Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,2,Mod(116,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.116");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.95633484952\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.226 |
Dual form | 245.2.e.f.116.2 |
$q$-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 \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | − | 1.22474i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(3\) | 0.207107 | + | 0.358719i | 0.119573 | + | 0.207107i | 0.919599 | − | 0.392859i | \(-0.128514\pi\) |
−0.800025 | + | 0.599966i | \(0.795181\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0.585786 | 0.239146 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.82843 | 1.00000 | ||||||||
\(9\) | 1.41421 | − | 2.44949i | 0.471405 | − | 0.816497i | ||||
\(10\) | 0.707107 | + | 1.22474i | 0.223607 | + | 0.387298i | ||||
\(11\) | 0.0857864 | + | 0.148586i | 0.0258656 | + | 0.0448005i | 0.878668 | − | 0.477432i | \(-0.158432\pi\) |
−0.852803 | + | 0.522233i | \(0.825099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.41421 | 1.22428 | 0.612141 | − | 0.790748i | \(-0.290308\pi\) | ||||
0.612141 | + | 0.790748i | \(0.290308\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.414214 | −0.106949 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | −1.62132 | − | 2.80821i | −0.393228 | − | 0.681091i | 0.599645 | − | 0.800266i | \(-0.295308\pi\) |
−0.992873 | + | 0.119175i | \(0.961975\pi\) | |||||||
\(18\) | −2.00000 | − | 3.46410i | −0.471405 | − | 0.816497i | ||||
\(19\) | −3.00000 | + | 5.19615i | −0.688247 | + | 1.19208i | 0.284157 | + | 0.958778i | \(0.408286\pi\) |
−0.972404 | + | 0.233301i | \(0.925047\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.242641 | 0.0517312 | ||||||||
\(23\) | −3.70711 | + | 6.42090i | −0.772985 | + | 1.33885i | 0.162935 | + | 0.986637i | \(0.447904\pi\) |
−0.935920 | + | 0.352213i | \(0.885429\pi\) | |||||||
\(24\) | 0.585786 | + | 1.01461i | 0.119573 | + | 0.207107i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 3.12132 | − | 5.40629i | 0.612141 | − | 1.06026i | ||||
\(27\) | 2.41421 | 0.464616 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.65685 | −1.60754 | −0.803769 | − | 0.594942i | \(-0.797175\pi\) | ||||
−0.803769 | + | 0.594942i | \(0.797175\pi\) | |||||||
\(30\) | −0.292893 | + | 0.507306i | −0.0534747 | + | 0.0926210i | ||||
\(31\) | −5.12132 | − | 8.87039i | −0.919816 | − | 1.59317i | −0.799693 | − | 0.600410i | \(-0.795004\pi\) |
−0.120124 | − | 0.992759i | \(-0.538329\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.0355339 | + | 0.0615465i | −0.00618566 | + | 0.0107139i | ||||
\(34\) | −4.58579 | −0.786456 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.12132 | + | 1.94218i | −0.184344 | + | 0.319293i | −0.943355 | − | 0.331784i | \(-0.892349\pi\) |
0.759011 | + | 0.651077i | \(0.225683\pi\) | |||||||
\(38\) | 4.24264 | + | 7.34847i | 0.688247 | + | 1.19208i | ||||
\(39\) | 0.914214 | + | 1.58346i | 0.146391 | + | 0.253557i | ||||
\(40\) | −1.41421 | + | 2.44949i | −0.223607 | + | 0.387298i | ||||
\(41\) | −6.24264 | −0.974937 | −0.487468 | − | 0.873141i | \(-0.662080\pi\) | ||||
−0.487468 | + | 0.873141i | \(0.662080\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.41421 | + | 2.44949i | 0.210819 | + | 0.365148i | ||||
\(46\) | 5.24264 | + | 9.08052i | 0.772985 | + | 1.33885i | ||||
\(47\) | 3.62132 | − | 6.27231i | 0.528224 | − | 0.914911i | −0.471235 | − | 0.882008i | \(-0.656192\pi\) |
0.999459 | − | 0.0329027i | \(-0.0104751\pi\) | |||||||
\(48\) | 1.65685 | 0.239146 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.41421 | −0.200000 | ||||||||
\(51\) | 0.671573 | − | 1.16320i | 0.0940390 | − | 0.162880i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.12132 | − | 3.67423i | −0.291386 | − | 0.504695i | 0.682752 | − | 0.730650i | \(-0.260783\pi\) |
−0.974138 | + | 0.225955i | \(0.927450\pi\) | |||||||
\(54\) | 1.70711 | − | 2.95680i | 0.232308 | − | 0.402369i | ||||
\(55\) | −0.171573 | −0.0231349 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.48528 | −0.329184 | ||||||||
\(58\) | −6.12132 | + | 10.6024i | −0.803769 | + | 1.39217i | ||||
\(59\) | 1.12132 | + | 1.94218i | 0.145983 | + | 0.252851i | 0.929739 | − | 0.368218i | \(-0.120032\pi\) |
−0.783756 | + | 0.621069i | \(0.786699\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.41421 | − | 2.44949i | 0.181071 | − | 0.313625i | −0.761174 | − | 0.648547i | \(-0.775377\pi\) |
0.942246 | + | 0.334922i | \(0.108710\pi\) | |||||||
\(62\) | −14.4853 | −1.83963 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | −2.20711 | + | 3.82282i | −0.273758 | + | 0.474163i | ||||
\(66\) | 0.0502525 | + | 0.0870399i | 0.00618566 | + | 0.0107139i | ||||
\(67\) | 4.12132 | + | 7.13834i | 0.503499 | + | 0.872087i | 0.999992 | + | 0.00404550i | \(0.00128773\pi\) |
−0.496492 | + | 0.868041i | \(0.665379\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.07107 | −0.369713 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.17157 | −0.376396 | −0.188198 | − | 0.982131i | \(-0.560265\pi\) | ||||
−0.188198 | + | 0.982131i | \(0.560265\pi\) | |||||||
\(72\) | 4.00000 | − | 6.92820i | 0.471405 | − | 0.816497i | ||||
\(73\) | 4.24264 | + | 7.34847i | 0.496564 | + | 0.860073i | 0.999992 | − | 0.00396356i | \(-0.00126164\pi\) |
−0.503429 | + | 0.864037i | \(0.667928\pi\) | |||||||
\(74\) | 1.58579 | + | 2.74666i | 0.184344 | + | 0.319293i | ||||
\(75\) | 0.207107 | − | 0.358719i | 0.0239146 | − | 0.0414214i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.58579 | 0.292783 | ||||||||
\(79\) | −0.742641 | + | 1.28629i | −0.0835536 | + | 0.144719i | −0.904774 | − | 0.425892i | \(-0.859960\pi\) |
0.821220 | + | 0.570611i | \(0.193294\pi\) | |||||||
\(80\) | 2.00000 | + | 3.46410i | 0.223607 | + | 0.387298i | ||||
\(81\) | −3.74264 | − | 6.48244i | −0.415849 | − | 0.720272i | ||||
\(82\) | −4.41421 | + | 7.64564i | −0.487468 | + | 0.844320i | ||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.24264 | 0.351714 | ||||||||
\(86\) | 1.41421 | − | 2.44949i | 0.152499 | − | 0.264135i | ||||
\(87\) | −1.79289 | − | 3.10538i | −0.192218 | − | 0.332932i | ||||
\(88\) | 0.242641 | + | 0.420266i | 0.0258656 | + | 0.0448005i | ||||
\(89\) | 4.00000 | − | 6.92820i | 0.423999 | − | 0.734388i | −0.572327 | − | 0.820025i | \(-0.693959\pi\) |
0.996326 | + | 0.0856373i | \(0.0272926\pi\) | |||||||
\(90\) | 4.00000 | 0.421637 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.12132 | − | 3.67423i | 0.219971 | − | 0.381000i | ||||
\(94\) | −5.12132 | − | 8.87039i | −0.528224 | − | 0.914911i | ||||
\(95\) | −3.00000 | − | 5.19615i | −0.307794 | − | 0.533114i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.2426 | 1.34459 | 0.672293 | − | 0.740285i | \(-0.265309\pi\) | ||||
0.672293 | + | 0.740285i | \(0.265309\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.485281 | 0.0487726 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.24264 | − | 2.15232i | −0.123647 | − | 0.214164i | 0.797556 | − | 0.603245i | \(-0.206126\pi\) |
−0.921203 | + | 0.389081i | \(0.872792\pi\) | |||||||
\(102\) | −0.949747 | − | 1.64501i | −0.0940390 | − | 0.162880i | ||||
\(103\) | −9.62132 | + | 16.6646i | −0.948017 | + | 1.64201i | −0.198422 | + | 0.980117i | \(0.563582\pi\) |
−0.749595 | + | 0.661897i | \(0.769752\pi\) | |||||||
\(104\) | 12.4853 | 1.22428 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | 1.24264 | − | 2.15232i | 0.120131 | − | 0.208072i | −0.799688 | − | 0.600415i | \(-0.795002\pi\) |
0.919819 | + | 0.392343i | \(0.128335\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.50000 | − | 4.33013i | −0.239457 | − | 0.414751i | 0.721102 | − | 0.692829i | \(-0.243636\pi\) |
−0.960558 | + | 0.278078i | \(0.910303\pi\) | |||||||
\(110\) | −0.121320 | + | 0.210133i | −0.0115674 | + | 0.0200354i | ||||
\(111\) | −0.928932 | −0.0881703 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.0711 | −1.22962 | −0.614811 | − | 0.788674i | \(-0.710768\pi\) | ||||
−0.614811 | + | 0.788674i | \(0.710768\pi\) | |||||||
\(114\) | −1.75736 | + | 3.04384i | −0.164592 | + | 0.285081i | ||||
\(115\) | −3.70711 | − | 6.42090i | −0.345689 | − | 0.598752i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.24264 | − | 10.8126i | 0.577132 | − | 0.999623i | ||||
\(118\) | 3.17157 | 0.291967 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.17157 | −0.106949 | ||||||||
