Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [840,2,Mod(209,840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("840.209");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 840.k (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: | \(6.70743376979\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.14 | ||
Character | \(\chi\) | \(=\) | 840.209 |
Dual form | 840.2.k.a.209.13 |
$q$-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 \(\left(\mathbb{Z}/840\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(281\) | \(337\) | \(421\) | \(631\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.325454 | + | 1.70120i | 0.187901 | + | 0.982188i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.34492 | − | 1.78639i | −0.601465 | − | 0.798899i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.53984 | + | 2.15149i | −0.582003 | + | 0.813186i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.78816 | + | 1.10732i | −0.929387 | + | 0.369108i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.00998i | − | 1.51057i | −0.655399 | − | 0.755283i | \(-0.727499\pi\) | ||
0.655399 | − | 0.755283i | \(-0.272501\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.62957 | −0.451961 | −0.225980 | − | 0.974132i | \(-0.572559\pi\) | ||||
−0.225980 | + | 0.974132i | \(0.572559\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.60130 | − | 2.86936i | 0.671653 | − | 0.740866i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.73603i | − | 1.14866i | −0.818625 | − | 0.574328i | \(-0.805263\pi\) | ||
0.818625 | − | 0.574328i | \(-0.194737\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.13979i | − | 0.490901i | −0.969409 | − | 0.245450i | \(-0.921064\pi\) | ||
0.969409 | − | 0.245450i | \(-0.0789359\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.16126 | − | 1.91936i | −0.908061 | − | 0.418838i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.46270 | 1.97311 | 0.986555 | − | 0.163429i | \(-0.0522555\pi\) | ||||
0.986555 | + | 0.163429i | \(0.0522555\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.38239 | + | 4.80510i | −0.276479 | + | 0.961020i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.79119 | − | 4.38283i | −0.537166 | − | 0.843477i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.96788i | − | 1.10821i | −0.832448 | − | 0.554103i | \(-0.813061\pi\) | ||
0.832448 | − | 0.554103i | \(-0.186939\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.38673i | − | 0.787880i | −0.919136 | − | 0.393940i | \(-0.871112\pi\) | ||
0.919136 | − | 0.393940i | \(-0.128888\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.52298 | − | 1.63052i | 1.48366 | − | 0.283837i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.91436 | − | 0.142824i | 0.999709 | − | 0.0241417i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.75323i | 0.617027i | 0.951220 | + | 0.308514i | \(0.0998315\pi\) | ||||
−0.951220 | + | 0.308514i | \(0.900168\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.530349 | − | 2.77222i | −0.0849238 | − | 0.443911i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.6255 | −1.65943 | −0.829716 | − | 0.558186i | \(-0.811497\pi\) | ||||
−0.829716 | + | 0.558186i | \(0.811497\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.74762i | − | 0.724005i | −0.932177 | − | 0.362002i | \(-0.882093\pi\) | ||
0.932177 | − | 0.362002i | \(-0.117907\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.72796 | + | 3.49149i | 0.853874 | + | 0.520480i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.64934i | 0.824041i | 0.911175 | + | 0.412021i | \(0.135177\pi\) | ||||
−0.911175 | + | 0.412021i | \(0.864823\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.25781 | − | 6.62588i | −0.322544 | − | 0.946554i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.05694 | − | 1.54136i | 1.12820 | − | 0.215834i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.69333 | −0.644679 | −0.322340 | − | 0.946624i | \(-0.604469\pi\) | ||||
−0.322340 | + | 0.946624i | \(0.604469\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.94979 | + | 6.73801i | −1.20679 | + | 0.908553i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.64020 | − | 0.696402i | 0.482157 | − | 0.0922406i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.66206 | −1.12770 | −0.563852 | − | 0.825876i | \(-0.690681\pi\) | ||||
−0.563852 | + | 0.825876i | \(0.690681\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.09779i | 0.268594i | 0.990941 | + | 0.134297i | \(0.0428776\pi\) | ||||
−0.990941 | + | 0.134297i | \(0.957122\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.91091 | − | 7.70379i | 0.240753 | − | 0.970587i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.19163 | + | 2.91105i | 0.271839 | + | 0.361071i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 6.20510i | − | 0.758073i | −0.925382 | − | 0.379037i | \(-0.876255\pi\) | ||
0.925382 | − | 0.379037i | \(-0.123745\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.07967 | + | 16.0979i | 0.370749 | + | 1.93797i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.65231i | − | 1.02684i | −0.858138 | − | 0.513420i | \(-0.828378\pi\) | ||
0.858138 | − | 0.513420i | \(-0.171622\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.5394 | 1.46763 | 0.733815 | − | 0.679349i | \(-0.237738\pi\) | ||||
0.733815 | + | 0.679349i | \(0.237738\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.62434 | − | 0.787891i | −0.995853 | − | 0.0909778i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.7789 | + | 7.71455i | 1.22837 | + | 0.879155i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.06070 | 0.119338 | 0.0596689 | − | 0.998218i | \(-0.480996\pi\) | ||||
0.0596689 | + | 0.998218i | \(0.480996\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.54767 | − | 6.17479i | 0.727519 | − | 0.686088i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 5.96483i | − | 0.654725i | −0.944899 | − | 0.327362i | \(-0.893840\pi\) | ||
0.944899 | − | 0.327362i | \(-0.106160\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.46041 | + | 6.36957i | −0.917661 | + | 0.690877i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.1525 | − | 1.94227i | 1.08847 | − | 0.208233i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.187117 | −0.0198344 | −0.00991719 | − | 0.999951i | \(-0.503157\pi\) | ||||
−0.00991719 | + | 0.999951i | \(0.503157\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.50927 | − | 3.50600i | 0.263043 | − | 0.367529i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.46270 | − | 1.42768i | 0.773846 | − | 0.148043i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.82250 | + | 2.87784i | −0.392180 | + | 0.295260i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.8671 | −1.10339 | −0.551693 | − | 0.834047i | \(-0.686018\pi\) | ||||
−0.551693 | + | 0.834047i | \(0.686018\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.54767 | + | 13.9686i | 0.557562 | + | 1.40390i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.64716 | 0.462409 | 0.231205 | − | 0.972905i | \(-0.425733\pi\) | ||||
0.231205 | + | 0.972905i | \(0.425733\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.674162 | 0.0664272 | 0.0332136 | − | 0.999448i | \(-0.489426\pi\) | ||||
0.0332136 | + | 0.999448i | \(0.489426\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.16782 | + | 10.0150i | 0.211558 | + | 0.977366i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.45930 | −0.817792 | −0.408896 | − | 0.912581i | \(-0.634086\pi\) | ||||
−0.408896 | + | 0.912581i | \(0.634086\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.32715 | 0.701814 | 0.350907 | − | 0.936410i | \(-0.385873\pi\) | ||||
