Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(769,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.769");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.k (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 769.20 | ||
Character | \(\chi\) | \(=\) | 1155.769 |
Dual form | 1155.2.k.b.769.19 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.567201 | −0.401072 | −0.200536 | − | 0.979686i | \(-0.564268\pi\) | ||||
−0.200536 | + | 0.979686i | \(0.564268\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.67828 | −0.839141 | ||||||||
\(5\) | −2.10264 | + | 0.760858i | −0.940329 | + | 0.340266i | ||||
\(6\) | −0.567201 | −0.231559 | ||||||||
\(7\) | −2.63586 | − | 0.228555i | −0.996262 | − | 0.0863855i | ||||
\(8\) | 2.08633 | 0.737628 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.19262 | − | 0.431559i | 0.377140 | − | 0.136471i | ||||
\(11\) | −0.727850 | + | 3.23577i | −0.219455 | + | 0.975623i | ||||
\(12\) | −1.67828 | −0.484478 | ||||||||
\(13\) | 4.44869i | 1.23384i | 0.787025 | + | 0.616922i | \(0.211620\pi\) | ||||
−0.787025 | + | 0.616922i | \(0.788380\pi\) | |||||||
\(14\) | 1.49506 | + | 0.129637i | 0.399573 | + | 0.0346468i | ||||
\(15\) | −2.10264 | + | 0.760858i | −0.542899 | + | 0.196453i | ||||
\(16\) | 2.17320 | 0.543299 | ||||||||
\(17\) | − | 3.87358i | − | 0.939481i | −0.882804 | − | 0.469741i | \(-0.844347\pi\) | ||
0.882804 | − | 0.469741i | \(-0.155653\pi\) | |||||||
\(18\) | −0.567201 | −0.133691 | ||||||||
\(19\) | 0.293716 | 0.0673830 | 0.0336915 | − | 0.999432i | \(-0.489274\pi\) | ||||
0.0336915 | + | 0.999432i | \(0.489274\pi\) | |||||||
\(20\) | 3.52882 | − | 1.27693i | 0.789069 | − | 0.285531i | ||||
\(21\) | −2.63586 | − | 0.228555i | −0.575192 | − | 0.0498747i | ||||
\(22\) | 0.412837 | − | 1.83534i | 0.0880172 | − | 0.391295i | ||||
\(23\) | − | 1.67062i | − | 0.348349i | −0.984715 | − | 0.174174i | \(-0.944274\pi\) | ||
0.984715 | − | 0.174174i | \(-0.0557256\pi\) | |||||||
\(24\) | 2.08633 | 0.425870 | ||||||||
\(25\) | 3.84219 | − | 3.19962i | 0.768438 | − | 0.639924i | ||||
\(26\) | − | 2.52330i | − | 0.494860i | ||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.42372 | + | 0.383579i | 0.836004 | + | 0.0724897i | ||||
\(29\) | 0.242329i | 0.0449993i | 0.999747 | + | 0.0224997i | \(0.00716247\pi\) | ||||
−0.999747 | + | 0.0224997i | \(0.992838\pi\) | |||||||
\(30\) | 1.19262 | − | 0.431559i | 0.217742 | − | 0.0787916i | ||||
\(31\) | − | 6.28613i | − | 1.12902i | −0.825426 | − | 0.564511i | \(-0.809065\pi\) | ||
0.825426 | − | 0.564511i | \(-0.190935\pi\) | |||||||
\(32\) | −5.40529 | −0.955530 | ||||||||
\(33\) | −0.727850 | + | 3.23577i | −0.126702 | + | 0.563276i | ||||
\(34\) | 2.19710i | 0.376800i | ||||||||
\(35\) | 5.71616 | − | 1.52495i | 0.966208 | − | 0.257763i | ||||
\(36\) | −1.67828 | −0.279714 | ||||||||
\(37\) | − | 11.3596i | − | 1.86751i | −0.357911 | − | 0.933756i | \(-0.616511\pi\) | ||
0.357911 | − | 0.933756i | \(-0.383489\pi\) | |||||||
\(38\) | −0.166596 | −0.0270254 | ||||||||
\(39\) | 4.44869i | 0.712360i | ||||||||
\(40\) | −4.38679 | + | 1.58740i | −0.693613 | + | 0.250990i | ||||
\(41\) | −5.68888 | −0.888455 | −0.444227 | − | 0.895914i | \(-0.646522\pi\) | ||||
−0.444227 | + | 0.895914i | \(0.646522\pi\) | |||||||
\(42\) | 1.49506 | + | 0.129637i | 0.230693 | + | 0.0200033i | ||||
\(43\) | −7.05842 | −1.07640 | −0.538200 | − | 0.842817i | \(-0.680895\pi\) | ||||
−0.538200 | + | 0.842817i | \(0.680895\pi\) | |||||||
\(44\) | 1.22154 | − | 5.43054i | 0.184154 | − | 0.818685i | ||||
\(45\) | −2.10264 | + | 0.760858i | −0.313443 | + | 0.113422i | ||||
\(46\) | 0.947579i | 0.139713i | ||||||||
\(47\) | −2.92937 | −0.427293 | −0.213646 | − | 0.976911i | \(-0.568534\pi\) | ||||
−0.213646 | + | 0.976911i | \(0.568534\pi\) | |||||||
\(48\) | 2.17320 | 0.313674 | ||||||||
\(49\) | 6.89553 | + | 1.20488i | 0.985075 | + | 0.172125i | ||||
\(50\) | −2.17930 | + | 1.81483i | −0.308199 | + | 0.256656i | ||||
\(51\) | − | 3.87358i | − | 0.542410i | ||||||
\(52\) | − | 7.46615i | − | 1.03537i | ||||||
\(53\) | − | 10.1514i | − | 1.39441i | −0.716873 | − | 0.697203i | \(-0.754427\pi\) | ||
0.716873 | − | 0.697203i | \(-0.245573\pi\) | |||||||
\(54\) | −0.567201 | −0.0771863 | ||||||||
\(55\) | −0.931557 | − | 7.35746i | −0.125611 | − | 0.992080i | ||||
\(56\) | −5.49927 | − | 0.476840i | −0.734871 | − | 0.0637204i | ||||
\(57\) | 0.293716 | 0.0389036 | ||||||||
\(58\) | − | 0.137449i | − | 0.0180480i | ||||||
\(59\) | 5.48413i | 0.713972i | 0.934110 | + | 0.356986i | \(0.116196\pi\) | ||||
−0.934110 | + | 0.356986i | \(0.883804\pi\) | |||||||
\(60\) | 3.52882 | − | 1.27693i | 0.455569 | − | 0.164851i | ||||
\(61\) | 5.57566 | 0.713889 | 0.356945 | − | 0.934125i | \(-0.383818\pi\) | ||||
0.356945 | + | 0.934125i | \(0.383818\pi\) | |||||||
\(62\) | 3.56550i | 0.452819i | ||||||||
\(63\) | −2.63586 | − | 0.228555i | −0.332087 | − | 0.0287952i | ||||
\(64\) | −1.28051 | −0.160063 | ||||||||
\(65\) | −3.38482 | − | 9.35398i | −0.419835 | − | 1.16022i | ||||
\(66\) | 0.412837 | − | 1.83534i | 0.0508168 | − | 0.225914i | ||||
\(67\) | − | 12.1655i | − | 1.48625i | −0.669153 | − | 0.743125i | \(-0.733343\pi\) | ||
0.669153 | − | 0.743125i | \(-0.266657\pi\) | |||||||
\(68\) | 6.50096i | 0.788358i | ||||||||
\(69\) | − | 1.67062i | − | 0.201119i | ||||||
\(70\) | −3.24222 | + | 0.864952i | −0.387519 | + | 0.103382i | ||||
\(71\) | 10.3614 | 1.22967 | 0.614836 | − | 0.788655i | \(-0.289222\pi\) | ||||
0.614836 | + | 0.788655i | \(0.289222\pi\) | |||||||
\(72\) | 2.08633 | 0.245876 | ||||||||
\(73\) | − | 4.76758i | − | 0.558003i | −0.960291 | − | 0.279001i | \(-0.909997\pi\) | ||
0.960291 | − | 0.279001i | \(-0.0900034\pi\) | |||||||
\(74\) | 6.44320i | 0.749006i | ||||||||
\(75\) | 3.84219 | − | 3.19962i | 0.443658 | − | 0.369460i | ||||
\(76\) | −0.492938 | −0.0565438 | ||||||||
\(77\) | 2.65806 | − | 8.36270i | 0.302914 | − | 0.953018i | ||||
\(78\) | − | 2.52330i | − | 0.285708i | ||||||
\(79\) | − | 7.37915i | − | 0.830219i | −0.909771 | − | 0.415110i | \(-0.863743\pi\) | ||
0.909771 | − | 0.415110i | \(-0.136257\pi\) | |||||||
\(80\) | −4.56945 | + | 1.65349i | −0.510880 | + | 0.184866i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.22674 | 0.356334 | ||||||||
\(83\) | 12.9770i | 1.42441i | 0.701971 | + | 0.712206i | \(0.252304\pi\) | ||||
−0.701971 | + | 0.712206i | \(0.747696\pi\) | |||||||
\(84\) | 4.42372 | + | 0.383579i | 0.482667 | + | 0.0418519i | ||||
\(85\) | 2.94724 | + | 8.14475i | 0.319673 | + | 0.883422i | ||||
\(86\) | 4.00355 | 0.431713 | ||||||||
\(87\) | 0.242329i | 0.0259804i | ||||||||
\(88\) | −1.51853 | + | 6.75088i | −0.161876 | + | 0.719646i | ||||
\(89\) | 13.0001i | 1.37801i | 0.724757 | + | 0.689004i | \(0.241952\pi\) | ||||
−0.724757 | + | 0.689004i | \(0.758048\pi\) | |||||||
\(90\) | 1.19262 | − | 0.431559i | 0.125713 | − | 0.0454904i | ||||
\(91\) | 1.01677 | − | 11.7261i | 0.106586 | − | 1.22923i | ||||
\(92\) | 2.80378i | 0.292314i | ||||||||
\(93\) | − | 6.28613i | − | 0.651841i | ||||||
\(94\) | 1.66154 | 0.171375 | ||||||||
\(95\) | −0.617578 | + | 0.223476i | −0.0633622 | + | 0.0229281i | ||||
\(96\) | −5.40529 | −0.551676 | ||||||||
\(97\) | −14.1192 | −1.43359 | −0.716794 | − | 0.697285i | \(-0.754391\pi\) | ||||
−0.716794 | + | 0.697285i | \(0.754391\pi\) | |||||||
\(98\) | −3.91115 | − | 0.683408i | −0.395086 | − | 0.0690346i | ||||
\(99\) | −0.727850 | + | 3.23577i | −0.0731517 | + | 0.325208i | ||||
\(100\) | −6.44828 | + | 5.36987i | −0.644828 | + | 0.536987i | ||||
\(101\) | 12.2453 | 1.21845 | 0.609226 | − | 0.792997i | \(-0.291480\pi\) | ||||
0.609226 | + | 0.792997i | \(0.291480\pi\) | |||||||
\(102\) | 2.19710i | 0.217545i | ||||||||
\(103\) | 6.50035 | 0.640498 | 0.320249 | − | 0.947333i | \(-0.396233\pi\) | ||||
0.320249 | + | 0.947333i | \(0.396233\pi\) | |||||||
\(104\) | 9.28141i | 0.910117i | ||||||||
\(105\) | 5.71616 | − | 1.52495i | 0.557841 | − | 0.148820i | ||||
\(106\) | 5.75791i | 0.559257i | ||||||||
\(107\) | 12.8529 | 1.24254 | 0.621269 | − | 0.783598i | \(-0.286617\pi\) | ||||
0.621269 | + | 0.783598i | \(0.286617\pi\) | |||||||
\(108\) | −1.67828 | −0.161493 | ||||||||
\(109\) | − | 7.31694i | − | 0.700836i | −0.936593 | − | 0.350418i | \(-0.886040\pi\) | ||
0.936593 | − | 0.350418i | \(-0.113960\pi\) | |||||||
\(110\) | 0.528380 | + | 4.17316i | 0.0503791 | + | 0.397895i | ||||
\(111\) | − | 11.3596i | − | 1.07821i | ||||||
\(112\) | −5.72825 | − | 0.496694i | −0.541268 | − | 0.0469332i | ||||
\(113\) | − | 5.30123i | − | 0.498698i | −0.968414 | − | 0.249349i | \(-0.919783\pi\) | ||
0.968414 | − | 0.249349i | \(-0.0802166\pi\) | |||||||
\(114\) | −0.166596 | −0.0156031 | ||||||||
