Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,2,Mod(47,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.y (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: | \(4.59938315643\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 335.18 | ||
Character | \(\chi\) | \(=\) | 576.335 |
Dual form | 576.2.y.a.239.18 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | 0 | ||||||||
\(3\) | 1.36987 | − | 1.05993i | 0.790895 | − | 0.611952i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.78704 | − | 0.746784i | −1.24640 | − | 0.333972i | −0.425456 | − | 0.904979i | \(-0.639886\pi\) |
−0.820945 | + | 0.571007i | \(0.806553\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.16672 | + | 2.02082i | −0.440979 | + | 0.763799i | −0.997762 | − | 0.0668592i | \(-0.978702\pi\) |
0.556783 | + | 0.830658i | \(0.312036\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.753089 | − | 2.90394i | 0.251030 | − | 0.967979i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.53982 | + | 1.48439i | −1.67032 | + | 0.447560i | −0.965196 | − | 0.261527i | \(-0.915774\pi\) |
−0.705121 | + | 0.709087i | \(0.749107\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.90572 | − | 1.04654i | −1.08325 | − | 0.290257i | −0.327325 | − | 0.944912i | \(-0.606147\pi\) |
−0.755928 | + | 0.654655i | \(0.772814\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.60942 | + | 1.93107i | −1.19015 | + | 0.498601i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.45489i | − | 1.56554i | −0.622310 | − | 0.782771i | \(-0.713806\pi\) | ||
0.622310 | − | 0.782771i | \(-0.286194\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.50499 | + | 1.50499i | 0.345267 | + | 0.345267i | 0.858343 | − | 0.513076i | \(-0.171494\pi\) |
−0.513076 | + | 0.858343i | \(0.671494\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.543676 | + | 4.00491i | 0.118640 | + | 0.873943i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.0418190 | − | 0.0241442i | 0.00871987 | − | 0.00503442i | −0.495634 | − | 0.868532i | \(-0.665064\pi\) |
0.504354 | + | 0.863497i | \(0.331731\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.87976 | + | 1.66263i | 0.575952 | + | 0.332526i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.04634 | − | 4.77624i | −0.393819 | − | 0.919188i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.08507 | + | 1.36254i | −0.944274 | + | 0.253018i | −0.697931 | − | 0.716165i | \(-0.745896\pi\) |
−0.246343 | + | 0.969183i | \(0.579229\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.65029 | − | 0.952797i | 0.296401 | − | 0.171127i | −0.344424 | − | 0.938814i | \(-0.611926\pi\) |
0.640825 | + | 0.767687i | \(0.278592\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.01548 | + | 7.90525i | −1.04716 | + | 1.37613i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.76082 | − | 4.76082i | 0.804725 | − | 0.804725i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.489763 | + | 0.489763i | 0.0805165 | + | 0.0805165i | 0.746218 | − | 0.665702i | \(-0.231868\pi\) |
−0.665702 | + | 0.746218i | \(0.731868\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.45959 | + | 2.70618i | −1.03436 | + | 0.433336i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.0155357 | + | 0.0269087i | 0.00242628 | + | 0.00420243i | 0.867236 | − | 0.497897i | \(-0.165894\pi\) |
−0.864810 | + | 0.502100i | \(0.832561\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.01892 | + | 3.80267i | 0.155384 | + | 0.579901i | 0.999072 | + | 0.0430675i | \(0.0137130\pi\) |
−0.843688 | + | 0.536834i | \(0.819620\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.26750 | + | 7.53099i | −0.636162 | + | 1.12265i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.0913288 | + | 0.158186i | −0.0133217 | + | 0.0230738i | −0.872609 | − | 0.488419i | \(-0.837574\pi\) |
0.859288 | + | 0.511493i | \(0.170907\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.777520 | + | 1.34670i | 0.111074 | + | 0.192386i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.84175 | − | 8.84237i | −0.958036 | − | 1.23818i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.62061 | − | 6.62061i | 0.909411 | − | 0.909411i | −0.0868136 | − | 0.996225i | \(-0.527668\pi\) |
0.996225 | + | 0.0868136i | \(0.0276684\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.5482 | 2.23136 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.65682 | + | 0.466453i | 0.484357 | + | 0.0617832i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.11363 | + | 4.15614i | −0.144983 | + | 0.541083i | 0.854773 | + | 0.519001i | \(0.173696\pi\) |
−0.999756 | + | 0.0220815i | \(0.992971\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.71427 | − | 6.39775i | −0.219490 | − | 0.819148i | −0.984537 | − | 0.175174i | \(-0.943951\pi\) |
0.765047 | − | 0.643974i | \(-0.222716\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.98970 | + | 4.90995i | 0.628643 | + | 0.618595i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.1039 | + | 5.83347i | 1.25323 | + | 0.723552i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.216578 | + | 0.808279i | −0.0264592 | + | 0.0987470i | −0.977893 | − | 0.209107i | \(-0.932944\pi\) |
0.951434 | + | 0.307854i | \(0.0996109\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.0316954 | − | 0.0773998i | 0.00381568 | − | 0.00931784i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.04372i | 0.123867i | 0.998080 | + | 0.0619333i | \(0.0197266\pi\) | ||||
−0.998080 | + | 0.0619333i | \(0.980273\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.74654i | 0.555540i | 0.960648 | + | 0.277770i | \(0.0895953\pi\) | ||||
−0.960648 | + | 0.277770i | \(0.910405\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.70717 | − | 0.774762i | 0.659008 | − | 0.0894618i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.46374 | − | 12.9269i | 0.394730 | − | 1.47315i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.29908 | − | 4.21413i | −0.821211 | − | 0.474126i | 0.0296228 | − | 0.999561i | \(-0.490569\pi\) |
−0.850834 | + | 0.525435i | \(0.823903\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.86571 | − | 4.37385i | −0.873968 | − | 0.485983i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.20973 | − | 11.9789i | −0.352313 | − | 1.31485i | −0.883832 | − | 0.467805i | \(-0.845045\pi\) |
0.531519 | − | 0.847047i | \(-0.321622\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.82041 | + | 17.9900i | −0.522847 | + | 1.95129i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.52169 | + | 7.25633i | −0.591987 | + | 0.777961i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.85193 | 0.302304 | 0.151152 | − | 0.988511i | \(-0.451702\pi\) | ||||
0.151152 | + | 0.988511i | \(0.451702\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.67175 | − | 6.67175i | 0.699390 | − | 0.699390i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.25079 | − | 3.05441i | 0.129701 | − | 0.316727i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.07055 | − | 5.31835i | −0.315032 | − | 0.545651i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.29818 | − | 5.71262i | 0.334880 | − | 0.580028i | −0.648582 | − | 0.761145i | \(-0.724638\pi\) |
0.983462 | + | 0.181116i | \(0.0579710\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.138600 | + | 17.2052i | 0.0139299 | + | 1.72918i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.15095 | − | 8.02745i | −0.214027 | − | 0.798761i | −0.986507 | − | 0.163721i | \(-0.947650\pi\) |
0.772479 | − | 0.635040i | \(-0.219016\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.39607 | − | 5.88217i | −0.334625 | − | 0.579588i | 0.648788 | − | 0.760970i | \(-0.275276\pi\) |
−0.983413 | + | 0.181382i | \(0.941943\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.47556 | − | 11.5678i | 0.144000 | − | 1.12891i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.9162 | − | 11.9162i | −1.15198 | − | 1.15198i | −0.986155 | − | 0.165828i | \(-0.946970\pi\) |
−0.165828 | − | 0.986155i | \(-0.553030\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.518803 | + | 0.518803i | −0.0496923 | + | 0.0496923i | −0.731516 | − | 0.681824i | \(-0.761187\pi\) |
0.681824 | + | 0.731516i | \(0.261187\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.19003 | + | 0.151796i | 0.112952 | + | 0.0144079i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.60012 | + | 5.54263i | −0.903103 | + | 0.521407i | −0.878206 | − | 0.478283i | \(-0.841259\pi\) |
