Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [810,3,Mod(269,810)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(810, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("810.269");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 810 = 2 \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 810.j (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: | \(22.0709014132\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 270) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.4 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 810.269 |
Dual form | 810.3.j.e.539.4 |
$q$-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 \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).
\(n\) | \(487\) | \(731\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 1.22474i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | − | 1.73205i | −0.250000 | − | 0.433013i | ||||
\(5\) | 4.82963 | + | 1.29410i | 0.965926 | + | 0.258819i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.33013 | + | 2.50000i | 0.618590 | + | 0.357143i | 0.776320 | − | 0.630339i | \(-0.217084\pi\) |
−0.157730 | + | 0.987482i | \(0.550418\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.00000 | − | 5.00000i | 0.500000 | − | 0.500000i | ||||
\(11\) | 1.22474 | + | 0.707107i | 0.111340 | + | 0.0642824i | 0.554636 | − | 0.832093i | \(-0.312857\pi\) |
−0.443296 | + | 0.896375i | \(0.646191\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.79423 | + | 4.50000i | −0.599556 | + | 0.346154i | −0.768867 | − | 0.639409i | \(-0.779179\pi\) |
0.169311 | + | 0.985563i | \(0.445846\pi\) | |||||||
\(14\) | 6.12372 | − | 3.53553i | 0.437409 | − | 0.252538i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | 11.3137 | 0.665512 | 0.332756 | − | 0.943013i | \(-0.392021\pi\) | ||||
0.332756 | + | 0.943013i | \(0.392021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 21.0000 | 1.10526 | 0.552632 | − | 0.833426i | \(-0.313624\pi\) | ||||
0.552632 | + | 0.833426i | \(0.313624\pi\) | |||||||
\(20\) | −2.58819 | − | 9.65926i | −0.129410 | − | 0.482963i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.73205 | − | 1.00000i | 0.0787296 | − | 0.0454545i | ||||
\(23\) | −0.707107 | − | 1.22474i | −0.0307438 | − | 0.0532498i | 0.850244 | − | 0.526389i | \(-0.176454\pi\) |
−0.880988 | + | 0.473139i | \(0.843121\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 21.6506 | + | 12.5000i | 0.866025 | + | 0.500000i | ||||
\(26\) | 12.7279i | 0.489535i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 10.0000i | − | 0.357143i | ||||||
\(29\) | 33.0681 | + | 19.0919i | 1.14028 | + | 0.658341i | 0.946500 | − | 0.322704i | \(-0.104592\pi\) |
0.193780 | + | 0.981045i | \(0.437925\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −20.0000 | − | 34.6410i | −0.645161 | − | 1.11745i | −0.984264 | − | 0.176703i | \(-0.943457\pi\) |
0.339103 | − | 0.940749i | \(-0.389876\pi\) | |||||||
\(32\) | 2.82843 | + | 4.89898i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.00000 | − | 13.8564i | 0.235294 | − | 0.407541i | ||||
\(35\) | 17.6777 | + | 17.6777i | 0.505076 | + | 0.505076i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 25.0000i | 0.675676i | 0.941204 | + | 0.337838i | \(0.109696\pi\) | ||||
−0.941204 | + | 0.337838i | \(0.890304\pi\) | |||||||
\(38\) | 14.8492 | − | 25.7196i | 0.390770 | − | 0.676833i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −13.6603 | − | 3.66025i | −0.341506 | − | 0.0915064i | ||||
\(41\) | −45.3156 | + | 26.1630i | −1.10526 | + | 0.638121i | −0.937597 | − | 0.347724i | \(-0.886955\pi\) |
−0.167661 | + | 0.985845i | \(0.553621\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 55.4256 | + | 32.0000i | 1.28897 | + | 0.744186i | 0.978470 | − | 0.206388i | \(-0.0661709\pi\) |
0.310498 | + | 0.950574i | \(0.399504\pi\) | |||||||
\(44\) | − | 2.82843i | − | 0.0642824i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.00000 | −0.0434783 | ||||||||
\(47\) | −11.3137 | + | 19.5959i | −0.240717 | + | 0.416934i | −0.960919 | − | 0.276830i | \(-0.910716\pi\) |
0.720202 | + | 0.693765i | \(0.244049\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −12.0000 | − | 20.7846i | −0.244898 | − | 0.424176i | ||||
\(50\) | 30.6186 | − | 17.6777i | 0.612372 | − | 0.353553i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 15.5885 | + | 9.00000i | 0.299778 | + | 0.173077i | ||||
\(53\) | 72.1249 | 1.36085 | 0.680424 | − | 0.732819i | \(-0.261796\pi\) | ||||
0.680424 | + | 0.732819i | \(0.261796\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.00000 | + | 5.00000i | 0.0909091 | + | 0.0909091i | ||||
\(56\) | −12.2474 | − | 7.07107i | −0.218704 | − | 0.126269i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 46.7654 | − | 27.0000i | 0.806300 | − | 0.465517i | ||||
\(59\) | −78.3837 | + | 45.2548i | −1.32854 | + | 0.767031i | −0.985073 | − | 0.172135i | \(-0.944933\pi\) |
−0.343463 | + | 0.939166i | \(0.611600\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 48.5000 | − | 84.0045i | 0.795082 | − | 1.37712i | −0.127705 | − | 0.991812i | \(-0.540761\pi\) |
0.922787 | − | 0.385310i | \(-0.125906\pi\) | |||||||
\(62\) | −56.5685 | −0.912396 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | −43.4667 | + | 11.6469i | −0.668718 | + | 0.179182i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 113.449 | − | 65.5000i | 1.69327 | − | 0.977612i | 0.741429 | − | 0.671032i | \(-0.234149\pi\) |
0.951845 | − | 0.306580i | \(-0.0991848\pi\) | |||||||
\(68\) | −11.3137 | − | 19.5959i | −0.166378 | − | 0.288175i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 34.1506 | − | 9.15064i | 0.487866 | − | 0.130723i | ||||
\(71\) | 89.0955i | 1.25487i | 0.778671 | + | 0.627433i | \(0.215894\pi\) | ||||
−0.778671 | + | 0.627433i | \(0.784106\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 17.0000i | 0.232877i | 0.993198 | + | 0.116438i | \(0.0371477\pi\) | ||||
−0.993198 | + | 0.116438i | \(0.962852\pi\) | |||||||
\(74\) | 30.6186 | + | 17.6777i | 0.413765 | + | 0.238887i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −21.0000 | − | 36.3731i | −0.276316 | − | 0.478593i | ||||
\(77\) | 3.53553 | + | 6.12372i | 0.0459160 | + | 0.0795289i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 58.5000 | − | 101.325i | 0.740506 | − | 1.28259i | −0.211759 | − | 0.977322i | \(-0.567919\pi\) |
0.952265 | − | 0.305273i | \(-0.0987476\pi\) | |||||||
\(80\) | −14.1421 | + | 14.1421i | −0.176777 | + | 0.176777i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 74.0000i | 0.902439i | ||||||||
\(83\) | 28.9914 | − | 50.2145i | 0.349294 | − | 0.604994i | −0.636830 | − | 0.771004i | \(-0.719755\pi\) |
0.986124 | + | 0.166009i | \(0.0530882\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 54.6410 | + | 14.6410i | 0.642835 | + | 0.172247i | ||||
\(86\) | 78.3837 | − | 45.2548i | 0.911438 | − | 0.526219i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.46410 | − | 2.00000i | −0.0393648 | − | 0.0227273i | ||||
\(89\) | − | 147.078i | − | 1.65256i | −0.563257 | − | 0.826282i | \(-0.690452\pi\) | ||
0.563257 | − | 0.826282i | \(-0.309548\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −45.0000 | −0.494505 | ||||||||
\(92\) | −1.41421 | + | 2.44949i | −0.0153719 | + | 0.0266249i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 16.0000 | + | 27.7128i | 0.170213 | + | 0.294817i | ||||
\(95\) | 101.422 | + | 27.1760i | 1.06760 | + | 0.286063i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −35.5070 | − | 20.5000i | −0.366052 | − | 0.211340i | 0.305680 | − | 0.952134i | \(-0.401116\pi\) |
−0.671732 | + | 0.740794i | \(0.734449\pi\) | |||||||
\(98\) | −33.9411 | −0.346338 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | − | 50.0000i | − | 0.500000i | ||||||
\(101\) | −78.3837 | − | 45.2548i | −0.776076 | − | 0.448068i | 0.0589618 | − | 0.998260i | \(-0.481221\pi\) |
−0.835038 | + | 0.550193i | \(0.814554\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.2583 | − | 6.50000i | 0.109304 | − | 0.0631068i | −0.444351 | − | 0.895853i | \(-0.646566\pi\) |
0.553655 | + | 0.832746i | \(0.313232\pi\) | |||||||
\(104\) | 22.0454 | − | 12.7279i | 0.211975 | − | 0.122384i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 51.0000 | − | 88.3346i | 0.481132 | − | 0.833345i | ||||
\(107\) | −123.037 | −1.14987 | −0.574937 | − | 0.818197i | \(-0.694974\pi\) | ||||
−0.574937 | + | 0.818197i | \(0.694974\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.00000 | 0.0733945 | 0.0366972 | − | 0.999326i | \(-0.488316\pi\) | ||||
0.0366972 | + | 0.999326i | \(0.488316\pi\) | |||||||
\(110\) | 9.65926 | − | 2.58819i | 0.0878114 | − | 0.0235290i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −17.3205 | + | 10.0000i | −0.154647 | + | 0.0892857i | ||||
