Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4410,2,Mod(881,4410)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4410, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("4410.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4410.b (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: | \(35.2140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.4 | ||
Root | \(0.923880 + 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4410.881 |
Dual form | 4410.2.b.d.881.5 |
$q$-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 \(\left(\mathbb{Z}/4410\mathbb{Z}\right)^\times\).
\(n\) | \(1081\) | \(2647\) | \(3431\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 1.00000i | − 0.316228i | ||||||||
\(11\) | − 0.152241i | − 0.0459024i | −0.999737 | − | 0.0229512i | \(-0.992694\pi\) | ||||
0.999737 | − | 0.0229512i | \(-0.00730623\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 5.19891i | − 1.44192i | −0.692977 | − | 0.720959i | \(-0.743701\pi\) | ||||
0.692977 | − | 0.720959i | \(-0.256299\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.881887 | −0.213889 | −0.106945 | − | 0.994265i | \(-0.534107\pi\) | ||||
−0.106945 | + | 0.994265i | \(0.534107\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.116520i | 0.0267316i | 0.999911 | + | 0.0133658i | \(0.00425459\pi\) | ||||
−0.999911 | + | 0.0133658i | \(0.995745\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.152241 | −0.0324579 | ||||||||
\(23\) | − 7.88764i | − 1.64469i | −0.568991 | − | 0.822344i | \(-0.692666\pi\) | ||||
0.568991 | − | 0.822344i | \(-0.307334\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.19891 | −1.01959 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 0.367542i | − 0.0682509i | −0.999418 | − | 0.0341254i | \(-0.989135\pi\) | ||||
0.999418 | − | 0.0341254i | \(-0.0108646\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.55007i | 0.817216i | 0.912710 | + | 0.408608i | \(0.133986\pi\) | ||||
−0.912710 | + | 0.408608i | \(0.866014\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.881887i | 0.151242i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.47727 | 0.242862 | 0.121431 | − | 0.992600i | \(-0.461252\pi\) | ||||
0.121431 | + | 0.992600i | \(0.461252\pi\) | |||||||
\(38\) | 0.116520 | 0.0189021 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | 3.38687 | 0.528941 | 0.264470 | − | 0.964394i | \(-0.414803\pi\) | ||||
0.264470 | + | 0.964394i | \(0.414803\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.54553 | −0.540688 | −0.270344 | − | 0.962764i | \(-0.587137\pi\) | ||||
−0.270344 | + | 0.962764i | \(0.587137\pi\) | |||||||
\(44\) | 0.152241i | 0.0229512i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.88764 | −1.16297 | ||||||||
\(47\) | −4.03572 | −0.588670 | −0.294335 | − | 0.955702i | \(-0.595098\pi\) | ||||
−0.294335 | + | 0.955702i | \(0.595098\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − 1.00000i | − 0.141421i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.19891i | 0.720959i | ||||||||
\(53\) | 8.80750i | 1.20980i | 0.796300 | + | 0.604902i | \(0.206788\pi\) | ||||
−0.796300 | + | 0.604902i | \(0.793212\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 0.152241i | − 0.0205282i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.367542 | −0.0482606 | ||||||||
\(59\) | 2.78016 | 0.361946 | 0.180973 | − | 0.983488i | \(-0.442075\pi\) | ||||
0.180973 | + | 0.983488i | \(0.442075\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 8.94495i | − 1.14528i | −0.819806 | − | 0.572642i | \(-0.805919\pi\) | ||||
0.819806 | − | 0.572642i | \(-0.194081\pi\) | |||||||
\(62\) | 4.55007 | 0.577859 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − 5.19891i | − 0.644846i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.82458 | −0.955925 | −0.477962 | − | 0.878380i | \(-0.658624\pi\) | ||||
−0.477962 | + | 0.878380i | \(0.658624\pi\) | |||||||
\(68\) | 0.881887 | 0.106945 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.6337i | 1.61802i | 0.587795 | + | 0.809010i | \(0.299996\pi\) | ||||
−0.587795 | + | 0.809010i | \(0.700004\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 11.6359i | − 1.36188i | −0.732338 | − | 0.680941i | \(-0.761571\pi\) | ||||
0.732338 | − | 0.680941i | \(-0.238429\pi\) | |||||||
\(74\) | − 1.47727i | − 0.171730i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 0.116520i | − 0.0133658i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.65685 | −0.636446 | −0.318223 | − | 0.948016i | \(-0.603086\pi\) | ||||
−0.318223 | + | 0.948016i | \(0.603086\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 3.38687i | − 0.374018i | ||||||||
\(83\) | 7.22625 | 0.793184 | 0.396592 | − | 0.917995i | \(-0.370193\pi\) | ||||
0.396592 | + | 0.917995i | \(0.370193\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.881887 | −0.0956541 | ||||||||
\(86\) | 3.54553i | 0.382324i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.152241 | 0.0162289 | ||||||||
\(89\) | −13.6241 | −1.44415 | −0.722075 | − | 0.691815i | \(-0.756811\pi\) | ||||
−0.722075 | + | 0.691815i | \(0.756811\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.88764i | 0.822344i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.03572i | 0.416253i | ||||||||
\(95\) | 0.116520i | 0.0119547i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 13.3910i | − 1.35965i | −0.733373 | − | 0.679827i | \(-0.762055\pi\) | ||||
0.733373 | − | 0.679827i | \(-0.237945\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 1.10973 | 0.110422 | 0.0552112 | − | 0.998475i | \(-0.482417\pi\) | ||||
0.0552112 | + | 0.998475i | \(0.482417\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 13.0984i | − 1.29062i | −0.763919 | − | 0.645312i | \(-0.776727\pi\) | ||||
0.763919 | − | 0.645312i | \(-0.223273\pi\) | |||||||
\(104\) | 5.19891 | 0.509795 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.80750 | 0.855460 | ||||||||
\(107\) | − 13.9359i | − 1.34723i | −0.739080 | − | 0.673617i | \(-0.764740\pi\) | ||||
0.739080 | − | 0.673617i | \(-0.235260\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.9587 | −1.81592 | −0.907958 | − | 0.419062i | \(-0.862359\pi\) | ||||
−0.907958 | + | 0.419062i | \(0.862359\pi\) | |||||||
\(110\) | −0.152241 | −0.0145156 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.59220i | 0.431998i | 0.976394 | + | 0.215999i | \(0.0693008\pi\) | ||||
