Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(1791,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.1791");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.k (of order \(2\), degree \(1\), not 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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 6 x^{14} + 68 x^{13} - 126 x^{12} - 148 x^{11} + 1006 x^{10} - 1516 x^{9} - 179 x^{8} + 3992 x^{7} - 5596 x^{6} - 488 x^{5} + 16080 x^{4} - 33776 x^{3} + \cdots + 5956 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{11} \) |
Twist minimal: | no (minimal twist has level 1120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1791.3 | ||
Root | \(2.23037 + 0.887196i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.1791 |
Dual form | 2240.2.k.f.1791.4 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.77439 | −1.02445 | −0.512223 | − | 0.858853i | \(-0.671178\pi\) | ||||
−0.512223 | + | 0.858853i | \(0.671178\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.829909 | − | 2.51222i | 0.313676 | − | 0.949530i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.148464 | 0.0494880 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.36631i | 1.91951i | 0.280832 | + | 0.959757i | \(0.409390\pi\) | ||||
−0.280832 | + | 0.959757i | \(0.590610\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 0.563705i | − | 0.156344i | −0.996940 | − | 0.0781718i | \(-0.975092\pi\) | ||
0.996940 | − | 0.0781718i | \(-0.0249083\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.77439i | 0.458146i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.12055i | − | 1.48445i | −0.670149 | − | 0.742226i | \(-0.733770\pi\) | ||
0.670149 | − | 0.742226i | \(-0.266230\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.694886 | 0.159418 | 0.0797088 | − | 0.996818i | \(-0.474601\pi\) | ||||
0.0797088 | + | 0.996818i | \(0.474601\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.47258 | + | 4.45766i | −0.321344 | + | 0.972741i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.964933i | 0.201202i | 0.994927 | + | 0.100601i | \(0.0320766\pi\) | ||||
−0.994927 | + | 0.100601i | \(0.967923\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.05974 | 0.973747 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.02585 | 0.376191 | 0.188095 | − | 0.982151i | \(-0.439769\pi\) | ||||
0.188095 | + | 0.982151i | \(0.439769\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.09745 | 1.45434 | 0.727172 | − | 0.686455i | \(-0.240834\pi\) | ||||
0.727172 | + | 0.686455i | \(0.240834\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 11.2963i | − | 1.96644i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.51222 | − | 0.829909i | −0.424643 | − | 0.140280i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.89633 | −0.311755 | −0.155877 | − | 0.987776i | \(-0.549820\pi\) | ||||
−0.155877 | + | 0.987776i | \(0.549820\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00023i | 0.160165i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.97453i | 0.308370i | 0.988042 | + | 0.154185i | \(0.0492752\pi\) | ||||
−0.988042 | + | 0.154185i | \(0.950725\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5.26331i | − | 0.802648i | −0.915936 | − | 0.401324i | \(-0.868550\pi\) | ||
0.915936 | − | 0.401324i | \(-0.131450\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 0.148464i | − | 0.0221317i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.03286 | 0.442388 | 0.221194 | − | 0.975230i | \(-0.429005\pi\) | ||||
0.221194 | + | 0.975230i | \(0.429005\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.62250 | − | 4.16983i | −0.803214 | − | 0.595690i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.8603i | 1.52074i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.73956 | −0.238947 | −0.119473 | − | 0.992837i | \(-0.538121\pi\) | ||||
−0.119473 | + | 0.992837i | \(0.538121\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.36631 | 0.858433 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.23300 | −0.163315 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.9168 | −1.68162 | −0.840810 | − | 0.541330i | \(-0.817921\pi\) | ||||
−0.840810 | + | 0.541330i | \(0.817921\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 9.96224i | − | 1.27553i | −0.770229 | − | 0.637767i | \(-0.779858\pi\) | ||
0.770229 | − | 0.637767i | \(-0.220142\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.123212 | − | 0.372974i | 0.0155232 | − | 0.0469904i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.563705 | −0.0699190 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.714651i | 0.0873085i | 0.999047 | + | 0.0436543i | \(0.0139000\pi\) | ||||
−0.999047 | + | 0.0436543i | \(0.986100\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 1.71217i | − | 0.206121i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.90688i | 0.938374i | 0.883099 | + | 0.469187i | \(0.155453\pi\) | ||||
−0.883099 | + | 0.469187i | \(0.844547\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.743450i | 0.0870143i | 0.999053 | + | 0.0435071i | \(0.0138531\pi\) | ||||
−0.999053 | + | 0.0435071i | \(0.986147\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.77439 | 0.204889 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 15.9936 | + | 5.28346i | 1.82264 | + | 0.602106i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.94493i | 0.443840i | 0.975065 | + | 0.221920i | \(0.0712324\pi\) | ||||
−0.975065 | + | 0.221920i | \(0.928768\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.42335 | −1.04704 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.5667 | −1.26962 | −0.634808 | − | 0.772670i | \(-0.718921\pi\) | ||||
−0.634808 | + | 0.772670i | \(0.718921\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.12055 | −0.663867 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.59465 | −0.385387 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 16.6650i | − | 1.76648i | −0.468919 | − | 0.883241i | \(-0.655356\pi\) | ||
0.468919 | − | 0.883241i | \(-0.344644\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.41615 | − | 0.467824i | −0.148453 | − | 0.0490413i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.3680 | −1.48990 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 0.694886i | − | 0.0712938i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9.54489i | − | 0.969137i | −0.874753 | − | 0.484568i | \(-0.838977\pi\) | ||
0.874753 | − | 0.484568i | \(-0.161023\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.945168i | 0.0949929i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 14.0637i | − | 1.39939i | −0.714441 | − | 0.699695i | \(-0.753319\pi\) | ||
0.714441 | − | 0.699695i | \(-0.246681\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.11405 | −0.799501 | −0.399751 | − | 0.916624i | \(-0.630903\pi\) | ||||
−0.399751 | + | 0.916624i | \(0.630903\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.45766 | + | 1.47258i | 0.435023 | + | 0.143709i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 10.6050i | − | 1.02522i | −0.858621 | − | 0.512611i | \(-0.828678\pi\) | ||
