Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(573,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.573");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.l (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: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 573.12 | ||
Character | \(\chi\) | \(=\) | 770.573 |
Dual form | 770.2.l.c.727.12 |
$q$-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 \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 | ||||
\(3\) | −1.65110 | + | 1.65110i | −0.953264 | + | 0.953264i | −0.998956 | − | 0.0456912i | \(-0.985451\pi\) |
0.0456912 | + | 0.998956i | \(0.485451\pi\) | |||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 2.15340 | + | 0.602381i | 0.963030 | + | 0.269393i | ||||
\(6\) | 2.33501i | 0.953264i | ||||||||
\(7\) | 0.00754262 | + | 2.64574i | 0.00285084 | + | 0.999996i | ||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | − | 2.45228i | − | 0.817426i | ||||||
\(10\) | 1.94863 | − | 1.09674i | 0.616212 | − | 0.346819i | ||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.65110 | + | 1.65110i | 0.476632 | + | 0.476632i | ||||
\(13\) | 0.174289 | − | 0.174289i | 0.0483390 | − | 0.0483390i | −0.682524 | − | 0.730863i | \(-0.739118\pi\) |
0.730863 | + | 0.682524i | \(0.239118\pi\) | |||||||
\(14\) | 1.87615 | + | 1.86549i | 0.501423 | + | 0.498573i | ||||
\(15\) | −4.55008 | + | 2.56089i | −1.17483 | + | 0.661220i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 5.60245 | + | 5.60245i | 1.35879 | + | 1.35879i | 0.875408 | + | 0.483385i | \(0.160593\pi\) |
0.483385 | + | 0.875408i | \(0.339407\pi\) | |||||||
\(18\) | −1.73402 | − | 1.73402i | −0.408713 | − | 0.408713i | ||||
\(19\) | −5.84195 | −1.34024 | −0.670118 | − | 0.742255i | \(-0.733756\pi\) | ||||
−0.670118 | + | 0.742255i | \(0.733756\pi\) | |||||||
\(20\) | 0.602381 | − | 2.15340i | 0.134696 | − | 0.481515i | ||||
\(21\) | −4.38084 | − | 4.35594i | −0.955978 | − | 0.950543i | ||||
\(22\) | −0.707107 | + | 0.707107i | −0.150756 | + | 0.150756i | ||||
\(23\) | −2.78391 | − | 2.78391i | −0.580486 | − | 0.580486i | 0.354551 | − | 0.935037i | \(-0.384634\pi\) |
−0.935037 | + | 0.354551i | \(0.884634\pi\) | |||||||
\(24\) | 2.33501 | 0.476632 | ||||||||
\(25\) | 4.27428 | + | 2.59433i | 0.854855 | + | 0.518867i | ||||
\(26\) | − | 0.246482i | − | 0.0483390i | ||||||
\(27\) | −0.904344 | − | 0.904344i | −0.174041 | − | 0.174041i | ||||
\(28\) | 2.64574 | − | 0.00754262i | 0.499998 | − | 0.00142542i | ||||
\(29\) | − | 1.55340i | − | 0.288460i | −0.989544 | − | 0.144230i | \(-0.953930\pi\) | ||
0.989544 | − | 0.144230i | \(-0.0460704\pi\) | |||||||
\(30\) | −1.40657 | + | 5.02822i | −0.256803 | + | 0.918023i | ||||
\(31\) | 5.97580i | 1.07329i | 0.843810 | + | 0.536643i | \(0.180308\pi\) | ||||
−0.843810 | + | 0.536643i | \(0.819692\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 1.65110 | − | 1.65110i | 0.287420 | − | 0.287420i | ||||
\(34\) | 7.92306 | 1.35879 | ||||||||
\(35\) | −1.57750 | + | 5.70188i | −0.266646 | + | 0.963794i | ||||
\(36\) | −2.45228 | −0.408713 | ||||||||
\(37\) | −3.47188 | + | 3.47188i | −0.570773 | + | 0.570773i | −0.932344 | − | 0.361571i | \(-0.882240\pi\) |
0.361571 | + | 0.932344i | \(0.382240\pi\) | |||||||
\(38\) | −4.13088 | + | 4.13088i | −0.670118 | + | 0.670118i | ||||
\(39\) | 0.575538i | 0.0921598i | ||||||||
\(40\) | −1.09674 | − | 1.94863i | −0.173409 | − | 0.308106i | ||||
\(41\) | 5.31279i | 0.829718i | 0.909886 | + | 0.414859i | \(0.136169\pi\) | ||||
−0.909886 | + | 0.414859i | \(0.863831\pi\) | |||||||
\(42\) | −6.17783 | + | 0.0176121i | −0.953261 | + | 0.00271761i | ||||
\(43\) | 2.57014 | + | 2.57014i | 0.391943 | + | 0.391943i | 0.875379 | − | 0.483437i | \(-0.160612\pi\) |
−0.483437 | + | 0.875379i | \(0.660612\pi\) | |||||||
\(44\) | 1.00000i | 0.150756i | ||||||||
\(45\) | 1.47721 | − | 5.28074i | 0.220209 | − | 0.787206i | ||||
\(46\) | −3.93704 | −0.580486 | ||||||||
\(47\) | 3.10826 | + | 3.10826i | 0.453387 | + | 0.453387i | 0.896477 | − | 0.443090i | \(-0.146118\pi\) |
−0.443090 | + | 0.896477i | \(0.646118\pi\) | |||||||
\(48\) | 1.65110 | − | 1.65110i | 0.238316 | − | 0.238316i | ||||
\(49\) | −6.99989 | + | 0.0399116i | −0.999984 | + | 0.00570166i | ||||
\(50\) | 4.85684 | − | 1.18790i | 0.686861 | − | 0.167994i | ||||
\(51\) | −18.5004 | −2.59058 | ||||||||
\(52\) | −0.174289 | − | 0.174289i | −0.0241695 | − | 0.0241695i | ||||
\(53\) | 6.13111 | + | 6.13111i | 0.842173 | + | 0.842173i | 0.989141 | − | 0.146968i | \(-0.0469516\pi\) |
−0.146968 | + | 0.989141i | \(0.546952\pi\) | |||||||
\(54\) | −1.27894 | −0.174041 | ||||||||
\(55\) | −2.15340 | − | 0.602381i | −0.290365 | − | 0.0812250i | ||||
\(56\) | 1.86549 | − | 1.87615i | 0.249286 | − | 0.250712i | ||||
\(57\) | 9.64566 | − | 9.64566i | 1.27760 | − | 1.27760i | ||||
\(58\) | −1.09842 | − | 1.09842i | −0.144230 | − | 0.144230i | ||||
\(59\) | −8.26608 | −1.07615 | −0.538076 | − | 0.842896i | \(-0.680849\pi\) | ||||
−0.538076 | + | 0.842896i | \(0.680849\pi\) | |||||||
\(60\) | 2.56089 | + | 4.55008i | 0.330610 | + | 0.587413i | ||||
\(61\) | 5.87018i | 0.751600i | 0.926701 | + | 0.375800i | \(0.122632\pi\) | ||||
−0.926701 | + | 0.375800i | \(0.877368\pi\) | |||||||
\(62\) | 4.22553 | + | 4.22553i | 0.536643 | + | 0.536643i | ||||
\(63\) | 6.48809 | − | 0.0184966i | 0.817423 | − | 0.00233035i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0.480302 | − | 0.270326i | 0.0595741 | − | 0.0335298i | ||||
\(66\) | − | 2.33501i | − | 0.287420i | ||||||
\(67\) | 6.82513 | − | 6.82513i | 0.833822 | − | 0.833822i | −0.154215 | − | 0.988037i | \(-0.549285\pi\) |
0.988037 | + | 0.154215i | \(0.0492848\pi\) | |||||||
\(68\) | 5.60245 | − | 5.60245i | 0.679397 | − | 0.679397i | ||||
\(69\) | 9.19304 | 1.10671 | ||||||||
\(70\) | 2.91638 | + | 5.14730i | 0.348574 | + | 0.615220i | ||||
\(71\) | 7.24081 | 0.859326 | 0.429663 | − | 0.902989i | \(-0.358632\pi\) | ||||
0.429663 | + | 0.902989i | \(0.358632\pi\) | |||||||
\(72\) | −1.73402 | + | 1.73402i | −0.204357 | + | 0.204357i | ||||
\(73\) | −0.699312 | + | 0.699312i | −0.0818483 | + | 0.0818483i | −0.746846 | − | 0.664997i | \(-0.768433\pi\) |
0.664997 | + | 0.746846i | \(0.268433\pi\) | |||||||
\(74\) | 4.90998i | 0.570773i | ||||||||
\(75\) | −11.3408 | + | 2.77375i | −1.30952 | + | 0.320286i | ||||
\(76\) | 5.84195i | 0.670118i | ||||||||
\(77\) | −0.00754262 | − | 2.64574i | −0.000859561 | − | 0.301510i | ||||
\(78\) | 0.406966 | + | 0.406966i | 0.0460799 | + | 0.0460799i | ||||
\(79\) | − | 7.29601i | − | 0.820865i | −0.911891 | − | 0.410433i | \(-0.865378\pi\) | ||
0.911891 | − | 0.410433i | \(-0.134622\pi\) | |||||||
\(80\) | −2.15340 | − | 0.602381i | −0.240758 | − | 0.0673482i | ||||
\(81\) | 10.3432 | 1.14924 | ||||||||
\(82\) | 3.75671 | + | 3.75671i | 0.414859 | + | 0.414859i | ||||
\(83\) | 8.97769 | − | 8.97769i | 0.985430 | − | 0.985430i | −0.0144656 | − | 0.999895i | \(-0.504605\pi\) |
0.999895 | + | 0.0144656i | \(0.00460470\pi\) | |||||||
\(84\) | −4.35594 | + | 4.38084i | −0.475271 | + | 0.477989i | ||||
\(85\) | 8.68951 | + | 15.4391i | 0.942510 | + | 1.67461i | ||||
\(86\) | 3.63473 | 0.391943 | ||||||||
\(87\) | 2.56483 | + | 2.56483i | 0.274978 | + | 0.274978i | ||||
\(88\) | 0.707107 | + | 0.707107i | 0.0753778 | + | 0.0753778i | ||||
\(89\) | −4.37218 | −0.463450 | −0.231725 | − | 0.972781i | \(-0.574437\pi\) | ||||
−0.231725 | + | 0.972781i | \(0.574437\pi\) | |||||||
\(90\) | −2.68951 | − | 4.77859i | −0.283499 | − | 0.503707i | ||||
\(91\) | 0.462438 | + | 0.459809i | 0.0484766 | + | 0.0482010i | ||||
\(92\) | −2.78391 | + | 2.78391i | −0.290243 | + | 0.290243i | ||||
\(93\) | −9.86666 | − | 9.86666i | −1.02312 | − | 1.02312i | ||||
\(94\) | 4.39575 | 0.453387 | ||||||||
\(95\) | −12.5801 | − | 3.51908i | −1.29069 | − | 0.361050i | ||||
\(96\) | − | 2.33501i | − | 0.238316i | ||||||
\(97\) | 0.622902 | + | 0.622902i | 0.0632461 | + | 0.0632461i | 0.738022 | − | 0.674776i | \(-0.235760\pi\) |
−0.674776 | + | 0.738022i | \(0.735760\pi\) | |||||||
\(98\) | −4.92145 | + | 4.97789i | −0.497141 | + | 0.502843i | ||||
\(99\) | 2.45228i | 0.246463i | ||||||||
\(100\) | 2.59433 | − | 4.27428i | 0.259433 | − | 0.427428i | ||||
\(101\) | 0.369909i | 0.0368073i | 0.999831 | + | 0.0184037i | \(0.00585840\pi\) | ||||
−0.999831 | + | 0.0184037i | \(0.994142\pi\) | |||||||
\(102\) | −13.0818 | + | 13.0818i | −1.29529 | + | 1.29529i | ||||
\(103\) | 8.40496 | − | 8.40496i | 0.828166 | − | 0.828166i | −0.159097 | − | 0.987263i | \(-0.550858\pi\) |
0.987263 | + | 0.159097i | \(0.0508584\pi\) | |||||||
\(104\) | −0.246482 | −0.0241695 | ||||||||
\(105\) | −6.80978 | − | 12.0190i | −0.664567 | − | 1.17294i | ||||
\(106\) | 8.67070 | 0.842173 | ||||||||
\(107\) | −3.66759 | + | 3.66759i | −0.354559 | + | 0.354559i | −0.861803 | − | 0.507243i | \(-0.830665\pi\) |
0.507243 | + | 0.861803i | \(0.330665\pi\) | |||||||
\(108\) | −0.904344 | + | 0.904344i | −0.0870206 | + | 0.0870206i | ||||
\(109\) | − | 18.7822i | − | 1.79901i | −0.436911 | − | 0.899505i | \(-0.643928\pi\) | ||
0.436911 | − | 0.899505i | \(-0.356072\pi\) | |||||||
\(110\) | −1.94863 | + | 1.09674i | −0.185795 | + | 0.104570i | ||||
\(111\) | − | 11.4649i | − | 1.08820i | ||||||
\(112\) | −0.00754262 | − | 2.64574i | −0.000712710 | − | 0.249999i | ||||
\(113\) | −8.65869 | − | 8.65869i | −0.814541 | − | 0.814541i | 0.170770 | − | 0.985311i | \(-0.445375\pi\) |
−0.985311 | + | 0.170770i | \(0.945375\pi\) | |||||||
\(114\) | − | 13.6410i | − | 1.27760i | ||||||