\(113\) | 19.0919 | + | 33.0681i | 0.168955 | + | 0.292638i | 0.938053 | − | 0.346493i | \(-0.112628\pi\) |
−0.769098 | + | 0.639131i | \(0.779294\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.83013 | − | 6.83013i | −0.0159141 | − | 0.0593924i | ||||
\(116\) | − | 76.3675i | − | 0.658341i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 128.000i | 1.08475i | ||||||||
\(119\) | 48.9898 | + | 28.2843i | 0.411679 | + | 0.237683i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −59.5000 | − | 103.057i | −0.491736 | − | 0.851711i | ||||
\(122\) | −68.5894 | − | 118.800i | −0.562208 | − | 0.973773i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −40.0000 | + | 69.2820i | −0.322581 | + | 0.558726i | ||||
\(125\) | 88.3883 | + | 88.3883i | 0.707107 | + | 0.707107i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.00000i | − | 0.0629921i | −0.999504 | − | 0.0314961i | \(-0.989973\pi\) | ||
0.999504 | − | 0.0314961i | \(-0.0100272\pi\) | |||||||
\(128\) | 5.65685 | − | 9.79796i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −16.4711 | + | 61.4711i | −0.126701 | + | 0.472855i | ||||
\(131\) | 117.576 | − | 67.8823i | 0.897523 | − | 0.518185i | 0.0211272 | − | 0.999777i | \(-0.493274\pi\) |
0.876396 | + | 0.481592i | \(0.159941\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 90.9327 | + | 52.5000i | 0.683704 | + | 0.394737i | ||||
\(134\) | − | 185.262i | − | 1.38255i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −32.0000 | −0.235294 | ||||||||
\(137\) | −133.643 | + | 231.477i | −0.975498 | + | 1.68961i | −0.297215 | + | 0.954811i | \(0.596058\pi\) |
−0.678283 | + | 0.734801i | \(0.737276\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.5000 | + | 32.0429i | 0.133094 | + | 0.230525i | 0.924868 | − | 0.380289i | \(-0.124176\pi\) |
−0.791774 | + | 0.610814i | \(0.790842\pi\) | |||||||
\(140\) | 12.9410 | − | 48.2963i | 0.0924354 | − | 0.344974i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 109.119 | + | 63.0000i | 0.768445 | + | 0.443662i | ||||
\(143\) | −12.7279 | −0.0890064 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 135.000 | + | 135.000i | 0.931034 | + | 0.931034i | ||||
\(146\) | 20.8207 | + | 12.0208i | 0.142607 | + | 0.0823344i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 43.3013 | − | 25.0000i | 0.292576 | − | 0.168919i | ||||
\(149\) | −225.353 | + | 130.108i | −1.51244 | + | 0.873206i | −0.512542 | + | 0.858662i | \(0.671296\pi\) |
−0.999894 | + | 0.0145438i | \(0.995370\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −54.5000 | + | 94.3968i | −0.360927 | + | 0.625144i | −0.988114 | − | 0.153725i | \(-0.950873\pi\) |
0.627187 | + | 0.778869i | \(0.284206\pi\) | |||||||
\(152\) | −59.3970 | −0.390770 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 10.0000 | 0.0649351 | ||||||||
\(155\) | −51.7638 | − | 193.185i | −0.333960 | − | 1.24636i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −102.191 | + | 59.0000i | −0.650898 | + | 0.375796i | −0.788800 | − | 0.614650i | \(-0.789297\pi\) |
0.137902 | + | 0.990446i | \(0.455964\pi\) | |||||||
\(158\) | −82.7315 | − | 143.295i | −0.523617 | − | 0.906931i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.32051 | + | 27.3205i | 0.0457532 | + | 0.170753i | ||||
\(161\) | − | 7.07107i | − | 0.0439197i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 203.000i | − | 1.24540i | −0.782461 | − | 0.622699i | \(-0.786036\pi\) | ||
0.782461 | − | 0.622699i | \(-0.213964\pi\) | |||||||
\(164\) | 90.6311 | + | 52.3259i | 0.552629 | + | 0.319060i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −41.0000 | − | 71.0141i | −0.246988 | − | 0.427796i | ||||
\(167\) | 50.9117 | + | 88.1816i | 0.304860 | + | 0.528034i | 0.977230 | − | 0.212182i | \(-0.0680569\pi\) |
−0.672370 | + | 0.740215i | \(0.734724\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −44.0000 | + | 76.2102i | −0.260355 | + | 0.450948i | ||||
\(170\) | 56.5685 | − | 56.5685i | 0.332756 | − | 0.332756i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 128.000i | − | 0.744186i | ||||||
\(173\) | −5.65685 | + | 9.79796i | −0.0326986 | + | 0.0566356i | −0.881912 | − | 0.471415i | \(-0.843743\pi\) |
0.849213 | + | 0.528050i | \(0.177077\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 62.5000 | + | 108.253i | 0.357143 | + | 0.618590i | ||||
\(176\) | −4.89898 | + | 2.82843i | −0.0278351 | + | 0.0160706i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −180.133 | − | 104.000i | −1.01198 | − | 0.584270i | ||||
\(179\) | 125.865i | 0.703156i | 0.936159 | + | 0.351578i | \(0.114355\pi\) | ||||
−0.936159 | + | 0.351578i | \(0.885645\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −127.000 | −0.701657 | −0.350829 | − | 0.936440i | \(-0.614100\pi\) | ||||
−0.350829 | + | 0.936440i | \(0.614100\pi\) | |||||||
\(182\) | −31.8198 | + | 55.1135i | −0.174834 | + | 0.302822i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.00000 | + | 3.46410i | 0.0108696 | + | 0.0188266i | ||||
\(185\) | −32.3524 | + | 120.741i | −0.174878 | + | 0.652653i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.8564 | + | 8.00000i | 0.0740984 | + | 0.0427807i | ||||
\(188\) | 45.2548 | 0.240717 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 105.000 | − | 105.000i | 0.552632 | − | 0.552632i | ||||
\(191\) | −88.1816 | − | 50.9117i | −0.461684 | − | 0.266553i | 0.251068 | − | 0.967969i | \(-0.419218\pi\) |
−0.712752 | + | 0.701416i | \(0.752552\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −234.693 | + | 135.500i | −1.21603 | + | 0.702073i | −0.964065 | − | 0.265665i | \(-0.914408\pi\) |
−0.251960 | + | 0.967738i | \(0.581075\pi\) | |||||||
\(194\) | −50.2145 | + | 28.9914i | −0.258838 | + | 0.149440i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −24.0000 | + | 41.5692i | −0.122449 | + | 0.212088i | ||||
\(197\) | −316.784 | −1.60804 | −0.804020 | − | 0.594602i | \(-0.797309\pi\) | ||||
−0.804020 | + | 0.594602i | \(0.797309\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 147.000 | 0.738693 | 0.369347 | − | 0.929292i | \(-0.379581\pi\) | ||||
0.369347 | + | 0.929292i | \(0.379581\pi\) | |||||||
\(200\) | −61.2372 | − | 35.3553i | −0.306186 | − | 0.176777i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −110.851 | + | 64.0000i | −0.548769 | + | 0.316832i | ||||
\(203\) | 95.4594 | + | 165.341i | 0.470243 | + | 0.814486i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −252.715 | + | 67.7147i | −1.23275 | + | 0.330316i | ||||
\(206\) | − | 18.3848i | − | 0.0892465i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 36.0000i | − | 0.173077i | ||||||
\(209\) | 25.7196 | + | 14.8492i | 0.123060 | + | 0.0710490i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −70.5000 | − | 122.110i | −0.334123 | − | 0.578718i | 0.649193 | − | 0.760624i | \(-0.275107\pi\) |
−0.983316 | + | 0.181906i | \(0.941774\pi\) | |||||||
\(212\) | −72.1249 | − | 124.924i | −0.340212 | − | 0.589264i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −87.0000 | + | 150.688i | −0.406542 | + | 0.704151i | ||||
\(215\) | 226.274 | + | 226.274i | 1.05244 | + | 1.05244i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 200.000i | − | 0.921659i | ||||||
\(218\) | 5.65685 | − | 9.79796i | 0.0259489 | − | 0.0449448i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.66025 | − | 13.6603i | 0.0166375 | − | 0.0620921i | ||||
\(221\) | −88.1816 | + | 50.9117i | −0.399012 | + | 0.230370i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.92820 | − | 4.00000i | −0.0310682 | − | 0.0179372i | 0.484385 | − | 0.874855i | \(-0.339043\pi\) |
−0.515454 | + | 0.856917i | \(0.672377\pi\) | |||||||
\(224\) | 28.2843i | 0.126269i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 54.0000 | 0.238938 | ||||||||
\(227\) | 34.6482 | − | 60.0125i | 0.152635 | − | 0.264372i | −0.779560 | − | 0.626327i | \(-0.784557\pi\) |
0.932196 | + | 0.361955i | \(0.117891\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.00000 | + | 6.92820i | 0.0174672 | + | 0.0302542i | 0.874627 | − | 0.484797i | \(-0.161106\pi\) |
−0.857160 | + | 0.515051i | \(0.827773\pi\) | |||||||
\(230\) | −9.65926 | − | 2.58819i | −0.0419968 | − | 0.0112530i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −93.5307 | − | 54.0000i | −0.403150 | − | 0.232759i | ||||
\(233\) | 316.784 | 1.35959 | 0.679794 | − | 0.733403i | \(-0.262069\pi\) | ||||
0.679794 | + | 0.733403i | \(0.262069\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −80.0000 | + | 80.0000i | −0.340426 | + | 0.340426i | ||||
\(236\) | 156.767 | + | 90.5097i | 0.664268 | + | 0.383516i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 69.2820 | − | 40.0000i | 0.291101 | − | 0.168067i | ||||
\(239\) | 177.588 | − | 102.530i | 0.743046 | − | 0.428998i | −0.0801297 | − | 0.996784i | \(-0.525533\pi\) |
