Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(493,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.493");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.f (of order \(4\), degree \(2\), 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 493.16 | ||
Character | \(\chi\) | \(=\) | 950.493 |
Dual form | 950.2.f.d.607.16 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 2.10096 | − | 2.10096i | 1.21299 | − | 1.21299i | 0.242951 | − | 0.970039i | \(-0.421885\pi\) |
0.970039 | − | 0.242951i | \(-0.0781153\pi\) | |||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.97120 | 1.21299 | ||||||||
\(7\) | 0.978377 | − | 0.978377i | 0.369792 | − | 0.369792i | −0.497609 | − | 0.867401i | \(-0.665789\pi\) |
0.867401 | + | 0.497609i | \(0.165789\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | − | 5.82806i | − | 1.94269i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.43153 | 0.733135 | 0.366567 | − | 0.930392i | \(-0.380533\pi\) | ||||
0.366567 | + | 0.930392i | \(0.380533\pi\) | |||||||
\(12\) | 2.10096 | + | 2.10096i | 0.606495 | + | 0.606495i | ||||
\(13\) | 1.31299 | − | 1.31299i | 0.364159 | − | 0.364159i | −0.501183 | − | 0.865341i | \(-0.667102\pi\) |
0.865341 | + | 0.501183i | \(0.167102\pi\) | |||||||
\(14\) | 1.38363 | 0.369792 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −5.11008 | + | 5.11008i | −1.23938 | + | 1.23938i | −0.279120 | + | 0.960256i | \(0.590043\pi\) |
−0.960256 | + | 0.279120i | \(0.909957\pi\) | |||||||
\(18\) | 4.12106 | − | 4.12106i | 0.971343 | − | 0.971343i | ||||
\(19\) | 3.48940 | − | 2.61229i | 0.800524 | − | 0.599301i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 4.11106i | − | 0.897107i | ||||||
\(22\) | 1.71935 | + | 1.71935i | 0.366567 | + | 0.366567i | ||||
\(23\) | −1.29579 | − | 1.29579i | −0.270192 | − | 0.270192i | 0.558986 | − | 0.829177i | \(-0.311191\pi\) |
−0.829177 | + | 0.558986i | \(0.811191\pi\) | |||||||
\(24\) | 2.97120i | 0.606495i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.85685 | 0.364159 | ||||||||
\(27\) | −5.94163 | − | 5.94163i | −1.14347 | − | 1.14347i | ||||
\(28\) | 0.978377 | + | 0.978377i | 0.184896 | + | 0.184896i | ||||
\(29\) | −0.448895 | −0.0833577 | −0.0416789 | − | 0.999131i | \(-0.513271\pi\) | ||||
−0.0416789 | + | 0.999131i | \(0.513271\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.46410i | − | 0.622171i | −0.950382 | − | 0.311086i | \(-0.899307\pi\) | ||
0.950382 | − | 0.311086i | \(-0.100693\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 5.10855 | − | 5.10855i | 0.889285 | − | 0.889285i | ||||
\(34\) | −7.22675 | −1.23938 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.82806 | 0.971343 | ||||||||
\(37\) | 4.60388 | + | 4.60388i | 0.756874 | + | 0.756874i | 0.975752 | − | 0.218878i | \(-0.0702397\pi\) |
−0.218878 | + | 0.975752i | \(0.570240\pi\) | |||||||
\(38\) | 4.31455 | + | 0.620212i | 0.699912 | + | 0.100612i | ||||
\(39\) | − | 5.51709i | − | 0.883441i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.28197i | 0.981079i | 0.871419 | + | 0.490540i | \(0.163200\pi\) | ||||
−0.871419 | + | 0.490540i | \(0.836800\pi\) | |||||||
\(42\) | 2.90696 | − | 2.90696i | 0.448553 | − | 0.448553i | ||||
\(43\) | −7.27794 | − | 7.27794i | −1.10987 | − | 1.10987i | −0.993166 | − | 0.116709i | \(-0.962766\pi\) |
−0.116709 | − | 0.993166i | \(-0.537234\pi\) | |||||||
\(44\) | 2.43153i | 0.366567i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 1.83253i | − | 0.270192i | ||||||
\(47\) | 6.15951 | − | 6.15951i | 0.898456 | − | 0.898456i | −0.0968433 | − | 0.995300i | \(-0.530875\pi\) |
0.995300 | + | 0.0968433i | \(0.0308746\pi\) | |||||||
\(48\) | −2.10096 | + | 2.10096i | −0.303247 | + | 0.303247i | ||||
\(49\) | 5.08556i | 0.726508i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 21.4721i | 3.00670i | ||||||||
\(52\) | 1.31299 | + | 1.31299i | 0.182079 | + | 0.182079i | ||||
\(53\) | −9.37595 | + | 9.37595i | −1.28789 | + | 1.28789i | −0.351816 | + | 0.936069i | \(0.614436\pi\) |
−0.936069 | + | 0.351816i | \(0.885564\pi\) | |||||||
\(54\) | − | 8.40274i | − | 1.14347i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.38363i | 0.184896i | ||||||||
\(57\) | 1.84278 | − | 12.8194i | 0.244082 | − | 1.69797i | ||||
\(58\) | −0.317417 | − | 0.317417i | −0.0416789 | − | 0.0416789i | ||||
\(59\) | 5.89371 | 0.767296 | 0.383648 | − | 0.923479i | \(-0.374668\pi\) | ||||
0.383648 | + | 0.923479i | \(0.374668\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 2.44949 | − | 2.44949i | 0.311086 | − | 0.311086i | ||||
\(63\) | −5.70204 | − | 5.70204i | −0.718389 | − | 0.718389i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.22458 | 0.889285 | ||||||||
\(67\) | −4.17716 | − | 4.17716i | −0.510322 | − | 0.510322i | 0.404303 | − | 0.914625i | \(-0.367514\pi\) |
−0.914625 | + | 0.404303i | \(0.867514\pi\) | |||||||
\(68\) | −5.11008 | − | 5.11008i | −0.619688 | − | 0.619688i | ||||
\(69\) | −5.44482 | −0.655479 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.6544i | 1.73916i | 0.493790 | + | 0.869581i | \(0.335611\pi\) | ||||
−0.493790 | + | 0.869581i | \(0.664389\pi\) | |||||||
\(72\) | 4.12106 | + | 4.12106i | 0.485671 | + | 0.485671i | ||||
\(73\) | 8.04521 | + | 8.04521i | 0.941621 | + | 0.941621i | 0.998387 | − | 0.0567667i | \(-0.0180791\pi\) |
−0.0567667 | + | 0.998387i | \(0.518079\pi\) | |||||||
\(74\) | 6.51088i | 0.756874i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.61229 | + | 3.48940i | 0.299650 | + | 0.400262i | ||||
\(77\) | 2.37896 | − | 2.37896i | 0.271107 | − | 0.271107i | ||||
\(78\) | 3.90117 | − | 3.90117i | 0.441721 | − | 0.441721i | ||||
\(79\) | 6.23137 | 0.701084 | 0.350542 | − | 0.936547i | \(-0.385997\pi\) | ||||
0.350542 | + | 0.936547i | \(0.385997\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.48208 | −0.831342 | ||||||||
\(82\) | −4.44203 | + | 4.44203i | −0.490540 | + | 0.490540i | ||||
\(83\) | −11.7200 | − | 11.7200i | −1.28643 | − | 1.28643i | −0.936938 | − | 0.349494i | \(-0.886353\pi\) |
−0.349494 | − | 0.936938i | \(-0.613647\pi\) | |||||||
\(84\) | 4.11106 | 0.448553 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 10.2926i | − | 1.10987i | ||||||
\(87\) | −0.943110 | + | 0.943110i | −0.101112 | + | 0.101112i | ||||
\(88\) | −1.71935 | + | 1.71935i | −0.183284 | + | 0.183284i | ||||
\(89\) | −3.31375 | −0.351257 | −0.175628 | − | 0.984457i | \(-0.556196\pi\) | ||||
−0.175628 | + | 0.984457i | \(0.556196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 2.56920i | − | 0.269326i | ||||||
\(92\) | 1.29579 | − | 1.29579i | 0.135096 | − | 0.135096i | ||||
\(93\) | −7.27794 | − | 7.27794i | −0.754687 | − | 0.754687i | ||||
\(94\) | 8.71086 | 0.898456 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.97120 | −0.303247 | ||||||||
\(97\) | −6.78718 | − | 6.78718i | −0.689134 | − | 0.689134i | 0.272907 | − | 0.962041i | \(-0.412015\pi\) |
−0.962041 | + | 0.272907i | \(0.912015\pi\) | |||||||
\(98\) | −3.59603 | + | 3.59603i | −0.363254 | + | 0.363254i | ||||
\(99\) | − | 14.1711i | − | 1.42425i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | −15.1831 | + | 15.1831i | −1.50335 | + | 1.50335i | ||||
\(103\) | −11.0298 | + | 11.0298i | −1.08680 | + | 1.08680i | −0.0909447 | + | 0.995856i | \(0.528989\pi\) |
−0.995856 | + | 0.0909447i | \(0.971011\pi\) | |||||||
\(104\) | 1.85685i | 0.182079i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −13.2596 | −1.28789 | ||||||||
\(107\) | 3.75484 | + | 3.75484i | 0.362994 | + | 0.362994i | 0.864914 | − | 0.501920i | \(-0.167373\pi\) |
−0.501920 | + | 0.864914i | \(0.667373\pi\) | |||||||
\(108\) | 5.94163 | − | 5.94163i | 0.571734 | − | 0.571734i | ||||
\(109\) | 10.9794 | 1.05163 | 0.525816 | − | 0.850598i | \(-0.323760\pi\) | ||||
0.525816 | + | 0.850598i | \(0.323760\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 19.3451 | 1.83616 | ||||||||
\(112\) | −0.978377 | + | 0.978377i | −0.0924479 | + | 0.0924479i | ||||
\(113\) | 2.52329 | − | 2.52329i | 0.237371 | − | 0.237371i | −0.578390 | − | 0.815761i | \(-0.696319\pi\) |
0.815761 | + | 0.578390i | \(0.196319\pi\) | |||||||
\(114\) | 10.3677 | − | 7.76165i | 0.971027 | − | 0.726945i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 0.448895i | − | 0.0416789i | ||||||
\(117\) | −7.65220 | − | 7.65220i | −0.707446 | − | 0.707446i | ||||
\(118\) | 4.16749 | + | 4.16749i | 0.383648 | + | 0.383648i | ||||
