Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,2,Mod(1268,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1575.1268");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.m (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.5764383184\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 18x^{10} + 107x^{8} + 240x^{6} + 151x^{4} + 30x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 315) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1268.1 | ||
Root | \(2.91021i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1268 |
Dual form | 1575.2.m.c.1457.1 |
$q$-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 \(\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(1226\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.45137 | − | 1.45137i | −1.02627 | − | 1.02627i | −0.999645 | − | 0.0266253i | \(-0.991524\pi\) |
−0.0266253 | − | 0.999645i | \(-0.508476\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.21293i | 1.10646i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.707107 | − | 0.707107i | 0.267261 | − | 0.267261i | ||||
\(8\) | 0.309035 | − | 0.309035i | 0.109260 | − | 0.109260i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.62971i | 1.69742i | 0.528857 | + | 0.848711i | \(0.322621\pi\) | ||||
−0.528857 | + | 0.848711i | \(0.677379\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.00747830 | + | 0.00747830i | 0.00207411 | + | 0.00207411i | 0.708143 | − | 0.706069i | \(-0.249533\pi\) |
−0.706069 | + | 0.708143i | \(0.749533\pi\) | |||||||
\(14\) | −2.05254 | −0.548565 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.52881 | 0.882202 | ||||||||
\(17\) | −1.20876 | − | 1.20876i | −0.293169 | − | 0.293169i | 0.545162 | − | 0.838331i | \(-0.316468\pi\) |
−0.838331 | + | 0.545162i | \(0.816468\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.69344i | − | 1.30616i | −0.757287 | − | 0.653082i | \(-0.773476\pi\) | ||
0.757287 | − | 0.653082i | \(-0.226524\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.17077 | − | 8.17077i | 1.74201 | − | 1.74201i | ||||
\(23\) | −4.96275 | + | 4.96275i | −1.03481 | + | 1.03481i | −0.0354333 | + | 0.999372i | \(0.511281\pi\) |
−0.999372 | + | 0.0354333i | \(0.988719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 0.0217075i | − | 0.00425719i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.56478 | + | 1.56478i | 0.295715 | + | 0.295715i | ||||
\(29\) | 1.55541 | 0.288831 | 0.144416 | − | 0.989517i | \(-0.453870\pi\) | ||||
0.144416 | + | 0.989517i | \(0.453870\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.84264 | −0.869763 | −0.434882 | − | 0.900488i | \(-0.643210\pi\) | ||||
−0.434882 | + | 0.900488i | \(0.643210\pi\) | |||||||
\(32\) | −5.73966 | − | 5.73966i | −1.01464 | − | 1.01464i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.50872i | 0.601741i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.14119 | + | 3.14119i | −0.516409 | + | 0.516409i | −0.916483 | − | 0.400074i | \(-0.868984\pi\) |
0.400074 | + | 0.916483i | \(0.368984\pi\) | |||||||
\(38\) | −8.26326 | + | 8.26326i | −1.34048 | + | 1.34048i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.02203i | − | 1.40900i | −0.709702 | − | 0.704502i | \(-0.751170\pi\) | ||
0.709702 | − | 0.704502i | \(-0.248830\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.78707 | − | 2.78707i | −0.425025 | − | 0.425025i | 0.461905 | − | 0.886929i | \(-0.347166\pi\) |
−0.886929 | + | 0.461905i | \(0.847166\pi\) | |||||||
\(44\) | −12.4581 | −1.87813 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 14.4055 | 2.12398 | ||||||||
\(47\) | −6.31695 | − | 6.31695i | −0.921421 | − | 0.921421i | 0.0757087 | − | 0.997130i | \(-0.475878\pi\) |
−0.997130 | + | 0.0757087i | \(0.975878\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.0165489 | + | 0.0165489i | −0.00229492 | + | 0.00229492i | ||||
\(53\) | 4.17043 | − | 4.17043i | 0.572853 | − | 0.572853i | −0.360072 | − | 0.932925i | \(-0.617248\pi\) |
0.932925 | + | 0.360072i | \(0.117248\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 0.437041i | − | 0.0584021i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.25746 | − | 2.25746i | −0.296419 | − | 0.296419i | ||||
\(59\) | −11.8204 | −1.53889 | −0.769444 | − | 0.638714i | \(-0.779467\pi\) | ||||
−0.769444 | + | 0.638714i | \(0.779467\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.82074 | 0.617232 | 0.308616 | − | 0.951187i | \(-0.400134\pi\) | ||||
0.308616 | + | 0.951187i | \(0.400134\pi\) | |||||||
\(62\) | 7.02844 | + | 7.02844i | 0.892613 | + | 0.892613i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 9.60309i | 1.20039i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.72058 | + | 1.72058i | −0.210203 | + | 0.210203i | −0.804354 | − | 0.594151i | \(-0.797488\pi\) |
0.594151 | + | 0.804354i | \(0.297488\pi\) | |||||||
\(68\) | 2.67491 | − | 2.67491i | 0.324380 | − | 0.324380i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.89804i | 0.581291i | 0.956831 | + | 0.290645i | \(0.0938700\pi\) | ||||
−0.956831 | + | 0.290645i | \(0.906130\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.69985 | − | 2.69985i | −0.315994 | − | 0.315994i | 0.531232 | − | 0.847226i | \(-0.321729\pi\) |
−0.847226 | + | 0.531232i | \(0.821729\pi\) | |||||||
\(74\) | 9.11804 | 1.05995 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 12.5992 | 1.44522 | ||||||||
\(77\) | 3.98081 | + | 3.98081i | 0.453655 | + | 0.453655i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 10.6179i | − | 1.19460i | −0.802016 | − | 0.597302i | \(-0.796239\pi\) | ||
0.802016 | − | 0.597302i | \(-0.203761\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −13.0943 | + | 13.0943i | −1.44602 | + | 1.44602i | ||||
\(83\) | 5.14537 | − | 5.14537i | 0.564778 | − | 0.564778i | −0.365883 | − | 0.930661i | \(-0.619233\pi\) |
0.930661 | + | 0.365883i | \(0.119233\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.09013i | 0.872381i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.73978 | + | 1.73978i | 0.185461 | + | 0.185461i | ||||
\(89\) | −16.4527 | −1.74398 | −0.871991 | − | 0.489521i | \(-0.837172\pi\) | ||||
−0.871991 | + | 0.489521i | \(0.837172\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0105759 | 0.00110866 | ||||||||
\(92\) | −10.9822 | − | 10.9822i | −1.14497 | − | 1.14497i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 18.3364i | 1.89126i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.91803 | + | 9.91803i | −1.00702 | + | 1.00702i | −0.00704778 | + | 0.999975i | \(0.502243\pi\) |
−0.999975 | + | 0.00704778i | \(0.997757\pi\) | |||||||
\(98\) | −1.45137 | + | 1.45137i | −0.146610 | + | 0.146610i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 12.8862i | − | 1.28223i | −0.767445 | − | 0.641115i | \(-0.778472\pi\) | ||
0.767445 | − | 0.641115i | \(-0.221528\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.93245 | − | 5.93245i | −0.584541 | − | 0.584541i | 0.351607 | − | 0.936148i | \(-0.385635\pi\) |
−0.936148 | + | 0.351607i | \(0.885635\pi\) | |||||||
\(104\) | 0.00462211 | 0.000453236 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.1057 | −1.17580 | ||||||||
