Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,4,Mod(146,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.146");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.c (of order \(2\), degree \(1\), 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: | \(8.67328077084\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 146.8 | ||
Character | \(\chi\) | \(=\) | 147.146 |
Dual form | 147.4.c.b.146.18 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.86969i | − | 1.01459i | −0.861773 | − | 0.507294i | \(-0.830646\pi\) | ||
0.861773 | − | 0.507294i | \(-0.169354\pi\) | |||||||
\(3\) | 2.76278 | − | 4.40080i | 0.531698 | − | 0.846934i | ||||
\(4\) | −0.235115 | −0.0293894 | ||||||||
\(5\) | 5.57059 | 0.498249 | 0.249124 | − | 0.968471i | \(-0.419857\pi\) | ||||
0.249124 | + | 0.968471i | \(0.419857\pi\) | |||||||
\(6\) | −12.6289 | − | 7.92832i | −0.859290 | − | 0.539454i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 22.2828i | − | 0.984770i | ||||||
\(9\) | −11.7341 | − | 24.3169i | −0.434596 | − | 0.900626i | ||||
\(10\) | − | 15.9859i | − | 0.505517i | ||||||
\(11\) | 42.7198i | 1.17095i | 0.810689 | + | 0.585477i | \(0.199093\pi\) | ||||
−0.810689 | + | 0.585477i | \(0.800907\pi\) | |||||||
\(12\) | −0.649571 | + | 1.03469i | −0.0156263 | + | 0.0248909i | ||||
\(13\) | − | 69.8357i | − | 1.48992i | −0.667110 | − | 0.744959i | \(-0.732469\pi\) | ||
0.667110 | − | 0.744959i | \(-0.267531\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 15.3903 | − | 24.5151i | 0.264918 | − | 0.421984i | ||||
\(16\) | −65.8256 | −1.02853 | ||||||||
\(17\) | 67.5034 | 0.963058 | 0.481529 | − | 0.876430i | \(-0.340082\pi\) | ||||
0.481529 | + | 0.876430i | \(0.340082\pi\) | |||||||
\(18\) | −69.7819 | + | 33.6732i | −0.913764 | + | 0.440936i | ||||
\(19\) | − | 79.3413i | − | 0.958008i | −0.877813 | − | 0.479004i | \(-0.840998\pi\) | ||
0.877813 | − | 0.479004i | \(-0.159002\pi\) | |||||||
\(20\) | −1.30973 | −0.0146432 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 122.593 | 1.18804 | ||||||||
\(23\) | 208.831i | 1.89323i | 0.322365 | + | 0.946615i | \(0.395522\pi\) | ||||
−0.322365 | + | 0.946615i | \(0.604478\pi\) | |||||||
\(24\) | −98.0622 | − | 61.5625i | −0.834036 | − | 0.523600i | ||||
\(25\) | −93.9685 | −0.751748 | ||||||||
\(26\) | −200.407 | −1.51165 | ||||||||
\(27\) | −139.432 | − | 15.5429i | −0.993844 | − | 0.110787i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.72587i | − | 0.0366644i | −0.999832 | − | 0.0183322i | \(-0.994164\pi\) | ||
0.999832 | − | 0.0183322i | \(-0.00583564\pi\) | |||||||
\(30\) | −70.3506 | − | 44.1655i | −0.428140 | − | 0.268782i | ||||
\(31\) | 193.293i | 1.11989i | 0.828531 | + | 0.559944i | \(0.189177\pi\) | ||||
−0.828531 | + | 0.559944i | \(0.810823\pi\) | |||||||
\(32\) | 10.6367i | 0.0587599i | ||||||||
\(33\) | 188.001 | + | 118.025i | 0.991722 | + | 0.622594i | ||||
