Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1357,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1357");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.x (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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | 16.0.478584585616890104119296.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 31x^{12} + 336x^{8} - 19375x^{4} + 390625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1693.3 | ||
Root | \(1.04705 - 1.97578i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1693 |
Dual form | 2100.2.x.c.1357.3 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.884806 | + | 2.49342i | −0.334425 | + | 0.942422i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.27492 | 0.987425 | 0.493712 | − | 0.869625i | \(-0.335640\pi\) | ||||
0.493712 | + | 0.869625i | \(0.335640\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.02282 | + | 3.02282i | −0.838380 | + | 0.838380i | −0.988646 | − | 0.150265i | \(-0.951987\pi\) |
0.150265 | + | 0.988646i | \(0.451987\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.41421 | + | 1.41421i | 0.342997 | + | 0.342997i | 0.857493 | − | 0.514496i | \(-0.172021\pi\) |
−0.514496 | + | 0.857493i | \(0.672021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.15068 | −0.493399 | −0.246700 | − | 0.969092i | \(-0.579346\pi\) | ||||
−0.246700 | + | 0.969092i | \(0.579346\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.13746 | − | 2.38876i | −0.248214 | − | 0.521271i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.296014 | + | 0.296014i | 0.0617231 | + | 0.0617231i | 0.737295 | − | 0.675571i | \(-0.236103\pi\) |
−0.675571 | + | 0.737295i | \(0.736103\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.725083i | 0.134644i | 0.997731 | + | 0.0673222i | \(0.0214456\pi\) | ||||
−0.997731 | + | 0.0673222i | \(0.978554\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.31342i | − | 0.235898i | −0.993020 | − | 0.117949i | \(-0.962368\pi\) | ||
0.993020 | − | 0.117949i | \(-0.0376319\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.31572 | + | 2.31572i | −0.403114 | + | 0.403114i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.56145 | + | 1.56145i | −0.256701 | + | 0.256701i | −0.823711 | − | 0.567010i | \(-0.808100\pi\) |
0.567010 | + | 0.823711i | \(0.308100\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 4.27492i | − | 0.684535i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.25370i | 0.820490i | 0.911975 | + | 0.410245i | \(0.134557\pi\) | ||||
−0.911975 | + | 0.410245i | \(0.865443\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.632717 | − | 0.632717i | −0.0964885 | − | 0.0964885i | 0.657215 | − | 0.753703i | \(-0.271734\pi\) |
−0.753703 | + | 0.657215i | \(0.771734\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.41421 | + | 1.41421i | 0.206284 | + | 0.206284i | 0.802686 | − | 0.596402i | \(-0.203403\pi\) |
−0.596402 | + | 0.802686i | \(0.703403\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.43424 | − | 4.41238i | −0.776320 | − | 0.630339i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | −0.280056 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.71492 | − | 3.71492i | −0.510284 | − | 0.510284i | 0.404329 | − | 0.914613i | \(-0.367505\pi\) |
−0.914613 | + | 0.404329i | \(0.867505\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.52076 | − | 1.52076i | 0.201429 | − | 0.201429i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.71780 | −1.13496 | −0.567480 | − | 0.823387i | \(-0.692082\pi\) | ||||
−0.567480 | + | 0.823387i | \(0.692082\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.31342i | 0.168167i | 0.996459 | + | 0.0840834i | \(0.0267962\pi\) | ||||
−0.996459 | + | 0.0840834i | \(0.973204\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.49342 | + | 0.884806i | 0.314141 | + | 0.111475i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.08221 | − | 3.08221i | 0.376552 | − | 0.376552i | −0.493305 | − | 0.869856i | \(-0.664211\pi\) |
0.869856 | + | 0.493305i | \(0.164211\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.418627 | −0.0503967 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.27492 | 1.10073 | 0.550365 | − | 0.834924i | \(-0.314489\pi\) | ||||
0.550365 | + | 0.834924i | \(0.314489\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.07107 | + | 7.07107i | −0.827606 | + | 0.827606i | −0.987185 | − | 0.159579i | \(-0.948986\pi\) |
0.159579 | + | 0.987185i | \(0.448986\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.89767 | + | 8.16573i | −0.330220 | + | 0.930571i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 11.8248i | − | 1.33039i | −0.746670 | − | 0.665194i | \(-0.768349\pi\) | ||
0.746670 | − | 0.665194i | \(-0.231651\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.7025 | + | 11.7025i | −1.28452 | + | 1.28452i | −0.346447 | + | 0.938070i | \(0.612612\pi\) |
−0.938070 | + | 0.346447i | \(0.887388\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.512711 | − | 0.512711i | −0.0549684 | − | 0.0549684i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −18.2728 | −1.93692 | −0.968459 | − | 0.249173i | \(-0.919841\pi\) | ||||
−0.968459 | + | 0.249173i | \(0.919841\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.86254 | − | 10.2118i | −0.509733 | − | 1.07048i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.928731 | + | 0.928731i | 0.0963049 | + | 0.0963049i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.26546 | + | 7.26546i | 0.737696 | + | 0.737696i | 0.972132 | − | 0.234436i | \(-0.0753242\pi\) |
−0.234436 | + | 0.972132i | \(0.575324\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 3.27492i | − | 0.329142i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.76546i | 0.772692i | 0.922354 | + | 0.386346i | \(0.126263\pi\) | ||||
−0.922354 | + | 0.386346i | \(0.873737\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.63143 | + | 4.63143i | −0.456349 | + | 0.456349i | −0.897455 | − | 0.441106i | \(-0.854586\pi\) |
0.441106 | + | 0.897455i | \(0.354586\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.30695 | + | 4.30695i | −0.416369 | + | 0.416369i | −0.883950 | − | 0.467581i | \(-0.845126\pi\) |
0.467581 | + | 0.883950i | \(0.345126\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.00000i | − | 0.0957826i | −0.998853 | − | 0.0478913i | \(-0.984750\pi\) | ||
