0.980779 | + | 0.195122i | \(0.937490\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −52.0000 | −1.20930 | −0.604651 | − | 0.796490i | \(-0.706687\pi\) | ||||
−0.604651 | + | 0.796490i | \(0.706687\pi\) | |||||||
\(44\) | −17.1464 | − | 9.89949i | −0.389692 | − | 0.224989i | ||||
\(45\) | 12.9350 | − | 33.5959i | 0.287445 | − | 0.746576i | ||||
\(46\) | −1.00000 | − | 1.73205i | −0.0217391 | − | 0.0376533i | ||||
\(47\) | −29.4449 | − | 17.0000i | −0.626486 | − | 0.361702i | 0.152904 | − | 0.988241i | \(-0.451138\pi\) |
−0.779390 | + | 0.626539i | \(0.784471\pi\) | |||||||
\(48\) | 11.3137 | − | 4.00000i | 0.235702 | − | 0.0833333i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 12.7279i | − | 0.254558i | ||||||
\(51\) | 94.3837 | + | 17.5420i | 1.85066 | + | 0.343961i | ||||
\(52\) | 12.7279 | + | 22.0454i | 0.244768 | + | 0.423950i | ||||
\(53\) | 39.1918 | − | 22.6274i | 0.739469 | − | 0.426932i | −0.0824075 | − | 0.996599i | \(-0.526261\pi\) |
0.821876 | + | 0.569666i | \(0.192928\pi\) | |||||||
\(54\) | 33.5840 | − | 18.1691i | 0.621925 | − | 0.336465i | ||||
\(55\) | 39.5980 | 0.719963 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 80.0000 | − | 28.2843i | 1.40351 | − | 0.496215i | ||||
\(58\) | −40.0000 | + | 69.2820i | −0.689655 | + | 1.19452i | ||||
\(59\) | −27.7128 | + | 16.0000i | −0.469709 | + | 0.271186i | −0.716118 | − | 0.697979i | \(-0.754083\pi\) |
0.246409 | + | 0.969166i | \(0.420749\pi\) | |||||||
\(60\) | −15.5959 | + | 18.2419i | −0.259932 | + | 0.304032i | ||||
\(61\) | 16.2635 | − | 28.1691i | 0.266614 | − | 0.461789i | −0.701371 | − | 0.712796i | \(-0.747428\pi\) |
0.967985 | + | 0.251007i | \(0.0807618\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | −44.0908 | − | 25.4558i | −0.678320 | − | 0.391628i | ||||
\(66\) | 31.9233 | + | 27.2929i | 0.483687 | + | 0.413528i | ||||
\(67\) | 6.00000 | + | 10.3923i | 0.0895522 | + | 0.155109i | 0.907322 | − | 0.420437i | \(-0.138123\pi\) |
−0.817770 | + | 0.575546i | \(0.804790\pi\) | |||||||
\(68\) | −55.4256 | − | 32.0000i | −0.815083 | − | 0.470588i | ||||
\(69\) | 1.41421 | + | 4.00000i | 0.0204958 | + | 0.0579710i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 89.0955i | − | 1.25487i | −0.778671 | − | 0.627433i | \(-0.784106\pi\) | ||
0.778671 | − | 0.627433i | \(-0.215894\pi\) | |||||||
\(72\) | −25.1464 | + | 3.95691i | −0.349256 | + | 0.0549571i | ||||
\(73\) | 16.2635 | + | 28.1691i | 0.222787 | + | 0.385879i | 0.955653 | − | 0.294494i | \(-0.0951512\pi\) |
−0.732866 | + | 0.680373i | \(0.761818\pi\) | |||||||
\(74\) | 61.2372 | − | 35.3553i | 0.827530 | − | 0.477775i | ||||
\(75\) | −4.93369 | + | 26.5454i | −0.0657826 | + | 0.353939i | ||||
\(76\) | −56.5685 | −0.744323 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −18.0000 | − | 50.9117i | −0.230769 | − | 0.652714i | ||||
\(79\) | 20.0000 | − | 34.6410i | 0.253165 | − | 0.438494i | −0.711231 | − | 0.702959i | \(-0.751862\pi\) |
0.964395 | + | 0.264465i | \(0.0851953\pi\) | |||||||
\(80\) | 13.8564 | − | 8.00000i | 0.173205 | − | 0.100000i | ||||
\(81\) | −77.0857 | + | 24.8755i | −0.951675 | + | 0.307106i | ||||
\(82\) | −11.3137 | + | 19.5959i | −0.137972 | + | 0.238975i | ||||
\(83\) | 62.0000i | 0.746988i | 0.927633 | + | 0.373494i | \(0.121840\pi\) | ||||
−0.927633 | + | 0.373494i | \(0.878160\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 128.000 | 1.50588 | ||||||||
\(86\) | −63.6867 | − | 36.7696i | −0.740543 | − | 0.427553i | ||||
\(87\) | 110.280 | − | 128.990i | 1.26758 | − | 1.48264i | ||||
\(88\) | −14.0000 | − | 24.2487i | −0.159091 | − | 0.275554i | ||||
\(89\) | −48.4974 | − | 28.0000i | −0.544915 | − | 0.314607i | 0.202154 | − | 0.979354i | \(-0.435206\pi\) |
−0.747068 | + | 0.664747i | \(0.768539\pi\) | |||||||
\(90\) | 39.5980 | − | 32.0000i | 0.439978 | − | 0.355556i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 2.82843i | − | 0.0307438i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −24.0416 | − | 41.6413i | −0.255762 | − | 0.442993i | ||||
\(95\) | 97.9796 | − | 56.5685i | 1.03136 | − | 0.595458i | ||||
\(96\) | 16.6848 | + | 3.10102i | 0.173800 | + | 0.0323023i | ||||
\(97\) | 24.0416 | 0.247852 | 0.123926 | − | 0.992291i | \(-0.460451\pi\) | ||||
0.123926 | + | 0.992291i | \(0.460451\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −56.0000 | − | 69.2965i | −0.565657 | − | 0.699964i | ||||
\(100\) | 9.00000 | − | 15.5885i | 0.0900000 | − | 0.155885i | ||||
\(101\) | 31.1769 | − | 18.0000i | 0.308682 | − | 0.178218i | −0.337654 | − | 0.941270i | \(-0.609633\pi\) |
0.646337 | + | 0.763052i | \(0.276300\pi\) | |||||||
\(102\) | 103.192 | + | 88.2238i | 1.01168 | + | 0.864940i | ||||
\(103\) | −36.7696 | + | 63.6867i | −0.356986 | + | 0.618318i | −0.987456 | − | 0.157896i | \(-0.949529\pi\) |
0.630470 | + | 0.776214i | \(0.282862\pi\) | |||||||
\(104\) | 36.0000i | 0.346154i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 64.0000 | 0.603774 | ||||||||
\(107\) | −126.149 | − | 72.8320i | −1.17896 | − | 0.680673i | −0.223186 | − | 0.974776i | \(-0.571646\pi\) |
−0.955774 | + | 0.294103i | \(0.904979\pi\) | |||||||
\(108\) | 53.9793 | + | 1.49490i | 0.499808 | + | 0.0138416i | ||||
\(109\) | 88.0000 | + | 152.420i | 0.807339 | + | 1.39835i | 0.914700 | + | 0.404133i | \(0.132427\pi\) |
−0.107361 | + | 0.994220i | \(0.534240\pi\) | |||||||
\(110\) | 48.4974 | + | 28.0000i | 0.440886 | + | 0.254545i | ||||
\(111\) | −141.421 | + | 50.0000i | −1.27407 | + | 0.450450i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 16.9706i | − | 0.150182i | −0.997177 | − | 0.0750910i | \(-0.976075\pi\) | ||
0.997177 | − | 0.0750910i | \(-0.0239247\pi\) | |||||||
\(114\) | 117.980 | + | 21.9275i | 1.03491 | + | 0.192347i | ||||
\(115\) | 2.82843 | + | 4.89898i | 0.0245950 | + | 0.0425998i | ||||
\(116\) | −97.9796 | + | 56.5685i | −0.844652 | + | 0.487660i | ||||
\(117\) | 17.8061 | + | 113.159i | 0.152189 | + | 0.967170i | ||||
\(118\) | −45.2548 | −0.383516 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −32.0000 | + | 11.3137i | −0.266667 | + | 0.0942809i | ||||
\(121\) | −11.5000 | + | 19.9186i | −0.0950413 | + | 0.164616i | ||||
\(122\) | 39.8372 | − | 23.0000i | 0.326534 | − | 0.188525i | ||||
\(123\) | 31.1918 | − | 36.4838i | 0.253592 | − | 0.296616i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 136.000i | 1.08800i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −104.000 | −0.818898 | −0.409449 | − | 0.912333i | \(-0.634279\pi\) | ||||
−0.409449 | + | 0.912333i | \(0.634279\pi\) | |||||||
\(128\) | −9.79796 | − | 5.65685i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 118.572 | + | 101.373i | 0.919166 | + | 0.785841i | ||||
\(130\) | −36.0000 | − | 62.3538i | −0.276923 | − | 0.479645i | ||||
\(131\) | −25.9808 | − | 15.0000i | −0.198326 | − | 0.114504i | 0.397548 | − | 0.917581i | \(-0.369861\pi\) |
−0.595875 | + | 0.803077i | \(0.703194\pi\) | |||||||
\(132\) | 19.7990 | + | 56.0000i | 0.149992 | + | 0.424242i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 16.9706i | 0.126646i | ||||||||
\(135\) | −94.9898 | + | 51.3901i | −0.703628 | + | 0.380667i | ||||
\(136\) | −45.2548 | − | 78.3837i | −0.332756 | − | 0.576351i | ||||
\(137\) | 58.7878 | − | 33.9411i | 0.429108 | − | 0.247745i | −0.269859 | − | 0.962900i | \(-0.586977\pi\) |
0.698966 | + | 0.715154i | \(0.253644\pi\) | |||||||
\(138\) | −1.09638 | + | 5.89898i | −0.00794476 | + | 0.0427462i | ||||
\(139\) | 214.960 | 1.54648 | 0.773239 | − | 0.634115i | \(-0.218635\pi\) | ||||
0.773239 | + | 0.634115i | \(0.218635\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 34.0000 | + | 96.1665i | 0.241135 | + | 0.682032i | ||||
\(142\) | 63.0000 | − | 109.119i | 0.443662 | − | 0.768445i | ||||
\(143\) | −109.119 | + | 63.0000i | −0.763071 | + | 0.440559i | ||||
\(144\) | −33.5959 | − | 12.9350i | −0.233305 | − | 0.0898264i | ||||
\(145\) | 113.137 | − | 195.959i | 0.780256 | − | 1.35144i | ||||
\(146\) | 46.0000i | 0.315068i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 100.000 | 0.675676 | ||||||||
\(149\) | 78.3837 | + | 45.2548i | 0.526065 | + | 0.303724i | 0.739413 | − | 0.673253i | \(-0.235103\pi\) |
−0.213348 | + | 0.976976i | \(0.568437\pi\) | |||||||
\(150\) | −24.8130 | + | 29.0227i | −0.165420 | + | 0.193485i | ||||
\(151\) | −76.0000 | − | 131.636i | −0.503311 | − | 0.871761i | −0.999993 | − | 0.00382774i | \(-0.998782\pi\) |
0.496681 | − | 0.867933i | \(-0.334552\pi\) | |||||||
\(152\) | −69.2820 | − | 40.0000i | −0.455803 | − | 0.263158i | ||||
\(153\) | −181.019 | − | 224.000i | −1.18313 | − | 1.46405i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 13.9546 | − | 75.0818i | 0.0894525 | − | 0.481293i | ||||
\(157\) | 85.5599 | + | 148.194i | 0.544968 | + | 0.943912i | 0.998609 | + | 0.0527273i | \(0.0167914\pi\) |
−0.453641 | + | 0.891184i | \(0.649875\pi\) | |||||||