−0.0248974 | + | 0.999690i | \(0.507926\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.134582 | + | 0.0360611i | −0.0125498 | + | 0.00336271i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.98043 | + | 10.5538i | −0.552891 | + | 0.975703i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.0442 | + | 7.53107i | 1.19576 | + | 0.690372i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.9599 | − | 10.9465i | 1.72362 | − | 0.995135i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.0498033 | + | 0.0203946i | 0.00449062 | + | 0.00183892i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.41689 | + | 3.41689i | 0.305616 | + | 0.305616i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.0823i | 1.07213i | 0.844176 | + | 0.536067i | \(0.180090\pi\) | ||||
−0.844176 | + | 0.536067i | \(0.819910\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.42636 | + | 4.12917i | 0.477764 | + | 0.363553i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.61991 | + | 0.702002i | 0.228902 | + | 0.0613342i | 0.371447 | − | 0.928454i | \(-0.378862\pi\) |
−0.142545 | + | 0.989788i | \(0.545528\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.79721 | + | 1.28541i | −0.415971 | + | 0.111459i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.13641 | + | 14.8397i | 0.183873 | + | 1.27720i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.51859 | + | 13.0226i | −0.642356 | + | 1.11259i | 0.342549 | + | 0.939500i | \(0.388710\pi\) |
−0.984905 | + | 0.173094i | \(0.944624\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.28951 | + | 2.22117i | 0.703107 | + | 0.188397i | 0.592622 | − | 0.805481i | \(-0.298093\pi\) |
0.110485 | + | 0.993878i | \(0.464760\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.0425579 | + | 0.313497i | 0.00358402 | + | 0.0264012i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 23.1905 | 1.93928 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.1898 | 1.26144 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.49251 | + | 1.02069i | 0.205579 | + | 0.0841852i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.977298 | − | 0.261866i | −0.0800634 | − | 0.0214529i | 0.218565 | − | 0.975822i | \(-0.429862\pi\) |
−0.298628 | + | 0.954369i | \(0.596529\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.29411 | − | 14.3658i | 0.674965 | − | 1.16907i | −0.301514 | − | 0.953462i | \(-0.597492\pi\) |
0.976479 | − | 0.215612i | \(-0.0691747\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −18.7446 | − | 4.86111i | −1.51541 | − | 0.392997i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.31096 | + | 1.42307i | −0.426587 | + | 0.114304i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.2306 | + | 5.68871i | 1.69438 | + | 0.454009i | 0.971515 | − | 0.236977i | \(-0.0761566\pi\) |
0.722868 | + | 0.690986i | \(0.242823\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.05198 | − | 16.0868i | 0.162733 | − | 1.27576i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.112678i | 0.00888030i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.153221 | − | 0.153221i | −0.0120012 | − | 0.0120012i | 0.701081 | − | 0.713082i | \(-0.252701\pi\) |
−0.713082 | + | 0.701081i | \(0.752701\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 22.6689 | − | 17.5400i | 1.76477 | − | 1.36548i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.83025 | + | 1.05669i | −0.141629 | + | 0.0817694i | −0.569140 | − | 0.822241i | \(-0.692724\pi\) |
0.427511 | + | 0.904010i | \(0.359390\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.90111 | + | 1.67495i | 0.223162 | + | 0.128843i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.50377 | − | 3.23700i | 0.420884 | − | 0.247539i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.17246 | − | 0.582108i | 0.165169 | − | 0.0442568i | −0.175287 | − | 0.984517i | \(-0.556085\pi\) |
0.340456 | + | 0.940261i | \(0.389419\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.71976 | + | 3.87966i | −0.507966 | + | 0.293274i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.87969 | + | 6.87374i | 0.216451 | + | 0.516662i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.33235 | + | 4.33235i | −0.323815 | + | 0.323815i | −0.850229 | − | 0.526413i | \(-0.823536\pi\) |
0.526413 | + | 0.850229i | \(0.323536\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.9507 | − | 13.9507i | −1.03695 | − | 1.03695i | −0.999291 | − | 0.0376558i | \(-0.988011\pi\) |
−0.0376558 | − | 0.999291i | \(-0.511989\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.12951 | − | 6.94708i | −0.674873 | − | 0.513543i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.999240 | − | 1.73073i | −0.0734656 | − | 0.127246i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.58157 | + | 35.7589i | 0.700674 | + | 2.61495i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.0394 | + | 1.43725i | 0.875741 | + | 0.104545i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.83161 | + | 6.63654i | −0.277246 | + | 0.480203i | −0.970699 | − | 0.240298i | \(-0.922755\pi\) |
0.693454 | + | 0.720501i | \(0.256088\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.79037 | − | 6.56511i | −0.272836 | − | 0.472567i | 0.696751 | − | 0.717314i | \(-0.254628\pi\) |
−0.969587 | + | 0.244747i | \(0.921295\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 20.0240 | − | 2.71831i | 1.43395 | − | 0.194662i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.6000 | − | 12.6000i | 0.897715 | − | 0.897715i | −0.0975188 | − | 0.995234i | \(-0.531091\pi\) |
0.995234 | + | 0.0975188i | \(0.0310906\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.1095 | −1.63819 | −0.819096 | − | 0.573656i | \(-0.805524\pi\) | ||||
−0.819096 | + | 0.573656i | \(0.805524\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.560037 | + | 1.33679i | 0.0395020 | + | 0.0942902i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.17941 | − | 11.8657i | 0.223151 | − | 0.832811i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.0232037 | − | 0.0865974i | −0.00162062 | − | 0.00604822i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.0386199 | − | 0.139623i | −0.00268427 | − | 0.00970444i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.5713 | − | 6.10336i | −0.731234 | − | 0.422178i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.42605 | + | 12.7862i | −0.235859 | + | 0.880238i | 0.741901 | + | 0.670510i | \(0.233925\pi\) |
−0.977760 | + | 0.209728i | \(0.932742\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.10627 | + | 1.42976i | 0.0758004 | + | 0.0979654i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 11.3591i | − | 0.774683i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.44660i | 0.301855i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.03100 | + | 6.50214i | 0.339964 | + | 0.439374i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.75527 | + | 25.2110i | −0.454409 | + | 1.69588i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.1219 | − | 8.15328i | −0.945672 | − | 0.545984i | −0.0539380 | − | 0.998544i | \(-0.517177\pi\) |
−0.891734 | + | 0.452561i | \(0.850511\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.99689 | − | 7.11054i | 0.466460 | − | 0.474036i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.96068 | + | 22.2456i | 0.395624 | + | 1.47649i | 0.820714 | + | 0.571339i | \(0.193576\pi\) |
−0.425090 | + | 0.905151i | \(0.639758\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.05838 | + | 18.8781i | −0.334267 | + | 1.24750i | 0.570394 | + | 0.821371i | \(0.306791\pi\) |
−0.904661 | + | 0.426131i | \(0.859876\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.95671 | − | 21.3794i | −0.589308 | − | 1.40666i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.4018 | −1.20554 | −0.602771 | − | 0.797914i | \(-0.705937\pi\) | ||||
−0.602771 | + | 0.797914i | \(0.705937\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.372668 | − | 0.372668i | 0.0243102 | − | 0.0243102i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.4655 | + | 1.96372i | −0.939634 | + | 0.127558i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.4328 | − | 21.5343i | −0.804212 | − | 1.39294i | −0.916821 | − | 0.399298i | \(-0.869254\pi\) |
