Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [351,2,Mod(71,351)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(351, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([10, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("351.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 351 = 3^{3} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 351.ba (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.80274911095\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 117) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 89.9 | ||
Character | \(\chi\) | \(=\) | 351.89 |
Dual form | 351.2.ba.a.71.9 |
$q$-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 \(\left(\mathbb{Z}/351\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(326\) |
\(\chi(n)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.841634 | − | 0.841634i | 0.595125 | − | 0.595125i | −0.343886 | − | 0.939011i | \(-0.611743\pi\) |
0.939011 | + | 0.343886i | \(0.111743\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.583303i | 0.291651i | ||||||||
\(5\) | 2.77680 | + | 0.744040i | 1.24182 | + | 0.332745i | 0.819172 | − | 0.573548i | \(-0.194433\pi\) |
0.422650 | + | 0.906293i | \(0.361100\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.42554 | − | 0.381973i | −0.538804 | − | 0.144372i | −0.0208532 | − | 0.999783i | \(-0.506638\pi\) |
−0.517951 | + | 0.855410i | \(0.673305\pi\) | |||||||
\(8\) | 2.17420 | + | 2.17420i | 0.768695 | + | 0.768695i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.96326 | − | 1.71084i | 0.937065 | − | 0.541014i | ||||
\(11\) | 1.23230 | + | 1.23230i | 0.371552 | + | 0.371552i | 0.868042 | − | 0.496491i | \(-0.165378\pi\) |
−0.496491 | + | 0.868042i | \(0.665378\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.60363 | + | 0.117561i | −0.999468 | + | 0.0326056i | ||||
\(14\) | −1.52127 | + | 0.878303i | −0.406575 | + | 0.234736i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.49315 | 0.623288 | ||||||||
\(17\) | −0.939625 | + | 1.62748i | −0.227893 | + | 0.394722i | −0.957183 | − | 0.289482i | \(-0.906517\pi\) |
0.729291 | + | 0.684204i | \(0.239850\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.34907 | − | 1.16533i | 0.997745 | − | 0.267345i | 0.277245 | − | 0.960799i | \(-0.410579\pi\) |
0.720501 | + | 0.693454i | \(0.243912\pi\) | |||||||
\(20\) | −0.434001 | + | 1.61971i | −0.0970455 | + | 0.362179i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.07429 | 0.442240 | ||||||||
\(23\) | 2.82588 | − | 4.89457i | 0.589237 | − | 1.02059i | −0.405096 | − | 0.914274i | \(-0.632762\pi\) |
0.994333 | − | 0.106314i | \(-0.0339048\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.82688 | + | 1.63210i | 0.565376 | + | 0.326420i | ||||
\(26\) | −2.93400 | + | 3.13189i | −0.575405 | + | 0.614213i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.222806 | − | 0.831522i | 0.0421063 | − | 0.157143i | ||||
\(29\) | − | 6.70089i | − | 1.24432i | −0.782888 | − | 0.622162i | \(-0.786254\pi\) | ||
0.782888 | − | 0.622162i | \(-0.213746\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.676611 | − | 2.52515i | 0.121523 | − | 0.453530i | −0.878169 | − | 0.478350i | \(-0.841235\pi\) |
0.999692 | + | 0.0248208i | \(0.00790153\pi\) | |||||||
\(32\) | −2.25007 | + | 2.25007i | −0.397760 | + | 0.397760i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.578921 | + | 2.16056i | 0.0992842 | + | 0.370534i | ||||
\(35\) | −3.67424 | − | 2.12132i | −0.621059 | − | 0.358569i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.1775 | − | 2.99499i | −1.83756 | − | 0.492374i | −0.838912 | − | 0.544267i | \(-0.816808\pi\) |
−0.998653 | + | 0.0518927i | \(0.983475\pi\) | |||||||
\(38\) | 2.67955 | − | 4.64111i | 0.434680 | − | 0.752888i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.41961 | + | 7.65499i | 0.698802 | + | 1.21036i | ||||
\(41\) | −0.168067 | − | 0.627234i | −0.0262476 | − | 0.0979574i | 0.951559 | − | 0.307465i | \(-0.0994806\pi\) |
−0.977807 | + | 0.209507i | \(0.932814\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.78065 | − | 1.02806i | 0.271547 | − | 0.156778i | −0.358044 | − | 0.933705i | \(-0.616556\pi\) |
0.629590 | + | 0.776927i | \(0.283223\pi\) | |||||||
\(44\) | −0.718802 | + | 0.718802i | −0.108364 | + | 0.108364i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.74108 | − | 6.49779i | −0.256708 | − | 0.958048i | ||||
\(47\) | −2.31288 | + | 0.619735i | −0.337369 | + | 0.0903977i | −0.423526 | − | 0.905884i | \(-0.639208\pi\) |
0.0861575 | + | 0.996282i | \(0.472541\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.17591 | − | 2.41096i | −0.596559 | − | 0.344424i | ||||
\(50\) | 3.75283 | − | 1.00557i | 0.530730 | − | 0.142209i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.0685738 | − | 2.10201i | −0.00950947 | − | 0.291496i | ||||
\(53\) | 11.5633i | 1.58834i | 0.607698 | + | 0.794168i | \(0.292093\pi\) | ||||
−0.607698 | + | 0.794168i | \(0.707907\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.50496 | + | 4.33872i | 0.337769 | + | 0.585033i | ||||
\(56\) | −2.26892 | − | 3.92989i | −0.303198 | − | 0.525154i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.63970 | − | 5.63970i | −0.740529 | − | 0.740529i | ||||
\(59\) | 9.15908 | + | 9.15908i | 1.19241 | + | 1.19241i | 0.976388 | + | 0.216023i | \(0.0693086\pi\) |
0.216023 | + | 0.976388i | \(0.430691\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.24278 | − | 9.08077i | −0.671269 | − | 1.16267i | −0.977544 | − | 0.210730i | \(-0.932416\pi\) |
0.306275 | − | 0.951943i | \(-0.400917\pi\) | |||||||
\(62\) | −1.55579 | − | 2.69471i | −0.197586 | − | 0.342228i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.77378i | 1.09672i | ||||||||
\(65\) | −10.0940 | − | 2.35481i | −1.25201 | − | 0.292078i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.50643 | − | 0.939544i | 0.428378 | − | 0.114784i | −0.0381866 | − | 0.999271i | \(-0.512158\pi\) |
0.466565 | + | 0.884487i | \(0.345491\pi\) | |||||||
\(68\) | −0.949313 | − | 0.548086i | −0.115121 | − | 0.0664652i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.87774 | + | 1.30699i | −0.583001 | + | 0.156215i | ||||
\(71\) | −2.99663 | − | 11.1836i | −0.355635 | − | 1.32725i | −0.879684 | − | 0.475559i | \(-0.842246\pi\) |
0.524049 | − | 0.851688i | \(-0.324421\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.97423 | + | 8.97423i | −1.05035 | + | 1.05035i | −0.0516906 | + | 0.998663i | \(0.516461\pi\) |
−0.998663 | + | 0.0516906i | \(0.983539\pi\) | |||||||
\(74\) | −11.9280 | + | 6.88665i | −1.38661 | + | 0.800557i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.679740 | + | 2.53683i | 0.0779716 | + | 0.290994i | ||||
\(77\) | −1.28599 | − | 2.22739i | −0.146552 | − | 0.253835i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.85927 | + | 8.41651i | −0.546711 | + | 0.946931i | 0.451786 | + | 0.892126i | \(0.350787\pi\) |
−0.998497 | + | 0.0548048i | \(0.982546\pi\) | |||||||
\(80\) | 6.92298 | + | 1.85501i | 0.774012 | + | 0.207396i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.669352 | − | 0.386451i | −0.0739176 | − | 0.0426763i | ||||
\(83\) | −0.712145 | − | 2.65776i | −0.0781681 | − | 0.291727i | 0.915765 | − | 0.401715i | \(-0.131586\pi\) |
−0.993933 | + | 0.109987i | \(0.964919\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.82006 | + | 3.82006i | −0.414344 | + | 0.414344i | ||||
\(86\) | 0.633407 | − | 2.36391i | 0.0683020 | − | 0.254907i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.35851i | 0.571219i | ||||||||
\(89\) | 1.57286 | − | 5.86998i | 0.166722 | − | 0.622217i | −0.831092 | − | 0.556135i | \(-0.812284\pi\) |
0.997814 | − | 0.0660814i | \(-0.0210497\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.18203 | + | 1.20890i | 0.543225 | + | 0.126727i | ||||
\(92\) | 2.85501 | + | 1.64834i | 0.297656 | + | 0.171852i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.42501 | + | 2.46819i | −0.146979 | + | 0.254575i | ||||
\(95\) | 12.9435 | 1.32798 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.35706 | + | 5.06463i | −0.137789 | + | 0.514235i | 0.862182 | + | 0.506599i | \(0.169097\pi\) |
−0.999971 | + | 0.00763623i | \(0.997569\pi\) | |||||||
\(98\) | −5.54374 | + | 1.48544i | −0.560003 | + | 0.150052i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.952008 | + | 1.64893i | −0.0952008 | + | 0.164893i | ||||
\(101\) | 3.02851 | 0.301348 | 0.150674 | − | 0.988584i | \(-0.451856\pi\) | ||||
0.150674 | + | 0.988584i | \(0.451856\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.9431 | − | 9.20475i | 1.57092 | − | 0.906971i | 0.574864 | − | 0.818249i | \(-0.305055\pi\) |
0.996056 | − | 0.0887220i | \(-0.0282783\pi\) | |||||||
\(104\) | −8.09061 | − | 7.57941i | −0.793350 | − | 0.743222i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.73204 | + | 9.73204i | 0.945259 | + | 0.945259i | ||||
