Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [855,2,Mod(647,855)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(855, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("855.647");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 855 = 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 855.n (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.82720937282\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 101x^{16} + 2922x^{12} + 18746x^{8} + 4405x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 647.3 | ||
Root | \(-1.20930 + 1.20930i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 855.647 |
Dual form | 855.2.n.d.818.3 |
$q$-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 \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).
\(n\) | \(172\) | \(191\) | \(496\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.20930 | + | 1.20930i | −0.855102 | + | 0.855102i | −0.990756 | − | 0.135654i | \(-0.956686\pi\) |
0.135654 | + | 0.990756i | \(0.456686\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 0.924801i | − | 0.462400i | ||||||
\(5\) | −1.20930 | + | 1.88085i | −0.540814 | + | 0.841142i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.18506 | + | 2.18506i | 0.825877 | + | 0.825877i | 0.986944 | − | 0.161067i | \(-0.0514934\pi\) |
−0.161067 | + | 0.986944i | \(0.551493\pi\) | |||||||
\(8\) | −1.30024 | − | 1.30024i | −0.459703 | − | 0.459703i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.812108 | − | 3.73691i | −0.256811 | − | 1.18171i | ||||
\(11\) | − | 6.39552i | − | 1.92832i | −0.265320 | − | 0.964160i | \(-0.585478\pi\) | ||
0.265320 | − | 0.964160i | \(-0.414522\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.18506 | − | 3.18506i | 0.883378 | − | 0.883378i | −0.110498 | − | 0.993876i | \(-0.535245\pi\) |
0.993876 | + | 0.110498i | \(0.0352447\pi\) | |||||||
\(14\) | −5.28479 | −1.41242 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.99435 | 1.24859 | ||||||||
\(17\) | 4.92813 | − | 4.92813i | 1.19525 | − | 1.19525i | 0.219673 | − | 0.975574i | \(-0.429501\pi\) |
0.975574 | − | 0.219673i | \(-0.0704991\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.00000i | − | 0.229416i | ||||||
\(20\) | 1.73941 | + | 1.11836i | 0.388944 | + | 0.250073i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.73408 | + | 7.73408i | 1.64891 | + | 1.64891i | ||||
\(23\) | 1.62276 | + | 1.62276i | 0.338369 | + | 0.338369i | 0.855753 | − | 0.517384i | \(-0.173094\pi\) |
−0.517384 | + | 0.855753i | \(0.673094\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.07520 | − | 4.54902i | −0.415040 | − | 0.909803i | ||||
\(26\) | 7.70338i | 1.51076i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.02075 | − | 2.02075i | 0.381886 | − | 0.381886i | ||||
\(29\) | −2.20338 | −0.409157 | −0.204578 | − | 0.978850i | \(-0.565582\pi\) | ||||
−0.204578 | + | 0.978850i | \(0.565582\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.59617 | −0.286680 | −0.143340 | − | 0.989673i | \(-0.545784\pi\) | ||||
−0.143340 | + | 0.989673i | \(0.545784\pi\) | |||||||
\(32\) | −3.43918 | + | 3.43918i | −0.607966 | + | 0.607966i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 11.9191i | 2.04412i | ||||||||
\(35\) | −6.75217 | + | 1.46739i | −1.14133 | + | 0.248034i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.56977 | − | 6.56977i | −1.08006 | − | 1.08006i | −0.996503 | − | 0.0835600i | \(-0.973371\pi\) |
−0.0835600 | − | 0.996503i | \(-0.526629\pi\) | |||||||
\(38\) | 1.20930 | + | 1.20930i | 0.196174 | + | 0.196174i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.01792 | − | 0.873178i | 0.635289 | − | 0.138062i | ||||
\(41\) | 5.32003i | 0.830849i | 0.909628 | + | 0.415424i | \(0.136367\pi\) | ||||
−0.909628 | + | 0.415424i | \(0.863633\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.02075 | − | 4.02075i | 0.613158 | − | 0.613158i | −0.330609 | − | 0.943768i | \(-0.607254\pi\) |
0.943768 | + | 0.330609i | \(0.107254\pi\) | |||||||
\(44\) | −5.91458 | −0.891656 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.92480 | −0.578680 | ||||||||
\(47\) | 2.10370 | − | 2.10370i | 0.306856 | − | 0.306856i | −0.536833 | − | 0.843689i | \(-0.680379\pi\) |
0.843689 | + | 0.536833i | \(0.180379\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.54902i | 0.364145i | ||||||||
\(50\) | 8.01065 | + | 2.99158i | 1.13288 | + | 0.423073i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.94555 | − | 2.94555i | −0.408474 | − | 0.408474i | ||||
\(53\) | 7.08100 | + | 7.08100i | 0.972651 | + | 0.972651i | 0.999636 | − | 0.0269852i | \(-0.00859071\pi\) |
−0.0269852 | + | 0.999636i | \(0.508591\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12.0290 | + | 7.73408i | 1.62199 | + | 1.04286i | ||||
\(56\) | − | 5.68220i | − | 0.759316i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.66454 | − | 2.66454i | 0.349871 | − | 0.349871i | ||||
\(59\) | 4.04550 | 0.526680 | 0.263340 | − | 0.964703i | \(-0.415176\pi\) | ||||
0.263340 | + | 0.964703i | \(0.415176\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.29493 | −0.293836 | −0.146918 | − | 0.989149i | \(-0.546935\pi\) | ||||
−0.146918 | + | 0.989149i | \(0.546935\pi\) | |||||||
\(62\) | 1.93024 | − | 1.93024i | 0.245141 | − | 0.245141i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.67071i | 0.208839i | ||||||||
\(65\) | 2.13894 | + | 9.84232i | 0.265303 | + | 1.22079i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.38470 | − | 3.38470i | −0.413507 | − | 0.413507i | 0.469451 | − | 0.882958i | \(-0.344452\pi\) |
−0.882958 | + | 0.469451i | \(0.844452\pi\) | |||||||
\(68\) | −4.55754 | − | 4.55754i | −0.552682 | − | 0.552682i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.39088 | − | 9.93989i | 0.763856 | − | 1.18804i | ||||
\(71\) | 10.9670i | 1.30154i | 0.759274 | + | 0.650771i | \(0.225554\pi\) | ||||
−0.759274 | + | 0.650771i | \(0.774446\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.68484 | − | 5.68484i | 0.665361 | − | 0.665361i | −0.291278 | − | 0.956639i | \(-0.594080\pi\) |
0.956639 | + | 0.291278i | \(0.0940804\pi\) | |||||||
\(74\) | 15.8896 | 1.84713 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.924801 | −0.106082 | ||||||||
\(77\) | 13.9746 | − | 13.9746i | 1.59256 | − | 1.59256i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.156054i | 0.0175574i | 0.999961 | + | 0.00877871i | \(0.00279439\pi\) | ||||
−0.999961 | + | 0.00877871i | \(0.997206\pi\) | |||||||
\(80\) | −6.03965 | + | 9.39362i | −0.675253 | + | 1.05024i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.43350 | − | 6.43350i | −0.710461 | − | 0.710461i | ||||
\(83\) | −8.12862 | − | 8.12862i | −0.892232 | − | 0.892232i | 0.102501 | − | 0.994733i | \(-0.467316\pi\) |
−0.994733 | + | 0.102501i | \(0.967316\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.30950 | + | 15.2286i | 0.358966 | + | 1.65178i | ||||
\(86\) | 9.72456i | 1.04863i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.31568 | + | 8.31568i | −0.886454 | + | 0.886454i | ||||
\(89\) | −14.9439 | −1.58405 | −0.792025 | − | 0.610488i | \(-0.790973\pi\) | ||||
−0.792025 | + | 0.610488i | \(0.790973\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.9191 | 1.45912 | ||||||||
\(92\) | 1.50073 | − | 1.50073i | 0.156462 | − | 0.156462i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.08800i | 0.524787i | ||||||||
\(95\) | 1.88085 | + | 1.20930i | 0.192971 | + | 0.124071i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.439151 | + | 0.439151i | 0.0445890 | + | 0.0445890i | 0.729050 | − | 0.684461i | \(-0.239962\pi\) |
−0.684461 | + | 0.729050i | \(0.739962\pi\) | |||||||
\(98\) | −3.08252 | − | 3.08252i | −0.311381 | − | 0.311381i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.20693 | + | 1.91915i | −0.420693 | + | 0.191915i | ||||
\(101\) | − | 10.9317i | − | 1.08775i | −0.839166 | − | 0.543875i | \(-0.816957\pi\) | ||
0.839166 | − | 0.543875i | \(-0.183043\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.29493 | − | 2.29493i | 0.226126 | − | 0.226126i | −0.584946 | − | 0.811072i | \(-0.698884\pi\) |
0.811072 | + | 0.584946i | \(0.198884\pi\) | |||||||
\(104\) | −8.28267 | −0.812183 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −17.1261 | −1.66343 | ||||||||