0.112609 | − | 0.993639i | \(-0.464079\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.256221 | − | 0.443788i | 0.0165047 | − | 0.0285869i | −0.857655 | − | 0.514225i | \(-0.828079\pi\) |
0.874160 | + | 0.485638i | \(0.161413\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.4110 | + | 2.34552i | −0.988615 | + | 0.150465i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.16128 | − | 4.33395i | −0.0741914 | − | 0.276886i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.30304 | − | 7.45308i | −0.273796 | − | 0.474228i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −17.0937 | − | 13.0074i | −1.08327 | − | 0.824310i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.88443 | + | 7.88443i | 0.497661 | + | 0.497661i | 0.910709 | − | 0.413048i | \(-0.135536\pi\) |
−0.413048 | + | 0.910709i | \(0.635536\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.195830 | + | 0.195830i | −0.0123117 | + | 0.0123117i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.4649 | + | 29.7533i | 0.780580 | + | 1.86322i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.6490 | − | 6.14820i | 0.664266 | − | 0.383514i | −0.129635 | − | 0.991562i | \(-0.541380\pi\) |
0.793900 | + | 0.608048i | \(0.208047\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.56114 | + | 0.418306i | −0.0970046 | + | 0.0259923i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.127223 | + | 15.7928i | 0.00787492 | + | 0.977553i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.46535 | + | 4.88747i | 0.521996 | + | 0.301375i | 0.737751 | − | 0.675073i | \(-0.235888\pi\) |
−0.215755 | + | 0.976448i | \(0.569221\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −23.3961 | + | 13.5077i | −1.43721 | + | 0.829773i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.90677 | − | 3.02285i | 0.239091 | − | 0.184995i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.64229 | + | 5.64229i | 0.344016 | + | 0.344016i | 0.857875 | − | 0.513859i | \(-0.171784\pi\) |
−0.513859 | + | 0.857875i | \(0.671784\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 11.0524i | − | 0.671386i | −0.941971 | − | 0.335693i | \(-0.891029\pi\) | ||
0.941971 | − | 0.335693i | \(-0.108971\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.06783 | − | 16.2110i | 0.125151 | − | 0.981137i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −18.4213 | − | 4.93598i | −1.11085 | − | 0.297651i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.2727 | − | 6.77180i | 1.51849 | − | 0.406878i | 0.599246 | − | 0.800565i | \(-0.295467\pi\) |
0.919245 | + | 0.393687i | \(0.128801\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.52405 | − | 5.50989i | −0.0912423 | − | 0.329869i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.8442 | + | 22.2468i | −0.766219 | + | 1.32713i | 0.173381 | + | 0.984855i | \(0.444531\pi\) |
−0.939600 | + | 0.342275i | \(0.888802\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −31.3627 | − | 8.40360i | −1.86432 | − | 0.499542i | −0.864323 | − | 0.502937i | \(-0.832253\pi\) |
−0.999994 | + | 0.00339463i | \(0.998919\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.84335 | − | 4.03088i | −0.583070 | − | 0.238768i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.0725036 | −0.00427975 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −24.6657 | −1.45092 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.53690 | − | 11.3214i | −0.0900950 | − | 0.663672i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.0583 | − | 5.91051i | −1.28866 | − | 0.345296i | −0.451510 | − | 0.892266i | \(-0.649114\pi\) |
−0.837152 | + | 0.546971i | \(0.815781\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.20747 | − | 10.7517i | 0.361413 | − | 0.625986i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.4262 | + | 23.4219i | 1.06919 | + | 1.35908i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.188601 | + | 0.0505356i | −0.0109071 | + | 0.00292255i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.87331 | − | 2.37760i | −0.511449 | − | 0.137042i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.4551 | − | 8.71670i | −0.658076 | − | 0.500761i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.1110i | 1.09429i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.3124 | − | 10.3124i | −0.588560 | − | 0.588560i | 0.348681 | − | 0.937241i | \(-0.386630\pi\) |
−0.937241 | + | 0.348681i | \(0.886630\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.8869 | − | 4.45821i | −0.619333 | − | 0.253619i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.887812 | − | 0.512578i | 0.0503432 | − | 0.0290656i | −0.474617 | − | 0.880192i | \(-0.657413\pi\) |
0.524960 | + | 0.851127i | \(0.324080\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.53399 | + | 5.50445i | 0.538893 | + | 0.311130i | 0.744630 | − | 0.667477i | \(-0.232626\pi\) |
−0.205737 | + | 0.978607i | \(0.565959\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10.2398 | − | 17.4104i | −0.576947 | − | 0.980967i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.3465 | − | 4.91593i | 1.03044 | − | 0.276106i | 0.296295 | − | 0.955096i | \(-0.404249\pi\) |
0.734147 | + | 0.678990i | \(0.237582\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 26.1478 | − | 15.0965i | 1.46400 | − | 0.845239i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −28.9540 | − | 3.69329i | −1.61605 | − | 0.206139i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.71452 | − | 9.71452i | 0.540531 | − | 0.540531i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.50755 | − | 9.50755i | −0.527384 | − | 0.527384i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.160797 | + | 1.26059i | −0.00889210 | + | 0.0697107i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.213111 | − | 0.369119i | −0.0117492 | − | 0.0203502i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.94329 | − | 18.4486i | −0.271708 | − | 1.01403i | −0.958015 | − | 0.286716i | \(-0.907436\pi\) |
0.686307 | − | 0.727312i | \(-0.259230\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.79108 | − | 1.05341i | 0.0981504 | − | 0.0577263i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.20722 | − | 2.09097i | 0.0659575 | − | 0.114242i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.6805 | − | 25.4274i | −0.799699 | − | 1.38512i | −0.919812 | − | 0.392359i | \(-0.871659\pi\) |
0.120113 | − | 0.992760i | \(-0.461674\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.27610 | + | 17.7682i | −0.395184 | + | 0.965034i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.72800 | + | 7.72800i | −0.418495 | + | 0.418495i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.9627 | −1.07788 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.146137 | + | 0.192046i | −0.00786776 | + | 0.0103394i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.49514 | + | 20.5081i | −0.294995 | + | 1.10093i | 0.646227 | + | 0.763145i | \(0.276346\pi\) |
−0.941222 | + | 0.337789i | \(0.890321\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.64137 | − | 24.7859i | −0.355504 | − | 1.32676i | −0.879849 | − | 0.475254i | \(-0.842356\pi\) |
0.524345 | − | 0.851506i | \(-0.324310\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.99394 | + | 20.7962i | 0.159805 | + | 1.11002i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.1119 | + | 11.0343i | 1.01723 | + | 0.587296i | 0.913299 | − | 0.407289i | \(-0.133526\pi\) |
0.103927 | + | 0.994585i | \(0.466859\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.779432 | − | 2.90888i | 0.0413680 | − | 0.154387i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 25.8513 | − | 3.50937i | 1.36819 | − | 0.185735i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.1522i | 0.694145i | 0.937838 | + | 0.347073i | \(0.112824\pi\) | ||||
−0.937838 | + | 0.347073i | \(0.887176\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 14.4700i | − | 0.761581i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.3700 | − | 35.0914i | 0.754231 | − | 1.84182i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.54464 | − | 13.2288i | 0.185535 | − | 0.692425i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.13483 | + | 2.96459i | 0.268036 | + | 0.154751i | 0.627995 | − | 0.778218i | \(-0.283876\pi\) |