\(115\) | −4.31790 | − | 7.67185i | −0.402647 | − | 0.715404i | ||||
\(116\) | −1.55340 | −0.144230 | ||||||||
\(117\) | −0.427405 | − | 0.427405i | −0.0395136 | − | 0.0395136i | ||||
\(118\) | −5.84500 | + | 5.84500i | −0.538076 | + | 0.538076i | ||||
\(119\) | −14.7804 | + | 14.8649i | −1.35491 | + | 1.36266i | ||||
\(120\) | 5.02822 | + | 1.40657i | 0.459011 | + | 0.128401i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 4.15084 | + | 4.15084i | 0.375800 | + | 0.375800i | ||||
\(123\) | −8.77196 | − | 8.77196i | −0.790941 | − | 0.790941i | ||||
\(124\) | 5.97580 | 0.536643 | ||||||||
\(125\) | 7.64145 | + | 8.16138i | 0.683472 | + | 0.729976i | ||||
\(126\) | 4.57470 | − | 4.60085i | 0.407546 | − | 0.409877i | ||||
\(127\) | −6.75899 | + | 6.75899i | −0.599764 | + | 0.599764i | −0.940250 | − | 0.340486i | \(-0.889408\pi\) |
0.340486 | + | 0.940250i | \(0.389408\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | −8.48713 | −0.747250 | ||||||||
\(130\) | 0.148476 | − | 0.530774i | 0.0130222 | − | 0.0465520i | ||||
\(131\) | 4.14114i | 0.361813i | 0.983500 | + | 0.180907i | \(0.0579032\pi\) | ||||
−0.983500 | + | 0.180907i | \(0.942097\pi\) | |||||||
\(132\) | −1.65110 | − | 1.65110i | −0.143710 | − | 0.143710i | ||||
\(133\) | −0.0440636 | − | 15.4563i | −0.00382080 | − | 1.34023i | ||||
\(134\) | − | 9.65219i | − | 0.833822i | ||||||
\(135\) | −1.40266 | − | 2.49218i | −0.120721 | − | 0.214492i | ||||
\(136\) | − | 7.92306i | − | 0.679397i | ||||||
\(137\) | 10.1281 | − | 10.1281i | 0.865301 | − | 0.865301i | −0.126647 | − | 0.991948i | \(-0.540422\pi\) |
0.991948 | + | 0.126647i | \(0.0404216\pi\) | |||||||
\(138\) | 6.50046 | − | 6.50046i | 0.553356 | − | 0.553356i | ||||
\(139\) | 12.4510 | 1.05608 | 0.528041 | − | 0.849219i | \(-0.322927\pi\) | ||||
0.528041 | + | 0.849219i | \(0.322927\pi\) | |||||||
\(140\) | 5.70188 | + | 1.57750i | 0.481897 | + | 0.133323i | ||||
\(141\) | −10.2641 | −0.864395 | ||||||||
\(142\) | 5.12003 | − | 5.12003i | 0.429663 | − | 0.429663i | ||||
\(143\) | −0.174289 | + | 0.174289i | −0.0145748 | + | 0.0145748i | ||||
\(144\) | 2.45228i | 0.204357i | ||||||||
\(145\) | 0.935739 | − | 3.34510i | 0.0777089 | − | 0.277795i | ||||
\(146\) | 0.988977i | 0.0818483i | ||||||||
\(147\) | 11.4916 | − | 11.6234i | 0.947814 | − | 0.958684i | ||||
\(148\) | 3.47188 | + | 3.47188i | 0.285387 | + | 0.285387i | ||||
\(149\) | − | 9.48708i | − | 0.777212i | −0.921404 | − | 0.388606i | \(-0.872957\pi\) | ||
0.921404 | − | 0.388606i | \(-0.127043\pi\) | |||||||
\(150\) | −6.05780 | + | 9.98048i | −0.494617 | + | 0.814903i | ||||
\(151\) | −0.184085 | −0.0149806 | −0.00749032 | − | 0.999972i | \(-0.502384\pi\) | ||||
−0.00749032 | + | 0.999972i | \(0.502384\pi\) | |||||||
\(152\) | 4.13088 | + | 4.13088i | 0.335059 | + | 0.335059i | ||||
\(153\) | 13.7388 | − | 13.7388i | 1.11071 | − | 1.11071i | ||||
\(154\) | −1.87615 | − | 1.86549i | −0.151185 | − | 0.150325i | ||||
\(155\) | −3.59971 | + | 12.8683i | −0.289135 | + | 1.03361i | ||||
\(156\) | 0.575538 | 0.0460799 | ||||||||
\(157\) | −9.08936 | − | 9.08936i | −0.725410 | − | 0.725410i | 0.244292 | − | 0.969702i | \(-0.421445\pi\) |
−0.969702 | + | 0.244292i | \(0.921445\pi\) | |||||||
\(158\) | −5.15906 | − | 5.15906i | −0.410433 | − | 0.410433i | ||||
\(159\) | −20.2462 | −1.60563 | ||||||||
\(160\) | −1.94863 | + | 1.09674i | −0.154053 | + | 0.0867047i | ||||
\(161\) | 7.34451 | − | 7.38650i | 0.578828 | − | 0.582138i | ||||
\(162\) | 7.31372 | − | 7.31372i | 0.574620 | − | 0.574620i | ||||
\(163\) | 6.69266 | + | 6.69266i | 0.524210 | + | 0.524210i | 0.918840 | − | 0.394630i | \(-0.129127\pi\) |
−0.394630 | + | 0.918840i | \(0.629127\pi\) | |||||||
\(164\) | 5.31279 | 0.414859 | ||||||||
\(165\) | 4.55008 | − | 2.56089i | 0.354223 | − | 0.199365i | ||||
\(166\) | − | 12.6964i | − | 0.985430i | ||||||
\(167\) | 5.27402 | + | 5.27402i | 0.408116 | + | 0.408116i | 0.881081 | − | 0.472965i | \(-0.156816\pi\) |
−0.472965 | + | 0.881081i | \(0.656816\pi\) | |||||||
\(168\) | 0.0176121 | + | 6.17783i | 0.00135880 | + | 0.476630i | ||||
\(169\) | 12.9392i | 0.995327i | ||||||||
\(170\) | 17.0615 | + | 4.77270i | 1.30856 | + | 0.366049i | ||||
\(171\) | 14.3261i | 1.09554i | ||||||||
\(172\) | 2.57014 | − | 2.57014i | 0.195971 | − | 0.195971i | ||||
\(173\) | 9.25971 | − | 9.25971i | 0.704003 | − | 0.704003i | −0.261264 | − | 0.965267i | \(-0.584139\pi\) |
0.965267 | + | 0.261264i | \(0.0841395\pi\) | |||||||
\(174\) | 3.62721 | 0.274978 | ||||||||
\(175\) | −6.83170 | + | 11.3282i | −0.516428 | + | 0.856331i | ||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 13.6481 | − | 13.6481i | 1.02586 | − | 1.02586i | ||||
\(178\) | −3.09160 | + | 3.09160i | −0.231725 | + | 0.231725i | ||||
\(179\) | − | 12.5815i | − | 0.940384i | −0.882564 | − | 0.470192i | \(-0.844185\pi\) | ||
0.882564 | − | 0.470192i | \(-0.155815\pi\) | |||||||
\(180\) | −5.28074 | − | 1.47721i | −0.393603 | − | 0.110104i | ||||
\(181\) | − | 22.1174i | − | 1.64397i | −0.569509 | − | 0.821985i | \(-0.692867\pi\) | ||
0.569509 | − | 0.821985i | \(-0.307133\pi\) | |||||||
\(182\) | 0.652127 | − | 0.00185912i | 0.0483388 | − | 0.000137807i | ||||
\(183\) | −9.69227 | − | 9.69227i | −0.716473 | − | 0.716473i | ||||
\(184\) | 3.93704i | 0.290243i | ||||||||
\(185\) | −9.56774 | + | 5.38496i | −0.703434 | + | 0.395910i | ||||
\(186\) | −13.9536 | −1.02312 | ||||||||
\(187\) | −5.60245 | − | 5.60245i | −0.409692 | − | 0.409692i | ||||
\(188\) | 3.10826 | − | 3.10826i | 0.226694 | − | 0.226694i | ||||
\(189\) | 2.38584 | − | 2.39948i | 0.173544 | − | 0.174537i | ||||
\(190\) | −11.3838 | + | 6.40709i | −0.825869 | + | 0.464819i | ||||
\(191\) | −6.49463 | −0.469935 | −0.234967 | − | 0.972003i | \(-0.575498\pi\) | ||||
−0.234967 | + | 0.972003i | \(0.575498\pi\) | |||||||
\(192\) | −1.65110 | − | 1.65110i | −0.119158 | − | 0.119158i | ||||
\(193\) | 9.30134 | + | 9.30134i | 0.669525 | + | 0.669525i | 0.957606 | − | 0.288081i | \(-0.0930173\pi\) |
−0.288081 | + | 0.957606i | \(0.593017\pi\) | |||||||
\(194\) | 0.880916 | 0.0632461 | ||||||||
\(195\) | −0.346693 | + | 1.23936i | −0.0248272 | + | 0.0887527i | ||||
\(196\) | 0.0399116 | + | 6.99989i | 0.00285083 | + | 0.499992i | ||||
\(197\) | 8.69365 | − | 8.69365i | 0.619397 | − | 0.619397i | −0.325980 | − | 0.945377i | \(-0.605694\pi\) |
0.945377 | + | 0.325980i | \(0.105694\pi\) | |||||||
\(198\) | 1.73402 | + | 1.73402i | 0.123232 | + | 0.123232i | ||||
\(199\) | 16.3032 | 1.15570 | 0.577851 | − | 0.816142i | \(-0.303892\pi\) | ||||
0.577851 | + | 0.816142i | \(0.303892\pi\) | |||||||
\(200\) | −1.18790 | − | 4.85684i | −0.0839970 | − | 0.343430i | ||||
\(201\) | 22.5380i | 1.58971i | ||||||||
\(202\) | 0.261565 | + | 0.261565i | 0.0184037 | + | 0.0184037i | ||||
\(203\) | 4.10990 | − | 0.0117167i | 0.288458 | − | 0.000822353i | ||||
\(204\) | 18.5004i | 1.29529i | ||||||||
\(205\) | −3.20032 | + | 11.4406i | −0.223520 | + | 0.799044i | ||||
\(206\) | − | 11.8864i | − | 0.828166i | ||||||
\(207\) | −6.82692 | + | 6.82692i | −0.474504 | + | 0.474504i | ||||
\(208\) | −0.174289 | + | 0.174289i | −0.0120848 | + | 0.0120848i | ||||
\(209\) | 5.84195 | 0.404096 | ||||||||
\(210\) | −13.3140 | − | 3.68348i | −0.918751 | − | 0.254184i | ||||
\(211\) | 28.5557 | 1.96586 | 0.982928 | − | 0.183991i | \(-0.0589016\pi\) | ||||
0.982928 | + | 0.183991i | \(0.0589016\pi\) | |||||||
\(212\) | 6.13111 | − | 6.13111i | 0.421086 | − | 0.421086i | ||||
\(213\) | −11.9553 | + | 11.9553i | −0.819165 | + | 0.819165i | ||||
\(214\) | 5.18676i | 0.354559i | ||||||||
\(215\) | 3.98634 | + | 7.08275i | 0.271866 | + | 0.483039i | ||||
\(216\) | 1.27894i | 0.0870206i | ||||||||
\(217\) | −15.8104 | + | 0.0450732i | −1.07328 | + | 0.00305977i | ||||
\(218\) | −13.2810 | − | 13.2810i | −0.899505 | − | 0.899505i | ||||
\(219\) | − | 2.30927i | − | 0.156046i | ||||||
\(220\) | −0.602381 | + | 2.15340i | −0.0406125 | + | 0.145182i | ||||
\(221\) | 1.95289 | 0.131365 | ||||||||
\(222\) | −8.10688 | − | 8.10688i | −0.544098 | − | 0.544098i | ||||
\(223\) | −11.1562 | + | 11.1562i | −0.747076 | + | 0.747076i | −0.973929 | − | 0.226853i | \(-0.927156\pi\) |
0.226853 | + | 0.973929i | \(0.427156\pi\) | |||||||
\(224\) | −1.87615 | − | 1.86549i | −0.125356 | − | 0.124643i | ||||
\(225\) | 6.36203 | − | 10.4817i | 0.424135 | − | 0.698781i | ||||
\(226\) | −12.2452 | −0.814541 | ||||||||
\(227\) | 17.0882 | + | 17.0882i | 1.13418 | + | 1.13418i | 0.989474 | + | 0.144708i | \(0.0462242\pi\) |
0.144708 | + | 0.989474i | \(0.453776\pi\) | |||||||
\(228\) | −9.64566 | − | 9.64566i | −0.638799 | − | 0.638799i | ||||
\(229\) | −22.2615 | −1.47108 | −0.735541 | − | 0.677480i | \(-0.763072\pi\) | ||||
−0.735541 | + | 0.677480i | \(0.763072\pi\) | |||||||
\(230\) | −8.47804 | − | 2.37160i | −0.559025 | − | 0.156379i | ||||
\(231\) | 4.38084 | + | 4.35594i | 0.288238 | + | 0.286599i | ||||
\(232\) | −1.09842 | + | 1.09842i | −0.0721149 | + | 0.0721149i | ||||
\(233\) | 11.7748 | + | 11.7748i | 0.771395 | + | 0.771395i | 0.978350 | − | 0.206955i | \(-0.0663554\pi\) |
−0.206955 | + | 0.978350i | \(0.566355\pi\) | |||||||
\(234\) | −0.604442 | −0.0395136 | ||||||||
\(235\) | 4.82098 | + | 8.56570i | 0.314486 | + | 0.558765i | ||||
\(236\) | 8.26608i | 0.538076i | ||||||||
\(237\) | 12.0465 | + | 12.0465i | 0.782502 | + | 0.782502i | ||||
\(238\) | 0.0597606 | + | 20.9624i | 0.00387370 | + | 1.35879i | ||||
\(239\) | 26.4952i | 1.71383i | 0.515454 | + | 0.856917i | \(0.327623\pi\) | ||||
−0.515454 | + | 0.856917i | \(0.672377\pi\) | |||||||