0.858621 | − | 0.512611i | \(-0.171322\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.4913 | 1.19645 | 0.598225 | − | 0.801328i | \(-0.295873\pi\) | ||||
0.598225 | + | 0.801328i | \(0.295873\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.36483 | 0.319376 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.9783 | 1.40904 | 0.704518 | − | 0.709686i | \(-0.251163\pi\) | ||||
0.704518 | + | 0.709686i | \(0.251163\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.964933 | 0.0899805 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 0.0836899i | − | 0.00773714i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −15.3762 | − | 5.07951i | −1.40953 | − | 0.465638i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −29.5299 | −2.68453 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 3.50359i | − | 0.315908i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 7.51224i | − | 0.666604i | −0.942820 | − | 0.333302i | \(-0.891837\pi\) | ||
0.942820 | − | 0.333302i | \(-0.108163\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.33918i | 0.822269i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.12485 | −0.797242 | −0.398621 | − | 0.917116i | \(-0.630511\pi\) | ||||
−0.398621 | + | 0.917116i | \(0.630511\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.576692 | − | 1.74571i | 0.0500055 | − | 0.151372i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 5.05974i | − | 0.435473i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.5030 | −1.32451 | −0.662255 | − | 0.749279i | \(-0.730400\pi\) | ||||
−0.662255 | + | 0.749279i | \(0.730400\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.4290 | 0.884574 | 0.442287 | − | 0.896874i | \(-0.354167\pi\) | ||||
0.442287 | + | 0.896874i | \(0.354167\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.38148 | −0.453202 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.58872 | 0.300104 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2.02585i | − | 0.168238i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.97652 | + | 7.39891i | 0.822849 | + | 0.610252i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.0129 | −1.47567 | −0.737837 | − | 0.674979i | \(-0.764153\pi\) | ||||
−0.737837 | + | 0.674979i | \(0.764153\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 15.7987i | − | 1.28568i | −0.765999 | − | 0.642842i | \(-0.777755\pi\) | ||
0.765999 | − | 0.642842i | \(-0.222245\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 0.908682i | − | 0.0734626i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 8.09745i | − | 0.650402i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 22.6822i | − | 1.81024i | −0.425157 | − | 0.905119i | \(-0.639781\pi\) | ||
0.425157 | − | 0.905119i | \(-0.360219\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.08666 | 0.244788 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.42412 | + | 0.800807i | 0.191048 | + | 0.0631124i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 17.7258i | − | 1.38839i | −0.719788 | − | 0.694194i | \(-0.755761\pi\) | ||
0.719788 | − | 0.694194i | \(-0.244239\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −11.2963 | −0.879417 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.6783 | 1.29061 | 0.645303 | − | 0.763927i | \(-0.276731\pi\) | ||||
0.645303 | + | 0.763927i | \(0.276731\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.6822 | 0.975557 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.103166 | 0.00788927 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.8854i | 1.28377i | 0.766800 | + | 0.641886i | \(0.221848\pi\) | ||||
−0.766800 | + | 0.641886i | \(0.778152\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.829909 | + | 2.51222i | −0.0627353 | + | 0.189906i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 22.9194 | 1.72273 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.2643i | 0.767193i | 0.923501 | + | 0.383596i | \(0.125315\pi\) | ||||
−0.923501 | + | 0.383596i | \(0.874685\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 0.656666i | − | 0.0488096i | −0.999702 | − | 0.0244048i | \(-0.992231\pi\) | ||
0.999702 | − | 0.0244048i | \(-0.00776906\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 17.6769i | 1.30672i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.89633i | 0.139421i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 38.9653 | 2.84943 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.19913 | − | 12.7112i | 0.305441 | − | 0.924602i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 25.4758i | − | 1.84337i | −0.387943 | − | 0.921683i | \(-0.626814\pi\) | ||
0.387943 | − | 0.921683i | \(-0.373186\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.8050 | 0.777760 | 0.388880 | − | 0.921288i | \(-0.372862\pi\) | ||||
0.388880 | + | 0.921288i | \(0.372862\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.00023 | 0.0716282 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.2699 | 0.874196 | 0.437098 | − | 0.899414i | \(-0.356006\pi\) | ||||
0.437098 | + | 0.899414i | \(0.356006\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.0170 | −1.20631 | −0.603153 | − | 0.797626i | \(-0.706089\pi\) | ||||
−0.603153 | + | 0.797626i | \(0.706089\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 1.26807i | − | 0.0894428i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.68127 | − | 5.08938i | 0.118002 | − | 0.357204i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.97453 | 0.137907 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.143258i | 0.00995711i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.42386i | 0.306004i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 16.4726i | − | 1.13402i | −0.823712 | − | 0.567009i | \(-0.808101\pi\) | ||
0.823712 | − | 0.567009i | \(-0.191899\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 14.0299i | − | 0.961313i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.26331 | −0.358955 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.72015 | − | 20.3426i | 0.456193 | − | 1.38094i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 1.31917i | − | 0.0891414i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.45019 | −0.232085 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.48939 | 0.300632 | 0.150316 | − | 0.988638i | \(-0.451971\pi\) | ||||
0.150316 | + | 0.988638i | \(0.451971\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.148464 | −0.00989760 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.6264 | −0.970791 | −0.485395 | − | 0.874295i | \(-0.661324\pi\) | ||||
−0.485395 | + | 0.874295i | \(0.661324\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.05959i | − | 0.0700195i | −0.999387 | − | 0.0350098i | \(-0.988854\pi\) | ||