−0.359959 | + | 0.932968i | \(0.617209\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.0898410 | − | 0.0248502i | 0.00467694 | − | 0.00129365i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.65466 | + | 21.1035i | 0.293575 | + | 1.09564i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.31148 | − | 34.7509i | 0.482130 | − | 1.79933i | −0.110520 | − | 0.993874i | \(-0.535252\pi\) |
0.592650 | − | 0.805460i | \(-0.298082\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.30237 | + | 1.05903i | 0.428732 | + | 0.0546878i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21.2868 | 1.09633 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.54655 | + | 4.54655i | −0.233540 | + | 0.233540i | −0.814169 | − | 0.580628i | \(-0.802807\pi\) |
0.580628 | + | 0.814169i | \(0.302807\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.8064 | + | 16.5512i | 0.656094 | + | 0.847945i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.4216 | + | 28.4430i | 0.839104 | + | 1.45337i | 0.890645 | + | 0.454700i | \(0.150253\pi\) |
−0.0515410 | + | 0.998671i | \(0.516413\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −19.3071 | + | 33.4409i | −0.983983 | + | 1.70431i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.8100 | − | 0.0951387i | 0.600338 | − | 0.00483617i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.46615 | + | 31.5961i | 0.429251 | + | 1.60199i | 0.754462 | + | 0.656344i | \(0.227898\pi\) |
−0.325211 | + | 0.945641i | \(0.605435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.155848 | − | 0.269937i | −0.00788159 | − | 0.0136513i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.33301 | − | 1.81527i | 0.218571 | − | 0.0915683i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 17.1958 | + | 17.1958i | 0.865213 | + | 0.865213i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.7370 | + | 26.7370i | −1.34189 | + | 1.34189i | −0.447720 | + | 0.894174i | \(0.647764\pi\) |
−0.894174 | + | 0.447720i | \(0.852236\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.20911 | + | 6.84556i | −0.260782 | + | 0.342706i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.15088 | − | 1.24181i | 0.107410 | − | 0.0620130i | −0.445333 | − | 0.895365i | \(-0.646915\pi\) |
0.552743 | + | 0.833352i | \(0.313581\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.44272 | + | 1.99427i | −0.370748 | + | 0.0993418i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.6557 | + | 18.0641i | 0.927010 | + | 0.897611i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.44020 | − | 1.98620i | −0.170524 | − | 0.0984522i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.04923 | − | 3.49252i | 0.299115 | − | 0.172694i | −0.342930 | − | 0.939361i | \(-0.611419\pi\) |
0.642045 | + | 0.766667i | \(0.278086\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.50355 | + | 25.8084i | 0.172818 | + | 1.27304i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.09951 | − | 7.09951i | −0.349344 | − | 0.349344i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 35.7825i | 1.75649i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.7098 | − | 5.74361i | 0.671374 | − | 0.281266i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.1858 | − | 7.82032i | −1.42582 | − | 0.382048i | −0.538276 | − | 0.842768i | \(-0.680924\pi\) |
−0.887545 | + | 0.460721i | \(0.847591\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.2445 | + | 8.37195i | −1.52277 | + | 0.408024i | −0.920651 | − | 0.390386i | \(-0.872341\pi\) |
−0.602114 | + | 0.798410i | \(0.705675\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.390584 | + | 0.384342i | 0.0189909 | + | 0.0186873i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.7321 | − | 18.5885i | 0.520584 | − | 0.901677i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.9288 | + | 4.00016i | 0.722455 | + | 0.193581i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 31.7679 | − | 24.5803i | 1.53377 | − | 1.18675i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.2342 | −1.45633 | −0.728164 | − | 0.685403i | \(-0.759626\pi\) | ||||
−0.728164 | + | 0.685403i | \(0.759626\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.5522 | 1.66047 | 0.830237 | − | 0.557410i | \(-0.188205\pi\) | ||||
0.830237 | + | 0.557410i | \(0.188205\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 20.8081 | − | 16.1002i | 0.997670 | − | 0.771944i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.0992738 | + | 0.0266003i | 0.00474891 | + | 0.00127247i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.65747 | + | 2.87082i | −0.0791066 | + | 0.137017i | −0.902865 | − | 0.429925i | \(-0.858540\pi\) |
0.823758 | + | 0.566941i | \(0.191873\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.49629 | − | 1.24368i | 0.214109 | − | 0.0592229i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.4752 | + | 4.14656i | −0.735248 | + | 0.197009i | −0.606965 | − | 0.794729i | \(-0.707613\pi\) |
−0.128283 | + | 0.991738i | \(0.540947\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.94843 | − | 2.12977i | −0.376792 | − | 0.100961i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.61633 | + | 0.677147i | −0.0764499 | + | 0.0320279i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 11.1511i | − | 0.526253i | −0.964761 | − | 0.263126i | \(-0.915246\pi\) | ||
0.964761 | − | 0.263126i | \(-0.0847536\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.126008 | − | 0.126008i | −0.00593349 | − | 0.00593349i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.86494 | − | 28.4705i | −0.181591 | − | 1.33766i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −23.5768 | + | 13.6121i | −1.10530 | + | 0.638143i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.6193 | − | 11.9046i | −0.964530 | − | 0.556872i | −0.0669658 | − | 0.997755i | \(-0.521332\pi\) |
−0.897564 | + | 0.440884i | \(0.854665\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −30.8301 | + | 13.2089i | −1.43903 | + | 0.616540i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.5986 | − | 3.10783i | 0.540199 | − | 0.144746i | 0.0216051 | − | 0.999767i | \(-0.493122\pi\) |
0.518594 | + | 0.855021i | \(0.326456\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.7247 | − | 6.76924i | 0.544892 | − | 0.314593i | −0.202168 | − | 0.979351i | \(-0.564799\pi\) |
0.747059 | + | 0.664758i | \(0.231465\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.76697 | + | 7.57868i | −0.267437 | + | 0.351453i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.6000 | − | 11.6000i | 0.536784 | − | 0.536784i | −0.385799 | − | 0.922583i | \(-0.626074\pi\) |
0.922583 | + | 0.385799i | \(0.126074\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.38070 | − | 1.38070i | −0.0637549 | − | 0.0637549i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 35.1128 | − | 14.7102i | 1.61791 | − | 0.677808i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.2893 | − | 19.5536i | −0.519081 | − | 0.899075i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.83176 | + | 6.83624i | 0.0840471 | + | 0.313668i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.2399 | − | 24.2118i | −0.652002 | − | 1.10858i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.09571 | − | 3.62988i | 0.0957555 | − | 0.165853i | −0.814168 | − | 0.580629i | \(-0.802807\pi\) |
0.909924 | + | 0.414776i | \(0.136140\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.40032 | − | 2.42543i | −0.0638493 | − | 0.110590i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.119431 | + | 0.154355i | 0.00543432 | + | 0.00702338i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.4582 | + | 13.4582i | −0.611107 | + | 0.611107i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.7152 | 1.21058 | 0.605291 | − | 0.796004i | \(-0.293057\pi\) | ||||
0.605291 | + | 0.796004i | \(0.293057\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.372296 | − | 0.0474890i | −0.0168358 | − | 0.00214753i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.681269 | − | 2.54253i | 0.0307452 | − | 0.114743i | −0.948848 | − | 0.315733i | \(-0.897749\pi\) |
0.979593 | + | 0.200991i | \(0.0644161\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.79506 | + | 32.8236i | 0.396109 | + | 1.47830i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.4623 | − | 48.0549i | 0.560137 | − | 2.15991i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.10917 | − | 1.21773i | −0.0946091 | − | 0.0546226i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.46533 | − | 9.20074i | 0.110363 | − | 0.411882i | −0.888535 | − | 0.458809i | \(-0.848276\pi\) |