\(107\) | −3.97340 | + | 2.29404i | −0.384123 | + | 0.221774i | −0.679611 | − | 0.733573i | \(-0.737851\pi\) |
0.295487 | + | 0.955347i | \(0.404518\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.138592 | + | 0.138592i | 0.0132747 | + | 0.0132747i | 0.713713 | − | 0.700438i | \(-0.247012\pi\) |
−0.700438 | + | 0.713713i | \(0.747012\pi\) | |||||||
\(110\) | 5.75988 | + | 1.54335i | 0.549183 | + | 0.147153i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.55409 | − | 0.952316i | −0.335830 | − | 0.0899854i | ||||
\(113\) | 7.46794i | 0.702524i | 0.936277 | + | 0.351262i | \(0.114247\pi\) | ||||
−0.936277 | + | 0.351262i | \(0.885753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.4887 | − | 11.4887i | 1.07132 | − | 1.07132i | ||||
\(116\) | 3.90865 | 0.362909 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 15.4172 | 1.41927 | ||||||||
\(119\) | 1.96113 | − | 1.96113i | 0.179776 | − | 0.179776i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 7.96289i | − | 0.723899i | ||||||
\(122\) | −12.0552 | − | 3.23018i | −1.09143 | − | 0.292447i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.47292 | + | 0.394669i | 0.132273 | + | 0.0354423i | ||||
\(125\) | −3.52846 | − | 3.52846i | −0.315595 | − | 0.315595i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.37062 | + | 5.41013i | −0.831508 | + | 0.480071i | −0.854369 | − | 0.519667i | \(-0.826056\pi\) |
0.0228608 | + | 0.999739i | \(0.492723\pi\) | |||||||
\(128\) | 2.88417 | + | 2.88417i | 0.254927 | + | 0.254927i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −10.4774 | + | 6.51360i | −0.918926 | + | 0.571280i | ||||
\(131\) | −6.84566 | + | 3.95234i | −0.598108 | + | 0.345318i | −0.768297 | − | 0.640094i | \(-0.778896\pi\) |
0.170189 | + | 0.985411i | \(0.445562\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.64490 | −0.576186 | ||||||||
\(134\) | 2.16038 | − | 3.74188i | 0.186628 | − | 0.323249i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.58139 | + | 1.49553i | −0.478600 | + | 0.128241i | ||||
\(137\) | 2.19061 | − | 8.17545i | 0.187156 | − | 0.698476i | −0.807003 | − | 0.590548i | \(-0.798912\pi\) |
0.994159 | − | 0.107928i | \(-0.0344216\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.469919 | 0.0398580 | 0.0199290 | − | 0.999801i | \(-0.493656\pi\) | ||||
0.0199290 | + | 0.999801i | \(0.493656\pi\) | |||||||
\(140\) | 1.23737 | − | 2.14319i | 0.104577 | − | 0.181133i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −11.9346 | − | 6.89042i | −1.00153 | − | 0.578231i | ||||
\(143\) | −4.58562 | − | 4.29588i | −0.383469 | − | 0.359239i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.98574 | − | 18.6070i | 0.414043 | − | 1.54523i | ||||
\(146\) | 15.1060i | 1.25018i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.74699 | − | 6.51985i | 0.143602 | − | 0.535928i | ||||
\(149\) | 3.83653 | − | 3.83653i | 0.314301 | − | 0.314301i | −0.532272 | − | 0.846573i | \(-0.678662\pi\) |
0.846573 | + | 0.532272i | \(0.178662\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.12016 | − | 19.1087i | −0.416673 | − | 1.55504i | −0.781462 | − | 0.623953i | \(-0.785525\pi\) |
0.364789 | − | 0.931090i | \(-0.381141\pi\) | |||||||
\(152\) | 11.9894 | + | 6.92208i | 0.972468 | + | 0.561455i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.95698 | − | 0.792321i | −0.238280 | − | 0.0638470i | ||||
\(155\) | 3.75762 | − | 6.50839i | 0.301819 | − | 0.522767i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.5326 | + | 19.9750i | 0.920401 | + | 1.59418i | 0.798796 | + | 0.601602i | \(0.205471\pi\) |
0.121605 | + | 0.992579i | \(0.461196\pi\) | |||||||
\(158\) | 2.99389 | + | 11.1734i | 0.238181 | + | 0.888904i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −7.92213 | + | 4.57384i | −0.626300 | + | 0.361594i | ||||
\(161\) | −5.89800 | + | 5.89800i | −0.464827 | + | 0.464827i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.15428 | + | 4.30782i | 0.0904100 | + | 0.337415i | 0.996284 | − | 0.0861334i | \(-0.0274511\pi\) |
−0.905874 | + | 0.423548i | \(0.860784\pi\) | |||||||
\(164\) | 0.365867 | − | 0.0980338i | 0.0285694 | − | 0.00765515i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.83623 | − | 1.63750i | −0.220134 | − | 0.127095i | ||||
\(167\) | −0.344237 | + | 0.0922379i | −0.0266378 | + | 0.00713759i | −0.272113 | − | 0.962265i | \(-0.587723\pi\) |
0.245476 | + | 0.969403i | \(0.421056\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9724 | − | 0.847295i | 0.997874 | − | 0.0651766i | ||||
\(170\) | 6.43019i | 0.493173i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.599670 | + | 1.03866i | 0.0457244 | + | 0.0791970i | ||||
\(173\) | 5.94881 | + | 10.3036i | 0.452280 | + | 0.783371i | 0.998527 | − | 0.0542525i | \(-0.0172776\pi\) |
−0.546248 | + | 0.837624i | \(0.683944\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.40641 | − | 3.40641i | −0.257501 | − | 0.257501i | ||||
\(176\) | 3.07230 | + | 3.07230i | 0.231584 | + | 0.231584i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.61661 | − | 6.26415i | −0.271076 | − | 0.469518i | ||||
\(179\) | 2.92970 | + | 5.07439i | 0.218976 | + | 0.379278i | 0.954495 | − | 0.298226i | \(-0.0963950\pi\) |
−0.735519 | + | 0.677504i | \(0.763062\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 8.29778i | − | 0.616769i | −0.951262 | − | 0.308384i | \(-0.900212\pi\) | ||
0.951262 | − | 0.308384i | \(-0.0997883\pi\) | |||||||
\(182\) | 5.37883 | − | 3.34393i | 0.398705 | − | 0.247868i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 16.7858 | − | 4.49773i | 1.23746 | − | 0.331577i | ||||
\(185\) | −28.8092 | − | 16.6330i | −2.11809 | − | 1.22288i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.16344 | + | 0.847640i | −0.231333 | + | 0.0619856i | ||||
\(188\) | −0.361493 | − | 1.34911i | −0.0263646 | − | 0.0983940i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.8937 | − | 10.8937i | 0.790314 | − | 0.790314i | ||||
\(191\) | 6.20085 | − | 3.58006i | 0.448678 | − | 0.259044i | −0.258594 | − | 0.965986i | \(-0.583259\pi\) |
0.707272 | + | 0.706942i | \(0.249926\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.709019 | − | 2.64609i | −0.0510363 | − | 0.190470i | 0.935701 | − | 0.352793i | \(-0.114768\pi\) |
−0.986738 | + | 0.162323i | \(0.948101\pi\) | |||||||
\(194\) | 3.12041 | + | 5.40471i | 0.224033 | + | 0.388036i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.40632 | − | 2.43582i | 0.100452 | − | 0.173987i | ||||
\(197\) | 23.1428 | + | 6.20110i | 1.64886 | + | 0.441810i | 0.959292 | − | 0.282414i | \(-0.0911353\pi\) |
0.689564 | + | 0.724224i | \(0.257802\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.08608 | + | 4.66850i | 0.573207 | + | 0.330941i | 0.758429 | − | 0.651755i | \(-0.225967\pi\) |
−0.185222 | + | 0.982697i | \(0.559300\pi\) | |||||||
\(200\) | 2.59768 | + | 9.69469i | 0.183684 | + | 0.685518i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.54890 | − | 2.54890i | 0.179340 | − | 0.179340i | ||||
\(203\) | −2.55956 | + | 9.55240i | −0.179646 | + | 0.670447i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 1.86675i | − | 0.130379i | ||||||
\(206\) | 5.67122 | − | 21.1653i | 0.395133 | − | 1.47466i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −8.98441 | + | 0.293098i | −0.622957 | + | 0.0203227i | ||||
\(209\) | 6.79538 | + | 3.92332i | 0.470046 | + | 0.271381i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.60557 | + | 4.51298i | −0.179375 | + | 0.310687i | −0.941667 | − | 0.336547i | \(-0.890741\pi\) |
0.762292 | + | 0.647234i | \(0.224074\pi\) | |||||||
\(212\) | −6.74488 | −0.463240 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.41341 | + | 5.27490i | −0.0966184 | + | 0.360585i | ||||
\(215\) | 5.70942 | − | 1.52984i | 0.389379 | − | 0.104334i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.92907 | + | 3.34125i | −0.130954 | + | 0.226819i | ||||
\(218\) | 0.233287 | 0.0158002 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.53079 | + | 1.46115i | −0.170626 | + | 0.0985107i | ||||
\(221\) | 3.19474 | − | 5.97530i | 0.214901 | − | 0.401942i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.83926 | + | 4.83926i | 0.324061 | + | 0.324061i | 0.850323 | − | 0.526262i | \(-0.176407\pi\) |
−0.526262 | + | 0.850323i | \(0.676407\pi\) | |||||||
\(224\) | 4.06703 | − | 2.34810i | 0.271740 | − | 0.156889i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.28527 | + | 6.28527i | 0.418090 | + | 0.418090i | ||||
\(227\) | 12.3360 | + | 3.30542i | 0.818769 | + | 0.219389i | 0.643808 | − | 0.765187i | \(-0.277353\pi\) |
0.174961 | + | 0.984575i | \(0.444020\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.6101 | + | 4.71861i | 1.16371 | + | 0.311815i | 0.788446 | − | 0.615104i | \(-0.210886\pi\) |
0.375263 | + | 0.926919i | \(0.377553\pi\) | |||||||
\(230\) | − | 19.3385i | − | 1.27514i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 14.5691 | − | 14.5691i | 0.956506 | − | 0.956506i | ||||
