Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(1457,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, 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("3150.1457");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.m (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: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.1698758656.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 2843.4 | ||
Root | \(-1.69230i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.2843 |
Dual form | 3150.2.m.i.1457.3 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.707107 | + | 0.707107i | −0.267261 | + | 0.267261i | ||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.36365i | 1.91871i | 0.282197 | + | 0.959356i | \(0.408937\pi\) | ||||
−0.282197 | + | 0.959356i | \(0.591063\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.69230 | + | 1.69230i | 0.469359 | + | 0.469359i | 0.901707 | − | 0.432348i | \(-0.142315\pi\) |
−0.432348 | + | 0.901707i | \(0.642315\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −0.979056 | − | 0.979056i | −0.237456 | − | 0.237456i | 0.578340 | − | 0.815796i | \(-0.303701\pi\) |
−0.815796 | + | 0.578340i | \(0.803701\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.49978 | + | 4.49978i | −0.959356 | + | 0.959356i | ||||
\(23\) | 1.38459 | − | 1.38459i | 0.288708 | − | 0.288708i | −0.547861 | − | 0.836569i | \(-0.684558\pi\) |
0.836569 | + | 0.547861i | \(0.184558\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.39327i | 0.469359i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.707107 | − | 0.707107i | −0.133631 | − | 0.133631i | ||||
\(29\) | −5.81975 | −1.08070 | −0.540350 | − | 0.841440i | \(-0.681708\pi\) | ||||
−0.540350 | + | 0.841440i | \(0.681708\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.36365 | 0.424524 | 0.212262 | − | 0.977213i | \(-0.431917\pi\) | ||||
0.212262 | + | 0.977213i | \(0.431917\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 1.38459i | − | 0.237456i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.157074 | + | 0.157074i | −0.0258227 | + | 0.0258227i | −0.719900 | − | 0.694078i | \(-0.755812\pi\) |
0.694078 | + | 0.719900i | \(0.255812\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.94944i | 1.39767i | 0.715284 | + | 0.698834i | \(0.246297\pi\) | ||||
−0.715284 | + | 0.698834i | \(0.753703\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.88438 | − | 5.88438i | −0.897359 | − | 0.897359i | 0.0978430 | − | 0.995202i | \(-0.468806\pi\) |
−0.995202 | + | 0.0978430i | \(0.968806\pi\) | |||||||
\(44\) | −6.36365 | −0.959356 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.95811 | 0.288708 | ||||||||
\(47\) | −3.05595 | − | 3.05595i | −0.445756 | − | 0.445756i | 0.448185 | − | 0.893941i | \(-0.352071\pi\) |
−0.893941 | + | 0.448185i | \(0.852071\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.69230 | + | 1.69230i | −0.234679 | + | 0.234679i | ||||
\(53\) | −0.192517 | + | 0.192517i | −0.0264442 | + | 0.0264442i | −0.720205 | − | 0.693761i | \(-0.755952\pi\) |
0.693761 | + | 0.720205i | \(0.255952\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 1.00000i | − | 0.133631i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.11519 | − | 4.11519i | −0.540350 | − | 0.540350i | ||||
\(59\) | 10.3842 | 1.35190 | 0.675951 | − | 0.736947i | \(-0.263733\pi\) | ||||
0.675951 | + | 0.736947i | \(0.263733\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.979056 | −0.125355 | −0.0626777 | − | 0.998034i | \(-0.519964\pi\) | ||||
−0.0626777 | + | 0.998034i | \(0.519964\pi\) | |||||||
\(62\) | 1.67135 | + | 1.67135i | 0.212262 | + | 0.212262i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.88438 | + | 9.88438i | −1.20757 | + | 1.20757i | −0.235756 | + | 0.971812i | \(0.575757\pi\) |
−0.971812 | + | 0.235756i | \(0.924243\pi\) | |||||||
\(68\) | 0.979056 | − | 0.979056i | 0.118728 | − | 0.118728i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.3423i | − | 1.46476i | −0.680897 | − | 0.732379i | \(-0.738410\pi\) | ||
0.680897 | − | 0.732379i | \(-0.261590\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.71324 | − | 4.71324i | −0.551643 | − | 0.551643i | 0.375272 | − | 0.926915i | \(-0.377549\pi\) |
−0.926915 | + | 0.375272i | \(0.877549\pi\) | |||||||
\(74\) | −0.222136 | −0.0258227 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.49978 | − | 4.49978i | −0.512798 | − | 0.512798i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.68541i | 0.752168i | 0.926586 | + | 0.376084i | \(0.122730\pi\) | ||||
−0.926586 | + | 0.376084i | \(0.877270\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.32821 | + | 6.32821i | −0.698834 | + | 0.698834i | ||||
\(83\) | −11.3427 | + | 11.3427i | −1.24502 | + | 1.24502i | −0.287133 | + | 0.957891i | \(0.592702\pi\) |
−0.957891 | + | 0.287133i | \(0.907298\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 8.32176i | − | 0.897359i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.49978 | − | 4.49978i | −0.479678 | − | 0.479678i | ||||
\(89\) | −11.8371 | −1.25473 | −0.627365 | − | 0.778725i | \(-0.715867\pi\) | ||||
−0.627365 | + | 0.778725i | \(0.715867\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.39327 | −0.250883 | ||||||||
\(92\) | 1.38459 | + | 1.38459i | 0.144354 | + | 0.144354i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 4.32176i | − | 0.445756i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.39866 | − | 9.39866i | 0.954289 | − | 0.954289i | −0.0447111 | − | 0.999000i | \(-0.514237\pi\) |
0.999000 | + | 0.0447111i | \(0.0142367\pi\) | |||||||
\(98\) | 0.707107 | − | 0.707107i | 0.0714286 | − | 0.0714286i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.0501i | 1.59705i | 0.601964 | + | 0.798524i | \(0.294385\pi\) | ||||
−0.601964 | + | 0.798524i | \(0.705615\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.706797 | + | 0.706797i | 0.0696427 | + | 0.0696427i | 0.741070 | − | 0.671428i | \(-0.234319\pi\) |
−0.671428 | + | 0.741070i | \(0.734319\pi\) | |||||||
\(104\) | −2.39327 | −0.234679 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.272260 | −0.0264442 | ||||||||
\(107\) | 9.51384 | + | 9.51384i | 0.919738 | + | 0.919738i | 0.997010 | − | 0.0772723i | \(-0.0246211\pi\) |
−0.0772723 | + | 0.997010i | \(0.524621\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 14.9577i | − | 1.43269i | −0.697749 | − | 0.716343i | \(-0.745815\pi\) | ||
0.697749 | − | 0.716343i | \(-0.254185\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.707107 | − | 0.707107i | 0.0668153 | − | 0.0668153i | ||||
\(113\) | −9.22170 | + | 9.22170i | −0.867504 | + | 0.867504i | −0.992196 | − | 0.124691i | \(-0.960206\pi\) |
0.124691 | + | 0.992196i | \(0.460206\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 5.81975i | − | 0.540350i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.34271 | + | 7.34271i | 0.675951 | + | 0.675951i | ||||