0.350907 | + | 0.936410i | \(0.385873\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.38499 | + | 1.22150i | −0.606037 | + | 0.115940i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.2229 | −0.961691 | −0.480845 | − | 0.876805i | \(-0.659670\pi\) | ||||
−0.480845 | + | 0.876805i | \(0.659670\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.7266 | − | 16.9041i | −1.18676 | − | 1.57632i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.54350 | − | 1.80446i | 0.420046 | − | 0.166822i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.1895 | + | 7.29271i | 0.934072 | + | 0.668522i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14.0999 | −1.28181 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.45812 | − | 18.0762i | −0.311808 | − | 1.62987i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.4430 | − | 3.99296i | 0.934050 | − | 0.357142i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.7565i | 1.75310i | 0.481307 | + | 0.876552i | \(0.340162\pi\) | ||||
−0.481307 | + | 0.876552i | \(0.659838\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.07664 | − | 1.54513i | 0.711109 | − | 0.136041i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.5174 | 1.53050 | 0.765251 | − | 0.643732i | \(-0.222615\pi\) | ||||
0.765251 | + | 0.643732i | \(0.222615\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.60373 | + | 3.29492i | 0.399194 | + | 0.285706i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.07553 | + | 10.8807i | −0.350766 | + | 0.936463i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −21.3696 | −1.82573 | −0.912863 | − | 0.408266i | \(-0.866134\pi\) | ||||
−0.912863 | + | 0.408266i | \(0.866134\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 3.32832i | − | 0.282305i | −0.989988 | − | 0.141152i | \(-0.954919\pi\) | ||
0.989988 | − | 0.141152i | \(-0.0450807\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.61066 | + | 1.83860i | −0.809363 | + | 0.154838i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.16411i | 0.682717i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.6610 | + | 8.02630i | −0.885345 | + | 0.666548i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.5371 | − | 5.99740i | 0.869088 | − | 0.494658i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.29916i | 0.352201i | 0.984372 | + | 0.176101i | \(0.0563484\pi\) | ||||
−0.984372 | + | 0.176101i | \(0.943652\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.59367 | −0.617964 | −0.308982 | − | 0.951068i | \(-0.599988\pi\) | ||||
−0.308982 | + | 0.951068i | \(0.599988\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.24432 | + | 13.2048i | 0.423978 | + | 1.06755i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.83642 | + | 5.89979i | −0.629436 | + | 0.473883i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.4164 | −1.23036 | −0.615181 | − | 0.788386i | \(-0.710917\pi\) | ||||
−0.615181 | + | 0.788386i | \(0.710917\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.52746 | − | 7.98430i | −0.121136 | − | 0.633196i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.5710 | + | 20.3589i | −1.14836 | + | 1.60451i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 7.60297i | − | 0.595511i | −0.954642 | − | 0.297755i | \(-0.903762\pi\) | ||
0.954642 | − | 0.297755i | \(-0.0962380\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −14.3754 | − | 13.0325i | −1.11913 | − | 1.01458i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.12412i | 0.241752i | 0.992668 | + | 0.120876i | \(0.0385703\pi\) | ||||
−0.992668 | + | 0.120876i | \(0.961430\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.3445 | −0.795731 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.36944 | + | 5.96607i | 0.181195 | + | 0.456237i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.28993i | 0.402186i | 0.979572 | + | 0.201093i | \(0.0644493\pi\) | ||||
−0.979572 | + | 0.201093i | \(0.935551\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.20946 | − | 10.3733i | −0.620577 | − | 0.784146i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.81910 | − | 14.7359i | −0.211897 | − | 1.10762i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 14.5042i | − | 1.08410i | −0.840348 | − | 0.542048i | \(-0.817649\pi\) | ||
0.840348 | − | 0.542048i | \(-0.182351\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 18.5082i | − | 1.37571i | −0.725850 | − | 0.687853i | \(-0.758554\pi\) | ||
0.725850 | − | 0.687853i | \(-0.241446\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.56875 | + | 0.682732i | −0.263810 | + | 0.0504690i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.70474 | − | 5.04778i | 0.492942 | − | 0.371120i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −23.7274 | −1.73512 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.7276 | + | 0.743619i | 0.998536 | + | 0.0540904i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.7342i | 0.921414i | 0.887552 | + | 0.460707i | \(0.152404\pi\) | ||||
−0.887552 | + | 0.460707i | \(0.847596\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.04248i | 0.290984i | 0.989359 | + | 0.145492i | \(0.0464765\pi\) | ||||
−0.989359 | + | 0.145492i | \(0.953523\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.23900 | + | 4.67582i | −0.303561 | + | 0.334842i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.44077 | 0.387639 | 0.193819 | − | 0.981037i | \(-0.437912\pi\) | ||||
0.193819 | + | 0.981037i | \(0.437912\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.8119i | 1.12087i | 0.828197 | + | 0.560437i | \(0.189367\pi\) | ||||
−0.828197 | + | 0.560437i | \(0.810633\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.5561 | − | 2.01947i | 0.744570 | − | 0.142443i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.8398 | + | 9.18955i | 0.901179 | + | 0.644980i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.2905 | + | 18.9814i | 0.998090 | + | 1.32572i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −26.3835 | + | 10.4783i | −1.83378 | + | 0.728290i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.7203 | −0.741538 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.7369 | 1.22106 | 0.610531 | − | 0.791993i | \(-0.290956\pi\) | ||||
0.610531 | + | 0.791993i | \(0.290956\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.7193 | − | 2.81593i | 1.00855 | − | 0.192944i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.48111 | + | 6.38515i | −0.578407 | + | 0.435464i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.43800 | + | 6.75484i | 0.640693 | + | 0.458549i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.08101 | + | 21.3321i | 0.275769 | + | 1.44149i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.71769i | 0.519148i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 28.0313 | 1.87711 | 0.938556 | − | 0.345126i | \(-0.112164\pi\) | ||||
0.938556 | + | 0.345126i | \(0.112164\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.46646 | − | 14.9281i | −0.0977643 | − | 0.995210i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.2192i | 1.14288i | 0.820645 | + | 0.571439i | \(0.193615\pi\) | ||||
−0.820645 | + | 0.571439i | \(0.806385\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.89863i | 0.323710i | 0.986815 | + | 0.161855i | \(0.0517477\pi\) | ||||
−0.986815 | + | 0.161855i | \(0.948252\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.61595 | + | 20.8478i | −0.632683 | + | 1.37169i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.0858 | 1.11933 | 0.559663 | − | 0.828720i | \(-0.310931\pi\) | ||||
0.559663 | + | 0.828720i | \(0.310931\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.0919 | − | 7.59790i | 0.658326 | − | 0.495632i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.345208 | + | 1.80446i | 0.0224237 | + | 0.117212i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 20.4559i | − | 1.32319i | −0.749863 | − | 0.661593i | \(-0.769881\pi\) | ||