\(119\) | 9.99917i | 0.916622i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.08765 | −0.462513 | ||||||||
\(122\) | −1.41421 | − | 1.41421i | −0.128037 | − | 0.128037i | ||||
\(123\) | 13.1982 | + | 13.1982i | 1.19004 | + | 1.19004i | ||||
\(124\) | 3.46410 | 0.311086 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | − | 8.06390i | − | 0.718389i | ||||||
\(127\) | 9.25728 | + | 9.25728i | 0.821451 | + | 0.821451i | 0.986316 | − | 0.164865i | \(-0.0527190\pi\) |
−0.164865 | + | 0.986316i | \(0.552719\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | −30.5813 | −2.69253 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.65611 | −0.319436 | −0.159718 | − | 0.987163i | \(-0.551059\pi\) | ||||
−0.159718 | + | 0.987163i | \(0.551059\pi\) | |||||||
\(132\) | 5.10855 | + | 5.10855i | 0.444642 | + | 0.444642i | ||||
\(133\) | 0.858147 | − | 5.96976i | 0.0744107 | − | 0.517644i | ||||
\(134\) | − | 5.90740i | − | 0.510322i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 7.22675i | − | 0.619688i | ||||||
\(137\) | 9.68455 | − | 9.68455i | 0.827407 | − | 0.827407i | −0.159751 | − | 0.987157i | \(-0.551069\pi\) |
0.987157 | + | 0.159751i | \(0.0510690\pi\) | |||||||
\(138\) | −3.85007 | − | 3.85007i | −0.327740 | − | 0.327740i | ||||
\(139\) | 4.36152i | 0.369939i | 0.982744 | + | 0.184969i | \(0.0592186\pi\) | ||||
−0.982744 | + | 0.184969i | \(0.940781\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 25.8817i | − | 2.17964i | ||||||
\(142\) | −10.3623 | + | 10.3623i | −0.869581 | + | 0.869581i | ||||
\(143\) | 3.19259 | − | 3.19259i | 0.266977 | − | 0.266977i | ||||
\(144\) | 5.82806i | 0.485671i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 11.3776i | 0.941621i | ||||||||
\(147\) | 10.6845 | + | 10.6845i | 0.881247 | + | 0.881247i | ||||
\(148\) | −4.60388 | + | 4.60388i | −0.378437 | + | 0.378437i | ||||
\(149\) | 10.8631i | 0.889937i | 0.895546 | + | 0.444969i | \(0.146785\pi\) | ||||
−0.895546 | + | 0.444969i | \(0.853215\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.85777i | 0.395320i | 0.980271 | + | 0.197660i | \(0.0633341\pi\) | ||||
−0.980271 | + | 0.197660i | \(0.936666\pi\) | |||||||
\(152\) | −0.620212 | + | 4.31455i | −0.0503058 | + | 0.349956i | ||||
\(153\) | 29.7818 | + | 29.7818i | 2.40772 | + | 2.40772i | ||||
\(154\) | 3.36435 | 0.271107 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.51709 | 0.441721 | ||||||||
\(157\) | −17.0054 | + | 17.0054i | −1.35718 | + | 1.35718i | −0.479795 | + | 0.877381i | \(0.659289\pi\) |
−0.877381 | + | 0.479795i | \(0.840711\pi\) | |||||||
\(158\) | 4.40624 | + | 4.40624i | 0.350542 | + | 0.350542i | ||||
\(159\) | 39.3970i | 3.12438i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.53555 | −0.199829 | ||||||||
\(162\) | −5.29063 | − | 5.29063i | −0.415671 | − | 0.415671i | ||||
\(163\) | −12.0706 | − | 12.0706i | −0.945442 | − | 0.945442i | 0.0531445 | − | 0.998587i | \(-0.483076\pi\) |
−0.998587 | + | 0.0531445i | \(0.983076\pi\) | |||||||
\(164\) | −6.28197 | −0.490540 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 16.5745i | − | 1.28643i | ||||||
\(167\) | 14.2631 | + | 14.2631i | 1.10371 | + | 1.10371i | 0.993959 | + | 0.109756i | \(0.0350068\pi\) |
0.109756 | + | 0.993959i | \(0.464993\pi\) | |||||||
\(168\) | 2.90696 | + | 2.90696i | 0.224277 | + | 0.224277i | ||||
\(169\) | 9.55210i | 0.734777i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −15.2246 | − | 20.3364i | −1.16425 | − | 1.55517i | ||||
\(172\) | 7.27794 | − | 7.27794i | 0.554937 | − | 0.554937i | ||||
\(173\) | −17.2504 | + | 17.2504i | −1.31152 | + | 1.31152i | −0.391226 | + | 0.920295i | \(0.627949\pi\) |
−0.920295 | + | 0.391226i | \(0.872051\pi\) | |||||||
\(174\) | −1.33376 | −0.101112 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.43153 | −0.183284 | ||||||||
\(177\) | 12.3825 | − | 12.3825i | 0.930722 | − | 0.930722i | ||||
\(178\) | −2.34317 | − | 2.34317i | −0.175628 | − | 0.175628i | ||||
\(179\) | −4.39957 | −0.328839 | −0.164420 | − | 0.986390i | \(-0.552575\pi\) | ||||
−0.164420 | + | 0.986390i | \(0.552575\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.74263i | 0.426847i | 0.976960 | + | 0.213423i | \(0.0684613\pi\) | ||||
−0.976960 | + | 0.213423i | \(0.931539\pi\) | |||||||
\(182\) | 1.81670 | − | 1.81670i | 0.134663 | − | 0.134663i | ||||
\(183\) | −4.20192 | + | 4.20192i | −0.310615 | + | 0.310615i | ||||
\(184\) | 1.83253 | 0.135096 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | − | 10.2926i | − | 0.754687i | ||||||
\(187\) | −12.4253 | + | 12.4253i | −0.908630 | + | 0.908630i | ||||
\(188\) | 6.15951 | + | 6.15951i | 0.449228 | + | 0.449228i | ||||
\(189\) | −11.6263 | −0.845690 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.3451 | 1.68920 | 0.844598 | − | 0.535401i | \(-0.179840\pi\) | ||||
0.844598 | + | 0.535401i | \(0.179840\pi\) | |||||||
\(192\) | −2.10096 | − | 2.10096i | −0.151624 | − | 0.151624i | ||||
\(193\) | 2.53207 | − | 2.53207i | 0.182263 | − | 0.182263i | −0.610078 | − | 0.792341i | \(-0.708862\pi\) |
0.792341 | + | 0.610078i | \(0.208862\pi\) | |||||||
\(194\) | − | 9.59852i | − | 0.689134i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.08556 | −0.363254 | ||||||||
\(197\) | 2.09885 | − | 2.09885i | 0.149537 | − | 0.149537i | −0.628374 | − | 0.777911i | \(-0.716279\pi\) |
0.777911 | + | 0.628374i | \(0.216279\pi\) | |||||||
\(198\) | 10.0205 | − | 10.0205i | 0.712125 | − | 0.712125i | ||||
\(199\) | − | 24.2238i | − | 1.71718i | −0.512666 | − | 0.858588i | \(-0.671342\pi\) | ||
0.512666 | − | 0.858588i | \(-0.328658\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −17.5521 | −1.23803 | ||||||||
\(202\) | −4.24264 | − | 4.24264i | −0.298511 | − | 0.298511i | ||||
\(203\) | −0.439189 | + | 0.439189i | −0.0308250 | + | 0.0308250i | ||||
\(204\) | −21.4721 | −1.50335 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −15.5985 | −1.08680 | ||||||||
\(207\) | −7.55196 | + | 7.55196i | −0.524898 | + | 0.524898i | ||||
\(208\) | −1.31299 | + | 1.31299i | −0.0910397 | + | 0.0910397i | ||||
\(209\) | 8.48460 | − | 6.35187i | 0.586892 | − | 0.439368i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 4.34969i | − | 0.299445i | −0.988728 | − | 0.149723i | \(-0.952162\pi\) | ||
0.988728 | − | 0.149723i | \(-0.0478381\pi\) | |||||||
\(212\) | −9.37595 | − | 9.37595i | −0.643943 | − | 0.643943i | ||||
\(213\) | 30.7884 | + | 30.7884i | 2.10959 | + | 2.10959i | ||||
\(214\) | 5.31014i | 0.362994i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 8.40274 | 0.571734 | ||||||||
\(217\) | −3.38920 | − | 3.38920i | −0.230074 | − | 0.230074i | ||||
\(218\) | 7.76358 | + | 7.76358i | 0.525816 | + | 0.525816i | ||||
\(219\) | 33.8053 | 2.28435 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.4190i | 0.902660i | ||||||||
\(222\) | 13.6791 | + | 13.6791i | 0.918080 | + | 0.918080i | ||||
\(223\) | 8.40384 | − | 8.40384i | 0.562762 | − | 0.562762i | −0.367329 | − | 0.930091i | \(-0.619728\pi\) |
0.930091 | + | 0.367329i | \(0.119728\pi\) | |||||||
\(224\) | −1.38363 | −0.0924479 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.56847 | 0.237371 | ||||||||
\(227\) | −8.32589 | − | 8.32589i | −0.552609 | − | 0.552609i | 0.374584 | − | 0.927193i | \(-0.377785\pi\) |
−0.927193 | + | 0.374584i | \(0.877785\pi\) | |||||||
\(228\) | 12.8194 | + | 1.84278i | 0.848986 | + | 0.122041i | ||||
\(229\) | − | 19.4833i | − | 1.28750i | −0.765238 | − | 0.643748i | \(-0.777379\pi\) | ||
0.765238 | − | 0.643748i | \(-0.222621\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 9.99618i | − | 0.657700i | ||||||
\(232\) | 0.317417 | − | 0.317417i | 0.0208394 | − | 0.0208394i | ||||
\(233\) | −13.2953 | − | 13.2953i | −0.871007 | − | 0.871007i | 0.121575 | − | 0.992582i | \(-0.461205\pi\) |
−0.992582 | + | 0.121575i | \(0.961205\pi\) | |||||||
\(234\) | − | 10.8218i | − | 0.707446i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.89371i | 0.383648i | ||||||||
\(237\) | 13.0919 | − | 13.0919i | 0.850407 | − | 0.850407i | ||||
\(238\) | −7.07048 | + | 7.07048i | −0.458311 | + | 0.458311i | ||||
\(239\) | 13.7943i | 0.892280i | 0.894963 | + | 0.446140i | \(0.147202\pi\) | ||||
−0.894963 | + | 0.446140i | \(0.852798\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 16.5745i | − | 1.06766i | −0.845592 | − | 0.533830i | \(-0.820752\pi\) | ||
0.845592 | − | 0.533830i | \(-0.179248\pi\) | |||||||
\(242\) | −3.59751 | − | 3.59751i | −0.231257 | − | 0.231257i | ||||
