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 | 431.2 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1170.431 |
Dual form | 1170.2.cu.c.1151.2 |
$q$-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 \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).
\(n\) | \(911\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) |
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 | −0.418740 | − | 0.908106i | \(-0.637528\pi\) |
0.0914134 | + | 0.995813i | \(0.470862\pi\) | |||||||
\(8\) | −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 | 0.110242 | − | 0.993905i | \(-0.464837\pi\) |
−0.401480 | + | 0.915868i | \(0.631504\pi\) | |||||||
\(12\) | 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 | 0.399586 | + | 0.916696i | \(0.369154\pi\) |
−0.993675 | + | 0.112296i | \(0.964180\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.232051 | + | 0.866025i | 0.0532361 | + | 0.198680i | 0.987422 | − | 0.158107i | \(-0.0505390\pi\) |
−0.934186 | + | 0.356787i | \(0.883872\pi\) | |||||||
\(20\) | −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 | 0.998255 | + | 0.0590435i | \(0.0188051\pi\) |
−0.447995 | + | 0.894036i | \(0.647862\pi\) | |||||||
\(24\) | 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 | −0.709880 | − | 0.704323i | \(-0.751251\pi\) |
0.255021 | + | 0.966935i | \(0.417918\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.26795 | − | 1.26795i | 0.227730 | − | 0.227730i | −0.584014 | − | 0.811744i | \(-0.698519\pi\) |
0.811744 | + | 0.584014i | \(0.198519\pi\) | |||||||
\(32\) | 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 | −0.700908 | − | 0.713252i | \(-0.747222\pi\) |
0.963630 | − | 0.267240i | \(-0.0861118\pi\) | |||||||
\(38\) | 0.896575 | 0.145444 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −1.03528 | + | 3.86370i | −0.161683 | + | 0.603409i | 0.836757 | + | 0.547574i | \(0.184449\pi\) |
−0.998440 | + | 0.0558348i | \(0.982218\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.92820 | − | 2.26795i | −0.599045 | − | 0.345859i | 0.169621 | − | 0.985509i | \(-0.445746\pi\) |
−0.768666 | + | 0.639650i | \(0.779079\pi\) | |||||||
\(44\) | 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 | −0.0243115 | + | 0.999704i | \(0.507739\pi\) |
−0.999704 | + | 0.0243115i | \(0.992261\pi\) | |||||||
\(48\) | 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 | \(0.344944\pi\) | ||||
−0.468085 | + | 0.883683i | \(0.655056\pi\) | |||||||
\(54\) | 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 | 0.999999 | + | 0.00161411i | \(0.000513789\pi\) |
−0.865217 | + | 0.501397i | \(0.832820\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.46410 | − | 4.26795i | 0.315496 | − | 0.546455i | −0.664047 | − | 0.747691i | \(-0.731162\pi\) |
0.979543 | + | 0.201236i | \(0.0644958\pi\) | |||||||
\(62\) | −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 | 0.820658 | − | 0.571420i | \(-0.193607\pi\) |
0.425000 | + | 0.905193i | \(0.360274\pi\) | |||||||
\(68\) | 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 | −0.142356 | − | 0.989816i | \(-0.545468\pi\) |
0.371624 | + | 0.928383i | \(0.378801\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.53590 | + | 2.53590i | 0.296804 | + | 0.296804i | 0.839761 | − | 0.542956i | \(-0.182695\pi\) |
−0.542956 | + | 0.839761i | \(0.682695\pi\) | |||||||
\(74\) | −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 | 0.998938 | + | 0.0460792i | \(0.0146726\pi\) |
0.0460792 | + | 0.998938i | \(0.485327\pi\) | |||||||
\(84\) | 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 | −0.422384 | − | 0.906417i | \(-0.638807\pi\) |
−0.819004 | + | 0.573788i | \(0.805473\pi\) | |||||||
\(90\) | 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 | −0.997557 | − | 0.0698518i | \(-0.977747\pi\) |
0.828984 | − | 0.559272i | \(-0.188919\pi\) | |||||||