\(107\) | 6.24014 | − | 6.24014i | 0.603257 | − | 0.603257i | −0.337918 | − | 0.941176i | \(-0.609723\pi\) |
0.941176 | + | 0.337918i | \(0.109723\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.54967i | 0.244214i | 0.992517 | + | 0.122107i | \(0.0389651\pi\) | ||||
−0.992517 | + | 0.122107i | \(0.961035\pi\) | |||||||
\(110\) | −23.8995 | + | 5.19385i | −2.27872 | + | 0.495214i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.9130 | + | 10.9130i | 1.03118 | + | 1.03118i | ||||
\(113\) | 13.5354 | + | 13.5354i | 1.27331 | + | 1.27331i | 0.944342 | + | 0.328965i | \(0.106700\pi\) |
0.328965 | + | 0.944342i | \(0.393300\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.01457 | + | 1.08977i | −0.467611 | + | 0.101622i | ||||
\(116\) | 2.03768i | 0.189194i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.89222 | + | 4.89222i | −0.450365 | + | 0.450365i | ||||
\(119\) | 21.5366 | 1.97425 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −29.9026 | −2.71842 | ||||||||
\(122\) | 2.77525 | − | 2.77525i | 0.251260 | − | 0.251260i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.47614i | 0.132561i | ||||||||
\(125\) | 11.0656 | + | 1.59797i | 0.989733 | + | 0.142927i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.0089 | + | 11.0089i | 0.976883 | + | 0.976883i | 0.999739 | − | 0.0228555i | \(-0.00727575\pi\) |
−0.0228555 | + | 0.999739i | \(0.507276\pi\) | |||||||
\(128\) | −8.89874 | − | 8.89874i | −0.786545 | − | 0.786545i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −14.4889 | − | 9.31568i | −1.27076 | − | 0.817039i | ||||
\(131\) | − | 7.61764i | − | 0.665556i | −0.943005 | − | 0.332778i | \(-0.892014\pi\) | ||
0.943005 | − | 0.332778i | \(-0.107986\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.18506 | − | 2.18506i | 0.189469 | − | 0.189469i | ||||
\(134\) | 8.18622 | 0.707182 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.8155 | −1.09892 | ||||||||
\(137\) | −10.5524 | + | 10.5524i | −0.901554 | + | 0.901554i | −0.995571 | − | 0.0940170i | \(-0.970029\pi\) |
0.0940170 | + | 0.995571i | \(0.470029\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.57750i | 0.557897i | 0.960306 | + | 0.278948i | \(0.0899858\pi\) | ||||
−0.960306 | + | 0.278948i | \(0.910014\pi\) | |||||||
\(140\) | 1.35704 | + | 6.24441i | 0.114691 | + | 0.527749i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −13.2623 | − | 13.2623i | −1.11295 | − | 1.11295i | ||||
\(143\) | −20.3701 | − | 20.3701i | −1.70344 | − | 1.70344i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.66454 | − | 4.14422i | 0.221278 | − | 0.344159i | ||||
\(146\) | 13.7493i | 1.13790i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.07572 | + | 6.07572i | −0.499421 | + | 0.499421i | ||||
\(149\) | 19.4713 | 1.59515 | 0.797577 | − | 0.603218i | \(-0.206115\pi\) | ||||
0.797577 | + | 0.603218i | \(0.206115\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.59051 | −0.780465 | −0.390232 | − | 0.920716i | \(-0.627605\pi\) | ||||
−0.390232 | + | 0.920716i | \(0.627605\pi\) | |||||||
\(152\) | −1.30024 | + | 1.30024i | −0.105463 | + | 0.105463i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 33.7989i | 2.72360i | ||||||||
\(155\) | 1.93024 | − | 3.00216i | 0.155041 | − | 0.241139i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.41319 | + | 7.41319i | 0.591637 | + | 0.591637i | 0.938073 | − | 0.346437i | \(-0.112608\pi\) |
−0.346437 | + | 0.938073i | \(0.612608\pi\) | |||||||
\(158\) | −0.188715 | − | 0.188715i | −0.0150134 | − | 0.0150134i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.30959 | − | 10.6276i | −0.182589 | − | 0.840183i | ||||
\(161\) | 7.09167i | 0.558902i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.43915 | − | 7.43915i | 0.582679 | − | 0.582679i | −0.352959 | − | 0.935639i | \(-0.614825\pi\) |
0.935639 | + | 0.352959i | \(0.114825\pi\) | |||||||
\(164\) | 4.91996 | 0.384185 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 19.6598 | 1.52590 | ||||||||
\(167\) | 6.44469 | − | 6.44469i | 0.498705 | − | 0.498705i | −0.412330 | − | 0.911035i | \(-0.635285\pi\) |
0.911035 | + | 0.412330i | \(0.135285\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 7.28928i | − | 0.560713i | ||||||
\(170\) | −22.4181 | − | 14.4138i | −1.71939 | − | 1.10549i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.71839 | − | 3.71839i | −0.283525 | − | 0.283525i | ||||
\(173\) | −1.85514 | − | 1.85514i | −0.141044 | − | 0.141044i | 0.633060 | − | 0.774103i | \(-0.281799\pi\) |
−0.774103 | + | 0.633060i | \(0.781799\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.40545 | − | 14.4743i | 0.408614 | − | 1.09416i | ||||
\(176\) | − | 31.9414i | − | 2.40767i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 18.0716 | − | 18.0716i | 1.35453 | − | 1.35453i | ||||
\(179\) | 5.73817 | 0.428891 | 0.214446 | − | 0.976736i | \(-0.431206\pi\) | ||||
0.214446 | + | 0.976736i | \(0.431206\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0124 | −1.04153 | −0.520765 | − | 0.853700i | \(-0.674353\pi\) | ||||
−0.520765 | + | 0.853700i | \(0.674353\pi\) | |||||||
\(182\) | −16.8324 | + | 16.8324i | −1.24770 | + | 1.24770i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 4.21994i | − | 0.311098i | ||||||
\(185\) | 20.3015 | − | 4.41195i | 1.49260 | − | 0.324373i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −31.5179 | − | 31.5179i | −2.30482 | − | 2.30482i | ||||
\(188\) | −1.94550 | − | 1.94550i | −0.141890 | − | 0.141890i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.73691 | + | 0.812108i | −0.271104 | + | 0.0589165i | ||||
\(191\) | − | 3.99218i | − | 0.288864i | −0.989515 | − | 0.144432i | \(-0.953865\pi\) | ||
0.989515 | − | 0.144432i | \(-0.0461355\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.2551 | − | 14.2551i | 1.02610 | − | 1.02610i | 0.0264509 | − | 0.999650i | \(-0.491579\pi\) |
0.999650 | − | 0.0264509i | \(-0.00842056\pi\) | |||||||
\(194\) | −1.06213 | −0.0762563 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.35733 | 0.168381 | ||||||||
\(197\) | 3.62026 | − | 3.62026i | 0.257933 | − | 0.257933i | −0.566280 | − | 0.824213i | \(-0.691618\pi\) |
0.824213 | + | 0.566280i | \(0.191618\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.999558i | 0.0708568i | 0.999372 | + | 0.0354284i | \(0.0112796\pi\) | ||||
−0.999372 | + | 0.0354284i | \(0.988720\pi\) | |||||||
\(200\) | −3.21655 | + | 8.61304i | −0.227444 | + | 0.609034i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 13.2197 | + | 13.2197i | 0.930137 | + | 0.930137i | ||||
\(203\) | −4.81452 | − | 4.81452i | −0.337913 | − | 0.337913i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.0062 | − | 6.43350i | −0.698862 | − | 0.449335i | ||||
\(206\) | 5.55051i | 0.386722i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 15.9073 | − | 15.9073i | 1.10297 | − | 1.10297i | ||||
\(209\) | −6.39552 | −0.442387 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.2847 | 0.708029 | 0.354015 | − | 0.935240i | \(-0.384816\pi\) | ||||
0.354015 | + | 0.935240i | \(0.384816\pi\) | |||||||
\(212\) | 6.54852 | − | 6.54852i | 0.449754 | − | 0.449754i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 15.0924i | 1.03169i | ||||||||
\(215\) | 2.70015 | + | 12.4247i | 0.184149 | + | 0.847358i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.48773 | − | 3.48773i | −0.236763 | − | 0.236763i | ||||
\(218\) | −3.08331 | − | 3.08331i | −0.208828 | − | 0.208828i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.15248 | − | 11.1244i | 0.482220 | − | 0.750009i | ||||
\(221\) | − | 31.3928i | − | 2.11171i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.24256 | + | 5.24256i | −0.351068 | + | 0.351068i | −0.860507 | − | 0.509439i | \(-0.829853\pi\) |
0.509439 | + | 0.860507i | \(0.329853\pi\) | |||||||
\(224\) | −15.0296 | −1.00421 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −32.7367 | −2.17762 | ||||||||
\(227\) | −14.1300 | + | 14.1300i | −0.937840 | + | 0.937840i | −0.998178 | − | 0.0603377i | \(-0.980782\pi\) |
0.0603377 | + | 0.998178i | \(0.480782\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 29.1157i | 1.92402i | 0.273021 | + | 0.962008i | \(0.411977\pi\) | ||||
−0.273021 | + | 0.962008i | \(0.588023\pi\) | |||||||