0.998853 | − | 0.0478913i | \(-0.0152501\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 2.20822i | − | 0.209595i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.3594 | − | 11.3594i | −1.06860 | − | 1.06860i | −0.997467 | − | 0.0711366i | \(-0.977337\pi\) |
−0.0711366 | − | 0.997467i | \(-0.522663\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.02282 | + | 3.02282i | 0.279460 | + | 0.279460i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.77753 | + | 2.27492i | −0.437955 | + | 0.208541i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.274917 | −0.0249925 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.71492 | − | 3.71492i | −0.334963 | − | 0.334963i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.50195 | − | 9.50195i | 0.843161 | − | 0.843161i | −0.146107 | − | 0.989269i | \(-0.546675\pi\) |
0.989269 | + | 0.146107i | \(0.0466745\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.894797 | 0.0787825 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 19.9474i | − | 1.74281i | −0.490566 | − | 0.871404i | \(-0.663210\pi\) | ||
0.490566 | − | 0.871404i | \(-0.336790\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.90293 | − | 5.36253i | 0.165005 | − | 0.464990i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.3703 | + | 15.3703i | −1.31318 | + | 1.31318i | −0.394117 | + | 0.919060i | \(0.628949\pi\) |
−0.919060 | + | 0.394117i | \(0.871051\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.46410 | −0.293821 | −0.146911 | − | 0.989150i | \(-0.546933\pi\) | ||||
−0.146911 | + | 0.989150i | \(0.546933\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.00000 | −0.168430 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.89949 | + | 9.89949i | −0.827837 | + | 0.827837i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.96261 | − | 0.722565i | 0.574266 | − | 0.0595962i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 23.2749i | 1.90676i | 0.301779 | + | 0.953378i | \(0.402419\pi\) | ||||
−0.301779 | + | 0.953378i | \(0.597581\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.0000 | −0.895167 | −0.447584 | − | 0.894242i | \(-0.647715\pi\) | ||||
−0.447584 | + | 0.894242i | \(0.647715\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.41421 | − | 1.41421i | 0.114332 | − | 0.114332i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.65426 | + | 7.65426i | 0.610876 | + | 0.610876i | 0.943174 | − | 0.332298i | \(-0.107824\pi\) |
−0.332298 | + | 0.943174i | \(0.607824\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.25370 | 0.416645 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | + | 0.476171i | −0.0788110 | + | 0.0375275i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.7070 | − | 15.7070i | −1.23027 | − | 1.23027i | −0.963859 | − | 0.266412i | \(-0.914162\pi\) |
−0.266412 | − | 0.963859i | \(-0.585838\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.45986 | − | 7.45986i | −0.577261 | − | 0.577261i | 0.356886 | − | 0.934148i | \(-0.383838\pi\) |
−0.934148 | + | 0.356886i | \(0.883838\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.27492i | − | 0.405763i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.15068i | 0.164466i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.5055 | − | 13.5055i | 1.02680 | − | 1.02680i | 0.0271738 | − | 0.999631i | \(-0.491349\pi\) |
0.999631 | − | 0.0271738i | \(-0.00865077\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.16441 | − | 6.16441i | 0.463346 | − | 0.463346i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.45017i | 0.556852i | 0.960458 | + | 0.278426i | \(0.0898126\pi\) | ||||
−0.960458 | + | 0.278426i | \(0.910187\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.10302i | − | 0.230646i | −0.993328 | − | 0.115323i | \(-0.963210\pi\) | ||
0.993328 | − | 0.115323i | \(-0.0367902\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.928731 | − | 0.928731i | −0.0686538 | − | 0.0686538i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.63143 | + | 4.63143i | 0.338684 | + | 0.338684i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.38876 | + | 1.13746i | −0.173757 | + | 0.0827379i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.5498 | 0.908074 | 0.454037 | − | 0.890983i | \(-0.349983\pi\) | ||||
0.454037 | + | 0.890983i | \(0.349983\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.5536 | + | 13.5536i | 0.975608 | + | 0.975608i | 0.999710 | − | 0.0241020i | \(-0.00767264\pi\) |
−0.0241020 | + | 0.999710i | \(0.507673\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.0328 | + | 12.0328i | −0.857303 | + | 0.857303i | −0.991020 | − | 0.133717i | \(-0.957309\pi\) |
0.133717 | + | 0.991020i | \(0.457309\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.1698 | 1.07536 | 0.537680 | − | 0.843149i | \(-0.319301\pi\) | ||||
0.537680 | + | 0.843149i | \(0.319301\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.35890i | 0.307453i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.80793 | − | 0.641557i | −0.126892 | − | 0.0450285i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.296014 | − | 0.296014i | 0.0205744 | − | 0.0205744i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.04329 | −0.487195 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.72508 | 0.118760 | 0.0593798 | − | 0.998235i | \(-0.481088\pi\) | ||||
0.0593798 | + | 0.998235i | \(0.481088\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.55836 | + | 6.55836i | −0.449371 | + | 0.449371i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.27491 | + | 1.16213i | 0.222315 | + | 0.0788902i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 10.0000i | − | 0.675737i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.54983 | −0.575124 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.41161 | − | 3.41161i | 0.228459 | − | 0.228459i | −0.583590 | − | 0.812049i | \(-0.698352\pi\) |
0.812049 | + | 0.583590i | \(0.198352\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.8943 | − | 13.8943i | −0.922197 | − | 0.922197i | 0.0749876 | − | 0.997184i | \(-0.476108\pi\) |
−0.997184 | + | 0.0749876i | \(0.976108\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.5430 | −0.828864 | −0.414432 | − | 0.910080i | \(-0.636020\pi\) | ||||
−0.414432 | + | 0.910080i | \(0.636020\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.72508 | − | 7.82300i | −0.245092 | − | 0.514716i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.46043 | + | 6.46043i | 0.423237 | + | 0.423237i | 0.886317 | − | 0.463080i | \(-0.153256\pi\) |