−0.976394 | + | 0.215999i | \(0.930699\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 7.88764i | − 0.735526i | ||||||||
\(116\) | 0.367542i | 0.0341254i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 2.78016i | − 0.255935i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9768 | 0.997893 | ||||||||
\(122\) | −8.94495 | −0.809837 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − 4.55007i | − 0.408608i | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.35237 | −0.474946 | −0.237473 | − | 0.971394i | \(-0.576319\pi\) | ||||
−0.237473 | + | 0.971394i | \(0.576319\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.19891 | −0.455975 | ||||||||
\(131\) | 0.679129 | 0.0593358 | 0.0296679 | − | 0.999560i | \(-0.490555\pi\) | ||||
0.0296679 | + | 0.999560i | \(0.490555\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 7.82458i | 0.675941i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − 0.881887i | − 0.0756212i | ||||||||
\(137\) | 0.619541i | 0.0529309i | 0.999650 | + | 0.0264655i | \(0.00842520\pi\) | ||||
−0.999650 | + | 0.0264655i | \(0.991575\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 2.29807i | − 0.194920i | −0.995239 | − | 0.0974598i | \(-0.968928\pi\) | ||||
0.995239 | − | 0.0974598i | \(-0.0310717\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 13.6337 | 1.14411 | ||||||||
\(143\) | −0.791487 | −0.0661875 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 0.367542i | − 0.0305227i | ||||||||
\(146\) | −11.6359 | −0.962996 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.47727 | −0.121431 | ||||||||
\(149\) | − 11.2092i | − 0.918294i | −0.888360 | − | 0.459147i | \(-0.848155\pi\) | ||||
0.888360 | − | 0.459147i | \(-0.151845\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.96096 | 0.729233 | 0.364616 | − | 0.931158i | \(-0.381200\pi\) | ||||
0.364616 | + | 0.931158i | \(0.381200\pi\) | |||||||
\(152\) | −0.116520 | −0.00945103 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.55007i | 0.365470i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 7.89308i | − 0.629936i | −0.949102 | − | 0.314968i | \(-0.898006\pi\) | ||||
0.949102 | − | 0.314968i | \(-0.101994\pi\) | |||||||
\(158\) | 5.65685i | 0.450035i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 1.00000i | − 0.0790569i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.86325 | −0.772549 | −0.386275 | − | 0.922384i | \(-0.626238\pi\) | ||||
−0.386275 | + | 0.922384i | \(0.626238\pi\) | |||||||
\(164\) | −3.38687 | −0.264470 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 7.22625i | − 0.560866i | ||||||||
\(167\) | −18.4924 | −1.43098 | −0.715492 | − | 0.698621i | \(-0.753797\pi\) | ||||
−0.715492 | + | 0.698621i | \(0.753797\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14.0287 | −1.07913 | ||||||||
\(170\) | 0.881887i | 0.0676376i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.54553 | 0.270344 | ||||||||
\(173\) | −9.09425 | −0.691423 | −0.345711 | − | 0.938341i | \(-0.612362\pi\) | ||||
−0.345711 | + | 0.938341i | \(0.612362\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 0.152241i | − 0.0114756i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 13.6241i | 1.02117i | ||||||||
\(179\) | 0.762181i | 0.0569681i | 0.999594 | + | 0.0284841i | \(0.00906798\pi\) | ||||
−0.999594 | + | 0.0284841i | \(0.990932\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 4.68682i | − 0.348369i | −0.984713 | − | 0.174184i | \(-0.944271\pi\) | ||||
0.984713 | − | 0.174184i | \(-0.0557288\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.88764 | 0.581485 | ||||||||
\(185\) | 1.47727 | 0.108611 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.134259i | 0.00981801i | ||||||||
\(188\) | 4.03572 | 0.294335 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.116520 | 0.00845326 | ||||||||
\(191\) | − 18.9533i | − 1.37141i | −0.727879 | − | 0.685705i | \(-0.759494\pi\) | ||||
0.727879 | − | 0.685705i | \(-0.240506\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.43060 | 0.606848 | 0.303424 | − | 0.952856i | \(-0.401870\pi\) | ||||
0.303424 | + | 0.952856i | \(0.401870\pi\) | |||||||
\(194\) | −13.3910 | −0.961420 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 0.108381i | − 0.00772185i | −0.999993 | − | 0.00386093i | \(-0.998771\pi\) | ||||
0.999993 | − | 0.00386093i | \(-0.00122897\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 23.4524i | − 1.66249i | −0.555903 | − | 0.831247i | \(-0.687627\pi\) | ||||
0.555903 | − | 0.831247i | \(-0.312373\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 1.10973i | − 0.0780804i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.38687 | 0.236550 | ||||||||
\(206\) | −13.0984 | −0.912609 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 5.19891i | − 0.360480i | ||||||||
\(209\) | 0.0177391 | 0.00122704 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.57128 | −0.177014 | −0.0885070 | − | 0.996076i | \(-0.528210\pi\) | ||||
−0.0885070 | + | 0.996076i | \(0.528210\pi\) | |||||||
\(212\) | − 8.80750i | − 0.604902i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −13.9359 | −0.952639 | ||||||||
\(215\) | −3.54553 | −0.241803 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 18.9587i | 1.28405i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.152241i | 0.0102641i | ||||||||
\(221\) | 4.58485i | 0.308411i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.97547i | 0.199252i | 0.995025 | + | 0.0996262i | \(0.0317647\pi\) | ||||
−0.995025 | + | 0.0996262i | \(0.968235\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.59220 | 0.305469 | ||||||||
\(227\) | −13.2809 | −0.881486 | −0.440743 | − | 0.897633i | \(-0.645285\pi\) | ||||
−0.440743 | + | 0.897633i | \(0.645285\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 7.17210i | − 0.473946i | −0.971516 | − | 0.236973i | \(-0.923845\pi\) | ||||
0.971516 | − | 0.236973i | \(-0.0761553\pi\) | |||||||
\(230\) | −7.88764 | −0.520096 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.367542 | 0.0241303 | ||||||||
\(233\) | 14.0160i | 0.918220i | 0.888380 | + | 0.459110i | \(0.151832\pi\) | ||||
−0.888380 | + | 0.459110i | \(0.848168\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.03572 | −0.263261 | ||||||||