\(98\) | 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 | 0.690300 | − | 0.723523i | \(-0.257478\pi\) |
−0.971739 | + | 0.236056i | \(0.924145\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 0.660254i | − | 0.0650568i | −0.999471 | − | 0.0325284i | \(-0.989644\pi\) | ||
0.999471 | − | 0.0325284i | \(-0.0103559\pi\) | |||||||
\(104\) | 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 | 0.115786 | − | 0.993274i | \(-0.463061\pi\) |
0.918094 | + | 0.396363i | \(0.129728\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.26795 | − | 3.26795i | 0.313013 | − | 0.313013i | −0.533063 | − | 0.846076i | \(-0.678959\pi\) |
0.846076 | + | 0.533063i | \(0.178959\pi\) | |||||||
\(110\) | −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 | 0.581966 | − | 0.813213i | \(-0.302284\pi\) |
−0.413280 | + | 0.910604i | \(0.635617\pi\) | |||||||
\(114\) | 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 | 0.0727855 | − | 0.997348i | \(-0.476811\pi\) |
0.900121 | + | 0.435640i | \(0.143478\pi\) | |||||||
\(128\) | −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 | \(-0.938697\pi\) | ||
0.981512 | − | 0.191400i | \(-0.0613027\pi\) | |||||||
\(132\) | 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 | −0.996220 | − | 0.0868620i | \(-0.972316\pi\) |
0.819321 | − | 0.573335i | \(-0.194351\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.33013 | + | 14.4282i | −0.706552 | + | 1.22378i | 0.259576 | + | 0.965723i | \(0.416417\pi\) |
−0.966128 | + | 0.258062i | \(0.916916\pi\) | |||||||
\(140\) | 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 | −0.162920 | − | 0.986639i | \(-0.552091\pi\) |
0.352227 | + | 0.935915i | \(0.385425\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.1962 | + | 10.1962i | 0.829751 | + | 0.829751i | 0.987482 | − | 0.157731i | \(-0.0504179\pi\) |
−0.157731 | + | 0.987482i | \(0.550418\pi\) | |||||||
\(152\) | −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 | −0.926237 | − | 0.376942i | \(-0.876975\pi\) |
−0.613673 | + | 0.789560i | \(0.710309\pi\) | |||||||
\(164\) | 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 | −0.0361899 | − | 0.999345i | \(-0.511522\pi\) |
−0.531014 | + | 0.847363i | \(0.678189\pi\) | |||||||
\(168\) | 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 | −0.998114 | − | 0.0613801i | \(-0.980450\pi\) |
0.552214 | + | 0.833702i | \(0.313783\pi\) | |||||||
\(174\) | 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 | 0.858858 | − | 0.512214i | \(-0.171175\pi\) |
−0.873019 | + | 0.487686i | \(0.837841\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 19.8564i | − | 1.47592i | −0.674847 | − | 0.737958i | \(-0.735790\pi\) | ||
0.674847 | − | 0.737958i | \(-0.264210\pi\) | |||||||
\(182\) | −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 | −0.999787 | − | 0.0206345i | \(-0.993431\pi\) |
−0.517764 | − | 0.855524i | \(-0.673235\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.339746 | + | 1.26795i | −0.0244554 | + | 0.0912690i | −0.977075 | − | 0.212896i | \(-0.931711\pi\) |
0.952620 | + | 0.304165i | \(0.0983773\pi\) | |||||||
\(194\) | −6.41473 | −0.460551 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.19615 | 0.442582 | ||||||||
\(197\) | −1.96404 | + | 7.32989i | −0.139932 | + | 0.522233i | 0.859997 | + | 0.510299i | \(0.170465\pi\) |
−0.999929 | + | 0.0119336i | \(0.996201\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.92820 | − | 2.26795i | −0.278463 | − | 0.160771i | 0.354264 | − | 0.935145i | \(-0.384731\pi\) |
−0.632727 | + | 0.774375i | \(0.718065\pi\) | |||||||
\(200\) | −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 | 0.984756 | − | 0.173939i | \(-0.0556495\pi\) |
−0.643014 | + | 0.765855i | \(0.722316\pi\) | |||||||
\(212\) | 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 | 0.179955 | − | 0.983675i | \(-0.442405\pi\) |
−0.335992 | + | 0.941865i | \(0.609071\pi\) | |||||||