\(115\) | 1.27111 | + | 3.51272i | 0.118531 | + | 0.327562i | ||||
\(116\) | − | 0.406696i | − | 0.0377608i | ||||||
\(117\) | 4.44869i | 0.411281i | ||||||||
\(118\) | − | 3.11060i | − | 0.286354i | ||||||
\(119\) | −0.885325 | + | 10.2102i | −0.0811576 | + | 0.935969i | ||||
\(120\) | −4.38679 | + | 1.58740i | −0.400458 | + | 0.144909i | ||||
\(121\) | −9.94047 | − | 4.71032i | −0.903679 | − | 0.428211i | ||||
\(122\) | −3.16252 | −0.286321 | ||||||||
\(123\) | −5.68888 | −0.512949 | ||||||||
\(124\) | 10.5499i | 0.947409i | ||||||||
\(125\) | −5.64429 | + | 9.65101i | −0.504841 | + | 0.863212i | ||||
\(126\) | 1.49506 | + | 0.129637i | 0.133191 | + | 0.0115489i | ||||
\(127\) | 4.15420 | 0.368626 | 0.184313 | − | 0.982868i | \(-0.440994\pi\) | ||||
0.184313 | + | 0.982868i | \(0.440994\pi\) | |||||||
\(128\) | 11.5369 | 1.01973 | ||||||||
\(129\) | −7.05842 | −0.621459 | ||||||||
\(130\) | 1.91987 | + | 5.30559i | 0.168384 | + | 0.465331i | ||||
\(131\) | −8.17994 | −0.714685 | −0.357343 | − | 0.933973i | \(-0.616317\pi\) | ||||
−0.357343 | + | 0.933973i | \(0.616317\pi\) | |||||||
\(132\) | 1.22154 | − | 5.43054i | 0.106321 | − | 0.472668i | ||||
\(133\) | −0.774193 | − | 0.0671301i | −0.0671311 | − | 0.00582091i | ||||
\(134\) | 6.90027i | 0.596093i | ||||||||
\(135\) | −2.10264 | + | 0.760858i | −0.180966 | + | 0.0654842i | ||||
\(136\) | − | 8.08156i | − | 0.692988i | ||||||
\(137\) | 7.72402i | 0.659908i | 0.943997 | + | 0.329954i | \(0.107033\pi\) | ||||
−0.943997 | + | 0.329954i | \(0.892967\pi\) | |||||||
\(138\) | 0.947579i | 0.0806633i | ||||||||
\(139\) | −3.34279 | −0.283532 | −0.141766 | − | 0.989900i | \(-0.545278\pi\) | ||||
−0.141766 | + | 0.989900i | \(0.545278\pi\) | |||||||
\(140\) | −9.59334 | + | 2.55929i | −0.810785 | + | 0.216300i | ||||
\(141\) | −2.92937 | −0.246697 | ||||||||
\(142\) | −5.87700 | −0.493187 | ||||||||
\(143\) | −14.3949 | − | 3.23798i | −1.20377 | − | 0.270773i | ||||
\(144\) | 2.17320 | 0.181100 | ||||||||
\(145\) | −0.184378 | − | 0.509530i | −0.0153117 | − | 0.0423142i | ||||
\(146\) | 2.70418i | 0.223799i | ||||||||
\(147\) | 6.89553 | + | 1.20488i | 0.568733 | + | 0.0993765i | ||||
\(148\) | 19.0647i | 1.56711i | ||||||||
\(149\) | − | 15.9689i | − | 1.30822i | −0.756399 | − | 0.654110i | \(-0.773043\pi\) | ||
0.756399 | − | 0.654110i | \(-0.226957\pi\) | |||||||
\(150\) | −2.17930 | + | 1.81483i | −0.177939 | + | 0.148180i | ||||
\(151\) | − | 11.4976i | − | 0.935662i | −0.883818 | − | 0.467831i | \(-0.845036\pi\) | ||
0.883818 | − | 0.467831i | \(-0.154964\pi\) | |||||||
\(152\) | 0.612787 | 0.0497036 | ||||||||
\(153\) | − | 3.87358i | − | 0.313160i | ||||||
\(154\) | −1.50766 | + | 4.74333i | −0.121490 | + | 0.382229i | ||||
\(155\) | 4.78285 | + | 13.2175i | 0.384168 | + | 1.06165i | ||||
\(156\) | − | 7.46615i | − | 0.597771i | ||||||
\(157\) | 11.5302 | 0.920207 | 0.460103 | − | 0.887865i | \(-0.347812\pi\) | ||||
0.460103 | + | 0.887865i | \(0.347812\pi\) | |||||||
\(158\) | 4.18546i | 0.332978i | ||||||||
\(159\) | − | 10.1514i | − | 0.805061i | ||||||
\(160\) | 11.3654 | − | 4.11266i | 0.898513 | − | 0.325134i | ||||
\(161\) | −0.381828 | + | 4.40353i | −0.0300923 | + | 0.347046i | ||||
\(162\) | −0.567201 | −0.0445635 | ||||||||
\(163\) | 11.0609i | 0.866357i | 0.901308 | + | 0.433178i | \(0.142608\pi\) | ||||
−0.901308 | + | 0.433178i | \(0.857392\pi\) | |||||||
\(164\) | 9.54756 | 0.745539 | ||||||||
\(165\) | −0.931557 | − | 7.35746i | −0.0725216 | − | 0.572777i | ||||
\(166\) | − | 7.36058i | − | 0.571292i | ||||||
\(167\) | 14.7919i | 1.14463i | 0.820033 | + | 0.572316i | \(0.193955\pi\) | ||||
−0.820033 | + | 0.572316i | \(0.806045\pi\) | |||||||
\(168\) | −5.49927 | − | 0.476840i | −0.424278 | − | 0.0367890i | ||||
\(169\) | −6.79080 | −0.522369 | ||||||||
\(170\) | −1.67168 | − | 4.61971i | −0.128212 | − | 0.354316i | ||||
\(171\) | 0.293716 | 0.0224610 | ||||||||
\(172\) | 11.8460 | 0.903251 | ||||||||
\(173\) | − | 18.2598i | − | 1.38827i | −0.719847 | − | 0.694133i | \(-0.755788\pi\) | ||
0.719847 | − | 0.694133i | \(-0.244212\pi\) | |||||||
\(174\) | − | 0.137449i | − | 0.0104200i | ||||||
\(175\) | −10.8588 | + | 7.55560i | −0.820846 | + | 0.571150i | ||||
\(176\) | −1.58176 | + | 7.03198i | −0.119230 | + | 0.530055i | ||||
\(177\) | 5.48413i | 0.412212i | ||||||||
\(178\) | − | 7.37368i | − | 0.552681i | ||||||
\(179\) | −3.28199 | −0.245307 | −0.122654 | − | 0.992450i | \(-0.539140\pi\) | ||||
−0.122654 | + | 0.992450i | \(0.539140\pi\) | |||||||
\(180\) | 3.52882 | − | 1.27693i | 0.263023 | − | 0.0951770i | ||||
\(181\) | − | 23.4137i | − | 1.74032i | −0.492766 | − | 0.870162i | \(-0.664014\pi\) | ||
0.492766 | − | 0.870162i | \(-0.335986\pi\) | |||||||
\(182\) | −0.576712 | + | 6.65107i | −0.0427487 | + | 0.493010i | ||||
\(183\) | 5.57566 | 0.412164 | ||||||||
\(184\) | − | 3.48546i | − | 0.256952i | ||||||
\(185\) | 8.64306 | + | 23.8852i | 0.635450 | + | 1.75608i | ||||
\(186\) | 3.56550i | 0.261435i | ||||||||
\(187\) | 12.5340 | + | 2.81939i | 0.916579 | + | 0.206174i | ||||
\(188\) | 4.91631 | 0.358559 | ||||||||
\(189\) | −2.63586 | − | 0.228555i | −0.191731 | − | 0.0166249i | ||||
\(190\) | 0.350291 | − | 0.126756i | 0.0254128 | − | 0.00919583i | ||||
\(191\) | −20.9902 | −1.51880 | −0.759400 | − | 0.650624i | \(-0.774508\pi\) | ||||
−0.759400 | + | 0.650624i | \(0.774508\pi\) | |||||||
\(192\) | −1.28051 | −0.0924125 | ||||||||
\(193\) | 19.3802 | 1.39502 | 0.697510 | − | 0.716575i | \(-0.254291\pi\) | ||||
0.697510 | + | 0.716575i | \(0.254291\pi\) | |||||||
\(194\) | 8.00843 | 0.574972 | ||||||||
\(195\) | −3.38482 | − | 9.35398i | −0.242392 | − | 0.669853i | ||||
\(196\) | −11.5726 | − | 2.02212i | −0.826617 | − | 0.144437i | ||||
\(197\) | −21.2474 | −1.51382 | −0.756908 | − | 0.653521i | \(-0.773291\pi\) | ||||
−0.756908 | + | 0.653521i | \(0.773291\pi\) | |||||||
\(198\) | 0.412837 | − | 1.83534i | 0.0293391 | − | 0.130432i | ||||
\(199\) | − | 24.9705i | − | 1.77011i | −0.465486 | − | 0.885055i | \(-0.654120\pi\) | ||
0.465486 | − | 0.885055i | \(-0.345880\pi\) | |||||||
\(200\) | 8.01607 | − | 6.67545i | 0.566822 | − | 0.472026i | ||||
\(201\) | − | 12.1655i | − | 0.858086i | ||||||
\(202\) | −6.94554 | −0.488687 | ||||||||
\(203\) | 0.0553853 | − | 0.638745i | 0.00388729 | − | 0.0448311i | ||||
\(204\) | 6.50096i | 0.455159i | ||||||||
\(205\) | 11.9617 | − | 4.32843i | 0.835440 | − | 0.302311i | ||||
\(206\) | −3.68700 | −0.256886 | ||||||||
\(207\) | − | 1.67062i | − | 0.116116i | ||||||
\(208\) | 9.66787i | 0.670346i | ||||||||
\(209\) | −0.213781 | + | 0.950397i | −0.0147875 | + | 0.0657404i | ||||
\(210\) | −3.24222 | + | 0.864952i | −0.223734 | + | 0.0596873i | ||||
\(211\) | 2.78208i | 0.191526i | 0.995404 | + | 0.0957631i | \(0.0305291\pi\) | ||||
−0.995404 | + | 0.0957631i | \(0.969471\pi\) | |||||||
\(212\) | 17.0370i | 1.17010i | ||||||||
\(213\) | 10.3614 | 0.709951 | ||||||||
\(214\) | −7.29019 | −0.498347 | ||||||||
\(215\) | 14.8413 | − | 5.37045i | 1.01217 | − | 0.366262i | ||||
\(216\) | 2.08633 | 0.141957 | ||||||||
\(217\) | −1.43672 | + | 16.5694i | −0.0975311 | + | 1.12480i | ||||
\(218\) | 4.15018i | 0.281086i | ||||||||
\(219\) | − | 4.76758i | − | 0.322163i | ||||||
\(220\) | 1.56342 | + | 12.3479i | 0.105405 | + | 0.832495i | ||||
\(221\) | 17.2323 | 1.15917 | ||||||||
\(222\) | 6.44320i | 0.432439i | ||||||||
\(223\) | 16.3794 | 1.09684 | 0.548422 | − | 0.836202i | \(-0.315229\pi\) | ||||
0.548422 | + | 0.836202i | \(0.315229\pi\) | |||||||
\(224\) | 14.2476 | + | 1.23541i | 0.951958 | + | 0.0825440i | ||||
\(225\) | 3.84219 | − | 3.19962i | 0.256146 | − | 0.213308i | ||||
\(226\) | 3.00687i | 0.200014i | ||||||||
\(227\) | − | 16.7625i | − | 1.11257i | −0.830993 | − | 0.556283i | \(-0.812227\pi\) | ||
0.830993 | − | 0.556283i | \(-0.187773\pi\) | |||||||
\(228\) | −0.492938 | −0.0326456 | ||||||||
\(229\) | − | 0.130024i | − | 0.00859224i | −0.999991 | − | 0.00429612i | \(-0.998632\pi\) | ||
0.999991 | − | 0.00429612i | \(-0.00136750\pi\) | |||||||
\(230\) | −0.720972 | − | 1.99242i | −0.0475395 | − | 0.131376i | ||||
\(231\) | 2.65806 | − | 8.36270i | 0.174888 | − | 0.550225i | ||||
\(232\) | 0.505577i | 0.0331927i | ||||||||
\(233\) | −5.89232 | −0.386019 | −0.193009 | − | 0.981197i | \(-0.561825\pi\) | ||||
−0.193009 | + | 0.981197i | \(0.561825\pi\) | |||||||
\(234\) | − | 2.52330i | − | 0.164953i | ||||||
\(235\) | 6.15941 | − | 2.22883i | 0.401796 | − | 0.145393i | ||||
\(236\) | − | 9.20391i | − | 0.599124i | ||||||
\(237\) | − | 7.37915i | − | 0.479327i | ||||||
\(238\) | 0.502158 | − | 5.79125i | 0.0325500 | − | 0.375391i | ||||
\(239\) | − | 2.70370i | − | 0.174888i | −0.996169 | − | 0.0874438i | \(-0.972130\pi\) | ||