\(230\) | 4.74625 | − | 7.38196i | 0.312959 | − | 0.486752i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.86491 | + | 2.86491i | 0.188090 | + | 0.188090i | ||||
\(233\) | −15.5695 | − | 15.5695i | −1.01999 | − | 1.01999i | −0.999796 | − | 0.0201964i | \(-0.993571\pi\) |
−0.0201964 | − | 0.999796i | \(-0.506429\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.41275 | + | 6.50074i | 0.0921574 | + | 0.424062i | ||||
\(236\) | − | 3.74128i | − | 0.243537i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −26.0441 | + | 26.0441i | −1.68819 | + | 1.68819i | ||||
\(239\) | 5.52295 | 0.357250 | 0.178625 | − | 0.983917i | \(-0.442835\pi\) | ||||
0.178625 | + | 0.983917i | \(0.442835\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.4116 | −0.670672 | −0.335336 | − | 0.942099i | \(-0.608850\pi\) | ||||
−0.335336 | + | 0.942099i | \(0.608850\pi\) | |||||||
\(242\) | 36.1612 | − | 36.1612i | 2.32453 | − | 2.32453i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.12235i | 0.135870i | ||||||||
\(245\) | −4.79432 | − | 3.08252i | −0.306298 | − | 0.196935i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.18506 | − | 3.18506i | −0.202661 | − | 0.202661i | ||||
\(248\) | 2.07540 | + | 2.07540i | 0.131788 | + | 0.131788i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −15.3140 | + | 11.4491i | −0.968541 | + | 0.724106i | ||||
\(251\) | 7.99887i | 0.504884i | 0.967612 | + | 0.252442i | \(0.0812337\pi\) | ||||
−0.967612 | + | 0.252442i | \(0.918766\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.3784 | − | 10.3784i | 0.652484 | − | 0.652484i | ||||
\(254\) | −26.6261 | −1.67067 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 18.1810 | 1.13631 | ||||||||
\(257\) | −9.46626 | + | 9.46626i | −0.590489 | + | 0.590489i | −0.937763 | − | 0.347275i | \(-0.887107\pi\) |
0.347275 | + | 0.937763i | \(0.387107\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 28.7107i | − | 1.78400i | ||||||
\(260\) | 9.10219 | − | 1.97809i | 0.564494 | − | 0.122676i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.21199 | + | 9.21199i | 0.569119 | + | 0.569119i | ||||
\(263\) | 6.95805 | + | 6.95805i | 0.429052 | + | 0.429052i | 0.888305 | − | 0.459254i | \(-0.151883\pi\) |
−0.459254 | + | 0.888305i | \(0.651883\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −21.8813 | + | 4.75527i | −1.34416 | + | 0.292114i | ||||
\(266\) | 5.28479i | 0.324031i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.13017 | + | 3.13017i | −0.191206 | + | 0.191206i | ||||
\(269\) | −28.3286 | −1.72722 | −0.863611 | − | 0.504158i | \(-0.831803\pi\) | ||||
−0.863611 | + | 0.504158i | \(0.831803\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.87830 | 0.174844 | 0.0874222 | − | 0.996171i | \(-0.472137\pi\) | ||||
0.0874222 | + | 0.996171i | \(0.472137\pi\) | |||||||
\(272\) | 24.6128 | − | 24.6128i | 1.49237 | − | 1.49237i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 25.5220i | − | 1.54184i | ||||||
\(275\) | −29.0933 | + | 13.2720i | −1.75439 | + | 0.800330i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.49248 | + | 5.49248i | 0.330011 | + | 0.330011i | 0.852591 | − | 0.522579i | \(-0.175030\pi\) |
−0.522579 | + | 0.852591i | \(0.675030\pi\) | |||||||
\(278\) | −7.95416 | − | 7.95416i | −0.477059 | − | 0.477059i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 10.6874 | + | 6.87147i | 0.638692 | + | 0.410649i | ||||
\(281\) | − | 28.3007i | − | 1.68828i | −0.536124 | − | 0.844139i | \(-0.680112\pi\) | ||
0.536124 | − | 0.844139i | \(-0.319888\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.55454 | − | 9.55454i | 0.567958 | − | 0.567958i | −0.363598 | − | 0.931556i | \(-0.618452\pi\) |
0.931556 | + | 0.363598i | \(0.118452\pi\) | |||||||
\(284\) | 10.1423 | 0.601833 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 49.2671 | 2.91322 | ||||||||
\(287\) | −11.6246 | + | 11.6246i | −0.686179 | + | 0.686179i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 31.5729i | − | 1.85723i | ||||||
\(290\) | 1.78938 | + | 8.23381i | 0.105076 | + | 0.483506i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.25735 | − | 5.25735i | −0.307663 | − | 0.307663i | ||||
\(293\) | −5.30807 | − | 5.30807i | −0.310101 | − | 0.310101i | 0.534848 | − | 0.844948i | \(-0.320369\pi\) |
−0.844948 | + | 0.534848i | \(0.820369\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.89222 | + | 7.60899i | −0.284836 | + | 0.443013i | ||||
\(296\) | 17.0845i | 0.993016i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −23.5466 | + | 23.5466i | −1.36402 | + | 1.36402i | ||||
\(299\) | 10.3372 | 0.597815 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.5712 | 1.01279 | ||||||||
\(302\) | 11.5978 | − | 11.5978i | 0.667378 | − | 0.667378i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 4.99435i | − | 0.286445i | ||||||
\(305\) | 2.77525 | − | 4.31642i | 0.158911 | − | 0.247158i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.2836 | + | 14.2836i | 0.815209 | + | 0.815209i | 0.985409 | − | 0.170200i | \(-0.0544415\pi\) |
−0.170200 | + | 0.985409i | \(0.554441\pi\) | |||||||
\(308\) | −12.9237 | − | 12.9237i | −0.736398 | − | 0.736398i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.29626 | + | 5.96474i | 0.0736227 | + | 0.338774i | ||||
\(311\) | 21.2935i | 1.20744i | 0.797196 | + | 0.603721i | \(0.206316\pi\) | ||||
−0.797196 | + | 0.603721i | \(0.793684\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.68594 | − | 1.68594i | 0.0952949 | − | 0.0952949i | −0.657852 | − | 0.753147i | \(-0.728535\pi\) |
0.753147 | + | 0.657852i | \(0.228535\pi\) | |||||||
\(314\) | −17.9295 | −1.01182 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.144319 | 0.00811856 | ||||||||
\(317\) | 7.57258 | − | 7.57258i | 0.425318 | − | 0.425318i | −0.461712 | − | 0.887030i | \(-0.652765\pi\) |
0.887030 | + | 0.461712i | \(0.152765\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.0917i | 0.788985i | ||||||||
\(320\) | −3.14236 | − | 2.02039i | −0.175664 | − | 0.112943i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.57594 | − | 8.57594i | −0.477919 | − | 0.477919i | ||||
\(323\) | −4.92813 | − | 4.92813i | −0.274208 | − | 0.274208i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −21.0986 | − | 7.87927i | −1.17034 | − | 0.437063i | ||||
\(326\) | 17.9923i | 0.996501i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.91729 | − | 6.91729i | 0.381943 | − | 0.381943i | ||||
\(329\) | 9.19344 | 0.506851 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.6766 | −0.751736 | −0.375868 | − | 0.926673i | \(-0.622655\pi\) | ||||
−0.375868 | + | 0.926673i | \(0.622655\pi\) | |||||||
\(332\) | −7.51736 | + | 7.51736i | −0.412568 | + | 0.412568i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 15.5871i | 0.852888i | ||||||||
\(335\) | 10.4592 | − | 2.27301i | 0.571449 | − | 0.124188i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.979251 | − | 0.979251i | −0.0533432 | − | 0.0533432i | 0.679932 | − | 0.733275i | \(-0.262009\pi\) |
−0.733275 | + | 0.679932i | \(0.762009\pi\) | |||||||
\(338\) | 8.81490 | + | 8.81490i | 0.479467 | + | 0.479467i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 14.0835 | − | 3.06063i | 0.763783 | − | 0.165986i | ||||
\(341\) | 10.2083i | 0.552812i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.72569 | − | 9.72569i | 0.525138 | − | 0.525138i | ||||
\(344\) | −10.4558 | −0.563741 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.48683 | 0.241213 | ||||||||
\(347\) | −17.5039 | + | 17.5039i | −0.939661 | + | 0.939661i | −0.998280 | − | 0.0586196i | \(-0.981330\pi\) |
0.0586196 | + | 0.998280i | \(0.481330\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 4.89631i | − | 0.262094i | −0.991376 | − | 0.131047i | \(-0.958166\pi\) | ||
0.991376 | − | 0.131047i | \(-0.0418338\pi\) | |||||||
\(350\) | 10.9670 | + | 24.0406i | 0.586210 | + | 1.28502i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 21.9953 | + | 21.9953i | 1.17235 | + | 1.17235i | ||||
\(353\) | −5.87829 | − | 5.87829i | −0.312870 | − | 0.312870i | 0.533151 | − | 0.846020i | \(-0.321008\pi\) |
−0.846020 | + | 0.533151i | \(0.821008\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.6273 | − | 13.2623i | −1.09478 | − | 0.703892i | ||||
\(356\) | 13.8201i | 0.732466i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.93916 | + | 6.93916i | −0.366746 | + | 0.366746i | ||||