\(243\) | 2.10535 | − | 2.10535i | 0.135058 | − | 0.135058i | ||||
\(244\) | − | 2.00000i | − | 0.128037i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 18.6650i | 1.19004i | ||||||||
\(247\) | 1.15164 | − | 8.01148i | 0.0732773 | − | 0.509758i | ||||
\(248\) | 2.44949 | + | 2.44949i | 0.155543 | + | 0.155543i | ||||
\(249\) | −49.2463 | −3.12086 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.63848 | −0.229659 | −0.114830 | − | 0.993385i | \(-0.536632\pi\) | ||||
−0.114830 | + | 0.993385i | \(0.536632\pi\) | |||||||
\(252\) | 5.70204 | − | 5.70204i | 0.359195 | − | 0.359195i | ||||
\(253\) | −3.15077 | − | 3.15077i | −0.198087 | − | 0.198087i | ||||
\(254\) | 13.0918i | 0.821451i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.1201 | − | 11.1201i | −0.693650 | − | 0.693650i | 0.269383 | − | 0.963033i | \(-0.413180\pi\) |
−0.963033 | + | 0.269383i | \(0.913180\pi\) | |||||||
\(258\) | −21.6242 | − | 21.6242i | −1.34627 | − | 1.34627i | ||||
\(259\) | 9.00867 | 0.559772 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.61619i | 0.161938i | ||||||||
\(262\) | −2.58526 | − | 2.58526i | −0.159718 | − | 0.159718i | ||||
\(263\) | −6.36300 | − | 6.36300i | −0.392359 | − | 0.392359i | 0.483168 | − | 0.875528i | \(-0.339486\pi\) |
−0.875528 | + | 0.483168i | \(0.839486\pi\) | |||||||
\(264\) | 7.22458i | 0.444642i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.82806 | − | 3.61445i | 0.296027 | − | 0.221616i | ||||
\(267\) | −6.96205 | + | 6.96205i | −0.426071 | + | 0.426071i | ||||
\(268\) | 4.17716 | − | 4.17716i | 0.255161 | − | 0.255161i | ||||
\(269\) | 10.6004 | 0.646318 | 0.323159 | − | 0.946345i | \(-0.395255\pi\) | ||||
0.323159 | + | 0.946345i | \(0.395255\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.38098 | −0.144635 | −0.0723173 | − | 0.997382i | \(-0.523039\pi\) | ||||
−0.0723173 | + | 0.997382i | \(0.523039\pi\) | |||||||
\(272\) | 5.11008 | − | 5.11008i | 0.309844 | − | 0.309844i | ||||
\(273\) | −5.39779 | − | 5.39779i | −0.326689 | − | 0.326689i | ||||
\(274\) | 13.6960 | 0.827407 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 5.44482i | − | 0.327740i | ||||||
\(277\) | −9.30625 | + | 9.30625i | −0.559159 | + | 0.559159i | −0.929068 | − | 0.369909i | \(-0.879389\pi\) |
0.369909 | + | 0.929068i | \(0.379389\pi\) | |||||||
\(278\) | −3.08406 | + | 3.08406i | −0.184969 | + | 0.184969i | ||||
\(279\) | −20.1890 | −1.20868 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.4627i | 0.743465i | 0.928340 | + | 0.371732i | \(0.121236\pi\) | ||||
−0.928340 | + | 0.371732i | \(0.878764\pi\) | |||||||
\(282\) | 18.3012 | − | 18.3012i | 1.08982 | − | 1.08982i | ||||
\(283\) | 9.26944 | + | 9.26944i | 0.551011 | + | 0.551011i | 0.926733 | − | 0.375722i | \(-0.122605\pi\) |
−0.375722 | + | 0.926733i | \(0.622605\pi\) | |||||||
\(284\) | −14.6544 | −0.869581 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.51500 | 0.266977 | ||||||||
\(287\) | 6.14614 | + | 6.14614i | 0.362795 | + | 0.362795i | ||||
\(288\) | −4.12106 | + | 4.12106i | −0.242836 | + | 0.242836i | ||||
\(289\) | − | 35.2258i | − | 2.07211i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −28.5192 | −1.67182 | ||||||||
\(292\) | −8.04521 | + | 8.04521i | −0.470810 | + | 0.470810i | ||||
\(293\) | 15.8630 | − | 15.8630i | 0.926724 | − | 0.926724i | −0.0707683 | − | 0.997493i | \(-0.522545\pi\) |
0.997493 | + | 0.0707683i | \(0.0225451\pi\) | |||||||
\(294\) | 15.1102i | 0.881247i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.51088 | −0.378437 | ||||||||
\(297\) | −14.4473 | − | 14.4473i | −0.838316 | − | 0.838316i | ||||
\(298\) | −7.68135 | + | 7.68135i | −0.444969 | + | 0.444969i | ||||
\(299\) | −3.40274 | −0.196785 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.2411 | −0.820845 | ||||||||
\(302\) | −3.43496 | + | 3.43496i | −0.197660 | + | 0.197660i | ||||
\(303\) | −12.6058 | + | 12.6058i | −0.724182 | + | 0.724182i | ||||
\(304\) | −3.48940 | + | 2.61229i | −0.200131 | + | 0.149825i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 42.1179i | 2.40772i | ||||||||
\(307\) | −15.6620 | − | 15.6620i | −0.893875 | − | 0.893875i | 0.101010 | − | 0.994885i | \(-0.467793\pi\) |
−0.994885 | + | 0.101010i | \(0.967793\pi\) | |||||||
\(308\) | 2.37896 | + | 2.37896i | 0.135554 | + | 0.135554i | ||||
\(309\) | 46.3464i | 2.63656i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.5676 | −0.599236 | −0.299618 | − | 0.954059i | \(-0.596859\pi\) | ||||
−0.299618 | + | 0.954059i | \(0.596859\pi\) | |||||||
\(312\) | 3.90117 | + | 3.90117i | 0.220860 | + | 0.220860i | ||||
\(313\) | −3.89448 | − | 3.89448i | −0.220129 | − | 0.220129i | 0.588424 | − | 0.808553i | \(-0.299749\pi\) |
−0.808553 | + | 0.588424i | \(0.799749\pi\) | |||||||
\(314\) | −24.0492 | −1.35718 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.23137i | 0.350542i | ||||||||
\(317\) | −3.77959 | − | 3.77959i | −0.212283 | − | 0.212283i | 0.592954 | − | 0.805237i | \(-0.297962\pi\) |
−0.805237 | + | 0.592954i | \(0.797962\pi\) | |||||||
\(318\) | −27.8579 | + | 27.8579i | −1.56219 | + | 1.56219i | ||||
\(319\) | −1.09150 | −0.0611124 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.7775 | 0.880615 | ||||||||
\(322\) | −1.79290 | − | 1.79290i | −0.0999147 | − | 0.0999147i | ||||
\(323\) | −4.48211 | + | 31.1801i | −0.249392 | + | 1.73491i | ||||
\(324\) | − | 7.48208i | − | 0.415671i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 17.0704i | − | 0.945442i | ||||||
\(327\) | 23.0672 | − | 23.0672i | 1.27562 | − | 1.27562i | ||||
\(328\) | −4.44203 | − | 4.44203i | −0.245270 | − | 0.245270i | ||||
\(329\) | − | 12.0526i | − | 0.664484i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.73087i | 0.369962i | 0.982742 | + | 0.184981i | \(0.0592224\pi\) | ||||
−0.982742 | + | 0.184981i | \(0.940778\pi\) | |||||||
\(332\) | 11.7200 | − | 11.7200i | 0.643216 | − | 0.643216i | ||||
\(333\) | 26.8317 | − | 26.8317i | 1.47037 | − | 1.47037i | ||||
\(334\) | 20.1711i | 1.10371i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.11106i | 0.224277i | ||||||||
\(337\) | −2.68796 | − | 2.68796i | −0.146423 | − | 0.146423i | 0.630095 | − | 0.776518i | \(-0.283016\pi\) |
−0.776518 | + | 0.630095i | \(0.783016\pi\) | |||||||
\(338\) | −6.75435 | + | 6.75435i | −0.367388 | + | 0.367388i | ||||
\(339\) | − | 10.6026i | − | 0.575857i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 8.42308i | − | 0.456135i | ||||||
\(342\) | 3.61463 | − | 25.1454i | 0.195457 | − | 1.35971i | ||||
\(343\) | 11.8242 | + | 11.8242i | 0.638448 | + | 0.638448i | ||||
\(344\) | 10.2926 | 0.554937 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −24.3957 | −1.31152 | ||||||||
\(347\) | −10.7345 | + | 10.7345i | −0.576258 | + | 0.576258i | −0.933870 | − | 0.357612i | \(-0.883591\pi\) |
0.357612 | + | 0.933870i | \(0.383591\pi\) | |||||||
\(348\) | −0.943110 | − | 0.943110i | −0.0505560 | − | 0.0505560i | ||||
\(349\) | − | 19.2111i | − | 1.02835i | −0.857686 | − | 0.514174i | \(-0.828098\pi\) | ||
0.857686 | − | 0.514174i | \(-0.171902\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.6026 | −0.832808 | ||||||||
\(352\) | −1.71935 | − | 1.71935i | −0.0916418 | − | 0.0916418i | ||||
\(353\) | −5.31409 | − | 5.31409i | −0.282840 | − | 0.282840i | 0.551400 | − | 0.834241i | \(-0.314094\pi\) |
−0.834241 | + | 0.551400i | \(0.814094\pi\) | |||||||
\(354\) | 17.5114 | 0.930722 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 3.31375i | − | 0.175628i | ||||||
\(357\) | 21.0078 | + | 21.0078i | 1.11185 | + | 1.11185i | ||||
\(358\) | −3.11097 | − | 3.11097i | −0.164420 | − | 0.164420i | ||||
\(359\) | 8.87861i | 0.468595i | 0.972165 | + | 0.234297i | \(0.0752790\pi\) | ||||
−0.972165 | + | 0.234297i | \(0.924721\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.35187 | − | 18.2307i | 0.281677 | − | 0.959509i | ||||
\(362\) | −4.06065 | + | 4.06065i | −0.213423 | + | 0.213423i | ||||
\(363\) | −10.6889 | + | 10.6889i | −0.561024 | + | 0.561024i | ||||
\(364\) | 2.56920 | 0.134663 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.94241 | −0.310615 | ||||||||
\(367\) | 3.22233 | − | 3.22233i | 0.168204 | − | 0.168204i | −0.617985 | − | 0.786190i | \(-0.712051\pi\) |
0.786190 | + | 0.617985i | \(0.212051\pi\) | |||||||
\(368\) | 1.29579 | + | 1.29579i | 0.0675479 | + | 0.0675479i | ||||
\(369\) | 36.6117 | 1.90593 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.3464i | 0.952499i | ||||||||