\(121\) | 5.48528 | − | 9.50079i | 0.498662 | − | 0.863708i | ||||
\(122\) | −2.00000 | − | 3.46410i | −0.181071 | − | 0.313625i | ||||
\(123\) | −1.29289 | − | 2.23936i | −0.116576 | − | 0.201916i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.24264 | 0.731416 | 0.365708 | − | 0.930730i | \(-0.380827\pi\) | ||||
0.365708 | + | 0.930730i | \(0.380827\pi\) | |||||||
\(128\) | 5.65685 | − | 9.79796i | 0.500000 | − | 0.866025i | ||||
\(129\) | 0.414214 | + | 0.717439i | 0.0364695 | + | 0.0631670i | ||||
\(130\) | 3.12132 | + | 5.40629i | 0.273758 | + | 0.474163i | ||||
\(131\) | −6.12132 | + | 10.6024i | −0.534822 | + | 0.926339i | 0.464350 | + | 0.885652i | \(0.346288\pi\) |
−0.999172 | + | 0.0406873i | \(0.987045\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 11.6569 | 1.00700 | ||||||||
\(135\) | −1.20711 | + | 2.09077i | −0.103891 | + | 0.179945i | ||||
\(136\) | −4.58579 | − | 7.94282i | −0.393228 | − | 0.681091i | ||||
\(137\) | −6.00000 | − | 10.3923i | −0.512615 | − | 0.887875i | −0.999893 | − | 0.0146279i | \(-0.995344\pi\) |
0.487278 | − | 0.873247i | \(-0.337990\pi\) | |||||||
\(138\) | −2.17157 | + | 3.76127i | −0.184857 | + | 0.320181i | ||||
\(139\) | 7.75736 | 0.657971 | 0.328985 | − | 0.944335i | \(-0.393293\pi\) | ||||
0.328985 | + | 0.944335i | \(0.393293\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00000 | 0.252646 | ||||||||
\(142\) | −2.24264 | + | 3.88437i | −0.188198 | + | 0.325969i | ||||
\(143\) | 0.378680 | + | 0.655892i | 0.0316668 | + | 0.0548485i | ||||
\(144\) | −5.65685 | − | 9.79796i | −0.471405 | − | 0.816497i | ||||
\(145\) | 4.32843 | − | 7.49706i | 0.359456 | − | 0.622597i | ||||
\(146\) | 12.0000 | 0.993127 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.58579 | − | 7.94282i | 0.375682 | − | 0.650701i | −0.614747 | − | 0.788725i | \(-0.710742\pi\) |
0.990429 | + | 0.138024i | \(0.0440751\pi\) | |||||||
\(150\) | −0.292893 | − | 0.507306i | −0.0239146 | − | 0.0414214i | ||||
\(151\) | 3.74264 | + | 6.48244i | 0.304572 | + | 0.527534i | 0.977166 | − | 0.212478i | \(-0.0681533\pi\) |
−0.672594 | + | 0.740012i | \(0.734820\pi\) | |||||||
\(152\) | −8.48528 | + | 14.6969i | −0.688247 | + | 1.19208i | ||||
\(153\) | −9.17157 | −0.741478 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.2426 | 0.822709 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.58579 | + | 13.1390i | 0.605412 | + | 1.04860i | 0.991986 | + | 0.126346i | \(0.0403248\pi\) |
−0.386575 | + | 0.922258i | \(0.626342\pi\) | |||||||
\(158\) | 1.05025 | + | 1.81909i | 0.0835536 | + | 0.144719i | ||||
\(159\) | 0.878680 | − | 1.52192i | 0.0696838 | − | 0.120696i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −10.5858 | −0.831698 | ||||||||
\(163\) | 5.12132 | − | 8.87039i | 0.401133 | − | 0.694782i | −0.592730 | − | 0.805401i | \(-0.701950\pi\) |
0.993863 | + | 0.110619i | \(0.0352833\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.0355339 | − | 0.0615465i | −0.00276631 | − | 0.00479139i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.757359 | 0.0586062 | 0.0293031 | − | 0.999571i | \(-0.490671\pi\) | ||||
0.0293031 | + | 0.999571i | \(0.490671\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.48528 | 0.498868 | ||||||||
\(170\) | 2.29289 | − | 3.97141i | 0.175857 | − | 0.304593i | ||||
\(171\) | 8.48528 | + | 14.6969i | 0.648886 | + | 1.12390i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.62132 | − | 6.27231i | 0.275324 | − | 0.476875i | −0.694893 | − | 0.719113i | \(-0.744548\pi\) |
0.970217 | + | 0.242238i | \(0.0778816\pi\) | |||||||
\(174\) | −5.07107 | −0.384437 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.686292 | 0.0517312 | ||||||||
\(177\) | −0.464466 | + | 0.804479i | −0.0349114 | + | 0.0604683i | ||||
\(178\) | −5.65685 | − | 9.79796i | −0.423999 | − | 0.734388i | ||||
\(179\) | 7.24264 | + | 12.5446i | 0.541340 | + | 0.937629i | 0.998827 | + | 0.0484128i | \(0.0154163\pi\) |
−0.457487 | + | 0.889216i | \(0.651250\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.7279 | −1.39204 | −0.696018 | − | 0.718025i | \(-0.745047\pi\) | ||||
−0.696018 | + | 0.718025i | \(0.745047\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.17157 | 0.0866052 | ||||||||
\(184\) | −10.4853 | + | 18.1610i | −0.772985 | + | 1.33885i | ||||
\(185\) | −1.12132 | − | 1.94218i | −0.0824411 | − | 0.142792i | ||||
\(186\) | −3.00000 | − | 5.19615i | −0.219971 | − | 0.381000i | ||||
\(187\) | 0.278175 | − | 0.481813i | 0.0203421 | − | 0.0352336i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.48528 | −0.615587 | ||||||||
\(191\) | −6.98528 | + | 12.0989i | −0.505437 | + | 0.875443i | 0.494543 | + | 0.869153i | \(0.335335\pi\) |
−0.999980 | + | 0.00628978i | \(0.997998\pi\) | |||||||
\(192\) | 1.65685 | + | 2.86976i | 0.119573 | + | 0.207107i | ||||
\(193\) | 8.00000 | + | 13.8564i | 0.575853 | + | 0.997406i | 0.995948 | + | 0.0899262i | \(0.0286631\pi\) |
−0.420096 | + | 0.907480i | \(0.638004\pi\) | |||||||
\(194\) | 9.36396 | − | 16.2189i | 0.672293 | − | 1.16445i | ||||
\(195\) | −1.82843 | −0.130936 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.4142 | 0.955723 | 0.477862 | − | 0.878435i | \(-0.341412\pi\) | ||||
0.477862 | + | 0.878435i | \(0.341412\pi\) | |||||||
\(198\) | 0.343146 | − | 0.594346i | 0.0243863 | − | 0.0422383i | ||||
\(199\) | 3.70711 | + | 6.42090i | 0.262790 | + | 0.455165i | 0.966982 | − | 0.254844i | \(-0.0820241\pi\) |
−0.704192 | + | 0.710009i | \(0.748691\pi\) | |||||||
\(200\) | −1.41421 | − | 2.44949i | −0.100000 | − | 0.173205i | ||||
\(201\) | −1.70711 | + | 2.95680i | −0.120410 | + | 0.208556i | ||||
\(202\) | −3.51472 | −0.247295 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.12132 | − | 5.40629i | 0.218002 | − | 0.377591i | ||||
\(206\) | 13.6066 | + | 23.5673i | 0.948017 | + | 1.64201i | ||||
\(207\) | 10.4853 | + | 18.1610i | 0.728777 | + | 1.26228i | ||||
\(208\) | 8.82843 | − | 15.2913i | 0.612141 | − | 1.06026i | ||||
\(209\) | −1.02944 | −0.0712077 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.00000 | 0.619586 | 0.309793 | − | 0.950804i | \(-0.399740\pi\) | ||||
0.309793 | + | 0.950804i | \(0.399740\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.656854 | − | 1.13770i | −0.0450069 | − | 0.0779543i | ||||
\(214\) | −1.75736 | − | 3.04384i | −0.120131 | − | 0.208072i | ||||
\(215\) | −1.00000 | + | 1.73205i | −0.0681994 | + | 0.118125i | ||||
\(216\) | 6.82843 | 0.464616 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.07107 | −0.478913 | ||||||||
\(219\) | −1.75736 | + | 3.04384i | −0.118751 | + | 0.205683i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.15685 | − | 12.3960i | −0.481422 | − | 0.833848i | ||||
\(222\) | −0.656854 | + | 1.13770i | −0.0440852 | + | 0.0763578i | ||||
\(223\) | −24.2132 | −1.62144 | −0.810718 | − | 0.585437i | \(-0.800923\pi\) | ||||
−0.810718 | + | 0.585437i | \(0.800923\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.82843 | −0.188562 | ||||||||
\(226\) | −9.24264 | + | 16.0087i | −0.614811 | + | 1.06488i | ||||
\(227\) | −7.86396 | − | 13.6208i | −0.521949 | − | 0.904043i | −0.999674 | − | 0.0255332i | \(-0.991872\pi\) |
0.477725 | − | 0.878510i | \(-0.341462\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.02082 | + | 15.6245i | −0.596112 | + | 1.03250i | 0.397277 | + | 0.917699i | \(0.369955\pi\) |
−0.993389 | + | 0.114798i | \(0.963378\pi\) | |||||||
\(230\) | −10.4853 | −0.691379 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −24.4853 | −1.60754 | ||||||||
\(233\) | 4.58579 | − | 7.94282i | 0.300425 | − | 0.520351i | −0.675807 | − | 0.737078i | \(-0.736205\pi\) |
0.976232 | + | 0.216727i | \(0.0695382\pi\) | |||||||
\(234\) | −8.82843 | − | 15.2913i | −0.577132 | − | 0.999623i | ||||
\(235\) | 3.62132 | + | 6.27231i | 0.236229 | + | 0.409160i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.615224 | −0.0399631 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.4853 | −1.13103 | −0.565514 | − | 0.824738i | \(-0.691322\pi\) | ||||
−0.565514 | + | 0.824738i | \(0.691322\pi\) | |||||||
\(240\) | −0.828427 | + | 1.43488i | −0.0534747 | + | 0.0926210i | ||||
\(241\) | 0.363961 | + | 0.630399i | 0.0234448 | + | 0.0406076i | 0.877510 | − | 0.479559i | \(-0.159203\pi\) |
−0.854065 | + | 0.520166i | \(0.825870\pi\) | |||||||
\(242\) | −7.75736 | − | 13.4361i | −0.498662 | − | 0.863708i | ||||
