Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5520,2,Mod(1471,5520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 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("5520.1471");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5520.be (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: | \(44.0774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.20 | ||
Character | \(\chi\) | \(=\) | 5520.1471 |
Dual form | 5520.2.be.c.1471.19 |
$q$-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 \(\left(\mathbb{Z}/5520\mathbb{Z}\right)^\times\).
\(n\) | \(1201\) | \(1381\) | \(1841\) | \(4417\) | \(4831\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.01693 | −0.762327 | −0.381163 | − | 0.924508i | \(-0.624476\pi\) | ||||
−0.381163 | + | 0.924508i | \(0.624476\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.697775 | −0.210387 | −0.105194 | − | 0.994452i | \(-0.533546\pi\) | ||||
−0.105194 | + | 0.994452i | \(0.533546\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.195235 | 0.0541486 | 0.0270743 | − | 0.999633i | \(-0.491381\pi\) | ||||
0.0270743 | + | 0.999633i | \(0.491381\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.430024i | 0.104296i | 0.998639 | + | 0.0521480i | \(0.0166068\pi\) | ||||
−0.998639 | + | 0.0521480i | \(0.983393\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.71006 | 1.76881 | 0.884405 | − | 0.466720i | \(-0.154564\pi\) | ||||
0.884405 | + | 0.466720i | \(0.154564\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 2.01693i | − | 0.440130i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.23049 | + | 2.25897i | −0.882119 | + | 0.471027i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.64181 | −1.79044 | −0.895220 | − | 0.445625i | \(-0.852982\pi\) | ||||
−0.895220 | + | 0.445625i | \(0.852982\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.05072i | − | 0.188714i | −0.995538 | − | 0.0943570i | \(-0.969920\pi\) | ||
0.995538 | − | 0.0943570i | \(-0.0300795\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.697775i | − | 0.121467i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 2.01693i | − | 0.340923i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.89822i | 0.805262i | 0.915362 | + | 0.402631i | \(0.131904\pi\) | ||||
−0.915362 | + | 0.402631i | \(0.868096\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.195235i | 0.0312627i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.71938 | −0.580870 | −0.290435 | − | 0.956895i | \(-0.593800\pi\) | ||||
−0.290435 | + | 0.956895i | \(0.593800\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.85669 | 0.893136 | 0.446568 | − | 0.894750i | \(-0.352646\pi\) | ||||
0.446568 | + | 0.894750i | \(0.352646\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 10.6764i | − | 1.55731i | −0.627452 | − | 0.778655i | \(-0.715902\pi\) | ||
0.627452 | − | 0.778655i | \(-0.284098\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.93201 | −0.418858 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.430024 | −0.0602154 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.464177i | 0.0637597i | 0.999492 | + | 0.0318798i | \(0.0101494\pi\) | ||||
−0.999492 | + | 0.0318798i | \(0.989851\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.697775i | − | 0.0940880i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.71006i | 1.02122i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.64910i | 0.995828i | 0.867226 | + | 0.497914i | \(0.165901\pi\) | ||||
−0.867226 | + | 0.497914i | \(0.834099\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.18983i | − | 0.536452i | −0.963356 | − | 0.268226i | \(-0.913563\pi\) | ||
0.963356 | − | 0.268226i | \(-0.0864375\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.01693 | 0.254109 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.195235i | 0.0242160i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.70657 | −0.452830 | −0.226415 | − | 0.974031i | \(-0.572700\pi\) | ||||
−0.226415 | + | 0.974031i | \(0.572700\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.25897 | − | 4.23049i | −0.271948 | − | 0.509292i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.69569i | − | 0.675954i | −0.941154 | − | 0.337977i | \(-0.890257\pi\) | ||
0.941154 | − | 0.337977i | \(-0.109743\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.51188 | −0.411034 | −0.205517 | − | 0.978654i | \(-0.565888\pi\) | ||||
−0.205517 | + | 0.978654i | \(0.565888\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 1.00000i | − | 0.115470i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.40736 | 0.160384 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.68233 | −1.08935 | −0.544674 | − | 0.838648i | \(-0.683346\pi\) | ||||
−0.544674 | + | 0.838648i | \(0.683346\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.982199 | 0.107810 | 0.0539052 | − | 0.998546i | \(-0.482833\pi\) | ||||
0.0539052 | + | 0.998546i | \(0.482833\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.430024 | −0.0466426 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 9.64181i | − | 1.03371i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 5.48101i | − | 0.580986i | −0.956877 | − | 0.290493i | \(-0.906181\pi\) | ||
0.956877 | − | 0.290493i | \(-0.0938192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.393776 | −0.0412789 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.05072 | 0.108954 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.71006i | 0.791036i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.5553i | 1.37634i | 0.725552 | + | 0.688168i | \(0.241585\pi\) | ||||
−0.725552 | + | 0.688168i | \(0.758415\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.697775 | 0.0701291 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.87390 | −0.982490 | −0.491245 | − | 0.871021i | \(-0.663458\pi\) | ||||
−0.491245 | + | 0.871021i | \(0.663458\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.65129 | 0.753904 | 0.376952 | − | 0.926233i | \(-0.376972\pi\) | ||||
0.376952 | + | 0.926233i | \(0.376972\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.01693 | 0.196832 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.7693 | 1.52448 | 0.762238 | − | 0.647296i | \(-0.224100\pi\) | ||||
0.762238 | + | 0.647296i | \(0.224100\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 7.29036i | − | 0.698289i | −0.937069 | − | 0.349145i | \(-0.886472\pi\) | ||
0.937069 | − | 0.349145i | \(-0.113528\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.89822 | −0.464918 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 11.6243i | − | 1.09352i | −0.837288 | − | 0.546762i | \(-0.815860\pi\) | ||
