Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(1065,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.1065");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.d (of order \(2\), degree \(1\), 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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 39 x^{18} + 531 x^{16} + 3488 x^{14} + 12661 x^{12} + 27027 x^{10} + 34540 x^{8} + 25909 x^{6} + \cdots + 144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1065.5 | ||
Root | \(1.20144i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1148.1065 |
Dual form | 1148.2.d.a.1065.16 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | − | 2.23543i | − | 1.29062i | −0.763919 | − | 0.645312i | \(-0.776727\pi\) | ||
0.763919 | − | 0.645312i | \(-0.223273\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.468853 | 0.209677 | 0.104839 | − | 0.994489i | \(-0.466567\pi\) | ||||
0.104839 | + | 0.994489i | \(0.466567\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.99714 | −0.665713 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.98364i | 1.50263i | 0.659946 | + | 0.751313i | \(0.270579\pi\) | ||||
−0.659946 | + | 0.751313i | \(0.729421\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.78611i | 1.05008i | 0.851078 | + | 0.525039i | \(0.175949\pi\) | ||||
−0.851078 | + | 0.525039i | \(0.824051\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1.04809i | − | 0.270615i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.22201i | 0.296381i | 0.988959 | + | 0.148191i | \(0.0473449\pi\) | ||||
−0.988959 | + | 0.148191i | \(0.952655\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.89875i | 1.81210i | 0.423173 | + | 0.906049i | \(0.360916\pi\) | ||||
−0.423173 | + | 0.906049i | \(0.639084\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.23543 | 0.487810 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.249482 | −0.0520206 | −0.0260103 | − | 0.999662i | \(-0.508280\pi\) | ||||
−0.0260103 | + | 0.999662i | \(0.508280\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.78018 | −0.956035 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 2.24183i | − | 0.431440i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.31531i | 1.54411i | 0.635553 | + | 0.772057i | \(0.280772\pi\) | ||||
−0.635553 | + | 0.772057i | \(0.719228\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.17006 | 0.569360 | 0.284680 | − | 0.958623i | \(-0.408113\pi\) | ||||
0.284680 | + | 0.958623i | \(0.408113\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 11.1406 | 1.93933 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.468853i | 0.0792506i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.74950 | −1.27401 | −0.637005 | − | 0.770860i | \(-0.719827\pi\) | ||||
−0.637005 | + | 0.770860i | \(0.719827\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.46357 | 1.35526 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.82365 | − | 5.13612i | −0.597153 | − | 0.802127i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.90962 | 0.748711 | 0.374355 | − | 0.927285i | \(-0.377864\pi\) | ||||
0.374355 | + | 0.927285i | \(0.377864\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.936364 | −0.139585 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.80770i | 0.263680i | 0.991271 | + | 0.131840i | \(0.0420885\pi\) | ||||
−0.991271 | + | 0.131840i | \(0.957911\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.73172 | 0.382517 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1.74173i | − | 0.239244i | −0.992819 | − | 0.119622i | \(-0.961832\pi\) | ||
0.992819 | − | 0.119622i | \(-0.0381683\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.33660i | 0.315066i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 17.6571 | 2.33874 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.25456 | 0.293519 | 0.146760 | − | 0.989172i | \(-0.453116\pi\) | ||||
0.146760 | + | 0.989172i | \(0.453116\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.09904 | −0.140718 | −0.0703589 | − | 0.997522i | \(-0.522414\pi\) | ||||
−0.0703589 | + | 0.997522i | \(0.522414\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.99714i | − | 0.251616i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.77513i | 0.220177i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 11.8286i | − | 1.44509i | −0.691323 | − | 0.722545i | \(-0.742972\pi\) | ||
0.691323 | − | 0.722545i | \(-0.257028\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.557699i | 0.0671391i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.3547i | − | 1.46624i | −0.680100 | − | 0.733119i | \(-0.738064\pi\) | ||
0.680100 | − | 0.733119i | \(-0.261936\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.91035 | −0.340630 | −0.170315 | − | 0.985390i | \(-0.554479\pi\) | ||||
−0.170315 | + | 0.985390i | \(0.554479\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.6857i | 1.23388i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.98364 | −0.567939 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3.79118i | − | 0.426542i | −0.976993 | − | 0.213271i | \(-0.931588\pi\) | ||
0.976993 | − | 0.213271i | \(-0.0684117\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0029 | −1.22254 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.75742 | 0.961252 | 0.480626 | − | 0.876926i | \(-0.340410\pi\) | ||||
0.480626 | + | 0.876926i | \(0.340410\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.572943i | 0.0621444i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 18.5883 | 1.99287 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.9289i | 1.68846i | 0.535982 | + | 0.844229i | \(0.319941\pi\) | ||||
−0.535982 | + | 0.844229i | \(0.680059\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.78611 | −0.396892 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 7.08645i | − | 0.734831i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.70335i | 0.379956i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.29519i | 0.436111i | 0.975936 | + | 0.218055i | \(0.0699713\pi\) | ||||
−0.975936 | + | 0.218055i | \(0.930029\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 9.95302i | − | 1.00032i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 4.42421i | − | 0.440225i | −0.975474 | − | 0.220113i | \(-0.929358\pi\) | ||
0.975474 | − | 0.220113i | \(-0.0706425\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.9664 | 1.47469 | 0.737343 | − | 0.675519i | \(-0.236080\pi\) | ||||
0.737343 | + | 0.675519i | \(0.236080\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.04809 | 0.102283 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.4446 | 1.68644 | 0.843218 | − | 0.537572i | \(-0.180658\pi\) | ||||