\(224\) | −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 | 0.123023 | − | 0.992404i | \(-0.460741\pi\) |
0.602743 | + | 0.797935i | \(0.294074\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.339746 | − | 0.339746i | −0.0224510 | − | 0.0224510i | 0.695792 | − | 0.718243i | \(-0.255053\pi\) |
−0.718243 | + | 0.695792i | \(0.755053\pi\) | |||||||
\(230\) | 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 | 0.959146 | − | 0.282913i | \(-0.0913008\pi\) |
−0.282913 | + | 0.959146i | \(0.591301\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.96410 | + | 1.59808i | −0.384182 | + | 0.102941i | −0.445740 | − | 0.895162i | \(-0.647060\pi\) |
0.0615587 | + | 0.998103i | \(0.480393\pi\) | |||||||
\(242\) | −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 | −0.235324 | − | 0.971917i | \(-0.575615\pi\) |
0.959367 | − | 0.282162i | \(-0.0910514\pi\) | |||||||
\(252\) | 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 | 0.879227 | + | 0.476404i | \(0.158060\pi\) |
−0.0270355 | + | 0.999634i | \(0.508607\pi\) | |||||||
\(258\) | 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 | 0.00116020 | − | 0.999999i | \(-0.499631\pi\) |
0.866605 | + | 0.498995i | \(0.166297\pi\) | |||||||
\(264\) | 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 | −0.145261 | − | 0.989393i | \(-0.546402\pi\) |
−0.929470 | + | 0.368897i | \(0.879735\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.07180 | − | 18.9282i | 0.308090 | − | 1.14981i | −0.622163 | − | 0.782888i | \(-0.713746\pi\) |
0.930253 | − | 0.366919i | \(-0.119587\pi\) | |||||||
\(272\) | −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 | −0.152943 | − | 0.988235i | \(-0.548875\pi\) |
−0.932308 | + | 0.361665i | \(0.882208\pi\) | |||||||
\(278\) | 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 | −0.521716 | − | 0.853119i | \(-0.674708\pi\) |
0.853119 | + | 0.521716i | \(0.174708\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.3923 | + | 14.6603i | −1.50942 | + | 0.871462i | −0.509476 | + | 0.860485i | \(0.670161\pi\) |
−0.999940 | + | 0.0109768i | \(0.996506\pi\) | |||||||
\(284\) | −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 | 0.987669 | + | 0.156554i | \(0.0500385\pi\) |
−0.777070 | + | 0.629414i | \(0.783295\pi\) | |||||||
\(294\) | 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 | 0.997334 | − | 0.0729708i | \(-0.0232480\pi\) |
−0.0729708 | + | 0.997334i | \(0.523248\pi\) | |||||||
\(308\) | −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 | 0.311842 | − | 0.950134i | \(-0.399054\pi\) |
−0.950134 | + | 0.311842i | \(0.899054\pi\) | |||||||
\(318\) | 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 | 0.973540 | − | 0.228515i | \(-0.0733869\pi\) |
−0.957368 | + | 0.288871i | \(0.906720\pi\) | |||||||
\(332\) | −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 | \(0.0394257\pi\) | ||||
−0.992339 | + | 0.123543i | \(0.960574\pi\) | |||||||
\(338\) | −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 | 0.597571 | − | 0.801816i | \(-0.296133\pi\) |
−0.395607 | + | 0.918420i | \(0.629466\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.679492 | + | 2.53590i | −0.0363724 | + | 0.135744i | −0.981725 | − | 0.190308i | \(-0.939051\pi\) |
0.945352 | + | 0.326051i | \(0.105718\pi\) | |||||||
\(350\) | −0.896575 | −0.0479240 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −6.86800 | + | 25.6317i | −0.365547 | + | 1.36424i | 0.501132 | + | 0.865371i | \(0.332917\pi\) |
−0.866678 | + | 0.498867i | \(0.833750\pi\) | |||||||
\(354\) | 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 | −0.600823 | − | 0.799382i | \(-0.705160\pi\) |
0.799382 | + | 0.600823i | \(0.205160\pi\) | |||||||
\(360\) | 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 | 0.718379 | − | 0.695652i | \(-0.244885\pi\) |
−0.961642 | + | 0.274308i | \(0.911551\pi\) | |||||||