\(107\) | −4.75259 | − | 4.75259i | −0.459450 | − | 0.459450i | 0.439025 | − | 0.898475i | \(-0.355324\pi\) |
−0.898475 | + | 0.439025i | \(0.855324\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.3430i | 1.18225i | 0.806581 | + | 0.591124i | \(0.201316\pi\) | ||||
−0.806581 | + | 0.591124i | \(0.798684\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.49524 | − | 2.49524i | 0.235778 | − | 0.235778i | ||||
\(113\) | −3.95944 | + | 3.95944i | −0.372472 | + | 0.372472i | −0.868377 | − | 0.495905i | \(-0.834837\pi\) |
0.495905 | + | 0.868377i | \(0.334837\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.44200i | 0.319581i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 17.1558 | + | 17.1558i | 1.57932 | + | 1.57932i | ||||
\(119\) | −1.70945 | −0.156705 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −20.6936 | −1.88124 | ||||||||
\(122\) | −6.99666 | − | 6.99666i | −0.633448 | − | 0.633448i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 10.7164i | − | 0.962361i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.55904 | − | 5.55904i | 0.493285 | − | 0.493285i | −0.416055 | − | 0.909340i | \(-0.636588\pi\) |
0.909340 | + | 0.416055i | \(0.136588\pi\) | |||||||
\(128\) | 2.45827 | − | 2.45827i | 0.217282 | − | 0.217282i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.36678i | 0.294157i | 0.989125 | + | 0.147079i | \(0.0469870\pi\) | ||||
−0.989125 | + | 0.147079i | \(0.953013\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.02587 | − | 4.02587i | −0.349087 | − | 0.349087i | ||||
\(134\) | 4.99439 | 0.431450 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.747101 | −0.0640634 | ||||||||
\(137\) | 16.3236 | + | 16.3236i | 1.39462 | + | 1.39462i | 0.814605 | + | 0.580016i | \(0.196954\pi\) |
0.580016 | + | 0.814605i | \(0.303046\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.6535i | 1.07325i | 0.843820 | + | 0.536626i | \(0.180301\pi\) | ||||
−0.843820 | + | 0.536626i | \(0.819699\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.10885 | − | 7.10885i | 0.596562 | − | 0.596562i | ||||
\(143\) | −0.0421007 | + | 0.0421007i | −0.00352064 | + | 0.00352064i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.83695i | 0.648591i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.95123 | − | 6.95123i | −0.571387 | − | 0.571387i | ||||
\(149\) | −7.42258 | −0.608081 | −0.304041 | − | 0.952659i | \(-0.598336\pi\) | ||||
−0.304041 | + | 0.952659i | \(0.598336\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.7952 | −1.04126 | −0.520628 | − | 0.853783i | \(-0.674302\pi\) | ||||
−0.520628 | + | 0.853783i | \(0.674302\pi\) | |||||||
\(152\) | −1.75947 | − | 1.75947i | −0.142712 | − | 0.142712i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 11.5552i | − | 0.931146i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.3508 | + | 10.3508i | −0.826085 | + | 0.826085i | −0.986973 | − | 0.160887i | \(-0.948564\pi\) |
0.160887 | + | 0.986973i | \(0.448564\pi\) | |||||||
\(158\) | −15.4104 | + | 15.4104i | −1.22599 | + | 1.22599i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.01839i | 0.553127i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.6689 | + | 14.6689i | 1.14896 | + | 1.14896i | 0.986757 | + | 0.162203i | \(0.0518599\pi\) |
0.162203 | + | 0.986757i | \(0.448140\pi\) | |||||||
\(164\) | 19.9651 | 1.55901 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.9356 | −1.15923 | ||||||||
\(167\) | 11.4412 | + | 11.4412i | 0.885344 | + | 0.885344i | 0.994072 | − | 0.108728i | \(-0.0346776\pi\) |
−0.108728 | + | 0.994072i | \(0.534678\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.9999i | − | 0.999991i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.16759 | − | 6.16759i | 0.470274 | − | 0.470274i | ||||
\(173\) | 7.83527 | − | 7.83527i | 0.595704 | − | 0.595704i | −0.343462 | − | 0.939166i | \(-0.611600\pi\) |
0.939166 | + | 0.343462i | \(0.111600\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 19.8662i | 1.49747i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 23.8789 | + | 23.8789i | 1.78980 | + | 1.78980i | ||||
\(179\) | −11.1315 | −0.832007 | −0.416003 | − | 0.909363i | \(-0.636570\pi\) | ||||
−0.416003 | + | 0.909363i | \(0.636570\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.8050 | 0.951788 | 0.475894 | − | 0.879503i | \(-0.342125\pi\) | ||||
0.475894 | + | 0.879503i | \(0.342125\pi\) | |||||||
\(182\) | −0.0153495 | − | 0.0153495i | −0.00113778 | − | 0.00113778i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.06733i | 0.226126i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.80500 | − | 6.80500i | 0.497631 | − | 0.497631i | ||||
\(188\) | 13.9789 | − | 13.9789i | 1.01952 | − | 1.01952i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.52585i | − | 0.110407i | −0.998475 | − | 0.0552033i | \(-0.982419\pi\) | ||
0.998475 | − | 0.0552033i | \(-0.0175807\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.00514 | + | 7.00514i | 0.504241 | + | 0.504241i | 0.912753 | − | 0.408512i | \(-0.133952\pi\) |
−0.408512 | + | 0.912753i | \(0.633952\pi\) | |||||||
\(194\) | 28.7894 | 2.06696 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.21293 | 0.158066 | ||||||||
\(197\) | −3.95944 | − | 3.95944i | −0.282098 | − | 0.282098i | 0.551847 | − | 0.833945i | \(-0.313923\pi\) |
−0.833945 | + | 0.551847i | \(0.813923\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.0634i | 1.35137i | 0.737193 | + | 0.675683i | \(0.236151\pi\) | ||||
−0.737193 | + | 0.675683i | \(0.763849\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −18.7027 | + | 18.7027i | −1.31591 | + | 1.31591i | ||||
\(203\) | 1.09984 | − | 1.09984i | 0.0771935 | − | 0.0771935i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 17.2203i | 1.19980i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.0263895 | + | 0.0263895i | 0.00182978 | + | 0.00182978i | ||||
\(209\) | 32.0524 | 2.21711 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.1156 | −0.971756 | −0.485878 | − | 0.874027i | \(-0.661500\pi\) | ||||
−0.485878 | + | 0.874027i | \(0.661500\pi\) | |||||||
\(212\) | 9.22886 | + | 9.22886i | 0.633841 | + | 0.633841i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 13.7955i | 0.943040i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.42426 | + | 3.42426i | −0.232454 | + | 0.232454i | ||||
\(218\) | 17.9143 | − | 17.9143i | 1.21331 | − | 1.21331i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 0.0180790i | − | 0.00121613i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.1021 | − | 20.1021i | −1.34613 | − | 1.34613i | −0.889818 | − | 0.456315i | \(-0.849169\pi\) |
−0.456315 | − | 0.889818i | \(-0.650831\pi\) | |||||||
\(224\) | −8.11711 | −0.542347 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.4932 | 0.764515 | ||||||||
\(227\) | −7.18784 | − | 7.18784i | −0.477074 | − | 0.477074i | 0.427121 | − | 0.904195i | \(-0.359528\pi\) |
−0.904195 | + | 0.427121i | \(0.859528\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 12.4777i | − | 0.824552i | −0.911059 | − | 0.412276i | \(-0.864734\pi\) | ||
0.911059 | − | 0.412276i | \(-0.135266\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.480675 | − | 0.480675i | 0.0315578 | − | 0.0315578i | ||||