0.837288 | − | 0.546762i | \(-0.184140\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.25897 | − | 4.23049i | −0.210650 | − | 0.394496i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.195235 | −0.0180495 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 0.867327i | − | 0.0795077i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5131 | −0.955737 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 3.71938i | − | 0.335365i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.20841i | 0.462172i | 0.972933 | + | 0.231086i | \(0.0742279\pi\) | ||||
−0.972933 | + | 0.231086i | \(0.925772\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.85669i | 0.515653i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.04355i | 0.178546i | 0.996007 | + | 0.0892728i | \(0.0284543\pi\) | ||||
−0.996007 | + | 0.0892728i | \(0.971546\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.5506 | −1.34841 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 21.0004i | − | 1.79419i | −0.441841 | − | 0.897093i | \(-0.645675\pi\) | ||
0.441841 | − | 0.897093i | \(-0.354325\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2.56106i | − | 0.217227i | −0.994084 | − | 0.108613i | \(-0.965359\pi\) | ||
0.994084 | − | 0.108613i | \(-0.0346410\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.6764 | 0.899113 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.136231 | −0.0113922 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 9.64181i | − | 0.800709i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 2.93201i | − | 0.241828i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 9.82277i | − | 0.804712i | −0.915483 | − | 0.402356i | \(-0.868191\pi\) | ||
0.915483 | − | 0.402356i | \(-0.131809\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 14.8419i | − | 1.20782i | −0.797054 | − | 0.603909i | \(-0.793609\pi\) | ||
0.797054 | − | 0.603909i | \(-0.206391\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 0.430024i | − | 0.0347654i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.05072 | 0.0843955 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 1.12666i | − | 0.0899172i | −0.998989 | − | 0.0449586i | \(-0.985684\pi\) | ||
0.998989 | − | 0.0449586i | \(-0.0143156\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.464177 | −0.0368117 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.53260 | − | 4.55617i | 0.672463 | − | 0.359077i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 17.1655i | − | 1.34451i | −0.740321 | − | 0.672254i | \(-0.765326\pi\) | ||
0.740321 | − | 0.672254i | \(-0.234674\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.697775 | 0.0543217 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.809244i | 0.0626212i | 0.999510 | + | 0.0313106i | \(0.00996809\pi\) | ||||
−0.999510 | + | 0.0313106i | \(0.990032\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9619 | −0.997068 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.71006 | −0.589603 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.192946 | 0.0146694 | 0.00733472 | − | 0.999973i | \(-0.497665\pi\) | ||||
0.00733472 | + | 0.999973i | \(0.497665\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.01693 | 0.152465 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.64910 | −0.574942 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 23.5203i | − | 1.75799i | −0.476832 | − | 0.878994i | \(-0.658215\pi\) | ||
0.476832 | − | 0.878994i | \(-0.341785\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 9.77478i | − | 0.726554i | −0.931681 | − | 0.363277i | \(-0.881658\pi\) | ||
0.931681 | − | 0.363277i | \(-0.118342\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.18983 | 0.309721 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.89822 | −0.360124 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.300060i | − | 0.0219426i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.01693i | 0.146710i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.21224 | 0.521859 | 0.260930 | − | 0.965358i | \(-0.415971\pi\) | ||||
0.260930 | + | 0.965358i | \(0.415971\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.9860 | 1.79853 | 0.899266 | − | 0.437402i | \(-0.144101\pi\) | ||||
0.899266 | + | 0.437402i | \(0.144101\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.195235 | −0.0139811 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.96165 | −0.495997 | −0.247998 | − | 0.968760i | \(-0.579773\pi\) | ||||
−0.247998 | + | 0.968760i | \(0.579773\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.94085 | 0.208471 | 0.104236 | − | 0.994553i | \(-0.466760\pi\) | ||||
0.104236 | + | 0.994553i | \(0.466760\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 3.70657i | − | 0.261441i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 19.4468 | 1.36490 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 3.71938i | − | 0.259773i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.23049 | − | 2.25897i | 0.294040 | − | 0.157009i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.37989 | −0.372135 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 28.0259i | − | 1.92938i | −0.263381 | − | 0.964692i | \(-0.584838\pi\) | ||
0.263381 | − | 0.964692i | \(-0.415162\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.69569 | 0.390262 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.85669i | 0.399423i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.11922i | 0.143862i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 3.51188i | − | 0.237311i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.0839559i | 0.00564748i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.81830i | 0.121763i | 0.998145 | + | 0.0608813i | \(0.0193911\pi\) | ||||
−0.998145 | + | 0.0608813i | \(0.980609\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.7824 | −1.04752 | −0.523758 | − | 0.851867i | \(-0.675470\pi\) | ||||
−0.523758 | + | 0.851867i | \(0.675470\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.05803i | 0.466408i | 0.972428 | + | 0.233204i | \(0.0749210\pi\) | ||||
−0.972428 | + | 0.233204i | \(0.925079\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.40736i | 0.0925976i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.71879 | −0.374650 | −0.187325 | − | 0.982298i | \(-0.559982\pi\) | ||||
−0.187325 | + | 0.982298i | \(0.559982\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.6764 | 0.696450 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 9.68233i | − | 0.628935i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.6125i | 1.33331i | 0.745365 | + | 0.666657i | \(0.232275\pi\) | ||||