\(359\) | 32.5369 | 1.71723 | 0.858616 | − | 0.512620i | \(-0.171325\pi\) | ||||
0.858616 | + | 0.512620i | \(0.171325\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 16.9451 | − | 16.9451i | 0.890615 | − | 0.890615i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 12.8724i | − | 0.674699i | ||||||
\(365\) | 3.81768 | + | 17.5670i | 0.199826 | + | 0.919499i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.4654 | + | 11.4654i | 0.598490 | + | 0.598490i | 0.939911 | − | 0.341420i | \(-0.110908\pi\) |
−0.341420 | + | 0.939911i | \(0.610908\pi\) | |||||||
\(368\) | 8.10463 | + | 8.10463i | 0.422483 | + | 0.422483i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −19.2153 | + | 29.8860i | −0.998953 | + | 1.55370i | ||||
\(371\) | 30.9449i | 1.60658i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.73452 | + | 7.73452i | −0.400478 | + | 0.400478i | −0.878402 | − | 0.477923i | \(-0.841390\pi\) |
0.477923 | + | 0.878402i | \(0.341390\pi\) | |||||||
\(374\) | 76.2291 | 3.94171 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.47061 | −0.282125 | ||||||||
\(377\) | −7.01789 | + | 7.01789i | −0.361440 | + | 0.361440i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 27.8974i | − | 1.43299i | −0.697590 | − | 0.716497i | \(-0.745744\pi\) | ||
0.697590 | − | 0.716497i | \(-0.254256\pi\) | |||||||
\(380\) | 1.11836 | − | 1.73941i | 0.0573706 | − | 0.0892299i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.82773 | + | 4.82773i | 0.247008 | + | 0.247008i | ||||
\(383\) | 22.3282 | + | 22.3282i | 1.14092 | + | 1.14092i | 0.988282 | + | 0.152638i | \(0.0487768\pi\) |
0.152638 | + | 0.988282i | \(0.451223\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.38470 | + | 43.1836i | 0.478289 | + | 2.20084i | ||||
\(386\) | 34.4772i | 1.75484i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.406127 | − | 0.406127i | 0.0206180 | − | 0.0206180i | ||||
\(389\) | 11.8101 | 0.598796 | 0.299398 | − | 0.954128i | \(-0.403214\pi\) | ||||
0.299398 | + | 0.954128i | \(0.403214\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.9943 | 0.808869 | ||||||||
\(392\) | 3.31432 | − | 3.31432i | 0.167399 | − | 0.167399i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.75595i | 0.441118i | ||||||||
\(395\) | −0.293514 | − | 0.188715i | −0.0147683 | − | 0.00949531i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.62987 | − | 6.62987i | −0.332744 | − | 0.332744i | 0.520884 | − | 0.853628i | \(-0.325602\pi\) |
−0.853628 | + | 0.520884i | \(0.825602\pi\) | |||||||
\(398\) | −1.20876 | − | 1.20876i | −0.0605898 | − | 0.0605898i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.3643 | − | 22.7194i | −0.518213 | − | 1.13597i | ||||
\(401\) | 19.4459i | 0.971080i | 0.874214 | + | 0.485540i | \(0.161377\pi\) | ||||
−0.874214 | + | 0.485540i | \(0.838623\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.08390 | + | 5.08390i | −0.253247 | + | 0.253247i | ||||
\(404\) | −10.1097 | −0.502976 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11.6444 | 0.577900 | ||||||||
\(407\) | −42.0170 | + | 42.0170i | −2.08271 | + | 2.08271i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.8272i | 0.980390i | 0.871613 | + | 0.490195i | \(0.163074\pi\) | ||||
−0.871613 | + | 0.490195i | \(0.836926\pi\) | |||||||
\(410\) | 19.8805 | − | 4.32044i | 0.981826 | − | 0.213371i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.12235 | − | 2.12235i | −0.104561 | − | 0.104561i | ||||
\(413\) | 8.83969 | + | 8.83969i | 0.434973 | + | 0.434973i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25.1187 | − | 5.45880i | 1.23303 | − | 0.267962i | ||||
\(416\) | 21.9080i | 1.07413i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.73408 | − | 7.73408i | 0.378286 | − | 0.378286i | ||||
\(419\) | 36.6414 | 1.79005 | 0.895026 | − | 0.446015i | \(-0.147157\pi\) | ||||
0.895026 | + | 0.446015i | \(0.147157\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.9548 | −0.875062 | −0.437531 | − | 0.899203i | \(-0.644147\pi\) | ||||
−0.437531 | + | 0.899203i | \(0.644147\pi\) | |||||||
\(422\) | −12.4373 | + | 12.4373i | −0.605437 | + | 0.605437i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 18.4139i | − | 0.894260i | ||||||
\(425\) | −32.6450 | − | 12.1913i | −1.58351 | − | 0.591364i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.01457 | − | 5.01457i | −0.242672 | − | 0.242672i | ||||
\(428\) | −5.77089 | − | 5.77089i | −0.278946 | − | 0.278946i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −18.2905 | − | 11.7599i | −0.882044 | − | 0.567112i | ||||
\(431\) | − | 40.3285i | − | 1.94256i | −0.237947 | − | 0.971278i | \(-0.576474\pi\) | ||
0.237947 | − | 0.971278i | \(-0.423526\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.97138 | + | 7.97138i | −0.383080 | + | 0.383080i | −0.872211 | − | 0.489130i | \(-0.837314\pi\) |
0.489130 | + | 0.872211i | \(0.337314\pi\) | |||||||
\(434\) | 8.43541 | 0.404913 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.35794 | 0.112925 | ||||||||
\(437\) | 1.62276 | − | 1.62276i | 0.0776272 | − | 0.0776272i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.3684i | 0.733493i | 0.930321 | + | 0.366746i | \(0.119528\pi\) | ||||
−0.930321 | + | 0.366746i | \(0.880472\pi\) | |||||||
\(440\) | −5.58442 | − | 25.6967i | −0.266227 | − | 1.22504i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 37.9633 | + | 37.9633i | 1.80573 | + | 1.80573i | ||||
\(443\) | 18.5975 | + | 18.5975i | 0.883594 | + | 0.883594i | 0.993898 | − | 0.110304i | \(-0.0351823\pi\) |
−0.110304 | + | 0.993898i | \(0.535182\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.0716 | − | 28.1073i | 0.856677 | − | 1.33241i | ||||
\(446\) | − | 12.6796i | − | 0.600398i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.65062 | + | 3.65062i | −0.172476 | + | 0.172476i | ||||
\(449\) | −8.21864 | −0.387861 | −0.193931 | − | 0.981015i | \(-0.562124\pi\) | ||||
−0.193931 | + | 0.981015i | \(0.562124\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 34.0243 | 1.60214 | ||||||||
\(452\) | 12.5176 | − | 12.5176i | 0.588778 | − | 0.588778i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 34.1747i | − | 1.60390i | ||||||
\(455\) | −16.8324 | + | 26.1798i | −0.789114 | + | 1.22733i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.5986 | + | 10.5986i | 0.495780 | + | 0.495780i | 0.910121 | − | 0.414342i | \(-0.135988\pi\) |
−0.414342 | + | 0.910121i | \(0.635988\pi\) | |||||||
\(458\) | −35.2095 | − | 35.2095i | −1.64523 | − | 1.64523i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.00782 | + | 4.63748i | 0.0469899 | + | 0.216224i | ||||
\(461\) | − | 17.6356i | − | 0.821372i | −0.911777 | − | 0.410686i | \(-0.865289\pi\) | ||
0.911777 | − | 0.410686i | \(-0.134711\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.0147 | + | 21.0147i | −0.976634 | + | 0.976634i | −0.999733 | − | 0.0230994i | \(-0.992647\pi\) |
0.0230994 | + | 0.999733i | \(0.492647\pi\) | |||||||
\(464\) | −11.0044 | −0.510867 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 37.6563 | 1.74440 | ||||||||
\(467\) | 1.31306 | − | 1.31306i | 0.0607613 | − | 0.0607613i | −0.676073 | − | 0.736834i | \(-0.736320\pi\) |
0.736834 | + | 0.676073i | \(0.236320\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 14.7916i | − | 0.683012i | ||||||
\(470\) | −9.56976 | − | 6.15290i | −0.441420 | − | 0.283812i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.26011 | − | 5.26011i | −0.242116 | − | 0.242116i | ||||
\(473\) | −25.7148 | − | 25.7148i | −1.18237 | − | 1.18237i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.54902 | + | 2.07520i | −0.208723 | + | 0.0952167i | ||||
\(476\) | − | 19.9170i | − | 0.912895i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.67889 | + | 6.67889i | −0.305486 | + | 0.305486i | ||||
\(479\) | 6.28928 | 0.287364 | 0.143682 | − | 0.989624i | \(-0.454106\pi\) | ||||
0.143682 | + | 0.989624i | \(0.454106\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −41.8503 | −1.90821 | ||||||||
\(482\) | 12.5908 | − | 12.5908i | 0.573493 | − | 0.573493i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 27.6540i | 1.25700i | ||||||||