\(233\) | −16.7330 | + | 16.7330i | −1.09622 | + | 1.09622i | −0.101367 | + | 0.994849i | \(0.532322\pi\) |
−0.994849 | + | 0.101367i | \(0.967678\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 26.1577i | − | 1.70272i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.48104 | + | 2.48104i | 0.160822 | + | 0.160822i | ||||
\(239\) | 3.43517 | 0.222203 | 0.111101 | − | 0.993809i | \(-0.464562\pi\) | ||||
0.111101 | + | 0.993809i | \(0.464562\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.7302 | 1.46418 | 0.732091 | − | 0.681206i | \(-0.238544\pi\) | ||||
0.732091 | + | 0.681206i | \(0.238544\pi\) | |||||||
\(242\) | 30.0340 | + | 30.0340i | 1.93066 | + | 1.93066i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.6679i | 0.682945i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0425773 | − | 0.0425773i | 0.00270913 | − | 0.00270913i | ||||
\(248\) | −1.49654 | + | 1.49654i | −0.0950306 | + | 0.0950306i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 1.13033i | − | 0.0713455i | −0.999364 | − | 0.0356727i | \(-0.988643\pi\) | ||
0.999364 | − | 0.0356727i | \(-0.0113574\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −27.9389 | − | 27.9389i | −1.75650 | − | 1.75650i | ||||
\(254\) | −16.1364 | −1.01249 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.0705 | 0.754405 | ||||||||
\(257\) | 1.03499 | + | 1.03499i | 0.0645611 | + | 0.0645611i | 0.738650 | − | 0.674089i | \(-0.235464\pi\) |
−0.674089 | + | 0.738650i | \(0.735464\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.44232i | 0.276032i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.88643 | − | 4.88643i | 0.301885 | − | 0.301885i | ||||
\(263\) | 5.31703 | − | 5.31703i | 0.327862 | − | 0.327862i | −0.523911 | − | 0.851773i | \(-0.675528\pi\) |
0.851773 | + | 0.523911i | \(0.175528\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 11.6860i | 0.716516i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.80753 | − | 3.80753i | −0.232582 | − | 0.232582i | ||||
\(269\) | 3.78057 | 0.230506 | 0.115253 | − | 0.993336i | \(-0.463232\pi\) | ||||
0.115253 | + | 0.993336i | \(0.463232\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.8404 | −1.69119 | −0.845593 | − | 0.533828i | \(-0.820753\pi\) | ||||
−0.845593 | + | 0.533828i | \(0.820753\pi\) | |||||||
\(272\) | −4.26550 | − | 4.26550i | −0.258634 | − | 0.258634i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 47.3831i | − | 2.86252i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.81486 | − | 1.81486i | 0.109044 | − | 0.109044i | −0.650480 | − | 0.759524i | \(-0.725432\pi\) |
0.759524 | + | 0.650480i | \(0.225432\pi\) | |||||||
\(278\) | 18.3648 | − | 18.3648i | 1.10145 | − | 1.10145i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 8.13136i | − | 0.485076i | −0.970142 | − | 0.242538i | \(-0.922020\pi\) | ||
0.970142 | − | 0.242538i | \(-0.0779800\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.85187 | + | 3.85187i | 0.228970 | + | 0.228970i | 0.812262 | − | 0.583292i | \(-0.198236\pi\) |
−0.583292 | + | 0.812262i | \(0.698236\pi\) | |||||||
\(284\) | −10.8390 | −0.643177 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.122207 | 0.00722625 | ||||||||
\(287\) | −6.37954 | − | 6.37954i | −0.376572 | − | 0.376572i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 14.0778i | − | 0.828104i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.97458 | − | 5.97458i | 0.349636 | − | 0.349636i | ||||
\(293\) | −9.16944 | + | 9.16944i | −0.535684 | + | 0.535684i | −0.922258 | − | 0.386574i | \(-0.873658\pi\) |
0.386574 | + | 0.922258i | \(0.373658\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.94148i | 0.112846i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.7729 | + | 10.7729i | 0.624056 | + | 0.624056i | ||||
\(299\) | −0.0742259 | −0.00429260 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.94152 | −0.227185 | ||||||||
\(302\) | 18.5705 | + | 18.5705i | 1.06861 | + | 1.06861i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 20.0911i | − | 1.15230i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.6101 | + | 11.6101i | −0.662626 | + | 0.662626i | −0.955998 | − | 0.293372i | \(-0.905222\pi\) |
0.293372 | + | 0.955998i | \(0.405222\pi\) | |||||||
\(308\) | −8.80923 | + | 8.80923i | −0.501953 | + | 0.501953i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 6.53623i | − | 0.370635i | −0.982679 | − | 0.185318i | \(-0.940669\pi\) | ||
0.982679 | − | 0.185318i | \(-0.0593314\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.80568 | − | 8.80568i | −0.497727 | − | 0.497727i | 0.413003 | − | 0.910730i | \(-0.364480\pi\) |
−0.910730 | + | 0.413003i | \(0.864480\pi\) | |||||||
\(314\) | 30.0457 | 1.69557 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 23.4966 | 1.32179 | ||||||||
\(317\) | −14.2899 | − | 14.2899i | −0.802602 | − | 0.802602i | 0.180899 | − | 0.983502i | \(-0.442099\pi\) |
−0.983502 | + | 0.180899i | \(0.942099\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.75648i | 0.490269i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.1863 | − | 10.1863i | 0.567658 | − | 0.567658i | ||||
\(323\) | −6.88203 | + | 6.88203i | −0.382926 | + | 0.382926i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 42.5800i | − | 2.35829i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.78812 | − | 2.78812i | −0.153948 | − | 0.153948i | ||||
\(329\) | −8.93351 | −0.492520 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.27002 | 0.289667 | 0.144833 | − | 0.989456i | \(-0.453735\pi\) | ||||
0.144833 | + | 0.989456i | \(0.453735\pi\) | |||||||
\(332\) | 11.3863 | + | 11.3863i | 0.624906 | + | 0.624906i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 33.2106i | − | 1.81721i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.55379 | + | 8.55379i | −0.465955 | + | 0.465955i | −0.900601 | − | 0.434646i | \(-0.856873\pi\) |
0.434646 | + | 0.900601i | \(0.356873\pi\) | |||||||
\(338\) | −18.8676 | + | 18.8676i | −1.02626 | + | 1.02626i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 27.2626i | − | 1.47635i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.707107 | − | 0.707107i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | −1.72261 | −0.0928767 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −22.7437 | −1.22271 | ||||||||
\(347\) | −4.78700 | − | 4.78700i | −0.256980 | − | 0.256980i | 0.566845 | − | 0.823824i | \(-0.308164\pi\) |
−0.823824 | + | 0.566845i | \(0.808164\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.62377i | 0.515149i | 0.966258 | + | 0.257574i | \(0.0829232\pi\) | ||||
−0.966258 | + | 0.257574i | \(0.917077\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 32.3126 | − | 32.3126i | 1.72227 | − | 1.72227i | ||||
\(353\) | 17.5108 | − | 17.5108i | 0.932003 | − | 0.932003i | −0.0658276 | − | 0.997831i | \(-0.520969\pi\) |
0.997831 | + | 0.0658276i | \(0.0209687\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 36.4086i | − | 1.92965i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 16.1559 | + | 16.1559i | 0.853864 | + | 0.853864i | ||||
\(359\) | −3.99422 | −0.210807 | −0.105403 | − | 0.994430i | \(-0.533613\pi\) | ||||
