Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,4,Mod(136,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.136");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(23.8957735523\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 2 x^{10} + 32 x^{9} + 583 x^{8} - 624 x^{7} + 594 x^{6} + 9450 x^{5} + 90513 x^{4} + \cdots + 746496 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 136.6 | ||
Root | \(-2.61824 + 2.61824i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.136 |
Dual form | 405.4.e.w.271.6 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.05867 | − | 3.56572i | 0.727850 | − | 1.26067i | −0.229940 | − | 0.973205i | \(-0.573853\pi\) |
0.957790 | − | 0.287468i | \(-0.0928136\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.47625 | − | 7.75309i | −0.559531 | − | 0.969137i | ||||
\(5\) | −2.50000 | − | 4.33013i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.0115 | − | 17.3404i | 0.540568 | − | 0.936291i | −0.458303 | − | 0.888796i | \(-0.651543\pi\) |
0.998871 | − | 0.0474955i | \(-0.0151240\pi\) | |||||||
\(8\) | −3.92177 | −0.173319 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −20.5867 | −0.651009 | ||||||||
\(11\) | 0.839133 | − | 1.45342i | 0.0230007 | − | 0.0398385i | −0.854296 | − | 0.519787i | \(-0.826011\pi\) |
0.877297 | + | 0.479948i | \(0.159345\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.55615 | − | 9.62353i | −0.118538 | − | 0.205314i | 0.800650 | − | 0.599132i | \(-0.204488\pi\) |
−0.919189 | + | 0.393818i | \(0.871154\pi\) | |||||||
\(14\) | −41.2206 | − | 71.3962i | −0.786905 | − | 1.36296i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 27.7364 | − | 48.0408i | 0.433381 | − | 0.750638i | ||||
\(17\) | 8.98682 | 0.128213 | 0.0641066 | − | 0.997943i | \(-0.479580\pi\) | ||||
0.0641066 | + | 0.997943i | \(0.479580\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −50.6419 | −0.611477 | −0.305738 | − | 0.952116i | \(-0.598903\pi\) | ||||
−0.305738 | + | 0.952116i | \(0.598903\pi\) | |||||||
\(20\) | −22.3812 | + | 38.7655i | −0.250230 | + | 0.433411i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.45500 | − | 5.98423i | −0.0334822 | − | 0.0579928i | ||||
\(23\) | −107.246 | − | 185.755i | −0.972272 | − | 1.68402i | −0.688658 | − | 0.725086i | \(-0.741800\pi\) |
−0.283614 | − | 0.958939i | \(-0.591533\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | −45.7531 | −0.345113 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −179.255 | −1.20986 | ||||||||
\(29\) | 38.4544 | − | 66.6050i | 0.246235 | − | 0.426491i | −0.716243 | − | 0.697851i | \(-0.754140\pi\) |
0.962478 | + | 0.271360i | \(0.0874733\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 136.769 | + | 236.890i | 0.792399 | + | 1.37247i | 0.924478 | + | 0.381236i | \(0.124501\pi\) |
−0.132079 | + | 0.991239i | \(0.542165\pi\) | |||||||
\(32\) | −129.887 | − | 224.971i | −0.717532 | − | 1.24280i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 18.5009 | − | 32.0445i | 0.0933200 | − | 0.161635i | ||||
\(35\) | −100.115 | −0.483499 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −137.283 | −0.609978 | −0.304989 | − | 0.952356i | \(-0.598653\pi\) | ||||
−0.304989 | + | 0.952356i | \(0.598653\pi\) | |||||||
\(38\) | −104.255 | + | 180.575i | −0.445063 | + | 0.770872i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 9.80442 | + | 16.9818i | 0.0387554 | + | 0.0671263i | ||||
\(41\) | 26.6729 | + | 46.1987i | 0.101600 | + | 0.175976i | 0.912344 | − | 0.409424i | \(-0.134270\pi\) |
−0.810744 | + | 0.585401i | \(0.800937\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −147.635 | + | 255.711i | −0.523584 | + | 0.906874i | 0.476039 | + | 0.879424i | \(0.342072\pi\) |
−0.999623 | + | 0.0274502i | \(0.991261\pi\) | |||||||
\(44\) | −15.0247 | −0.0514785 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −883.134 | −2.83067 | ||||||||
\(47\) | 97.4916 | − | 168.860i | 0.302566 | − | 0.524060i | −0.674150 | − | 0.738594i | \(-0.735490\pi\) |
0.976716 | + | 0.214534i | \(0.0688234\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −28.9587 | − | 50.1579i | −0.0844276 | − | 0.146233i | ||||
\(50\) | 51.4668 | + | 89.1431i | 0.145570 | + | 0.252135i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −49.7414 | + | 86.1547i | −0.132652 | + | 0.229760i | ||||
\(53\) | −450.173 | −1.16672 | −0.583359 | − | 0.812214i | \(-0.698262\pi\) | ||||
−0.583359 | + | 0.812214i | \(0.698262\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.39133 | −0.0205725 | ||||||||
\(56\) | −39.2626 | + | 68.0048i | −0.0936909 | + | 0.162277i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −158.330 | − | 274.236i | −0.358444 | − | 0.620843i | ||||
\(59\) | −240.572 | − | 416.684i | −0.530845 | − | 0.919451i | −0.999352 | − | 0.0359910i | \(-0.988541\pi\) |
0.468507 | − | 0.883460i | \(-0.344792\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −337.927 | + | 585.307i | −0.709297 | + | 1.22854i | 0.255821 | + | 0.966724i | \(0.417654\pi\) |
−0.965118 | + | 0.261814i | \(0.915679\pi\) | |||||||
\(62\) | 1126.25 | 2.30699 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −625.798 | −1.22226 | ||||||||
\(65\) | −27.7807 | + | 48.1177i | −0.0530120 | + | 0.0918194i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −447.295 | − | 774.737i | −0.815608 | − | 1.41267i | −0.908890 | − | 0.417035i | \(-0.863069\pi\) |
0.0932823 | − | 0.995640i | \(-0.470264\pi\) | |||||||
\(68\) | −40.2273 | − | 69.6757i | −0.0717393 | − | 0.124256i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −206.103 | + | 356.981i | −0.351915 | + | 0.609534i | ||||
\(71\) | 721.947 | 1.20675 | 0.603376 | − | 0.797457i | \(-0.293822\pi\) | ||||
0.603376 | + | 0.797457i | \(0.293822\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 915.175 | 1.46730 | 0.733651 | − | 0.679526i | \(-0.237815\pi\) | ||||
0.733651 | + | 0.679526i | \(0.237815\pi\) | |||||||
\(74\) | −282.621 | + | 489.513i | −0.443973 | + | 0.768983i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 226.686 | + | 392.632i | 0.342140 | + | 0.592604i | ||||
\(77\) | −16.8019 | − | 29.1017i | −0.0248669 | − | 0.0430708i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −29.8321 | + | 51.6707i | −0.0424858 | + | 0.0735875i | −0.886486 | − | 0.462755i | \(-0.846861\pi\) |
0.844001 | + | 0.536342i | \(0.180194\pi\) | |||||||
\(80\) | −277.364 | −0.387628 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 219.643 | 0.295798 | ||||||||
\(83\) | −371.438 | + | 643.349i | −0.491212 | + | 0.850803i | −0.999949 | − | 0.0101184i | \(-0.996779\pi\) |
0.508737 | + | 0.860922i | \(0.330112\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −22.4671 | − | 38.9141i | −0.0286693 | − | 0.0496568i | ||||
\(86\) | 607.863 | + | 1052.85i | 0.762181 | + | 1.32014i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.29089 | + | 5.69998i | −0.00398647 | + | 0.00690477i | ||||
\(89\) | 1540.72 | 1.83501 | 0.917505 | − | 0.397723i | \(-0.130200\pi\) | ||||
0.917505 | + | 0.397723i | \(0.130200\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −222.501 | −0.256312 | ||||||||
\(92\) | −960.116 | + | 1662.97i | −1.08803 | + | 1.88453i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −401.406 | − | 695.256i | −0.440445 | − | 0.762874i | ||||
\(95\) | 126.605 | + | 219.286i | 0.136730 | + | 0.236824i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 560.783 | − | 971.305i | 0.586999 | − | 1.01671i | −0.407624 | − | 0.913150i | \(-0.633643\pi\) |
0.994623 | − | 0.103562i | \(-0.0330240\pi\) | |||||||
\(98\) | −238.465 | −0.245802 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 223.812 | 0.223812 | ||||||||
\(101\) | 879.236 | − | 1522.88i | 0.866211 | − | 1.50032i | 0.000370864 | − | 1.00000i | \(-0.499882\pi\) |
0.865840 | − | 0.500321i | \(-0.166785\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −528.242 | − | 914.941i | −0.505332 | − | 0.875261i | −0.999981 | − | 0.00616773i | \(-0.998037\pi\) |
0.494649 | − | 0.869093i | \(-0.335297\pi\) | |||||||
\(104\) | 21.7899 | + | 37.7413i | 0.0205450 | + | 0.0355850i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −926.759 | + | 1605.19i | −0.849196 | + | 1.47085i | ||||
\(107\) | 1470.03 | 1.32816 | 0.664081 | − | 0.747661i | \(-0.268823\pi\) | ||||
0.664081 | + | 0.747661i | \(0.268823\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 918.889 | 0.807464 | 0.403732 | − | 0.914877i | \(-0.367713\pi\) | ||||