\(372\) | 7.27794 | − | 7.27794i | 0.377343 | − | 0.377343i | ||||
\(373\) | 14.8413 | − | 14.8413i | 0.768456 | − | 0.768456i | −0.209379 | − | 0.977835i | \(-0.567144\pi\) |
0.977835 | + | 0.209379i | \(0.0671442\pi\) | |||||||
\(374\) | −17.5721 | −0.908630 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.71086i | 0.449228i | ||||||||
\(377\) | −0.589396 | + | 0.589396i | −0.0303554 | + | 0.0303554i | ||||
\(378\) | −8.22105 | − | 8.22105i | −0.422845 | − | 0.422845i | ||||
\(379\) | 17.7572 | 0.912126 | 0.456063 | − | 0.889947i | \(-0.349259\pi\) | ||||
0.456063 | + | 0.889947i | \(0.349259\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 38.8983 | 1.99282 | ||||||||
\(382\) | 16.5075 | + | 16.5075i | 0.844598 | + | 0.844598i | ||||
\(383\) | −7.73086 | + | 7.73086i | −0.395028 | + | 0.395028i | −0.876475 | − | 0.481447i | \(-0.840111\pi\) |
0.481447 | + | 0.876475i | \(0.340111\pi\) | |||||||
\(384\) | − | 2.97120i | − | 0.151624i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.58089 | 0.182263 | ||||||||
\(387\) | −42.4162 | + | 42.4162i | −2.15614 | + | 2.15614i | ||||
\(388\) | 6.78718 | − | 6.78718i | 0.344567 | − | 0.344567i | ||||
\(389\) | − | 9.37806i | − | 0.475487i | −0.971328 | − | 0.237743i | \(-0.923592\pi\) | ||
0.971328 | − | 0.237743i | \(-0.0764077\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.2432 | 0.669738 | ||||||||
\(392\) | −3.59603 | − | 3.59603i | −0.181627 | − | 0.181627i | ||||
\(393\) | −7.68135 | + | 7.68135i | −0.387473 | + | 0.387473i | ||||
\(394\) | 2.96822 | 0.149537 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 14.1711 | 0.712125 | ||||||||
\(397\) | −22.6813 | + | 22.6813i | −1.13834 | + | 1.13834i | −0.149593 | + | 0.988748i | \(0.547796\pi\) |
−0.988748 | + | 0.149593i | \(0.952204\pi\) | |||||||
\(398\) | 17.1288 | − | 17.1288i | 0.858588 | − | 0.858588i | ||||
\(399\) | −10.7393 | − | 14.3451i | −0.537637 | − | 0.718156i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 5.38418i | − | 0.268873i | −0.990922 | − | 0.134437i | \(-0.957078\pi\) | ||
0.990922 | − | 0.134437i | \(-0.0429225\pi\) | |||||||
\(402\) | −12.4112 | − | 12.4112i | −0.619015 | − | 0.619015i | ||||
\(403\) | −4.54834 | − | 4.54834i | −0.226569 | − | 0.226569i | ||||
\(404\) | − | 6.00000i | − | 0.298511i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.621107 | −0.0308250 | ||||||||
\(407\) | 11.1945 | + | 11.1945i | 0.554891 | + | 0.554891i | ||||
\(408\) | −15.1831 | − | 15.1831i | −0.751675 | − | 0.751675i | ||||
\(409\) | 32.0256 | 1.58356 | 0.791781 | − | 0.610805i | \(-0.209154\pi\) | ||||
0.791781 | + | 0.610805i | \(0.209154\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 40.6937i | − | 2.00727i | ||||||
\(412\) | −11.0298 | − | 11.0298i | −0.543400 | − | 0.543400i | ||||
\(413\) | 5.76627 | − | 5.76627i | 0.283740 | − | 0.283740i | ||||
\(414\) | −10.6801 | −0.524898 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.85685 | −0.0910397 | ||||||||
\(417\) | 9.16337 | + | 9.16337i | 0.448732 | + | 0.448732i | ||||
\(418\) | 10.4910 | + | 1.50807i | 0.513130 | + | 0.0737619i | ||||
\(419\) | − | 11.8096i | − | 0.576937i | −0.957489 | − | 0.288468i | \(-0.906854\pi\) | ||
0.957489 | − | 0.288468i | \(-0.0931460\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 19.1530i | − | 0.933462i | −0.884399 | − | 0.466731i | \(-0.845432\pi\) | ||
0.884399 | − | 0.466731i | \(-0.154568\pi\) | |||||||
\(422\) | 3.07570 | − | 3.07570i | 0.149723 | − | 0.149723i | ||||
\(423\) | −35.8980 | − | 35.8980i | −1.74542 | − | 1.74542i | ||||
\(424\) | − | 13.2596i | − | 0.643943i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 43.5414i | 2.10959i | ||||||||
\(427\) | −1.95675 | + | 1.95675i | −0.0946940 | + | 0.0946940i | ||||
\(428\) | −3.75484 | + | 3.75484i | −0.181497 | + | 0.181497i | ||||
\(429\) | − | 13.4150i | − | 0.647682i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 26.3206i | − | 1.26782i | −0.773407 | − | 0.633909i | \(-0.781449\pi\) | ||
0.773407 | − | 0.633909i | \(-0.218551\pi\) | |||||||
\(432\) | 5.94163 | + | 5.94163i | 0.285867 | + | 0.285867i | ||||
\(433\) | 27.9402 | − | 27.9402i | 1.34272 | − | 1.34272i | 0.449379 | − | 0.893341i | \(-0.351645\pi\) |
0.893341 | − | 0.449379i | \(-0.148355\pi\) | |||||||
\(434\) | − | 4.79305i | − | 0.230074i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.9794i | 0.525816i | ||||||||
\(437\) | −7.90654 | − | 1.13656i | −0.378221 | − | 0.0543689i | ||||
\(438\) | 23.9040 | + | 23.9040i | 1.14218 | + | 1.14218i | ||||
\(439\) | −19.8071 | −0.945343 | −0.472671 | − | 0.881239i | \(-0.656710\pi\) | ||||
−0.472671 | + | 0.881239i | \(0.656710\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 29.6389 | 1.41138 | ||||||||
\(442\) | −9.48867 | + | 9.48867i | −0.451330 | + | 0.451330i | ||||
\(443\) | −21.6600 | − | 21.6600i | −1.02910 | − | 1.02910i | −0.999564 | − | 0.0295348i | \(-0.990597\pi\) |
−0.0295348 | − | 0.999564i | \(-0.509403\pi\) | |||||||
\(444\) | 19.3451i | 0.918080i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 11.8848 | 0.562762 | ||||||||
\(447\) | 22.8229 | + | 22.8229i | 1.07948 | + | 1.07948i | ||||
\(448\) | −0.978377 | − | 0.978377i | −0.0462240 | − | 0.0462240i | ||||
\(449\) | 38.7528 | 1.82886 | 0.914429 | − | 0.404746i | \(-0.132640\pi\) | ||||
0.914429 | + | 0.404746i | \(0.132640\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.2748i | 0.719263i | ||||||||
\(452\) | 2.52329 | + | 2.52329i | 0.118685 | + | 0.118685i | ||||
\(453\) | 10.2060 | + | 10.2060i | 0.479518 | + | 0.479518i | ||||
\(454\) | − | 11.7746i | − | 0.552609i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.76165 | + | 10.3677i | 0.363473 | + | 0.485514i | ||||
\(457\) | −1.12501 | + | 1.12501i | −0.0526257 | + | 0.0526257i | −0.732930 | − | 0.680304i | \(-0.761848\pi\) |
0.680304 | + | 0.732930i | \(0.261848\pi\) | |||||||
\(458\) | 13.7768 | − | 13.7768i | 0.643748 | − | 0.643748i | ||||
\(459\) | 60.7244 | 2.83437 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.58920 | 0.400039 | 0.200019 | − | 0.979792i | \(-0.435899\pi\) | ||||
0.200019 | + | 0.979792i | \(0.435899\pi\) | |||||||
\(462\) | 7.06837 | − | 7.06837i | 0.328850 | − | 0.328850i | ||||
\(463\) | −4.18856 | − | 4.18856i | −0.194659 | − | 0.194659i | 0.603047 | − | 0.797706i | \(-0.293953\pi\) |
−0.797706 | + | 0.603047i | \(0.793953\pi\) | |||||||
\(464\) | 0.448895 | 0.0208394 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 18.8025i | − | 0.871007i | ||||||
\(467\) | 12.3180 | − | 12.3180i | 0.570008 | − | 0.570008i | −0.362122 | − | 0.932131i | \(-0.617948\pi\) |
0.932131 | + | 0.362122i | \(0.117948\pi\) | |||||||
\(468\) | 7.65220 | − | 7.65220i | 0.353723 | − | 0.353723i | ||||
\(469\) | −8.17368 | −0.377426 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 71.4551i | 3.29248i | ||||||||
\(472\) | −4.16749 | + | 4.16749i | −0.191824 | + | 0.191824i | ||||
\(473\) | −17.6965 | − | 17.6965i | −0.813688 | − | 0.813688i | ||||
\(474\) | 18.5147 | 0.850407 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −9.99917 | −0.458311 | ||||||||
\(477\) | 54.6436 | + | 54.6436i | 2.50196 | + | 2.50196i | ||||
\(478\) | −9.75405 | + | 9.75405i | −0.446140 | + | 0.446140i | ||||
\(479\) | 29.5368i | 1.34957i | 0.738014 | + | 0.674786i | \(0.235764\pi\) | ||||
−0.738014 | + | 0.674786i | \(0.764236\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.0897 | 0.551245 | ||||||||
\(482\) | 11.7200 | − | 11.7200i | 0.533830 | − | 0.533830i | ||||
\(483\) | −5.32709 | + | 5.32709i | −0.242391 | + | 0.242391i | ||||
\(484\) | − | 5.08765i | − | 0.231257i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.97742 | 0.135058 | ||||||||
\(487\) | −20.2288 | − | 20.2288i | −0.916655 | − | 0.916655i | 0.0801298 | − | 0.996784i | \(-0.474467\pi\) |
−0.996784 | + | 0.0801298i | \(0.974467\pi\) | |||||||
\(488\) | 1.41421 | − | 1.41421i | 0.0640184 | − | 0.0640184i | ||||
\(489\) | −50.7197 | −2.29362 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.5192 | 1.19679 | 0.598397 | − | 0.801200i | \(-0.295805\pi\) | ||||
0.598397 | + | 0.801200i | \(0.295805\pi\) | |||||||
\(492\) | −13.1982 | + | 13.1982i | −0.595019 | + | 0.595019i | ||||
\(493\) | 2.29389 | − | 2.29389i | 0.103312 | − | 0.103312i | ||||
\(494\) | 6.47931 | − | 4.85064i | 0.291518 | − | 0.218241i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.46410i | 0.155543i | ||||||||