\(236\) | −2.78016 | −0.180973 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.8895i | 0.963123i | 0.876412 | + | 0.481562i | \(0.159930\pi\) | ||||
−0.876412 | + | 0.481562i | \(0.840070\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 23.1405i | − 1.49061i | −0.666722 | − | 0.745307i | \(-0.732303\pi\) | ||||
0.666722 | − | 0.745307i | \(-0.267697\pi\) | |||||||
\(242\) | − 10.9768i | − 0.705617i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.94495i | 0.572642i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.605778 | 0.0385447 | ||||||||
\(248\) | −4.55007 | −0.288929 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 1.00000i | − 0.0632456i | ||||||||
\(251\) | −2.66364 | −0.168128 | −0.0840638 | − | 0.996460i | \(-0.526790\pi\) | ||||
−0.0840638 | + | 0.996460i | \(0.526790\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.20082 | −0.0754950 | ||||||||
\(254\) | 5.35237i | 0.335838i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.239169 | 0.0149190 | 0.00745948 | − | 0.999972i | \(-0.497626\pi\) | ||||
0.00745948 | + | 0.999972i | \(0.497626\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5.19891i | 0.322423i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 0.679129i | − 0.0419567i | ||||||||
\(263\) | 21.1139i | 1.30194i | 0.759104 | + | 0.650969i | \(0.225637\pi\) | ||||
−0.759104 | + | 0.650969i | \(0.774363\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.80750i | 0.541041i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.82458 | 0.477962 | ||||||||
\(269\) | 19.6233 | 1.19646 | 0.598228 | − | 0.801326i | \(-0.295872\pi\) | ||||
0.598228 | + | 0.801326i | \(0.295872\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 15.8648i | − 0.963715i | −0.876250 | − | 0.481857i | \(-0.839962\pi\) | ||||
0.876250 | − | 0.481857i | \(-0.160038\pi\) | |||||||
\(272\) | −0.881887 | −0.0534723 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.619541 | 0.0374278 | ||||||||
\(275\) | − 0.152241i | − 0.00918047i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.0508 | 0.784149 | 0.392074 | − | 0.919934i | \(-0.371758\pi\) | ||||
0.392074 | + | 0.919934i | \(0.371758\pi\) | |||||||
\(278\) | −2.29807 | −0.137829 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.3133i | 1.21179i | 0.795544 | + | 0.605896i | \(0.207185\pi\) | ||||
−0.795544 | + | 0.605896i | \(0.792815\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.7412i | 1.58960i | 0.606874 | + | 0.794798i | \(0.292423\pi\) | ||||
−0.606874 | + | 0.794798i | \(0.707577\pi\) | |||||||
\(284\) | − 13.6337i | − 0.809010i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.791487i | 0.0468016i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.2223 | −0.954251 | ||||||||
\(290\) | −0.367542 | −0.0215828 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.6359i | 0.680941i | ||||||||
\(293\) | 22.1435 | 1.29364 | 0.646819 | − | 0.762644i | \(-0.276099\pi\) | ||||
0.646819 | + | 0.762644i | \(0.276099\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.78016 | 0.161867 | ||||||||
\(296\) | 1.47727i | 0.0858648i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −11.2092 | −0.649332 | ||||||||
\(299\) | −41.0072 | −2.37151 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − 8.96096i | − 0.515645i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.116520i | 0.00668289i | ||||||||
\(305\) | − 8.94495i | − 0.512186i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 26.5458i | − 1.51505i | −0.652805 | − | 0.757526i | \(-0.726408\pi\) | ||||
0.652805 | − | 0.757526i | \(-0.273592\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.55007 | 0.258426 | ||||||||
\(311\) | 19.9310 | 1.13018 | 0.565092 | − | 0.825028i | \(-0.308841\pi\) | ||||
0.565092 | + | 0.825028i | \(0.308841\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 30.3170i | − 1.71362i | −0.515635 | − | 0.856808i | \(-0.672444\pi\) | ||||
0.515635 | − | 0.856808i | \(-0.327556\pi\) | |||||||
\(314\) | −7.89308 | −0.445432 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.65685 | 0.318223 | ||||||||
\(317\) | − 27.6593i | − 1.55350i | −0.629809 | − | 0.776750i | \(-0.716867\pi\) | ||||
0.629809 | − | 0.776750i | \(-0.283133\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.0559550 | −0.00313288 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 0.102758i | − 0.00571759i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 5.19891i | − 0.288384i | ||||||||
\(326\) | 9.86325i | 0.546275i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.38687i | 0.187009i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.0428 | −1.10165 | −0.550827 | − | 0.834620i | \(-0.685687\pi\) | ||||
−0.550827 | + | 0.834620i | \(0.685687\pi\) | |||||||
\(332\) | −7.22625 | −0.396592 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 18.4924i | 1.01186i | ||||||||
\(335\) | −7.82458 | −0.427503 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.5368 | −1.33660 | −0.668302 | − | 0.743890i | \(-0.732978\pi\) | ||||
−0.668302 | + | 0.743890i | \(0.732978\pi\) | |||||||
\(338\) | 14.0287i | 0.763060i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.881887 | 0.0478270 | ||||||||
\(341\) | 0.692706 | 0.0375121 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − 3.54553i | − 0.191162i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.09425i | 0.488910i | ||||||||
\(347\) | 30.4845i | 1.63650i | 0.574866 | + | 0.818248i | \(0.305054\pi\) | ||||
−0.574866 | + | 0.818248i | \(0.694946\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.0443i | 1.50118i | 0.660769 | + | 0.750589i | \(0.270230\pi\) | ||||
−0.660769 | + | 0.750589i | \(0.729770\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.152241 | −0.00811447 | ||||||||
\(353\) | −31.7437 | −1.68955 | −0.844774 | − | 0.535123i | \(-0.820265\pi\) | ||||
−0.844774 | + | 0.535123i | \(0.820265\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.6337i | 0.723600i | ||||||||
\(356\) | 13.6241 | 0.722075 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.762181 | 0.0402825 | ||||||||
\(359\) | 24.8245i | 1.31018i | 0.755549 | + | 0.655092i | \(0.227370\pi\) | ||||
−0.755549 | + | 0.655092i | \(0.772630\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9864 | 0.999285 | ||||||||