\(119\) | 1.38459 | 0.126926 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −29.4961 | −2.68146 | ||||||||
\(122\) | −0.692297 | − | 0.692297i | −0.0626777 | − | 0.0626777i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.36365i | 0.212262i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.38459 | − | 5.38459i | 0.477806 | − | 0.477806i | −0.426624 | − | 0.904429i | \(-0.640297\pi\) |
0.904429 | + | 0.426624i | \(0.140297\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.2718i | 1.15956i | 0.814772 | + | 0.579782i | \(0.196862\pi\) | ||||
−0.814772 | + | 0.579782i | \(0.803138\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −13.9786 | −1.20757 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.38459 | 0.118728 | ||||||||
\(137\) | 3.56484 | + | 3.56484i | 0.304565 | + | 0.304565i | 0.842797 | − | 0.538232i | \(-0.180908\pi\) |
−0.538232 | + | 0.842797i | \(0.680908\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.41359i | 0.119899i | 0.998201 | + | 0.0599497i | \(0.0190940\pi\) | ||||
−0.998201 | + | 0.0599497i | \(0.980906\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.72730 | − | 8.72730i | 0.732379 | − | 0.732379i | ||||
\(143\) | −10.7692 | + | 10.7692i | −0.900565 | + | 0.900565i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 6.66553i | − | 0.551643i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.157074 | − | 0.157074i | −0.0129114 | − | 0.0129114i | ||||
\(149\) | −20.0609 | −1.64345 | −0.821726 | − | 0.569882i | \(-0.806989\pi\) | ||||
−0.821726 | + | 0.569882i | \(0.806989\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.81108 | 0.717035 | 0.358518 | − | 0.933523i | \(-0.383282\pi\) | ||||
0.358518 | + | 0.933523i | \(0.383282\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 6.36365i | − | 0.512798i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.2654 | + | 15.2654i | −1.21831 | + | 1.21831i | −0.250086 | + | 0.968224i | \(0.580459\pi\) |
−0.968224 | + | 0.250086i | \(0.919541\pi\) | |||||||
\(158\) | −4.72730 | + | 4.72730i | −0.376084 | + | 0.376084i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.95811i | 0.154321i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.11519 | − | 7.11519i | −0.557304 | − | 0.557304i | 0.371235 | − | 0.928539i | \(-0.378935\pi\) |
−0.928539 | + | 0.371235i | \(0.878935\pi\) | |||||||
\(164\) | −8.94944 | −0.698834 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.0410 | −1.24502 | ||||||||
\(167\) | 16.7128 | + | 16.7128i | 1.29328 | + | 1.29328i | 0.932749 | + | 0.360527i | \(0.117403\pi\) |
0.360527 | + | 0.932749i | \(0.382597\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 7.27226i | − | 0.559405i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.88438 | − | 5.88438i | 0.448679 | − | 0.448679i | ||||
\(173\) | −14.7843 | + | 14.7843i | −1.12403 | + | 1.12403i | −0.132901 | + | 0.991129i | \(0.542429\pi\) |
−0.991129 | + | 0.132901i | \(0.957571\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 6.36365i | − | 0.479678i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.37010 | − | 8.37010i | −0.627365 | − | 0.627365i | ||||
\(179\) | 12.0205 | 0.898455 | 0.449227 | − | 0.893417i | \(-0.351699\pi\) | ||||
0.449227 | + | 0.893417i | \(0.351699\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.5236 | 1.30252 | 0.651259 | − | 0.758856i | \(-0.274241\pi\) | ||||
0.651259 | + | 0.758856i | \(0.274241\pi\) | |||||||
\(182\) | −1.69230 | − | 1.69230i | −0.125441 | − | 0.125441i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.95811i | 0.144354i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.23037 | − | 6.23037i | 0.455610 | − | 0.455610i | ||||
\(188\) | 3.05595 | − | 3.05595i | 0.222878 | − | 0.222878i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 6.30038i | − | 0.455880i | −0.973675 | − | 0.227940i | \(-0.926801\pi\) | ||
0.973675 | − | 0.227940i | \(-0.0731989\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.6435 | + | 11.6435i | 0.838119 | + | 0.838119i | 0.988611 | − | 0.150492i | \(-0.0480857\pi\) |
−0.150492 | + | 0.988611i | \(0.548086\pi\) | |||||||
\(194\) | 13.2917 | 0.954289 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 1.92849 | + | 1.92849i | 0.137399 | + | 0.137399i | 0.772461 | − | 0.635062i | \(-0.219025\pi\) |
−0.635062 | + | 0.772461i | \(0.719025\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 5.67736i | − | 0.402457i | −0.979544 | − | 0.201229i | \(-0.935507\pi\) | ||
0.979544 | − | 0.201229i | \(-0.0644934\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11.3492 | + | 11.3492i | −0.798524 | + | 0.798524i | ||||
\(203\) | 4.11519 | − | 4.11519i | 0.288829 | − | 0.288829i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.999561i | 0.0696427i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.69230 | − | 1.69230i | −0.117340 | − | 0.117340i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.91622 | 0.544975 | 0.272488 | − | 0.962159i | \(-0.412154\pi\) | ||||
0.272488 | + | 0.962159i | \(0.412154\pi\) | |||||||
\(212\) | −0.192517 | − | 0.192517i | −0.0132221 | − | 0.0132221i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 13.4546i | 0.919738i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.67135 | + | 1.67135i | −0.113459 | + | 0.113459i | ||||
\(218\) | 10.5767 | − | 10.5767i | 0.716343 | − | 0.716343i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 3.31371i | − | 0.222904i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.34227 | − | 8.34227i | −0.558640 | − | 0.558640i | 0.370280 | − | 0.928920i | \(-0.379262\pi\) |
−0.928920 | + | 0.370280i | \(0.879262\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.0414 | −0.867504 | ||||||||
\(227\) | 3.27270 | + | 3.27270i | 0.217217 | + | 0.217217i | 0.807324 | − | 0.590108i | \(-0.200915\pi\) |
−0.590108 | + | 0.807324i | \(0.700915\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 23.0901i | − | 1.52584i | −0.646496 | − | 0.762918i | \(-0.723766\pi\) | ||
0.646496 | − | 0.762918i | \(-0.276234\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.11519 | − | 4.11519i | 0.270175 | − | 0.270175i | ||||
\(233\) | −5.23081 | + | 5.23081i | −0.342682 | + | 0.342682i | −0.857375 | − | 0.514693i | \(-0.827906\pi\) |
0.514693 | + | 0.857375i | \(0.327906\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 10.3842i | 0.675951i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.979056 | + | 0.979056i | 0.0634628 | + | 0.0634628i | ||||
\(239\) | −5.27182 | −0.341006 | −0.170503 | − | 0.985357i | \(-0.554539\pi\) | ||||
−0.170503 | + | 0.985357i | \(0.554539\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.27270 | −0.339644 | −0.169822 | − | 0.985475i | \(-0.554319\pi\) | ||||