\(158\) | 48.9898 | − | 28.2843i | 0.310062 | − | 0.179014i | ||||
\(159\) | −133.479 | − | 24.8082i | −0.839488 | − | 0.156026i | ||||
\(160\) | 22.6274 | 0.141421 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −112.000 | − | 24.0416i | −0.691358 | − | 0.148405i | ||||
\(163\) | −122.000 | + | 211.310i | −0.748466 | + | 1.29638i | 0.200091 | + | 0.979777i | \(0.435876\pi\) |
−0.948558 | + | 0.316604i | \(0.897457\pi\) | |||||||
\(164\) | −27.7128 | + | 16.0000i | −0.168981 | + | 0.0975610i | ||||
\(165\) | −90.2929 | − | 77.1959i | −0.547229 | − | 0.467854i | ||||
\(166\) | −43.8406 | + | 75.9342i | −0.264100 | + | 0.457435i | ||||
\(167\) | − | 226.000i | − | 1.35329i | −0.736308 | − | 0.676647i | \(-0.763432\pi\) | ||
0.736308 | − | 0.676647i | \(-0.236568\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.00000 | −0.0414201 | ||||||||
\(170\) | 156.767 | + | 90.5097i | 0.922161 | + | 0.532410i | ||||
\(171\) | −237.559 | − | 91.4643i | −1.38923 | − | 0.534879i | ||||
\(172\) | −52.0000 | − | 90.0666i | −0.302326 | − | 0.523643i | ||||
\(173\) | 114.315 | + | 66.0000i | 0.660782 | + | 0.381503i | 0.792575 | − | 0.609774i | \(-0.208740\pi\) |
−0.131793 | + | 0.991277i | \(0.542073\pi\) | |||||||
\(174\) | 226.274 | − | 80.0000i | 1.30043 | − | 0.459770i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 39.5980i | − | 0.224989i | ||||||
\(177\) | 94.3837 | + | 17.5420i | 0.533241 | + | 0.0991075i | ||||
\(178\) | −39.5980 | − | 68.5857i | −0.222461 | − | 0.385313i | ||||
\(179\) | −194.734 | + | 112.430i | −1.08790 | + | 0.628100i | −0.933017 | − | 0.359832i | \(-0.882834\pi\) |
−0.154885 | + | 0.987933i | \(0.549501\pi\) | |||||||
\(180\) | 71.1248 | − | 11.1918i | 0.395138 | − | 0.0621769i | ||||
\(181\) | −182.434 | −1.00792 | −0.503960 | − | 0.863727i | \(-0.668124\pi\) | ||||
−0.503960 | + | 0.863727i | \(0.668124\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −92.0000 | + | 32.5269i | −0.502732 | + | 0.177743i | ||||
\(184\) | 2.00000 | − | 3.46410i | 0.0108696 | − | 0.0188266i | ||||
\(185\) | −173.205 | + | 100.000i | −0.936244 | + | 0.540541i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 158.392 | − | 274.343i | 0.847016 | − | 1.46707i | ||||
\(188\) | − | 68.0000i | − | 0.361702i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 160.000 | 0.842105 | ||||||||
\(191\) | −8.57321 | − | 4.94975i | −0.0448859 | − | 0.0259149i | 0.477389 | − | 0.878692i | \(-0.341583\pi\) |
−0.522275 | + | 0.852777i | \(0.674917\pi\) | |||||||
\(192\) | 18.2419 | + | 15.5959i | 0.0950100 | + | 0.0812287i | ||||
\(193\) | 80.0000 | + | 138.564i | 0.414508 | + | 0.717949i | 0.995377 | − | 0.0960486i | \(-0.0306204\pi\) |
−0.580869 | + | 0.813997i | \(0.697287\pi\) | |||||||
\(194\) | 29.4449 | + | 17.0000i | 0.151778 | + | 0.0876289i | ||||
\(195\) | 50.9117 | + | 144.000i | 0.261086 | + | 0.738462i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 107.480i | 0.545585i | 0.962073 | + | 0.272792i | \(0.0879472\pi\) | ||||
−0.962073 | + | 0.272792i | \(0.912053\pi\) | |||||||
\(198\) | −19.5857 | − | 124.468i | −0.0989177 | − | 0.628629i | ||||
\(199\) | −110.309 | − | 191.060i | −0.554315 | − | 0.960102i | −0.997956 | − | 0.0638972i | \(-0.979647\pi\) |
0.443642 | − | 0.896204i | \(-0.353686\pi\) | |||||||
\(200\) | 22.0454 | − | 12.7279i | 0.110227 | − | 0.0636396i | ||||
\(201\) | 6.57826 | − | 35.3939i | 0.0327277 | − | 0.176089i | ||||
\(202\) | 50.9117 | 0.252038 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 64.0000 | + | 181.019i | 0.313725 | + | 0.887350i | ||||
\(205\) | 32.0000 | − | 55.4256i | 0.156098 | − | 0.270369i | ||||
\(206\) | −90.0666 | + | 52.0000i | −0.437217 | + | 0.252427i | ||||
\(207\) | 4.57321 | − | 11.8780i | 0.0220928 | − | 0.0573814i | ||||
\(208\) | −25.4558 | + | 44.0908i | −0.122384 | + | 0.211975i | ||||
\(209\) | − | 280.000i | − | 1.33971i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −372.000 | −1.76303 | −0.881517 | − | 0.472153i | \(-0.843477\pi\) | ||||
−0.881517 | + | 0.472153i | \(0.843477\pi\) | |||||||
\(212\) | 78.3837 | + | 45.2548i | 0.369734 | + | 0.213466i | ||||
\(213\) | −173.691 | + | 203.159i | −0.815449 | + | 0.953798i | ||||
\(214\) | −103.000 | − | 178.401i | −0.481308 | − | 0.833651i | ||||
\(215\) | 180.133 | + | 104.000i | 0.837829 | + | 0.483721i | ||||
\(216\) | 65.0538 | + | 40.0000i | 0.301175 | + | 0.185185i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 248.902i | 1.14175i | ||||||||
\(219\) | 17.8309 | − | 95.9378i | 0.0814195 | − | 0.438072i | ||||
\(220\) | 39.5980 | + | 68.5857i | 0.179991 | + | 0.311753i | ||||
\(221\) | −352.727 | + | 203.647i | −1.59605 | + | 0.921479i | ||||
\(222\) | −208.560 | − | 38.7628i | −0.939461 | − | 0.174607i | ||||
\(223\) | 16.9706 | 0.0761012 | 0.0380506 | − | 0.999276i | \(-0.487885\pi\) | ||||
0.0380506 | + | 0.999276i | \(0.487885\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 63.0000 | − | 50.9117i | 0.280000 | − | 0.226274i | ||||
\(226\) | 12.0000 | − | 20.7846i | 0.0530973 | − | 0.0919673i | ||||
\(227\) | 332.554 | − | 192.000i | 1.46499 | − | 0.845815i | 0.465759 | − | 0.884912i | \(-0.345781\pi\) |
0.999235 | + | 0.0390966i | \(0.0124480\pi\) | |||||||
\(228\) | 128.990 | + | 110.280i | 0.565745 | + | 0.483683i | ||||
\(229\) | −125.158 | + | 216.780i | −0.546541 | + | 0.946637i | 0.451967 | + | 0.892035i | \(0.350722\pi\) |
−0.998508 | + | 0.0546023i | \(0.982611\pi\) | |||||||
\(230\) | 8.00000i | 0.0347826i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −160.000 | −0.689655 | ||||||||
\(233\) | 279.242 | + | 161.220i | 1.19846 | + | 0.691933i | 0.960212 | − | 0.279271i | \(-0.0900928\pi\) |
0.238250 | + | 0.971204i | \(0.423426\pi\) | |||||||
\(234\) | −58.2075 | + | 151.182i | −0.248750 | + | 0.646075i | ||||
\(235\) | 68.0000 | + | 117.779i | 0.289362 | + | 0.501189i | ||||
\(236\) | −55.4256 | − | 32.0000i | −0.234854 | − | 0.135593i | ||||
\(237\) | −113.137 | + | 40.0000i | −0.477372 | + | 0.168776i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 284.257i | 1.18936i | 0.803963 | + | 0.594680i | \(0.202721\pi\) | ||||
−0.803963 | + | 0.594680i | \(0.797279\pi\) | |||||||
\(240\) | −47.1918 | − | 8.77101i | −0.196633 | − | 0.0365459i | ||||
\(241\) | 23.3345 | + | 40.4166i | 0.0968238 | + | 0.167704i | 0.910368 | − | 0.413799i | \(-0.135798\pi\) |
−0.813545 | + | 0.581503i | \(0.802465\pi\) | |||||||
\(242\) | −28.1691 | + | 16.2635i | −0.116401 | + | 0.0672044i | ||||
\(243\) | 224.268 | + | 93.5556i | 0.922916 | + | 0.385003i | ||||
\(244\) | 65.0538 | 0.266614 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 64.0000 | − | 22.6274i | 0.260163 | − | 0.0919814i | ||||
\(247\) | −180.000 | + | 311.769i | −0.728745 | + | 1.26222i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 120.868 | − | 141.375i | 0.485415 | − | 0.567770i | ||||
\(250\) | −96.1665 | + | 166.565i | −0.384666 | + | 0.666261i | ||||
\(251\) | 224.000i | 0.892430i | 0.894926 | + | 0.446215i | \(0.147228\pi\) | ||||
−0.894926 | + | 0.446215i | \(0.852772\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.0000 | 0.0553360 | ||||||||
\(254\) | −127.373 | − | 73.5391i | −0.501470 | − | 0.289524i | ||||
\(255\) | −291.871 | − | 249.535i | −1.14459 | − | 0.978567i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −103.923 | − | 60.0000i | −0.404370 | − | 0.233463i | 0.283998 | − | 0.958825i | \(-0.408339\pi\) |
−0.688368 | + | 0.725362i | \(0.741672\pi\) | |||||||
\(258\) | 73.5391 | + | 208.000i | 0.285035 | + | 0.806202i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 101.823i | − | 0.391628i | ||||||
\(261\) | −502.929 | + | 79.1382i | −1.92693 | + | 0.303212i | ||||
\(262\) | −21.2132 | − | 36.7423i | −0.0809664 | − | 0.140238i | ||||
\(263\) | 194.734 | − | 112.430i | 0.740435 | − | 0.427490i | −0.0817924 | − | 0.996649i | \(-0.526064\pi\) |
0.822227 | + | 0.569159i | \(0.192731\pi\) | |||||||
\(264\) | −15.3493 | + | 82.5857i | −0.0581412 | + | 0.312825i | ||||
\(265\) | −181.019 | −0.683092 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 56.0000 | + | 158.392i | 0.209738 | + | 0.593228i | ||||
\(268\) | −12.0000 | + | 20.7846i | −0.0447761 | + | 0.0775545i | ||||
\(269\) | 142.028 | − | 82.0000i | 0.527986 | − | 0.304833i | −0.212210 | − | 0.977224i | \(-0.568066\pi\) |
0.740196 | + | 0.672391i | \(0.234733\pi\) | |||||||
\(270\) | −152.677 | − | 4.22821i | −0.565469 | − | 0.0156600i | ||||
\(271\) | −115.966 | + | 200.858i | −0.427917 | + | 0.741174i | −0.996688 | − | 0.0813220i | \(-0.974086\pi\) |
0.568771 | + | 0.822496i | \(0.307419\pi\) | |||||||
\(272\) | − | 128.000i | − | 0.470588i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 96.0000 | 0.350365 | ||||||||
\(275\) | 77.1589 | + | 44.5477i | 0.280578 | + | 0.161992i | ||||
\(276\) | −5.51399 | + | 6.44949i | −0.0199782 | + | 0.0233677i | ||||