0.843218 | + | 0.537572i | \(0.180658\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 5.31886i | − | 0.509455i | −0.967013 | − | 0.254727i | \(-0.918014\pi\) | ||
0.967013 | − | 0.254727i | \(-0.0819857\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17.3234i | 1.64427i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.843987 | 0.0793957 | 0.0396978 | − | 0.999212i | \(-0.487360\pi\) | ||||
0.0396978 | + | 0.999212i | \(0.487360\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.116970 | −0.0109075 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 7.56138i | − | 0.699050i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.22201 | −0.112022 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.8367 | −1.25788 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.4814 | + | 8.54748i | −1.03525 | + | 0.770701i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.58546 | −0.410136 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.18810 | −0.726576 | −0.363288 | − | 0.931677i | \(-0.618346\pi\) | ||||
−0.363288 | + | 0.931677i | \(0.618346\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 10.9751i | − | 0.966304i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.65452 | 0.494038 | 0.247019 | − | 0.969011i | \(-0.420549\pi\) | ||||
0.247019 | + | 0.969011i | \(0.420549\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.89875 | −0.684909 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 1.05109i | − | 0.0904631i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 3.57141i | − | 0.305126i | −0.988294 | − | 0.152563i | \(-0.951247\pi\) | ||
0.988294 | − | 0.152563i | \(-0.0487528\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.9095 | 1.77352 | 0.886759 | − | 0.462232i | \(-0.152951\pi\) | ||||
0.886759 | + | 0.462232i | \(0.152951\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.04098 | 0.340312 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −18.8686 | −1.57787 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.89866i | 0.323766i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.23543i | 0.184375i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.6546i | 1.20055i | 0.799792 | + | 0.600277i | \(0.204943\pi\) | ||||
−0.799792 | + | 0.600277i | \(0.795057\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1.70827i | − | 0.139017i | −0.997581 | − | 0.0695087i | \(-0.977857\pi\) | ||
0.997581 | − | 0.0695087i | \(-0.0221431\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.44052i | − | 0.197305i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.48629 | 0.119382 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 14.1603i | − | 1.13011i | −0.825052 | − | 0.565057i | \(-0.808854\pi\) | ||
0.825052 | − | 0.565057i | \(-0.191146\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.89350 | −0.308775 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 0.249482i | − | 0.0196619i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.0614 | −1.57133 | −0.785664 | − | 0.618654i | \(-0.787678\pi\) | ||||
−0.785664 | + | 0.618654i | \(0.787678\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.22329 | 0.406633 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.5991i | 0.974946i | 0.873138 | + | 0.487473i | \(0.162081\pi\) | ||||
−0.873138 | + | 0.487473i | \(0.837919\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.33461 | −0.102662 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 15.7749i | − | 1.20634i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.134256 | 0.0102073 | 0.00510364 | − | 0.999987i | \(-0.498375\pi\) | ||||
0.00510364 | + | 0.999987i | \(0.498375\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4.78018i | − | 0.361347i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 5.03992i | − | 0.378823i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 14.9327i | − | 1.11613i | −0.829799 | − | 0.558063i | \(-0.811545\pi\) | ||
0.829799 | − | 0.558063i | \(-0.188455\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.6490i | 1.68349i | 0.539878 | + | 0.841744i | \(0.318471\pi\) | ||||
−0.539878 | + | 0.841744i | \(0.681529\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.45683i | 0.181614i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.63337 | −0.267131 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.09007 | −0.445350 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.24183 | 0.163069 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.7885i | 1.43185i | 0.698178 | + | 0.715924i | \(0.253994\pi\) | ||||
−0.698178 | + | 0.715924i | \(0.746006\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 23.4346i | − | 1.68686i | −0.537237 | − | 0.843431i | \(-0.680532\pi\) | ||
0.537237 | − | 0.843431i | \(-0.319468\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.96817 | 0.284166 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.6808 | 1.11721 | 0.558606 | − | 0.829433i | \(-0.311336\pi\) | ||||
0.558606 | + | 0.829433i | \(0.311336\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.6879i | 1.32475i | 0.749171 | + | 0.662376i | \(0.230452\pi\) | ||||
−0.749171 | + | 0.662376i | \(0.769548\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −26.4419 | −1.86507 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.31531 | −0.583621 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.79273 | − | 2.40808i | −0.125209 | − | 0.168188i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.498250 | 0.0346308 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −39.3646 | −2.72290 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 17.8016i | − | 1.22551i | −0.790272 | − | 0.612756i | \(-0.790061\pi\) | ||
0.790272 | − | 0.612756i | \(-0.209939\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −27.6181 | −1.89236 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.30189 | 0.156988 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.17006i | 0.215198i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.50587i | 0.439626i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.62666 | −0.311223 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.4729 | −1.23704 | −0.618518 | − | 0.785771i | \(-0.712267\pi\) | ||||
−0.618518 | + | 0.785771i | \(0.712267\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.54667 | 0.636445 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 11.1615i | − | 0.740816i | −0.928869 | − | 0.370408i | \(-0.879218\pi\) | ||
0.928869 | − | 0.370408i | \(-0.120782\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.2692i | 0.810774i | 0.914145 | + | 0.405387i | \(0.132863\pi\) | ||||