−0.169822 | + | 0.985475i | \(0.554319\pi\) | |||||||
\(242\) | −20.8569 | − | 20.8569i | −1.34073 | − | 1.34073i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 0.979056i | − | 0.0626777i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1.67135 | + | 1.67135i | −0.106131 | + | 0.106131i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 20.3423i | − | 1.28399i | −0.766708 | − | 0.641996i | \(-0.778106\pi\) | ||
0.766708 | − | 0.641996i | \(-0.221894\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.81108 | + | 8.81108i | 0.553948 | + | 0.553948i | ||||
\(254\) | 7.61497 | 0.477806 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.50201 | − | 2.50201i | −0.156071 | − | 0.156071i | 0.624752 | − | 0.780823i | \(-0.285200\pi\) |
−0.780823 | + | 0.624752i | \(0.785200\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 0.222136i | − | 0.0138028i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.38459 | + | 9.38459i | −0.579782 | + | 0.579782i | ||||
\(263\) | 12.6983 | − | 12.6983i | 0.783011 | − | 0.783011i | −0.197327 | − | 0.980338i | \(-0.563226\pi\) |
0.980338 | + | 0.197327i | \(0.0632260\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.88438 | − | 9.88438i | −0.603784 | − | 0.603784i | ||||
\(269\) | 26.9196 | 1.64131 | 0.820657 | − | 0.571421i | \(-0.193608\pi\) | ||||
0.820657 | + | 0.571421i | \(0.193608\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.1320 | 1.40517 | 0.702583 | − | 0.711601i | \(-0.252030\pi\) | ||||
0.702583 | + | 0.711601i | \(0.252030\pi\) | |||||||
\(272\) | 0.979056 | + | 0.979056i | 0.0593640 | + | 0.0593640i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.04145i | 0.304565i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.2271 | + | 12.2271i | −0.734654 | + | 0.734654i | −0.971538 | − | 0.236884i | \(-0.923874\pi\) |
0.236884 | + | 0.971538i | \(0.423874\pi\) | |||||||
\(278\) | −0.999561 | + | 0.999561i | −0.0599497 | + | 0.0599497i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.4428i | 0.622964i | 0.950252 | + | 0.311482i | \(0.100825\pi\) | ||||
−0.950252 | + | 0.311482i | \(0.899175\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.9577 | − | 22.9577i | −1.36469 | − | 1.36469i | −0.867829 | − | 0.496863i | \(-0.834485\pi\) |
−0.496863 | − | 0.867829i | \(-0.665515\pi\) | |||||||
\(284\) | 12.3423 | 0.732379 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −15.2299 | −0.900565 | ||||||||
\(287\) | −6.32821 | − | 6.32821i | −0.373542 | − | 0.373542i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 15.0829i | − | 0.887229i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.71324 | − | 4.71324i | 0.275822 | − | 0.275822i | ||||
\(293\) | 18.6413 | − | 18.6413i | 1.08904 | − | 1.08904i | 0.0934082 | − | 0.995628i | \(-0.470224\pi\) |
0.995628 | − | 0.0934082i | \(-0.0297762\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 0.222136i | − | 0.0129114i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.1852 | − | 14.1852i | −0.821726 | − | 0.821726i | ||||
\(299\) | 4.68629 | 0.271015 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.32176 | 0.479658 | ||||||||
\(302\) | 6.23037 | + | 6.23037i | 0.358518 | + | 0.358518i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.727302 | + | 0.727302i | −0.0415093 | + | 0.0415093i | −0.727557 | − | 0.686047i | \(-0.759344\pi\) |
0.686047 | + | 0.727557i | \(0.259344\pi\) | |||||||
\(308\) | 4.49978 | − | 4.49978i | 0.256399 | − | 0.256399i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.2295i | 1.37393i | 0.726691 | + | 0.686964i | \(0.241057\pi\) | ||||
−0.726691 | + | 0.686964i | \(0.758943\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.44054 | − | 3.44054i | −0.194471 | − | 0.194471i | 0.603154 | − | 0.797625i | \(-0.293910\pi\) |
−0.797625 | + | 0.603154i | \(0.793910\pi\) | |||||||
\(314\) | −21.5885 | −1.21831 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.68541 | −0.376084 | ||||||||
\(317\) | 12.9198 | + | 12.9198i | 0.725649 | + | 0.725649i | 0.969750 | − | 0.244101i | \(-0.0784927\pi\) |
−0.244101 | + | 0.969750i | \(0.578493\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 37.0349i | − | 2.07355i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.38459 | + | 1.38459i | −0.0771604 | + | 0.0771604i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 10.0624i | − | 0.557304i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.32821 | − | 6.32821i | −0.349417 | − | 0.349417i | ||||
\(329\) | 4.32176 | 0.238267 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.76831 | 0.481950 | 0.240975 | − | 0.970531i | \(-0.422533\pi\) | ||||
0.240975 | + | 0.970531i | \(0.422533\pi\) | |||||||
\(332\) | −11.3427 | − | 11.3427i | −0.622512 | − | 0.622512i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 23.6355i | 1.29328i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.3427 | − | 12.3427i | 0.672350 | − | 0.672350i | −0.285907 | − | 0.958257i | \(-0.592295\pi\) |
0.958257 | + | 0.285907i | \(0.0922949\pi\) | |||||||
\(338\) | 5.14226 | − | 5.14226i | 0.279702 | − | 0.279702i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.0414i | 0.814540i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | 8.32176 | 0.448679 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.9082 | −1.12403 | ||||||||
\(347\) | 5.17157 | + | 5.17157i | 0.277625 | + | 0.277625i | 0.832160 | − | 0.554535i | \(-0.187104\pi\) |
−0.554535 | + | 0.832160i | \(0.687104\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.9363i | 1.54892i | 0.632620 | + | 0.774462i | \(0.281979\pi\) | ||||
−0.632620 | + | 0.774462i | \(0.718021\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.49978 | − | 4.49978i | 0.239839 | − | 0.239839i | ||||
\(353\) | 10.3637 | − | 10.3637i | 0.551601 | − | 0.551601i | −0.375301 | − | 0.926903i | \(-0.622461\pi\) |
0.926903 | + | 0.375301i | \(0.122461\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 11.8371i | − | 0.627365i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.49978 | + | 8.49978i | 0.449227 | + | 0.449227i | ||||
\(359\) | 13.2308 | 0.698295 | 0.349148 | − | 0.937068i | \(-0.386471\pi\) | ||||
0.349148 | + | 0.937068i | \(0.386471\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.0000 | 1.00000 | ||||||||
\(362\) | 12.3910 | + | 12.3910i | 0.651259 | + | 0.651259i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 2.39327i | − | 0.125441i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.20943 | − | 3.20943i | 0.167531 | − | 0.167531i | −0.618362 | − | 0.785893i | \(-0.712204\pi\) |
0.785893 | + | 0.618362i | \(0.212204\pi\) | |||||||
\(368\) | −1.38459 | + | 1.38459i | −0.0721770 | + | 0.0721770i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 0.272260i | − | 0.0141350i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.26897 | + | 2.26897i | 0.117483 | + | 0.117483i | 0.763404 | − | 0.645921i | \(-0.223527\pi\) |