0.403732 | + | 0.914877i | \(0.367713\pi\) | |||||||
\(110\) | −17.2750 | + | 29.9212i | −0.0149737 | + | 0.0259352i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −555.363 | − | 961.917i | −0.468544 | − | 0.811541i | ||||
\(113\) | −493.609 | − | 854.955i | −0.410927 | − | 0.711747i | 0.584064 | − | 0.811708i | \(-0.301462\pi\) |
−0.994991 | + | 0.0999606i | \(0.968128\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −536.228 | + | 928.774i | −0.434813 | + | 0.753119i | ||||
\(116\) | −688.526 | −0.551104 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1981.04 | −1.54550 | ||||||||
\(119\) | 89.9712 | − | 155.835i | 0.0693080 | − | 0.120045i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 664.092 | + | 1150.24i | 0.498942 | + | 0.864193i | ||||
\(122\) | 1391.36 | + | 2409.91i | 1.03252 | + | 1.78838i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1224.42 | − | 2120.76i | 0.886744 | − | 1.53589i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1480.10 | 1.03415 | 0.517077 | − | 0.855939i | \(-0.327020\pi\) | ||||
0.517077 | + | 0.855939i | \(0.327020\pi\) | |||||||
\(128\) | −249.214 | + | 431.651i | −0.172091 | + | 0.298070i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 114.383 | + | 198.117i | 0.0771695 | + | 0.133662i | ||||
\(131\) | 253.298 | + | 438.724i | 0.168937 | + | 0.292607i | 0.938046 | − | 0.346510i | \(-0.112633\pi\) |
−0.769110 | + | 0.639117i | \(0.779300\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −507.000 | + | 878.149i | −0.330545 | + | 0.572520i | ||||
\(134\) | −3683.33 | −2.37456 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −35.2442 | −0.0222218 | ||||||||
\(137\) | −487.861 | + | 845.001i | −0.304240 | + | 0.526958i | −0.977092 | − | 0.212819i | \(-0.931736\pi\) |
0.672852 | + | 0.739777i | \(0.265069\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 944.413 | + | 1635.77i | 0.576288 | + | 0.998160i | 0.995900 | + | 0.0904566i | \(0.0288327\pi\) |
−0.419612 | + | 0.907703i | \(0.637834\pi\) | |||||||
\(140\) | 448.138 | + | 776.198i | 0.270533 | + | 0.468576i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1486.25 | − | 2574.26i | 0.878334 | − | 1.52132i | ||||
\(143\) | −18.6494 | −0.0109059 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −384.544 | −0.220239 | ||||||||
\(146\) | 1884.04 | − | 3263.26i | 1.06798 | − | 1.84979i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 614.513 | + | 1064.37i | 0.341302 | + | 0.591152i | ||||
\(149\) | −1291.15 | − | 2236.33i | −0.709898 | − | 1.22958i | −0.964895 | − | 0.262637i | \(-0.915408\pi\) |
0.254997 | − | 0.966942i | \(-0.417926\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1268.96 | + | 2197.91i | −0.683885 | + | 1.18452i | 0.289901 | + | 0.957057i | \(0.406378\pi\) |
−0.973786 | + | 0.227467i | \(0.926956\pi\) | |||||||
\(152\) | 198.606 | 0.105981 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −138.358 | −0.0723976 | ||||||||
\(155\) | 683.843 | − | 1184.45i | 0.354372 | − | 0.613789i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −52.5175 | − | 90.9630i | −0.0266965 | − | 0.0462397i | 0.852368 | − | 0.522942i | \(-0.175165\pi\) |
−0.879065 | + | 0.476702i | \(0.841832\pi\) | |||||||
\(158\) | 122.829 | + | 212.746i | 0.0618465 | + | 0.107121i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −649.436 | + | 1124.86i | −0.320890 | + | 0.555798i | ||||
\(161\) | −4294.74 | −2.10232 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2228.88 | 1.07104 | 0.535519 | − | 0.844523i | \(-0.320116\pi\) | ||||
0.535519 | + | 0.844523i | \(0.320116\pi\) | |||||||
\(164\) | 238.789 | − | 413.594i | 0.113697 | − | 0.196929i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1529.34 | + | 2648.89i | 0.715057 | + | 1.23851i | ||||
\(167\) | −1406.90 | − | 2436.82i | −0.651911 | − | 1.12914i | −0.982659 | − | 0.185424i | \(-0.940634\pi\) |
0.330748 | − | 0.943719i | \(-0.392699\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1036.76 | − | 1795.72i | 0.471897 | − | 0.817350i | ||||
\(170\) | −185.009 | −0.0834679 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2643.40 | 1.17185 | ||||||||
\(173\) | 1642.22 | − | 2844.41i | 0.721711 | − | 1.25004i | −0.238603 | − | 0.971117i | \(-0.576689\pi\) |
0.960314 | − | 0.278922i | \(-0.0899772\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 250.286 | + | 433.509i | 0.108114 | + | 0.187258i | ||||
\(176\) | −46.5490 | − | 80.6253i | −0.0199362 | − | 0.0345304i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3171.83 | − | 5493.78i | 1.33561 | − | 2.31335i | ||||
\(179\) | 1268.62 | 0.529726 | 0.264863 | − | 0.964286i | \(-0.414673\pi\) | ||||
0.264863 | + | 0.964286i | \(0.414673\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1080.10 | 0.443554 | 0.221777 | − | 0.975097i | \(-0.428814\pi\) | ||||
0.221777 | + | 0.975097i | \(0.428814\pi\) | |||||||
\(182\) | −458.056 | + | 793.376i | −0.186557 | + | 0.323126i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 420.592 | + | 728.487i | 0.168513 | + | 0.291874i | ||||
\(185\) | 343.208 | + | 594.453i | 0.136395 | + | 0.236243i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.54114 | − | 13.0616i | 0.00294900 | − | 0.00510782i | ||||
\(188\) | −1745.59 | −0.677181 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1042.55 | 0.398077 | ||||||||
\(191\) | −143.357 | + | 248.302i | −0.0543087 | + | 0.0940654i | −0.891902 | − | 0.452229i | \(-0.850629\pi\) |
0.837593 | + | 0.546295i | \(0.183962\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2325.35 | + | 4027.63i | 0.867267 | + | 1.50215i | 0.864779 | + | 0.502153i | \(0.167459\pi\) |
0.00248836 | + | 0.999997i | \(0.499208\pi\) | |||||||
\(194\) | −2308.93 | − | 3999.19i | −0.854494 | − | 1.48003i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −259.252 | + | 449.038i | −0.0944797 | + | 0.163644i | ||||
\(197\) | 1694.82 | 0.612947 | 0.306474 | − | 0.951879i | \(-0.400851\pi\) | ||||
0.306474 | + | 0.951879i | \(0.400851\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3249.77 | −1.15764 | −0.578819 | − | 0.815456i | \(-0.696486\pi\) | ||||
−0.578819 | + | 0.815456i | \(0.696486\pi\) | |||||||
\(200\) | 49.0221 | − | 84.9088i | 0.0173319 | − | 0.0300198i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3620.12 | − | 6270.23i | −1.26094 | − | 2.18402i | ||||
\(203\) | −769.970 | − | 1333.63i | −0.266213 | − | 0.461095i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 133.364 | − | 230.994i | 0.0454369 | − | 0.0786990i | ||||
\(206\) | −4349.90 | −1.47122 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −616.430 | −0.205489 | ||||||||
\(209\) | −42.4953 | + | 73.6041i | −0.0140644 | + | 0.0243603i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 539.279 | + | 934.059i | 0.175950 | + | 0.304755i | 0.940490 | − | 0.339822i | \(-0.110367\pi\) |
−0.764539 | + | 0.644577i | \(0.777034\pi\) | |||||||
\(212\) | 2015.09 | + | 3490.24i | 0.652815 | + | 1.13071i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3026.31 | − | 5241.72i | 0.966702 | − | 1.67438i | ||||
\(215\) | 1476.35 | 0.468308 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5477.01 | 1.71338 | ||||||||
\(218\) | 1891.69 | − | 3276.50i | 0.587713 | − | 1.01795i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 37.5617 | + | 65.0588i | 0.0115110 | + | 0.0199376i | ||||
\(221\) | −49.9321 | − | 86.4850i | −0.0151982 | − | 0.0263240i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2571.64 | − | 4454.21i | 0.772241 | − | 1.33756i | −0.164091 | − | 0.986445i | \(-0.552469\pi\) |
0.936332 | − | 0.351115i | \(-0.114197\pi\) | |||||||
\(224\) | −5201.44 | −1.55150 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4064.71 | −1.19637 | ||||||||
\(227\) | −1454.83 | + | 2519.84i | −0.425377 | + | 0.736774i | −0.996456 | − | 0.0841209i | \(-0.973192\pi\) |
0.571079 | + | 0.820895i | \(0.306525\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −862.910 | − | 1494.60i | −0.249007 | − | 0.431293i | 0.714243 | − | 0.699897i | \(-0.246771\pi\) |
−0.963251 | + | 0.268604i | \(0.913438\pi\) | |||||||
\(230\) | 2207.83 | + | 3824.08i | 0.632958 | + | 1.09631i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −150.809 | + | 261.209i | −0.0426772 | + | 0.0739191i | ||||
\(233\) | 1087.48 | 0.305765 | 0.152882 | − | 0.988244i | \(-0.451144\pi\) | ||||
0.152882 | + | 0.988244i | \(0.451144\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −974.916 | −0.270623 | ||||||||
