Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1170,2,Mod(71,1170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1170, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1170.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1170.cu (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.34249703649\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 1151.2 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1170.1151 |
Dual form | 1170.2.cu.c.431.2 |
$q$-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 \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).
\(n\) | \(911\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.258819 | + | 0.965926i | 0.183013 | + | 0.683013i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.866025 | + | 0.500000i | −0.433013 | + | 0.250000i | ||||
\(5\) | 0.707107 | − | 0.707107i | 0.316228 | − | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.866025 | − | 0.232051i | −0.327327 | − | 0.0877070i | 0.0914134 | − | 0.995813i | \(-0.470862\pi\) |
−0.418740 | + | 0.908106i | \(0.637528\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.866025 | + | 0.500000i | 0.273861 | + | 0.158114i | ||||
\(11\) | −0.965926 | + | 0.258819i | −0.291238 | + | 0.0780369i | −0.401480 | − | 0.915868i | \(-0.631504\pi\) |
0.110242 | + | 0.993905i | \(0.464837\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.59808 | − | 2.50000i | −0.720577 | − | 0.693375i | ||||
\(14\) | − | 0.896575i | − | 0.239620i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | −2.44949 | − | 4.24264i | −0.594089 | − | 1.02899i | −0.993675 | − | 0.112296i | \(-0.964180\pi\) |
0.399586 | − | 0.916696i | \(-0.369154\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.232051 | − | 0.866025i | 0.0532361 | − | 0.198680i | −0.934186 | − | 0.356787i | \(-0.883872\pi\) |
0.987422 | + | 0.158107i | \(0.0505390\pi\) | |||||||
\(20\) | −0.258819 | + | 0.965926i | −0.0578737 | + | 0.215988i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.500000 | − | 0.866025i | −0.106600 | − | 0.184637i | ||||
\(23\) | 2.63896 | − | 4.57081i | 0.550261 | − | 0.953080i | −0.447995 | − | 0.894036i | \(-0.647862\pi\) |
0.998255 | − | 0.0590435i | \(-0.0188051\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | 1.74238 | − | 3.15660i | 0.341709 | − | 0.619060i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.866025 | − | 0.232051i | 0.163663 | − | 0.0438535i | ||||
\(29\) | −2.44949 | − | 1.41421i | −0.454859 | − | 0.262613i | 0.255021 | − | 0.966935i | \(-0.417918\pi\) |
−0.709880 | + | 0.704323i | \(0.751251\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.26795 | + | 1.26795i | 0.227730 | + | 0.227730i | 0.811744 | − | 0.584014i | \(-0.198519\pi\) |
−0.584014 | + | 0.811744i | \(0.698519\pi\) | |||||||
\(32\) | 0.965926 | + | 0.258819i | 0.170753 | + | 0.0457532i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.46410 | − | 3.46410i | 0.594089 | − | 0.594089i | ||||
\(35\) | −0.776457 | + | 0.448288i | −0.131245 | + | 0.0757745i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.59808 | + | 5.96410i | 0.262722 | + | 0.980492i | 0.963630 | + | 0.267240i | \(0.0861118\pi\) |
−0.700908 | + | 0.713252i | \(0.747222\pi\) | |||||||
\(38\) | 0.896575 | 0.145444 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −1.03528 | − | 3.86370i | −0.161683 | − | 0.603409i | −0.998440 | − | 0.0558348i | \(-0.982218\pi\) |
0.836757 | − | 0.547574i | \(-0.184449\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.92820 | + | 2.26795i | −0.599045 | + | 0.345859i | −0.768666 | − | 0.639650i | \(-0.779079\pi\) |
0.169621 | + | 0.985509i | \(0.445746\pi\) | |||||||
\(44\) | 0.707107 | − | 0.707107i | 0.106600 | − | 0.106600i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.09808 | + | 1.36603i | 0.751670 | + | 0.201409i | ||||
\(47\) | −7.02030 | − | 7.02030i | −1.02402 | − | 1.02402i | −0.999704 | − | 0.0243115i | \(-0.992261\pi\) |
−0.0243115 | − | 0.999704i | \(-0.507739\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.36603 | − | 3.09808i | −0.766575 | − | 0.442582i | ||||
\(50\) | 0.965926 | − | 0.258819i | 0.136603 | − | 0.0366025i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.50000 | + | 0.866025i | 0.485363 | + | 0.120096i | ||||
\(53\) | − | 12.8666i | − | 1.76737i | −0.468085 | − | 0.883683i | \(-0.655056\pi\) | ||
0.468085 | − | 0.883683i | \(-0.344944\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.500000 | + | 0.866025i | −0.0674200 | + | 0.116775i | ||||
\(56\) | 0.448288 | + | 0.776457i | 0.0599050 | + | 0.103758i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.732051 | − | 2.73205i | 0.0961230 | − | 0.358736i | ||||
\(59\) | 1.03528 | − | 3.86370i | 0.134781 | − | 0.503011i | −0.865217 | − | 0.501397i | \(-0.832820\pi\) |
0.999999 | − | 0.00161411i | \(-0.000513789\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.46410 | + | 4.26795i | 0.315496 | + | 0.546455i | 0.979543 | − | 0.201236i | \(-0.0644958\pi\) |
−0.664047 | + | 0.747691i | \(0.731162\pi\) | |||||||
\(62\) | −0.896575 | + | 1.55291i | −0.113865 | + | 0.197220i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −3.60488 | + | 0.0693504i | −0.447131 | + | 0.00860185i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.1962 | − | 2.73205i | 1.24566 | − | 0.333773i | 0.425000 | − | 0.905193i | \(-0.360274\pi\) |
0.820658 | + | 0.571420i | \(0.193607\pi\) | |||||||
\(68\) | 4.24264 | + | 2.44949i | 0.514496 | + | 0.297044i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.633975 | − | 0.633975i | −0.0757745 | − | 0.0757745i | ||||
\(71\) | 1.93185 | + | 0.517638i | 0.229269 | + | 0.0614323i | 0.371624 | − | 0.928383i | \(-0.378801\pi\) |
−0.142356 | + | 0.989816i | \(0.545468\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.53590 | − | 2.53590i | 0.296804 | − | 0.296804i | −0.542956 | − | 0.839761i | \(-0.682695\pi\) |
0.839761 | + | 0.542956i | \(0.182695\pi\) | |||||||
\(74\) | −5.34727 | + | 3.08725i | −0.621607 | + | 0.358885i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.232051 | + | 0.866025i | 0.0266181 | + | 0.0993399i | ||||
\(77\) | 0.896575 | 0.102174 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | 0.225018 | 0.112509 | − | 0.993651i | \(-0.464111\pi\) | ||||
0.112509 | + | 0.993651i | \(0.464111\pi\) | |||||||
\(80\) | −0.258819 | − | 0.965926i | −0.0289368 | − | 0.107994i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.46410 | − | 2.00000i | 0.382546 | − | 0.220863i | ||||
\(83\) | 9.52056 | − | 9.52056i | 1.04502 | − | 1.04502i | 0.0460792 | − | 0.998938i | \(-0.485327\pi\) |
0.998938 | − | 0.0460792i | \(-0.0146726\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.73205 | − | 1.26795i | −0.513263 | − | 0.137528i | ||||
\(86\) | −3.20736 | − | 3.20736i | −0.345859 | − | 0.345859i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.866025 | + | 0.500000i | 0.0923186 | + | 0.0533002i | ||||
\(89\) | −11.7112 | + | 3.13801i | −1.24139 | + | 0.332629i | −0.819004 | − | 0.573788i | \(-0.805473\pi\) |
−0.422384 | + | 0.906417i | \(0.638807\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.66987 | + | 2.76795i | 0.175050 | + | 0.290160i | ||||
\(92\) | 5.27792i | 0.550261i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.96410 | − | 8.59808i | 0.512008 | − | 0.886824i | ||||
\(95\) | −0.448288 | − | 0.776457i | −0.0459934 | − | 0.0796628i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.66025 | + | 6.19615i | −0.168573 | + | 0.629124i | 0.828984 | + | 0.559272i | \(0.188919\pi\) |
−0.997557 | + | 0.0698518i | \(0.977747\pi\) | |||||||
\(98\) | 1.60368 | − | 5.98502i | 0.161996 | − | 0.604579i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | −2.82843 | + | 4.89898i | −0.281439 | + | 0.487467i | −0.971739 | − | 0.236056i | \(-0.924145\pi\) |
0.690300 | + | 0.723523i | \(0.257478\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.660254i | 0.0650568i | 0.999471 | + | 0.0325284i | \(0.0103559\pi\) | ||||
−0.999471 | + | 0.0325284i | \(0.989644\pi\) | |||||||
\(104\) | 0.0693504 | + | 3.60488i | 0.00680036 | + | 0.353488i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.4282 | − | 3.33013i | 1.20713 | − | 0.323451i | ||||
\(107\) | 10.6945 | + | 6.17449i | 1.03388 | + | 0.596911i | 0.918094 | − | 0.396363i | \(-0.129728\pi\) |
0.115786 | + | 0.993274i | \(0.463061\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.26795 | + | 3.26795i | 0.313013 | + | 0.313013i | 0.846076 | − | 0.533063i | \(-0.178959\pi\) |
−0.533063 | + | 0.846076i | \(0.678959\pi\) | |||||||
\(110\) | −0.965926 | − | 0.258819i | −0.0920974 | − | 0.0246774i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.633975 | + | 0.633975i | −0.0599050 | + | 0.0599050i | ||||
\(113\) | 1.79315 | − | 1.03528i | 0.168685 | − | 0.0973906i | −0.413280 | − | 0.910604i | \(-0.635617\pi\) |