\(497\) | 14.3376 | + | 14.3376i | 0.643128 | + | 0.643128i | ||||
\(498\) | −34.8224 | − | 34.8224i | −1.56043 | − | 1.56043i | ||||
\(499\) | 8.51500i | 0.381184i | 0.981669 | + | 0.190592i | \(0.0610407\pi\) | ||||
−0.981669 | + | 0.190592i | \(0.938959\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 59.9325 | 2.67759 | ||||||||
\(502\) | −2.57280 | − | 2.57280i | −0.114830 | − | 0.114830i | ||||
\(503\) | 25.6567 | + | 25.6567i | 1.14398 | + | 1.14398i | 0.987716 | + | 0.156261i | \(0.0499440\pi\) |
0.156261 | + | 0.987716i | \(0.450056\pi\) | |||||||
\(504\) | 8.06390 | 0.359195 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 4.45585i | − | 0.198087i | ||||||
\(507\) | 20.0686 | + | 20.0686i | 0.891276 | + | 0.891276i | ||||
\(508\) | −9.25728 | + | 9.25728i | −0.410725 | + | 0.410725i | ||||
\(509\) | 21.5712 | 0.956126 | 0.478063 | − | 0.878326i | \(-0.341339\pi\) | ||||
0.478063 | + | 0.878326i | \(0.341339\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.7425 | 0.696407 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −36.2540 | − | 5.21148i | −1.60065 | − | 0.230092i | ||||
\(514\) | − | 15.7261i | − | 0.693650i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 30.5813i | − | 1.34627i | ||||||
\(517\) | 14.9770 | − | 14.9770i | 0.658690 | − | 0.658690i | ||||
\(518\) | 6.37009 | + | 6.37009i | 0.279886 | + | 0.279886i | ||||
\(519\) | 72.4846i | 3.18172i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.17976i | 0.314551i | 0.987555 | + | 0.157276i | \(0.0502711\pi\) | ||||
−0.987555 | + | 0.157276i | \(0.949729\pi\) | |||||||
\(522\) | −1.84992 | + | 1.84992i | −0.0809689 | + | 0.0809689i | ||||
\(523\) | 28.0501 | − | 28.0501i | 1.22654 | − | 1.22654i | 0.261281 | − | 0.965263i | \(-0.415855\pi\) |
0.965263 | − | 0.261281i | \(-0.0841451\pi\) | |||||||
\(524\) | − | 3.65611i | − | 0.159718i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 8.99864i | − | 0.392359i | ||||||
\(527\) | 17.7018 | + | 17.7018i | 0.771104 | + | 0.771104i | ||||
\(528\) | −5.10855 | + | 5.10855i | −0.222321 | + | 0.222321i | ||||
\(529\) | − | 19.6418i | − | 0.853993i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 34.3489i | − | 1.49062i | ||||||
\(532\) | 5.96976 | + | 0.858147i | 0.258822 | + | 0.0372054i | ||||
\(533\) | 8.24819 | + | 8.24819i | 0.357269 | + | 0.357269i | ||||
\(534\) | −9.84582 | −0.426071 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.90740 | 0.255161 | ||||||||
\(537\) | −9.24331 | + | 9.24331i | −0.398878 | + | 0.398878i | ||||
\(538\) | 7.49562 | + | 7.49562i | 0.323159 | + | 0.323159i | ||||
\(539\) | 12.3657i | 0.532628i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.8272 | 0.852439 | 0.426220 | − | 0.904620i | \(-0.359845\pi\) | ||||
0.426220 | + | 0.904620i | \(0.359845\pi\) | |||||||
\(542\) | −1.68361 | − | 1.68361i | −0.0723173 | − | 0.0723173i | ||||
\(543\) | 12.0650 | + | 12.0650i | 0.517760 | + | 0.517760i | ||||
\(544\) | 7.22675 | 0.309844 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | − | 7.63363i | − | 0.326689i | ||||||
\(547\) | −0.784465 | − | 0.784465i | −0.0335413 | − | 0.0335413i | 0.690137 | − | 0.723679i | \(-0.257550\pi\) |
−0.723679 | + | 0.690137i | \(0.757550\pi\) | |||||||
\(548\) | 9.68455 | + | 9.68455i | 0.413703 | + | 0.413703i | ||||
\(549\) | 11.6561i | 0.497471i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.56638 | + | 1.17264i | −0.0667299 | + | 0.0499563i | ||||
\(552\) | 3.85007 | − | 3.85007i | 0.163870 | − | 0.163870i | ||||
\(553\) | 6.09663 | − | 6.09663i | 0.259255 | − | 0.259255i | ||||
\(554\) | −13.1610 | −0.559159 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.36152 | −0.184969 | ||||||||
\(557\) | 17.5686 | − | 17.5686i | 0.744407 | − | 0.744407i | −0.229016 | − | 0.973423i | \(-0.573551\pi\) |
0.973423 | + | 0.229016i | \(0.0735508\pi\) | |||||||
\(558\) | −14.2758 | − | 14.2758i | −0.604341 | − | 0.604341i | ||||
\(559\) | −19.1118 | −0.808341 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 52.2102i | 2.20432i | ||||||||
\(562\) | −8.81249 | + | 8.81249i | −0.371732 | + | 0.371732i | ||||
\(563\) | 9.66803 | − | 9.66803i | 0.407459 | − | 0.407459i | −0.473393 | − | 0.880852i | \(-0.656971\pi\) |
0.880852 | + | 0.473393i | \(0.156971\pi\) | |||||||
\(564\) | 25.8817 | 1.08982 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 13.1090i | 0.551011i | ||||||||
\(567\) | −7.32030 | + | 7.32030i | −0.307424 | + | 0.307424i | ||||
\(568\) | −10.3623 | − | 10.3623i | −0.434791 | − | 0.434791i | ||||
\(569\) | −34.9880 | −1.46677 | −0.733387 | − | 0.679812i | \(-0.762061\pi\) | ||||
−0.733387 | + | 0.679812i | \(0.762061\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.1053 | −1.17617 | −0.588085 | − | 0.808799i | \(-0.700118\pi\) | ||||
−0.588085 | + | 0.808799i | \(0.700118\pi\) | |||||||
\(572\) | 3.19259 | + | 3.19259i | 0.133489 | + | 0.133489i | ||||
\(573\) | 49.0472 | − | 49.0472i | 2.04898 | − | 2.04898i | ||||
\(574\) | 8.69195i | 0.362795i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −5.82806 | −0.242836 | ||||||||
\(577\) | 11.4812 | − | 11.4812i | 0.477969 | − | 0.477969i | −0.426513 | − | 0.904482i | \(-0.640258\pi\) |
0.904482 | + | 0.426513i | \(0.140258\pi\) | |||||||
\(578\) | 24.9084 | − | 24.9084i | 1.03605 | − | 1.03605i | ||||
\(579\) | − | 10.6396i | − | 0.442165i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.9331 | −0.951425 | ||||||||
\(582\) | −20.1661 | − | 20.1661i | −0.835912 | − | 0.835912i | ||||
\(583\) | −22.7979 | + | 22.7979i | −0.944193 | + | 0.944193i | ||||
\(584\) | −11.3776 | −0.470810 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22.4336 | 0.926724 | ||||||||
\(587\) | 11.5256 | − | 11.5256i | 0.475713 | − | 0.475713i | −0.428045 | − | 0.903758i | \(-0.640797\pi\) |
0.903758 | + | 0.428045i | \(0.140797\pi\) | |||||||
\(588\) | −10.6845 | + | 10.6845i | −0.440623 | + | 0.440623i | ||||
\(589\) | −9.04924 | − | 12.0876i | −0.372867 | − | 0.498063i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 8.81920i | − | 0.362774i | ||||||
\(592\) | −4.60388 | − | 4.60388i | −0.189219 | − | 0.189219i | ||||
\(593\) | 9.63025 | + | 9.63025i | 0.395467 | + | 0.395467i | 0.876631 | − | 0.481164i | \(-0.159786\pi\) |
−0.481164 | + | 0.876631i | \(0.659786\pi\) | |||||||
\(594\) | − | 20.4315i | − | 0.838316i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10.8631 | −0.444969 | ||||||||
\(597\) | −50.8931 | − | 50.8931i | −2.08292 | − | 2.08292i | ||||
\(598\) | −2.40610 | − | 2.40610i | −0.0983927 | − | 0.0983927i | ||||
\(599\) | −26.3407 | −1.07625 | −0.538125 | − | 0.842865i | \(-0.680867\pi\) | ||||
−0.538125 | + | 0.842865i | \(0.680867\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 4.31129i | − | 0.175861i | −0.996127 | − | 0.0879306i | \(-0.971975\pi\) | ||
0.996127 | − | 0.0879306i | \(-0.0280254\pi\) | |||||||
\(602\) | −10.0700 | − | 10.0700i | −0.410423 | − | 0.410423i | ||||
\(603\) | −24.3447 | + | 24.3447i | −0.991395 | + | 0.991395i | ||||
\(604\) | −4.85777 | −0.197660 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −17.8272 | −0.724182 | ||||||||
\(607\) | 1.98494 | + | 1.98494i | 0.0805664 | + | 0.0805664i | 0.746242 | − | 0.665675i | \(-0.231856\pi\) |
−0.665675 | + | 0.746242i | \(0.731856\pi\) | |||||||
\(608\) | −4.31455 | − | 0.620212i | −0.174978 | − | 0.0251529i | ||||
\(609\) | 1.84543i | 0.0747808i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 16.1748i | − | 0.654362i | ||||||
\(612\) | −29.7818 | + | 29.7818i | −1.20386 | + | 1.20386i | ||||
\(613\) | −4.06979 | − | 4.06979i | −0.164377 | − | 0.164377i | 0.620125 | − | 0.784503i | \(-0.287082\pi\) |
−0.784503 | + | 0.620125i | \(0.787082\pi\) | |||||||
\(614\) | − | 22.1494i | − | 0.893875i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.36435i | 0.135554i | ||||||||
\(617\) | −24.2219 | + | 24.2219i | −0.975137 | + | 0.975137i | −0.999698 | − | 0.0245613i | \(-0.992181\pi\) |
0.0245613 | + | 0.999698i | \(0.492181\pi\) | |||||||
\(618\) | −32.7719 | + | 32.7719i | −1.31828 | + | 1.31828i | ||||
\(619\) | − | 39.0342i | − | 1.56892i | −0.620182 | − | 0.784458i | \(-0.712941\pi\) | ||
0.620182 | − | 0.784458i | \(-0.287059\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.3983i | 0.617911i | ||||||||
\(622\) | −7.47245 | − | 7.47245i | −0.299618 | − | 0.299618i | ||||
\(623\) | −3.24210 | + | 3.24210i | −0.129892 | + | 0.129892i | ||||
