Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [608,2,Mod(305,608)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(608, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("608.305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 608 = 2^{5} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 608.c (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: | \(4.85490444289\) |
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: | \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 4 x^{12} + 4 x^{11} - 10 x^{10} + 24 x^{9} - 40 x^{8} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{13} \) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 305.9 | ||
Root | \(-0.466170 - 1.33517i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 608.305 |
Dual form | 608.2.c.b.305.8 |
$q$-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 \(\left(\mathbb{Z}/608\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.579017i | 0.334296i | 0.985932 | + | 0.167148i | \(0.0534557\pi\) | ||||
−0.985932 | + | 0.167148i | \(0.946544\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.10882i | 0.943091i | 0.881842 | + | 0.471546i | \(0.156304\pi\) | ||||
−0.881842 | + | 0.471546i | \(0.843696\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.73436 | 1.03349 | 0.516745 | − | 0.856140i | \(-0.327144\pi\) | ||||
0.516745 | + | 0.856140i | \(0.327144\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.66474 | 0.888246 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.66474i | 1.40647i | 0.710957 | + | 0.703236i | \(0.248262\pi\) | ||||
−0.710957 | + | 0.703236i | \(0.751738\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.47791i | − 1.24195i | −0.783831 | − | 0.620974i | \(-0.786737\pi\) | ||||
0.783831 | − | 0.620974i | \(-0.213263\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.22104 | −0.315271 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.85237 | −1.66194 | −0.830972 | − | 0.556314i | \(-0.812215\pi\) | ||||
−0.830972 | + | 0.556314i | \(0.812215\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1.00000i | − 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.58324i | 0.345491i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.20416 | 0.251085 | 0.125543 | − | 0.992088i | \(-0.459933\pi\) | ||||
0.125543 | + | 0.992088i | \(0.459933\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.552894 | 0.110579 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.27998i | 0.631233i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.57484i | 1.77800i | 0.457904 | + | 0.889002i | \(0.348600\pi\) | ||||
−0.457904 | + | 0.889002i | \(0.651400\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.35842 | 0.962400 | 0.481200 | − | 0.876611i | \(-0.340201\pi\) | ||||
0.481200 | + | 0.876611i | \(0.340201\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.70096 | −0.470178 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.76625i | 0.974675i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 1.09693i | − 0.180335i | −0.995927 | − | 0.0901674i | \(-0.971260\pi\) | ||||
0.995927 | − | 0.0901674i | \(-0.0287402\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.59279 | 0.415178 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.33797 | 1.14600 | 0.573000 | − | 0.819556i | \(-0.305780\pi\) | ||||
0.573000 | + | 0.819556i | \(0.305780\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.64408i | 1.16571i | 0.812576 | + | 0.582856i | \(0.198065\pi\) | ||||
−0.812576 | + | 0.582856i | \(0.801935\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.61945i | 0.837697i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.56486 | −1.10345 | −0.551724 | − | 0.834027i | \(-0.686030\pi\) | ||||
−0.551724 | + | 0.834027i | \(0.686030\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.476702 | 0.0681003 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 3.96764i | − 0.555581i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 3.11949i | − 0.428495i | −0.976779 | − | 0.214248i | \(-0.931270\pi\) | ||||
0.976779 | − | 0.214248i | \(-0.0687300\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.83708 | −1.32643 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.579017 | 0.0766927 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 10.2442i | − 1.33368i | −0.745201 | − | 0.666840i | \(-0.767646\pi\) | ||||
0.745201 | − | 0.666840i | \(-0.232354\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 0.722061i | − 0.0924504i | −0.998931 | − | 0.0462252i | \(-0.985281\pi\) | ||||
0.998931 | − | 0.0462252i | \(-0.0147192\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.28634 | 0.917993 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.44309 | 1.17127 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 6.13698i | − 0.749752i | −0.927075 | − | 0.374876i | \(-0.877685\pi\) | ||||
0.927075 | − | 0.374876i | \(-0.122315\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.697232i | 0.0839368i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.62247 | −0.548587 | −0.274293 | − | 0.961646i | \(-0.588444\pi\) | ||||
−0.274293 | + | 0.961646i | \(0.588444\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.19270 | −0.724801 | −0.362400 | − | 0.932022i | \(-0.618043\pi\) | ||||
−0.362400 | + | 0.932022i | \(0.618043\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.320135i | 0.0369660i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.7551i | 1.45357i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.26723 | 0.367592 | 0.183796 | − | 0.982964i | \(-0.441161\pi\) | ||||
0.183796 | + | 0.982964i | \(0.441161\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.09505 | 0.677228 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 8.97934i | − 0.985611i | −0.870140 | − | 0.492805i | \(-0.835971\pi\) | ||||
0.870140 | − | 0.492805i | \(-0.164029\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 14.4504i | − 1.56736i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.54400 | −0.594379 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.620707 | 0.0657948 | 0.0328974 | − | 0.999459i | \(-0.489527\pi\) | ||||
0.0328974 | + | 0.999459i | \(0.489527\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 12.2442i | − 1.28354i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.10262i | 0.321726i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.10882 | 0.216360 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.67284 | −0.169851 | −0.0849257 | − | 0.996387i | \(-0.527065\pi\) | ||||
−0.0849257 | + | 0.996387i | \(0.527065\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.4303i | 1.24929i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 7.30571i | − 0.726946i | −0.931605 | − | 0.363473i | \(-0.881591\pi\) | ||||