0.581966 | + | 0.813213i | \(0.302284\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.36603 | − | 5.09808i | −0.127383 | − | 0.475398i | ||||
\(116\) | 2.82843 | 0.262613 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.00000 | 0.368230 | ||||||||
\(119\) | 1.13681 | + | 4.24264i | 0.104211 | + | 0.388922i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.66025 | + | 5.00000i | −0.787296 | + | 0.454545i | ||||
\(122\) | −3.48477 | + | 3.48477i | −0.315496 | + | 0.315496i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.73205 | − | 0.464102i | −0.155543 | − | 0.0416776i | ||||
\(125\) | −0.707107 | − | 0.707107i | −0.0632456 | − | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.9641 | + | 6.33013i | 0.972907 | + | 0.561708i | 0.900121 | − | 0.435640i | \(-0.143478\pi\) |
0.0727855 | + | 0.997348i | \(0.476811\pi\) | |||||||
\(128\) | −0.965926 | + | 0.258819i | −0.0853766 | + | 0.0228766i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.00000 | − | 3.46410i | −0.0877058 | − | 0.303822i | ||||
\(131\) | 4.38134i | 0.382800i | 0.981512 | + | 0.191400i | \(0.0613027\pi\) | ||||
−0.981512 | + | 0.191400i | \(0.938697\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.401924 | + | 0.696152i | −0.0348512 | + | 0.0603641i | ||||
\(134\) | 5.27792 | + | 9.14162i | 0.455943 | + | 0.789716i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.26795 | + | 4.73205i | −0.108726 | + | 0.405770i | ||||
\(137\) | −2.07055 | + | 7.72741i | −0.176899 | + | 0.660197i | 0.819321 | + | 0.573335i | \(0.194351\pi\) |
−0.996220 | + | 0.0868620i | \(0.972316\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.33013 | − | 14.4282i | −0.706552 | − | 1.22378i | −0.966128 | − | 0.258062i | \(-0.916916\pi\) |
0.259576 | − | 0.965723i | \(-0.416417\pi\) | |||||||
\(140\) | 0.448288 | − | 0.776457i | 0.0378872 | − | 0.0656226i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.00000i | 0.167836i | ||||||||
\(143\) | 3.15660 | + | 1.74238i | 0.263968 | + | 0.145705i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.73205 | + | 0.732051i | −0.226884 | + | 0.0607935i | ||||
\(146\) | 3.10583 | + | 1.79315i | 0.257040 | + | 0.148402i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.36603 | − | 4.36603i | −0.358885 | − | 0.358885i | ||||
\(149\) | 2.31079 | + | 0.619174i | 0.189307 | + | 0.0507247i | 0.352227 | − | 0.935915i | \(-0.385425\pi\) |
−0.162920 | + | 0.986639i | \(0.552091\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.1962 | − | 10.1962i | 0.829751 | − | 0.829751i | −0.157731 | − | 0.987482i | \(-0.550418\pi\) |
0.987482 | + | 0.157731i | \(0.0504179\pi\) | |||||||
\(152\) | −0.776457 | + | 0.448288i | −0.0629790 | + | 0.0363609i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.232051 | + | 0.866025i | 0.0186992 | + | 0.0697863i | ||||
\(155\) | 1.79315 | 0.144029 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.80385 | −0.543006 | −0.271503 | − | 0.962438i | \(-0.587521\pi\) | ||||
−0.271503 | + | 0.962438i | \(0.587521\pi\) | |||||||
\(158\) | 0.517638 | + | 1.93185i | 0.0411811 | + | 0.153690i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.866025 | − | 0.500000i | 0.0684653 | − | 0.0395285i | ||||
\(161\) | −3.34607 | + | 3.34607i | −0.263707 | + | 0.263707i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.6603 | − | 5.26795i | −1.53991 | − | 0.412618i | −0.613673 | − | 0.789560i | \(-0.710309\pi\) |
−0.926237 | + | 0.376942i | \(0.876975\pi\) | |||||||
\(164\) | 2.82843 | + | 2.82843i | 0.220863 | + | 0.220863i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.6603 | + | 6.73205i | 0.905011 | + | 0.522508i | ||||
\(167\) | −7.32989 | + | 1.96404i | −0.567204 | + | 0.151982i | −0.531014 | − | 0.847363i | \(-0.678189\pi\) |
−0.0361899 | + | 0.999345i | \(0.511522\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.500000 | + | 12.9904i | 0.0384615 | + | 0.999260i | ||||
\(170\) | − | 4.89898i | − | 0.375735i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.26795 | − | 3.92820i | 0.172930 | − | 0.299523i | ||||
\(173\) | −5.86491 | − | 10.1583i | −0.445900 | − | 0.772322i | 0.552214 | − | 0.833702i | \(-0.313783\pi\) |
−0.998114 | + | 0.0613801i | \(0.980450\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.232051 | + | 0.866025i | −0.0175414 | + | 0.0654654i | ||||
\(176\) | −0.258819 | + | 0.965926i | −0.0195092 | + | 0.0728094i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.06218 | − | 10.5000i | −0.454379 | − | 0.787008i | ||||
\(179\) | −0.189469 | + | 0.328169i | −0.0141616 | + | 0.0245285i | −0.873019 | − | 0.487686i | \(-0.837841\pi\) |
0.858858 | + | 0.512214i | \(0.171175\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.8564i | 1.47592i | 0.674847 | + | 0.737958i | \(0.264210\pi\) | ||||
−0.674847 | + | 0.737958i | \(0.735790\pi\) | |||||||
\(182\) | −2.24144 | + | 2.32937i | −0.166146 | + | 0.172664i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.09808 | + | 1.36603i | −0.375835 | + | 0.100705i | ||||
\(185\) | 5.34727 | + | 3.08725i | 0.393139 | + | 0.226979i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.46410 | + | 3.46410i | 0.253320 | + | 0.253320i | ||||
\(188\) | 9.58991 | + | 2.56961i | 0.699416 | + | 0.187408i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.633975 | − | 0.633975i | 0.0459934 | − | 0.0459934i | ||||
\(191\) | −20.9730 | + | 12.1087i | −1.51755 | + | 0.876158i | −0.517764 | + | 0.855524i | \(0.673235\pi\) |
−0.999787 | + | 0.0206345i | \(0.993431\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.339746 | − | 1.26795i | −0.0244554 | − | 0.0912690i | 0.952620 | − | 0.304165i | \(-0.0983773\pi\) |
−0.977075 | + | 0.212896i | \(0.931711\pi\) | |||||||
\(194\) | −6.41473 | −0.460551 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.19615 | 0.442582 | ||||||||
\(197\) | −1.96404 | − | 7.32989i | −0.139932 | − | 0.522233i | −0.999929 | − | 0.0119336i | \(-0.996201\pi\) |
0.859997 | − | 0.510299i | \(-0.170465\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.92820 | + | 2.26795i | −0.278463 | + | 0.160771i | −0.632727 | − | 0.774375i | \(-0.718065\pi\) |
0.354264 | + | 0.935145i | \(0.384731\pi\) | |||||||
\(200\) | −0.707107 | + | 0.707107i | −0.0500000 | + | 0.0500000i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.46410 | − | 1.46410i | −0.384453 | − | 0.103014i | ||||
\(203\) | 1.79315 | + | 1.79315i | 0.125855 | + | 0.125855i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.46410 | − | 2.00000i | −0.241943 | − | 0.139686i | ||||
\(206\) | −0.637756 | + | 0.170886i | −0.0444346 | + | 0.0119062i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.46410 | + | 1.00000i | −0.240192 | + | 0.0693375i | ||||
\(209\) | 0.896575i | 0.0620174i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.96410 | − | 8.59808i | 0.341743 | − | 0.591916i | −0.643014 | − | 0.765855i | \(-0.722316\pi\) |
0.984756 | + | 0.173939i | \(0.0556495\pi\) | |||||||
\(212\) | 6.43331 | + | 11.1428i | 0.441842 | + | 0.765292i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.19615 | + | 11.9282i | −0.218484 | + | 0.815395i | ||||
\(215\) | −1.17398 | + | 4.38134i | −0.0800646 | + | 0.298805i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.803848 | − | 1.39230i | −0.0545687 | − | 0.0945158i | ||||
\(218\) | −2.31079 | + | 4.00240i | −0.156506 | + | 0.271077i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 1.00000i | − | 0.0674200i | ||||||
\(221\) | −4.24264 | + | 17.1464i | −0.285391 | + | 1.15339i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.33013 | + | 0.624356i | −0.156037 | + | 0.0418099i | −0.335992 | − | 0.941865i | \(-0.609071\pi\) |
0.179955 | + | 0.983675i | \(0.442405\pi\) | |||||||
\(224\) | −0.776457 | − | 0.448288i | −0.0518792 | − | 0.0299525i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.46410 | + | 1.46410i | 0.0973906 | + | 0.0973906i | ||||
\(227\) | 10.9348 | + | 2.92996i | 0.725766 | + | 0.194468i | 0.602743 | − | 0.797935i | \(-0.294074\pi\) |
0.123023 | + | 0.992404i | \(0.460741\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.339746 | + | 0.339746i | −0.0224510 | + | 0.0224510i | −0.718243 | − | 0.695792i | \(-0.755053\pi\) |
0.695792 | + | 0.718243i | \(0.255053\pi\) | |||||||
\(230\) | 4.57081 | − | 2.63896i | 0.301390 | − | 0.174008i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.732051 | + | 2.73205i | 0.0480615 | + | 0.179368i | ||||
\(233\) | 8.76268 | 0.574062 | 0.287031 | − | 0.957921i | \(-0.407332\pi\) | ||||
0.287031 | + | 0.957921i | \(0.407332\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.92820 | −0.647645 | ||||||||
\(236\) | 1.03528 | + | 3.86370i | 0.0673907 | + | 0.251506i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.80385 | + | 2.19615i | −0.246567 | + | 0.142355i | ||||