\(277\) | 232.000 | + | 401.836i | 0.837545 | + | 1.45067i | 0.891941 | + | 0.452151i | \(0.149343\pi\) |
−0.0543961 | + | 0.998519i | \(0.517323\pi\) | |||||||
\(278\) | 263.272 | + | 152.000i | 0.947021 | + | 0.546763i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 39.5980i | − | 0.140918i | −0.997515 | − | 0.0704590i | \(-0.977554\pi\) | ||
0.997515 | − | 0.0704590i | \(-0.0224464\pi\) | |||||||
\(282\) | −26.3587 | + | 141.821i | −0.0934705 | + | 0.502912i | ||||
\(283\) | 124.451 | + | 215.555i | 0.439755 | + | 0.761679i | 0.997670 | − | 0.0682194i | \(-0.0217318\pi\) |
−0.557915 | + | 0.829898i | \(0.688398\pi\) | |||||||
\(284\) | 154.318 | − | 89.0955i | 0.543373 | − | 0.313716i | ||||
\(285\) | −333.697 | − | 62.0204i | −1.17087 | − | 0.217615i | ||||
\(286\) | −178.191 | −0.623045 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −32.0000 | − | 39.5980i | −0.111111 | − | 0.137493i | ||||
\(289\) | 367.500 | − | 636.529i | 1.27163 | − | 2.20252i | ||||
\(290\) | 277.128 | − | 160.000i | 0.955614 | − | 0.551724i | ||||
\(291\) | −54.8207 | − | 46.8689i | −0.188387 | − | 0.161062i | ||||
\(292\) | −32.5269 | + | 56.3383i | −0.111394 | + | 0.192939i | ||||
\(293\) | − | 316.000i | − | 1.07850i | −0.842146 | − | 0.539249i | \(-0.818708\pi\) | ||
0.842146 | − | 0.539249i | \(-0.181292\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 128.000 | 0.433898 | ||||||||
\(296\) | 122.474 | + | 70.7107i | 0.413765 | + | 0.238887i | ||||
\(297\) | −7.39936 | + | 267.184i | −0.0249137 | + | 0.899609i | ||||
\(298\) | 64.0000 | + | 110.851i | 0.214765 | + | 0.371984i | ||||
\(299\) | −15.5885 | − | 9.00000i | −0.0521353 | − | 0.0301003i | ||||
\(300\) | −50.9117 | + | 18.0000i | −0.169706 | + | 0.0600000i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 214.960i | − | 0.711790i | ||||||
\(303\) | −106.182 | − | 19.7348i | −0.350434 | − | 0.0651313i | ||||
\(304\) | −56.5685 | − | 97.9796i | −0.186081 | − | 0.322301i | ||||
\(305\) | −112.677 | + | 65.0538i | −0.369431 | + | 0.213291i | ||||
\(306\) | −63.3106 | − | 402.343i | −0.206897 | − | 1.31485i | ||||
\(307\) | 345.068 | 1.12400 | 0.562000 | − | 0.827137i | \(-0.310032\pi\) | ||||
0.562000 | + | 0.827137i | \(0.310032\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 208.000 | − | 73.5391i | 0.673139 | − | 0.237991i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 458.993 | − | 265.000i | 1.47586 | − | 0.852090i | 0.476234 | − | 0.879319i | \(-0.342002\pi\) |
0.999629 | + | 0.0272286i | \(0.00866819\pi\) | |||||||
\(312\) | 70.1816 | − | 82.0886i | 0.224941 | − | 0.263104i | ||||
\(313\) | 74.2462 | − | 128.598i | 0.237208 | − | 0.410857i | −0.722704 | − | 0.691158i | \(-0.757101\pi\) |
0.959912 | + | 0.280301i | \(0.0904343\pi\) | |||||||
\(314\) | 242.000i | 0.770701i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 80.0000 | 0.253165 | ||||||||
\(317\) | −97.9796 | − | 56.5685i | −0.309084 | − | 0.178450i | 0.337433 | − | 0.941350i | \(-0.390441\pi\) |
−0.646516 | + | 0.762900i | \(0.723775\pi\) | |||||||
\(318\) | −145.935 | − | 124.767i | −0.458916 | − | 0.392350i | ||||
\(319\) | −280.000 | − | 484.974i | −0.877743 | − | 1.52030i | ||||
\(320\) | 27.7128 | + | 16.0000i | 0.0866025 | + | 0.0500000i | ||||
\(321\) | 145.664 | + | 412.000i | 0.453782 | + | 1.28349i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 905.097i | − | 2.80216i | ||||||
\(324\) | −120.171 | − | 108.641i | −0.370899 | − | 0.335311i | ||||
\(325\) | −57.2756 | − | 99.2043i | −0.176233 | − | 0.305244i | ||||
\(326\) | −298.838 | + | 172.534i | −0.916680 | + | 0.529246i | ||||
\(327\) | 96.4811 | − | 519.110i | 0.295049 | − | 1.58749i | ||||
\(328\) | −45.2548 | −0.137972 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −56.0000 | − | 158.392i | −0.169697 | − | 0.479976i | ||||
\(331\) | −26.0000 | + | 45.0333i | −0.0785498 | + | 0.136052i | −0.902624 | − | 0.430429i | \(-0.858362\pi\) |
0.824075 | + | 0.566481i | \(0.191696\pi\) | |||||||
\(332\) | −107.387 | + | 62.0000i | −0.323455 | + | 0.186747i | ||||
\(333\) | 419.949 | + | 161.688i | 1.26111 | + | 0.485548i | ||||
\(334\) | 159.806 | − | 276.792i | 0.478461 | − | 0.828720i | ||||
\(335\) | − | 48.0000i | − | 0.143284i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 80.0000 | 0.237389 | 0.118694 | − | 0.992931i | \(-0.462129\pi\) | ||||
0.118694 | + | 0.992931i | \(0.462129\pi\) | |||||||
\(338\) | −8.57321 | − | 4.94975i | −0.0253645 | − | 0.0146442i | ||||
\(339\) | −33.0839 | + | 38.6969i | −0.0975927 | + | 0.114150i | ||||
\(340\) | 128.000 | + | 221.703i | 0.376471 | + | 0.652066i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −226.274 | − | 280.000i | −0.661620 | − | 0.818713i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 147.078i | − | 0.427553i | ||||||
\(345\) | 3.10102 | − | 16.6848i | 0.00898847 | − | 0.0483618i | ||||
\(346\) | 93.3381 | + | 161.666i | 0.269763 | + | 0.467244i | ||||
\(347\) | 187.386 | − | 108.187i | 0.540017 | − | 0.311779i | −0.205069 | − | 0.978748i | \(-0.565742\pi\) |
0.745086 | + | 0.666969i | \(0.232408\pi\) | |||||||
\(348\) | 333.697 | + | 62.0204i | 0.958898 | + | 0.178220i | ||||
\(349\) | −12.7279 | −0.0364697 | −0.0182348 | − | 0.999834i | \(-0.505805\pi\) | ||||
−0.0182348 | + | 0.999834i | \(0.505805\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 180.000 | − | 292.742i | 0.512821 | − | 0.834023i | ||||
\(352\) | 28.0000 | − | 48.4974i | 0.0795455 | − | 0.137777i | ||||
\(353\) | 55.4256 | − | 32.0000i | 0.157013 | − | 0.0906516i | −0.419435 | − | 0.907785i | \(-0.637772\pi\) |
0.576448 | + | 0.817134i | \(0.304438\pi\) | |||||||
\(354\) | 103.192 | + | 88.2238i | 0.291502 | + | 0.249220i | ||||
\(355\) | −178.191 | + | 308.636i | −0.501946 | + | 0.869396i | ||||
\(356\) | − | 112.000i | − | 0.314607i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −318.000 | −0.888268 | ||||||||
\(359\) | 155.543 | + | 89.8026i | 0.433266 | + | 0.250146i | 0.700737 | − | 0.713420i | \(-0.252855\pi\) |
−0.267471 | + | 0.963566i | \(0.586188\pi\) | |||||||
\(360\) | 95.0236 | + | 36.5857i | 0.263954 | + | 0.101627i | ||||
\(361\) | −219.500 | − | 380.185i | −0.608033 | − | 1.05314i | ||||
\(362\) | −223.435 | − | 129.000i | −0.617223 | − | 0.356354i | ||||
\(363\) | 65.0538 | − | 23.0000i | 0.179212 | − | 0.0633609i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 130.108i | − | 0.356459i | ||||||
\(366\) | −135.677 | − | 25.2167i | −0.370701 | − | 0.0688980i | ||||
\(367\) | 65.0538 | + | 112.677i | 0.177258 | + | 0.307021i | 0.940941 | − | 0.338572i | \(-0.109944\pi\) |
−0.763682 | + | 0.645592i | \(0.776611\pi\) | |||||||
\(368\) | 4.89898 | − | 2.82843i | 0.0133124 | − | 0.00768594i | ||||
\(369\) | −142.250 | + | 22.3837i | −0.385500 | + | 0.0606604i | ||||
\(370\) | −282.843 | −0.764440 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.00000 | − | 12.1244i | 0.0187668 | − | 0.0325050i | −0.856490 | − | 0.516164i | \(-0.827359\pi\) |
0.875256 | + | 0.483659i | \(0.160693\pi\) | |||||||
\(374\) | 387.979 | − | 224.000i | 1.03738 | − | 0.598930i | ||||
\(375\) | 265.131 | − | 310.112i | 0.707015 | − | 0.826967i | ||||
\(376\) | 48.0833 | − | 83.2827i | 0.127881 | − | 0.221496i | ||||
\(377\) | 720.000i | 1.90981i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 148.000 | 0.390501 | 0.195251 | − | 0.980753i | \(-0.437448\pi\) | ||||
0.195251 | + | 0.980753i | \(0.437448\pi\) | |||||||
\(380\) | 195.959 | + | 113.137i | 0.515682 | + | 0.297729i | ||||
\(381\) | 237.145 | + | 202.747i | 0.622427 | + | 0.532144i | ||||
\(382\) | −7.00000 | − | 12.1244i | −0.0183246 | − | 0.0317392i | ||||
\(383\) | 96.9948 | + | 56.0000i | 0.253250 | + | 0.146214i | 0.621252 | − | 0.783611i | \(-0.286624\pi\) |
−0.368001 | + | 0.929825i | \(0.619958\pi\) | |||||||
\(384\) | 11.3137 | + | 32.0000i | 0.0294628 | + | 0.0833333i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 226.274i | 0.586203i | ||||||||
\(387\) | −72.7469 | − | 462.311i | −0.187977 | − | 1.19460i | ||||
\(388\) | 24.0416 | + | 41.6413i | 0.0619630 | + | 0.107323i | ||||
\(389\) | 372.322 | − | 214.960i | 0.957127 | − | 0.552598i | 0.0618394 | − | 0.998086i | \(-0.480303\pi\) |
0.895288 | + | 0.445489i | \(0.146970\pi\) | |||||||
\(390\) | −39.4695 | + | 212.363i | −0.101204 | + | 0.544521i | ||||
\(391\) | 45.2548 | 0.115741 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 30.0000 | + | 84.8528i | 0.0763359 | + | 0.215910i | ||||
\(394\) | −76.0000 | + | 131.636i | −0.192893 | + | 0.334101i | ||||
\(395\) | −138.564 | + | 80.0000i | −0.350795 | + | 0.202532i | ||||
\(396\) | 64.0250 | − | 166.291i | 0.161679 | − | 0.419928i | ||||
\(397\) | 17.6777 | − | 30.6186i | 0.0445281 | − | 0.0771250i | −0.842902 | − | 0.538067i | \(-0.819155\pi\) |
0.887430 | + | 0.460942i | \(0.152488\pi\) | |||||||