0.823176 | + | 0.567787i | \(0.192200\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −39.5000 | + | 68.4160i | −0.163900 | + | 0.283884i | −0.936264 | − | 0.351297i | \(-0.885741\pi\) |
0.772364 | + | 0.635180i | \(0.219074\pi\) | |||||||
\(242\) | −168.291 | −0.695419 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −194.000 | −0.795082 | ||||||||
\(245\) | −31.0583 | − | 115.911i | −0.126769 | − | 0.473107i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −163.679 | + | 94.5000i | −0.662667 | + | 0.382591i | ||||
\(248\) | 56.5685 | + | 97.9796i | 0.228099 | + | 0.395079i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 170.753 | − | 45.7532i | 0.683013 | − | 0.183013i | ||||
\(251\) | 46.6690i | 0.185932i | 0.995669 | + | 0.0929662i | \(0.0296349\pi\) | ||||
−0.995669 | + | 0.0929662i | \(0.970365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.00000i | − | 0.00790514i | ||||||
\(254\) | −9.79796 | − | 5.65685i | −0.0385746 | − | 0.0222711i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −84.8528 | − | 146.969i | −0.330167 | − | 0.571865i | 0.652378 | − | 0.757894i | \(-0.273772\pi\) |
−0.982544 | + | 0.186029i | \(0.940438\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −62.5000 | + | 108.253i | −0.241313 | + | 0.417966i | ||||
\(260\) | 63.6396 | + | 63.6396i | 0.244768 | + | 0.244768i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 192.000i | − | 0.732824i | ||||||
\(263\) | 141.421 | − | 244.949i | 0.537724 | − | 0.931365i | −0.461302 | − | 0.887243i | \(-0.652618\pi\) |
0.999026 | − | 0.0441219i | \(-0.0140490\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 348.336 | + | 93.3365i | 1.31448 | + | 0.352213i | ||||
\(266\) | 128.598 | − | 74.2462i | 0.483452 | − | 0.279121i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −226.899 | − | 131.000i | −0.846637 | − | 0.488806i | ||||
\(269\) | 101.823i | 0.378526i | 0.981926 | + | 0.189263i | \(0.0606098\pi\) | ||||
−0.981926 | + | 0.189263i | \(0.939390\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −221.000 | −0.815498 | −0.407749 | − | 0.913094i | \(-0.633686\pi\) | ||||
−0.407749 | + | 0.913094i | \(0.633686\pi\) | |||||||
\(272\) | −22.6274 | + | 39.1918i | −0.0831890 | + | 0.144088i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 189.000 | + | 327.358i | 0.689781 | + | 1.19474i | ||||
\(275\) | 17.6777 | + | 30.6186i | 0.0642824 | + | 0.111340i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −76.2102 | − | 44.0000i | −0.275127 | − | 0.158845i | 0.356088 | − | 0.934452i | \(-0.384110\pi\) |
−0.631215 | + | 0.775608i | \(0.717444\pi\) | |||||||
\(278\) | 52.3259 | 0.188223 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −50.0000 | − | 50.0000i | −0.178571 | − | 0.178571i | ||||
\(281\) | 176.363 | + | 101.823i | 0.627627 | + | 0.362361i | 0.779833 | − | 0.625988i | \(-0.215304\pi\) |
−0.152205 | + | 0.988349i | \(0.548638\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.7128 | + | 16.0000i | −0.0979251 | + | 0.0565371i | −0.548163 | − | 0.836372i | \(-0.684673\pi\) |
0.450238 | + | 0.892909i | \(0.351339\pi\) | |||||||
\(284\) | 154.318 | − | 89.0955i | 0.543373 | − | 0.313716i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.00000 | + | 15.5885i | −0.0314685 | + | 0.0545051i | ||||
\(287\) | −261.630 | −0.911601 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −161.000 | −0.557093 | ||||||||
\(290\) | 260.800 | − | 69.8811i | 0.899310 | − | 0.240969i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 29.4449 | − | 17.0000i | 0.100839 | − | 0.0582192i | ||||
\(293\) | 86.9741 | + | 150.644i | 0.296840 | + | 0.514142i | 0.975411 | − | 0.220393i | \(-0.0707338\pi\) |
−0.678571 | + | 0.734535i | \(0.737401\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −437.128 | + | 117.128i | −1.48179 | + | 0.397045i | ||||
\(296\) | − | 70.7107i | − | 0.238887i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 368.000i | 1.23490i | ||||||||
\(299\) | 11.0227 | + | 6.36396i | 0.0368652 | + | 0.0212842i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 160.000 | + | 277.128i | 0.531561 | + | 0.920691i | ||||
\(302\) | 77.0746 | + | 133.497i | 0.255214 | + | 0.442044i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −42.0000 | + | 72.7461i | −0.138158 | + | 0.239296i | ||||
\(305\) | 342.947 | − | 342.947i | 1.12442 | − | 1.12442i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 486.000i | 1.58306i | 0.611129 | + | 0.791531i | \(0.290716\pi\) | ||||
−0.611129 | + | 0.791531i | \(0.709284\pi\) | |||||||
\(308\) | 7.07107 | − | 12.2474i | 0.0229580 | − | 0.0397644i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −273.205 | − | 73.2051i | −0.881307 | − | 0.236145i | ||||
\(311\) | −58.7878 | + | 33.9411i | −0.189028 | + | 0.109135i | −0.591528 | − | 0.806285i | \(-0.701475\pi\) |
0.402499 | + | 0.915420i | \(0.368142\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −243.353 | − | 140.500i | −0.777486 | − | 0.448882i | 0.0580525 | − | 0.998314i | \(-0.481511\pi\) |
−0.835539 | + | 0.549432i | \(0.814844\pi\) | |||||||
\(314\) | 166.877i | 0.531456i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −234.000 | −0.740506 | ||||||||
\(317\) | −260.215 | + | 450.706i | −0.820868 | + | 1.42179i | 0.0841679 | + | 0.996452i | \(0.473177\pi\) |
−0.905036 | + | 0.425334i | \(0.860157\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.0000 | + | 46.7654i | 0.0846395 | + | 0.146600i | ||||
\(320\) | 38.6370 | + | 10.3528i | 0.120741 | + | 0.0323524i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.66025 | − | 5.00000i | −0.0268952 | − | 0.0155280i | ||||
\(323\) | 237.588 | 0.735566 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −225.000 | −0.692308 | ||||||||
\(326\) | −248.623 | − | 143.543i | −0.762648 | − | 0.440315i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 128.172 | − | 74.0000i | 0.390768 | − | 0.225610i | ||||
\(329\) | −97.9796 | + | 56.5685i | −0.297810 | + | 0.171941i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.5000 | − | 51.0955i | 0.0891239 | − | 0.154367i | −0.818017 | − | 0.575194i | \(-0.804927\pi\) |
0.907141 | + | 0.420827i | \(0.138260\pi\) | |||||||
\(332\) | −115.966 | −0.349294 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 144.000 | 0.431138 | ||||||||
\(335\) | 632.681 | − | 169.526i | 1.88860 | − | 0.506049i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 47.6314 | − | 27.5000i | 0.141339 | − | 0.0816024i | −0.427663 | − | 0.903938i | \(-0.640663\pi\) |
0.569002 | + | 0.822336i | \(0.307330\pi\) | |||||||
\(338\) | 62.2254 | + | 107.778i | 0.184099 | + | 0.318868i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −29.2820 | − | 109.282i | −0.0861236 | − | 0.321418i | ||||
\(341\) | − | 56.5685i | − | 0.165890i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 365.000i | − | 1.06414i | ||||||
\(344\) | −156.767 | − | 90.5097i | −0.455719 | − | 0.263109i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.00000 | + | 13.8564i | 0.0231214 | + | 0.0400474i | ||||
\(347\) | −299.106 | − | 518.067i | −0.861977 | − | 1.49299i | −0.870017 | − | 0.493021i | \(-0.835893\pi\) |
0.00803996 | − | 0.999968i | \(-0.497441\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 219.500 | − | 380.185i | 0.628940 | − | 1.08936i | −0.358825 | − | 0.933405i | \(-0.616823\pi\) |
0.987765 | − | 0.155951i | \(-0.0498442\pi\) | |||||||
\(350\) | 176.777 | 0.505076 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.00000i | 0.0227273i | ||||||||
\(353\) | −260.215 | + | 450.706i | −0.737154 | + | 1.27679i | 0.216618 | + | 0.976256i | \(0.430497\pi\) |
−0.953772 | + | 0.300531i | \(0.902836\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −115.298 | + | 430.298i | −0.324783 | + | 1.21211i | ||||
\(356\) | −254.747 | + | 147.078i | −0.715581 | + | 0.413141i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 154.153 | + | 89.0000i | 0.430594 | + | 0.248603i | ||||
\(359\) | 55.1543i | 0.153633i | 0.997045 | + | 0.0768166i | \(0.0244756\pi\) | ||||
−0.997045 | + | 0.0768166i | \(0.975524\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 80.0000 | 0.221607 | ||||||||
\(362\) | −89.8026 | + | 155.543i | −0.248073 | + | 0.429676i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 45.0000 | + | 77.9423i | 0.123626 | + | 0.214127i | ||||
\(365\) | −21.9996 | + | 82.1037i | −0.0602729 | + | 0.224942i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −510.089 | − | 294.500i | −1.38989 | − | 0.802452i | −0.396586 | − | 0.917998i | \(-0.629805\pi\) |
−0.993302 | + | 0.115545i | \(0.963138\pi\) | |||||||
\(368\) | 5.65685 | 0.0153719 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 125.000 | + | 125.000i | 0.337838 | + | 0.337838i | ||||