−0.463080 | + | 0.886317i | \(0.653256\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.36136 | + | 8.36136i | 0.543129 | + | 0.543129i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.09967i | 0.588609i | 0.955712 | + | 0.294304i | \(0.0950879\pi\) | ||||
−0.955712 | + | 0.294304i | \(0.904912\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.1890i | 1.81581i | 0.419174 | + | 0.907906i | \(0.362320\pi\) | ||||
−0.419174 | + | 0.907906i | \(0.637680\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.50112 | − | 6.50112i | 0.413656 | − | 0.413656i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 16.5498i | − | 1.04880i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.09095i | 0.384457i | 0.981350 | + | 0.192229i | \(0.0615715\pi\) | ||||
−0.981350 | + | 0.192229i | \(0.938428\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.969421 | + | 0.969421i | 0.0609470 | + | 0.0609470i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.60601 | − | 3.60601i | −0.224937 | − | 0.224937i | 0.585637 | − | 0.810574i | \(-0.300844\pi\) |
−0.810574 | + | 0.585637i | \(0.800844\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.51176 | − | 5.27492i | −0.156073 | − | 0.327767i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.725083 | 0.0448815 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.05246 | + | 7.05246i | 0.434873 | + | 0.434873i | 0.890282 | − | 0.455409i | \(-0.150507\pi\) |
−0.455409 | + | 0.890282i | \(0.650507\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.9209 | − | 12.9209i | 0.790744 | − | 0.790744i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.1578 | 1.10710 | 0.553549 | − | 0.832817i | \(-0.313273\pi\) | ||||
0.553549 | + | 0.832817i | \(0.313273\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 22.5742i | − | 1.37129i | −0.727938 | − | 0.685643i | \(-0.759521\pi\) | ||
0.727938 | − | 0.685643i | \(-0.240479\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.6591 | + | 3.78247i | 0.645121 | + | 0.228926i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.97025 | + | 3.97025i | −0.238549 | + | 0.238549i | −0.816249 | − | 0.577700i | \(-0.803950\pi\) |
0.577700 | + | 0.816249i | \(0.303950\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.31342 | −0.0786326 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.7251 | 0.759115 | 0.379557 | − | 0.925168i | \(-0.376076\pi\) | ||||
0.379557 | + | 0.925168i | \(0.376076\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.9680 | + | 18.9680i | −1.12753 | + | 1.12753i | −0.136951 | + | 0.990578i | \(0.543730\pi\) |
−0.990578 | + | 0.136951i | \(0.956270\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.0996 | − | 4.64850i | −0.773248 | − | 0.274392i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 13.0000i | − | 0.764706i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.2749 | −0.602326 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.6771 | − | 10.6771i | 0.623762 | − | 0.623762i | −0.322730 | − | 0.946491i | \(-0.604600\pi\) |
0.946491 | + | 0.322730i | \(0.104600\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.31572 | + | 2.31572i | 0.134371 | + | 0.134371i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.78959 | −0.103495 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.13746 | − | 1.01779i | 0.123201 | − | 0.0586647i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.49101 | − | 5.49101i | −0.315450 | − | 0.315450i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.1193 | − | 11.1193i | −0.634613 | − | 0.634613i | 0.314609 | − | 0.949221i | \(-0.398127\pi\) |
−0.949221 | + | 0.314609i | \(0.898127\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 6.54983i | − | 0.372607i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 33.0816i | 1.87589i | 0.346790 | + | 0.937943i | \(0.387271\pi\) | ||||
−0.346790 | + | 0.937943i | \(0.612729\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.6046 | − | 19.6046i | 1.10812 | − | 1.10812i | 0.114719 | − | 0.993398i | \(-0.463403\pi\) |
0.993398 | − | 0.114719i | \(-0.0365968\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.64448 | − | 7.64448i | 0.429357 | − | 0.429357i | −0.459052 | − | 0.888409i | \(-0.651811\pi\) |
0.888409 | + | 0.459052i | \(0.151811\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.37459i | 0.132951i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 6.09095i | − | 0.339964i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.04152 | − | 3.04152i | −0.169235 | − | 0.169235i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.707107 | + | 0.707107i | 0.0391031 | + | 0.0391031i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.77753 | + | 2.27492i | −0.263394 | + | 0.125420i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.3746 | 0.570239 | 0.285119 | − | 0.958492i | \(-0.407967\pi\) | ||||
0.285119 | + | 0.958492i | \(0.407967\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.56145 | + | 1.56145i | 0.0855668 | + | 0.0855668i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.5842 | − | 12.5842i | 0.685502 | − | 0.685502i | −0.275732 | − | 0.961235i | \(-0.588920\pi\) |
0.961235 | + | 0.275732i | \(0.0889203\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.0646 | 0.872511 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 4.30136i | − | 0.232931i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.8101 | − | 9.64572i | 0.853667 | − | 0.520820i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.50195 | + | 9.50195i | −0.510091 | + | 0.510091i | −0.914554 | − | 0.404463i | \(-0.867458\pi\) |
0.404463 | + | 0.914554i | \(0.367458\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.2728 | 0.978123 | 0.489062 | − | 0.872249i | \(-0.337339\pi\) | ||||
0.489062 | + | 0.872249i | \(0.337339\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.27492 | −0.228178 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.26806 | + | 5.26806i | −0.280391 | + | 0.280391i | −0.833265 | − | 0.552874i | \(-0.813531\pi\) |
0.552874 | + | 0.833265i | \(0.313531\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.76961 | − | 4.98683i | 0.0936578 | − | 0.263931i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.3746i | 1.39200i | 0.718043 | + | 0.695999i | \(0.245038\pi\) | ||||
−0.718043 | + | 0.695999i | \(0.754962\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.3746 | −0.756557 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.194396 | − | 0.194396i | 0.0102031 | − | 0.0102031i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.9680 | − | 18.9680i | −0.990120 | − | 0.990120i | 0.00983201 | − | 0.999952i | \(-0.496870\pi\) |