0.996169 | − | 0.0874438i | \(-0.0278698\pi\) | |||||||
\(240\) | −4.56945 | + | 1.65349i | −0.294957 | + | 0.106733i | ||||
\(241\) | −26.4906 | −1.70641 | −0.853205 | − | 0.521575i | \(-0.825345\pi\) | ||||
−0.853205 | + | 0.521575i | \(0.825345\pi\) | |||||||
\(242\) | 5.63825 | + | 2.67170i | 0.362440 | + | 0.171743i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −9.35753 | −0.599054 | ||||||||
\(245\) | −15.4155 | + | 2.71309i | −0.984863 | + | 0.173333i | ||||
\(246\) | 3.22674 | 0.205730 | ||||||||
\(247\) | 1.30665i | 0.0831400i | ||||||||
\(248\) | − | 13.1149i | − | 0.832798i | ||||||
\(249\) | 12.9770i | 0.822385i | ||||||||
\(250\) | 3.20145 | − | 5.47407i | 0.202477 | − | 0.346210i | ||||
\(251\) | − | 0.841941i | − | 0.0531428i | −0.999647 | − | 0.0265714i | \(-0.991541\pi\) | ||
0.999647 | − | 0.0265714i | \(-0.00845894\pi\) | |||||||
\(252\) | 4.42372 | + | 0.383579i | 0.278668 | + | 0.0241632i | ||||
\(253\) | 5.40575 | + | 1.21596i | 0.339857 | + | 0.0764469i | ||||
\(254\) | −2.35627 | −0.147845 | ||||||||
\(255\) | 2.94724 | + | 8.14475i | 0.184564 | + | 0.510044i | ||||
\(256\) | −3.98273 | −0.248921 | ||||||||
\(257\) | −22.7075 | −1.41646 | −0.708228 | − | 0.705984i | \(-0.750505\pi\) | ||||
−0.708228 | + | 0.705984i | \(0.750505\pi\) | |||||||
\(258\) | 4.00355 | 0.249250 | ||||||||
\(259\) | −2.59630 | + | 29.9424i | −0.161326 | + | 1.86053i | ||||
\(260\) | 5.68068 | + | 15.6986i | 0.352301 | + | 0.973588i | ||||
\(261\) | 0.242329i | 0.0149998i | ||||||||
\(262\) | 4.63968 | 0.286640 | ||||||||
\(263\) | −17.2218 | −1.06194 | −0.530972 | − | 0.847389i | \(-0.678173\pi\) | ||||
−0.530972 | + | 0.847389i | \(0.678173\pi\) | |||||||
\(264\) | −1.51853 | + | 6.75088i | −0.0934592 | + | 0.415488i | ||||
\(265\) | 7.72380 | + | 21.3448i | 0.474469 | + | 1.31120i | ||||
\(266\) | 0.439124 | + | 0.0380763i | 0.0269244 | + | 0.00233461i | ||||
\(267\) | 13.0001i | 0.795594i | ||||||||
\(268\) | 20.4171i | 1.24717i | ||||||||
\(269\) | 1.77799i | 0.108406i | 0.998530 | + | 0.0542029i | \(0.0172618\pi\) | ||||
−0.998530 | + | 0.0542029i | \(0.982738\pi\) | |||||||
\(270\) | 1.19262 | − | 0.431559i | 0.0725806 | − | 0.0262639i | ||||
\(271\) | −24.0555 | −1.46126 | −0.730632 | − | 0.682771i | \(-0.760775\pi\) | ||||
−0.730632 | + | 0.682771i | \(0.760775\pi\) | |||||||
\(272\) | − | 8.41806i | − | 0.510420i | ||||||
\(273\) | 1.01677 | − | 11.7261i | 0.0615376 | − | 0.709697i | ||||
\(274\) | − | 4.38107i | − | 0.264670i | ||||||
\(275\) | 7.55671 | + | 14.7613i | 0.455687 | + | 0.890140i | ||||
\(276\) | 2.80378i | 0.168767i | ||||||||
\(277\) | −21.5534 | −1.29502 | −0.647509 | − | 0.762058i | \(-0.724189\pi\) | ||||
−0.647509 | + | 0.762058i | \(0.724189\pi\) | |||||||
\(278\) | 1.89604 | 0.113717 | ||||||||
\(279\) | − | 6.28613i | − | 0.376341i | ||||||
\(280\) | 11.9258 | − | 3.18154i | 0.712702 | − | 0.190133i | ||||
\(281\) | 7.14637i | 0.426317i | 0.977018 | + | 0.213158i | \(0.0683750\pi\) | ||||
−0.977018 | + | 0.213158i | \(0.931625\pi\) | |||||||
\(282\) | 1.66154 | 0.0989434 | ||||||||
\(283\) | 24.3695i | 1.44862i | 0.689475 | + | 0.724309i | \(0.257841\pi\) | ||||
−0.689475 | + | 0.724309i | \(0.742159\pi\) | |||||||
\(284\) | −17.3893 | −1.03187 | ||||||||
\(285\) | −0.617578 | + | 0.223476i | −0.0365822 | + | 0.0132376i | ||||
\(286\) | 8.16483 | + | 1.83658i | 0.482797 | + | 0.108599i | ||||
\(287\) | 14.9951 | + | 1.30022i | 0.885133 | + | 0.0767496i | ||||
\(288\) | −5.40529 | −0.318510 | ||||||||
\(289\) | 1.99537 | 0.117375 | ||||||||
\(290\) | 0.104579 | + | 0.289006i | 0.00614110 | + | 0.0169710i | ||||
\(291\) | −14.1192 | −0.827683 | ||||||||
\(292\) | 8.00134i | 0.468243i | ||||||||
\(293\) | 25.4567i | 1.48720i | 0.668625 | + | 0.743599i | \(0.266883\pi\) | ||||
−0.668625 | + | 0.743599i | \(0.733117\pi\) | |||||||
\(294\) | −3.91115 | − | 0.683408i | −0.228103 | − | 0.0398571i | ||||
\(295\) | −4.17264 | − | 11.5311i | −0.242940 | − | 0.671369i | ||||
\(296\) | − | 23.6999i | − | 1.37753i | ||||||
\(297\) | −0.727850 | + | 3.23577i | −0.0422341 | + | 0.187759i | ||||
\(298\) | 9.05756i | 0.524690i | ||||||||
\(299\) | 7.43207 | 0.429808 | ||||||||
\(300\) | −6.44828 | + | 5.36987i | −0.372292 | + | 0.310029i | ||||
\(301\) | 18.6050 | + | 1.61323i | 1.07238 | + | 0.0929853i | ||||
\(302\) | 6.52146i | 0.375268i | ||||||||
\(303\) | 12.2453 | 0.703473 | ||||||||
\(304\) | 0.638302 | 0.0366091 | ||||||||
\(305\) | −11.7236 | + | 4.24228i | −0.671291 | + | 0.242912i | ||||
\(306\) | 2.19710i | 0.125600i | ||||||||
\(307\) | − | 26.5078i | − | 1.51288i | −0.654062 | − | 0.756441i | \(-0.726936\pi\) | ||
0.654062 | − | 0.756441i | \(-0.273064\pi\) | |||||||
\(308\) | −4.46098 | + | 14.0350i | −0.254188 | + | 0.799717i | ||||
\(309\) | 6.50035 | 0.369792 | ||||||||
\(310\) | −2.71284 | − | 7.49696i | −0.154079 | − | 0.425799i | ||||
\(311\) | 14.0105i | 0.794464i | 0.917718 | + | 0.397232i | \(0.130029\pi\) | ||||
−0.917718 | + | 0.397232i | \(0.869971\pi\) | |||||||
\(312\) | 9.28141i | 0.525456i | ||||||||
\(313\) | −26.0111 | −1.47023 | −0.735116 | − | 0.677941i | \(-0.762873\pi\) | ||||
−0.735116 | + | 0.677941i | \(0.762873\pi\) | |||||||
\(314\) | −6.53992 | −0.369069 | ||||||||
\(315\) | 5.71616 | − | 1.52495i | 0.322069 | − | 0.0859210i | ||||
\(316\) | 12.3843i | 0.696671i | ||||||||
\(317\) | 8.25895i | 0.463869i | 0.972731 | + | 0.231934i | \(0.0745055\pi\) | ||||
−0.972731 | + | 0.231934i | \(0.925495\pi\) | |||||||
\(318\) | 5.75791i | 0.322887i | ||||||||
\(319\) | −0.784121 | − | 0.176379i | −0.0439023 | − | 0.00987532i | ||||
\(320\) | 2.69244 | − | 0.974282i | 0.150512 | − | 0.0544640i | ||||
\(321\) | 12.8529 | 0.717379 | ||||||||
\(322\) | 0.216574 | − | 2.49769i | 0.0120692 | − | 0.139191i | ||||
\(323\) | − | 1.13773i | − | 0.0633051i | ||||||
\(324\) | −1.67828 | −0.0932379 | ||||||||
\(325\) | 14.2341 | + | 17.0927i | 0.789566 | + | 0.948132i | ||||
\(326\) | − | 6.27376i | − | 0.347471i | ||||||
\(327\) | − | 7.31694i | − | 0.404628i | ||||||
\(328\) | −11.8689 | −0.655349 | ||||||||
\(329\) | 7.72141 | + | 0.669521i | 0.425695 | + | 0.0369119i | ||||
\(330\) | 0.528380 | + | 4.17316i | 0.0290864 | + | 0.229725i | ||||
\(331\) | 21.0761 | 1.15845 | 0.579223 | − | 0.815169i | \(-0.303356\pi\) | ||||
0.579223 | + | 0.815169i | \(0.303356\pi\) | |||||||
\(332\) | − | 21.7791i | − | 1.19528i | ||||||
\(333\) | − | 11.3596i | − | 0.622504i | ||||||
\(334\) | − | 8.38999i | − | 0.459080i | ||||||
\(335\) | 9.25619 | + | 25.5796i | 0.505720 | + | 1.39756i | ||||
\(336\) | −5.72825 | − | 0.496694i | −0.312502 | − | 0.0270969i | ||||
\(337\) | −2.95010 | −0.160702 | −0.0803512 | − | 0.996767i | \(-0.525604\pi\) | ||||
−0.0803512 | + | 0.996767i | \(0.525604\pi\) | |||||||
\(338\) | 3.85175 | 0.209508 | ||||||||
\(339\) | − | 5.30123i | − | 0.287923i | ||||||
\(340\) | −4.94631 | − | 13.6692i | −0.268251 | − | 0.741316i | ||||
\(341\) | 20.3405 | + | 4.57536i | 1.10150 | + | 0.247769i | ||||
\(342\) | −0.166596 | −0.00900847 | ||||||||
\(343\) | −17.9003 | − | 4.75189i | −0.966524 | − | 0.256578i | ||||
\(344\) | −14.7262 | −0.793982 | ||||||||
\(345\) | 1.27111 | + | 3.51272i | 0.0684340 | + | 0.189118i | ||||
\(346\) | 10.3570i | 0.556795i | ||||||||
\(347\) | 15.9201 | 0.854637 | 0.427318 | − | 0.904101i | \(-0.359458\pi\) | ||||
0.427318 | + | 0.904101i | \(0.359458\pi\) | |||||||
\(348\) | − | 0.406696i | − | 0.0218012i | ||||||
\(349\) | 35.0032 | 1.87368 | 0.936840 | − | 0.349758i | \(-0.113736\pi\) | ||||
0.936840 | + | 0.349758i | \(0.113736\pi\) | |||||||
\(350\) | 6.15911 | − | 4.28555i | 0.329218 | − | 0.229072i | ||||
\(351\) | 4.44869i | 0.237453i | ||||||||
\(352\) | 3.93424 | − | 17.4903i | 0.209696 | − | 0.932237i | ||||
\(353\) | −15.8285 | −0.842469 | −0.421234 | − | 0.906952i | \(-0.638403\pi\) | ||||
−0.421234 | + | 0.906952i | \(0.638403\pi\) | |||||||
\(354\) | − | 3.11060i | − | 0.165327i | ||||||
\(355\) | −21.7863 | + | 7.88354i | −1.15630 | + | 0.418415i | ||||
\(356\) | − | 21.8179i | − | 1.15634i | ||||||
\(357\) | −0.885325 | + | 10.2102i | −0.0468564 | + | 0.540382i | ||||
\(358\) | 1.86155 | 0.0983858 | ||||||||
\(359\) | − | 20.5387i | − | 1.08399i | −0.840382 | − | 0.541995i | \(-0.817669\pi\) | ||
0.840382 | − | 0.541995i | \(-0.182331\pi\) | |||||||
\(360\) | −4.38679 | + | 1.58740i | −0.231204 | + | 0.0836632i | ||||
\(361\) | −18.9137 | −0.995460 | ||||||||
\(362\) | 13.2803i | 0.697995i | ||||||||
\(363\) | −9.94047 | − | 4.71032i | −0.521739 | − | 0.247227i | ||||
\(364\) | −1.70642 | + | 19.6797i | −0.0894409 | + | 1.03150i | ||||
\(365\) | 3.62745 | + | 10.0245i | 0.189869 | + | 0.524706i | ||||
\(366\) | −3.16252 | −0.165308 | ||||||||