−0.745365 | + | 0.666657i | \(0.767725\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.5987i | 1.52013i | 0.649849 | + | 0.760063i | \(0.274832\pi\) | ||||
−0.649849 | + | 0.760063i | \(0.725168\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 2.93201i | − | 0.187319i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.50528 | 0.0957785 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.982199i | 0.0622443i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.45913 | 0.0920994 | 0.0460497 | − | 0.998939i | \(-0.485337\pi\) | ||||
0.0460497 | + | 0.998939i | \(0.485337\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.95193 | − | 1.57625i | 0.185587 | − | 0.0990981i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 0.430024i | − | 0.0269291i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.3730 | −1.27083 | −0.635417 | − | 0.772169i | \(-0.719172\pi\) | ||||
−0.635417 | + | 0.772169i | \(0.719172\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 9.87935i | − | 0.613873i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.64181 | 0.596813 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.84599 | 0.422142 | 0.211071 | − | 0.977471i | \(-0.432305\pi\) | ||||
0.211071 | + | 0.977471i | \(0.432305\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.464177 | −0.0285142 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.48101 | 0.335432 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.7765 | −0.961912 | −0.480956 | − | 0.876745i | \(-0.659710\pi\) | ||||
−0.480956 | + | 0.876745i | \(0.659710\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 15.4121i | − | 0.936216i | −0.883671 | − | 0.468108i | \(-0.844936\pi\) | ||
0.883671 | − | 0.468108i | \(-0.155064\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 0.393776i | − | 0.0238324i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.697775 | 0.0420774 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.24637 | 0.435392 | 0.217696 | − | 0.976017i | \(-0.430146\pi\) | ||||
0.217696 | + | 0.976017i | \(0.430146\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.05072i | 0.0629047i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 0.321739i | − | 0.0191933i | −0.999954 | − | 0.00959666i | \(-0.996945\pi\) | ||
0.999954 | − | 0.00959666i | \(-0.00305476\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.0317 | 0.952988 | 0.476494 | − | 0.879178i | \(-0.341907\pi\) | ||||
0.476494 | + | 0.879178i | \(0.341907\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.71006 | −0.456705 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.50172 | 0.442812 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.8151 | 0.989122 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.5553 | −0.794628 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 6.96765i | − | 0.407055i | −0.979069 | − | 0.203527i | \(-0.934759\pi\) | ||
0.979069 | − | 0.203527i | \(-0.0652406\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.64910 | −0.445348 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.697775i | 0.0404890i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.825942 | + | 0.441030i | −0.0477655 | + | 0.0255054i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.8125 | −0.680862 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 9.87390i | − | 0.567241i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.18983 | 0.239909 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.8378i | 1.36049i | 0.732983 | + | 0.680246i | \(0.238127\pi\) | ||||
−0.732983 | + | 0.680246i | \(0.761873\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.65129i | 0.435266i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.02594i | 0.114880i | 0.998349 | + | 0.0574401i | \(0.0182938\pi\) | ||||
−0.998349 | + | 0.0574401i | \(0.981706\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.4162i | 0.927900i | 0.885861 | + | 0.463950i | \(0.153568\pi\) | ||||
−0.885861 | + | 0.463950i | \(0.846432\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.01693i | 0.113641i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.2081 | −1.19117 | −0.595583 | − | 0.803294i | \(-0.703079\pi\) | ||||
−0.595583 | + | 0.803294i | \(0.703079\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.72782 | 0.376686 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.7693i | 0.880157i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.31551i | 0.184480i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.195235 | −0.0108297 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.29036 | 0.403158 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 21.5335i | 1.18718i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.15797i | 0.118613i | 0.998240 | + | 0.0593063i | \(0.0188889\pi\) | ||||
−0.998240 | + | 0.0593063i | \(0.981111\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 4.89822i | − | 0.268421i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 3.70657i | − | 0.202512i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.24431i | 0.176729i | 0.996088 | + | 0.0883645i | \(0.0281640\pi\) | ||||
−0.996088 | + | 0.0883645i | \(0.971836\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.6243 | 0.631346 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.733163i | 0.0397030i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0321 | 1.08163 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.23049 | − | 2.25897i | 0.227762 | − | 0.121619i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 24.8303i | − | 1.33296i | −0.745524 | − | 0.666479i | \(-0.767800\pi\) | ||
0.745524 | − | 0.666479i | \(-0.232200\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.69841 | 0.144442 | 0.0722212 | − | 0.997389i | \(-0.476991\pi\) | ||||
0.0722212 | + | 0.997389i | \(0.476991\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 0.195235i | − | 0.0104209i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.10284 | 0.324821 | 0.162411 | − | 0.986723i | \(-0.448073\pi\) | ||||
0.162411 | + | 0.986723i | \(0.448073\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.69569 | 0.302296 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.867327 | 0.0459038 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.7445 | 0.725406 | 0.362703 | − | 0.931905i | \(-0.381854\pi\) | ||||
0.362703 | + | 0.931905i | \(0.381854\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 40.4451 | 2.12869 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 10.5131i | − | 0.551795i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 3.51188i | − | 0.183820i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.83223 | −0.147841 | −0.0739206 | − | 0.997264i | \(-0.523551\pi\) | ||||