0.999387 | − | 0.0350098i | \(-0.0111462\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −28.3788 | − | 9.37492i | −1.86719 | − | 0.616825i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.856456 | −0.0561083 | −0.0280542 | − | 0.999606i | \(-0.508931\pi\) | ||||
−0.0280542 | + | 0.999606i | \(0.508931\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 3.03286i | − | 0.197842i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 6.99986i | − | 0.454690i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 4.54240i | − | 0.293824i | −0.989150 | − | 0.146912i | \(-0.953067\pi\) | ||
0.989150 | − | 0.146912i | \(-0.0469333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.1050i | 1.16625i | 0.812384 | + | 0.583123i | \(0.198169\pi\) | ||||
−0.812384 | + | 0.583123i | \(0.801831\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.54149 | 0.0988866 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.16983 | + | 5.62250i | −0.266401 | + | 0.359208i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 0.391710i | − | 0.0249239i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 20.5239 | 1.30065 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.2709 | 1.34261 | 0.671303 | − | 0.741183i | \(-0.265735\pi\) | ||||
0.671303 | + | 0.741183i | \(0.265735\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.14306 | −0.386211 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.8603 | 0.680096 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.1582i | 1.19506i | 0.801848 | + | 0.597528i | \(0.203850\pi\) | ||||
−0.801848 | + | 0.597528i | \(0.796150\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.57378 | + | 4.76400i | −0.0977900 | + | 0.296020i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.300766 | 0.0186169 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.9902i | 1.29431i | 0.762358 | + | 0.647155i | \(0.224041\pi\) | ||||
−0.762358 | + | 0.647155i | \(0.775959\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.73956i | 0.106860i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 29.5702i | 1.80966i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.17835i | 0.437672i | 0.975762 | + | 0.218836i | \(0.0702259\pi\) | ||||
−0.975762 | + | 0.218836i | \(0.929774\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.3174 | −1.29494 | −0.647470 | − | 0.762091i | \(-0.724173\pi\) | ||||
−0.647470 | + | 0.762091i | \(0.724173\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.51281 | + | 0.830103i | 0.152082 | + | 0.0502401i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 6.36631i | − | 0.383903i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.2723 | −0.677284 | −0.338642 | − | 0.940915i | \(-0.609968\pi\) | ||||
−0.338642 | + | 0.940915i | \(0.609968\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.20218 | 0.0719726 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.0380 | −1.07606 | −0.538029 | − | 0.842926i | \(-0.680831\pi\) | ||||
−0.538029 | + | 0.842926i | \(0.680831\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.3421 | −1.68476 | −0.842380 | − | 0.538883i | \(-0.818846\pi\) | ||||
−0.842380 | + | 0.538883i | \(0.818846\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.23300i | 0.0730366i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.96046 | + | 1.63868i | 0.292806 | + | 0.0967283i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −20.4612 | −1.20360 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.9364i | 0.992828i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 23.6862i | − | 1.38376i | −0.722011 | − | 0.691881i | \(-0.756782\pi\) | ||
0.722011 | − | 0.691881i | \(-0.243218\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.9168i | 0.752044i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 32.2119i | 1.86912i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.543938 | 0.0314567 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.2226 | − | 4.36807i | −0.762138 | − | 0.251772i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 24.9545i | 1.43360i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.96224 | −0.570436 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.87125 | −0.506309 | −0.253155 | − | 0.967426i | \(-0.581468\pi\) | ||||
−0.253155 | + | 0.967426i | \(0.581468\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.3975 | 0.819045 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.465767 | 0.0264112 | 0.0132056 | − | 0.999913i | \(-0.495796\pi\) | ||||
0.0132056 | + | 0.999913i | \(0.495796\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.7351i | 0.889398i | 0.895680 | + | 0.444699i | \(0.146689\pi\) | ||||
−0.895680 | + | 0.444699i | \(0.853311\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.372974 | − | 0.123212i | −0.0210147 | − | 0.00694219i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.9122 | 1.34304 | 0.671521 | − | 0.740986i | \(-0.265641\pi\) | ||||
0.671521 | + | 0.740986i | \(0.265641\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.8972i | 0.722103i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.8174i | 1.05028i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4.25309i | − | 0.236648i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.563705i | 0.0312687i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −22.1645 | −1.22570 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.51700 | − | 7.61921i | 0.138767 | − | 0.420061i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 1.69904i | − | 0.0933874i | −0.998909 | − | 0.0466937i | \(-0.985132\pi\) | ||
0.998909 | − | 0.0466937i | \(-0.0148685\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.281537 | −0.0154281 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.714651 | 0.0390456 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.7339 | 1.45629 | 0.728145 | − | 0.685423i | \(-0.240383\pi\) | ||||
0.728145 | + | 0.685423i | \(0.240383\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −26.5773 | −1.44348 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 51.5508i | 2.79163i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.1417 | + | 10.6644i | −0.817575 | + | 0.575822i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.71217 | −0.0921801 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 13.2342i | − | 0.710448i | −0.934781 | − | 0.355224i | \(-0.884405\pi\) | ||
0.934781 | − | 0.355224i | \(-0.115595\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 18.8288i | − | 1.00788i | −0.863738 | − | 0.503941i | \(-0.831883\pi\) | ||
0.863738 | − | 0.503941i | \(-0.168117\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 2.85220i | − | 0.152239i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 19.4969i | − | 1.03771i | −0.854861 | − | 0.518856i | \(-0.826358\pi\) | ||
0.854861 | − | 0.518856i | \(-0.173642\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.90688 | 0.419654 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 27.2834 | + | 9.01303i | 1.44399 | + | 0.477020i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.76471i | 0.515362i | 0.966230 | + | 0.257681i | \(0.0829583\pi\) | ||||