0.998898 | + | 0.0469272i | \(0.0149429\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.38718 | + | 3.38747i | −0.0619745 | + | 0.151341i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.5953i | 0.517010i | 0.966010 | + | 0.258505i | \(0.0832299\pi\) | ||||
−0.966010 | + | 0.258505i | \(0.916770\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.9791i | 1.06706i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.74948 | − | 0.780505i | 0.255343 | − | 0.0346634i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.97882 | − | 11.1171i | 0.132034 | − | 0.492757i | −0.867959 | − | 0.496637i | \(-0.834568\pi\) |
0.999992 | + | 0.00387934i | \(0.00123484\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.59190 | − | 5.53789i | −0.424321 | − | 0.244982i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.10846 | − | 10.2679i | 0.181393 | − | 0.453339i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.07227 | + | 18.9300i | 0.223511 | + | 0.834154i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.271135 | − | 1.01189i | 0.0119245 | − | 0.0445029i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.35899 | − | 3.10007i | 0.103548 | − | 0.136078i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.7808 | 0.559939 | 0.279969 | − | 0.960009i | \(-0.409676\pi\) | ||||
0.279969 | + | 0.960009i | \(0.409676\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.1010 | − | 22.1010i | 0.966409 | − | 0.966409i | −0.0330445 | − | 0.999454i | \(-0.510520\pi\) |
0.999454 | + | 0.0330445i | \(0.0105203\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.09303 | + | 12.4371i | −0.222278 | + | 0.542800i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.15020 | − | 10.6525i | −0.267907 | − | 0.464029i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.4988 | + | 19.9166i | −0.499949 | + | 0.865938i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.2305 | + | 6.36386i | 0.487362 | + | 0.276168i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.0325174 | − | 0.121357i | −0.00140849 | − | 0.00525654i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.3121 | + | 42.1097i | 1.05110 | + | 1.82056i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.34276 | + | 10.5268i | −0.0579445 | + | 0.454263i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.30635 | − | 6.30635i | −0.271634 | − | 0.271634i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.90029 | − | 4.90029i | 0.210680 | − | 0.210680i | −0.593876 | − | 0.804556i | \(-0.702403\pi\) |
0.804556 | + | 0.593876i | \(0.202403\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −33.8974 | − | 4.32385i | −1.45468 | − | 0.185554i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.83336 | − | 1.05849i | 0.0785324 | − | 0.0453407i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.1873 | − | 7.82071i | 1.24796 | − | 0.334390i | 0.426411 | − | 0.904529i | \(-0.359778\pi\) |
0.821548 | + | 0.570140i | \(0.193111\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −19.8697 | + | 0.160065i | −0.848017 | + | 0.00683141i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.70357 | − | 5.60236i | −0.413386 | − | 0.238668i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.0320 | − | 9.83343i | 0.724275 | − | 0.418160i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.20329 | − | 1.31176i | −0.135972 | − | 0.0556809i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.23259 | + | 5.23259i | 0.221712 | + | 0.221712i | 0.809219 | − | 0.587507i | \(-0.199891\pi\) |
−0.587507 | + | 0.809219i | \(0.699891\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 15.9185i | − | 0.673281i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 51.0275 | + | 38.8293i | 2.15438 | + | 1.63937i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.0312 | + | 6.70709i | 1.05494 | + | 0.282670i | 0.744291 | − | 0.667855i | \(-0.232787\pi\) |
0.310648 | + | 0.950525i | \(0.399454\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.8950 | − | 8.27830i | 1.29976 | − | 0.348271i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.0159 | − | 10.7921i | 0.756595 | − | 0.453227i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.2193 | − | 21.1644i | 0.512259 | − | 0.887259i | −0.487640 | − | 0.873045i | \(-0.662142\pi\) |
0.999899 | − | 0.0142138i | \(-0.00452456\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.29056 | − | 1.41760i | −0.221403 | − | 0.0593248i | 0.146412 | − | 0.989224i | \(-0.453227\pi\) |
−0.367815 | + | 0.929899i | \(0.619894\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.78548 | + | 13.1525i | 0.0745893 | + | 0.549452i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.160572 | 0.00669630 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.8956 | 0.786634 | 0.393317 | − | 0.919403i | \(-0.371327\pi\) | ||||
0.393317 | + | 0.919403i | \(0.371327\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.1509 | − | 4.97581i | −0.504973 | − | 0.206788i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27.9520 | + | 7.48972i | 1.15964 | + | 0.310726i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −26.8494 | + | 46.5045i | −1.11199 | + | 1.92602i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 24.5491 | − | 24.9479i | 1.01498 | − | 1.03147i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 40.3694 | − | 10.8169i | 1.66622 | − | 0.446463i | 0.702133 | − | 0.712045i | \(-0.252231\pi\) |
0.964088 | + | 0.265583i | \(0.0855643\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.91761 | + | 1.04972i | 0.161422 | + | 0.0432530i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.90523 | − | 30.6156i | 0.160640 | − | 1.25936i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.51816i | 0.349799i | 0.984586 | + | 0.174899i | \(0.0559600\pi\) | ||||
−0.984586 | + | 0.174899i | \(0.944040\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −30.7306 | − | 30.7306i | −1.25983 | − | 1.25983i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −31.6571 | + | 24.4945i | −1.29564 | + | 1.00249i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.1886 | − | 17.4294i | 1.23347 | − | 0.712145i | 0.265719 | − | 0.964051i | \(-0.414391\pi\) |
0.967752 | + | 0.251906i | \(0.0810573\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.4933 | − | 10.0997i | −0.713565 | − | 0.411977i | 0.0988146 | − | 0.995106i | \(-0.468495\pi\) |
−0.812380 | + | 0.583129i | \(0.801828\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.18409 | + | 1.23763i | 0.0889430 | + | 0.0504004i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −61.0165 | + | 16.3493i | −2.48067 | + | 0.664695i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.0948018 | + | 0.0547339i | −0.00384789 | + | 0.00222158i | −0.501923 | − | 0.864912i | \(-0.667374\pi\) |
0.498075 | + | 0.867134i | \(0.334040\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.22148 | − | 19.6245i | −0.333151 | − | 0.795224i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.522253 | − | 0.522253i | 0.0211281 | − | 0.0211281i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.4094 | + | 13.4094i | 0.541603 | + | 0.541603i | 0.923999 | − | 0.382396i | \(-0.124901\pi\) |
−0.382396 | + | 0.923999i | \(0.624901\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.123573 | − | 0.0940328i | −0.00498296 | − | 0.00379177i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.92944 | + | 3.34190i | 0.0776765 | + | 0.134540i | 0.902247 | − | 0.431219i | \(-0.141917\pi\) |
−0.824571 | + | 0.565759i | \(0.808583\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.30529 | − | 4.87142i | −0.0524642 | − | 0.195799i | 0.934720 | − | 0.355386i | \(-0.115650\pi\) |
−0.987184 | + | 0.159587i | \(0.948984\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.200895 | − | 0.150330i | −0.00806163 | − | 0.00603255i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.32741 | + | 5.76324i | −0.133310 | + | 0.230899i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.2845 | − | 26.4735i | −0.611379 | − | 1.05894i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −20.9505 | + | 2.84408i | −0.836682 | + | 0.113582i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.16137 | − | 3.16137i | 0.126052 | − | 0.126052i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.0513 | −1.31575 | −0.657876 | − | 0.753127i | \(-0.728545\pi\) | ||||