−0.645921 | + | 0.763404i | \(0.723527\pi\) | |||||||
\(374\) | 8.81108 | 0.455610 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.32176 | 0.222878 | ||||||||
\(377\) | −9.84875 | − | 9.84875i | −0.507236 | − | 0.507236i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2.39792i | − | 0.123173i | −0.998102 | − | 0.0615865i | \(-0.980384\pi\) | ||
0.998102 | − | 0.0615865i | \(-0.0196160\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.45504 | − | 4.45504i | 0.227940 | − | 0.227940i | ||||
\(383\) | −16.6838 | + | 16.6838i | −0.852503 | + | 0.852503i | −0.990441 | − | 0.137938i | \(-0.955952\pi\) |
0.137938 | + | 0.990441i | \(0.455952\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.4664i | 0.838119i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.39866 | + | 9.39866i | 0.477144 | + | 0.477144i | ||||
\(389\) | −22.0782 | −1.11941 | −0.559706 | − | 0.828691i | \(-0.689086\pi\) | ||||
−0.559706 | + | 0.828691i | \(0.689086\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.71119 | −0.137111 | ||||||||
\(392\) | 0.707107 | + | 0.707107i | 0.0357143 | + | 0.0357143i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.72730i | 0.137399i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.9717 | + | 20.9717i | −1.05254 | + | 1.05254i | −0.0540003 | + | 0.998541i | \(0.517197\pi\) |
−0.998541 | + | 0.0540003i | \(0.982803\pi\) | |||||||
\(398\) | 4.01450 | − | 4.01450i | 0.201229 | − | 0.201229i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.29574i | 0.464207i | 0.972691 | + | 0.232103i | \(0.0745608\pi\) | ||||
−0.972691 | + | 0.232103i | \(0.925439\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.00000 | + | 4.00000i | 0.199254 | + | 0.199254i | ||||
\(404\) | −16.0501 | −0.798524 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.81975 | 0.288829 | ||||||||
\(407\) | −0.999561 | − | 0.999561i | −0.0495464 | − | 0.0495464i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.2367i | 1.69289i | 0.532472 | + | 0.846447i | \(0.321263\pi\) | ||||
−0.532472 | + | 0.846447i | \(0.678737\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.706797 | + | 0.706797i | −0.0348214 | + | 0.0348214i | ||||
\(413\) | −7.34271 | + | 7.34271i | −0.361311 | + | 0.361311i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 2.39327i | − | 0.117340i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.7753 | 0.672969 | 0.336484 | − | 0.941689i | \(-0.390762\pi\) | ||||
0.336484 | + | 0.941689i | \(0.390762\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.6283 | 0.517991 | 0.258996 | − | 0.965878i | \(-0.416608\pi\) | ||||
0.258996 | + | 0.965878i | \(0.416608\pi\) | |||||||
\(422\) | 5.59762 | + | 5.59762i | 0.272488 | + | 0.272488i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 0.272260i | − | 0.0132221i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.692297 | − | 0.692297i | 0.0335026 | − | 0.0335026i | ||||
\(428\) | −9.51384 | + | 9.51384i | −0.459869 | + | 0.459869i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 18.8877i | − | 0.909787i | −0.890546 | − | 0.454893i | \(-0.849677\pi\) | ||
0.890546 | − | 0.454893i | \(-0.150323\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.3697 | + | 19.3697i | 0.930846 | + | 0.930846i | 0.997759 | − | 0.0669125i | \(-0.0213149\pi\) |
−0.0669125 | + | 0.997759i | \(0.521315\pi\) | |||||||
\(434\) | −2.36365 | −0.113459 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.9577 | 0.716343 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 4.86628i | − | 0.232255i | −0.993234 | − | 0.116127i | \(-0.962952\pi\) | ||
0.993234 | − | 0.116127i | \(-0.0370481\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.34315 | − | 2.34315i | 0.111452 | − | 0.111452i | ||||
\(443\) | −7.17070 | + | 7.17070i | −0.340690 | + | 0.340690i | −0.856627 | − | 0.515937i | \(-0.827444\pi\) |
0.515937 | + | 0.856627i | \(0.327444\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 11.7977i | − | 0.558640i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.707107 | + | 0.707107i | 0.0334077 | + | 0.0334077i | ||||
\(449\) | −8.87093 | −0.418645 | −0.209323 | − | 0.977847i | \(-0.567126\pi\) | ||||
−0.209323 | + | 0.977847i | \(0.567126\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −56.9511 | −2.68172 | ||||||||
\(452\) | −9.22170 | − | 9.22170i | −0.433752 | − | 0.433752i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.62829i | 0.217217i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.27270 | + | 4.27270i | −0.199868 | + | 0.199868i | −0.799944 | − | 0.600075i | \(-0.795137\pi\) |
0.600075 | + | 0.799944i | \(0.295137\pi\) | |||||||
\(458\) | 16.3271 | − | 16.3271i | 0.762918 | − | 0.762918i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 0.771724i | − | 0.0359428i | −0.999839 | − | 0.0179714i | \(-0.994279\pi\) | ||
0.999839 | − | 0.0179714i | \(-0.00572077\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.6150 | + | 19.6150i | 0.911585 | + | 0.911585i | 0.996397 | − | 0.0848121i | \(-0.0270290\pi\) |
−0.0848121 | + | 0.996397i | \(0.527029\pi\) | |||||||
\(464\) | 5.81975 | 0.270175 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.39748 | −0.342682 | ||||||||
\(467\) | 8.18848 | + | 8.18848i | 0.378918 | + | 0.378918i | 0.870712 | − | 0.491794i | \(-0.163659\pi\) |
−0.491794 | + | 0.870712i | \(0.663659\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 13.9786i | − | 0.645473i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.34271 | + | 7.34271i | −0.337975 | + | 0.337975i | ||||
\(473\) | 37.4461 | − | 37.4461i | 1.72177 | − | 1.72177i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.38459i | 0.0634628i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.72774 | − | 3.72774i | −0.170503 | − | 0.170503i | ||||
\(479\) | 21.0833 | 0.963322 | 0.481661 | − | 0.876358i | \(-0.340034\pi\) | ||||
0.481661 | + | 0.876358i | \(0.340034\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.531630 | −0.0242403 | ||||||||
\(482\) | −3.72836 | − | 3.72836i | −0.169822 | − | 0.169822i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 29.4961i | − | 1.34073i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.6983 | − | 20.6983i | 0.937930 | − | 0.937930i | −0.0602535 | − | 0.998183i | \(-0.519191\pi\) |
0.998183 | + | 0.0602535i | \(0.0191909\pi\) | |||||||
\(488\) | 0.692297 | − | 0.692297i | 0.0313388 | − | 0.0313388i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.2799i | 0.463924i | 0.972725 | + | 0.231962i | \(0.0745146\pi\) | ||||
−0.972725 | + | 0.231962i | \(0.925485\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.69786 | + | 5.69786i | 0.256619 | + | 0.256619i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.36365 | −0.106131 | ||||||||
