Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,2,Mod(881,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1680.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.f (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: | \(13.4148675396\) |
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: | \( x^{16} - 2 x^{15} + x^{14} - 4 x^{13} + 10 x^{12} - 32 x^{11} + 71 x^{10} - 70 x^{9} + 74 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | no (minimal twist has level 840) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.14 | ||
Root | \(-1.12510 - 1.31688i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.881 |
Dual form | 1680.2.f.l.881.13 |
$q$-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 \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.31688 | + | 1.12510i | 0.760298 | + | 0.649574i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.64497 | − | 0.0644212i | −0.999704 | − | 0.0243489i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.468322 | + | 2.96322i | 0.156107 | + | 0.987740i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.69896i | − | 0.813767i | −0.913480 | − | 0.406884i | \(-0.866615\pi\) | ||
0.913480 | − | 0.406884i | \(-0.133385\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.61014i | 1.83332i | 0.399665 | + | 0.916661i | \(0.369127\pi\) | ||||
−0.399665 | + | 0.916661i | \(0.630873\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.31688 | + | 1.12510i | 0.340016 | + | 0.290498i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.03420 | −1.70604 | −0.853022 | − | 0.521875i | \(-0.825233\pi\) | ||||
−0.853022 | + | 0.521875i | \(0.825233\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.22748i | 0.740435i | 0.928945 | + | 0.370217i | \(0.120717\pi\) | ||||
−0.928945 | + | 0.370217i | \(0.879283\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.41061 | − | 3.06067i | −0.744257 | − | 0.667894i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.56574i | − | 0.534993i | −0.963559 | − | 0.267496i | \(-0.913804\pi\) | ||
0.963559 | − | 0.267496i | \(-0.0861964\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.71718 | + | 4.42910i | −0.522922 | + | 0.852381i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.21890i | 1.52621i | 0.646273 | + | 0.763106i | \(0.276327\pi\) | ||||
−0.646273 | + | 0.763106i | \(0.723673\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.87007i | − | 0.515481i | −0.966214 | − | 0.257740i | \(-0.917022\pi\) | ||
0.966214 | − | 0.257740i | \(-0.0829779\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.03659 | − | 3.55419i | 0.528602 | − | 0.618706i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.64497 | − | 0.0644212i | −0.447081 | − | 0.0108892i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.79684 | −1.11739 | −0.558697 | − | 0.829372i | \(-0.688699\pi\) | ||||
−0.558697 | + | 0.829372i | \(0.688699\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.43703 | + | 8.70473i | −1.19088 | + | 1.39387i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.0478 | 1.56920 | 0.784600 | − | 0.620002i | \(-0.212868\pi\) | ||||
0.784600 | + | 0.620002i | \(0.212868\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.6680 | −1.77935 | −0.889673 | − | 0.456599i | \(-0.849068\pi\) | ||||
−0.889673 | + | 0.456599i | \(0.849068\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.468322 | + | 2.96322i | 0.0698133 | + | 0.441731i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.56626 | 0.374328 | 0.187164 | − | 0.982329i | \(-0.440070\pi\) | ||||
0.187164 | + | 0.982329i | \(0.440070\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.99170 | + | 0.340784i | 0.998814 | + | 0.0486834i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.26316 | − | 7.91414i | −1.29710 | − | 1.10820i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.70121i | 0.371040i | 0.982641 | + | 0.185520i | \(0.0593969\pi\) | ||||
−0.982641 | + | 0.185520i | \(0.940603\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.69896i | − | 0.363928i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.63122 | + | 4.25019i | −0.480967 | + | 0.562951i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.03797 | 0.395510 | 0.197755 | − | 0.980251i | \(-0.436635\pi\) | ||||
0.197755 | + | 0.980251i | \(0.436635\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.83481i | 1.00315i | 0.865116 | + | 0.501573i | \(0.167245\pi\) | ||||
−0.865116 | + | 0.501573i | \(0.832755\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.04780 | − | 7.86779i | −0.132011 | − | 0.991248i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.61014i | 0.819887i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.5077 | 1.52805 | 0.764027 | − | 0.645184i | \(-0.223219\pi\) | ||||
0.764027 | + | 0.645184i | \(0.223219\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.88670 | − | 3.37875i | 0.347517 | − | 0.406754i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.0203i | 1.66391i | 0.554846 | + | 0.831953i | \(0.312777\pi\) | ||||
−0.554846 | + | 0.831953i | \(0.687223\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.81228i | − | 0.212111i | −0.994360 | − | 0.106056i | \(-0.966178\pi\) | ||
0.994360 | − | 0.106056i | \(-0.0338222\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.31688 | + | 1.12510i | 0.152060 | + | 0.129915i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.173870 | + | 7.13866i | −0.0198143 | + | 0.813526i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.4166 | −1.50949 | −0.754744 | − | 0.656020i | \(-0.772239\pi\) | ||||
−0.754744 | + | 0.656020i | \(0.772239\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.56135 | + | 2.77548i | −0.951261 | + | 0.308387i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.01554 | −0.330998 | −0.165499 | − | 0.986210i | \(-0.552924\pi\) | ||||
−0.165499 | + | 0.986210i | \(0.552924\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.03420 | −0.762966 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.24705 | + | 10.8233i | −0.991388 | + | 1.16038i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.17450 | 0.442496 | 0.221248 | − | 0.975218i | \(-0.428987\pi\) | ||||
0.221248 | + | 0.975218i | \(0.428987\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.425833 | − | 17.4836i | 0.0446394 | − | 1.83278i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.22911 | − | 3.77953i | 0.334843 | − | 0.391919i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.22748i | 0.331133i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9.55176i | − | 0.969834i | −0.874560 | − | 0.484917i | \(-0.838850\pi\) | ||
0.874560 | − | 0.484917i | \(-0.161150\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.99761 | − | 1.26398i | 0.803790 | − | 0.127035i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.5849 | 1.05324 | 0.526620 | − | 0.850101i | \(-0.323459\pi\) | ||||
0.526620 | + | 0.850101i | \(0.323459\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.89424i | 0.186645i | 0.995636 | + | 0.0933226i | \(0.0297488\pi\) | ||||
−0.995636 | + | 0.0933226i | \(0.970251\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.41061 | − | 3.06067i | −0.332842 | − | 0.298691i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.25101i | 0.507634i | 0.967252 | + | 0.253817i | \(0.0816861\pi\) | ||||
−0.967252 | + | 0.253817i | \(0.918314\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.53893 | −0.243185 | −0.121593 | − | 0.992580i | \(-0.538800\pi\) | ||||