\(239\) | 10.4543 | − | 10.4543i | 0.676232 | − | 0.676232i | −0.282913 | − | 0.959146i | \(-0.591301\pi\) |
0.959146 | + | 0.282913i | \(0.0913008\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.96410 | − | 1.59808i | −0.384182 | − | 0.102941i | 0.0615587 | − | 0.998103i | \(-0.480393\pi\) |
−0.445740 | + | 0.895162i | \(0.647060\pi\) | |||||||
\(242\) | −7.07107 | − | 7.07107i | −0.454545 | − | 0.454545i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.26795 | − | 2.46410i | −0.273227 | − | 0.157748i | ||||
\(245\) | −5.98502 | + | 1.60368i | −0.382369 | + | 0.102456i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.76795 | + | 1.66987i | −0.176120 | + | 0.106251i | ||||
\(248\) | − | 1.79315i | − | 0.113865i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.500000 | − | 0.866025i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | 11.4710 | + | 19.8683i | 0.724043 | + | 1.25408i | 0.959367 | + | 0.282162i | \(0.0910514\pi\) |
−0.235324 | + | 0.971917i | \(0.575615\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.36603 | + | 5.09808i | −0.0858813 | + | 0.320513i | ||||
\(254\) | −3.27671 | + | 12.2289i | −0.205599 | + | 0.767307i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 13.6617 | − | 23.6627i | 0.852191 | − | 1.47604i | −0.0270355 | − | 0.999634i | \(-0.508607\pi\) |
0.879227 | − | 0.476404i | \(-0.158060\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 5.53590i | − | 0.343984i | ||||||
\(260\) | 3.08725 | − | 1.86250i | 0.191463 | − | 0.115507i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.23205 | + | 1.13397i | −0.261457 | + | 0.0700572i | ||||
\(263\) | 14.0728 | + | 8.12493i | 0.867765 | + | 0.501004i | 0.866605 | − | 0.498995i | \(-0.166297\pi\) |
0.00116020 | + | 0.999999i | \(0.499631\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.09808 | − | 9.09808i | −0.558890 | − | 0.558890i | ||||
\(266\) | −0.776457 | − | 0.208051i | −0.0476076 | − | 0.0127564i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.46410 | + | 7.46410i | −0.455943 | + | 0.455943i | ||||
\(269\) | −17.6269 | + | 10.1769i | −1.07473 | + | 0.620496i | −0.929470 | − | 0.368897i | \(-0.879735\pi\) |
−0.145261 | + | 0.989393i | \(0.546402\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.07180 | + | 18.9282i | 0.308090 | + | 1.14981i | 0.930253 | + | 0.366919i | \(0.119587\pi\) |
−0.622163 | + | 0.782888i | \(0.713746\pi\) | |||||||
\(272\) | −4.89898 | −0.297044 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.00000 | −0.483298 | ||||||||
\(275\) | 0.258819 | + | 0.965926i | 0.0156074 | + | 0.0582475i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.0622 | + | 10.4282i | −1.08525 | + | 0.626570i | −0.932308 | − | 0.361665i | \(-0.882208\pi\) |
−0.152943 | + | 0.988235i | \(0.548875\pi\) | |||||||
\(278\) | 11.7806 | − | 11.7806i | 0.706552 | − | 0.706552i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.866025 | + | 0.232051i | 0.0517549 | + | 0.0138677i | ||||
\(281\) | 5.55532 | + | 5.55532i | 0.331403 | + | 0.331403i | 0.853119 | − | 0.521716i | \(-0.174708\pi\) |
−0.521716 | + | 0.853119i | \(0.674708\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.3923 | − | 14.6603i | −1.50942 | − | 0.871462i | −0.999940 | − | 0.0109768i | \(-0.996506\pi\) |
−0.509476 | − | 0.860485i | \(-0.670161\pi\) | |||||||
\(284\) | −1.93185 | + | 0.517638i | −0.114634 | + | 0.0307162i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.866025 | + | 3.50000i | −0.0512092 | + | 0.206959i | ||||
\(287\) | 3.58630i | 0.211693i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.50000 | + | 6.06218i | −0.205882 | + | 0.356599i | ||||
\(290\) | −1.41421 | − | 2.44949i | −0.0830455 | − | 0.143839i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.928203 | + | 3.46410i | −0.0543190 | + | 0.202721i | ||||
\(293\) | 3.60488 | − | 13.4536i | 0.210600 | − | 0.785968i | −0.777070 | − | 0.629414i | \(-0.783295\pi\) |
0.987669 | − | 0.156554i | \(-0.0500385\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.00000 | − | 3.46410i | −0.116445 | − | 0.201688i | ||||
\(296\) | 3.08725 | − | 5.34727i | 0.179443 | − | 0.310804i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.39230i | 0.138582i | ||||||||
\(299\) | −18.2832 | + | 5.27792i | −1.05735 | + | 0.305230i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.92820 | − | 1.05256i | 0.226418 | − | 0.0606685i | ||||
\(302\) | 12.4877 | + | 7.20977i | 0.718586 | + | 0.414876i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.633975 | − | 0.633975i | −0.0363609 | − | 0.0363609i | ||||
\(305\) | 4.76028 | + | 1.27551i | 0.272573 | + | 0.0730357i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.1962 | − | 16.1962i | 0.924363 | − | 0.924363i | −0.0729708 | − | 0.997334i | \(-0.523248\pi\) |
0.997334 | + | 0.0729708i | \(0.0232480\pi\) | |||||||
\(308\) | −0.776457 | + | 0.448288i | −0.0442428 | + | 0.0255436i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.464102 | + | 1.73205i | 0.0263592 | + | 0.0983739i | ||||
\(311\) | 0.554803 | 0.0314600 | 0.0157300 | − | 0.999876i | \(-0.494993\pi\) | ||||
0.0157300 | + | 0.999876i | \(0.494993\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.0000 | −0.565233 | −0.282617 | − | 0.959233i | \(-0.591202\pi\) | ||||
−0.282617 | + | 0.959233i | \(0.591202\pi\) | |||||||
\(314\) | −1.76097 | − | 6.57201i | −0.0993770 | − | 0.370880i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.73205 | + | 1.00000i | −0.0974355 | + | 0.0562544i | ||||
\(317\) | −11.3645 | + | 11.3645i | −0.638293 | + | 0.638293i | −0.950134 | − | 0.311842i | \(-0.899054\pi\) |
0.311842 | + | 0.950134i | \(0.399054\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.73205 | + | 0.732051i | 0.152965 | + | 0.0409870i | ||||
\(320\) | 0.707107 | + | 0.707107i | 0.0395285 | + | 0.0395285i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.09808 | − | 2.36603i | −0.228377 | − | 0.131853i | ||||
\(323\) | −4.24264 | + | 1.13681i | −0.236067 | + | 0.0632539i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.50000 | + | 2.59808i | −0.138675 | + | 0.144115i | ||||
\(326\) | − | 20.3538i | − | 1.12729i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.00000 | + | 3.46410i | −0.110432 | + | 0.191273i | ||||
\(329\) | 4.45069 | + | 7.70882i | 0.245375 | + | 0.425001i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.294229 | − | 1.09808i | 0.0161723 | − | 0.0603557i | −0.957368 | − | 0.288871i | \(-0.906720\pi\) |
0.973540 | + | 0.228515i | \(0.0733869\pi\) | |||||||
\(332\) | −3.48477 | + | 13.0053i | −0.191251 | + | 0.713760i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.79423 | − | 6.57180i | −0.207611 | − | 0.359593i | ||||
\(335\) | 5.27792 | − | 9.14162i | 0.288363 | − | 0.499460i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 4.53590i | − | 0.247086i | −0.992339 | − | 0.123543i | \(-0.960574\pi\) | ||
0.992339 | − | 0.123543i | \(-0.0394257\pi\) | |||||||
\(338\) | −12.4183 | + | 3.84512i | −0.675468 | + | 0.209147i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.73205 | − | 1.26795i | 0.256631 | − | 0.0687642i | ||||
\(341\) | −1.55291 | − | 0.896575i | −0.0840950 | − | 0.0485523i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.36603 | + | 8.36603i | 0.451723 | + | 0.451723i | ||||
\(344\) | 4.38134 | + | 1.17398i | 0.236226 | + | 0.0632966i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.29423 | − | 8.29423i | 0.445900 | − | 0.445900i | ||||
\(347\) | 3.76217 | − | 2.17209i | 0.201964 | − | 0.116604i | −0.395607 | − | 0.918420i | \(-0.629466\pi\) |
0.597571 | + | 0.801816i | \(0.296133\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.679492 | − | 2.53590i | −0.0363724 | − | 0.135744i | 0.945352 | − | 0.326051i | \(-0.105718\pi\) |
−0.981725 | + | 0.190308i | \(0.939051\pi\) | |||||||
\(350\) | −0.896575 | −0.0479240 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −6.86800 | − | 25.6317i | −0.365547 | − | 1.36424i | −0.866678 | − | 0.498867i | \(-0.833750\pi\) |
0.501132 | − | 0.865371i | \(-0.332917\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.73205 | − | 1.00000i | 0.0919277 | − | 0.0530745i | ||||
\(356\) | 8.57321 | − | 8.57321i | 0.454379 | − | 0.454379i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.366025 | − | 0.0980762i | −0.0193450 | − | 0.00518349i | ||||
\(359\) | 3.76217 | + | 3.76217i | 0.198560 | + | 0.198560i | 0.799382 | − | 0.600823i | \(-0.205160\pi\) |
−0.600823 | + | 0.799382i | \(0.705160\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.7583 | + | 9.09808i | 0.829386 | + | 0.478846i | ||||
\(362\) | −19.1798 | + | 5.13922i | −1.00807 | + | 0.270111i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.83013 | − | 1.56218i | −0.148339 | − | 0.0818804i | ||||