\(243\) | 5.17157 | − | 8.95743i | 0.331757 | − | 0.574619i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.65685 | −0.233153 | ||||||||
\(247\) | −13.2426 | + | 22.9369i | −0.842609 | + | 1.45944i | ||||
\(248\) | −14.4853 | − | 25.0892i | −0.919816 | − | 1.59317i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.707107 | − | 1.22474i | 0.0447214 | − | 0.0774597i | ||||
\(251\) | 17.2132 | 1.08649 | 0.543244 | − | 0.839575i | \(-0.317196\pi\) | ||||
0.543244 | + | 0.839575i | \(0.317196\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.27208 | −0.0799749 | ||||||||
\(254\) | 5.82843 | − | 10.0951i | 0.365708 | − | 0.633425i | ||||
\(255\) | 0.671573 | + | 1.16320i | 0.0420555 | + | 0.0728423i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.75736 | − | 8.23999i | 0.296756 | − | 0.513996i | −0.678636 | − | 0.734475i | \(-0.737429\pi\) |
0.975392 | + | 0.220479i | \(0.0707619\pi\) | |||||||
\(258\) | 1.17157 | 0.0729389 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.2426 | + | 21.2049i | −0.757800 | + | 1.31255i | ||||
\(262\) | 8.65685 | + | 14.9941i | 0.534822 | + | 0.926339i | ||||
\(263\) | 8.31371 | + | 14.3998i | 0.512645 | + | 0.887928i | 0.999892 | + | 0.0146635i | \(0.00466771\pi\) |
−0.487247 | + | 0.873264i | \(0.661999\pi\) | |||||||
\(264\) | −0.100505 | + | 0.174080i | −0.00618566 | + | 0.0107139i | ||||
\(265\) | 4.24264 | 0.260623 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.31371 | 0.202796 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.12132 | + | 14.0665i | 0.495166 | + | 0.857652i | 0.999984 | − | 0.00557327i | \(-0.00177404\pi\) |
−0.504819 | + | 0.863225i | \(0.668441\pi\) | |||||||
\(270\) | 1.70711 | + | 2.95680i | 0.103891 | + | 0.179945i | ||||
\(271\) | 0.343146 | − | 0.594346i | 0.0208446 | − | 0.0361039i | −0.855415 | − | 0.517943i | \(-0.826698\pi\) |
0.876260 | + | 0.481839i | \(0.160031\pi\) | |||||||
\(272\) | −12.9706 | −0.786456 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.9706 | −1.02523 | ||||||||
\(275\) | 0.0857864 | − | 0.148586i | 0.00517312 | − | 0.00896010i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.60660 | − | 13.1750i | −0.457036 | − | 0.791610i | 0.541766 | − | 0.840529i | \(-0.317756\pi\) |
−0.998803 | + | 0.0489189i | \(0.984422\pi\) | |||||||
\(278\) | 5.48528 | − | 9.50079i | 0.328985 | − | 0.569819i | ||||
\(279\) | −28.9706 | −1.73442 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.31371 | 0.138024 | 0.0690121 | − | 0.997616i | \(-0.478015\pi\) | ||||
0.0690121 | + | 0.997616i | \(0.478015\pi\) | |||||||
\(282\) | 2.12132 | − | 3.67423i | 0.126323 | − | 0.218797i | ||||
\(283\) | −12.2782 | − | 21.2664i | −0.729862 | − | 1.26416i | −0.956941 | − | 0.290281i | \(-0.906251\pi\) |
0.227080 | − | 0.973876i | \(-0.427082\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.24264 | − | 2.15232i | 0.0736077 | − | 0.127492i | ||||
\(286\) | 1.07107 | 0.0633336 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.24264 | − | 5.61642i | 0.190744 | − | 0.330378i | ||||
\(290\) | −6.12132 | − | 10.6024i | −0.359456 | − | 0.622597i | ||||
\(291\) | 2.74264 | + | 4.75039i | 0.160776 | + | 0.278473i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.7279 | 1.50304 | 0.751521 | − | 0.659710i | \(-0.229321\pi\) | ||||
0.751521 | + | 0.659710i | \(0.229321\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.24264 | −0.130572 | ||||||||
\(296\) | −3.17157 | + | 5.49333i | −0.184344 | + | 0.319293i | ||||
\(297\) | 0.207107 | + | 0.358719i | 0.0120176 | + | 0.0208150i | ||||
\(298\) | −6.48528 | − | 11.2328i | −0.375682 | − | 0.650701i | ||||
\(299\) | −16.3640 | + | 28.3432i | −0.946352 | + | 1.63913i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 10.5858 | 0.609144 | ||||||||
\(303\) | 0.514719 | − | 0.891519i | 0.0295698 | − | 0.0512164i | ||||
\(304\) | 12.0000 | + | 20.7846i | 0.688247 | + | 1.19208i | ||||
\(305\) | 1.41421 | + | 2.44949i | 0.0809776 | + | 0.140257i | ||||
\(306\) | −6.48528 | + | 11.2328i | −0.370739 | + | 0.642139i | ||||
\(307\) | 30.8995 | 1.76353 | 0.881764 | − | 0.471691i | \(-0.156356\pi\) | ||||
0.881764 | + | 0.471691i | \(0.156356\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.97056 | −0.453429 | ||||||||
\(310\) | 7.24264 | − | 12.5446i | 0.411354 | − | 0.712487i | ||||
\(311\) | 5.00000 | + | 8.66025i | 0.283524 | + | 0.491078i | 0.972250 | − | 0.233944i | \(-0.0751631\pi\) |
−0.688726 | + | 0.725022i | \(0.741830\pi\) | |||||||
\(312\) | 2.58579 | + | 4.47871i | 0.146391 | + | 0.253557i | ||||
\(313\) | 9.10660 | − | 15.7731i | 0.514736 | − | 0.891548i | −0.485118 | − | 0.874449i | \(-0.661223\pi\) |
0.999854 | − | 0.0170996i | \(-0.00544323\pi\) | |||||||
\(314\) | 21.4558 | 1.21082 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.171573 | − | 0.297173i | 0.00963649 | − | 0.0166909i | −0.861167 | − | 0.508322i | \(-0.830266\pi\) |
0.870803 | + | 0.491631i | \(0.163599\pi\) | |||||||
\(318\) | −1.24264 | − | 2.15232i | −0.0696838 | − | 0.120696i | ||||
\(319\) | −0.742641 | − | 1.28629i | −0.0415799 | − | 0.0720185i | ||||
\(320\) | −4.00000 | + | 6.92820i | −0.223607 | + | 0.387298i | ||||
\(321\) | 1.02944 | 0.0574576 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.4558 | 1.08255 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.20711 | − | 3.82282i | −0.122428 | − | 0.212052i | ||||
\(326\) | −7.24264 | − | 12.5446i | −0.401133 | − | 0.694782i | ||||
\(327\) | 1.03553 | − | 1.79360i | 0.0572652 | − | 0.0991862i | ||||
\(328\) | −17.6569 | −0.974937 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.100505 | −0.00553262 | ||||||||
\(331\) | 13.7279 | − | 23.7775i | 0.754555 | − | 1.30693i | −0.191040 | − | 0.981582i | \(-0.561186\pi\) |
0.945595 | − | 0.325345i | \(-0.105480\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.17157 | + | 5.49333i | 0.173801 | + | 0.301032i | ||||
\(334\) | 0.535534 | − | 0.927572i | 0.0293031 | − | 0.0507545i | ||||
\(335\) | −8.24264 | −0.450344 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.2426 | 1.21163 | 0.605817 | − | 0.795604i | \(-0.292846\pi\) | ||||
0.605817 | + | 0.795604i | \(0.292846\pi\) | |||||||
\(338\) | 4.58579 | − | 7.94282i | 0.249434 | − | 0.432032i | ||||
\(339\) | −2.70711 | − | 4.68885i | −0.147030 | − | 0.254663i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.878680 | − | 1.52192i | 0.0475832 | − | 0.0824165i | ||||
\(342\) | 24.0000 | 1.29777 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.65685 | 0.304997 | ||||||||
\(345\) | 1.53553 | − | 2.65962i | 0.0826704 | − | 0.143189i | ||||
\(346\) | −5.12132 | − | 8.87039i | −0.275324 | − | 0.476875i | ||||
\(347\) | −6.53553 | − | 11.3199i | −0.350846 | − | 0.607683i | 0.635552 | − | 0.772058i | \(-0.280773\pi\) |
−0.986398 | + | 0.164375i | \(0.947439\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.9706 | −0.587241 | −0.293620 | − | 0.955922i | \(-0.594860\pi\) | ||||
−0.293620 | + | 0.955922i | \(0.594860\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.6569 | 0.568821 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.10660 | + | 5.38079i | 0.165348 | + | 0.286391i | 0.936779 | − | 0.349922i | \(-0.113792\pi\) |
−0.771431 | + | 0.636313i | \(0.780459\pi\) | |||||||
\(354\) | 0.656854 | + | 1.13770i | 0.0349114 | + | 0.0604683i | ||||
\(355\) | 1.58579 | − | 2.74666i | 0.0841648 | − | 0.145778i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 20.4853 | 1.08268 | ||||||||
\(359\) | 5.65685 | − | 9.79796i | 0.298557 | − | 0.517116i | −0.677249 | − | 0.735754i | \(-0.736828\pi\) |
0.975806 | + | 0.218638i | \(0.0701613\pi\) | |||||||
\(360\) | 4.00000 | + | 6.92820i | 0.210819 | + | 0.365148i | ||||
\(361\) | −8.50000 | − | 14.7224i | −0.447368 | − | 0.774865i | ||||
\(362\) | −13.2426 | + | 22.9369i | −0.696018 | + | 1.20554i | ||||
\(363\) | 4.54416 | 0.238506 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.48528 | −0.444140 | ||||||||
\(366\) | 0.828427 | − | 1.43488i | 0.0433026 | − | 0.0750023i | ||||
\(367\) | 11.9350 | + | 20.6721i | 0.623003 | + | 1.07907i | 0.988923 | + | 0.148427i | \(0.0474211\pi\) |
−0.365920 | + | 0.930646i | \(0.619246\pi\) | |||||||
\(368\) | 14.8284 | + | 25.6836i | 0.772985 | + | 1.33885i | ||||
\(369\) | −8.82843 | + | 15.2913i | −0.459590 | + | 0.796032i | ||||
\(370\) | −3.17157 | −0.164882 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.24264 | − | 14.2767i | 0.426788 | − | 0.739218i | −0.569798 | − | 0.821785i | \(-0.692978\pi\) |