\(233\) | −4.27048 | −0.279769 | −0.139884 | − | 0.990168i | \(-0.544673\pi\) | ||||
−0.139884 | + | 0.990168i | \(0.544673\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.88351 | −0.449031 | ||||||||
\(236\) | −5.34252 | + | 5.34252i | −0.347768 | + | 0.347768i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 3.30110i | − | 0.213979i | ||||||
\(239\) | 1.08816 | + | 0.291572i | 0.0703874 | + | 0.0188603i | 0.293841 | − | 0.955854i | \(-0.405066\pi\) |
−0.223453 | + | 0.974715i | \(0.571733\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.52710 | + | 2.28483i | 0.549279 | + | 0.147179i | 0.522776 | − | 0.852470i | \(-0.324896\pi\) |
0.0265026 | + | 0.999649i | \(0.491563\pi\) | |||||||
\(242\) | −6.70184 | − | 6.70184i | −0.430811 | − | 0.430811i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.29684 | − | 3.05813i | 0.339095 | − | 0.195777i | ||||
\(245\) | −9.80181 | − | 9.80181i | −0.626215 | − | 0.626215i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.5355 | + | 4.71071i | −0.988498 | + | 0.299735i | ||||
\(248\) | 6.96125 | − | 4.01908i | 0.442040 | − | 0.255212i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.93935 | −0.375638 | ||||||||
\(251\) | −8.72352 | + | 15.1096i | −0.550624 | + | 0.953708i | 0.447606 | + | 0.894231i | \(0.352277\pi\) |
−0.998230 | + | 0.0594773i | \(0.981057\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.51388 | − | 2.54924i | 0.598133 | − | 0.160269i | ||||
\(254\) | −3.33328 | + | 12.4400i | −0.209149 | + | 0.780554i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.6927 | −0.793295 | ||||||||
\(257\) | −1.62517 | + | 2.81488i | −0.101376 | + | 0.175588i | −0.912252 | − | 0.409630i | \(-0.865658\pi\) |
0.810876 | + | 0.585218i | \(0.198991\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.7899 | + | 8.53897i | 0.919002 | + | 0.530586i | ||||
\(260\) | 1.37356 | − | 5.88788i | 0.0851849 | − | 0.365151i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.43511 | + | 9.08797i | −0.150442 | + | 0.561457i | ||||
\(263\) | 18.0770i | 1.11467i | 0.830286 | + | 0.557337i | \(0.188177\pi\) | ||||
−0.830286 | + | 0.557337i | \(0.811823\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.60353 | + | 32.1088i | −0.528511 | + | 1.97243i | ||||
\(266\) | −5.59258 | + | 5.59258i | −0.342903 | + | 0.342903i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.548039 | + | 2.04531i | 0.0334768 | + | 0.124937i | ||||
\(269\) | 0.992035 | + | 0.572752i | 0.0604854 | + | 0.0349213i | 0.529938 | − | 0.848037i | \(-0.322215\pi\) |
−0.469452 | + | 0.882958i | \(0.655549\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.64641 | − | 2.31680i | −0.525232 | − | 0.140736i | −0.0135464 | − | 0.999908i | \(-0.504312\pi\) |
−0.511686 | + | 0.859173i | \(0.670979\pi\) | |||||||
\(272\) | −2.34263 | + | 4.05755i | −0.142043 | + | 0.246025i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.03705 | − | 8.72443i | −0.304299 | − | 0.527062i | ||||
\(275\) | 1.47232 | + | 5.49478i | 0.0887844 | + | 0.331348i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.2593 | + | 12.8514i | −1.33743 | + | 0.772165i | −0.986426 | − | 0.164209i | \(-0.947493\pi\) |
−0.351003 | + | 0.936374i | \(0.614159\pi\) | |||||||
\(278\) | 0.395500 | − | 0.395500i | 0.0237205 | − | 0.0237205i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.37634 | − | 12.6007i | −0.201775 | − | 0.753035i | ||||
\(281\) | −0.868838 | + | 0.232804i | −0.0518305 | + | 0.0138879i | −0.284641 | − | 0.958634i | \(-0.591874\pi\) |
0.232811 | + | 0.972522i | \(0.425208\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.7574 | − | 9.09752i | −0.936678 | − | 0.540791i | −0.0477608 | − | 0.998859i | \(-0.515209\pi\) |
−0.888917 | + | 0.458067i | \(0.848542\pi\) | |||||||
\(284\) | 6.52341 | − | 1.74794i | 0.387093 | − | 0.103721i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.47497 | + | 0.243856i | −0.442004 | + | 0.0144195i | ||||
\(287\) | 0.958344i | 0.0565693i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.73421 | + | 11.6640i | 0.396130 | + | 0.686117i | ||||
\(290\) | −11.4641 | − | 19.8565i | −0.673198 | − | 1.16601i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.23469 | − | 5.23469i | −0.306337 | − | 0.306337i | ||||
\(293\) | 3.24724 | + | 3.24724i | 0.189706 | + | 0.189706i | 0.795569 | − | 0.605863i | \(-0.207172\pi\) |
−0.605863 | + | 0.795569i | \(0.707172\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.6182 | + | 32.2476i | 1.08399 | + | 1.87753i | ||||
\(296\) | −17.7903 | − | 30.8137i | −1.03404 | − | 1.79101i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 6.45792i | − | 0.374097i | ||||||
\(299\) | −9.60803 | + | 17.9704i | −0.555646 | + | 1.03926i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.93108 | + | 0.785381i | −0.168945 | + | 0.0452686i | ||||
\(302\) | −20.3918 | − | 11.7732i | −1.17342 | − | 0.677474i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 10.8429 | − | 2.90535i | 0.621883 | − | 0.166633i | ||||
\(305\) | −7.80168 | − | 29.1163i | −0.446723 | − | 1.66719i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.93098 | − | 3.93098i | 0.224353 | − | 0.224353i | −0.585976 | − | 0.810329i | \(-0.699289\pi\) |
0.810329 | + | 0.585976i | \(0.199289\pi\) | |||||||
\(308\) | 1.29925 | − | 0.750119i | 0.0740314 | − | 0.0427420i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.31514 | − | 8.64023i | −0.131491 | − | 0.490732i | ||||
\(311\) | 10.9466 | + | 18.9600i | 0.620724 | + | 1.07513i | 0.989351 | + | 0.145548i | \(0.0464945\pi\) |
−0.368627 | + | 0.929577i | \(0.620172\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.78444 | + | 6.55485i | −0.213909 | + | 0.370502i | −0.952935 | − | 0.303176i | \(-0.901953\pi\) |
0.739025 | + | 0.673678i | \(0.235286\pi\) | |||||||
\(314\) | 26.5179 | + | 7.10545i | 1.49649 | + | 0.400984i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.90937 | − | 2.83443i | −0.276174 | − | 0.159449i | ||||
\(317\) | −7.64018 | − | 28.5136i | −0.429116 | − | 1.60148i | −0.754768 | − | 0.655992i | \(-0.772251\pi\) |
0.325653 | − | 0.945489i | \(-0.394416\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.25749 | − | 8.25749i | 0.462331 | − | 0.462331i | ||||
\(320\) | −6.52805 | + | 24.3630i | −0.364929 | + | 1.36193i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 9.92792i | 0.553261i | ||||||||
\(323\) | −2.18995 | + | 8.17300i | −0.121852 | + | 0.454758i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.3789 | − | 5.54916i | −0.575718 | − | 0.307812i | ||||
\(326\) | 4.59709 | + | 2.65413i | 0.254609 | + | 0.146999i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.998319 | − | 1.72914i | 0.0551230 | − | 0.0954758i | ||||
\(329\) | 3.53383 | 0.194826 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.98513 | − | 18.6048i | 0.274008 | − | 1.02261i | −0.682496 | − | 0.730890i | \(-0.739105\pi\) |
0.956503 | − | 0.291721i | \(-0.0942280\pi\) | |||||||
\(332\) | 1.55028 | − | 0.415396i | 0.0850827 | − | 0.0227978i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.212091 | + | 0.367352i | −0.0116051 | + | 0.0201006i | ||||
\(335\) | 10.4357 | 0.570163 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.6291 | + | 9.02348i | −0.851373 | + | 0.491541i | −0.861114 | − | 0.508412i | \(-0.830233\pi\) |
0.00974077 | + | 0.999953i | \(0.496899\pi\) | |||||||
\(338\) | 10.2049 | − | 11.6311i | 0.555072 | − | 0.632648i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.22825 | − | 2.22825i | −0.120844 | − | 0.120844i | ||||
\(341\) | 3.94552 | − | 2.27794i | 0.213662 | − | 0.123358i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.3370 | + | 12.3370i | 0.666135 | + | 0.666135i | ||||
\(344\) | 6.10669 | + | 1.63628i | 0.329251 | + | 0.0882224i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.6786 | + | 3.66518i | 0.735367 | + | 0.197041i | ||||
\(347\) | − | 25.1292i | − | 1.34901i | −0.738272 | − | 0.674503i | \(-0.764358\pi\) | ||
0.738272 | − | 0.674503i | \(-0.235642\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.5014 | + | 16.5014i | −0.883300 | + | 0.883300i | −0.993868 | − | 0.110569i | \(-0.964733\pi\) |
0.110569 | + | 0.993868i | \(0.464733\pi\) | |||||||
\(350\) | −5.73391 | −0.306490 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.54551 | −0.295577 | ||||||||
\(353\) | −14.1500 | + | 14.1500i | −0.753127 | + | 0.753127i | −0.975061 | − | 0.221935i | \(-0.928763\pi\) |
0.221935 | + | 0.975061i | \(0.428763\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 33.2841i | − | 1.76654i | ||||||
\(356\) | 3.42398 | + | 0.917452i | 0.181470 | + | 0.0486248i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.73652 | + | 1.80504i | 0.356036 | + | 0.0953996i | ||||
\(359\) | 1.97346 | + | 1.97346i | 0.104155 | + | 0.104155i | 0.757264 | − | 0.653109i | \(-0.226536\pi\) |