\(34\) | − | 193.714i | − | 0.977108i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.75886 | + | 5.71727i | 0.0127725 | + | 0.0264688i | ||||
\(37\) | 163.609 | 0.726949 | 0.363474 | − | 0.931604i | \(-0.381590\pi\) | ||||
0.363474 | + | 0.931604i | \(0.381590\pi\) | |||||||
\(38\) | −227.685 | −0.971983 | ||||||||
\(39\) | −307.333 | − | 192.941i | −1.26186 | − | 0.792186i | ||||
\(40\) | − | 124.128i | − | 0.490661i | ||||||
\(41\) | 58.1164 | 0.221372 | 0.110686 | − | 0.993855i | \(-0.464695\pi\) | ||||
0.110686 | + | 0.993855i | \(0.464695\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 58.9508 | 0.209068 | 0.104534 | − | 0.994521i | \(-0.466665\pi\) | ||||
0.104534 | + | 0.994521i | \(0.466665\pi\) | |||||||
\(44\) | − | 10.0441i | − | 0.0344136i | ||||||
\(45\) | −65.3658 | − | 135.460i | −0.216537 | − | 0.448736i | ||||
\(46\) | 599.280 | 1.92085 | ||||||||
\(47\) | 148.572 | 0.461094 | 0.230547 | − | 0.973061i | \(-0.425948\pi\) | ||||
0.230547 | + | 0.973061i | \(0.425948\pi\) | |||||||
\(48\) | −181.862 | + | 289.685i | −0.546865 | + | 0.871094i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 269.660i | 0.762715i | ||||||||
\(51\) | 186.497 | − | 297.069i | 0.512056 | − | 0.815647i | ||||
\(52\) | 16.4194i | 0.0437878i | ||||||||
\(53\) | 100.642i | 0.260834i | 0.991459 | + | 0.130417i | \(0.0416316\pi\) | ||||
−0.991459 | + | 0.130417i | \(0.958368\pi\) | |||||||
\(54\) | −44.6034 | + | 400.128i | −0.112403 | + | 1.00834i | ||||
\(55\) | 237.975i | 0.583427i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −349.165 | − | 219.203i | −0.811370 | − | 0.509370i | ||||
\(58\) | −16.4315 | −0.0371993 | ||||||||
\(59\) | 738.690 | 1.62999 | 0.814994 | − | 0.579469i | \(-0.196740\pi\) | ||||
0.814994 | + | 0.579469i | \(0.196740\pi\) | |||||||
\(60\) | −3.61850 | + | 5.76386i | −0.00778577 | + | 0.0124019i | ||||
\(61\) | − | 356.946i | − | 0.749218i | −0.927183 | − | 0.374609i | \(-0.877777\pi\) | ||
0.927183 | − | 0.374609i | \(-0.122223\pi\) | |||||||
\(62\) | 554.692 | 1.13622 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −496.081 | −0.968909 | ||||||||
\(65\) | − | 389.026i | − | 0.742350i | ||||||
\(66\) | 338.696 | − | 539.505i | 0.631676 | − | 1.00619i | ||||
\(67\) | 721.159 | 1.31498 | 0.657489 | − | 0.753464i | \(-0.271619\pi\) | ||||
0.657489 | + | 0.753464i | \(0.271619\pi\) | |||||||
\(68\) | −15.8711 | −0.0283037 | ||||||||
\(69\) | 919.024 | + | 576.955i | 1.60344 | + | 1.00663i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 308.915i | − | 0.516359i | −0.966097 | − | 0.258180i | \(-0.916877\pi\) | ||
0.966097 | − | 0.258180i | \(-0.0831226\pi\) | |||||||
\(72\) | −541.849 | + | 261.468i | −0.886909 | + | 0.427977i | ||||
\(73\) | 827.134i | 1.32615i | 0.748555 | + | 0.663073i | \(0.230748\pi\) | ||||
−0.748555 | + | 0.663073i | \(0.769252\pi\) | |||||||
\(74\) | − | 469.506i | − | 0.737554i | ||||||