−0.657876 | + | 0.753127i | \(0.728545\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.85925 | + | 21.1468i | 0.352123 | + | 0.840510i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.02289 | − | 33.6739i | 0.358063 | − | 1.33631i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.62740 | − | 6.07355i | −0.0644801 | − | 0.240643i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.03089 | + | 0.786012i | 0.119900 | + | 0.0310942i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.03668 | + | 1.75323i | 0.119942 | + | 0.0692483i | 0.558770 | − | 0.829322i | \(-0.311273\pi\) |
−0.438829 | + | 0.898571i | \(0.644607\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.373234 | + | 1.39293i | −0.0147189 | + | 0.0549318i | −0.972895 | − | 0.231248i | \(-0.925719\pi\) |
0.958176 | + | 0.286180i | \(0.0923856\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.0399 | − | 15.5605i | −0.474069 | − | 0.612693i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.3282i | 0.681241i | 0.940201 | + | 0.340621i | \(0.110637\pi\) | ||||
−0.940201 | + | 0.340621i | \(0.889363\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 24.6773i | − | 0.968668i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.71309 | + | 6.09126i | 0.184721 | + | 0.238735i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.08794 | + | 4.06026i | −0.0425745 | + | 0.158890i | −0.983940 | − | 0.178497i | \(-0.942877\pi\) |
0.941366 | + | 0.337387i | \(0.109543\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.77753 | − | 3.91301i | −0.264820 | − | 0.152894i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.7836 | + | 3.57456i | 0.537751 | + | 0.139457i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.1404 | − | 45.3085i | −0.472922 | − | 1.76497i | −0.629187 | − | 0.777254i | \(-0.716612\pi\) |
0.156265 | − | 0.987715i | \(-0.450055\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.48771 | + | 31.6766i | −0.330134 | + | 1.23208i | 0.578915 | + | 0.815388i | \(0.303476\pi\) |
−0.909049 | + | 0.416689i | \(0.863191\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 17.4681 | + | 41.6960i | 0.678406 | + | 1.61934i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.3299 | 0.555690 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.179755 | + | 0.179755i | −0.00696015 | + | 0.00696015i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −27.9871 | + | 3.79931i | −1.08204 | + | 0.146890i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.9935 | + | 32.8977i | 0.733236 | + | 1.27000i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.37128 | + | 2.37512i | −0.0528588 | + | 0.0915541i | −0.891244 | − | 0.453524i | \(-0.850167\pi\) |
0.838385 | + | 0.545078i | \(0.183500\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.04815 | − | 17.1567i | 0.0788333 | − | 0.660363i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.17117 | + | 34.2273i | 0.352477 | + | 1.31546i | 0.883630 | + | 0.468185i | \(0.155092\pi\) |
−0.531154 | + | 0.847276i | \(0.678241\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.69612 | + | 13.3301i | 0.295350 | + | 0.511561i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 31.7441 | + | 24.1556i | 1.21644 | + | 0.925645i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.646566 | + | 0.646566i | 0.0247402 | + | 0.0247402i | 0.719369 | − | 0.694628i | \(-0.244431\pi\) |
−0.694628 | + | 0.719369i | \(0.744431\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 30.6796 | − | 30.6796i | 1.17221 | − | 1.17221i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.0802 | + | 31.2221i | 0.499041 | + | 1.19120i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −32.7870 | + | 18.9296i | −1.24908 | + | 0.721159i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.5305 | − | 9.25241i | 1.31360 | − | 0.351978i | 0.467024 | − | 0.884245i | \(-0.345326\pi\) |
0.846577 | + | 0.532266i | \(0.178659\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −34.9303 | − | 19.7936i | −1.32689 | − | 0.751895i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.4444 | − | 12.3810i | −0.813434 | − | 0.469636i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.173693 | − | 0.100282i | 0.00657908 | − | 0.00379844i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −25.2081 | + | 19.5047i | −0.953458 | + | 0.737734i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.7079 | − | 25.7079i | −0.970975 | − | 0.970975i | 0.0286153 | − | 0.999590i | \(-0.490890\pi\) |
−0.999590 | + | 0.0286153i | \(0.990890\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.47417i | 0.0555995i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.115504 | − | 0.905509i | 0.00435013 | − | 0.0341034i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.7316 | + | 5.01912i | 0.704474 | + | 0.188763i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.0199 | − | 6.43610i | 0.902085 | − | 0.241713i | 0.222173 | − | 0.975007i | \(-0.428685\pi\) |
0.679911 | + | 0.733294i | \(0.262018\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17.7344 | + | 18.0225i | −0.665093 | + | 0.675896i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.0460091 | − | 0.0796901i | 0.00172305 | − | 0.00298442i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −64.6326 | − | 17.3183i | −2.41712 | − | 0.647666i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −39.8562 | − | 16.3212i | −1.48846 | − | 0.609527i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.00765 | −0.112167 | −0.0560833 | − | 0.998426i | \(-0.517861\pi\) | ||||
−0.0560833 | + | 0.998426i | \(0.517861\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.8491 | 0.590251 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.119395 | − | 0.879510i | −0.00444036 | − | 0.0327093i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16.9092 | − | 4.53080i | −0.627992 | − | 0.168270i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.1265 | − | 33.1281i | 0.709363 | − | 1.22865i | −0.255730 | − | 0.966748i | \(-0.582316\pi\) |
0.965094 | − | 0.261905i | \(-0.0843507\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.6250 | + | 19.5477i | −0.689814 | + | 0.723987i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.5458 | − | 6.57703i | 0.907859 | − | 0.243260i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.4887 | − | 3.07838i | −0.424343 | − | 0.113702i | 0.0403263 | − | 0.999187i | \(-0.487160\pi\) |
−0.464670 | + | 0.885484i | \(0.653827\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.18449 | − | 4.70608i | −0.228119 | − | 0.173586i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 4.79920i | − | 0.176781i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.0692 | + | 30.0692i | 1.10611 | + | 1.10611i | 0.993657 | + | 0.112457i | \(0.0358720\pi\) |
0.112457 | + | 0.993657i | \(0.464128\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.7944 | − | 5.64883i | −0.506748 | − | 0.207515i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.00273 | − | 2.31098i | 0.146846 | − | 0.0847815i | −0.424777 | − | 0.905298i | \(-0.639647\pi\) |
0.571623 | + | 0.820517i | \(0.306314\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.52821 | + | 1.45966i | 0.0926264 | + | 0.0534779i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −37.2031 | + | 0.299699i | −1.36119 | + | 0.0109654i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 37.9834 | − | 10.1776i | 1.38788 | − | 0.371882i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.7097 | + | 6.18323i | −0.390801 | + | 0.225629i | −0.682507 | − | 0.730879i | \(-0.739110\pi\) |
0.291706 | + | 0.956508i | \(0.405777\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.1576 | + | 2.44369i | 0.698142 | + | 0.0890529i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −33.8442 | + | 33.8442i | −1.23172 | + | 1.23172i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.8033 | + | 15.8033i | 0.574380 | + | 0.574380i | 0.933349 | − | 0.358969i | \(-0.116872\pi\) |
−0.358969 | + | 0.933349i | \(0.616872\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.0606953 | + | 0.475829i | −0.00220310 | + | 0.0172715i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.67823 | − | 6.37089i | −0.133336 | − | 0.230944i | 0.791625 | − | 0.611008i | \(-0.209236\pi\) |