−0.999952 | + | 0.00983201i | \(0.996870\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.25370 | 0.273497 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.5498 | − | 5.97586i | 0.651555 | − | 0.310251i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.9615 | + | 12.9615i | 0.671123 | + | 0.671123i | 0.957975 | − | 0.286852i | \(-0.0926087\pi\) |
−0.286852 | + | 0.957975i | \(0.592609\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.19180 | − | 2.19180i | −0.112883 | − | 0.112883i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.0000i | 0.770498i | 0.922813 | + | 0.385249i | \(0.125884\pi\) | ||||
−0.922813 | + | 0.385249i | \(0.874116\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.4378i | 0.688438i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.1676 | − | 15.1676i | 0.775026 | − | 0.775026i | −0.203954 | − | 0.978980i | \(-0.565379\pi\) |
0.978980 | + | 0.203954i | \(0.0653794\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.632717 | + | 0.632717i | −0.0321628 | + | 0.0321628i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.3746i | 0.931628i | 0.884883 | + | 0.465814i | \(0.154239\pi\) | ||||
−0.884883 | + | 0.465814i | \(0.845761\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.837253i | 0.0423417i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.1049 | + | 14.1049i | 0.711499 | + | 0.711499i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.43704 | + | 4.43704i | 0.222688 | + | 0.222688i | 0.809630 | − | 0.586941i | \(-0.199668\pi\) |
−0.586941 | + | 0.809630i | \(0.699668\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.44631 | + | 5.13746i | 0.122469 | + | 0.257195i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.27492 | −0.0636663 | −0.0318332 | − | 0.999493i | \(-0.510135\pi\) | ||||
−0.0318332 | + | 0.999493i | \(0.510135\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.97025 | + | 3.97025i | 0.197772 | + | 0.197772i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.11361 | + | 5.11361i | −0.253472 | + | 0.253472i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.7682 | 1.57084 | 0.785418 | − | 0.618966i | \(-0.212448\pi\) | ||||
0.785418 | + | 0.618966i | \(0.212448\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 21.7370i | − | 1.07220i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.71356 | − | 21.7371i | 0.379559 | − | 1.06961i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.44949 | − | 2.44949i | 0.119952 | − | 0.119952i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.1819 | 0.595125 | 0.297562 | − | 0.954702i | \(-0.403826\pi\) | ||||
0.297562 | + | 0.954702i | \(0.403826\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.725083 | 0.0353384 | 0.0176692 | − | 0.999844i | \(-0.494375\pi\) | ||||
0.0176692 | + | 0.999844i | \(0.494375\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.41421 | − | 1.41421i | 0.0687614 | − | 0.0687614i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.27491 | − | 1.16213i | −0.158484 | − | 0.0562392i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 14.0000i | − | 0.675926i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.6495 | 1.23549 | 0.617747 | − | 0.786377i | \(-0.288046\pi\) | ||||
0.617747 | + | 0.786377i | \(0.288046\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.43704 | − | 4.43704i | 0.213230 | − | 0.213230i | −0.592408 | − | 0.805638i | \(-0.701823\pi\) |
0.805638 | + | 0.592408i | \(0.201823\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.636630 | − | 0.636630i | −0.0304542 | − | 0.0304542i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 33.4427 | 1.59613 | 0.798066 | − | 0.602570i | \(-0.205857\pi\) | ||||
0.798066 | + | 0.602570i | \(0.205857\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.41238 | + | 5.43424i | −0.210113 | + | 0.258773i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.0039 | + | 19.0039i | 0.902902 | + | 0.902902i | 0.995686 | − | 0.0927842i | \(-0.0295767\pi\) |
−0.0927842 | + | 0.995686i | \(0.529577\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.4579 | − | 16.4579i | −0.778430 | − | 0.778430i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.82475i | 0.369273i | 0.982807 | + | 0.184636i | \(0.0591108\pi\) | ||||
−0.982807 | + | 0.184636i | \(0.940889\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.2054i | 0.810172i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.77817 | − | 7.77817i | 0.365451 | − | 0.365451i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.86840 | + | 5.86840i | −0.274512 | + | 0.274512i | −0.830914 | − | 0.556401i | \(-0.812182\pi\) |
0.556401 | + | 0.830914i | \(0.312182\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.00000i | 0.0933520i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.6219i | 1.00703i | 0.863986 | + | 0.503515i | \(0.167960\pi\) | ||||
−0.863986 | + | 0.503515i | \(0.832040\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.7783 | + | 14.7783i | 0.686807 | + | 0.686807i | 0.961525 | − | 0.274718i | \(-0.0885845\pi\) |
−0.274718 | + | 0.961525i | \(0.588585\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.388792 | − | 0.388792i | −0.0179911 | − | 0.0179911i | 0.698054 | − | 0.716045i | \(-0.254050\pi\) |
−0.716045 | + | 0.698054i | \(0.754050\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.95807 | + | 10.4124i | 0.228942 | + | 0.480799i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.8248 | −0.498778 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.07210 | − | 2.07210i | −0.0952751 | − | 0.0952751i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.71492 | + | 3.71492i | −0.170095 | + | 0.170095i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.2487 | 1.10795 | 0.553976 | − | 0.832533i | \(-0.313110\pi\) | ||||
0.553976 | + | 0.832533i | \(0.313110\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 9.43996i | − | 0.430425i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.370403 | − | 1.04381i | 0.0168539 | − | 0.0474950i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.4110 | − | 15.4110i | 0.698341 | − | 0.698341i | −0.265712 | − | 0.964052i | \(-0.585607\pi\) |
0.964052 | + | 0.265712i | \(0.0856070\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22.2131 | 1.00451 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.9244 | 1.30534 | 0.652670 | − | 0.757642i | \(-0.273649\pi\) | ||||