0.996586 | + | 0.0825669i | \(0.0263118\pi\) | |||||||
\(374\) | −0.393398 | − | 0.681386i | −0.0203421 | − | 0.0352336i | ||||
\(375\) | 0.207107 | + | 0.358719i | 0.0106949 | + | 0.0185242i | ||||
\(376\) | 10.2426 | − | 17.7408i | 0.528224 | − | 0.914911i | ||||
\(377\) | −38.2132 | −1.96808 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.00000 | 0.102733 | 0.0513665 | − | 0.998680i | \(-0.483642\pi\) | ||||
0.0513665 | + | 0.998680i | \(0.483642\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.70711 | + | 2.95680i | 0.0874577 | + | 0.151481i | ||||
\(382\) | 9.87868 | + | 17.1104i | 0.505437 | + | 0.875443i | ||||
\(383\) | −2.24264 | + | 3.88437i | −0.114594 | + | 0.198482i | −0.917617 | − | 0.397465i | \(-0.869890\pi\) |
0.803024 | + | 0.595947i | \(0.203223\pi\) | |||||||
\(384\) | 4.68629 | 0.239146 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 22.6274 | 1.15171 | ||||||||
\(387\) | 2.82843 | − | 4.89898i | 0.143777 | − | 0.249029i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.42893 | + | 5.93908i | 0.173854 | + | 0.301124i | 0.939764 | − | 0.341824i | \(-0.111045\pi\) |
−0.765910 | + | 0.642948i | \(0.777711\pi\) | |||||||
\(390\) | −1.29289 | + | 2.23936i | −0.0654682 | + | 0.113394i | ||||
\(391\) | 24.0416 | 1.21584 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.07107 | −0.255802 | ||||||||
\(394\) | 9.48528 | − | 16.4290i | 0.477862 | − | 0.827681i | ||||
\(395\) | −0.742641 | − | 1.28629i | −0.0373663 | − | 0.0647203i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.792893 | + | 1.37333i | −0.0397942 | + | 0.0689255i | −0.885237 | − | 0.465141i | \(-0.846004\pi\) |
0.845442 | + | 0.534067i | \(0.179337\pi\) | |||||||
\(398\) | 10.4853 | 0.525580 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | −5.91421 | + | 10.2437i | −0.295342 | + | 0.511547i | −0.975064 | − | 0.221922i | \(-0.928767\pi\) |
0.679723 | + | 0.733469i | \(0.262100\pi\) | |||||||
\(402\) | 2.41421 | + | 4.18154i | 0.120410 | + | 0.208556i | ||||
\(403\) | −22.6066 | − | 39.1558i | −1.12612 | − | 1.95049i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.48528 | 0.371947 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.384776 | −0.0190727 | ||||||||
\(408\) | 1.89949 | − | 3.29002i | 0.0940390 | − | 0.162880i | ||||
\(409\) | −1.24264 | − | 2.15232i | −0.0614446 | − | 0.106425i | 0.833667 | − | 0.552268i | \(-0.186237\pi\) |
−0.895111 | + | 0.445843i | \(0.852904\pi\) | |||||||
\(410\) | −4.41421 | − | 7.64564i | −0.218002 | − | 0.377591i | ||||
\(411\) | 2.48528 | − | 4.30463i | 0.122590 | − | 0.212332i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 29.6569 | 1.45755 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.60660 | + | 2.78272i | 0.0786756 | + | 0.136270i | ||||
\(418\) | −0.727922 | + | 1.26080i | −0.0356038 | + | 0.0616676i | ||||
\(419\) | 18.7279 | 0.914919 | 0.457459 | − | 0.889230i | \(-0.348759\pi\) | ||||
0.457459 | + | 0.889230i | \(0.348759\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.0000 | −0.926003 | −0.463002 | − | 0.886357i | \(-0.653228\pi\) | ||||
−0.463002 | + | 0.886357i | \(0.653228\pi\) | |||||||
\(422\) | 6.36396 | − | 11.0227i | 0.309793 | − | 0.536577i | ||||
\(423\) | −10.2426 | − | 17.7408i | −0.498014 | − | 0.862586i | ||||
\(424\) | −6.00000 | − | 10.3923i | −0.291386 | − | 0.504695i | ||||
\(425\) | −1.62132 | + | 2.80821i | −0.0786456 | + | 0.136218i | ||||
\(426\) | −1.85786 | −0.0900138 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.156854 | + | 0.271680i | −0.00757299 | + | 0.0131168i | ||||
\(430\) | 1.41421 | + | 2.44949i | 0.0681994 | + | 0.118125i | ||||
\(431\) | 14.3995 | + | 24.9407i | 0.693599 | + | 1.20135i | 0.970651 | + | 0.240494i | \(0.0773095\pi\) |
−0.277051 | + | 0.960855i | \(0.589357\pi\) | |||||||
\(432\) | 4.82843 | − | 8.36308i | 0.232308 | − | 0.402369i | ||||
\(433\) | 10.9706 | 0.527212 | 0.263606 | − | 0.964630i | \(-0.415088\pi\) | ||||
0.263606 | + | 0.964630i | \(0.415088\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.58579 | 0.171925 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −22.2426 | − | 38.5254i | −1.06401 | − | 1.84292i | ||||
\(438\) | 2.48528 | + | 4.30463i | 0.118751 | + | 0.205683i | ||||
\(439\) | 15.1924 | − | 26.3140i | 0.725093 | − | 1.25590i | −0.233843 | − | 0.972274i | \(-0.575130\pi\) |
0.958936 | − | 0.283624i | \(-0.0915366\pi\) | |||||||
\(440\) | −0.485281 | −0.0231349 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −20.2426 | −0.962844 | ||||||||
\(443\) | −7.58579 | + | 13.1390i | −0.360412 | + | 0.624251i | −0.988029 | − | 0.154271i | \(-0.950697\pi\) |
0.627617 | + | 0.778522i | \(0.284030\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.00000 | + | 6.92820i | 0.189618 | + | 0.328428i | ||||
\(446\) | −17.1213 | + | 29.6550i | −0.810718 | + | 1.40420i | ||||
\(447\) | 3.79899 | 0.179686 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.1716 | −1.14073 | −0.570364 | − | 0.821392i | \(-0.693198\pi\) | ||||
−0.570364 | + | 0.821392i | \(0.693198\pi\) | |||||||
\(450\) | −2.00000 | + | 3.46410i | −0.0942809 | + | 0.163299i | ||||
\(451\) | −0.535534 | − | 0.927572i | −0.0252173 | − | 0.0436777i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.55025 | + | 2.68512i | −0.0728372 | + | 0.126158i | ||||
\(454\) | −22.2426 | −1.04390 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.02944 | −0.329184 | ||||||||
\(457\) | 5.87868 | − | 10.1822i | 0.274993 | − | 0.476302i | −0.695140 | − | 0.718874i | \(-0.744658\pi\) |
0.970133 | + | 0.242572i | \(0.0779911\pi\) | |||||||
\(458\) | 12.7574 | + | 22.0964i | 0.596112 | + | 1.03250i | ||||
\(459\) | −3.91421 | − | 6.77962i | −0.182700 | − | 0.316445i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.02944 | 0.141095 | 0.0705475 | − | 0.997508i | \(-0.477525\pi\) | ||||
0.0705475 | + | 0.997508i | \(0.477525\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.4558 | −0.997138 | −0.498569 | − | 0.866850i | \(-0.666141\pi\) | ||||
−0.498569 | + | 0.866850i | \(0.666141\pi\) | |||||||
\(464\) | −17.3137 | + | 29.9882i | −0.803769 | + | 1.39217i | ||||
\(465\) | 2.12132 | + | 3.67423i | 0.0983739 | + | 0.170389i | ||||
\(466\) | −6.48528 | − | 11.2328i | −0.300425 | − | 0.520351i | ||||
\(467\) | 2.86396 | − | 4.96053i | 0.132528 | − | 0.229546i | −0.792122 | − | 0.610362i | \(-0.791024\pi\) |
0.924651 | + | 0.380817i | \(0.124357\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 10.2426 | 0.472458 | ||||||||
\(471\) | −3.14214 | + | 5.44234i | −0.144782 | + | 0.250770i | ||||
\(472\) | 3.17157 | + | 5.49333i | 0.145983 | + | 0.252851i | ||||
\(473\) | 0.171573 | + | 0.297173i | 0.00788893 | + | 0.0136640i | ||||
\(474\) | −0.435029 | + | 0.753492i | −0.0199815 | + | 0.0346090i | ||||
\(475\) | 6.00000 | 0.275299 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.0000 | −0.549442 | ||||||||
\(478\) | −12.3640 | + | 21.4150i | −0.565514 | + | 0.979500i | ||||
\(479\) | −5.87868 | − | 10.1822i | −0.268604 | − | 0.465235i | 0.699898 | − | 0.714243i | \(-0.253229\pi\) |
−0.968501 | + | 0.249008i | \(0.919896\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.94975 | + | 8.57321i | −0.225689 | + | 0.390905i | ||||
\(482\) | 1.02944 | 0.0468896 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.62132 | + | 11.4685i | −0.300659 | + | 0.520756i | ||||
\(486\) | −7.31371 | − | 12.6677i | −0.331757 | − | 0.574619i | ||||
\(487\) | −13.8492 | − | 23.9876i | −0.627569 | − | 1.08698i | −0.988038 | − | 0.154210i | \(-0.950717\pi\) |
0.360469 | − | 0.932771i | \(-0.382617\pi\) | |||||||
\(488\) | 4.00000 | − | 6.92820i | 0.181071 | − | 0.313625i | ||||
\(489\) | 4.24264 | 0.191859 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.2843 | −1.68262 | −0.841308 | − | 0.540556i | \(-0.818214\pi\) | ||||
−0.841308 | + | 0.540556i | \(0.818214\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.0355 | + | 24.3103i | 0.632129 | + | 1.09488i | ||||
\(494\) | 18.7279 | + | 32.4377i | 0.842609 | + | 1.45944i | ||||
\(495\) | −0.242641 | + | 0.420266i | −0.0109059 | + | 0.0188896i | ||||
\(496\) | −40.9706 | −1.83963 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.50000 | + | 2.59808i | −0.0671492 | + | 0.116306i | −0.897645 | − | 0.440719i | \(-0.854724\pi\) |