\(624\) | 5.51709i | 0.220860i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 5.50762i | − | 0.220129i | ||||||
\(627\) | 4.48077 | − | 31.1708i | 0.178945 | − | 1.24484i | ||||
\(628\) | −17.0054 | − | 17.0054i | −0.678588 | − | 0.678588i | ||||
\(629\) | −47.0524 | −1.87610 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.9507 | −0.634988 | −0.317494 | − | 0.948260i | \(-0.602841\pi\) | ||||
−0.317494 | + | 0.948260i | \(0.602841\pi\) | |||||||
\(632\) | −4.40624 | + | 4.40624i | −0.175271 | + | 0.175271i | ||||
\(633\) | −9.13853 | − | 9.13853i | −0.363224 | − | 0.363224i | ||||
\(634\) | − | 5.34515i | − | 0.212283i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −39.3970 | −1.56219 | ||||||||
\(637\) | 6.67730 | + | 6.67730i | 0.264564 | + | 0.264564i | ||||
\(638\) | −0.771809 | − | 0.771809i | −0.0305562 | − | 0.0305562i | ||||
\(639\) | 85.4070 | 3.37865 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.1678i | 1.66553i | 0.553629 | + | 0.832763i | \(0.313242\pi\) | ||||
−0.553629 | + | 0.832763i | \(0.686758\pi\) | |||||||
\(642\) | 11.1564 | + | 11.1564i | 0.440307 | + | 0.440307i | ||||
\(643\) | −3.77141 | − | 3.77141i | −0.148730 | − | 0.148730i | 0.628821 | − | 0.777550i | \(-0.283538\pi\) |
−0.777550 | + | 0.628821i | \(0.783538\pi\) | |||||||
\(644\) | − | 2.53555i | − | 0.0999147i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −25.2170 | + | 18.8784i | −0.992151 | + | 0.742759i | ||||
\(647\) | 4.69344 | − | 4.69344i | 0.184518 | − | 0.184518i | −0.608803 | − | 0.793321i | \(-0.708350\pi\) |
0.793321 | + | 0.608803i | \(0.208350\pi\) | |||||||
\(648\) | 5.29063 | − | 5.29063i | 0.207836 | − | 0.207836i | ||||
\(649\) | 14.3308 | 0.562532 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.2411 | −0.558154 | ||||||||
\(652\) | 12.0706 | − | 12.0706i | 0.472721 | − | 0.472721i | ||||
\(653\) | 18.6820 | + | 18.6820i | 0.731084 | + | 0.731084i | 0.970834 | − | 0.239751i | \(-0.0770658\pi\) |
−0.239751 | + | 0.970834i | \(0.577066\pi\) | |||||||
\(654\) | 32.6219 | 1.27562 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 6.28197i | − | 0.245270i | ||||||
\(657\) | 46.8880 | − | 46.8880i | 1.82927 | − | 1.82927i | ||||
\(658\) | 8.52250 | − | 8.52250i | 0.332242 | − | 0.332242i | ||||
\(659\) | −6.58693 | −0.256590 | −0.128295 | − | 0.991736i | \(-0.540950\pi\) | ||||
−0.128295 | + | 0.991736i | \(0.540950\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 6.27981i | − | 0.244256i | −0.992514 | − | 0.122128i | \(-0.961028\pi\) | ||
0.992514 | − | 0.122128i | \(-0.0389719\pi\) | |||||||
\(662\) | −4.75944 | + | 4.75944i | −0.184981 | + | 0.184981i | ||||
\(663\) | 28.1928 | + | 28.1928i | 1.09492 | + | 1.09492i | ||||
\(664\) | 16.5745 | 0.643216 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 37.9458 | 1.47037 | ||||||||
\(667\) | 0.581675 | + | 0.581675i | 0.0225226 | + | 0.0225226i | ||||
\(668\) | −14.2631 | + | 14.2631i | −0.551857 | + | 0.551857i | ||||
\(669\) | − | 35.3122i | − | 1.36525i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.86307 | −0.187737 | ||||||||
\(672\) | −2.90696 | + | 2.90696i | −0.112138 | + | 0.112138i | ||||
\(673\) | −21.3284 | + | 21.3284i | −0.822148 | + | 0.822148i | −0.986416 | − | 0.164268i | \(-0.947474\pi\) |
0.164268 | + | 0.986416i | \(0.447474\pi\) | |||||||
\(674\) | − | 3.80135i | − | 0.146423i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.55210 | −0.367388 | ||||||||
\(677\) | −0.766712 | − | 0.766712i | −0.0294671 | − | 0.0294671i | 0.692220 | − | 0.721687i | \(-0.256633\pi\) |
−0.721687 | + | 0.692220i | \(0.756633\pi\) | |||||||
\(678\) | 7.49720 | − | 7.49720i | 0.287928 | − | 0.287928i | ||||
\(679\) | −13.2808 | −0.509672 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −34.9847 | −1.34062 | ||||||||
\(682\) | 5.95601 | − | 5.95601i | 0.228068 | − | 0.228068i | ||||
\(683\) | −3.22088 | + | 3.22088i | −0.123244 | + | 0.123244i | −0.766038 | − | 0.642795i | \(-0.777775\pi\) |
0.642795 | + | 0.766038i | \(0.277775\pi\) | |||||||
\(684\) | 20.3364 | − | 15.2246i | 0.777583 | − | 0.582126i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 16.7220i | 0.638448i | ||||||||
\(687\) | −40.9337 | − | 40.9337i | −1.56172 | − | 1.56172i | ||||
\(688\) | 7.27794 | + | 7.27794i | 0.277469 | + | 0.277469i | ||||
\(689\) | 24.6211i | 0.937989i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.2588 | −1.07501 | −0.537507 | − | 0.843259i | \(-0.680634\pi\) | ||||
−0.537507 | + | 0.843259i | \(0.680634\pi\) | |||||||
\(692\) | −17.2504 | − | 17.2504i | −0.655760 | − | 0.655760i | ||||
\(693\) | −13.8647 | − | 13.8647i | −0.526676 | − | 0.526676i | ||||
\(694\) | −15.1809 | −0.576258 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 1.33376i | − | 0.0505560i | ||||||
\(697\) | −32.1014 | − | 32.1014i | −1.21593 | − | 1.21593i | ||||
\(698\) | 13.5843 | − | 13.5843i | 0.514174 | − | 0.514174i | ||||
\(699\) | −55.8659 | −2.11304 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.5844 | 1.11739 | 0.558694 | − | 0.829374i | \(-0.311302\pi\) | ||||
0.558694 | + | 0.829374i | \(0.311302\pi\) | |||||||
\(702\) | −11.0327 | − | 11.0327i | −0.416404 | − | 0.416404i | ||||
\(703\) | 28.0915 | + | 4.03812i | 1.05949 | + | 0.152301i | ||||
\(704\) | − | 2.43153i | − | 0.0916418i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 7.51525i | − | 0.282840i | ||||||
\(707\) | −5.87026 | + | 5.87026i | −0.220774 | + | 0.220774i | ||||
\(708\) | 12.3825 | + | 12.3825i | 0.465361 | + | 0.465361i | ||||
\(709\) | − | 36.4475i | − | 1.36881i | −0.729100 | − | 0.684407i | \(-0.760061\pi\) | ||
0.729100 | − | 0.684407i | \(-0.239939\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 36.3168i | − | 1.36199i | ||||||
\(712\) | 2.34317 | − | 2.34317i | 0.0878142 | − | 0.0878142i | ||||
\(713\) | −4.48876 | + | 4.48876i | −0.168105 | + | 0.168105i | ||||
\(714\) | 29.7096i | 1.11185i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 4.39957i | − | 0.164420i | ||||||
\(717\) | 28.9813 | + | 28.9813i | 1.08233 | + | 1.08233i | ||||
\(718\) | −6.27812 | + | 6.27812i | −0.234297 | + | 0.234297i | ||||
\(719\) | 23.3451i | 0.870627i | 0.900279 | + | 0.435314i | \(0.143362\pi\) | ||||
−0.900279 | + | 0.435314i | \(0.856638\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.5827i | 0.803780i | ||||||||
\(722\) | 16.6754 | − | 9.10669i | 0.620593 | − | 0.338916i | ||||
\(723\) | −34.8224 | − | 34.8224i | −1.29506 | − | 1.29506i | ||||
\(724\) | −5.74263 | −0.213423 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −15.1164 | −0.561024 | ||||||||
\(727\) | 34.8179 | − | 34.8179i | 1.29132 | − | 1.29132i | 0.357355 | − | 0.933969i | \(-0.383679\pi\) |
0.933969 | − | 0.357355i | \(-0.116321\pi\) | |||||||
\(728\) | 1.81670 | + | 1.81670i | 0.0673315 | + | 0.0673315i | ||||
\(729\) | − | 31.2928i | − | 1.15899i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 74.3817 | 2.75111 | ||||||||
\(732\) | −4.20192 | − | 4.20192i | −0.155307 | − | 0.155307i | ||||
\(733\) | −8.05487 | − | 8.05487i | −0.297513 | − | 0.297513i | 0.542526 | − | 0.840039i | \(-0.317468\pi\) |
−0.840039 | + | 0.542526i | \(0.817468\pi\) | |||||||
\(734\) | 4.55706 | 0.168204 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.83253i | 0.0675479i | ||||||||
\(737\) | −10.1569 | − | 10.1569i | −0.374135 | − | 0.374135i | ||||
\(738\) | 25.8884 | + | 25.8884i | 0.952965 | + | 0.952965i | ||||
\(739\) | − | 14.0042i | − | 0.515152i | −0.966258 | − | 0.257576i | \(-0.917076\pi\) | ||
0.966258 | − | 0.257576i | \(-0.0829238\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14.4122 | − | 19.2514i | −0.529447 | − | 0.707216i | ||||
\(742\) | −12.9729 | + | 12.9729i | −0.476249 | + | 0.476249i | ||||
\(743\) | −19.1875 | + | 19.1875i | −0.703922 | + | 0.703922i | −0.965250 | − | 0.261328i | \(-0.915840\pi\) |
0.261328 | + | 0.965250i | \(0.415840\pi\) | |||||||
\(744\) | 10.2926 | 0.377343 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 20.9888 | 0.768456 | ||||||||
\(747\) | −68.3046 | + | 68.3046i | −2.49913 | + | 2.49913i | ||||
\(748\) | −12.4253 | − | 12.4253i | −0.454315 | − | 0.454315i | ||||
\(749\) | 7.34729 | 0.268464 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 0.675311i | − | 0.0246424i | −0.999924 | − | 0.0123212i | \(-0.996078\pi\) | ||
0.999924 | − | 0.0123212i | \(-0.00392207\pi\) | |||||||
\(752\) | −6.15951 | + | 6.15951i | −0.224614 | + | 0.224614i | ||||
\(753\) | −7.64431 | + | 7.64431i | −0.278574 | + | 0.278574i | ||||