\(236\) | −2153.72 | + | 3730.36i | −0.594049 | + | 1.02892i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −370.442 | − | 641.625i | −0.100892 | − | 0.174749i | ||||
\(239\) | 159.672 | + | 276.561i | 0.0432149 | + | 0.0748504i | 0.886824 | − | 0.462108i | \(-0.152907\pi\) |
−0.843609 | + | 0.536958i | \(0.819573\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1822.91 | + | 3157.38i | −0.487238 | + | 0.843920i | −0.999892 | − | 0.0146745i | \(-0.995329\pi\) |
0.512655 | + | 0.858595i | \(0.328662\pi\) | |||||||
\(242\) | 5468.58 | 1.45262 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6050.58 | 1.58750 | ||||||||
\(245\) | −144.793 | + | 250.789i | −0.0377572 | + | 0.0653973i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 281.374 | + | 487.354i | 0.0724834 | + | 0.125545i | ||||
\(248\) | −536.375 | − | 929.028i | −0.137338 | − | 0.237876i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 257.334 | − | 445.715i | 0.0651009 | − | 0.112758i | ||||
\(251\) | −572.874 | −0.144062 | −0.0720309 | − | 0.997402i | \(-0.522948\pi\) | ||||
−0.0720309 | + | 0.997402i | \(0.522948\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −359.973 | −0.0894519 | ||||||||
\(254\) | 3047.04 | − | 5277.62i | 0.752709 | − | 1.30373i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1477.09 | − | 2558.40i | −0.360618 | − | 0.624609i | ||||
\(257\) | 1838.83 | + | 3184.94i | 0.446315 | + | 0.773040i | 0.998143 | − | 0.0609179i | \(-0.0194028\pi\) |
−0.551828 | + | 0.833958i | \(0.686069\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1374.40 | + | 2380.54i | −0.329735 | + | 0.571117i | ||||
\(260\) | 497.414 | 0.118647 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2085.83 | 0.491842 | ||||||||
\(263\) | −1000.86 | + | 1733.53i | −0.234659 | + | 0.406442i | −0.959174 | − | 0.282818i | \(-0.908731\pi\) |
0.724514 | + | 0.689260i | \(0.242064\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1125.43 | + | 1949.31i | 0.260886 | + | 0.451868i | ||||
\(266\) | 2087.49 | + | 3615.64i | 0.481174 | + | 0.833418i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4004.41 | + | 6935.83i | −0.912716 | + | 1.58087i | ||||
\(269\) | −20.1629 | −0.00457009 | −0.00228504 | − | 0.999997i | \(-0.500727\pi\) | ||||
−0.00228504 | + | 0.999997i | \(0.500727\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4733.12 | 1.06095 | 0.530474 | − | 0.847701i | \(-0.322014\pi\) | ||||
0.530474 | + | 0.847701i | \(0.322014\pi\) | |||||||
\(272\) | 249.262 | − | 431.734i | 0.0555651 | − | 0.0962416i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2008.69 | + | 3479.16i | 0.442881 | + | 0.767093i | ||||
\(275\) | 20.9783 | + | 36.3355i | 0.00460015 | + | 0.00796769i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2514.56 | + | 4355.34i | −0.545434 | + | 0.944719i | 0.453146 | + | 0.891436i | \(0.350302\pi\) |
−0.998579 | + | 0.0532826i | \(0.983032\pi\) | |||||||
\(278\) | 7776.94 | 1.67780 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 392.626 | 0.0837996 | ||||||||
\(281\) | −2904.16 | + | 5030.14i | −0.616539 | + | 1.06788i | 0.373574 | + | 0.927600i | \(0.378132\pi\) |
−0.990112 | + | 0.140276i | \(0.955201\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −106.512 | − | 184.483i | −0.0223726 | − | 0.0387505i | 0.854622 | − | 0.519250i | \(-0.173789\pi\) |
−0.876995 | + | 0.480500i | \(0.840455\pi\) | |||||||
\(284\) | −3231.62 | − | 5597.32i | −0.675215 | − | 1.16951i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −38.3930 | + | 66.4986i | −0.00793785 | + | 0.0137488i | ||||
\(287\) | 1068.14 | 0.219687 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4832.24 | −0.983561 | ||||||||
\(290\) | −791.650 | + | 1371.18i | −0.160301 | + | 0.277649i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4096.55 | − | 7095.43i | −0.821002 | − | 1.42202i | ||||
\(293\) | 1796.55 | + | 3111.71i | 0.358210 | + | 0.620437i | 0.987662 | − | 0.156602i | \(-0.0500540\pi\) |
−0.629452 | + | 0.777039i | \(0.716721\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1202.86 | + | 2083.42i | −0.237401 | + | 0.411191i | ||||
\(296\) | 538.392 | 0.105721 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10632.2 | −2.06680 | ||||||||
\(299\) | −1191.75 | + | 2064.16i | −0.230503 | + | 0.399243i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2956.08 | + | 5120.09i | 0.566066 | + | 0.980455i | ||||
\(302\) | 5224.75 | + | 9049.53i | 0.995531 | + | 1.72431i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1404.62 | + | 2432.88i | −0.265002 | + | 0.458997i | ||||
\(305\) | 3379.27 | 0.634415 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2403.23 | 0.446774 | 0.223387 | − | 0.974730i | \(-0.428289\pi\) | ||||
0.223387 | + | 0.974730i | \(0.428289\pi\) | |||||||
\(308\) | −150.419 | + | 260.533i | −0.0278277 | + | 0.0481989i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2815.61 | − | 4876.79i | −0.515859 | − | 0.893493i | ||||
\(311\) | 804.080 | + | 1392.71i | 0.146608 | + | 0.253933i | 0.929972 | − | 0.367631i | \(-0.119831\pi\) |
−0.783363 | + | 0.621564i | \(0.786498\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1390.27 | + | 2408.02i | −0.251063 | + | 0.434855i | −0.963819 | − | 0.266558i | \(-0.914114\pi\) |
0.712755 | + | 0.701413i | \(0.247447\pi\) | |||||||
\(314\) | −432.465 | −0.0777242 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 534.144 | 0.0950885 | ||||||||
\(317\) | −2767.85 | + | 4794.05i | −0.490403 | + | 0.849403i | −0.999939 | − | 0.0110461i | \(-0.996484\pi\) |
0.509536 | + | 0.860449i | \(0.329817\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −64.5368 | − | 111.781i | −0.0113272 | − | 0.0196192i | ||||
\(320\) | 1564.49 | + | 2709.78i | 0.273306 | + | 0.473380i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8841.46 | + | 15313.9i | −1.53017 | + | 2.65033i | ||||
\(323\) | −455.110 | −0.0783994 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 277.807 | 0.0474153 | ||||||||
\(326\) | 4588.53 | − | 7947.56i | 0.779555 | − | 1.35023i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −104.605 | − | 181.181i | −0.0176092 | − | 0.0305001i | ||||
\(329\) | −1952.07 | − | 3381.08i | −0.327115 | − | 0.566580i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4808.37 | − | 8328.35i | 0.798466 | − | 1.38298i | −0.122149 | − | 0.992512i | \(-0.538979\pi\) |
0.920615 | − | 0.390471i | \(-0.127688\pi\) | |||||||
\(332\) | 6650.59 | 1.09939 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11585.4 | −1.89797 | ||||||||
\(335\) | −2236.47 | + | 3873.69i | −0.364751 | + | 0.631767i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1042.23 | + | 1805.19i | 0.168468 | + | 0.291795i | 0.937881 | − | 0.346956i | \(-0.112785\pi\) |
−0.769413 | + | 0.638751i | \(0.779451\pi\) | |||||||
\(338\) | −4268.69 | − | 7393.58i | −0.686941 | − | 1.18982i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −201.136 | + | 348.378i | −0.0320828 | + | 0.0555690i | ||||
\(341\) | 459.068 | 0.0729030 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5708.19 | 0.898581 | ||||||||
\(344\) | 578.990 | − | 1002.84i | 0.0907472 | − | 0.157179i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6761.59 | − | 11711.4i | −1.05059 | − | 1.81968i | ||||
\(347\) | 3056.71 | + | 5294.38i | 0.472890 | + | 0.819070i | 0.999519 | − | 0.0310257i | \(-0.00987737\pi\) |
−0.526628 | + | 0.850096i | \(0.676544\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1094.53 | + | 1895.78i | −0.167877 | + | 0.290771i | −0.937673 | − | 0.347519i | \(-0.887024\pi\) |
0.769797 | + | 0.638289i | \(0.220358\pi\) | |||||||
\(350\) | 2061.03 | 0.314762 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −435.971 | −0.0660151 | ||||||||
\(353\) | 1250.10 | − | 2165.24i | 0.188488 | − | 0.326471i | −0.756258 | − | 0.654273i | \(-0.772975\pi\) |
0.944746 | + | 0.327802i | \(0.106308\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1804.87 | − | 3126.12i | −0.269838 | − | 0.467373i | ||||
\(356\) | −6896.65 | − | 11945.3i | −1.02675 | − | 1.77838i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2611.67 | − | 4523.54i | 0.385561 | − | 0.667812i | ||||
\(359\) | 841.607 | 0.123728 | 0.0618639 | − | 0.998085i | \(-0.480296\pi\) | ||||
0.0618639 | + | 0.998085i | \(0.480296\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4294.40 | −0.626096 | ||||||||