\(398\) | − | 312.000i | − | 0.783920i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 36.0000 | 0.0900000 | ||||||||
\(401\) | −117.576 | − | 67.8823i | −0.293206 | − | 0.169282i | 0.346181 | − | 0.938168i | \(-0.387478\pi\) |
−0.639387 | + | 0.768885i | \(0.720812\pi\) | |||||||
\(402\) | 33.0839 | − | 38.6969i | 0.0822984 | − | 0.0962610i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 62.3538 | + | 36.0000i | 0.154341 | + | 0.0891089i | ||||
\(405\) | 316.784 | + | 68.0000i | 0.782182 | + | 0.167901i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 494.975i | 1.21615i | ||||||||
\(408\) | −49.6163 | + | 266.957i | −0.121609 | + | 0.654307i | ||||
\(409\) | 163.342 | + | 282.916i | 0.399368 | + | 0.691726i | 0.993648 | − | 0.112532i | \(-0.0358961\pi\) |
−0.594280 | + | 0.804258i | \(0.702563\pi\) | |||||||
\(410\) | 78.3837 | − | 45.2548i | 0.191180 | − | 0.110378i | ||||
\(411\) | −200.218 | − | 37.2122i | −0.487148 | − | 0.0905407i | ||||
\(412\) | −147.078 | −0.356986 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 14.0000 | − | 11.3137i | 0.0338164 | − | 0.0273278i | ||||
\(415\) | 124.000 | − | 214.774i | 0.298795 | − | 0.517528i | ||||
\(416\) | −62.3538 | + | 36.0000i | −0.149889 | + | 0.0865385i | ||||
\(417\) | −490.161 | − | 419.063i | −1.17545 | − | 1.00495i | ||||
\(418\) | 197.990 | − | 342.929i | 0.473660 | − | 0.820403i | ||||
\(419\) | 352.000i | 0.840095i | 0.907502 | + | 0.420048i | \(0.137987\pi\) | ||||
−0.907502 | + | 0.420048i | \(0.862013\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 240.000 | 0.570071 | 0.285036 | − | 0.958517i | \(-0.407995\pi\) | ||||
0.285036 | + | 0.958517i | \(0.407995\pi\) | |||||||
\(422\) | −455.605 | − | 263.044i | −1.07963 | − | 0.623326i | ||||
\(423\) | 109.948 | − | 285.565i | 0.259923 | − | 0.675095i | ||||
\(424\) | 64.0000 | + | 110.851i | 0.150943 | + | 0.261442i | ||||
\(425\) | 249.415 | + | 144.000i | 0.586860 | + | 0.338824i | ||||
\(426\) | −356.382 | + | 126.000i | −0.836577 | + | 0.295775i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 291.328i | − | 0.680673i | ||||||
\(429\) | 371.636 | + | 69.0717i | 0.866284 | + | 0.161006i | ||||
\(430\) | 147.078 | + | 254.747i | 0.342042 | + | 0.592435i | ||||
\(431\) | −635.643 | + | 366.988i | −1.47481 | + | 0.851481i | −0.999597 | − | 0.0283901i | \(-0.990962\pi\) |
−0.475212 | + | 0.879871i | \(0.657629\pi\) | |||||||
\(432\) | 51.3901 | + | 94.9898i | 0.118958 | + | 0.219884i | ||||
\(433\) | −428.507 | −0.989623 | −0.494811 | − | 0.869000i | \(-0.664763\pi\) | ||||
−0.494811 | + | 0.869000i | \(0.664763\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −640.000 | + | 226.274i | −1.47126 | + | 0.520171i | ||||
\(436\) | −176.000 | + | 304.841i | −0.403670 | + | 0.699176i | ||||
\(437\) | 34.6410 | − | 20.0000i | 0.0792701 | − | 0.0457666i | ||||
\(438\) | 89.6765 | − | 104.891i | 0.204741 | − | 0.239477i | ||||
\(439\) | −203.647 | + | 352.727i | −0.463888 | + | 0.803477i | −0.999151 | − | 0.0412083i | \(-0.986879\pi\) |
0.535263 | + | 0.844686i | \(0.320213\pi\) | |||||||
\(440\) | 112.000i | 0.254545i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −576.000 | −1.30317 | ||||||||
\(443\) | 344.153 | + | 198.697i | 0.776870 | + | 0.448526i | 0.835320 | − | 0.549764i | \(-0.185282\pi\) |
−0.0584500 | + | 0.998290i | \(0.518616\pi\) | |||||||
\(444\) | −228.024 | − | 194.949i | −0.513567 | − | 0.439074i | ||||
\(445\) | 112.000 | + | 193.990i | 0.251685 | + | 0.435932i | ||||
\(446\) | 20.7846 | + | 12.0000i | 0.0466023 | + | 0.0269058i | ||||
\(447\) | −90.5097 | − | 256.000i | −0.202482 | − | 0.572707i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 16.9706i | − | 0.0377964i | −0.999821 | − | 0.0188982i | \(-0.993984\pi\) | ||
0.999821 | − | 0.0188982i | \(-0.00601583\pi\) | |||||||
\(450\) | 113.159 | − | 17.8061i | 0.251464 | − | 0.0395691i | ||||
\(451\) | −79.1960 | − | 137.171i | −0.175601 | − | 0.304150i | ||||
\(452\) | 29.3939 | − | 16.9706i | 0.0650307 | − | 0.0375455i | ||||
\(453\) | −83.3246 | + | 448.322i | −0.183940 | + | 0.989674i | ||||
\(454\) | 543.058 | 1.19616 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 80.0000 | + | 226.274i | 0.175439 | + | 0.496215i | ||||
\(457\) | 63.0000 | − | 109.119i | 0.137856 | − | 0.238773i | −0.788829 | − | 0.614613i | \(-0.789312\pi\) |
0.926685 | + | 0.375840i | \(0.122646\pi\) | |||||||
\(458\) | −306.573 | + | 177.000i | −0.669373 | + | 0.386463i | ||||
\(459\) | −23.9184 | + | 863.669i | −0.0521097 | + | 1.88163i | ||||
\(460\) | −5.65685 | + | 9.79796i | −0.0122975 | + | 0.0212999i | ||||
\(461\) | − | 580.000i | − | 1.25813i | −0.777351 | − | 0.629067i | \(-0.783437\pi\) | ||
0.777351 | − | 0.629067i | \(-0.216563\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 112.000 | 0.241901 | 0.120950 | − | 0.992659i | \(-0.461406\pi\) | ||||
0.120950 | + | 0.992659i | \(0.461406\pi\) | |||||||
\(464\) | −195.959 | − | 113.137i | −0.422326 | − | 0.243830i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 228.000 | + | 394.908i | 0.489270 | + | 0.847441i | ||||
\(467\) | 110.851 | + | 64.0000i | 0.237369 | + | 0.137045i | 0.613967 | − | 0.789332i | \(-0.289573\pi\) |
−0.376598 | + | 0.926377i | \(0.622906\pi\) | |||||||
\(468\) | −178.191 | + | 144.000i | −0.380750 | + | 0.307692i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 192.333i | 0.409219i | ||||||||
\(471\) | 93.8059 | − | 504.716i | 0.199163 | − | 1.07158i | ||||
\(472\) | −45.2548 | − | 78.3837i | −0.0958789 | − | 0.166067i | ||||
\(473\) | 445.807 | − | 257.387i | 0.942510 | − | 0.544158i | ||||
\(474\) | −166.848 | − | 31.0102i | −0.352001 | − | 0.0654224i | ||||
\(475\) | 254.558 | 0.535913 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 256.000 | + | 316.784i | 0.536688 | + | 0.664117i | ||||
\(478\) | −201.000 | + | 348.142i | −0.420502 | + | 0.728331i | ||||
\(479\) | −417.424 | + | 241.000i | −0.871449 | + | 0.503132i | −0.867830 | − | 0.496862i | \(-0.834486\pi\) |
−0.00361975 | + | 0.999993i | \(0.501152\pi\) | |||||||
\(480\) | −51.5959 | − | 44.1119i | −0.107491 | − | 0.0918998i | ||||
\(481\) | 318.198 | − | 551.135i | 0.661534 | − | 1.14581i | ||||
\(482\) | 66.0000i | 0.136929i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −46.0000 | −0.0950413 | ||||||||
\(485\) | −83.2827 | − | 48.0833i | −0.171717 | − | 0.0991407i | ||||
\(486\) | 208.518 | + | 273.164i | 0.429049 | + | 0.562065i | ||||
\(487\) | 60.0000 | + | 103.923i | 0.123203 | + | 0.213394i | 0.921029 | − | 0.389494i | \(-0.127350\pi\) |
−0.797826 | + | 0.602888i | \(0.794017\pi\) | |||||||
\(488\) | 79.6743 | + | 46.0000i | 0.163267 | + | 0.0942623i | ||||
\(489\) | 690.136 | − | 244.000i | 1.41132 | − | 0.498978i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 623.668i | 1.27020i | 0.772430 | + | 0.635100i | \(0.219041\pi\) | ||||
−0.772430 | + | 0.635100i | \(0.780959\pi\) | |||||||
\(492\) | 94.3837 | + | 17.5420i | 0.191837 | + | 0.0356545i | ||||
\(493\) | −905.097 | − | 1567.67i | −1.83590 | − | 3.17986i | ||||
\(494\) | −440.908 | + | 254.558i | −0.892527 | + | 0.515300i | ||||
\(495\) | 55.3968 | + | 352.050i | 0.111913 | + | 0.711212i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 248.000 | − | 87.6812i | 0.497992 | − | 0.176067i | ||||
\(499\) | −142.000 | + | 245.951i | −0.284569 | + | 0.492888i | −0.972505 | − | 0.232884i | \(-0.925184\pi\) |
0.687935 | + | 0.725772i | \(0.258517\pi\) | |||||||
\(500\) | −235.559 | + | 136.000i | −0.471118 | + | 0.272000i | ||||
\(501\) | −440.585 | + | 515.334i | −0.879411 | + | 1.02861i | ||||
\(502\) | −158.392 | + | 274.343i | −0.315522 | + | 0.546500i | ||||
\(503\) | − | 16.0000i | − | 0.0318091i | −0.999874 | − | 0.0159046i | \(-0.994937\pi\) | ||
0.999874 | − | 0.0159046i | \(-0.00506280\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −144.000 | −0.285149 | ||||||||
\(506\) | 17.1464 | + | 9.89949i | 0.0338862 | + | 0.0195642i | ||||
\(507\) | 15.9617 | + | 13.6464i | 0.0314826 | + | 0.0269160i | ||||
\(508\) | −104.000 | − | 180.133i | −0.204724 | − | 0.354593i | ||||
\(509\) | −308.305 | − | 178.000i | −0.605707 | − | 0.349705i | 0.165576 | − | 0.986197i | \(-0.447052\pi\) |
−0.771284 | + | 0.636492i | \(0.780385\pi\) | |||||||
\(510\) | −181.019 | − | 512.000i | −0.354940 | − | 1.00392i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 363.383 | + | 671.679i | 0.708348 | + | 1.30932i | ||||
\(514\) | −84.8528 | − | 146.969i | −0.165083 | − | 0.285933i | ||||
\(515\) | 254.747 | − | 147.078i | 0.494654 | − | 0.285589i | ||||
\(516\) | −57.0116 | + | 306.747i | −0.110488 | + | 0.594471i | ||||
\(517\) | 336.583 | 0.651031 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −132.000 | − | 373.352i | −0.254335 | − | 0.719369i | ||||
\(520\) | 72.0000 | − | 124.708i | 0.138462 | − | 0.239822i | ||||
\(521\) | −214.774 | + | 124.000i | −0.412235 | + | 0.238004i | −0.691749 | − | 0.722138i | \(-0.743160\pi\) |