\(365\) | − | 3.58630i | − | 0.187716i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.66025 | + | 8.07180i | −0.243263 | + | 0.421344i | −0.961642 | − | 0.274308i | \(-0.911551\pi\) |
0.718379 | + | 0.695652i | \(0.244885\pi\) | |||||||
\(368\) | −2.63896 | − | 4.57081i | −0.137565 | − | 0.238270i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.59808 | + | 5.96410i | −0.0830800 | + | 0.310059i | ||||
\(371\) | −2.98571 | + | 11.1428i | −0.155010 | + | 0.578507i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.3923 | − | 31.8564i | −0.952317 | − | 1.64946i | −0.740391 | − | 0.672177i | \(-0.765360\pi\) |
−0.211927 | − | 0.977286i | \(-0.567974\pi\) | |||||||
\(374\) | −2.44949 | + | 4.24264i | −0.126660 | + | 0.219382i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.92820i | 0.512008i | ||||||||
\(377\) | 2.82843 | + | 9.79796i | 0.145671 | + | 0.504621i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.5526 | − | 9.79423i | 1.87758 | − | 0.503096i | 0.877872 | − | 0.478896i | \(-0.158963\pi\) |
0.999707 | − | 0.0241998i | \(-0.00770379\pi\) | |||||||
\(380\) | 0.776457 | + | 0.448288i | 0.0398314 | + | 0.0229967i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −17.1244 | − | 17.1244i | −0.876158 | − | 0.876158i | ||||
\(383\) | 30.1146 | + | 8.06918i | 1.53878 | + | 0.412316i | 0.925872 | − | 0.377836i | \(-0.123332\pi\) |
0.612911 | + | 0.790152i | \(0.289998\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.633975 | − | 0.633975i | 0.0323103 | − | 0.0323103i | ||||
\(386\) | 1.13681 | − | 0.656339i | 0.0578622 | − | 0.0334068i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.66025 | − | 6.19615i | −0.0842866 | − | 0.314562i | ||||
\(389\) | 26.0106 | 1.31879 | 0.659396 | − | 0.751796i | \(-0.270812\pi\) | ||||
0.659396 | + | 0.751796i | \(0.270812\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.8564 | −1.30761 | ||||||||
\(392\) | 1.60368 | + | 5.98502i | 0.0809982 | + | 0.302289i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.57180 | − | 3.79423i | 0.331082 | − | 0.191150i | ||||
\(395\) | 1.41421 | − | 1.41421i | 0.0711568 | − | 0.0711568i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.3564 | + | 8.13397i | 1.52354 | + | 0.408232i | 0.920907 | − | 0.389783i | \(-0.127450\pi\) |
0.602637 | + | 0.798015i | \(0.294117\pi\) | |||||||
\(398\) | −3.20736 | − | 3.20736i | −0.160771 | − | 0.160771i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.866025 | − | 0.500000i | −0.0433013 | − | 0.0250000i | ||||
\(401\) | −32.7721 | + | 8.78127i | −1.63656 | + | 0.438515i | −0.955807 | − | 0.293996i | \(-0.905015\pi\) |
−0.680755 | + | 0.732511i | \(0.738348\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.124356 | − | 6.46410i | −0.00619460 | − | 0.322000i | ||||
\(404\) | − | 5.65685i | − | 0.281439i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.26795 | + | 2.19615i | −0.0629273 | + | 0.108993i | ||||
\(407\) | −3.08725 | − | 5.34727i | −0.153029 | − | 0.265054i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.64359 | + | 21.0622i | −0.279058 | + | 1.04146i | 0.674015 | + | 0.738717i | \(0.264568\pi\) |
−0.953073 | + | 0.302740i | \(0.902099\pi\) | |||||||
\(410\) | 1.03528 | − | 3.86370i | 0.0511286 | − | 0.190815i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.330127 | − | 0.571797i | −0.0162642 | − | 0.0281704i | ||||
\(413\) | −1.79315 | + | 3.10583i | −0.0882352 | + | 0.152828i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 13.4641i | − | 0.660927i | ||||||
\(416\) | −1.86250 | − | 3.08725i | −0.0913166 | − | 0.151365i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.866025 | + | 0.232051i | −0.0423587 | + | 0.0113500i | ||||
\(419\) | −6.53983 | − | 3.77577i | −0.319491 | − | 0.184458i | 0.331674 | − | 0.943394i | \(-0.392386\pi\) |
−0.651166 | + | 0.758935i | \(0.725720\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.53590 | + | 2.53590i | 0.123592 | + | 0.123592i | 0.766197 | − | 0.642605i | \(-0.222146\pi\) |
−0.642605 | + | 0.766197i | \(0.722146\pi\) | |||||||
\(422\) | 9.58991 | + | 2.56961i | 0.466829 | + | 0.125087i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.09808 | + | 9.09808i | −0.441842 | + | 0.441842i | ||||
\(425\) | −4.24264 | + | 2.44949i | −0.205798 | + | 0.118818i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.14359 | − | 4.26795i | −0.0553424 | − | 0.206541i | ||||
\(428\) | −12.3490 | −0.596911 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.53590 | −0.218740 | ||||||||
\(431\) | 2.44949 | + | 9.14162i | 0.117988 | + | 0.440336i | 0.999493 | − | 0.0318378i | \(-0.0101360\pi\) |
−0.881505 | + | 0.472174i | \(0.843469\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.6603 | + | 13.6603i | −1.13704 | + | 0.656470i | −0.945696 | − | 0.325053i | \(-0.894618\pi\) |
−0.191344 | + | 0.981523i | \(0.561284\pi\) | |||||||
\(434\) | 1.13681 | − | 1.13681i | 0.0545687 | − | 0.0545687i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.46410 | − | 1.19615i | −0.213792 | − | 0.0572853i | ||||
\(437\) | −3.34607 | − | 3.34607i | −0.160064 | − | 0.160064i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.8038 | + | 7.39230i | 0.611094 | + | 0.352815i | 0.773394 | − | 0.633926i | \(-0.218558\pi\) |
−0.162299 | + | 0.986742i | \(0.551891\pi\) | |||||||
\(440\) | 0.965926 | − | 0.258819i | 0.0460487 | − | 0.0123387i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17.6603 | + | 0.339746i | −0.840013 | + | 0.0161601i | ||||
\(443\) | 10.2784i | 0.488343i | 0.969732 | + | 0.244172i | \(0.0785160\pi\) | ||||
−0.969732 | + | 0.244172i | \(0.921484\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.06218 | + | 10.5000i | −0.287375 | + | 0.497748i | ||||
\(446\) | −1.20616 | − | 2.08913i | −0.0571134 | − | 0.0989234i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.232051 | − | 0.866025i | 0.0109634 | − | 0.0409159i | ||||
\(449\) | 0.448288 | − | 1.67303i | 0.0211560 | − | 0.0789553i | −0.954541 | − | 0.298080i | \(-0.903654\pi\) |
0.975697 | + | 0.219125i | \(0.0703203\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.00000 | + | 3.46410i | 0.0941763 | + | 0.163118i | ||||
\(452\) | −1.03528 | + | 1.79315i | −0.0486953 | + | 0.0843427i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.3205i | 0.531298i | ||||||||
\(455\) | 3.13801 | + | 0.776457i | 0.147112 | + | 0.0364009i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.0526 | − | 9.92820i | 1.73325 | − | 0.464422i | 0.752319 | − | 0.658799i | \(-0.228935\pi\) |
0.980927 | + | 0.194377i | \(0.0622687\pi\) | |||||||
\(458\) | −0.416102 | − | 0.240237i | −0.0194432 | − | 0.0112255i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.73205 | + | 3.73205i | 0.174008 | + | 0.174008i | ||||
\(461\) | 13.0053 | + | 3.48477i | 0.605718 | + | 0.162302i | 0.548627 | − | 0.836067i | \(-0.315151\pi\) |
0.0570913 | + | 0.998369i | \(0.481817\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.1244 | − | 16.1244i | 0.749362 | − | 0.749362i | −0.224997 | − | 0.974359i | \(-0.572237\pi\) |
0.974359 | + | 0.224997i | \(0.0722373\pi\) | |||||||
\(464\) | −2.44949 | + | 1.41421i | −0.113715 | + | 0.0656532i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.26795 | + | 8.46410i | 0.105061 | + | 0.392092i | ||||
\(467\) | 4.14110 | 0.191627 | 0.0958137 | − | 0.995399i | \(-0.469455\pi\) | ||||
0.0958137 | + | 0.995399i | \(0.469455\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.46410 | −0.437012 | ||||||||
\(470\) | −2.56961 | − | 9.58991i | −0.118527 | − | 0.442349i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.46410 | + | 2.00000i | −0.159448 | + | 0.0920575i | ||||
\(473\) | 3.20736 | − | 3.20736i | 0.147475 | − | 0.147475i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.866025 | − | 0.232051i | −0.0397360 | − | 0.0106472i | ||||
\(476\) | −3.10583 | − | 3.10583i | −0.142355 | − | 0.142355i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12.8038 | + | 7.39230i | 0.585634 | + | 0.338116i | ||||
\(479\) | 9.89949 | − | 2.65256i | 0.452319 | − | 0.121199i | −0.0254650 | − | 0.999676i | \(-0.508107\pi\) |
0.477784 | + | 0.878477i | \(0.341440\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.7583 | − | 19.4904i | 0.490538 | − | 0.888685i | ||||
\(482\) | − | 6.17449i | − | 0.281240i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.00000 | − | 8.66025i | 0.227273 | − | 0.393648i | ||||
\(485\) | 3.20736 | + | 5.55532i | 0.145639 | + | 0.252254i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.20577 | − | 15.6962i | 0.190582 | − | 0.711261i | −0.802785 | − | 0.596269i | \(-0.796649\pi\) |
0.993366 | − | 0.114992i | \(-0.0366841\pi\) | |||||||
\(488\) | 1.27551 | − | 4.76028i | 0.0577398 | − | 0.215488i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.09808 | − | 5.36603i | −0.139957 | − | 0.242412i | ||||