−0.966230 | + | 0.257681i | \(0.917042\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5171 | −0.974586 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 52.3975 | 2.75016 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.743450 | 0.0389140 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.80647 | 0.303095 | 0.151548 | − | 0.988450i | \(-0.451574\pi\) | ||||
0.151548 | + | 0.988450i | \(0.451574\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.293147i | 0.0152606i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.44368 | + | 4.37015i | −0.0749519 | + | 0.226887i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.7648 | −0.971604 | −0.485802 | − | 0.874069i | \(-0.661472\pi\) | ||||
−0.485802 | + | 0.874069i | \(0.661472\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 1.77439i | − | 0.0916292i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 1.14198i | − | 0.0588150i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.91732i | 0.303952i | 0.988384 | + | 0.151976i | \(0.0485637\pi\) | ||||
−0.988384 | + | 0.151976i | \(0.951436\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.3297i | 0.682899i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.2320 | 1.34039 | 0.670196 | − | 0.742184i | \(-0.266210\pi\) | ||||
0.670196 | + | 0.742184i | \(0.266210\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.28346 | − | 15.9936i | 0.269270 | − | 0.815108i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 0.781413i | − | 0.0397215i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.9320 | 1.61902 | 0.809508 | − | 0.587109i | \(-0.199734\pi\) | ||||
0.809508 | + | 0.587109i | \(0.199734\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.90593 | 0.298676 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.1911 | 0.816731 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.94493 | 0.198491 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 19.0500i | − | 0.956094i | −0.878334 | − | 0.478047i | \(-0.841345\pi\) | ||
0.878334 | − | 0.478047i | \(-0.158655\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.02328 | + | 3.09756i | −0.0512279 | + | 0.155072i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.6227 | −1.52923 | −0.764613 | − | 0.644489i | \(-0.777070\pi\) | ||||
−0.764613 | + | 0.644489i | \(0.777070\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 4.56457i | − | 0.227377i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.42335i | 0.468250i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 12.0726i | − | 0.598417i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.2209i | 1.44488i | 0.691434 | + | 0.722440i | \(0.256979\pi\) | ||||
−0.691434 | + | 0.722440i | \(0.743021\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 27.5084 | 1.35689 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.7198 | + | 32.4498i | −0.527485 | + | 1.59675i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.5667i | 0.567789i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.5051 | −0.906198 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.35398 | 0.212706 | 0.106353 | − | 0.994328i | \(-0.466083\pi\) | ||||
0.106353 | + | 0.994328i | \(0.466083\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.8255 | 1.25866 | 0.629328 | − | 0.777140i | \(-0.283330\pi\) | ||||
0.629328 | + | 0.777140i | \(0.283330\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.450271 | 0.0218929 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.12055i | 0.296890i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −25.0273 | − | 8.26776i | −1.21116 | − | 0.400105i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.36779 | −0.307440 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 4.84144i | − | 0.233204i | −0.993179 | − | 0.116602i | \(-0.962800\pi\) | ||
0.993179 | − | 0.116602i | \(-0.0372002\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.54916i | − | 0.122505i | −0.998122 | − | 0.0612524i | \(-0.980491\pi\) | ||
0.998122 | − | 0.0612524i | \(-0.0195094\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.59465i | 0.172350i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.670518i | 0.0320752i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.9908 | 0.524564 | 0.262282 | − | 0.964991i | \(-0.415525\pi\) | ||||
0.262282 | + | 0.964991i | \(0.415525\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.834739 | − | 0.619070i | −0.0397495 | − | 0.0294795i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 36.3209i | 1.72566i | 0.505495 | + | 0.862830i | \(0.331310\pi\) | ||||
−0.505495 | + | 0.862830i | \(0.668690\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.6650 | −0.789995 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 31.9619 | 1.51175 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.05482 | 0.380131 | 0.190065 | − | 0.981771i | \(-0.439130\pi\) | ||||
0.190065 | + | 0.981771i | \(0.439130\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.5705 | −0.591920 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 28.0331i | 1.31711i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.467824 | + | 1.41615i | −0.0219319 | + | 0.0663902i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.7790 | 0.691333 | 0.345667 | − | 0.938357i | \(-0.387653\pi\) | ||||
0.345667 | + | 0.938357i | \(0.387653\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 30.9684i | − | 1.44548i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.08795i | 0.0972457i | 0.998817 | + | 0.0486229i | \(0.0154832\pi\) | ||||
−0.998817 | + | 0.0486229i | \(0.984517\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 37.0568i | − | 1.72217i | −0.508458 | − | 0.861087i | \(-0.669784\pi\) | ||
0.508458 | − | 0.861087i | \(-0.330216\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 14.3680i | 0.666302i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.16280 | 0.192631 | 0.0963156 | − | 0.995351i | \(-0.469294\pi\) | ||||
0.0963156 | + | 0.995351i | \(0.469294\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.79536 | + | 0.593096i | 0.0829020 | + | 0.0273866i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 40.2471i | 1.85449i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 33.5079 | 1.54069 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.694886 | −0.0318835 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.258262 | −0.0118250 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.5746 | 1.71683 | 0.858414 | − | 0.512957i | \(-0.171450\pi\) | ||||
0.858414 | + | 0.512957i | \(0.171450\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.06897i | 0.0487409i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.30135 | − | 1.42095i | −0.195718 | − | 0.0646552i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.54489 | −0.433411 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.821825i | 0.0372405i | 0.999827 | + | 0.0186202i | \(0.00592735\pi\) | ||||