0.279515 | + | 0.960141i | \(0.409826\pi\) | |||||||
\(522\) | −671.918 | − | 258.700i | −1.28720 | − | 0.495594i | ||||
\(523\) | −25.4558 | + | 44.0908i | −0.0486727 | + | 0.0843037i | −0.889335 | − | 0.457256i | \(-0.848832\pi\) |
0.840663 | + | 0.541559i | \(0.182166\pi\) | |||||||
\(524\) | − | 60.0000i | − | 0.114504i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 318.000 | 0.604563 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −77.1959 | + | 90.2929i | −0.146204 | + | 0.171009i | ||||
\(529\) | −263.500 | − | 456.395i | −0.498110 | − | 0.862751i | ||||
\(530\) | −221.703 | − | 128.000i | −0.418307 | − | 0.241509i | ||||
\(531\) | −181.019 | − | 224.000i | −0.340903 | − | 0.421846i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 203.647i | 0.382076i | ||||||||
\(534\) | −43.4143 | + | 233.588i | −0.0813002 | + | 0.437430i | ||||
\(535\) | 291.328 | + | 504.595i | 0.544538 | + | 0.943168i | ||||
\(536\) | −29.3939 | + | 16.9706i | −0.0548393 | + | 0.0316615i | ||||
\(537\) | 663.222 | + | 123.266i | 1.23505 | + | 0.229545i | ||||
\(538\) | 231.931 | 0.431099 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −184.000 | − | 113.137i | −0.340741 | − | 0.209513i | ||||
\(541\) | −200.000 | + | 346.410i | −0.369686 | + | 0.640315i | −0.989516 | − | 0.144421i | \(-0.953868\pi\) |
0.619831 | + | 0.784736i | \(0.287201\pi\) | |||||||
\(542\) | −284.056 | + | 164.000i | −0.524089 | + | 0.302583i | ||||
\(543\) | 415.992 | + | 355.652i | 0.766100 | + | 0.654977i | ||||
\(544\) | 90.5097 | − | 156.767i | 0.166378 | − | 0.288175i | ||||
\(545\) | − | 704.000i | − | 1.29174i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 820.000 | 1.49909 | 0.749543 | − | 0.661956i | \(-0.230273\pi\) | ||||
0.749543 | + | 0.661956i | \(0.230273\pi\) | |||||||
\(548\) | 117.576 | + | 67.8823i | 0.214554 | + | 0.123873i | ||||
\(549\) | 273.193 | + | 105.184i | 0.497619 | + | 0.191592i | ||||
\(550\) | 63.0000 | + | 109.119i | 0.114545 | + | 0.198399i | ||||
\(551\) | −1385.64 | − | 800.000i | −2.51477 | − | 1.45191i | ||||
\(552\) | −11.3137 | + | 4.00000i | −0.0204958 | + | 0.00724638i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 656.195i | 1.18447i | ||||||||
\(555\) | 589.898 | + | 109.638i | 1.06288 | + | 0.197545i | ||||
\(556\) | 214.960 | + | 372.322i | 0.386620 | + | 0.669645i | ||||
\(557\) | −911.210 | + | 526.087i | −1.63592 | + | 0.944502i | −0.653709 | + | 0.756746i | \(0.726788\pi\) |
−0.982216 | + | 0.187756i | \(0.939879\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −661.852 | −1.18399 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −896.000 | + | 316.784i | −1.59715 | + | 0.564677i | ||||
\(562\) | 28.0000 | − | 48.4974i | 0.0498221 | − | 0.0862943i | ||||
\(563\) | −942.236 | + | 544.000i | −1.67360 | + | 0.966252i | −0.708000 | + | 0.706212i | \(0.750402\pi\) |
−0.965598 | + | 0.260040i | \(0.916264\pi\) | |||||||
\(564\) | −132.565 | + | 155.056i | −0.235045 | + | 0.274922i | ||||
\(565\) | −33.9411 | + | 58.7878i | −0.0600728 | + | 0.104049i | ||||
\(566\) | 352.000i | 0.621908i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 252.000 | 0.443662 | ||||||||
\(569\) | −436.009 | − | 251.730i | −0.766273 | − | 0.442408i | 0.0652707 | − | 0.997868i | \(-0.479209\pi\) |
−0.831543 | + | 0.555460i | \(0.812542\pi\) | |||||||
\(570\) | −364.838 | − | 311.918i | −0.640067 | − | 0.547225i | ||||
\(571\) | −410.000 | − | 710.141i | −0.718039 | − | 1.24368i | −0.961776 | − | 0.273838i | \(-0.911707\pi\) |
0.243737 | − | 0.969841i | \(-0.421627\pi\) | |||||||
\(572\) | −218.238 | − | 126.000i | −0.381536 | − | 0.220280i | ||||
\(573\) | 9.89949 | + | 28.0000i | 0.0172766 | + | 0.0488656i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.7279i | 0.0221355i | ||||||||
\(576\) | −11.1918 | − | 71.1248i | −0.0194303 | − | 0.123481i | ||||
\(577\) | −146.371 | − | 253.522i | −0.253676 | − | 0.439380i | 0.710859 | − | 0.703335i | \(-0.248306\pi\) |
−0.964535 | + | 0.263955i | \(0.914973\pi\) | |||||||
\(578\) | 900.187 | − | 519.723i | 1.55742 | − | 0.899176i | ||||
\(579\) | 87.7101 | − | 471.918i | 0.151486 | − | 0.815058i | ||||
\(580\) | 452.548 | 0.780256 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −34.0000 | − | 96.1665i | −0.0584192 | − | 0.165235i | ||||
\(583\) | −224.000 | + | 387.979i | −0.384220 | + | 0.665488i | ||||
\(584\) | −79.6743 | + | 46.0000i | −0.136429 | + | 0.0787671i | ||||
\(585\) | 164.636 | − | 427.606i | 0.281429 | − | 0.730951i | ||||
\(586\) | 223.446 | − | 387.019i | 0.381307 | − | 0.660443i | ||||
\(587\) | − | 480.000i | − | 0.817717i | −0.912598 | − | 0.408859i | \(-0.865927\pi\) | ||
0.912598 | − | 0.408859i | \(-0.134073\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 156.767 | + | 90.5097i | 0.265707 | + | 0.153406i | ||||
\(591\) | 209.532 | − | 245.081i | 0.354537 | − | 0.414688i | ||||
\(592\) | 100.000 | + | 173.205i | 0.168919 | + | 0.292576i | ||||
\(593\) | 928.379 | + | 536.000i | 1.56556 | + | 0.903879i | 0.996676 | + | 0.0814631i | \(0.0259593\pi\) |
0.568887 | + | 0.822416i | \(0.307374\pi\) | |||||||
\(594\) | −197.990 | + | 322.000i | −0.333316 | + | 0.542088i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 181.019i | 0.303724i | ||||||||
\(597\) | −120.940 | + | 650.709i | −0.202579 | + | 1.08996i | ||||
\(598\) | −12.7279 | − | 22.0454i | −0.0212842 | − | 0.0368652i | ||||
\(599\) | 353.951 | − | 204.354i | 0.590904 | − | 0.341158i | −0.174551 | − | 0.984648i | \(-0.555847\pi\) |
0.765455 | + | 0.643490i | \(0.222514\pi\) | |||||||
\(600\) | −75.0818 | − | 13.9546i | −0.125136 | − | 0.0232577i | ||||
\(601\) | 326.683 | 0.543566 | 0.271783 | − | 0.962359i | \(-0.412387\pi\) | ||||
0.271783 | + | 0.962359i | \(0.412387\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −84.0000 | + | 67.8823i | −0.139303 | + | 0.112574i | ||||
\(604\) | 152.000 | − | 263.272i | 0.251656 | − | 0.435880i | ||||
\(605\) | 79.6743 | − | 46.0000i | 0.131693 | − | 0.0760331i | ||||
\(606\) | −116.091 | − | 99.2518i | −0.191569 | − | 0.163782i | ||||
\(607\) | −127.279 | + | 220.454i | −0.209686 | + | 0.363186i | −0.951616 | − | 0.307291i | \(-0.900577\pi\) |
0.741930 | + | 0.670478i | \(0.233911\pi\) | |||||||
\(608\) | − | 160.000i | − | 0.263158i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −184.000 | −0.301639 | ||||||||
\(611\) | −374.772 | − | 216.375i | −0.613375 | − | 0.354132i | ||||
\(612\) | 206.960 | − | 537.535i | 0.338170 | − | 0.878325i | ||||
\(613\) | 168.000 | + | 290.985i | 0.274062 | + | 0.474689i | 0.969898 | − | 0.243511i | \(-0.0782993\pi\) |
−0.695836 | + | 0.718201i | \(0.744966\pi\) | |||||||
\(614\) | 422.620 | + | 244.000i | 0.688307 | + | 0.397394i | ||||
\(615\) | −181.019 | + | 64.0000i | −0.294340 | + | 0.104065i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 384.666i | 0.623446i | 0.950173 | + | 0.311723i | \(0.100906\pi\) | ||||
−0.950173 | + | 0.311723i | \(0.899094\pi\) | |||||||
\(618\) | 306.747 | + | 57.0116i | 0.496354 | + | 0.0922517i | ||||
\(619\) | 308.299 | + | 533.989i | 0.498059 | + | 0.862664i | 0.999997 | − | 0.00223976i | \(-0.000712938\pi\) |
−0.501938 | + | 0.864903i | \(0.667380\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −33.5840 | + | 18.1691i | −0.0540805 | + | 0.0292579i | ||||
\(622\) | 749.533 | 1.20504 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 144.000 | − | 50.9117i | 0.230769 | − | 0.0815892i | ||||
\(625\) | 159.500 | − | 276.262i | 0.255200 | − | 0.442019i | ||||
\(626\) | 181.865 | − | 105.000i | 0.290520 | − | 0.167732i | ||||
\(627\) | −545.857 | + | 638.467i | −0.870586 | + | 1.01829i | ||||
\(628\) | −171.120 | + | 296.388i | −0.272484 | + | 0.471956i | ||||
\(629\) | 1600.00i | 2.54372i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −712.000 | −1.12837 | −0.564184 | − | 0.825649i | \(-0.690809\pi\) | ||||
−0.564184 | + | 0.825649i | \(0.690809\pi\) | |||||||
\(632\) | 97.9796 | + | 56.5685i | 0.155031 | + | 0.0895072i | ||||
\(633\) | 848.249 | + | 725.210i | 1.34005 | + | 1.14567i | ||||
\(634\) | −80.0000 | − | 138.564i | −0.126183 | − | 0.218555i | ||||
\(635\) | 360.267 | + | 208.000i | 0.567349 | + | 0.327559i | ||||
\(636\) | −90.5097 | − | 256.000i | −0.142311 | − | 0.402516i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 791.960i | − | 1.24132i | ||||||
\(639\) | 792.112 | − | 124.643i | 1.23961 | − | 0.195059i | ||||
\(640\) | 22.6274 | + | 39.1918i | 0.0353553 | + | 0.0612372i | ||||
\(641\) | 489.898 | − | 282.843i | 0.764271 | − | 0.441252i | −0.0665559 | − | 0.997783i | \(-0.521201\pi\) |
0.830827 | + | 0.556530i | \(0.187868\pi\) | |||||||
\(642\) | −112.927 | + | 607.595i | −0.175898 | + | 0.946409i | ||||
\(643\) | −837.214 | −1.30204 | −0.651022 | − | 0.759059i | \(-0.725659\pi\) | ||||