\(362\) | 2223.57 | − | 3851.34i | 0.322841 | − | 0.559176i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 995.969 | + | 1725.07i | 0.143415 | + | 0.248402i | ||||
\(365\) | −2287.94 | − | 3962.82i | −0.328099 | − | 0.568284i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2807.21 | − | 4862.23i | 0.399278 | − | 0.691571i | −0.594359 | − | 0.804200i | \(-0.702594\pi\) |
0.993637 | + | 0.112630i | \(0.0359273\pi\) | |||||||
\(368\) | −11898.4 | −1.68546 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2826.21 | 0.397101 | ||||||||
\(371\) | −4506.89 | + | 7806.17i | −0.630691 | + | 1.09239i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −659.587 | − | 1142.44i | −0.0915607 | − | 0.158588i | 0.816607 | − | 0.577194i | \(-0.195852\pi\) |
−0.908168 | + | 0.418606i | \(0.862519\pi\) | |||||||
\(374\) | −31.0495 | − | 53.7792i | −0.00429286 | − | 0.00743545i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −382.339 | + | 662.231i | −0.0524405 | + | 0.0908297i | ||||
\(377\) | −854.634 | −0.116753 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5002.07 | −0.677939 | −0.338970 | − | 0.940797i | \(-0.610078\pi\) | ||||
−0.338970 | + | 0.940797i | \(0.610078\pi\) | |||||||
\(380\) | 1133.43 | − | 1963.16i | 0.153010 | − | 0.265021i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 590.251 | + | 1022.34i | 0.0790572 | + | 0.136931i | ||||
\(383\) | −1121.22 | − | 1942.02i | −0.149587 | − | 0.259092i | 0.781488 | − | 0.623920i | \(-0.214461\pi\) |
−0.931075 | + | 0.364828i | \(0.881128\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −84.0095 | + | 145.509i | −0.0111208 | + | 0.0192618i | ||||
\(386\) | 19148.5 | 2.52496 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10040.8 | −1.31378 | ||||||||
\(389\) | −5696.89 | + | 9867.30i | −0.742529 | + | 1.28610i | 0.208811 | + | 0.977956i | \(0.433041\pi\) |
−0.951340 | + | 0.308142i | \(0.900293\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −963.797 | − | 1669.35i | −0.124658 | − | 0.215914i | ||||
\(392\) | 113.569 | + | 196.707i | 0.0146329 | + | 0.0253450i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3489.07 | − | 6043.24i | 0.446134 | − | 0.772726i | ||||
\(395\) | 298.321 | 0.0380004 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14926.0 | −1.88694 | −0.943472 | − | 0.331454i | \(-0.892461\pi\) | ||||
−0.943472 | + | 0.331454i | \(0.892461\pi\) | |||||||
\(398\) | −6690.20 | + | 11587.8i | −0.842586 | + | 1.45940i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 693.409 | + | 1201.02i | 0.0866762 | + | 0.150128i | ||||
\(401\) | −3582.82 | − | 6205.62i | −0.446178 | − | 0.772803i | 0.551955 | − | 0.833874i | \(-0.313882\pi\) |
−0.998133 | + | 0.0610707i | \(0.980548\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1519.81 | − | 2632.39i | 0.187859 | − | 0.325382i | ||||
\(404\) | −15742.7 | −1.93869 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6340.46 | −0.775053 | ||||||||
\(407\) | −115.199 | + | 199.530i | −0.0140299 | + | 0.0243006i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5662.05 | + | 9806.96i | 0.684524 | + | 1.18563i | 0.973586 | + | 0.228321i | \(0.0733234\pi\) |
−0.289062 | + | 0.957310i | \(0.593343\pi\) | |||||||
\(410\) | −549.106 | − | 951.080i | −0.0661425 | − | 0.114562i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4729.08 | + | 8191.01i | −0.565498 | + | 0.979471i | ||||
\(413\) | −9633.93 | −1.14783 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3714.38 | 0.439353 | ||||||||
\(416\) | −1443.35 | + | 2499.95i | −0.170110 | + | 0.294639i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 174.968 | + | 303.053i | 0.0204736 | + | 0.0354613i | ||||
\(419\) | −6349.90 | − | 10998.4i | −0.740365 | − | 1.28235i | −0.952329 | − | 0.305072i | \(-0.901319\pi\) |
0.211964 | − | 0.977277i | \(-0.432014\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8581.39 | − | 14863.4i | 0.993424 | − | 1.72066i | 0.397557 | − | 0.917577i | \(-0.369858\pi\) |
0.595867 | − | 0.803083i | \(-0.296809\pi\) | |||||||
\(422\) | 4440.79 | 0.512261 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1765.48 | 0.202215 | ||||||||
\(425\) | −112.335 | + | 194.570i | −0.0128213 | + | 0.0222072i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6766.29 | + | 11719.6i | 0.766847 | + | 1.32822i | ||||
\(428\) | −6580.23 | − | 11397.3i | −0.743148 | − | 1.28717i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3039.32 | − | 5264.25i | 0.340858 | − | 0.590383i | ||||
\(431\) | 11130.9 | 1.24399 | 0.621994 | − | 0.783022i | \(-0.286323\pi\) | ||||
0.621994 | + | 0.783022i | \(0.286323\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7675.55 | 0.851878 | 0.425939 | − | 0.904752i | \(-0.359944\pi\) | ||||
0.425939 | + | 0.904752i | \(0.359944\pi\) | |||||||
\(434\) | 11275.4 | − | 19529.5i | 1.24708 | − | 2.16001i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4113.17 | − | 7124.23i | −0.451801 | − | 0.782543i | ||||
\(437\) | 5431.12 | + | 9406.98i | 0.594522 | + | 1.02974i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1681.90 | + | 2913.13i | −0.182853 | + | 0.316711i | −0.942851 | − | 0.333214i | \(-0.891867\pi\) |
0.759998 | + | 0.649926i | \(0.225200\pi\) | |||||||
\(440\) | 32.9089 | 0.00356561 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −411.175 | −0.0442480 | ||||||||
\(443\) | 3947.03 | − | 6836.46i | 0.423316 | − | 0.733205i | −0.572945 | − | 0.819594i | \(-0.694199\pi\) |
0.996262 | + | 0.0863883i | \(0.0275326\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3851.80 | − | 6671.51i | −0.410321 | − | 0.710697i | ||||
\(446\) | −10588.3 | − | 18339.5i | −1.12415 | − | 1.94709i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6265.15 | + | 10851.6i | −0.660715 | + | 1.14439i | ||||
\(449\) | −2244.52 | −0.235914 | −0.117957 | − | 0.993019i | \(-0.537634\pi\) | ||||
−0.117957 | + | 0.993019i | \(0.537634\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 89.5283 | 0.00934750 | ||||||||
\(452\) | −4419.03 | + | 7653.99i | −0.459853 | + | 0.796489i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5990.04 | + | 10375.1i | 0.619221 | + | 1.07252i | ||||
\(455\) | 556.252 | + | 963.456i | 0.0573131 | + | 0.0992693i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7374.65 | + | 12773.3i | −0.754862 | + | 1.30746i | 0.190581 | + | 0.981671i | \(0.438963\pi\) |
−0.945443 | + | 0.325787i | \(0.894371\pi\) | |||||||
\(458\) | −7105.79 | −0.724960 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9601.16 | 0.973166 | ||||||||
\(461\) | 6239.75 | − | 10807.6i | 0.630400 | − | 1.09188i | −0.357070 | − | 0.934078i | \(-0.616224\pi\) |
0.987470 | − | 0.157807i | \(-0.0504424\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4839.56 | + | 8382.37i | 0.485774 | + | 0.841386i | 0.999866 | − | 0.0163492i | \(-0.00520436\pi\) |
−0.514092 | + | 0.857735i | \(0.671871\pi\) | |||||||
\(464\) | −2133.17 | − | 3694.76i | −0.213427 | − | 0.369666i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2238.76 | − | 3877.65i | 0.222551 | − | 0.385469i | ||||
\(467\) | −6714.33 | −0.665315 | −0.332658 | − | 0.943048i | \(-0.607945\pi\) | ||||
−0.332658 | + | 0.943048i | \(0.607945\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17912.3 | −1.76357 | ||||||||
\(470\) | −2007.03 | + | 3476.28i | −0.196973 | + | 0.341168i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 943.469 | + | 1634.14i | 0.0920057 | + | 0.159359i | ||||
\(473\) | 247.771 | + | 429.152i | 0.0240857 | + | 0.0417176i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 633.024 | − | 1096.43i | 0.0611477 | − | 0.105911i | ||||
\(476\) | −1610.93 | −0.155120 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1314.85 | 0.125816 | ||||||||
\(479\) | 1063.74 | − | 1842.45i | 0.101469 | − | 0.175749i | −0.810821 | − | 0.585294i | \(-0.800979\pi\) |
0.912290 | + | 0.409545i | \(0.134313\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 762.765 | + | 1321.15i | 0.0723058 | + | 0.125237i | ||||
\(482\) | 7505.56 | + | 13000.0i | 0.709272 | + | 1.22849i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5945.28 | − | 10297.5i | 0.558347 | − | 0.967086i | ||||
\(485\) | −5607.83 | −0.525028 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6549.04 | −0.609375 | −0.304687 | − | 0.952452i | \(-0.598552\pi\) | ||||
−0.304687 | + | 0.952452i | \(0.598552\pi\) | |||||||