\(485\) | −1.35704 | + | 0.294913i | −0.0616201 | + | 0.0133913i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.1874 | + | 25.1874i | 1.14135 | + | 1.14135i | 0.988204 | + | 0.153144i | \(0.0489400\pi\) |
0.153144 | + | 0.988204i | \(0.451060\pi\) | |||||||
\(488\) | 2.98395 | + | 2.98395i | 0.135077 | + | 0.135077i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9.52544 | − | 2.07008i | 0.430315 | − | 0.0935165i | ||||
\(491\) | 17.0077i | 0.767547i | 0.923427 | + | 0.383773i | \(0.125376\pi\) | ||||
−0.923427 | + | 0.383773i | \(0.874624\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.8585 | + | 10.8585i | −0.489043 | + | 0.489043i | ||||
\(494\) | 7.70338 | 0.346592 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.97182 | −0.357945 | ||||||||
\(497\) | −23.9636 | + | 23.9636i | −1.07491 | + | 1.07491i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 12.3888i | − | 0.554601i | −0.960783 | − | 0.277300i | \(-0.910560\pi\) | ||
0.960783 | − | 0.277300i | \(-0.0894397\pi\) | |||||||
\(500\) | 1.47781 | − | 10.2334i | 0.0660895 | − | 0.457653i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.67301 | − | 9.67301i | −0.431728 | − | 0.431728i | ||||
\(503\) | 9.81969 | + | 9.81969i | 0.437838 | + | 0.437838i | 0.891284 | − | 0.453446i | \(-0.149805\pi\) |
−0.453446 | + | 0.891284i | \(0.649805\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.5610 | + | 13.2197i | 0.914952 | + | 0.588270i | ||||
\(506\) | 25.1011i | 1.11588i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.1811 | − | 10.1811i | 0.451711 | − | 0.451711i | ||||
\(509\) | −9.12486 | −0.404452 | −0.202226 | − | 0.979339i | \(-0.564818\pi\) | ||||
−0.202226 | + | 0.979339i | \(0.564818\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.8435 | 1.09901 | ||||||||
\(512\) | −4.18878 | + | 4.18878i | −0.185120 | + | 0.185120i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 22.8950i | − | 1.00986i | ||||||
\(515\) | 1.54117 | + | 7.09167i | 0.0679120 | + | 0.312497i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.4542 | − | 13.4542i | −0.591717 | − | 0.591717i | ||||
\(518\) | 34.7198 | + | 34.7198i | 1.52550 | + | 1.52550i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.0162 | − | 15.5785i | 0.439240 | − | 0.683161i | ||||
\(521\) | − | 21.2160i | − | 0.929491i | −0.885444 | − | 0.464746i | \(-0.846146\pi\) | ||
0.885444 | − | 0.464746i | \(-0.153854\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.23842 | + | 6.23842i | −0.272787 | + | 0.272787i | −0.830221 | − | 0.557434i | \(-0.811786\pi\) |
0.557434 | + | 0.830221i | \(0.311786\pi\) | |||||||
\(524\) | −7.04480 | −0.307753 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.8287 | −0.733766 | ||||||||
\(527\) | −7.86613 | + | 7.86613i | −0.342654 | + | 0.342654i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 17.7333i | − | 0.771013i | ||||||
\(530\) | 20.7105 | − | 32.2116i | 0.899608 | − | 1.39918i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.02075 | − | 2.02075i | −0.0876106 | − | 0.0876106i | ||||
\(533\) | 16.9446 | + | 16.9446i | 0.733954 | + | 0.733954i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.19059 | + | 19.2830i | 0.181175 | + | 0.833675i | ||||
\(536\) | 8.80182i | 0.380181i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 34.2577 | − | 34.2577i | 1.47695 | − | 1.47695i | ||||
\(539\) | 16.3023 | 0.702189 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.261229 | −0.0112311 | −0.00561556 | − | 0.999984i | \(-0.501787\pi\) | ||||
−0.00561556 | + | 0.999984i | \(0.501787\pi\) | |||||||
\(542\) | −3.48072 | + | 3.48072i | −0.149510 | + | 0.149510i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 33.8974i | 1.45334i | ||||||||
\(545\) | −4.79555 | − | 3.08331i | −0.205419 | − | 0.132074i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.61835 | + | 7.61835i | 0.325737 | + | 0.325737i | 0.850963 | − | 0.525226i | \(-0.176019\pi\) |
−0.525226 | + | 0.850963i | \(0.676019\pi\) | |||||||
\(548\) | 9.75888 | + | 9.75888i | 0.416879 | + | 0.416879i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 19.1327 | − | 51.2322i | 0.815821 | − | 2.18455i | ||||
\(551\) | 2.20338i | 0.0938670i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.340988 | + | 0.340988i | −0.0145003 | + | 0.0145003i | ||||
\(554\) | −13.2841 | −0.564387 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.08288 | 0.257972 | ||||||||
\(557\) | −3.56267 | + | 3.56267i | −0.150955 | + | 0.150955i | −0.778544 | − | 0.627589i | \(-0.784042\pi\) |
0.627589 | + | 0.778544i | \(0.284042\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 25.6127i | − | 1.08330i | ||||||
\(560\) | −33.7227 | + | 7.32864i | −1.42504 | + | 0.309692i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 34.2240 | + | 34.2240i | 1.44365 | + | 1.44365i | ||||
\(563\) | 2.50019 | + | 2.50019i | 0.105370 | + | 0.105370i | 0.757826 | − | 0.652456i | \(-0.226261\pi\) |
−0.652456 | + | 0.757826i | \(0.726261\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −41.8265 | + | 9.08977i | −1.75965 | + | 0.382410i | ||||
\(566\) | 23.1086i | 0.971325i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.2597 | − | 14.2597i | 0.598322 | − | 0.598322i | ||||
\(569\) | 11.7470 | 0.492461 | 0.246231 | − | 0.969211i | \(-0.420808\pi\) | ||||
0.246231 | + | 0.969211i | \(0.420808\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.0111305 | −0.000465796 | −0.000232898 | − | 1.00000i | \(-0.500074\pi\) | ||||
−0.000232898 | 1.00000i | \(0.500074\pi\) | ||||||||
\(572\) | −18.8383 | + | 18.8383i | −0.787669 | + | 0.787669i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 28.1152i | − | 1.17351i | ||||||
\(575\) | 4.01441 | − | 10.7495i | 0.167413 | − | 0.448286i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.1867 | − | 19.1867i | −0.798753 | − | 0.798753i | 0.184146 | − | 0.982899i | \(-0.441048\pi\) |
−0.982899 | + | 0.184146i | \(0.941048\pi\) | |||||||
\(578\) | 38.1810 | + | 38.1810i | 1.58812 | + | 1.58812i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.83258 | − | 2.46416i | −0.159139 | − | 0.102319i | ||||
\(581\) | − | 35.5231i | − | 1.47375i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 45.2867 | − | 45.2867i | 1.87558 | − | 1.87558i | ||||
\(584\) | −14.7833 | −0.611736 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.8381 | 0.530335 | ||||||||
\(587\) | 26.8789 | − | 26.8789i | 1.10941 | − | 1.10941i | 0.116185 | − | 0.993228i | \(-0.462933\pi\) |
0.993228 | − | 0.116185i | \(-0.0370666\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.59617i | 0.0657690i | ||||||||
\(590\) | −3.28539 | − | 15.1177i | −0.135257 | − | 0.622385i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −32.8117 | − | 32.8117i | −1.34855 | − | 1.34855i | ||||
\(593\) | −6.59487 | − | 6.59487i | −0.270819 | − | 0.270819i | 0.558611 | − | 0.829430i | \(-0.311334\pi\) |
−0.829430 | + | 0.558611i | \(0.811334\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −26.0441 | + | 40.5071i | −1.06770 | + | 1.66063i | ||||
\(596\) | − | 18.0071i | − | 0.737599i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12.5007 | + | 12.5007i | −0.511193 | + | 0.511193i | ||||
\(599\) | −21.8982 | −0.894737 | −0.447368 | − | 0.894350i | \(-0.647639\pi\) | ||||
−0.447368 | + | 0.894350i | \(0.647639\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.9509 | 1.34409 | 0.672047 | − | 0.740508i | \(-0.265415\pi\) | ||||
0.672047 | + | 0.740508i | \(0.265415\pi\) | |||||||
\(602\) | −21.2488 | + | 21.2488i | −0.866036 | + | 0.866036i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.86931i | 0.360887i | ||||||||
\(605\) | 36.1612 | − | 56.2424i | 1.47016 | − | 2.28658i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.1956 | + | 20.1956i | 0.819714 | + | 0.819714i | 0.986066 | − | 0.166352i | \(-0.0531989\pi\) |
−0.166352 | + | 0.986066i | \(0.553199\pi\) | |||||||
\(608\) | 3.43918 | + | 3.43918i | 0.139477 | + | 0.139477i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.86373 | + | 8.57594i | 0.0754602 | + | 0.347230i | ||||
\(611\) | − | 13.4008i | − | 0.542140i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.4951 | + | 19.4951i | −0.787399 | + | 0.787399i | −0.981067 | − | 0.193668i | \(-0.937962\pi\) |
0.193668 | + | 0.981067i | \(0.437962\pi\) | |||||||
\(614\) | −34.5463 | −1.39417 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −36.3406 | −1.46420 | ||||||||