\(240\) | 4.55008 | − | 2.56089i | 0.293706 | − | 0.165305i | ||||
\(241\) | − | 15.2640i | − | 0.983239i | −0.870810 | − | 0.491620i | \(-0.836405\pi\) | ||
0.870810 | − | 0.491620i | \(-0.163595\pi\) | |||||||
\(242\) | 0.707107 | − | 0.707107i | 0.0454545 | − | 0.0454545i | ||||
\(243\) | −14.3646 | + | 14.3646i | −0.921489 | + | 0.921489i | ||||
\(244\) | 5.87018 | 0.375800 | ||||||||
\(245\) | −15.0976 | − | 4.13065i | −0.964551 | − | 0.263898i | ||||
\(246\) | −12.4054 | −0.790941 | ||||||||
\(247\) | −1.01819 | + | 1.01819i | −0.0647857 | + | 0.0647857i | ||||
\(248\) | 4.22553 | − | 4.22553i | 0.268321 | − | 0.268321i | ||||
\(249\) | 29.6462i | 1.87875i | ||||||||
\(250\) | 11.1743 | + | 0.367646i | 0.706724 | + | 0.0232520i | ||||
\(251\) | − | 5.99446i | − | 0.378367i | −0.981942 | − | 0.189184i | \(-0.939416\pi\) | ||
0.981942 | − | 0.189184i | \(-0.0605841\pi\) | |||||||
\(252\) | −0.0184966 | − | 6.48809i | −0.00116518 | − | 0.408711i | ||||
\(253\) | 2.78391 | + | 2.78391i | 0.175023 | + | 0.175023i | ||||
\(254\) | 9.55866i | 0.599764i | ||||||||
\(255\) | −39.8388 | − | 11.1443i | −2.49481 | − | 0.697883i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.1867 | − | 10.1867i | −0.635427 | − | 0.635427i | 0.313997 | − | 0.949424i | \(-0.398332\pi\) |
−0.949424 | + | 0.313997i | \(0.898332\pi\) | |||||||
\(258\) | −6.00131 | + | 6.00131i | −0.373625 | + | 0.373625i | ||||
\(259\) | −9.21188 | − | 9.15950i | −0.572398 | − | 0.569144i | ||||
\(260\) | −0.270326 | − | 0.480302i | −0.0167649 | − | 0.0297871i | ||||
\(261\) | −3.80937 | −0.235794 | ||||||||
\(262\) | 2.92823 | + | 2.92823i | 0.180907 | + | 0.180907i | ||||
\(263\) | −1.12520 | − | 1.12520i | −0.0693827 | − | 0.0693827i | 0.671564 | − | 0.740947i | \(-0.265623\pi\) |
−0.740947 | + | 0.671564i | \(0.765623\pi\) | |||||||
\(264\) | −2.33501 | −0.143710 | ||||||||
\(265\) | 9.50948 | + | 16.8960i | 0.584163 | + | 1.03791i | ||||
\(266\) | −10.9604 | − | 10.8981i | −0.672025 | − | 0.668205i | ||||
\(267\) | 7.21892 | − | 7.21892i | 0.441790 | − | 0.441790i | ||||
\(268\) | −6.82513 | − | 6.82513i | −0.416911 | − | 0.416911i | ||||
\(269\) | −24.9262 | −1.51978 | −0.759889 | − | 0.650053i | \(-0.774747\pi\) | ||||
−0.759889 | + | 0.650053i | \(0.774747\pi\) | |||||||
\(270\) | −2.75406 | − | 0.770406i | −0.167607 | − | 0.0468854i | ||||
\(271\) | − | 19.9841i | − | 1.21395i | −0.794722 | − | 0.606973i | \(-0.792384\pi\) | ||
0.794722 | − | 0.606973i | \(-0.207616\pi\) | |||||||
\(272\) | −5.60245 | − | 5.60245i | −0.339698 | − | 0.339698i | ||||
\(273\) | −1.52272 | + | 0.00434106i | −0.0921594 | + | 0.000262733i | ||||
\(274\) | − | 14.3233i | − | 0.865301i | ||||||
\(275\) | −4.27428 | − | 2.59433i | −0.257748 | − | 0.156444i | ||||
\(276\) | − | 9.19304i | − | 0.553356i | ||||||
\(277\) | 12.2107 | − | 12.2107i | 0.733670 | − | 0.733670i | −0.237674 | − | 0.971345i | \(-0.576385\pi\) |
0.971345 | + | 0.237674i | \(0.0763851\pi\) | |||||||
\(278\) | 8.80421 | − | 8.80421i | 0.528041 | − | 0.528041i | ||||
\(279\) | 14.6543 | 0.877332 | ||||||||
\(280\) | 5.14730 | − | 2.91638i | 0.307610 | − | 0.174287i | ||||
\(281\) | −12.1194 | −0.722984 | −0.361492 | − | 0.932375i | \(-0.617733\pi\) | ||||
−0.361492 | + | 0.932375i | \(0.617733\pi\) | |||||||
\(282\) | −7.25783 | + | 7.25783i | −0.432198 | + | 0.432198i | ||||
\(283\) | 2.54038 | − | 2.54038i | 0.151010 | − | 0.151010i | −0.627559 | − | 0.778569i | \(-0.715946\pi\) |
0.778569 | + | 0.627559i | \(0.215946\pi\) | |||||||
\(284\) | − | 7.24081i | − | 0.429663i | ||||||
\(285\) | 26.5813 | − | 14.9606i | 1.57454 | − | 0.886191i | ||||
\(286\) | 0.246482i | 0.0145748i | ||||||||
\(287\) | −14.0563 | + | 0.0400723i | −0.829715 | + | 0.00236539i | ||||
\(288\) | 1.73402 | + | 1.73402i | 0.102178 | + | 0.102178i | ||||
\(289\) | 45.7748i | 2.69264i | ||||||||
\(290\) | −1.70367 | − | 3.02701i | −0.100043 | − | 0.177752i | ||||
\(291\) | −2.05695 | −0.120580 | ||||||||
\(292\) | 0.699312 | + | 0.699312i | 0.0409241 | + | 0.0409241i | ||||
\(293\) | −5.00456 | + | 5.00456i | −0.292370 | + | 0.292370i | −0.838016 | − | 0.545646i | \(-0.816284\pi\) |
0.545646 | + | 0.838016i | \(0.316284\pi\) | |||||||
\(294\) | −0.0931941 | − | 16.3448i | −0.00543519 | − | 0.953249i | ||||
\(295\) | −17.8002 | − | 4.97933i | −1.03637 | − | 0.289908i | ||||
\(296\) | 4.90998 | 0.285387 | ||||||||
\(297\) | 0.904344 | + | 0.904344i | 0.0524754 | + | 0.0524754i | ||||
\(298\) | −6.70838 | − | 6.70838i | −0.388606 | − | 0.388606i | ||||
\(299\) | −0.970409 | −0.0561202 | ||||||||
\(300\) | 2.77375 | + | 11.3408i | 0.160143 | + | 0.654760i | ||||
\(301\) | −6.78054 | + | 6.81931i | −0.390824 | + | 0.393058i | ||||
\(302\) | −0.130168 | + | 0.130168i | −0.00749032 | + | 0.00749032i | ||||
\(303\) | −0.610758 | − | 0.610758i | −0.0350871 | − | 0.0350871i | ||||
\(304\) | 5.84195 | 0.335059 | ||||||||
\(305\) | −3.53608 | + | 12.6409i | −0.202476 | + | 0.723813i | ||||
\(306\) | − | 19.4295i | − | 1.11071i | ||||||
\(307\) | 23.8030 | + | 23.8030i | 1.35851 | + | 1.35851i | 0.875757 | + | 0.482753i | \(0.160363\pi\) |
0.482753 | + | 0.875757i | \(0.339637\pi\) | |||||||
\(308\) | −2.64574 | + | 0.00754262i | −0.150755 | + | 0.000429781i | ||||
\(309\) | 27.7549i | 1.57892i | ||||||||
\(310\) | 6.55388 | + | 11.6446i | 0.372236 | + | 0.661371i | ||||
\(311\) | 17.3594i | 0.984360i | 0.870494 | + | 0.492180i | \(0.163800\pi\) | ||||
−0.870494 | + | 0.492180i | \(0.836200\pi\) | |||||||
\(312\) | 0.406966 | − | 0.406966i | 0.0230399 | − | 0.0230399i | ||||
\(313\) | 8.06269 | − | 8.06269i | 0.455730 | − | 0.455730i | −0.441521 | − | 0.897251i | \(-0.645561\pi\) |
0.897251 | + | 0.441521i | \(0.145561\pi\) | |||||||
\(314\) | −12.8543 | −0.725410 | ||||||||
\(315\) | 13.9826 | + | 3.86847i | 0.787831 | + | 0.217964i | ||||
\(316\) | −7.29601 | −0.410433 | ||||||||
\(317\) | 0.307140 | − | 0.307140i | 0.0172507 | − | 0.0172507i | −0.698429 | − | 0.715680i | \(-0.746117\pi\) |
0.715680 | + | 0.698429i | \(0.246117\pi\) | |||||||
\(318\) | −14.3162 | + | 14.3162i | −0.802813 | + | 0.802813i | ||||
\(319\) | 1.55340i | 0.0869738i | ||||||||
\(320\) | −0.602381 | + | 2.15340i | −0.0336741 | + | 0.120379i | ||||
\(321\) | − | 12.1111i | − | 0.675978i | ||||||
\(322\) | −0.0296956 | − | 10.4164i | −0.00165487 | − | 0.580483i | ||||
\(323\) | −32.7292 | − | 32.7292i | −1.82110 | − | 1.82110i | ||||
\(324\) | − | 10.3432i | − | 0.574620i | ||||||
\(325\) | 1.19712 | − | 0.292795i | 0.0664044 | − | 0.0162413i | ||||
\(326\) | 9.46485 | 0.524210 | ||||||||
\(327\) | 31.0114 | + | 31.0114i | 1.71493 | + | 1.71493i | ||||
\(328\) | 3.75671 | − | 3.75671i | 0.207430 | − | 0.207430i | ||||
\(329\) | −8.20022 | + | 8.24711i | −0.452093 | + | 0.454678i | ||||
\(330\) | 1.40657 | − | 5.02822i | 0.0774289 | − | 0.276794i | ||||
\(331\) | 26.9515 | 1.48139 | 0.740695 | − | 0.671841i | \(-0.234496\pi\) | ||||
0.740695 | + | 0.671841i | \(0.234496\pi\) | |||||||
\(332\) | −8.97769 | − | 8.97769i | −0.492715 | − | 0.492715i | ||||
\(333\) | 8.51401 | + | 8.51401i | 0.466565 | + | 0.466565i | ||||
\(334\) | 7.45859 | 0.408116 | ||||||||
\(335\) | 18.8086 | − | 10.5859i | 1.02762 | − | 0.578370i | ||||
\(336\) | 4.38084 | + | 4.35594i | 0.238995 | + | 0.237636i | ||||
\(337\) | 23.9680 | − | 23.9680i | 1.30562 | − | 1.30562i | 0.381076 | − | 0.924544i | \(-0.375554\pi\) |
0.924544 | − | 0.381076i | \(-0.124446\pi\) | |||||||
\(338\) | 9.14943 | + | 9.14943i | 0.497663 | + | 0.497663i | ||||
\(339\) | 28.5928 | 1.55295 | ||||||||
\(340\) | 15.4391 | − | 8.68951i | 0.837304 | − | 0.471255i | ||||
\(341\) | − | 5.97580i | − | 0.323608i | ||||||
\(342\) | 10.1301 | + | 10.1301i | 0.547772 | + | 0.547772i | ||||
\(343\) | −0.158393 | − | 18.5196i | −0.00855243 | − | 0.999963i | ||||
\(344\) | − | 3.63473i | − | 0.195971i | ||||||
\(345\) | 19.7963 | + | 5.53771i | 1.06580 | + | 0.298140i | ||||
\(346\) | − | 13.0952i | − | 0.704003i | ||||||
\(347\) | −17.6258 | + | 17.6258i | −0.946205 | + | 0.946205i | −0.998625 | − | 0.0524200i | \(-0.983307\pi\) |
0.0524200 | + | 0.998625i | \(0.483307\pi\) | |||||||
\(348\) | 2.56483 | − | 2.56483i | 0.137489 | − | 0.137489i | ||||
\(349\) | 32.5283 | 1.74120 | 0.870599 | − | 0.491993i | \(-0.163731\pi\) | ||||
0.870599 | + | 0.491993i | \(0.163731\pi\) | |||||||
\(350\) | 3.17950 | + | 12.8410i | 0.169952 | + | 0.686379i | ||||
\(351\) | −0.315234 | −0.0168260 | ||||||||
\(352\) | 0.707107 | − | 0.707107i | 0.0376889 | − | 0.0376889i | ||||
\(353\) | −19.7589 | + | 19.7589i | −1.05166 | + | 1.05166i | −0.0530679 | + | 0.998591i | \(0.516900\pi\) |
−0.998591 | + | 0.0530679i | \(0.983100\pi\) | |||||||
\(354\) | − | 19.3014i | − | 1.02586i | ||||||
\(355\) | 15.5924 | + | 4.36172i | 0.827557 | + | 0.231496i | ||||
\(356\) | 4.37218i | 0.231725i | ||||||||
\(357\) | −0.139542 | − | 48.9473i | −0.00738533 | − | 2.59057i | ||||
\(358\) | −8.89645 | − | 8.89645i | −0.470192 | − | 0.470192i | ||||
\(359\) | 0.613084i | 0.0323573i | 0.999869 | + | 0.0161787i | \(0.00515005\pi\) | ||||
−0.999869 | + | 0.0161787i | \(0.994850\pi\) | |||||||
\(360\) | −4.77859 | + | 2.68951i | −0.251854 | + | 0.141749i | ||||
\(361\) | 15.1284 | 0.796231 | ||||||||
\(362\) | −15.6393 | − | 15.6393i | −0.821985 | − | 0.821985i | ||||
\(363\) | −1.65110 | + | 1.65110i | −0.0866604 | + | 0.0866604i | ||||
\(364\) | 0.459809 | − | 0.462438i | 0.0241005 | − | 0.0242383i | ||||
\(365\) | −1.92715 | + | 1.08465i | −0.100872 | + | 0.0567731i | ||||
\(366\) | −13.7069 | −0.716473 | ||||||||