\(362\) | −4.68682 | −0.246334 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 11.6359i | − 0.609052i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 7.06147i | − 0.368606i | −0.982870 | − | 0.184303i | \(-0.940997\pi\) | ||||
0.982870 | − | 0.184303i | \(-0.0590027\pi\) | |||||||
\(368\) | − 7.88764i | − 0.411172i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 1.47727i | − 0.0767998i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.3300 | 1.15621 | 0.578103 | − | 0.815964i | \(-0.303793\pi\) | ||||
0.578103 | + | 0.815964i | \(0.303793\pi\) | |||||||
\(374\) | 0.134259 | 0.00694238 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − 4.03572i | − 0.208126i | ||||||||
\(377\) | −1.91082 | −0.0984122 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.4625 | −1.61612 | −0.808059 | − | 0.589101i | \(-0.799482\pi\) | ||||
−0.808059 | + | 0.589101i | \(0.799482\pi\) | |||||||
\(380\) | − 0.116520i | − 0.00597736i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −18.9533 | −0.969734 | ||||||||
\(383\) | −5.01389 | −0.256198 | −0.128099 | − | 0.991761i | \(-0.540888\pi\) | ||||
−0.128099 | + | 0.991761i | \(0.540888\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 8.43060i | − 0.429106i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.3910i | 0.679827i | ||||||||
\(389\) | 10.4490i | 0.529787i | 0.964278 | + | 0.264893i | \(0.0853368\pi\) | ||||
−0.964278 | + | 0.264893i | \(0.914663\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.95601i | 0.351781i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.108381 | −0.00546018 | ||||||||
\(395\) | −5.65685 | −0.284627 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 10.9191i | − 0.548012i | −0.961728 | − | 0.274006i | \(-0.911651\pi\) | ||||
0.961728 | − | 0.274006i | \(-0.0883489\pi\) | |||||||
\(398\) | −23.4524 | −1.17556 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 8.87351i | 0.443122i | 0.975147 | + | 0.221561i | \(0.0711151\pi\) | ||||
−0.975147 | + | 0.221561i | \(0.928885\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.6554 | 1.17836 | ||||||||
\(404\) | −1.10973 | −0.0552112 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 0.224902i | − 0.0111480i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.54924i | 0.0766052i | 0.999266 | + | 0.0383026i | \(0.0121951\pi\) | ||||
−0.999266 | + | 0.0383026i | \(0.987805\pi\) | |||||||
\(410\) | − 3.38687i | − 0.167266i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.0984i | 0.645312i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.22625 | 0.354723 | ||||||||
\(416\) | −5.19891 | −0.254898 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 0.0177391i | 0 0.000867650i | ||||||||
\(419\) | 7.71604 | 0.376953 | 0.188477 | − | 0.982078i | \(-0.439645\pi\) | ||||
0.188477 | + | 0.982078i | \(0.439645\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.1546 | −1.66459 | −0.832297 | − | 0.554330i | \(-0.812975\pi\) | ||||
−0.832297 | + | 0.554330i | \(0.812975\pi\) | |||||||
\(422\) | 2.57128i | 0.125168i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.80750 | −0.427730 | ||||||||
\(425\) | −0.881887 | −0.0427778 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 13.9359i | 0.673617i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.54553i | 0.170981i | ||||||||
\(431\) | 38.3931i | 1.84933i | 0.380781 | + | 0.924665i | \(0.375655\pi\) | ||||
−0.380781 | + | 0.924665i | \(0.624345\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 7.93869i | − 0.381509i | −0.981638 | − | 0.190754i | \(-0.938907\pi\) | ||||
0.981638 | − | 0.190754i | \(-0.0610934\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.9587 | 0.907958 | ||||||||
\(437\) | 0.919069 | 0.0439651 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 38.4010i | 1.83278i | 0.400289 | + | 0.916389i | \(0.368910\pi\) | ||||
−0.400289 | + | 0.916389i | \(0.631090\pi\) | |||||||
\(440\) | 0.152241 | 0.00725780 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.58485 | 0.218079 | ||||||||
\(443\) | − 24.0926i | − 1.14467i | −0.820019 | − | 0.572337i | \(-0.806037\pi\) | ||||
0.820019 | − | 0.572337i | \(-0.193963\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.6241 | −0.645843 | ||||||||
\(446\) | 2.97547 | 0.140893 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 40.1788i | − 1.89615i | −0.318041 | − | 0.948077i | \(-0.603025\pi\) | ||||
0.318041 | − | 0.948077i | \(-0.396975\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 0.515621i | − 0.0242796i | ||||||||
\(452\) | − 4.59220i | − 0.215999i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.2809i | 0.623305i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.8309 | 0.600203 | 0.300101 | − | 0.953907i | \(-0.402980\pi\) | ||||
0.300101 | + | 0.953907i | \(0.402980\pi\) | |||||||
\(458\) | −7.17210 | −0.335130 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.88764i | 0.367763i | ||||||||
\(461\) | −7.96722 | −0.371071 | −0.185535 | − | 0.982638i | \(-0.559402\pi\) | ||||
−0.185535 | + | 0.982638i | \(0.559402\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.2773 | 1.22121 | 0.610605 | − | 0.791935i | \(-0.290926\pi\) | ||||
0.610605 | + | 0.791935i | \(0.290926\pi\) | |||||||
\(464\) | − 0.367542i | − 0.0170627i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.0160 | 0.649279 | ||||||||
\(467\) | 22.5709 | 1.04446 | 0.522229 | − | 0.852805i | \(-0.325101\pi\) | ||||
0.522229 | + | 0.852805i | \(0.325101\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.03572i | 0.186154i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.78016i | 0.127967i | ||||||||
\(473\) | 0.539775i | 0.0248189i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.116520i | 0.00534631i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14.8895 | 0.681031 | ||||||||
\(479\) | 23.9665 | 1.09506 | 0.547528 | − | 0.836787i | \(-0.315569\pi\) | ||||
0.547528 | + | 0.836787i | \(0.315569\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 7.68022i | − 0.350188i | ||||||||
\(482\) | −23.1405 | −1.05402 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.9768 | −0.498946 | ||||||||
\(485\) | − 13.3910i | − 0.608056i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.3699 | 1.73871 | 0.869354 | − | 0.494191i | \(-0.164535\pi\) | ||||
0.869354 | + | 0.494191i | \(0.164535\pi\) | |||||||