0.749863 | − | 0.661593i | \(-0.230119\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.8088i | 0.696253i | 0.937448 | + | 0.348127i | \(0.113182\pi\) | ||||
−0.937448 | + | 0.348127i | \(0.886818\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.6355 | + | 9.12929i | 0.810568 | + | 0.585644i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.79985 | + | 12.9446i | −0.562202 | + | 0.827000i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.48693i | 0.221868i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.1474 | − | 1.94128i | 0.643063 | − | 0.123023i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.7407 | 1.87722 | 0.938609 | − | 0.344982i | \(-0.112115\pi\) | ||||
0.938609 | + | 0.344982i | \(0.112115\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 47.4080i | − | 2.98051i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −13.5894 | − | 12.3198i | −0.851001 | − | 0.771499i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 28.1376i | − | 1.75518i | −0.479415 | − | 0.877589i | \(-0.659151\pi\) | ||
0.479415 | − | 0.877589i | \(-0.340849\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.07503 | − | 5.77936i | −0.501758 | − | 0.359112i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.60837 | + | 16.6394i | 0.409048 | + | 1.02995i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.0985 | −1.30099 | −0.650496 | − | 0.759510i | \(-0.725439\pi\) | ||||
−0.650496 | + | 0.759510i | \(0.725439\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.31215 | + | 8.38414i | 0.387752 | + | 0.515033i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.0608979 | − | 0.318324i | −0.00372689 | − | 0.0194811i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.42683 | −0.330880 | −0.165440 | − | 0.986220i | \(-0.552904\pi\) | ||||
−0.165440 | + | 0.986220i | \(0.552904\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.0004i | 1.03270i | 0.856377 | + | 0.516351i | \(0.172710\pi\) | ||||
−0.856377 | + | 0.516351i | \(0.827290\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.78105 | + | 3.12773i | 0.410408 | + | 0.189299i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 24.0735 | + | 6.92577i | 1.45168 | + | 0.417640i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 0.897874i | − | 0.0539480i | −0.999636 | − | 0.0269740i | \(-0.991413\pi\) | ||
0.999636 | − | 0.0269740i | \(-0.00858714\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.85753 | + | 12.2309i | 0.290813 | + | 0.732245i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.6282i | 0.753338i | 0.926348 | + | 0.376669i | \(0.122931\pi\) | ||||
−0.926348 | + | 0.376669i | \(0.877069\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.82856 | −0.108696 | −0.0543482 | − | 0.998522i | \(-0.517308\pi\) | ||||
−0.0543482 | + | 0.998522i | \(0.517308\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.13982 | − | 5.56623i | −0.363692 | − | 0.329715i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.3616 | − | 22.8607i | 0.965794 | − | 1.34943i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.43001 | −0.319413 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.53674 | − | 18.4871i | −0.207327 | − | 1.08373i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.26878i | 0.366226i | 0.983092 | + | 0.183113i | \(0.0586175\pi\) | ||||
−0.983092 | + | 0.183113i | \(0.941383\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.6498 | + | 15.4738i | 0.678275 | + | 0.900922i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −21.9579 | + | 13.9838i | −1.27413 | + | 0.811424i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.4201 | −0.891769 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.2144 | + | 7.31055i | 0.588751 | + | 0.421373i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.51243 | + | 7.90574i | 0.0868871 | + | 0.454173i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.74747 | − | 2.82135i | 0.214579 | − | 0.161550i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.5040 | 1.05608 | 0.528039 | − | 0.849220i | \(-0.322927\pi\) | ||||
0.528039 | + | 0.849220i | \(0.322927\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.219409 | + | 1.14688i | 0.0124817 | + | 0.0652440i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.3348 | 1.09637 | 0.548187 | − | 0.836356i | \(-0.315318\pi\) | ||||
0.548187 | + | 0.836356i | \(0.315318\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.6125 | −0.599856 | −0.299928 | − | 0.953962i | \(-0.596963\pi\) | ||||
−0.299928 | + | 0.953962i | \(0.596963\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −16.3320 | + | 6.94732i | −0.920205 | + | 0.391437i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.68654 | −0.150891 | −0.0754455 | − | 0.997150i | \(-0.524038\pi\) | ||||
−0.0754455 | + | 0.997150i | \(0.524038\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −29.8990 | −1.67402 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.75311 | − | 14.3910i | −0.153664 | − | 0.803225i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.1341 | −0.563877 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.25271 | − | 7.83024i | 0.124958 | − | 0.434344i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.38465 | + | 12.4649i | 0.131871 | + | 0.689313i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.1545 | − | 8.69906i | −0.670099 | − | 0.479595i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.6637 | −0.860954 | −0.430477 | − | 0.902602i | \(-0.641655\pi\) | ||||
−0.430477 | + | 0.902602i | \(0.641655\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.15604 | − | 10.4646i | −0.227749 | − | 0.573457i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.0847 | + | 8.34534i | −0.605624 | + | 0.455955i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 8.05239i | − | 0.438642i | −0.975653 | − | 0.219321i | \(-0.929616\pi\) | ||
0.975653 | − | 0.219321i | \(-0.0703842\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.32708 | − | 17.3912i | −0.180702 | − | 0.944561i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.9774 | −1.19015 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.7322 | + | 5.34511i | 0.957447 | + | 0.288609i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 24.6153 | − | 27.1519i | 1.32525 | − | 1.46181i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.814731 | −0.0437370 | −0.0218685 | − | 0.999761i | \(-0.506962\pi\) | ||||
−0.0218685 | + | 0.999761i | \(0.506962\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 20.6841i | − | 1.10719i | −0.832785 | − | 0.553597i | \(-0.813255\pi\) | ||
0.832785 | − | 0.553597i | \(-0.186745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.54844 | + | 7.14213i | 0.242778 | + | 0.381219i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 13.1361i | − | 0.699163i | −0.936906 | − | 0.349581i | \(-0.886324\pi\) | ||
0.936906 | − | 0.349581i | \(-0.113676\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.4564 | + | 11.6366i | −0.820341 | + | 0.617609i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.09014 | + | 19.7079i | −0.481101 | + | 1.04305i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 15.6128i | − | 0.824014i | −0.911181 | − | 0.412007i | \(-0.864828\pi\) | ||
0.911181 | − | 0.412007i | \(-0.135172\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.4213 | 0.759016 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.58887 | − | 23.9868i | −0.240853 | − | 1.25898i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.8645 | − | 22.4004i | −0.882729 | − | 1.17249i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.40534 | 0.490955 | 0.245477 | − | 0.969402i | \(-0.421055\pi\) | ||||