−0.653109 | + | 0.757264i | \(0.726536\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.10195 | − | 0.636209i | 0.0579972 | − | 0.0334847i | ||||
\(362\) | −6.98370 | − | 6.98370i | −0.367055 | − | 0.367055i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.705155 | + | 3.02269i | −0.0369602 | + | 0.158432i | ||||
\(365\) | −31.5968 | + | 18.2424i | −1.65385 | + | 0.954852i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −32.9892 | −1.72202 | −0.861011 | − | 0.508587i | \(-0.830168\pi\) | ||||
−0.861011 | + | 0.508587i | \(0.830168\pi\) | |||||||
\(368\) | 7.04535 | − | 12.2029i | 0.367264 | − | 0.636120i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −38.2457 | + | 10.2479i | −1.98830 | + | 0.532763i | ||||
\(371\) | 4.41685 | − | 16.4839i | 0.229311 | − | 0.855802i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.70461 | −0.243596 | −0.121798 | − | 0.992555i | \(-0.538866\pi\) | ||||
−0.121798 | + | 0.992555i | \(0.538866\pi\) | |||||||
\(374\) | −1.94905 | + | 3.37586i | −0.100783 | + | 0.174562i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.37609 | − | 3.68124i | −0.328822 | − | 0.189845i | ||||
\(377\) | 0.787765 | + | 24.1476i | 0.0405720 | + | 1.24366i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.09903 | − | 19.0299i | 0.261920 | − | 0.977498i | −0.702189 | − | 0.711991i | \(-0.747794\pi\) |
0.964109 | − | 0.265507i | \(-0.0855394\pi\) | |||||||
\(380\) | 7.55000i | 0.387307i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.20574 | − | 8.23195i | 0.112856 | − | 0.421183i | ||||
\(383\) | −4.04582 | + | 4.04582i | −0.206732 | + | 0.206732i | −0.802877 | − | 0.596145i | \(-0.796698\pi\) |
0.596145 | + | 0.802877i | \(0.296698\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.91365 | − | 7.14185i | −0.0975287 | − | 0.363982i | ||||
\(386\) | −2.82378 | − | 1.63031i | −0.143727 | − | 0.0829806i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.95421 | − | 0.791578i | −0.149977 | − | 0.0401863i | ||||
\(389\) | −8.59884 | + | 14.8936i | −0.435978 | + | 0.755137i | −0.997375 | − | 0.0724102i | \(-0.976931\pi\) |
0.561397 | + | 0.827547i | \(0.310264\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.31054 | + | 9.19812i | 0.268565 | + | 0.465169i | ||||
\(392\) | −3.83735 | − | 14.3212i | −0.193815 | − | 0.723328i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 24.6968 | − | 14.2587i | 1.24421 | − | 0.718344i | ||||
\(395\) | −19.7554 | + | 19.7554i | −0.994004 | + | 0.994004i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.701121 | − | 2.61662i | −0.0351882 | − | 0.131324i | 0.946097 | − | 0.323882i | \(-0.104988\pi\) |
−0.981286 | + | 0.192558i | \(0.938322\pi\) | |||||||
\(398\) | 10.7347 | − | 2.87635i | 0.538082 | − | 0.144179i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.04784 | + | 4.06907i | 0.352392 | + | 0.203454i | ||||
\(401\) | −7.48577 | + | 2.00581i | −0.373822 | + | 0.100165i | −0.440838 | − | 0.897587i | \(-0.645319\pi\) |
0.0670163 | + | 0.997752i | \(0.478652\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.14140 | + | 9.17925i | −0.106671 | + | 0.457251i | ||||
\(404\) | 1.76654i | 0.0878886i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.88542 | + | 10.1938i | 0.292088 | + | 0.505912i | ||||
\(407\) | −10.0832 | − | 17.4647i | −0.499808 | − | 0.865692i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.60298 | − | 5.60298i | −0.277050 | − | 0.277050i | 0.554880 | − | 0.831930i | \(-0.312764\pi\) |
−0.831930 | + | 0.554880i | \(0.812764\pi\) | |||||||
\(410\) | −1.57112 | − | 1.57112i | −0.0775921 | − | 0.0775921i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.36916 | + | 9.29965i | 0.264519 | + | 0.458161i | ||||
\(413\) | −9.55813 | − | 16.5552i | −0.470325 | − | 0.814627i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 7.90993i | − | 0.388283i | ||||||
\(416\) | 7.84391 | − | 8.37295i | 0.384579 | − | 0.410518i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9.02123 | − | 2.41723i | 0.441243 | − | 0.118231i | ||||
\(419\) | 26.4028 | + | 15.2436i | 1.28986 | + | 0.744700i | 0.978629 | − | 0.205634i | \(-0.0659257\pi\) |
0.311230 | + | 0.950335i | \(0.399259\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.53981 | + | 2.02029i | −0.367468 | + | 0.0984628i | −0.437828 | − | 0.899059i | \(-0.644252\pi\) |
0.0703596 | + | 0.997522i | \(0.477585\pi\) | |||||||
\(422\) | 1.60534 | + | 5.99122i | 0.0781469 | + | 0.291648i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −25.1408 | + | 25.1408i | −1.22095 | + | 1.22095i | ||||
\(425\) | −5.31241 | + | 3.06712i | −0.257690 | + | 0.148777i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.00520 | + | 14.9476i | 0.193825 | + | 0.723365i | ||||
\(428\) | −1.33812 | − | 2.31770i | −0.0646806 | − | 0.112030i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.51769 | − | 6.09281i | 0.169638 | − | 0.293821i | ||||
\(431\) | −30.9395 | − | 8.29022i | −1.49030 | − | 0.399326i | −0.580465 | − | 0.814285i | \(-0.697129\pi\) |
−0.909840 | + | 0.414960i | \(0.863796\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.6303 | + | 11.3335i | 0.943371 | + | 0.544655i | 0.891015 | − | 0.453973i | \(-0.149994\pi\) |
0.0523555 | + | 0.998629i | \(0.483327\pi\) | |||||||
\(434\) | 1.18854 | + | 4.43569i | 0.0570517 | + | 0.212920i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.0808408 | + | 0.0808408i | −0.00387157 | + | 0.00387157i | ||||
\(437\) | 6.58617 | − | 24.5799i | 0.315059 | − | 1.17582i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 32.3810i | − | 1.54546i | −0.634735 | − | 0.772730i | \(-0.718891\pi\) | ||
0.634735 | − | 0.772730i | \(-0.281109\pi\) | |||||||
\(440\) | −3.98695 | + | 14.8795i | −0.190070 | + | 0.709352i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.34022 | − | 7.71782i | −0.111313 | − | 0.367099i | ||||
\(443\) | −21.0067 | − | 12.1282i | −0.998059 | − | 0.576230i | −0.0903854 | − | 0.995907i | \(-0.528810\pi\) |
−0.907673 | + | 0.419677i | \(0.862143\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.73501 | − | 15.1295i | 0.414079 | − | 0.717206i | ||||
\(446\) | 8.14578 | 0.385714 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.35134 | − | 12.5074i | 0.158336 | − | 0.590918i | ||||
\(449\) | 10.4048 | − | 2.78796i | 0.491032 | − | 0.131572i | −0.00480262 | − | 0.999988i | \(-0.501529\pi\) |
0.495835 | + | 0.868417i | \(0.334862\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.565830 | − | 0.980046i | 0.0266439 | − | 0.0461486i | ||||
\(452\) | −4.35607 | −0.204892 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.1644 | − | 7.60045i | 0.617834 | − | 0.356707i | ||||
\(455\) | 13.4900 | + | 7.21252i | 0.632420 | + | 0.338128i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.0357 | − | 17.0357i | −0.796895 | − | 0.796895i | 0.185710 | − | 0.982605i | \(-0.440541\pi\) |
−0.982605 | + | 0.185710i | \(0.940541\pi\) | |||||||
\(458\) | 18.7926 | − | 10.8499i | 0.878122 | − | 0.506984i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.70136 | + | 6.70136i | 0.312453 | + | 0.312453i | ||||
\(461\) | −2.85339 | − | 0.764563i | −0.132896 | − | 0.0356092i | 0.191758 | − | 0.981442i | \(-0.438581\pi\) |
−0.324654 | + | 0.945833i | \(0.605248\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.79433 | + | 0.480789i | 0.0833896 | + | 0.0223442i | 0.300273 | − | 0.953853i | \(-0.402922\pi\) |
−0.216883 | + | 0.976198i | \(0.569589\pi\) | |||||||
\(464\) | − | 16.7064i | − | 0.775573i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.59419 | + | 3.59419i | −0.166497 | + | 0.166497i | ||||
\(467\) | 16.0374 | 0.742122 | 0.371061 | − | 0.928608i | \(-0.378994\pi\) | ||||
0.371061 | + | 0.928608i | \(0.378994\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.35743 | −0.247383 | ||||||||
\(470\) | −5.79340 | + | 5.79340i | −0.267230 | + | 0.267230i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 39.8273i | 1.83320i | ||||||||
\(473\) | 3.46117 | + | 0.927416i | 0.159145 | + | 0.0426427i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.1962 | + | 3.80387i | 0.651368 | + | 0.174533i | ||||
\(476\) | 1.14393 | + | 1.14393i | 0.0524320 | + | 0.0524320i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.16123 | − | 0.670438i | 0.0531136 | − | 0.0306651i | ||||
\(479\) | 26.1930 | + | 26.1930i | 1.19679 | + | 1.19679i | 0.975123 | + | 0.221664i | \(0.0711489\pi\) |
0.221664 | + | 0.975123i | \(0.428851\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 40.6316 | + | 9.47883i | 1.85264 | + | 0.432197i | ||||
\(482\) | 9.09969 | − | 5.25371i | 0.414480 | − | 0.239300i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.64477 | 0.211126 | ||||||||
\(485\) | −7.53657 | + | 13.0537i | −0.342218 | + | 0.592739i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.5635 | − | 5.24201i | 0.886505 | − | 0.237538i | 0.213293 | − | 0.976988i | \(-0.431581\pi\) |
0.673212 | + | 0.739450i | \(0.264914\pi\) | |||||||