−0.924961 | + | 0.380063i | \(0.875902\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.443110 | − | 1.65371i | −0.0160416 | − | 0.0598682i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 48.6117 | + | 27.5463i | 1.75756 | + | 0.995938i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.69908 | − | 15.0673i | 0.314106 | − | 0.544047i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.792301 | + | 1.37231i | 0.0285711 | + | 0.0494866i | 0.879957 | − | 0.475053i | \(-0.157571\pi\) |
−0.851386 | + | 0.524539i | \(0.824238\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.07107 | − | 19.7094i | 0.290672 | − | 0.709818i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.11545 | + | 6.11545i | −0.219958 | + | 0.219958i | −0.808481 | − | 0.588523i | \(-0.799710\pi\) |
0.588523 | + | 0.808481i | \(0.299710\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.33660 | 0.227617 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.69518 | + | 2.22773i | −0.0608144 | + | 0.0799193i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.0171161 | + | 0.0638783i | −0.000613249 | + | 0.00228868i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.54928 | − | 5.78201i | −0.0554377 | − | 0.206896i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 16.9136 | + | 21.4993i | 0.604444 | + | 0.768323i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −54.9221 | − | 31.7093i | −1.96025 | − | 1.13175i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.49992 | + | 27.9901i | −0.267343 | + | 0.997739i | 0.693457 | + | 0.720498i | \(0.256087\pi\) |
−0.960800 | + | 0.277241i | \(0.910580\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.7768 | − | 2.27749i | 0.597271 | − | 0.0810809i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 25.8668i | − | 0.919719i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.7819i | 0.951053i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −17.7323 | + | 43.3021i | −0.628900 | + | 1.53577i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.6075 | + | 43.3197i | −0.411158 | + | 1.53446i | 0.381250 | + | 0.924472i | \(0.375494\pi\) |
−0.792408 | + | 0.609991i | \(0.791173\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.02107 | + | 0.589518i | 0.0361230 | + | 0.0208556i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.14776 | − | 8.28182i | 0.0758872 | − | 0.292624i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.04571 | − | 26.2949i | −0.248638 | − | 0.927928i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0841464 | − | 0.314039i | 0.00296577 | − | 0.0110684i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.7096 | + | 1.74876i | 0.482602 | + | 0.0615593i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.6588 | 0.620851 | 0.310426 | − | 0.950598i | \(-0.399528\pi\) | ||||
0.310426 | + | 0.950598i | \(0.399528\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.326636 | − | 0.326636i | 0.0114697 | − | 0.0114697i | −0.701349 | − | 0.712818i | \(-0.747418\pi\) |
0.712818 | + | 0.701349i | \(0.247418\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.7148 | − | 15.1404i | −0.410856 | − | 0.530996i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.312609 | + | 0.541455i | 0.0109502 | + | 0.0189663i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.18950 | + | 7.25642i | −0.146572 | + | 0.253870i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14.3499 | − | 24.3988i | −0.501427 | − | 0.852563i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.5662 | − | 39.4337i | −0.368764 | − | 1.37625i | −0.862246 | − | 0.506490i | \(-0.830943\pi\) |
0.493482 | − | 0.869756i | \(-0.335724\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.27150 | − | 5.66640i | −0.114037 | − | 0.197518i | 0.803357 | − | 0.595497i | \(-0.203045\pi\) |
−0.917394 | + | 0.397979i | \(0.869712\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −30.4666 | + | 12.7637i | −1.06071 | + | 0.444375i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.510932 | + | 0.510932i | 0.0177668 | + | 0.0177668i | 0.715934 | − | 0.698168i | \(-0.246001\pi\) |
−0.698168 | + | 0.715934i | \(0.746001\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.210205 | − | 0.210205i | 0.00730073 | − | 0.00730073i | −0.703447 | − | 0.710748i | \(-0.748357\pi\) |
0.710748 | + | 0.703447i | \(0.248357\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.4427 | − | 36.0639i | 0.951976 | − | 1.25104i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.69283 | − | 5.01881i | 0.301189 | − | 0.173891i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.89009 | − | 1.57824i | 0.203835 | − | 0.0546174i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.92785 | − | 5.93245i | −0.274027 | − | 0.205055i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.1098 | − | 14.4971i | −0.866885 | − | 0.500496i | −0.000573152 | − | 1.00000i | \(-0.500182\pi\) |
−0.866312 | + | 0.499504i | \(0.833516\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.11330 | + | 0.642762i | −0.0383895 | + | 0.0221642i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.98520 | + | 44.0891i | 0.206141 | + | 1.51851i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.83466 | − | 6.83466i | −0.235119 | − | 0.235119i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 51.0860i | 1.75534i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −51.8700 | + | 21.7304i | −1.78018 | + | 0.745787i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.0323063 | + | 0.00865646i | 0.00110745 | + | 0.000296740i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.1702 | − | 7.28025i | 0.930292 | − | 0.249271i | 0.238313 | − | 0.971189i | \(-0.423406\pi\) |
0.691979 | + | 0.721918i | \(0.256739\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −17.7566 | + | 4.91150i | −0.607262 | + | 0.167970i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.3745 | − | 49.1461i | 0.969256 | − | 1.67880i | 0.271537 | − | 0.962428i | \(-0.412468\pi\) |
0.697719 | − | 0.716372i | \(-0.254198\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.27967 | + | 1.68263i | 0.214259 | + | 0.0574106i | 0.364352 | − | 0.931261i | \(-0.381291\pi\) |
−0.150093 | + | 0.988672i | \(0.547957\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.0993205 | + | 0.0768489i | −0.00338483 | + | 0.00261900i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.7093 | −0.432629 | −0.216314 | − | 0.976324i | \(-0.569404\pi\) | ||||
−0.216314 | + | 0.976324i | \(0.569404\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.48942 | −0.220647 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −33.7887 | + | 26.1439i | −1.14753 | + | 0.887894i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 46.6910 | + | 12.5108i | 1.58388 | + | 0.424400i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.69178 | − | 2.93026i | 0.0573239 | − | 0.0992880i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.1053 | − | 13.8798i | −0.477391 | − | 0.469761i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.8915 | + | 2.91836i | −0.368199 | + | 0.0986587i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.3558 | + | 9.47357i | 1.19388 | + | 0.319900i | 0.800419 | − | 0.599441i | \(-0.204610\pi\) |
0.393463 | + | 0.919341i | \(0.371277\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −36.4818 | + | 15.2837i | −1.23050 | + | 0.515506i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 39.6546i | − | 1.33600i | −0.744163 | − | 0.667998i | \(-0.767151\pi\) | ||
0.744163 | − | 0.667998i | \(-0.232849\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.6423 | − | 16.6423i | −0.560060 | − | 0.560060i | 0.369265 | − | 0.929324i | \(-0.379610\pi\) |
−0.929324 | + | 0.369265i | \(0.879610\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.89259 | − | 21.3079i | −0.0972334 | − | 0.716256i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.0199051 | + | 0.0114922i | −0.000668349 | + | 0.000385871i | −0.500334 | − | 0.865832i | \(-0.666789\pi\) |