\(617\) | −17.7580 | + | 17.7580i | −0.714909 | + | 0.714909i | −0.967558 | − | 0.252649i | \(-0.918698\pi\) |
0.252649 | + | 0.967558i | \(0.418698\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 47.3008i | 1.90118i | 0.310450 | + | 0.950590i | \(0.399520\pi\) | ||||
−0.310450 | + | 0.950590i | \(0.600480\pi\) | |||||||
\(620\) | −2.77640 | − | 1.78509i | −0.111503 | − | 0.0716910i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −25.7501 | − | 25.7501i | −1.03249 | − | 1.03249i | ||||
\(623\) | −32.6534 | − | 32.6534i | −1.30823 | − | 1.30823i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.3871 | + | 18.8802i | −0.655484 | + | 0.755209i | ||||
\(626\) | 4.07761i | 0.162974i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.85572 | − | 6.85572i | 0.273573 | − | 0.273573i | ||||
\(629\) | −64.7533 | −2.58188 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.6544 | −1.26014 | −0.630071 | − | 0.776538i | \(-0.716974\pi\) | ||||
−0.630071 | + | 0.776538i | \(0.716974\pi\) | |||||||
\(632\) | 0.202907 | − | 0.202907i | 0.00807120 | − | 0.00807120i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18.3150i | 0.727382i | ||||||||
\(635\) | −34.0192 | + | 7.39307i | −1.35001 | + | 0.293385i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.11878 | + | 8.11878i | 0.321678 | + | 0.321678i | ||||
\(638\) | −17.0411 | − | 17.0411i | −0.674663 | − | 0.674663i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 27.4984 | − | 5.97598i | 1.08697 | − | 0.236221i | ||||
\(641\) | − | 40.9546i | − | 1.61761i | −0.588078 | − | 0.808804i | \(-0.700115\pi\) | ||
0.588078 | − | 0.808804i | \(-0.299885\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.0553 | − | 20.0553i | 0.790903 | − | 0.790903i | −0.190738 | − | 0.981641i | \(-0.561088\pi\) |
0.981641 | + | 0.190738i | \(0.0610880\pi\) | |||||||
\(644\) | 6.55838 | 0.258437 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.9191 | 0.468953 | ||||||||
\(647\) | −7.34757 | + | 7.34757i | −0.288863 | + | 0.288863i | −0.836631 | − | 0.547768i | \(-0.815478\pi\) |
0.547768 | + | 0.836631i | \(0.315478\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 25.8731i | − | 1.01561i | ||||||
\(650\) | 35.0428 | − | 15.9861i | 1.37449 | − | 0.627025i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.87973 | − | 6.87973i | −0.269431 | − | 0.269431i | ||||
\(653\) | 5.51837 | + | 5.51837i | 0.215950 | + | 0.215950i | 0.806789 | − | 0.590839i | \(-0.201203\pi\) |
−0.590839 | + | 0.806789i | \(0.701203\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.3276 | + | 9.21199i | 0.559827 | + | 0.359942i | ||||
\(656\) | 26.5701i | 1.03739i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −11.1176 | + | 11.1176i | −0.433409 | + | 0.433409i | ||||
\(659\) | −15.2922 | −0.595701 | −0.297850 | − | 0.954613i | \(-0.596270\pi\) | ||||
−0.297850 | + | 0.954613i | \(0.596270\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.1834 | −0.512777 | −0.256388 | − | 0.966574i | \(-0.582533\pi\) | ||||
−0.256388 | + | 0.966574i | \(0.582533\pi\) | |||||||
\(662\) | 16.5391 | − | 16.5391i | 0.642811 | − | 0.642811i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 21.1383i | 0.820323i | ||||||||
\(665\) | 1.46739 | + | 6.75217i | 0.0569028 | + | 0.261838i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.57555 | − | 3.57555i | −0.138446 | − | 0.138446i | ||||
\(668\) | −5.96005 | − | 5.96005i | −0.230601 | − | 0.230601i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −9.89957 | + | 15.3971i | −0.382454 | + | 0.594840i | ||||
\(671\) | 14.6773i | 0.566609i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.4137 | + | 14.4137i | −0.555608 | + | 0.555608i | −0.928054 | − | 0.372446i | \(-0.878519\pi\) |
0.372446 | + | 0.928054i | \(0.378519\pi\) | |||||||
\(674\) | 2.36841 | 0.0912278 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.74113 | −0.259274 | ||||||||
\(677\) | 2.47514 | − | 2.47514i | 0.0951275 | − | 0.0951275i | −0.657942 | − | 0.753069i | \(-0.728573\pi\) |
0.753069 | + | 0.657942i | \(0.228573\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.91915i | 0.0736500i | ||||||||
\(680\) | 15.4977 | − | 24.1040i | 0.594310 | − | 0.924345i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.3449 | − | 12.3449i | −0.472711 | − | 0.472711i | ||||
\(683\) | 12.4204 | + | 12.4204i | 0.475255 | + | 0.475255i | 0.903610 | − | 0.428355i | \(-0.140907\pi\) |
−0.428355 | + | 0.903610i | \(0.640907\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.08651 | − | 32.6085i | −0.270762 | − | 1.24591i | ||||
\(686\) | 23.5225i | 0.898093i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 20.0810 | − | 20.0810i | 0.765581 | − | 0.765581i | ||||
\(689\) | 45.1069 | 1.71844 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 47.1413 | 1.79334 | 0.896669 | − | 0.442701i | \(-0.145980\pi\) | ||||
0.896669 | + | 0.442701i | \(0.145980\pi\) | |||||||
\(692\) | −1.71563 | + | 1.71563i | −0.0652186 | + | 0.0652186i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 42.3349i | − | 1.60701i | ||||||
\(695\) | −12.3713 | − | 7.95416i | −0.469270 | − | 0.301718i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26.2178 | + | 26.2178i | 0.993069 | + | 0.993069i | ||||
\(698\) | 5.92110 | + | 5.92110i | 0.224117 | + | 0.224117i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −13.3859 | − | 4.99896i | −0.505939 | − | 0.188943i | ||||
\(701\) | 17.3056i | 0.653624i | 0.945089 | + | 0.326812i | \(0.105974\pi\) | ||||
−0.945089 | + | 0.326812i | \(0.894026\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.56977 | + | 6.56977i | −0.247783 | + | 0.247783i | ||||
\(704\) | 10.6851 | 0.402709 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.2172 | 0.535071 | ||||||||
\(707\) | 23.8866 | − | 23.8866i | 0.898347 | − | 0.898347i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 35.1056i | − | 1.31842i | −0.751960 | − | 0.659209i | \(-0.770891\pi\) | ||
0.751960 | − | 0.659209i | \(-0.229109\pi\) | |||||||
\(710\) | 40.9826 | − | 8.90637i | 1.53805 | − | 0.334250i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 19.4306 | + | 19.4306i | 0.728193 | + | 0.728193i | ||||
\(713\) | −2.59020 | − | 2.59020i | −0.0970038 | − | 0.0970038i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 62.9467 | − | 13.6796i | 2.35407 | − | 0.511589i | ||||
\(716\) | − | 5.30667i | − | 0.198319i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −39.3468 | + | 39.3468i | −1.46841 | + | 1.46841i | ||||
\(719\) | −25.7773 | −0.961331 | −0.480666 | − | 0.876904i | \(-0.659605\pi\) | ||||
−0.480666 | + | 0.876904i | \(0.659605\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.0291 | 0.373505 | ||||||||
\(722\) | 1.20930 | − | 1.20930i | 0.0450054 | − | 0.0450054i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.9586i | 0.481604i | ||||||||
\(725\) | 4.57244 | + | 10.0232i | 0.169816 | + | 0.372252i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.6889 | + | 11.6889i | 0.433516 | + | 0.433516i | 0.889823 | − | 0.456307i | \(-0.150828\pi\) |
−0.456307 | + | 0.889823i | \(0.650828\pi\) | |||||||
\(728\) | −18.0982 | − | 18.0982i | −0.670763 | − | 0.670763i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −25.8604 | − | 16.6270i | −0.957138 | − | 0.615394i | ||||
\(731\) | − | 39.6295i | − | 1.46575i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.0206 | + | 25.0206i | −0.924158 | + | 0.924158i | −0.997320 | − | 0.0731624i | \(-0.976691\pi\) |
0.0731624 | + | 0.997320i | \(0.476691\pi\) | |||||||
\(734\) | −27.7302 | −1.02354 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11.1619 | −0.411434 | ||||||||
\(737\) | −21.6469 | + | 21.6469i | −0.797374 | + | 0.797374i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.1672i | 0.852219i | 0.904672 | + | 0.426109i | \(0.140116\pi\) | ||||
−0.904672 | + | 0.426109i | \(0.859884\pi\) | |||||||
\(740\) | −4.08017 | − | 18.7749i | −0.149990 | − | 0.690178i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −37.4216 | − | 37.4216i | −1.37379 | − | 1.37379i | ||||
\(743\) | −26.0695 | − | 26.0695i | −0.956395 | − | 0.956395i | 0.0426929 | − | 0.999088i | \(-0.486406\pi\) |