\(367\) | 9.21581 | + | 9.21581i | 0.481061 | + | 0.481061i | 0.905470 | − | 0.424409i | \(-0.139518\pi\) |
−0.424409 | + | 0.905470i | \(0.639518\pi\) | |||||||
\(368\) | 2.78391 | + | 2.78391i | 0.145121 | + | 0.145121i | ||||
\(369\) | 13.0284 | 0.678233 | ||||||||
\(370\) | −2.95768 | + | 10.5732i | −0.153762 | + | 0.549672i | ||||
\(371\) | −16.1751 | + | 16.2676i | −0.839768 | + | 0.844570i | ||||
\(372\) | −9.86666 | + | 9.86666i | −0.511562 | + | 0.511562i | ||||
\(373\) | 23.1619 | + | 23.1619i | 1.19928 | + | 1.19928i | 0.974382 | + | 0.224898i | \(0.0722048\pi\) |
0.224898 | + | 0.974382i | \(0.427795\pi\) | |||||||
\(374\) | −7.92306 | −0.409692 | ||||||||
\(375\) | −26.0921 | − | 0.858458i | −1.34739 | − | 0.0443306i | ||||
\(376\) | − | 4.39575i | − | 0.226694i | ||||||
\(377\) | −0.270741 | − | 0.270741i | −0.0139439 | − | 0.0139439i | ||||
\(378\) | −0.00964653 | − | 3.38373i | −0.000496164 | − | 0.174040i | ||||
\(379\) | − | 18.6719i | − | 0.959109i | −0.877512 | − | 0.479554i | \(-0.840798\pi\) | ||
0.877512 | − | 0.479554i | \(-0.159202\pi\) | |||||||
\(380\) | −3.51908 | + | 12.5801i | −0.180525 | + | 0.645344i | ||||
\(381\) | − | 22.3196i | − | 1.14347i | ||||||
\(382\) | −4.59239 | + | 4.59239i | −0.234967 | + | 0.234967i | ||||
\(383\) | 4.83162 | − | 4.83162i | 0.246884 | − | 0.246884i | −0.572807 | − | 0.819691i | \(-0.694145\pi\) |
0.819691 | + | 0.572807i | \(0.194145\pi\) | |||||||
\(384\) | −2.33501 | −0.119158 | ||||||||
\(385\) | 1.57750 | − | 5.70188i | 0.0803969 | − | 0.290595i | ||||
\(386\) | 13.1541 | 0.669525 | ||||||||
\(387\) | 6.30270 | − | 6.30270i | 0.320384 | − | 0.320384i | ||||
\(388\) | 0.622902 | − | 0.622902i | 0.0316230 | − | 0.0316230i | ||||
\(389\) | 32.0514i | 1.62507i | 0.582911 | + | 0.812536i | \(0.301914\pi\) | ||||
−0.582911 | + | 0.812536i | \(0.698086\pi\) | |||||||
\(390\) | 0.631214 | + | 1.12151i | 0.0319627 | + | 0.0567899i | ||||
\(391\) | − | 31.1934i | − | 1.57752i | ||||||
\(392\) | 4.97789 | + | 4.92145i | 0.251421 | + | 0.248571i | ||||
\(393\) | −6.83745 | − | 6.83745i | −0.344904 | − | 0.344904i | ||||
\(394\) | − | 12.2947i | − | 0.619397i | ||||||
\(395\) | 4.39497 | − | 15.7112i | 0.221135 | − | 0.790518i | ||||
\(396\) | 2.45228 | 0.123232 | ||||||||
\(397\) | −21.1347 | − | 21.1347i | −1.06072 | − | 1.06072i | −0.998033 | − | 0.0626889i | \(-0.980032\pi\) |
−0.0626889 | − | 0.998033i | \(-0.519968\pi\) | |||||||
\(398\) | 11.5281 | − | 11.5281i | 0.577851 | − | 0.577851i | ||||
\(399\) | 25.5927 | + | 25.4472i | 1.28124 | + | 1.27395i | ||||
\(400\) | −4.27428 | − | 2.59433i | −0.213714 | − | 0.129717i | ||||
\(401\) | −34.0114 | −1.69845 | −0.849223 | − | 0.528034i | \(-0.822929\pi\) | ||||
−0.849223 | + | 0.528034i | \(0.822929\pi\) | |||||||
\(402\) | 15.9368 | + | 15.9368i | 0.794853 | + | 0.794853i | ||||
\(403\) | 1.04152 | + | 1.04152i | 0.0518816 | + | 0.0518816i | ||||
\(404\) | 0.369909 | 0.0184037 | ||||||||
\(405\) | 22.2730 | + | 6.23052i | 1.10675 | + | 0.309597i | ||||
\(406\) | 2.89785 | − | 2.91442i | 0.143818 | − | 0.144640i | ||||
\(407\) | 3.47188 | − | 3.47188i | 0.172095 | − | 0.172095i | ||||
\(408\) | 13.0818 | + | 13.0818i | 0.647645 | + | 0.647645i | ||||
\(409\) | 4.11314 | 0.203382 | 0.101691 | − | 0.994816i | \(-0.467575\pi\) | ||||
0.101691 | + | 0.994816i | \(0.467575\pi\) | |||||||
\(410\) | 5.82673 | + | 10.3527i | 0.287762 | + | 0.511282i | ||||
\(411\) | 33.4450i | 1.64972i | ||||||||
\(412\) | −8.40496 | − | 8.40496i | −0.414083 | − | 0.414083i | ||||
\(413\) | −0.0623479 | − | 21.8699i | −0.00306794 | − | 1.07615i | ||||
\(414\) | 9.65473i | 0.474504i | ||||||||
\(415\) | 24.7406 | − | 13.9246i | 1.21447 | − | 0.683531i | ||||
\(416\) | 0.246482i | 0.0120848i | ||||||||
\(417\) | −20.5579 | + | 20.5579i | −1.00673 | + | 1.00673i | ||||
\(418\) | 4.13088 | − | 4.13088i | 0.202048 | − | 0.202048i | ||||
\(419\) | −7.61620 | −0.372076 | −0.186038 | − | 0.982543i | \(-0.559565\pi\) | ||||
−0.186038 | + | 0.982543i | \(0.559565\pi\) | |||||||
\(420\) | −12.0190 | + | 6.80978i | −0.586468 | + | 0.332283i | ||||
\(421\) | −31.1762 | −1.51943 | −0.759717 | − | 0.650254i | \(-0.774663\pi\) | ||||
−0.759717 | + | 0.650254i | \(0.774663\pi\) | |||||||
\(422\) | 20.1919 | − | 20.1919i | 0.982928 | − | 0.982928i | ||||
\(423\) | 7.62233 | − | 7.62233i | 0.370610 | − | 0.370610i | ||||
\(424\) | − | 8.67070i | − | 0.421086i | ||||||
\(425\) | 9.41178 | + | 38.4810i | 0.456538 | + | 1.86660i | ||||
\(426\) | 16.9074i | 0.819165i | ||||||||
\(427\) | −15.5310 | + | 0.0442765i | −0.751596 | + | 0.00214269i | ||||
\(428\) | 3.66759 | + | 3.66759i | 0.177280 | + | 0.177280i | ||||
\(429\) | − | 0.575538i | − | 0.0277872i | ||||||
\(430\) | 7.82703 | + | 2.18949i | 0.377453 | + | 0.105587i | ||||
\(431\) | 2.40923 | 0.116049 | 0.0580243 | − | 0.998315i | \(-0.481520\pi\) | ||||
0.0580243 | + | 0.998315i | \(0.481520\pi\) | |||||||
\(432\) | 0.904344 | + | 0.904344i | 0.0435103 | + | 0.0435103i | ||||
\(433\) | −7.56995 | + | 7.56995i | −0.363788 | + | 0.363788i | −0.865206 | − | 0.501417i | \(-0.832812\pi\) |
0.501417 | + | 0.865206i | \(0.332812\pi\) | |||||||
\(434\) | −11.1478 | + | 11.2115i | −0.535111 | + | 0.538170i | ||||
\(435\) | 3.97810 | + | 7.06810i | 0.190735 | + | 0.338890i | ||||
\(436\) | −18.7822 | −0.899505 | ||||||||
\(437\) | 16.2635 | + | 16.2635i | 0.777987 | + | 0.777987i | ||||
\(438\) | −1.63290 | − | 1.63290i | −0.0780231 | − | 0.0780231i | ||||
\(439\) | 1.17868 | 0.0562555 | 0.0281277 | − | 0.999604i | \(-0.491045\pi\) | ||||
0.0281277 | + | 0.999604i | \(0.491045\pi\) | |||||||
\(440\) | 1.09674 | + | 1.94863i | 0.0522849 | + | 0.0928974i | ||||
\(441\) | 0.0978744 | + | 17.1657i | 0.00466069 | + | 0.817413i | ||||
\(442\) | 1.38090 | − | 1.38090i | 0.0656827 | − | 0.0656827i | ||||
\(443\) | −20.5251 | − | 20.5251i | −0.975175 | − | 0.975175i | 0.0245246 | − | 0.999699i | \(-0.492193\pi\) |
−0.999699 | + | 0.0245246i | \(0.992193\pi\) | |||||||
\(444\) | −11.4649 | −0.544098 | ||||||||
\(445\) | −9.41506 | − | 2.63372i | −0.446317 | − | 0.124850i | ||||
\(446\) | 15.7773i | 0.747076i | ||||||||
\(447\) | 15.6641 | + | 15.6641i | 0.740888 | + | 0.740888i | ||||
\(448\) | −2.64574 | + | 0.00754262i | −0.124999 | + | 0.000356355i | ||||
\(449\) | − | 20.3061i | − | 0.958303i | −0.877732 | − | 0.479151i | \(-0.840944\pi\) | ||
0.877732 | − | 0.479151i | \(-0.159056\pi\) | |||||||
\(450\) | −2.91306 | − | 11.9103i | −0.137323 | − | 0.561458i | ||||
\(451\) | − | 5.31279i | − | 0.250169i | ||||||
\(452\) | −8.65869 | + | 8.65869i | −0.407271 | + | 0.407271i | ||||
\(453\) | 0.303944 | − | 0.303944i | 0.0142805 | − | 0.0142805i | ||||
\(454\) | 24.1663 | 1.13418 | ||||||||
\(455\) | 0.718834 | + | 1.26872i | 0.0336995 | + | 0.0594783i | ||||
\(456\) | −13.6410 | −0.638799 | ||||||||
\(457\) | −12.7759 | + | 12.7759i | −0.597633 | + | 0.597633i | −0.939682 | − | 0.342049i | \(-0.888879\pi\) |
0.342049 | + | 0.939682i | \(0.388879\pi\) | |||||||
\(458\) | −15.7413 | + | 15.7413i | −0.735541 | + | 0.735541i | ||||
\(459\) | − | 10.1331i | − | 0.472972i | ||||||
\(460\) | −7.67185 | + | 4.31790i | −0.357702 | + | 0.201323i | ||||
\(461\) | 2.72914i | 0.127108i | 0.997978 | + | 0.0635542i | \(0.0202436\pi\) | ||||
−0.997978 | + | 0.0635542i | \(0.979756\pi\) | |||||||
\(462\) | 6.17783 | − | 0.0176121i | 0.287419 | − | 0.000819389i | ||||
\(463\) | 20.9039 | + | 20.9039i | 0.971486 | + | 0.971486i | 0.999605 | − | 0.0281184i | \(-0.00895154\pi\) |
−0.0281184 | + | 0.999605i | \(0.508952\pi\) | |||||||
\(464\) | 1.55340i | 0.0721149i | ||||||||
\(465\) | −15.3034 | − | 27.1904i | −0.709678 | − | 1.26092i | ||||
\(466\) | 16.6521 | 0.771395 | ||||||||
\(467\) | 7.04339 | + | 7.04339i | 0.325929 | + | 0.325929i | 0.851036 | − | 0.525107i | \(-0.175975\pi\) |
−0.525107 | + | 0.851036i | \(0.675975\pi\) | |||||||
\(468\) | −0.427405 | + | 0.427405i | −0.0197568 | + | 0.0197568i | ||||
\(469\) | 18.1090 | + | 18.0060i | 0.836196 | + | 0.831442i | ||||
\(470\) | 9.46581 | + | 2.64791i | 0.436625 | + | 0.122139i | ||||
\(471\) | 30.0149 | 1.38302 | ||||||||
\(472\) | 5.84500 | + | 5.84500i | 0.269038 | + | 0.269038i | ||||
\(473\) | −2.57014 | − | 2.57014i | −0.118175 | − | 0.118175i | ||||
\(474\) | 17.0363 | 0.782502 | ||||||||
\(475\) | −24.9701 | − | 15.1560i | −1.14571 | − | 0.695404i | ||||
\(476\) | 14.8649 | + | 14.7804i | 0.681331 | + | 0.677457i | ||||
\(477\) | 15.0352 | − | 15.0352i | 0.688414 | − | 0.688414i | ||||
\(478\) | 18.7350 | + | 18.7350i | 0.856917 | + | 0.856917i | ||||
\(479\) | −28.4335 | −1.29916 | −0.649579 | − | 0.760294i | \(-0.725055\pi\) | ||||
−0.649579 | + | 0.760294i | \(0.725055\pi\) | |||||||
\(480\) | 1.40657 | − | 5.02822i | 0.0642006 | − | 0.229506i | ||||
\(481\) | 1.21022i | 0.0551813i | ||||||||
\(482\) | −10.7933 | − | 10.7933i | −0.491620 | − | 0.491620i | ||||
\(483\) | 0.0693396 | + | 24.3224i | 0.00315506 | + | 1.10671i | ||||
\(484\) | − | 1.00000i | − | 0.0454545i | ||||||
\(485\) | 0.966133 | + | 1.71658i | 0.0438699 | + | 0.0779459i | ||||
\(486\) | 20.3146i | 0.921489i | ||||||||
\(487\) | 2.98613 | − | 2.98613i | 0.135314 | − | 0.135314i | −0.636205 | − | 0.771520i | \(-0.719497\pi\) |
0.771520 | + | 0.636205i | \(0.219497\pi\) | |||||||
\(488\) | 4.15084 | − | 4.15084i | 0.187900 | − | 0.187900i | ||||
\(489\) | −22.1005 | −0.999421 | ||||||||
\(490\) | −13.5964 | + | 7.75481i | −0.614224 | + | 0.350327i | ||||
\(491\) | −41.7259 | −1.88306 | −0.941531 | − | 0.336927i | \(-0.890612\pi\) | ||||