−0.999827 | + | 0.0186202i | \(0.994073\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 31.4524i | 1.42233i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.6087i | 0.704409i | 0.935923 | + | 0.352204i | \(0.114568\pi\) | ||||
−0.935923 | + | 0.352204i | \(0.885432\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 12.3993i | − | 0.558437i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.945168 | 0.0424821 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.8638 | + | 6.56199i | 0.891014 | + | 0.294346i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.6642i | 1.59655i | 0.602293 | + | 0.798275i | \(0.294254\pi\) | ||||
−0.602293 | + | 0.798275i | \(0.705746\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −29.5938 | −1.32216 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.1203 | 1.52135 | 0.760675 | − | 0.649133i | \(-0.224868\pi\) | ||||
0.760675 | + | 0.649133i | \(0.224868\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.0637 | −0.625826 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −22.5032 | −0.999404 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 40.7563i | 1.80649i | 0.429124 | + | 0.903246i | \(0.358822\pi\) | ||||
−0.429124 | + | 0.903246i | \(0.641178\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.86771 | + | 0.616996i | 0.0826227 | + | 0.0272943i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.51594 | 0.155233 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.11405i | 0.357548i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.3081i | 0.849170i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 29.9613i | − | 1.31515i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 11.0375i | − | 0.483562i | −0.970331 | − | 0.241781i | \(-0.922268\pi\) | ||
0.970331 | − | 0.241781i | \(-0.0777315\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.55759 | −0.286744 | −0.143372 | − | 0.989669i | \(-0.545794\pi\) | ||||
−0.143372 | + | 0.989669i | \(0.545794\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.47258 | − | 4.45766i | 0.0642688 | − | 0.194548i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 49.5609i | − | 2.15890i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.0689 | 0.959518 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.91768 | −0.0832201 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.11305 | 0.0482117 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.6050 | −0.458494 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 18.2130i | − | 0.785947i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 26.5464 | − | 35.7946i | 1.14344 | − | 1.54178i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.7600 | −0.892541 | −0.446271 | − | 0.894898i | \(-0.647248\pi\) | ||||
−0.446271 | + | 0.894898i | \(0.647248\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.16518i | 0.0500027i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 12.4913i | − | 0.535069i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.20675i | 0.179868i | 0.995948 | + | 0.0899338i | \(0.0286655\pi\) | ||||
−0.995948 | + | 0.0899338i | \(0.971334\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 1.47903i | − | 0.0631237i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.40773 | 0.0599714 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.91055 | + | 3.27394i | 0.421439 | + | 0.139222i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 3.36483i | − | 0.142829i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.1465 | 0.811265 | 0.405633 | − | 0.914036i | \(-0.367051\pi\) | ||||
0.405633 | + | 0.914036i | \(0.367051\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.96696 | −0.125489 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −69.1397 | −2.91908 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −34.3646 | −1.44829 | −0.724147 | − | 0.689646i | \(-0.757766\pi\) | ||||
−0.724147 | + | 0.689646i | \(0.757766\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 14.9783i | − | 0.630140i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.82053 | + | 23.6735i | −0.328431 | + | 0.994195i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.965245 | −0.0404652 | −0.0202326 | − | 0.999795i | \(-0.506441\pi\) | ||||
−0.0202326 | + | 0.999795i | \(0.506441\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1.72034i | − | 0.0719939i | −0.999352 | − | 0.0359969i | \(-0.988539\pi\) | ||
0.999352 | − | 0.0359969i | \(-0.0114607\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 45.2041i | 1.88843i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 0.964933i | − | 0.0402405i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 1.83237i | − | 0.0762826i | −0.999272 | − | 0.0381413i | \(-0.987856\pi\) | ||
0.999272 | − | 0.0381413i | \(-0.0121437\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.1723 | −0.796773 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.59935 | + | 29.0582i | −0.398248 | + | 1.20554i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 11.0746i | − | 0.458661i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.0836899 | −0.00346015 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.03942 | −0.290548 | −0.145274 | − | 0.989391i | \(-0.546406\pi\) | ||||
−0.145274 | + | 0.989391i | \(0.546406\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.62680 | 0.231848 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.7716 | −0.895565 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 5.37760i | − | 0.220832i | −0.993885 | − | 0.110416i | \(-0.964782\pi\) | ||
0.993885 | − | 0.110416i | \(-0.0352182\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.07951 | + | 15.3762i | −0.208239 | + | 0.630362i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 30.1949 | 1.23579 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 19.2945i | − | 0.788350i | −0.919035 | − | 0.394175i | \(-0.871030\pi\) | ||
0.919035 | − | 0.394175i | \(-0.128970\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 19.2218i | − | 0.784075i | −0.919949 | − | 0.392038i | \(-0.871770\pi\) | ||
0.919949 | − | 0.392038i | \(-0.128230\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.106100i | 0.00432073i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 29.5299i | 1.20056i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.04592 | −0.367163 | −0.183581 | − | 0.983005i | \(-0.558769\pi\) | ||||
−0.183581 | + | 0.983005i | \(0.558769\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.98323 | + | 9.03055i | −0.120887 | + | 0.365936i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1.70964i | − | 0.0691645i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.7177 | 0.675221 | 0.337611 | − | 0.941286i | \(-0.390381\pi\) | ||||
0.337611 | + | 0.941286i | \(0.390381\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.50359 | −0.141278 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.6742 | 1.03361 | 0.516803 | − | 0.856104i | \(-0.327122\pi\) | ||||