\(491\) | −0.877993 | + | 1.52073i | −0.0396233 | + | 0.0686295i | −0.885157 | − | 0.465293i | \(-0.845949\pi\) |
0.845534 | + | 0.533922i | \(0.179282\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.8564i | 0.624061i | ||||||||
\(494\) | −2.32937 | − | 2.24144i | −0.104803 | − | 0.100847i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.73205 | − | 0.464102i | 0.0777714 | − | 0.0208388i | ||||
\(497\) | −1.55291 | − | 0.896575i | −0.0696577 | − | 0.0402169i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.1962 | + | 23.1962i | 1.03840 | + | 1.03840i | 0.999233 | + | 0.0391698i | \(0.0124713\pi\) |
0.0391698 | + | 0.999233i | \(0.487529\pi\) | |||||||
\(500\) | 0.965926 | + | 0.258819i | 0.0431975 | + | 0.0115747i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −16.2224 | + | 16.2224i | −0.724043 | + | 0.724043i | ||||
\(503\) | −30.5629 | + | 17.6455i | −1.36273 | + | 0.786773i | −0.989987 | − | 0.141161i | \(-0.954917\pi\) |
−0.372745 | + | 0.927934i | \(0.621583\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.46410 | + | 5.46410i | 0.0651517 | + | 0.243149i | ||||
\(506\) | −5.27792 | −0.234632 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −12.6603 | −0.561708 | ||||||||
\(509\) | −1.17398 | − | 4.38134i | −0.0520356 | − | 0.194200i | 0.935015 | − | 0.354608i | \(-0.115386\pi\) |
−0.987051 | + | 0.160408i | \(0.948719\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.78461 | + | 1.60770i | −0.123184 | + | 0.0711202i | ||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 26.3923 | + | 7.07180i | 1.16411 | + | 0.311924i | ||||
\(515\) | 0.466870 | + | 0.466870i | 0.0205728 | + | 0.0205728i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.59808 | + | 4.96410i | 0.378143 | + | 0.218321i | ||||
\(518\) | 5.34727 | − | 1.43280i | 0.234945 | − | 0.0629534i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.59808 | + | 2.50000i | 0.113933 | + | 0.109632i | ||||
\(521\) | 3.72500i | 0.163195i | 0.996665 | + | 0.0815977i | \(0.0260023\pi\) | ||||
−0.996665 | + | 0.0815977i | \(0.973998\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.7846 | − | 34.2679i | 0.865121 | − | 1.49843i | −0.00180682 | − | 0.999998i | \(-0.500575\pi\) |
0.866927 | − | 0.498434i | \(-0.166092\pi\) | |||||||
\(524\) | −2.19067 | − | 3.79435i | −0.0956999 | − | 0.165757i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.20577 | + | 15.6962i | −0.183380 | + | 0.684385i | ||||
\(527\) | 2.27362 | − | 8.48528i | 0.0990406 | − | 0.369625i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.42820 | − | 4.20577i | −0.105574 | − | 0.182860i | ||||
\(530\) | 6.43331 | − | 11.1428i | 0.279445 | − | 0.484013i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 0.803848i | − | 0.0348512i | ||||||
\(533\) | −6.96953 | + | 12.6264i | −0.301884 | + | 0.546909i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.9282 | − | 3.19615i | 0.515701 | − | 0.138182i | ||||
\(536\) | −9.14162 | − | 5.27792i | −0.394858 | − | 0.227971i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −14.3923 | − | 14.3923i | −0.620496 | − | 0.620496i | ||||
\(539\) | 5.98502 | + | 1.60368i | 0.257793 | + | 0.0690755i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.80385 | − | 7.80385i | 0.335514 | − | 0.335514i | −0.519162 | − | 0.854676i | \(-0.673756\pi\) |
0.854676 | + | 0.519162i | \(0.173756\pi\) | |||||||
\(542\) | −16.9706 | + | 9.79796i | −0.728948 | + | 0.420858i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.26795 | − | 4.73205i | −0.0543629 | − | 0.202885i | ||||
\(545\) | 4.62158 | 0.197967 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.7128 | 1.44146 | 0.720728 | − | 0.693218i | \(-0.243808\pi\) | ||||
0.720728 | + | 0.693218i | \(0.243808\pi\) | |||||||
\(548\) | −2.07055 | − | 7.72741i | −0.0884496 | − | 0.330098i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.866025 | + | 0.500000i | −0.0369274 | + | 0.0213201i | ||||
\(551\) | −1.79315 | + | 1.79315i | −0.0763908 | + | 0.0763908i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.73205 | − | 0.464102i | −0.0736543 | − | 0.0197356i | ||||
\(554\) | −14.7477 | − | 14.7477i | −0.626570 | − | 0.626570i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.4282 | + | 8.33013i | 0.611892 | + | 0.353276i | ||||
\(557\) | −2.19067 | + | 0.586988i | −0.0928217 | + | 0.0248715i | −0.304931 | − | 0.952374i | \(-0.598633\pi\) |
0.212109 | + | 0.977246i | \(0.431967\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.8756 | + | 3.92820i | 0.671468 | + | 0.166145i | ||||
\(560\) | 0.896575i | 0.0378872i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.92820 | + | 6.80385i | −0.165701 | + | 0.287003i | ||||
\(563\) | −0.757875 | − | 1.31268i | −0.0319406 | − | 0.0553228i | 0.849613 | − | 0.527406i | \(-0.176835\pi\) |
−0.881554 | + | 0.472084i | \(0.843502\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.535898 | − | 2.00000i | 0.0225454 | − | 0.0841406i | ||||
\(566\) | 7.58871 | − | 28.3214i | 0.318977 | − | 1.19044i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.00000 | − | 1.73205i | −0.0419591 | − | 0.0726752i | ||||
\(569\) | 18.3018 | − | 31.6997i | 0.767252 | − | 1.32892i | −0.171795 | − | 0.985133i | \(-0.554957\pi\) |
0.939048 | − | 0.343787i | \(-0.111710\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 32.6603i | − | 1.36679i | −0.730049 | − | 0.683395i | \(-0.760503\pi\) | ||
0.730049 | − | 0.683395i | \(-0.239497\pi\) | |||||||
\(572\) | −3.60488 | + | 0.0693504i | −0.150728 | + | 0.00289968i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.46410 | + | 0.928203i | −0.144589 | + | 0.0387425i | ||||
\(575\) | −4.57081 | − | 2.63896i | −0.190616 | − | 0.110052i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.66025 | + | 7.66025i | 0.318901 | + | 0.318901i | 0.848345 | − | 0.529444i | \(-0.177600\pi\) |
−0.529444 | + | 0.848345i | \(0.677600\pi\) | |||||||
\(578\) | −6.76148 | − | 1.81173i | −0.281241 | − | 0.0753582i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.00000 | − | 2.00000i | 0.0830455 | − | 0.0830455i | ||||
\(581\) | −10.4543 | + | 6.03579i | −0.433717 | + | 0.250407i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.33013 | + | 12.4282i | 0.137920 | + | 0.514724i | ||||
\(584\) | −3.58630 | −0.148402 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.9282 | 0.575369 | ||||||||
\(587\) | −10.5930 | − | 39.5336i | −0.437220 | − | 1.63173i | −0.735698 | − | 0.677310i | \(-0.763146\pi\) |
0.298478 | − | 0.954417i | \(-0.403521\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.39230 | − | 0.803848i | 0.0573689 | − | 0.0331220i | ||||
\(590\) | 2.82843 | − | 2.82843i | 0.116445 | − | 0.116445i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.96410 | + | 1.59808i | 0.245123 | + | 0.0656805i | ||||
\(593\) | −28.0812 | − | 28.0812i | −1.15316 | − | 1.15316i | −0.985916 | − | 0.167241i | \(-0.946514\pi\) |
−0.167241 | − | 0.985916i | \(-0.553486\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.80385 | + | 2.19615i | 0.155943 | + | 0.0900335i | ||||
\(596\) | −2.31079 | + | 0.619174i | −0.0946536 | + | 0.0253624i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.83013 | − | 16.2942i | −0.401984 | − | 0.666321i | ||||
\(599\) | − | 26.4911i | − | 1.08240i | −0.840895 | − | 0.541199i | \(-0.817971\pi\) | ||
0.840895 | − | 0.541199i | \(-0.182029\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.42820 | + | 16.3301i | −0.384584 | + | 0.666120i | −0.991711 | − | 0.128485i | \(-0.958989\pi\) |
0.607127 | + | 0.794605i | \(0.292322\pi\) | |||||||
\(602\) | 2.03339 | + | 3.52193i | 0.0828747 | + | 0.143543i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.73205 | + | 13.9282i | −0.151855 | + | 0.566731i | ||||
\(605\) | −2.58819 | + | 9.65926i | −0.105225 | + | 0.392705i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.93782 | − | 10.2846i | −0.241009 | − | 0.417439i | 0.719993 | − | 0.693981i | \(-0.244145\pi\) |
−0.961002 | + | 0.276542i | \(0.910812\pi\) | |||||||
\(608\) | 0.448288 | − | 0.776457i | 0.0181805 | − | 0.0314895i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.92820i | 0.199537i | ||||||||
\(611\) | 0.688524 | + | 35.7900i | 0.0278547 | + | 1.44791i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.89230 | − | 2.38269i | 0.359157 | − | 0.0962358i | −0.0747284 | − | 0.997204i | \(-0.523809\pi\) |
0.433885 | + | 0.900968i | \(0.357142\pi\) | |||||||
\(614\) | 19.8362 | + | 11.4524i | 0.800522 | + | 0.462182i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.633975 | − | 0.633975i | −0.0255436 | − | 0.0255436i | ||||
\(617\) | 12.8666 | + | 3.44760i | 0.517991 | + | 0.138795i | 0.508337 | − | 0.861158i | \(-0.330260\pi\) |