0.652670 | + | 0.757642i | \(0.273649\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.02542 | + | 1.02542i | −0.0461827 | + | 0.0461827i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.20650 | + | 23.1262i | −0.368112 | + | 1.03735i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 9.17525i | − | 0.410741i | −0.978684 | − | 0.205370i | \(-0.934160\pi\) | ||
0.978684 | − | 0.205370i | \(-0.0658399\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.5498 | 0.471332 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.48528 | − | 8.48528i | 0.378340 | − | 0.378340i | −0.492163 | − | 0.870503i | \(-0.663794\pi\) |
0.870503 | + | 0.492163i | \(0.163794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.72993 | + | 3.72993i | 0.165652 | + | 0.165652i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.3205 | −0.767718 | −0.383859 | − | 0.923392i | \(-0.625405\pi\) | ||||
−0.383859 | + | 0.923392i | \(0.625405\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.3746 | − | 23.8876i | −0.503182 | − | 1.05673i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.52076 | − | 1.52076i | −0.0671431 | − | 0.0671431i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.63143 | + | 4.63143i | 0.203690 | + | 0.203690i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.0997i | 0.838382i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.0142i | 1.40257i | 0.712883 | + | 0.701283i | \(0.247389\pi\) | ||||
−0.712883 | + | 0.701283i | \(0.752611\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.1343 | − | 20.1343i | 0.880413 | − | 0.880413i | −0.113163 | − | 0.993576i | \(-0.536098\pi\) |
0.993576 | + | 0.113163i | \(0.0360983\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.85746 | − | 1.85746i | 0.0809123 | − | 0.0809123i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 22.8248i | − | 0.992381i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.71780i | 0.378320i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.8810 | − | 15.8810i | −0.687882 | − | 0.687882i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.26806 | − | 5.26806i | −0.227334 | − | 0.227334i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17.7967 | − | 14.4502i | −0.766557 | − | 0.622413i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.1993 | −1.42735 | −0.713676 | − | 0.700476i | \(-0.752971\pi\) | ||||
−0.713676 | + | 0.700476i | \(0.752971\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.19417 | + | 2.19417i | 0.0941607 | + | 0.0941607i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.19499 | − | 5.19499i | 0.222122 | − | 0.222122i | −0.587270 | − | 0.809391i | \(-0.699797\pi\) |
0.809391 | + | 0.587270i | \(0.199797\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.31342 | 0.0560556 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1.55942i | − | 0.0664335i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 29.4840 | + | 10.4626i | 1.25379 | + | 0.444915i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.9318 | − | 16.9318i | 0.717423 | − | 0.717423i | −0.250654 | − | 0.968077i | \(-0.580646\pi\) |
0.968077 | + | 0.250654i | \(0.0806455\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.82518 | 0.161788 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.54983 | −0.276534 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.4102 | + | 19.4102i | −0.818042 | + | 0.818042i | −0.985824 | − | 0.167782i | \(-0.946340\pi\) |
0.167782 | + | 0.985824i | \(0.446340\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.884806 | − | 2.49342i | 0.0371583 | − | 0.104714i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 41.8248i | 1.75338i | 0.481051 | + | 0.876692i | \(0.340255\pi\) | ||||
−0.481051 | + | 0.876692i | \(0.659745\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.0997 | 0.757448 | 0.378724 | − | 0.925510i | \(-0.376363\pi\) | ||||
0.378724 | + | 0.925510i | \(0.376363\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.87407 | + | 8.87407i | −0.370720 | + | 0.370720i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.67968 | − | 8.67968i | −0.361340 | − | 0.361340i | 0.502966 | − | 0.864306i | \(-0.332242\pi\) |
−0.864306 | + | 0.502966i | \(0.832242\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.1676 | −0.796580 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.8248 | − | 39.5336i | −0.780982 | − | 1.64013i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.1661 | − | 12.1661i | −0.503867 | − | 0.503867i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.63143 | − | 4.63143i | −0.191160 | − | 0.191160i | 0.605037 | − | 0.796197i | \(-0.293158\pi\) |
−0.796197 | + | 0.605037i | \(0.793158\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.82475i | 0.116392i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 17.0170i | − | 0.699985i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.1421 | − | 14.1421i | 0.580748 | − | 0.580748i | −0.354361 | − | 0.935109i | \(-0.615302\pi\) |
0.935109 | + | 0.354361i | \(0.115302\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.7267 | + | 10.7267i | −0.439014 | + | 0.439014i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.3746i | 0.914201i | 0.889415 | + | 0.457100i | \(0.151112\pi\) | ||||
−0.889415 | + | 0.457100i | \(0.848888\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.0027i | 0.979091i | 0.871978 | + | 0.489546i | \(0.162837\pi\) | ||||
−0.871978 | + | 0.489546i | \(0.837163\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.08221 | − | 3.08221i | −0.125517 | − | 0.125517i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.40902 | − | 5.40902i | −0.219545 | − | 0.219545i | 0.588762 | − | 0.808307i | \(-0.299616\pi\) |
−0.808307 | + | 0.588762i | \(0.799616\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.73205 | − | 0.824752i | 0.0701862 | − | 0.0334206i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.54983 | −0.345889 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.7713 | − | 29.7713i | −1.20245 | − | 1.20245i | −0.973419 | − | 0.229031i | \(-0.926444\pi\) |
−0.229031 | − | 0.973419i | \(-0.573556\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.27637 | − | 5.27637i | 0.212419 | − | 0.212419i | −0.592875 | − | 0.805294i | \(-0.702007\pi\) |
0.805294 | + | 0.592875i | \(0.202007\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.12654 | 0.326633 | 0.163317 | − | 0.986574i | \(-0.447781\pi\) | ||||