0.516803 | + | 0.856104i | \(0.327122\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.03441 | 0.322930 | 0.161465 | − | 0.986878i | \(-0.448378\pi\) | ||||
0.161465 | + | 0.986878i | \(0.448378\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.88231i | 0.195920i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −41.8661 | − | 13.8304i | −1.67733 | − | 0.554104i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 7.84965i | − | 0.313485i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.6066i | 0.462785i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.22789i | 0.327547i | 0.986498 | + | 0.163774i | \(0.0523667\pi\) | ||||
−0.986498 | + | 0.163774i | \(0.947633\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 29.2288i | 1.16174i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.51224 | −0.298114 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.35055 | + | 3.16943i | −0.0931323 | + | 0.125577i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.17389i | 0.0464383i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.4651 | 1.47978 | 0.739891 | − | 0.672727i | \(-0.234877\pi\) | ||||
0.739891 | + | 0.672727i | \(0.234877\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.50809 | −0.217218 | −0.108609 | − | 0.994085i | \(-0.534640\pi\) | ||||
−0.108609 | + | 0.994085i | \(0.534640\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.33918 | 0.367730 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −39.9344 | −1.56998 | −0.784992 | − | 0.619506i | \(-0.787333\pi\) | ||||
−0.784992 | + | 0.619506i | \(0.787333\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 82.2322i | − | 3.22789i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.9242 | + | 36.0957i | −0.467345 | + | 1.41470i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 37.5904 | 1.47103 | 0.735513 | − | 0.677510i | \(-0.236941\pi\) | ||||
0.735513 | + | 0.677510i | \(0.236941\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.12485i | 0.356537i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.110376i | 0.00430616i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 2.81823i | − | 0.109783i | −0.998492 | − | 0.0548913i | \(-0.982519\pi\) | ||
0.998492 | − | 0.0548913i | \(-0.0174812\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 19.0129i | − | 0.739518i | −0.929128 | − | 0.369759i | \(-0.879440\pi\) | ||
0.929128 | − | 0.369759i | \(-0.120560\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.12198 | 0.237758 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.74571 | − | 0.576692i | −0.0676956 | − | 0.0223632i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.95481i | 0.0756905i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.96594 | −0.307981 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 63.4227 | 2.44841 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.0799 | −1.35223 | −0.676115 | − | 0.736796i | \(-0.736338\pi\) | ||||
−0.676115 | + | 0.736796i | \(0.736338\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.05974 | −0.194749 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 20.1811i | − | 0.775623i | −0.921739 | − | 0.387812i | \(-0.873231\pi\) | ||
0.921739 | − | 0.387812i | \(-0.126769\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −23.9789 | − | 7.92140i | −0.920225 | − | 0.303995i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 25.9530 | 0.994522 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 11.6160i | − | 0.444473i | −0.974993 | − | 0.222236i | \(-0.928664\pi\) | ||
0.974993 | − | 0.222236i | \(-0.0713356\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.5030i | 0.592339i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.88012i | 0.0717312i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.980597i | 0.0373578i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.5766 | 0.820812 | 0.410406 | − | 0.911903i | \(-0.365387\pi\) | ||||
0.410406 | + | 0.911903i | \(0.365387\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.37447 | + | 0.784404i | 0.0901986 | + | 0.0297970i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 10.4290i | − | 0.395594i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.0852 | 0.457760 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.51969 | 0.0574799 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.7329 | 0.556453 | 0.278226 | − | 0.960516i | \(-0.410253\pi\) | ||||
0.278226 | + | 0.960516i | \(0.410253\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.31773 | −0.0496992 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.38148i | 0.202678i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −35.3311 | − | 11.6716i | −1.32876 | − | 0.438956i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.4666 | 1.44464 | 0.722321 | − | 0.691558i | \(-0.243075\pi\) | ||||
0.722321 | + | 0.691558i | \(0.243075\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.585681i | 0.0219648i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.81349i | 0.292618i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 3.58872i | − | 0.134210i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.06000i | 0.301006i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.0175 | 0.895700 | 0.447850 | − | 0.894109i | \(-0.352190\pi\) | ||||
0.447850 | + | 0.894109i | \(0.352190\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.73393 | + | 20.3843i | −0.250785 | + | 0.759150i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 32.1254i | − | 1.19476i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.02585 | −0.0752381 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.65598 | 0.358121 | 0.179060 | − | 0.983838i | \(-0.442694\pi\) | ||||
0.179060 | + | 0.983838i | \(0.442694\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.5348 | 0.945735 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −32.2144 | −1.19149 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 15.2522i | − | 0.563355i | −0.959509 | − | 0.281677i | \(-0.909109\pi\) | ||
0.959509 | − | 0.281677i | \(-0.0908907\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.39891 | − | 9.97652i | 0.272913 | − | 0.367989i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.54969 | −0.167590 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.4632i | 0.715964i | 0.933729 | + | 0.357982i | \(0.116535\pi\) | ||||
−0.933729 | + | 0.357982i | \(0.883465\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.695048i | 0.0255332i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.0393i | 1.06535i | 0.846320 | + | 0.532674i | \(0.178813\pi\) | ||||
−0.846320 | + | 0.532674i | \(0.821187\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.0129i | 0.659941i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.71725 | −0.0628307 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −26.6421 | − | 8.80118i | −0.973480 | − | 0.321588i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.883907i | 0.0322542i | 0.999870 | + | 0.0161271i | \(0.00513364\pi\) | ||||