\(754\) | −0.833532 | −0.0303554 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | − | 11.6263i | − | 0.422845i | ||||||
\(757\) | 11.3477 | − | 11.3477i | 0.412440 | − | 0.412440i | −0.470148 | − | 0.882588i | \(-0.655799\pi\) |
0.882588 | + | 0.470148i | \(0.155799\pi\) | |||||||
\(758\) | 12.5562 | + | 12.5562i | 0.456063 | + | 0.456063i | ||||
\(759\) | −13.2393 | −0.480555 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.0715 | −0.981342 | −0.490671 | − | 0.871345i | \(-0.663248\pi\) | ||||
−0.490671 | + | 0.871345i | \(0.663248\pi\) | |||||||
\(762\) | 27.5053 | + | 27.5053i | 0.996411 | + | 0.996411i | ||||
\(763\) | 10.7419 | − | 10.7419i | 0.388885 | − | 0.388885i | ||||
\(764\) | 23.3451i | 0.844598i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.9331 | −0.395028 | ||||||||
\(767\) | 7.73841 | − | 7.73841i | 0.279418 | − | 0.279418i | ||||
\(768\) | 2.10096 | − | 2.10096i | 0.0758118 | − | 0.0758118i | ||||
\(769\) | 33.4854i | 1.20752i | 0.797168 | + | 0.603758i | \(0.206331\pi\) | ||||
−0.797168 | + | 0.603758i | \(0.793669\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −46.7256 | −1.68278 | ||||||||
\(772\) | 2.53207 | + | 2.53207i | 0.0911313 | + | 0.0911313i | ||||
\(773\) | 12.2649 | − | 12.2649i | 0.441137 | − | 0.441137i | −0.451257 | − | 0.892394i | \(-0.649024\pi\) |
0.892394 | + | 0.451257i | \(0.149024\pi\) | |||||||
\(774\) | −59.9856 | −2.15614 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.59852 | 0.344567 | ||||||||
\(777\) | 18.9268 | − | 18.9268i | 0.678997 | − | 0.678997i | ||||
\(778\) | 6.63129 | − | 6.63129i | 0.237743 | − | 0.237743i | ||||
\(779\) | 16.4103 | + | 21.9203i | 0.587962 | + | 0.785378i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35.6328i | 1.27504i | ||||||||
\(782\) | 9.36437 | + | 9.36437i | 0.334869 | + | 0.334869i | ||||
\(783\) | 2.66717 | + | 2.66717i | 0.0953169 | + | 0.0953169i | ||||
\(784\) | − | 5.08556i | − | 0.181627i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −10.8631 | −0.387473 | ||||||||
\(787\) | 20.4103 | + | 20.4103i | 0.727549 | + | 0.727549i | 0.970131 | − | 0.242582i | \(-0.0779944\pi\) |
−0.242582 | + | 0.970131i | \(0.577994\pi\) | |||||||
\(788\) | 2.09885 | + | 2.09885i | 0.0747685 | + | 0.0747685i | ||||
\(789\) | −26.7368 | −0.951855 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 4.93745i | − | 0.175556i | ||||||
\(792\) | 10.0205 | + | 10.0205i | 0.356063 | + | 0.356063i | ||||
\(793\) | −2.62599 | + | 2.62599i | −0.0932515 | + | 0.0932515i | ||||
\(794\) | −32.0762 | −1.13834 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 24.2238 | 0.858588 | ||||||||
\(797\) | −15.8630 | − | 15.8630i | −0.561895 | − | 0.561895i | 0.367950 | − | 0.929845i | \(-0.380060\pi\) |
−0.929845 | + | 0.367950i | \(0.880060\pi\) | |||||||
\(798\) | 2.54973 | − | 17.7374i | 0.0902594 | − | 0.627896i | ||||
\(799\) | 62.9511i | 2.22705i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 19.3127i | 0.682381i | ||||||||
\(802\) | 3.80719 | − | 3.80719i | 0.134437 | − | 0.134437i | ||||
\(803\) | 19.5622 | + | 19.5622i | 0.690335 | + | 0.690335i | ||||
\(804\) | − | 17.5521i | − | 0.619015i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 6.43233i | − | 0.226569i | ||||||
\(807\) | 22.2710 | − | 22.2710i | 0.783977 | − | 0.783977i | ||||
\(808\) | 4.24264 | − | 4.24264i | 0.149256 | − | 0.149256i | ||||
\(809\) | − | 0.0173772i | − | 0.000610952i | −1.00000 | 0.000305476i | \(-0.999903\pi\) | |||
1.00000 | 0.000305476i | \(-9.72360e-5\pi\) | ||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 18.4034i | − | 0.646232i | −0.946359 | − | 0.323116i | \(-0.895270\pi\) | ||
0.946359 | − | 0.323116i | \(-0.104730\pi\) | |||||||
\(812\) | −0.439189 | − | 0.439189i | −0.0154125 | − | 0.0154125i | ||||
\(813\) | −5.00235 | + | 5.00235i | −0.175440 | + | 0.175440i | ||||
\(814\) | 15.8314i | 0.554891i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 21.4721i | − | 0.751675i | ||||||
\(817\) | −44.4077 | − | 6.38357i | −1.55363 | − | 0.223333i | ||||
\(818\) | 22.6455 | + | 22.6455i | 0.791781 | + | 0.791781i | ||||
\(819\) | −14.9735 | −0.523215 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.2364 | −1.02036 | −0.510178 | − | 0.860069i | \(-0.670421\pi\) | ||||
−0.510178 | + | 0.860069i | \(0.670421\pi\) | |||||||
\(822\) | 28.7748 | − | 28.7748i | 1.00364 | − | 1.00364i | ||||
\(823\) | −14.4582 | − | 14.4582i | −0.503980 | − | 0.503980i | 0.408692 | − | 0.912672i | \(-0.365985\pi\) |
−0.912672 | + | 0.408692i | \(0.865985\pi\) | |||||||
\(824\) | − | 15.5985i | − | 0.543400i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.15474 | 0.283740 | ||||||||
\(827\) | 18.5102 | + | 18.5102i | 0.643663 | + | 0.643663i | 0.951454 | − | 0.307791i | \(-0.0995898\pi\) |
−0.307791 | + | 0.951454i | \(0.599590\pi\) | |||||||
\(828\) | −7.55196 | − | 7.55196i | −0.262449 | − | 0.262449i | ||||
\(829\) | −38.5469 | −1.33879 | −0.669394 | − | 0.742907i | \(-0.733446\pi\) | ||||
−0.669394 | + | 0.742907i | \(0.733446\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 39.1041i | 1.35651i | ||||||||
\(832\) | −1.31299 | − | 1.31299i | −0.0455198 | − | 0.0455198i | ||||
\(833\) | −25.9876 | − | 25.9876i | −0.900417 | − | 0.900417i | ||||
\(834\) | 12.9590i | 0.448732i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.35187 | + | 8.48460i | 0.219684 | + | 0.293446i | ||||
\(837\) | −20.5824 | + | 20.5824i | −0.711432 | + | 0.711432i | ||||
\(838\) | 8.35065 | − | 8.35065i | 0.288468 | − | 0.288468i | ||||
\(839\) | 24.0478 | 0.830221 | 0.415110 | − | 0.909771i | \(-0.363743\pi\) | ||||
0.415110 | + | 0.909771i | \(0.363743\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7985 | −0.993051 | ||||||||
\(842\) | 13.5432 | − | 13.5432i | 0.466731 | − | 0.466731i | ||||
\(843\) | 26.1837 | + | 26.1837i | 0.901815 | + | 0.901815i | ||||
\(844\) | 4.34969 | 0.149723 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 50.7674i | − | 1.74542i | ||||||
\(847\) | −4.97764 | + | 4.97764i | −0.171034 | + | 0.171034i | ||||
\(848\) | 9.37595 | − | 9.37595i | 0.321971 | − | 0.321971i | ||||
\(849\) | 38.9494 | 1.33674 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 11.9314i | − | 0.409002i | ||||||
\(852\) | −30.7884 | + | 30.7884i | −1.05479 | + | 1.05479i | ||||
\(853\) | 34.3807 | + | 34.3807i | 1.17717 | + | 1.17717i | 0.980462 | + | 0.196710i | \(0.0630257\pi\) |
0.196710 | + | 0.980462i | \(0.436974\pi\) | |||||||
\(854\) | −2.76727 | −0.0946940 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.31014 | −0.181497 | ||||||||
\(857\) | 15.0795 | + | 15.0795i | 0.515107 | + | 0.515107i | 0.916087 | − | 0.400980i | \(-0.131330\pi\) |
−0.400980 | + | 0.916087i | \(0.631330\pi\) | |||||||
\(858\) | 9.48583 | − | 9.48583i | 0.323841 | − | 0.323841i | ||||
\(859\) | − | 15.4674i | − | 0.527740i | −0.964558 | − | 0.263870i | \(-0.915001\pi\) | ||
0.964558 | − | 0.263870i | \(-0.0849990\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 25.8256 | 0.880133 | ||||||||
\(862\) | 18.6115 | − | 18.6115i | 0.633909 | − | 0.633909i | ||||
\(863\) | −15.3381 | + | 15.3381i | −0.522116 | + | 0.522116i | −0.918210 | − | 0.396094i | \(-0.870365\pi\) |
0.396094 | + | 0.918210i | \(0.370365\pi\) | |||||||
\(864\) | 8.40274i | 0.285867i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 39.5134 | 1.34272 | ||||||||
\(867\) | −74.0081 | − | 74.0081i | −2.51345 | − | 2.51345i | ||||
\(868\) | 3.38920 | − | 3.38920i | 0.115037 | − | 0.115037i | ||||
\(869\) | 15.1518 | 0.513989 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.9692 | −0.371676 | ||||||||
\(872\) | −7.76358 | + | 7.76358i | −0.262908 | + | 0.262908i | ||||
\(873\) | −39.5561 | + | 39.5561i | −1.33877 | + | 1.33877i | ||||
\(874\) | −4.78710 | − | 6.39443i | −0.161926 | − | 0.216295i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 33.8053i | 1.14218i | ||||||||
\(877\) | −9.56444 | − | 9.56444i | −0.322968 | − | 0.322968i | 0.526936 | − | 0.849905i | \(-0.323341\pi\) |
−0.849905 | + | 0.526936i | \(0.823341\pi\) | |||||||
\(878\) | −14.0058 | − | 14.0058i | −0.472671 | − | 0.472671i | ||||
\(879\) | − | 66.6549i | − | 2.24821i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.53681 | −0.186540 | −0.0932700 | − | 0.995641i | \(-0.529732\pi\) | ||||
−0.0932700 | + | 0.995641i | \(0.529732\pi\) | |||||||
\(882\) | 20.9579 | + | 20.9579i | 0.705688 | + | 0.705688i | ||||