0.163317 | + | 0.986574i | \(0.447781\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.418627i | 0.0167989i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.1679 | − | 45.5618i | 0.647754 | − | 1.82539i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.98036 | − | 4.98036i | 0.198896 | − | 0.198896i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.41644 | −0.176095 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.0000 | −1.15447 | −0.577236 | − | 0.816577i | \(-0.695869\pi\) | ||||
−0.577236 | + | 0.816577i | \(0.695869\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.21982 | + | 1.21982i | −0.0484834 | + | 0.0484834i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 29.7646 | − | 3.08891i | 1.17932 | − | 0.122387i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 9.27492i | − | 0.366910i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.2749 | −0.524328 | −0.262164 | − | 0.965023i | \(-0.584436\pi\) | ||||
−0.262164 | + | 0.965023i | \(0.584436\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.3542 | + | 21.3542i | −0.842126 | + | 0.842126i | −0.989135 | − | 0.147009i | \(-0.953035\pi\) |
0.147009 | + | 0.989135i | \(0.453035\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.7481 | − | 17.7481i | −0.697752 | − | 0.697752i | 0.266174 | − | 0.963925i | \(-0.414241\pi\) |
−0.963925 | + | 0.266174i | \(0.914241\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −28.5501 | −1.12069 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.13746 | + | 1.49397i | −0.122967 | + | 0.0585531i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.0235 | + | 14.0235i | 0.548783 | + | 0.548783i | 0.926089 | − | 0.377306i | \(-0.123149\pi\) |
−0.377306 | + | 0.926089i | \(0.623149\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.07107 | + | 7.07107i | 0.275869 | + | 0.275869i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 33.0997i | − | 1.28938i | −0.764444 | − | 0.644690i | \(-0.776986\pi\) | ||
0.764444 | − | 0.644690i | \(-0.223014\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.8038i | 1.31481i | 0.753536 | + | 0.657407i | \(0.228347\pi\) | ||||
−0.753536 | + | 0.657407i | \(0.771653\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.04565 | − | 6.04565i | 0.234793 | − | 0.234793i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.214635 | + | 0.214635i | −0.00831068 | + | 0.00831068i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.82475i | 0.186536i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.30136i | 0.166052i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.26709 | + | 7.26709i | 0.280126 | + | 0.280126i | 0.833159 | − | 0.553033i | \(-0.186530\pi\) |
−0.553033 | + | 0.833159i | \(0.686530\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.26806 | − | 5.26806i | −0.202468 | − | 0.202468i | 0.598589 | − | 0.801057i | \(-0.295728\pi\) |
−0.801057 | + | 0.598589i | \(0.795728\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.5443 | + | 11.6873i | −0.941925 | + | 0.448517i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.6495 | 0.752971 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.7275 | + | 13.7275i | 0.525269 | + | 0.525269i | 0.919158 | − | 0.393889i | \(-0.128871\pi\) |
−0.393889 | + | 0.919158i | \(0.628871\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.86923 | − | 8.86923i | 0.338382 | − | 0.338382i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.4591 | 0.855624 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 47.7753i | − | 1.81746i | −0.417388 | − | 0.908728i | \(-0.637055\pi\) | ||
0.417388 | − | 0.908728i | \(-0.362945\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.16573 | + | 2.89767i | 0.310190 | + | 0.110073i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.42985 | + | 7.42985i | −0.281426 | + | 0.281426i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.13642 | −0.345571 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −45.2990 | −1.71092 | −0.855460 | − | 0.517869i | \(-0.826725\pi\) | ||||
−0.855460 | + | 0.517869i | \(0.826725\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.35817 | − | 3.35817i | 0.126656 | − | 0.126656i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.3625 | − | 6.87092i | −0.728202 | − | 0.258408i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 4.27492i | − | 0.160548i | −0.996773 | − | 0.0802739i | \(-0.974420\pi\) | ||
0.996773 | − | 0.0802739i | \(-0.0255795\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.8248 | −0.443463 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.388792 | − | 0.388792i | 0.0145604 | − | 0.0145604i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.43444 | − | 6.43444i | −0.240298 | − | 0.240298i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.2443 | 1.20251 | 0.601256 | − | 0.799057i | \(-0.294667\pi\) | ||||
0.601256 | + | 0.799057i | \(0.294667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.45017 | − | 15.6460i | −0.277459 | − | 0.582688i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19.9326 | − | 19.9326i | −0.741302 | − | 0.741302i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.7710 | − | 20.7710i | −0.770353 | − | 0.770353i | 0.207815 | − | 0.978168i | \(-0.433365\pi\) |
−0.978168 | + | 0.207815i | \(0.933365\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1.78959i | − | 0.0661905i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.5818 | − | 16.5818i | 0.612462 | − | 0.612462i | −0.331125 | − | 0.943587i | \(-0.607428\pi\) |
0.943587 | + | 0.331125i | \(0.107428\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.0940 | − | 10.0940i | 0.371816 | − | 0.371816i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.6254i | 0.501219i | 0.968088 | + | 0.250609i | \(0.0806310\pi\) | ||||
−0.968088 | + | 0.250609i | \(0.919369\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.19397i | 0.337749i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.30695 | − | 4.30695i | −0.158007 | − | 0.158007i | 0.623676 | − | 0.781683i | \(-0.285638\pi\) |
−0.781683 | + | 0.623676i | \(0.785638\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.7025 | + | 11.7025i | 0.428172 | + | 0.428172i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.92820 | − | 14.5498i | −0.253151 | − | 0.531639i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.0000 | 0.875772 | 0.437886 | − | 0.899030i | \(-0.355727\pi\) | ||||