0.931605 | − | 0.363473i | \(-0.118409\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.77332 | 0.864461 | 0.432231 | − | 0.901763i | \(-0.357727\pi\) | ||||
0.432231 | + | 0.901763i | \(0.357727\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.33876 | −0.325830 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 9.91355i | − 0.958379i | −0.877711 | − | 0.479190i | \(-0.840931\pi\) | ||||
0.877711 | − | 0.479190i | \(-0.159069\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 2.84589i | − 0.272587i | −0.990669 | − | 0.136293i | \(-0.956481\pi\) | ||||
0.990669 | − | 0.136293i | \(-0.0435189\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.635143 | 0.0602851 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.58487 | −0.149092 | −0.0745462 | − | 0.997218i | \(-0.523751\pi\) | ||||
−0.0745462 | + | 0.997218i | \(0.523751\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.53936i | 0.236797i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 11.9325i | − 1.10316i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −18.7368 | −1.71760 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7598 | −0.978163 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.24881i | 0.383103i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.7100i | 1.04738i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.2933 | −1.26833 | −0.634163 | − | 0.773199i | \(-0.718655\pi\) | ||||
−0.634163 | + | 0.773199i | \(0.718655\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.42605 | −0.389692 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 0.609006i | − 0.0532091i | −0.999646 | − | 0.0266046i | \(-0.991531\pi\) | ||||
0.999646 | − | 0.0266046i | \(-0.00846949\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 2.73436i | − 0.237099i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.91688 | −0.595310 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.1589 | 1.55142 | 0.775710 | − | 0.631089i | \(-0.217392\pi\) | ||||
0.775710 | + | 0.631089i | \(0.217392\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.93421i | 0.164058i | 0.996630 | + | 0.0820289i | \(0.0261400\pi\) | ||||
−0.996630 | + | 0.0820289i | \(0.973860\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 4.38018i | − 0.368878i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 20.8883 | 1.74677 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20.1916 | −1.67682 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.276019i | 0.0227656i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 15.5775i | − 1.27616i | −0.769970 | − | 0.638080i | \(-0.779729\pi\) | ||||
0.769970 | − | 0.638080i | \(-0.220271\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.9746 | 1.62551 | 0.812756 | − | 0.582605i | \(-0.197966\pi\) | ||||
0.812756 | + | 0.582605i | \(0.197966\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −18.2598 | −1.47622 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.2999i | 0.907631i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 20.8872i | − 1.66698i | −0.552536 | − | 0.833489i | \(-0.686340\pi\) | ||||
0.552536 | − | 0.833489i | \(-0.313660\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.80624 | 0.143244 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.29261 | 0.259494 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.54835i | 0.199602i | 0.995007 | + | 0.0998010i | \(0.0318206\pi\) | ||||
−0.995007 | + | 0.0998010i | \(0.968179\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 5.69584i | − 0.443420i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.6644 | 1.44429 | 0.722146 | − | 0.691740i | \(-0.243156\pi\) | ||||
0.722146 | + | 0.691740i | \(0.243156\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.05167 | −0.542436 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 2.66474i | − 0.203778i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 8.42370i | − 0.640442i | −0.947343 | − | 0.320221i | \(-0.896243\pi\) | ||||
0.947343 | − | 0.320221i | \(-0.103757\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.51181 | 0.114282 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.93157 | 0.445844 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 16.6809i | − 1.24679i | −0.781908 | − | 0.623394i | \(-0.785753\pi\) | ||||
0.781908 | − | 0.623394i | \(-0.214247\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 4.65888i | − 0.346292i | −0.984896 | − | 0.173146i | \(-0.944607\pi\) | ||||
0.984896 | − | 0.173146i | \(-0.0553932\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.418086 | 0.0309058 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.31323 | 0.170072 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 31.9645i | − 2.33748i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.96864i | 0.652372i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.0609 | −1.45155 | −0.725777 | − | 0.687930i | \(-0.758520\pi\) | ||||
−0.725777 | + | 0.687930i | \(0.758520\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.85117 | 0.133250 | 0.0666251 | − | 0.997778i | \(-0.478777\pi\) | ||||
0.0666251 | + | 0.997778i | \(0.478777\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.46771i | 0.391551i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 0.224883i | − 0.0160222i | −0.999968 | − | 0.00801112i | \(-0.997450\pi\) | ||||
0.999968 | − | 0.00801112i | \(-0.00255005\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.77685 | 0.125957 | 0.0629787 | − | 0.998015i | \(-0.479940\pi\) | ||||
0.0629787 | + | 0.998015i | \(0.479940\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.55342 | 0.250639 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 26.1810i | 1.83755i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.4744i | 1.08078i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.20878 | 0.223026 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.66474 | 0.322667 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.0194i | 1.17166i | 0.810433 | + | 0.585831i | \(0.199232\pi\) | ||||
−0.810433 | + | 0.585831i | \(0.800768\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 2.67649i | − 0.183390i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.1200 | −1.09937 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.6518 | 0.994630 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 3.58568i | − 0.242298i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 30.6843i | 2.06405i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.6634 | −0.914971 | −0.457486 | − | 0.889217i | \(-0.651250\pi\) | ||||
−0.457486 | + | 0.889217i | \(0.651250\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.47332 | 0.0982212 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 5.46152i | − 0.362494i | −0.983438 | − | 0.181247i | \(-0.941987\pi\) | ||||