−0.651022 | + | 0.759059i | \(0.725659\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −208.000 | − | 588.313i | −0.322481 | − | 0.912113i | ||||
\(646\) | 640.000 | − | 1108.51i | 0.990712 | − | 1.71596i | ||||
\(647\) | −805.404 | + | 465.000i | −1.24483 | + | 0.718702i | −0.970073 | − | 0.242813i | \(-0.921930\pi\) |
−0.274755 | + | 0.961514i | \(0.588597\pi\) | |||||||
\(648\) | −70.3587 | − | 218.031i | −0.108578 | − | 0.336468i | ||||
\(649\) | 158.392 | − | 274.343i | 0.244055 | − | 0.422716i | ||||
\(650\) | − | 162.000i | − | 0.249231i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −488.000 | −0.748466 | ||||||||
\(653\) | −455.605 | − | 263.044i | −0.697711 | − | 0.402823i | 0.108783 | − | 0.994065i | \(-0.465304\pi\) |
−0.806494 | + | 0.591242i | \(0.798638\pi\) | |||||||
\(654\) | 485.231 | − | 567.555i | 0.741944 | − | 0.867821i | ||||
\(655\) | 60.0000 | + | 103.923i | 0.0916031 | + | 0.158661i | ||||
\(656\) | −55.4256 | − | 32.0000i | −0.0844903 | − | 0.0487805i | ||||
\(657\) | −227.688 | + | 184.000i | −0.346558 | + | 0.280061i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 46.6690i | − | 0.0708180i | −0.999373 | − | 0.0354090i | \(-0.988727\pi\) | ||
0.999373 | − | 0.0354090i | \(-0.0112734\pi\) | |||||||
\(660\) | 43.4143 | − | 233.588i | 0.0657792 | − | 0.353921i | ||||
\(661\) | −248.194 | − | 429.885i | −0.375483 | − | 0.650356i | 0.614916 | − | 0.788593i | \(-0.289190\pi\) |
−0.990399 | + | 0.138236i | \(0.955857\pi\) | |||||||
\(662\) | −63.6867 | + | 36.7696i | −0.0962035 | + | 0.0555431i | ||||
\(663\) | 1201.31 | + | 223.273i | 1.81193 | + | 0.336762i | ||||
\(664\) | −175.362 | −0.264100 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 400.000 | + | 494.975i | 0.600601 | + | 0.743205i | ||||
\(667\) | 40.0000 | − | 69.2820i | 0.0599700 | − | 0.103871i | ||||
\(668\) | 391.443 | − | 226.000i | 0.585993 | − | 0.338323i | ||||
\(669\) | −38.6969 | − | 33.0839i | −0.0578430 | − | 0.0494528i | ||||
\(670\) | 33.9411 | − | 58.7878i | 0.0506584 | − | 0.0877429i | ||||
\(671\) | 322.000i | 0.479881i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −498.000 | −0.739970 | −0.369985 | − | 0.929038i | \(-0.620637\pi\) | ||||
−0.369985 | + | 0.929038i | \(0.620637\pi\) | |||||||
\(674\) | 97.9796 | + | 56.5685i | 0.145370 | + | 0.0839296i | ||||
\(675\) | −242.907 | − | 6.72704i | −0.359862 | − | 0.00996598i | ||||
\(676\) | −7.00000 | − | 12.1244i | −0.0103550 | − | 0.0179354i | ||||
\(677\) | −883.346 | − | 510.000i | −1.30479 | − | 0.753323i | −0.323572 | − | 0.946203i | \(-0.604884\pi\) |
−0.981222 | + | 0.192880i | \(0.938217\pi\) | |||||||
\(678\) | −67.8823 | + | 24.0000i | −0.100121 | + | 0.0353982i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 362.039i | 0.532410i | ||||||||
\(681\) | −1132.60 | − | 210.504i | −1.66315 | − | 0.309111i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 400.492 | − | 231.224i | 0.586371 | − | 0.338542i | −0.177290 | − | 0.984159i | \(-0.556733\pi\) |
0.763661 | + | 0.645617i | \(0.223400\pi\) | |||||||
\(684\) | −79.1382 | − | 502.929i | −0.115699 | − | 0.735276i | ||||
\(685\) | −271.529 | −0.396393 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 708.000 | − | 250.316i | 1.03057 | − | 0.364361i | ||||
\(688\) | 104.000 | − | 180.133i | 0.151163 | − | 0.261822i | ||||
\(689\) | 498.831 | − | 288.000i | 0.723992 | − | 0.417997i | ||||
\(690\) | 15.5959 | − | 18.2419i | 0.0226028 | − | 0.0264376i | ||||
\(691\) | 271.529 | − | 470.302i | 0.392951 | − | 0.680611i | −0.599886 | − | 0.800085i | \(-0.704788\pi\) |
0.992837 | + | 0.119474i | \(0.0381209\pi\) | |||||||
\(692\) | 264.000i | 0.381503i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 306.000 | 0.440922 | ||||||||
\(695\) | −744.645 | − | 429.921i | −1.07143 | − | 0.618591i | ||||
\(696\) | 364.838 | + | 311.918i | 0.524193 | + | 0.448159i | ||||
\(697\) | −256.000 | − | 443.405i | −0.367288 | − | 0.636162i | ||||
\(698\) | −15.5885 | − | 9.00000i | −0.0223330 | − | 0.0128940i | ||||
\(699\) | −322.441 | − | 912.000i | −0.461289 | − | 1.30472i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 797.616i | − | 1.13783i | −0.822398 | − | 0.568913i | \(-0.807364\pi\) | ||
0.822398 | − | 0.568913i | \(-0.192636\pi\) | |||||||
\(702\) | 427.454 | − | 231.255i | 0.608909 | − | 0.329423i | ||||
\(703\) | 707.107 | + | 1224.74i | 1.00584 | + | 1.74217i | ||||
\(704\) | 68.5857 | − | 39.5980i | 0.0974229 | − | 0.0562471i | ||||
\(705\) | 74.5536 | − | 401.131i | 0.105750 | − | 0.568980i | ||||
\(706\) | 90.5097 | 0.128201 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 64.0000 | + | 181.019i | 0.0903955 | + | 0.255677i | ||||
\(709\) | −440.000 | + | 762.102i | −0.620592 | + | 1.07490i | 0.368783 | + | 0.929515i | \(0.379774\pi\) |
−0.989376 | + | 0.145382i | \(0.953559\pi\) | |||||||
\(710\) | −436.477 | + | 252.000i | −0.614756 | + | 0.354930i | ||||
\(711\) | 335.959 | + | 129.350i | 0.472516 | + | 0.181927i | ||||
\(712\) | 79.1960 | − | 137.171i | 0.111230 | − | 0.192656i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 504.000 | 0.704895 | ||||||||
\(716\) | −389.469 | − | 224.860i | −0.543951 | − | 0.314050i | ||||
\(717\) | 554.156 | − | 648.174i | 0.772881 | − | 0.904008i | ||||
\(718\) | 127.000 | + | 219.970i | 0.176880 | + | 0.306366i | ||||
\(719\) | 568.113 | + | 328.000i | 0.790143 | + | 0.456189i | 0.840013 | − | 0.542567i | \(-0.182547\pi\) |
−0.0498700 | + | 0.998756i | \(0.515881\pi\) | |||||||
\(720\) | 90.5097 | + | 112.000i | 0.125708 | + | 0.155556i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 620.840i | − | 0.859889i | ||||||
\(723\) | 25.5834 | − | 137.650i | 0.0353851 | − | 0.190387i | ||||
\(724\) | −182.434 | − | 315.984i | −0.251980 | − | 0.436442i | ||||
\(725\) | 440.908 | − | 254.558i | 0.608149 | − | 0.351115i | ||||
\(726\) | 95.9378 | + | 17.8309i | 0.132146 | + | 0.0245604i | ||||
\(727\) | −786.303 | −1.08157 | −0.540786 | − | 0.841160i | \(-0.681873\pi\) | ||||
−0.540786 | + | 0.841160i | \(0.681873\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −329.000 | − | 650.538i | −0.451303 | − | 0.892371i | ||||
\(730\) | 92.0000 | − | 159.349i | 0.126027 | − | 0.218286i | ||||
\(731\) | 1441.07 | − | 832.000i | 1.97136 | − | 1.13817i | ||||
\(732\) | −148.338 | − | 126.822i | −0.202648 | − | 0.173254i | ||||
\(733\) | −617.304 | + | 1069.20i | −0.842161 | + | 1.45867i | 0.0459025 | + | 0.998946i | \(0.485384\pi\) |
−0.888064 | + | 0.459720i | \(0.847950\pi\) | |||||||
\(734\) | 184.000i | 0.250681i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.00000 | 0.0108696 | ||||||||
\(737\) | −102.879 | − | 59.3970i | −0.139591 | − | 0.0805929i | ||||
\(738\) | −190.047 | − | 73.1714i | −0.257517 | − | 0.0991483i | ||||
\(739\) | 78.0000 | + | 135.100i | 0.105548 | + | 0.182815i | 0.913962 | − | 0.405800i | \(-0.133007\pi\) |
−0.808414 | + | 0.588614i | \(0.799674\pi\) | |||||||
\(740\) | −346.410 | − | 200.000i | −0.468122 | − | 0.270270i | ||||
\(741\) | 1018.23 | − | 360.000i | 1.37413 | − | 0.485830i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 858.428i | − | 1.15535i | −0.816266 | − | 0.577677i | \(-0.803959\pi\) | ||
0.816266 | − | 0.577677i | \(-0.196041\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −181.019 | − | 313.535i | −0.242979 | − | 0.420852i | ||||
\(746\) | 17.1464 | − | 9.89949i | 0.0229845 | − | 0.0132701i | ||||
\(747\) | −551.218 | + | 86.7367i | −0.737908 | + | 0.116113i | ||||
\(748\) | 633.568 | 0.847016 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 544.000 | − | 192.333i | 0.725333 | − | 0.256444i | ||||
\(751\) | −40.0000 | + | 69.2820i | −0.0532623 | + | 0.0922530i | −0.891427 | − | 0.453164i | \(-0.850295\pi\) |
0.838165 | + | 0.545417i | \(0.183629\pi\) | |||||||
\(752\) | 117.779 | − | 68.0000i | 0.156622 | − | 0.0904255i | ||||
\(753\) | 436.686 | − | 510.774i | 0.579928 | − | 0.678318i | ||||
\(754\) | −509.117 | + | 881.816i | −0.675221 | + | 1.16952i | ||||
\(755\) | 608.000i | 0.805298i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.0000 | −0.0211361 | −0.0105680 | − | 0.999944i | \(-0.503364\pi\) | ||||
−0.0105680 | + | 0.999944i | \(0.503364\pi\) | |||||||
\(758\) | 181.262 | + | 104.652i | 0.239132 | + | 0.138063i | ||||
\(759\) | −31.9233 | − | 27.2929i | −0.0420597 | − | 0.0359590i | ||||
\(760\) | 160.000 | + | 277.128i | 0.210526 | + | 0.364642i | ||||
\(761\) | −588.897 | − | 340.000i | −0.773847 | − | 0.446781i | 0.0603985 | − | 0.998174i | \(-0.480763\pi\) |
−0.834245 | + | 0.551394i | \(0.814096\pi\) | |||||||
\(762\) | 147.078 | + | 416.000i | 0.193016 | + | 0.545932i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 19.7990i | − | 0.0259149i | ||||||
\(765\) | 179.069 | + | 1138.00i | 0.234078 | + | 1.48758i | ||||
\(766\) | 79.1960 | + | 137.171i | 0.103389 | + | 0.179075i | ||||
\(767\) | −352.727 | + | 203.647i | −0.459878 | + | 0.265511i | ||||