−0.914145 | + | 0.405387i | \(0.867137\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.1406i | 0.732996i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.38249i | 0.352619i | 0.984335 | + | 0.176309i | \(0.0564159\pi\) | ||||
−0.984335 | + | 0.176309i | \(0.943584\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.847545i | 0.0552878i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.47492 | −0.550505 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.79783i | 0.116292i | 0.998308 | + | 0.0581461i | \(0.0185189\pi\) | ||||
−0.998308 | + | 0.0581461i | \(0.981481\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.4358 | −1.05873 | −0.529363 | − | 0.848396i | \(-0.677569\pi\) | ||||
−0.529363 | + | 0.848396i | \(0.677569\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 17.8706i | 1.14640i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.468853 | −0.0299539 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −29.9055 | −1.90284 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 19.5766i | − | 1.24062i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.8489 | 1.31597 | 0.657986 | − | 0.753031i | \(-0.271409\pi\) | ||||
0.657986 | + | 0.753031i | \(0.271409\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 1.24333i | − | 0.0781675i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.28077 | 0.0802051 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 11.7446i | − | 0.732606i | −0.930496 | − | 0.366303i | \(-0.880623\pi\) | ||
0.930496 | − | 0.366303i | \(-0.119377\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 7.74950i | − | 0.481530i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 16.6068i | − | 1.02794i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.4258i | 1.32117i | 0.750750 | + | 0.660586i | \(0.229692\pi\) | ||||
−0.750750 | + | 0.660586i | \(0.770308\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.816613i | − | 0.0501641i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 35.6079 | 2.17917 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.9515 | 0.972580 | 0.486290 | − | 0.873797i | \(-0.338350\pi\) | ||||
0.486290 | + | 0.873797i | \(0.338350\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.5899 | −1.49373 | −0.746865 | − | 0.664976i | \(-0.768442\pi\) | ||||
−0.746865 | + | 0.664976i | \(0.768442\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.46357i | 0.512239i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 23.8227i | − | 1.43656i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 31.9459 | 1.91944 | 0.959721 | − | 0.280956i | \(-0.0906514\pi\) | ||||
0.959721 | + | 0.280956i | \(0.0906514\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.33106 | −0.379030 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 14.0011i | − | 0.835235i | −0.908623 | − | 0.417618i | \(-0.862865\pi\) | ||
0.908623 | − | 0.417618i | \(-0.137135\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.43345 | 0.0852097 | 0.0426049 | − | 0.999092i | \(-0.486434\pi\) | ||||
0.0426049 | + | 0.999092i | \(0.486434\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.27858 | 0.490381 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.13612 | − | 3.82365i | 0.303176 | − | 0.225703i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.5067 | 0.912158 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.60159 | 0.562855 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 14.0309i | − | 0.819695i | −0.912154 | − | 0.409847i | \(-0.865582\pi\) | ||
0.912154 | − | 0.409847i | \(-0.134418\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.05706 | 0.0615444 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.1725 | 0.648292 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 0.944566i | − | 0.0546257i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.90962i | 0.282986i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.89000 | −0.568166 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.515289 | −0.0295053 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.11435 | −0.348964 | −0.174482 | − | 0.984660i | \(-0.555825\pi\) | ||||
−0.174482 | + | 0.984660i | \(0.555825\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 33.4564i | − | 1.90327i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.22194i | 0.125995i | 0.998014 | + | 0.0629973i | \(0.0200660\pi\) | ||||
−0.998014 | + | 0.0629973i | \(0.979934\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 4.57533i | − | 0.258613i | −0.991605 | − | 0.129307i | \(-0.958725\pi\) | ||
0.991605 | − | 0.129307i | \(-0.0412751\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 0.936364i | − | 0.0527581i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.39003i | 0.415066i | 0.978228 | + | 0.207533i | \(0.0665434\pi\) | ||||
−0.978228 | + | 0.207533i | \(0.933457\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −41.4406 | −2.32023 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 38.9962i | − | 2.17656i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.65236 | −0.537072 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 18.0983i | − | 1.00391i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.8899 | −0.657515 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.80770 | −0.0996617 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 4.35261i | − | 0.239241i | −0.992820 | − | 0.119620i | \(-0.961832\pi\) | ||
0.992820 | − | 0.119620i | \(-0.0381678\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.4768 | 0.848124 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 5.54586i | − | 0.303003i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.788204 | 0.0429362 | 0.0214681 | − | 0.999770i | \(-0.493166\pi\) | ||||
0.0214681 | + | 0.999770i | \(0.493166\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 1.88667i | − | 0.102470i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.7985i | 0.855535i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.261479i | 0.0140775i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.37888i | 0.235070i | 0.993069 | + | 0.117535i | \(0.0374993\pi\) | ||||
−0.993069 | + | 0.117535i | \(0.962501\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.5805 | −0.941061 | −0.470530 | − | 0.882384i | \(-0.655937\pi\) | ||||
−0.470530 | + | 0.882384i | \(0.655937\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.48779 | 0.453045 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.6489 | 1.73773 | 0.868864 | − | 0.495052i | \(-0.164851\pi\) | ||||
0.868864 | + | 0.495052i | \(0.164851\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 5.79255i | − | 0.307437i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.73172i | 0.144578i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.0591 | 1.48090 | 0.740450 | − | 0.672111i | \(-0.234612\pi\) | ||||