\(488\) | 8.94495 | 0.404919 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 7.83834i | − 0.353740i | −0.984234 | − | 0.176870i | \(-0.943403\pi\) | ||||
0.984234 | − | 0.176870i | \(-0.0565971\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.324131i | 0.0145981i | ||||||||
\(494\) | − 0.605778i | − 0.0272552i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.55007i | 0.204304i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.7056 | −0.613549 | −0.306775 | − | 0.951782i | \(-0.599250\pi\) | ||||
−0.306775 | + | 0.951782i | \(0.599250\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.66364i | 0.118884i | ||||||||
\(503\) | −3.02437 | −0.134850 | −0.0674249 | − | 0.997724i | \(-0.521478\pi\) | ||||
−0.0674249 | + | 0.997724i | \(0.521478\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.10973 | 0.0493824 | ||||||||
\(506\) | 1.20082i | 0.0533830i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.35237 | 0.237473 | ||||||||
\(509\) | 14.2914 | 0.633457 | 0.316728 | − | 0.948516i | \(-0.397416\pi\) | ||||
0.316728 | + | 0.948516i | \(0.397416\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 0.239169i | − 0.0105493i | ||||||||
\(515\) | − 13.0984i | − 0.577185i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.614402i | 0.0270214i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.19891 | 0.227987 | ||||||||
\(521\) | 13.8158 | 0.605279 | 0.302640 | − | 0.953105i | \(-0.402132\pi\) | ||||
0.302640 | + | 0.953105i | \(0.402132\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 7.48213i | − 0.327171i | −0.986529 | − | 0.163585i | \(-0.947694\pi\) | ||||
0.986529 | − | 0.163585i | \(-0.0523059\pi\) | |||||||
\(524\) | −0.679129 | −0.0296679 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.1139 | 0.920610 | ||||||||
\(527\) | − 4.01264i | − 0.174794i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −39.2149 | −1.70500 | ||||||||
\(530\) | 8.80750 | 0.382573 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 17.6081i | − 0.762690i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 13.9359i | − 0.602502i | ||||||||
\(536\) | − 7.82458i | − 0.337970i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 19.6233i | − 0.846022i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.0780 | −0.863222 | −0.431611 | − | 0.902060i | \(-0.642055\pi\) | ||||
−0.431611 | + | 0.902060i | \(0.642055\pi\) | |||||||
\(542\) | −15.8648 | −0.681449 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.881887i | 0.0378106i | ||||||||
\(545\) | −18.9587 | −0.812102 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.897902 | −0.0383915 | −0.0191958 | − | 0.999816i | \(-0.506111\pi\) | ||||
−0.0191958 | + | 0.999816i | \(0.506111\pi\) | |||||||
\(548\) | − 0.619541i | − 0.0264655i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.152241 | −0.00649158 | ||||||||
\(551\) | 0.0428261 | 0.00182445 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − 13.0508i | − 0.554477i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.29807i | 0.0974598i | ||||||||
\(557\) | − 19.2977i | − 0.817670i | −0.912608 | − | 0.408835i | \(-0.865935\pi\) | ||||
0.912608 | − | 0.408835i | \(-0.134065\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.4329i | 0.779629i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20.3133 | 0.856866 | ||||||||
\(563\) | 2.18155 | 0.0919412 | 0.0459706 | − | 0.998943i | \(-0.485362\pi\) | ||||
0.0459706 | + | 0.998943i | \(0.485362\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.59220i | 0.193195i | ||||||||
\(566\) | 26.7412 | 1.12401 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −13.6337 | −0.572056 | ||||||||
\(569\) | − 3.27133i | − 0.137141i | −0.997646 | − | 0.0685707i | \(-0.978156\pi\) | ||||
0.997646 | − | 0.0685707i | \(-0.0218439\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.91270 | −0.121893 | −0.0609463 | − | 0.998141i | \(-0.519412\pi\) | ||||
−0.0609463 | + | 0.998141i | \(0.519412\pi\) | |||||||
\(572\) | 0.791487 | 0.0330937 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 7.88764i | − 0.328937i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.29639i | 0.0955998i | 0.998857 | + | 0.0477999i | \(0.0152210\pi\) | ||||
−0.998857 | + | 0.0477999i | \(0.984779\pi\) | |||||||
\(578\) | 16.2223i | 0.674758i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.367542i | 0.0152614i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.34086 | 0.0555328 | ||||||||
\(584\) | 11.6359 | 0.481498 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − 22.1435i | − 0.914740i | ||||||||
\(587\) | 11.1071 | 0.458438 | 0.229219 | − | 0.973375i | \(-0.426383\pi\) | ||||
0.229219 | + | 0.973375i | \(0.426383\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.530174 | −0.0218455 | ||||||||
\(590\) | − 2.78016i | − 0.114457i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.47727 | 0.0607156 | ||||||||
\(593\) | 18.3789 | 0.754730 | 0.377365 | − | 0.926065i | \(-0.376830\pi\) | ||||
0.377365 | + | 0.926065i | \(0.376830\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.2092i | 0.459147i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 41.0072i | 1.67691i | ||||||||
\(599\) | − 48.8861i | − 1.99743i | −0.0506712 | − | 0.998715i | \(-0.516136\pi\) | ||||
0.0506712 | − | 0.998715i | \(-0.483864\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 6.21975i | − 0.253709i | −0.991921 | − | 0.126854i | \(-0.959512\pi\) | ||||
0.991921 | − | 0.126854i | \(-0.0404881\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.96096 | −0.364616 | ||||||||
\(605\) | 10.9768 | 0.446271 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 44.0234i | 1.78685i | 0.449209 | + | 0.893427i | \(0.351706\pi\) | ||||
−0.449209 | + | 0.893427i | \(0.648294\pi\) | |||||||
\(608\) | 0.116520 | 0.00472552 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.94495 | −0.362170 | ||||||||
\(611\) | 20.9814i | 0.848815i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 46.5712 | 1.88099 | 0.940496 | − | 0.339805i | \(-0.110361\pi\) | ||||
0.940496 | + | 0.339805i | \(0.110361\pi\) | |||||||
\(614\) | −26.5458 | −1.07130 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 19.6155i | − 0.789688i | −0.918748 | − | 0.394844i | \(-0.870799\pi\) | ||||