0.245477 | + | 0.969402i | \(0.421055\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 29.6257 | − | 11.7659i | 1.54225 | − | 0.612509i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.22697 | − | 10.0977i | 0.375205 | − | 0.524244i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 8.98592i | − | 0.465273i | −0.972564 | − | 0.232637i | \(-0.925265\pi\) | ||
0.972564 | − | 0.232637i | \(-0.0747353\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.1915 | + | 16.4661i | 0.526289 | + | 0.850306i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.72506i | 0.500866i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.6705 | 0.907671 | 0.453836 | − | 0.891085i | \(-0.350055\pi\) | ||||
0.453836 | + | 0.891085i | \(0.350055\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −33.6097 | + | 6.42982i | −1.72188 | + | 0.329410i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 9.60898i | − | 0.490996i | −0.969397 | − | 0.245498i | \(-0.921049\pi\) | ||
0.969397 | − | 0.245498i | \(-0.0789515\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.715548 | − | 29.6308i | −0.0364677 | − | 1.51013i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.25715 | + | 13.2371i | 0.267236 | + | 0.672880i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 31.1675i | − | 1.58026i | −0.612942 | − | 0.790128i | \(-0.710014\pi\) | ||
0.612942 | − | 0.790128i | \(-0.289986\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 44.8157i | − | 2.26643i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.70110 | + | 29.8006i | 0.287583 | + | 1.50324i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.42655 | − | 1.89482i | −0.0717776 | − | 0.0953389i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.58833 | 0.280470 | 0.140235 | − | 0.990118i | \(-0.455214\pi\) | ||||
0.140235 | + | 0.990118i | \(0.455214\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.10702 | + | 8.90421i | −0.205608 | + | 0.445768i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.0883i | 0.953224i | 0.879114 | + | 0.476612i | \(0.158135\pi\) | ||||
−0.879114 | + | 0.476612i | \(0.841865\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.14848i | 0.356091i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −19.8367 | − | 3.39213i | −0.985692 | − | 0.168556i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.8036 | 0.932060 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.53326i | 0.273602i | 0.990599 | + | 0.136801i | \(0.0436821\pi\) | ||||
−0.990599 | + | 0.136801i | \(0.956318\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.95481 | − | 36.3539i | −0.343055 | − | 1.79321i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.3382 | − | 18.6363i | 0.656328 | − | 0.917034i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.6555 | + | 8.02220i | −0.523059 | + | 0.393794i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.66214 | − | 1.08321i | 0.277276 | − | 0.0530452i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.0661 | −0.833734 | −0.416867 | − | 0.908968i | \(-0.636872\pi\) | ||||
−0.416867 | + | 0.908968i | \(0.636872\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.1421 | −1.27409 | −0.637045 | − | 0.770827i | \(-0.719843\pi\) | ||||
−0.637045 | + | 0.770827i | \(0.719843\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.25565 | − | 15.7513i | −0.304160 | − | 0.765853i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 22.7571 | + | 6.54706i | 1.10388 | + | 0.317579i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.51336 | − | 3.23024i | −0.218417 | − | 0.156323i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13.8888 | + | 2.65704i | −0.670557 | + | 0.128283i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 15.4016i | − | 0.741869i | −0.928659 | − | 0.370934i | \(-0.879037\pi\) | ||
0.928659 | − | 0.370934i | \(-0.120963\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.0966 | 0.725494 | 0.362747 | − | 0.931888i | \(-0.381839\pi\) | ||||
0.362747 | + | 0.931888i | \(0.381839\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17.1240 | − | 15.5242i | −0.821032 | − | 0.744330i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 20.2482i | − | 0.968601i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.0500i | 0.813751i | 0.913484 | + | 0.406875i | \(0.133382\pi\) | ||||
−0.913484 | + | 0.406875i | \(0.866618\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.6321 | + | 15.9739i | 0.649149 | + | 0.760661i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.8460 | 1.03793 | 0.518967 | − | 0.854794i | \(-0.326317\pi\) | ||||
0.518967 | + | 0.854794i | \(0.326317\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.251657 | + | 0.334265i | 0.0119297 | + | 0.0158457i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.31374 | + | 1.39918i | −0.345928 | + | 0.0661789i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 14.4240i | − | 0.680710i | −0.940297 | − | 0.340355i | \(-0.889453\pi\) | ||
0.940297 | − | 0.340355i | \(-0.110547\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 53.2338i | 2.50668i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.47139 | − | 12.9184i | −0.116116 | − | 0.606957i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.63785 | + | 0.232742i | −0.451829 | + | 0.0109111i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 9.40452i | − | 0.439925i | −0.975508 | − | 0.219962i | \(-0.929406\pi\) | ||
0.975508 | − | 0.219962i | \(-0.0705935\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −20.7572 | + | 13.2192i | −0.968865 | + | 0.617019i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.63026 | 0.401951 | 0.200976 | − | 0.979596i | \(-0.435589\pi\) | ||||
0.200976 | + | 0.979596i | \(0.435589\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.9809i | 1.16096i | 0.814275 | + | 0.580479i | \(0.197135\pi\) | ||||
−0.814275 | + | 0.580479i | \(0.802865\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.5871 | − | 11.4112i | −0.583713 | − | 0.529182i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.52170i | 0.255514i | 0.991806 | + | 0.127757i | \(0.0407777\pi\) | ||||
−0.991806 | + | 0.127757i | \(0.959222\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.3502 | + | 9.55483i | 0.616455 | + | 0.441201i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.01732 | − | 26.2264i | −0.231186 | − | 1.20845i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −23.7855 | −1.09366 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.2819 | + | 2.95803i | 0.471766 | + | 0.135724i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.0858 | − | 5.19704i | 0.599156 | − | 0.237956i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.15027 | −0.143940 | −0.0719699 | − | 0.997407i | \(-0.522929\pi\) | ||||
−0.0719699 | + | 0.997407i | \(0.522929\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 6.11614i | − | 0.278872i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −39.3767 | − | 18.1623i | −1.79170 | − | 0.826414i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.6153 | + | 19.4129i | 0.663649 | + | 0.881494i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 31.1480i | − | 1.41145i | −0.708485 | − | 0.705726i | \(-0.750621\pi\) | ||
0.708485 | − | 0.705726i | \(-0.249379\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.9342 | − | 2.47442i | 0.584903 | − | 0.111897i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 7.82187i | − | 0.352996i | −0.984301 | − | 0.176498i | \(-0.943523\pi\) | ||
0.984301 | − | 0.176498i | \(-0.0564769\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −28.2641 | −1.27295 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 17.4923 | − | 28.6970i | 0.786220 | − | 1.28983i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.6153 | + | 13.3231i | 0.835012 | + | 0.597624i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.8804 | 1.29286 | 0.646432 | − | 0.762971i | \(-0.276260\pi\) | ||||