0.983438 | − | 0.181247i | \(-0.0580133\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 3.22791i | − 0.213306i | −0.994296 | − | 0.106653i | \(-0.965987\pi\) | ||||
0.994296 | − | 0.106653i | \(-0.0340135\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.38540 | −0.485923 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.8344 | −1.16837 | −0.584185 | − | 0.811621i | \(-0.698586\pi\) | ||||
−0.584185 | + | 0.811621i | \(0.698586\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 15.9529i | − 1.04065i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.89178i | 0.122884i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.82556 | −0.118086 | −0.0590428 | − | 0.998255i | \(-0.518805\pi\) | ||||
−0.0590428 | + | 0.998255i | \(0.518805\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.47608 | 0.417161 | 0.208581 | − | 0.978005i | \(-0.433116\pi\) | ||||
0.208581 | + | 0.978005i | \(0.433116\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.3691i | 0.857627i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00528i | 0.0642248i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.47791 | −0.284923 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.19919 | 0.329485 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.10899i | 0.196238i | 0.995175 | + | 0.0981189i | \(0.0312825\pi\) | ||||
−0.995175 | + | 0.0981189i | \(0.968717\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.61711i | 0.353145i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.36702 | 0.523963 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.75606 | 0.359053 | 0.179526 | − | 0.983753i | \(-0.442543\pi\) | ||||
0.179526 | + | 0.983753i | \(0.442543\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 2.99941i | − 0.186374i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 25.5145i | 1.57931i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.58595 | 0.282782 | 0.141391 | − | 0.989954i | \(-0.454843\pi\) | ||||
0.141391 | + | 0.989954i | \(0.454843\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.57844 | 0.404110 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.359400i | 0.0219949i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.3913i | 0.694542i | 0.937765 | + | 0.347271i | \(0.112892\pi\) | ||||
−0.937765 | + | 0.347271i | \(0.887108\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.1252 | −1.52625 | −0.763124 | − | 0.646252i | \(-0.776336\pi\) | ||||
−0.763124 | + | 0.646252i | \(0.776336\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.08960 | 0.429082 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.57910i | 0.155526i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 18.2998i | − 1.09953i | −0.835321 | − | 0.549763i | \(-0.814718\pi\) | ||||
0.835321 | − | 0.549763i | \(-0.185282\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.2788 | 0.854848 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.0708 | −1.07802 | −0.539008 | − | 0.842301i | \(-0.681201\pi\) | ||||
−0.539008 | + | 0.842301i | \(0.681201\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.3972i | 0.915269i | 0.889140 | + | 0.457634i | \(0.151303\pi\) | ||||
−0.889140 | + | 0.457634i | \(0.848697\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.22104i | 0.0723282i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.0646 | 1.18438 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 29.9550 | 1.76206 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 0.968605i | − 0.0567806i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 11.4407i | − 0.668374i | −0.942507 | − | 0.334187i | \(-0.891538\pi\) | ||||
0.942507 | − | 0.334187i | \(-0.108462\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.6031 | 1.25778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −15.3003 | −0.887811 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 5.39214i | − 0.311835i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.9016i | 1.20475i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.23013 | 0.243015 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.52269 | 0.0871892 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 21.3453i | − 1.21824i | −0.793077 | − | 0.609122i | \(-0.791522\pi\) | ||||
0.793077 | − | 0.609122i | \(-0.208478\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.07991i | 0.288986i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.7295 | 1.23216 | 0.616082 | − | 0.787682i | \(-0.288719\pi\) | ||||
0.616082 | + | 0.787682i | \(0.288719\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 34.1009 | 1.92750 | 0.963748 | − | 0.266814i | \(-0.0859710\pi\) | ||||
0.963748 | + | 0.266814i | \(0.0859710\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 15.3656i | 0.865751i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.2281i | 1.24845i | 0.781244 | + | 0.624226i | \(0.214586\pi\) | ||||
−0.781244 | + | 0.624226i | \(0.785414\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −44.6641 | −2.50071 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.74012 | 0.320382 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.85237i | 0.381276i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 2.47581i | − 0.137333i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.64782 | 0.0911245 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −20.6850 | −1.14040 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.1969i | 1.32998i | 0.746852 | + | 0.664991i | \(0.231564\pi\) | ||||
−0.746852 | + | 0.664991i | \(0.768436\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 2.92304i | − 0.160182i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.9418 | 0.707084 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −34.2735 | −1.86700 | −0.933498 | − | 0.358583i | \(-0.883260\pi\) | ||||
−0.933498 | + | 0.358583i | \(0.883260\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 0.917670i | − 0.0498410i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.9956i | 1.35359i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.8370 | −0.963108 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.47033 | −0.0791601 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.9233i | 1.44532i | 0.691206 | + | 0.722658i | \(0.257080\pi\) | ||||
−0.691206 | + | 0.722658i | \(0.742920\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 8.65769i | − 0.463436i | −0.972783 | − | 0.231718i | \(-0.925565\pi\) | ||||
0.972783 | − | 0.231718i | \(-0.0744346\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.6875 | 0.783959 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.11265 | −0.485018 | −0.242509 | − | 0.970149i | \(-0.577970\pi\) | ||||