−0.0739206 | + | 0.997264i | \(0.523551\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.71938 | 0.193623 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 0.936212i | − | 0.0486057i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 13.7736i | − | 0.713168i | −0.934263 | − | 0.356584i | \(-0.883941\pi\) | ||
0.934263 | − | 0.356584i | \(-0.116059\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.88242 | −0.0969498 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.0709 | 0.620040 | 0.310020 | − | 0.950730i | \(-0.399664\pi\) | ||||
0.310020 | + | 0.950730i | \(0.399664\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.20841 | −0.266835 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.1553 | −0.518910 | −0.259455 | − | 0.965755i | \(-0.583543\pi\) | ||||
−0.259455 | + | 0.965755i | \(0.583543\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.40736i | 0.0717258i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.85669 | −0.297712 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 12.2653i | − | 0.621877i | −0.950430 | − | 0.310939i | \(-0.899357\pi\) | ||
0.950430 | − | 0.310939i | \(-0.100643\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.971409 | − | 1.81921i | −0.0491263 | − | 0.0920015i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.04355 | −0.103083 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 9.68233i | − | 0.487171i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.7383 | −0.538942 | −0.269471 | − | 0.963008i | \(-0.586849\pi\) | ||||
−0.269471 | + | 0.963008i | \(0.586849\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 15.5506i | − | 0.778506i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 18.0035i | − | 0.899049i | −0.893268 | − | 0.449525i | \(-0.851593\pi\) | ||
0.893268 | − | 0.449525i | \(-0.148407\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 0.205137i | − | 0.0102186i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3.41786i | − | 0.169417i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.4255 | −0.960527 | −0.480264 | − | 0.877124i | \(-0.659459\pi\) | ||||
−0.480264 | + | 0.877124i | \(0.659459\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.0004 | 1.03587 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 15.4277i | − | 0.759147i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.982199i | 0.0482143i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.56106 | 0.125416 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.8285 | −0.968685 | −0.484343 | − | 0.874878i | \(-0.660941\pi\) | ||||
−0.484343 | + | 0.874878i | \(0.660941\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 14.9197i | − | 0.727140i | −0.931567 | − | 0.363570i | \(-0.881558\pi\) | ||
0.931567 | − | 0.363570i | \(-0.118442\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.6764i | 0.519103i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 0.430024i | − | 0.0208592i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.45058i | 0.408952i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 0.136231i | − | 0.00657727i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −37.3682 | −1.79996 | −0.899982 | − | 0.435926i | \(-0.856421\pi\) | ||||
−0.899982 | + | 0.435926i | \(0.856421\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.24734i | 0.204114i | 0.994779 | + | 0.102057i | \(0.0325425\pi\) | ||||
−0.994779 | + | 0.102057i | \(0.967458\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.64181 | 0.462290 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −32.6174 | + | 17.4168i | −1.56030 | + | 0.833157i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 36.0964i | − | 1.72278i | −0.507940 | − | 0.861392i | \(-0.669593\pi\) | ||
0.507940 | − | 0.861392i | \(-0.330407\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.93201 | 0.139619 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 8.68329i | − | 0.412556i | −0.978493 | − | 0.206278i | \(-0.933865\pi\) | ||
0.978493 | − | 0.206278i | \(-0.0661350\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.48101 | 0.259825 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.82277 | 0.464601 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.7648 | 0.649599 | 0.324799 | − | 0.945783i | \(-0.394703\pi\) | ||||
0.324799 | + | 0.945783i | \(0.394703\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.59529 | 0.122208 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.8419 | 0.697334 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 0.393776i | − | 0.0184605i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.9155i | 0.650939i | 0.945553 | + | 0.325469i | \(0.105522\pi\) | ||||
−0.945553 | + | 0.325469i | \(0.894478\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.430024 | 0.0200718 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.7166 | −1.10459 | −0.552296 | − | 0.833648i | \(-0.686248\pi\) | ||||
−0.552296 | + | 0.833648i | \(0.686248\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.78160i | 0.454589i | 0.973826 | + | 0.227295i | \(0.0729881\pi\) | ||||
−0.973826 | + | 0.227295i | \(0.927012\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.05072i | 0.0487258i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −37.7537 | −1.74703 | −0.873516 | − | 0.486795i | \(-0.838166\pi\) | ||||
−0.873516 | + | 0.486795i | \(0.838166\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.47588 | 0.345204 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.12666 | 0.0519137 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.08665 | −0.187904 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.71006 | −0.353762 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 0.464177i | − | 0.0212532i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.8613 | 0.633337 | 0.316668 | − | 0.948536i | \(-0.397436\pi\) | ||||
0.316668 | + | 0.948536i | \(0.397436\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.956306i | 0.0436038i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.55617 | + | 8.53260i | 0.207313 | + | 0.388247i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.5553 | −0.615516 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 20.7362i | − | 0.939646i | −0.882761 | − | 0.469823i | \(-0.844318\pi\) | ||
0.882761 | − | 0.469823i | \(-0.155682\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.1655 | 0.776252 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 32.8875i | − | 1.48419i | −0.670295 | − | 0.742095i | \(-0.733832\pi\) | ||