\(371\) | 312.310 | + | 180.312i | 0.841806 | + | 0.486017i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.79423 | + | 4.50000i | −0.0208961 | + | 0.0120643i | −0.510412 | − | 0.859930i | \(-0.670507\pi\) |
0.489516 | + | 0.871995i | \(0.337174\pi\) | |||||||
\(374\) | 19.5959 | − | 11.3137i | 0.0523955 | − | 0.0302506i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 32.0000 | − | 55.4256i | 0.0851064 | − | 0.147409i | ||||
\(377\) | −343.654 | −0.911549 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 157.000 | 0.414248 | 0.207124 | − | 0.978315i | \(-0.433590\pi\) | ||||
0.207124 | + | 0.978315i | \(0.433590\pi\) | |||||||
\(380\) | −54.3520 | − | 202.844i | −0.143032 | − | 0.533801i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −124.708 | + | 72.0000i | −0.326460 | + | 0.188482i | ||||
\(383\) | −141.421 | − | 244.949i | −0.369246 | − | 0.639553i | 0.620202 | − | 0.784443i | \(-0.287051\pi\) |
−0.989448 | + | 0.144889i | \(0.953717\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.15064 | + | 34.1506i | 0.0237679 | + | 0.0887029i | ||||
\(386\) | 383.252i | 0.992881i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 82.0000i | 0.211340i | ||||||||
\(389\) | −519.292 | − | 299.813i | −1.33494 | − | 0.770728i | −0.348888 | − | 0.937164i | \(-0.613441\pi\) |
−0.986052 | + | 0.166436i | \(0.946774\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.00000 | − | 13.8564i | −0.0204604 | − | 0.0354384i | ||||
\(392\) | 33.9411 | + | 58.7878i | 0.0865845 | + | 0.149969i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −224.000 | + | 387.979i | −0.568528 | + | 0.984719i | ||||
\(395\) | 413.657 | − | 413.657i | 1.04723 | − | 1.04723i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 296.000i | − | 0.745592i | −0.927913 | − | 0.372796i | \(-0.878399\pi\) | ||
0.927913 | − | 0.372796i | \(-0.121601\pi\) | |||||||
\(398\) | 103.945 | − | 180.037i | 0.261168 | − | 0.452356i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −86.6025 | + | 50.0000i | −0.216506 | + | 0.125000i | ||||
\(401\) | −336.805 | + | 194.454i | −0.839912 | + | 0.484924i | −0.857234 | − | 0.514926i | \(-0.827819\pi\) |
0.0173221 | + | 0.999850i | \(0.494486\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 311.769 | + | 180.000i | 0.773621 | + | 0.446650i | ||||
\(404\) | 181.019i | 0.448068i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 270.000 | 0.665025 | ||||||||
\(407\) | −17.6777 | + | 30.6186i | −0.0434341 | + | 0.0752300i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −72.5000 | − | 125.574i | −0.177262 | − | 0.307026i | 0.763680 | − | 0.645595i | \(-0.223391\pi\) |
−0.940942 | + | 0.338569i | \(0.890057\pi\) | |||||||
\(410\) | −95.7630 | + | 357.393i | −0.233568 | + | 0.871689i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −22.5167 | − | 13.0000i | −0.0546521 | − | 0.0315534i | ||||
\(413\) | −452.548 | −1.09576 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 205.000 | − | 205.000i | 0.493976 | − | 0.493976i | ||||
\(416\) | −44.0908 | − | 25.4558i | −0.105988 | − | 0.0611919i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 36.3731 | − | 21.0000i | 0.0870169 | − | 0.0502392i | ||||
\(419\) | 607.473 | − | 350.725i | 1.44982 | − | 0.837052i | 0.451347 | − | 0.892348i | \(-0.350944\pi\) |
0.998470 | + | 0.0552959i | \(0.0176102\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −252.500 | + | 437.343i | −0.599762 | + | 1.03882i | 0.393093 | + | 0.919499i | \(0.371405\pi\) |
−0.992856 | + | 0.119320i | \(0.961928\pi\) | |||||||
\(422\) | −199.404 | −0.472522 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −204.000 | −0.481132 | ||||||||
\(425\) | 244.949 | + | 141.421i | 0.576351 | + | 0.332756i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 420.022 | − | 242.500i | 0.983659 | − | 0.567916i | ||||
\(428\) | 123.037 | + | 213.106i | 0.287469 | + | 0.497910i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 437.128 | − | 117.128i | 1.01658 | − | 0.272391i | ||||
\(431\) | − | 43.8406i | − | 0.101718i | −0.998706 | − | 0.0508592i | \(-0.983804\pi\) | ||
0.998706 | − | 0.0508592i | \(-0.0161960\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.0000i | 0.0739030i | 0.999317 | + | 0.0369515i | \(0.0117647\pi\) | ||||
−0.999317 | + | 0.0369515i | \(0.988235\pi\) | |||||||
\(434\) | −244.949 | − | 141.421i | −0.564399 | − | 0.325856i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.00000 | − | 13.8564i | −0.0183486 | − | 0.0317807i | ||||
\(437\) | −14.8492 | − | 25.7196i | −0.0339800 | − | 0.0588550i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 252.000 | − | 436.477i | 0.574032 | − | 0.994252i | −0.422114 | − | 0.906543i | \(-0.638712\pi\) |
0.996146 | − | 0.0877097i | \(-0.0279548\pi\) | |||||||
\(440\) | −14.1421 | − | 14.1421i | −0.0321412 | − | 0.0321412i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 144.000i | 0.325792i | ||||||||
\(443\) | 118.794 | − | 205.757i | 0.268158 | − | 0.464463i | −0.700228 | − | 0.713919i | \(-0.746918\pi\) |
0.968386 | + | 0.249456i | \(0.0802518\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 190.333 | − | 710.333i | 0.427715 | − | 1.59625i | ||||
\(446\) | −9.79796 | + | 5.65685i | −0.0219685 | + | 0.0126835i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 34.6410 | + | 20.0000i | 0.0773237 | + | 0.0446429i | ||||
\(449\) | 67.8823i | 0.151185i | 0.997139 | + | 0.0755927i | \(0.0240849\pi\) | ||||
−0.997139 | + | 0.0755927i | \(0.975915\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −74.0000 | −0.164080 | ||||||||
\(452\) | 38.1838 | − | 66.1362i | 0.0844774 | − | 0.146319i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −49.0000 | − | 84.8705i | −0.107930 | − | 0.186939i | ||||
\(455\) | −217.333 | − | 58.2343i | −0.477656 | − | 0.127987i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 651.251 | + | 376.000i | 1.42506 | + | 0.822757i | 0.996725 | − | 0.0808643i | \(-0.0257680\pi\) |
0.428332 | + | 0.903621i | \(0.359101\pi\) | |||||||
\(458\) | 11.3137 | 0.0247024 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −10.0000 | + | 10.0000i | −0.0217391 | + | 0.0217391i | ||||
\(461\) | −529.090 | − | 305.470i | −1.14770 | − | 0.662625i | −0.199374 | − | 0.979923i | \(-0.563891\pi\) |
−0.948326 | + | 0.317298i | \(0.897224\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −517.017 | + | 298.500i | −1.11667 | + | 0.644708i | −0.940548 | − | 0.339660i | \(-0.889688\pi\) |
−0.176120 | + | 0.984369i | \(0.556355\pi\) | |||||||
\(464\) | −132.272 | + | 76.3675i | −0.285070 | + | 0.164585i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 224.000 | − | 387.979i | 0.480687 | − | 0.832574i | ||||
\(467\) | −848.528 | −1.81698 | −0.908488 | − | 0.417910i | \(-0.862763\pi\) | ||||
−0.908488 | + | 0.417910i | \(0.862763\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 655.000 | 1.39659 | ||||||||
\(470\) | 41.4110 | + | 154.548i | 0.0881086 | + | 0.328826i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 221.703 | − | 128.000i | 0.469709 | − | 0.271186i | ||||
\(473\) | 45.2548 | + | 78.3837i | 0.0956762 | + | 0.165716i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 454.663 | + | 262.500i | 0.957186 | + | 0.552632i | ||||
\(476\) | − | 113.137i | − | 0.237683i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 290.000i | − | 0.606695i | ||||||
\(479\) | 145.745 | + | 84.1457i | 0.304269 | + | 0.175670i | 0.644359 | − | 0.764723i | \(-0.277124\pi\) |
−0.340090 | + | 0.940393i | \(0.610458\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −112.500 | − | 194.856i | −0.233888 | − | 0.405105i | ||||
\(482\) | 55.8614 | + | 96.7548i | 0.115895 | + | 0.200736i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −119.000 | + | 206.114i | −0.245868 | + | 0.425855i | ||||
\(485\) | −144.957 | − | 144.957i | −0.298880 | − | 0.298880i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 507.000i | 1.04107i | 0.853841 | + | 0.520534i | \(0.174267\pi\) | ||||
−0.853841 | + | 0.520534i | \(0.825733\pi\) | |||||||
\(488\) | −137.179 | + | 237.601i | −0.281104 | + | 0.486886i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −163.923 | − | 43.9230i | −0.334537 | − | 0.0896389i | ||||
\(491\) | 371.098 | − | 214.253i | 0.755800 | − | 0.436361i | −0.0719859 | − | 0.997406i | \(-0.522934\pi\) |
0.827786 | + | 0.561044i | \(0.189600\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 374.123 | + | 216.000i | 0.758870 | + | 0.438134i | ||||
\(494\) | 267.286i | 0.541066i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 160.000 | 0.322581 | ||||||||
\(497\) | −222.739 | + | 385.795i | −0.448166 | + | 0.776247i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −435.000 | − | 753.442i | −0.871743 | − | 1.50990i | −0.860192 | − | 0.509971i | \(-0.829656\pi\) |