−0.121593 | + | 0.992580i | \(0.538800\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.95060 | − | 7.64709i | −0.849553 | − | 0.725830i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 8.73583i | − | 0.821798i | −0.911681 | − | 0.410899i | \(-0.865215\pi\) | ||
0.911681 | − | 0.410899i | \(-0.134785\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2.56574i | − | 0.239256i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −19.5873 | + | 3.09567i | −1.81085 | + | 0.286195i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.6052 | + | 0.453151i | 1.70554 | + | 0.0415403i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.71562 | 0.337783 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.2317 | + | 11.3047i | 1.19306 | + | 1.01931i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.71266 | −0.684388 | −0.342194 | − | 0.939629i | \(-0.611170\pi\) | ||||
−0.342194 | + | 0.939629i | \(0.611170\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.3652 | − | 13.1276i | −1.35283 | − | 1.15582i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.91632 | −0.254800 | −0.127400 | − | 0.991851i | \(-0.540663\pi\) | ||||
−0.127400 | + | 0.991851i | \(0.540663\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.207918 | − | 8.53658i | 0.0180288 | − | 0.740215i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.71718 | + | 4.42910i | −0.233858 | + | 0.381196i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 18.7142i | − | 1.59886i | −0.600759 | − | 0.799430i | \(-0.705135\pi\) | ||
0.600759 | − | 0.799430i | \(-0.294865\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 19.5502i | − | 1.65823i | −0.559080 | − | 0.829114i | \(-0.688845\pi\) | ||
0.559080 | − | 0.829114i | \(-0.311155\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.37945 | + | 2.88729i | 0.284601 | + | 0.243154i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.8405 | 1.49190 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.21890i | 0.682543i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.82378 | + | 8.31510i | 0.727773 | + | 0.685818i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.35377i | 0.274751i | 0.990519 | + | 0.137376i | \(0.0438667\pi\) | ||||
−0.990519 | + | 0.137376i | \(0.956133\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.20015 | 0.504561 | 0.252280 | − | 0.967654i | \(-0.418819\pi\) | ||||
0.252280 | + | 0.967654i | \(0.418819\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.29427 | − | 20.8439i | −0.266326 | − | 1.68513i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 2.87007i | − | 0.230530i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.90178i | 0.790248i | 0.918628 | + | 0.395124i | \(0.129298\pi\) | ||||
−0.918628 | + | 0.395124i | \(0.870702\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.03912 | + | 3.55716i | −0.241018 | + | 0.282101i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.165288 | + | 6.78629i | −0.0130265 | + | 0.534834i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.4953 | 1.05703 | 0.528515 | − | 0.848924i | \(-0.322749\pi\) | ||||
0.528515 | + | 0.848924i | \(0.322749\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.03659 | − | 3.55419i | 0.236398 | − | 0.276694i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.40548 | 0.340907 | 0.170453 | − | 0.985366i | \(-0.445477\pi\) | ||||
0.170453 | + | 0.985366i | \(0.445477\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −30.6939 | −2.36107 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.56374 | + | 1.51150i | −0.731357 | + | 0.115587i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.90091 | 0.448638 | 0.224319 | − | 0.974516i | \(-0.427984\pi\) | ||||
0.224319 | + | 0.974516i | \(0.427984\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.64497 | − | 0.0644212i | −0.199941 | − | 0.00486978i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.00063 | + | 3.41801i | 0.300706 | + | 0.256913i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.34159i | 0.548736i | 0.961625 | + | 0.274368i | \(0.0884687\pi\) | ||||
−0.961625 | + | 0.274368i | \(0.911531\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.0168i | 1.26485i | 0.774623 | + | 0.632423i | \(0.217940\pi\) | ||||
−0.774623 | + | 0.632423i | \(0.782060\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.81491 | + | 10.3175i | −0.651617 | + | 0.762690i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.79684 | −0.499714 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.9850i | 1.38832i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.47219 | − | 11.5398i | 0.543522 | − | 0.839395i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.75110i | 0.126705i | 0.997991 | + | 0.0633525i | \(0.0201792\pi\) | ||||
−0.997991 | + | 0.0633525i | \(0.979821\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.8740 | −0.926694 | −0.463347 | − | 0.886177i | \(-0.653352\pi\) | ||||
−0.463347 | + | 0.886177i | \(0.653352\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.43703 | + | 8.70473i | −0.532577 | + | 0.623359i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 7.93648i | − | 0.565451i | −0.959201 | − | 0.282725i | \(-0.908762\pi\) | ||
0.959201 | − | 0.282725i | \(-0.0912385\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.56247i | 0.606977i | 0.952835 | + | 0.303489i | \(0.0981515\pi\) | ||||
−0.952835 | + | 0.303489i | \(0.901849\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.4710 | + | 14.0723i | 1.16178 | + | 0.992585i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.529471 | − | 21.7387i | 0.0371616 | − | 1.52576i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.0478 | 0.701768 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.60284 | − | 1.20159i | 0.528434 | − | 0.0835163i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.71084 | 0.602541 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.30759 | 0.640761 | 0.320380 | − | 0.947289i | \(-0.396189\pi\) | ||||
0.320380 | + | 0.947289i | \(0.396189\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15.7742 | + | 18.4630i | −1.08083 | + | 1.26507i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.6680 | −0.795748 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.184894 | + | 7.59125i | −0.0125514 | + | 0.515328i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.03899 | − | 2.38655i | 0.137782 | − | 0.161268i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 46.4970i | − | 3.12773i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 19.9132i | − | 1.33349i | −0.745287 | − | 0.666744i | \(-0.767687\pi\) | ||
0.745287 | − | 0.666744i | \(-0.232313\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.468322 | + | 2.96322i | 0.0312215 | + | 0.197548i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.8987 | 0.856116 | 0.428058 | − | 0.903751i | \(-0.359198\pi\) | ||||
0.428058 | + | 0.903751i | \(0.359198\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 6.88453i | − | 0.454942i | −0.973785 | − | 0.227471i | \(-0.926954\pi\) | ||
0.973785 | − | 0.227471i | \(-0.0730458\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.26064 | + | 9.20511i | −0.543510 | + | 0.605651i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.3574i | 1.00610i | 0.864258 | + | 0.503049i | \(0.167788\pi\) | ||||