0.670295 | − | 0.742095i | \(-0.266168\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 4.14621i | − | 0.186736i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.697775i | 0.0313627i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.4878i | 0.515298i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 0.150831i | − | 0.00675210i | −0.999994 | − | 0.00337605i | \(-0.998925\pi\) | ||
0.999994 | − | 0.00337605i | \(-0.00107463\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.809244 | −0.0361543 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.93423 | 0.309182 | 0.154591 | − | 0.987979i | \(-0.450594\pi\) | ||||
0.154591 | + | 0.987979i | \(0.450594\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 9.87390i | − | 0.439383i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 12.9619i | − | 0.575657i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.6312 | −0.471220 | −0.235610 | − | 0.971848i | \(-0.575709\pi\) | ||||
−0.235610 | + | 0.971848i | \(0.575709\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.08320 | 0.313343 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 7.71006i | − | 0.340408i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.65129i | 0.337156i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.44971i | 0.327638i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.192946i | 0.00846941i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.6607i | 0.554673i | 0.960773 | + | 0.277337i | \(0.0894517\pi\) | ||||
−0.960773 | + | 0.277337i | \(0.910548\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.9210 | 1.57072 | 0.785358 | − | 0.619042i | \(-0.212479\pi\) | ||||
0.785358 | + | 0.619042i | \(0.212479\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.01693i | 0.0880259i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.451833 | 0.0196821 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.7941 | − | 19.1131i | 0.556267 | − | 0.831004i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 7.64910i | − | 0.331943i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.726155 | −0.0314533 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.7693i | 0.681767i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 23.5203 | 1.01498 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.04588 | 0.0881224 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.5417 | −0.668191 | −0.334095 | − | 0.942539i | \(-0.608431\pi\) | ||||
−0.334095 | + | 0.942539i | \(0.608431\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.77478 | 0.419476 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.29036 | 0.312285 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.4468i | 0.532187i | 0.963947 | + | 0.266093i | \(0.0857330\pi\) | ||||
−0.963947 | + | 0.266093i | \(0.914267\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.18983i | 0.178817i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −74.3390 | −3.16695 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.5286 | 0.830438 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 4.89822i | − | 0.207918i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.8342i | 1.05226i | 0.850404 | + | 0.526130i | \(0.176357\pi\) | ||||
−0.850404 | + | 0.526130i | \(0.823643\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.14343 | 0.0483621 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.300060 | 0.0126685 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 41.0729 | 1.73101 | 0.865507 | − | 0.500896i | \(-0.166996\pi\) | ||||
0.865507 | + | 0.500896i | \(0.166996\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.6243 | 0.489038 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.01693 | −0.0847030 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.8724i | 1.37808i | 0.724722 | + | 0.689041i | \(0.241968\pi\) | ||||
−0.724722 | + | 0.689041i | \(0.758032\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.5411 | −1.61290 | −0.806448 | − | 0.591305i | \(-0.798613\pi\) | ||||
−0.806448 | + | 0.591305i | \(0.798613\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.21224i | 0.301296i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.23049 | − | 2.25897i | 0.176424 | − | 0.0942054i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.2323 | 1.38348 | 0.691740 | − | 0.722147i | \(-0.256844\pi\) | ||||
0.691740 | + | 0.722147i | \(0.256844\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.9860i | 1.03838i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.98102 | −0.0821867 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 0.323892i | − | 0.0134142i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 0.195235i | − | 0.00807199i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.1033i | 0.417008i | 0.978021 | + | 0.208504i | \(0.0668595\pi\) | ||||
−0.978021 | + | 0.208504i | \(0.933141\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 8.10108i | − | 0.333799i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 6.96165i | − | 0.286364i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.289921 | −0.0119056 | −0.00595281 | − | 0.999982i | \(-0.501895\pi\) | ||||
−0.00595281 | + | 0.999982i | \(0.501895\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.867327 | 0.0355569 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.94085i | 0.120361i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.0346i | 1.51319i | 0.653883 | + | 0.756596i | \(0.273139\pi\) | ||||
−0.653883 | + | 0.756596i | \(0.726861\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −38.1805 | −1.55742 | −0.778708 | − | 0.627387i | \(-0.784125\pi\) | ||||
−0.778708 | + | 0.627387i | \(0.784125\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.70657 | 0.150943 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 10.5131i | − | 0.427419i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 39.4410i | − | 1.60086i | −0.599426 | − | 0.800430i | \(-0.704605\pi\) | ||
0.599426 | − | 0.800430i | \(-0.295395\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19.4468i | 0.788025i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 2.08441i | − | 0.0843261i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.2889i | 0.496345i | 0.968716 | + | 0.248173i | \(0.0798300\pi\) | ||||
−0.968716 | + | 0.248173i | \(0.920170\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.71938 | 0.149980 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 10.2034i | − | 0.410773i | −0.978681 | − | 0.205386i | \(-0.934155\pi\) | ||