−0.999870 | + | 0.0161271i | \(0.994866\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −37.7428 | −1.37543 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.7987 | −0.574975 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.1875 | −1.02449 | −0.512246 | − | 0.858839i | \(-0.671186\pi\) | ||||
−0.512246 | + | 0.858839i | \(0.671186\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.9002 | 0.395652 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.5553i | 0.817629i | 0.912618 | + | 0.408814i | \(0.134058\pi\) | ||||
−0.912618 | + | 0.408814i | \(0.865942\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.3667 | − | 31.3809i | 0.375298 | − | 1.13607i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.908682 | −0.0328535 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.28125i | 0.262911i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 4.68731i | − | 0.169029i | −0.996422 | − | 0.0845144i | \(-0.973066\pi\) | ||
0.996422 | − | 0.0845144i | \(-0.0269339\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 33.9942i | − | 1.22427i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 38.9796i | − | 1.40200i | −0.713162 | − | 0.700999i | \(-0.752738\pi\) | ||
0.713162 | − | 0.700999i | \(-0.247262\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.09745 | −0.290869 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.79250 | − | 8.45320i | 0.100181 | − | 0.303257i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.37207i | 0.0491596i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −50.3376 | −1.80122 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.2503 | 0.366315 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.6822 | −0.809563 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.6892 | −0.416674 | −0.208337 | − | 0.978057i | \(-0.566805\pi\) | ||||
−0.208337 | + | 0.978057i | \(0.566805\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 37.2448i | − | 1.32595i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.4306 | − | 37.6287i | 0.441981 | − | 1.33792i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.61576 | −0.199422 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 3.08666i | − | 0.109472i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.6177i | 0.907427i | 0.891148 | + | 0.453714i | \(0.149901\pi\) | ||||
−0.891148 | + | 0.453714i | \(0.850099\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 18.5628i | − | 0.656704i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 2.47415i | − | 0.0874197i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.73303 | −0.167025 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.800807 | − | 2.42412i | 0.0282247 | − | 0.0854392i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 12.7372i | − | 0.448371i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −41.7251 | −1.46698 | −0.733488 | − | 0.679702i | \(-0.762109\pi\) | ||||
−0.733488 | + | 0.679702i | \(0.762109\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.9122 | 0.909899 | 0.454950 | − | 0.890517i | \(-0.349657\pi\) | ||||
0.454950 | + | 0.890517i | \(0.349657\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 37.8254 | 1.32659 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.7258 | −0.620906 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 3.65740i | − | 0.127956i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.210248 | − | 0.0694550i | −0.00734664 | − | 0.00242696i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.4953 | −1.02939 | −0.514697 | − | 0.857372i | \(-0.672096\pi\) | ||||
−0.514697 | + | 0.857372i | \(0.672096\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 34.2637i | − | 1.19436i | −0.802109 | − | 0.597178i | \(-0.796289\pi\) | ||
0.802109 | − | 0.597178i | \(-0.203711\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.2963i | 0.393287i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 53.5268i | 1.86131i | 0.365899 | + | 0.930655i | \(0.380762\pi\) | ||||
−0.365899 | + | 0.930655i | \(0.619238\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.4570i | 1.16201i | 0.813900 | + | 0.581005i | \(0.197340\pi\) | ||||
−0.813900 | + | 0.581005i | \(0.802660\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.0014 | 0.693841 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −25.5217 | + | 34.4128i | −0.884274 | + | 1.19233i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 16.6783i | − | 0.577177i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 40.9710 | 1.41616 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.7494 | 0.785397 | 0.392699 | − | 0.919667i | \(-0.371542\pi\) | ||||
0.392699 | + | 0.919667i | \(0.371542\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.8959 | −0.858481 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 32.0065 | 1.10236 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 12.6822i | − | 0.436282i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.5071 | + | 74.1855i | −0.842074 | + | 2.54905i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 50.2899 | 1.72595 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1.82983i | − | 0.0627258i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 39.0172i | − | 1.33592i | −0.744196 | − | 0.667961i | \(-0.767167\pi\) | ||
0.744196 | − | 0.667961i | \(-0.232833\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 0.103166i | − | 0.00352819i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 28.8131i | − | 0.984238i | −0.870528 | − | 0.492119i | \(-0.836222\pi\) | ||
0.870528 | − | 0.492119i | \(-0.163778\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.9381 | 0.646159 | 0.323079 | − | 0.946372i | \(-0.395282\pi\) | ||||
0.323079 | + | 0.946372i | \(0.395282\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.80179 | − | 2.90766i | −0.299964 | − | 0.0990928i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 11.0291i | − | 0.375435i | −0.982223 | − | 0.187717i | \(-0.939891\pi\) | ||
0.982223 | − | 0.187717i | \(-0.0601089\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.8854 | 0.574121 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 36.3061 | 1.23302 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −25.1147 | −0.851957 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.402852 | 0.0136501 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 1.41707i | − | 0.0479607i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.51222 | + | 0.829909i | 0.0849285 | + | 0.0280561i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.186515 | 0.00629815 | 0.00314908 | − | 0.999995i | \(-0.498998\pi\) | ||||
0.00314908 | + | 0.999995i | \(0.498998\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 42.0286i | 1.41759i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.4366i | 0.958055i | 0.877800 | + | 0.479027i | \(0.159011\pi\) | ||||