0.646432 | + | 0.762971i | \(0.276260\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.31475 | + | 1.01676i | −0.237445 | + | 0.0454253i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.7497i | 1.23730i | 0.785668 | + | 0.618648i | \(0.212319\pi\) | ||||
−0.785668 | + | 0.618648i | \(0.787681\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.25004 | − | 8.30164i | −0.278123 | − | 0.369418i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.36666 | − | 17.5981i | −0.149519 | − | 0.781558i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.57553 | −0.424428 | −0.212214 | − | 0.977223i | \(-0.568067\pi\) | ||||
−0.212214 | + | 0.977223i | \(0.568067\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.3087 | + | 26.9785i | −0.854166 | + | 1.19346i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.37833 | + | 5.97256i | −0.414063 | + | 0.263695i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.906693 | − | 1.20432i | −0.0399536 | − | 0.0530686i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 28.3031 | 1.24477 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.99923 | + | 1.72163i | −0.395022 | + | 0.0755711i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.0936 | −1.09937 | −0.549685 | − | 0.835372i | \(-0.685252\pi\) | ||||
−0.549685 | + | 0.835372i | \(0.685252\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.7296 | 1.38744 | 0.693720 | − | 0.720245i | \(-0.255971\pi\) | ||||
0.693720 | + | 0.720245i | \(0.255971\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 14.9752 | − | 17.3419i | 0.653572 | − | 0.756865i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.7757 | −0.905004 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 66.5428 | 2.89316 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 24.1512 | − | 9.59170i | 1.04807 | − | 0.416244i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.3151 | 0.749998 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.3771 | + | 15.1116i | 0.491873 | + | 0.653333i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 24.6745 | − | 4.72045i | 1.06479 | − | 0.203702i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −33.1955 | + | 11.3116i | −1.42983 | + | 0.487225i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.5457 | 1.52823 | 0.764115 | − | 0.645080i | \(-0.223176\pi\) | ||||
0.764115 | + | 0.645080i | \(0.223176\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 31.4862 | − | 6.02357i | 1.35120 | − | 0.258496i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.85442 | − | 13.0892i | −0.422117 | − | 0.560678i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.24333i | 0.395216i | 0.980281 | + | 0.197608i | \(0.0633174\pi\) | ||||
−0.980281 | + | 0.197608i | \(0.936683\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.32293 | − | 5.84896i | −0.0991401 | − | 0.249628i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.7700 | −0.544020 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.63330 | + | 2.28208i | −0.0694550 | + | 0.0970439i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.7694 | + | 9.76328i | 0.457134 | + | 0.414428i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.8645 | −0.714572 | −0.357286 | − | 0.933995i | \(-0.616298\pi\) | ||||
−0.357286 | + | 0.933995i | \(0.616298\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.73657i | 0.327222i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.72218 | − | 40.3651i | −0.326031 | − | 1.70422i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.9764i | 0.673325i | 0.941625 | + | 0.336662i | \(0.109298\pi\) | ||||
−0.941625 | + | 0.336662i | \(0.890702\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.7490 | + | 18.2621i | 0.578424 | + | 0.768293i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.20265 | + | 23.5954i | 0.134499 | + | 0.990914i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 17.2766i | − | 0.724272i | −0.932125 | − | 0.362136i | \(-0.882048\pi\) | ||
0.932125 | − | 0.362136i | \(-0.117952\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.5387 | 0.733973 | 0.366987 | − | 0.930226i | \(-0.380389\pi\) | ||||
0.366987 | + | 0.930226i | \(0.380389\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.6634 | + | 4.14439i | −0.905002 | + | 0.173134i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.0812 | + | 45.4692i | −0.545523 | + | 1.89620i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.5820 | 0.690316 | 0.345158 | − | 0.938545i | \(-0.387825\pi\) | ||||
0.345158 | + | 0.938545i | \(0.387825\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.87707 | + | 1.31564i | −0.285801 | + | 0.0546761i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.8333 | + | 9.18486i | 0.532413 | + | 0.381052i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.5135i | 0.973831i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.33410 | − | 5.68962i | −0.385918 | − | 0.235237i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 31.5221i | − | 1.30106i | −0.759481 | − | 0.650529i | \(-0.774547\pi\) | ||
0.759481 | − | 0.650529i | \(-0.225453\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.38667 | −0.386771 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.77072 | + | 9.25583i | 0.0728376 | + | 0.380734i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.5290i | 1.29474i | 0.762176 | + | 0.647370i | \(0.224131\pi\) | ||||
−0.762176 | + | 0.647370i | \(0.775869\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.676421 | − | 28.0106i | −0.0277306 | − | 1.14832i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −26.8992 | + | 5.14603i | −1.10091 | + | 0.210613i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 34.3090i | − | 1.40183i | −0.713246 | − | 0.700913i | \(-0.752776\pi\) | ||
0.713246 | − | 0.700913i | \(-0.247224\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 37.5135i | − | 1.53021i | −0.643907 | − | 0.765103i | \(-0.722688\pi\) | ||
0.643907 | − | 0.765103i | \(-0.277312\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.87105 | + | 17.3008i | 0.279811 | + | 0.704543i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.9632 | + | 25.1880i | 0.770965 | + | 1.02404i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.56064 | 0.103933 | 0.0519666 | − | 0.998649i | \(-0.483451\pi\) | ||||
0.0519666 | + | 0.998649i | \(0.483451\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.4545 | + | 24.8339i | −0.464159 | + | 1.00632i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 9.20599i | − | 0.372434i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 6.36050i | − | 0.256898i | −0.991716 | − | 0.128449i | \(-0.959000\pi\) | ||
0.991716 | − | 0.128449i | \(-0.0409999\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −27.6402 | + | 30.4885i | −1.11456 | + | 1.22942i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.0824 | 0.486418 | 0.243209 | − | 0.969974i | \(-0.421800\pi\) | ||||
0.243209 | + | 0.969974i | \(0.421800\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 38.9476i | − | 1.56543i | −0.622378 | − | 0.782717i | \(-0.713833\pi\) | ||
0.622378 | − | 0.782717i | \(-0.286167\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −26.4122 | − | 41.4735i | −1.05989 | − | 1.66427i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.288130 | − | 0.402580i | 0.0115437 | − | 0.0161290i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.1780 | − | 13.2851i | −0.847119 | − | 0.531403i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.48896 | − | 18.2374i | −0.139336 | − | 0.728330i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17.7754 | 0.708752 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.62832 | 0.383297 | 0.191649 | − | 0.981464i | \(-0.438617\pi\) | ||||