−0.864258 | + | 0.503049i | \(0.832212\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.56626 | 0.167405 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −17.6680 | − | 15.0950i | −1.14766 | − | 0.980524i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.0305i | 1.42504i | 0.701654 | + | 0.712518i | \(0.252445\pi\) | ||||
−0.701654 | + | 0.712518i | \(0.747555\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.25586i | 0.467391i | 0.972310 | + | 0.233695i | \(0.0750819\pi\) | ||||
−0.972310 | + | 0.233695i | \(0.924918\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.3969 | − | 5.97737i | −0.923562 | − | 0.383448i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.99170 | + | 0.340784i | 0.446683 | + | 0.0217719i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.3341 | −1.35746 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.97109 | − | 3.39277i | −0.251658 | − | 0.215008i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.87952 | 0.497351 | 0.248676 | − | 0.968587i | \(-0.420005\pi\) | ||||
0.248676 | + | 0.968587i | \(0.420005\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.92482 | −0.435360 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.26316 | − | 7.91414i | −0.580082 | − | 0.495603i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.11492 | −0.319060 | −0.159530 | − | 0.987193i | \(-0.550998\pi\) | ||||
−0.159530 | + | 0.987193i | \(0.550998\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 17.9774 | + | 0.437861i | 1.11706 | + | 0.0272073i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −24.3544 | + | 3.84909i | −1.50750 | + | 0.238253i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.14488i | 0.255584i | 0.991801 | + | 0.127792i | \(0.0407890\pi\) | ||||
−0.991801 | + | 0.127792i | \(0.959211\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.70121i | 0.165934i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.49730 | + | 4.69671i | 0.336429 | + | 0.287434i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.3797 | 1.54743 | 0.773714 | − | 0.633535i | \(-0.218397\pi\) | ||||
0.773714 | + | 0.633535i | \(0.218397\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4.50193i | − | 0.273473i | −0.990607 | − | 0.136736i | \(-0.956339\pi\) | ||
0.990607 | − | 0.136736i | \(-0.0436613\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 20.2315 | − | 22.5446i | 1.22446 | − | 1.36446i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 2.69896i | − | 0.162753i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.75704 | 0.285823 | 0.142911 | − | 0.989736i | \(-0.454354\pi\) | ||||
0.142911 | + | 0.989736i | \(0.454354\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.50466 | − | 1.34412i | 0.509161 | − | 0.0804703i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.5156i | 0.627310i | 0.949537 | + | 0.313655i | \(0.101553\pi\) | ||||
−0.949537 | + | 0.313655i | \(0.898447\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.59242i | 0.154103i | 0.997027 | + | 0.0770517i | \(0.0245506\pi\) | ||||
−0.997027 | + | 0.0770517i | \(0.975449\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.63122 | + | 4.25019i | −0.215095 | + | 0.251760i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −26.5761 | − | 0.647290i | −1.56874 | − | 0.0382083i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.4800 | 1.91059 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.7466 | − | 12.5785i | 0.629979 | − | 0.737364i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.7742 | 0.687856 | 0.343928 | − | 0.938996i | \(-0.388242\pi\) | ||||
0.343928 | + | 0.938996i | \(0.388242\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.03797 | 0.176878 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.9540 | + | 7.33357i | 0.693639 | + | 0.425537i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.9599 | 0.980815 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 30.8613 | + | 0.751663i | 1.77882 | + | 0.0433251i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.9390 | + | 11.9090i | 0.800776 | + | 0.684157i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.83481i | 0.448620i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.4395i | 1.56606i | 0.621986 | + | 0.783028i | \(0.286326\pi\) | ||||
−0.621986 | + | 0.783028i | \(0.713674\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.13120 | + | 2.49448i | −0.121240 | + | 0.141906i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.5480 | −0.881645 | −0.440822 | − | 0.897594i | \(-0.645313\pi\) | ||||
−0.440822 | + | 0.897594i | \(0.645313\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 12.6650i | − | 0.715869i | −0.933747 | − | 0.357935i | \(-0.883481\pi\) | ||
0.933747 | − | 0.357935i | \(-0.116519\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.04780 | − | 7.86779i | −0.0590370 | − | 0.443300i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.2682i | 1.02604i | 0.858376 | + | 0.513021i | \(0.171474\pi\) | ||||
−0.858376 | + | 0.513021i | \(0.828526\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.1825 | 1.24198 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.90789 | + | 6.91493i | −0.329746 | + | 0.385954i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 22.7027i | − | 1.26321i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.61014i | 0.366665i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.34345 | − | 2.85654i | −0.184893 | − | 0.157967i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.78768 | − | 0.165322i | −0.374217 | − | 0.00911448i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.7692 | 0.866751 | 0.433376 | − | 0.901213i | \(-0.357322\pi\) | ||||
0.433376 | + | 0.901213i | \(0.357322\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.18311 | − | 20.1405i | −0.174433 | − | 1.10369i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.5077 | 0.683367 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.90831 | 0.212899 | 0.106450 | − | 0.994318i | \(-0.466052\pi\) | ||||
0.106450 | + | 0.994318i | \(0.466052\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.82864 | − | 11.5040i | 0.533819 | − | 0.624812i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.74622 | −0.419481 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.4709 | − | 1.35178i | −0.997333 | − | 0.0729890i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.88670 | − | 3.37875i | 0.155415 | − | 0.181906i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 18.5501i | − | 0.995821i | −0.867228 | − | 0.497911i | \(-0.834101\pi\) | ||
0.867228 | − | 0.497911i | \(-0.165899\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 27.1665i | − | 1.45419i | −0.686537 | − | 0.727095i | \(-0.740870\pi\) | ||
0.686537 | − | 0.727095i | \(-0.259130\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −29.2770 | − | 17.9610i | −1.56269 | − | 0.958685i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.1433 | 1.55114 | 0.775569 | − | 0.631262i | \(-0.217463\pi\) | ||||
0.775569 | + | 0.631262i | \(0.217463\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.0203i | 0.744121i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 23.9909 | + | 21.5294i | 1.26973 | + | 1.13946i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 23.0333i | − | 1.21565i | −0.794070 | − | 0.607827i | \(-0.792042\pi\) | ||