−0.105403 | + | 0.994430i | \(0.533613\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.4153 | −0.706066 | ||||||||
\(362\) | −18.5847 | − | 18.5847i | −0.976792 | − | 0.976792i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.0234037i | 0.00122669i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.18932 | − | 8.18932i | 0.427479 | − | 0.427479i | −0.460290 | − | 0.887769i | \(-0.652254\pi\) |
0.887769 | + | 0.460290i | \(0.152254\pi\) | |||||||
\(368\) | −17.5126 | + | 17.5126i | −0.912907 | + | 0.912907i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 5.89788i | − | 0.306203i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.6414 | − | 13.6414i | −0.706326 | − | 0.706326i | 0.259434 | − | 0.965761i | \(-0.416464\pi\) |
−0.965761 | + | 0.259434i | \(0.916464\pi\) | |||||||
\(374\) | −19.7531 | −1.02141 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.90431 | −0.201350 | ||||||||
\(377\) | 0.0116318 | + | 0.0116318i | 0.000599068 | + | 0.000599068i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.05127i | 0.156733i | 0.996925 | + | 0.0783666i | \(0.0249705\pi\) | ||||
−0.996925 | + | 0.0783666i | \(0.975030\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.21457 | + | 2.21457i | −0.113307 | + | 0.113307i | ||||
\(383\) | 1.55390 | − | 1.55390i | 0.0794006 | − | 0.0794006i | −0.666291 | − | 0.745692i | \(-0.732119\pi\) |
0.745692 | + | 0.666291i | \(0.232119\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 20.3340i | − | 1.03498i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −21.9479 | − | 21.9479i | −1.11423 | − | 1.11423i | ||||
\(389\) | 20.5833 | 1.04361 | 0.521807 | − | 0.853064i | \(-0.325258\pi\) | ||||
0.521807 | + | 0.853064i | \(0.325258\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.9976 | 0.606745 | ||||||||
\(392\) | −0.309035 | − | 0.309035i | −0.0156086 | − | 0.0156086i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.4932i | 0.579018i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.62748 | − | 7.62748i | 0.382812 | − | 0.382812i | −0.489302 | − | 0.872114i | \(-0.662748\pi\) |
0.872114 | + | 0.489302i | \(0.162748\pi\) | |||||||
\(398\) | 27.6679 | − | 27.6679i | 1.38687 | − | 1.38687i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 19.2725i | − | 0.962421i | −0.876605 | − | 0.481211i | \(-0.840197\pi\) | ||
0.876605 | − | 0.481211i | \(-0.159803\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0362147 | − | 0.0362147i | −0.00180398 | − | 0.00180398i | ||||
\(404\) | 28.5163 | 1.41874 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.19253 | −0.158443 | ||||||||
\(407\) | −17.6840 | − | 17.6840i | −0.876563 | − | 0.876563i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 16.5809i | − | 0.819875i | −0.912114 | − | 0.409938i | \(-0.865551\pi\) | ||
0.912114 | − | 0.409938i | \(-0.134449\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.1281 | − | 13.1281i | 0.646774 | − | 0.646774i | ||||
\(413\) | −8.35830 | + | 8.35830i | −0.411285 | + | 0.411285i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 0.0858459i | − | 0.00420894i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −46.5198 | − | 46.5198i | −2.27536 | − | 2.27536i | ||||
\(419\) | 4.61274 | 0.225347 | 0.112674 | − | 0.993632i | \(-0.464059\pi\) | ||||
0.112674 | + | 0.993632i | \(0.464059\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.9277 | −0.971215 | −0.485608 | − | 0.874177i | \(-0.661402\pi\) | ||||
−0.485608 | + | 0.874177i | \(0.661402\pi\) | |||||||
\(422\) | 20.4869 | + | 20.4869i | 0.997285 | + | 0.997285i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 2.57762i | − | 0.125180i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.40878 | − | 3.40878i | 0.164962 | − | 0.164962i | ||||
\(428\) | 10.5171 | − | 10.5171i | 0.508364 | − | 0.508364i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.8886i | 1.29518i | 0.761990 | + | 0.647589i | \(0.224222\pi\) | ||||
−0.761990 | + | 0.647589i | \(0.775778\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.2612 | + | 20.2612i | 0.973692 | + | 0.973692i | 0.999663 | − | 0.0259707i | \(-0.00826765\pi\) |
−0.0259707 | + | 0.999663i | \(0.508268\pi\) | |||||||
\(434\) | 9.93971 | 0.477122 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −27.3142 | −1.30811 | ||||||||
\(437\) | 28.2551 | + | 28.2551i | 1.35163 | + | 1.35163i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.0619i | 1.48250i | 0.671228 | + | 0.741251i | \(0.265767\pi\) | ||||
−0.671228 | + | 0.741251i | \(0.734233\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.0262393 | + | 0.0262393i | −0.00124808 | + | 0.00124808i | ||||
\(443\) | 25.6712 | − | 25.6712i | 1.21968 | − | 1.21968i | 0.251933 | − | 0.967745i | \(-0.418934\pi\) |
0.967745 | − | 0.251933i | \(-0.0810663\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 58.3509i | 2.76299i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.79041 | + | 6.79041i | 0.320817 | + | 0.320817i | ||||
\(449\) | −23.6055 | −1.11401 | −0.557007 | − | 0.830508i | \(-0.688050\pi\) | ||||
−0.557007 | + | 0.830508i | \(0.688050\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 50.7914 | 2.39167 | ||||||||
\(452\) | −8.76194 | − | 8.76194i | −0.412127 | − | 0.412127i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 20.8644i | 0.979214i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.8226 | − | 17.8226i | 0.833708 | − | 0.833708i | −0.154314 | − | 0.988022i | \(-0.549317\pi\) |
0.988022 | + | 0.154314i | \(0.0493168\pi\) | |||||||
\(458\) | −18.1098 | + | 18.1098i | −0.846214 | + | 0.846214i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 7.13491i | − | 0.332306i | −0.986100 | − | 0.166153i | \(-0.946865\pi\) | ||
0.986100 | − | 0.166153i | \(-0.0531345\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.46573 | + | 7.46573i | 0.346962 | + | 0.346962i | 0.858977 | − | 0.512015i | \(-0.171101\pi\) |
−0.512015 | + | 0.858977i | \(0.671101\pi\) | |||||||
\(464\) | 5.48873 | 0.254808 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 48.5715 | 2.25003 | ||||||||
\(467\) | −28.5436 | − | 28.5436i | −1.32084 | − | 1.32084i | −0.913094 | − | 0.407748i | \(-0.866314\pi\) |
−0.407748 | − | 0.913094i | \(-0.633686\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.43327i | 0.112358i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.65292 | + | 3.65292i | −0.168139 | + | 0.168139i | ||||
\(473\) | 15.6904 | − | 15.6904i | 0.721446 | − | 0.721446i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 3.78289i | − | 0.173389i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.98570 | − | 4.98570i | −0.228040 | − | 0.228040i | ||||
\(479\) | −6.46156 | −0.295236 | −0.147618 | − | 0.989044i | \(-0.547161\pi\) | ||||
−0.147618 | + | 0.989044i | \(0.547161\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0469816 | −0.00214217 | ||||||||
\(482\) | −32.9899 | − | 32.9899i | −1.50265 | − | 1.50265i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 45.7935i | − | 2.08152i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.192093 | + | 0.192093i | −0.00870456 | + | 0.00870456i | −0.711446 | − | 0.702741i | \(-0.751959\pi\) |