\(367\) | −10.8338 | −0.565519 | −0.282759 | − | 0.959191i | \(-0.591250\pi\) | ||||
−0.282759 | + | 0.959191i | \(0.591250\pi\) | |||||||
\(368\) | − | 3.63059i | − | 0.189258i | ||||||
\(369\) | −5.68888 | −0.296152 | ||||||||
\(370\) | −4.90236 | − | 13.5477i | −0.254861 | − | 0.704313i | ||||
\(371\) | −2.32016 | + | 26.7578i | −0.120457 | + | 1.38919i | ||||
\(372\) | 10.5499i | 0.546987i | ||||||||
\(373\) | −4.55950 | −0.236082 | −0.118041 | − | 0.993009i | \(-0.537661\pi\) | ||||
−0.118041 | + | 0.993009i | \(0.537661\pi\) | |||||||
\(374\) | −7.10932 | − | 1.59916i | −0.367614 | − | 0.0826906i | ||||
\(375\) | −5.64429 | + | 9.65101i | −0.291470 | + | 0.498376i | ||||
\(376\) | −6.11162 | −0.315183 | ||||||||
\(377\) | −1.07804 | −0.0555221 | ||||||||
\(378\) | 1.49506 | + | 0.129637i | 0.0768978 | + | 0.00666778i | ||||
\(379\) | 8.64377 | 0.444001 | 0.222000 | − | 0.975047i | \(-0.428741\pi\) | ||||
0.222000 | + | 0.975047i | \(0.428741\pi\) | |||||||
\(380\) | 1.03647 | − | 0.375055i | 0.0531698 | − | 0.0192399i | ||||
\(381\) | 4.15420 | 0.212826 | ||||||||
\(382\) | 11.9057 | 0.609148 | ||||||||
\(383\) | 14.1718 | 0.724143 | 0.362071 | − | 0.932150i | \(-0.382070\pi\) | ||||
0.362071 | + | 0.932150i | \(0.382070\pi\) | |||||||
\(384\) | 11.5369 | 0.588740 | ||||||||
\(385\) | 0.773873 | + | 19.6062i | 0.0394402 | + | 0.999222i | ||||
\(386\) | −10.9925 | −0.559504 | ||||||||
\(387\) | −7.05842 | −0.358800 | ||||||||
\(388\) | 23.6960 | 1.20298 | ||||||||
\(389\) | 18.9857 | 0.962612 | 0.481306 | − | 0.876553i | \(-0.340163\pi\) | ||||
0.481306 | + | 0.876553i | \(0.340163\pi\) | |||||||
\(390\) | 1.91987 | + | 5.30559i | 0.0972165 | + | 0.268659i | ||||
\(391\) | −6.47129 | −0.327267 | ||||||||
\(392\) | 14.3863 | + | 2.51377i | 0.726619 | + | 0.126964i | ||||
\(393\) | −8.17994 | −0.412624 | ||||||||
\(394\) | 12.0516 | 0.607149 | ||||||||
\(395\) | 5.61448 | + | 15.5157i | 0.282495 | + | 0.780680i | ||||
\(396\) | 1.22154 | − | 5.43054i | 0.0613846 | − | 0.272895i | ||||
\(397\) | 12.3940 | 0.622035 | 0.311018 | − | 0.950404i | \(-0.399330\pi\) | ||||
0.311018 | + | 0.950404i | \(0.399330\pi\) | |||||||
\(398\) | 14.1633i | 0.709942i | ||||||||
\(399\) | −0.774193 | − | 0.0671301i | −0.0387581 | − | 0.00336071i | ||||
\(400\) | 8.34984 | − | 6.95341i | 0.417492 | − | 0.347670i | ||||
\(401\) | −10.3186 | −0.515287 | −0.257643 | − | 0.966240i | \(-0.582946\pi\) | ||||
−0.257643 | + | 0.966240i | \(0.582946\pi\) | |||||||
\(402\) | 6.90027i | 0.344154i | ||||||||
\(403\) | 27.9650 | 1.39304 | ||||||||
\(404\) | −20.5511 | −1.02245 | ||||||||
\(405\) | −2.10264 | + | 0.760858i | −0.104481 | + | 0.0378073i | ||||
\(406\) | −0.0314146 | + | 0.362297i | −0.00155908 | + | 0.0179805i | ||||
\(407\) | 36.7572 | + | 8.26810i | 1.82199 | + | 0.409835i | ||||
\(408\) | − | 8.08156i | − | 0.400097i | ||||||
\(409\) | −21.9324 | −1.08449 | −0.542243 | − | 0.840222i | \(-0.682425\pi\) | ||||
−0.542243 | + | 0.840222i | \(0.682425\pi\) | |||||||
\(410\) | −6.78468 | + | 2.45509i | −0.335071 | + | 0.121248i | ||||
\(411\) | 7.72402i | 0.380998i | ||||||||
\(412\) | −10.9094 | −0.537468 | ||||||||
\(413\) | 1.25342 | − | 14.4554i | 0.0616769 | − | 0.711303i | ||||
\(414\) | 0.947579i | 0.0465710i | ||||||||
\(415\) | −9.87366 | − | 27.2860i | −0.484679 | − | 1.33942i | ||||
\(416\) | − | 24.0465i | − | 1.17897i | ||||||
\(417\) | −3.34279 | −0.163697 | ||||||||
\(418\) | 0.121257 | − | 0.539067i | 0.00593086 | − | 0.0263666i | ||||
\(419\) | − | 1.82773i | − | 0.0892904i | −0.999003 | − | 0.0446452i | \(-0.985784\pi\) | ||
0.999003 | − | 0.0446452i | \(-0.0142157\pi\) | |||||||
\(420\) | −9.59334 | + | 2.55929i | −0.468107 | + | 0.124881i | ||||
\(421\) | −7.93395 | −0.386677 | −0.193339 | − | 0.981132i | \(-0.561932\pi\) | ||||
−0.193339 | + | 0.981132i | \(0.561932\pi\) | |||||||
\(422\) | − | 1.57800i | − | 0.0768158i | ||||||
\(423\) | −2.92937 | −0.142431 | ||||||||
\(424\) | − | 21.1792i | − | 1.02855i | ||||||
\(425\) | −12.3940 | − | 14.8830i | −0.601197 | − | 0.721934i | ||||
\(426\) | −5.87700 | −0.284741 | ||||||||
\(427\) | −14.6967 | − | 1.27434i | −0.711221 | − | 0.0616697i | ||||
\(428\) | −21.5708 | −1.04266 | ||||||||
\(429\) | −14.3949 | − | 3.23798i | −0.694994 | − | 0.156331i | ||||
\(430\) | −8.41802 | + | 3.04613i | −0.405953 | + | 0.146897i | ||||
\(431\) | − | 15.5772i | − | 0.750327i | −0.926959 | − | 0.375164i | \(-0.877587\pi\) | ||
0.926959 | − | 0.375164i | \(-0.122413\pi\) | |||||||
\(432\) | 2.17320 | 0.104558 | ||||||||
\(433\) | 18.2940 | 0.879153 | 0.439576 | − | 0.898205i | \(-0.355129\pi\) | ||||
0.439576 | + | 0.898205i | \(0.355129\pi\) | |||||||
\(434\) | 0.814911 | − | 9.39816i | 0.0391170 | − | 0.451126i | ||||
\(435\) | −0.184378 | − | 0.509530i | −0.00884023 | − | 0.0244301i | ||||
\(436\) | 12.2799i | 0.588100i | ||||||||
\(437\) | − | 0.490688i | − | 0.0234728i | ||||||
\(438\) | 2.70418i | 0.129211i | ||||||||
\(439\) | 5.99399 | 0.286078 | 0.143039 | − | 0.989717i | \(-0.454313\pi\) | ||||
0.143039 | + | 0.989717i | \(0.454313\pi\) | |||||||
\(440\) | −1.94353 | − | 15.3501i | −0.0926543 | − | 0.731786i | ||||
\(441\) | 6.89553 | + | 1.20488i | 0.328358 | + | 0.0573751i | ||||
\(442\) | −9.77421 | −0.464912 | ||||||||
\(443\) | − | 15.4074i | − | 0.732027i | −0.930610 | − | 0.366013i | \(-0.880722\pi\) | ||
0.930610 | − | 0.366013i | \(-0.119278\pi\) | |||||||
\(444\) | 19.0647i | 0.904769i | ||||||||
\(445\) | −9.89123 | − | 27.3345i | −0.468889 | − | 1.29578i | ||||
\(446\) | −9.29040 | −0.439913 | ||||||||
\(447\) | − | 15.9689i | − | 0.755301i | ||||||
\(448\) | 3.37523 | + | 0.292665i | 0.159465 | + | 0.0138271i | ||||
\(449\) | −9.10949 | −0.429904 | −0.214952 | − | 0.976625i | \(-0.568959\pi\) | ||||
−0.214952 | + | 0.976625i | \(0.568959\pi\) | |||||||
\(450\) | −2.17930 | + | 1.81483i | −0.102733 | + | 0.0855518i | ||||
\(451\) | 4.14065 | − | 18.4079i | 0.194976 | − | 0.866796i | ||||
\(452\) | 8.89697i | 0.418478i | ||||||||
\(453\) | − | 11.4976i | − | 0.540204i | ||||||
\(454\) | 9.50771i | 0.446219i | ||||||||
\(455\) | 6.78401 | + | 25.4294i | 0.318039 | + | 1.19215i | ||||
\(456\) | 0.612787 | 0.0286964 | ||||||||
\(457\) | 15.6456 | 0.731869 | 0.365934 | − | 0.930641i | \(-0.380749\pi\) | ||||
0.365934 | + | 0.930641i | \(0.380749\pi\) | |||||||
\(458\) | 0.0737499i | 0.00344611i | ||||||||
\(459\) | − | 3.87358i | − | 0.180803i | ||||||
\(460\) | −2.13327 | − | 5.89533i | −0.0994644 | − | 0.274871i | ||||
\(461\) | −16.4860 | −0.767831 | −0.383916 | − | 0.923368i | \(-0.625425\pi\) | ||||
−0.383916 | + | 0.923368i | \(0.625425\pi\) | |||||||
\(462\) | −1.50766 | + | 4.74333i | −0.0701425 | + | 0.220680i | ||||
\(463\) | 19.9642i | 0.927816i | 0.885883 | + | 0.463908i | \(0.153553\pi\) | ||||
−0.885883 | + | 0.463908i | \(0.846447\pi\) | |||||||
\(464\) | 0.526628i | 0.0244481i | ||||||||
\(465\) | 4.78285 | + | 13.2175i | 0.221799 | + | 0.612945i | ||||
\(466\) | 3.34213 | 0.154821 | ||||||||
\(467\) | 3.73472 | 0.172822 | 0.0864112 | − | 0.996260i | \(-0.472460\pi\) | ||||
0.0864112 | + | 0.996260i | \(0.472460\pi\) | |||||||
\(468\) | − | 7.46615i | − | 0.345123i | ||||||
\(469\) | −2.78048 | + | 32.0665i | −0.128390 | + | 1.48069i | ||||
\(470\) | −3.49363 | + | 1.26420i | −0.161149 | + | 0.0583131i | ||||
\(471\) | 11.5302 | 0.531282 | ||||||||
\(472\) | 11.4417i | 0.526646i | ||||||||
\(473\) | 5.13747 | − | 22.8395i | 0.236221 | − | 1.05016i | ||||
\(474\) | 4.18546i | 0.192245i | ||||||||
\(475\) | 1.12851 | − | 0.939778i | 0.0517797 | − | 0.0431200i | ||||
\(476\) | 1.48583 | − | 17.1356i | 0.0681027 | − | 0.785411i | ||||
\(477\) | − | 10.1514i | − | 0.464802i | ||||||
\(478\) | 1.53354i | 0.0701425i | ||||||||
\(479\) | −18.9654 | −0.866550 | −0.433275 | − | 0.901262i | \(-0.642642\pi\) | ||||
−0.433275 | + | 0.901262i | \(0.642642\pi\) | |||||||
\(480\) | 11.3654 | − | 4.11266i | 0.518757 | − | 0.187716i | ||||
\(481\) | 50.5354 | 2.30422 | ||||||||
\(482\) | 15.0255 | 0.684393 | ||||||||
\(483\) | −0.381828 | + | 4.40353i | −0.0173738 | + | 0.200367i | ||||
\(484\) | 16.6829 | + | 7.90524i | 0.758314 | + | 0.359329i | ||||
\(485\) | 29.6876 | − | 10.7427i | 1.34805 | − | 0.487801i | ||||
\(486\) | −0.567201 | −0.0257288 | ||||||||
\(487\) | 6.48529i | 0.293877i | 0.989146 | + | 0.146938i | \(0.0469419\pi\) | ||||
−0.989146 | + | 0.146938i | \(0.953058\pi\) | |||||||
\(488\) | 11.6326 | 0.526585 | ||||||||
\(489\) | 11.0609i | 0.500191i | ||||||||
\(490\) | 8.74372 | − | 1.53887i | 0.395001 | − | 0.0695190i | ||||
\(491\) | 10.6943i | 0.482627i | 0.970447 | + | 0.241314i | \(0.0775782\pi\) | ||||
−0.970447 | + | 0.241314i | \(0.922422\pi\) | |||||||
\(492\) | 9.54756 | 0.430437 | ||||||||