0.794070 | − | 0.607827i | \(-0.207958\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.58337 | 0.451756 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.89300 | + | 4.18042i | 0.256816 | + | 0.219415i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 1.81228i | − | 0.0948591i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.3177i | 1.11277i | 0.830923 | + | 0.556387i | \(0.187813\pi\) | ||||
−0.830923 | + | 0.556387i | \(0.812187\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.70560 | + | 29.7738i | 0.244964 | + | 1.54996i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.174015 | − | 7.14461i | 0.00903442 | − | 0.370930i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.49852 | 0.0775906 | 0.0387953 | − | 0.999247i | \(-0.487648\pi\) | ||||
0.0387953 | + | 0.999247i | \(0.487648\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.31688 | + | 1.12510i | 0.0680032 | + | 0.0580997i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −54.3281 | −2.79804 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.44524 | −0.485170 | −0.242585 | − | 0.970130i | \(-0.577995\pi\) | ||||
−0.242585 | + | 0.970130i | \(0.577995\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.1566 | − | 8.67748i | −0.520339 | − | 0.444561i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.6101 | 1.15532 | 0.577662 | − | 0.816276i | \(-0.303965\pi\) | ||||
0.577662 | + | 0.816276i | \(0.303965\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.173870 | + | 7.13866i | −0.00886124 | + | 0.363820i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.46436 | − | 34.5747i | −0.277769 | − | 1.75753i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 19.4779i | − | 0.987569i | −0.869584 | − | 0.493784i | \(-0.835613\pi\) | ||
0.869584 | − | 0.493784i | \(-0.164387\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.0479i | 0.912721i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.84043 | − | 3.28113i | −0.193724 | − | 0.165511i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.4166 | −0.675063 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 4.10316i | − | 0.205932i | −0.994685 | − | 0.102966i | \(-0.967167\pi\) | ||
0.994685 | − | 0.102966i | \(-0.0328333\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.87827 | − | 11.0077i | 0.494532 | − | 0.551074i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.69031i | 0.134348i | 0.997741 | + | 0.0671738i | \(0.0213982\pi\) | ||||
−0.997741 | + | 0.0671738i | \(0.978602\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.9716 | 0.945042 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.56135 | + | 2.77548i | −0.425417 | + | 0.137915i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.3444i | 0.909298i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 22.9345i | − | 1.13404i | −0.823705 | − | 0.567019i | \(-0.808097\pi\) | ||
0.823705 | − | 0.567019i | \(-0.191903\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.0552 | − | 24.6442i | 1.03858 | − | 1.21561i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.03533 | − | 0.195710i | −0.395393 | − | 0.00963024i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.01554 | −0.148027 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 21.9959 | − | 25.7452i | 1.07714 | − | 1.26075i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.76656 | 0.379421 | 0.189711 | − | 0.981840i | \(-0.439245\pi\) | ||||
0.189711 | + | 0.981840i | \(0.439245\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.86035 | 0.188142 | 0.0940710 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940710 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.20184 | + | 7.60441i | 0.0584354 | + | 0.369739i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.03420 | −0.341209 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.504728 | − | 20.7228i | 0.0244255 | − | 1.00285i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 23.4937 | + | 20.0723i | 1.13429 | + | 0.969098i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.05754i | 0.243613i | 0.992554 | + | 0.121807i | \(0.0388688\pi\) | ||||
−0.992554 | + | 0.121807i | \(0.961131\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.7647i | 1.81486i | 0.420208 | + | 0.907428i | \(0.361957\pi\) | ||||
−0.420208 | + | 0.907428i | \(0.638043\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.24705 | + | 10.8233i | −0.443362 | + | 0.518936i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.28086 | 0.396127 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.03026i | 0.335536i | 0.985827 | + | 0.167768i | \(0.0536559\pi\) | ||||
−0.985827 | + | 0.167768i | \(0.946344\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.26455 | + | 20.8775i | 0.107836 | + | 0.994169i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 24.2815i | − | 1.15365i | −0.816869 | − | 0.576824i | \(-0.804292\pi\) | ||
0.816869 | − | 0.576824i | \(-0.195708\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.17450 | 0.197890 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.77330 | + | 4.41649i | −0.178471 | + | 0.208893i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 19.0341i | − | 0.898276i | −0.893462 | − | 0.449138i | \(-0.851731\pi\) | ||
0.893462 | − | 0.449138i | \(-0.148269\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 27.1186i | − | 1.27696i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.16482 | + | 6.97575i | 0.383617 | + | 0.327750i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.425833 | − | 17.4836i | 0.0199634 | − | 0.819644i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.29974 | 0.341467 | 0.170734 | − | 0.985317i | \(-0.445386\pi\) | ||||
0.170734 | + | 0.985317i | \(0.445386\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 19.1132 | − | 31.1552i | 0.892128 | − | 1.45420i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.3544 | 1.04115 | 0.520575 | − | 0.853816i | \(-0.325718\pi\) | ||||
0.520575 | + | 0.853816i | \(0.325718\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.45971 | −0.393156 | −0.196578 | − | 0.980488i | \(-0.562983\pi\) | ||||
−0.196578 | + | 0.980488i | \(0.562983\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.22911 | − | 3.77953i | 0.149746 | − | 0.175272i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.9314 | −0.552120 | −0.276060 | − | 0.961140i | \(-0.589029\pi\) | ||||
−0.276060 | + | 0.961140i | \(0.589029\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −33.0824 | − | 0.805759i | −1.52760 | − | 0.0372065i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.1404 | + | 13.0394i | −0.513325 | + | 0.600824i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 31.4913i | 1.44797i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.22748i | 0.148087i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.00428 | + | 1.26504i | −0.366491 | + | 0.0579221i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.4398 | 0.751155 | 0.375578 | − | 0.926791i | \(-0.377444\pi\) | ||||
0.375578 | + | 0.926791i | \(0.377444\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 44.9281i | − | 2.04854i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.85288 | + | 8.75073i | −0.357318 | + | 0.398172i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 9.55176i | − | 0.433723i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.41408 | −0.200021 | −0.100011 | − | 0.994986i | \(-0.531888\pi\) | ||||