\(488\) | 1325.27 | − | 2295.44i | 0.122935 | − | 0.212929i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 596.163 | + | 1032.59i | 0.0549631 | + | 0.0951989i | ||||
\(491\) | 6466.86 | + | 11200.9i | 0.594389 | + | 1.02951i | 0.993633 | + | 0.112668i | \(0.0359396\pi\) |
−0.399243 | + | 0.916845i | \(0.630727\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 345.583 | − | 598.567i | 0.0315705 | − | 0.0546818i | ||||
\(494\) | 2317.03 | 0.211028 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15173.9 | 1.37364 | ||||||||
\(497\) | 7227.74 | − | 12518.8i | 0.652331 | − | 1.12987i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2560.33 | − | 4434.62i | −0.229692 | − | 0.397837i | 0.728025 | − | 0.685550i | \(-0.240438\pi\) |
−0.957717 | + | 0.287713i | \(0.907105\pi\) | |||||||
\(500\) | −559.531 | − | 969.137i | −0.0500460 | − | 0.0866822i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1179.36 | + | 2042.71i | −0.104855 | + | 0.181615i | ||||
\(503\) | −10809.6 | −0.958204 | −0.479102 | − | 0.877759i | \(-0.659038\pi\) | ||||
−0.479102 | + | 0.877759i | \(0.659038\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8792.36 | −0.774762 | ||||||||
\(506\) | −741.067 | + | 1283.57i | −0.0651076 | + | 0.112770i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6625.29 | − | 11475.3i | −0.578642 | − | 1.00224i | ||||
\(509\) | 7378.46 | + | 12779.9i | 0.642524 | + | 1.11288i | 0.984868 | + | 0.173309i | \(0.0554459\pi\) |
−0.342344 | + | 0.939575i | \(0.611221\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9162.24 | − | 15869.5i | 0.793177 | − | 1.37382i | ||||
\(512\) | −16150.8 | −1.39409 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15142.2 | 1.29940 | ||||||||
\(515\) | −2641.21 | + | 4574.71i | −0.225991 | + | 0.391428i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −163.617 | − | 283.393i | −0.0139185 | − | 0.0241075i | ||||
\(518\) | 5658.89 | + | 9801.48i | 0.479995 | + | 0.831375i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 108.950 | − | 188.706i | 0.00918800 | − | 0.0159141i | ||||
\(521\) | 1742.68 | 0.146542 | 0.0732709 | − | 0.997312i | \(-0.476656\pi\) | ||||
0.0732709 | + | 0.997312i | \(0.476656\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10304.8 | 0.861565 | 0.430782 | − | 0.902456i | \(-0.358238\pi\) | ||||
0.430782 | + | 0.902456i | \(0.358238\pi\) | |||||||
\(524\) | 2267.65 | − | 3927.68i | 0.189051 | − | 0.327446i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4120.87 | + | 7137.55i | 0.341594 | + | 0.591658i | ||||
\(527\) | 1229.11 | + | 2128.89i | 0.101596 | + | 0.175969i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16919.7 | + | 29305.9i | −1.39063 | + | 2.40863i | ||||
\(530\) | 9267.59 | 0.759544 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 9077.83 | 0.739800 | ||||||||
\(533\) | 296.397 | − | 513.374i | 0.0240870 | − | 0.0417199i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3675.08 | − | 6365.42i | −0.296986 | − | 0.514395i | ||||
\(536\) | 1754.19 | + | 3038.34i | 0.141361 | + | 0.244844i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −41.5087 | + | 71.8953i | −0.00332634 | + | 0.00576138i | ||||
\(539\) | −97.2007 | −0.00776759 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3966.86 | 0.315247 | 0.157623 | − | 0.987499i | \(-0.449617\pi\) | ||||
0.157623 | + | 0.987499i | \(0.449617\pi\) | |||||||
\(542\) | 9743.94 | − | 16877.0i | 0.772211 | − | 1.33751i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1167.27 | − | 2021.78i | −0.0919971 | − | 0.159344i | ||||
\(545\) | −2297.22 | − | 3978.90i | −0.180554 | − | 0.312729i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2904.36 | − | 5030.50i | 0.227023 | − | 0.393215i | −0.729902 | − | 0.683552i | \(-0.760434\pi\) |
0.956924 | + | 0.290337i | \(0.0937675\pi\) | |||||||
\(548\) | 8735.16 | 0.680926 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 172.750 | 0.0133929 | ||||||||
\(551\) | −1947.41 | + | 3373.01i | −0.150567 | + | 0.260789i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 597.326 | + | 1034.60i | 0.0459329 | + | 0.0795581i | ||||
\(554\) | 10353.3 | + | 17932.4i | 0.793988 | + | 1.37523i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8454.85 | − | 14644.2i | 0.644902 | − | 1.11700i | ||||
\(557\) | 3563.91 | 0.271109 | 0.135554 | − | 0.990770i | \(-0.456718\pi\) | ||||
0.135554 | + | 0.990770i | \(0.456718\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3281.13 | 0.248259 | ||||||||
\(560\) | −2776.82 | + | 4809.59i | −0.209539 | + | 0.362932i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11957.4 | + | 20710.8i | 0.897495 | + | 1.55451i | ||||
\(563\) | 255.772 | + | 443.010i | 0.0191466 | + | 0.0331628i | 0.875440 | − | 0.483327i | \(-0.160572\pi\) |
−0.856293 | + | 0.516490i | \(0.827238\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2468.04 | + | 4274.78i | −0.183772 | + | 0.318303i | ||||
\(566\) | −877.089 | −0.0651357 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2831.31 | −0.209153 | ||||||||
\(569\) | −4058.27 | + | 7029.13i | −0.299001 | + | 0.517885i | −0.975908 | − | 0.218184i | \(-0.929987\pi\) |
0.676907 | + | 0.736069i | \(0.263320\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7539.06 | − | 13058.0i | −0.552539 | − | 0.957026i | −0.998090 | − | 0.0617692i | \(-0.980326\pi\) |
0.445551 | − | 0.895256i | \(-0.353008\pi\) | |||||||
\(572\) | 83.4794 | + | 144.591i | 0.00610218 | + | 0.0105693i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2198.94 | − | 3808.68i | 0.159899 | − | 0.276953i | ||||
\(575\) | 5362.28 | 0.388909 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27101.5 | 1.95537 | 0.977685 | − | 0.210077i | \(-0.0673716\pi\) | ||||
0.977685 | + | 0.210077i | \(0.0673716\pi\) | |||||||
\(578\) | −9947.98 | + | 17230.4i | −0.715885 | + | 1.23995i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1721.32 | + | 2981.41i | 0.123231 | + | 0.213442i | ||||
\(581\) | 7437.26 | + | 12881.7i | 0.531067 | + | 0.919834i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −377.755 | + | 654.292i | −0.0268354 | + | 0.0464803i | ||||
\(584\) | −3589.10 | −0.254312 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14794.0 | 1.04289 | ||||||||
\(587\) | −51.0411 | + | 88.4057i | −0.00358891 | + | 0.00621617i | −0.867814 | − | 0.496889i | \(-0.834476\pi\) |
0.864225 | + | 0.503105i | \(0.167809\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6926.22 | − | 11996.6i | −0.484533 | − | 0.839236i | ||||
\(590\) | 4952.59 | + | 8578.15i | 0.345585 | + | 0.598571i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3807.73 | + | 6595.19i | −0.264353 | + | 0.457872i | ||||
\(593\) | 16467.2 | 1.14035 | 0.570174 | − | 0.821524i | \(-0.306876\pi\) | ||||
0.570174 | + | 0.821524i | \(0.306876\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −899.712 | −0.0619909 | ||||||||
\(596\) | −11559.0 | + | 20020.7i | −0.794420 | + | 1.37598i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4906.82 | + | 8498.87i | 0.335543 | + | 0.581178i | ||||
\(599\) | −11608.1 | − | 20105.8i | −0.791809 | − | 1.37145i | −0.924846 | − | 0.380342i | \(-0.875806\pi\) |
0.133038 | − | 0.991111i | \(-0.457527\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 839.147 | − | 1453.45i | 0.0569543 | − | 0.0986477i | −0.836143 | − | 0.548512i | \(-0.815194\pi\) |
0.893097 | + | 0.449865i | \(0.148528\pi\) | |||||||
\(602\) | 24342.4 | 1.64804 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 22720.8 | 1.53062 | ||||||||
\(605\) | 3320.46 | − | 5751.20i | 0.223134 | − | 0.386479i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9653.64 | − | 16720.6i | −0.645517 | − | 1.11807i | −0.984182 | − | 0.177162i | \(-0.943308\pi\) |
0.338664 | − | 0.940907i | \(-0.390025\pi\) | |||||||
\(608\) | 6577.74 | + | 11393.0i | 0.438754 | + | 0.759944i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6956.80 | − | 12049.5i | 0.461759 | − | 0.799789i | ||||
\(611\) | −2166.71 | −0.143463 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13659.9 | 0.900032 | 0.450016 | − | 0.893020i | \(-0.351418\pi\) | ||||
0.450016 | + | 0.893020i | \(0.351418\pi\) | |||||||
\(614\) | 4947.46 | − | 8569.26i | 0.325185 | − | 0.563236i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 65.8931 | + | 114.130i | 0.00430992 | + | 0.00746500i | ||||
\(617\) | 7301.84 | + | 12647.2i | 0.476436 | + | 0.825211i | 0.999635 | − | 0.0269990i | \(-0.00859510\pi\) |