0.830496 | + | 0.557024i | \(0.188057\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.156854 | + | 0.271680i | 0.00700773 | + | 0.0121377i | ||||
\(502\) | 12.1716 | − | 21.0818i | 0.543244 | − | 0.940926i | ||||
\(503\) | −41.2426 | −1.83892 | −0.919459 | − | 0.393185i | \(-0.871373\pi\) | ||||
−0.919459 | + | 0.393185i | \(0.871373\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.48528 | 0.110594 | ||||||||
\(506\) | −0.899495 | + | 1.55797i | −0.0399874 | + | 0.0692603i | ||||
\(507\) | 1.34315 | + | 2.32640i | 0.0596512 | + | 0.103319i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.6066 | − | 21.8353i | 0.558778 | − | 0.967832i | −0.438821 | − | 0.898574i | \(-0.644604\pi\) |
0.997599 | − | 0.0692571i | \(-0.0220629\pi\) | |||||||
\(510\) | 1.89949 | 0.0841110 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6274 | 1.00000 | ||||||||
\(513\) | −7.24264 | + | 12.5446i | −0.319770 | + | 0.553859i | ||||
\(514\) | −6.72792 | − | 11.6531i | −0.296756 | − | 0.513996i | ||||
\(515\) | −9.62132 | − | 16.6646i | −0.423966 | − | 0.734331i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.24264 | 0.0546513 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.00000 | 0.131685 | ||||||||
\(520\) | −6.24264 | + | 10.8126i | −0.273758 | + | 0.474163i | ||||
\(521\) | −7.48528 | − | 12.9649i | −0.327936 | − | 0.568002i | 0.654166 | − | 0.756351i | \(-0.273020\pi\) |
−0.982102 | + | 0.188349i | \(0.939686\pi\) | |||||||
\(522\) | 17.3137 | + | 29.9882i | 0.757800 | + | 1.31255i | ||||
\(523\) | −16.2426 | + | 28.1331i | −0.710241 | + | 1.23017i | 0.254525 | + | 0.967066i | \(0.418081\pi\) |
−0.964767 | + | 0.263108i | \(0.915253\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.5147 | 1.02529 | ||||||||
\(527\) | −16.6066 | + | 28.7635i | −0.723395 | + | 1.25296i | ||||
\(528\) | 0.142136 | + | 0.246186i | 0.00618566 | + | 0.0107139i | ||||
\(529\) | −15.9853 | − | 27.6873i | −0.695012 | − | 1.20380i | ||||
\(530\) | 3.00000 | − | 5.19615i | 0.130312 | − | 0.225706i | ||||
\(531\) | 6.34315 | 0.275269 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −27.5563 | −1.19360 | ||||||||
\(534\) | 2.34315 | − | 4.05845i | 0.101398 | − | 0.175626i | ||||
\(535\) | 1.24264 | + | 2.15232i | 0.0537240 | + | 0.0930528i | ||||
\(536\) | 11.6569 | + | 20.1903i | 0.503499 | + | 0.872087i | ||||
\(537\) | −3.00000 | + | 5.19615i | −0.129460 | + | 0.224231i | ||||
\(538\) | 22.9706 | 0.990331 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.9853 | − | 19.0271i | 0.472294 | − | 0.818037i | −0.527203 | − | 0.849739i | \(-0.676759\pi\) |
0.999497 | + | 0.0317018i | \(0.0100927\pi\) | |||||||
\(542\) | −0.485281 | − | 0.840532i | −0.0208446 | − | 0.0361039i | ||||
\(543\) | −3.87868 | − | 6.71807i | −0.166450 | − | 0.288300i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.00000 | 0.214176 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.4853 | −1.04692 | −0.523458 | − | 0.852052i | \(-0.675358\pi\) | ||||
−0.523458 | + | 0.852052i | \(0.675358\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.00000 | − | 6.92820i | −0.170716 | − | 0.295689i | ||||
\(550\) | −0.121320 | − | 0.210133i | −0.00517312 | − | 0.00896010i | ||||
\(551\) | 25.9706 | − | 44.9823i | 1.10638 | − | 1.91631i | ||||
\(552\) | −8.68629 | −0.369713 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −21.5147 | −0.914073 | ||||||||
\(555\) | 0.464466 | − | 0.804479i | 0.0197155 | − | 0.0341482i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.89949 | + | 6.75412i | 0.165227 | + | 0.286181i | 0.936736 | − | 0.350037i | \(-0.113831\pi\) |
−0.771509 | + | 0.636218i | \(0.780498\pi\) | |||||||
\(558\) | −20.4853 | + | 35.4815i | −0.867211 | + | 1.50205i | ||||
\(559\) | 8.82843 | 0.373403 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.230447 | 0.00972950 | ||||||||
\(562\) | 1.63604 | − | 2.83370i | 0.0690121 | − | 0.119533i | ||||
\(563\) | 15.9706 | + | 27.6618i | 0.673079 | + | 1.16581i | 0.977026 | + | 0.213118i | \(0.0683619\pi\) |
−0.303947 | + | 0.952689i | \(0.598305\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.53553 | − | 11.3199i | 0.274952 | − | 0.476231i | ||||
\(566\) | −34.7279 | −1.45972 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.97056 | −0.376396 | ||||||||
\(569\) | −13.0711 | + | 22.6398i | −0.547968 | + | 0.949108i | 0.450446 | + | 0.892804i | \(0.351265\pi\) |
−0.998414 | + | 0.0563042i | \(0.982068\pi\) | |||||||
\(570\) | −1.75736 | − | 3.04384i | −0.0736077 | − | 0.127492i | ||||
\(571\) | 8.75736 | + | 15.1682i | 0.366484 | + | 0.634769i | 0.989013 | − | 0.147828i | \(-0.0472281\pi\) |
−0.622529 | + | 0.782597i | \(0.713895\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.78680 | −0.241747 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.41421 | 0.309194 | ||||||||
\(576\) | 11.3137 | − | 19.5959i | 0.471405 | − | 0.816497i | ||||
\(577\) | −7.86396 | − | 13.6208i | −0.327381 | − | 0.567040i | 0.654610 | − | 0.755966i | \(-0.272833\pi\) |
−0.981991 | + | 0.188926i | \(0.939499\pi\) | |||||||
\(578\) | −4.58579 | − | 7.94282i | −0.190744 | − | 0.330378i | ||||
\(579\) | −3.31371 | + | 5.73951i | −0.137713 | + | 0.238526i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7.75736 | 0.321553 | ||||||||
\(583\) | 0.363961 | − | 0.630399i | 0.0150737 | − | 0.0261085i | ||||
\(584\) | 12.0000 | + | 20.7846i | 0.496564 | + | 0.860073i | ||||
\(585\) | 6.24264 | + | 10.8126i | 0.258101 | + | 0.447045i | ||||
\(586\) | 18.1924 | − | 31.5101i | 0.751521 | − | 1.30167i | ||||
\(587\) | −37.4558 | −1.54597 | −0.772984 | − | 0.634425i | \(-0.781237\pi\) | ||||
−0.772984 | + | 0.634425i | \(0.781237\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 61.4558 | 2.53224 | ||||||||
\(590\) | −1.58579 | + | 2.74666i | −0.0652858 | + | 0.113078i | ||||
\(591\) | 2.77817 | + | 4.81194i | 0.114279 | + | 0.197937i | ||||
\(592\) | 4.48528 | + | 7.76874i | 0.184344 | + | 0.319293i | ||||
\(593\) | −9.62132 | + | 16.6646i | −0.395100 | + | 0.684334i | −0.993114 | − | 0.117152i | \(-0.962623\pi\) |
0.598014 | + | 0.801486i | \(0.295957\pi\) | |||||||
\(594\) | 0.585786 | 0.0240351 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.53553 | + | 2.65962i | −0.0628452 | + | 0.108851i | ||||
\(598\) | 23.1421 | + | 40.0834i | 0.946352 | + | 1.63913i | ||||
\(599\) | 8.91421 | + | 15.4399i | 0.364225 | + | 0.630856i | 0.988651 | − | 0.150228i | \(-0.0480006\pi\) |
−0.624427 | + | 0.781084i | \(0.714667\pi\) | |||||||
\(600\) | 0.585786 | − | 1.01461i | 0.0239146 | − | 0.0414214i | ||||
\(601\) | −10.9706 | −0.447499 | −0.223749 | − | 0.974647i | \(-0.571830\pi\) | ||||
−0.223749 | + | 0.974647i | \(0.571830\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 23.3137 | 0.949408 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.48528 | + | 9.50079i | 0.223008 | + | 0.386262i | ||||
\(606\) | −0.727922 | − | 1.26080i | −0.0295698 | − | 0.0512164i | ||||
\(607\) | 2.55025 | − | 4.41717i | 0.103512 | − | 0.179287i | −0.809618 | − | 0.586958i | \(-0.800325\pi\) |
0.913129 | + | 0.407670i | \(0.133659\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.00000 | 0.161955 | ||||||||
\(611\) | 15.9853 | − | 27.6873i | 0.646695 | − | 1.12011i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.9706 | + | 20.7336i | 0.483486 | + | 0.837423i | 0.999820 | − | 0.0189643i | \(-0.00603690\pi\) |
−0.516334 | + | 0.856387i | \(0.672704\pi\) | |||||||
\(614\) | 21.8492 | − | 37.8440i | 0.881764 | − | 1.52726i | ||||
\(615\) | 2.58579 | 0.104269 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.58579 | 0.184617 | 0.0923084 | − | 0.995730i | \(-0.470575\pi\) | ||||
0.0923084 | + | 0.995730i | \(0.470575\pi\) | |||||||
\(618\) | −5.63604 | + | 9.76191i | −0.226715 | + | 0.392681i | ||||
\(619\) | −8.46447 | − | 14.6609i | −0.340216 | − | 0.589271i | 0.644257 | − | 0.764809i | \(-0.277167\pi\) |
−0.984473 | + | 0.175538i | \(0.943833\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.94975 | + | 15.5014i | −0.359141 | + | 0.622050i | ||||
\(622\) | 14.1421 | 0.567048 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 7.31371 | 0.292783 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −12.8787 | − | 22.3065i | −0.514736 | − | 0.891548i | ||||
\(627\) | −0.213203 | − | 0.369279i | −0.00851453 | − | 0.0147476i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.27208 | 0.289957 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.4558 | −1.69014 | −0.845070 | − | 0.534655i | \(-0.820441\pi\) | ||||