\(488\) | 8.34453 | − | 31.1422i | 0.377739 | − | 1.40974i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −16.4991 | −0.745352 | ||||||||
\(491\) | −5.66933 | + | 9.81958i | −0.255854 | + | 0.443151i | −0.965127 | − | 0.261782i | \(-0.915690\pi\) |
0.709273 | + | 0.704933i | \(0.249023\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.9056 | + | 6.29633i | 0.491162 | + | 0.283572i | ||||
\(494\) | −9.11049 | + | 17.0399i | −0.409900 | + | 0.766660i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.68689 | − | 6.29557i | 0.0757438 | − | 0.282680i | ||||
\(497\) | 17.0873i | 0.766469i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.32264 | + | 4.93618i | −0.0592097 | + | 0.220974i | −0.989191 | − | 0.146634i | \(-0.953156\pi\) |
0.929981 | + | 0.367607i | \(0.119823\pi\) | |||||||
\(500\) | 2.05816 | − | 2.05816i | 0.0920438 | − | 0.0920438i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.37473 | + | 20.0588i | 0.239886 | + | 0.895266i | ||||
\(503\) | 16.1644 | + | 9.33251i | 0.720734 | + | 0.416116i | 0.815023 | − | 0.579429i | \(-0.196724\pi\) |
−0.0942889 | + | 0.995545i | \(0.530058\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.40956 | + | 2.25333i | 0.374220 | + | 0.100272i | ||||
\(506\) | 5.86169 | − | 10.1527i | 0.260584 | − | 0.451344i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.15574 | − | 5.46591i | −0.140013 | − | 0.242510i | ||||
\(509\) | −0.836359 | − | 3.12134i | −0.0370710 | − | 0.138351i | 0.944910 | − | 0.327330i | \(-0.106149\pi\) |
−0.981981 | + | 0.188979i | \(0.939482\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.2210 | − | 9.36522i | 0.717576 | − | 0.414293i | ||||
\(512\) | −16.4510 | + | 16.4510i | −0.727037 | + | 0.727037i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.00130 | + | 3.73691i | 0.0441655 | + | 0.164828i | ||||
\(515\) | 51.1195 | − | 13.6974i | 2.25259 | − | 0.603580i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.61386 | − | 2.08646i | −0.158937 | − | 0.0917625i | ||||
\(518\) | 19.6344 | − | 5.26103i | 0.862687 | − | 0.231156i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −16.8266 | − | 27.0662i | −0.737895 | − | 1.18693i | ||||
\(521\) | 21.9128i | 0.960018i | 0.877263 | + | 0.480009i | \(0.159367\pi\) | ||||
−0.877263 | + | 0.480009i | \(0.840633\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.66002 | + | 16.7316i | 0.422403 | + | 0.731624i | 0.996174 | − | 0.0873922i | \(-0.0278533\pi\) |
−0.573771 | + | 0.819016i | \(0.694520\pi\) | |||||||
\(524\) | −2.30541 | − | 3.99309i | −0.100712 | − | 0.174439i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.2142 | + | 15.2142i | 0.663371 | + | 0.663371i | ||||
\(527\) | 3.47386 | + | 3.47386i | 0.151324 | + | 0.151324i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.47119 | − | 7.74433i | −0.194400 | − | 0.336710i | ||||
\(530\) | 19.7829 | + | 34.2649i | 0.859313 | + | 1.48837i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 3.87599i | − | 0.168046i | ||||||
\(533\) | 0.679389 | + | 2.24056i | 0.0294276 | + | 0.0970495i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.7402 | + | 3.41372i | −0.550807 | + | 0.147588i | ||||
\(536\) | 9.66641 | + | 5.58091i | 0.417525 | + | 0.241058i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.31698 | − | 0.352883i | 0.0567790 | − | 0.0152139i | ||||
\(539\) | −2.17494 | − | 8.11699i | −0.0936814 | − | 0.349624i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.88126 | + | 1.88126i | −0.0808815 | + | 0.0808815i | −0.746390 | − | 0.665509i | \(-0.768215\pi\) |
0.665509 | + | 0.746390i | \(0.268215\pi\) | |||||||
\(542\) | −9.22702 | + | 5.32722i | −0.396334 | + | 0.228824i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.54772 | − | 5.77617i | −0.0663579 | − | 0.247651i | ||||
\(545\) | 0.281723 | + | 0.487958i | 0.0120677 | + | 0.0209018i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.0438 | − | 24.3246i | 0.600469 | − | 1.04004i | −0.392281 | − | 0.919846i | \(-0.628314\pi\) |
0.992750 | − | 0.120198i | \(-0.0383529\pi\) | |||||||
\(548\) | 4.76876 | + | 1.27779i | 0.203711 | + | 0.0545843i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.86376 | + | 3.38544i | 0.250031 | + | 0.144356i | ||||
\(551\) | −7.80876 | − | 29.1427i | −0.332664 | − | 1.24152i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.1420 | − | 10.1420i | 0.431280 | − | 0.431280i | ||||
\(554\) | −7.91798 | + | 29.5503i | −0.336403 | + | 1.25547i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.274105i | 0.0116246i | ||||||||
\(557\) | 3.91190 | − | 14.5994i | 0.165753 | − | 0.618597i | −0.832190 | − | 0.554490i | \(-0.812913\pi\) |
0.997943 | − | 0.0641073i | \(-0.0204200\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.29595 | + | 3.91408i | −0.266290 | + | 0.165548i | ||||
\(560\) | −9.16043 | − | 5.28878i | −0.387099 | − | 0.223492i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.535308 | + | 0.927180i | −0.0225806 | + | 0.0391107i | ||||
\(563\) | 25.4105 | 1.07093 | 0.535463 | − | 0.844558i | \(-0.320137\pi\) | ||||
0.535463 | + | 0.844558i | \(0.320137\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.55645 | + | 20.7369i | −0.233762 | + | 0.872410i | ||||
\(566\) | −20.9187 | + | 5.60516i | −0.879280 | + | 0.235602i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 17.8000 | − | 30.8306i | 0.746873 | − | 1.29362i | ||||
\(569\) | −25.0364 | −1.04958 | −0.524789 | − | 0.851232i | \(-0.675856\pi\) | ||||
−0.524789 | + | 0.851232i | \(0.675856\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.2909 | + | 13.4470i | −0.974693 | + | 0.562739i | −0.900664 | − | 0.434517i | \(-0.856919\pi\) |
−0.0740294 | + | 0.997256i | \(0.523586\pi\) | |||||||
\(572\) | 2.50580 | − | 2.67480i | 0.104773 | − | 0.111839i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.806576 | + | 0.806576i | 0.0336658 | + | 0.0336658i | ||||
\(575\) | 15.9768 | − | 9.22423i | 0.666280 | − | 0.384677i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.8490 | − | 12.8490i | −0.534912 | − | 0.534912i | 0.387118 | − | 0.922030i | \(-0.373470\pi\) |
−0.922030 | + | 0.387118i | \(0.873470\pi\) | |||||||
\(578\) | 15.4846 | + | 4.14907i | 0.644073 | + | 0.172579i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10.8535 | + | 2.90819i | 0.450668 | + | 0.120756i | ||||
\(581\) | 4.06077i | 0.168469i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.2494 | + | 14.2494i | −0.590149 | + | 0.590149i | ||||
\(584\) | −39.0235 | −1.61480 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.46598 | 0.225797 | ||||||||
\(587\) | 10.0666 | − | 10.0666i | 0.415495 | − | 0.415495i | −0.468153 | − | 0.883648i | \(-0.655080\pi\) |
0.883648 | + | 0.468153i | \(0.155080\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 11.7705i | − | 0.484996i | ||||||
\(590\) | 42.8104 | + | 11.4710i | 1.76248 | + | 0.472255i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −27.8671 | − | 7.46698i | −1.14533 | − | 0.306891i | ||||
\(593\) | 14.8629 | + | 14.8629i | 0.610345 | + | 0.610345i | 0.943036 | − | 0.332691i | \(-0.107957\pi\) |
−0.332691 | + | 0.943036i | \(0.607957\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.90481 | − | 3.98649i | 0.283070 | − | 0.163430i | ||||
\(596\) | 2.23786 | + | 2.23786i | 0.0916664 | + | 0.0916664i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.03810 | + | 23.2110i | 0.287809 | + | 0.949168i | ||||
\(599\) | 29.6012 | − | 17.0903i | 1.20947 | − | 0.698289i | 0.246828 | − | 0.969059i | \(-0.420612\pi\) |
0.962644 | + | 0.270770i | \(0.0872783\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.94270 | 0.364780 | 0.182390 | − | 0.983226i | \(-0.441617\pi\) | ||||
0.182390 | + | 0.983226i | \(0.441617\pi\) | |||||||
\(602\) | −1.80590 | + | 3.12790i | −0.0736028 | + | 0.127484i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11.1462 | − | 2.98660i | 0.453531 | − | 0.121523i | ||||
\(605\) | 5.92471 | − | 22.1113i | 0.240874 | − | 0.898953i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.16628 | 0.372048 | 0.186024 | − | 0.982545i | \(-0.440440\pi\) | ||||
0.186024 | + | 0.982545i | \(0.440440\pi\) | |||||||
\(608\) | −7.16364 | + | 12.4078i | −0.290524 | + | 0.503202i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −31.0714 | − | 17.9391i | −1.25805 | − | 0.726333i | ||||
\(611\) | 8.26193 | − | 2.50520i | 0.334242 | − | 0.101350i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.197913 | + | 0.738622i | −0.00799364 | + | 0.0298327i | −0.969807 | − | 0.243872i | \(-0.921582\pi\) |
0.961814 | + | 0.273705i | \(0.0882490\pi\) | |||||||
\(614\) | − | 6.61690i | − | 0.267037i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.04680 | − | 7.63878i | 0.0824681 | − | 0.307775i | ||||
\(617\) | −11.7973 | + | 11.7973i | −0.474940 | + | 0.474940i | −0.903509 | − | 0.428569i | \(-0.859018\pi\) |