0.740450 | + | 0.672111i | \(0.234612\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −43.3903 | −2.28370 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 30.9310i | 1.62345i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.36452 | −0.0714224 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.8918 | 1.03834 | 0.519172 | − | 0.854670i | \(-0.326240\pi\) | ||||
0.519172 | + | 0.854670i | \(0.326240\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.63635 | + | 10.2575i | 0.397532 | + | 0.533986i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.74173 | 0.0904259 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.48402 | 0.128617 | 0.0643087 | − | 0.997930i | \(-0.479516\pi\) | ||||
0.0643087 | + | 0.997930i | \(0.479516\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.2505i | 0.529332i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −31.4827 | −1.62144 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.5135 | −0.591409 | −0.295705 | − | 0.955279i | \(-0.595554\pi\) | ||||
−0.295705 | + | 0.955279i | \(0.595554\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.3039i | 0.937738i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 36.6688i | 1.87369i | 0.349745 | + | 0.936845i | \(0.386268\pi\) | ||||
−0.349745 | + | 0.936845i | \(0.613732\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.33660 | −0.119084 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.80519 | −0.498426 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.4388 | 1.18839 | 0.594197 | − | 0.804319i | \(-0.297470\pi\) | ||||
0.594197 | + | 0.804319i | \(0.297470\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 0.304870i | − | 0.0154179i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 12.6403i | − | 0.637618i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 1.77751i | − | 0.0894361i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 32.4793i | − | 1.63009i | −0.579397 | − | 0.815046i | \(-0.696712\pi\) | ||
0.579397 | − | 0.815046i | \(-0.303288\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 17.6571i | 0.883960i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.98971 | −0.249174 | −0.124587 | − | 0.992209i | \(-0.539761\pi\) | ||||
−0.124587 | + | 0.992209i | \(0.539761\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.0022i | 0.597873i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.15872 | −0.256339 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 38.6207i | − | 1.91436i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.2544 | 1.05096 | 0.525481 | − | 0.850805i | \(-0.323885\pi\) | ||||
0.525481 | + | 0.850805i | \(0.323885\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.98364 | −0.393804 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.25456i | 0.110940i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.10594 | 0.201553 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 46.7416i | − | 2.28895i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.415097 | 0.0202788 | 0.0101394 | − | 0.999949i | \(-0.496772\pi\) | ||||
0.0101394 | + | 0.999949i | \(0.496772\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 24.4243i | − | 1.19037i | −0.803590 | − | 0.595183i | \(-0.797079\pi\) | ||
0.803590 | − | 0.595183i | \(-0.202921\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 3.61023i | − | 0.175535i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 5.84143i | − | 0.283351i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 1.09904i | − | 0.0531863i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 42.1794i | 2.03644i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.4445 | 1.61096 | 0.805482 | − | 0.592620i | \(-0.201907\pi\) | ||||
0.805482 | + | 0.592620i | \(0.201907\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.74246 | 0.275965 | 0.137983 | − | 0.990435i | \(-0.455938\pi\) | ||||
0.137983 | + | 0.990435i | \(0.455938\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.71517 | 0.417860 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 1.97060i | − | 0.0942664i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.9479i | 0.856606i | 0.903635 | + | 0.428303i | \(0.140888\pi\) | ||||
−0.903635 | + | 0.428303i | \(0.859112\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.99714 | 0.0951018 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.7389 | −0.605245 | −0.302622 | − | 0.953111i | \(-0.597862\pi\) | ||||
−0.302622 | + | 0.953111i | \(0.597862\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.46830i | 0.354032i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 32.7593 | 1.54946 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.6046 | −1.58590 | −0.792949 | − | 0.609289i | \(-0.791455\pi\) | ||||
−0.792949 | + | 0.609289i | \(0.791455\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.5966 | − | 19.0557i | 1.20530 | − | 0.897297i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.81872 | −0.179419 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.77513 | −0.0832193 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.3766i | 1.42096i | 0.703718 | + | 0.710480i | \(0.251522\pi\) | ||||
−0.703718 | + | 0.710480i | \(0.748478\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.73954 | 0.127871 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.4830 | −0.488244 | −0.244122 | − | 0.969745i | \(-0.578500\pi\) | ||||
−0.244122 | + | 0.969745i | \(0.578500\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16.9928i | − | 0.789723i | −0.918741 | − | 0.394862i | \(-0.870792\pi\) | ||
0.918741 | − | 0.394862i | \(-0.129208\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 3.32250i | − | 0.154077i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.3701 | 1.17399 | 0.586994 | − | 0.809591i | \(-0.300311\pi\) | ||||
0.586994 | + | 0.809591i | \(0.300311\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.8286 | 0.546193 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −31.6543 | −1.45855 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.4678i | 1.12503i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 37.7574i | − | 1.73243i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.47847i | 0.159268i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.92313i | 0.270635i | 0.990802 | + | 0.135317i | \(0.0432054\pi\) | ||||