−0.242509 | + | 0.970149i | \(0.577970\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 9.74795i | − 0.517367i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 10.8489i | − 0.574187i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.29978 | −0.226934 | −0.113467 | − | 0.993542i | \(-0.536196\pi\) | ||||
−0.113467 | + | 0.993542i | \(0.536196\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 6.23010i | − 0.326996i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 13.0593i | − 0.683553i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.2873 | 1.11119 | 0.555594 | − | 0.831454i | \(-0.312491\pi\) | ||||
0.555594 | + | 0.831454i | \(0.312491\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 19.5538 | 1.01793 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 8.52980i | − 0.442845i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.1076i | 0.575129i | 0.957761 | + | 0.287565i | \(0.0928456\pi\) | ||||
−0.957761 | + | 0.287565i | \(0.907154\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.78031 | −0.350134 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 42.8753 | 2.20819 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 20.6908i | − 1.06281i | −0.847117 | − | 0.531407i | \(-0.821664\pi\) | ||||
0.847117 | − | 0.531407i | \(-0.178336\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 8.27608i | − 0.423996i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.1869 | 0.622720 | 0.311360 | − | 0.950292i | \(-0.399215\pi\) | ||||
0.311360 | + | 0.950292i | \(0.399215\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −26.8981 | −1.37085 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 20.3695i | 1.03544i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 26.1769i | − 1.32722i | −0.748078 | − | 0.663611i | \(-0.769023\pi\) | ||||
0.748078 | − | 0.663611i | \(-0.230977\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.25137 | −0.417290 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.352625 | 0.0177876 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.88999i | 0.346673i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.8451i | 0.745055i | 0.928021 | + | 0.372528i | \(0.121509\pi\) | ||||
−0.928021 | + | 0.372528i | \(0.878491\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.58324 | 0.0792611 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 34.4111 | 1.71841 | 0.859205 | − | 0.511632i | \(-0.170959\pi\) | ||||
0.859205 | + | 0.511632i | \(0.170959\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 23.9945i | − 1.19525i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12.8533i | 0.638688i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.11691 | 0.253636 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.43283 | 0.0708487 | 0.0354243 | − | 0.999372i | \(-0.488722\pi\) | ||||
0.0354243 | + | 0.999372i | \(0.488722\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.5143i | 0.518633i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 28.0113i | − 1.37834i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.9358 | 0.929521 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.11994 | −0.0548438 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.6886i | 1.64579i | 0.568190 | + | 0.822897i | \(0.307644\pi\) | ||||
−0.568190 | + | 0.822897i | \(0.692356\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 0.237430i | − 0.0115716i | −0.999983 | − | 0.00578582i | \(-0.998158\pi\) | ||||
0.999983 | − | 0.00578582i | \(-0.00184169\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −20.1584 | −0.980134 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.78863 | −0.183776 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 1.97437i | − 0.0955465i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.0947i | 0.583936i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.0743 | −0.629766 | −0.314883 | − | 0.949130i | \(-0.601965\pi\) | ||||
−0.314883 | + | 0.949130i | \(0.601965\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.67718 | −0.465056 | −0.232528 | − | 0.972590i | \(-0.574700\pi\) | ||||
−0.232528 | + | 0.972590i | \(0.574700\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 11.6913i | − 0.560554i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 1.20416i | − 0.0576030i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.7983 | −0.849468 | −0.424734 | − | 0.905318i | \(-0.639632\pi\) | ||||
−0.424734 | + | 0.905318i | \(0.639632\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.27029 | 0.0604898 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 3.30468i | − 0.157010i | −0.996914 | − | 0.0785050i | \(-0.974985\pi\) | ||||
0.996914 | − | 0.0785050i | \(-0.0250147\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.30896i | 0.0620505i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.01966 | 0.426615 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.6543 | −1.39947 | −0.699735 | − | 0.714402i | \(-0.746699\pi\) | ||||
−0.699735 | + | 0.714402i | \(0.746699\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 34.2297i | 1.61182i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.5656i | 0.543402i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 25.8208 | 1.21050 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.2310 | −0.946368 | −0.473184 | − | 0.880964i | \(-0.656895\pi\) | ||||
−0.473184 | + | 0.880964i | \(0.656895\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 22.4756i | − 1.04907i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 41.2429i | 1.92087i | 0.278502 | + | 0.960436i | \(0.410162\pi\) | ||||
−0.278502 | + | 0.960436i | \(0.589838\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.5232 | 0.767896 | 0.383948 | − | 0.923355i | \(-0.374564\pi\) | ||||
0.383948 | + | 0.923355i | \(0.374564\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.54285 | −0.303417 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 24.9967i | − 1.15671i | −0.815786 | − | 0.578355i | \(-0.803695\pi\) | ||||
0.815786 | − | 0.578355i | \(-0.196305\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 16.7807i | − 0.774860i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.0940 | 0.557264 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −35.6576 | −1.63954 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 0.552894i | − 0.0253685i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 8.31263i | − 0.380609i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.0298 | −0.458273 | −0.229137 | − | 0.973394i | \(-0.573590\pi\) | ||||
−0.229137 | + | 0.973394i | \(0.573590\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.91197 | −0.223966 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.90648i | 0.0867478i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 3.52772i | − 0.160185i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −41.6248 | −1.88620 | −0.943101 | − | 0.332508i | \(-0.892105\pi\) | ||||