−0.0115517 | − | 0.999933i | \(-0.503677\pi\) | |||||||
\(500\) | 64.7048 | − | 241.481i | 0.129410 | − | 0.482963i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 57.1577 | + | 33.0000i | 0.113860 | + | 0.0657371i | ||||
\(503\) | 462.448 | 0.919379 | 0.459690 | − | 0.888080i | \(-0.347961\pi\) | ||||
0.459690 | + | 0.888080i | \(0.347961\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −320.000 | − | 320.000i | −0.633663 | − | 0.633663i | ||||
\(506\) | −2.44949 | − | 1.41421i | −0.00484089 | − | 0.00279489i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −13.8564 | + | 8.00000i | −0.0272764 | + | 0.0157480i | ||||
\(509\) | 709.127 | − | 409.415i | 1.39318 | − | 0.804351i | 0.399512 | − | 0.916728i | \(-0.369180\pi\) |
0.993666 | + | 0.112377i | \(0.0358464\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −42.5000 | + | 73.6122i | −0.0831703 | + | 0.144055i | ||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −240.000 | −0.466926 | ||||||||
\(515\) | 62.7852 | − | 16.8232i | 0.121913 | − | 0.0326665i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.7128 | + | 16.0000i | −0.0536031 | + | 0.0309478i | ||||
\(518\) | 88.3883 | + | 153.093i | 0.170634 | + | 0.295547i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 122.942 | − | 32.9423i | 0.236427 | − | 0.0633506i | ||||
\(521\) | − | 864.084i | − | 1.65851i | −0.558869 | − | 0.829256i | \(-0.688765\pi\) | ||
0.558869 | − | 0.829256i | \(-0.311235\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 163.000i | 0.311663i | 0.987784 | + | 0.155832i | \(0.0498058\pi\) | ||||
−0.987784 | + | 0.155832i | \(0.950194\pi\) | |||||||
\(524\) | −235.151 | − | 135.765i | −0.448761 | − | 0.259093i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −200.000 | − | 346.410i | −0.380228 | − | 0.658574i | ||||
\(527\) | −226.274 | − | 391.918i | −0.429363 | − | 0.743678i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 263.500 | − | 456.395i | 0.498110 | − | 0.862751i | ||||
\(530\) | 360.624 | − | 360.624i | 0.680424 | − | 0.680424i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 210.000i | − | 0.394737i | ||||||
\(533\) | 235.467 | − | 407.840i | 0.441776 | − | 0.765178i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −594.221 | − | 159.221i | −1.11069 | − | 0.297609i | ||||
\(536\) | −320.883 | + | 185.262i | −0.598663 | + | 0.345638i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 124.708 | + | 72.0000i | 0.231799 | + | 0.133829i | ||||
\(539\) | − | 33.9411i | − | 0.0629705i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 697.000 | 1.28835 | 0.644177 | − | 0.764876i | \(-0.277200\pi\) | ||||
0.644177 | + | 0.764876i | \(0.277200\pi\) | |||||||
\(542\) | −156.271 | + | 270.669i | −0.288322 | + | 0.499389i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 32.0000 | + | 55.4256i | 0.0588235 | + | 0.101885i | ||||
\(545\) | 38.6370 | + | 10.3528i | 0.0708936 | + | 0.0189959i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 336.884 | + | 194.500i | 0.615875 | + | 0.355576i | 0.775261 | − | 0.631640i | \(-0.217618\pi\) |
−0.159386 | + | 0.987216i | \(0.550951\pi\) | |||||||
\(548\) | 534.573 | 0.975498 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 50.0000 | 0.0909091 | ||||||||
\(551\) | 694.430 | + | 400.930i | 1.26031 | + | 0.727640i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 506.625 | − | 292.500i | 0.916139 | − | 0.528933i | ||||
\(554\) | −107.778 | + | 62.2254i | −0.194544 | + | 0.112320i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 37.0000 | − | 64.0859i | 0.0665468 | − | 0.115262i | ||||
\(557\) | −1086.12 | −1.94994 | −0.974969 | − | 0.222339i | \(-0.928631\pi\) | ||||
−0.974969 | + | 0.222339i | \(0.928631\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −576.000 | −1.03041 | ||||||||
\(560\) | −96.5926 | + | 25.8819i | −0.172487 | + | 0.0462177i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 249.415 | − | 144.000i | 0.443799 | − | 0.256228i | ||||
\(563\) | −311.127 | − | 538.888i | −0.552623 | − | 0.957172i | −0.998084 | − | 0.0618704i | \(-0.980293\pi\) |
0.445461 | − | 0.895301i | \(-0.353040\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 49.4134 | + | 184.413i | 0.0874574 | + | 0.326395i | ||||
\(566\) | 45.2548i | 0.0799555i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 252.000i | − | 0.443662i | ||||||
\(569\) | −401.716 | − | 231.931i | −0.706004 | − | 0.407612i | 0.103576 | − | 0.994622i | \(-0.466972\pi\) |
−0.809580 | + | 0.587010i | \(0.800305\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 461.500 | + | 799.341i | 0.808231 | + | 1.39990i | 0.914088 | + | 0.405516i | \(0.132908\pi\) |
−0.105857 | + | 0.994381i | \(0.533758\pi\) | |||||||
\(572\) | 12.7279 | + | 22.0454i | 0.0222516 | + | 0.0385409i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −185.000 | + | 320.429i | −0.322300 | + | 0.558239i | ||||
\(575\) | − | 35.3553i | − | 0.0614875i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 247.000i | 0.428076i | 0.976825 | + | 0.214038i | \(0.0686617\pi\) | ||||
−0.976825 | + | 0.214038i | \(0.931338\pi\) | |||||||
\(578\) | −113.844 | + | 197.184i | −0.196962 | + | 0.341149i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 98.8269 | − | 368.827i | 0.170391 | − | 0.635908i | ||||
\(581\) | 251.073 | − | 144.957i | 0.432139 | − | 0.249496i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 88.3346 | + | 51.0000i | 0.151517 | + | 0.0874786i | ||||
\(584\) | − | 48.0833i | − | 0.0823344i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 246.000 | 0.419795 | ||||||||
\(587\) | −226.981 | + | 393.143i | −0.386680 | + | 0.669750i | −0.992001 | − | 0.126232i | \(-0.959712\pi\) |
0.605321 | + | 0.795982i | \(0.293045\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −420.000 | − | 727.461i | −0.713073 | − | 1.23508i | ||||
\(590\) | −165.644 | + | 618.193i | −0.280753 | + | 1.04778i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −86.6025 | − | 50.0000i | −0.146288 | − | 0.0844595i | ||||
\(593\) | 4.24264 | 0.00715454 | 0.00357727 | − | 0.999994i | \(-0.498861\pi\) | ||||
0.00357727 | + | 0.999994i | \(0.498861\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 200.000 | + | 200.000i | 0.336134 | + | 0.336134i | ||||
\(596\) | 450.706 | + | 260.215i | 0.756218 | + | 0.436603i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 15.5885 | − | 9.00000i | 0.0260677 | − | 0.0150502i | ||||
\(599\) | 194.734 | − | 112.430i | 0.325099 | − | 0.187696i | −0.328564 | − | 0.944482i | \(-0.606565\pi\) |
0.653663 | + | 0.756786i | \(0.273231\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 368.000 | − | 637.395i | 0.612313 | − | 1.06056i | −0.378537 | − | 0.925586i | \(-0.623573\pi\) |
0.990850 | − | 0.134971i | \(-0.0430940\pi\) | |||||||
\(602\) | 452.548 | 0.751741 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 218.000 | 0.360927 | ||||||||
\(605\) | −153.997 | − | 574.726i | −0.254541 | − | 0.949960i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 378.453 | − | 218.500i | 0.623481 | − | 0.359967i | −0.154742 | − | 0.987955i | \(-0.549455\pi\) |
0.778223 | + | 0.627988i | \(0.216121\pi\) | |||||||
\(608\) | 59.3970 | + | 102.879i | 0.0976924 | + | 0.169208i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −177.522 | − | 662.522i | −0.291020 | − | 1.08610i | ||||
\(611\) | − | 203.647i | − | 0.333301i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 335.000i | 0.546493i | 0.961944 | + | 0.273246i | \(0.0880974\pi\) | ||||
−0.961944 | + | 0.273246i | \(0.911903\pi\) | |||||||
\(614\) | 595.226 | + | 343.654i | 0.969423 | + | 0.559697i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.0000 | − | 17.3205i | −0.0162338 | − | 0.0281177i | ||||
\(617\) | 127.986 | + | 221.679i | 0.207433 | + | 0.359285i | 0.950905 | − | 0.309482i | \(-0.100156\pi\) |
−0.743472 | + | 0.668767i | \(0.766822\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 482.500 | − | 835.715i | 0.779483 | − | 1.35010i | −0.152757 | − | 0.988264i | \(-0.548815\pi\) |
0.932240 | − | 0.361840i | \(-0.117851\pi\) | |||||||
\(620\) | −282.843 | + | 282.843i | −0.456198 | + | 0.456198i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 96.0000i | 0.154341i | ||||||||
\(623\) | 367.696 | − | 636.867i | 0.590201 | − | 1.02226i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 312.500 | + | 541.266i | 0.500000 | + | 0.866025i | ||||
\(626\) | −344.153 | + | 198.697i | −0.549766 | + | 0.317407i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 204.382 | + | 118.000i | 0.325449 | + | 0.187898i | ||||
\(629\) | 282.843i | 0.449670i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 275.000 | 0.435816 | 0.217908 | − | 0.975969i | \(-0.430077\pi\) | ||||
0.217908 | + | 0.975969i | \(0.430077\pi\) | |||||||