−0.990802 | + | 0.135317i | \(0.956795\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 29.3404i | − | 1.33781i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.557699 | −0.0253762 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.01381i | 0.0914425i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.12441 | 0.232209 | 0.116105 | − | 0.993237i | \(-0.462959\pi\) | ||||
0.116105 | + | 0.993237i | \(0.462959\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 44.8457i | 2.02799i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.8111 | 0.848933 | 0.424467 | − | 0.905444i | \(-0.360462\pi\) | ||||
0.424467 | + | 0.905444i | \(0.360462\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.1614 | −0.457646 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 4.66650i | − | 0.209744i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.3547 | 0.554186 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.07851i | 0.0930470i | 0.998917 | + | 0.0465235i | \(0.0148142\pi\) | ||||
−0.998917 | + | 0.0465235i | \(0.985186\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 28.1643 | 1.25829 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.1912i | 1.16781i | 0.811822 | + | 0.583905i | \(0.198476\pi\) | ||||
−0.811822 | + | 0.583905i | \(0.801524\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 2.07430i | − | 0.0923053i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.98343i | 0.132499i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 31.6951i | 1.40486i | 0.711752 | + | 0.702431i | \(0.247902\pi\) | ||||
−0.711752 | + | 0.702431i | \(0.752098\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 2.91035i | − | 0.128746i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.7076 | 0.781811 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.01705 | 0.309208 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.00893 | −0.396212 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 0.300119i | − | 0.0131738i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.0562i | 1.62346i | 0.584033 | + | 0.811730i | \(0.301474\pi\) | ||||
−0.584033 | + | 0.811730i | \(0.698526\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.75364 | 0.164135 | 0.0820676 | − | 0.996627i | \(-0.473848\pi\) | ||||
0.0820676 | + | 0.996627i | \(0.473848\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −10.6857 | −0.466364 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.87385i | 0.168748i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9378 | −0.997294 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.50268 | −0.195400 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.4459 | − | 14.4767i | 0.842296 | − | 0.627057i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.17896 | 0.353607 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −33.3811 | −1.44050 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 4.98364i | − | 0.214661i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.0339 | 0.517380 | 0.258690 | − | 0.965960i | \(-0.416709\pi\) | ||||
0.258690 | + | 0.965960i | \(0.416709\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 50.6302 | 2.17275 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 2.49376i | − | 0.106821i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.14839i | 0.220129i | 0.993924 | + | 0.110065i | \(0.0351058\pi\) | ||||
−0.993924 | + | 0.110065i | \(0.964894\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.19494 | 0.0936776 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −65.6806 | −2.79809 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.79118 | 0.161218 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.12214i | 0.344766i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 46.7199i | 1.97959i | 0.142508 | + | 0.989794i | \(0.454483\pi\) | ||||
−0.142508 | + | 0.989794i | \(0.545517\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.5884i | 0.786204i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.6139i | 0.574779i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.4210i | 0.818496i | 0.912423 | + | 0.409248i | \(0.134209\pi\) | ||||
−0.912423 | + | 0.409248i | \(0.865791\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.395706 | 0.0166475 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 11.0029i | − | 0.462076i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.9853 | −0.502451 | −0.251225 | − | 0.967929i | \(-0.580833\pi\) | ||||
−0.251225 | + | 0.967929i | \(0.580833\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 28.2952i | − | 1.18412i | −0.805895 | − | 0.592059i | \(-0.798315\pi\) | ||
0.805895 | − | 0.592059i | \(-0.201685\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 44.2359 | 1.84798 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.19257 | 0.0497335 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.4014i | 0.433016i | 0.976281 | + | 0.216508i | \(0.0694667\pi\) | ||||
−0.976281 | + | 0.216508i | \(0.930533\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −52.3864 | −2.17711 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.75742i | 0.363319i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.68014 | 0.359495 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 3.54517i | − | 0.146575i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.5780i | 0.890619i | 0.895377 | + | 0.445310i | \(0.146906\pi\) | ||||
−0.895377 | + | 0.445310i | \(0.853094\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25.0396i | 1.03174i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 35.0534i | − | 1.44190i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 14.5336i | − | 0.596823i | −0.954437 | − | 0.298412i | \(-0.903543\pi\) | ||
0.954437 | − | 0.298412i | \(-0.0964568\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.572943 | −0.0234884 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 41.7755 | 1.70976 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.12899 | 0.209565 | 0.104782 | − | 0.994495i | \(-0.466585\pi\) | ||||
0.104782 | + | 0.994495i | \(0.466585\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.80002i | 0.195797i | 0.995196 | + | 0.0978984i | \(0.0312120\pi\) | ||||
−0.995196 | + | 0.0978984i | \(0.968788\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 23.6233i | 0.962015i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.48738 | −0.263750 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.8802 | −0.725735 | −0.362868 | − | 0.931841i | \(-0.618202\pi\) | ||||
−0.362868 | + | 0.931841i | \(0.618202\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18.5883i | 0.753235i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.84415 | −0.276885 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.92497 | −0.400866 | −0.200433 | − | 0.979707i | \(-0.564235\pi\) | ||||