\(493\) | 0.938680 | 0.0422760 | ||||||||
\(494\) | − | 0.741133i | − | 0.0333451i | ||||||
\(495\) | −0.931557 | − | 7.35746i | −0.0418704 | − | 0.330693i | ||||
\(496\) | − | 13.6610i | − | 0.613397i | ||||||
\(497\) | −27.3112 | − | 2.36814i | −1.22507 | − | 0.106226i | ||||
\(498\) | − | 7.36058i | − | 0.329835i | ||||||
\(499\) | −23.0123 | −1.03017 | −0.515087 | − | 0.857138i | \(-0.672240\pi\) | ||||
−0.515087 | + | 0.857138i | \(0.672240\pi\) | |||||||
\(500\) | 9.47272 | − | 16.1971i | 0.423633 | − | 0.724357i | ||||
\(501\) | 14.7919i | 0.660854i | ||||||||
\(502\) | 0.477550i | 0.0213141i | ||||||||
\(503\) | 34.8954i | 1.55591i | 0.628320 | + | 0.777955i | \(0.283743\pi\) | ||||
−0.628320 | + | 0.777955i | \(0.716257\pi\) | |||||||
\(504\) | −5.49927 | − | 0.476840i | −0.244957 | − | 0.0212401i | ||||
\(505\) | −25.7474 | + | 9.31692i | −1.14575 | + | 0.414598i | ||||
\(506\) | −3.06615 | − | 0.689695i | −0.136307 | − | 0.0306607i | ||||
\(507\) | −6.79080 | −0.301590 | ||||||||
\(508\) | −6.97193 | −0.309329 | ||||||||
\(509\) | − | 28.7970i | − | 1.27641i | −0.769868 | − | 0.638203i | \(-0.779678\pi\) | ||
0.769868 | − | 0.638203i | \(-0.220322\pi\) | |||||||
\(510\) | −1.67168 | − | 4.61971i | −0.0740233 | − | 0.204564i | ||||
\(511\) | −1.08965 | + | 12.5667i | −0.0482034 | + | 0.555917i | ||||
\(512\) | −20.8148 | −0.919892 | ||||||||
\(513\) | 0.293716 | 0.0129679 | ||||||||
\(514\) | 12.8797 | 0.568101 | ||||||||
\(515\) | −13.6679 | + | 4.94584i | −0.602279 | + | 0.217940i | ||||
\(516\) | 11.8460 | 0.521492 | ||||||||
\(517\) | 2.13214 | − | 9.47878i | 0.0937715 | − | 0.416876i | ||||
\(518\) | 1.47262 | − | 16.9834i | 0.0647033 | − | 0.746206i | ||||
\(519\) | − | 18.2598i | − | 0.801516i | ||||||
\(520\) | −7.06183 | − | 19.5155i | −0.309682 | − | 0.855810i | ||||
\(521\) | − | 14.7346i | − | 0.645534i | −0.946478 | − | 0.322767i | \(-0.895387\pi\) | ||
0.946478 | − | 0.322767i | \(-0.104613\pi\) | |||||||
\(522\) | − | 0.137449i | − | 0.00601599i | ||||||
\(523\) | − | 6.03297i | − | 0.263803i | −0.991263 | − | 0.131902i | \(-0.957892\pi\) | ||
0.991263 | − | 0.131902i | \(-0.0421083\pi\) | |||||||
\(524\) | 13.7283 | 0.599722 | ||||||||
\(525\) | −10.8588 | + | 7.55560i | −0.473916 | + | 0.329753i | ||||
\(526\) | 9.76825 | 0.425916 | ||||||||
\(527\) | −24.3498 | −1.06069 | ||||||||
\(528\) | −1.58176 | + | 7.03198i | −0.0688373 | + | 0.306028i | ||||
\(529\) | 20.2090 | 0.878653 | ||||||||
\(530\) | −4.38095 | − | 12.1068i | −0.190296 | − | 0.525886i | ||||
\(531\) | 5.48413i | 0.237991i | ||||||||
\(532\) | 1.29932 | + | 0.112663i | 0.0563325 | + | 0.00488457i | ||||
\(533\) | − | 25.3081i | − | 1.09621i | ||||||
\(534\) | − | 7.37368i | − | 0.319090i | ||||||
\(535\) | −27.0250 | + | 9.77923i | −1.16839 | + | 0.422793i | ||||
\(536\) | − | 25.3812i | − | 1.09630i | ||||||
\(537\) | −3.28199 | −0.141628 | ||||||||
\(538\) | − | 1.00848i | − | 0.0434785i | ||||||
\(539\) | −8.91762 | + | 21.4354i | −0.384109 | + | 0.923288i | ||||
\(540\) | 3.52882 | − | 1.27693i | 0.151856 | − | 0.0549505i | ||||
\(541\) | − | 31.3633i | − | 1.34841i | −0.738543 | − | 0.674206i | \(-0.764486\pi\) | ||
0.738543 | − | 0.674206i | \(-0.235514\pi\) | |||||||
\(542\) | 13.6443 | 0.586072 | ||||||||
\(543\) | − | 23.4137i | − | 1.00478i | ||||||
\(544\) | 20.9378i | 0.897703i | ||||||||
\(545\) | 5.56715 | + | 15.3849i | 0.238470 | + | 0.659016i | ||||
\(546\) | −0.576712 | + | 6.65107i | −0.0246810 | + | 0.284639i | ||||
\(547\) | −9.01256 | −0.385349 | −0.192675 | − | 0.981263i | \(-0.561716\pi\) | ||||
−0.192675 | + | 0.981263i | \(0.561716\pi\) | |||||||
\(548\) | − | 12.9631i | − | 0.553756i | ||||||
\(549\) | 5.57566 | 0.237963 | ||||||||
\(550\) | −4.28617 | − | 8.37263i | −0.182763 | − | 0.357010i | ||||
\(551\) | 0.0711757i | 0.00303219i | ||||||||
\(552\) | − | 3.48546i | − | 0.148351i | ||||||
\(553\) | −1.68654 | + | 19.4504i | −0.0717189 | + | 0.827116i | ||||
\(554\) | 12.2251 | 0.519395 | ||||||||
\(555\) | 8.64306 | + | 23.8852i | 0.366877 | + | 1.01387i | ||||
\(556\) | 5.61015 | 0.237923 | ||||||||
\(557\) | 15.2949 | 0.648066 | 0.324033 | − | 0.946046i | \(-0.394961\pi\) | ||||
0.324033 | + | 0.946046i | \(0.394961\pi\) | |||||||
\(558\) | 3.56550i | 0.150940i | ||||||||
\(559\) | − | 31.4007i | − | 1.32811i | ||||||
\(560\) | 12.4224 | − | 3.31401i | 0.524940 | − | 0.140043i | ||||
\(561\) | 12.5340 | + | 2.81939i | 0.529187 | + | 0.119035i | ||||
\(562\) | − | 4.05343i | − | 0.170984i | ||||||
\(563\) | − | 6.61395i | − | 0.278745i | −0.990240 | − | 0.139372i | \(-0.955491\pi\) | ||
0.990240 | − | 0.139372i | \(-0.0445085\pi\) | |||||||
\(564\) | 4.91631 | 0.207014 | ||||||||
\(565\) | 4.03348 | + | 11.1466i | 0.169690 | + | 0.468940i | ||||
\(566\) | − | 13.8224i | − | 0.581000i | ||||||
\(567\) | −2.63586 | − | 0.228555i | −0.110696 | − | 0.00959839i | ||||
\(568\) | 21.6173 | 0.907040 | ||||||||
\(569\) | − | 19.8797i | − | 0.833400i | −0.909044 | − | 0.416700i | \(-0.863187\pi\) | ||
0.909044 | − | 0.416700i | \(-0.136813\pi\) | |||||||
\(570\) | 0.350291 | − | 0.126756i | 0.0146721 | − | 0.00530921i | ||||
\(571\) | − | 14.4599i | − | 0.605127i | −0.953129 | − | 0.302563i | \(-0.902158\pi\) | ||
0.953129 | − | 0.302563i | \(-0.0978424\pi\) | |||||||
\(572\) | 24.1588 | + | 5.43424i | 1.01013 | + | 0.227217i | ||||
\(573\) | −20.9902 | −0.876880 | ||||||||
\(574\) | −8.50525 | − | 0.737487i | −0.355002 | − | 0.0307821i | ||||
\(575\) | −5.34535 | − | 6.41885i | −0.222917 | − | 0.267684i | ||||
\(576\) | −1.28051 | −0.0533544 | ||||||||
\(577\) | 2.85370 | 0.118801 | 0.0594005 | − | 0.998234i | \(-0.481081\pi\) | ||||
0.0594005 | + | 0.998234i | \(0.481081\pi\) | |||||||
\(578\) | −1.13178 | −0.0470756 | ||||||||
\(579\) | 19.3802 | 0.805415 | ||||||||
\(580\) | 0.309438 | + | 0.855135i | 0.0128487 | + | 0.0355076i | ||||
\(581\) | 2.96596 | − | 34.2056i | 0.123049 | − | 1.41909i | ||||
\(582\) | 8.00843 | 0.331960 | ||||||||
\(583\) | 32.8477 | + | 7.38872i | 1.36041 | + | 0.306010i | ||||
\(584\) | − | 9.94672i | − | 0.411598i | ||||||
\(585\) | −3.38482 | − | 9.35398i | −0.139945 | − | 0.386740i | ||||
\(586\) | − | 14.4391i | − | 0.596474i | ||||||
\(587\) | −8.41194 | −0.347198 | −0.173599 | − | 0.984816i | \(-0.555540\pi\) | ||||
−0.173599 | + | 0.984816i | \(0.555540\pi\) | |||||||
\(588\) | −11.5726 | − | 2.02212i | −0.477248 | − | 0.0833910i | ||||
\(589\) | − | 1.84633i | − | 0.0760768i | ||||||
\(590\) | 2.36673 | + | 6.54048i | 0.0974366 | + | 0.269267i | ||||
\(591\) | −21.2474 | −0.874002 | ||||||||
\(592\) | − | 24.6867i | − | 1.01462i | ||||||
\(593\) | − | 18.3022i | − | 0.751583i | −0.926704 | − | 0.375791i | \(-0.877371\pi\) | ||
0.926704 | − | 0.375791i | \(-0.122629\pi\) | |||||||
\(594\) | 0.412837 | − | 1.83534i | 0.0169389 | − | 0.0753047i | ||||
\(595\) | −5.90700 | − | 22.1420i | −0.242164 | − | 0.907735i | ||||
\(596\) | 26.8003i | 1.09778i | ||||||||
\(597\) | − | 24.9705i | − | 1.02197i | ||||||
\(598\) | −4.21548 | −0.172384 | ||||||||
\(599\) | 4.67527 | 0.191027 | 0.0955133 | − | 0.995428i | \(-0.469551\pi\) | ||||
0.0955133 | + | 0.995428i | \(0.469551\pi\) | |||||||
\(600\) | 8.01607 | − | 6.67545i | 0.327255 | − | 0.272524i | ||||
\(601\) | −27.1569 | −1.10775 | −0.553876 | − | 0.832599i | \(-0.686852\pi\) | ||||
−0.553876 | + | 0.832599i | \(0.686852\pi\) | |||||||
\(602\) | −10.5528 | − | 0.915029i | −0.430100 | − | 0.0372938i | ||||
\(603\) | − | 12.1655i | − | 0.495416i | ||||||
\(604\) | 19.2962i | 0.785152i | ||||||||
\(605\) | 24.4851 | + | 2.34082i | 0.995461 | + | 0.0951678i | ||||
\(606\) | −6.94554 | −0.282143 | ||||||||
\(607\) | 6.98908i | 0.283678i | 0.989890 | + | 0.141839i | \(0.0453015\pi\) | ||||
−0.989890 | + | 0.141839i | \(0.954698\pi\) | |||||||
\(608\) | −1.58762 | −0.0643865 | ||||||||
\(609\) | 0.0553853 | − | 0.638745i | 0.00224433 | − | 0.0258832i | ||||
\(610\) | 6.64964 | − | 2.40623i | 0.269236 | − | 0.0974253i | ||||
\(611\) | − | 13.0318i | − | 0.527212i | ||||||
\(612\) | 6.50096i | 0.262786i | ||||||||
\(613\) | −43.5667 | −1.75964 | −0.879822 | − | 0.475304i | \(-0.842338\pi\) | ||||
−0.879822 | + | 0.475304i | \(0.842338\pi\) | |||||||
\(614\) | 15.0353i | 0.606774i | ||||||||
\(615\) | 11.9617 | − | 4.32843i | 0.482341 | − | 0.174539i | ||||
\(616\) | 5.54559 | − | 17.4473i | 0.223438 | − | 0.702973i | ||||
\(617\) | − | 29.3838i | − | 1.18295i | −0.806325 | − | 0.591473i | \(-0.798546\pi\) | ||
0.806325 | − | 0.591473i | \(-0.201454\pi\) | |||||||
\(618\) | −3.68700 | −0.148313 | ||||||||
\(619\) | 23.0883i | 0.927997i | 0.885836 | + | 0.463999i | \(0.153586\pi\) | ||||
−0.885836 | + | 0.463999i | \(0.846414\pi\) | |||||||