0.702741 | + | 0.711446i | \(0.251959\pi\) | |||||||
\(488\) | 1.48978 | − | 1.48978i | 0.0674390 | − | 0.0674390i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 20.9550i | − | 0.945688i | −0.881146 | − | 0.472844i | \(-0.843227\pi\) | ||
0.881146 | − | 0.472844i | \(-0.156773\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.88012 | − | 1.88012i | −0.0846763 | − | 0.0846763i | ||||
\(494\) | −0.123590 | −0.00556059 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −17.0887 | −0.767307 | ||||||||
\(497\) | 3.46344 | + | 3.46344i | 0.155356 | + | 0.155356i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 6.23105i | − | 0.278940i | −0.990226 | − | 0.139470i | \(-0.955460\pi\) | ||
0.990226 | − | 0.139470i | \(-0.0445399\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.64052 | + | 1.64052i | −0.0732198 | + | 0.0732198i | ||||
\(503\) | −5.72261 | + | 5.72261i | −0.255158 | + | 0.255158i | −0.823082 | − | 0.567923i | \(-0.807747\pi\) |
0.567923 | + | 0.823082i | \(0.307747\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 81.0990i | 3.60529i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.3017 | + | 12.3017i | 0.545802 | + | 0.545802i | ||||
\(509\) | 5.37263 | 0.238138 | 0.119069 | − | 0.992886i | \(-0.462009\pi\) | ||||
0.119069 | + | 0.992886i | \(0.462009\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.81817 | −0.168906 | ||||||||
\(512\) | −22.4352 | − | 22.4352i | −0.991506 | − | 0.991506i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 3.00431i | − | 0.132514i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 35.5626 | − | 35.5626i | 1.56404 | − | 1.56404i | ||||
\(518\) | 6.44743 | − | 6.44743i | 0.283284 | − | 0.283284i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 12.7159i | − | 0.557095i | −0.960422 | − | 0.278548i | \(-0.910147\pi\) | ||
0.960422 | − | 0.278548i | \(-0.0898530\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.11255 | + | 8.11255i | 0.354737 | + | 0.354737i | 0.861869 | − | 0.507132i | \(-0.169294\pi\) |
−0.507132 | + | 0.861869i | \(0.669294\pi\) | |||||||
\(524\) | −7.45044 | −0.325474 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.4339 | −0.672951 | ||||||||
\(527\) | 5.85361 | + | 5.85361i | 0.254987 | + | 0.254987i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 26.2578i | − | 1.14164i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.90896 | − | 8.90896i | 0.386252 | − | 0.386252i | ||||
\(533\) | 0.0674694 | − | 0.0674694i | 0.00292243 | − | 0.00292243i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.06344i | 0.0459336i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.48699 | − | 5.48699i | −0.236561 | − | 0.236561i | ||||
\(539\) | 5.62971 | 0.242489 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.73394 | −0.0745479 | −0.0372740 | − | 0.999305i | \(-0.511867\pi\) | ||||
−0.0372740 | + | 0.999305i | \(0.511867\pi\) | |||||||
\(542\) | 40.4067 | + | 40.4067i | 1.73562 | + | 1.73562i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 13.8758i | 0.594920i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.8819 | + | 17.8819i | −0.764574 | + | 0.764574i | −0.977145 | − | 0.212572i | \(-0.931816\pi\) |
0.212572 | + | 0.977145i | \(0.431816\pi\) | |||||||
\(548\) | −36.1230 | + | 36.1230i | −1.54310 | + | 1.54310i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 8.85560i | − | 0.377261i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.50797 | − | 7.50797i | −0.319272 | − | 0.319272i | ||||
\(554\) | −5.26805 | −0.223818 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −28.0012 | −1.18751 | ||||||||
\(557\) | −18.4069 | − | 18.4069i | −0.779925 | − | 0.779925i | 0.199893 | − | 0.979818i | \(-0.435941\pi\) |
−0.979818 | + | 0.199893i | \(0.935941\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 0.0416852i | − | 0.00176309i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11.8016 | + | 11.8016i | −0.497820 | + | 0.497820i | ||||
\(563\) | −6.57537 | + | 6.57537i | −0.277119 | + | 0.277119i | −0.831958 | − | 0.554839i | \(-0.812780\pi\) |
0.554839 | + | 0.831958i | \(0.312780\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 11.1809i | − | 0.469970i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.51367 | + | 1.51367i | 0.0635120 | + | 0.0635120i | ||||
\(569\) | −2.00559 | −0.0840787 | −0.0420393 | − | 0.999116i | \(-0.513385\pi\) | ||||
−0.0420393 | + | 0.999116i | \(0.513385\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.05799 | −0.253519 | −0.126759 | − | 0.991933i | \(-0.540458\pi\) | ||||
−0.126759 | + | 0.991933i | \(0.540458\pi\) | |||||||
\(572\) | −0.0931657 | − | 0.0931657i | −0.00389545 | − | 0.00389545i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 18.5181i | 0.772930i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.1731 | − | 21.1731i | 0.881446 | − | 0.881446i | −0.112236 | − | 0.993682i | \(-0.535801\pi\) |
0.993682 | + | 0.112236i | \(0.0358012\pi\) | |||||||
\(578\) | −20.4320 | + | 20.4320i | −0.849859 | + | 0.849859i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 7.27666i | − | 0.301887i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.4783 | + | 23.4783i | 0.972373 | + | 0.972373i | ||||
\(584\) | −1.66870 | −0.0690512 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 26.6164 | 1.09951 | ||||||||
\(587\) | 25.2367 | + | 25.2367i | 1.04163 | + | 1.04163i | 0.999095 | + | 0.0425335i | \(0.0135429\pi\) |
0.0425335 | + | 0.999095i | \(0.486457\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.5713i | 1.13605i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −11.0847 | + | 11.0847i | −0.455577 | + | 0.455577i | ||||
\(593\) | 28.2414 | − | 28.2414i | 1.15973 | − | 1.15973i | 0.175202 | − | 0.984533i | \(-0.443942\pi\) |
0.984533 | − | 0.175202i | \(-0.0560577\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 16.4256i | − | 0.672820i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.107729 | + | 0.107729i | 0.00440537 | + | 0.00440537i | ||||
\(599\) | −15.8076 | −0.645881 | −0.322940 | − | 0.946419i | \(-0.604671\pi\) | ||||
−0.322940 | + | 0.946419i | \(0.604671\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.49573 | −0.101803 | −0.0509016 | − | 0.998704i | \(-0.516209\pi\) | ||||
−0.0509016 | + | 0.998704i | \(0.516209\pi\) | |||||||
\(602\) | 5.72058 | + | 5.72058i | 0.233154 | + | 0.233154i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 28.3148i | − | 1.15211i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.4046 | + | 15.4046i | −0.625253 | + | 0.625253i | −0.946870 | − | 0.321617i | \(-0.895774\pi\) |
0.321617 | + | 0.946870i | \(0.395774\pi\) | |||||||
\(608\) | −32.6784 | + | 32.6784i | −1.32528 | + | 1.32528i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 0.0944801i | − | 0.00382225i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.8394 | + | 12.8394i | 0.518580 | + | 0.518580i | 0.917142 | − | 0.398561i | \(-0.130490\pi\) |
−0.398561 | + | 0.917142i | \(0.630490\pi\) | |||||||
\(614\) | 33.7011 | 1.36007 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.46042 | 0.0991330 | ||||||||
\(617\) | 14.5354 | + | 14.5354i | 0.585173 | + | 0.585173i | 0.936320 | − | 0.351147i | \(-0.114208\pi\) |