−0.200433 | + | 0.979707i | \(0.564235\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.38310 | + | 4.00751i | −0.217068 | + | 0.161598i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.0895 | 1.09058 | 0.545291 | − | 0.838247i | \(-0.316419\pi\) | ||||
0.545291 | + | 0.838247i | \(0.316419\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.1664 | −0.730170 | −0.365085 | − | 0.930974i | \(-0.618960\pi\) | ||||
−0.365085 | + | 0.930974i | \(0.618960\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.559295i | 0.0224437i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15.9289 | −0.638177 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.7510 | 0.870039 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 87.9966i | 3.51425i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 9.46997i | − | 0.377592i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.1736 | 0.444812 | 0.222406 | − | 0.974954i | \(-0.428609\pi\) | ||||
0.222406 | + | 0.974954i | \(0.428609\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −39.7942 | −1.58168 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.83901 | −0.152347 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 3.78611i | − | 0.150011i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.6741i | 0.976093i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 23.0981i | − | 0.912320i | −0.889898 | − | 0.456160i | \(-0.849224\pi\) | ||
0.889898 | − | 0.456160i | \(-0.150776\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.28421i | 0.326697i | 0.986568 | + | 0.163349i | \(0.0522295\pi\) | ||||
−0.986568 | + | 0.163349i | \(0.947770\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 5.14571i | − | 0.202612i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 49.0736 | 1.92928 | 0.964642 | − | 0.263565i | \(-0.0848985\pi\) | ||||
0.964642 | + | 0.263565i | \(0.0848985\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.2359i | 0.441050i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.08645 | 0.277740 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 33.5708i | − | 1.31373i | −0.754010 | − | 0.656863i | \(-0.771883\pi\) | ||
0.754010 | − | 0.656863i | \(-0.228117\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.65114 | 0.103589 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.81236 | 0.226762 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 28.9895i | − | 1.12927i | −0.825341 | − | 0.564635i | \(-0.809017\pi\) | ||
0.825341 | − | 0.564635i | \(-0.190983\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.64974 | −0.0641673 | −0.0320836 | − | 0.999485i | \(-0.510214\pi\) | ||||
−0.0320836 | + | 0.999485i | \(0.510214\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.3426i | 0.401672i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.70335 | −0.143610 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 2.07452i | − | 0.0803258i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 41.2948i | 1.59655i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 5.47723i | − | 0.211446i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 38.9087i | − | 1.49982i | −0.661540 | − | 0.749910i | \(-0.730097\pi\) | ||
0.661540 | − | 0.749910i | \(-0.269903\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.7163i | 0.412472i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.5432 | 0.635805 | 0.317903 | − | 0.948123i | \(-0.397021\pi\) | ||||
0.317903 | + | 0.948123i | \(0.397021\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.29519 | −0.164834 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24.9508 | −0.956116 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.1382i | 0.808830i | 0.914576 | + | 0.404415i | \(0.132525\pi\) | ||||
−0.914576 | + | 0.404415i | \(0.867475\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1.67447i | − | 0.0639781i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27.4270 | 1.04641 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.59436 | 0.251225 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 39.5315i | − | 1.50385i | −0.659250 | − | 0.751924i | \(-0.729126\pi\) | ||
0.659250 | − | 0.751924i | \(-0.270874\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.95302 | 0.378084 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.80346 | 0.371867 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.27639 | − | 4.67253i | 0.237735 | − | 0.176985i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.0322 | 0.455099 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.9383 | −0.979675 | −0.489838 | − | 0.871814i | \(-0.662944\pi\) | ||||
−0.489838 | + | 0.871814i | \(0.662944\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 61.2113i | − | 2.30863i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.89463 | 0.0713557 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.42421 | 0.166389 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.6216i | 1.11246i | 0.831028 | + | 0.556231i | \(0.187753\pi\) | ||||
−0.831028 | + | 0.556231i | \(0.812247\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.57152i | 0.283954i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.790874 | −0.0296185 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.84660 | −0.330844 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.01893 | 0.150090 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 27.4212i | − | 1.02264i | −0.859391 | − | 0.511318i | \(-0.829157\pi\) | ||
0.859391 | − | 0.511318i | \(-0.170843\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.9664i | 0.557379i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 36.7411i | 1.36642i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 39.7487i | − | 1.47623i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 45.9715i | − | 1.70499i | −0.522738 | − | 0.852493i | \(-0.675089\pi\) | ||
0.522738 | − | 0.852493i | \(-0.324911\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6.93989 | 0.257033 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.99961i | 0.221904i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.9746 | −1.10714 | −0.553569 | − | 0.832803i | \(-0.686734\pi\) | ||||
−0.553569 | + | 0.832803i | \(0.686734\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.04809i | 0.0386593i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 58.9494 | 2.17143 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.1355 | −0.483196 | −0.241598 | − | 0.970376i | \(-0.577672\pi\) | ||||
−0.241598 | + | 0.970376i | \(0.577672\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 66.8516i | 2.45586i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.72772 | 0.173443 | 0.0867216 | − | 0.996233i | \(-0.472361\pi\) | ||||