0.00965369 | + | 0.999953i | \(0.496927\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.8827 | − | 26.8827i | 1.08051 | − | 1.08051i | 0.0840444 | − | 0.996462i | \(-0.473216\pi\) |
0.996462 | − | 0.0840444i | \(-0.0267837\pi\) | |||||||
\(620\) | −1.55291 | + | 0.896575i | −0.0623665 | + | 0.0360073i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.143594 | + | 0.535898i | 0.00575758 | + | 0.0214876i | ||||
\(623\) | 10.8704 | 0.435513 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | −2.58819 | − | 9.65926i | −0.103445 | − | 0.386062i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.89230 | − | 3.40192i | 0.235129 | − | 0.135752i | ||||
\(629\) | 21.3891 | − | 21.3891i | 0.852838 | − | 0.852838i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.1962 | + | 3.80385i | 0.565140 | + | 0.151429i | 0.530067 | − | 0.847956i | \(-0.322167\pi\) |
0.0350732 | + | 0.999385i | \(0.488834\pi\) | |||||||
\(632\) | −1.41421 | − | 1.41421i | −0.0562544 | − | 0.0562544i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −13.9186 | − | 8.03590i | −0.552778 | − | 0.319146i | ||||
\(635\) | 12.2289 | − | 3.27671i | 0.485288 | − | 0.130032i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.19615 | + | 21.4641i | 0.245500 | + | 0.850439i | ||||
\(638\) | 2.82843i | 0.111979i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.500000 | + | 0.866025i | −0.0197642 | + | 0.0342327i | ||||
\(641\) | 2.62038 | + | 4.53862i | 0.103499 | + | 0.179265i | 0.913124 | − | 0.407682i | \(-0.133663\pi\) |
−0.809625 | + | 0.586947i | \(0.800330\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.66025 | − | 21.1244i | 0.223219 | − | 0.833063i | −0.759892 | − | 0.650050i | \(-0.774748\pi\) |
0.983110 | − | 0.183014i | \(-0.0585852\pi\) | |||||||
\(644\) | 1.22474 | − | 4.57081i | 0.0482617 | − | 0.180115i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.19615 | − | 3.80385i | −0.0864065 | − | 0.149660i | ||||
\(647\) | 4.17329 | − | 7.22835i | 0.164069 | − | 0.284176i | −0.772255 | − | 0.635312i | \(-0.780871\pi\) |
0.936324 | + | 0.351137i | \(0.114205\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.00000i | 0.157014i | ||||||||
\(650\) | −3.15660 | − | 1.74238i | −0.123812 | − | 0.0683419i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 19.6603 | − | 5.26795i | 0.769955 | − | 0.206309i | ||||
\(653\) | −4.29839 | − | 2.48168i | −0.168209 | − | 0.0971155i | 0.413532 | − | 0.910490i | \(-0.364295\pi\) |
−0.581741 | + | 0.813374i | \(0.697628\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.09808 | + | 3.09808i | 0.121052 | + | 0.121052i | ||||
\(656\) | −3.86370 | − | 1.03528i | −0.150852 | − | 0.0404207i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.29423 | + | 6.29423i | −0.245375 | + | 0.245375i | ||||
\(659\) | 34.2693 | − | 19.7854i | 1.33494 | − | 0.770729i | 0.348890 | − | 0.937164i | \(-0.386559\pi\) |
0.986053 | + | 0.166435i | \(0.0532255\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.41154 | − | 23.9282i | −0.249380 | − | 0.930699i | −0.971131 | − | 0.238546i | \(-0.923329\pi\) |
0.721751 | − | 0.692153i | \(-0.243338\pi\) | |||||||
\(662\) | 1.13681 | 0.0441835 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13.4641 | −0.522508 | ||||||||
\(665\) | 0.208051 | + | 0.776457i | 0.00806787 | + | 0.0301097i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.9282 | + | 7.46410i | −0.500582 | + | 0.289011i | ||||
\(668\) | 5.36585 | − | 5.36585i | 0.207611 | − | 0.207611i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.1962 | + | 2.73205i | 0.393912 | + | 0.105548i | ||||
\(671\) | −3.48477 | − | 3.48477i | −0.134528 | − | 0.134528i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.1769 | + | 21.4641i | 1.43306 | + | 0.827380i | 0.997353 | − | 0.0727061i | \(-0.0231635\pi\) |
0.435711 | + | 0.900086i | \(0.356497\pi\) | |||||||
\(674\) | 4.38134 | − | 1.17398i | 0.168763 | − | 0.0452199i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.92820 | − | 11.0000i | −0.266469 | − | 0.423077i | ||||
\(677\) | − | 30.8081i | − | 1.18405i | −0.805919 | − | 0.592026i | \(-0.798328\pi\) | ||
0.805919 | − | 0.592026i | \(-0.201672\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.87564 | − | 4.98076i | 0.110357 | − | 0.191144i | ||||
\(680\) | 2.44949 | + | 4.24264i | 0.0939336 | + | 0.162698i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.464102 | − | 1.73205i | 0.0177714 | − | 0.0663237i | ||||
\(683\) | −2.20925 | + | 8.24504i | −0.0845347 | + | 0.315488i | −0.995226 | − | 0.0976005i | \(-0.968883\pi\) |
0.910691 | + | 0.413088i | \(0.135550\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.00000 | + | 6.92820i | 0.152832 | + | 0.264713i | ||||
\(686\) | −5.91567 | + | 10.2462i | −0.225861 | + | 0.391204i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.53590i | 0.172930i | ||||||||
\(689\) | −32.1666 | + | 33.4285i | −1.22545 | + | 1.27352i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.1603 | − | 3.25833i | 0.462598 | − | 0.123953i | −0.0199902 | − | 0.999800i | \(-0.506364\pi\) |
0.482588 | + | 0.875847i | \(0.339697\pi\) | |||||||
\(692\) | 10.1583 | + | 5.86491i | 0.386161 | + | 0.222950i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.07180 | + | 3.07180i | 0.116604 | + | 0.116604i | ||||
\(695\) | −16.0926 | − | 4.31199i | −0.610426 | − | 0.163563i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.8564 | + | 13.8564i | −0.524849 | + | 0.524849i | ||||
\(698\) | 2.27362 | − | 1.31268i | 0.0860579 | − | 0.0496856i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.232051 | − | 0.866025i | −0.00877070 | − | 0.0327327i | ||||
\(701\) | −34.4959 | −1.30289 | −0.651447 | − | 0.758694i | \(-0.725838\pi\) | ||||
−0.651447 | + | 0.758694i | \(0.725838\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.53590 | 0.208790 | ||||||||
\(704\) | −0.258819 | − | 0.965926i | −0.00975461 | − | 0.0364047i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 22.9808 | − | 13.2679i | 0.864892 | − | 0.499346i | ||||
\(707\) | 3.58630 | − | 3.58630i | 0.134877 | − | 0.134877i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.6603 | + | 6.33975i | 0.888579 | + | 0.238094i | 0.674105 | − | 0.738635i | \(-0.264529\pi\) |
0.214474 | + | 0.976730i | \(0.431196\pi\) | |||||||
\(710\) | 1.41421 | + | 1.41421i | 0.0530745 | + | 0.0530745i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.5000 | + | 6.06218i | 0.393504 | + | 0.227190i | ||||
\(713\) | 9.14162 | − | 2.44949i | 0.342356 | − | 0.0917341i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.46410 | − | 1.00000i | 0.129550 | − | 0.0373979i | ||||
\(716\) | − | 0.378937i | − | 0.0141616i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.66025 | + | 4.60770i | −0.0992798 | + | 0.171958i | ||||
\(719\) | 4.79744 | + | 8.30942i | 0.178914 | + | 0.309889i | 0.941509 | − | 0.336988i | \(-0.109408\pi\) |
−0.762595 | + | 0.646877i | \(0.776075\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.153212 | − | 0.571797i | 0.00570593 | − | 0.0212948i | ||||
\(722\) | −4.70951 | + | 17.5761i | −0.175270 | + | 0.654116i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.92820 | − | 17.1962i | −0.368979 | − | 0.639090i | ||||
\(725\) | −1.41421 | + | 2.44949i | −0.0525226 | + | 0.0909718i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 7.92820i | − | 0.294041i | −0.989133 | − | 0.147020i | \(-0.953032\pi\) | ||
0.989133 | − | 0.147020i | \(-0.0469683\pi\) | |||||||
\(728\) | 0.776457 | − | 3.13801i | 0.0287774 | − | 0.116303i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.46410 | − | 0.928203i | 0.128212 | − | 0.0343543i | ||||
\(731\) | 19.2442 | + | 11.1106i | 0.711772 | + | 0.410942i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.8301 | + | 14.8301i | 0.547763 | + | 0.547763i | 0.925793 | − | 0.378030i | \(-0.123398\pi\) |
−0.378030 | + | 0.925793i | \(0.623398\pi\) | |||||||
\(734\) | −9.00292 | − | 2.41233i | −0.332304 | − | 0.0890405i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.73205 | − | 3.73205i | 0.137565 | − | 0.137565i | ||||
\(737\) | −9.14162 | + | 5.27792i | −0.336736 | + | 0.194415i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.3301 | − | 38.5526i | −0.380000 | − | 1.41818i | −0.845900 | − | 0.533342i | \(-0.820936\pi\) |
0.465900 | − | 0.884837i | \(-0.345731\pi\) | |||||||
\(740\) | −6.17449 | −0.226979 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.5359 | −0.423496 | ||||||||
\(743\) | −2.13492 | − | 7.96764i | −0.0783228 | − | 0.292304i | 0.915643 | − | 0.401991i | \(-0.131682\pi\) |
−0.993966 | + | 0.109687i | \(0.965015\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.07180 | − | 1.19615i | 0.0759048 | − | 0.0438236i | ||||
\(746\) | 26.0106 | − | 26.0106i | 0.952317 | − | 0.952317i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.73205 | − | 1.26795i | −0.173021 | − | 0.0463608i | ||||