−0.351147 | + | 0.936320i | \(0.614208\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 10.1884i | − | 0.409506i | −0.978814 | − | 0.204753i | \(-0.934361\pi\) | ||
0.978814 | − | 0.204753i | \(-0.0656391\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9.48646 | + | 9.48646i | −0.380372 | + | 0.380372i | ||||
\(623\) | −11.6338 | + | 11.6338i | −0.466099 | + | 0.466099i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 25.5605i | 1.02160i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −22.9056 | − | 22.9056i | −0.914033 | − | 0.914033i | ||||
\(629\) | 7.59392 | 0.302790 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.95627 | −0.276925 | −0.138462 | − | 0.990368i | \(-0.544216\pi\) | ||||
−0.138462 | + | 0.990368i | \(0.544216\pi\) | |||||||
\(632\) | −3.28130 | − | 3.28130i | −0.130523 | − | 0.130523i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 41.4798i | 1.64737i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.00747830 | − | 0.00747830i | 0.000296301 | − | 0.000296301i | ||||
\(638\) | 12.7089 | − | 12.7089i | 0.503149 | − | 0.503149i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.2049i | 1.43001i | 0.699120 | + | 0.715004i | \(0.253575\pi\) | ||||
−0.699120 | + | 0.715004i | \(0.746425\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.93368 | − | 4.93368i | −0.194565 | − | 0.194565i | 0.603100 | − | 0.797665i | \(-0.293932\pi\) |
−0.797665 | + | 0.603100i | \(0.793932\pi\) | |||||||
\(644\) | −15.5312 | −0.612015 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 19.9767 | 0.785972 | ||||||||
\(647\) | 10.7433 | + | 10.7433i | 0.422364 | + | 0.422364i | 0.886017 | − | 0.463653i | \(-0.153462\pi\) |
−0.463653 | + | 0.886017i | \(0.653462\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 66.5455i | − | 2.61214i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −32.4613 | + | 32.4613i | −1.27128 | + | 1.27128i | ||||
\(653\) | 14.0006 | − | 14.0006i | 0.547884 | − | 0.547884i | −0.377944 | − | 0.925828i | \(-0.623369\pi\) |
0.925828 | + | 0.377944i | \(0.123369\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 31.8370i | − | 1.24303i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.9658 | + | 12.9658i | 0.505459 | + | 0.505459i | ||||
\(659\) | −6.35539 | −0.247571 | −0.123785 | − | 0.992309i | \(-0.539503\pi\) | ||||
−0.123785 | + | 0.992309i | \(0.539503\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.73321 | 0.145205 | 0.0726025 | − | 0.997361i | \(-0.476870\pi\) | ||||
0.0726025 | + | 0.997361i | \(0.476870\pi\) | |||||||
\(662\) | −7.64873 | − | 7.64873i | −0.297276 | − | 0.297276i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 3.18020i | − | 0.123416i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.71909 | + | 7.71909i | −0.298884 | + | 0.298884i | ||||
\(668\) | −25.3185 | + | 25.3185i | −0.979601 | + | 0.979601i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.1394i | 1.04770i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.2398 | + | 32.2398i | 1.24275 | + | 1.24275i | 0.958854 | + | 0.283901i | \(0.0916288\pi\) |
0.283901 | + | 0.958854i | \(0.408371\pi\) | |||||||
\(674\) | 24.8294 | 0.956392 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 28.7678 | 1.10645 | ||||||||
\(677\) | 4.36523 | + | 4.36523i | 0.167769 | + | 0.167769i | 0.785998 | − | 0.618229i | \(-0.212149\pi\) |
−0.618229 | + | 0.785998i | \(0.712149\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.0262i | 0.538276i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −39.5681 | + | 39.5681i | −1.51514 | + | 1.51514i | ||||
\(683\) | −13.0185 | + | 13.0185i | −0.498138 | + | 0.498138i | −0.910858 | − | 0.412720i | \(-0.864579\pi\) |
0.412720 | + | 0.910858i | \(0.364579\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.05254i | 0.0783664i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.83505 | − | 9.83505i | −0.374958 | − | 0.374958i | ||||
\(689\) | 0.0623755 | 0.00237632 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.404163 | −0.0153751 | −0.00768755 | − | 0.999970i | \(-0.502447\pi\) | ||||
−0.00768755 | + | 0.999970i | \(0.502447\pi\) | |||||||
\(692\) | 17.3389 | + | 17.3389i | 0.659125 | + | 0.659125i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.8954i | 0.527461i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.9055 | + | 10.9055i | −0.413076 | + | 0.413076i | ||||
\(698\) | 13.9676 | − | 13.9676i | 0.528682 | − | 0.528682i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 21.5747i | − | 0.814864i | −0.913236 | − | 0.407432i | \(-0.866424\pi\) | ||
0.913236 | − | 0.407432i | \(-0.133576\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.8842 | + | 17.8842i | 0.674515 | + | 0.674515i | ||||
\(704\) | −54.0626 | −2.03756 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −50.8290 | −1.91298 | ||||||||
\(707\) | −9.11195 | − | 9.11195i | −0.342690 | − | 0.342690i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 51.3287i | 1.92769i | 0.266461 | + | 0.963846i | \(0.414146\pi\) | ||||
−0.266461 | + | 0.963846i | \(0.585854\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.08446 | + | 5.08446i | −0.190548 | + | 0.190548i | ||||
\(713\) | 24.0328 | − | 24.0328i | 0.900036 | − | 0.900036i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 24.6332i | − | 0.920585i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.79708 | + | 5.79708i | 0.216345 | + | 0.216345i | ||||
\(719\) | 18.4190 | 0.686911 | 0.343456 | − | 0.939169i | \(-0.388402\pi\) | ||||
0.343456 | + | 0.939169i | \(0.388402\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.38975 | −0.312450 | ||||||||
\(722\) | 19.4704 | + | 19.4704i | 0.724615 | + | 0.724615i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 28.3365i | 1.05312i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.2891 | + | 28.2891i | −1.04918 | + | 1.04918i | −0.0504586 | + | 0.998726i | \(0.516068\pi\) |
−0.998726 | + | 0.0504586i | \(0.983932\pi\) | |||||||
\(728\) | 0.00326833 | − | 0.00326833i | 0.000121132 | − | 0.000121132i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.73783i | 0.249208i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.6024 | + | 13.6024i | 0.502416 | + | 0.502416i | 0.912188 | − | 0.409772i | \(-0.134392\pi\) |
−0.409772 | + | 0.912188i | \(0.634392\pi\) | |||||||
\(734\) | −23.7714 | −0.877419 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 56.9690 | 2.09991 | ||||||||
\(737\) | −9.68639 | − | 9.68639i | −0.356803 | − | 0.356803i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.2219i | 1.00137i | 0.865629 | + | 0.500686i | \(0.166919\pi\) | ||||
−0.865629 | + | 0.500686i | \(0.833081\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.55999 | + | 8.55999i | −0.314247 | + | 0.314247i | ||||
\(743\) | 0.997164 | − | 0.997164i | 0.0365824 | − | 0.0365824i | −0.688579 | − | 0.725161i | \(-0.741765\pi\) |
0.725161 | + | 0.688579i | \(0.241765\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 39.5974i | 1.44976i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 15.0590 | + | 15.0590i | 0.550610 | + | 0.550610i | ||||