\(620\) | −8.02697 | − | 22.1826i | −0.322371 | − | 0.890876i | ||||
\(621\) | − | 1.67062i | − | 0.0670397i | ||||||
\(622\) | − | 7.94678i | − | 0.318637i | ||||||
\(623\) | 2.97124 | − | 34.2665i | 0.119040 | − | 1.37286i | ||||
\(624\) | 9.66787i | 0.387025i | ||||||||
\(625\) | 4.52487 | − | 24.5871i | 0.180995 | − | 0.983484i | ||||
\(626\) | 14.7535 | 0.589669 | ||||||||
\(627\) | −0.213781 | + | 0.950397i | −0.00853758 | + | 0.0379552i | ||||
\(628\) | −19.3509 | −0.772184 | ||||||||
\(629\) | −44.0024 | −1.75449 | ||||||||
\(630\) | −3.24222 | + | 0.864952i | −0.129173 | + | 0.0344605i | ||||
\(631\) | −18.8289 | −0.749566 | −0.374783 | − | 0.927113i | \(-0.622283\pi\) | ||||
−0.374783 | + | 0.927113i | \(0.622283\pi\) | |||||||
\(632\) | − | 15.3953i | − | 0.612393i | ||||||
\(633\) | 2.78208i | 0.110578i | ||||||||
\(634\) | − | 4.68449i | − | 0.186045i | ||||||
\(635\) | −8.73479 | + | 3.16076i | −0.346630 | + | 0.125431i | ||||
\(636\) | 17.0370i | 0.675560i | ||||||||
\(637\) | −5.36012 | + | 30.6760i | −0.212376 | + | 1.21543i | ||||
\(638\) | 0.444754 | + | 0.100042i | 0.0176080 | + | 0.00396071i | ||||
\(639\) | 10.3614 | 0.409890 | ||||||||
\(640\) | −24.2579 | + | 8.77793i | −0.958879 | + | 0.346978i | ||||
\(641\) | 32.9736 | 1.30238 | 0.651190 | − | 0.758915i | \(-0.274270\pi\) | ||||
0.651190 | + | 0.758915i | \(0.274270\pi\) | |||||||
\(642\) | −7.29019 | −0.287721 | ||||||||
\(643\) | 5.85837 | 0.231032 | 0.115516 | − | 0.993306i | \(-0.463148\pi\) | ||||
0.115516 | + | 0.993306i | \(0.463148\pi\) | |||||||
\(644\) | 0.640816 | − | 7.39036i | 0.0252517 | − | 0.291221i | ||||
\(645\) | 14.8413 | − | 5.37045i | 0.584376 | − | 0.211461i | ||||
\(646\) | 0.645323i | 0.0253899i | ||||||||
\(647\) | −21.6502 | −0.851156 | −0.425578 | − | 0.904922i | \(-0.639929\pi\) | ||||
−0.425578 | + | 0.904922i | \(0.639929\pi\) | |||||||
\(648\) | 2.08633 | 0.0819587 | ||||||||
\(649\) | −17.7454 | − | 3.99162i | −0.696568 | − | 0.156685i | ||||
\(650\) | −8.07360 | − | 9.69500i | −0.316673 | − | 0.380269i | ||||
\(651\) | −1.43672 | + | 16.5694i | −0.0563096 | + | 0.649404i | ||||
\(652\) | − | 18.5633i | − | 0.726996i | ||||||
\(653\) | − | 49.1478i | − | 1.92330i | −0.274276 | − | 0.961651i | \(-0.588438\pi\) | ||
0.274276 | − | 0.961651i | \(-0.411562\pi\) | |||||||
\(654\) | 4.15018i | 0.162285i | ||||||||
\(655\) | 17.1995 | − | 6.22377i | 0.672039 | − | 0.243183i | ||||
\(656\) | −12.3631 | −0.482697 | ||||||||
\(657\) | − | 4.76758i | − | 0.186001i | ||||||
\(658\) | −4.37960 | − | 0.379753i | −0.170734 | − | 0.0148043i | ||||
\(659\) | − | 44.7970i | − | 1.74504i | −0.488576 | − | 0.872521i | \(-0.662484\pi\) | ||
0.488576 | − | 0.872521i | \(-0.337516\pi\) | |||||||
\(660\) | 1.56342 | + | 12.3479i | 0.0608559 | + | 0.480641i | ||||
\(661\) | 8.39566i | 0.326553i | 0.986580 | + | 0.163277i | \(0.0522063\pi\) | ||||
−0.986580 | + | 0.163277i | \(0.947794\pi\) | |||||||
\(662\) | −11.9544 | −0.464620 | ||||||||
\(663\) | 17.2323 | 0.669249 | ||||||||
\(664\) | 27.0743i | 1.05069i | ||||||||
\(665\) | 1.67893 | − | 0.447901i | 0.0651060 | − | 0.0173688i | ||||
\(666\) | 6.44320i | 0.249669i | ||||||||
\(667\) | 0.404839 | 0.0156754 | ||||||||
\(668\) | − | 24.8250i | − | 0.960508i | ||||||
\(669\) | 16.3794 | 0.633263 | ||||||||
\(670\) | −5.25013 | − | 14.5088i | −0.202830 | − | 0.560524i | ||||
\(671\) | −4.05824 | + | 18.0416i | −0.156667 | + | 0.696487i | ||||
\(672\) | 14.2476 | + | 1.23541i | 0.549613 | + | 0.0476568i | ||||
\(673\) | 7.01933 | 0.270575 | 0.135288 | − | 0.990806i | \(-0.456804\pi\) | ||||
0.135288 | + | 0.990806i | \(0.456804\pi\) | |||||||
\(674\) | 1.67330 | 0.0644532 | ||||||||
\(675\) | 3.84219 | − | 3.19962i | 0.147886 | − | 0.123153i | ||||
\(676\) | 11.3969 | 0.438342 | ||||||||
\(677\) | 2.31998i | 0.0891642i | 0.999006 | + | 0.0445821i | \(0.0141956\pi\) | ||||
−0.999006 | + | 0.0445821i | \(0.985804\pi\) | |||||||
\(678\) | 3.00687i | 0.115478i | ||||||||
\(679\) | 37.2163 | + | 3.22701i | 1.42823 | + | 0.123841i | ||||
\(680\) | 6.14891 | + | 16.9926i | 0.235800 | + | 0.651637i | ||||
\(681\) | − | 16.7625i | − | 0.642340i | ||||||
\(682\) | −11.5372 | − | 2.59515i | −0.441780 | − | 0.0993734i | ||||
\(683\) | 20.1258i | 0.770091i | 0.922898 | + | 0.385045i | \(0.125814\pi\) | ||||
−0.922898 | + | 0.385045i | \(0.874186\pi\) | |||||||
\(684\) | −0.492938 | −0.0188479 | ||||||||
\(685\) | −5.87688 | − | 16.2408i | −0.224544 | − | 0.620530i | ||||
\(686\) | 10.1531 | + | 2.69528i | 0.387645 | + | 0.102906i | ||||
\(687\) | − | 0.130024i | − | 0.00496073i | ||||||
\(688\) | −15.3393 | −0.584807 | ||||||||
\(689\) | 45.1605 | 1.72048 | ||||||||
\(690\) | −0.720972 | − | 1.99242i | −0.0274470 | − | 0.0758500i | ||||
\(691\) | 33.8892i | 1.28920i | 0.764518 | + | 0.644602i | \(0.222977\pi\) | ||||
−0.764518 | + | 0.644602i | \(0.777023\pi\) | |||||||
\(692\) | 30.6451i | 1.16495i | ||||||||
\(693\) | 2.65806 | − | 8.36270i | 0.100971 | − | 0.317673i | ||||
\(694\) | −9.02992 | −0.342771 | ||||||||
\(695\) | 7.02869 | − | 2.54339i | 0.266613 | − | 0.0964762i | ||||
\(696\) | 0.505577i | 0.0191638i | ||||||||
\(697\) | 22.0364i | 0.834687i | ||||||||
\(698\) | −19.8539 | −0.751480 | ||||||||
\(699\) | −5.89232 | −0.222868 | ||||||||
\(700\) | 18.2241 | − | 12.6804i | 0.688806 | − | 0.479275i | ||||
\(701\) | − | 10.4432i | − | 0.394434i | −0.980360 | − | 0.197217i | \(-0.936810\pi\) | ||
0.980360 | − | 0.197217i | \(-0.0631903\pi\) | |||||||
\(702\) | − | 2.52330i | − | 0.0952358i | ||||||
\(703\) | − | 3.33650i | − | 0.125838i | ||||||
\(704\) | 0.932016 | − | 4.14343i | 0.0351267 | − | 0.156161i | ||||
\(705\) | 6.15941 | − | 2.22883i | 0.231977 | − | 0.0839427i | ||||
\(706\) | 8.97797 | 0.337890 | ||||||||
\(707\) | −32.2769 | − | 2.79872i | −1.21390 | − | 0.105257i | ||||
\(708\) | − | 9.20391i | − | 0.345904i | ||||||
\(709\) | −6.53089 | −0.245273 | −0.122636 | − | 0.992452i | \(-0.539135\pi\) | ||||
−0.122636 | + | 0.992452i | \(0.539135\pi\) | |||||||
\(710\) | 12.3572 | − | 4.47156i | 0.463758 | − | 0.167815i | ||||
\(711\) | − | 7.37915i | − | 0.276740i | ||||||
\(712\) | 27.1225i | 1.01646i | ||||||||
\(713\) | −10.5017 | −0.393293 | ||||||||
\(714\) | 0.502158 | − | 5.79125i | 0.0187928 | − | 0.216732i | ||||
\(715\) | 32.7310 | − | 4.14420i | 1.22407 | − | 0.154984i | ||||
\(716\) | 5.50810 | 0.205847 | ||||||||
\(717\) | − | 2.70370i | − | 0.100971i | ||||||
\(718\) | 11.6496i | 0.434758i | ||||||||
\(719\) | − | 5.95963i | − | 0.222257i | −0.993806 | − | 0.111128i | \(-0.964554\pi\) | ||
0.993806 | − | 0.111128i | \(-0.0354465\pi\) | |||||||
\(720\) | −4.56945 | + | 1.65349i | −0.170293 | + | 0.0616221i | ||||
\(721\) | −17.1340 | − | 1.48568i | −0.638104 | − | 0.0553298i | ||||
\(722\) | 10.7279 | 0.399251 | ||||||||
\(723\) | −26.4906 | −0.985197 | ||||||||
\(724\) | 39.2947i | 1.46038i | ||||||||
\(725\) | 0.775360 | + | 0.931073i | 0.0287961 | + | 0.0345792i | ||||
\(726\) | 5.63825 | + | 2.67170i | 0.209255 | + | 0.0991560i | ||||
\(727\) | 19.8405 | 0.735845 | 0.367922 | − | 0.929856i | \(-0.380069\pi\) | ||||
0.367922 | + | 0.929856i | \(0.380069\pi\) | |||||||
\(728\) | 2.12131 | − | 24.4645i | 0.0786210 | − | 0.906715i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.05749 | − | 5.68591i | −0.0761512 | − | 0.210445i | ||||
\(731\) | 27.3414i | 1.01126i | ||||||||
\(732\) | −9.35753 | −0.345864 | ||||||||
\(733\) | − | 36.0282i | − | 1.33073i | −0.746517 | − | 0.665366i | \(-0.768275\pi\) | ||
0.746517 | − | 0.665366i | \(-0.231725\pi\) | |||||||
\(734\) | 6.14493 | 0.226814 | ||||||||
\(735\) | −15.4155 | + | 2.71309i | −0.568611 | + | 0.100074i | ||||
\(736\) | 9.03020i | 0.332858i | ||||||||
\(737\) | 39.3647 | + | 8.85464i | 1.45002 | + | 0.326165i | ||||
\(738\) | 3.22674 | 0.118778 | ||||||||
\(739\) | 15.1483i | 0.557239i | 0.960402 | + | 0.278619i | \(0.0898768\pi\) | ||||
−0.960402 | + | 0.278619i | \(0.910123\pi\) | |||||||
\(740\) | −14.5055 | − | 40.0861i | −0.533233 | − | 1.47360i | ||||
\(741\) | 1.30665i | 0.0480009i | ||||||||
\(742\) | 1.31600 | − | 15.1770i | 0.0483117 | − | 0.557167i | ||||
\(743\) | −17.7211 | −0.650126 | −0.325063 | − | 0.945692i | \(-0.605385\pi\) | ||||
−0.325063 | + | 0.945692i | \(0.605385\pi\) | |||||||
\(744\) | − | 13.1149i | − | 0.480816i | ||||||
\(745\) | 12.1500 | + | 33.5768i | 0.445143 | + | 1.23016i | ||||
\(746\) | 2.58616 | 0.0946859 | ||||||||
\(747\) | 12.9770i | 0.474804i | ||||||||
\(748\) | −21.0357 | − | 4.73173i | −0.769140 | − | 0.173009i | ||||
\(749\) | −33.8785 | − | 2.93759i | −1.23789 | − | 0.107337i | ||||
\(750\) | 3.20145 | − | 5.47407i | 0.116900 | − | 0.199885i | ||||