\(768\) | −8.77101 | + | 47.1918i | −0.0114206 | + | 0.0614477i | ||||
\(769\) | −1336.43 | −1.73788 | −0.868941 | − | 0.494915i | \(-0.835199\pi\) | ||||
−0.868941 | + | 0.494915i | \(0.835199\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 120.000 | + | 339.411i | 0.155642 | + | 0.440222i | ||||
\(772\) | −160.000 | + | 277.128i | −0.207254 | + | 0.358974i | ||||
\(773\) | −1001.13 | + | 578.000i | −1.29512 | + | 0.747736i | −0.979556 | − | 0.201169i | \(-0.935526\pi\) |
−0.315560 | + | 0.948905i | \(0.602193\pi\) | |||||||
\(774\) | 237.807 | − | 617.653i | 0.307244 | − | 0.798002i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 68.0000i | 0.0876289i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 608.000 | 0.781491 | ||||||||
\(779\) | −391.918 | − | 226.274i | −0.503104 | − | 0.290467i | ||||
\(780\) | −198.504 | + | 232.182i | −0.254492 | + | 0.297669i | ||||
\(781\) | 441.000 | + | 763.834i | 0.564661 | + | 0.978021i | ||||
\(782\) | 55.4256 | + | 32.0000i | 0.0708768 | + | 0.0409207i | ||||
\(783\) | 1301.08 | + | 800.000i | 1.66166 | + | 1.02171i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 684.479i | − | 0.871948i | ||||||
\(786\) | −23.2577 | + | 125.136i | −0.0295899 | + | 0.159206i | ||||
\(787\) | 260.215 | + | 450.706i | 0.330642 | + | 0.572689i | 0.982638 | − | 0.185534i | \(-0.0594014\pi\) |
−0.651996 | + | 0.758223i | \(0.726068\pi\) | |||||||
\(788\) | −186.161 | + | 107.480i | −0.236245 | + | 0.136396i | ||||
\(789\) | −663.222 | − | 123.266i | −0.840586 | − | 0.156230i | ||||
\(790\) | −226.274 | −0.286423 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 196.000 | − | 158.392i | 0.247475 | − | 0.199990i | ||||
\(793\) | 207.000 | − | 358.535i | 0.261034 | − | 0.452124i | ||||
\(794\) | 43.3013 | − | 25.0000i | 0.0545356 | − | 0.0314861i | ||||
\(795\) | 412.767 | + | 352.895i | 0.519204 | + | 0.443894i | ||||
\(796\) | 220.617 | − | 382.120i | 0.277157 | − | 0.480051i | ||||
\(797\) | − | 60.0000i | − | 0.0752823i | −0.999291 | − | 0.0376412i | \(-0.988016\pi\) | ||
0.999291 | − | 0.0376412i | \(-0.0119844\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1088.00 | 1.36170 | ||||||||
\(800\) | 44.0908 | + | 25.4558i | 0.0551135 | + | 0.0318198i | ||||
\(801\) | 181.090 | − | 470.343i | 0.226080 | − | 0.587195i | ||||
\(802\) | −96.0000 | − | 166.277i | −0.119701 | − | 0.207328i | ||||
\(803\) | −278.860 | − | 161.000i | −0.347273 | − | 0.200498i | ||||
\(804\) | 67.8823 | − | 24.0000i | 0.0844307 | − | 0.0298507i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −483.716 | − | 89.9029i | −0.599401 | − | 0.111404i | ||||
\(808\) | 50.9117 | + | 88.1816i | 0.0630095 | + | 0.109136i | ||||
\(809\) | −553.585 | + | 319.612i | −0.684283 | + | 0.395071i | −0.801467 | − | 0.598039i | \(-0.795947\pi\) |
0.117184 | + | 0.993110i | \(0.462613\pi\) | |||||||
\(810\) | 339.896 | + | 307.283i | 0.419625 | + | 0.379361i | ||||
\(811\) | 458.205 | 0.564988 | 0.282494 | − | 0.959269i | \(-0.408838\pi\) | ||||
0.282494 | + | 0.959269i | \(0.408838\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 656.000 | − | 231.931i | 0.806888 | − | 0.285278i | ||||
\(814\) | −350.000 | + | 606.218i | −0.429975 | + | 0.744739i | ||||
\(815\) | 845.241 | − | 488.000i | 1.03711 | − | 0.598773i | ||||
\(816\) | −249.535 | + | 291.871i | −0.305802 | + | 0.357685i | ||||
\(817\) | 735.391 | − | 1273.73i | 0.900111 | − | 1.55904i | ||||
\(818\) | 462.000i | 0.564792i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 128.000 | 0.156098 | ||||||||
\(821\) | 323.333 | + | 186.676i | 0.393828 | + | 0.227377i | 0.683817 | − | 0.729653i | \(-0.260318\pi\) |
−0.289990 | + | 0.957030i | \(0.593652\pi\) | |||||||
\(822\) | −218.903 | − | 187.151i | −0.266305 | − | 0.227678i | ||||
\(823\) | 700.000 | + | 1212.44i | 0.850547 | + | 1.47319i | 0.880716 | + | 0.473645i | \(0.157062\pi\) |
−0.0301688 | + | 0.999545i | \(0.509604\pi\) | |||||||
\(824\) | −180.133 | − | 104.000i | −0.218608 | − | 0.126214i | ||||
\(825\) | −89.0955 | − | 252.000i | −0.107994 | − | 0.305455i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 55.1543i | − | 0.0666921i | −0.999444 | − | 0.0333460i | \(-0.989384\pi\) | ||
0.999444 | − | 0.0333460i | \(-0.0106163\pi\) | |||||||
\(828\) | 25.1464 | − | 3.95691i | 0.0303701 | − | 0.00477888i | ||||
\(829\) | −548.008 | − | 949.177i | −0.661047 | − | 1.14497i | −0.980341 | − | 0.197311i | \(-0.936779\pi\) |
0.319294 | − | 0.947656i | \(-0.396554\pi\) | |||||||
\(830\) | 303.737 | − | 175.362i | 0.365948 | − | 0.211280i | ||||
\(831\) | 254.359 | − | 1368.56i | 0.306088 | − | 1.64689i | ||||
\(832\) | −101.823 | −0.122384 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −304.000 | − | 859.842i | −0.364508 | − | 1.03099i | ||||
\(835\) | −452.000 | + | 782.887i | −0.541317 | + | 0.937589i | ||||
\(836\) | 484.974 | − | 280.000i | 0.580113 | − | 0.334928i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −248.902 | + | 431.110i | −0.297019 | + | 0.514451i | ||||
\(839\) | − | 1250.00i | − | 1.48987i | −0.667138 | − | 0.744934i | \(-0.732481\pi\) | ||
0.667138 | − | 0.744934i | \(-0.267519\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2359.00 | −2.80499 | ||||||||
\(842\) | 293.939 | + | 169.706i | 0.349096 | + | 0.201551i | ||||
\(843\) | −77.1959 | + | 90.2929i | −0.0915728 | + | 0.107109i | ||||
\(844\) | −372.000 | − | 644.323i | −0.440758 | − | 0.763416i | ||||
\(845\) | 24.2487 | + | 14.0000i | 0.0286967 | + | 0.0165680i | ||||
\(846\) | 336.583 | − | 272.000i | 0.397852 | − | 0.321513i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 181.019i | 0.213466i | ||||||||
\(849\) | 136.445 | − | 734.133i | 0.160712 | − | 0.864703i | ||||
\(850\) | 203.647 | + | 352.727i | 0.239584 | + | 0.414972i | ||||
\(851\) | −61.2372 | + | 35.3553i | −0.0719592 | + | 0.0415456i | ||||
\(852\) | −525.572 | − | 97.6821i | −0.616869 | − | 0.114650i | ||||
\(853\) | 250.316 | 0.293453 | 0.146727 | − | 0.989177i | \(-0.453126\pi\) | ||||
0.146727 | + | 0.989177i | \(0.453126\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 640.000 | + | 791.960i | 0.748538 | + | 0.926269i | ||||
\(856\) | 206.000 | − | 356.802i | 0.240654 | − | 0.416825i | ||||
\(857\) | −221.703 | + | 128.000i | −0.258696 | + | 0.149358i | −0.623740 | − | 0.781632i | \(-0.714387\pi\) |
0.365044 | + | 0.930990i | \(0.381054\pi\) | |||||||
\(858\) | 406.318 | + | 347.381i | 0.473564 | + | 0.404873i | ||||
\(859\) | −393.151 | + | 680.958i | −0.457685 | + | 0.792734i | −0.998838 | − | 0.0481904i | \(-0.984655\pi\) |
0.541153 | + | 0.840924i | \(0.317988\pi\) | |||||||
\(860\) | 416.000i | 0.483721i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1038.00 | −1.20418 | ||||||||
\(863\) | 1402.33 | + | 809.637i | 1.62495 | + | 0.938166i | 0.985568 | + | 0.169277i | \(0.0541434\pi\) |
0.639383 | + | 0.768889i | \(0.279190\pi\) | |||||||
\(864\) | −4.22821 | + | 152.677i | −0.00489376 | + | 0.176709i | ||||
\(865\) | −264.000 | − | 457.261i | −0.305202 | − | 0.528626i | ||||
\(866\) | −524.811 | − | 303.000i | −0.606018 | − | 0.349885i | ||||
\(867\) | −2078.89 | + | 735.000i | −2.39780 | + | 0.847751i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 395.980i | 0.455673i | ||||||||
\(870\) | −943.837 | − | 175.420i | −1.08487 | − | 0.201632i | ||||
\(871\) | 76.3675 | + | 132.272i | 0.0876780 | + | 0.151863i | ||||
\(872\) | −431.110 | + | 248.902i | −0.494392 | + | 0.285438i | ||||
\(873\) | 33.6337 | + | 213.745i | 0.0385266 | + | 0.244839i | ||||
\(874\) | 56.5685 | 0.0647237 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 184.000 | − | 65.0538i | 0.210046 | − | 0.0742624i | ||||
\(877\) | 632.000 | − | 1094.66i | 0.720639 | − | 1.24818i | −0.240106 | − | 0.970747i | \(-0.577182\pi\) |
0.960744 | − | 0.277436i | \(-0.0894846\pi\) | |||||||
\(878\) | −498.831 | + | 288.000i | −0.568144 | + | 0.328018i | ||||
\(879\) | −616.039 | + | 720.556i | −0.700840 | + | 0.819745i | ||||
\(880\) | −79.1960 | + | 137.171i | −0.0899954 | + | 0.155877i | ||||
\(881\) | 264.000i | 0.299659i | 0.988712 | + | 0.149830i | \(0.0478726\pi\) | ||||
−0.988712 | + | 0.149830i | \(0.952127\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1148.00 | 1.30011 | 0.650057 | − | 0.759886i | \(-0.274745\pi\) | ||||
0.650057 | + | 0.759886i | \(0.274745\pi\) | |||||||
\(884\) | −705.453 | − | 407.294i | −0.798024 | − | 0.460739i | ||||
\(885\) | −291.871 | − | 249.535i | −0.329797 | − | 0.281960i | ||||
\(886\) | 281.000 | + | 486.706i | 0.317156 | + | 0.549330i | ||||
\(887\) | 1110.24 | + | 641.000i | 1.25168 | + | 0.722661i | 0.971444 | − | 0.237269i | \(-0.0762523\pi\) |
0.280241 | + | 0.959930i | \(0.409586\pi\) | |||||||
\(888\) | −141.421 | − | 400.000i | −0.159258 | − | 0.450450i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 316.784i | 0.355937i | ||||||||