\(749\) | −7.82894 | − | 7.82894i | −0.286063 | − | 0.286063i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.9282 | − | 7.46410i | −0.471757 | − | 0.272369i | 0.245218 | − | 0.969468i | \(-0.421140\pi\) |
−0.716975 | + | 0.697099i | \(0.754474\pi\) | |||||||
\(752\) | −9.58991 | + | 2.56961i | −0.349708 | + | 0.0937040i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.73205 | + | 5.26795i | −0.318003 | + | 0.191847i | ||||
\(755\) | − | 14.4195i | − | 0.524781i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.50000 | + | 12.9904i | −0.272592 | + | 0.472143i | −0.969525 | − | 0.244993i | \(-0.921214\pi\) |
0.696933 | + | 0.717137i | \(0.254548\pi\) | |||||||
\(758\) | 18.9210 | + | 32.7721i | 0.687242 | + | 1.19034i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.232051 | + | 0.866025i | −0.00841737 | + | 0.0314140i | ||||
\(761\) | 7.89829 | − | 29.4768i | 0.286313 | − | 1.06853i | −0.661562 | − | 0.749891i | \(-0.730106\pi\) |
0.947875 | − | 0.318644i | \(-0.103227\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.07180 | − | 3.58846i | −0.0750041 | − | 0.129911i | ||||
\(764\) | 12.1087 | − | 20.9730i | 0.438079 | − | 0.758775i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 31.1769i | 1.12647i | ||||||||
\(767\) | −12.3490 | + | 7.45001i | −0.445896 | + | 0.269004i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.56218 | + | 2.02628i | −0.272699 | + | 0.0730695i | −0.392577 | − | 0.919719i | \(-0.628416\pi\) |
0.119878 | + | 0.992789i | \(0.461750\pi\) | |||||||
\(770\) | 0.776457 | + | 0.448288i | 0.0279816 | + | 0.0161552i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.928203 | + | 0.928203i | 0.0334068 | + | 0.0334068i | ||||
\(773\) | 7.79676 | + | 2.08913i | 0.280430 | + | 0.0751410i | 0.396293 | − | 0.918124i | \(-0.370297\pi\) |
−0.115863 | + | 0.993265i | \(0.536963\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.26795 | − | 1.26795i | 0.0455461 | − | 0.0455461i | ||||
\(776\) | 5.55532 | − | 3.20736i | 0.199424 | − | 0.115138i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.73205 | + | 25.1244i | 0.241356 | + | 0.900752i | ||||
\(779\) | −3.58630 | −0.128493 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.00000 | −0.0715656 | ||||||||
\(782\) | −6.69213 | − | 24.9754i | −0.239310 | − | 0.893117i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.36603 | + | 3.09808i | −0.191644 | + | 0.110646i | ||||
\(785\) | −4.81105 | + | 4.81105i | −0.171714 | + | 0.171714i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.6603 | − | 7.94744i | −1.05727 | − | 0.283296i | −0.312019 | − | 0.950076i | \(-0.601005\pi\) |
−0.745255 | + | 0.666780i | \(0.767672\pi\) | |||||||
\(788\) | 5.36585 | + | 5.36585i | 0.191150 | + | 0.191150i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.73205 | + | 1.00000i | 0.0616236 | + | 0.0355784i | ||||
\(791\) | −1.79315 | + | 0.480473i | −0.0637571 | + | 0.0170837i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.26795 | − | 17.2487i | 0.151559 | − | 0.612520i | ||||
\(794\) | 31.4273i | 1.11531i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.26795 | − | 3.92820i | 0.0803853 | − | 0.139231i | ||||
\(797\) | −5.50455 | − | 9.53416i | −0.194981 | − | 0.337717i | 0.751913 | − | 0.659262i | \(-0.229131\pi\) |
−0.946894 | + | 0.321545i | \(0.895798\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.5885 | + | 46.9808i | −0.445348 | + | 1.66206i | ||||
\(800\) | 0.258819 | − | 0.965926i | 0.00915064 | − | 0.0341506i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −16.9641 | − | 29.3827i | −0.599023 | − | 1.03754i | ||||
\(803\) | −1.79315 | + | 3.10583i | −0.0632789 | + | 0.109602i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.73205i | 0.166783i | ||||||||
\(806\) | 6.21166 | − | 1.79315i | 0.218796 | − | 0.0631610i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.46410 | − | 1.46410i | 0.192226 | − | 0.0515069i | ||||
\(809\) | −23.7506 | − | 13.7124i | −0.835028 | − | 0.482103i | 0.0205434 | − | 0.999789i | \(-0.493460\pi\) |
−0.855571 | + | 0.517686i | \(0.826794\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.16987 | − | 8.16987i | −0.286883 | − | 0.286883i | 0.548963 | − | 0.835846i | \(-0.315023\pi\) |
−0.835846 | + | 0.548963i | \(0.815023\pi\) | |||||||
\(812\) | −2.44949 | − | 0.656339i | −0.0859602 | − | 0.0230330i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.36603 | − | 4.36603i | 0.153029 | − | 0.153029i | ||||
\(815\) | −17.6269 | + | 10.1769i | −0.617443 | + | 0.356481i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.05256 | + | 3.92820i | 0.0368244 | + | 0.137430i | ||||
\(818\) | −21.8052 | −0.762400 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.00000 | 0.139686 | ||||||||
\(821\) | −12.4877 | − | 46.6047i | −0.435823 | − | 1.62651i | −0.739089 | − | 0.673608i | \(-0.764744\pi\) |
0.303265 | − | 0.952906i | \(-0.401923\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.8205 | + | 19.5263i | −1.17891 | + | 0.680643i | −0.955762 | − | 0.294142i | \(-0.904966\pi\) |
−0.223147 | + | 0.974785i | \(0.571633\pi\) | |||||||
\(824\) | 0.466870 | − | 0.466870i | 0.0162642 | − | 0.0162642i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.46410 | − | 0.928203i | −0.120532 | − | 0.0322963i | ||||
\(827\) | 24.1160 | + | 24.1160i | 0.838594 | + | 0.838594i | 0.988674 | − | 0.150080i | \(-0.0479531\pi\) |
−0.150080 | + | 0.988674i | \(0.547953\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.9090 | − | 20.7321i | −1.24717 | − | 0.720054i | −0.276626 | − | 0.960978i | \(-0.589216\pi\) |
−0.970544 | + | 0.240924i | \(0.922550\pi\) | |||||||
\(830\) | 13.0053 | − | 3.48477i | 0.451421 | − | 0.120958i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.50000 | − | 2.59808i | 0.0866719 | − | 0.0900721i | ||||
\(833\) | 30.3548i | 1.05173i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.79423 | + | 6.57180i | −0.131305 | + | 0.227426i | ||||
\(836\) | −0.448288 | − | 0.776457i | −0.0155044 | − | 0.0268543i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.95448 | − | 7.29423i | 0.0675165 | − | 0.251975i | ||||
\(839\) | 11.4524 | − | 42.7410i | 0.395381 | − | 1.47558i | −0.425749 | − | 0.904841i | \(-0.639989\pi\) |
0.821130 | − | 0.570741i | \(-0.193344\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.5000 | − | 18.1865i | −0.362069 | − | 0.627122i | ||||
\(842\) | −1.79315 | + | 3.10583i | −0.0617961 | + | 0.107034i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.92820i | 0.341743i | ||||||||
\(845\) | 9.53914 | + | 8.83203i | 0.328156 | + | 0.303831i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.66025 | − | 2.32051i | 0.297570 | − | 0.0797336i | ||||
\(848\) | −11.1428 | − | 6.43331i | −0.382646 | − | 0.220921i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.46410 | − | 3.46410i | −0.118818 | − | 0.118818i | ||||
\(851\) | 31.4780 | + | 8.43451i | 1.07905 | + | 0.289131i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.0000 | − | 15.0000i | 0.513590 | − | 0.513590i | −0.402034 | − | 0.915625i | \(-0.631697\pi\) |
0.915625 | + | 0.402034i | \(0.131697\pi\) | |||||||
\(854\) | 3.82654 | − | 2.20925i | 0.130941 | − | 0.0755991i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.19615 | − | 11.9282i | −0.109242 | − | 0.407698i | ||||
\(857\) | −28.7647 | −0.982585 | −0.491292 | − | 0.870995i | \(-0.663475\pi\) | ||||
−0.491292 | + | 0.870995i | \(0.663475\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.00000 | −0.102359 | −0.0511793 | − | 0.998689i | \(-0.516298\pi\) | ||||
−0.0511793 | + | 0.998689i | \(0.516298\pi\) | |||||||
\(860\) | −1.17398 | − | 4.38134i | −0.0400323 | − | 0.149403i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.19615 | + | 4.73205i | −0.279162 | + | 0.161174i | ||||
\(863\) | −25.6317 | + | 25.6317i | −0.872514 | + | 0.872514i | −0.992746 | − | 0.120232i | \(-0.961636\pi\) |
0.120232 | + | 0.992746i | \(0.461636\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.3301 | − | 3.03590i | −0.385236 | − | 0.103224i | ||||
\(866\) | −19.3185 | − | 19.3185i | −0.656470 | − | 0.656470i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.39230 | + | 0.803848i | 0.0472579 | + | 0.0272844i | ||||
\(869\) | −1.93185 | + | 0.517638i | −0.0655336 | + | 0.0175597i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −33.3205 | − | 18.3923i | −1.12902 | − | 0.623199i | ||||
\(872\) | − | 4.62158i | − | 0.156506i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.36603 | − | 4.09808i | 0.0800320 | − | 0.138619i | ||||
\(875\) | 0.448288 | + | 0.776457i | 0.0151549 | + | 0.0262490i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.63397 | − | 13.5622i | 0.122711 | − | 0.457962i | −0.877037 | − | 0.480423i | \(-0.840483\pi\) |