−0.999088 | + | 0.0426929i | \(0.986406\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.5466 | + | 36.6227i | −0.862681 | + | 1.34175i | ||||
\(746\) | − | 18.7067i | − | 0.684900i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −29.1478 | + | 29.1478i | −1.06575 | + | 1.06575i | ||||
\(749\) | 27.2702 | 0.996433 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.3705 | −1.07175 | −0.535873 | − | 0.844299i | \(-0.680017\pi\) | ||||
−0.535873 | + | 0.844299i | \(0.680017\pi\) | |||||||
\(752\) | 10.5066 | − | 10.5066i | 0.383136 | − | 0.383136i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 16.9734i | − | 0.618136i | ||||||
\(755\) | 11.5978 | − | 18.0383i | 0.422087 | − | 0.656482i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.5892 | − | 16.5892i | −0.602945 | − | 0.602945i | 0.338148 | − | 0.941093i | \(-0.390200\pi\) |
−0.941093 | + | 0.338148i | \(0.890200\pi\) | |||||||
\(758\) | 33.7363 | + | 33.7363i | 1.22536 | + | 1.22536i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.873178 | − | 4.01792i | −0.0316735 | − | 0.145745i | ||||
\(761\) | 2.62004i | 0.0949765i | 0.998872 | + | 0.0474882i | \(0.0151217\pi\) | ||||
−0.998872 | + | 0.0474882i | \(0.984878\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.57119 | + | 5.57119i | −0.201691 | + | 0.201691i | ||||
\(764\) | −3.69197 | −0.133571 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −54.0030 | −1.95121 | ||||||||
\(767\) | 12.8852 | − | 12.8852i | 0.465257 | − | 0.465257i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.0002i | 0.829408i | 0.909956 | + | 0.414704i | \(0.136115\pi\) | ||||
−0.909956 | + | 0.414704i | \(0.863885\pi\) | |||||||
\(770\) | −63.5708 | − | 40.8730i | −2.29093 | − | 1.47296i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13.1831 | − | 13.1831i | −0.474469 | − | 0.474469i | ||||
\(773\) | 9.06485 | + | 9.06485i | 0.326040 | + | 0.326040i | 0.851078 | − | 0.525039i | \(-0.175949\pi\) |
−0.525039 | + | 0.851078i | \(0.675949\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.31237 | + | 7.26100i | 0.118984 | + | 0.260823i | ||||
\(776\) | − | 1.14200i | − | 0.0409954i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14.2819 | + | 14.2819i | −0.512032 | + | 0.512032i | ||||
\(779\) | 5.32003 | 0.190610 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 70.1395 | 2.50979 | ||||||||
\(782\) | −19.3419 | + | 19.3419i | −0.691666 | + | 0.691666i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 12.7307i | 0.454667i | ||||||||
\(785\) | −22.9079 | + | 4.97835i | −0.817616 | + | 0.177685i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.8659 | − | 23.8659i | −0.850726 | − | 0.850726i | 0.139496 | − | 0.990223i | \(-0.455452\pi\) |
−0.990223 | + | 0.139496i | \(0.955452\pi\) | |||||||
\(788\) | −3.34802 | − | 3.34802i | −0.119268 | − | 0.119268i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.583159 | − | 0.126733i | 0.0207479 | − | 0.00450894i | ||||
\(791\) | 59.1516i | 2.10319i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.30950 | + | 7.30950i | −0.259568 | + | 0.259568i | ||||
\(794\) | 16.0350 | 0.569060 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.924392 | 0.0327642 | ||||||||
\(797\) | 36.2931 | − | 36.2931i | 1.28557 | − | 1.28557i | 0.348115 | − | 0.937452i | \(-0.386822\pi\) |
0.937452 | − | 0.348115i | \(-0.113178\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 20.7346i | − | 0.733538i | ||||||
\(800\) | 22.7818 | + | 8.50789i | 0.805460 | + | 0.300799i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −23.5158 | − | 23.5158i | −0.830373 | − | 0.830373i | ||||
\(803\) | −36.3575 | − | 36.3575i | −1.28303 | − | 1.28303i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.3384 | − | 8.57594i | −0.470116 | − | 0.302262i | ||||
\(806\) | − | 12.2959i | − | 0.433105i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −14.2138 | + | 14.2138i | −0.500041 | + | 0.500041i | ||||
\(809\) | −13.2271 | −0.465039 | −0.232520 | − | 0.972592i | \(-0.574697\pi\) | ||||
−0.232520 | + | 0.972592i | \(0.574697\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.4012 | −0.646154 | −0.323077 | − | 0.946373i | \(-0.604717\pi\) | ||||
−0.323077 | + | 0.946373i | \(0.604717\pi\) | |||||||
\(812\) | −4.45247 | + | 4.45247i | −0.156251 | + | 0.156251i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 101.622i | − | 3.56186i | ||||||
\(815\) | 4.99579 | + | 22.9881i | 0.174995 | + | 0.805237i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.02075 | − | 4.02075i | −0.140668 | − | 0.140668i | ||||
\(818\) | −23.9769 | − | 23.9769i | −0.838334 | − | 0.838334i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.94970 | + | 9.25372i | −0.207773 | + | 0.323154i | ||||
\(821\) | 6.38333i | 0.222780i | 0.993777 | + | 0.111390i | \(0.0355302\pi\) | ||||
−0.993777 | + | 0.111390i | \(0.964470\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.6349 | − | 32.6349i | 1.13758 | − | 1.13758i | 0.148700 | − | 0.988882i | \(-0.452491\pi\) |
0.988882 | − | 0.148700i | \(-0.0475088\pi\) | |||||||
\(824\) | −5.96790 | −0.207902 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −21.3796 | −0.743892 | ||||||||
\(827\) | −12.6859 | + | 12.6859i | −0.441131 | + | 0.441131i | −0.892392 | − | 0.451261i | \(-0.850974\pi\) |
0.451261 | + | 0.892392i | \(0.350974\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 24.2254i | − | 0.841382i | −0.907204 | − | 0.420691i | \(-0.861788\pi\) | ||
0.907204 | − | 0.420691i | \(-0.138212\pi\) | |||||||
\(830\) | −23.7746 | + | 36.9772i | −0.825228 | + | 1.28350i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.32133 | + | 5.32133i | 0.184484 | + | 0.184484i | ||||
\(833\) | 12.5619 | + | 12.5619i | 0.435243 | + | 0.435243i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.32795 | + | 19.9151i | 0.149775 | + | 0.689189i | ||||
\(836\) | 5.91458i | 0.204560i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −44.3104 | + | 44.3104i | −1.53068 | + | 1.53068i | ||||
\(839\) | 35.9297 | 1.24043 | 0.620215 | − | 0.784432i | \(-0.287045\pi\) | ||||
0.620215 | + | 0.784432i | \(0.287045\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.1451 | −0.832591 | ||||||||
\(842\) | 21.7127 | − | 21.7127i | 0.748268 | − | 0.748268i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 9.51131i | − | 0.327393i | ||||||
\(845\) | 13.7100 | + | 8.81490i | 0.471640 | + | 0.303242i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −65.3392 | − | 65.3392i | −2.24508 | − | 2.24508i | ||||
\(848\) | 35.3650 | + | 35.3650i | 1.21444 | + | 1.21444i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 54.2204 | − | 24.7346i | 1.85974 | − | 0.848390i | ||||
\(851\) | − | 21.3223i | − | 0.730919i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.89045 | − | 7.89045i | 0.270164 | − | 0.270164i | −0.559002 | − | 0.829166i | \(-0.688816\pi\) |
0.829166 | + | 0.559002i | \(0.188816\pi\) | |||||||
\(854\) | 12.1282 | 0.415019 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.2273 | −0.554638 | ||||||||
\(857\) | 11.8794 | − | 11.8794i | 0.405792 | − | 0.405792i | −0.474476 | − | 0.880268i | \(-0.657363\pi\) |
0.880268 | + | 0.474476i | \(0.157363\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.1067i | 1.67550i | 0.546056 | + | 0.837749i | \(0.316129\pi\) | ||||
−0.546056 | + | 0.837749i | \(0.683871\pi\) | |||||||
\(860\) | 11.4904 | − | 2.49710i | 0.391819 | − | 0.0851503i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 48.7692 | + | 48.7692i | 1.66108 | + | 1.66108i | ||||
\(863\) | −22.8690 | − | 22.8690i | −0.778471 | − | 0.778471i | 0.201100 | − | 0.979571i | \(-0.435548\pi\) |
−0.979571 | + | 0.201100i | \(0.935548\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.73265 | − | 1.24582i | 0.194916 | − | 0.0423593i | ||||
\(866\) | − | 19.2795i | − | 0.655146i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.22546 | + | 3.22546i | −0.109479 | + | 0.109479i | ||||
\(869\) | 0.998045 | 0.0338563 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.5610 | −0.730566 | ||||||||
\(872\) | 3.31517 | − | 3.31517i | 0.112266 | − | 0.112266i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.92480i | 0.132758i | ||||||||
\(875\) | 20.6873 | + | 27.6706i | 0.699358 | + | 0.935438i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.9799 | − | 24.9799i | −0.843511 | − | 0.843511i | 0.145802 | − | 0.989314i | \(-0.453424\pi\) |