\(75\) | −259.614 | + | 413.537i | −0.399703 | + | 0.636681i | ||||
\(76\) | 18.6543i | 0.0281552i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −553.680 | + | 881.950i | −0.803743 | + | 1.28027i | ||||
\(79\) | 467.203 | 0.665373 | 0.332686 | − | 0.943038i | \(-0.392045\pi\) | ||||
0.332686 | + | 0.943038i | \(0.392045\pi\) | |||||||
\(80\) | −366.688 | −0.512462 | ||||||||
\(81\) | −453.623 | + | 570.673i | −0.622253 | + | 0.782816i | ||||
\(82\) | − | 166.776i | − | 0.224602i | ||||||
\(83\) | −274.704 | −0.363285 | −0.181643 | − | 0.983365i | \(-0.558141\pi\) | ||||
−0.181643 | + | 0.983365i | \(0.558141\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 376.034 | 0.479843 | ||||||||
\(86\) | − | 169.170i | − | 0.212118i | ||||||
\(87\) | −25.1984 | − | 15.8193i | −0.0310523 | − | 0.0194944i | ||||
\(88\) | 951.917 | 1.15312 | ||||||||
\(89\) | 541.074 | 0.644424 | 0.322212 | − | 0.946668i | \(-0.395574\pi\) | ||||
0.322212 | + | 0.946668i | \(0.395574\pi\) | |||||||
\(90\) | −388.727 | + | 187.579i | −0.455282 | + | 0.219696i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 49.0993i | − | 0.0556409i | ||||||
\(93\) | 850.645 | + | 534.027i | 0.948471 | + | 0.595441i | ||||
\(94\) | − | 426.355i | − | 0.467821i | ||||||
\(95\) | − | 441.978i | − | 0.477326i | ||||||
\(96\) | 46.8099 | + | 29.3868i | 0.0497658 | + | 0.0312425i | ||||
\(97\) | − | 41.4658i | − | 0.0434042i | −0.999764 | − | 0.0217021i | \(-0.993091\pi\) | ||
0.999764 | − | 0.0217021i | \(-0.00690854\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1038.81 | − | 501.277i | 1.05459 | − | 0.508892i | ||||
\(100\) | 22.0934 | 0.0220934 | ||||||||
\(101\) | −1263.68 | −1.24496 | −0.622479 | − | 0.782637i | \(-0.713874\pi\) | ||||
−0.622479 | + | 0.782637i | \(0.713874\pi\) | |||||||
\(102\) | −852.496 | − | 535.189i | −0.827546 | − | 0.519526i | ||||
\(103\) | − | 309.423i | − | 0.296003i | −0.988987 | − | 0.148001i | \(-0.952716\pi\) | ||
0.988987 | − | 0.148001i | \(-0.0472840\pi\) | |||||||
\(104\) | −1556.14 | −1.46723 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 288.810 | 0.264639 | ||||||||
\(107\) | − | 895.715i | − | 0.809272i | −0.914478 | − | 0.404636i | \(-0.867398\pi\) | ||
0.914478 | − | 0.404636i | \(-0.132602\pi\) | |||||||
\(108\) | 32.7827 | + | 3.65438i | 0.0292085 | + | 0.00325595i | ||||
\(109\) | −1590.61 | −1.39773 | −0.698865 | − | 0.715254i | \(-0.746311\pi\) | ||||
−0.698865 | + | 0.715254i | \(0.746311\pi\) | |||||||
\(110\) | 682.913 | 0.591938 | ||||||||
\(111\) | 452.015 | − | 720.009i | 0.386517 | − | 0.615678i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 859.839i | 0.715812i | 0.933758 | + | 0.357906i | \(0.116509\pi\) | ||||
−0.933758 | + | 0.357906i | \(0.883491\pi\) | |||||||
\(114\) | −629.044 | + | 1002.00i | −0.516801 | + | 0.823206i | ||||
\(115\) | 1163.31i | 0.943300i | ||||||||
\(116\) | 1.34624i | 0.00107754i | ||||||||