\(497\) | 8.72730 | + | 8.72730i | 0.391473 | + | 0.391473i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.16711i | 0.231312i | 0.993289 | + | 0.115656i | \(0.0368970\pi\) | ||||
−0.993289 | + | 0.115656i | \(0.963103\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14.3842 | − | 14.3842i | 0.641996 | − | 0.641996i | ||||
\(503\) | −0.741801 | + | 0.741801i | −0.0330753 | + | 0.0330753i | −0.723451 | − | 0.690376i | \(-0.757445\pi\) |
0.690376 | + | 0.723451i | \(0.257445\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 12.4607i | 0.553948i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.38459 | + | 5.38459i | 0.238903 | + | 0.238903i | ||||
\(509\) | 1.96723 | 0.0871958 | 0.0435979 | − | 0.999049i | \(-0.486118\pi\) | ||||
0.0435979 | + | 0.999049i | \(0.486118\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.66553 | 0.294866 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 3.53838i | − | 0.156071i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.4470 | − | 19.4470i | 0.855278 | − | 0.855278i | ||||
\(518\) | 0.157074 | − | 0.157074i | 0.00690142 | − | 0.00690142i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 5.19146i | − | 0.227442i | −0.993513 | − | 0.113721i | \(-0.963723\pi\) | ||
0.993513 | − | 0.113721i | \(-0.0362770\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.2295 | + | 28.2295i | 1.23439 | + | 1.23439i | 0.962261 | + | 0.272129i | \(0.0877277\pi\) |
0.272129 | + | 0.962261i | \(0.412272\pi\) | |||||||
\(524\) | −13.2718 | −0.579782 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.9581 | 0.783011 | ||||||||
\(527\) | −2.31415 | − | 2.31415i | −0.100806 | − | 0.100806i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.1658i | 0.833295i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.1451 | + | 15.1451i | −0.656007 | + | 0.656007i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 13.9786i | − | 0.603784i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 19.0350 | + | 19.0350i | 0.820657 | + | 0.820657i | ||||
\(539\) | 6.36365 | 0.274102 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.9167 | −0.641317 | −0.320659 | − | 0.947195i | \(-0.603904\pi\) | ||||
−0.320659 | + | 0.947195i | \(0.603904\pi\) | |||||||
\(542\) | 16.3568 | + | 16.3568i | 0.702583 | + | 0.702583i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.38459i | 0.0593640i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.8839 | − | 14.8839i | 0.636391 | − | 0.636391i | −0.313272 | − | 0.949663i | \(-0.601425\pi\) |
0.949663 | + | 0.313272i | \(0.101425\pi\) | |||||||
\(548\) | −3.56484 | + | 3.56484i | −0.152283 | + | 0.152283i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.72730 | − | 4.72730i | −0.201025 | − | 0.201025i | ||||
\(554\) | −17.2917 | −0.734654 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.41359 | −0.0599497 | ||||||||
\(557\) | −16.1925 | − | 16.1925i | −0.686099 | − | 0.686099i | 0.275268 | − | 0.961367i | \(-0.411233\pi\) |
−0.961367 | + | 0.275268i | \(0.911233\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 19.9162i | − | 0.842367i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.38416 | + | 7.38416i | −0.311482 | + | 0.311482i | ||||
\(563\) | −4.69830 | + | 4.69830i | −0.198010 | + | 0.198010i | −0.799146 | − | 0.601136i | \(-0.794715\pi\) |
0.601136 | + | 0.799146i | \(0.294715\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 32.4671i | − | 1.36469i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.72730 | + | 8.72730i | 0.366189 | + | 0.366189i | ||||
\(569\) | 38.1643 | 1.59993 | 0.799965 | − | 0.600046i | \(-0.204851\pi\) | ||||
0.799965 | + | 0.600046i | \(0.204851\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.6008 | −1.02951 | −0.514755 | − | 0.857337i | \(-0.672117\pi\) | ||||
−0.514755 | + | 0.857337i | \(0.672117\pi\) | |||||||
\(572\) | −10.7692 | − | 10.7692i | −0.450282 | − | 0.450282i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 8.94944i | − | 0.373542i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.01318 | − | 8.01318i | 0.333593 | − | 0.333593i | −0.520356 | − | 0.853949i | \(-0.674201\pi\) |
0.853949 | + | 0.520356i | \(0.174201\pi\) | |||||||
\(578\) | 10.6652 | − | 10.6652i | 0.443615 | − | 0.443615i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 16.0410i | − | 0.665493i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.22511 | − | 1.22511i | −0.0507388 | − | 0.0507388i | ||||
\(584\) | 6.66553 | 0.275822 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 26.3628 | 1.08904 | ||||||||
\(587\) | 7.42648 | + | 7.42648i | 0.306524 | + | 0.306524i | 0.843559 | − | 0.537036i | \(-0.180456\pi\) |
−0.537036 | + | 0.843559i | \(0.680456\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.157074 | − | 0.157074i | 0.00645568 | − | 0.00645568i | ||||
\(593\) | −13.8157 | + | 13.8157i | −0.567344 | + | 0.567344i | −0.931383 | − | 0.364040i | \(-0.881397\pi\) |
0.364040 | + | 0.931383i | \(0.381397\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 20.0609i | − | 0.821726i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.31371 | + | 3.31371i | 0.135508 | + | 0.135508i | ||||
\(599\) | −0.643527 | −0.0262938 | −0.0131469 | − | 0.999914i | \(-0.504185\pi\) | ||||
−0.0131469 | + | 0.999914i | \(0.504185\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.0548 | 0.818051 | 0.409026 | − | 0.912523i | \(-0.365869\pi\) | ||||
0.409026 | + | 0.912523i | \(0.365869\pi\) | |||||||
\(602\) | 5.88438 | + | 5.88438i | 0.239829 | + | 0.239829i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.81108i | 0.358518i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.3423 | − | 16.3423i | 0.663312 | − | 0.663312i | −0.292847 | − | 0.956159i | \(-0.594603\pi\) |
0.956159 | + | 0.292847i | \(0.0946027\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 10.3431i | − | 0.418439i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.29797 | − | 6.29797i | −0.254373 | − | 0.254373i | 0.568388 | − | 0.822761i | \(-0.307567\pi\) |
−0.822761 | + | 0.568388i | \(0.807567\pi\) | |||||||
\(614\) | −1.02856 | −0.0415093 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.36365 | 0.256399 | ||||||||
\(617\) | −15.3632 | − | 15.3632i | −0.618500 | − | 0.618500i | 0.326647 | − | 0.945146i | \(-0.394081\pi\) |
−0.945146 | + | 0.326647i | \(0.894081\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.1462i | 1.41264i | 0.707891 | + | 0.706322i | \(0.249647\pi\) | ||||
−0.707891 | + | 0.706322i | \(0.750353\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −17.1328 | + | 17.1328i | −0.686964 | + | 0.686964i | ||||
\(623\) | 8.37010 | − | 8.37010i | 0.335341 | − | 0.335341i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 4.86566i | − | 0.194471i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15.2654 | − | 15.2654i | −0.609155 | − | 0.609155i | ||||