−0.100011 | + | 0.994986i | \(0.531888\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.7716 | + | 15.1835i | 0.803659 | + | 0.686620i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.2188i | 0.686817i | 0.939186 | + | 0.343408i | \(0.111581\pi\) | ||||
−0.939186 | + | 0.343408i | \(0.888419\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 57.8134i | − | 2.60378i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.99761 | − | 1.26398i | 0.359466 | − | 0.0568118i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.903206 | − | 37.0833i | 0.0405143 | − | 1.66341i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.3095 | −1.49114 | −0.745570 | − | 0.666427i | \(-0.767823\pi\) | ||||
−0.745570 | + | 0.666427i | \(0.767823\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.80147 | + | 4.95659i | 0.259191 | + | 0.221444i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.24941 | 0.412411 | 0.206205 | − | 0.978509i | \(-0.433889\pi\) | ||||
0.206205 | + | 0.978509i | \(0.433889\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.5849 | 0.471023 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −40.4201 | − | 34.5336i | −1.79512 | − | 1.53369i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.0016 | −0.576286 | −0.288143 | − | 0.957587i | \(-0.593038\pi\) | ||||
−0.288143 | + | 0.957587i | \(0.593038\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.116749 | + | 4.79342i | −0.00516468 | + | 0.212048i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −14.2948 | − | 8.76965i | −0.631132 | − | 0.387190i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.89424i | 0.0834702i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 6.92624i | − | 0.304616i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.77076 | + | 6.63908i | 0.341099 | + | 0.291423i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.37469 | −0.0602262 | −0.0301131 | − | 0.999546i | \(-0.509587\pi\) | ||||
−0.0301131 | + | 0.999546i | \(0.509587\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.30714i | 0.188338i | 0.995556 | + | 0.0941690i | \(0.0300194\pi\) | ||||
−0.995556 | + | 0.0941690i | \(0.969981\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.41061 | − | 3.06067i | −0.148851 | − | 0.133579i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.1887i | 0.879432i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.4170 | 0.713783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.42275 | + | 9.00218i | 0.0617421 | + | 0.390661i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 66.4173i | 2.87685i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.25101i | 0.227021i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.25999 | + | 9.66796i | −0.356445 | + | 0.417203i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.919762 | − | 18.8703i | 0.0396169 | − | 0.812802i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.7698 | −0.592011 | −0.296006 | − | 0.955186i | \(-0.595655\pi\) | ||||
−0.296006 | + | 0.955186i | \(0.595655\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −19.1455 | + | 22.4090i | −0.821611 | + | 0.961660i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.53893 | −0.108756 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.9601 | −0.511375 | −0.255688 | − | 0.966759i | \(-0.582302\pi\) | ||||
−0.255688 | + | 0.966759i | \(0.582302\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −23.2163 | + | 3.66922i | −0.990847 | + | 0.156598i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −26.5263 | −1.13006 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 35.4865 | + | 0.864314i | 1.50904 | + | 0.0367544i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.95060 | − | 7.64709i | −0.379932 | − | 0.324601i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.97976i | 0.380485i | 0.981737 | + | 0.190242i | \(0.0609274\pi\) | ||||
−0.981737 | + | 0.190242i | \(0.939073\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 77.1268i | − | 3.26211i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21.3600 | + | 25.0009i | −0.901818 | + | 1.05554i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.48868 | −0.273465 | −0.136733 | − | 0.990608i | \(-0.543660\pi\) | ||||
−0.136733 | + | 0.990608i | \(0.543660\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 8.73583i | − | 0.367519i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 22.8233 | − | 6.78953i | 0.958488 | − | 0.285133i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 22.1663i | − | 0.929260i | −0.885505 | − | 0.464630i | \(-0.846187\pi\) | ||
0.885505 | − | 0.464630i | \(-0.153813\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.6346 | 0.989077 | 0.494539 | − | 0.869156i | \(-0.335337\pi\) | ||||
0.494539 | + | 0.869156i | \(0.335337\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.97015 | + | 2.30598i | −0.0823043 | + | 0.0963336i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 2.56574i | − | 0.106999i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.1403i | 1.46291i | 0.681890 | + | 0.731455i | \(0.261158\pi\) | ||||
−0.681890 | + | 0.731455i | \(0.738842\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.9535 | − | 14.4845i | −0.704564 | − | 0.601956i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.97600 | + | 0.194265i | 0.330900 | + | 0.00805945i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.29046 | 0.301940 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −19.5873 | + | 3.09567i | −0.809835 | + | 0.127990i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.59955 | 0.272393 | 0.136196 | − | 0.990682i | \(-0.456512\pi\) | ||||
0.136196 | + | 0.990682i | \(0.456512\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.26311 | 0.381680 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.92929 | − | 10.4514i | 0.367302 | − | 0.429911i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.20187 | −0.377876 | −0.188938 | − | 0.981989i | \(-0.560504\pi\) | ||||
−0.188938 | + | 0.981989i | \(0.560504\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.6052 | + | 0.453151i | 0.762740 | + | 0.0185774i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.63359 | + | 11.2757i | −0.394277 | + | 0.461484i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 23.7274i | − | 0.969476i | −0.874659 | − | 0.484738i | \(-0.838915\pi\) | ||
0.874659 | − | 0.484738i | \(-0.161085\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.04185i | 0.246452i | 0.992379 | + | 0.123226i | \(0.0393240\pi\) | ||||
−0.992379 | + | 0.123226i | \(0.960676\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.85762 | + | 37.0630i | 0.238541 | + | 1.50932i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.71562 | 0.151061 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.3266i | 1.71799i | 0.511988 | + | 0.858993i | \(0.328909\pi\) | ||||
−0.511988 | + | 0.858993i | \(0.671091\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 25.1554 | − | 28.0315i | 1.01935 | − | 1.13589i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.9634i | 0.686264i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.8987 | 1.08643 | 0.543215 | − | 0.839594i | \(-0.317207\pi\) | ||||
0.543215 | + | 0.839594i | \(0.317207\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13.2317 | + | 11.3047i | 0.533553 | + | 0.455850i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.3624i | 1.62493i | 0.583010 | + | 0.812465i | \(0.301875\pi\) | ||||
−0.583010 | + | 0.812465i | \(0.698125\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.1095i | 0.969042i | 0.874780 | + | 0.484521i | \(0.161006\pi\) | ||||