−0.941531 | + | 0.336927i | \(0.890612\pi\) | |||||||
\(492\) | −8.77196 | + | 8.77196i | −0.395470 | + | 0.395470i | ||||
\(493\) | 8.70285 | − | 8.70285i | 0.391957 | − | 0.391957i | ||||
\(494\) | 1.43993i | 0.0647857i | ||||||||
\(495\) | −1.47721 | + | 5.28074i | −0.0663954 | + | 0.237352i | ||||
\(496\) | − | 5.97580i | − | 0.268321i | ||||||
\(497\) | 0.0546147 | + | 19.1573i | 0.00244980 | + | 0.859323i | ||||
\(498\) | 20.9630 | + | 20.9630i | 0.939375 | + | 0.939375i | ||||
\(499\) | − | 22.5409i | − | 1.00907i | −0.863392 | − | 0.504534i | \(-0.831664\pi\) | ||
0.863392 | − | 0.504534i | \(-0.168336\pi\) | |||||||
\(500\) | 8.16138 | − | 7.64145i | 0.364988 | − | 0.341736i | ||||
\(501\) | −17.4159 | −0.778085 | ||||||||
\(502\) | −4.23872 | − | 4.23872i | −0.189184 | − | 0.189184i | ||||
\(503\) | 16.1802 | − | 16.1802i | 0.721438 | − | 0.721438i | −0.247460 | − | 0.968898i | \(-0.579596\pi\) |
0.968898 | + | 0.247460i | \(0.0795960\pi\) | |||||||
\(504\) | −4.60085 | − | 4.57470i | −0.204938 | − | 0.203773i | ||||
\(505\) | −0.222826 | + | 0.796563i | −0.00991563 | + | 0.0354466i | ||||
\(506\) | 3.93704 | 0.175023 | ||||||||
\(507\) | −21.3640 | − | 21.3640i | −0.948810 | − | 0.948810i | ||||
\(508\) | 6.75899 | + | 6.75899i | 0.299882 | + | 0.299882i | ||||
\(509\) | −23.9927 | −1.06346 | −0.531729 | − | 0.846914i | \(-0.678458\pi\) | ||||
−0.531729 | + | 0.846914i | \(0.678458\pi\) | |||||||
\(510\) | −36.0505 | + | 20.2901i | −1.59634 | + | 0.898461i | ||||
\(511\) | −1.85547 | − | 1.84492i | −0.0820813 | − | 0.0816146i | ||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 5.28313 | + | 5.28313i | 0.233256 | + | 0.233256i | ||||
\(514\) | −14.4061 | −0.635427 | ||||||||
\(515\) | 23.1622 | − | 13.0363i | 1.02065 | − | 0.574447i | ||||
\(516\) | 8.48713i | 0.373625i | ||||||||
\(517\) | −3.10826 | − | 3.10826i | −0.136701 | − | 0.136701i | ||||
\(518\) | −12.9905 | + | 0.0370341i | −0.570771 | + | 0.00162718i | ||||
\(519\) | 30.5775i | 1.34220i | ||||||||
\(520\) | −0.530774 | − | 0.148476i | −0.0232760 | − | 0.00651109i | ||||
\(521\) | − | 36.3625i | − | 1.59307i | −0.604591 | − | 0.796536i | \(-0.706663\pi\) | ||
0.604591 | − | 0.796536i | \(-0.293337\pi\) | |||||||
\(522\) | −2.69363 | + | 2.69363i | −0.117897 | + | 0.117897i | ||||
\(523\) | −2.72002 | + | 2.72002i | −0.118938 | + | 0.118938i | −0.764071 | − | 0.645133i | \(-0.776802\pi\) |
0.645133 | + | 0.764071i | \(0.276802\pi\) | |||||||
\(524\) | 4.14114 | 0.180907 | ||||||||
\(525\) | −7.42417 | − | 29.9838i | −0.324017 | − | 1.30860i | ||||
\(526\) | −1.59127 | −0.0693827 | ||||||||
\(527\) | −33.4791 | + | 33.4791i | −1.45837 | + | 1.45837i | ||||
\(528\) | −1.65110 | + | 1.65110i | −0.0718550 | + | 0.0718550i | ||||
\(529\) | − | 7.49968i | − | 0.326073i | ||||||
\(530\) | 18.6715 | + | 5.22306i | 0.811038 | + | 0.226875i | ||||
\(531\) | 20.2707i | 0.879675i | ||||||||
\(532\) | −15.4563 | + | 0.0440636i | −0.670115 | + | 0.00191040i | ||||
\(533\) | 0.925960 | + | 0.925960i | 0.0401078 | + | 0.0401078i | ||||
\(534\) | − | 10.2091i | − | 0.441790i | ||||||
\(535\) | −10.1071 | + | 5.68851i | −0.436967 | + | 0.245936i | ||||
\(536\) | −9.65219 | −0.416911 | ||||||||
\(537\) | 20.7733 | + | 20.7733i | 0.896434 | + | 0.896434i | ||||
\(538\) | −17.6255 | + | 17.6255i | −0.759889 | + | 0.759889i | ||||
\(539\) | 6.99989 | − | 0.0399116i | 0.301506 | − | 0.00171912i | ||||
\(540\) | −2.49218 | + | 1.40266i | −0.107246 | + | 0.0603607i | ||||
\(541\) | −0.196243 | −0.00843715 | −0.00421857 | − | 0.999991i | \(-0.501343\pi\) | ||||
−0.00421857 | + | 0.999991i | \(0.501343\pi\) | |||||||
\(542\) | −14.1309 | − | 14.1309i | −0.606973 | − | 0.606973i | ||||
\(543\) | 36.5180 | + | 36.5180i | 1.56714 | + | 1.56714i | ||||
\(544\) | −7.92306 | −0.339698 | ||||||||
\(545\) | 11.3140 | − | 40.4456i | 0.484640 | − | 1.73250i | ||||
\(546\) | −1.07366 | + | 1.07980i | −0.0459483 | + | 0.0462111i | ||||
\(547\) | −13.3227 | + | 13.3227i | −0.569639 | + | 0.569639i | −0.932027 | − | 0.362388i | \(-0.881961\pi\) |
0.362388 | + | 0.932027i | \(0.381961\pi\) | |||||||
\(548\) | −10.1281 | − | 10.1281i | −0.432650 | − | 0.432650i | ||||
\(549\) | 14.3953 | 0.614377 | ||||||||
\(550\) | −4.85684 | + | 1.18790i | −0.207096 | + | 0.0506521i | ||||
\(551\) | 9.07490i | 0.386604i | ||||||||
\(552\) | −6.50046 | − | 6.50046i | −0.276678 | − | 0.276678i | ||||
\(553\) | 19.3033 | − | 0.0550310i | 0.820862 | − | 0.00234016i | ||||
\(554\) | − | 17.2686i | − | 0.733670i | ||||||
\(555\) | 6.90621 | − | 24.6884i | 0.293152 | − | 1.04797i | ||||
\(556\) | − | 12.4510i | − | 0.528041i | ||||||
\(557\) | 5.60100 | − | 5.60100i | 0.237322 | − | 0.237322i | −0.578418 | − | 0.815740i | \(-0.696330\pi\) |
0.815740 | + | 0.578418i | \(0.196330\pi\) | |||||||
\(558\) | 10.3622 | − | 10.3622i | 0.438666 | − | 0.438666i | ||||
\(559\) | 0.895894 | 0.0378923 | ||||||||
\(560\) | 1.57750 | − | 5.70188i | 0.0666616 | − | 0.240949i | ||||
\(561\) | 18.5004 | 0.781089 | ||||||||
\(562\) | −8.56973 | + | 8.56973i | −0.361492 | + | 0.361492i | ||||
\(563\) | −15.0915 | + | 15.0915i | −0.636032 | + | 0.636032i | −0.949574 | − | 0.313542i | \(-0.898484\pi\) |
0.313542 | + | 0.949574i | \(0.398484\pi\) | |||||||
\(564\) | 10.2641i | 0.432198i | ||||||||
\(565\) | −13.4298 | − | 23.8615i | −0.564997 | − | 1.00386i | ||||
\(566\) | − | 3.59264i | − | 0.151010i | ||||||
\(567\) | 0.0780146 | + | 27.3653i | 0.00327630 | + | 1.14924i | ||||
\(568\) | −5.12003 | − | 5.12003i | −0.214832 | − | 0.214832i | ||||
\(569\) | 0.116714i | 0.00489292i | 0.999997 | + | 0.00244646i | \(0.000778734\pi\) | ||||
−0.999997 | + | 0.00244646i | \(0.999221\pi\) | |||||||
\(570\) | 8.21709 | − | 29.3746i | 0.344176 | − | 1.23037i | ||||
\(571\) | 16.3706 | 0.685090 | 0.342545 | − | 0.939501i | \(-0.388711\pi\) | ||||
0.342545 | + | 0.939501i | \(0.388711\pi\) | |||||||
\(572\) | 0.174289 | + | 0.174289i | 0.00728738 | + | 0.00728738i | ||||
\(573\) | 10.7233 | − | 10.7233i | 0.447972 | − | 0.447972i | ||||
\(574\) | −9.91094 | + | 9.96761i | −0.413675 | + | 0.416040i | ||||
\(575\) | −4.67681 | − | 19.1216i | −0.195036 | − | 0.797426i | ||||
\(576\) | 2.45228 | 0.102178 | ||||||||
\(577\) | 4.06513 | + | 4.06513i | 0.169234 | + | 0.169234i | 0.786642 | − | 0.617409i | \(-0.211818\pi\) |
−0.617409 | + | 0.786642i | \(0.711818\pi\) | |||||||
\(578\) | 32.3677 | + | 32.3677i | 1.34632 | + | 1.34632i | ||||
\(579\) | −30.7149 | −1.27647 | ||||||||
\(580\) | −3.34510 | − | 0.935739i | −0.138898 | − | 0.0388545i | ||||
\(581\) | 23.8204 | + | 23.6849i | 0.988235 | + | 0.982616i | ||||
\(582\) | −1.45448 | + | 1.45448i | −0.0602902 | + | 0.0602902i | ||||
\(583\) | −6.13111 | − | 6.13111i | −0.253925 | − | 0.253925i | ||||
\(584\) | 0.988977 | 0.0409241 | ||||||||
\(585\) | −0.662914 | − | 1.17783i | −0.0274081 | − | 0.0486975i | ||||
\(586\) | 7.07752i | 0.292370i | ||||||||
\(587\) | −5.94212 | − | 5.94212i | −0.245257 | − | 0.245257i | 0.573764 | − | 0.819021i | \(-0.305483\pi\) |
−0.819021 | + | 0.573764i | \(0.805483\pi\) | |||||||
\(588\) | −11.6234 | − | 11.4916i | −0.479342 | − | 0.473907i | ||||
\(589\) | − | 34.9103i | − | 1.43846i | ||||||
\(590\) | −16.1075 | + | 9.06572i | −0.663137 | + | 0.373230i | ||||
\(591\) | 28.7082i | 1.18090i | ||||||||
\(592\) | 3.47188 | − | 3.47188i | 0.142693 | − | 0.142693i | ||||
\(593\) | −30.1675 | + | 30.1675i | −1.23883 | + | 1.23883i | −0.278350 | + | 0.960480i | \(0.589787\pi\) |
−0.960480 | + | 0.278350i | \(0.910213\pi\) | |||||||
\(594\) | 1.27894 | 0.0524754 | ||||||||
\(595\) | −40.7824 | + | 23.1066i | −1.67191 | + | 0.947280i | ||||
\(596\) | −9.48708 | −0.388606 | ||||||||
\(597\) | −26.9182 | + | 26.9182i | −1.10169 | + | 1.10169i | ||||
\(598\) | −0.686183 | + | 0.686183i | −0.0280601 | + | 0.0280601i | ||||
\(599\) | − | 44.7384i | − | 1.82796i | −0.405760 | − | 0.913980i | \(-0.632993\pi\) | ||
0.405760 | − | 0.913980i | \(-0.367007\pi\) | |||||||
\(600\) | 9.98048 | + | 6.05780i | 0.407451 | + | 0.247309i | ||||
\(601\) | − | 20.5386i | − | 0.837786i | −0.908036 | − | 0.418893i | \(-0.862418\pi\) | ||
0.908036 | − | 0.418893i | \(-0.137582\pi\) | |||||||
\(602\) | 0.0274154 | + | 9.61654i | 0.00111737 | + | 0.391941i | ||||
\(603\) | −16.7371 | − | 16.7371i | −0.681588 | − | 0.681588i | ||||
\(604\) | 0.184085i | 0.00749032i | ||||||||
\(605\) | 2.15340 | + | 0.602381i | 0.0875482 | + | 0.0244903i | ||||
\(606\) | −0.863742 | −0.0350871 | ||||||||
\(607\) | 7.82014 | + | 7.82014i | 0.317410 | + | 0.317410i | 0.847771 | − | 0.530362i | \(-0.177944\pi\) |
−0.530362 | + | 0.847771i | \(0.677944\pi\) | |||||||
\(608\) | 4.13088 | − | 4.13088i | 0.167529 | − | 0.167529i | ||||
\(609\) | −6.76652 | + | 6.80521i | −0.274193 | + | 0.275761i | ||||
\(610\) | 6.43805 | + | 11.4388i | 0.260669 | + | 0.463144i | ||||
\(611\) | 1.08347 | 0.0438326 | ||||||||
\(612\) | −13.7388 | − | 13.7388i | −0.555356 | − | 0.555356i | ||||
\(613\) | −23.6072 | − | 23.6072i | −0.953487 | − | 0.953487i | 0.0454782 | − | 0.998965i | \(-0.485519\pi\) |
−0.998965 | + | 0.0454782i | \(0.985519\pi\) | |||||||
\(614\) | 33.6625 | 1.35851 | ||||||||
\(615\) | −13.6055 | − | 24.1736i | −0.548626 | − | 0.974774i | ||||
\(616\) | −1.86549 | + | 1.87615i | −0.0751626 | + | 0.0755924i | ||||
\(617\) | 21.0998 | − | 21.0998i | 0.849445 | − | 0.849445i | −0.140619 | − | 0.990064i | \(-0.544909\pi\) |
0.990064 | + | 0.140619i | \(0.0449092\pi\) | |||||||
\(618\) | 19.6257 | + | 19.6257i | 0.789461 | + | 0.789461i | ||||