\(629\) | 0.307568 | 0.0122635 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.5864 | 0.899151 | 0.449575 | − | 0.893242i | \(-0.351575\pi\) | ||||
0.449575 | + | 0.893242i | \(0.351575\pi\) | |||||||
\(632\) | −4.72730 | − | 4.72730i | −0.188042 | − | 0.188042i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18.2714i | 0.725649i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.69230 | − | 1.69230i | 0.0670513 | − | 0.0670513i | ||||
\(638\) | 26.1876 | − | 26.1876i | 1.03678 | − | 1.03678i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 6.90352i | − | 0.272673i | −0.990663 | − | 0.136336i | \(-0.956467\pi\) | ||
0.990663 | − | 0.136336i | \(-0.0435328\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.4542 | − | 30.4542i | −1.20100 | − | 1.20100i | −0.973864 | − | 0.227131i | \(-0.927066\pi\) |
−0.227131 | − | 0.973864i | \(-0.572934\pi\) | |||||||
\(644\) | −1.95811 | −0.0771604 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.9726 | − | 13.9726i | −0.549320 | − | 0.549320i | 0.376924 | − | 0.926244i | \(-0.376982\pi\) |
−0.926244 | + | 0.376924i | \(0.876982\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 66.0811i | 2.59391i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.11519 | − | 7.11519i | 0.278652 | − | 0.278652i | ||||
\(653\) | 7.99597 | − | 7.99597i | 0.312906 | − | 0.312906i | −0.533128 | − | 0.846035i | \(-0.678984\pi\) |
0.846035 | + | 0.533128i | \(0.178984\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 8.94944i | − | 0.349417i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.05595 | + | 3.05595i | 0.119133 | + | 0.119133i | ||||
\(659\) | 27.9020 | 1.08691 | 0.543454 | − | 0.839439i | \(-0.317116\pi\) | ||||
0.543454 | + | 0.839439i | \(0.317116\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.294519 | −0.0114555 | −0.00572774 | − | 0.999984i | \(-0.501823\pi\) | ||||
−0.00572774 | + | 0.999984i | \(0.501823\pi\) | |||||||
\(662\) | 6.20013 | + | 6.20013i | 0.240975 | + | 0.240975i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 16.0410i | − | 0.622512i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.05800 | + | 8.05800i | −0.312007 | + | 0.312007i | ||||
\(668\) | −16.7128 | + | 16.7128i | −0.646638 | + | 0.646638i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 6.23037i | − | 0.240521i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.6569 | + | 24.6569i | 0.950452 | + | 0.950452i | 0.998829 | − | 0.0483773i | \(-0.0154050\pi\) |
−0.0483773 | + | 0.998829i | \(0.515405\pi\) | |||||||
\(674\) | 17.4552 | 0.672350 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.27226 | 0.279702 | ||||||||
\(677\) | 28.7195 | + | 28.7195i | 1.10378 | + | 1.10378i | 0.993950 | + | 0.109831i | \(0.0350311\pi\) |
0.109831 | + | 0.993950i | \(0.464969\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.2917i | 0.510089i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10.6359 | + | 10.6359i | −0.407270 | + | 0.407270i | ||||
\(683\) | −0.221515 | + | 0.221515i | −0.00847605 | + | 0.00847605i | −0.711332 | − | 0.702856i | \(-0.751908\pi\) |
0.702856 | + | 0.711332i | \(0.251908\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.00000i | 0.0381802i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.88438 | + | 5.88438i | 0.224340 | + | 0.224340i | ||||
\(689\) | −0.651591 | −0.0248236 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.2648 | −1.37958 | −0.689789 | − | 0.724010i | \(-0.742297\pi\) | ||||
−0.689789 | + | 0.724010i | \(0.742297\pi\) | |||||||
\(692\) | −14.7843 | − | 14.7843i | −0.562015 | − | 0.562015i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.31371i | 0.277625i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.76200 | − | 8.76200i | 0.331885 | − | 0.331885i | ||||
\(698\) | −20.4610 | + | 20.4610i | −0.774462 | + | 0.774462i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 21.0497i | − | 0.795036i | −0.917594 | − | 0.397518i | \(-0.869872\pi\) | ||
0.917594 | − | 0.397518i | \(-0.130128\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 6.36365 | 0.239839 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.6564 | 0.551601 | ||||||||
\(707\) | −11.3492 | − | 11.3492i | −0.426829 | − | 0.426829i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.3617i | 0.539366i | 0.962949 | + | 0.269683i | \(0.0869190\pi\) | ||||
−0.962949 | + | 0.269683i | \(0.913081\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.37010 | − | 8.37010i | 0.313683 | − | 0.313683i | ||||
\(713\) | 3.27270 | − | 3.27270i | 0.122564 | − | 0.122564i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.0205i | 0.449227i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.35560 | + | 9.35560i | 0.349148 | + | 0.349148i | ||||
\(719\) | −16.9706 | −0.632895 | −0.316448 | − | 0.948610i | \(-0.602490\pi\) | ||||
−0.316448 | + | 0.948610i | \(0.602490\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.999561 | −0.0372256 | ||||||||
\(722\) | 13.4350 | + | 13.4350i | 0.500000 | + | 0.500000i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 17.5236i | 0.651259i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.42692 | − | 2.42692i | 0.0900095 | − | 0.0900095i | −0.660668 | − | 0.750678i | \(-0.729727\pi\) |
0.750678 | + | 0.660668i | \(0.229727\pi\) | |||||||
\(728\) | 1.69230 | − | 1.69230i | 0.0627207 | − | 0.0627207i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.5223i | 0.426167i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.3701 | + | 14.3701i | 0.530772 | + | 0.530772i | 0.920802 | − | 0.390030i | \(-0.127536\pi\) |
−0.390030 | + | 0.920802i | \(0.627536\pi\) | |||||||
\(734\) | 4.53882 | 0.167531 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.95811 | −0.0721770 | ||||||||
\(737\) | −62.9007 | − | 62.9007i | −2.31698 | − | 2.31698i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 38.0886i | − | 1.40111i | −0.713598 | − | 0.700556i | \(-0.752935\pi\) | ||
0.713598 | − | 0.700556i | \(-0.247065\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.192517 | − | 0.192517i | 0.00706751 | − | 0.00706751i | ||||
\(743\) | 31.4965 | − | 31.4965i | 1.15549 | − | 1.15549i | 0.170061 | − | 0.985434i | \(-0.445604\pi\) |
0.985434 | − | 0.170061i | \(-0.0543963\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.20881i | 0.117483i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.23037 | + | 6.23037i | 0.227805 | + | 0.227805i | ||||
\(749\) | −13.4546 | −0.491621 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.9511 | 0.618554 | 0.309277 | − | 0.950972i | \(-0.399913\pi\) | ||||
0.309277 | + | 0.950972i | \(0.399913\pi\) | |||||||