\(632\) | −165.463 | + | 286.590i | −0.261809 | + | 0.453466i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 368.000 | + | 637.395i | 0.580442 | + | 1.00535i | ||||
\(635\) | 10.3528 | − | 38.6370i | 0.0163036 | − | 0.0608457i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 187.061 | + | 108.000i | 0.293660 | + | 0.169545i | ||||
\(638\) | 76.3675 | 0.119698 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 40.0000 | − | 40.0000i | 0.0625000 | − | 0.0625000i | ||||
\(641\) | −421.312 | − | 243.245i | −0.657273 | − | 0.379477i | 0.133964 | − | 0.990986i | \(-0.457229\pi\) |
−0.791237 | + | 0.611509i | \(0.790563\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 997.661 | − | 576.000i | 1.55157 | − | 0.895801i | 0.553559 | − | 0.832810i | \(-0.313269\pi\) |
0.998014 | − | 0.0629907i | \(-0.0200639\pi\) | |||||||
\(644\) | −12.2474 | + | 7.07107i | −0.0190178 | + | 0.0109799i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 168.000 | − | 290.985i | 0.260062 | − | 0.450440i | ||||
\(647\) | 691.550 | 1.06886 | 0.534428 | − | 0.845214i | \(-0.320527\pi\) | ||||
0.534428 | + | 0.845214i | \(0.320527\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −128.000 | −0.197227 | ||||||||
\(650\) | −159.099 | + | 275.568i | −0.244768 | + | 0.423950i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −351.606 | + | 203.000i | −0.539273 | + | 0.311350i | ||||
\(653\) | 175.362 | + | 303.737i | 0.268549 | + | 0.465140i | 0.968487 | − | 0.249063i | \(-0.0801226\pi\) |
−0.699938 | + | 0.714203i | \(0.746789\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 655.692 | − | 175.692i | 1.00106 | − | 0.268232i | ||||
\(656\) | − | 209.304i | − | 0.319060i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 160.000i | 0.243161i | ||||||||
\(659\) | 431.110 | + | 248.902i | 0.654188 | + | 0.377696i | 0.790059 | − | 0.613031i | \(-0.210050\pi\) |
−0.135871 | + | 0.990727i | \(0.543383\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 288.500 | + | 499.697i | 0.436460 | + | 0.755971i | 0.997414 | − | 0.0718765i | \(-0.0228987\pi\) |
−0.560954 | + | 0.827847i | \(0.689565\pi\) | |||||||
\(662\) | −41.7193 | − | 72.2599i | −0.0630201 | − | 0.109154i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −82.0000 | + | 142.028i | −0.123494 | + | 0.213898i | ||||
\(665\) | 371.231 | + | 371.231i | 0.558242 | + | 0.558242i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 54.0000i | − | 0.0809595i | ||||||
\(668\) | 101.823 | − | 176.363i | 0.152430 | − | 0.264017i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 239.747 | − | 894.747i | 0.357831 | − | 1.33544i | ||||
\(671\) | 118.800 | − | 68.5894i | 0.177050 | − | 0.102220i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −423.486 | − | 244.500i | −0.629252 | − | 0.363299i | 0.151210 | − | 0.988502i | \(-0.451683\pi\) |
−0.780462 | + | 0.625203i | \(0.785016\pi\) | |||||||
\(674\) | − | 77.7817i | − | 0.115403i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 176.000 | 0.260355 | ||||||||
\(677\) | 299.813 | − | 519.292i | 0.442856 | − | 0.767048i | −0.555044 | − | 0.831821i | \(-0.687299\pi\) |
0.997900 | + | 0.0647722i | \(0.0206321\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −102.500 | − | 177.535i | −0.150957 | − | 0.261466i | ||||
\(680\) | −154.548 | − | 41.4110i | −0.227277 | − | 0.0608986i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −69.2820 | − | 40.0000i | −0.101587 | − | 0.0586510i | ||||
\(683\) | −236.174 | −0.345789 | −0.172894 | − | 0.984940i | \(-0.555312\pi\) | ||||
−0.172894 | + | 0.984940i | \(0.555312\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −945.000 | + | 945.000i | −1.37956 | + | 1.37956i | ||||
\(686\) | −447.032 | − | 258.094i | −0.651650 | − | 0.376230i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −221.703 | + | 128.000i | −0.322242 | + | 0.186047i | ||||
\(689\) | −562.158 | + | 324.562i | −0.815904 | + | 0.471062i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −320.000 | + | 554.256i | −0.463097 | + | 0.802107i | −0.999113 | − | 0.0421001i | \(-0.986595\pi\) |
0.536016 | + | 0.844208i | \(0.319928\pi\) | |||||||
\(692\) | 22.6274 | 0.0326986 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −846.000 | −1.21902 | ||||||||
\(695\) | 47.8815 | + | 178.696i | 0.0688943 | + | 0.257117i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −512.687 | + | 296.000i | −0.735562 | + | 0.424677i | ||||
\(698\) | −310.420 | − | 537.663i | −0.444728 | − | 0.770291i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 125.000 | − | 216.506i | 0.178571 | − | 0.309295i | ||||
\(701\) | 1093.19i | 1.55947i | 0.626111 | + | 0.779734i | \(0.284646\pi\) | ||||
−0.626111 | + | 0.779734i | \(0.715354\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 525.000i | 0.746799i | ||||||||
\(704\) | 9.79796 | + | 5.65685i | 0.0139176 | + | 0.00803530i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 368.000 | + | 637.395i | 0.521246 | + | 0.902825i | ||||
\(707\) | −226.274 | − | 391.918i | −0.320048 | − | 0.554340i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 244.500 | − | 423.486i | 0.344852 | − | 0.597301i | −0.640475 | − | 0.767979i | \(-0.721262\pi\) |
0.985327 | + | 0.170678i | \(0.0545958\pi\) | |||||||
\(710\) | 445.477 | + | 445.477i | 0.627433 | + | 0.627433i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 416.000i | 0.584270i | ||||||||
\(713\) | −28.2843 | + | 48.9898i | −0.0396694 | + | 0.0687094i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −61.4711 | − | 16.4711i | −0.0859736 | − | 0.0230366i | ||||
\(716\) | 218.005 | − | 125.865i | 0.304476 | − | 0.175789i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 67.5500 | + | 39.0000i | 0.0940808 | + | 0.0543175i | ||||
\(719\) | 620.840i | 0.863477i | 0.901999 | + | 0.431738i | \(0.142100\pi\) | ||||
−0.901999 | + | 0.431738i | \(0.857900\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 65.0000 | 0.0901526 | ||||||||
\(722\) | 56.5685 | − | 97.9796i | 0.0783498 | − | 0.135706i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 127.000 | + | 219.970i | 0.175414 | + | 0.303827i | ||||
\(725\) | 477.297 | + | 826.703i | 0.658341 | + | 1.14028i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −935.307 | − | 540.000i | −1.28653 | − | 0.742779i | −0.308496 | − | 0.951225i | \(-0.599826\pi\) |
−0.978034 | + | 0.208447i | \(0.933159\pi\) | |||||||
\(728\) | 127.279 | 0.174834 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 85.0000 | + | 85.0000i | 0.116438 | + | 0.116438i | ||||
\(731\) | 627.069 | + | 362.039i | 0.857824 | + | 0.495265i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −214.774 | + | 124.000i | −0.293007 | + | 0.169168i | −0.639297 | − | 0.768960i | \(-0.720775\pi\) |
0.346290 | + | 0.938128i | \(0.387441\pi\) | |||||||
\(734\) | −721.375 | + | 416.486i | −0.982799 | + | 0.567419i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.00000 | − | 6.92820i | 0.00543478 | − | 0.00941332i | ||||
\(737\) | 185.262 | 0.251373 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 848.000 | 1.14750 | 0.573748 | − | 0.819032i | \(-0.305489\pi\) | ||||
0.573748 | + | 0.819032i | \(0.305489\pi\) | |||||||
\(740\) | 241.481 | − | 64.7048i | 0.326326 | − | 0.0874389i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 441.673 | − | 255.000i | 0.595247 | − | 0.343666i | ||||
\(743\) | 16.9706 | + | 29.3939i | 0.0228406 | + | 0.0395611i | 0.877220 | − | 0.480089i | \(-0.159396\pi\) |
−0.854379 | + | 0.519650i | \(0.826062\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1256.74 | + | 336.743i | −1.68690 | + | 0.452005i | ||||
\(746\) | 12.7279i | 0.0170616i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 32.0000i | − | 0.0427807i | ||||||
\(749\) | −532.764 | − | 307.591i | −0.711300 | − | 0.410669i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 66.5000 | + | 115.181i | 0.0885486 | + | 0.153371i | 0.906898 | − | 0.421351i | \(-0.138444\pi\) |
−0.818349 | + | 0.574721i | \(0.805110\pi\) | |||||||
\(752\) | −45.2548 | − | 78.3837i | −0.0601793 | − | 0.104234i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −243.000 | + | 420.888i | −0.322281 | + | 0.558207i | ||||
\(755\) | −385.373 | + | 385.373i | −0.510428 | + | 0.510428i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1271.00i | − | 1.67900i | −0.543363 | − | 0.839498i | \(-0.682849\pi\) | ||
0.543363 | − | 0.839498i | \(-0.317151\pi\) | |||||||
\(758\) | 111.016 | − | 192.285i | 0.146459 | − | 0.253674i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −286.865 | − | 76.8653i | −0.377454 | − | 0.101139i | ||||
\(761\) | 466.628 | − | 269.408i | 0.613177 | − | 0.354018i | −0.161031 | − | 0.986949i | \(-0.551482\pi\) |