0.191649 | + | 0.981464i | \(0.438617\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.77255 | + | 30.1741i | 0.229438 | + | 1.19931i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 35.2928 | − | 26.5708i | 1.40055 | − | 1.05443i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.67926 | + | 10.7973i | 0.145777 | + | 0.427806i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.58090 | + | 24.1240i | 0.379015 | + | 0.954331i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 4.14281i | − | 0.163631i | −0.996647 | − | 0.0818155i | \(-0.973928\pi\) | ||
0.996647 | − | 0.0818155i | \(-0.0260718\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.6519 | −0.853869 | −0.426934 | − | 0.904283i | \(-0.640406\pi\) | ||||
−0.426934 | + | 0.904283i | \(0.640406\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −13.6226 | − | 12.3500i | −0.536390 | − | 0.486280i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 12.8648i | − | 0.505766i | −0.967497 | − | 0.252883i | \(-0.918621\pi\) | ||
0.967497 | − | 0.252883i | \(-0.0813788\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 43.3968i | 1.70347i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.41971 | + | 18.2543i | −0.329994 | + | 0.715443i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.82708 | 0.345430 | 0.172715 | − | 0.984972i | \(-0.444746\pi\) | ||||
0.172715 | + | 0.984972i | \(0.444746\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23.5595 | − | 31.2929i | −0.920544 | − | 1.22272i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −34.9620 | + | 13.8852i | −1.36400 | + | 0.541714i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.3918i | 0.989123i | 0.869143 | + | 0.494561i | \(0.164671\pi\) | ||||
−0.869143 | + | 0.494561i | \(0.835329\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.2661i | 1.06053i | 0.847833 | + | 0.530264i | \(0.177907\pi\) | ||||
−0.847833 | + | 0.530264i | \(0.822093\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13.1293 | + | 2.51175i | −0.509901 | + | 0.0975483i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.305614 | − | 12.6555i | −0.0118512 | − | 0.490758i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 56.4722i | − | 2.18661i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.12288 | + | 47.6868i | 0.352711 | + | 1.84368i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.5099 | 0.405729 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 24.5127i | − | 0.944895i | −0.881359 | − | 0.472447i | \(-0.843371\pi\) | ||
0.881359 | − | 0.472447i | \(-0.156629\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 24.9185 | − | 7.35317i | 0.959113 | − | 0.283024i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.5932i | 1.21423i | 0.794615 | + | 0.607114i | \(0.207673\pi\) | ||||
−0.794615 | + | 0.607114i | \(0.792327\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.7335 | − | 23.3804i | 0.642174 | − | 0.897259i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −29.2933 | + | 5.60405i | −1.12252 | + | 0.214748i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.3252 | −0.548139 | −0.274069 | − | 0.961710i | \(-0.588370\pi\) | ||||
−0.274069 | + | 0.961710i | \(0.588370\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.7403 | + | 38.1744i | 1.09811 | + | 1.45857i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.33354 | + | 1.59428i | −0.317944 | + | 0.0608254i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.64811 | 0.291370 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1.69810i | − | 0.0645986i | −0.999478 | − | 0.0322993i | \(-0.989717\pi\) | ||
0.999478 | − | 0.0322993i | \(-0.0102830\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −38.5959 | − | 9.57365i | −1.46614 | − | 0.363673i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.94569 | + | 4.47632i | −0.225533 | + | 0.169796i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 50.3229i | 1.90612i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.56063 | + | 29.0663i | 0.210322 | + | 1.09939i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.8839i | 0.864314i | 0.901798 | + | 0.432157i | \(0.142247\pi\) | ||||
−0.901798 | + | 0.432157i | \(0.857753\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.03111 | 0.302899 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.2100 | + | 14.6956i | 0.610504 | + | 0.553470i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.15586 | + | 9.99831i | −0.269124 | + | 0.376025i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −43.3163 | −1.62678 | −0.813389 | − | 0.581720i | \(-0.802380\pi\) | ||||
−0.813389 | + | 0.581720i | \(0.802380\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.95740 | + | 1.17454i | −0.110911 | + | 0.0440485i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 41.5103i | − | 1.55457i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.5843 | − | 10.9801i | 0.545422 | − | 0.410631i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 34.7997 | − | 6.65746i | 1.29962 | − | 0.248628i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.7322 | 1.10882 | 0.554412 | − | 0.832242i | \(-0.312943\pi\) | ||||
0.554412 | + | 0.832242i | \(0.312943\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.03810 | + | 1.45045i | −0.0386608 | + | 0.0540177i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18.3879 | + | 3.51775i | −0.683852 | + | 0.130827i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 28.6762 | + | 8.24996i | 1.06501 | + | 0.306396i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.6211 | −0.579355 | −0.289677 | − | 0.957124i | \(-0.593548\pi\) | ||||
−0.289677 | + | 0.957124i | \(0.593548\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.4185 | + | 24.4667i | −0.422906 | + | 0.906174i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −22.4849 | −0.831633 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.8068 | −1.17481 | −0.587406 | − | 0.809292i | \(-0.699851\pi\) | ||||
−0.587406 | + | 0.809292i | \(0.699851\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −24.8853 | − | 10.7574i | −0.917908 | − | 0.396794i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −31.0874 | −1.14512 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.0016 | −1.54505 | −0.772527 | − | 0.634982i | \(-0.781008\pi\) | ||||
−0.772527 | + | 0.634982i | \(0.781008\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.93196 | + | 1.13483i | −0.217916 | + | 0.0416892i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.5031 | −0.972305 | −0.486152 | − | 0.873874i | \(-0.661600\pi\) | ||||
−0.486152 | + | 0.873874i | \(0.661600\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.67999 | − | 5.78202i | 0.281373 | − | 0.211837i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.60499 | + | 16.6309i | 0.241664 | + | 0.608492i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.0259 | − | 18.2001i | 0.475958 | − | 0.665017i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.4006 | 1.21881 | 0.609403 | − | 0.792861i | \(-0.291409\pi\) | ||||
0.609403 | + | 0.792861i | \(0.291409\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.67923 | + | 50.5949i | 0.352731 | + | 1.84378i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.2129 | + | 13.5653i | 0.371684 | + | 0.493691i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.34496i | 0.121575i | 0.998151 | + | 0.0607873i | \(0.0193611\pi\) | ||||
−0.998151 | + | 0.0607873i | \(0.980639\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 80.6504 | − | 15.4291i | 2.92743 | − | 0.560041i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.4992 | −0.525595 | −0.262798 | − | 0.964851i | \(-0.584645\pi\) | ||||