0.0867216 | + | 0.996233i | \(0.472361\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.87086i | 0.251729i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −17.4898 | −0.639917 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.4446i | 0.637413i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.5122i | 1.29586i | 0.761701 | + | 0.647929i | \(0.224364\pi\) | ||||
−0.761701 | + | 0.647929i | \(0.775636\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 46.6062i | − | 1.69843i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 0.800929i | − | 0.0291488i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.9485i | 1.67003i | 0.550230 | + | 0.835013i | \(0.314540\pi\) | ||||
−0.550230 | + | 0.835013i | \(0.685460\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.77937 | −0.100885 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.9598 | 1.19479 | 0.597396 | − | 0.801947i | \(-0.296202\pi\) | ||||
0.597396 | + | 0.801947i | \(0.296202\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.31886 | 0.192556 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 1.14425i | − | 0.0413703i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.53603i | 0.308218i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.4944 | −0.739046 | −0.369523 | − | 0.929222i | \(-0.620479\pi\) | ||||
−0.369523 | + | 0.929222i | \(0.620479\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26.2541 | −0.945520 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.62253i | 0.238196i | 0.992883 | + | 0.119098i | \(0.0380002\pi\) | ||||
−0.992883 | + | 0.119098i | \(0.962000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.1535 | −0.544329 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17.3234 | −0.621475 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 40.5689 | − | 30.2020i | 1.45353 | − | 1.08210i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 61.5716 | 2.20321 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 18.6415 | 0.666192 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 6.63909i | − | 0.236959i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.6191 | 1.09145 | 0.545726 | − | 0.837964i | \(-0.316254\pi\) | ||||
0.545726 | + | 0.837964i | \(0.316254\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 47.8959 | 1.70514 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.843987i | 0.0300087i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 4.16109i | − | 0.147765i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.82548 | −0.0647431 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.0187 | 0.992475 | 0.496237 | − | 0.868187i | \(-0.334715\pi\) | ||||
0.496237 | + | 0.868187i | \(0.334715\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.20903 | −0.0781498 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 31.8122i | − | 1.12403i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 14.5041i | − | 0.511840i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 0.116970i | − | 0.00412266i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 35.6584i | − | 1.25524i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 47.4452i | − | 1.66808i | −0.551701 | − | 0.834042i | \(-0.686021\pi\) | ||
0.551701 | − | 0.834042i | \(-0.313979\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.0681 | −1.12606 | −0.563031 | − | 0.826435i | \(-0.690365\pi\) | ||||
−0.563031 | + | 0.826435i | \(0.690365\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 54.9689i | 1.92784i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.40583 | −0.329472 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 38.7799i | 1.35674i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.56138 | 0.264216 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.7166 | 1.03711 | 0.518557 | − | 0.855043i | \(-0.326469\pi\) | ||||
0.518557 | + | 0.855043i | \(0.326469\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 21.9764i | − | 0.766048i | −0.923738 | − | 0.383024i | \(-0.874883\pi\) | ||
0.923738 | − | 0.383024i | \(-0.125117\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −53.2539 | −1.85406 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 11.1796i | − | 0.388754i | −0.980927 | − | 0.194377i | \(-0.937731\pi\) | ||
0.980927 | − | 0.194377i | \(-0.0622686\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.82399 | −0.202276 | −0.101138 | − | 0.994872i | \(-0.532248\pi\) | ||||
−0.101138 | + | 0.994872i | \(0.532248\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 71.4127i | − | 2.47728i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1.22201i | − | 0.0423402i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.90711i | 0.204424i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 7.10673i | − | 0.245645i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 20.5442i | − | 0.709265i | −0.935006 | − | 0.354632i | \(-0.884606\pi\) | ||
0.935006 | − | 0.354632i | \(-0.115394\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −40.1444 | −1.38429 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −31.2984 | −1.07798 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.625737 | −0.0215260 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 13.8367i | − | 0.475435i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 3.20437i | − | 0.109974i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.93336 | 0.0662747 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.64795 | 0.0564246 | 0.0282123 | − | 0.999602i | \(-0.491019\pi\) | ||||
0.0282123 | + | 0.999602i | \(0.491019\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 7.39610i | − | 0.252941i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.3334 | 0.455460 | 0.227730 | − | 0.973724i | \(-0.426870\pi\) | ||||
0.227730 | + | 0.973724i | \(0.426870\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.6900 | 0.910652 | 0.455326 | − | 0.890325i | \(-0.349523\pi\) | ||||
0.455326 | + | 0.890325i | \(0.349523\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.54748 | − | 11.4814i | −0.291297 | − | 0.391286i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39.3025 | −1.33787 | −0.668936 | − | 0.743320i | \(-0.733250\pi\) | ||||
−0.668936 | + | 0.743320i | \(0.733250\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.0629462 | 0.00214023 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 34.6641i | − | 1.17725i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.8939 | 0.640932 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 44.7843 | 1.51746 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 8.57809i | − | 0.290324i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 4.58546i | − | 0.155017i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.86125 | 0.0966176 | 0.0483088 | − | 0.998832i | \(-0.484617\pi\) | ||||