\(752\) | 3.05595 | + | 3.05595i | 0.111439 | + | 0.111439i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 13.9282i | − | 0.507236i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.34644 | − | 2.34644i | 0.0852826 | − | 0.0852826i | −0.663179 | − | 0.748461i | \(-0.730793\pi\) |
0.748461 | + | 0.663179i | \(0.230793\pi\) | |||||||
\(758\) | 1.69559 | − | 1.69559i | 0.0615865 | − | 0.0615865i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.07510i | 0.111472i | 0.998446 | + | 0.0557361i | \(0.0177506\pi\) | ||||
−0.998446 | + | 0.0557361i | \(0.982249\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.5767 | + | 10.5767i | 0.382901 | + | 0.382901i | ||||
\(764\) | 6.30038 | 0.227940 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −23.5945 | −0.852503 | ||||||||
\(767\) | 17.5731 | + | 17.5731i | 0.634527 | + | 0.634527i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.4666i | 0.629862i | 0.949115 | + | 0.314931i | \(0.101981\pi\) | ||||
−0.949115 | + | 0.314931i | \(0.898019\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11.6435 | + | 11.6435i | −0.419060 | + | 0.419060i | ||||
\(773\) | −38.6076 | + | 38.6076i | −1.38862 | + | 1.38862i | −0.560395 | + | 0.828225i | \(0.689351\pi\) |
−0.828225 | + | 0.560395i | \(0.810649\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 13.2917i | 0.477144i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.6117 | − | 15.6117i | −0.559706 | − | 0.559706i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 78.5419 | 2.81045 | ||||||||
\(782\) | −1.91710 | − | 1.91710i | −0.0685554 | − | 0.0685554i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000i | 0.0357143i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.3076 | − | 12.3076i | 0.438717 | − | 0.438717i | −0.452863 | − | 0.891580i | \(-0.649597\pi\) |
0.891580 | + | 0.452863i | \(0.149597\pi\) | |||||||
\(788\) | −1.92849 | + | 1.92849i | −0.0686997 | + | 0.0686997i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 13.0414i | − | 0.463701i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.65685 | − | 1.65685i | −0.0588366 | − | 0.0588366i | ||||
\(794\) | −29.6585 | −1.05254 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.67736 | 0.201229 | ||||||||
\(797\) | 4.88543 | + | 4.88543i | 0.173051 | + | 0.173051i | 0.788318 | − | 0.615267i | \(-0.210952\pi\) |
−0.615267 | + | 0.788318i | \(0.710952\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.98389i | 0.211695i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.57308 | + | 6.57308i | −0.232103 | + | 0.232103i | ||||
\(803\) | 29.9934 | − | 29.9934i | 1.05844 | − | 1.05844i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.65685i | 0.199254i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.3492 | − | 11.3492i | −0.399262 | − | 0.399262i | ||||
\(809\) | −6.30907 | −0.221815 | −0.110907 | − | 0.993831i | \(-0.535376\pi\) | ||||
−0.110907 | + | 0.993831i | \(0.535376\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.6632 | 1.46299 | 0.731496 | − | 0.681846i | \(-0.238823\pi\) | ||||
0.731496 | + | 0.681846i | \(0.238823\pi\) | |||||||
\(812\) | 4.11519 | + | 4.11519i | 0.144415 | + | 0.144415i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 1.41359i | − | 0.0495464i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −24.2090 | + | 24.2090i | −0.846447 | + | 0.846447i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 46.4552i | 1.62130i | 0.585532 | + | 0.810649i | \(0.300886\pi\) | ||||
−0.585532 | + | 0.810649i | \(0.699114\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.2942 | + | 27.2942i | 0.951417 | + | 0.951417i | 0.998873 | − | 0.0474559i | \(-0.0151114\pi\) |
−0.0474559 | + | 0.998873i | \(0.515111\pi\) | |||||||
\(824\) | −0.999561 | −0.0348214 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.3842 | −0.361311 | ||||||||
\(827\) | −37.6528 | − | 37.6528i | −1.30932 | − | 1.30932i | −0.921908 | − | 0.387409i | \(-0.873370\pi\) |
−0.387409 | − | 0.921908i | \(-0.626630\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.9791i | 0.589707i | 0.955542 | + | 0.294853i | \(0.0952708\pi\) | ||||
−0.955542 | + | 0.294853i | \(0.904729\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.69230 | − | 1.69230i | 0.0586699 | − | 0.0586699i | ||||
\(833\) | −0.979056 | + | 0.979056i | −0.0339223 | + | 0.0339223i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 9.74063 | + | 9.74063i | 0.336484 | + | 0.336484i | ||||
\(839\) | 2.63064 | 0.0908197 | 0.0454099 | − | 0.998968i | \(-0.485541\pi\) | ||||
0.0454099 | + | 0.998968i | \(0.485541\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.86951 | 0.167914 | ||||||||
\(842\) | 7.51534 | + | 7.51534i | 0.258996 | + | 0.258996i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.91622i | 0.272488i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.8569 | − | 20.8569i | 0.716650 | − | 0.716650i | ||||
\(848\) | 0.192517 | − | 0.192517i | 0.00661105 | − | 0.00661105i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.434966i | 0.0149105i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.6700 | + | 35.6700i | 1.22132 | + | 1.22132i | 0.967163 | + | 0.254155i | \(0.0817975\pi\) |
0.254155 | + | 0.967163i | \(0.418203\pi\) | |||||||
\(854\) | 0.979056 | 0.0335026 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.4546 | −0.459869 | ||||||||
\(857\) | 2.97818 | + | 2.97818i | 0.101733 | + | 0.101733i | 0.756141 | − | 0.654409i | \(-0.227082\pi\) |
−0.654409 | + | 0.756141i | \(0.727082\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.9634i | 1.05646i | 0.849102 | + | 0.528228i | \(0.177144\pi\) | ||||
−0.849102 | + | 0.528228i | \(0.822856\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.3556 | − | 13.3556i | 0.454893 | − | 0.454893i | ||||
\(863\) | 0.602516 | − | 0.602516i | 0.0205099 | − | 0.0205099i | −0.696777 | − | 0.717287i | \(-0.745383\pi\) |
0.717287 | + | 0.696777i | \(0.245383\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 27.3928i | 0.930846i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.67135 | − | 1.67135i | −0.0567294 | − | 0.0567294i | ||||
\(869\) | −42.5436 | −1.44319 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −33.4546 | −1.13357 | ||||||||
\(872\) | 10.5767 | + | 10.5767i | 0.358171 | + | 0.358171i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.7369 | + | 28.7369i | −0.970376 | + | 0.970376i | −0.999574 | − | 0.0291975i | \(-0.990705\pi\) |
0.0291975 | + | 0.999574i | \(0.490705\pi\) | |||||||
\(878\) | 3.44098 | − | 3.44098i | 0.116127 | − | 0.116127i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46.7691i | 1.57569i | 0.615873 | + | 0.787845i | \(0.288803\pi\) | ||||
−0.615873 | + | 0.787845i | \(0.711197\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.4285 | + | 27.4285i | 0.923041 | + | 0.923041i | 0.997243 | − | 0.0742022i | \(-0.0236410\pi\) |