−0.845070 | + | 0.534655i | \(0.820441\pi\) | |||||||
\(632\) | −2.10051 | + | 3.63818i | −0.0835536 | + | 0.144719i | ||||
\(633\) | 1.86396 | + | 3.22848i | 0.0740858 | + | 0.128320i | ||||
\(634\) | −0.242641 | − | 0.420266i | −0.00963649 | − | 0.0166909i | ||||
\(635\) | −4.12132 | + | 7.13834i | −0.163550 | + | 0.283276i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.10051 | −0.0831598 | ||||||||
\(639\) | −4.48528 | + | 7.76874i | −0.177435 | + | 0.307326i | ||||
\(640\) | 5.65685 | + | 9.79796i | 0.223607 | + | 0.387298i | ||||
\(641\) | 11.6569 | + | 20.1903i | 0.460418 | + | 0.797467i | 0.998982 | − | 0.0451174i | \(-0.0143662\pi\) |
−0.538564 | + | 0.842585i | \(0.681033\pi\) | |||||||
\(642\) | 0.727922 | − | 1.26080i | 0.0287288 | − | 0.0497597i | ||||
\(643\) | 2.27208 | 0.0896020 | 0.0448010 | − | 0.998996i | \(-0.485735\pi\) | ||||
0.0448010 | + | 0.998996i | \(0.485735\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.828427 | −0.0326193 | ||||||||
\(646\) | 13.7574 | − | 23.8284i | 0.541276 | − | 0.937518i | ||||
\(647\) | 5.75736 | + | 9.97204i | 0.226345 | + | 0.392041i | 0.956722 | − | 0.291003i | \(-0.0939889\pi\) |
−0.730377 | + | 0.683044i | \(0.760656\pi\) | |||||||
\(648\) | −10.5858 | − | 18.3351i | −0.415849 | − | 0.720272i | ||||
\(649\) | −0.192388 | + | 0.333226i | −0.00755190 | + | 0.0130803i | ||||
\(650\) | −6.24264 | −0.244857 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.4853 | + | 30.2854i | −0.684252 | + | 1.18516i | 0.289419 | + | 0.957202i | \(0.406538\pi\) |
−0.973671 | + | 0.227957i | \(0.926796\pi\) | |||||||
\(654\) | −1.46447 | − | 2.53653i | −0.0572652 | − | 0.0991862i | ||||
\(655\) | −6.12132 | − | 10.6024i | −0.239180 | − | 0.414272i | ||||
\(656\) | −12.4853 | + | 21.6251i | −0.487468 | + | 0.844320i | ||||
\(657\) | 24.0000 | 0.936329 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.9706 | 0.777943 | 0.388971 | − | 0.921250i | \(-0.372831\pi\) | ||||
0.388971 | + | 0.921250i | \(0.372831\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.72792 | − | 11.6531i | −0.261686 | − | 0.453253i | 0.705004 | − | 0.709203i | \(-0.250945\pi\) |
−0.966690 | + | 0.255950i | \(0.917612\pi\) | |||||||
\(662\) | −19.4142 | − | 33.6264i | −0.754555 | − | 1.30693i | ||||
\(663\) | 2.96447 | − | 5.13461i | 0.115130 | − | 0.199412i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.97056 | 0.347602 | ||||||||
\(667\) | 32.0919 | − | 55.5848i | 1.24260 | − | 2.15225i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.01472 | − | 8.68575i | −0.193880 | − | 0.335810i | ||||
\(670\) | −5.82843 | + | 10.0951i | −0.225172 | + | 0.390009i | ||||
\(671\) | 0.485281 | 0.0187341 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.51472 | 0.135482 | 0.0677412 | − | 0.997703i | \(-0.478421\pi\) | ||||
0.0677412 | + | 0.997703i | \(0.478421\pi\) | |||||||
\(674\) | 15.7279 | − | 27.2416i | 0.605817 | − | 1.04931i | ||||
\(675\) | −1.20711 | − | 2.09077i | −0.0464616 | − | 0.0804738i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.1066 | + | 38.2898i | −0.849626 | + | 1.47159i | 0.0319169 | + | 0.999491i | \(0.489839\pi\) |
−0.881543 | + | 0.472104i | \(0.843495\pi\) | |||||||
\(678\) | −7.65685 | −0.294060 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 9.17157 | 0.351714 | ||||||||
\(681\) | 3.25736 | − | 5.64191i | 0.124822 | − | 0.216199i | ||||
\(682\) | −1.24264 | − | 2.15232i | −0.0475832 | − | 0.0824165i | ||||
\(683\) | −15.8995 | − | 27.5387i | −0.608377 | − | 1.05374i | −0.991508 | − | 0.130046i | \(-0.958487\pi\) |
0.383131 | − | 0.923694i | \(-0.374846\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.0000 | 0.458496 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.47309 | −0.285116 | ||||||||
\(688\) | 4.00000 | − | 6.92820i | 0.152499 | − | 0.264135i | ||||
\(689\) | −9.36396 | − | 16.2189i | −0.356739 | − | 0.617889i | ||||
\(690\) | −2.17157 | − | 3.76127i | −0.0826704 | − | 0.143189i | ||||
\(691\) | −7.41421 | + | 12.8418i | −0.282050 | + | 0.488525i | −0.971890 | − | 0.235437i | \(-0.924348\pi\) |
0.689840 | + | 0.723962i | \(0.257681\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.4853 | −0.701692 | ||||||||
\(695\) | −3.87868 | + | 6.71807i | −0.147127 | + | 0.254831i | ||||
\(696\) | −5.07107 | − | 8.78335i | −0.192218 | − | 0.332932i | ||||
\(697\) | 10.1213 | + | 17.5306i | 0.383372 | + | 0.664020i | ||||
\(698\) | −7.75736 | + | 13.4361i | −0.293620 | + | 0.508565i | ||||
\(699\) | 3.79899 | 0.143691 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.4558 | 1.75461 | 0.877307 | − | 0.479931i | \(-0.159338\pi\) | ||||
0.877307 | + | 0.479931i | \(0.159338\pi\) | |||||||
\(702\) | 7.53553 | − | 13.0519i | 0.284410 | − | 0.492613i | ||||
\(703\) | −6.72792 | − | 11.6531i | −0.253748 | − | 0.439505i | ||||
\(704\) | 0.686292 | + | 1.18869i | 0.0258656 | + | 0.0448005i | ||||
\(705\) | −1.50000 | + | 2.59808i | −0.0564933 | + | 0.0978492i | ||||
\(706\) | 8.78680 | 0.330695 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.50000 | + | 14.7224i | −0.319224 | + | 0.552913i | −0.980326 | − | 0.197383i | \(-0.936756\pi\) |
0.661102 | + | 0.750296i | \(0.270089\pi\) | |||||||
\(710\) | −2.24264 | − | 3.88437i | −0.0841648 | − | 0.145778i | ||||
\(711\) | 2.10051 | + | 3.63818i | 0.0787751 | + | 0.136442i | ||||
\(712\) | 11.3137 | − | 19.5959i | 0.423999 | − | 0.734388i | ||||
\(713\) | 75.9411 | 2.84402 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.757359 | −0.0283236 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.62132 | − | 6.27231i | −0.135241 | − | 0.234244i | ||||
\(718\) | −8.00000 | − | 13.8564i | −0.298557 | − | 0.517116i | ||||
\(719\) | 12.6066 | − | 21.8353i | 0.470147 | − | 0.814318i | −0.529270 | − | 0.848453i | \(-0.677534\pi\) |
0.999417 | + | 0.0341349i | \(0.0108676\pi\) | |||||||
\(720\) | 11.3137 | 0.421637 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −24.0416 | −0.894737 | ||||||||
\(723\) | −0.150758 | + | 0.261120i | −0.00560674 | + | 0.00971115i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.32843 | + | 7.49706i | 0.160754 | + | 0.278434i | ||||
\(726\) | 3.21320 | − | 5.56543i | 0.119253 | − | 0.206553i | ||||
\(727\) | −6.68629 | −0.247981 | −0.123990 | − | 0.992283i | \(-0.539569\pi\) | ||||
−0.123990 | + | 0.992283i | \(0.539569\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.1716 | −0.673021 | ||||||||
\(730\) | −6.00000 | + | 10.3923i | −0.222070 | + | 0.384636i | ||||
\(731\) | −3.24264 | − | 5.61642i | −0.119933 | − | 0.207731i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.34924 | + | 12.7293i | −0.271450 | + | 0.470166i | −0.969233 | − | 0.246143i | \(-0.920837\pi\) |
0.697783 | + | 0.716309i | \(0.254170\pi\) | |||||||
\(734\) | 33.7574 | 1.24601 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.707107 | + | 1.22474i | −0.0260466 | + | 0.0451141i | ||||
\(738\) | 12.4853 | + | 21.6251i | 0.459590 | + | 0.796032i | ||||
\(739\) | −14.9853 | − | 25.9553i | −0.551242 | − | 0.954780i | −0.998185 | − | 0.0602175i | \(-0.980821\pi\) |
0.446943 | − | 0.894563i | \(-0.352513\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.9706 | −0.403014 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.2721 | 0.413532 | 0.206766 | − | 0.978390i | \(-0.433706\pi\) | ||||
0.206766 | + | 0.978390i | \(0.433706\pi\) | |||||||
\(744\) | 6.00000 | − | 10.3923i | 0.219971 | − | 0.381000i | ||||
\(745\) | 4.58579 | + | 7.94282i | 0.168010 | + | 0.291002i | ||||
\(746\) | −11.6569 | − | 20.1903i | −0.426788 | − | 0.739218i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0.585786 | 0.0213899 | ||||||||
\(751\) | −14.7426 | + | 25.5350i | −0.537967 | + | 0.931785i | 0.461047 | + | 0.887376i | \(0.347474\pi\) |
−0.999013 | + | 0.0444097i | \(0.985859\pi\) | |||||||
\(752\) | −14.4853 | − | 25.0892i | −0.528224 | − | 0.914911i | ||||
\(753\) | 3.56497 | + | 6.17471i | 0.129915 | + | 0.225019i | ||||
\(754\) | −27.0208 | + | 46.8014i | −0.984040 | + | 1.70441i | ||||
\(755\) | −7.48528 | −0.272417 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.485281 | 0.0176379 | 0.00881893 | − | 0.999961i | \(-0.497193\pi\) | ||||
0.00881893 | + | 0.999961i | \(0.497193\pi\) | |||||||
\(758\) | 1.41421 | − | 2.44949i | 0.0513665 | − | 0.0889695i | ||||
\(759\) | −0.263456 | − | 0.456319i | −0.00956285 | − | 0.0165633i | ||||