0.0483088 | + | 0.998832i | \(0.484617\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −31.3651 | −1.05792 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.9699 | −0.369587 | −0.184793 | − | 0.982777i | \(-0.559162\pi\) | ||||
−0.184793 | + | 0.982777i | \(0.559162\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 50.6462i | − | 1.70438i | −0.523232 | − | 0.852190i | \(-0.675274\pi\) | ||
0.523232 | − | 0.852190i | \(-0.324726\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 2.36298i | − | 0.0794307i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 2.98749i | − | 0.100310i | −0.998741 | − | 0.0501550i | \(-0.984028\pi\) | ||
0.998741 | − | 0.0501550i | \(-0.0159715\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 8.18810i | − | 0.274620i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 54.8343i | − | 1.83702i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.2786 | −0.477814 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 7.00126i | − | 0.234026i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.11151 | −0.0705012 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26.3601i | 0.879158i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.12841 | 0.0709075 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.9751 | 0.365229 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.6190i | 0.352989i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.38010 | 0.0790300 | 0.0395150 | − | 0.999219i | \(-0.487419\pi\) | ||||
0.0395150 | + | 0.999219i | \(0.487419\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.83575i | 0.293063i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.6679 | −1.28112 | −0.640562 | − | 0.767907i | \(-0.721298\pi\) | ||||
−0.640562 | + | 0.767907i | \(0.721298\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 43.6439i | 1.44440i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.15189i | 0.0380803i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.65452i | 0.186729i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.1173i | 1.48828i | 0.668023 | + | 0.744141i | \(0.267141\pi\) | ||||
−0.668023 | + | 0.744141i | \(0.732859\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.6682i | 0.450382i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 46.7764 | 1.53966 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 37.0440 | 1.21800 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −29.8900 | −0.981717 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 27.6620i | − | 0.907561i | −0.891113 | − | 0.453781i | \(-0.850075\pi\) | ||
0.891113 | − | 0.453781i | \(-0.149925\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 7.89875i | − | 0.258871i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.96698 | 0.162612 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.85534 | −0.0933798 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.64793i | 0.184510i | 0.995735 | + | 0.0922549i | \(0.0294075\pi\) | ||||
−0.995735 | + | 0.0922549i | \(0.970593\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.2278 | −0.333773 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40.3099 | −1.31406 | −0.657032 | − | 0.753862i | \(-0.728188\pi\) | ||||
−0.657032 | + | 0.753862i | \(0.728188\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.953931 | + | 1.28137i | 0.0310643 | + | 0.0417271i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.05109 | 0.0341918 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.4019 | −0.565487 | −0.282743 | − | 0.959196i | \(-0.591245\pi\) | ||||
−0.282743 | + | 0.959196i | \(0.591245\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 11.0189i | − | 0.357688i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.5199 | 0.535694 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.3681 | −0.497823 | −0.248911 | − | 0.968526i | \(-0.580073\pi\) | ||||
−0.248911 | + | 0.968526i | \(0.580073\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.27791i | 0.300226i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 92.6374i | 2.99454i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.57141 | 0.115327 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.9507 | −0.675829 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −34.8393 | −1.12268 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 10.9874i | − | 0.353697i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 46.0434i | − | 1.48065i | −0.672246 | − | 0.740327i | \(-0.734670\pi\) | ||
0.672246 | − | 0.740327i | \(-0.265330\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21.5771i | 0.693158i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 30.8722i | − | 0.990736i | −0.868683 | − | 0.495368i | \(-0.835033\pi\) | ||
0.868683 | − | 0.495368i | \(-0.164967\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.9095i | 0.670327i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −40.4574 | −1.29567 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 4.31882i | − | 0.138171i | −0.997611 | − | 0.0690857i | \(-0.977992\pi\) | ||
0.997611 | − | 0.0690857i | \(-0.0220082\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −79.3839 | −2.53712 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.6225i | 0.339150i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.3025 | 0.870814 | 0.435407 | − | 0.900234i | \(-0.356605\pi\) | ||||
0.435407 | + | 0.900234i | \(0.356605\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.35200 | 0.234254 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.04098i | 0.128626i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.22486 | −0.0389484 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 50.4305i | − | 1.60198i | −0.598678 | − | 0.800989i | \(-0.704307\pi\) | ||
0.598678 | − | 0.800989i | \(-0.295693\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.72994 | −0.308770 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.76189i | 0.277771i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.64486i | 0.147104i | 0.997291 | + | 0.0735521i | \(0.0234335\pi\) | ||||
−0.997291 | + | 0.0735521i | \(0.976566\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 17.3730i | 0.549658i |
(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 | 1148.2.d.a.1065.5 | ✓ | 20 | |
41.40 | even | 2 | inner | 1148.2.d.a.1065.16 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.d.a.1065.5 | ✓ | 20 | 1.1 | even | 1 | trivial | |
1148.2.d.a.1065.16 | yes | 20 | 41.40 | even | 2 | inner |