−0.943101 | + | 0.332508i | \(0.892105\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.47554 | −0.0667261 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.6939i | 1.56572i | 0.622200 | + | 0.782858i | \(0.286239\pi\) | ||||
−0.622200 | + | 0.782858i | \(0.713761\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 65.6104i | − 2.95494i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −26.2132 | −1.17820 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.6395 | −0.566959 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 14.1270i | − 0.632413i | −0.948690 | − | 0.316207i | \(-0.897591\pi\) | ||||
0.948690 | − | 0.316207i | \(-0.102409\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.8070i | 0.482821i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.01157 | −0.134279 | −0.0671395 | − | 0.997744i | \(-0.521387\pi\) | ||||
−0.0671395 | + | 0.997744i | \(0.521387\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.4064 | 0.685576 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 4.08304i | − 0.181334i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.38122i | 0.105546i | 0.998607 | + | 0.0527730i | \(0.0168060\pi\) | ||||
−0.998607 | + | 0.0527730i | \(0.983194\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.9330 | −0.749074 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.27998 | 0.144815 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.5013i | 0.815266i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 35.2881i | − 1.55197i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.87747 | 0.214097 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.9133 | 0.784798 | 0.392399 | − | 0.919795i | \(-0.371645\pi\) | ||||
0.392399 | + | 0.919795i | \(0.371645\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 18.9602i | − 0.829071i | −0.910033 | − | 0.414536i | \(-0.863944\pi\) | ||||
0.910033 | − | 0.414536i | \(-0.136056\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.875363i | 0.0382040i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −36.7178 | −1.59945 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.5500 | −0.936956 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 27.2981i | − 1.18464i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 32.8588i | − 1.42327i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20.9059 | 0.903839 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.65852 | 0.416796 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.22369i | 0.0957811i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.2027i | 1.47049i | 0.677802 | + | 0.735245i | \(0.262933\pi\) | ||||
−0.677802 | + | 0.735245i | \(0.737067\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.69757 | 0.115764 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.00145 | 0.257074 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 0.645113i | − 0.0275830i | −0.999905 | − | 0.0137915i | \(-0.995610\pi\) | ||||
0.999905 | − | 0.0137915i | \(-0.00439011\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 1.92410i | − 0.0821187i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.57484 | 0.407902 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.93377 | 0.379903 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.33940i | 0.0568544i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 10.2596i | − 0.434714i | −0.976092 | − | 0.217357i | \(-0.930256\pi\) | ||||
0.976092 | − | 0.217357i | \(-0.0697436\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.2295 | 1.44775 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.5080 | 0.781409 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 12.9293i | − 0.544906i | −0.962169 | − | 0.272453i | \(-0.912165\pi\) | ||||
0.962169 | − | 0.272453i | \(-0.0878350\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 3.34221i | − 0.140608i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 16.6660 | 0.699908 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.32637 | 0.265215 | 0.132608 | − | 0.991169i | \(-0.457665\pi\) | ||||
0.132608 | + | 0.991169i | \(0.457665\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 31.1997i | − 1.30566i | −0.757502 | − | 0.652832i | \(-0.773581\pi\) | ||||
0.757502 | − | 0.652832i | \(-0.226419\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 11.6156i | − 0.485248i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.665774 | 0.0277647 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.48996 | 0.228550 | 0.114275 | − | 0.993449i | \(-0.463545\pi\) | ||||
0.114275 | + | 0.993449i | \(0.463545\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.07186i | 0.0445450i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 24.5527i | − 1.01862i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.5516 | 0.602666 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 25.1634 | 1.04038 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 17.4576i | − 0.720552i | −0.932846 | − | 0.360276i | \(-0.882683\pi\) | ||||
0.932846 | − | 0.360276i | \(-0.117317\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 5.35842i | − 0.220790i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.130211 | 0.00535617 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.7657 | −0.688486 | −0.344243 | − | 0.938881i | \(-0.611864\pi\) | ||||
−0.344243 | + | 0.938881i | \(0.611864\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 39.5125i | − 1.61985i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.02883i | 0.0421070i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.357982 | 0.0146267 | 0.00731337 | − | 0.999973i | \(-0.497672\pi\) | ||||
0.00731337 | + | 0.999973i | \(0.497672\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.8949 | 0.933903 | 0.466952 | − | 0.884283i | \(-0.345352\pi\) | ||||
0.466952 | + | 0.884283i | \(0.345352\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 16.3535i | − 0.665964i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 22.6904i | − 0.922497i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.33917 | −0.0543551 | −0.0271775 | − | 0.999631i | \(-0.508652\pi\) | ||||
−0.0271775 | + | 0.999631i | \(0.508652\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15.1593 | −0.614284 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 33.8747i | 1.37043i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.8667i | 1.20631i | 0.797625 | + | 0.603153i | \(0.206089\pi\) | ||||
−0.797625 | + | 0.603153i | \(0.793911\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.95997 | −0.361301 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.4935 | −1.46917 | −0.734587 | − | 0.678514i | \(-0.762624\pi\) | ||||