−0.262798 | + | 0.964851i | \(0.584645\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.2826 | + | 15.7643i | −0.408458 | + | 0.570706i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 16.5358 | − | 27.1278i | 0.597853 | − | 0.980808i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.1154 | 0.509678 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.7135i | 1.03544i | 0.855551 | + | 0.517718i | \(0.173218\pi\) | ||||
−0.855551 | + | 0.517718i | \(0.826782\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 47.8677 | − | 9.15750i | 1.72391 | − | 0.329799i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 13.0728i | − | 0.470196i | −0.971972 | − | 0.235098i | \(-0.924459\pi\) | ||
0.971972 | − | 0.235098i | \(-0.0755411\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.0787 | + | 6.06419i | 0.757168 | + | 0.217832i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.20379 | − | 15.6182i | 0.258435 | − | 0.560298i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.7364i | 0.814616i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −43.3479 | −1.55111 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −26.1562 | + | 16.6575i | −0.934747 | + | 0.595291i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.7338 | + | 27.5397i | 0.740020 | + | 0.982935i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.4820 | −0.908337 | −0.454168 | − | 0.890916i | \(-0.650064\pi\) | ||||
−0.454168 | + | 0.890916i | \(0.650064\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.86660 | − | 35.8928i | −0.244457 | − | 1.27782i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.7416 | − | 21.9945i | 0.559707 | − | 0.782034i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 3.41848i | − | 0.121394i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.2088 | + | 13.4669i | −0.433001 | + | 0.477621i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.96431i | 0.282110i | 0.990002 | + | 0.141055i | \(0.0450495\pi\) | ||||
−0.990002 | + | 0.141055i | \(0.954950\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.7555 | 0.946541 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.521712 | − | 0.207199i | 0.0184338 | − | 0.00732102i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 62.8224i | − | 2.21695i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 55.9658 | − | 1.35151i | 1.97254 | − | 0.0476343i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.76618 | − | 9.23212i | −0.0621726 | − | 0.324986i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 40.8966i | 1.43785i | 0.695088 | + | 0.718924i | \(0.255365\pi\) | ||||
−0.695088 | + | 0.718924i | \(0.744635\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 39.9526i | − | 1.40293i | −0.712705 | − | 0.701464i | \(-0.752530\pi\) | ||
0.712705 | − | 0.701464i | \(-0.247470\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −28.9211 | + | 5.53285i | −1.01431 | + | 0.194045i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.5819 | + | 10.2254i | −0.475753 | + | 0.358179i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.1589 | −0.355415 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.11397 | + | 12.5539i | −0.108811 | + | 0.438667i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 28.4551i | − | 0.993091i | −0.868011 | − | 0.496546i | \(-0.834602\pi\) | ||
0.868011 | − | 0.496546i | \(-0.165398\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.837012i | 0.0291764i | 0.999894 | + | 0.0145882i | \(0.00464373\pi\) | ||||
−0.999894 | + | 0.0145882i | \(0.995356\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.94732 | + | 43.2078i | −0.137428 | + | 1.50430i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.2414 | 0.738637 | 0.369319 | − | 0.929303i | \(-0.379591\pi\) | ||||
0.369319 | + | 0.929303i | \(0.379591\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 26.3174i | − | 0.914041i | −0.889456 | − | 0.457021i | \(-0.848917\pi\) | ||
0.889456 | − | 0.457021i | \(-0.151083\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.52746 | − | 0.292216i | 0.0529871 | − | 0.0101369i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −31.3804 | + | 10.6931i | −1.08727 | + | 0.370493i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.58090 | − | 4.20168i | 0.193135 | − | 0.145405i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −19.2263 | + | 12.2442i | −0.664558 | + | 0.423222i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.0138 | −1.07071 | −0.535357 | − | 0.844626i | \(-0.679823\pi\) | ||||
−0.535357 | + | 0.844626i | \(0.679823\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.61554 | −0.228122 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −21.4832 | + | 4.10991i | −0.739919 | + | 0.141553i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.9125 | + | 18.4793i | 0.478605 | + | 0.635709i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.7116 | − | 30.3358i | 0.746018 | − | 1.04235i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.595110 | − | 3.11074i | −0.0204241 | − | 0.106760i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 35.5157i | 1.21746i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.6808 | −0.776576 | −0.388288 | − | 0.921538i | \(-0.626933\pi\) | ||||
−0.388288 | + | 0.921538i | \(0.626933\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.47104 | − | 12.2566i | 0.255504 | − | 0.419167i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.68694i | 0.194262i | 0.995272 | + | 0.0971310i | \(0.0309666\pi\) | ||||
−0.995272 | + | 0.0971310i | \(0.969033\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.2123i | 1.13319i | 0.823997 | + | 0.566595i | \(0.191739\pi\) | ||||
−0.823997 | + | 0.566595i | \(0.808261\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 44.2156 | + | 20.3942i | 1.50686 | + | 0.695033i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.78646 | 0.162933 | 0.0814665 | − | 0.996676i | \(-0.474040\pi\) | ||||
0.0814665 | + | 0.996676i | \(0.474040\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.44989 | − | 7.11452i | 0.321306 | − | 0.241901i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.76722 | − | 9.23754i | −0.0600179 | − | 0.313723i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 5.31408i | − | 0.180268i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.1116i | 0.342619i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 30.2992 | − | 12.0334i | 1.02547 | − | 0.407268i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.48968 | + | 28.6165i | −0.253198 | + | 0.967415i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.0778i | 0.340303i | 0.985418 | + | 0.170151i | \(0.0544257\pi\) | ||||
−0.985418 | + | 0.170151i | \(0.945574\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.6645 | + | 2.04020i | −0.359703 | + | 0.0688142i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.6439 | 0.931346 | 0.465673 | − | 0.884957i | \(-0.345812\pi\) | ||||
0.465673 | + | 0.884957i | \(0.345812\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.04074i | 0.304245i | 0.988362 | + | 0.152123i | \(0.0486108\pi\) | ||||
−0.988362 | + | 0.152123i | \(0.951389\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −22.5326 | + | 24.8546i | −0.757426 | + | 0.835478i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.6139i | 1.22937i | 0.788771 | + | 0.614687i | \(0.210718\pi\) | ||||