0.918748 | − | 0.394844i | \(-0.129201\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 23.6497i | − 0.950561i | −0.879834 | − | 0.475281i | \(-0.842347\pi\) | ||||
0.879834 | − | 0.475281i | \(-0.157653\pi\) | |||||||
\(620\) | − 4.55007i | − 0.182735i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 19.9310i | − 0.799160i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −30.3170 | −1.21171 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.89308i | 0.314968i | ||||||||
\(629\) | −1.30279 | −0.0519456 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.0156 | 0.597763 | 0.298882 | − | 0.954290i | \(-0.403386\pi\) | ||||
0.298882 | + | 0.954290i | \(0.403386\pi\) | |||||||
\(632\) | − 5.65685i | − 0.225018i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −27.6593 | −1.09849 | ||||||||
\(635\) | −5.35237 | −0.212402 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.0559550i | 0.00221528i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000i | 0.0395285i | ||||||||
\(641\) | 19.3652i | 0.764878i | 0.923981 | + | 0.382439i | \(0.124916\pi\) | ||||
−0.923981 | + | 0.382439i | \(0.875084\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.76486i | 0.266780i | 0.991064 | + | 0.133390i | \(0.0425863\pi\) | ||||
−0.991064 | + | 0.133390i | \(0.957414\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.102758 | −0.00404294 | ||||||||
\(647\) | 10.7335 | 0.421978 | 0.210989 | − | 0.977488i | \(-0.432332\pi\) | ||||
0.210989 | + | 0.977488i | \(0.432332\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 0.423255i | − 0.0166142i | ||||||||
\(650\) | −5.19891 | −0.203918 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.86325 | 0.386275 | ||||||||
\(653\) | 28.2027i | 1.10366i | 0.833958 | + | 0.551828i | \(0.186070\pi\) | ||||
−0.833958 | + | 0.551828i | \(0.813930\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.679129 | 0.0265358 | ||||||||
\(656\) | 3.38687 | 0.132235 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.7176i | 0.417497i | 0.977969 | + | 0.208748i | \(0.0669389\pi\) | ||||
−0.977969 | + | 0.208748i | \(0.933061\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.8951i | 1.27947i | 0.768594 | + | 0.639736i | \(0.220956\pi\) | ||||
−0.768594 | + | 0.639736i | \(0.779044\pi\) | |||||||
\(662\) | 20.0428i | 0.778987i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.22625i | 0.280433i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.89904 | −0.112251 | ||||||||
\(668\) | 18.4924 | 0.715492 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.82458i | 0.302290i | ||||||||
\(671\) | −1.36179 | −0.0525712 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.14123 | −0.275274 | −0.137637 | − | 0.990483i | \(-0.543951\pi\) | ||||
−0.137637 | + | 0.990483i | \(0.543951\pi\) | |||||||
\(674\) | 24.5368i | 0.945121i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 14.0287 | 0.539565 | ||||||||
\(677\) | 31.0775 | 1.19440 | 0.597202 | − | 0.802091i | \(-0.296279\pi\) | ||||
0.597202 | + | 0.802091i | \(0.296279\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − 0.881887i | − 0.0338188i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 0.692706i | − 0.0265251i | ||||||||
\(683\) | 33.3984i | 1.27795i | 0.769226 | + | 0.638977i | \(0.220642\pi\) | ||||
−0.769226 | + | 0.638977i | \(0.779358\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.619541i | 0.0236714i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.54553 | −0.135172 | ||||||||
\(689\) | 45.7894 | 1.74444 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.8000i | 1.39994i | 0.714173 | + | 0.699969i | \(0.246803\pi\) | ||||
−0.714173 | + | 0.699969i | \(0.753197\pi\) | |||||||
\(692\) | 9.09425 | 0.345711 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30.4845 | 1.15718 | ||||||||
\(695\) | − 2.29807i | − 0.0871707i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.98684 | −0.113135 | ||||||||
\(698\) | 28.0443 | 1.06149 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 28.3473i | − 1.07066i | −0.844643 | − | 0.535330i | \(-0.820187\pi\) | ||||
0.844643 | − | 0.535330i | \(-0.179813\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.172132i | 0.00649209i | ||||||||
\(704\) | 0.152241i | 0.00573780i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 31.7437i | 1.19469i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.1618 | −0.569412 | −0.284706 | − | 0.958615i | \(-0.591896\pi\) | ||||
−0.284706 | + | 0.958615i | \(0.591896\pi\) | |||||||
\(710\) | 13.6337 | 0.511663 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 13.6241i | − 0.510584i | ||||||||
\(713\) | 35.8893 | 1.34406 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.791487 | −0.0295999 | ||||||||
\(716\) | − 0.762181i | − 0.0284841i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 24.8245 | 0.926440 | ||||||||
\(719\) | −43.1993 | −1.61106 | −0.805532 | − | 0.592553i | \(-0.798120\pi\) | ||||
−0.805532 | + | 0.592553i | \(0.798120\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − 18.9864i | − 0.706601i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.68682i | 0.174184i | ||||||||
\(725\) | − 0.367542i | − 0.0136502i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.9829i | 1.03783i | 0.854826 | + | 0.518914i | \(0.173664\pi\) | ||||
−0.854826 | + | 0.518914i | \(0.826336\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −11.6359 | −0.430665 | ||||||||
\(731\) | 3.12676 | 0.115647 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 36.1041i | − 1.33354i | −0.745266 | − | 0.666768i | \(-0.767677\pi\) | ||||
0.745266 | − | 0.666768i | \(-0.232323\pi\) | |||||||
\(734\) | −7.06147 | −0.260644 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.88764 | −0.290742 | ||||||||
\(737\) | 1.19122i | 0.0438792i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.3495 | −0.380713 | −0.190357 | − | 0.981715i | \(-0.560964\pi\) | ||||
−0.190357 | + | 0.981715i | \(0.560964\pi\) | |||||||
\(740\) | −1.47727 | −0.0543057 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 31.7753i | − 1.16572i | −0.812572 | − | 0.582861i | \(-0.801933\pi\) | ||||
0.812572 | − | 0.582861i | \(-0.198067\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 11.2092i | − 0.410673i | ||||||||