0.978681 | − | 0.205386i | \(-0.0658451\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.5655 | −1.26873 | −0.634363 | − | 0.773036i | \(-0.718737\pi\) | ||||
−0.634363 | + | 0.773036i | \(0.718737\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.25897 | + | 4.23049i | 0.0906492 | + | 0.169764i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.0548i | 0.442901i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 5.37989i | − | 0.214852i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.10635 | −0.0839857 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.4861 | 0.735919 | 0.367960 | − | 0.929842i | \(-0.380057\pi\) | ||||
0.367960 | + | 0.929842i | \(0.380057\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 28.0259 | 1.11393 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.20841 | −0.206690 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.572431 | −0.0226806 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.69569i | 0.225318i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 31.0234i | − | 1.22535i | −0.790335 | − | 0.612674i | \(-0.790094\pi\) | ||
0.790335 | − | 0.612674i | \(-0.209906\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.62461 | 0.182377 | 0.0911884 | − | 0.995834i | \(-0.470933\pi\) | ||||
0.0911884 | + | 0.995834i | \(0.470933\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.85669 | −0.230607 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.6906i | 0.813433i | 0.913554 | + | 0.406716i | \(0.133326\pi\) | ||||
−0.913554 | + | 0.406716i | \(0.866674\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 5.33736i | − | 0.209510i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.11922 | −0.0830586 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −44.7001 | −1.74925 | −0.874626 | − | 0.484799i | \(-0.838893\pi\) | ||||
−0.874626 | + | 0.484799i | \(0.838893\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.04355 | −0.0798480 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.51188 | 0.137011 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.80658 | −0.187238 | −0.0936190 | − | 0.995608i | \(-0.529844\pi\) | ||||
−0.0936190 | + | 0.995608i | \(0.529844\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.6532i | 1.46454i | 0.681014 | + | 0.732270i | \(0.261539\pi\) | ||||
−0.681014 | + | 0.732270i | \(0.738461\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.0839559 | −0.00326058 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 15.5506i | − | 0.603028i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 40.7896 | − | 21.7805i | 1.57938 | − | 0.843346i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.81830 | −0.0702997 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.92356i | 0.112863i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.9838 | −1.15579 | −0.577895 | − | 0.816111i | \(-0.696126\pi\) | ||||
−0.577895 | + | 0.816111i | \(0.696126\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000i | 0.0384900i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.9203i | 1.03463i | 0.855794 | + | 0.517316i | \(0.173069\pi\) | ||||
−0.855794 | + | 0.517316i | \(0.826931\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 27.3401i | − | 1.04922i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 15.7824i | − | 0.604783i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.8703i | 1.33427i | 0.744935 | + | 0.667137i | \(0.232480\pi\) | ||||
−0.744935 | + | 0.667137i | \(0.767520\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.0004 | 0.802385 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.05803 | −0.269281 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.0906239i | 0.00345250i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.22615i | 0.198812i | 0.995047 | + | 0.0994061i | \(0.0316943\pi\) | ||||
−0.995047 | + | 0.0994061i | \(0.968306\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.40736 | −0.0534613 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.56106 | 0.0971467 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1.59942i | − | 0.0605824i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 5.71879i | − | 0.216305i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 15.5942i | − | 0.588985i | −0.955654 | − | 0.294493i | \(-0.904849\pi\) | ||
0.955654 | − | 0.294493i | \(-0.0951507\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 37.7656i | 1.42436i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.6764i | 0.402096i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19.9149 | 0.748978 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 31.2212i | − | 1.17254i | −0.810117 | − | 0.586268i | \(-0.800596\pi\) | ||
0.810117 | − | 0.586268i | \(-0.199404\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.68233 | 0.363116 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.37353 | + | 4.44504i | 0.0888894 | + | 0.166468i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 0.136231i | − | 0.00509473i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.6125 | −0.769789 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 2.74815i | − | 0.102489i | −0.998686 | − | 0.0512443i | \(-0.983681\pi\) | ||
0.998686 | − | 0.0512443i | \(-0.0163187\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.4321 | −0.574721 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −23.5987 | −0.877646 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.64181 | 0.358088 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.4656 | −1.05573 | −0.527865 | − | 0.849328i | \(-0.677007\pi\) | ||||
−0.527865 | + | 0.849328i | \(0.677007\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.51852i | 0.0931506i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 31.8684i | − | 1.17709i | −0.808466 | − | 0.588543i | \(-0.799702\pi\) | ||
0.808466 | − | 0.588543i | \(-0.200298\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.93201 | 0.108149 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.58635 | 0.0952695 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 19.4238i | − | 0.714515i | −0.934006 | − | 0.357258i | \(-0.883712\pi\) | ||
0.934006 | − | 0.357258i | \(-0.116288\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.50528i | 0.0552978i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.2199 | −0.668425 | −0.334212 | − | 0.942498i | \(-0.608470\pi\) | ||||
−0.334212 | + | 0.942498i | \(0.608470\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.82277 | 0.359878 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.982199 | −0.0359368 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −31.8055 | −1.16215 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −50.1935 | −1.83159 | −0.915794 | − | 0.401649i | \(-0.868437\pi\) | ||||