−0.874780 | + | 0.484521i | \(0.838994\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.3639 | + | 6.97157i | 0.456018 | + | 0.279760i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.0414 | − | 0.268926i | −0.442365 | − | 0.0107743i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.4711 | + | 9.80052i | 0.458111 | + | 0.391395i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 47.8103 | 1.90632 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.34458 | −0.292383 | −0.146191 | − | 0.989256i | \(-0.546702\pi\) | ||||
−0.146191 | + | 0.989256i | \(0.546702\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.2569 | + | 10.4719i | 0.487170 | + | 0.416222i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.71266 | −0.306068 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.25263 | + | 46.2161i | −0.0892524 | + | 1.83115i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −41.5453 | + | 6.56603i | −1.64351 | + | 0.259748i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 20.2949i | − | 0.801601i | −0.916165 | − | 0.400800i | \(-0.868732\pi\) | ||
0.916165 | − | 0.400800i | \(-0.131268\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 43.6248i | 1.72040i | 0.509961 | + | 0.860198i | \(0.329660\pi\) | ||||
−0.509961 | + | 0.860198i | \(0.670340\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −15.3652 | − | 13.1276i | −0.605006 | − | 0.516897i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.1667 | −0.674894 | −0.337447 | − | 0.941345i | \(-0.609563\pi\) | ||||
−0.337447 | + | 0.941345i | \(0.609563\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 8.19936i | − | 0.321853i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.78436 | + | 9.78871i | −0.344286 | + | 0.383650i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 19.3345i | − | 0.756619i | −0.925679 | − | 0.378309i | \(-0.876506\pi\) | ||
0.925679 | − | 0.378309i | \(-0.123494\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.91632 | −0.113950 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.37019 | − | 0.848731i | 0.209511 | − | 0.0331122i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1.43175i | − | 0.0557731i | −0.999611 | − | 0.0278866i | \(-0.991122\pi\) | ||
0.999611 | − | 0.0278866i | \(-0.00887772\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 33.9771i | − | 1.32156i | −0.750582 | − | 0.660778i | \(-0.770227\pi\) | ||
0.750582 | − | 0.660778i | \(-0.229773\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 52.3136 | − | 61.2308i | 2.03169 | − | 2.37801i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.207918 | − | 8.53658i | 0.00806272 | − | 0.331034i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.0875 | 0.816513 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 22.4043 | − | 26.2232i | 0.866199 | − | 1.01385i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.1458 | 0.816326 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.78793 | −0.223108 | −0.111554 | − | 0.993758i | \(-0.535583\pi\) | ||||
−0.111554 | + | 0.993758i | \(0.535583\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.71718 | + | 4.42910i | −0.104584 | + | 0.170476i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.3272 | 0.819672 | 0.409836 | − | 0.912159i | \(-0.365586\pi\) | ||||
0.409836 | + | 0.912159i | \(0.365586\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.615336 | + | 25.2641i | −0.0236144 | + | 0.969547i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.9860 | + | 14.5122i | 0.650904 | + | 0.556111i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.4723i | 1.20425i | 0.798401 | + | 0.602127i | \(0.205680\pi\) | ||||
−0.798401 | + | 0.602127i | \(0.794320\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 18.7142i | − | 0.715032i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.74575 | − | 9.06607i | 0.295519 | − | 0.345892i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −17.8554 | −0.680236 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.8993i | 1.36568i | 0.730570 | + | 0.682838i | \(0.239254\pi\) | ||||
−0.730570 | + | 0.682838i | \(0.760746\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −21.2348 | + | 2.82798i | −0.806645 | + | 0.107426i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 19.5502i | − | 0.741582i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −70.6781 | −2.67713 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17.2786 | + | 20.2238i | −0.653535 | + | 0.764934i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 41.8942i | − | 1.58232i | −0.611609 | − | 0.791160i | \(-0.709477\pi\) | ||
0.611609 | − | 0.791160i | \(-0.290523\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 21.9367i | − | 0.827357i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.37945 | + | 2.88729i | 0.127277 | + | 0.108742i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −27.9968 | − | 0.681893i | −1.05293 | − | 0.0256452i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.6731 | −1.07684 | −0.538420 | − | 0.842676i | \(-0.680979\pi\) | ||||
−0.538420 | + | 0.842676i | \(0.680979\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.28330 | − | 39.7564i | −0.235642 | − | 1.49098i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.36385 | −0.275778 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.8405 | 0.667197 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.7864 | + | 29.0114i | −0.925666 | + | 1.08345i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.6353 | −1.17980 | −0.589899 | − | 0.807477i | \(-0.700832\pi\) | ||||
−0.589899 | + | 0.807477i | \(0.700832\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.122029 | − | 5.01021i | 0.00454461 | − | 0.186590i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.16353 | + | 9.55506i | −0.303605 | + | 0.355357i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.21890i | 0.305242i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3.14677i | − | 0.116707i | −0.998296 | − | 0.0583536i | \(-0.981415\pi\) | ||
0.998296 | − | 0.0583536i | \(-0.0185851\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.2338 | − | 24.0693i | −0.453105 | − | 0.891457i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 82.0747 | 3.03564 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 12.4598i | − | 0.460213i | −0.973165 | − | 0.230106i | \(-0.926093\pi\) | ||
0.973165 | − | 0.230106i | \(-0.0739074\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.82378 | + | 8.31510i | 0.325470 | + | 0.306707i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 33.7577i | − | 1.24348i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.1373 | −0.851118 | −0.425559 | − | 0.904931i | \(-0.639923\pi\) | ||||
−0.425559 | + | 0.904931i | \(0.639923\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −28.0943 | − | 24.0029i | −1.03207 | − | 0.881768i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.0418i | 1.06544i | 0.846292 | + | 0.532720i | \(0.178830\pi\) | ||||
−0.846292 | + | 0.532720i | \(0.821170\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.35377i | 0.122872i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.41224 | − | 8.93571i | −0.0516713 | − | 0.326940i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.338276 | − | 13.8887i | 0.0123603 | − | 0.507484i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.94574 | 0.216963 | 0.108482 | − | 0.994098i | \(-0.465401\pi\) | ||||