−0.734587 | + | 0.678514i | \(0.762624\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 8.88669i | − 0.357186i | −0.983923 | − | 0.178593i | \(-0.942845\pi\) | ||||
0.983923 | − | 0.178593i | \(-0.0571546\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.94963i | 0.158493i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.69723 | 0.0679982 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.9298 | −0.877194 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.70096i | 0.107866i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.51659i | 0.299706i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.1724 | 1.12153 | 0.560763 | − | 0.827977i | \(-0.310508\pi\) | ||||
0.560763 | + | 0.827977i | \(0.310508\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.85452 | −0.391682 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 30.1420i | − 1.19615i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 2.13463i | − 0.0845771i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.3177 | −0.487280 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.58435 | 0.141573 | 0.0707867 | − | 0.997491i | \(-0.477449\pi\) | ||||
0.0707867 | + | 0.997491i | \(0.477449\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.8837i | 0.784137i | 0.919936 | + | 0.392069i | \(0.128240\pi\) | ||||
−0.919936 | + | 0.392069i | \(0.871760\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 9.33373i | − 0.367515i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −35.7712 | −1.40631 | −0.703156 | − | 0.711036i | \(-0.748226\pi\) | ||||
−0.703156 | + | 0.711036i | \(0.748226\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 47.7865 | 1.87578 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.48365i | 0.332501i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.57378i | 0.335518i | 0.985828 | + | 0.167759i | \(0.0536531\pi\) | ||||
−0.985828 | + | 0.167759i | \(0.946347\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.28428 | 0.0501810 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.5019 | −0.643802 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 22.9993i | − 0.895927i | −0.894052 | − | 0.447964i | \(-0.852149\pi\) | ||||
0.894052 | − | 0.447964i | \(-0.147851\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.4720i | 1.10743i | 0.832706 | + | 0.553716i | \(0.186791\pi\) | ||||
−0.832706 | + | 0.553716i | \(0.813209\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.7667 | −0.690003 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.76625 | 0.223606 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.5297i | 0.446431i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 7.91136i | − 0.305871i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.36822 | 0.130029 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.63685 | 0.255832 | 0.127916 | − | 0.991785i | \(-0.459171\pi\) | ||||
0.127916 | + | 0.991785i | \(0.459171\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.81348i | 0.0698009i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 29.0823i | − 1.11772i | −0.829261 | − | 0.558862i | \(-0.811238\pi\) | ||||
0.829261 | − | 0.558862i | \(-0.188762\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.57415 | −0.175540 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.16231 | 0.121180 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.63939i | 0.177521i | 0.996053 | + | 0.0887607i | \(0.0282906\pi\) | ||||
−0.996053 | + | 0.0887607i | \(0.971709\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 38.2938i | 1.46313i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.86902 | 0.0713074 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.9688 | −0.532169 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.11245i | 0.194487i | 0.995261 | + | 0.0972434i | \(0.0310025\pi\) | ||||
−0.995261 | + | 0.0972434i | \(0.968997\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 33.9889i | 1.29113i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.07890 | −0.154721 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −50.2825 | −1.90459 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 10.3264i | − 0.390581i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 5.27938i | − 0.199399i | −0.995018 | − | 0.0996997i | \(-0.968212\pi\) | ||||
0.995018 | − | 0.0996997i | \(-0.0317882\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.09693 | −0.0413716 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.23700 | 0.347886 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 19.9764i | − 0.751290i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.1441i | 1.05697i | 0.848942 | + | 0.528486i | \(0.177240\pi\) | ||||
−0.848942 | + | 0.528486i | \(0.822760\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.70632 | 0.326512 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.45241 | 0.241645 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 44.0495i | 1.64736i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 1.05703i | − 0.0394755i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.51160 | −0.354723 | −0.177361 | − | 0.984146i | \(-0.556756\pi\) | ||||
−0.177361 | + | 0.984146i | \(0.556756\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.9894 | 0.893412 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.74976i | 0.139455i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.29387i | 0.196609i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.06196 | −0.261914 | −0.130957 | − | 0.991388i | \(-0.541805\pi\) | ||||
−0.130957 | + | 0.991388i | \(0.541805\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10.5442 | 0.390527 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 52.3801i | − 1.93735i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 7.62443i | − 0.281615i | −0.990037 | − | 0.140807i | \(-0.955030\pi\) | ||||
0.990037 | − | 0.140807i | \(-0.0449698\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.582073 | −0.0214701 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28.6274 | 1.05450 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 45.0131i | 1.65583i | 0.560851 | + | 0.827917i | \(0.310474\pi\) | ||||
−0.560851 | + | 0.827917i | \(0.689526\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 2.59279i | − 0.0952484i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.3137 | −0.561805 | −0.280903 | − | 0.959736i | \(-0.590634\pi\) | ||||
−0.280903 | + | 0.959736i | \(0.590634\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 32.8501 | 1.20354 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 23.9276i | − 0.875465i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 27.1072i | − 0.990475i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.09580 | −0.149458 | −0.0747290 | − | 0.997204i | \(-0.523809\pi\) | ||||