−0.523200 | + | 0.852210i | \(0.675262\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13194.1 | − | 22852.9i | 0.856732 | − | 1.48390i | −0.0182965 | − | 0.999833i | \(-0.505824\pi\) |
0.875029 | − | 0.484071i | \(-0.160842\pi\) | |||||||
\(620\) | −12244.2 | −0.793128 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6621.35 | 0.426836 | ||||||||
\(623\) | 15424.9 | − | 26716.6i | 0.991948 | − | 1.71810i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 5724.23 | + | 9914.65i | 0.365473 | + | 0.633018i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −470.163 | + | 814.346i | −0.0298751 | + | 0.0517451i | ||||
\(629\) | −1233.74 | −0.0782072 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14241.1 | 0.898459 | 0.449229 | − | 0.893416i | \(-0.351699\pi\) | ||||
0.449229 | + | 0.893416i | \(0.351699\pi\) | |||||||
\(632\) | 116.995 | − | 202.641i | 0.00736360 | − | 0.0127541i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11396.2 | + | 19738.8i | 0.713880 | + | 1.23648i | ||||
\(635\) | −3700.25 | − | 6409.02i | −0.231244 | − | 0.400526i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −321.797 | + | 557.369i | −0.0200158 | + | 0.0346684i | ||||
\(638\) | −531.440 | −0.0329779 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2492.14 | 0.153923 | ||||||||
\(641\) | −9480.23 | + | 16420.2i | −0.584160 | + | 1.01180i | 0.410819 | + | 0.911717i | \(0.365243\pi\) |
−0.994980 | + | 0.100078i | \(0.968091\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5527.13 | − | 9573.26i | −0.338987 | − | 0.587143i | 0.645256 | − | 0.763967i | \(-0.276751\pi\) |
−0.984242 | + | 0.176824i | \(0.943418\pi\) | |||||||
\(644\) | 19224.3 | + | 33297.5i | 1.17631 | + | 2.03743i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −936.922 | + | 1622.80i | −0.0570630 | + | 0.0988360i | ||||
\(647\) | −19310.1 | −1.17335 | −0.586677 | − | 0.809821i | \(-0.699564\pi\) | ||||
−0.586677 | + | 0.809821i | \(0.699564\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −807.489 | −0.0488393 | ||||||||
\(650\) | 571.914 | − | 990.584i | 0.0345113 | − | 0.0597753i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9977.02 | − | 17280.7i | −0.599280 | − | 1.03798i | ||||
\(653\) | 3467.13 | + | 6005.24i | 0.207778 | + | 0.359883i | 0.951014 | − | 0.309147i | \(-0.100043\pi\) |
−0.743236 | + | 0.669029i | \(0.766710\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1266.49 | − | 2193.62i | 0.0755508 | − | 0.130858i | ||||
\(656\) | 2959.23 | 0.176126 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −16074.6 | −0.952363 | ||||||||
\(659\) | −7939.35 | + | 13751.4i | −0.469307 | + | 0.812863i | −0.999384 | − | 0.0350862i | \(-0.988829\pi\) |
0.530078 | + | 0.847949i | \(0.322163\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4709.16 | + | 8156.51i | 0.277103 | + | 0.479957i | 0.970664 | − | 0.240442i | \(-0.0772923\pi\) |
−0.693561 | + | 0.720398i | \(0.743959\pi\) | |||||||
\(662\) | −19797.7 | − | 34290.7i | −1.16233 | − | 2.01321i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1456.69 | − | 2523.06i | 0.0851364 | − | 0.147461i | ||||
\(665\) | 5070.00 | 0.295648 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16496.3 | −0.957628 | ||||||||
\(668\) | −12595.3 | + | 21815.6i | −0.729529 | + | 1.26358i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9208.32 | + | 15949.3i | 0.530968 | + | 0.919664i | ||||
\(671\) | 567.132 | + | 982.301i | 0.0326287 | + | 0.0565146i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9196.17 | − | 15928.2i | 0.526726 | − | 0.912316i | −0.472789 | − | 0.881176i | \(-0.656753\pi\) |
0.999515 | − | 0.0311403i | \(-0.00991387\pi\) | |||||||
\(674\) | 8582.41 | 0.490478 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −18563.2 | −1.05617 | ||||||||
\(677\) | 5285.34 | − | 9154.49i | 0.300048 | − | 0.519698i | −0.676099 | − | 0.736811i | \(-0.736331\pi\) |
0.976146 | + | 0.217113i | \(0.0696641\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11228.5 | − | 19448.4i | −0.634626 | − | 1.09920i | ||||
\(680\) | 88.1106 | + | 152.612i | 0.00496895 | + | 0.00860647i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 945.070 | − | 1636.91i | 0.0530625 | − | 0.0919069i | ||||
\(683\) | 23975.0 | 1.34316 | 0.671579 | − | 0.740933i | \(-0.265616\pi\) | ||||
0.671579 | + | 0.740933i | \(0.265616\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4878.61 | 0.272120 | ||||||||
\(686\) | 11751.3 | − | 20353.8i | 0.654032 | − | 1.13282i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8189.72 | + | 14185.0i | 0.453823 | + | 0.786044i | ||||
\(689\) | 2501.23 | + | 4332.26i | 0.138301 | + | 0.239544i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9820.49 | + | 17009.6i | −0.540650 | + | 0.936433i | 0.458217 | + | 0.888840i | \(0.348488\pi\) |
−0.998867 | + | 0.0475927i | \(0.984845\pi\) | |||||||
\(692\) | −29404.0 | −1.61528 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 25171.1 | 1.37677 | ||||||||
\(695\) | 4722.06 | − | 8178.85i | 0.257724 | − | 0.446391i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 239.704 | + | 415.180i | 0.0130265 | + | 0.0225625i | ||||
\(698\) | 4506.56 | + | 7805.59i | 0.244378 | + | 0.423275i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2240.69 | − | 3880.99i | 0.120986 | − | 0.209554i | ||||
\(701\) | −36098.2 | −1.94495 | −0.972475 | − | 0.233007i | \(-0.925143\pi\) | ||||
−0.972475 | + | 0.233007i | \(0.925143\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6952.28 | 0.372987 | ||||||||
\(704\) | −525.128 | + | 909.548i | −0.0281129 | + | 0.0486930i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5147.10 | − | 8915.04i | −0.274382 | − | 0.475243i | ||||
\(707\) | −17604.9 | − | 30492.5i | −0.936492 | − | 1.62205i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17617.1 | + | 30513.6i | −0.933177 | + | 1.61631i | −0.155323 | + | 0.987864i | \(0.549642\pi\) |
−0.777853 | + | 0.628446i | \(0.783691\pi\) | |||||||
\(710\) | −14862.5 | −0.785606 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6042.34 | −0.318043 | ||||||||
\(713\) | 29335.7 | − | 50810.9i | 1.54085 | − | 2.66884i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 46.6235 | + | 80.7543i | 0.00243863 | + | 0.00422383i | ||||
\(716\) | −5678.65 | − | 9835.71i | −0.296398 | − | 0.513377i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1732.59 | − | 3000.94i | 0.0900553 | − | 0.155980i | ||||
\(719\) | 22089.7 | 1.14577 | 0.572885 | − | 0.819636i | \(-0.305824\pi\) | ||||
0.572885 | + | 0.819636i | \(0.305824\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21153.9 | −1.09267 | ||||||||
\(722\) | −8840.75 | + | 15312.6i | −0.455704 | + | 0.789303i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4834.80 | − | 8374.12i | −0.248182 | − | 0.429864i | ||||
\(725\) | 961.360 | + | 1665.13i | 0.0492469 | + | 0.0852982i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9717.61 | − | 16831.4i | 0.495744 | − | 0.858654i | −0.504244 | − | 0.863561i | \(-0.668229\pi\) |
0.999988 | + | 0.00490721i | \(0.00156202\pi\) | |||||||
\(728\) | 872.596 | 0.0444238 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −18840.4 | −0.955227 | ||||||||
\(731\) | −1326.77 | + | 2298.03i | −0.0671304 | + | 0.116273i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7487.10 | − | 12968.0i | −0.377275 | − | 0.653459i | 0.613390 | − | 0.789780i | \(-0.289805\pi\) |
−0.990665 | + | 0.136321i | \(0.956472\pi\) | |||||||
\(734\) | −11558.2 | − | 20019.5i | −0.581230 | − | 1.00672i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −27859.7 | + | 48254.3i | −1.39527 | + | 2.41668i | ||||
\(737\) | −1501.36 | −0.0750384 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30663.4 | −1.52635 | −0.763174 | − | 0.646193i | \(-0.776360\pi\) | ||||
−0.763174 | + | 0.646193i | \(0.776360\pi\) | |||||||
\(740\) | 3072.57 | − | 5321.84i | 0.152635 | − | 0.264371i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 18556.4 | + | 32140.7i | 0.918096 | + | 1.59019i | ||||
\(743\) | 1707.34 | + | 2957.20i | 0.0843018 | + | 0.146015i | 0.905093 | − | 0.425213i | \(-0.139801\pi\) |
−0.820792 | + | 0.571228i | \(0.806467\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6455.73 | + | 11181.6i | −0.317476 | + | 0.549884i | ||||
\(746\) | −5431.49 | −0.266570 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −135.024 | −0.00660023 | ||||||||