\(619\) | 21.5632 | 0.866698 | 0.433349 | − | 0.901226i | \(-0.357332\pi\) | ||||
0.433349 | + | 0.901226i | \(0.357332\pi\) | |||||||
\(620\) | 12.8683 | + | 3.59971i | 0.516803 | + | 0.144568i | ||||
\(621\) | 5.03523i | 0.202057i | ||||||||
\(622\) | 12.2749 | + | 12.2749i | 0.492180 | + | 0.492180i | ||||
\(623\) | −0.0329777 | − | 11.5677i | −0.00132122 | − | 0.463448i | ||||
\(624\) | − | 0.575538i | − | 0.0230399i | ||||||
\(625\) | 11.5389 | + | 22.1778i | 0.461554 | + | 0.887112i | ||||
\(626\) | − | 11.4024i | − | 0.455730i | ||||||
\(627\) | −9.64566 | + | 9.64566i | −0.385211 | + | 0.385211i | ||||
\(628\) | −9.08936 | + | 9.08936i | −0.362705 | + | 0.362705i | ||||
\(629\) | −38.9020 | −1.55113 | ||||||||
\(630\) | 12.6226 | − | 7.15178i | 0.502897 | − | 0.284934i | ||||
\(631\) | −1.20140 | −0.0478271 | −0.0239135 | − | 0.999714i | \(-0.507613\pi\) | ||||
−0.0239135 | + | 0.999714i | \(0.507613\pi\) | |||||||
\(632\) | −5.15906 | + | 5.15906i | −0.205216 | + | 0.205216i | ||||
\(633\) | −47.1484 | + | 47.1484i | −1.87398 | + | 1.87398i | ||||
\(634\) | − | 0.434362i | − | 0.0172507i | ||||||
\(635\) | −18.6263 | + | 10.4833i | −0.739163 | + | 0.416019i | ||||
\(636\) | 20.2462i | 0.802813i | ||||||||
\(637\) | −1.21305 | + | 1.22696i | −0.0480626 | + | 0.0486139i | ||||
\(638\) | 1.09842 | + | 1.09842i | 0.0434869 | + | 0.0434869i | ||||
\(639\) | − | 17.7565i | − | 0.702436i | ||||||
\(640\) | 1.09674 | + | 1.94863i | 0.0433523 | + | 0.0770264i | ||||
\(641\) | 38.7703 | 1.53133 | 0.765667 | − | 0.643237i | \(-0.222409\pi\) | ||||
0.765667 | + | 0.643237i | \(0.222409\pi\) | |||||||
\(642\) | −8.56387 | − | 8.56387i | −0.337989 | − | 0.337989i | ||||
\(643\) | −23.7814 | + | 23.7814i | −0.937845 | + | 0.937845i | −0.998178 | − | 0.0603332i | \(-0.980784\pi\) |
0.0603332 | + | 0.998178i | \(0.480784\pi\) | |||||||
\(644\) | −7.38650 | − | 7.34451i | −0.291069 | − | 0.289414i | ||||
\(645\) | −18.2762 | − | 5.11248i | −0.719624 | − | 0.201304i | ||||
\(646\) | −46.2861 | −1.82110 | ||||||||
\(647\) | 16.5759 | + | 16.5759i | 0.651665 | + | 0.651665i | 0.953394 | − | 0.301729i | \(-0.0975636\pi\) |
−0.301729 | + | 0.953394i | \(0.597564\pi\) | |||||||
\(648\) | −7.31372 | − | 7.31372i | −0.287310 | − | 0.287310i | ||||
\(649\) | 8.26608 | 0.324472 | ||||||||
\(650\) | 0.639456 | − | 1.05353i | 0.0250815 | − | 0.0413229i | ||||
\(651\) | 26.0302 | − | 26.1790i | 1.02020 | − | 1.02604i | ||||
\(652\) | 6.69266 | − | 6.69266i | 0.262105 | − | 0.262105i | ||||
\(653\) | −8.93778 | − | 8.93778i | −0.349762 | − | 0.349762i | 0.510259 | − | 0.860021i | \(-0.329550\pi\) |
−0.860021 | + | 0.510259i | \(0.829550\pi\) | |||||||
\(654\) | 43.8567 | 1.71493 | ||||||||
\(655\) | −2.49454 | + | 8.91755i | −0.0974699 | + | 0.348437i | ||||
\(656\) | − | 5.31279i | − | 0.207430i | ||||||
\(657\) | 1.71491 | + | 1.71491i | 0.0669049 | + | 0.0669049i | ||||
\(658\) | 0.0331555 | + | 11.6300i | 0.00129253 | + | 0.453385i | ||||
\(659\) | 39.7412i | 1.54810i | 0.633126 | + | 0.774049i | \(0.281772\pi\) | ||||
−0.633126 | + | 0.774049i | \(0.718228\pi\) | |||||||
\(660\) | −2.56089 | − | 4.55008i | −0.0996827 | − | 0.177112i | ||||
\(661\) | − | 4.69774i | − | 0.182721i | −0.995818 | − | 0.0913605i | \(-0.970878\pi\) | ||
0.995818 | − | 0.0913605i | \(-0.0291216\pi\) | |||||||
\(662\) | 19.0576 | − | 19.0576i | 0.740695 | − | 0.740695i | ||||
\(663\) | −3.22442 | + | 3.22442i | −0.125226 | + | 0.125226i | ||||
\(664\) | −12.6964 | −0.492715 | ||||||||
\(665\) | 9.21568 | − | 33.3101i | 0.357369 | − | 1.29171i | ||||
\(666\) | 12.0406 | 0.466565 | ||||||||
\(667\) | −4.32453 | + | 4.32453i | −0.167447 | + | 0.167447i | ||||
\(668\) | 5.27402 | − | 5.27402i | 0.204058 | − | 0.204058i | ||||
\(669\) | − | 36.8401i | − | 1.42432i | ||||||
\(670\) | 5.81429 | − | 20.7850i | 0.224626 | − | 0.802996i | ||||
\(671\) | − | 5.87018i | − | 0.226616i | ||||||
\(672\) | 6.17783 | − | 0.0176121i | 0.238315 | − | 0.000679402i | ||||
\(673\) | −0.821891 | − | 0.821891i | −0.0316816 | − | 0.0316816i | 0.691089 | − | 0.722770i | \(-0.257131\pi\) |
−0.722770 | + | 0.691089i | \(0.757131\pi\) | |||||||
\(674\) | − | 33.8959i | − | 1.30562i | ||||||
\(675\) | −1.51924 | − | 6.21159i | −0.0584758 | − | 0.239084i | ||||
\(676\) | 12.9392 | 0.497663 | ||||||||
\(677\) | 22.1594 | + | 22.1594i | 0.851656 | + | 0.851656i | 0.990337 | − | 0.138681i | \(-0.0442863\pi\) |
−0.138681 | + | 0.990337i | \(0.544286\pi\) | |||||||
\(678\) | 20.2181 | − | 20.2181i | 0.776473 | − | 0.776473i | ||||
\(679\) | −1.64334 | + | 1.65273i | −0.0630655 | + | 0.0634261i | ||||
\(680\) | 4.77270 | − | 17.0615i | 0.183025 | − | 0.654279i | ||||
\(681\) | −56.4287 | −2.16235 | ||||||||
\(682\) | −4.22553 | − | 4.22553i | −0.161804 | − | 0.161804i | ||||
\(683\) | −13.5920 | − | 13.5920i | −0.520082 | − | 0.520082i | 0.397514 | − | 0.917596i | \(-0.369873\pi\) |
−0.917596 | + | 0.397514i | \(0.869873\pi\) | |||||||
\(684\) | 14.3261 | 0.547772 | ||||||||
\(685\) | 27.9108 | − | 15.7089i | 1.06642 | − | 0.600205i | ||||
\(686\) | −13.2073 | − | 12.9833i | −0.504258 | − | 0.495705i | ||||
\(687\) | 36.7561 | − | 36.7561i | 1.40233 | − | 1.40233i | ||||
\(688\) | −2.57014 | − | 2.57014i | −0.0979857 | − | 0.0979857i | ||||
\(689\) | 2.13717 | 0.0814196 | ||||||||
\(690\) | 17.9139 | − | 10.0824i | 0.681969 | − | 0.383829i | ||||
\(691\) | − | 36.0061i | − | 1.36974i | −0.728667 | − | 0.684868i | \(-0.759860\pi\) | ||
0.728667 | − | 0.684868i | \(-0.240140\pi\) | |||||||
\(692\) | −9.25971 | − | 9.25971i | −0.352001 | − | 0.352001i | ||||
\(693\) | −6.48809 | + | 0.0184966i | −0.246462 | + | 0.000702628i | ||||
\(694\) | 24.9267i | 0.946205i | ||||||||
\(695\) | 26.8121 | + | 7.50026i | 1.01704 | + | 0.284501i | ||||
\(696\) | − | 3.62721i | − | 0.137489i | ||||||
\(697\) | −29.7646 | + | 29.7646i | −1.12742 | + | 1.12742i | ||||
\(698\) | 23.0010 | − | 23.0010i | 0.870599 | − | 0.870599i | ||||
\(699\) | −38.8829 | −1.47069 | ||||||||
\(700\) | 11.3282 | + | 6.83170i | 0.428165 | + | 0.258214i | ||||
\(701\) | 28.1878 | 1.06464 | 0.532319 | − | 0.846544i | \(-0.321321\pi\) | ||||
0.532319 | + | 0.846544i | \(0.321321\pi\) | |||||||
\(702\) | −0.222904 | + | 0.222904i | −0.00841298 | + | 0.00841298i | ||||
\(703\) | 20.2825 | − | 20.2825i | 0.764971 | − | 0.764971i | ||||
\(704\) | − | 1.00000i | − | 0.0376889i | ||||||
\(705\) | −22.1028 | − | 6.18291i | −0.832439 | − | 0.232862i | ||||
\(706\) | 27.9433i | 1.05166i | ||||||||
\(707\) | −0.978683 | + | 0.00279008i | −0.0368072 | + | 0.000104932i | ||||
\(708\) | −13.6481 | − | 13.6481i | −0.512929 | − | 0.512929i | ||||
\(709\) | − | 13.3379i | − | 0.500916i | −0.968127 | − | 0.250458i | \(-0.919419\pi\) | ||
0.968127 | − | 0.250458i | \(-0.0805813\pi\) | |||||||
\(710\) | 14.1097 | − | 7.94127i | 0.529527 | − | 0.298030i | ||||
\(711\) | −17.8918 | −0.670997 | ||||||||
\(712\) | 3.09160 | + | 3.09160i | 0.115863 | + | 0.115863i | ||||
\(713\) | 16.6361 | − | 16.6361i | 0.623027 | − | 0.623027i | ||||
\(714\) | −34.7097 | − | 34.5123i | −1.29898 | − | 1.29159i | ||||
\(715\) | −0.480302 | + | 0.270326i | −0.0179623 | + | 0.0101096i | ||||
\(716\) | −12.5815 | −0.470192 | ||||||||
\(717\) | −43.7463 | − | 43.7463i | −1.63374 | − | 1.63374i | ||||
\(718\) | 0.433516 | + | 0.433516i | 0.0161787 | + | 0.0161787i | ||||
\(719\) | 16.0240 | 0.597594 | 0.298797 | − | 0.954317i | \(-0.403415\pi\) | ||||
0.298797 | + | 0.954317i | \(0.403415\pi\) | |||||||
\(720\) | −1.47721 | + | 5.28074i | −0.0550522 | + | 0.196802i | ||||
\(721\) | 22.3007 | + | 22.1740i | 0.830523 | + | 0.825801i | ||||
\(722\) | 10.6974 | − | 10.6974i | 0.398115 | − | 0.398115i | ||||
\(723\) | 25.2024 | + | 25.2024i | 0.937287 | + | 0.937287i | ||||
\(724\) | −22.1174 | −0.821985 | ||||||||
\(725\) | 4.03004 | − | 6.63967i | 0.149672 | − | 0.246591i | ||||
\(726\) | 2.33501i | 0.0866604i | ||||||||
\(727\) | 14.4143 | + | 14.4143i | 0.534595 | + | 0.534595i | 0.921936 | − | 0.387341i | \(-0.126606\pi\) |
−0.387341 | + | 0.921936i | \(0.626606\pi\) | |||||||
\(728\) | −0.00185912 | − | 0.652127i | −6.89035e−5 | − | 0.0241694i | ||||
\(729\) | − | 16.4053i | − | 0.607605i | ||||||
\(730\) | −0.595740 | + | 2.12966i | −0.0220493 | + | 0.0788224i | ||||
\(731\) | 28.7981i | 1.06514i | ||||||||
\(732\) | −9.69227 | + | 9.69227i | −0.358237 | + | 0.358237i | ||||
\(733\) | 12.1058 | − | 12.1058i | 0.447138 | − | 0.447138i | −0.447264 | − | 0.894402i | \(-0.647601\pi\) |
0.894402 | + | 0.447264i | \(0.147601\pi\) | |||||||
\(734\) | 13.0331 | 0.481061 | ||||||||
\(735\) | 31.7478 | − | 18.1076i | 1.17104 | − | 0.667908i | ||||
\(736\) | 3.93704 | 0.145121 | ||||||||
\(737\) | −6.82513 | + | 6.82513i | −0.251407 | + | 0.251407i | ||||
\(738\) | 9.21249 | − | 9.21249i | 0.339117 | − | 0.339117i | ||||
\(739\) | − | 52.7975i | − | 1.94219i | −0.238702 | − | 0.971093i | \(-0.576722\pi\) | ||
0.238702 | − | 0.971093i | \(-0.423278\pi\) | |||||||
\(740\) | 5.38496 | + | 9.56774i | 0.197955 | + | 0.351717i | ||||
\(741\) | − | 3.36226i | − | 0.123516i | ||||||
\(742\) | 0.0653998 | + | 22.9404i | 0.00240090 | + | 0.842169i | ||||
\(743\) | 18.8400 | + | 18.8400i | 0.691172 | + | 0.691172i | 0.962490 | − | 0.271318i | \(-0.0874594\pi\) |
−0.271318 | + | 0.962490i | \(0.587459\pi\) | |||||||
\(744\) | 13.9536i | 0.511562i | ||||||||
\(745\) | 5.71483 | − | 20.4295i | 0.209375 | − | 0.748478i | ||||
\(746\) | 32.7559 | 1.19928 | ||||||||
\(747\) | −22.0158 | − | 22.0158i | −0.805516 | − | 0.805516i | ||||