\(746\) | − 22.3300i | − 0.817561i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 0.134259i | − 0.00490901i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.0292 | 0.475443 | 0.237721 | − | 0.971333i | \(-0.423599\pi\) | ||||
0.237721 | + | 0.971333i | \(0.423599\pi\) | |||||||
\(752\) | −4.03572 | −0.147168 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.91082i | 0.0695879i | ||||||||
\(755\) | 8.96096 | 0.326123 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.26385 | 0.300355 | 0.150177 | − | 0.988659i | \(-0.452016\pi\) | ||||
0.150177 | + | 0.988659i | \(0.452016\pi\) | |||||||
\(758\) | 31.4625i | 1.14277i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.116520 | −0.00422663 | ||||||||
\(761\) | 50.8346 | 1.84275 | 0.921377 | − | 0.388670i | \(-0.127066\pi\) | ||||
0.921377 | + | 0.388670i | \(0.127066\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 18.9533i | 0.685705i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.01389i | 0.181159i | ||||||||
\(767\) | − 14.4538i | − 0.521897i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.8781i | 1.61835i | 0.587570 | + | 0.809174i | \(0.300085\pi\) | ||||
−0.587570 | + | 0.809174i | \(0.699915\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.43060 | −0.303424 | ||||||||
\(773\) | −3.43559 | −0.123569 | −0.0617847 | − | 0.998089i | \(-0.519679\pi\) | ||||
−0.0617847 | + | 0.998089i | \(0.519679\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.55007i | 0.163443i | ||||||||
\(776\) | 13.3910 | 0.480710 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.4490 | 0.374616 | ||||||||
\(779\) | 0.394639i | 0.0141394i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.07560 | 0.0742709 | ||||||||
\(782\) | 6.95601 | 0.248746 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 7.89308i | − 0.281716i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.5020i | 0.516942i | 0.966019 | + | 0.258471i | \(0.0832187\pi\) | ||||
−0.966019 | + | 0.258471i | \(0.916781\pi\) | |||||||
\(788\) | 0.108381i | 0.00386093i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.65685i | 0.201262i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −46.5040 | −1.65141 | ||||||||
\(794\) | −10.9191 | −0.387503 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 23.4524i | 0.831247i | ||||||||
\(797\) | −36.3121 | −1.28624 | −0.643120 | − | 0.765766i | \(-0.722360\pi\) | ||||
−0.643120 | + | 0.765766i | \(0.722360\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.55905 | 0.125910 | ||||||||
\(800\) | − 1.00000i | − 0.0353553i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.87351 | 0.313334 | ||||||||
\(803\) | −1.77146 | −0.0625136 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 23.6554i | − 0.833226i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.10973i | 0.0390402i | ||||||||
\(809\) | − 11.8145i | − 0.415375i | −0.978195 | − | 0.207687i | \(-0.933406\pi\) | ||||
0.978195 | − | 0.207687i | \(-0.0665937\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 47.7615i | − 1.67713i | −0.544799 | − | 0.838566i | \(-0.683394\pi\) | ||||
0.544799 | − | 0.838566i | \(-0.316606\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.224902 | −0.00788280 | ||||||||
\(815\) | −9.86325 | −0.345494 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 0.413126i | − 0.0144534i | ||||||||
\(818\) | 1.54924 | 0.0541680 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.38687 | −0.118275 | ||||||||
\(821\) | 40.7291i | 1.42146i | 0.703467 | + | 0.710728i | \(0.251635\pi\) | ||||
−0.703467 | + | 0.710728i | \(0.748365\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 50.8205 | 1.77149 | 0.885745 | − | 0.464172i | \(-0.153648\pi\) | ||||
0.885745 | + | 0.464172i | \(0.153648\pi\) | |||||||
\(824\) | 13.0984 | 0.456305 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.3852i | 1.23046i | 0.788347 | + | 0.615231i | \(0.210937\pi\) | ||||
−0.788347 | + | 0.615231i | \(0.789063\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 46.4408i | − 1.61296i | −0.591263 | − | 0.806478i | \(-0.701371\pi\) | ||||
0.591263 | − | 0.806478i | \(-0.298629\pi\) | |||||||
\(830\) | − 7.22625i | − 0.250827i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.19891i | 0.180240i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.4924 | −0.639955 | ||||||||
\(836\) | −0.0177391 | −0.000613521 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 7.71604i | − 0.266546i | ||||||||
\(839\) | −28.1665 | −0.972416 | −0.486208 | − | 0.873843i | \(-0.661620\pi\) | ||||
−0.486208 | + | 0.873843i | \(0.661620\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.8649 | 0.995342 | ||||||||
\(842\) | 34.1546i | 1.17705i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.57128 | 0.0885070 | ||||||||
\(845\) | −14.0287 | −0.482602 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.80750i | 0.302451i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.881887i | 0.0302485i | ||||||||
\(851\) | − 11.6522i | − 0.399433i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 19.1972i | − 0.657301i | −0.944452 | − | 0.328650i | \(-0.893406\pi\) | ||||
0.944452 | − | 0.328650i | \(-0.106594\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.9359 | 0.476319 | ||||||||
\(857\) | −0.0426640 | −0.00145738 | −0.000728688 | − | 1.00000i | \(-0.500232\pi\) | ||||
−0.000728688 | 1.00000i | \(0.500232\pi\) | ||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.9055i | 1.53216i | 0.642747 | + | 0.766079i | \(0.277795\pi\) | ||||
−0.642747 | + | 0.766079i | \(0.722205\pi\) | |||||||
\(860\) | 3.54553 | 0.120902 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 38.3931 | 1.30767 | ||||||||
\(863\) | 2.04004i | 0.0694439i | 0.999397 | + | 0.0347220i | \(0.0110546\pi\) | ||||
−0.999397 | + | 0.0347220i | \(0.988945\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.09425 | −0.309214 | ||||||||
\(866\) | −7.93869 | −0.269768 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.861205i | 0.0292144i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40.6793i | 1.37837i | ||||||||
\(872\) | − 18.9587i | − 0.642023i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − 0.919069i | − 0.0310880i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.5037 | 0.861200 | 0.430600 | − | 0.902543i | \(-0.358302\pi\) | ||||
0.430600 | + | 0.902543i | \(0.358302\pi\) | |||||||