−0.989314 | + | 0.145802i | \(0.953424\pi\) | |||||||
\(878\) | −18.5849 | − | 18.5849i | −0.627211 | − | 0.627211i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 60.0770 | + | 38.6267i | 2.02520 | + | 1.30210i | ||||
\(881\) | − | 5.29063i | − | 0.178246i | −0.996021 | − | 0.0891229i | \(-0.971594\pi\) | ||
0.996021 | − | 0.0891229i | \(-0.0284064\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.33371 | + | 1.33371i | −0.0448830 | + | 0.0448830i | −0.729192 | − | 0.684309i | \(-0.760104\pi\) |
0.684309 | + | 0.729192i | \(0.260104\pi\) | |||||||
\(884\) | −29.0321 | −0.976455 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −44.9798 | −1.51113 | ||||||||
\(887\) | −8.13572 | + | 8.13572i | −0.273171 | + | 0.273171i | −0.830375 | − | 0.557205i | \(-0.811874\pi\) |
0.557205 | + | 0.830375i | \(0.311874\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 48.1104i | 1.61357i | ||||||||
\(890\) | 12.1361 | + | 55.8440i | 0.406802 | + | 1.87190i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.84833 | + | 4.84833i | 0.162334 | + | 0.162334i | ||||
\(893\) | −2.10370 | − | 2.10370i | −0.0703976 | − | 0.0703976i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.93916 | + | 10.7926i | −0.231951 | + | 0.360758i | ||||
\(896\) | − | 38.8887i | − | 1.29918i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.93878 | − | 9.93878i | 0.331661 | − | 0.331661i | ||||
\(899\) | 3.51696 | 0.117297 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 69.7922 | 2.32511 | ||||||||
\(902\) | −41.1455 | + | 41.1455i | −1.37000 | + | 1.37000i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 35.1985i | − | 1.17069i | ||||||
\(905\) | 16.9451 | − | 26.3552i | 0.563274 | − | 0.876075i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.43185 | + | 3.43185i | 0.113953 | + | 0.113953i | 0.761784 | − | 0.647831i | \(-0.224324\pi\) |
−0.647831 | + | 0.761784i | \(0.724324\pi\) | |||||||
\(908\) | 13.0674 | + | 13.0674i | 0.433658 | + | 0.433658i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −11.3038 | − | 52.0146i | −0.374719 | − | 1.72427i | ||||
\(911\) | − | 32.6667i | − | 1.08230i | −0.840927 | − | 0.541149i | \(-0.817990\pi\) | ||
0.840927 | − | 0.541149i | \(-0.182010\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −51.9867 | + | 51.9867i | −1.72051 | + | 1.72051i | ||||
\(914\) | −25.6336 | −0.847885 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 26.9262 | 0.889666 | ||||||||
\(917\) | 16.6450 | − | 16.6450i | 0.549668 | − | 0.549668i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47.1389i | 1.55497i | 0.628902 | + | 0.777485i | \(0.283505\pi\) | ||||
−0.628902 | + | 0.777485i | \(0.716495\pi\) | |||||||
\(920\) | 7.93708 | + | 5.10317i | 0.261678 | + | 0.168246i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 21.3267 | + | 21.3267i | 0.702357 | + | 0.702357i | ||||
\(923\) | 34.9306 | + | 34.9306i | 1.14975 | + | 1.14975i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.2524 | + | 43.5195i | −0.534375 | + | 1.43091i | ||||
\(926\) | − | 50.8259i | − | 1.67024i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.57780 | − | 7.57780i | 0.248753 | − | 0.248753i | ||||
\(929\) | −41.9076 | −1.37494 | −0.687471 | − | 0.726211i | \(-0.741279\pi\) | ||||
−0.687471 | + | 0.726211i | \(0.741279\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.54902 | 0.0835406 | ||||||||
\(932\) | −14.3987 | + | 14.3987i | −0.471645 | + | 0.471645i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.17577i | 0.103914i | ||||||||
\(935\) | 97.3951 | − | 21.1660i | 3.18516 | − | 0.692201i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.49144 | + | 4.49144i | 0.146729 | + | 0.146729i | 0.776655 | − | 0.629926i | \(-0.216915\pi\) |
−0.629926 | + | 0.776655i | \(0.716915\pi\) | |||||||
\(938\) | 17.8874 | + | 17.8874i | 0.584045 | + | 0.584045i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.01189 | − | 1.30651i | 0.196086 | − | 0.0426136i | ||||
\(941\) | − | 8.57988i | − | 0.279696i | −0.990173 | − | 0.139848i | \(-0.955339\pi\) | ||
0.990173 | − | 0.139848i | \(-0.0446614\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.63313 | + | 8.63313i | −0.281133 | + | 0.281133i | ||||
\(944\) | 20.2046 | 0.657605 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 62.1936 | 2.02209 | ||||||||
\(947\) | −12.8953 | + | 12.8953i | −0.419042 | + | 0.419042i | −0.884873 | − | 0.465832i | \(-0.845755\pi\) |
0.465832 | + | 0.884873i | \(0.345755\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 36.2132i | − | 1.17553i | ||||||
\(950\) | 2.99158 | − | 8.01065i | 0.0970597 | − | 0.259900i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −28.0026 | − | 28.0026i | −0.907570 | − | 0.907570i | ||||
\(953\) | 20.1541 | + | 20.1541i | 0.652854 | + | 0.652854i | 0.953679 | − | 0.300825i | \(-0.0972621\pi\) |
−0.300825 | + | 0.953679i | \(0.597262\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.50870 | + | 4.82773i | 0.242976 | + | 0.156222i | ||||
\(956\) | − | 5.10763i | − | 0.165193i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.60561 | + | 7.60561i | −0.245726 | + | 0.245726i | ||||
\(959\) | −46.1154 | −1.48914 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.4522 | −0.917814 | ||||||||
\(962\) | 50.6094 | − | 50.6094i | 1.63171 | − | 1.63171i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.62868i | 0.310119i | ||||||||
\(965\) | 9.57303 | + | 44.0502i | 0.308167 | + | 1.41803i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.56041 | + | 9.56041i | 0.307442 | + | 0.307442i | 0.843917 | − | 0.536475i | \(-0.180244\pi\) |
−0.536475 | + | 0.843917i | \(0.680244\pi\) | |||||||
\(968\) | 38.8805 | + | 38.8805i | 1.24967 | + | 1.24967i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.28443 | − | 1.99770i | 0.0412405 | − | 0.0641424i | ||||
\(971\) | 29.6220i | 0.950615i | 0.879820 | + | 0.475308i | \(0.157663\pi\) | ||||
−0.879820 | + | 0.475308i | \(0.842337\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.3723 | + | 14.3723i | −0.460754 | + | 0.460754i | ||||
\(974\) | −60.9180 | −1.95194 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.4617 | −0.366879 | ||||||||
\(977\) | −1.69779 | + | 1.69779i | −0.0543172 | + | 0.0543172i | −0.733744 | − | 0.679426i | \(-0.762229\pi\) |
0.679426 | + | 0.733744i | \(0.262229\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 95.5740i | 3.05456i | ||||||||
\(980\) | −2.85071 | + | 4.43379i | −0.0910628 | + | 0.141632i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −20.5674 | − | 20.5674i | −0.656331 | − | 0.656331i | ||||
\(983\) | 26.6829 | + | 26.6829i | 0.851051 | + | 0.851051i | 0.990263 | − | 0.139212i | \(-0.0444569\pi\) |
−0.139212 | + | 0.990263i | \(0.544457\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.43120 | + | 11.1871i | 0.0774645 | + | 0.356452i | ||||
\(986\) | − | 26.2624i | − | 0.836364i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.94555 | + | 2.94555i | −0.0937104 | + | 0.0937104i | ||||
\(989\) | 13.0494 | 0.414948 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.11083 | 0.130585 | 0.0652924 | − | 0.997866i | \(-0.479202\pi\) | ||||
0.0652924 | + | 0.997866i | \(0.479202\pi\) | |||||||
\(992\) | 5.48951 | − | 5.48951i | 0.174292 | − | 0.174292i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 57.9582i | − | 1.83832i | ||||||
\(995\) | −1.88002 | − | 1.20876i | −0.0596007 | − | 0.0383204i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.53028 | − | 5.53028i | −0.175146 | − | 0.175146i | 0.614090 | − | 0.789236i | \(-0.289523\pi\) |
−0.789236 | + | 0.614090i | \(0.789523\pi\) | |||||||
\(998\) | 14.9818 | + | 14.9818i | 0.474241 | + | 0.474241i | ||||
\(999\) | 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 | 855.2.n.d.647.3 | ✓ | 20 | |
3.2 | odd | 2 | inner | 855.2.n.d.647.8 | yes | 20 | |
5.3 | odd | 4 | inner | 855.2.n.d.818.8 | yes | 20 | |
15.8 | even | 4 | inner | 855.2.n.d.818.3 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
855.2.n.d.647.3 | ✓ | 20 | 1.1 | even | 1 | trivial | |
855.2.n.d.647.8 | yes | 20 | 3.2 | odd | 2 | inner | |
855.2.n.d.818.3 | yes | 20 | 15.8 | even | 4 | inner | |
855.2.n.d.818.8 | yes | 20 | 5.3 | odd | 4 | inner |