\(751\) | −28.1754 | −1.02813 | −0.514067 | − | 0.857750i | \(-0.671862\pi\) | ||||
−0.514067 | + | 0.857750i | \(0.671862\pi\) | |||||||
\(752\) | −6.36610 | −0.232148 | ||||||||
\(753\) | − | 0.841941i | − | 0.0306820i | ||||||
\(754\) | 0.611468 | 0.0222684 | ||||||||
\(755\) | 8.74804 | + | 24.1753i | 0.318374 | + | 0.879830i | ||||
\(756\) | 4.42372 | + | 0.383579i | 0.160889 | + | 0.0139506i | ||||
\(757\) | − | 3.33748i | − | 0.121303i | −0.998159 | − | 0.0606514i | \(-0.980682\pi\) | ||
0.998159 | − | 0.0606514i | \(-0.0193178\pi\) | |||||||
\(758\) | −4.90276 | −0.178076 | ||||||||
\(759\) | 5.40575 | + | 1.21596i | 0.196216 | + | 0.0441366i | ||||
\(760\) | −1.28847 | + | 0.466243i | −0.0467377 | + | 0.0169124i | ||||
\(761\) | 20.3177 | 0.736517 | 0.368259 | − | 0.929723i | \(-0.379954\pi\) | ||||
0.368259 | + | 0.929723i | \(0.379954\pi\) | |||||||
\(762\) | −2.35627 | −0.0853586 | ||||||||
\(763\) | −1.67232 | + | 19.2864i | −0.0605421 | + | 0.698216i | ||||
\(764\) | 35.2276 | 1.27449 | ||||||||
\(765\) | 2.94724 | + | 8.14475i | 0.106558 | + | 0.294474i | ||||
\(766\) | −8.03824 | −0.290433 | ||||||||
\(767\) | −24.3972 | −0.880930 | ||||||||
\(768\) | −3.98273 | −0.143714 | ||||||||
\(769\) | −15.4946 | −0.558748 | −0.279374 | − | 0.960182i | \(-0.590127\pi\) | ||||
−0.279374 | + | 0.960182i | \(0.590127\pi\) | |||||||
\(770\) | −0.438942 | − | 11.1206i | −0.0158184 | − | 0.400760i | ||||
\(771\) | −22.7075 | −0.817791 | ||||||||
\(772\) | −32.5255 | −1.17062 | ||||||||
\(773\) | 20.9096 | 0.752066 | 0.376033 | − | 0.926606i | \(-0.377288\pi\) | ||||
0.376033 | + | 0.926606i | \(0.377288\pi\) | |||||||
\(774\) | 4.00355 | 0.143904 | ||||||||
\(775\) | −20.1132 | − | 24.1525i | −0.722488 | − | 0.867583i | ||||
\(776\) | −29.4573 | −1.05745 | ||||||||
\(777\) | −2.59630 | + | 29.9424i | −0.0931416 | + | 1.07418i | ||||
\(778\) | −10.7687 | −0.386077 | ||||||||
\(779\) | −1.67091 | −0.0598667 | ||||||||
\(780\) | 5.68068 | + | 15.6986i | 0.203401 | + | 0.562101i | ||||
\(781\) | −7.54154 | + | 33.5271i | −0.269857 | + | 1.19970i | ||||
\(782\) | 3.67052 | 0.131258 | ||||||||
\(783\) | 0.242329i | 0.00866012i | ||||||||
\(784\) | 14.9853 | + | 2.61844i | 0.535191 | + | 0.0935155i | ||||
\(785\) | −24.2438 | + | 8.77281i | −0.865298 | + | 0.313115i | ||||
\(786\) | 4.63968 | 0.165492 | ||||||||
\(787\) | − | 16.8501i | − | 0.600640i | −0.953838 | − | 0.300320i | \(-0.902906\pi\) | ||
0.953838 | − | 0.300320i | \(-0.0970935\pi\) | |||||||
\(788\) | 35.6592 | 1.27031 | ||||||||
\(789\) | −17.2218 | −0.613114 | ||||||||
\(790\) | −3.18454 | − | 8.80053i | −0.113301 | − | 0.313109i | ||||
\(791\) | −1.21162 | + | 13.9733i | −0.0430803 | + | 0.496834i | ||||
\(792\) | −1.51853 | + | 6.75088i | −0.0539587 | + | 0.239882i | ||||
\(793\) | 24.8043i | 0.880828i | ||||||||
\(794\) | −7.02987 | −0.249481 | ||||||||
\(795\) | 7.72380 | + | 21.3448i | 0.273935 | + | 0.757023i | ||||
\(796\) | 41.9075i | 1.48537i | ||||||||
\(797\) | 53.7507 | 1.90395 | 0.951974 | − | 0.306180i | \(-0.0990510\pi\) | ||||
0.951974 | + | 0.306180i | \(0.0990510\pi\) | |||||||
\(798\) | 0.439124 | + | 0.0380763i | 0.0155448 | + | 0.00134789i | ||||
\(799\) | 11.3472i | 0.401433i | ||||||||
\(800\) | −20.7682 | + | 17.2949i | −0.734266 | + | 0.611467i | ||||
\(801\) | 13.0001i | 0.459336i | ||||||||
\(802\) | 5.85273 | 0.206667 | ||||||||
\(803\) | 15.4268 | + | 3.47008i | 0.544400 | + | 0.122456i | ||||
\(804\) | 20.4171i | 0.720056i | ||||||||
\(805\) | −2.54761 | − | 9.54955i | −0.0897914 | − | 0.336577i | ||||
\(806\) | −15.8618 | −0.558708 | ||||||||
\(807\) | 1.77799i | 0.0625882i | ||||||||
\(808\) | 25.5477 | 0.898764 | ||||||||
\(809\) | 35.6740i | 1.25423i | 0.778927 | + | 0.627115i | \(0.215764\pi\) | ||||
−0.778927 | + | 0.627115i | \(0.784236\pi\) | |||||||
\(810\) | 1.19262 | − | 0.431559i | 0.0419044 | − | 0.0151635i | ||||
\(811\) | 49.5430 | 1.73969 | 0.869845 | − | 0.493324i | \(-0.164218\pi\) | ||||
0.869845 | + | 0.493324i | \(0.164218\pi\) | |||||||
\(812\) | −0.0929523 | + | 1.07199i | −0.00326199 | + | 0.0376196i | ||||
\(813\) | −24.0555 | −0.843662 | ||||||||
\(814\) | −20.8487 | − | 4.68968i | −0.730748 | − | 0.164373i | ||||
\(815\) | −8.41577 | − | 23.2571i | −0.294792 | − | 0.814661i | ||||
\(816\) | − | 8.41806i | − | 0.294691i | ||||||
\(817\) | −2.07317 | −0.0725310 | ||||||||
\(818\) | 12.4401 | 0.434957 | ||||||||
\(819\) | 1.01677 | − | 11.7261i | 0.0355287 | − | 0.409744i | ||||
\(820\) | −20.0751 | + | 7.26433i | −0.701052 | + | 0.253681i | ||||
\(821\) | 22.5260i | 0.786164i | 0.919503 | + | 0.393082i | \(0.128591\pi\) | ||||
−0.919503 | + | 0.393082i | \(0.871409\pi\) | |||||||
\(822\) | − | 4.38107i | − | 0.152808i | ||||||
\(823\) | 43.3588i | 1.51139i | 0.654922 | + | 0.755696i | \(0.272701\pi\) | ||||
−0.654922 | + | 0.755696i | \(0.727299\pi\) | |||||||
\(824\) | 13.5618 | 0.472449 | ||||||||
\(825\) | 7.55671 | + | 14.7613i | 0.263091 | + | 0.513923i | ||||
\(826\) | −0.710943 | + | 8.19912i | −0.0247369 | + | 0.285284i | ||||
\(827\) | −19.3870 | −0.674152 | −0.337076 | − | 0.941477i | \(-0.609438\pi\) | ||||
−0.337076 | + | 0.941477i | \(0.609438\pi\) | |||||||
\(828\) | 2.80378i | 0.0974379i | ||||||||
\(829\) | − | 35.3424i | − | 1.22749i | −0.789504 | − | 0.613746i | \(-0.789662\pi\) | ||
0.789504 | − | 0.613746i | \(-0.210338\pi\) | |||||||
\(830\) | 5.60035 | + | 15.4766i | 0.194391 | + | 0.537202i | ||||
\(831\) | −21.5534 | −0.747679 | ||||||||
\(832\) | − | 5.69657i | − | 0.197493i | ||||||
\(833\) | 4.66719 | − | 26.7104i | 0.161708 | − | 0.925460i | ||||
\(834\) | 1.89604 | 0.0656543 | ||||||||
\(835\) | −11.2545 | − | 31.1021i | −0.389479 | − | 1.07633i | ||||
\(836\) | 0.358785 | − | 1.59504i | 0.0124088 | − | 0.0551654i | ||||
\(837\) | − | 6.28613i | − | 0.217280i | ||||||
\(838\) | 1.03669i | 0.0358119i | ||||||||
\(839\) | 6.53422i | 0.225586i | 0.993618 | + | 0.112793i | \(0.0359797\pi\) | ||||
−0.993618 | + | 0.112793i | \(0.964020\pi\) | |||||||
\(840\) | 11.9258 | − | 3.18154i | 0.411479 | − | 0.109773i | ||||
\(841\) | 28.9413 | 0.997975 | ||||||||
\(842\) | 4.50015 | 0.155085 | ||||||||
\(843\) | 7.14637i | 0.246134i | ||||||||
\(844\) | − | 4.66911i | − | 0.160718i | ||||||
\(845\) | 14.2786 | − | 5.16683i | 0.491199 | − | 0.177744i | ||||
\(846\) | 1.66154 | 0.0571250 | ||||||||
\(847\) | 25.1251 | + | 14.6877i | 0.863310 | + | 0.504675i | ||||
\(848\) | − | 22.0611i | − | 0.757580i | ||||||
\(849\) | 24.3695i | 0.836360i | ||||||||
\(850\) | 7.02989 | + | 8.44168i | 0.241123 | + | 0.289547i | ||||
\(851\) | −18.9776 | −0.650545 | ||||||||
\(852\) | −17.3893 | −0.595749 | ||||||||
\(853\) | 9.26467i | 0.317216i | 0.987342 | + | 0.158608i | \(0.0507006\pi\) | ||||
−0.987342 | + | 0.158608i | \(0.949299\pi\) | |||||||
\(854\) | 8.33596 | + | 0.722808i | 0.285251 | + | 0.0247340i | ||||
\(855\) | −0.617578 | + | 0.223476i | −0.0211207 | + | 0.00764271i | ||||
\(856\) | 26.8154 | 0.916530 | ||||||||
\(857\) | − | 52.4191i | − | 1.79060i | −0.445460 | − | 0.895302i | \(-0.646960\pi\) | ||
0.445460 | − | 0.895302i | \(-0.353040\pi\) | |||||||
\(858\) | 8.16483 | + | 1.83658i | 0.278743 | + | 0.0626999i | ||||
\(859\) | − | 4.69044i | − | 0.160036i | −0.996793 | − | 0.0800178i | \(-0.974502\pi\) | ||
0.996793 | − | 0.0800178i | \(-0.0254977\pi\) | |||||||
\(860\) | −24.9079 | + | 9.01314i | −0.849353 | + | 0.307345i | ||||
\(861\) | 14.9951 | + | 1.30022i | 0.511032 | + | 0.0443114i | ||||
\(862\) | 8.83541i | 0.300935i | ||||||||
\(863\) | 34.5431i | 1.17586i | 0.808911 | + | 0.587931i | \(0.200057\pi\) | ||||
−0.808911 | + | 0.587931i | \(0.799943\pi\) | |||||||
\(864\) | −5.40529 | −0.183892 | ||||||||
\(865\) | 13.8931 | + | 38.3938i | 0.472380 | + | 1.30543i | ||||
\(866\) | −10.3764 | −0.352603 | ||||||||
\(867\) | 1.99537 | 0.0677662 | ||||||||
\(868\) | 2.41123 | − | 27.8081i | 0.0818424 | − | 0.943867i | ||||
\(869\) | 23.8773 | + | 5.37091i | 0.809981 | + | 0.182196i | ||||
\(870\) | 0.104579 | + | 0.289006i | 0.00354557 | + | 0.00979822i | ||||
\(871\) | 54.1204 | 1.83380 | ||||||||
\(872\) | − | 15.2655i | − | 0.516956i | ||||||
\(873\) | −14.1192 | −0.477863 | ||||||||
\(874\) | 0.278319i | 0.00941427i | ||||||||
\(875\) | 17.0833 | − | 24.1487i | 0.577523 | − | 0.816375i | ||||
\(876\) | 8.00134i | 0.270340i | ||||||||
\(877\) | 20.6612 | 0.697679 | 0.348840 | − | 0.937182i | \(-0.386576\pi\) | ||||
0.348840 | + | 0.937182i | \(0.386576\pi\) | |||||||
\(878\) | −3.39980 | −0.114738 | ||||||||
\(879\) | 25.4567i | 0.858635i | ||||||||
\(880\) | −2.02446 | − | 15.9892i | −0.0682445 | − | 0.538996i | ||||
\(881\) | − | 11.5976i | − | 0.390732i | −0.980730 | − | 0.195366i | \(-0.937410\pi\) | ||
0.980730 | − | 0.195366i | \(-0.0625895\pi\) | |||||||