0.499666 | + | 0.866218i | \(0.333456\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.4162 | − | 14.0967i | −0.818894 | − | 0.472789i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 50.0671 | + | 12.5545i | 1.67731 | + | 0.420593i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.375517 | + | 0.100619i | −0.0125662 | + | 0.00336710i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.3098 | − | 8.83910i | 0.511749 | − | 0.295458i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.204795 | + | 0.269132i | −0.00683791 | + | 0.00898605i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.09363 | + | 7.09363i | −0.236586 | + | 0.236586i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −42.7353 | − | 42.7353i | −1.42372 | − | 1.42372i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14.6754 | + | 6.14810i | −0.488366 | + | 0.204596i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 28.4629 | + | 49.2992i | 0.946140 | + | 1.63876i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.2175 | − | 38.1323i | −0.339267 | − | 1.26616i | −0.899169 | − | 0.437602i | \(-0.855828\pi\) |
0.559902 | − | 0.828559i | \(-0.310839\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −24.9311 | + | 0.200838i | −0.826911 | + | 0.00666139i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.7704 | + | 39.4395i | −0.754417 | + | 1.30669i | 0.191246 | + | 0.981542i | \(0.438747\pi\) |
−0.945664 | + | 0.325147i | \(0.894586\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 35.5626 | + | 61.5962i | 1.17695 | + | 2.03854i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 20.2563 | + | 26.1795i | 0.669653 | + | 0.865469i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.47532 | + | 4.47532i | −0.147788 | + | 0.147788i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.2611 | 0.371468 | 0.185734 | − | 0.982600i | \(-0.440534\pi\) | ||||
0.185734 | + | 0.982600i | \(0.440534\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.0571 | − | 3.19621i | −0.825659 | − | 0.105319i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.09229 | − | 4.07647i | 0.0359531 | − | 0.134179i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.596105 | + | 2.22469i | 0.0195998 | + | 0.0731475i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.6390 | + | 5.43219i | −0.645030 | + | 0.178417i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.8724 | − | 9.74127i | −0.553564 | − | 0.319601i | 0.196994 | − | 0.980405i | \(-0.436882\pi\) |
−0.750558 | + | 0.660804i | \(0.770215\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.856614 | + | 3.19693i | −0.0280744 | + | 0.104775i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.672889 | − | 1.64319i | 0.0220294 | − | 0.0537955i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 106.817i | − | 3.49328i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 5.47240i | − | 0.178775i | −0.995997 | − | 0.0893877i | \(-0.971509\pi\) | ||
0.995997 | − | 0.0893877i | \(-0.0284910\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.8947 | − | 2.56499i | 0.616604 | − | 0.0837054i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.21380 | − | 11.9941i | 0.104767 | − | 0.390995i | −0.893552 | − | 0.448960i | \(-0.851795\pi\) |
0.998319 | + | 0.0579650i | \(0.0184612\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.00129938 | 0.000750197i | 4.23136e−5 | 2.44298e-5i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −32.4811 | − | 12.9965i | −1.05661 | − | 0.422778i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.00640230 | − | 0.0238937i | −0.000208047 | − | 0.000776441i | 0.965822 | − | 0.259207i | \(-0.0834613\pi\) |
−0.966030 | + | 0.258431i | \(0.916795\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.96742 | − | 18.5387i | 0.161249 | − | 0.601790i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.9218 | − | 26.1802i | 0.646008 | − | 0.848952i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −47.9215 | −1.55233 | −0.776164 | − | 0.630531i | \(-0.782837\pi\) | ||||
−0.776164 | + | 0.630531i | \(0.782837\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.6349 | − | 15.6349i | 0.505934 | − | 0.505934i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 19.8179 | − | 48.3951i | 0.640622 | − | 1.56439i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.5442 | − | 30.3875i | −0.566532 | − | 0.981262i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.6844 | + | 23.7020i | −0.441431 | + | 0.764581i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −43.5779 | + | 25.6299i | −1.40428 | + | 0.825913i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.66117 | + | 21.1278i | 0.182240 | + | 0.680127i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.27580 | − | 10.8700i | −0.201816 | − | 0.349556i | 0.747297 | − | 0.664490i | \(-0.231351\pi\) |
−0.949114 | + | 0.314934i | \(0.898018\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.01090 | − | 23.6044i | 0.0967242 | − | 0.758282i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.0701 | − | 16.0701i | −0.515715 | − | 0.515715i | 0.400557 | − | 0.916272i | \(-0.368817\pi\) |
−0.916272 | + | 0.400557i | \(0.868817\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.1601 | + | 14.1601i | −0.453953 | + | 0.453953i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −23.1015 | − | 2.94675i | −0.739839 | − | 0.0943716i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 47.1397 | − | 27.2161i | 1.50813 | − | 0.870721i | 0.508178 | − | 0.861252i | \(-0.330319\pi\) |
0.999955 | − | 0.00946892i | \(-0.00301410\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.7992 | + | 4.23337i | −0.504943 | + | 0.135299i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.11587 | + | 1.89728i | 0.0356269 | + | 0.0605754i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.9623 | − | 9.79319i | −0.541014 | − | 0.312354i | 0.204476 | − | 0.978872i | \(-0.434451\pi\) |
−0.745490 | + | 0.666517i | \(0.767784\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −44.5262 | + | 25.7072i | −1.41872 | + | 0.819101i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.683175 | − | 0.279762i | −0.0217457 | − | 0.00890491i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.134423 | + | 0.134423i | 0.00427439 | + | 0.00427439i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.8539i | 0.948341i | 0.880433 | + | 0.474171i | \(0.157252\pi\) | ||||
−0.880433 | + | 0.474171i | \(0.842748\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26.3260 | − | 20.0327i | −0.835429 | − | 0.635717i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 64.4071 | + | 17.2578i | 2.04184 | + | 0.547110i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.6880 | − | 7.41898i | 0.876888 | − | 0.234961i | 0.207824 | − | 0.978166i | \(-0.433362\pi\) |
0.669064 | + | 0.743205i | \(0.266695\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.33700 | − | 3.34145i | 0.0423009 | − | 0.105719i |
(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 | 576.2.y.a.335.18 | 88 | ||
3.2 | odd | 2 | 1728.2.z.a.143.19 | 88 | |||
4.3 | odd | 2 | 144.2.u.a.11.2 | ✓ | 88 | ||
9.4 | even | 3 | 1728.2.z.a.719.19 | 88 | |||
9.5 | odd | 6 | inner | 576.2.y.a.527.7 | 88 | ||
12.11 | even | 2 | 432.2.v.a.251.21 | 88 | |||
16.3 | odd | 4 | inner | 576.2.y.a.47.7 | 88 | ||
16.13 | even | 4 | 144.2.u.a.83.10 | yes | 88 | ||
36.23 | even | 6 | 144.2.u.a.59.10 | yes | 88 | ||
36.31 | odd | 6 | 432.2.v.a.395.13 | 88 | |||
48.29 | odd | 4 | 432.2.v.a.35.13 | 88 | |||
48.35 | even | 4 | 1728.2.z.a.1007.19 | 88 | |||
144.13 | even | 12 | 432.2.v.a.179.21 | 88 | |||
144.67 | odd | 12 | 1728.2.z.a.1583.19 | 88 | |||
144.77 | odd | 12 | 144.2.u.a.131.2 | yes | 88 | ||
144.131 | even | 12 | inner | 576.2.y.a.239.18 | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.u.a.11.2 | ✓ | 88 | 4.3 | odd | 2 | ||
144.2.u.a.59.10 | yes | 88 | 36.23 | even | 6 | ||
144.2.u.a.83.10 | yes | 88 | 16.13 | even | 4 | ||
144.2.u.a.131.2 | yes | 88 | 144.77 | odd | 12 | ||
432.2.v.a.35.13 | 88 | 48.29 | odd | 4 | |||
432.2.v.a.179.21 | 88 | 144.13 | even | 12 | |||
432.2.v.a.251.21 | 88 | 12.11 | even | 2 | |||
432.2.v.a.395.13 | 88 | 36.31 | odd | 6 | |||
576.2.y.a.47.7 | 88 | 16.3 | odd | 4 | inner | ||
576.2.y.a.239.18 | 88 | 144.131 | even | 12 | inner | ||
576.2.y.a.335.18 | 88 | 1.1 | even | 1 | trivial | ||
576.2.y.a.527.7 | 88 | 9.5 | odd | 6 | inner | ||
1728.2.z.a.143.19 | 88 | 3.2 | odd | 2 | |||
1728.2.z.a.719.19 | 88 | 9.4 | even | 3 | |||
1728.2.z.a.1007.19 | 88 | 48.35 | even | 4 | |||
1728.2.z.a.1583.19 | 88 | 144.67 | odd | 12 |