\(878\) | 38.4010 | 1.29597 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − 0.152241i | − 0.00513204i | ||||||||
\(881\) | −20.2983 | −0.683866 | −0.341933 | − | 0.939724i | \(-0.611082\pi\) | ||||
−0.341933 | + | 0.939724i | \(0.611082\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 50.1046 | 1.68615 | 0.843077 | − | 0.537793i | \(-0.180742\pi\) | ||||
0.843077 | + | 0.537793i | \(0.180742\pi\) | |||||||
\(884\) | − 4.58485i | − 0.154205i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.0926 | −0.809407 | ||||||||
\(887\) | 48.6881 | 1.63479 | 0.817394 | − | 0.576079i | \(-0.195418\pi\) | ||||
0.817394 | + | 0.576079i | \(0.195418\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 13.6241i | 0.456680i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 2.97547i | − 0.0996262i | ||||||||
\(893\) | − 0.470243i | − 0.0157361i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.762181i | 0.0254769i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −40.1788 | −1.34078 | ||||||||
\(899\) | 1.67234 | 0.0557757 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 7.76722i | − 0.258764i | ||||||||
\(902\) | −0.515621 | −0.0171683 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.59220 | −0.152734 | ||||||||
\(905\) | − 4.68682i | − 0.155795i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.77309 | −0.0588744 | −0.0294372 | − | 0.999567i | \(-0.509372\pi\) | ||||
−0.0294372 | + | 0.999567i | \(0.509372\pi\) | |||||||
\(908\) | 13.2809 | 0.440743 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.2998i | 1.26893i | 0.772953 | + | 0.634464i | \(0.218779\pi\) | ||||
−0.772953 | + | 0.634464i | \(0.781221\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 1.10013i | − 0.0364090i | ||||||||
\(914\) | − 12.8309i | − 0.424407i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.17210i | 0.236973i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.1356 | −1.38993 | −0.694963 | − | 0.719046i | \(-0.744579\pi\) | ||||
−0.694963 | + | 0.719046i | \(0.744579\pi\) | |||||||
\(920\) | 7.88764 | 0.260048 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.96722i | 0.262386i | ||||||||
\(923\) | 70.8803 | 2.33305 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.47727 | 0.0485725 | ||||||||
\(926\) | − 26.2773i | − 0.863527i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.367542 | −0.0120652 | ||||||||
\(929\) | 19.5499 | 0.641413 | 0.320706 | − | 0.947179i | \(-0.396080\pi\) | ||||
0.320706 | + | 0.947179i | \(0.396080\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − 14.0160i | − 0.459110i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 22.5709i | − 0.738544i | ||||||||
\(935\) | 0.134259i | 0.00439075i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 33.1018i | − 1.08139i | −0.841219 | − | 0.540695i | \(-0.818161\pi\) | ||||
0.841219 | − | 0.540695i | \(-0.181839\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.03572 | 0.131631 | ||||||||
\(941\) | −39.8510 | −1.29911 | −0.649553 | − | 0.760316i | \(-0.725044\pi\) | ||||
−0.649553 | + | 0.760316i | \(0.725044\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 26.7145i | − 0.869942i | ||||||||
\(944\) | 2.78016 | 0.0904866 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.539775 | 0.0175496 | ||||||||
\(947\) | − 28.4239i | − 0.923652i | −0.886970 | − | 0.461826i | \(-0.847194\pi\) | ||||
0.886970 | − | 0.461826i | \(-0.152806\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −60.4942 | −1.96372 | ||||||||
\(950\) | 0.116520 | 0.00378041 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 28.1026i | − 0.910333i | −0.890406 | − | 0.455166i | \(-0.849580\pi\) | ||||
0.890406 | − | 0.455166i | \(-0.150420\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 18.9533i | − 0.613313i | ||||||||
\(956\) | − 14.8895i | − 0.481562i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 23.9665i | − 0.774322i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.2969 | 0.332158 | ||||||||
\(962\) | −7.68022 | −0.247620 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 23.1405i | 0.745307i | ||||||||
\(965\) | 8.43060 | 0.271391 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.0721 | 1.35295 | 0.676473 | − | 0.736467i | \(-0.263507\pi\) | ||||
0.676473 | + | 0.736467i | \(0.263507\pi\) | |||||||
\(968\) | 10.9768i | 0.352808i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −13.3910 | −0.429960 | ||||||||
\(971\) | 53.8665 | 1.72866 | 0.864329 | − | 0.502927i | \(-0.167743\pi\) | ||||
0.864329 | + | 0.502927i | \(0.167743\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − 38.3699i | − 1.22945i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 8.94495i | − 0.286321i | ||||||||
\(977\) | − 44.6475i | − 1.42840i | −0.699941 | − | 0.714200i | \(-0.746791\pi\) | ||||
0.699941 | − | 0.714200i | \(-0.253209\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.07414i | 0.0662899i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.83834 | −0.250132 | ||||||||
\(983\) | −7.90394 | −0.252097 | −0.126048 | − | 0.992024i | \(-0.540229\pi\) | ||||
−0.126048 | + | 0.992024i | \(0.540229\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 0.108381i | − 0.00345332i | ||||||||
\(986\) | 0.324131 | 0.0103224 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.605778 | −0.0192724 | ||||||||
\(989\) | 27.9659i | 0.889263i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.3935 | 1.50550 | 0.752752 | − | 0.658304i | \(-0.228726\pi\) | ||||
0.752752 | + | 0.658304i | \(0.228726\pi\) | |||||||
\(992\) | 4.55007 | 0.144465 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 23.4524i | − 0.743490i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 26.9514i | − 0.853558i | −0.904356 | − | 0.426779i | \(-0.859648\pi\) | ||||
0.904356 | − | 0.426779i | \(-0.140352\pi\) | |||||||
\(998\) | 13.7056i | 0.433845i | ||||||||
\(999\) | 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 | 4410.2.b.d.881.4 | yes | 8 | |
3.2 | odd | 2 | 4410.2.b.a.881.5 | yes | 8 | ||
7.6 | odd | 2 | 4410.2.b.a.881.4 | ✓ | 8 | ||
21.20 | even | 2 | inner | 4410.2.b.d.881.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4410.2.b.a.881.4 | ✓ | 8 | 7.6 | odd | 2 | ||
4410.2.b.a.881.5 | yes | 8 | 3.2 | odd | 2 | ||
4410.2.b.d.881.4 | yes | 8 | 1.1 | even | 1 | trivial | |
4410.2.b.d.881.5 | yes | 8 | 21.20 | even | 2 | inner |