\(760\) | −8.48528 | − | 14.6969i | −0.307794 | − | 0.533114i | ||||
\(761\) | 6.36396 | − | 11.0227i | 0.230693 | − | 0.399573i | −0.727319 | − | 0.686300i | \(-0.759234\pi\) |
0.958012 | + | 0.286727i | \(0.0925672\pi\) | |||||||
\(762\) | 4.82843 | 0.174915 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.58579 | − | 7.94282i | 0.165799 | − | 0.287173i | ||||
\(766\) | 3.17157 | + | 5.49333i | 0.114594 | + | 0.198482i | ||||
\(767\) | 4.94975 | + | 8.57321i | 0.178725 | + | 0.309561i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.82843 | −0.318361 | −0.159181 | − | 0.987249i | \(-0.550885\pi\) | ||||
−0.159181 | + | 0.987249i | \(0.550885\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.94113 | 0.141936 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.10660 | + | 5.38079i | 0.111737 | + | 0.193534i | 0.916471 | − | 0.400102i | \(-0.131025\pi\) |
−0.804734 | + | 0.593636i | \(0.797692\pi\) | |||||||
\(774\) | −4.00000 | − | 6.92820i | −0.143777 | − | 0.249029i | ||||
\(775\) | −5.12132 | + | 8.87039i | −0.183963 | + | 0.318634i | ||||
\(776\) | 37.4558 | 1.34459 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.69848 | 0.347708 | ||||||||
\(779\) | 18.7279 | − | 32.4377i | 0.670997 | − | 1.16220i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.272078 | − | 0.471253i | −0.00973571 | − | 0.0168628i | ||||
\(782\) | 17.0000 | − | 29.4449i | 0.607919 | − | 1.05295i | ||||
\(783\) | −20.8995 | −0.746887 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.1716 | −0.541497 | ||||||||
\(786\) | −3.58579 | + | 6.21076i | −0.127901 | + | 0.221531i | ||||
\(787\) | −10.1360 | − | 17.5561i | −0.361311 | − | 0.625809i | 0.626866 | − | 0.779127i | \(-0.284337\pi\) |
−0.988177 | + | 0.153318i | \(0.951004\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.44365 | + | 5.96458i | −0.122597 | + | 0.212345i | ||||
\(790\) | −2.10051 | −0.0747326 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.37258 | 0.0487726 | ||||||||
\(793\) | 6.24264 | − | 10.8126i | 0.221683 | − | 0.383966i | ||||
\(794\) | 1.12132 | + | 1.94218i | 0.0397942 | + | 0.0689255i | ||||
\(795\) | 0.878680 | + | 1.52192i | 0.0311636 | + | 0.0539769i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.1838 | −0.750367 | −0.375184 | − | 0.926950i | \(-0.622420\pi\) | ||||
−0.375184 | + | 0.926950i | \(0.622420\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.4853 | −0.830850 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.3137 | − | 19.5959i | −0.399750 | − | 0.692388i | ||||
\(802\) | 8.36396 | + | 14.4868i | 0.295342 | + | 0.511547i | ||||
\(803\) | −0.727922 | + | 1.26080i | −0.0256878 | + | 0.0444926i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −63.9411 | −2.25223 | ||||||||
\(807\) | −3.36396 | + | 5.82655i | −0.118417 | + | 0.205104i | ||||
\(808\) | −3.51472 | − | 6.08767i | −0.123647 | − | 0.214164i | ||||
\(809\) | 24.2990 | + | 42.0871i | 0.854307 | + | 1.47970i | 0.877286 | + | 0.479967i | \(0.159351\pi\) |
−0.0229795 | + | 0.999736i | \(0.507315\pi\) | |||||||
\(810\) | 5.29289 | − | 9.16756i | 0.185973 | − | 0.322115i | ||||
\(811\) | 47.3553 | 1.66287 | 0.831435 | − | 0.555621i | \(-0.187520\pi\) | ||||
0.831435 | + | 0.555621i | \(0.187520\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.284271 | 0.00996983 | ||||||||
\(814\) | −0.272078 | + | 0.471253i | −0.00953633 | + | 0.0165174i | ||||
\(815\) | 5.12132 | + | 8.87039i | 0.179392 | + | 0.310716i | ||||
\(816\) | −2.68629 | − | 4.65279i | −0.0940390 | − | 0.162880i | ||||
\(817\) | −6.00000 | + | 10.3923i | −0.209913 | + | 0.363581i | ||||
\(818\) | −3.51472 | −0.122889 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.7426 | − | 20.3389i | 0.409821 | − | 0.709831i | −0.585048 | − | 0.810998i | \(-0.698925\pi\) |
0.994869 | + | 0.101168i | \(0.0322578\pi\) | |||||||
\(822\) | −3.51472 | − | 6.08767i | −0.122590 | − | 0.212332i | ||||
\(823\) | −8.36396 | − | 14.4868i | −0.291549 | − | 0.504978i | 0.682627 | − | 0.730767i | \(-0.260837\pi\) |
−0.974176 | + | 0.225789i | \(0.927504\pi\) | |||||||
\(824\) | −27.2132 | + | 47.1347i | −0.948017 | + | 1.64201i | ||||
\(825\) | 0.0710678 | 0.00247426 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42.0416 | 1.46193 | 0.730965 | − | 0.682415i | \(-0.239070\pi\) | ||||
0.730965 | + | 0.682415i | \(0.239070\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.97918 | − | 5.16010i | −0.103471 | − | 0.179218i | 0.809641 | − | 0.586925i | \(-0.199662\pi\) |
−0.913113 | + | 0.407707i | \(0.866328\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.15076 | − | 5.45727i | 0.109299 | − | 0.189311i | ||||
\(832\) | 35.3137 | 1.22428 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.54416 | 0.157351 | ||||||||
\(835\) | −0.378680 | + | 0.655892i | −0.0131047 | + | 0.0226981i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −12.3640 | − | 21.4150i | −0.427361 | − | 0.740211i | ||||
\(838\) | 13.2426 | − | 22.9369i | 0.457459 | − | 0.792343i | ||||
\(839\) | −23.2721 | −0.803441 | −0.401721 | − | 0.915762i | \(-0.631588\pi\) | ||||
−0.401721 | + | 0.915762i | \(0.631588\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 45.9411 | 1.58418 | ||||||||
\(842\) | −13.4350 | + | 23.2702i | −0.463002 | + | 0.801942i | ||||
\(843\) | 0.479185 | + | 0.829972i | 0.0165040 | + | 0.0285858i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.24264 | + | 5.61642i | −0.111550 | + | 0.193211i | ||||
\(846\) | −28.9706 | −0.996028 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −16.9706 | −0.582772 | ||||||||
\(849\) | 5.08579 | − | 8.80884i | 0.174544 | − | 0.302319i | ||||
\(850\) | 2.29289 | + | 3.97141i | 0.0786456 | + | 0.136218i | ||||
\(851\) | −8.31371 | − | 14.3998i | −0.284990 | − | 0.493618i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.9706 | 0.375625 | 0.187812 | − | 0.982205i | \(-0.439860\pi\) | ||||
0.187812 | + | 0.982205i | \(0.439860\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.9706 | −0.580381 | ||||||||
\(856\) | 3.51472 | − | 6.08767i | 0.120131 | − | 0.208072i | ||||
\(857\) | 11.2426 | + | 19.4728i | 0.384041 | + | 0.665179i | 0.991636 | − | 0.129068i | \(-0.0411987\pi\) |
−0.607594 | + | 0.794247i | \(0.707865\pi\) | |||||||
\(858\) | 0.221825 | + | 0.384213i | 0.00757299 | + | 0.0131168i | ||||
\(859\) | 12.3848 | − | 21.4511i | 0.422563 | − | 0.731901i | −0.573626 | − | 0.819117i | \(-0.694464\pi\) |
0.996189 | + | 0.0872164i | \(0.0277971\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 40.7279 | 1.38720 | ||||||||
\(863\) | −9.19239 | + | 15.9217i | −0.312913 | + | 0.541980i | −0.978992 | − | 0.203901i | \(-0.934638\pi\) |
0.666079 | + | 0.745881i | \(0.267971\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.62132 | + | 6.27231i | 0.123129 | + | 0.213265i | ||||
\(866\) | 7.75736 | − | 13.4361i | 0.263606 | − | 0.456579i | ||||
\(867\) | 2.68629 | 0.0912312 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.254834 | −0.00864465 | ||||||||
\(870\) | 2.53553 | − | 4.39167i | 0.0859627 | − | 0.148892i | ||||
\(871\) | 18.1924 | + | 31.5101i | 0.616426 | + | 1.06768i | ||||
\(872\) | −7.07107 | − | 12.2474i | −0.239457 | − | 0.414751i | ||||
\(873\) | 18.7279 | − | 32.4377i | 0.633844 | − | 1.09785i | ||||
\(874\) | −62.9117 | −2.12802 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.51472 | + | 11.2838i | −0.219986 | + | 0.381028i | −0.954804 | − | 0.297238i | \(-0.903935\pi\) |
0.734817 | + | 0.678265i | \(0.237268\pi\) | |||||||
\(878\) | −21.4853 | − | 37.2136i | −0.725093 | − | 1.25590i | ||||
\(879\) | 5.32843 | + | 9.22911i | 0.179723 | + | 0.311290i | ||||
\(880\) | −0.343146 | + | 0.594346i | −0.0115674 | + | 0.0200354i | ||||
\(881\) | −52.9706 | −1.78462 | −0.892312 | − | 0.451420i | \(-0.850918\pi\) | ||||
−0.892312 | + | 0.451420i | \(0.850918\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.5147 | 1.06055 | 0.530277 | − | 0.847824i | \(-0.322088\pi\) | ||||
0.530277 | + | 0.847824i | \(0.322088\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.464466 | − | 0.804479i | −0.0156129 | − | 0.0270423i | ||||
\(886\) | 10.7279 | + | 18.5813i | 0.360412 | + | 0.624251i | ||||
\(887\) | −1.48528 | + | 2.57258i | −0.0498709 | + | 0.0863789i | −0.889883 | − | 0.456188i | \(-0.849214\pi\) |
0.840012 | + | 0.542567i | \(0.182548\pi\) | |||||||
\(888\) | −2.62742 | −0.0881703 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 11.3137 | 0.379236 | ||||||||