\(749\) | −6.72117 | −0.245586 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 53.3536 | 1.94690 | 0.973451 | − | 0.228895i | \(-0.0735113\pi\) | ||||
0.973451 | + | 0.228895i | \(0.0735113\pi\) | |||||||
\(752\) | −22.2913 | − | 22.2913i | −0.812880 | − | 0.812880i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 0.0337640i | − | 0.00122961i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.8721 | + | 11.8721i | −0.431497 | + | 0.431497i | −0.889138 | − | 0.457640i | \(-0.848695\pi\) |
0.457640 | + | 0.889138i | \(0.348695\pi\) | |||||||
\(758\) | 4.42851 | − | 4.42851i | 0.160851 | − | 0.160851i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.9016i | 1.37393i | 0.726690 | + | 0.686965i | \(0.241058\pi\) | ||||
−0.726690 | + | 0.686965i | \(0.758942\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.72784 | + | 8.72784i | 0.315969 | + | 0.315969i | ||||
\(764\) | 3.37660 | 0.122161 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.51056 | −0.162973 | ||||||||
\(767\) | −0.0883967 | − | 0.0883967i | −0.00319182 | − | 0.00319182i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 50.8876i | 1.83505i | 0.397673 | + | 0.917527i | \(0.369818\pi\) | ||||
−0.397673 | + | 0.917527i | \(0.630182\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −15.5019 | + | 15.5019i | −0.557924 | + | 0.557924i | ||||
\(773\) | 17.4266 | − | 17.4266i | 0.626790 | − | 0.626790i | −0.320469 | − | 0.947259i | \(-0.603841\pi\) |
0.947259 | + | 0.320469i | \(0.103841\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.13003i | 0.220055i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −29.8739 | − | 29.8739i | −1.07103 | − | 1.07103i | ||||
\(779\) | −51.3664 | −1.84039 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.5746 | −0.986695 | ||||||||
\(782\) | −17.4129 | − | 17.4129i | −0.622684 | − | 0.622684i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 3.52881i | − | 0.126029i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.7795 | − | 18.7795i | 0.669416 | − | 0.669416i | −0.288165 | − | 0.957581i | \(-0.593045\pi\) |
0.957581 | + | 0.288165i | \(0.0930451\pi\) | |||||||
\(788\) | 8.76194 | − | 8.76194i | 0.312131 | − | 0.312131i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.59949i | 0.199095i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.0360509 | + | 0.0360509i | 0.00128021 | + | 0.00128021i | ||||
\(794\) | −22.1405 | −0.785738 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −42.1858 | −1.49524 | ||||||||
\(797\) | −5.50268 | − | 5.50268i | −0.194915 | − | 0.194915i | 0.602901 | − | 0.797816i | \(-0.294011\pi\) |
−0.797816 | + | 0.602901i | \(0.794011\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.2714i | 0.540263i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −27.9714 | + | 27.9714i | −0.987705 | + | 0.987705i | ||||
\(803\) | 15.1994 | − | 15.1994i | 0.536375 | − | 0.536375i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.105122i | 0.00370275i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.98230 | − | 3.98230i | −0.140097 | − | 0.140097i | ||||
\(809\) | 13.0716 | 0.459574 | 0.229787 | − | 0.973241i | \(-0.426197\pi\) | ||||
0.229787 | + | 0.973241i | \(0.426197\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.00662423 | 0.000232608 | 0.000116304 | − | 1.00000i | \(-0.499963\pi\) | ||||
0.000116304 | 1.00000i | \(0.499963\pi\) | ||||||||
\(812\) | 2.43386 | + | 2.43386i | 0.0854117 | + | 0.0854117i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 51.3319i | 1.79918i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.8680 | + | 15.8680i | −0.555152 | + | 0.555152i | ||||
\(818\) | −24.0650 | + | 24.0650i | −0.841414 | + | 0.841414i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.3629i | 0.501270i | 0.968082 | + | 0.250635i | \(0.0806394\pi\) | ||||
−0.968082 | + | 0.250635i | \(0.919361\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.50624 | − | 5.50624i | −0.191936 | − | 0.191936i | 0.604596 | − | 0.796532i | \(-0.293334\pi\) |
−0.796532 | + | 0.604596i | \(0.793334\pi\) | |||||||
\(824\) | −3.66667 | −0.127734 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 24.2619 | 0.844180 | ||||||||
\(827\) | −6.58070 | − | 6.58070i | −0.228833 | − | 0.228833i | 0.583372 | − | 0.812205i | \(-0.301733\pi\) |
−0.812205 | + | 0.583372i | \(0.801733\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 37.1189i | − | 1.28919i | −0.764522 | − | 0.644597i | \(-0.777025\pi\) | ||
0.764522 | − | 0.644597i | \(-0.222975\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.0718148 | + | 0.0718148i | −0.00248973 | + | 0.00248973i | ||||
\(833\) | −1.20876 | + | 1.20876i | −0.0418812 | + | 0.0418812i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 70.9296i | 2.45315i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.69477 | − | 6.69477i | −0.231267 | − | 0.231267i | ||||
\(839\) | −36.8376 | −1.27178 | −0.635888 | − | 0.771782i | \(-0.719366\pi\) | ||||
−0.635888 | + | 0.771782i | \(0.719366\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.5807 | −0.916576 | ||||||||
\(842\) | 28.9223 | + | 28.9223i | 0.996730 | + | 0.996730i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 31.2367i | − | 1.07521i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.6326 | + | 14.6326i | −0.502782 | + | 0.502782i | ||||
\(848\) | 14.7167 | − | 14.7167i | 0.505372 | − | 0.505372i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 31.1779i | − | 1.06876i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36.7552 | − | 36.7552i | −1.25848 | − | 1.25848i | −0.951821 | − | 0.306655i | \(-0.900790\pi\) |
−0.306655 | − | 0.951821i | \(-0.599210\pi\) | |||||||
\(854\) | −9.89477 | −0.338592 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.93743 | −0.100399 | ||||||||
\(857\) | −12.2360 | − | 12.2360i | −0.417974 | − | 0.417974i | 0.466531 | − | 0.884505i | \(-0.345504\pi\) |
−0.884505 | + | 0.466531i | \(0.845504\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.9638i | 1.22707i | 0.789668 | + | 0.613535i | \(0.210253\pi\) | ||||
−0.789668 | + | 0.613535i | \(0.789747\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 39.0252 | − | 39.0252i | 1.32920 | − | 1.32920i | ||||
\(863\) | −8.62624 | + | 8.62624i | −0.293641 | + | 0.293641i | −0.838517 | − | 0.544876i | \(-0.816577\pi\) |
0.544876 | + | 0.838517i | \(0.316577\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 58.8129i | − | 1.99854i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.57764 | − | 7.57764i | −0.257202 | − | 0.257202i | ||||
\(869\) | 59.7756 | 2.02775 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.0257341 | −0.000871966 | ||||||||
\(872\) | 3.81443 | + | 3.81443i | 0.129173 | + | 0.129173i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 82.0171i | − | 2.77427i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.42813 | − | 2.42813i | 0.0819920 | − | 0.0819920i | −0.664921 | − | 0.746913i | \(-0.731535\pi\) |
0.746913 | + | 0.664921i | \(0.231535\pi\) | |||||||
\(878\) | 45.0821 | − | 45.0821i | 1.52145 | − | 1.52145i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.54850i | 0.220625i | 0.993897 | + | 0.110312i | \(0.0351851\pi\) | ||||