\(749\) | 14717.2 | − | 25490.9i | 0.717962 | − | 1.24355i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 373.129 | + | 646.279i | 0.0181301 | + | 0.0314022i | 0.874948 | − | 0.484217i | \(-0.160895\pi\) |
−0.856818 | + | 0.515619i | \(0.827562\pi\) | |||||||
\(752\) | −5408.12 | − | 9367.15i | −0.262253 | − | 0.454235i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1759.41 | + | 3047.39i | −0.0849787 | + | 0.147187i | ||||
\(755\) | 12689.6 | 0.611685 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22929.5 | −1.10091 | −0.550454 | − | 0.834865i | \(-0.685546\pi\) | ||||
−0.550454 | + | 0.834865i | \(0.685546\pi\) | |||||||
\(758\) | −10297.6 | + | 17836.0i | −0.493438 | + | 0.854660i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −496.515 | − | 859.989i | −0.0236980 | − | 0.0410461i | ||||
\(761\) | −10588.3 | − | 18339.5i | −0.504370 | − | 0.873595i | −0.999987 | − | 0.00505384i | \(-0.998391\pi\) |
0.495617 | − | 0.868541i | \(-0.334942\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9199.42 | − | 15933.9i | 0.436489 | − | 0.756021i | ||||
\(764\) | 2566.81 | 0.121550 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9232.92 | −0.435508 | ||||||||
\(767\) | −2673.31 | + | 4630.31i | −0.125851 | + | 0.217980i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1387.09 | − | 2402.51i | −0.0650453 | − | 0.112662i | 0.831669 | − | 0.555272i | \(-0.187386\pi\) |
−0.896714 | + | 0.442610i | \(0.854053\pi\) | |||||||
\(770\) | 345.896 | + | 599.109i | 0.0161886 | + | 0.0280395i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 20817.7 | − | 36057.3i | 0.970526 | − | 1.68100i | ||||
\(773\) | −28891.7 | −1.34433 | −0.672163 | − | 0.740403i | \(-0.734635\pi\) | ||||
−0.672163 | + | 0.740403i | \(0.734635\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6838.43 | −0.316960 | ||||||||
\(776\) | −2199.26 | + | 3809.23i | −0.101738 | + | 0.176216i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23456.0 | + | 40627.1i | 1.08090 | + | 1.87217i | ||||
\(779\) | −1350.76 | − | 2339.59i | −0.0621260 | − | 0.107605i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 605.810 | − | 1049.29i | 0.0277562 | − | 0.0480751i | ||||
\(782\) | −7936.56 | −0.362930 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3212.83 | −0.146357 | ||||||||
\(785\) | −262.588 | + | 454.815i | −0.0119390 | + | 0.0206790i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4404.37 | − | 7628.60i | −0.199490 | − | 0.345527i | 0.748873 | − | 0.662714i | \(-0.230595\pi\) |
−0.948363 | + | 0.317186i | \(0.897262\pi\) | |||||||
\(788\) | −7586.42 | − | 13140.1i | −0.342963 | − | 0.594029i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 614.145 | − | 1063.73i | 0.0276586 | − | 0.0479061i | ||||
\(791\) | −19767.0 | −0.888537 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7510.29 | 0.336316 | ||||||||
\(794\) | −30727.8 | + | 53222.1i | −1.37341 | + | 2.37882i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14546.8 | + | 25195.7i | 0.647734 | + | 1.12191i | ||||
\(797\) | −390.251 | − | 675.935i | −0.0173443 | − | 0.0300412i | 0.857223 | − | 0.514945i | \(-0.172188\pi\) |
−0.874567 | + | 0.484904i | \(0.838854\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 876.139 | − | 1517.52i | 0.0387930 | − | 0.0671914i | ||||
\(800\) | 6494.36 | 0.287013 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −29503.4 | −1.29900 | ||||||||
\(803\) | 767.954 | − | 1330.13i | 0.0337491 | − | 0.0584551i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10736.9 | + | 18596.8i | 0.470092 | + | 0.814224i | ||||
\(806\) | −6257.59 | − | 10838.5i | −0.273467 | − | 0.473658i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3448.16 | + | 5972.39i | −0.150131 | + | 0.260035i | ||||
\(809\) | −15234.0 | −0.662051 | −0.331025 | − | 0.943622i | \(-0.607395\pi\) | ||||
−0.331025 | + | 0.943622i | \(0.607395\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10825.2 | 0.468711 | 0.234356 | − | 0.972151i | \(-0.424702\pi\) | ||||
0.234356 | + | 0.972151i | \(0.424702\pi\) | |||||||
\(812\) | −6893.15 | + | 11939.3i | −0.297909 | + | 0.515994i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 474.313 | + | 821.533i | 0.0204234 | + | 0.0353744i | ||||
\(815\) | −5572.20 | − | 9651.33i | −0.239492 | − | 0.414811i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7476.52 | − | 12949.7i | 0.320159 | − | 0.554532i | ||||
\(818\) | 46625.2 | 1.99292 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2387.89 | −0.101693 | ||||||||
\(821\) | 19985.6 | − | 34616.1i | 0.849577 | − | 1.47151i | −0.0320090 | − | 0.999488i | \(-0.510191\pi\) |
0.881586 | − | 0.472023i | \(-0.156476\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14310.3 | − | 24786.2i | −0.606107 | − | 1.04981i | −0.991876 | − | 0.127212i | \(-0.959397\pi\) |
0.385769 | − | 0.922595i | \(-0.373936\pi\) | |||||||
\(824\) | 2071.64 | + | 3588.19i | 0.0875838 | + | 0.151700i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −19833.1 | + | 34351.9i | −0.835449 | + | 1.44704i | ||||
\(827\) | −2265.62 | −0.0952639 | −0.0476320 | − | 0.998865i | \(-0.515167\pi\) | ||||
−0.0476320 | + | 0.998865i | \(0.515167\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14651.6 | −0.613839 | −0.306919 | − | 0.951736i | \(-0.599298\pi\) | ||||
−0.306919 | + | 0.951736i | \(0.599298\pi\) | |||||||
\(830\) | 7646.68 | − | 13244.4i | 0.319783 | − | 0.553881i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3477.03 | + | 6022.39i | 0.144885 | + | 0.250948i | ||||
\(833\) | −260.246 | − | 450.760i | −0.0108247 | − | 0.0187490i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7034.49 | + | 12184.1i | −0.291543 | + | 0.504968i | ||||
\(836\) | 760.879 | 0.0314779 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −52289.4 | −2.15550 | ||||||||
\(839\) | −11233.2 | + | 19456.5i | −0.462233 | + | 0.800611i | −0.999072 | − | 0.0430736i | \(-0.986285\pi\) |
0.536839 | + | 0.843685i | \(0.319618\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9237.02 | + | 15999.0i | 0.378737 | + | 0.655992i | ||||
\(842\) | −35332.5 | − | 61197.7i | −1.44613 | − | 2.50477i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4827.89 | − | 8362.16i | 0.196899 | − | 0.341040i | ||||
\(845\) | −10367.6 | −0.422078 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26594.1 | 1.07885 | ||||||||
\(848\) | −12486.2 | + | 21626.7i | −0.505633 | + | 0.875783i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 462.523 | + | 801.113i | 0.0186640 | + | 0.0323270i | ||||
\(851\) | 14723.0 | + | 25501.0i | 0.593065 | + | 1.02722i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22235.5 | + | 38513.0i | −0.892531 | + | 1.54591i | −0.0557007 | + | 0.998448i | \(0.517739\pi\) |
−0.836831 | + | 0.547462i | \(0.815594\pi\) | |||||||
\(854\) | 55718.2 | 2.23260 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5765.12 | −0.230196 | ||||||||
\(857\) | −15740.3 | + | 27263.0i | −0.627396 | + | 1.08668i | 0.360676 | + | 0.932691i | \(0.382546\pi\) |
−0.988072 | + | 0.153991i | \(0.950787\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21491.5 | − | 37224.5i | −0.853646 | − | 1.47856i | −0.877895 | − | 0.478853i | \(-0.841053\pi\) |
0.0242490 | − | 0.999706i | \(-0.492281\pi\) | |||||||
\(860\) | −6608.51 | − | 11446.3i | −0.262033 | − | 0.453854i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 22914.9 | − | 39689.9i | 0.905436 | − | 1.56826i | ||||
\(863\) | 25203.4 | 0.994131 | 0.497065 | − | 0.867713i | \(-0.334411\pi\) | ||||
0.497065 | + | 0.867713i | \(0.334411\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16422.2 | −0.645518 | ||||||||
\(866\) | 15801.4 | − | 27368.9i | 0.620039 | − | 1.07394i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −24516.5 | − | 42463.8i | −0.958691 | − | 1.66050i | ||||
\(869\) | 50.0662 | + | 86.7173i | 0.00195441 | + | 0.00338514i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4970.47 | + | 8609.11i | −0.193362 | + | 0.334912i | ||||
\(872\) | −3603.67 | −0.139949 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 44723.6 | 1.73089 | ||||||||
\(875\) | 1251.43 | − | 2167.54i | 0.0483499 | − | 0.0837444i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1736.36 | − | 3007.46i | −0.0668558 | − | 0.115798i | 0.830660 | − | 0.556780i | \(-0.187963\pi\) |
−0.897516 | + | 0.440982i | \(0.854630\pi\) | |||||||
\(878\) | 6924.95 | + | 11994.4i | 0.266180 | + | 0.461037i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −232.745 | + | 403.126i | −0.00891572 | + | 0.0154425i | ||||