−0.0742022 | + | 0.997243i | \(0.523641\pi\) | |||||||
\(884\) | 3.31371 | 0.111452 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.1409 | −0.340690 | ||||||||
\(887\) | 16.1393 | + | 16.1393i | 0.541904 | + | 0.541904i | 0.924087 | − | 0.382183i | \(-0.124827\pi\) |
−0.382183 | + | 0.924087i | \(0.624827\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.61497i | 0.255398i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.34227 | − | 8.34227i | 0.279320 | − | 0.279320i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.00000i | 0.0334077i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.27270 | − | 6.27270i | −0.209323 | − | 0.209323i | ||||
\(899\) | −13.7559 | −0.458784 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.376969 | 0.0125587 | ||||||||
\(902\) | −40.2705 | − | 40.2705i | −1.34086 | − | 1.34086i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 13.0414i | − | 0.433752i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.57067 | − | 2.57067i | 0.0853576 | − | 0.0853576i | −0.663139 | − | 0.748496i | \(-0.730776\pi\) |
0.748496 | + | 0.663139i | \(0.230776\pi\) | |||||||
\(908\) | −3.27270 | + | 3.27270i | −0.108608 | + | 0.108608i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 37.2138i | − | 1.23295i | −0.787375 | − | 0.616474i | \(-0.788560\pi\) | ||
0.787375 | − | 0.616474i | \(-0.211440\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −72.1810 | − | 72.1810i | −2.38884 | − | 2.38884i | ||||
\(914\) | −6.04251 | −0.199868 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 23.0901 | 0.762918 | ||||||||
\(917\) | −9.38459 | − | 9.38459i | −0.309907 | − | 0.309907i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.126540i | 0.00417416i | 0.999998 | + | 0.00208708i | \(0.000664339\pi\) | ||||
−0.999998 | + | 0.00208708i | \(0.999336\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.545691 | − | 0.545691i | 0.0179714 | − | 0.0179714i | ||||
\(923\) | 20.8868 | − | 20.8868i | 0.687497 | − | 0.687497i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 27.7398i | 0.911585i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.11519 | + | 4.11519i | 0.135088 | + | 0.135088i | ||||
\(929\) | −44.7882 | −1.46945 | −0.734727 | − | 0.678363i | \(-0.762690\pi\) | ||||
−0.734727 | + | 0.678363i | \(0.762690\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −5.23081 | − | 5.23081i | −0.171341 | − | 0.171341i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.5803i | 0.378918i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.9303 | − | 27.9303i | 0.912443 | − | 0.912443i | −0.0840213 | − | 0.996464i | \(-0.526776\pi\) |
0.996464 | + | 0.0840213i | \(0.0267764\pi\) | |||||||
\(938\) | 9.88438 | − | 9.88438i | 0.322736 | − | 0.322736i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.3233i | 0.597321i | 0.954359 | + | 0.298661i | \(0.0965399\pi\) | ||||
−0.954359 | + | 0.298661i | \(0.903460\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.3913 | + | 12.3913i | 0.403518 | + | 0.403518i | ||||
\(944\) | −10.3842 | −0.337975 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 52.9568 | 1.72177 | ||||||||
\(947\) | −32.1360 | − | 32.1360i | −1.04428 | − | 1.04428i | −0.998973 | − | 0.0453061i | \(-0.985574\pi\) |
−0.0453061 | − | 0.998973i | \(-0.514426\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 15.9524i | − | 0.517837i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.979056 | + | 0.979056i | −0.0317314 | + | 0.0317314i | ||||
\(953\) | 1.74001 | − | 1.74001i | 0.0563644 | − | 0.0563644i | −0.678363 | − | 0.734727i | \(-0.737310\pi\) |
0.734727 | + | 0.678363i | \(0.237310\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 5.27182i | − | 0.170503i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 14.9082 | + | 14.9082i | 0.481661 | + | 0.481661i | ||||
\(959\) | −5.04145 | −0.162797 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.4132 | −0.819779 | ||||||||
\(962\) | −0.375919 | − | 0.375919i | −0.0121201 | − | 0.0121201i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 5.27270i | − | 0.169822i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.7140 | + | 19.7140i | −0.633959 | + | 0.633959i | −0.949059 | − | 0.315100i | \(-0.897962\pi\) |
0.315100 | + | 0.949059i | \(0.397962\pi\) | |||||||
\(968\) | 20.8569 | − | 20.8569i | 0.670365 | − | 0.670365i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 21.2308i | − | 0.681329i | −0.940185 | − | 0.340665i | \(-0.889348\pi\) | ||
0.940185 | − | 0.340665i | \(-0.110652\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.999561 | − | 0.999561i | −0.0320445 | − | 0.0320445i | ||||
\(974\) | 29.2718 | 0.937930 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.979056 | 0.0313388 | ||||||||
\(977\) | −12.3013 | − | 12.3013i | −0.393552 | − | 0.393552i | 0.482399 | − | 0.875951i | \(-0.339765\pi\) |
−0.875951 | + | 0.482399i | \(0.839765\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 75.3272i | − | 2.40747i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.26897 | + | 7.26897i | −0.231962 | + | 0.231962i | ||||
\(983\) | 23.3087 | − | 23.3087i | 0.743433 | − | 0.743433i | −0.229804 | − | 0.973237i | \(-0.573808\pi\) |
0.973237 | + | 0.229804i | \(0.0738084\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 8.05800i | 0.256619i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.2949 | −0.518149 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.5606 | 0.335469 | 0.167735 | − | 0.985832i | \(-0.446355\pi\) | ||||
0.167735 | + | 0.985832i | \(0.446355\pi\) | |||||||
\(992\) | −1.67135 | − | 1.67135i | −0.0530655 | − | 0.0530655i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 12.3423i | 0.391473i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.3973 | + | 28.3973i | −0.899353 | + | 0.899353i | −0.995379 | − | 0.0960261i | \(-0.969387\pi\) |
0.0960261 | + | 0.995379i | \(0.469387\pi\) | |||||||
\(998\) | −3.65370 | + | 3.65370i | −0.115656 | + | 0.115656i | ||||
\(999\) | 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 | 3150.2.m.i.2843.4 | 8 | ||
3.2 | odd | 2 | 3150.2.m.j.2843.1 | 8 | |||
5.2 | odd | 4 | 3150.2.m.j.1457.2 | 8 | |||
5.3 | odd | 4 | 630.2.m.d.197.3 | yes | 8 | ||
5.4 | even | 2 | 630.2.m.c.323.2 | yes | 8 | ||
15.2 | even | 4 | inner | 3150.2.m.i.1457.3 | 8 | ||
15.8 | even | 4 | 630.2.m.c.197.2 | ✓ | 8 | ||
15.14 | odd | 2 | 630.2.m.d.323.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.m.c.197.2 | ✓ | 8 | 15.8 | even | 4 | ||
630.2.m.c.323.2 | yes | 8 | 5.4 | even | 2 | ||
630.2.m.d.197.3 | yes | 8 | 5.3 | odd | 4 | ||
630.2.m.d.323.3 | yes | 8 | 15.14 | odd | 2 | ||
3150.2.m.i.1457.3 | 8 | 15.2 | even | 4 | inner | ||
3150.2.m.i.2843.4 | 8 | 1.1 | even | 1 | trivial | ||
3150.2.m.j.1457.2 | 8 | 5.2 | odd | 4 | |||
3150.2.m.j.2843.1 | 8 | 3.2 | odd | 2 |