\(891\) | 537.745 | − | 594.818i | 0.603529 | − | 0.667585i | ||||
\(892\) | 16.9706 | + | 29.3939i | 0.0190253 | + | 0.0329528i | ||||
\(893\) | 832.827 | − | 480.833i | 0.932616 | − | 0.538446i | ||||
\(894\) | 70.1681 | − | 377.535i | 0.0784878 | − | 0.422298i | ||||
\(895\) | 899.440 | 1.00496 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.0000 | + | 50.9117i | 0.0200669 | + | 0.0567577i | ||||
\(898\) | 12.0000 | − | 20.7846i | 0.0133630 | − | 0.0231454i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 151.182 | + | 58.2075i | 0.167980 | + | 0.0646750i | ||||
\(901\) | −724.077 | + | 1254.14i | −0.803637 | + | 1.39194i | ||||
\(902\) | − | 224.000i | − | 0.248337i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 48.0000 | 0.0530973 | ||||||||
\(905\) | 631.968 | + | 364.867i | 0.698308 | + | 0.403168i | ||||
\(906\) | −419.063 | + | 490.161i | −0.462542 | + | 0.541017i | ||||
\(907\) | −434.000 | − | 751.710i | −0.478501 | − | 0.828787i | 0.521196 | − | 0.853437i | \(-0.325486\pi\) |
−0.999696 | + | 0.0246500i | \(0.992153\pi\) | |||||||
\(908\) | 665.108 | + | 384.000i | 0.732497 | + | 0.422907i | ||||
\(909\) | 203.647 | + | 252.000i | 0.224034 | + | 0.277228i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1231.78i | 1.35212i | 0.736847 | + | 0.676059i | \(0.236314\pi\) | ||||
−0.736847 | + | 0.676059i | \(0.763686\pi\) | |||||||
\(912\) | −62.0204 | + | 333.697i | −0.0680048 | + | 0.365895i | ||||
\(913\) | −306.884 | − | 531.539i | −0.336127 | − | 0.582190i | ||||
\(914\) | 154.318 | − | 89.0955i | 0.168838 | − | 0.0974786i | ||||
\(915\) | 383.751 | + | 71.3235i | 0.419400 | + | 0.0779491i | ||||
\(916\) | −500.632 | −0.546541 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −640.000 | + | 1040.86i | −0.697168 | + | 1.13384i | ||||
\(919\) | 64.0000 | − | 110.851i | 0.0696409 | − | 0.120622i | −0.829102 | − | 0.559097i | \(-0.811148\pi\) |
0.898743 | + | 0.438475i | \(0.144481\pi\) | |||||||
\(920\) | −13.8564 | + | 8.00000i | −0.0150613 | + | 0.00869565i | ||||
\(921\) | −786.838 | − | 672.707i | −0.854330 | − | 0.730409i | ||||
\(922\) | 410.122 | − | 710.352i | 0.444818 | − | 0.770447i | ||||
\(923\) | − | 1134.00i | − | 1.22860i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −450.000 | −0.486486 | ||||||||
\(926\) | 137.171 | + | 79.1960i | 0.148133 | + | 0.0855248i | ||||
\(927\) | −617.653 | − | 237.807i | −0.666293 | − | 0.256534i | ||||
\(928\) | −160.000 | − | 277.128i | −0.172414 | − | 0.298629i | ||||
\(929\) | 1274.79 | + | 736.000i | 1.37222 | + | 0.792250i | 0.991207 | − | 0.132321i | \(-0.0422430\pi\) |
0.381010 | + | 0.924571i | \(0.375576\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 644.881i | 0.691933i | ||||||||
\(933\) | −1563.23 | − | 290.540i | −1.67549 | − | 0.311404i | ||||
\(934\) | 90.5097 | + | 156.767i | 0.0969054 | + | 0.167845i | ||||
\(935\) | −1097.37 | + | 633.568i | −1.17366 | + | 0.677612i | ||||
\(936\) | −320.062 | + | 50.3633i | −0.341946 | + | 0.0538069i | ||||
\(937\) | 507.703 | 0.541838 | 0.270919 | − | 0.962602i | \(-0.412672\pi\) | ||||
0.270919 | + | 0.962602i | \(0.412672\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −420.000 | + | 148.492i | −0.447284 | + | 0.158139i | ||||
\(940\) | −136.000 | + | 235.559i | −0.144681 | + | 0.250595i | ||||
\(941\) | 959.556 | − | 554.000i | 1.01972 | − | 0.588735i | 0.105697 | − | 0.994398i | \(-0.466293\pi\) |
0.914023 | + | 0.405663i | \(0.132959\pi\) | |||||||
\(942\) | 471.777 | − | 551.818i | 0.500824 | − | 0.585794i | ||||
\(943\) | 11.3137 | − | 19.5959i | 0.0119976 | − | 0.0207804i | ||||
\(944\) | − | 128.000i | − | 0.135593i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 728.000 | 0.769556 | ||||||||
\(947\) | 216.780 | + | 125.158i | 0.228912 | + | 0.132163i | 0.610070 | − | 0.792347i | \(-0.291141\pi\) |
−0.381158 | + | 0.924510i | \(0.624475\pi\) | |||||||
\(948\) | −182.419 | − | 155.959i | −0.192425 | − | 0.164514i | ||||
\(949\) | 207.000 | + | 358.535i | 0.218124 | + | 0.377802i | ||||
\(950\) | 311.769 | + | 180.000i | 0.328178 | + | 0.189474i | ||||
\(951\) | 113.137 | + | 320.000i | 0.118966 | + | 0.336488i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 497.803i | − | 0.522354i | −0.965291 | − | 0.261177i | \(-0.915889\pi\) | ||
0.965291 | − | 0.261177i | \(-0.0841106\pi\) | |||||||
\(954\) | 89.5347 | + | 568.999i | 0.0938519 | + | 0.596435i | ||||
\(955\) | 19.7990 | + | 34.2929i | 0.0207319 | + | 0.0359088i | ||||
\(956\) | −492.347 | + | 284.257i | −0.515008 | + | 0.297340i | ||||
\(957\) | −306.985 | + | 1651.71i | −0.320779 | + | 1.72593i | ||||
\(958\) | −681.651 | −0.711535 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −32.0000 | − | 90.5097i | −0.0333333 | − | 0.0942809i | ||||
\(961\) | 480.500 | − | 832.250i | 0.500000 | − | 0.866025i | ||||
\(962\) | 779.423 | − | 450.000i | 0.810211 | − | 0.467775i | ||||
\(963\) | 471.041 | − | 1223.43i | 0.489139 | − | 1.27044i | ||||
\(964\) | −46.6690 | + | 80.8332i | −0.0484119 | + | 0.0838518i | ||||
\(965\) | − | 640.000i | − | 0.663212i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −384.000 | −0.397104 | −0.198552 | − | 0.980090i | \(-0.563624\pi\) | ||||
−0.198552 | + | 0.980090i | \(0.563624\pi\) | |||||||
\(968\) | −56.3383 | − | 32.5269i | −0.0582007 | − | 0.0336022i | ||||
\(969\) | −1764.48 | + | 2063.84i | −1.82093 | + | 2.12986i | ||||
\(970\) | −68.0000 | − | 117.779i | −0.0701031 | − | 0.121422i | ||||
\(971\) | −289.252 | − | 167.000i | −0.297891 | − | 0.171988i | 0.343604 | − | 0.939115i | \(-0.388352\pi\) |
−0.641495 | + | 0.767127i | \(0.721686\pi\) | |||||||
\(972\) | 62.2254 | + | 482.000i | 0.0640179 | + | 0.495885i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 169.706i | 0.174236i | ||||||||
\(975\) | −62.7957 | + | 337.868i | −0.0644058 | + | 0.346531i | ||||
\(976\) | 65.0538 | + | 112.677i | 0.0666535 | + | 0.115447i | ||||
\(977\) | −44.0908 | + | 25.4558i | −0.0451288 | + | 0.0260551i | −0.522395 | − | 0.852704i | \(-0.674961\pi\) |
0.477266 | + | 0.878759i | \(0.341628\pi\) | |||||||
\(978\) | 1017.77 | + | 189.162i | 1.04067 | + | 0.193417i | ||||
\(979\) | 554.372 | 0.566263 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1232.00 | + | 995.606i | −1.25586 | + | 1.01489i | ||||
\(982\) | −441.000 | + | 763.834i | −0.449084 | + | 0.777835i | ||||
\(983\) | −969.948 | + | 560.000i | −0.986723 | + | 0.569685i | −0.904293 | − | 0.426912i | \(-0.859601\pi\) |
−0.0824297 | + | 0.996597i | \(0.526268\pi\) | |||||||
\(984\) | 103.192 | + | 88.2238i | 0.104870 | + | 0.0896584i | ||||
\(985\) | 214.960 | − | 372.322i | 0.218234 | − | 0.377992i | ||||
\(986\) | − | 2560.00i | − | 2.59635i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −720.000 | −0.728745 | ||||||||
\(989\) | 63.6867 | + | 36.7696i | 0.0643951 | + | 0.0371785i | ||||
\(990\) | −181.090 | + | 470.343i | −0.182919 | + | 0.475094i | ||||
\(991\) | −508.000 | − | 879.882i | −0.512614 | − | 0.887873i | −0.999893 | − | 0.0146266i | \(-0.995344\pi\) |
0.487280 | − | 0.873246i | \(-0.337989\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 147.078 | − | 52.0000i | 0.148115 | − | 0.0523666i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 882.469i | 0.886904i | ||||||||
\(996\) | 365.737 | + | 67.9753i | 0.367206 | + | 0.0682483i | ||||
\(997\) | 610.233 | + | 1056.95i | 0.612069 | + | 1.06014i | 0.990891 | + | 0.134666i | \(0.0429960\pi\) |
−0.378822 | + | 0.925470i | \(0.623671\pi\) | |||||||
\(998\) | −347.828 | + | 200.818i | −0.348525 | + | 0.201221i | ||||
\(999\) | −642.376 | − | 1187.37i | −0.643019 | − | 1.18856i |
(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 | 294.3.h.e.275.3 | 8 | ||
3.2 | odd | 2 | inner | 294.3.h.e.275.1 | 8 | ||
7.2 | even | 3 | 294.3.b.g.197.2 | yes | 4 | ||
7.3 | odd | 6 | inner | 294.3.h.e.263.2 | 8 | ||
7.4 | even | 3 | inner | 294.3.h.e.263.1 | 8 | ||
7.5 | odd | 6 | 294.3.b.g.197.1 | ✓ | 4 | ||
7.6 | odd | 2 | inner | 294.3.h.e.275.4 | 8 | ||
21.2 | odd | 6 | 294.3.b.g.197.4 | yes | 4 | ||
21.5 | even | 6 | 294.3.b.g.197.3 | yes | 4 | ||
21.11 | odd | 6 | inner | 294.3.h.e.263.3 | 8 | ||
21.17 | even | 6 | inner | 294.3.h.e.263.4 | 8 | ||
21.20 | even | 2 | inner | 294.3.h.e.275.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
294.3.b.g.197.1 | ✓ | 4 | 7.5 | odd | 6 | ||
294.3.b.g.197.2 | yes | 4 | 7.2 | even | 3 | ||
294.3.b.g.197.3 | yes | 4 | 21.5 | even | 6 | ||
294.3.b.g.197.4 | yes | 4 | 21.2 | odd | 6 | ||
294.3.h.e.263.1 | 8 | 7.4 | even | 3 | inner | ||
294.3.h.e.263.2 | 8 | 7.3 | odd | 6 | inner | ||
294.3.h.e.263.3 | 8 | 21.11 | odd | 6 | inner | ||
294.3.h.e.263.4 | 8 | 21.17 | even | 6 | inner | ||
294.3.h.e.275.1 | 8 | 3.2 | odd | 2 | inner | ||
294.3.h.e.275.2 | 8 | 21.20 | even | 2 | inner | ||
294.3.h.e.275.3 | 8 | 1.1 | even | 1 | trivial | ||
294.3.h.e.275.4 | 8 | 7.6 | odd | 2 | inner |