−0.0747290 | + | 0.997204i | \(0.523809\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.80016 | −0.0656015 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 42.1228i | 1.53301i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.51720i | 0.345909i | 0.984930 | + | 0.172954i | \(0.0553313\pi\) | ||||
−0.984930 | + | 0.172954i | \(0.944669\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.25240 | −0.118055 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.4841 | −1.39505 | −0.697523 | − | 0.716562i | \(-0.745715\pi\) | ||||
−0.697523 | + | 0.716562i | \(0.745715\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 7.78167i | − 0.281715i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 38.5065i | − 1.39221i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −45.8726 | −1.65636 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.0210 | 0.541670 | 0.270835 | − | 0.962626i | \(-0.412700\pi\) | ||||
0.270835 | + | 0.962626i | \(0.412700\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.33286i | 0.120030i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.4471i | 1.38285i | 0.722451 | + | 0.691423i | \(0.243016\pi\) | ||||
−0.722451 | + | 0.691423i | \(0.756984\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.96263 | 0.106421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.73671 | 0.0623040 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 7.33797i | − 0.262910i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 21.5626i | − 0.771572i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −31.4053 | −1.12233 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 44.0472 | 1.57211 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 30.8457i | − 1.09953i | −0.835319 | − | 0.549765i | \(-0.814717\pi\) | ||||
0.835319 | − | 0.549765i | \(-0.185283\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.65535i | 0.0945328i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.33361 | −0.154085 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.23332 | −0.114819 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.80903i | 0.135092i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.1285i | 1.20889i | 0.796646 | + | 0.604446i | \(0.206606\pi\) | ||||
−0.796646 | + | 0.604446i | \(0.793394\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 51.8372 | 1.83387 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.65402 | 0.0584420 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 28.8873i | − 1.01941i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.94351i | 0.244727i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.59578 | −0.232182 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.9170 | −0.911192 | −0.455596 | − | 0.890187i | \(-0.650574\pi\) | ||||
−0.455596 | + | 0.890187i | \(0.650574\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.7874i | 1.18644i | 0.805041 | + | 0.593219i | \(0.202143\pi\) | ||||
−0.805041 | + | 0.593219i | \(0.797857\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 14.5479i | − 0.510218i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.37400 | −0.188243 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.64408 | 0.267432 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 32.6276i | − 1.14010i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.6475i | 0.964903i | 0.875923 | + | 0.482451i | \(0.160254\pi\) | ||||
−0.875923 | + | 0.482451i | \(0.839746\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.4983 | 0.435665 | 0.217832 | − | 0.975986i | \(-0.430101\pi\) | ||||
0.217832 | + | 0.975986i | \(0.430101\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.49335 | −0.0519916 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.03084i | 0.314033i | 0.987596 | + | 0.157017i | \(0.0501876\pi\) | ||||
−0.987596 | + | 0.157017i | \(0.949812\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 55.7684i | − 1.93692i | −0.249175 | − | 0.968458i | \(-0.580159\pi\) | ||||
0.249175 | − | 0.968458i | \(-0.419841\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.5959 | 0.367567 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.26654 | −0.113179 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 39.3597i | 1.36210i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 17.5755i | 0.607498i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.3128 | 0.494134 | 0.247067 | − | 0.968998i | \(-0.420533\pi\) | ||||
0.247067 | + | 0.968998i | \(0.420533\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −62.6776 | −2.16130 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 10.4633i | − 0.360376i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 14.8707i | − 0.511567i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −29.4211 | −1.01092 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.91525 | −0.305971 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1.32089i | − 0.0452794i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.0325i | 1.30221i | 0.758988 | + | 0.651105i | \(0.225694\pi\) | ||||
−0.758988 | + | 0.651105i | \(0.774306\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.61945 | 0.192181 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.1869 | −0.792048 | −0.396024 | − | 0.918240i | \(-0.629610\pi\) | ||||
−0.396024 | + | 0.918240i | \(0.629610\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46.5870i | 1.58953i | 0.606919 | + | 0.794764i | \(0.292405\pi\) | ||||
−0.606919 | + | 0.794764i | \(0.707595\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.6178i | 0.395933i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 54.3149 | 1.84890 | 0.924451 | − | 0.381301i | \(-0.124524\pi\) | ||||
0.924451 | + | 0.381301i | \(0.124524\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.7640 | 0.603995 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.3444i | 0.589048i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.2408i | 0.517008i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27.4808 | −0.931153 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.45769 | −0.150870 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 32.0194i | 1.08245i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 1.80324i | − 0.0608910i | −0.999536 | − | 0.0304455i | \(-0.990307\pi\) | ||||
0.999536 | − | 0.0304455i | \(-0.00969260\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.62438 | 0.223435 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.6372 | 0.425759 | 0.212880 | − | 0.977078i | \(-0.431716\pi\) | ||||
0.212880 | + | 0.977078i | \(0.431716\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.9276i | 1.34367i | 0.740700 | + | 0.671835i | \(0.234494\pi\) | ||||