0.999748 | + | 0.0224604i | \(0.00714997\pi\) | |||||||
\(878\) | −3.82654 | + | 14.2808i | −0.129139 | + | 0.481955i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.500000 | + | 0.866025i | 0.0168550 | + | 0.0291937i | ||||
\(881\) | −3.51695 | + | 6.09154i | −0.118489 | + | 0.205229i | −0.919169 | − | 0.393863i | \(-0.871138\pi\) |
0.800680 | + | 0.599092i | \(0.204472\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.3205i | 0.852103i | 0.904699 | + | 0.426051i | \(0.140096\pi\) | ||||
−0.904699 | + | 0.426051i | \(0.859904\pi\) | |||||||
\(884\) | −4.89898 | − | 16.9706i | −0.164771 | − | 0.570782i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.92820 | + | 2.66025i | −0.333545 | + | 0.0893730i | ||||
\(887\) | 45.5880 | + | 26.3202i | 1.53069 | + | 0.883747i | 0.999330 | + | 0.0366039i | \(0.0116540\pi\) |
0.531365 | + | 0.847143i | \(0.321679\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.02628 | − | 8.02628i | −0.269193 | − | 0.269193i | ||||
\(890\) | −11.7112 | − | 3.13801i | −0.392561 | − | 0.105186i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.70577 | − | 1.70577i | 0.0571134 | − | 0.0571134i | ||||
\(893\) | −7.70882 | + | 4.45069i | −0.257966 | + | 0.148937i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.0980762 | + | 0.366025i | 0.00327833 | + | 0.0122349i | ||||
\(896\) | 0.896575 | 0.0299525 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.73205 | 0.0577993 | ||||||||
\(899\) | −1.31268 | − | 4.89898i | −0.0437802 | − | 0.163390i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −54.5885 | + | 31.5167i | −1.81861 | + | 1.04997i | ||||
\(902\) | −2.82843 | + | 2.82843i | −0.0941763 | + | 0.0941763i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.00000 | − | 0.535898i | −0.0665190 | − | 0.0178237i | ||||
\(905\) | 14.0406 | + | 14.0406i | 0.466725 | + | 0.466725i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.32051 | − | 4.80385i | −0.276278 | − | 0.159509i | 0.355459 | − | 0.934692i | \(-0.384324\pi\) |
−0.631737 | + | 0.775183i | \(0.717658\pi\) | |||||||
\(908\) | −10.9348 | + | 2.92996i | −0.362883 | + | 0.0972342i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.0621778 | + | 3.23205i | 0.00206117 | + | 0.107141i | ||||
\(911\) | 12.8295i | 0.425059i | 0.977155 | + | 0.212529i | \(0.0681701\pi\) | ||||
−0.977155 | + | 0.212529i | \(0.931830\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.73205 | + | 11.6603i | −0.222798 | + | 0.385898i | ||||
\(914\) | 19.1798 | + | 33.2204i | 0.634412 | + | 1.09883i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.124356 | − | 0.464102i | 0.00410883 | − | 0.0153343i | ||||
\(917\) | 1.01669 | − | 3.79435i | 0.0335742 | − | 0.125301i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.58846 | + | 16.6077i | 0.316294 | + | 0.547837i | 0.979712 | − | 0.200412i | \(-0.0642281\pi\) |
−0.663418 | + | 0.748249i | \(0.730895\pi\) | |||||||
\(920\) | −2.63896 | + | 4.57081i | −0.0870039 | + | 0.150695i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13.4641i | 0.443417i | ||||||||
\(923\) | −3.72500 | − | 6.17449i | −0.122610 | − | 0.203236i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.96410 | − | 1.59808i | 0.196098 | − | 0.0525444i | ||||
\(926\) | 19.7482 | + | 11.4016i | 0.648967 | + | 0.374681i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.00000 | − | 2.00000i | −0.0656532 | − | 0.0656532i | ||||
\(929\) | 50.8473 | + | 13.6245i | 1.66825 | + | 0.447005i | 0.964637 | − | 0.263582i | \(-0.0849039\pi\) |
0.703609 | + | 0.710587i | \(0.251571\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.92820 | + | 3.92820i | −0.128742 | + | 0.128742i | ||||
\(932\) | −7.58871 | + | 4.38134i | −0.248576 | + | 0.143516i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.07180 | + | 4.00000i | 0.0350703 | + | 0.130884i | ||||
\(935\) | 4.89898 | 0.160214 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.92820 | −0.160997 | −0.0804987 | − | 0.996755i | \(-0.525651\pi\) | ||||
−0.0804987 | + | 0.996755i | \(0.525651\pi\) | |||||||
\(938\) | −2.44949 | − | 9.14162i | −0.0799787 | − | 0.298484i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.59808 | − | 4.96410i | 0.280438 | − | 0.161911i | ||||
\(941\) | −0.277401 | + | 0.277401i | −0.00904303 | + | 0.00904303i | −0.711614 | − | 0.702571i | \(-0.752035\pi\) |
0.702571 | + | 0.711614i | \(0.252035\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.3923 | − | 5.46410i | −0.664065 | − | 0.177936i | ||||
\(944\) | −2.82843 | − | 2.82843i | −0.0920575 | − | 0.0920575i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.92820 | + | 2.26795i | 0.127717 | + | 0.0737374i | ||||
\(947\) | −1.65445 | + | 0.443309i | −0.0537624 | + | 0.0144056i | −0.285600 | − | 0.958349i | \(-0.592193\pi\) |
0.231838 | + | 0.972755i | \(0.425526\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.9282 | + | 0.248711i | −0.419667 | + | 0.00807351i | ||||
\(950\) | − | 0.896575i | − | 0.0290887i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.19615 | − | 3.80385i | 0.0711777 | − | 0.123283i | ||||
\(953\) | −0.896575 | − | 1.55291i | −0.0290429 | − | 0.0503038i | 0.851139 | − | 0.524941i | \(-0.175913\pi\) |
−0.880182 | + | 0.474637i | \(0.842579\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.26795 | + | 23.3923i | −0.202826 | + | 0.756957i | ||||
\(956\) | −3.82654 | + | 14.2808i | −0.123759 | + | 0.461875i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.12436 | + | 8.87564i | 0.165560 | + | 0.286759i | ||||
\(959\) | 3.58630 | − | 6.21166i | 0.115808 | − | 0.200585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 27.7846i | − | 0.896278i | ||||||
\(962\) | 21.6107 | + | 5.34727i | 0.696758 | + | 0.172403i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.96410 | − | 1.59808i | 0.192091 | − | 0.0514706i | ||||
\(965\) | −1.13681 | − | 0.656339i | −0.0365953 | − | 0.0211283i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.5429 | + | 31.5429i | 1.01435 | + | 1.01435i | 0.999895 | + | 0.0144571i | \(0.00460199\pi\) |
0.0144571 | + | 0.999895i | \(0.495398\pi\) | |||||||
\(968\) | 9.65926 | + | 2.58819i | 0.310460 | + | 0.0831876i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.53590 | + | 4.53590i | −0.145639 | + | 0.145639i | ||||
\(971\) | −26.0800 | + | 15.0573i | −0.836947 | + | 0.483212i | −0.856225 | − | 0.516603i | \(-0.827196\pi\) |
0.0192783 | + | 0.999814i | \(0.493863\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.86603 | + | 14.4282i | 0.123939 | + | 0.462547i | ||||
\(974\) | 16.2499 | 0.520679 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.92820 | 0.157748 | ||||||||
\(977\) | −3.66063 | − | 13.6617i | −0.117114 | − | 0.437075i | 0.882322 | − | 0.470646i | \(-0.155979\pi\) |
−0.999436 | + | 0.0335702i | \(0.989312\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.5000 | − | 6.06218i | 0.335581 | − | 0.193748i | ||||
\(980\) | 4.38134 | − | 4.38134i | 0.139957 | − | 0.139957i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.69615 | − | 0.454483i | −0.0541264 | − | 0.0145031i | ||||
\(983\) | 10.0890 | + | 10.0890i | 0.321788 | + | 0.321788i | 0.849453 | − | 0.527665i | \(-0.176932\pi\) |
−0.527665 | + | 0.849453i | \(0.676932\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.57180 | − | 3.79423i | −0.209395 | − | 0.120894i | ||||
\(986\) | −13.3843 | + | 3.58630i | −0.426242 | + | 0.114211i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.56218 | − | 2.83013i | 0.0496995 | − | 0.0900383i | ||||
\(989\) | 23.9401i | 0.761251i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.1962 | + | 43.6410i | −0.800382 | + | 1.38630i | 0.118983 | + | 0.992896i | \(0.462037\pi\) |
−0.919365 | + | 0.393406i | \(0.871297\pi\) | |||||||
\(992\) | 0.896575 | + | 1.55291i | 0.0284663 | + | 0.0493051i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.464102 | − | 1.73205i | 0.0147204 | − | 0.0549373i | ||||
\(995\) | −1.17398 | + | 4.38134i | −0.0372176 | + | 0.138898i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.3564 | − | 30.0622i | −0.549683 | − | 0.952079i | −0.998296 | − | 0.0583527i | \(-0.981415\pi\) |
0.448613 | − | 0.893726i | \(-0.351918\pi\) | |||||||
\(998\) | −16.4022 | + | 28.4094i | −0.519201 | + | 0.899283i | ||||
\(999\) | 0 | 0 |
(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 | 1170.2.cu.c.1151.2 | yes | 8 | |
3.2 | odd | 2 | inner | 1170.2.cu.c.1151.1 | yes | 8 | |
13.2 | odd | 12 | inner | 1170.2.cu.c.431.1 | ✓ | 8 | |
39.2 | even | 12 | inner | 1170.2.cu.c.431.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1170.2.cu.c.431.1 | ✓ | 8 | 13.2 | odd | 12 | inner | |
1170.2.cu.c.431.2 | yes | 8 | 39.2 | even | 12 | inner | |
1170.2.cu.c.1151.1 | yes | 8 | 3.2 | odd | 2 | inner | |
1170.2.cu.c.1151.2 | yes | 8 | 1.1 | even | 1 | trivial |