−0.915794 | + | 0.401649i | \(0.868437\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.45913i | 0.0531736i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.8419 | 0.540152 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.7967i | 0.901250i | 0.892713 | + | 0.450625i | \(0.148799\pi\) | ||||
−0.892713 | + | 0.450625i | \(0.851201\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.57625 | + | 2.95193i | 0.0572143 | + | 0.107148i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.6359 | −1.11055 | −0.555275 | − | 0.831667i | \(-0.687387\pi\) | ||||
−0.555275 | + | 0.831667i | \(0.687387\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.7041i | 0.532325i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.430024 | 0.0155475 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.49338i | 0.0539227i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.2375i | 1.27070i | 0.772226 | + | 0.635348i | \(0.219143\pi\) | ||||
−0.772226 | + | 0.635348i | \(0.780857\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 20.3730i | − | 0.733716i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 51.1400i | − | 1.83938i | −0.392650 | − | 0.919688i | \(-0.628441\pi\) | ||
0.392650 | − | 0.919688i | \(-0.371559\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.05072i | 0.0377428i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.87935 | 0.354420 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −28.6767 | −1.02745 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.97431i | 0.142212i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.64181i | 0.344570i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.12666 | 0.0402122 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.8424 | −1.31329 | −0.656645 | − | 0.754200i | \(-0.728025\pi\) | ||||
−0.656645 | + | 0.754200i | \(0.728025\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.84599i | 0.243724i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.4454i | 0.833622i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 0.818003i | − | 0.0290481i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 0.464177i | − | 0.0164627i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 24.8874i | − | 0.881556i | −0.897616 | − | 0.440778i | \(-0.854703\pi\) | ||
0.897616 | − | 0.440778i | \(-0.145297\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.59110 | 0.162421 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.48101i | 0.193662i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.45050 | 0.0864764 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.55617 | + | 8.53260i | 0.160584 | + | 0.300734i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 15.7765i | − | 0.555360i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39.4308 | −1.38631 | −0.693156 | − | 0.720787i | \(-0.743780\pi\) | ||||
−0.693156 | + | 0.720787i | \(0.743780\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.8345i | 0.836943i | 0.908230 | + | 0.418471i | \(0.137434\pi\) | ||||
−0.908230 | + | 0.418471i | \(0.862566\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.4121 | 0.540524 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.1655 | 0.601282 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 45.1554 | 1.57979 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.393776 | 0.0137596 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.770729 | 0.0268986 | 0.0134493 | − | 0.999910i | \(-0.495719\pi\) | ||||
0.0134493 | + | 0.999910i | \(0.495719\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 15.2384i | − | 0.531177i | −0.964086 | − | 0.265589i | \(-0.914434\pi\) | ||
0.964086 | − | 0.265589i | \(-0.0855663\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.697775i | 0.0242934i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.9491 | 0.867567 | 0.433783 | − | 0.901017i | \(-0.357178\pi\) | ||||
0.433783 | + | 0.901017i | \(0.357178\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.4879 | 0.954695 | 0.477348 | − | 0.878715i | \(-0.341598\pi\) | ||||
0.477348 | + | 0.878715i | \(0.341598\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.24637i | 0.251374i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1.26083i | − | 0.0436853i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.809244 | −0.0280050 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.05072 | −0.0363180 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.34476 | 0.322617 | 0.161309 | − | 0.986904i | \(-0.448429\pi\) | ||||
0.161309 | + | 0.986904i | \(0.448429\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 63.9646 | 2.20567 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.321739 | 0.0110813 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 12.9619i | − | 0.445902i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.2042 | 0.728584 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.0317i | 0.550208i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.0649 | − | 20.7219i | −0.379300 | − | 0.710337i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.9627 | 0.786228 | 0.393114 | − | 0.919490i | \(-0.371398\pi\) | ||||
0.393114 | + | 0.919490i | \(0.371398\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 7.71006i | − | 0.263679i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.9504 | 0.783972 | 0.391986 | − | 0.919971i | \(-0.371788\pi\) | ||||
0.391986 | + | 0.919971i | \(0.371788\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.21344i | 0.109641i | 0.998496 | + | 0.0548206i | \(0.0174587\pi\) | ||||
−0.998496 | + | 0.0548206i | \(0.982541\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.50172i | 0.255658i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 47.8566i | 1.62906i | 0.580122 | + | 0.814529i | \(0.303005\pi\) | ||||
−0.580122 | + | 0.814529i | \(0.696995\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.192946i | 0.00656038i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.8151i | 0.571070i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.75609 | 0.229185 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.723654 | −0.0245201 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 13.5553i | − | 0.458779i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.01693i | 0.0681846i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.5419 | 0.423512 | 0.211756 | − | 0.977323i | \(-0.432082\pi\) | ||||
0.211756 | + | 0.977323i | \(0.432082\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.96765 | 0.235013 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 14.1413i | − | 0.476431i | −0.971212 | − | 0.238216i | \(-0.923437\pi\) | ||