\(368\) | −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 | −0.211927 | + | 0.977286i | \(0.567974\pi\) |
−0.740391 | + | 0.672177i | \(0.765360\pi\) | |||||||
\(374\) | −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 | 0.999707 | + | 0.0241998i | \(0.00770379\pi\) |
0.877872 | + | 0.478896i | \(0.158963\pi\) | |||||||
\(380\) | 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 | 0.612911 | − | 0.790152i | \(-0.289998\pi\) |
0.925872 | + | 0.377836i | \(0.123332\pi\) | |||||||
\(384\) | 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 | 0.602637 | − | 0.798015i | \(-0.294117\pi\) |
0.920907 | + | 0.389783i | \(0.127450\pi\) | |||||||
\(398\) | −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 | −0.680755 | − | 0.732511i | \(-0.738348\pi\) |
−0.955807 | + | 0.293996i | \(0.905015\pi\) | |||||||
\(402\) | 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 | −0.953073 | − | 0.302740i | \(-0.902099\pi\) |
0.674015 | − | 0.738717i | \(-0.264568\pi\) | |||||||
\(410\) | 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 | −0.651166 | − | 0.758935i | \(-0.725720\pi\) |
0.331674 | + | 0.943394i | \(0.392386\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.53590 | − | 2.53590i | 0.123592 | − | 0.123592i | −0.642605 | − | 0.766197i | \(-0.722146\pi\) |
0.766197 | + | 0.642605i | \(0.222146\pi\) | |||||||
\(422\) | 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 | −0.881505 | − | 0.472174i | \(-0.843469\pi\) |
0.999493 | + | 0.0318378i | \(0.0101360\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.6603 | − | 13.6603i | −1.13704 | − | 0.656470i | −0.191344 | − | 0.981523i | \(-0.561284\pi\) |
−0.945696 | + | 0.325053i | \(0.894618\pi\) | |||||||
\(434\) | 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 | −0.162299 | − | 0.986742i | \(-0.551891\pi\) |
0.773394 | + | 0.633926i | \(0.218558\pi\) | |||||||
\(440\) | 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 | \(-0.921484\pi\) | ||
0.969732 | − | 0.244172i | \(-0.0785160\pi\) | |||||||
\(444\) | 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 | 0.975697 | − | 0.219125i | \(-0.0703203\pi\) |
−0.954541 | + | 0.298080i | \(0.903654\pi\) | |||||||
\(450\) | 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 | 0.980927 | − | 0.194377i | \(-0.0622687\pi\) |
0.752319 | + | 0.658799i | \(0.228935\pi\) | |||||||
\(458\) | −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 | 0.0570913 | − | 0.998369i | \(-0.481817\pi\) |
0.548627 | + | 0.836067i | \(0.315151\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.1244 | + | 16.1244i | 0.749362 | + | 0.749362i | 0.974359 | − | 0.224997i | \(-0.0722373\pi\) |
−0.224997 | + | 0.974359i | \(0.572237\pi\) | |||||||
\(464\) | −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 | 0.477784 | − | 0.878477i | \(-0.341440\pi\) |
−0.0254650 | + | 0.999676i | \(0.508107\pi\) | |||||||
\(480\) | 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 | 0.993366 | + | 0.114992i | \(0.0366841\pi\) |
−0.802785 | + | 0.596269i | \(0.796649\pi\) | |||||||
\(488\) | 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 | 0.845534 | − | 0.533922i | \(-0.179282\pi\) |
−0.885157 | + | 0.465293i | \(0.845949\pi\) | |||||||
\(492\) | 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 | 0.0391698 | − | 0.999233i | \(-0.487529\pi\) |
0.999233 | − | 0.0391698i | \(-0.0124713\pi\) | |||||||
\(500\) | 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 | −0.372745 | − | 0.927934i | \(-0.621583\pi\) |
−0.989987 | + | 0.141161i | \(0.954917\pi\) | |||||||
\(504\) | 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 | −0.987051 | − | 0.160408i | \(-0.948719\pi\) |
0.935015 | + | 0.354608i | \(0.115386\pi\) | |||||||
\(510\) | 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 | \(-0.973998\pi\) | ||