\(882\) | −3.91115 | − | 0.683408i | −0.131695 | − | 0.0230115i | ||||
\(883\) | 21.6925i | 0.730011i | 0.931005 | + | 0.365006i | \(0.118933\pi\) | ||||
−0.931005 | + | 0.365006i | \(0.881067\pi\) | |||||||
\(884\) | −28.9207 | −0.972710 | ||||||||
\(885\) | −4.17264 | − | 11.5311i | −0.140262 | − | 0.387615i | ||||
\(886\) | 8.73909i | 0.293595i | ||||||||
\(887\) | 30.7127i | 1.03123i | 0.856820 | + | 0.515616i | \(0.172437\pi\) | ||||
−0.856820 | + | 0.515616i | \(0.827563\pi\) | |||||||
\(888\) | − | 23.6999i | − | 0.795317i | ||||||
\(889\) | −10.9499 | − | 0.949462i | −0.367248 | − | 0.0318439i | ||||
\(890\) | 5.61032 | + | 15.5042i | 0.188058 | + | 0.519702i | ||||
\(891\) | −0.727850 | + | 3.23577i | −0.0243839 | + | 0.108403i | ||||
\(892\) | −27.4892 | −0.920407 | ||||||||
\(893\) | −0.860402 | −0.0287922 | ||||||||
\(894\) | 9.05756i | 0.302930i | ||||||||
\(895\) | 6.90084 | − | 2.49712i | 0.230670 | − | 0.0834697i | ||||
\(896\) | −30.4096 | − | 2.63681i | −1.01591 | − | 0.0880897i | ||||
\(897\) | 7.43207 | 0.248150 | ||||||||
\(898\) | 5.16692 | 0.172422 | ||||||||
\(899\) | 1.52331 | 0.0508052 | ||||||||
\(900\) | −6.44828 | + | 5.36987i | −0.214943 | + | 0.178996i | ||||
\(901\) | −39.3224 | −1.31002 | ||||||||
\(902\) | −2.34858 | + | 10.4410i | −0.0781993 | + | 0.347648i | ||||
\(903\) | 18.6050 | + | 1.61323i | 0.619136 | + | 0.0536851i | ||||
\(904\) | − | 11.0601i | − | 0.367854i | ||||||
\(905\) | 17.8145 | + | 49.2305i | 0.592173 | + | 1.63648i | ||||
\(906\) | 6.52146i | 0.216661i | ||||||||
\(907\) | 3.30534i | 0.109752i | 0.998493 | + | 0.0548761i | \(0.0174764\pi\) | ||||
−0.998493 | + | 0.0548761i | \(0.982524\pi\) | |||||||
\(908\) | 28.1322i | 0.933600i | ||||||||
\(909\) | 12.2453 | 0.406151 | ||||||||
\(910\) | −3.84790 | − | 14.4236i | −0.127557 | − | 0.478138i | ||||
\(911\) | 34.8475 | 1.15455 | 0.577275 | − | 0.816550i | \(-0.304116\pi\) | ||||
0.577275 | + | 0.816550i | \(0.304116\pi\) | |||||||
\(912\) | 0.638302 | 0.0211363 | ||||||||
\(913\) | −41.9907 | − | 9.44531i | −1.38969 | − | 0.312594i | ||||
\(914\) | −8.87419 | −0.293532 | ||||||||
\(915\) | −11.7236 | + | 4.24228i | −0.387570 | + | 0.140245i | ||||
\(916\) | 0.218217i | 0.00721011i | ||||||||
\(917\) | 21.5612 | + | 1.86956i | 0.712013 | + | 0.0617385i | ||||
\(918\) | 2.19710i | 0.0725151i | ||||||||
\(919\) | 7.59218i | 0.250443i | 0.992129 | + | 0.125222i | \(0.0399642\pi\) | ||||
−0.992129 | + | 0.125222i | \(0.960036\pi\) | |||||||
\(920\) | 2.65194 | + | 7.32867i | 0.0874319 | + | 0.241619i | ||||
\(921\) | − | 26.5078i | − | 0.873463i | ||||||
\(922\) | 9.35090 | 0.307956 | ||||||||
\(923\) | 46.0946i | 1.51722i | ||||||||
\(924\) | −4.46098 | + | 14.0350i | −0.146755 | + | 0.461717i | ||||
\(925\) | −36.3465 | − | 43.6459i | −1.19507 | − | 1.43507i | ||||
\(926\) | − | 11.3237i | − | 0.372121i | ||||||
\(927\) | 6.50035 | 0.213499 | ||||||||
\(928\) | − | 1.30986i | − | 0.0429982i | ||||||
\(929\) | − | 48.9705i | − | 1.60667i | −0.595528 | − | 0.803334i | \(-0.703057\pi\) | ||
0.595528 | − | 0.803334i | \(-0.296943\pi\) | |||||||
\(930\) | −2.71284 | − | 7.49696i | −0.0889574 | − | 0.245835i | ||||
\(931\) | 2.02532 | + | 0.353891i | 0.0663773 | + | 0.0115983i | ||||
\(932\) | 9.88898 | 0.323924 | ||||||||
\(933\) | 14.0105i | 0.458684i | ||||||||
\(934\) | −2.11834 | −0.0693142 | ||||||||
\(935\) | −28.4997 | + | 3.60846i | −0.932040 | + | 0.118009i | ||||
\(936\) | 9.28141i | 0.303372i | ||||||||
\(937\) | − | 35.3138i | − | 1.15365i | −0.816868 | − | 0.576825i | \(-0.804291\pi\) | ||
0.816868 | − | 0.576825i | \(-0.195709\pi\) | |||||||
\(938\) | 1.57709 | − | 18.1882i | 0.0514938 | − | 0.593865i | ||||
\(939\) | −26.0111 | −0.848839 | ||||||||
\(940\) | −10.3372 | + | 3.74061i | −0.337163 | + | 0.122005i | ||||
\(941\) | −58.8989 | −1.92005 | −0.960024 | − | 0.279918i | \(-0.909693\pi\) | ||||
−0.960024 | + | 0.279918i | \(0.909693\pi\) | |||||||
\(942\) | −6.53992 | −0.213082 | ||||||||
\(943\) | 9.50397i | 0.309492i | ||||||||
\(944\) | 11.9181i | 0.387901i | ||||||||
\(945\) | 5.71616 | − | 1.52495i | 0.185947 | − | 0.0496065i | ||||
\(946\) | −2.91398 | + | 12.9546i | −0.0947417 | + | 0.421189i | ||||
\(947\) | 45.3395i | 1.47334i | 0.676254 | + | 0.736668i | \(0.263602\pi\) | ||||
−0.676254 | + | 0.736668i | \(0.736398\pi\) | |||||||
\(948\) | 12.3843i | 0.402223i | ||||||||
\(949\) | 21.2094 | 0.688488 | ||||||||
\(950\) | −0.640093 | + | 0.533043i | −0.0207674 | + | 0.0172942i | ||||
\(951\) | 8.25895i | 0.267815i | ||||||||
\(952\) | −1.84708 | + | 21.3019i | −0.0598641 | + | 0.690397i | ||||
\(953\) | 23.0721 | 0.747380 | 0.373690 | − | 0.927554i | \(-0.378092\pi\) | ||||
0.373690 | + | 0.927554i | \(0.378092\pi\) | |||||||
\(954\) | 5.75791i | 0.186419i | ||||||||
\(955\) | 44.1349 | − | 15.9706i | 1.42817 | − | 0.516796i | ||||
\(956\) | 4.53757i | 0.146755i | ||||||||
\(957\) | −0.784121 | − | 0.176379i | −0.0253470 | − | 0.00570152i | ||||
\(958\) | 10.7572 | 0.347549 | ||||||||
\(959\) | 1.76536 | − | 20.3594i | 0.0570065 | − | 0.657441i | ||||
\(960\) | 2.69244 | − | 0.974282i | 0.0868982 | − | 0.0314448i | ||||
\(961\) | −8.51538 | −0.274690 | ||||||||
\(962\) | −28.6638 | −0.924157 | ||||||||
\(963\) | 12.8529 | 0.414179 | ||||||||
\(964\) | 44.4587 | 1.43192 | ||||||||
\(965\) | −40.7497 | + | 14.7456i | −1.31178 | + | 0.474678i | ||||
\(966\) | 0.216574 | − | 2.49769i | 0.00696814 | − | 0.0803617i | ||||
\(967\) | 6.94580 | 0.223362 | 0.111681 | − | 0.993744i | \(-0.464377\pi\) | ||||
0.111681 | + | 0.993744i | \(0.464377\pi\) | |||||||
\(968\) | −20.7391 | − | 9.82726i | −0.666579 | − | 0.315860i | ||||
\(969\) | − | 1.13773i | − | 0.0365492i | ||||||
\(970\) | −16.8389 | + | 6.09328i | −0.540663 | + | 0.195643i | ||||
\(971\) | 58.1686i | 1.86672i | 0.358942 | + | 0.933360i | \(0.383138\pi\) | ||||
−0.358942 | + | 0.933360i | \(0.616862\pi\) | |||||||
\(972\) | −1.67828 | −0.0538309 | ||||||||
\(973\) | 8.81113 | + | 0.764010i | 0.282472 | + | 0.0244930i | ||||
\(974\) | − | 3.67847i | − | 0.117866i | ||||||
\(975\) | 14.2341 | + | 17.0927i | 0.455856 | + | 0.547405i | ||||
\(976\) | 12.1170 | 0.387856 | ||||||||
\(977\) | − | 21.2862i | − | 0.681005i | −0.940244 | − | 0.340503i | \(-0.889403\pi\) | ||
0.940244 | − | 0.340503i | \(-0.110597\pi\) | |||||||
\(978\) | − | 6.27376i | − | 0.200613i | ||||||
\(979\) | −42.0654 | − | 9.46213i | −1.34442 | − | 0.302411i | ||||
\(980\) | 25.8716 | − | 4.55333i | 0.826439 | − | 0.145451i | ||||
\(981\) | − | 7.31694i | − | 0.233612i | ||||||
\(982\) | − | 6.06582i | − | 0.193568i | ||||||
\(983\) | −29.6052 | −0.944259 | −0.472130 | − | 0.881529i | \(-0.656515\pi\) | ||||
−0.472130 | + | 0.881529i | \(0.656515\pi\) | |||||||
\(984\) | −11.8689 | −0.378366 | ||||||||
\(985\) | 44.6757 | − | 16.1663i | 1.42349 | − | 0.515100i | ||||
\(986\) | −0.532420 | −0.0169557 | ||||||||
\(987\) | 7.72141 | + | 0.669521i | 0.245775 | + | 0.0213111i | ||||
\(988\) | − | 2.19293i | − | 0.0697662i | ||||||
\(989\) | 11.7919i | 0.374962i | ||||||||
\(990\) | 0.528380 | + | 4.17316i | 0.0167930 | + | 0.132632i | ||||
\(991\) | −14.2985 | −0.454208 | −0.227104 | − | 0.973870i | \(-0.572926\pi\) | ||||
−0.227104 | + | 0.973870i | \(0.572926\pi\) | |||||||
\(992\) | 33.9784i | 1.07881i | ||||||||
\(993\) | 21.0761 | 0.668829 | ||||||||
\(994\) | 15.4909 | + | 1.34321i | 0.491343 | + | 0.0426042i | ||||
\(995\) | 18.9990 | + | 52.5039i | 0.602308 | + | 1.66449i | ||||
\(996\) | − | 21.7791i | − | 0.690097i | ||||||
\(997\) | − | 42.2847i | − | 1.33917i | −0.742736 | − | 0.669585i | \(-0.766472\pi\) | ||
0.742736 | − | 0.669585i | \(-0.233528\pi\) | |||||||
\(998\) | 13.0526 | 0.413174 | ||||||||
\(999\) | − | 11.3596i | − | 0.359403i |
(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 | 1155.2.k.b.769.20 | yes | 48 | |
5.4 | even | 2 | 1155.2.k.a.769.29 | yes | 48 | ||
7.6 | odd | 2 | 1155.2.k.a.769.19 | ✓ | 48 | ||
11.10 | odd | 2 | inner | 1155.2.k.b.769.29 | yes | 48 | |
35.34 | odd | 2 | inner | 1155.2.k.b.769.30 | yes | 48 | |
55.54 | odd | 2 | 1155.2.k.a.769.20 | yes | 48 | ||
77.76 | even | 2 | 1155.2.k.a.769.30 | yes | 48 | ||
385.384 | even | 2 | inner | 1155.2.k.b.769.19 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.k.a.769.19 | ✓ | 48 | 7.6 | odd | 2 | ||
1155.2.k.a.769.20 | yes | 48 | 55.54 | odd | 2 | ||
1155.2.k.a.769.29 | yes | 48 | 5.4 | even | 2 | ||
1155.2.k.a.769.30 | yes | 48 | 77.76 | even | 2 | ||
1155.2.k.b.769.19 | yes | 48 | 385.384 | even | 2 | inner | |
1155.2.k.b.769.20 | yes | 48 | 1.1 | even | 1 | trivial | |
1155.2.k.b.769.29 | yes | 48 | 11.10 | odd | 2 | inner | |
1155.2.k.b.769.30 | yes | 48 | 35.34 | odd | 2 | inner |