\(891\) | 0.642136 | − | 1.11221i | 0.0215124 | − | 0.0372605i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21.7279 | + | 37.6339i | 0.727097 | + | 1.25937i | ||||
\(894\) | 2.68629 | − | 4.65279i | 0.0898430 | − | 0.155613i | ||||
\(895\) | −14.4853 | −0.484190 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −13.5563 | −0.452633 | ||||||||
\(898\) | −17.0919 | + | 29.6040i | −0.570364 | + | 0.987899i | ||||
\(899\) | 44.3345 | + | 76.7896i | 1.47864 | + | 2.56108i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.87868 | + | 11.9142i | −0.229162 | + | 0.396920i | ||||
\(902\) | −1.51472 | −0.0504346 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −36.9706 | −1.22962 | ||||||||
\(905\) | 9.36396 | − | 16.2189i | 0.311269 | − | 0.539133i | ||||
\(906\) | 2.19239 | + | 3.79733i | 0.0728372 | + | 0.126158i | ||||
\(907\) | 22.0919 | + | 38.2643i | 0.733549 | + | 1.27054i | 0.955357 | + | 0.295454i | \(0.0954708\pi\) |
−0.221808 | + | 0.975090i | \(0.571196\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.02944 | −0.233152 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.65685 | 0.187420 | 0.0937100 | − | 0.995600i | \(-0.470127\pi\) | ||||
0.0937100 | + | 0.995600i | \(0.470127\pi\) | |||||||
\(912\) | −4.97056 | + | 8.60927i | −0.164592 | + | 0.285081i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −8.31371 | − | 14.3998i | −0.274993 | − | 0.476302i | ||||
\(915\) | −0.585786 | + | 1.01461i | −0.0193655 | + | 0.0335420i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −11.0711 | −0.365400 | ||||||||
\(919\) | −6.22792 | + | 10.7871i | −0.205440 | + | 0.355833i | −0.950273 | − | 0.311418i | \(-0.899196\pi\) |
0.744833 | + | 0.667251i | \(0.232529\pi\) | |||||||
\(920\) | −10.4853 | − | 18.1610i | −0.345689 | − | 0.598752i | ||||
\(921\) | 6.39949 | + | 11.0843i | 0.210871 | + | 0.365238i | ||||
\(922\) | 2.14214 | − | 3.71029i | 0.0705475 | − | 0.122192i | ||||
\(923\) | −14.0000 | −0.460816 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.24264 | 0.0737376 | ||||||||
\(926\) | −15.1716 | + | 26.2779i | −0.498569 | + | 0.863547i | ||||
\(927\) | 27.2132 | + | 47.1347i | 0.893799 | + | 1.54811i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.6360 | + | 25.3504i | −0.480193 | + | 0.831718i | −0.999742 | − | 0.0227223i | \(-0.992767\pi\) |
0.519549 | + | 0.854441i | \(0.326100\pi\) | |||||||
\(930\) | 6.00000 | 0.196748 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.07107 | + | 3.58719i | −0.0678037 | + | 0.117439i | ||||
\(934\) | −4.05025 | − | 7.01524i | −0.132528 | − | 0.229546i | ||||
\(935\) | 0.278175 | + | 0.481813i | 0.00909728 | + | 0.0157570i | ||||
\(936\) | 17.6569 | − | 30.5826i | 0.577132 | − | 0.999623i | ||||
\(937\) | −48.5563 | −1.58627 | −0.793133 | − | 0.609048i | \(-0.791552\pi\) | ||||
−0.793133 | + | 0.609048i | \(0.791552\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.54416 | 0.246194 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.4853 | − | 25.0892i | −0.472207 | − | 0.817886i | 0.527288 | − | 0.849687i | \(-0.323209\pi\) |
−0.999494 | + | 0.0318010i | \(0.989876\pi\) | |||||||
\(942\) | 4.44365 | + | 7.69663i | 0.144782 | + | 0.250770i | ||||
\(943\) | 23.1421 | − | 40.0834i | 0.753612 | − | 1.30529i | ||||
\(944\) | 8.97056 | 0.291967 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.485281 | 0.0157779 | ||||||||
\(947\) | 26.1213 | − | 45.2435i | 0.848829 | − | 1.47021i | −0.0334253 | − | 0.999441i | \(-0.510642\pi\) |
0.882254 | − | 0.470773i | \(-0.156025\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.7279 | + | 32.4377i | 0.607934 | + | 1.05297i | ||||
\(950\) | 4.24264 | − | 7.34847i | 0.137649 | − | 0.238416i | ||||
\(951\) | 0.142136 | 0.00460906 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 53.0122 | 1.71723 | 0.858617 | − | 0.512618i | \(-0.171324\pi\) | ||||
0.858617 | + | 0.512618i | \(0.171324\pi\) | |||||||
\(954\) | −8.48528 | + | 14.6969i | −0.274721 | + | 0.475831i | ||||
\(955\) | −6.98528 | − | 12.0989i | −0.226038 | − | 0.391510i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.307612 | − | 0.532799i | 0.00994368 | − | 0.0172230i | ||||
\(958\) | −16.6274 | −0.537207 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.31371 | −0.106949 | ||||||||
\(961\) | −36.9558 | + | 64.0094i | −1.19212 | + | 2.06482i | ||||
\(962\) | 7.00000 | + | 12.1244i | 0.225689 | + | 0.390905i | ||||
\(963\) | −3.51472 | − | 6.08767i | −0.113260 | − | 0.196172i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −16.0000 | −0.515058 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −60.4264 | −1.94318 | −0.971591 | − | 0.236666i | \(-0.923945\pi\) | ||||
−0.971591 | + | 0.236666i | \(0.923945\pi\) | |||||||
\(968\) | 15.5147 | − | 26.8723i | 0.498662 | − | 0.863708i | ||||
\(969\) | 4.02944 | + | 6.97919i | 0.129444 | + | 0.224204i | ||||
\(970\) | 9.36396 | + | 16.2189i | 0.300659 | + | 0.520756i | ||||
\(971\) | 8.63604 | − | 14.9581i | 0.277144 | − | 0.480027i | −0.693530 | − | 0.720428i | \(-0.743946\pi\) |
0.970674 | + | 0.240401i | \(0.0772789\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −39.1716 | −1.25514 | ||||||||
\(975\) | 0.914214 | − | 1.58346i | 0.0292783 | − | 0.0507114i | ||||
\(976\) | −5.65685 | − | 9.79796i | −0.181071 | − | 0.313625i | ||||
\(977\) | −21.3848 | − | 37.0395i | −0.684160 | − | 1.18500i | −0.973700 | − | 0.227833i | \(-0.926836\pi\) |
0.289541 | − | 0.957166i | \(-0.406498\pi\) | |||||||
\(978\) | 3.00000 | − | 5.19615i | 0.0959294 | − | 0.166155i | ||||
\(979\) | 1.37258 | 0.0438679 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.1421 | −0.451524 | ||||||||
\(982\) | −26.3640 | + | 45.6637i | −0.841308 | + | 1.45719i | ||||
\(983\) | −0.106602 | − | 0.184640i | −0.00340007 | − | 0.00588909i | 0.864320 | − | 0.502942i | \(-0.167749\pi\) |
−0.867720 | + | 0.497053i | \(0.834416\pi\) | |||||||
\(984\) | −3.65685 | − | 6.33386i | −0.116576 | − | 0.201916i | ||||
\(985\) | −6.70711 | + | 11.6170i | −0.213706 | + | 0.370150i | ||||
\(986\) | 39.6985 | 1.26426 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.41421 | + | 12.8418i | −0.235758 | + | 0.408345i | ||||
\(990\) | 0.343146 | + | 0.594346i | 0.0109059 | + | 0.0188896i | ||||
\(991\) | −9.97056 | − | 17.2695i | −0.316725 | − | 0.548584i | 0.663077 | − | 0.748551i | \(-0.269250\pi\) |
−0.979803 | + | 0.199966i | \(0.935917\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.3726 | 0.360898 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.41421 | −0.235046 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.8640 | + | 18.8169i | 0.344065 | + | 0.595938i | 0.985183 | − | 0.171504i | \(-0.0548626\pi\) |
−0.641118 | + | 0.767442i | \(0.721529\pi\) | |||||||
\(998\) | 2.12132 | + | 3.67423i | 0.0671492 | + | 0.116306i | ||||
\(999\) | −2.70711 | + | 4.68885i | −0.0856491 | + | 0.148349i |
(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 | 245.2.e.f.226.2 | 4 | ||
7.2 | even | 3 | 245.2.a.f.1.1 | yes | 2 | ||
7.3 | odd | 6 | 245.2.e.g.116.2 | 4 | |||
7.4 | even | 3 | inner | 245.2.e.f.116.2 | 4 | ||
7.5 | odd | 6 | 245.2.a.e.1.1 | ✓ | 2 | ||
7.6 | odd | 2 | 245.2.e.g.226.2 | 4 | |||
21.2 | odd | 6 | 2205.2.a.t.1.2 | 2 | |||
21.5 | even | 6 | 2205.2.a.v.1.2 | 2 | |||
28.19 | even | 6 | 3920.2.a.bw.1.1 | 2 | |||
28.23 | odd | 6 | 3920.2.a.br.1.2 | 2 | |||
35.2 | odd | 12 | 1225.2.b.j.99.1 | 4 | |||
35.9 | even | 6 | 1225.2.a.p.1.2 | 2 | |||
35.12 | even | 12 | 1225.2.b.i.99.2 | 4 | |||
35.19 | odd | 6 | 1225.2.a.r.1.2 | 2 | |||
35.23 | odd | 12 | 1225.2.b.j.99.4 | 4 | |||
35.33 | even | 12 | 1225.2.b.i.99.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
245.2.a.e.1.1 | ✓ | 2 | 7.5 | odd | 6 | ||
245.2.a.f.1.1 | yes | 2 | 7.2 | even | 3 | ||
245.2.e.f.116.2 | 4 | 7.4 | even | 3 | inner | ||
245.2.e.f.226.2 | 4 | 1.1 | even | 1 | trivial | ||
245.2.e.g.116.2 | 4 | 7.3 | odd | 6 | |||
245.2.e.g.226.2 | 4 | 7.6 | odd | 2 | |||
1225.2.a.p.1.2 | 2 | 35.9 | even | 6 | |||
1225.2.a.r.1.2 | 2 | 35.19 | odd | 6 | |||
1225.2.b.i.99.2 | 4 | 35.12 | even | 12 | |||
1225.2.b.i.99.3 | 4 | 35.33 | even | 12 | |||
1225.2.b.j.99.1 | 4 | 35.2 | odd | 12 | |||
1225.2.b.j.99.4 | 4 | 35.23 | odd | 12 | |||
2205.2.a.t.1.2 | 2 | 21.2 | odd | 6 | |||
2205.2.a.v.1.2 | 2 | 21.5 | even | 6 | |||
3920.2.a.br.1.2 | 2 | 28.23 | odd | 6 | |||
3920.2.a.bw.1.1 | 2 | 28.19 | even | 6 |