0.996665 | − | 0.0815977i | \(-0.0260023\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.7846 | + | 34.2679i | 0.865121 | + | 1.49843i | 0.866927 | + | 0.498434i | \(0.166092\pi\) |
−0.00180682 | + | 0.999998i | \(0.500575\pi\) | |||||||
\(524\) | −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 | 0.854676 | − | 0.519162i | \(-0.173756\pi\) |
−0.519162 | + | 0.854676i | \(0.673756\pi\) | |||||||
\(542\) | −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 | 0.212109 | − | 0.977246i | \(-0.431967\pi\) |
−0.304931 | + | 0.952374i | \(0.598633\pi\) | |||||||
\(558\) | 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 | −0.881554 | − | 0.472084i | \(-0.843502\pi\) |
0.849613 | + | 0.527406i | \(0.176835\pi\) | |||||||
\(564\) | 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 | 0.939048 | + | 0.343787i | \(0.111710\pi\) |
−0.171795 | + | 0.985133i | \(0.554957\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.6603i | 1.36679i | 0.730049 | + | 0.683395i | \(0.239497\pi\) | ||||
−0.730049 | + | 0.683395i | \(0.760503\pi\) | |||||||
\(572\) | −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 | −0.529444 | − | 0.848345i | \(-0.677600\pi\) |
0.848345 | + | 0.529444i | \(0.177600\pi\) | |||||||
\(578\) | −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 | 0.298478 | + | 0.954417i | \(0.403521\pi\) |
−0.735698 | + | 0.677310i | \(0.763146\pi\) | |||||||
\(588\) | 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 | −0.167241 | + | 0.985916i | \(0.553486\pi\) |
−0.985916 | + | 0.167241i | \(0.946514\pi\) | |||||||
\(594\) | 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 | \(0.182029\pi\) | ||||
−0.840895 | + | 0.541199i | \(0.817971\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.42820 | − | 16.3301i | −0.384584 | − | 0.666120i | 0.607127 | − | 0.794605i | \(-0.292322\pi\) |
−0.991711 | + | 0.128485i | \(0.958989\pi\) | |||||||
\(602\) | 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 | −0.961002 | − | 0.276542i | \(-0.910812\pi\) |
0.719993 | + | 0.693981i | \(0.244145\pi\) | |||||||
\(608\) | 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 | 0.433885 | − | 0.900968i | \(-0.357142\pi\) |
−0.0747284 | + | 0.997204i | \(0.523809\pi\) | |||||||
\(614\) | 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 | 0.00965369 | − | 0.999953i | \(-0.496927\pi\) |
0.508337 | + | 0.861158i | \(0.330260\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.8827 | + | 26.8827i | 1.08051 | + | 1.08051i | 0.996462 | + | 0.0840444i | \(0.0267837\pi\) |
0.0840444 | + | 0.996462i | \(0.473216\pi\) | |||||||
\(620\) | −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 | 0.0350732 | − | 0.999385i | \(-0.488834\pi\) |
0.530067 | + | 0.847956i | \(0.322167\pi\) | |||||||
\(632\) | −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 | −0.809625 | − | 0.586947i | \(-0.800330\pi\) |
0.913124 | + | 0.407682i | \(0.133663\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.66025 | + | 21.1244i | 0.223219 | + | 0.833063i | 0.983110 | + | 0.183014i | \(0.0585852\pi\) |
−0.759892 | + | 0.650050i | \(0.774748\pi\) | |||||||
\(644\) | 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 | 0.936324 | − | 0.351137i | \(-0.114205\pi\) |
−0.772255 | + | 0.635312i | \(0.780871\pi\) | |||||||
\(648\) | 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 | −0.581741 | − | 0.813374i | \(-0.697628\pi\) |
0.413532 | + | 0.910490i | \(0.364295\pi\) | |||||||
\(654\) | 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 | 0.986053 | − | 0.166435i | \(-0.0532255\pi\) |
0.348890 | + | 0.937164i | \(0.386559\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.41154 | + | 23.9282i | −0.249380 | + | 0.930699i | 0.721751 | + | 0.692153i | \(0.243338\pi\) |
−0.971131 | + | 0.238546i | \(0.923329\pi\) | |||||||
\(662\) | 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 | 0.435711 | − | 0.900086i | \(-0.356497\pi\) |