0.428569 | + | 0.903509i | \(0.359018\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.995076 | − | 3.71367i | −0.0399955 | − | 0.149265i | 0.943041 | − | 0.332678i | \(-0.107952\pi\) |
−0.983036 | + | 0.183413i | \(0.941286\pi\) | |||||||
\(620\) | 3.79636 | + | 2.19183i | 0.152466 | + | 0.0880261i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 25.1704 | + | 6.74440i | 1.00924 | + | 0.270426i | ||||
\(623\) | −4.48434 | + | 7.76711i | −0.179661 | + | 0.311183i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.3330 | − | 26.5575i | −0.613320 | − | 1.06230i | ||||
\(626\) | 2.33167 | + | 8.70190i | 0.0931922 | + | 0.347798i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.6515 | + | 6.72699i | −0.464945 | + | 0.268436i | ||||
\(629\) | 15.3769 | − | 15.3769i | 0.613118 | − | 0.613118i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.46710 | + | 12.9394i | 0.138023 | + | 0.515110i | 0.999967 | + | 0.00810607i | \(0.00258027\pi\) |
−0.861944 | + | 0.507004i | \(0.830753\pi\) | |||||||
\(632\) | −28.8642 | + | 7.73413i | −1.14815 | + | 0.307647i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −30.4282 | − | 17.5678i | −1.20846 | − | 0.697705i | ||||
\(635\) | −30.0457 | + | 8.05071i | −1.19233 | + | 0.319483i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.3319 | + | 8.19731i | 0.607472 | + | 0.324789i | ||||
\(638\) | − | 13.8996i | − | 0.550290i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.86282 | + | 10.1547i | 0.231748 | + | 0.401400i | ||||
\(641\) | 12.7444 | + | 22.0740i | 0.503375 | + | 0.871870i | 0.999992 | + | 0.00390095i | \(0.00124172\pi\) |
−0.496618 | + | 0.867969i | \(0.665425\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.94884 | − | 3.94884i | −0.155727 | − | 0.155727i | 0.624943 | − | 0.780670i | \(-0.285122\pi\) |
−0.780670 | + | 0.624943i | \(0.785122\pi\) | |||||||
\(644\) | −3.44032 | − | 3.44032i | −0.135568 | − | 0.135568i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.03554 | + | 8.72181i | 0.198121 | + | 0.343155i | ||||
\(647\) | −1.23117 | − | 2.13245i | −0.0484024 | − | 0.0838354i | 0.840809 | − | 0.541332i | \(-0.182080\pi\) |
−0.889212 | + | 0.457496i | \(0.848746\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.5734i | 0.886085i | ||||||||
\(650\) | −13.4056 | + | 4.06488i | −0.525811 | + | 0.159438i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.51276 | + | 0.673293i | −0.0984075 | + | 0.0263682i | ||||
\(653\) | −27.7948 | − | 16.0473i | −1.08769 | − | 0.627981i | −0.154733 | − | 0.987956i | \(-0.549452\pi\) |
−0.932962 | + | 0.359975i | \(0.882785\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.9497 | + | 5.88141i | −0.857646 | + | 0.229806i | ||||
\(656\) | −0.419016 | − | 1.56379i | −0.0163598 | − | 0.0610557i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.97419 | − | 2.97419i | 0.115946 | − | 0.115946i | ||||
\(659\) | −4.60604 | + | 2.65930i | −0.179426 | + | 0.103591i | −0.587023 | − | 0.809570i | \(-0.699700\pi\) |
0.407597 | + | 0.913162i | \(0.366367\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.92362 | − | 22.1073i | −0.230402 | − | 0.859872i | −0.980168 | − | 0.198169i | \(-0.936500\pi\) |
0.749766 | − | 0.661703i | \(-0.230166\pi\) | |||||||
\(662\) | −11.4628 | − | 19.8541i | −0.445513 | − | 0.771651i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.23015 | − | 7.32684i | 0.164162 | − | 0.284337i | ||||
\(665\) | −18.4516 | − | 4.94408i | −0.715520 | − | 0.191723i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −32.7980 | − | 18.9359i | −1.26994 | − | 0.733202i | ||||
\(668\) | −0.0538026 | − | 0.200794i | −0.00208169 | − | 0.00776896i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.78304 | − | 8.78304i | 0.339318 | − | 0.339318i | ||||
\(671\) | 4.72954 | − | 17.6509i | 0.182582 | − | 0.681404i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.4168i | 1.09539i | 0.836679 | + | 0.547693i | \(0.184494\pi\) | ||||
−0.836679 | + | 0.547693i | \(0.815506\pi\) | |||||||
\(674\) | −5.55954 | + | 20.7485i | −0.214146 | + | 0.799202i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.494230 | + | 7.56681i | 0.0190088 | + | 0.291031i | ||||
\(677\) | −19.5004 | − | 11.2586i | −0.749461 | − | 0.432701i | 0.0760383 | − | 0.997105i | \(-0.475773\pi\) |
−0.825499 | + | 0.564404i | \(0.809106\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.86910 | − | 6.70147i | 0.148482 | − | 0.257179i | ||||
\(680\) | −16.6111 | −0.637007 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.40349 | − | 5.23788i | 0.0537422 | − | 0.200569i | ||||
\(683\) | −38.9958 | + | 10.4489i | −1.49213 | + | 0.399816i | −0.910457 | − | 0.413604i | \(-0.864270\pi\) |
−0.581677 | + | 0.813420i | \(0.697603\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.1657 | − | 21.0717i | 0.464829 | − | 0.805107i | ||||
\(686\) | 20.7665 | 0.792868 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.43943 | − | 2.56311i | 0.169252 | − | 0.0977176i | ||||
\(689\) | −1.35939 | − | 41.6698i | −0.0517887 | − | 1.58749i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.7637 | + | 23.7637i | 0.904015 | + | 0.904015i | 0.995781 | − | 0.0917661i | \(-0.0292512\pi\) |
−0.0917661 | + | 0.995781i | \(0.529251\pi\) | |||||||
\(692\) | −6.01014 | + | 3.46996i | −0.228471 | + | 0.131908i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.1496 | − | 21.1496i | −0.802828 | − | 0.802828i | ||||
\(695\) | 1.30487 | + | 0.349639i | 0.0494965 | + | 0.0132625i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.17873 | + | 0.315840i | 0.0446476 | + | 0.0119633i | ||||
\(698\) | 27.7763i | 1.05135i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.98697 | − | 1.98697i | 0.0751004 | − | 0.0751004i | ||||
\(701\) | 34.8493 | 1.31624 | 0.658120 | − | 0.752913i | \(-0.271352\pi\) | ||||
0.658120 | + | 0.752913i | \(0.271352\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −52.1018 | −1.96506 | ||||||||
\(704\) | −10.8119 | + | 10.8119i | −0.407489 | + | 0.407489i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23.8182i | 0.896410i | ||||||||
\(707\) | −4.31727 | − | 1.15681i | −0.162367 | − | 0.0435062i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.53384 | + | 2.28664i | 0.320495 | + | 0.0858764i | 0.415480 | − | 0.909602i | \(-0.363614\pi\) |
−0.0949849 | + | 0.995479i | \(0.530280\pi\) | |||||||
\(710\) | −28.0131 | − | 28.0131i | −1.05131 | − | 1.05131i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 16.1822 | − | 9.34279i | 0.606453 | − | 0.350136i | ||||
\(713\) | −10.4475 | − | 10.4475i | −0.391261 | − | 0.391261i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.53702 | − | 15.3407i | −0.356664 | − | 0.573708i | ||||
\(716\) | −2.95991 | + | 1.70890i | −0.110617 | + | 0.0638647i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.32187 | 0.123971 | ||||||||
\(719\) | −12.4677 | + | 21.5947i | −0.464966 | + | 0.805345i | −0.999200 | − | 0.0399915i | \(-0.987267\pi\) |
0.534234 | + | 0.845337i | \(0.320600\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.2435 | + | 7.03193i | −0.977359 | + | 0.261883i | ||||
\(722\) | 0.391981 | − | 1.46289i | 0.0145880 | − | 0.0544432i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.84012 | 0.179882 | ||||||||
\(725\) | 10.9365 | − | 18.9426i | 0.406172 | − | 0.703511i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.7972 | + | 9.12055i | 0.585888 | + | 0.338262i | 0.763470 | − | 0.645844i | \(-0.223494\pi\) |
−0.177582 | + | 0.984106i | \(0.556828\pi\) | |||||||
\(728\) | 8.63837 | + | 13.8951i | 0.320159 | + | 0.514989i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −11.2395 | + | 41.9464i | −0.415993 | + | 1.55251i | ||||
\(731\) | 3.86396i | 0.142914i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.98357 | − | 22.3310i | 0.221008 | − | 0.824814i | −0.762956 | − | 0.646450i | \(-0.776253\pi\) |
0.983965 | − | 0.178364i | \(-0.0570805\pi\) | |||||||
\(734\) | −27.7648 | + | 27.7648i | −1.02482 | + | 1.02482i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.65469 | + | 17.3715i | 0.171574 | + | 0.640324i | ||||
\(737\) | 5.47876 | + | 3.16316i | 0.201813 | + | 0.116517i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.4323 | + | 3.06326i | 0.420542 | + | 0.112684i | 0.462883 | − | 0.886419i | \(-0.346815\pi\) |
−0.0423409 | + | 0.999103i | \(0.513482\pi\) | |||||||
\(740\) | 9.70206 | − | 16.8045i | 0.356655 | − | 0.617745i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.1560 | − | 17.5908i | −0.372840 | − | 0.645778i | ||||
\(743\) | −11.3842 | − | 42.4865i | −0.417647 | − | 1.55868i | −0.779474 | − | 0.626434i | \(-0.784514\pi\) |
0.361827 | − | 0.932245i | \(-0.382153\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.5078 | − | 7.79874i | 0.494888 | − | 0.285724i | ||||
\(746\) | −3.95957 | + | 3.95957i | −0.144970 | + | 0.144970i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.494431 | − | 1.84524i | −0.0180782 | − | 0.0674687i | ||||