0.437886 | + | 0.899030i | \(0.355727\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.30695 | − | 4.30695i | −0.156954 | − | 0.156954i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.16524 | + | 9.16524i | −0.333116 | + | 0.333116i | −0.853769 | − | 0.520652i | \(-0.825689\pi\) |
0.520652 | + | 0.853769i | \(0.325689\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.37097 | −0.0497630 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.8564i | 0.502294i | 0.967949 | + | 0.251147i | \(0.0808078\pi\) | ||||
−0.967949 | + | 0.251147i | \(0.919192\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.49342 | + | 0.884806i | 0.0902677 | + | 0.0320321i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 26.3524 | − | 26.3524i | 0.951529 | − | 0.951529i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.8591 | 1.36523 | 0.682617 | − | 0.730776i | \(-0.260842\pi\) | ||||
0.682617 | + | 0.730776i | \(0.260842\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.09967 | 0.183660 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.9706 | + | 16.9706i | −0.610389 | + | 0.610389i | −0.943047 | − | 0.332659i | \(-0.892054\pi\) |
0.332659 | + | 0.943047i | \(0.392054\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.50601 | + | 1.95385i | 0.197527 | + | 0.0700939i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 11.2990i | − | 0.404829i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.3746 | 1.08689 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.512711 | + | 0.512711i | −0.0183228 | + | 0.0183228i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.3770 | + | 24.3770i | 0.868945 | + | 0.868945i | 0.992356 | − | 0.123410i | \(-0.0393831\pi\) |
−0.123410 | + | 0.992356i | \(0.539383\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.97368 | −0.355072 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 38.3746 | − | 18.2728i | 1.36444 | − | 0.649708i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.97025 | − | 3.97025i | −0.140988 | − | 0.140988i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.1167 | + | 13.1167i | 0.464618 | + | 0.464618i | 0.900166 | − | 0.435548i | \(-0.143445\pi\) |
−0.435548 | + | 0.900166i | \(0.643445\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.00000i | 0.141510i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18.2728i | 0.645639i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −23.1572 | + | 23.1572i | −0.817198 | + | 0.817198i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.8395 | + | 12.8395i | −0.451971 | + | 0.451971i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.72508i | 0.236441i | 0.992987 | + | 0.118221i | \(0.0377190\pi\) | ||||
−0.992987 | + | 0.118221i | \(0.962281\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.4712i | 0.683726i | 0.939750 | + | 0.341863i | \(0.111058\pi\) | ||||
−0.939750 | + | 0.341863i | \(0.888942\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.9624 | + | 15.9624i | 0.559825 | + | 0.559825i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.36077 | + | 1.36077i | 0.0476073 | + | 0.0476073i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.2118 | + | 4.86254i | −0.356828 | + | 0.169911i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34.0000 | −1.18661 | −0.593304 | − | 0.804978i | \(-0.702177\pi\) | ||||
−0.593304 | + | 0.804978i | \(0.702177\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.20510 | − | 6.20510i | −0.216296 | − | 0.216296i | 0.590639 | − | 0.806936i | \(-0.298876\pi\) |
−0.806936 | + | 0.590639i | \(0.798876\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.2011 | + | 37.2011i | −1.29361 | + | 1.29361i | −0.361072 | + | 0.932538i | \(0.617589\pi\) |
−0.932538 | + | 0.361072i | \(0.882411\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.7084 | −1.24021 | −0.620103 | − | 0.784521i | \(-0.712909\pi\) | ||||
−0.620103 | + | 0.784521i | \(0.712909\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 5.61478i | − | 0.194775i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.44513 | − | 13.9252i | −0.0500708 | − | 0.482480i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.928731 | − | 0.928731i | 0.0321016 | − | 0.0321016i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.2252 | 0.663727 | 0.331864 | − | 0.943327i | \(-0.392323\pi\) | ||||
0.331864 | + | 0.943327i | \(0.392323\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.4743 | 0.981871 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.99799 | + | 8.99799i | −0.309907 | + | 0.309907i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.243248 | − | 0.685483i | 0.00835811 | − | 0.0235535i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 26.8248i | − | 0.920623i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.924421 | −0.0316887 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.2360 | + | 24.2360i | −0.829826 | + | 0.829826i | −0.987492 | − | 0.157667i | \(-0.949603\pi\) |
0.157667 | + | 0.987492i | \(0.449603\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.26286 | + | 9.26286i | 0.316413 | + | 0.316413i | 0.847388 | − | 0.530974i | \(-0.178174\pi\) |
−0.530974 | + | 0.847388i | \(0.678174\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −51.3544 | −1.75219 | −0.876096 | − | 0.482138i | \(-0.839861\pi\) | ||||
−0.876096 | + | 0.482138i | \(0.839861\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.5498 | − | 5.97586i | 0.427697 | − | 0.203657i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.7713 | + | 29.7713i | 1.01343 | + | 1.01343i | 0.999909 | + | 0.0135172i | \(0.00430278\pi\) |
0.0135172 | + | 0.999909i | \(0.495697\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.19239 | + | 9.19239i | 0.312190 | + | 0.312190i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 38.7251i | − | 1.31366i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.6339i | 0.631387i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.26546 | − | 7.26546i | 0.245899 | − | 0.245899i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.0555 | + | 23.0555i | −0.778530 | + | 0.778530i | −0.979581 | − | 0.201051i | \(-0.935564\pi\) |
0.201051 | + | 0.979581i | \(0.435564\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.0997i | 0.509299i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 45.1484i | − | 1.52109i | −0.649286 | − | 0.760544i | \(-0.724932\pi\) | ||
0.649286 | − | 0.760544i | \(-0.275068\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.9834 | − | 20.9834i | −0.706148 | − | 0.706148i | 0.259575 | − | 0.965723i | \(-0.416418\pi\) |