−0.993897 | + | 0.110312i | \(0.964815\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.8913 | − | 11.8913i | −0.400175 | − | 0.400175i | 0.478120 | − | 0.878295i | \(-0.341318\pi\) |
−0.878295 | + | 0.478120i | \(0.841318\pi\) | |||||||
\(884\) | 0.0400076 | 0.00134560 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −74.5168 | −2.50344 | ||||||||
\(887\) | 10.2116 | + | 10.2116i | 0.342872 | + | 0.342872i | 0.857446 | − | 0.514574i | \(-0.172050\pi\) |
−0.514574 | + | 0.857446i | \(0.672050\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 7.86167i | − | 0.263672i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 44.4844 | − | 44.4844i | 1.48945 | − | 1.48945i | ||||
\(893\) | −35.9651 | + | 35.9651i | −1.20353 | + | 1.20353i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 3.47652i | − | 0.116142i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 34.2603 | + | 34.2603i | 1.14328 | + | 1.14328i | ||||
\(899\) | −7.53226 | −0.251215 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.0821 | −0.335885 | ||||||||
\(902\) | −73.7169 | − | 73.7169i | −2.45450 | − | 2.45450i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.44721i | 0.0813929i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.9887 | − | 25.9887i | 0.862942 | − | 0.862942i | −0.128737 | − | 0.991679i | \(-0.541092\pi\) |
0.991679 | + | 0.128737i | \(0.0410922\pi\) | |||||||
\(908\) | 15.9062 | − | 15.9062i | 0.527865 | − | 0.527865i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51.9902i | 1.72251i | 0.508172 | + | 0.861256i | \(0.330322\pi\) | ||||
−0.508172 | + | 0.861256i | \(0.669678\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.9670 | + | 28.9670i | 0.958666 | + | 0.958666i | ||||
\(914\) | −51.7343 | −1.71122 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 27.6123 | 0.912337 | ||||||||
\(917\) | 2.38067 | + | 2.38067i | 0.0786168 | + | 0.0786168i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.77384i | 0.223448i | 0.993739 | + | 0.111724i | \(0.0356373\pi\) | ||||
−0.993739 | + | 0.111724i | \(0.964363\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10.3554 | + | 10.3554i | −0.341036 | + | 0.341036i | ||||
\(923\) | −0.0366290 | + | 0.0366290i | −0.00120566 | + | 0.00120566i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 21.6710i | − | 0.712154i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.92750 | − | 8.92750i | −0.293060 | − | 0.293060i | ||||
\(929\) | 22.6568 | 0.743347 | 0.371673 | − | 0.928364i | \(-0.378784\pi\) | ||||
0.371673 | + | 0.928364i | \(0.378784\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.69344 | −0.186595 | ||||||||
\(932\) | −37.0289 | − | 37.0289i | −1.21292 | − | 1.21292i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 82.8546i | 2.71108i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.1664 | − | 18.1664i | 0.593470 | − | 0.593470i | −0.345097 | − | 0.938567i | \(-0.612154\pi\) |
0.938567 | + | 0.345097i | \(0.112154\pi\) | |||||||
\(938\) | 3.53157 | − | 3.53157i | 0.115310 | − | 0.115310i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 12.6080i | − | 0.411010i | −0.978656 | − | 0.205505i | \(-0.934116\pi\) | ||
0.978656 | − | 0.205505i | \(-0.0658837\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44.7741 | + | 44.7741i | 1.45804 | + | 1.45804i | ||||
\(944\) | −41.7120 | −1.35761 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −45.5451 | −1.48080 | ||||||||
\(947\) | 6.67439 | + | 6.67439i | 0.216889 | + | 0.216889i | 0.807186 | − | 0.590297i | \(-0.200989\pi\) |
−0.590297 | + | 0.807186i | \(0.700989\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 0.0403806i | − | 0.00131081i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.528280 | + | 0.528280i | −0.0171217 | + | 0.0171217i | ||||
\(953\) | −12.6293 | + | 12.6293i | −0.409104 | + | 0.409104i | −0.881426 | − | 0.472322i | \(-0.843416\pi\) |
0.472322 | + | 0.881426i | \(0.343416\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7.60179i | 0.245859i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.37809 | + | 9.37809i | 0.302992 | + | 0.302992i | ||||
\(959\) | 23.0851 | 0.745456 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.54887 | −0.243512 | ||||||||
\(962\) | 0.0681874 | + | 0.0681874i | 0.00219845 | + | 0.00219845i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 50.3003i | 1.62006i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.9926 | + | 28.9926i | −0.932340 | + | 0.932340i | −0.997852 | − | 0.0655119i | \(-0.979132\pi\) |
0.0655119 | + | 0.997852i | \(0.479132\pi\) | |||||||
\(968\) | −6.39506 | + | 6.39506i | −0.205545 | + | 0.205545i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.51860i | 0.0808259i | 0.999183 | + | 0.0404129i | \(0.0128673\pi\) | ||||
−0.999183 | + | 0.0404129i | \(0.987133\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.94734 | + | 8.94734i | 0.286839 | + | 0.286839i | ||||
\(974\) | 0.557594 | 0.0178665 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 17.0115 | 0.544524 | ||||||||
\(977\) | 27.3808 | + | 27.3808i | 0.875990 | + | 0.875990i | 0.993117 | − | 0.117127i | \(-0.0373686\pi\) |
−0.117127 | + | 0.993117i | \(0.537369\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 92.6239i | − | 2.96027i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −30.4134 | + | 30.4134i | −0.970532 | + | 0.970532i | ||||
\(983\) | −24.7375 | + | 24.7375i | −0.789005 | + | 0.789005i | −0.981331 | − | 0.192326i | \(-0.938397\pi\) |
0.192326 | + | 0.981331i | \(0.438397\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.45748i | 0.173802i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.0942204 | + | 0.0942204i | 0.00299755 | + | 0.00299755i | ||||
\(989\) | 27.6631 | 0.879636 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.57525 | −0.272402 | −0.136201 | − | 0.990681i | \(-0.543489\pi\) | ||||
−0.136201 | + | 0.990681i | \(0.543489\pi\) | |||||||
\(992\) | 27.7951 | + | 27.7951i | 0.882495 | + | 0.882495i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 10.0534i | − | 0.318876i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.7299 | − | 10.7299i | 0.339820 | − | 0.339820i | −0.516480 | − | 0.856299i | \(-0.672758\pi\) |
0.856299 | + | 0.516480i | \(0.172758\pi\) | |||||||
\(998\) | −9.04353 | + | 9.04353i | −0.286268 | + | 0.286268i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1575.2.m.c.1268.1 | 12 | ||
3.2 | odd | 2 | 1575.2.m.d.1268.6 | 12 | |||
5.2 | odd | 4 | 1575.2.m.d.1457.6 | 12 | |||
5.3 | odd | 4 | 315.2.m.b.197.1 | yes | 12 | ||
5.4 | even | 2 | 315.2.m.a.8.6 | ✓ | 12 | ||
15.2 | even | 4 | inner | 1575.2.m.c.1457.1 | 12 | ||
15.8 | even | 4 | 315.2.m.a.197.6 | yes | 12 | ||
15.14 | odd | 2 | 315.2.m.b.8.1 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.m.a.8.6 | ✓ | 12 | 5.4 | even | 2 | ||
315.2.m.a.197.6 | yes | 12 | 15.8 | even | 4 | ||
315.2.m.b.8.1 | yes | 12 | 15.14 | odd | 2 | ||
315.2.m.b.197.1 | yes | 12 | 5.3 | odd | 4 | ||
1575.2.m.c.1268.1 | 12 | 1.1 | even | 1 | trivial | ||
1575.2.m.c.1457.1 | 12 | 15.2 | even | 4 | inner | ||
1575.2.m.d.1268.6 | 12 | 3.2 | odd | 2 | |||
1575.2.m.d.1457.6 | 12 | 5.2 | odd | 4 |