0.971212 | − | 0.238216i | \(-0.0765625\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.3945i | 1.05651i | 0.849086 | + | 0.528255i | \(0.177154\pi\) | ||||
−0.849086 | + | 0.528255i | \(0.822846\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 7.64910i | − | 0.257122i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.6407i | 1.02881i | 0.857546 | + | 0.514407i | \(0.171988\pi\) | ||||
−0.857546 | + | 0.514407i | \(0.828012\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 10.5050i | − | 0.352326i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.697775 | −0.0233764 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 82.3156i | − | 2.75459i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.5203 | 0.786196 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.441030 | − | 0.825942i | −0.0147256 | − | 0.0275774i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.1308i | 0.337881i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.199607 | −0.00664988 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 11.8125i | − | 0.393096i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.77478 | 0.324925 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.7078 | −0.886818 | −0.443409 | − | 0.896319i | \(-0.646231\pi\) | ||||
−0.443409 | + | 0.896319i | \(0.646231\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.87390 | 0.327497 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.5901 | −0.350865 | −0.175432 | − | 0.984492i | \(-0.556132\pi\) | ||||
−0.175432 | + | 0.984492i | \(0.556132\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.685354 | −0.0226819 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.18983i | 0.138511i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 4.12169i | − | 0.136110i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.8569 | −1.08385 | −0.541925 | − | 0.840427i | \(-0.682304\pi\) | ||||
−0.541925 | + | 0.840427i | \(0.682304\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −23.8378 | −0.785481 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1.11200i | − | 0.0366019i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 4.89822i | − | 0.161052i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.65129 | −0.251301 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.6352 | 1.13634 | 0.568172 | − | 0.822910i | \(-0.307651\pi\) | ||||
0.568172 | + | 0.822910i | \(0.307651\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.6060 | −0.740880 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.02594 | −0.0663262 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.300060 | 0.00981301 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 39.0172i | − | 1.27464i | −0.770601 | − | 0.637318i | \(-0.780044\pi\) | ||
0.770601 | − | 0.637318i | \(-0.219956\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.4162 | −0.535723 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.3857i | 0.534159i | 0.963675 | + | 0.267079i | \(0.0860586\pi\) | ||||
−0.963675 | + | 0.267079i | \(0.913941\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.7348 | − | 8.40195i | 0.512396 | − | 0.273605i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.01693 | −0.0656106 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 48.1701i | 1.56532i | 0.622451 | + | 0.782658i | \(0.286137\pi\) | ||||
−0.622451 | + | 0.782658i | \(0.713863\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.685643 | −0.0222569 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 21.2081i | − | 0.687720i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.1941i | 1.20483i | 0.798181 | + | 0.602417i | \(0.205796\pi\) | ||||
−0.798181 | + | 0.602417i | \(0.794204\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.21224i | 0.233383i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.72782i | 0.217480i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 42.3563i | 1.36776i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.8960 | 0.964387 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.7693 | −0.508159 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24.9860i | 0.804328i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.39440i | 0.302103i | 0.988526 | + | 0.151052i | \(0.0482660\pi\) | ||||
−0.988526 | + | 0.151052i | \(0.951734\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.31551 | −0.106510 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50.5564 | −1.62243 | −0.811216 | − | 0.584747i | \(-0.801194\pi\) | ||||
−0.811216 | + | 0.584747i | \(0.801194\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.16548i | 0.165598i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 0.195235i | − | 0.00625254i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 23.7373i | − | 0.759424i | −0.925105 | − | 0.379712i | \(-0.876023\pi\) | ||
0.925105 | − | 0.379712i | \(-0.123977\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.82451i | 0.122232i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.29036i | 0.232763i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.88451 | 0.283372 | 0.141686 | − | 0.989912i | \(-0.454748\pi\) | ||||
0.141686 | + | 0.989912i | \(0.454748\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 6.96165i | − | 0.221816i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21.5335 | −0.685418 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24.7767 | + | 13.2301i | −0.787852 | + | 0.420691i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.2770i | 0.961781i | 0.876781 | + | 0.480890i | \(0.159686\pi\) | ||||
−0.876781 | + | 0.480890i | \(0.840314\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.15797 | −0.0684810 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.94085i | 0.0932312i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46.1127 | −1.46040 | −0.730202 | − | 0.683232i | \(-0.760574\pi\) | ||||
−0.730202 | + | 0.683232i | \(0.760574\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.89822 | 0.154973 |
(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 | 5520.2.be.c.1471.20 | yes | 32 | |
4.3 | odd | 2 | 5520.2.be.d.1471.19 | yes | 32 | ||
23.22 | odd | 2 | 5520.2.be.d.1471.20 | yes | 32 | ||
92.91 | even | 2 | inner | 5520.2.be.c.1471.19 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5520.2.be.c.1471.19 | ✓ | 32 | 92.91 | even | 2 | inner | |
5520.2.be.c.1471.20 | yes | 32 | 1.1 | even | 1 | trivial | |
5520.2.be.d.1471.19 | yes | 32 | 4.3 | odd | 2 | ||
5520.2.be.d.1471.20 | yes | 32 | 23.22 | odd | 2 |