\(881\) | −26066.1 | −0.996811 | −0.498405 | − | 0.866944i | \(-0.666081\pi\) | ||||
−0.498405 | + | 0.866944i | \(0.666081\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3032.93 | −0.115590 | −0.0577952 | − | 0.998328i | \(-0.518407\pi\) | ||||
−0.0577952 | + | 0.998328i | \(0.518407\pi\) | |||||||
\(884\) | −447.017 | + | 774.257i | −0.0170077 | + | 0.0294582i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16251.3 | − | 28148.0i | −0.616221 | − | 1.06733i | ||||
\(887\) | −21169.7 | − | 36667.0i | −0.801363 | − | 1.38800i | −0.918719 | − | 0.394911i | \(-0.870775\pi\) |
0.117357 | − | 0.993090i | \(-0.462558\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14818.0 | − | 25665.5i | 0.559031 | − | 0.968270i | ||||
\(890\) | −31718.3 | −1.19461 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −46045.2 | −1.72837 | ||||||||
\(893\) | −4937.16 | + | 8551.41i | −0.185012 | + | 0.320450i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3171.55 | − | 5493.28i | −0.118450 | − | 0.205162i | ||||
\(896\) | 4989.99 | + | 8642.92i | 0.186054 | + | 0.322254i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4620.72 | + | 8003.32i | −0.171710 | + | 0.297410i | ||||
\(899\) | 21037.4 | 0.780464 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4045.63 | −0.149589 | ||||||||
\(902\) | 184.309 | − | 319.233i | 0.00680358 | − | 0.0117841i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1935.82 | + | 3352.93i | 0.0712216 | + | 0.123359i | ||||
\(905\) | −2700.25 | − | 4676.97i | −0.0991816 | − | 0.171788i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10104.9 | − | 17502.2i | 0.369931 | − | 0.640739i | −0.619624 | − | 0.784899i | \(-0.712715\pi\) |
0.989554 | + | 0.144160i | \(0.0460481\pi\) | |||||||
\(908\) | 26048.8 | 0.952047 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4580.56 | 0.166861 | ||||||||
\(911\) | −5627.30 | + | 9746.78i | −0.204655 | + | 0.354473i | −0.950023 | − | 0.312180i | \(-0.898941\pi\) |
0.745368 | + | 0.666654i | \(0.232274\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 623.371 | + | 1079.71i | 0.0225965 | + | 0.0391382i | ||||
\(914\) | 30364.0 | + | 52591.9i | 1.09885 | + | 1.90327i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7725.20 | + | 13380.4i | −0.278655 | + | 0.482644i | ||||
\(917\) | 10143.5 | 0.365287 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17825.9 | −0.639851 | −0.319925 | − | 0.947443i | \(-0.603658\pi\) | ||||
−0.319925 | + | 0.947443i | \(0.603658\pi\) | |||||||
\(920\) | 2102.96 | − | 3642.44i | 0.0753615 | − | 0.130530i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −25691.2 | − | 44498.5i | −0.917673 | − | 1.58946i | ||||
\(923\) | −4011.25 | − | 6947.68i | −0.143046 | − | 0.247764i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1716.04 | − | 2972.26i | 0.0609978 | − | 0.105651i | ||||
\(926\) | 39852.3 | 1.41428 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −19978.9 | −0.706725 | ||||||||
\(929\) | 1042.12 | − | 1805.00i | 0.0368039 | − | 0.0637461i | −0.847037 | − | 0.531534i | \(-0.821616\pi\) |
0.883841 | + | 0.467788i | \(0.154949\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1466.52 | + | 2540.09i | 0.0516255 | + | 0.0894180i | ||||
\(932\) | −4867.83 | − | 8431.33i | −0.171085 | − | 0.296328i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13822.6 | + | 23941.4i | −0.484250 | + | 0.838745i | ||||
\(935\) | −75.4114 | −0.00263767 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5419.51 | −0.188952 | −0.0944758 | − | 0.995527i | \(-0.530117\pi\) | ||||
−0.0944758 | + | 0.995527i | \(0.530117\pi\) | |||||||
\(938\) | −36875.5 | + | 63870.3i | −1.28361 | + | 2.22328i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4363.97 | + | 7558.61i | 0.151422 | + | 0.262271i | ||||
\(941\) | 23206.9 | + | 40195.6i | 0.803958 | + | 1.39250i | 0.916993 | + | 0.398904i | \(0.130609\pi\) |
−0.113035 | + | 0.993591i | \(0.536057\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5721.09 | − | 9909.23i | 0.197566 | − | 0.342194i | ||||
\(944\) | −26690.4 | −0.920232 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2040.31 | 0.0701230 | ||||||||
\(947\) | −9391.53 | + | 16266.6i | −0.322264 | + | 0.558177i | −0.980955 | − | 0.194237i | \(-0.937777\pi\) |
0.658691 | + | 0.752413i | \(0.271110\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5084.85 | − | 8807.22i | −0.173932 | − | 0.301258i | ||||
\(950\) | −2606.38 | − | 4514.38i | −0.0890126 | − | 0.154174i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −352.846 | + | 611.147i | −0.0120124 | + | 0.0208061i | ||||
\(953\) | −11796.7 | −0.400979 | −0.200489 | − | 0.979696i | \(-0.564253\pi\) | ||||
−0.200489 | + | 0.979696i | \(0.564253\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1433.57 | 0.0485752 | ||||||||
\(956\) | 1429.47 | − | 2475.91i | 0.0483601 | − | 0.0837622i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4379.78 | − | 7586.00i | −0.147708 | − | 0.255838i | ||||
\(959\) | 9768.41 | + | 16919.4i | 0.328924 | + | 0.569714i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22515.8 | + | 38998.5i | −0.755792 | + | 1.30907i | ||||
\(962\) | 6281.13 | 0.210511 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 32639.3 | 1.09050 | ||||||||
\(965\) | 11626.8 | − | 20138.1i | 0.387854 | − | 0.671782i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5080.87 | + | 8800.33i | 0.168966 | + | 0.292657i | 0.938057 | − | 0.346482i | \(-0.112624\pi\) |
−0.769091 | + | 0.639140i | \(0.779291\pi\) | |||||||
\(968\) | −2604.41 | − | 4510.98i | −0.0864763 | − | 0.149781i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11544.7 | + | 19996.0i | −0.382141 | + | 0.661888i | ||||
\(971\) | 36614.9 | 1.21012 | 0.605060 | − | 0.796180i | \(-0.293149\pi\) | ||||
0.605060 | + | 0.796180i | \(0.293149\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 37819.8 | 1.24609 | ||||||||
\(974\) | −13482.3 | + | 23352.1i | −0.443533 | + | 0.768222i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 18745.7 | + | 32468.6i | 0.614791 | + | 1.06485i | ||||
\(977\) | 25495.4 | + | 44159.4i | 0.834874 | + | 1.44604i | 0.894133 | + | 0.447801i | \(0.147793\pi\) |
−0.0592594 | + | 0.998243i | \(0.518874\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1292.87 | − | 2239.32i | 0.0422066 | − | 0.0731040i | ||||
\(980\) | 2592.52 | 0.0845052 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 53252.5 | 1.73051 | ||||||||
\(983\) | 10891.9 | − | 18865.4i | 0.353406 | − | 0.612117i | −0.633438 | − | 0.773794i | \(-0.718357\pi\) |
0.986844 | + | 0.161676i | \(0.0516901\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4237.04 | − | 7338.76i | −0.137059 | − | 0.237393i | ||||
\(986\) | −1422.88 | − | 2464.51i | −0.0459572 | − | 0.0796003i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2519.00 | − | 4363.04i | 0.0811135 | − | 0.140493i | ||||
\(989\) | 63332.8 | 2.03626 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50955.6 | −1.63336 | −0.816679 | − | 0.577092i | \(-0.804187\pi\) | ||||
−0.816679 | + | 0.577092i | \(0.804187\pi\) | |||||||
\(992\) | 35529.0 | − | 61538.0i | 1.13714 | − | 1.96959i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −29759.1 | − | 51544.3i | −0.949599 | − | 1.64475i | ||||
\(995\) | 8124.42 | + | 14071.9i | 0.258856 | + | 0.448351i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9581.42 | − | 16595.5i | 0.304360 | − | 0.527167i | −0.672759 | − | 0.739862i | \(-0.734891\pi\) |
0.977119 | + | 0.212695i | \(0.0682242\pi\) | |||||||
\(998\) | −21083.5 | −0.668724 | ||||||||
\(999\) | 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 | 405.4.e.w.136.6 | 12 | ||
3.2 | odd | 2 | 405.4.e.x.136.1 | 12 | |||
9.2 | odd | 6 | 405.4.a.k.1.6 | ✓ | 6 | ||
9.4 | even | 3 | inner | 405.4.e.w.271.6 | 12 | ||
9.5 | odd | 6 | 405.4.e.x.271.1 | 12 | |||
9.7 | even | 3 | 405.4.a.l.1.1 | yes | 6 | ||
45.29 | odd | 6 | 2025.4.a.z.1.1 | 6 | |||
45.34 | even | 6 | 2025.4.a.y.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
405.4.a.k.1.6 | ✓ | 6 | 9.2 | odd | 6 | ||
405.4.a.l.1.1 | yes | 6 | 9.7 | even | 3 | ||
405.4.e.w.136.6 | 12 | 1.1 | even | 1 | trivial | ||
405.4.e.w.271.6 | 12 | 9.4 | even | 3 | inner | ||
405.4.e.x.136.1 | 12 | 3.2 | odd | 2 | |||
405.4.e.x.271.1 | 12 | 9.5 | odd | 6 | |||
2025.4.a.y.1.6 | 6 | 45.34 | even | 6 | |||
2025.4.a.z.1.1 | 6 | 45.29 | odd | 6 |