−0.877800 | + | 0.479027i | \(0.840989\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 6.76938i | − | 0.227808i | −0.993492 | − | 0.113904i | \(-0.963664\pi\) | ||
0.993492 | − | 0.113904i | \(-0.0363356\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 22.9194i | − | 0.770428i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31.0752 | −1.04340 | −0.521701 | − | 0.853128i | \(-0.674702\pi\) | ||||
−0.521701 | + | 0.853128i | \(0.674702\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.8724 | − | 6.23448i | −0.632960 | − | 0.209098i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 59.9919i | − | 2.00981i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.10749 | 0.0705245 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.2643 | 0.343099 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.965158 | −0.0322257 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.4042 | 0.547111 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.6471i | 0.354705i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 23.4621 | + | 7.75067i | 0.780769 | + | 0.257926i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.656666 | −0.0218283 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 39.5879i | − | 1.31450i | −0.753674 | − | 0.657248i | \(-0.771720\pi\) | ||
0.753674 | − | 0.657248i | \(-0.228280\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 2.08795i | − | 0.0692531i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.9338i | 0.991750i | 0.868394 | + | 0.495875i | \(0.165153\pi\) | ||||
−0.868394 | + | 0.495875i | \(0.834847\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 73.6375i | − | 2.43704i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 17.6769 | 0.584381 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.57280 | + | 22.9236i | −0.250076 | + | 0.757005i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 18.1442i | − | 0.598524i | −0.954171 | − | 0.299262i | \(-0.903260\pi\) | ||
0.954171 | − | 0.299262i | \(-0.0967404\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.7411 | 0.518686 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.45715 | 0.146709 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.89633 | 0.0623509 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.20465 | −0.0395657 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.33330i | 0.142171i | 0.997470 | + | 0.0710854i | \(0.0226463\pi\) | ||||
−0.997470 | + | 0.0710854i | \(0.977354\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.90699 | − | 2.89756i | −0.128047 | − | 0.0949635i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.826453 | −0.0270569 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 38.9653i | − | 1.27430i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 20.1249i | − | 0.657451i | −0.944426 | − | 0.328725i | \(-0.893381\pi\) | ||
0.944426 | − | 0.328725i | \(-0.106619\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 27.9201i | − | 0.911139i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 16.2874i | − | 0.530955i | −0.964117 | − | 0.265478i | \(-0.914470\pi\) | ||
0.964117 | − | 0.265478i | \(-0.0855296\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.90529 | −0.0620448 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −12.7112 | − | 4.19913i | −0.413495 | − | 0.136598i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.2240i | 0.592201i | 0.955157 | + | 0.296101i | \(0.0956864\pi\) | ||||
−0.955157 | + | 0.296101i | \(0.904314\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.419087 | 0.0136041 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −42.4296 | −1.37587 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.0976 | 0.456667 | 0.228334 | − | 0.973583i | \(-0.426672\pi\) | ||||
0.228334 | + | 0.973583i | \(0.426672\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.4758 | −0.824379 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 22.8846i | − | 0.739755i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.8661 | + | 38.9469i | −0.415467 | + | 1.25766i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 34.5686 | 1.11512 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 1.57446i | − | 0.0507362i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 10.8050i | − | 0.347825i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 57.2233i | 1.84018i | 0.391709 | + | 0.920089i | \(0.371884\pi\) | ||||
−0.391709 | + | 0.920089i | \(0.628116\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.54664i | 0.242433i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.0148 | −0.963220 | −0.481610 | − | 0.876386i | \(-0.659948\pi\) | ||||
−0.481610 | + | 0.876386i | \(0.659948\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.65510 | − | 26.1999i | 0.277470 | − | 0.839930i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 1.00023i | − | 0.0320331i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.1481 | 0.740574 | 0.370287 | − | 0.928917i | \(-0.379259\pi\) | ||||
0.370287 | + | 0.928917i | \(0.379259\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 106.094 | 3.39079 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.85451 | 0.0592100 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.3460 | −0.553250 | −0.276625 | − | 0.960978i | \(-0.589216\pi\) | ||||
−0.276625 | + | 0.960978i | \(0.589216\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 12.2699i | − | 0.390952i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.46614 | + | 13.5195i | −0.142159 | + | 0.430329i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.07875 | 0.161495 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 29.7547i | − | 0.945188i | −0.881280 | − | 0.472594i | \(-0.843318\pi\) | ||
0.881280 | − | 0.472594i | \(-0.156682\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.01475i | 0.0956703i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.0170i | 0.539476i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 36.4069i | − | 1.15302i | −0.817091 | − | 0.576509i | \(-0.804415\pi\) | ||
0.817091 | − | 0.576509i | \(-0.195585\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.59494 | −0.303570 |
(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 | 2240.2.k.f.1791.3 | 16 | ||
4.3 | odd | 2 | 2240.2.k.g.1791.13 | 16 | |||
7.6 | odd | 2 | 2240.2.k.g.1791.14 | 16 | |||
8.3 | odd | 2 | 1120.2.k.b.671.4 | yes | 16 | ||
8.5 | even | 2 | 1120.2.k.a.671.14 | yes | 16 | ||
28.27 | even | 2 | inner | 2240.2.k.f.1791.4 | 16 | ||
56.13 | odd | 2 | 1120.2.k.b.671.3 | yes | 16 | ||
56.27 | even | 2 | 1120.2.k.a.671.13 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1120.2.k.a.671.13 | ✓ | 16 | 56.27 | even | 2 | ||
1120.2.k.a.671.14 | yes | 16 | 8.5 | even | 2 | ||
1120.2.k.b.671.3 | yes | 16 | 56.13 | odd | 2 | ||
1120.2.k.b.671.4 | yes | 16 | 8.3 | odd | 2 | ||
2240.2.k.f.1791.3 | 16 | 1.1 | even | 1 | trivial | ||
2240.2.k.f.1791.4 | 16 | 28.27 | even | 2 | inner | ||
2240.2.k.g.1791.13 | 16 | 4.3 | odd | 2 | |||
2240.2.k.g.1791.14 | 16 | 7.6 | odd | 2 |