0.997353 | + | 0.0727061i | \(0.0231635\pi\) | |||||||
\(674\) | 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 | \(0.201672\pi\) | ||||
−0.805919 | + | 0.592026i | \(0.798328\pi\) | |||||||
\(678\) | 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 | 0.910691 | − | 0.413088i | \(-0.135550\pi\) |
−0.995226 | + | 0.0976005i | \(0.968883\pi\) | |||||||
\(684\) | 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 | 0.482588 | − | 0.875847i | \(-0.339697\pi\) |
−0.0199902 | + | 0.999800i | \(0.506364\pi\) | |||||||
\(692\) | 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 | 0.214474 | − | 0.976730i | \(-0.431196\pi\) |
0.674105 | + | 0.738635i | \(0.264529\pi\) | |||||||
\(710\) | 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 | −0.762595 | − | 0.646877i | \(-0.776075\pi\) |
0.941509 | + | 0.336988i | \(0.109408\pi\) | |||||||
\(720\) | 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 | \(0.0469683\pi\) | ||||
−0.989133 | + | 0.147020i | \(0.953032\pi\) | |||||||
\(728\) | 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 | −0.378030 | − | 0.925793i | \(-0.623398\pi\) |
0.925793 | + | 0.378030i | \(0.123398\pi\) | |||||||
\(734\) | −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 | 0.465900 | + | 0.884837i | \(0.345731\pi\) |
−0.845900 | + | 0.533342i | \(0.820936\pi\) | |||||||
\(740\) | −6.17449 | −0.226979 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.5359 | −0.423496 | ||||||||
\(743\) | −2.13492 | + | 7.96764i | −0.0783228 | + | 0.292304i | −0.993966 | − | 0.109687i | \(-0.965015\pi\) |
0.915643 | + | 0.401991i | \(0.131682\pi\) | |||||||
\(744\) | 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 | −0.716975 | − | 0.697099i | \(-0.754474\pi\) |
0.245218 | + | 0.969468i | \(0.421140\pi\) | |||||||
\(752\) | −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 | 0.696933 | − | 0.717137i | \(-0.254548\pi\) |
−0.969525 | + | 0.244993i | \(0.921214\pi\) | |||||||
\(758\) | 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 | 0.947875 | + | 0.318644i | \(0.103227\pi\) |
−0.661562 | + | 0.749891i | \(0.730106\pi\) | |||||||
\(762\) | 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 | 0.119878 | − | 0.992789i | \(-0.461750\pi\) |
−0.392577 | + | 0.919719i | \(0.628416\pi\) | |||||||
\(770\) | 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 | −0.115863 | − | 0.993265i | \(-0.536963\pi\) |
0.396293 | + | 0.918124i | \(0.370297\pi\) | |||||||
\(774\) | 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 | −0.745255 | − | 0.666780i | \(-0.767672\pi\) |
−0.312019 | + | 0.950076i | \(0.601005\pi\) | |||||||
\(788\) | 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 | −0.946894 | − | 0.321545i | \(-0.895798\pi\) |
0.751913 | + | 0.659262i | \(0.229131\pi\) | |||||||
\(798\) | 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 | −0.855571 | − | 0.517686i | \(-0.826794\pi\) |
0.0205434 | + | 0.999789i | \(0.493460\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.16987 | + | 8.16987i | −0.286883 | + | 0.286883i | −0.835846 | − | 0.548963i | \(-0.815023\pi\) |
0.548963 | + | 0.835846i | \(0.315023\pi\) | |||||||
\(812\) | −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 | 0.303265 | + | 0.952906i | \(0.401923\pi\) |
−0.739089 | + | 0.673608i | \(0.764744\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.8205 | − | 19.5263i | −1.17891 | − | 0.680643i | −0.223147 | − | 0.974785i | \(-0.571633\pi\) |
−0.955762 | + | 0.294142i | \(0.904966\pi\) | |||||||
\(824\) | 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 | −0.150080 | − | 0.988674i | \(-0.547953\pi\) |
0.988674 | + | 0.150080i | \(0.0479531\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.9090 | + | 20.7321i | −1.24717 | + | 0.720054i | −0.970544 | − | 0.240924i | \(-0.922550\pi\) |
−0.276626 | + | 0.960978i | \(0.589216\pi\) | |||||||