0.108482 | + | 0.994098i | \(0.465401\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.3764 | + | 8.86521i | 0.378135 | + | 0.323066i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.20015 | 0.225646 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.8676 | −1.59439 | −0.797197 | − | 0.603719i | \(-0.793685\pi\) | ||||
−0.797197 | + | 0.603719i | \(0.793685\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.11912 | − | 7.79108i | −0.331003 | − | 0.282798i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.6453 | −0.965893 | −0.482946 | − | 0.875650i | \(-0.660433\pi\) | ||||
−0.482946 | + | 0.875650i | \(0.660433\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.71538 | + | 0.163561i | 0.243113 | + | 0.00592130i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.29427 | − | 20.8439i | −0.119105 | − | 0.753612i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.0814i | 0.725098i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.3596i | 0.662065i | 0.943619 | + | 0.331032i | \(0.107397\pi\) | ||||
−0.943619 | + | 0.331032i | \(0.892603\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.73571 | − | 5.75477i | −0.242581 | − | 0.207253i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.57902 | 0.0927610 | 0.0463805 | − | 0.998924i | \(-0.485231\pi\) | ||||
0.0463805 | + | 0.998924i | \(0.485231\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 2.87007i | − | 0.103096i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 23.1814 | + | 20.8029i | 0.831628 | + | 0.746301i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 32.4290i | 1.16189i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 37.8403 | 1.35403 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −36.4023 | − | 22.3323i | −1.30091 | − | 0.798090i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.90178i | 0.353410i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 31.5892i | − | 1.12603i | −0.826446 | − | 0.563016i | \(-0.809641\pi\) | ||
0.826446 | − | 0.563016i | \(-0.190359\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.66338 | + | 5.45829i | −0.166021 | + | 0.194320i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.562773 | + | 23.1060i | −0.0200099 | + | 0.821555i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −51.7892 | −1.83909 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.03912 | + | 3.55716i | −0.107786 | + | 0.126159i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.2603 | −0.611393 | −0.305696 | − | 0.952129i | \(-0.598889\pi\) | ||||
−0.305696 | + | 0.952129i | \(0.598889\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.0516 | −0.638620 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.95501 | + | 12.3700i | 0.0690769 | + | 0.437071i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.89127 | −0.172609 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.165288 | + | 6.78629i | −0.00582563 | + | 0.239185i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 33.4219 | + | 28.5546i | 1.17651 | + | 1.00517i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.6539i | 0.726152i | 0.931760 | + | 0.363076i | \(0.118273\pi\) | ||||
−0.931760 | + | 0.363076i | \(0.881727\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 21.0641i | − | 0.739660i | −0.929099 | − | 0.369830i | \(-0.879416\pi\) | ||
0.929099 | − | 0.369830i | \(-0.120584\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.06510 | − | 5.92848i | 0.177641 | − | 0.207921i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.4953 | 0.472718 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 37.6581i | − | 1.31749i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 52.0072 | − | 6.92612i | 1.81728 | − | 0.242018i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.7909i | 1.42361i | 0.702376 | + | 0.711806i | \(0.252123\pi\) | ||||
−0.702376 | + | 0.711806i | \(0.747877\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.5422 | 0.437194 | 0.218597 | − | 0.975815i | \(-0.429852\pi\) | ||||
0.218597 | + | 0.975815i | \(0.429852\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.03659 | − | 3.55419i | 0.105720 | − | 0.123741i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.0641i | 0.349964i | 0.984572 | + | 0.174982i | \(0.0559867\pi\) | ||||
−0.984572 | + | 0.174982i | \(0.944013\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.1382i | 0.907816i | 0.891049 | + | 0.453908i | \(0.149971\pi\) | ||||
−0.891049 | + | 0.453908i | \(0.850029\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.26442 | + | 5.35212i | 0.217310 | + | 0.185663i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −49.1810 | − | 2.39714i | −1.70402 | − | 0.0830560i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.40548 | 0.152458 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.7118 | + | 7.79852i | 0.439386 | + | 0.269556i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35.0785 | −1.21105 | −0.605523 | − | 0.795828i | \(-0.707036\pi\) | ||||
−0.605523 | + | 0.795828i | \(0.707036\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −38.5504 | −1.32932 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.8311 | + | 13.8478i | −0.407484 | + | 0.476943i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −30.6939 | −1.05590 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.82768 | − | 0.239364i | −0.337683 | − | 0.00822465i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.91672 | + | 3.41389i | −0.100101 | + | 0.117165i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.4389i | 0.597798i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.2995i | 0.386889i | 0.981111 | + | 0.193444i | \(0.0619659\pi\) | ||||
−0.981111 | + | 0.193444i | \(0.938034\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.56374 | + | 1.51150i | −0.327073 | + | 0.0516922i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 45.4081 | 1.55111 | 0.775556 | − | 0.631279i | \(-0.217470\pi\) | ||||
0.775556 | + | 0.631279i | \(0.217470\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 5.83938i | − | 0.199237i | −0.995026 | − | 0.0996186i | \(-0.968238\pi\) | ||
0.995026 | − | 0.0996186i | \(-0.0317623\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −34.2691 | − | 30.7530i | −1.16789 | − | 1.04806i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 40.2731i | − | 1.37091i | −0.728113 | − | 0.685457i | \(-0.759603\pi\) | ||
0.728113 | − | 0.685457i | \(-0.240397\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.90091 | 0.200637 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 42.7721 | + | 36.5430i | 1.45262 | + | 1.24107i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 36.2109i | 1.22837i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 82.6774i | 2.80142i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 28.3040 | − | 4.47330i | 0.957944 | − | 0.151398i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.64497 | − | 0.0644212i | −0.0894162 | − | 0.00217783i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.2384 | −1.05484 | −0.527422 | − | 0.849603i | \(-0.676841\pi\) | ||||
−0.527422 | + | 0.849603i | \(0.676841\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.5052 | + | 13.2471i | 0.522976 | + | 0.446813i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.3074 | −1.05477 | −0.527387 | − | 0.849625i | \(-0.676828\pi\) | ||||