\(749\) | 6.54051 | − | 1.75252i | 0.238985 | − | 0.0640358i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.0454 | + | 18.5014i | 1.16935 | + | 0.675126i | 0.953528 | − | 0.301306i | \(-0.0974225\pi\) |
0.215825 | + | 0.976432i | \(0.430756\pi\) | |||||||
\(752\) | −5.76637 | + | 1.54509i | −0.210278 | + | 0.0563438i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 20.9864 | + | 19.6604i | 0.764281 | + | 0.715990i | ||||
\(755\) | − | 56.8706i | − | 2.06973i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.2842 | − | 40.3294i | −0.846278 | − | 1.46580i | −0.884507 | − | 0.466527i | \(-0.845505\pi\) |
0.0382287 | − | 0.999269i | \(-0.487828\pi\) | |||||||
\(758\) | −11.7247 | − | 20.3077i | −0.425859 | − | 0.737609i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 28.1418 | + | 28.1418i | 1.02081 | + | 1.02081i | ||||
\(761\) | 21.4108 | + | 21.4108i | 0.776142 | + | 0.776142i | 0.979172 | − | 0.203031i | \(-0.0650792\pi\) |
−0.203031 | + | 0.979172i | \(0.565079\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.144630 | − | 0.250506i | −0.00523595 | − | 0.00906893i | ||||
\(764\) | 2.08826 | + | 3.61697i | 0.0755506 | + | 0.130857i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.81020i | 0.246062i | ||||||||
\(767\) | −34.0827 | − | 31.9292i | −1.23066 | − | 1.15290i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −50.7997 | + | 13.6117i | −1.83188 | + | 0.490852i | −0.998121 | − | 0.0612700i | \(-0.980485\pi\) |
−0.833763 | + | 0.552122i | \(0.813818\pi\) | |||||||
\(770\) | −7.62142 | − | 4.40023i | −0.274657 | − | 0.158573i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.54347 | − | 0.413573i | 0.0555508 | − | 0.0148848i | ||||
\(773\) | −5.09988 | − | 19.0330i | −0.183430 | − | 0.684570i | −0.994961 | − | 0.100261i | \(-0.968032\pi\) |
0.811531 | − | 0.584309i | \(-0.198634\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.03398 | − | 6.03398i | 0.216747 | − | 0.216747i | ||||
\(776\) | −13.9620 | + | 8.06097i | −0.501207 | + | 0.289372i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.29791 | + | 19.7721i | 0.189939 | + | 0.708863i | ||||
\(779\) | −1.46187 | − | 2.53203i | −0.0523769 | − | 0.0907194i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.0888 | − | 17.4742i | 0.361004 | − | 0.625277i | ||||
\(782\) | 12.2110 | + | 3.27192i | 0.436664 | + | 0.117004i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −10.4112 | − | 6.01090i | −0.371828 | − | 0.214675i | ||||
\(785\) | 17.1614 | + | 64.0473i | 0.612517 | + | 2.28595i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.17503 | + | 7.17503i | −0.255762 | + | 0.255762i | −0.823328 | − | 0.567566i | \(-0.807885\pi\) |
0.567566 | + | 0.823328i | \(0.307885\pi\) | |||||||
\(788\) | −3.61712 | + | 13.4993i | −0.128854 | + | 0.480891i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 33.2537i | 1.18311i | ||||||||
\(791\) | 2.85255 | − | 10.6459i | 0.101425 | − | 0.378523i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.9606 | + | 32.1074i | 0.708822 | + | 1.14017i | ||||
\(794\) | −2.79232 | − | 1.61215i | −0.0990958 | − | 0.0572130i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.72315 | + | 4.71663i | −0.0965195 | + | 0.167177i | ||||
\(797\) | 41.2377 | 1.46072 | 0.730358 | − | 0.683065i | \(-0.239353\pi\) | ||||
0.730358 | + | 0.683065i | \(0.239353\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.16464 | − | 4.34649i | 0.0412019 | − | 0.153768i | ||||
\(800\) | −10.0330 | + | 2.68834i | −0.354720 | + | 0.0950471i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.61213 | + | 7.98844i | −0.162860 | + | 0.282082i | ||||
\(803\) | −22.1178 | −0.780521 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.7659 | + | 11.9892i | −0.731902 | + | 0.422564i | ||||
\(806\) | 5.92330 | + | 9.52785i | 0.208639 | + | 0.335604i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.58458 | + | 6.58458i | 0.231645 | + | 0.231645i | ||||
\(809\) | 22.9401 | − | 13.2445i | 0.806532 | − | 0.465651i | −0.0392184 | − | 0.999231i | \(-0.512487\pi\) |
0.845750 | + | 0.533579i | \(0.179153\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.7759 | − | 27.7759i | −0.975343 | − | 0.975343i | 0.0243602 | − | 0.999703i | \(-0.492245\pi\) |
−0.999703 | + | 0.0243602i | \(0.992245\pi\) | |||||||
\(812\) | −5.57194 | − | 1.49300i | −0.195537 | − | 0.0523939i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −23.1853 | − | 6.21248i | −0.812644 | − | 0.217747i | ||||
\(815\) | 12.8208i | 0.449092i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.54615 | − | 6.54615i | 0.229021 | − | 0.229021i | ||||
\(818\) | −9.43133 | −0.329759 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.08888 | 0.0380253 | ||||||||
\(821\) | 20.0159 | − | 20.0159i | 0.698561 | − | 0.698561i | −0.265539 | − | 0.964100i | \(-0.585550\pi\) |
0.964100 | + | 0.265539i | \(0.0855501\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.18802i | 0.111127i | 0.998455 | + | 0.0555636i | \(0.0176956\pi\) | ||||
−0.998455 | + | 0.0555636i | \(0.982304\pi\) | |||||||
\(824\) | 54.6764 | + | 14.6505i | 1.90474 | + | 0.510374i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −21.9779 | − | 5.88895i | −0.764707 | − | 0.204903i | ||||
\(827\) | −40.4226 | − | 40.4226i | −1.40563 | − | 1.40563i | −0.780603 | − | 0.625027i | \(-0.785088\pi\) |
−0.625027 | − | 0.780603i | \(-0.714912\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.372721 | − | 0.215190i | 0.0129451 | − | 0.00747387i | −0.493513 | − | 0.869738i | \(-0.664288\pi\) |
0.506459 | + | 0.862264i | \(0.330954\pi\) | |||||||
\(830\) | −6.65727 | − | 6.65727i | −0.231077 | − | 0.231077i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.03146 | − | 31.6175i | −0.0357593 | − | 1.09614i | ||||
\(833\) | 7.84759 | − | 4.53081i | 0.271903 | − | 0.156983i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.02450 | −0.0354544 | ||||||||
\(836\) | −2.28848 | + | 3.96376i | −0.0791488 | + | 0.137090i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 35.0510 | − | 9.39190i | 1.21082 | − | 0.324438i | ||||
\(839\) | −1.25045 | + | 4.66673i | −0.0431702 | + | 0.161113i | −0.984146 | − | 0.177361i | \(-0.943244\pi\) |
0.940976 | + | 0.338474i | \(0.109911\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.9020 | −0.548345 | ||||||||
\(842\) | −4.64542 | + | 8.04611i | −0.160092 | + | 0.277287i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.63244 | − | 1.51984i | −0.0906122 | − | 0.0523150i | ||||
\(845\) | 36.6520 | + | 7.29919i | 1.26087 | + | 0.251100i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.04160 | + | 11.3514i | −0.104511 | + | 0.390040i | ||||
\(848\) | 28.8290i | 0.989991i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.88971 | + | 7.05251i | −0.0648166 | + | 0.241899i | ||||
\(851\) | −46.2454 | + | 46.2454i | −1.58527 | + | 1.58527i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.5603 | − | 43.1437i | −0.395818 | − | 1.47721i | −0.820383 | − | 0.571815i | \(-0.806240\pi\) |
0.424565 | − | 0.905397i | \(-0.360427\pi\) | |||||||
\(854\) | 15.9513 | + | 9.20951i | 0.545843 | + | 0.315143i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.6267 | − | 3.65125i | −0.465750 | − | 0.124797i | ||||
\(857\) | −25.1388 | + | 43.5417i | −0.858725 | + | 1.48736i | 0.0144207 | + | 0.999896i | \(0.495410\pi\) |
−0.873146 | + | 0.487459i | \(0.837924\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.1679 | + | 43.5920i | 0.858717 | + | 1.48734i | 0.873153 | + | 0.487445i | \(0.162071\pi\) |
−0.0144366 | + | 0.999896i | \(0.504595\pi\) | |||||||
\(860\) | 0.892357 | + | 3.33032i | 0.0304291 | + | 0.113563i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −33.0171 | + | 19.0624i | −1.12457 | + | 0.649269i | ||||
\(863\) | 29.3689 | − | 29.3689i | 0.999728 | − | 0.999728i | −0.000272025 | − | 1.00000i | \(-0.500087\pi\) |
1.00000 | 0.000272025i | \(8.65883e-5\pi\) | ||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.85231 | + | 33.0373i | 0.300988 | + | 1.12330i | ||||
\(866\) | 26.0602 | − | 6.98281i | 0.885562 | − | 0.237286i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.94896 | − | 1.12523i | −0.0661521 | − | 0.0381929i | ||||
\(869\) | −16.3597 | + | 4.38357i | −0.554965 | + | 0.148702i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.5254 | + | 3.79799i | −0.424408 | + | 0.128690i | ||||
\(872\) | 0.602650i | 0.0204083i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −15.1442 | − | 26.2304i | −0.512259 | − | 0.887258i | ||||
\(875\) | 3.68219 | + | 6.37775i | 0.124481 | + | 0.215607i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.4238 | − | 12.4238i | −0.419523 | − | 0.419523i | 0.465516 | − | 0.885039i | \(-0.345869\pi\) |
−0.885039 | + | 0.465516i | \(0.845869\pi\) | |||||||
\(878\) | −27.2529 | − | 27.2529i | −0.919742 | − | 0.919742i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.24525 | + | 10.8171i | 0.210527 | + | 0.364644i | ||||