\(830\) | 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 | 0.821130 | + | 0.570741i | \(0.193344\pi\) |
−0.425749 | + | 0.904841i | \(0.639989\pi\) | |||||||
\(840\) | 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 | 0.915625 | − | 0.402034i | \(-0.131697\pi\) |
−0.402034 | + | 0.915625i | \(0.631697\pi\) | |||||||
\(854\) | 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 | 0.120232 | − | 0.992746i | \(-0.461636\pi\) |
−0.992746 | + | 0.120232i | \(0.961636\pi\) | |||||||
\(864\) | 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 | 0.999748 | − | 0.0224604i | \(-0.00714997\pi\) |
−0.877037 | + | 0.480423i | \(0.840483\pi\) | |||||||
\(878\) | −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 | 0.800680 | − | 0.599092i | \(-0.204472\pi\) |
−0.919169 | + | 0.393863i | \(0.871138\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 25.3205i | − | 0.852103i | −0.904699 | − | 0.426051i | \(-0.859904\pi\) | ||
0.904699 | − | 0.426051i | \(-0.140096\pi\) | |||||||
\(884\) | −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 | 0.531365 | − | 0.847143i | \(-0.321679\pi\) |
0.999330 | − | 0.0366039i | \(-0.0116540\pi\) | |||||||
\(888\) | 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 | −0.631737 | − | 0.775183i | \(-0.717658\pi\) |
0.355459 | + | 0.934692i | \(0.384324\pi\) | |||||||
\(908\) | −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 | \(-0.931830\pi\) | ||
0.977155 | − | 0.212529i | \(-0.0681701\pi\) | |||||||
\(912\) | 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 | −0.663418 | − | 0.748249i | \(-0.730895\pi\) |
0.979712 | + | 0.200412i | \(0.0642281\pi\) | |||||||
\(920\) | −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 | 0.703609 | − | 0.710587i | \(-0.251571\pi\) |
0.964637 | + | 0.263582i | \(0.0849039\pi\) | |||||||
\(930\) | 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 | 0.702571 | − | 0.711614i | \(-0.252035\pi\) |
−0.711614 | + | 0.702571i | \(0.752035\pi\) | |||||||
\(942\) | 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 | 0.231838 | − | 0.972755i | \(-0.425526\pi\) |
−0.285600 | + | 0.958349i | \(0.592193\pi\) | |||||||
\(948\) | 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 | −0.880182 | − | 0.474637i | \(-0.842579\pi\) |
0.851139 | + | 0.524941i | \(0.175913\pi\) | |||||||
\(954\) | 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 | 0.0144571 | − | 0.999895i | \(-0.495398\pi\) |
0.999895 | − | 0.0144571i | \(-0.00460199\pi\) | |||||||
\(968\) | 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 | 0.0192783 | − | 0.999814i | \(-0.493863\pi\) |
−0.856225 | + | 0.516603i | \(0.827196\pi\) | |||||||
\(972\) | 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 | −0.999436 | − | 0.0335702i | \(-0.989312\pi\) |
0.882322 | + | 0.470646i | \(0.155979\pi\) | |||||||
\(978\) | 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 | −0.527665 | − | 0.849453i | \(-0.676932\pi\) |
0.849453 | + | 0.527665i | \(0.176932\pi\) | |||||||
\(984\) | 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 | −0.919365 | − | 0.393406i | \(-0.871297\pi\) |
0.118983 | − | 0.992896i | \(-0.462037\pi\) | |||||||
\(992\) | 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 | 0.448613 | + | 0.893726i | \(0.351918\pi\) |
−0.998296 | + | 0.0583527i | \(0.981415\pi\) | |||||||
\(998\) | −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.431.2 | yes | 8 | |
3.2 | odd | 2 | inner | 1170.2.cu.c.431.1 | ✓ | 8 | |
13.7 | odd | 12 | inner | 1170.2.cu.c.1151.1 | yes | 8 | |
39.20 | even | 12 | inner | 1170.2.cu.c.1151.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1170.2.cu.c.431.1 | ✓ | 8 | 3.2 | odd | 2 | inner | |
1170.2.cu.c.431.2 | yes | 8 | 1.1 | even | 1 | trivial | |
1170.2.cu.c.1151.1 | yes | 8 | 13.7 | odd | 12 | inner | |
1170.2.cu.c.1151.2 | yes | 8 | 39.20 | even | 12 | inner |