\(883\) | 23.6873 | + | 23.6873i | 0.797141 | + | 0.797141i | 0.982644 | − | 0.185502i | \(-0.0593913\pi\) |
−0.185502 | + | 0.982644i | \(0.559391\pi\) | |||||||
\(884\) | −13.4190 | −0.451330 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 30.6319i | − | 1.02910i | ||||||
\(887\) | 21.1405 | + | 21.1405i | 0.709830 | + | 0.709830i | 0.966499 | − | 0.256669i | \(-0.0826251\pi\) |
−0.256669 | + | 0.966499i | \(0.582625\pi\) | |||||||
\(888\) | −13.6791 | + | 13.6791i | −0.459040 | + | 0.459040i | ||||
\(889\) | 18.1142 | 0.607531 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.1929 | −0.609486 | ||||||||
\(892\) | 8.40384 | + | 8.40384i | 0.281381 | + | 0.281381i | ||||
\(893\) | 5.40258 | − | 37.5834i | 0.180790 | − | 1.25768i | ||||
\(894\) | 32.2764i | 1.07948i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 1.38363i | − | 0.0462240i | ||||||
\(897\) | −7.14901 | + | 7.14901i | −0.238699 | + | 0.238699i | ||||
\(898\) | 27.4024 | + | 27.4024i | 0.914429 | + | 0.914429i | ||||
\(899\) | 1.55502i | 0.0518628i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 95.8237i | − | 3.19235i | ||||||
\(902\) | −10.8009 | + | 10.8009i | −0.359632 | + | 0.359632i | ||||
\(903\) | −29.9200 | + | 29.9200i | −0.995676 | + | 0.995676i | ||||
\(904\) | 3.56847i | 0.118685i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 14.4334i | 0.479518i | ||||||||
\(907\) | 13.3405 | + | 13.3405i | 0.442965 | + | 0.442965i | 0.893007 | − | 0.450042i | \(-0.148591\pi\) |
−0.450042 | + | 0.893007i | \(0.648591\pi\) | |||||||
\(908\) | 8.32589 | − | 8.32589i | 0.276304 | − | 0.276304i | ||||
\(909\) | 34.9683i | 1.15983i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 18.8154i | − | 0.623381i | −0.950184 | − | 0.311691i | \(-0.899105\pi\) | ||
0.950184 | − | 0.311691i | \(-0.100895\pi\) | |||||||
\(912\) | −1.84278 | + | 12.8194i | −0.0610204 | + | 0.424493i | ||||
\(913\) | −28.4975 | − | 28.4975i | −0.943129 | − | 0.943129i | ||||
\(914\) | −1.59100 | −0.0526257 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.4833 | 0.643748 | ||||||||
\(917\) | −3.57706 | + | 3.57706i | −0.118125 | + | 0.118125i | ||||
\(918\) | 42.9387 | + | 42.9387i | 1.41719 | + | 1.41719i | ||||
\(919\) | 12.6764i | 0.418156i | 0.977899 | + | 0.209078i | \(0.0670463\pi\) | ||||
−0.977899 | + | 0.209078i | \(0.932954\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −65.8103 | −2.16852 | ||||||||
\(922\) | 6.07348 | + | 6.07348i | 0.200019 | + | 0.200019i | ||||
\(923\) | 19.2412 | + | 19.2412i | 0.633331 | + | 0.633331i | ||||
\(924\) | 9.99618 | 0.328850 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 5.92352i | − | 0.194659i | ||||||
\(927\) | 64.2824 | + | 64.2824i | 2.11131 | + | 2.11131i | ||||
\(928\) | 0.317417 | + | 0.317417i | 0.0104197 | + | 0.0104197i | ||||
\(929\) | − | 9.79013i | − | 0.321204i | −0.987019 | − | 0.160602i | \(-0.948656\pi\) | ||
0.987019 | − | 0.160602i | \(-0.0513435\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.2850 | + | 17.7456i | 0.435397 | + | 0.581587i | ||||
\(932\) | 13.2953 | − | 13.2953i | 0.435503 | − | 0.435503i | ||||
\(933\) | −22.2022 | + | 22.2022i | −0.726867 | + | 0.726867i | ||||
\(934\) | 17.4203 | 0.570008 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 10.8218 | 0.353723 | ||||||||
\(937\) | 2.50430 | − | 2.50430i | 0.0818121 | − | 0.0818121i | −0.665017 | − | 0.746829i | \(-0.731576\pi\) |
0.746829 | + | 0.665017i | \(0.231576\pi\) | |||||||
\(938\) | −5.77967 | − | 5.77967i | −0.188713 | − | 0.188713i | ||||
\(939\) | −16.3643 | −0.534028 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 42.9543i | − | 1.40027i | −0.714010 | − | 0.700135i | \(-0.753123\pi\) | ||
0.714010 | − | 0.700135i | \(-0.246877\pi\) | |||||||
\(942\) | −50.5264 | + | 50.5264i | −1.64624 | + | 1.64624i | ||||
\(943\) | 8.14014 | − | 8.14014i | 0.265079 | − | 0.265079i | ||||
\(944\) | −5.89371 | −0.191824 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 25.0267i | − | 0.813688i | ||||||
\(947\) | −18.0614 | + | 18.0614i | −0.586916 | + | 0.586916i | −0.936795 | − | 0.349879i | \(-0.886223\pi\) |
0.349879 | + | 0.936795i | \(0.386223\pi\) | |||||||
\(948\) | 13.0919 | + | 13.0919i | 0.425204 | + | 0.425204i | ||||
\(949\) | 21.1266 | 0.685799 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.8815 | −0.514994 | ||||||||
\(952\) | −7.07048 | − | 7.07048i | −0.229156 | − | 0.229156i | ||||
\(953\) | −26.3730 | + | 26.3730i | −0.854307 | + | 0.854307i | −0.990660 | − | 0.136353i | \(-0.956462\pi\) |
0.136353 | + | 0.990660i | \(0.456462\pi\) | |||||||
\(954\) | 77.2777i | 2.50196i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −13.7943 | −0.446140 | ||||||||
\(957\) | −2.29320 | + | 2.29320i | −0.0741287 | + | 0.0741287i | ||||
\(958\) | −20.8857 | + | 20.8857i | −0.674786 | + | 0.674786i | ||||
\(959\) | − | 18.9503i | − | 0.611936i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.0000 | 0.612903 | ||||||||
\(962\) | 8.54874 | + | 8.54874i | 0.275622 | + | 0.275622i | ||||
\(963\) | 21.8834 | − | 21.8834i | 0.705183 | − | 0.705183i | ||||
\(964\) | 16.5745 | 0.533830 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −7.53364 | −0.242391 | ||||||||
\(967\) | −33.7448 | + | 33.7448i | −1.08516 | + | 1.08516i | −0.0891408 | + | 0.996019i | \(0.528412\pi\) |
−0.996019 | + | 0.0891408i | \(0.971588\pi\) | |||||||
\(968\) | 3.59751 | − | 3.59751i | 0.115628 | − | 0.115628i | ||||
\(969\) | 56.0915 | + | 74.9250i | 1.80192 | + | 2.40694i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 31.7048i | − | 1.01746i | −0.860928 | − | 0.508728i | \(-0.830116\pi\) | ||
0.860928 | − | 0.508728i | \(-0.169884\pi\) | |||||||
\(972\) | 2.10535 | + | 2.10535i | 0.0675292 | + | 0.0675292i | ||||
\(973\) | 4.26721 | + | 4.26721i | 0.136800 | + | 0.136800i | ||||
\(974\) | − | 28.6079i | − | 0.916655i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | −21.1530 | − | 21.1530i | −0.676745 | − | 0.676745i | 0.282517 | − | 0.959262i | \(-0.408831\pi\) |
−0.959262 | + | 0.282517i | \(0.908831\pi\) | |||||||
\(978\) | −35.8642 | − | 35.8642i | −1.14681 | − | 1.14681i | ||||
\(979\) | −8.05749 | −0.257518 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 63.9883i | − | 2.04299i | ||||||
\(982\) | 18.7519 | + | 18.7519i | 0.598397 | + | 0.598397i | ||||
\(983\) | 43.3066 | − | 43.3066i | 1.38127 | − | 1.38127i | 0.538887 | − | 0.842378i | \(-0.318845\pi\) |
0.842378 | − | 0.538887i | \(-0.181155\pi\) | |||||||
\(984\) | −18.6650 | −0.595019 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.24405 | 0.103312 | ||||||||
\(987\) | −25.3221 | − | 25.3221i | −0.806011 | − | 0.806011i | ||||
\(988\) | 8.01148 | + | 1.15164i | 0.254879 | + | 0.0366386i | ||||
\(989\) | 18.8614i | 0.599758i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.3181i | 0.867789i | 0.900964 | + | 0.433895i | \(0.142861\pi\) | ||||
−0.900964 | + | 0.433895i | \(0.857139\pi\) | |||||||
\(992\) | −2.44949 | + | 2.44949i | −0.0777714 | + | 0.0777714i | ||||
\(993\) | 14.1413 | + | 14.1413i | 0.448760 | + | 0.448760i | ||||
\(994\) | 20.2764i | 0.643128i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 49.2463i | − | 1.56043i | ||||||
\(997\) | −16.4984 | + | 16.4984i | −0.522511 | + | 0.522511i | −0.918329 | − | 0.395818i | \(-0.870461\pi\) |
0.395818 | + | 0.918329i | \(0.370461\pi\) | |||||||
\(998\) | −6.02101 | + | 6.02101i | −0.190592 | + | 0.190592i | ||||
\(999\) | − | 54.7092i | − | 1.73092i |
(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 | 950.2.f.d.493.16 | yes | 32 | |
5.2 | odd | 4 | inner | 950.2.f.d.607.2 | yes | 32 | |
5.3 | odd | 4 | inner | 950.2.f.d.607.15 | yes | 32 | |
5.4 | even | 2 | inner | 950.2.f.d.493.1 | ✓ | 32 | |
19.18 | odd | 2 | inner | 950.2.f.d.493.2 | yes | 32 | |
95.18 | even | 4 | inner | 950.2.f.d.607.1 | yes | 32 | |
95.37 | even | 4 | inner | 950.2.f.d.607.16 | yes | 32 | |
95.94 | odd | 2 | inner | 950.2.f.d.493.15 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.f.d.493.1 | ✓ | 32 | 5.4 | even | 2 | inner | |
950.2.f.d.493.2 | yes | 32 | 19.18 | odd | 2 | inner | |
950.2.f.d.493.15 | yes | 32 | 95.94 | odd | 2 | inner | |
950.2.f.d.493.16 | yes | 32 | 1.1 | even | 1 | trivial | |
950.2.f.d.607.1 | yes | 32 | 95.18 | even | 4 | inner | |
950.2.f.d.607.2 | yes | 32 | 5.2 | odd | 4 | inner | |
950.2.f.d.607.15 | yes | 32 | 5.3 | odd | 4 | inner | |
950.2.f.d.607.16 | yes | 32 | 95.37 | even | 4 | inner |