\(748\) | −5.60245 | + | 5.60245i | −0.204846 | + | 0.204846i | ||||
\(749\) | −9.73116 | − | 9.67583i | −0.355569 | − | 0.353547i | ||||
\(750\) | −19.0569 | + | 17.8429i | −0.695861 | + | 0.651530i | ||||
\(751\) | 26.1515 | 0.954281 | 0.477141 | − | 0.878827i | \(-0.341673\pi\) | ||||
0.477141 | + | 0.878827i | \(0.341673\pi\) | |||||||
\(752\) | −3.10826 | − | 3.10826i | −0.113347 | − | 0.113347i | ||||
\(753\) | 9.89747 | + | 9.89747i | 0.360684 | + | 0.360684i | ||||
\(754\) | −0.382885 | −0.0139439 | ||||||||
\(755\) | −0.396409 | − | 0.110889i | −0.0144268 | − | 0.00403568i | ||||
\(756\) | −2.39948 | − | 2.38584i | −0.0872683 | − | 0.0867721i | ||||
\(757\) | −3.83287 | + | 3.83287i | −0.139308 | + | 0.139308i | −0.773322 | − | 0.634014i | \(-0.781406\pi\) |
0.634014 | + | 0.773322i | \(0.281406\pi\) | |||||||
\(758\) | −13.2030 | − | 13.2030i | −0.479554 | − | 0.479554i | ||||
\(759\) | −9.19304 | −0.333686 | ||||||||
\(760\) | 6.40709 | + | 11.3838i | 0.232409 | + | 0.412934i | ||||
\(761\) | 21.4031i | 0.775862i | 0.921688 | + | 0.387931i | \(0.126810\pi\) | ||||
−0.921688 | + | 0.387931i | \(0.873190\pi\) | |||||||
\(762\) | −15.7823 | − | 15.7823i | −0.571733 | − | 0.571733i | ||||
\(763\) | 49.6929 | − | 0.141667i | 1.79900 | − | 0.00512869i | ||||
\(764\) | 6.49463i | 0.234967i | ||||||||
\(765\) | 37.8610 | − | 21.3091i | 1.36887 | − | 0.770432i | ||||
\(766\) | − | 6.83294i | − | 0.246884i | ||||||
\(767\) | −1.44069 | + | 1.44069i | −0.0520201 | + | 0.0520201i | ||||
\(768\) | −1.65110 | + | 1.65110i | −0.0595790 | + | 0.0595790i | ||||
\(769\) | −30.0882 | −1.08501 | −0.542505 | − | 0.840053i | \(-0.682524\pi\) | ||||
−0.542505 | + | 0.840053i | \(0.682524\pi\) | |||||||
\(770\) | −2.91638 | − | 5.14730i | −0.105099 | − | 0.185496i | ||||
\(771\) | 33.6385 | 1.21146 | ||||||||
\(772\) | 9.30134 | − | 9.30134i | 0.334762 | − | 0.334762i | ||||
\(773\) | −28.3430 | + | 28.3430i | −1.01943 | + | 1.01943i | −0.0196183 | + | 0.999808i | \(0.506245\pi\) |
−0.999808 | + | 0.0196183i | \(0.993755\pi\) | |||||||
\(774\) | − | 8.91336i | − | 0.320384i | ||||||
\(775\) | −15.5032 | + | 25.5422i | −0.556892 | + | 0.917503i | ||||
\(776\) | − | 0.880916i | − | 0.0316230i | ||||||
\(777\) | 30.3330 | − | 0.0864750i | 1.08819 | − | 0.00310227i | ||||
\(778\) | 22.6638 | + | 22.6638i | 0.812536 | + | 0.812536i | ||||
\(779\) | − | 31.0370i | − | 1.11202i | ||||||
\(780\) | 1.23936 | + | 0.346693i | 0.0443763 | + | 0.0124136i | ||||
\(781\) | −7.24081 | −0.259097 | ||||||||
\(782\) | −22.0571 | − | 22.0571i | −0.788760 | − | 0.788760i | ||||
\(783\) | −1.40481 | + | 1.40481i | −0.0502038 | + | 0.0502038i | ||||
\(784\) | 6.99989 | − | 0.0399116i | 0.249996 | − | 0.00142542i | ||||
\(785\) | −14.0978 | − | 25.0483i | −0.503172 | − | 0.894012i | ||||
\(786\) | −9.66962 | −0.344904 | ||||||||
\(787\) | −25.2455 | − | 25.2455i | −0.899904 | − | 0.899904i | 0.0955234 | − | 0.995427i | \(-0.469548\pi\) |
−0.995427 | + | 0.0955234i | \(0.969548\pi\) | |||||||
\(788\) | −8.69365 | − | 8.69365i | −0.309699 | − | 0.309699i | ||||
\(789\) | 3.71564 | 0.132280 | ||||||||
\(790\) | −8.00181 | − | 14.2172i | −0.284691 | − | 0.505827i | ||||
\(791\) | 22.8433 | − | 22.9740i | 0.812216 | − | 0.816860i | ||||
\(792\) | 1.73402 | − | 1.73402i | 0.0616158 | − | 0.0616158i | ||||
\(793\) | 1.02311 | + | 1.02311i | 0.0363316 | + | 0.0363316i | ||||
\(794\) | −29.8890 | −1.06072 | ||||||||
\(795\) | −43.5982 | − | 12.1959i | −1.54627 | − | 0.432544i | ||||
\(796\) | − | 16.3032i | − | 0.577851i | ||||||
\(797\) | 0.829786 | + | 0.829786i | 0.0293925 | + | 0.0293925i | 0.721650 | − | 0.692258i | \(-0.243384\pi\) |
−0.692258 | + | 0.721650i | \(0.743384\pi\) | |||||||
\(798\) | 36.0906 | − | 0.102889i | 1.27759 | − | 0.00364223i | ||||
\(799\) | 34.8278i | 1.23212i | ||||||||
\(800\) | −4.85684 | + | 1.18790i | −0.171715 | + | 0.0419985i | ||||
\(801\) | 10.7218i | 0.378836i | ||||||||
\(802\) | −24.0497 | + | 24.0497i | −0.849223 | + | 0.849223i | ||||
\(803\) | 0.699312 | − | 0.699312i | 0.0246782 | − | 0.0246782i | ||||
\(804\) | 22.5380 | 0.794853 | ||||||||
\(805\) | 20.2652 | − | 11.4819i | 0.714253 | − | 0.404684i | ||||
\(806\) | 1.47293 | 0.0518816 | ||||||||
\(807\) | 41.1557 | − | 41.1557i | 1.44875 | − | 1.44875i | ||||
\(808\) | 0.261565 | − | 0.261565i | 0.00920183 | − | 0.00920183i | ||||
\(809\) | 13.0221i | 0.457834i | 0.973446 | + | 0.228917i | \(0.0735185\pi\) | ||||
−0.973446 | + | 0.228917i | \(0.926482\pi\) | |||||||
\(810\) | 20.1550 | − | 11.3437i | 0.708175 | − | 0.398578i | ||||
\(811\) | 13.6474i | 0.479226i | 0.970869 | + | 0.239613i | \(0.0770205\pi\) | ||||
−0.970869 | + | 0.239613i | \(0.922979\pi\) | |||||||
\(812\) | −0.0117167 | − | 4.10990i | −0.000411176 | − | 0.144229i | ||||
\(813\) | 32.9958 | + | 32.9958i | 1.15721 | + | 1.15721i | ||||
\(814\) | − | 4.90998i | − | 0.172095i | ||||||
\(815\) | 10.3805 | + | 18.4435i | 0.363612 | + | 0.646048i | ||||
\(816\) | 18.5004 | 0.647645 | ||||||||
\(817\) | −15.0146 | − | 15.0146i | −0.525295 | − | 0.525295i | ||||
\(818\) | 2.90843 | − | 2.90843i | 0.101691 | − | 0.101691i | ||||
\(819\) | 1.12758 | − | 1.13403i | 0.0394008 | − | 0.0396261i | ||||
\(820\) | 11.4406 | + | 3.20032i | 0.399522 | + | 0.111760i | ||||
\(821\) | 16.9473 | 0.591463 | 0.295732 | − | 0.955271i | \(-0.404437\pi\) | ||||
0.295732 | + | 0.955271i | \(0.404437\pi\) | |||||||
\(822\) | 23.6492 | + | 23.6492i | 0.824860 | + | 0.824860i | ||||
\(823\) | 9.35366 | + | 9.35366i | 0.326048 | + | 0.326048i | 0.851082 | − | 0.525034i | \(-0.175947\pi\) |
−0.525034 | + | 0.851082i | \(0.675947\pi\) | |||||||
\(824\) | −11.8864 | −0.414083 | ||||||||
\(825\) | 11.3408 | − | 2.77375i | 0.394835 | − | 0.0965697i | ||||
\(826\) | −15.5084 | − | 15.4203i | −0.539608 | − | 0.536540i | ||||
\(827\) | −10.2275 | + | 10.2275i | −0.355645 | + | 0.355645i | −0.862205 | − | 0.506560i | \(-0.830917\pi\) |
0.506560 | + | 0.862205i | \(0.330917\pi\) | |||||||
\(828\) | 6.82692 | + | 6.82692i | 0.237252 | + | 0.237252i | ||||
\(829\) | 7.06038 | 0.245217 | 0.122609 | − | 0.992455i | \(-0.460874\pi\) | ||||
0.122609 | + | 0.992455i | \(0.460874\pi\) | |||||||
\(830\) | 7.64805 | − | 27.3404i | 0.265468 | − | 0.948999i | ||||
\(831\) | 40.3223i | 1.39876i | ||||||||
\(832\) | 0.174289 | + | 0.174289i | 0.00604238 | + | 0.00604238i | ||||
\(833\) | −39.4401 | − | 38.9929i | −1.36652 | − | 1.35102i | ||||
\(834\) | 29.0733i | 1.00673i | ||||||||
\(835\) | 8.18012 | + | 14.5341i | 0.283085 | + | 0.502972i | ||||
\(836\) | − | 5.84195i | − | 0.202048i | ||||||
\(837\) | 5.40418 | − | 5.40418i | 0.186796 | − | 0.186796i | ||||
\(838\) | −5.38547 | + | 5.38547i | −0.186038 | + | 0.186038i | ||||
\(839\) | 8.36005 | 0.288621 | 0.144310 | − | 0.989532i | \(-0.453904\pi\) | ||||
0.144310 | + | 0.989532i | \(0.453904\pi\) | |||||||
\(840\) | −3.68348 | + | 13.3140i | −0.127092 | + | 0.459375i | ||||
\(841\) | 26.5869 | 0.916791 | ||||||||
\(842\) | −22.0449 | + | 22.0449i | −0.759717 | + | 0.759717i | ||||
\(843\) | 20.0104 | − | 20.0104i | 0.689195 | − | 0.689195i | ||||
\(844\) | − | 28.5557i | − | 0.982928i | ||||||
\(845\) | −7.79435 | + | 27.8634i | −0.268134 | + | 0.958530i | ||||
\(846\) | − | 10.7796i | − | 0.370610i | ||||||
\(847\) | 0.00754262 | + | 2.64574i | 0.000259167 | + | 0.0909087i | ||||
\(848\) | −6.13111 | − | 6.13111i | −0.210543 | − | 0.210543i | ||||
\(849\) | 8.38886i | 0.287905i | ||||||||
\(850\) | 33.8653 | + | 20.5551i | 1.16157 | + | 0.705033i | ||||
\(851\) | 19.3308 | 0.662651 | ||||||||
\(852\) | 11.9553 | + | 11.9553i | 0.409583 | + | 0.409583i | ||||
\(853\) | −14.5398 | + | 14.5398i | −0.497834 | + | 0.497834i | −0.910763 | − | 0.412929i | \(-0.864506\pi\) |
0.412929 | + | 0.910763i | \(0.364506\pi\) | |||||||
\(854\) | −10.9507 | + | 11.0134i | −0.374727 | + | 0.376870i | ||||
\(855\) | −8.62976 | + | 30.8498i | −0.295132 | + | 1.05504i | ||||
\(856\) | 5.18676 | 0.177280 | ||||||||
\(857\) | −7.95621 | − | 7.95621i | −0.271779 | − | 0.271779i | 0.558037 | − | 0.829816i | \(-0.311555\pi\) |
−0.829816 | + | 0.558037i | \(0.811555\pi\) | |||||||
\(858\) | −0.406966 | − | 0.406966i | −0.0138936 | − | 0.0138936i | ||||
\(859\) | −18.9137 | −0.645326 | −0.322663 | − | 0.946514i | \(-0.604578\pi\) | ||||
−0.322663 | + | 0.946514i | \(0.604578\pi\) | |||||||
\(860\) | 7.08275 | − | 3.98634i | 0.241520 | − | 0.135933i | ||||
\(861\) | 23.1422 | − | 23.2745i | 0.788683 | − | 0.793192i | ||||
\(862\) | 1.70358 | − | 1.70358i | 0.0580243 | − | 0.0580243i | ||||
\(863\) | −0.296888 | − | 0.296888i | −0.0101062 | − | 0.0101062i | 0.702036 | − | 0.712142i | \(-0.252275\pi\) |
−0.712142 | + | 0.702036i | \(0.752275\pi\) | |||||||
\(864\) | 1.27894 | 0.0435103 | ||||||||
\(865\) | 25.5177 | − | 14.3620i | 0.867629 | − | 0.488323i | ||||
\(866\) | 10.7055i | 0.363788i | ||||||||
\(867\) | −75.5789 | − | 75.5789i | −2.56679 | − | 2.56679i | ||||
\(868\) | 0.0450732 | + | 15.8104i | 0.00152988 | + | 0.536641i | ||||
\(869\) | 7.29601i | 0.247500i | ||||||||
\(870\) | 7.81084 | + | 2.18496i | 0.264812 | + | 0.0740772i | ||||
\(871\) | − | 2.37909i | − | 0.0806123i | ||||||
\(872\) | −13.2810 | + | 13.2810i | −0.449752 | + | 0.449752i | ||||
\(873\) | 1.52753 | − | 1.52753i | 0.0516990 | − | 0.0516990i | ||||
\(874\) | 23.0000 | 0.777987 | ||||||||
\(875\) | −21.5353 | + | 20.2789i | −0.728025 | + | 0.685551i | ||||
\(876\) | −2.30927 | −0.0780231 | ||||||||
\(877\) | 15.9103 | − | 15.9103i | 0.537253 | − | 0.537253i | −0.385468 | − | 0.922721i | \(-0.625960\pi\) |