−0.965723 | + | 0.259575i | \(0.916418\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.26806 | + | 5.26806i | 0.176884 | + | 0.176884i | 0.789996 | − | 0.613112i | \(-0.210083\pi\) |
−0.613112 | + | 0.789996i | \(0.710083\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.2849 | + | 32.0997i | 0.512640 | + | 1.07659i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.27492 | −0.109714 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.04152 | − | 3.04152i | −0.101780 | − | 0.101780i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.26543 | − | 1.26543i | 0.0422516 | − | 0.0422516i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.952341 | 0.0317624 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 10.5074i | − | 0.350052i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.791722 | + | 2.23110i | −0.0263469 | + | 0.0742464i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.2082 | + | 22.2082i | −0.737410 | + | 0.737410i | −0.972076 | − | 0.234666i | \(-0.924600\pi\) |
0.234666 | + | 0.972076i | \(0.424600\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.76546 | 0.257564 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.7251 | −0.421601 | −0.210800 | − | 0.977529i | \(-0.567607\pi\) | ||||
−0.210800 | + | 0.977529i | \(0.567607\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −38.3247 | + | 38.3247i | −1.26836 | + | 1.26836i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 49.7370 | + | 17.6495i | 1.64246 | + | 0.582839i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.2990i | 1.19739i | 0.800976 | + | 0.598697i | \(0.204315\pi\) | ||||
−0.800976 | + | 0.598697i | \(0.795685\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.7251 | 0.518159 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −28.0364 | + | 28.0364i | −0.922830 | + | 0.922830i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.63143 | + | 4.63143i | 0.152116 | + | 0.152116i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −39.7796 | −1.30513 | −0.652564 | − | 0.757734i | \(-0.726306\pi\) | ||||
−0.652564 | + | 0.757734i | \(0.726306\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.6873 | + | 9.48960i | 0.383036 | + | 0.311009i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23.3922 | − | 23.3922i | −0.765827 | − | 0.765827i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.6248 | + | 24.6248i | 0.804458 | + | 0.804458i | 0.983789 | − | 0.179331i | \(-0.0573933\pi\) |
−0.179331 | + | 0.983789i | \(0.557393\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.7251i | 0.904774i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.65037i | 0.249395i | 0.992195 | + | 0.124697i | \(0.0397960\pi\) | ||||
−0.992195 | + | 0.124697i | \(0.960204\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.55517 | + | 1.55517i | −0.0506432 | + | 0.0506432i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.71658 | − | 9.71658i | 0.315746 | − | 0.315746i | −0.531384 | − | 0.847131i | \(-0.678328\pi\) |
0.847131 | + | 0.531384i | \(0.178328\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 42.7492i | − | 1.38770i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.8109i | 0.350568i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.42057 | − | 9.42057i | −0.305162 | − | 0.305162i | 0.537867 | − | 0.843029i | \(-0.319230\pi\) |
−0.843029 | + | 0.537867i | \(0.819230\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.67909 | − | 1.67909i | −0.0542771 | − | 0.0542771i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24.7249 | − | 51.9244i | −0.798408 | − | 1.67673i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.2749 | 0.944352 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.30695 | + | 4.30695i | 0.138790 | + | 0.138790i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.5763 | + | 24.5763i | −0.790320 | + | 0.790320i | −0.981546 | − | 0.191226i | \(-0.938754\pi\) |
0.191226 | + | 0.981546i | \(0.438754\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.30136 | 0.138179 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 25.9232i | − | 0.831916i | −0.909384 | − | 0.415958i | \(-0.863446\pi\) | ||
0.909384 | − | 0.415958i | \(-0.136554\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.06506 | − | 8.63744i | 0.0982612 | − | 0.276904i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.0328 | + | 12.0328i | −0.384964 | + | 0.384964i | −0.872887 | − | 0.487923i | \(-0.837755\pi\) |
0.487923 | + | 0.872887i | \(0.337755\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −59.8421 | −1.91256 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.00000 | −0.0319275 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.6170 | + | 30.6170i | −0.976531 | + | 0.976531i | −0.999731 | − | 0.0231995i | \(-0.992615\pi\) |
0.0231995 | + | 0.999731i | \(0.492615\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.76961 | − | 4.98683i | 0.0563274 | − | 0.158733i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 0.374586i | − | 0.0119111i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.5498 | −0.684553 | −0.342277 | − | 0.939599i | \(-0.611198\pi\) | ||||
−0.342277 | + | 0.939599i | \(0.611198\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.33594 | + | 7.33594i | −0.232799 | + | 0.232799i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.0312 | − | 32.0312i | −1.01444 | − | 1.01444i | −0.999894 | − | 0.0145452i | \(-0.995370\pi\) |
−0.0145452 | − | 0.999894i | \(-0.504630\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.20822 | −0.0698650 |
(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 | 2100.2.x.c.1693.3 | yes | 16 | |
5.2 | odd | 4 | inner | 2100.2.x.c.1357.5 | yes | 16 | |
5.3 | odd | 4 | inner | 2100.2.x.c.1357.4 | yes | 16 | |
5.4 | even | 2 | inner | 2100.2.x.c.1693.6 | yes | 16 | |
7.6 | odd | 2 | inner | 2100.2.x.c.1693.5 | yes | 16 | |
35.13 | even | 4 | inner | 2100.2.x.c.1357.6 | yes | 16 | |
35.27 | even | 4 | inner | 2100.2.x.c.1357.3 | ✓ | 16 | |
35.34 | odd | 2 | inner | 2100.2.x.c.1693.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.x.c.1357.3 | ✓ | 16 | 35.27 | even | 4 | inner | |
2100.2.x.c.1357.4 | yes | 16 | 5.3 | odd | 4 | inner | |
2100.2.x.c.1357.5 | yes | 16 | 5.2 | odd | 4 | inner | |
2100.2.x.c.1357.6 | yes | 16 | 35.13 | even | 4 | inner | |
2100.2.x.c.1693.3 | yes | 16 | 1.1 | even | 1 | trivial | |
2100.2.x.c.1693.4 | yes | 16 | 35.34 | odd | 2 | inner | |
2100.2.x.c.1693.5 | yes | 16 | 7.6 | odd | 2 | inner | |
2100.2.x.c.1693.6 | yes | 16 | 5.4 | even | 2 | inner |