\(881\) | 11.7668 | + | 20.3807i | 0.396434 | + | 0.686644i | 0.993283 | − | 0.115710i | \(-0.0369142\pi\) |
−0.596849 | + | 0.802354i | \(0.703581\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.09275i | 0.171385i | 0.996322 | + | 0.0856923i | \(0.0273102\pi\) | ||||
−0.996322 | + | 0.0856923i | \(0.972690\pi\) | |||||||
\(884\) | 3.48541 | + | 1.86350i | 0.117227 | + | 0.0626763i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −27.8875 | + | 7.47243i | −0.936899 | + | 0.251041i | ||||
\(887\) | −11.4511 | − | 6.61127i | −0.384489 | − | 0.221985i | 0.295281 | − | 0.955411i | \(-0.404587\pi\) |
−0.679769 | + | 0.733426i | \(0.737920\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.4247 | − | 4.13304i | 0.517329 | − | 0.138618i | ||||
\(890\) | −5.38181 | − | 20.0852i | −0.180399 | − | 0.673256i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.82276 | + | 2.82276i | −0.0945129 | + | 0.0945129i | ||||
\(893\) | −9.33670 | + | 5.39054i | −0.312441 | + | 0.180388i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.35963 | + | 16.2704i | 0.145726 | + | 0.543858i | ||||
\(896\) | −3.00983 | − | 5.21318i | −0.100551 | − | 0.174160i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.41059 | − | 11.1035i | 0.213924 | − | 0.370528i | ||||
\(899\) | −16.9207 | − | 4.53390i | −0.564338 | − | 0.151214i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.8190 | − | 10.8651i | −0.626951 | − | 0.361970i | ||||
\(902\) | −0.348619 | − | 1.30106i | −0.0116077 | − | 0.0433207i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16.2368 | + | 16.2368i | −0.540027 | + | 0.540027i | ||||
\(905\) | 6.17388 | − | 23.0412i | 0.205227 | − | 0.765917i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 9.89130i | − | 0.328435i | −0.986424 | − | 0.164218i | \(-0.947490\pi\) | ||
0.986424 | − | 0.164218i | \(-0.0525099\pi\) | |||||||
\(908\) | −1.92806 | + | 7.19562i | −0.0639850 | + | 0.238795i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 17.4239 | − | 5.28333i | 0.577598 | − | 0.175141i | ||||
\(911\) | 10.2559 | + | 5.92123i | 0.339792 | + | 0.196179i | 0.660180 | − | 0.751107i | \(-0.270480\pi\) |
−0.320388 | + | 0.947286i | \(0.603813\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.39758 | − | 4.15273i | 0.0793483 | − | 0.137435i | ||||
\(914\) | −28.6756 | −0.948504 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.75238 | + | 10.2720i | −0.0909412 | + | 0.339397i | ||||
\(917\) | 11.2685 | − | 3.01937i | 0.372117 | − | 0.0997085i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.00599 | + | 1.74243i | −0.0331846 | + | 0.0574775i | −0.882141 | − | 0.470986i | \(-0.843898\pi\) |
0.848956 | + | 0.528463i | \(0.177232\pi\) | |||||||
\(920\) | 49.9572 | 1.64704 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.04499 | + | 1.75803i | −0.100281 | + | 0.0578975i | ||||
\(923\) | 12.1135 | + | 39.9492i | 0.398721 | + | 1.31495i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −26.7092 | − | 26.7092i | −0.878194 | − | 0.878194i | ||||
\(926\) | 1.91482 | − | 1.10552i | 0.0629248 | − | 0.0363297i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 15.0775 | + | 15.0775i | 0.494943 | + | 0.494943i | ||||
\(929\) | 40.2389 | + | 10.7820i | 1.32019 | + | 0.353745i | 0.849051 | − | 0.528311i | \(-0.177175\pi\) |
0.471144 | + | 0.882056i | \(0.343841\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.9709 | − | 5.61914i | −0.687294 | − | 0.184160i | ||||
\(932\) | − | 2.49098i | − | 0.0815949i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13.4976 | − | 13.4976i | 0.441656 | − | 0.441656i | ||||
\(935\) | −9.41490 | −0.307900 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.9819 | 1.56750 | 0.783750 | − | 0.621077i | \(-0.213304\pi\) | ||||
0.783750 | + | 0.621077i | \(0.213304\pi\) | |||||||
\(938\) | −4.50900 | + | 4.50900i | −0.147224 | + | 0.147224i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | − | 4.01517i | − | 0.130960i | ||||||
\(941\) | −23.7536 | − | 6.36477i | −0.774346 | − | 0.207485i | −0.150056 | − | 0.988678i | \(-0.547945\pi\) |
−0.624291 | + | 0.781192i | \(0.714612\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.54497 | − | 0.949873i | −0.115440 | − | 0.0309321i | ||||
\(944\) | 22.8350 | + | 22.8350i | 0.743216 | + | 0.743216i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.69358 | − | 2.13249i | 0.120089 | − | 0.0693332i | ||||
\(947\) | 29.5660 | + | 29.5660i | 0.960767 | + | 0.960767i | 0.999259 | − | 0.0384921i | \(-0.0122554\pi\) |
−0.0384921 | + | 0.999259i | \(0.512255\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.2848 | − | 33.3949i | 1.01555 | − | 1.08404i | ||||
\(950\) | 15.1495 | − | 8.74657i | 0.491515 | − | 0.283776i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.52775 | 0.276386 | ||||||||
\(953\) | 3.67150 | − | 6.35923i | 0.118932 | − | 0.205996i | −0.800413 | − | 0.599449i | \(-0.795386\pi\) |
0.919345 | + | 0.393453i | \(0.128720\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.8822 | − | 5.32742i | 0.643373 | − | 0.172391i | ||||
\(956\) | −0.170075 | + | 0.634729i | −0.00550062 | + | 0.0205286i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 44.0898 | 1.42448 | ||||||||
\(959\) | −6.24560 | + | 10.8177i | −0.201681 | + | 0.349321i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.9282 | + | 12.0829i | 0.675104 | + | 0.389772i | ||||
\(962\) | 42.1747 | − | 26.2193i | 1.35977 | − | 0.845343i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.33275 | + | 4.97388i | −0.0429249 | + | 0.160198i | ||||
\(965\) | − | 7.87520i | − | 0.253512i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.78898 | − | 25.3368i | 0.218319 | − | 0.814778i | −0.766653 | − | 0.642062i | \(-0.778079\pi\) |
0.984972 | − | 0.172716i | \(-0.0552542\pi\) | |||||||
\(968\) | 17.3129 | − | 17.3129i | 0.556457 | − | 0.556457i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.64343 | + | 17.3295i | 0.149091 | + | 0.556417i | ||||
\(971\) | 11.1860 | + | 6.45823i | 0.358975 | + | 0.207255i | 0.668631 | − | 0.743594i | \(-0.266880\pi\) |
−0.309656 | + | 0.950849i | \(0.600214\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.669888 | − | 0.179496i | −0.0214756 | − | 0.00575438i | ||||
\(974\) | 12.0534 | − | 20.8771i | 0.386217 | − | 0.668947i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.0711 | − | 22.6397i | −0.418394 | − | 0.724680i | ||||
\(977\) | −8.97618 | − | 33.4996i | −0.287174 | − | 1.07175i | −0.947236 | − | 0.320536i | \(-0.896137\pi\) |
0.660063 | − | 0.751210i | \(-0.270530\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.17179 | − | 5.29533i | 0.293132 | − | 0.169240i | ||||
\(980\) | 5.71742 | − | 5.71742i | 0.182636 | − | 0.182636i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.49299 | + | 13.0360i | 0.111466 | + | 0.415996i | ||||
\(983\) | −27.3813 | + | 7.33678i | −0.873326 | + | 0.234007i | −0.667526 | − | 0.744587i | \(-0.732647\pi\) |
−0.205801 | + | 0.978594i | \(0.565980\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 59.6490 | + | 34.4384i | 1.90058 | + | 1.09730i | ||||
\(986\) | 14.4777 | − | 3.87929i | 0.461064 | − | 0.123542i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.74777 | − | 9.06188i | −0.0874181 | − | 0.288297i | ||||
\(989\) | − | 11.6207i | − | 0.369516i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.249119 | + | 0.431486i | 0.00791352 | + | 0.0137066i | 0.869955 | − | 0.493131i | \(-0.164148\pi\) |
−0.862042 | + | 0.506838i | \(0.830814\pi\) | |||||||
\(992\) | 4.15933 | + | 7.20418i | 0.132059 | + | 0.228733i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 14.3812 | + | 14.3812i | 0.456145 | + | 0.456145i | ||||
\(995\) | 18.9798 | + | 18.9798i | 0.601702 | + | 0.601702i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.9952 | − | 34.6328i | −0.633255 | − | 1.09683i | −0.986882 | − | 0.161444i | \(-0.948385\pi\) |
0.353626 | − | 0.935387i | \(-0.384948\pi\) | |||||||
\(998\) | 3.04127 | + | 5.26764i | 0.0962698 | + | 0.166744i | ||||
\(999\) | 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 | 351.2.ba.a.89.9 | 48 | ||
3.2 | odd | 2 | 117.2.x.a.11.4 | ✓ | 48 | ||
9.4 | even | 3 | 117.2.bc.a.50.9 | yes | 48 | ||
9.5 | odd | 6 | 351.2.bf.a.206.4 | 48 | |||
13.6 | odd | 12 | 351.2.bf.a.305.4 | 48 | |||
39.32 | even | 12 | 117.2.bc.a.110.9 | yes | 48 | ||
117.32 | even | 12 | inner | 351.2.ba.a.71.9 | 48 | ||
117.58 | odd | 12 | 117.2.x.a.32.4 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.2.x.a.11.4 | ✓ | 48 | 3.2 | odd | 2 | ||
117.2.x.a.32.4 | yes | 48 | 117.58 | odd | 12 | ||
117.2.bc.a.50.9 | yes | 48 | 9.4 | even | 3 | ||
117.2.bc.a.110.9 | yes | 48 | 39.32 | even | 12 | ||
351.2.ba.a.71.9 | 48 | 117.32 | even | 12 | inner | ||
351.2.ba.a.89.9 | 48 | 1.1 | even | 1 | trivial | ||
351.2.bf.a.206.4 | 48 | 9.5 | odd | 6 | |||
351.2.bf.a.305.4 | 48 | 13.6 | odd | 12 |