−0.788771 | + | 0.614687i | \(0.789282\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −42.5059 | − | 30.4217i | −1.42560 | − | 1.02031i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −30.9356 | − | 32.8037i | −1.03638 | − | 1.09897i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.0884 | 0.404523 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.9102 | + | 19.5070i | −0.866082 | + | 0.652046i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.01854 | − | 26.2327i | −0.167564 | − | 0.875885i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −26.1795 | −0.873134 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.2278i | 0.740515i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.11238 | + | 19.7561i | −0.303241 | + | 0.657440i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −33.0629 | + | 24.8920i | −1.09905 | + | 0.827439i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.95247i | 0.197648i | 0.995105 | + | 0.0988242i | \(0.0315081\pi\) | ||||
−0.995105 | + | 0.0988242i | \(0.968492\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12.9570 | + | 5.14591i | −0.429757 | + | 0.170679i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.3197i | 0.375039i | 0.982261 | + | 0.187519i | \(0.0600447\pi\) | ||||
−0.982261 | + | 0.187519i | \(0.939955\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −29.8837 | −0.989005 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.01930 | + | 5.45697i | 0.198992 | + | 0.180402i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −26.9739 | + | 37.6885i | −0.890757 | + | 1.24458i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.97971 | 0.263226 | 0.131613 | − | 0.991301i | \(-0.457984\pi\) | ||||
0.131613 | + | 0.991301i | \(0.457984\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.02219 | + | 31.4790i | 0.198438 | + | 1.03727i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.0995i | 0.464092i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.0346 | − | 5.18844i | −0.592975 | − | 0.170595i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.87967 | + | 0.746516i | −0.0617365 | + | 0.0245188i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.7309 | −1.04106 | −0.520529 | − | 0.853844i | \(-0.674265\pi\) | ||||
−0.520529 | + | 0.853844i | \(0.674265\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.1780 | + | 4.83123i | −0.464664 | + | 0.158337i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.29257 | + | 32.8923i | 0.206010 | + | 1.07685i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 31.9115 | + | 42.3865i | 1.04362 | + | 1.38619i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.1916 | 1.28033 | 0.640167 | − | 0.768236i | \(-0.278865\pi\) | ||||
0.640167 | + | 0.768236i | \(0.278865\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.45389 | − | 18.0541i | −0.112713 | − | 0.589172i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.7755 | 0.481667 | 0.240834 | − | 0.970566i | \(-0.422579\pi\) | ||||
0.240834 | + | 0.970566i | \(0.422579\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −100.546 | −3.27424 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −17.1341 | − | 25.5230i | −0.557372 | − | 0.830263i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −38.4136 | −1.24827 | −0.624137 | − | 0.781315i | \(-0.714549\pi\) | ||||
−0.624137 | + | 0.781315i | \(0.714549\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.4339 | −0.663312 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.874343 | − | 4.57033i | −0.0283525 | − | 0.148203i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −31.2446 | −1.01211 | −0.506056 | − | 0.862500i | \(-0.668897\pi\) | ||||
−0.506056 | + | 0.862500i | \(0.668897\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.7483 | − | 17.1264i | 0.736117 | − | 0.554199i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.73072 | − | 50.8641i | −0.314550 | − | 1.64420i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 32.9056 | − | 45.9764i | 1.06258 | − | 1.48466i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.7566 | 0.379245 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 23.5859 | − | 9.36719i | 0.760045 | − | 0.301853i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.22146 | − | 5.43680i | 0.232467 | − | 0.175017i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 16.9272i | − | 0.544341i | −0.962249 | − | 0.272170i | \(-0.912259\pi\) | ||
0.962249 | − | 0.272170i | \(-0.0877414\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.29818 | − | 17.2401i | −0.105953 | − | 0.553833i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.4041 | 1.36081 | 0.680406 | − | 0.732836i | \(-0.261804\pi\) | ||||
0.680406 | + | 0.732836i | \(0.261804\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.16085 | + | 5.12507i | 0.229566 | + | 0.164302i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.0540 | + | 1.28392i | 0.450087 | + | 0.0411184i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42.3945 | 1.35632 | 0.678160 | − | 0.734914i | \(-0.262778\pi\) | ||||
0.678160 | + | 0.734914i | \(0.262778\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.937453i | 0.0299611i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −20.4293 | + | 8.11353i | −0.652256 | + | 0.259045i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 27.5443i | − | 0.878525i | −0.898359 | − | 0.439263i | \(-0.855240\pi\) | ||
0.898359 | − | 0.439263i | \(-0.144760\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.31738 | − | 9.71935i | −0.233151 | − | 0.309684i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.8431 | − | 23.5084i | 0.345140 | − | 0.748280i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 44.9253i | − | 1.42854i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.3366 | 1.05897 | 0.529486 | − | 0.848319i | \(-0.322385\pi\) | ||||
0.529486 | + | 0.848319i | \(0.322385\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.09780 | − | 26.6470i | −0.161774 | − | 0.845618i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 28.2462 | − | 21.2657i | 0.895465 | − | 0.674167i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.4732 | 1.34514 | 0.672570 | − | 0.740033i | \(-0.265190\pi\) | ||||
0.672570 | + | 0.740033i | \(0.265190\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16.4498 | − | 10.4760i | 0.520448 | − | 0.331446i |
(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 | 840.2.k.a.209.14 | yes | 24 | |
3.2 | odd | 2 | 840.2.k.b.209.13 | yes | 24 | ||
4.3 | odd | 2 | 1680.2.k.i.209.11 | 24 | |||
5.4 | even | 2 | 840.2.k.b.209.11 | yes | 24 | ||
7.6 | odd | 2 | inner | 840.2.k.a.209.11 | ✓ | 24 | |
12.11 | even | 2 | 1680.2.k.h.209.12 | 24 | |||
15.14 | odd | 2 | inner | 840.2.k.a.209.12 | yes | 24 | |
20.19 | odd | 2 | 1680.2.k.h.209.14 | 24 | |||
21.20 | even | 2 | 840.2.k.b.209.12 | yes | 24 | ||
28.27 | even | 2 | 1680.2.k.i.209.14 | 24 | |||
35.34 | odd | 2 | 840.2.k.b.209.14 | yes | 24 | ||
60.59 | even | 2 | 1680.2.k.i.209.13 | 24 | |||
84.83 | odd | 2 | 1680.2.k.h.209.13 | 24 | |||
105.104 | even | 2 | inner | 840.2.k.a.209.13 | yes | 24 | |
140.139 | even | 2 | 1680.2.k.h.209.11 | 24 | |||
420.419 | odd | 2 | 1680.2.k.i.209.12 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.k.a.209.11 | ✓ | 24 | 7.6 | odd | 2 | inner | |
840.2.k.a.209.12 | yes | 24 | 15.14 | odd | 2 | inner | |
840.2.k.a.209.13 | yes | 24 | 105.104 | even | 2 | inner | |
840.2.k.a.209.14 | yes | 24 | 1.1 | even | 1 | trivial | |
840.2.k.b.209.11 | yes | 24 | 5.4 | even | 2 | ||
840.2.k.b.209.12 | yes | 24 | 21.20 | even | 2 | ||
840.2.k.b.209.13 | yes | 24 | 3.2 | odd | 2 | ||
840.2.k.b.209.14 | yes | 24 | 35.34 | odd | 2 | ||
1680.2.k.h.209.11 | 24 | 140.139 | even | 2 | |||
1680.2.k.h.209.12 | 24 | 12.11 | even | 2 | |||
1680.2.k.h.209.13 | 24 | 84.83 | odd | 2 | |||
1680.2.k.h.209.14 | 24 | 20.19 | odd | 2 | |||
1680.2.k.i.209.11 | 24 | 4.3 | odd | 2 | |||
1680.2.k.i.209.12 | 24 | 420.419 | odd | 2 | |||
1680.2.k.i.209.13 | 24 | 60.59 | even | 2 | |||
1680.2.k.i.209.14 | 24 | 28.27 | even | 2 |