−0.527387 | + | 0.849625i | \(0.676828\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43.3854 | −1.46003 | −0.730017 | − | 0.683429i | \(-0.760488\pi\) | ||||
−0.730017 | + | 0.683429i | \(0.760488\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.00063 | + | 3.41801i | 0.134480 | + | 0.114895i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.2749 | −0.613609 | −0.306805 | − | 0.951772i | \(-0.599260\pi\) | ||||
−0.306805 | + | 0.951772i | \(0.599260\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.3997 | + | 0.496859i | 0.684185 | + | 0.0166641i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.49092 | + | 23.1067i | 0.250955 | + | 0.774105i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.28257i | 0.277166i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.34159i | 0.245402i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 22.3340 | + | 19.0815i | 0.745712 | + | 0.637112i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 23.5889 | 0.786733 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 19.0009i | − | 0.633010i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 39.7949 | + | 35.7118i | 1.32429 | + | 1.18841i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.0168i | 0.565656i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.4276 | −1.37558 | −0.687790 | − | 0.725910i | \(-0.741419\pi\) | ||||
−0.687790 | + | 0.725910i | \(0.741419\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.95715 | + | 31.3655i | 0.164418 | + | 1.04033i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.58416i | 0.118748i | 0.998236 | + | 0.0593742i | \(0.0189105\pi\) | ||||
−0.998236 | + | 0.0593742i | \(0.981089\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.13882i | 0.269356i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.81491 | + | 10.3175i | −0.291412 | + | 0.341085i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.71356 | + | 0.187873i | 0.254724 | + | 0.00620410i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.5460 | 0.677749 | 0.338874 | − | 0.940832i | \(-0.389954\pi\) | ||||
0.338874 | + | 0.940832i | \(0.389954\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.8721 | + | 36.1344i | −1.01727 | + | 1.19067i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −92.6763 | −3.05048 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.79684 | −0.223479 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.61305 | + | 0.887115i | −0.184357 | + | 0.0291367i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.6332 | −0.676953 | −0.338477 | − | 0.940975i | \(-0.609912\pi\) | ||||
−0.338477 | + | 0.940975i | \(0.609912\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.09987 | + | 22.5656i | −0.0360469 | + | 0.739557i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20.4747 | − | 17.4929i | −0.670313 | − | 0.572693i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18.9850i | 0.620877i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.9657i | 0.619581i | 0.950805 | + | 0.309791i | \(0.100259\pi\) | ||||
−0.950805 | + | 0.309791i | \(0.899741\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.2493 | − | 16.6782i | 0.465010 | − | 0.544274i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.1459 | −0.689337 | −0.344668 | − | 0.938725i | \(-0.612009\pi\) | ||||
−0.344668 | + | 0.938725i | \(0.612009\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 25.7800i | − | 0.839511i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.47219 | − | 11.5398i | 0.243070 | − | 0.375389i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43.7955i | 1.42316i | 0.702604 | + | 0.711581i | \(0.252021\pi\) | ||||
−0.702604 | + | 0.711581i | \(0.747979\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.9794 | 0.388869 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20.5534 | + | 24.0569i | −0.666490 | + | 0.780098i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.0324i | 0.713701i | 0.934162 | + | 0.356850i | \(0.116149\pi\) | ||||
−0.934162 | + | 0.356850i | \(0.883851\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.75110i | 0.0566642i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 29.2116 | + | 24.9574i | 0.944276 | + | 0.806758i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.20559 | + | 49.4984i | −0.0389305 | + | 1.59839i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.7627 | 0.734280 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.5599 | + | 2.45916i | −0.501411 | + | 0.0792455i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.8740 | −0.414430 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.8422 | −1.05613 | −0.528066 | − | 0.849203i | \(-0.677083\pi\) | ||||
−0.528066 | + | 0.849203i | \(0.677083\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25.5427 | − | 29.8967i | 0.820551 | − | 0.960420i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.7928 | 1.21283 | 0.606414 | − | 0.795149i | \(-0.292607\pi\) | ||||
0.606414 | + | 0.795149i | \(0.292607\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.25945 | + | 51.7097i | −0.0403761 | + | 1.65774i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.43703 | + | 8.70473i | −0.238176 | + | 0.278774i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.8791i | 0.508017i | 0.967202 | + | 0.254008i | \(0.0817491\pi\) | ||||
−0.967202 | + | 0.254008i | \(0.918251\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 11.2668i | − | 0.360089i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.18904 | − | 7.52341i | −0.0379630 | − | 0.240204i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.7320 | 0.693142 | 0.346571 | − | 0.938024i | \(-0.387346\pi\) | ||||
0.346571 | + | 0.938024i | \(0.387346\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 7.93648i | − | 0.252877i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.75253 | − | 7.85450i | −0.278596 | − | 0.250011i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29.9369i | 0.951937i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.1739 | 1.05380 | 0.526902 | − | 0.849926i | \(-0.323354\pi\) | ||||
0.526902 | + | 0.849926i | \(0.323354\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.7660 | + | 17.7418i | 0.658990 | + | 0.563019i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.56247i | 0.271449i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.50680i | 0.111061i | 0.998457 | + | 0.0555307i | \(0.0176851\pi\) | ||||
−0.998457 | + | 0.0555307i | \(0.982315\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 18.4683 | − | 30.1039i | 0.584310 | − | 0.952445i |
(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 | 1680.2.f.l.881.14 | 16 | ||
3.2 | odd | 2 | 1680.2.f.k.881.4 | 16 | |||
4.3 | odd | 2 | 840.2.f.b.41.3 | yes | 16 | ||
7.6 | odd | 2 | 1680.2.f.k.881.3 | 16 | |||
12.11 | even | 2 | 840.2.f.a.41.13 | ✓ | 16 | ||
21.20 | even | 2 | inner | 1680.2.f.l.881.13 | 16 | ||
28.27 | even | 2 | 840.2.f.a.41.14 | yes | 16 | ||
84.83 | odd | 2 | 840.2.f.b.41.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.f.a.41.13 | ✓ | 16 | 12.11 | even | 2 | ||
840.2.f.a.41.14 | yes | 16 | 28.27 | even | 2 | ||
840.2.f.b.41.3 | yes | 16 | 4.3 | odd | 2 | ||
840.2.f.b.41.4 | yes | 16 | 84.83 | odd | 2 | ||
1680.2.f.k.881.3 | 16 | 7.6 | odd | 2 | |||
1680.2.f.k.881.4 | 16 | 3.2 | odd | 2 | |||
1680.2.f.l.881.13 | 16 | 21.20 | even | 2 | inner | ||
1680.2.f.l.881.14 | 16 | 1.1 | even | 1 | trivial |