0.774208 | + | 0.632931i | \(0.218148\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 34.6410 | + | 20.0000i | 0.0454011 | + | 0.0262123i | ||||
\(764\) | 203.647i | 0.266553i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −400.000 | −0.522193 | ||||||||
\(767\) | 407.294 | − | 705.453i | 0.531022 | − | 0.919756i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.5000 | + | 70.1481i | 0.0526658 | + | 0.0912198i | 0.891156 | − | 0.453696i | \(-0.149895\pi\) |
−0.838491 | + | 0.544916i | \(0.816562\pi\) | |||||||
\(770\) | 48.2963 | + | 12.9410i | 0.0627225 | + | 0.0168064i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 469.386 | + | 271.000i | 0.608013 | + | 0.351036i | ||||
\(773\) | −445.477 | −0.576297 | −0.288148 | − | 0.957586i | \(-0.593040\pi\) | ||||
−0.288148 | + | 0.957586i | \(0.593040\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1000.00i | − | 1.29032i | ||||||
\(776\) | 100.429 | + | 57.9828i | 0.129419 | + | 0.0747200i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −734.390 | + | 424.000i | −0.943945 | + | 0.544987i | ||||
\(779\) | −951.627 | + | 549.422i | −1.22160 | + | 0.705291i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −63.0000 | + | 109.119i | −0.0806658 | + | 0.139717i | ||||
\(782\) | −22.6274 | −0.0289353 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 96.0000 | 0.122449 | ||||||||
\(785\) | −569.896 | + | 152.703i | −0.725982 | + | 0.194526i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −342.080 | + | 197.500i | −0.434663 | + | 0.250953i | −0.701331 | − | 0.712835i | \(-0.747411\pi\) |
0.266668 | + | 0.963788i | \(0.414077\pi\) | |||||||
\(788\) | 316.784 | + | 548.686i | 0.402010 | + | 0.696302i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −214.125 | − | 799.125i | −0.271044 | − | 1.01155i | ||||
\(791\) | 190.919i | 0.241364i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 873.000i | 1.10088i | ||||||||
\(794\) | −362.524 | − | 209.304i | −0.456580 | − | 0.263607i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −147.000 | − | 254.611i | −0.184673 | − | 0.319864i | ||||
\(797\) | 537.401 | + | 930.806i | 0.674280 | + | 1.16789i | 0.976679 | + | 0.214706i | \(0.0688792\pi\) |
−0.302399 | + | 0.953181i | \(0.597787\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −128.000 | + | 221.703i | −0.160200 | + | 0.277475i | ||||
\(800\) | 141.421i | 0.176777i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 550.000i | 0.685786i | ||||||||
\(803\) | −12.0208 | + | 20.8207i | −0.0149699 | + | 0.0259286i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.15064 | − | 34.1506i | 0.0113672 | − | 0.0424231i | ||||
\(806\) | 440.908 | − | 254.558i | 0.547032 | − | 0.315829i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 221.703 | + | 128.000i | 0.274384 | + | 0.158416i | ||||
\(809\) | − | 1255.82i | − | 1.55231i | −0.630540 | − | 0.776157i | \(-0.717167\pi\) | ||
0.630540 | − | 0.776157i | \(-0.282833\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −752.000 | −0.927250 | −0.463625 | − | 0.886031i | \(-0.653452\pi\) | ||||
−0.463625 | + | 0.886031i | \(0.653452\pi\) | |||||||
\(812\) | 190.919 | − | 330.681i | 0.235122 | − | 0.407243i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 25.0000 | + | 43.3013i | 0.0307125 | + | 0.0531957i | ||||
\(815\) | 262.701 | − | 980.415i | 0.322333 | − | 1.20296i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1163.94 | + | 672.000i | 1.42465 | + | 0.822521i | ||||
\(818\) | −205.061 | −0.250686 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 370.000 | + | 370.000i | 0.451220 | + | 0.451220i | ||||
\(821\) | −431.110 | − | 248.902i | −0.525104 | − | 0.303169i | 0.213917 | − | 0.976852i | \(-0.431378\pi\) |
−0.739020 | + | 0.673683i | \(0.764711\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 459.859 | − | 265.500i | 0.558760 | − | 0.322600i | −0.193888 | − | 0.981024i | \(-0.562110\pi\) |
0.752648 | + | 0.658423i | \(0.228776\pi\) | |||||||
\(824\) | −31.8434 | + | 18.3848i | −0.0386449 | + | 0.0223116i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −320.000 | + | 554.256i | −0.387409 | + | 0.671012i | ||||
\(827\) | 350.725 | 0.424093 | 0.212047 | − | 0.977260i | \(-0.431987\pi\) | ||||
0.212047 | + | 0.977260i | \(0.431987\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −705.000 | −0.850422 | −0.425211 | − | 0.905094i | \(-0.639800\pi\) | ||||
−0.425211 | + | 0.905094i | \(0.639800\pi\) | |||||||
\(830\) | −106.116 | − | 396.030i | −0.127850 | − | 0.477144i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −62.3538 | + | 36.0000i | −0.0749445 | + | 0.0432692i | ||||
\(833\) | −135.765 | − | 235.151i | −0.162983 | − | 0.282294i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 131.769 | + | 491.769i | 0.157807 | + | 0.588945i | ||||
\(836\) | − | 59.3970i | − | 0.0710490i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 992.000i | − | 1.18377i | ||||||
\(839\) | 1401.11 | + | 808.930i | 1.66997 | + | 0.964160i | 0.967648 | + | 0.252304i | \(0.0811885\pi\) |
0.702326 | + | 0.711855i | \(0.252145\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 308.500 | + | 534.338i | 0.366825 | + | 0.635360i | ||||
\(842\) | 357.089 | + | 618.496i | 0.424096 | + | 0.734556i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −141.000 | + | 244.219i | −0.167062 | + | 0.289359i | ||||
\(845\) | −311.127 | + | 311.127i | −0.368198 | + | 0.368198i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 595.000i | − | 0.702479i | ||||||
\(848\) | −144.250 | + | 249.848i | −0.170106 | + | 0.294632i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 346.410 | − | 200.000i | 0.407541 | − | 0.235294i | ||||
\(851\) | 30.6186 | − | 17.6777i | 0.0359796 | − | 0.0207728i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1419.42 | − | 819.500i | −1.66403 | − | 0.960727i | −0.970762 | − | 0.240045i | \(-0.922838\pi\) |
−0.693266 | − | 0.720682i | \(-0.743829\pi\) | |||||||
\(854\) | − | 685.894i | − | 0.803154i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 348.000 | 0.406542 | ||||||||
\(857\) | −494.268 | + | 856.097i | −0.576742 | + | 0.998946i | 0.419108 | + | 0.907936i | \(0.362343\pi\) |
−0.995850 | + | 0.0910097i | \(0.970991\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −177.500 | − | 307.439i | −0.206636 | − | 0.357903i | 0.744017 | − | 0.668161i | \(-0.232918\pi\) |
−0.950653 | + | 0.310257i | \(0.899585\pi\) | |||||||
\(860\) | 165.644 | − | 618.193i | 0.192610 | − | 0.718829i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −53.6936 | − | 31.0000i | −0.0622895 | − | 0.0359629i | ||||
\(863\) | 1459.47 | 1.69116 | 0.845578 | − | 0.533851i | \(-0.179256\pi\) | ||||
0.845578 | + | 0.533851i | \(0.179256\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −40.0000 | + | 40.0000i | −0.0462428 | + | 0.0462428i | ||||
\(866\) | 39.1918 | + | 22.6274i | 0.0452562 | + | 0.0261287i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −346.410 | + | 200.000i | −0.399090 | + | 0.230415i | ||||
\(869\) | 143.295 | − | 82.7315i | 0.164897 | − | 0.0952031i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −589.500 | + | 1021.04i | −0.676808 | + | 1.17227i | ||||
\(872\) | −22.6274 | −0.0259489 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −42.0000 | −0.0480549 | ||||||||
\(875\) | 161.762 | + | 603.704i | 0.184871 | + | 0.689947i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −977.743 | + | 564.500i | −1.11487 | + | 0.643672i | −0.940087 | − | 0.340935i | \(-0.889256\pi\) |
−0.174785 | + | 0.984607i | \(0.555923\pi\) | |||||||
\(878\) | −356.382 | − | 617.271i | −0.405902 | − | 0.703043i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −27.3205 | + | 7.32051i | −0.0310460 | + | 0.00831876i | ||||
\(881\) | 165.463i | 0.187813i | 0.995581 | + | 0.0939063i | \(0.0299354\pi\) | ||||
−0.995581 | + | 0.0939063i | \(0.970065\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1227.00i | − | 1.38958i | −0.719212 | − | 0.694790i | \(-0.755497\pi\) | ||
0.719212 | − | 0.694790i | \(-0.244503\pi\) | |||||||
\(884\) | 176.363 | + | 101.823i | 0.199506 | + | 0.115185i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −168.000 | − | 290.985i | −0.189616 | − | 0.328425i | ||||
\(887\) | 118.794 | + | 205.757i | 0.133928 | + | 0.231970i | 0.925187 | − | 0.379511i | \(-0.123908\pi\) |
−0.791260 | + | 0.611480i | \(0.790574\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.0000 | − | 34.6410i | 0.0224972 | − | 0.0389663i | ||||
\(890\) | −735.391 | − | 735.391i | −0.826282 | − | 0.826282i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16.0000i | 0.0179372i | ||||||||
\(893\) | −237.588 | + | 411.514i | −0.266056 | + | 0.460822i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −162.881 | + | 607.881i | −0.181990 | + | 0.679197i | ||||