0.922721 | + | 0.385468i | \(0.125960\pi\) | |||||||
\(878\) | 0.833455 | − | 0.833455i | 0.0281277 | − | 0.0281277i | ||||
\(879\) | − | 16.5261i | − | 0.557411i | ||||||
\(880\) | 2.15340 | + | 0.602381i | 0.0725911 | + | 0.0203062i | ||||
\(881\) | 16.7161i | 0.563180i | 0.959535 | + | 0.281590i | \(0.0908617\pi\) | ||||
−0.959535 | + | 0.281590i | \(0.909138\pi\) | |||||||
\(882\) | 12.2072 | + | 12.0688i | 0.411037 | + | 0.406376i | ||||
\(883\) | −25.8566 | − | 25.8566i | −0.870144 | − | 0.870144i | 0.122344 | − | 0.992488i | \(-0.460959\pi\) |
−0.992488 | + | 0.122344i | \(0.960959\pi\) | |||||||
\(884\) | − | 1.95289i | − | 0.0656827i | ||||||
\(885\) | 37.6113 | − | 21.1686i | 1.26429 | − | 0.711573i | ||||
\(886\) | −29.0268 | −0.975175 | ||||||||
\(887\) | −36.7666 | − | 36.7666i | −1.23450 | − | 1.23450i | −0.962217 | − | 0.272283i | \(-0.912221\pi\) |
−0.272283 | − | 0.962217i | \(-0.587779\pi\) | |||||||
\(888\) | −8.10688 | + | 8.10688i | −0.272049 | + | 0.272049i | ||||
\(889\) | −17.9335 | − | 17.8316i | −0.601471 | − | 0.598051i | ||||
\(890\) | −8.51977 | + | 4.79513i | −0.285583 | + | 0.160733i | ||||
\(891\) | −10.3432 | −0.346509 | ||||||||
\(892\) | 11.1562 | + | 11.1562i | 0.373538 | + | 0.373538i | ||||
\(893\) | −18.1583 | − | 18.1583i | −0.607645 | − | 0.607645i | ||||
\(894\) | 22.1524 | 0.740888 | ||||||||
\(895\) | 7.57884 | − | 27.0930i | 0.253333 | − | 0.905618i | ||||
\(896\) | −1.86549 | + | 1.87615i | −0.0623216 | + | 0.0626779i | ||||
\(897\) | 1.60225 | − | 1.60225i | 0.0534974 | − | 0.0534974i | ||||
\(898\) | −14.3586 | − | 14.3586i | −0.479151 | − | 0.479151i | ||||
\(899\) | 9.28282 | 0.309599 | ||||||||
\(900\) | −10.4817 | − | 6.36203i | −0.349390 | − | 0.212068i | ||||
\(901\) | 68.6984i | 2.28868i | ||||||||
\(902\) | −3.75671 | − | 3.75671i | −0.125085 | − | 0.125085i | ||||
\(903\) | −0.0640152 | − | 22.4547i | −0.00213029 | − | 0.747247i | ||||
\(904\) | 12.2452i | 0.407271i | ||||||||
\(905\) | 13.3231 | − | 47.6275i | 0.442874 | − | 1.58319i | ||||
\(906\) | − | 0.429841i | − | 0.0142805i | ||||||
\(907\) | −23.9547 | + | 23.9547i | −0.795403 | + | 0.795403i | −0.982367 | − | 0.186963i | \(-0.940135\pi\) |
0.186963 | + | 0.982367i | \(0.440135\pi\) | |||||||
\(908\) | 17.0882 | − | 17.0882i | 0.567091 | − | 0.567091i | ||||
\(909\) | 0.907120 | 0.0300873 | ||||||||
\(910\) | 1.40541 | + | 0.388825i | 0.0465889 | + | 0.0128894i | ||||
\(911\) | −8.04984 | −0.266703 | −0.133351 | − | 0.991069i | \(-0.542574\pi\) | ||||
−0.133351 | + | 0.991069i | \(0.542574\pi\) | |||||||
\(912\) | −9.64566 | + | 9.64566i | −0.319400 | + | 0.319400i | ||||
\(913\) | −8.97769 | + | 8.97769i | −0.297118 | + | 0.297118i | ||||
\(914\) | 18.0679i | 0.597633i | ||||||||
\(915\) | −15.0329 | − | 26.7098i | −0.496973 | − | 0.882998i | ||||
\(916\) | 22.2615i | 0.735541i | ||||||||
\(917\) | −10.9564 | + | 0.0312351i | −0.361812 | + | 0.00103147i | ||||
\(918\) | −7.16517 | − | 7.16517i | −0.236486 | − | 0.236486i | ||||
\(919\) | − | 38.1618i | − | 1.25884i | −0.777065 | − | 0.629420i | \(-0.783292\pi\) | ||
0.777065 | − | 0.629420i | \(-0.216708\pi\) | |||||||
\(920\) | −2.37160 | + | 8.47804i | −0.0781893 | + | 0.279513i | ||||
\(921\) | −78.6024 | −2.59004 | ||||||||
\(922\) | 1.92979 | + | 1.92979i | 0.0635542 | + | 0.0635542i | ||||
\(923\) | 1.26199 | − | 1.26199i | 0.0415390 | − | 0.0415390i | ||||
\(924\) | 4.35594 | − | 4.38084i | 0.143300 | − | 0.144119i | ||||
\(925\) | −23.8470 | + | 5.83255i | −0.784084 | + | 0.191773i | ||||
\(926\) | 29.5626 | 0.971486 | ||||||||
\(927\) | −20.6113 | − | 20.6113i | −0.676964 | − | 0.676964i | ||||
\(928\) | 1.09842 | + | 1.09842i | 0.0360574 | + | 0.0360574i | ||||
\(929\) | −44.9165 | −1.47366 | −0.736831 | − | 0.676077i | \(-0.763679\pi\) | ||||
−0.736831 | + | 0.676077i | \(0.763679\pi\) | |||||||
\(930\) | −30.0476 | − | 8.40536i | −0.985300 | − | 0.275622i | ||||
\(931\) | 40.8930 | − | 0.233162i | 1.34021 | − | 0.00764157i | ||||
\(932\) | 11.7748 | − | 11.7748i | 0.385698 | − | 0.385698i | ||||
\(933\) | −28.6621 | − | 28.6621i | −0.938355 | − | 0.938355i | ||||
\(934\) | 9.96086 | 0.325929 | ||||||||
\(935\) | −8.68951 | − | 15.4391i | −0.284177 | − | 0.504913i | ||||
\(936\) | 0.604442i | 0.0197568i | ||||||||
\(937\) | 17.2385 | + | 17.2385i | 0.563158 | + | 0.563158i | 0.930203 | − | 0.367045i | \(-0.119631\pi\) |
−0.367045 | + | 0.930203i | \(0.619631\pi\) | |||||||
\(938\) | 25.5372 | − | 0.0728028i | 0.833819 | − | 0.00237710i | ||||
\(939\) | 26.6246i | 0.868863i | ||||||||
\(940\) | 8.56570 | − | 4.82098i | 0.279382 | − | 0.157243i | ||||
\(941\) | − | 7.51266i | − | 0.244906i | −0.992474 | − | 0.122453i | \(-0.960924\pi\) | ||
0.992474 | − | 0.122453i | \(-0.0390761\pi\) | |||||||
\(942\) | 21.2238 | − | 21.2238i | 0.691508 | − | 0.691508i | ||||
\(943\) | 14.7903 | − | 14.7903i | 0.481639 | − | 0.481639i | ||||
\(944\) | 8.26608 | 0.269038 | ||||||||
\(945\) | 6.58307 | − | 3.72986i | 0.214147 | − | 0.121332i | ||||
\(946\) | −3.63473 | −0.118175 | ||||||||
\(947\) | −20.7575 | + | 20.7575i | −0.674528 | + | 0.674528i | −0.958757 | − | 0.284228i | \(-0.908263\pi\) |
0.284228 | + | 0.958757i | \(0.408263\pi\) | |||||||
\(948\) | 12.0465 | − | 12.0465i | 0.391251 | − | 0.391251i | ||||
\(949\) | 0.243765i | 0.00791294i | ||||||||
\(950\) | −28.3734 | + | 6.93964i | −0.920555 | + | 0.225152i | ||||
\(951\) | 1.01424i | 0.0328890i | ||||||||
\(952\) | 20.9624 | − | 0.0597606i | 0.679394 | − | 0.00193685i | ||||
\(953\) | −4.37098 | − | 4.37098i | −0.141590 | − | 0.141590i | 0.632759 | − | 0.774349i | \(-0.281922\pi\) |
−0.774349 | + | 0.632759i | \(0.781922\pi\) | |||||||
\(954\) | − | 21.2630i | − | 0.688414i | ||||||
\(955\) | −13.9855 | − | 3.91224i | −0.452561 | − | 0.126597i | ||||
\(956\) | 26.4952 | 0.856917 | ||||||||
\(957\) | −2.56483 | − | 2.56483i | −0.0829091 | − | 0.0829091i | ||||
\(958\) | −20.1055 | + | 20.1055i | −0.649579 | + | 0.649579i | ||||
\(959\) | 26.8727 | + | 26.7199i | 0.867764 | + | 0.862830i | ||||
\(960\) | −2.56089 | − | 4.55008i | −0.0826525 | − | 0.146853i | ||||
\(961\) | −4.71019 | −0.151942 | ||||||||
\(962\) | 0.855754 | + | 0.855754i | 0.0275906 | + | 0.0275906i | ||||
\(963\) | 8.99396 | + | 8.99396i | 0.289826 | + | 0.289826i | ||||
\(964\) | −15.2640 | −0.491620 | ||||||||
\(965\) | 14.4266 | + | 25.6325i | 0.464408 | + | 0.825138i | ||||
\(966\) | 17.2476 | + | 17.1495i | 0.554931 | + | 0.551776i | ||||
\(967\) | −2.91714 | + | 2.91714i | −0.0938089 | + | 0.0938089i | −0.752454 | − | 0.658645i | \(-0.771130\pi\) |
0.658645 | + | 0.752454i | \(0.271130\pi\) | |||||||
\(968\) | −0.707107 | − | 0.707107i | −0.0227273 | − | 0.0227273i | ||||
\(969\) | 108.079 | 3.47198 | ||||||||
\(970\) | 1.89697 | + | 0.530647i | 0.0609079 | + | 0.0170380i | ||||
\(971\) | − | 52.8711i | − | 1.69672i | −0.529423 | − | 0.848358i | \(-0.677592\pi\) | ||
0.529423 | − | 0.848358i | \(-0.322408\pi\) | |||||||
\(972\) | 14.3646 | + | 14.3646i | 0.460745 | + | 0.460745i | ||||
\(973\) | 0.0939134 | + | 32.9422i | 0.00301073 | + | 1.05608i | ||||
\(974\) | − | 4.22302i | − | 0.135314i | ||||||
\(975\) | −1.49314 | + | 2.46001i | −0.0478187 | + | 0.0787832i | ||||
\(976\) | − | 5.87018i | − | 0.187900i | ||||||
\(977\) | −1.30914 | + | 1.30914i | −0.0418832 | + | 0.0418832i | −0.727738 | − | 0.685855i | \(-0.759428\pi\) |
0.685855 | + | 0.727738i | \(0.259428\pi\) | |||||||
\(978\) | −15.6274 | + | 15.6274i | −0.499710 | + | 0.499710i | ||||
\(979\) | 4.37218 | 0.139735 | ||||||||
\(980\) | −4.13065 | + | 15.0976i | −0.131949 | + | 0.482275i | ||||
\(981\) | −46.0592 | −1.47056 | ||||||||
\(982\) | −29.5046 | + | 29.5046i | −0.941531 | + | 0.941531i | ||||
\(983\) | 6.95163 | − | 6.95163i | 0.221723 | − | 0.221723i | −0.587501 | − | 0.809224i | \(-0.699888\pi\) |
0.809224 | + | 0.587501i | \(0.199888\pi\) | |||||||
\(984\) | 12.4054i | 0.395470i | ||||||||
\(985\) | 23.9578 | − | 13.4840i | 0.763359 | − | 0.429637i | ||||
\(986\) | − | 12.3077i | − | 0.391957i | ||||||
\(987\) | −0.0774184 | − | 27.1562i | −0.00246425 | − | 0.864392i | ||||
\(988\) | 1.01819 | + | 1.01819i | 0.0323928 | + | 0.0323928i | ||||
\(989\) | − | 14.3101i | − | 0.455034i | ||||||
\(990\) | 2.68951 | + | 4.77859i | 0.0854781 | + | 0.151874i | ||||
\(991\) | −15.7718 | −0.501007 | −0.250503 | − | 0.968116i | \(-0.580596\pi\) | ||||
−0.250503 | + | 0.968116i | \(0.580596\pi\) | |||||||
\(992\) | −4.22553 | − | 4.22553i | −0.134161 | − | 0.134161i | ||||
\(993\) | −44.4998 | + | 44.4998i | −1.41216 | + | 1.41216i | ||||
\(994\) | 13.5849 | + | 13.5076i | 0.430886 | + | 0.428436i | ||||
\(995\) | 35.1073 | + | 9.82072i | 1.11298 | + | 0.311338i | ||||
\(996\) | 29.6462 | 0.939375 | ||||||||
\(997\) | −4.36904 | − | 4.36904i | −0.138369 | − | 0.138369i | 0.634530 | − | 0.772899i | \(-0.281194\pi\) |
−0.772899 | + | 0.634530i | \(0.781194\pi\) | |||||||
\(998\) | −15.9388 | − | 15.9388i | −0.504534 | − | 0.504534i | ||||
\(999\) | 6.27955 | 0.198676 |
(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 | 770.2.l.c.573.12 | ✓ | 40 | |
5.2 | odd | 4 | inner | 770.2.l.c.727.19 | yes | 40 | |
7.6 | odd | 2 | inner | 770.2.l.c.573.19 | yes | 40 | |
35.27 | even | 4 | inner | 770.2.l.c.727.12 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.l.c.573.12 | ✓ | 40 | 1.1 | even | 1 | trivial | |
770.2.l.c.573.19 | yes | 40 | 7.6 | odd | 2 | inner | |
770.2.l.c.727.12 | yes | 40 | 35.27 | even | 4 | inner | |
770.2.l.c.727.19 | yes | 40 | 5.2 | odd | 4 | inner |