−0.740700 | + | 0.671835i | \(0.765506\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.5086i | 0.420471i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.3642 | 0.482304 | 0.241152 | − | 0.970487i | \(-0.422475\pi\) | ||||
0.241152 | + | 0.970487i | \(0.422475\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −39.0830 | −1.31080 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 28.4318i | 0.952502i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.56486i | 0.253148i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 35.1769 | 1.17584 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.12214 | 0.104245 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 51.3060i | 1.71115i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.3759i | 0.712135i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.1024 | −0.402743 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.82473 | 0.326585 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 3.32787i | − 0.110500i | −0.998473 | − | 0.0552501i | \(-0.982404\pi\) | ||||
0.998473 | − | 0.0552501i | \(-0.0175956\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 19.4678i | − 0.645707i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.8252 | 1.18694 | 0.593471 | − | 0.804855i | \(-0.297757\pi\) | ||||
0.593471 | + | 0.804855i | \(0.297757\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 41.8863 | 1.38623 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.881666i | 0.0291470i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 1.66524i | − 0.0549910i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 48.3186 | 1.59388 | 0.796942 | − | 0.604055i | \(-0.206449\pi\) | ||||
0.796942 | + | 0.604055i | \(0.206449\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.3593 | 0.407254 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 20.6990i | 0.681316i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 0.606487i | − 0.0199412i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 23.3786 | 0.767855 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.2127 | −0.761585 | −0.380792 | − | 0.924661i | \(-0.624349\pi\) | ||||
−0.380792 | + | 0.924661i | \(0.624349\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 0.476702i | − 0.0156233i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.5817i | 0.411908i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 67.4073 | 2.20445 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.10467 | 0.232099 | 0.116050 | − | 0.993243i | \(-0.462977\pi\) | ||||
0.116050 | + | 0.993243i | \(0.462977\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.7450i | 0.644354i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 55.5352i | − 1.81040i | −0.424989 | − | 0.905199i | \(-0.639722\pi\) | ||||
0.424989 | − | 0.905199i | \(-0.360278\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.83612 | 0.287744 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −18.9132 | −0.615247 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 15.5988i | − 0.506894i | −0.967349 | − | 0.253447i | \(-0.918436\pi\) | ||||
0.967349 | − | 0.253447i | \(-0.0815643\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27.7304i | 0.900165i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.8704 | −0.417352 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.1243 | 0.684282 | 0.342141 | − | 0.939649i | \(-0.388848\pi\) | ||||
0.342141 | + | 0.939649i | \(0.388848\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 42.3047i | − 1.36895i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 25.8613i | − 0.835977i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 49.6529 | 1.60338 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.28738 | −0.0737863 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 26.4170i | − 0.851277i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.90378i | 0.125667i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.1207 | −1.48314 | −0.741570 | − | 0.670875i | \(-0.765919\pi\) | ||||
−0.741570 | + | 0.670875i | \(0.765919\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.96764 | −0.127459 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.3253i | 0.716454i | 0.933635 | + | 0.358227i | \(0.116619\pi\) | ||||
−0.933635 | + | 0.358227i | \(0.883381\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.28882i | 0.169552i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.43354 | 0.0459099 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.2650 | 0.456379 | 0.228190 | − | 0.973617i | \(-0.426719\pi\) | ||||
0.228190 | + | 0.973617i | \(0.426719\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.89544i | 0.0925385i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 7.58355i | − 0.242124i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.7242 | −0.405838 | −0.202919 | − | 0.979196i | \(-0.565043\pi\) | ||||
−0.202919 | + | 0.979196i | \(0.565043\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.474237 | 0.0151104 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 11.9770i | − 0.381232i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.20472i | 0.292693i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.8169 | 0.343611 | 0.171806 | − | 0.985131i | \(-0.445040\pi\) | ||||
0.171806 | + | 0.985131i | \(0.445040\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.0104 | −0.444607 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.74705i | 0.118789i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 5.39134i | − 0.170746i | −0.996349 | − | 0.0853728i | \(-0.972792\pi\) | ||||
0.996349 | − | 0.0853728i | \(-0.0272081\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.59792 | 0.113833 |
(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 | 608.2.c.b.305.9 | 16 | ||
3.2 | odd | 2 | 5472.2.g.b.2737.5 | 16 | |||
4.3 | odd | 2 | 152.2.c.b.77.16 | yes | 16 | ||
8.3 | odd | 2 | 152.2.c.b.77.15 | ✓ | 16 | ||
8.5 | even | 2 | inner | 608.2.c.b.305.8 | 16 | ||
12.11 | even | 2 | 1368.2.g.b.685.1 | 16 | |||
16.3 | odd | 4 | 4864.2.a.bo.1.5 | 8 | |||
16.5 | even | 4 | 4864.2.a.bp.1.5 | 8 | |||
16.11 | odd | 4 | 4864.2.a.bq.1.4 | 8 | |||
16.13 | even | 4 | 4864.2.a.bn.1.4 | 8 | |||
24.5 | odd | 2 | 5472.2.g.b.2737.12 | 16 | |||
24.11 | even | 2 | 1368.2.g.b.685.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.c.b.77.15 | ✓ | 16 | 8.3 | odd | 2 | ||
152.2.c.b.77.16 | yes | 16 | 4.3 | odd | 2 | ||
608.2.c.b.305.8 | 16 | 8.5 | even | 2 | inner | ||
608.2.c.b.305.9 | 16 | 1.1 | even | 1 | trivial | ||
1368.2.g.b.685.1 | 16 | 12.11 | even | 2 | |||
1368.2.g.b.685.2 | 16 | 24.11 | even | 2 | |||
4864.2.a.bn.1.4 | 8 | 16.13 | even | 4 | |||
4864.2.a.bo.1.5 | 8 | 16.3 | odd | 4 | |||
4864.2.a.bp.1.5 | 8 | 16.5 | even | 4 | |||
4864.2.a.bq.1.4 | 8 | 16.11 | odd | 4 | |||
5472.2.g.b.2737.5 | 16 | 3.2 | odd | 2 | |||
5472.2.g.b.2737.12 | 16 | 24.5 | odd | 2 |