\(896\) | 48.9898 | − | 28.2843i | 0.0546761 | − | 0.0315673i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 83.1384 | + | 48.0000i | 0.0925818 | + | 0.0534521i | ||||
\(899\) | − | 1527.35i | − | 1.69894i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 816.000 | 0.905660 | ||||||||
\(902\) | −52.3259 | + | 90.6311i | −0.0580110 | + | 0.100478i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −54.0000 | − | 93.5307i | −0.0597345 | − | 0.103463i | ||||
\(905\) | −613.363 | − | 164.350i | −0.677749 | − | 0.181602i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −870.356 | − | 502.500i | −0.959598 | − | 0.554024i | −0.0635488 | − | 0.997979i | \(-0.520242\pi\) |
−0.896049 | + | 0.443954i | \(0.853575\pi\) | |||||||
\(908\) | −138.593 | −0.152635 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −225.000 | + | 225.000i | −0.247253 | + | 0.247253i | ||||
\(911\) | −676.059 | − | 390.323i | −0.742107 | − | 0.428455i | 0.0807281 | − | 0.996736i | \(-0.474275\pi\) |
−0.822835 | + | 0.568281i | \(0.807609\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 71.0141 | − | 41.0000i | 0.0777810 | − | 0.0449069i | ||||
\(914\) | 921.008 | − | 531.744i | 1.00767 | − | 0.581777i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.00000 | − | 13.8564i | 0.00873362 | − | 0.0151271i | ||||
\(917\) | 678.823 | 0.740264 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 600.000 | 0.652884 | 0.326442 | − | 0.945217i | \(-0.394150\pi\) | ||||
0.326442 | + | 0.945217i | \(0.394150\pi\) | |||||||
\(920\) | 5.17638 | + | 19.3185i | 0.00562650 | + | 0.0209984i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −748.246 | + | 432.000i | −0.811547 | + | 0.468547i | ||||
\(923\) | −400.930 | − | 694.430i | −0.434377 | − | 0.752362i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −312.500 | + | 541.266i | −0.337838 | + | 0.585152i | ||||
\(926\) | 844.285i | 0.911755i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 216.000i | 0.232759i | ||||||||
\(929\) | 1091.25 | + | 630.032i | 1.17465 | + | 0.678183i | 0.954770 | − | 0.297344i | \(-0.0961009\pi\) |
0.219877 | + | 0.975528i | \(0.429434\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −252.000 | − | 436.477i | −0.270677 | − | 0.468826i | ||||
\(932\) | −316.784 | − | 548.686i | −0.339897 | − | 0.588719i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −600.000 | + | 1039.23i | −0.642398 | + | 1.11267i | ||||
\(935\) | 56.5685 | + | 56.5685i | 0.0605011 | + | 0.0605011i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1465.00i | − | 1.56350i | −0.623592 | − | 0.781750i | \(-0.714327\pi\) | ||
0.623592 | − | 0.781750i | \(-0.285673\pi\) | |||||||
\(938\) | 463.155 | − | 802.208i | 0.493769 | − | 0.855232i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 218.564 | + | 58.5641i | 0.232515 | + | 0.0623022i | ||||
\(941\) | −221.679 | + | 127.986i | −0.235578 | + | 0.136011i | −0.613143 | − | 0.789972i | \(-0.710095\pi\) |
0.377565 | + | 0.925983i | \(0.376762\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 64.0859 | + | 37.0000i | 0.0679596 | + | 0.0392365i | ||||
\(944\) | − | 362.039i | − | 0.383516i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 128.000 | 0.135307 | ||||||||
\(947\) | 203.647 | − | 352.727i | 0.215044 | − | 0.372467i | −0.738242 | − | 0.674536i | \(-0.764344\pi\) |
0.953286 | + | 0.302069i | \(0.0976771\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −76.5000 | − | 132.502i | −0.0806112 | − | 0.139623i | ||||
\(950\) | 642.991 | − | 371.231i | 0.676833 | − | 0.390770i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −138.564 | − | 80.0000i | −0.145550 | − | 0.0840336i | ||||
\(953\) | −497.803 | −0.522354 | −0.261177 | − | 0.965291i | \(-0.584111\pi\) | ||||
−0.261177 | + | 0.965291i | \(0.584111\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −360.000 | − | 360.000i | −0.376963 | − | 0.376963i | ||||
\(956\) | −355.176 | − | 205.061i | −0.371523 | − | 0.214499i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 206.114 | − | 119.000i | 0.215150 | − | 0.124217i | ||||
\(959\) | −1157.38 | + | 668.216i | −1.20687 | + | 0.696784i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −319.500 | + | 553.390i | −0.332466 | + | 0.575848i | ||||
\(962\) | −318.198 | −0.330767 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 158.000 | 0.163900 | ||||||||
\(965\) | −1308.83 | + | 350.700i | −1.35630 | + | 0.363419i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 425.218 | − | 245.500i | 0.439730 | − | 0.253878i | −0.263753 | − | 0.964590i | \(-0.584961\pi\) |
0.703483 | + | 0.710712i | \(0.251627\pi\) | |||||||
\(968\) | 168.291 | + | 291.489i | 0.173855 | + | 0.301125i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −280.035 | + | 75.0352i | −0.288696 | + | 0.0773559i | ||||
\(971\) | − | 509.117i | − | 0.524322i | −0.965024 | − | 0.262161i | \(-0.915565\pi\) | ||
0.965024 | − | 0.262161i | \(-0.0844352\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 185.000i | 0.190134i | ||||||||
\(974\) | 620.946 | + | 358.503i | 0.637521 | + | 0.368073i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 194.000 | + | 336.018i | 0.198770 | + | 0.344281i | ||||
\(977\) | −235.467 | − | 407.840i | −0.241010 | − | 0.417441i | 0.719992 | − | 0.693982i | \(-0.244145\pi\) |
−0.961002 | + | 0.276541i | \(0.910812\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 104.000 | − | 180.133i | 0.106231 | − | 0.183997i | ||||
\(980\) | −169.706 | + | 169.706i | −0.173169 | + | 0.173169i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 606.000i | − | 0.617108i | ||||||
\(983\) | −300.520 | + | 520.517i | −0.305718 | + | 0.529518i | −0.977421 | − | 0.211302i | \(-0.932230\pi\) |
0.671703 | + | 0.740820i | \(0.265563\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1529.95 | − | 409.948i | −1.55325 | − | 0.416191i | ||||
\(986\) | 529.090 | − | 305.470i | 0.536602 | − | 0.309807i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 327.358 | + | 189.000i | 0.331334 | + | 0.191296i | ||||
\(989\) | − | 90.5097i | − | 0.0915163i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −755.000 | −0.761857 | −0.380928 | − | 0.924605i | \(-0.624396\pi\) | ||||
−0.380928 | + | 0.924605i | \(0.624396\pi\) | |||||||
\(992\) | 113.137 | − | 195.959i | 0.114049 | − | 0.197539i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 315.000 | + | 545.596i | 0.316901 | + | 0.548889i | ||||
\(995\) | 709.955 | + | 190.232i | 0.713523 | + | 0.191188i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.7846 | + | 12.0000i | 0.0208472 | + | 0.0120361i | 0.510387 | − | 0.859945i | \(-0.329502\pi\) |
−0.489540 | + | 0.871981i | \(0.662835\pi\) | |||||||
\(998\) | −1230.37 | −1.23283 | ||||||||
\(999\) | 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 | 810.3.j.e.269.4 | 8 | ||
3.2 | odd | 2 | inner | 810.3.j.e.269.1 | 8 | ||
5.4 | even | 2 | inner | 810.3.j.e.269.2 | 8 | ||
9.2 | odd | 6 | 270.3.b.c.269.3 | yes | 4 | ||
9.4 | even | 3 | inner | 810.3.j.e.539.3 | 8 | ||
9.5 | odd | 6 | inner | 810.3.j.e.539.2 | 8 | ||
9.7 | even | 3 | 270.3.b.c.269.2 | yes | 4 | ||
15.14 | odd | 2 | inner | 810.3.j.e.269.3 | 8 | ||
36.7 | odd | 6 | 2160.3.c.i.1889.2 | 4 | |||
36.11 | even | 6 | 2160.3.c.i.1889.3 | 4 | |||
45.2 | even | 12 | 1350.3.d.g.701.2 | 2 | |||
45.4 | even | 6 | inner | 810.3.j.e.539.1 | 8 | ||
45.7 | odd | 12 | 1350.3.d.g.701.1 | 2 | |||
45.14 | odd | 6 | inner | 810.3.j.e.539.4 | 8 | ||
45.29 | odd | 6 | 270.3.b.c.269.1 | ✓ | 4 | ||
45.34 | even | 6 | 270.3.b.c.269.4 | yes | 4 | ||
45.38 | even | 12 | 1350.3.d.f.701.1 | 2 | |||
45.43 | odd | 12 | 1350.3.d.f.701.2 | 2 | |||
180.79 | odd | 6 | 2160.3.c.i.1889.4 | 4 | |||
180.119 | even | 6 | 2160.3.c.i.1889.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
270.3.b.c.269.1 | ✓ | 4 | 45.29 | odd | 6 | ||
270.3.b.c.269.2 | yes | 4 | 9.7 | even | 3 | ||
270.3.b.c.269.3 | yes | 4 | 9.2 | odd | 6 | ||
270.3.b.c.269.4 | yes | 4 | 45.34 | even | 6 | ||
810.3.j.e.269.1 | 8 | 3.2 | odd | 2 | inner | ||
810.3.j.e.269.2 | 8 | 5.4 | even | 2 | inner | ||
810.3.j.e.269.3 | 8 | 15.14 | odd | 2 | inner | ||
810.3.j.e.269.4 | 8 | 1.1 | even | 1 | trivial | ||
810.3.j.e.539.1 | 8 | 45.4 | even | 6 | inner | ||
810.3.j.e.539.2 | 8 | 9.5 | odd | 6 | inner | ||
810.3.j.e.539.3 | 8 | 9.4 | even | 3 | inner | ||
810.3.j.e.539.4 | 8 | 45.14 | odd | 6 | inner | ||
1350.3.d.f.701.1 | 2 | 45.38 | even | 12 | |||
1350.3.d.f.701.2 | 2 | 45.43 | odd | 12 | |||
1350.3.d.g.701.1 | 2 | 45.7 | odd | 12 | |||
1350.3.d.g.701.2 | 2 | 45.2 | even | 12 | |||
2160.3.c.i.1889.1 | 4 | 180.119 | even | 6 | |||
2160.3.c.i.1889.2 | 4 | 36.7 | odd | 6 | |||
2160.3.c.i.1889.3 | 4 | 36.11 | even | 6 | |||
2160.3.c.i.1889.4 | 4 | 180.79 | odd | 6 |