\(117\) | −1698.19 | + | 819.458i | −1.34186 | + | 0.647512i | ||||
\(118\) | − | 2119.81i | − | 1.65377i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −546.264 | − | 342.940i | −0.415557 | − | 0.260883i | ||||
\(121\) | −493.980 | −0.371135 | ||||||||
\(122\) | −1024.32 | −0.760147 | ||||||||
\(123\) | 160.563 | − | 255.759i | 0.117703 | − | 0.187488i | ||||
\(124\) | − | 45.4462i | − | 0.0329128i | ||||||
\(125\) | −1219.78 | −0.872807 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1382.66 | 0.966075 | 0.483038 | − | 0.875600i | \(-0.339533\pi\) | ||||
0.483038 | + | 0.875600i | \(0.339533\pi\) | |||||||
\(128\) | 1508.69i | 1.04180i | ||||||||
\(129\) | 162.868 | − | 259.431i | 0.111161 | − | 0.177067i | ||||
\(130\) | −1116.38 | −0.753180 | ||||||||
\(131\) | −879.895 | −0.586846 | −0.293423 | − | 0.955983i | \(-0.594794\pi\) | ||||
−0.293423 | + | 0.955983i | \(0.594794\pi\) | |||||||
\(132\) | −44.2019 | − | 27.7496i | −0.0291461 | − | 0.0182976i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 2069.50i | − | 1.33416i | ||||||
\(135\) | −776.721 | − | 86.5833i | −0.495182 | − | 0.0551993i | ||||
\(136\) | − | 1504.17i | − | 0.948391i | ||||||
\(137\) | 3037.41i | 1.89419i | 0.320958 | + | 0.947093i | \(0.395995\pi\) | ||||
−0.320958 | + | 0.947093i | \(0.604005\pi\) | |||||||
\(138\) | 1655.68 | − | 2637.31i | 1.02131 | − | 1.62683i | ||||
\(139\) | 652.162i | 0.397954i | 0.980004 | + | 0.198977i | \(0.0637620\pi\) | ||||
−0.980004 | + | 0.198977i | \(0.936238\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 410.472 | − | 653.835i | 0.245163 | − | 0.390517i | ||||
\(142\) | −886.491 | −0.523892 | ||||||||
\(143\) | 2983.37 | 1.74463 | ||||||||
\(144\) | 772.403 | + | 1600.68i | 0.446993 | + | 0.926317i | ||||
\(145\) | − | 31.8965i | − | 0.0182680i | ||||||
\(146\) | 2373.62 | 1.34549 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −38.4669 | −0.0213646 | ||||||||
\(149\) | − | 395.474i | − | 0.217440i | −0.994072 | − | 0.108720i | \(-0.965325\pi\) | ||
0.994072 | − | 0.108720i | \(-0.0346752\pi\) | |||||||
\(150\) | 1186.72 | + | 745.013i | 0.645969 | + | 0.405534i | ||||
\(151\) | −705.128 | −0.380017 | −0.190008 | − | 0.981782i | \(-0.560852\pi\) | ||||
−0.190008 | + | 0.981782i | \(0.560852\pi\) | |||||||
\(152\) | −1767.95 | −0.943417 | ||||||||
\(153\) | −792.091 | − | 1641.47i | −0.418541 | − | 0.867355i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1076.76i | 0.557983i | ||||||||
\(156\) | 72.2586 | + | 45.3633i | 0.0370854 | + | 0.0232819i | ||||
\(157\) | − | 1597.79i | − | 0.812214i | −0.913825 | − | 0.406107i | \(-0.866886\pi\) | ||
0.913825 | − | 0.406107i | \(-0.133114\pi\) | |||||||
\(158\) | − | 1340.73i | − | 0.675079i | ||||||
\(159\) | 442.903 | + | 278.051i | 0.220909 | + | 0.138685i | ||||
\(160\) | 59.2526i | 0.0292771i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1637.65 | + | 1301.76i | 0.794236 | + | 0.631331i | ||||
\(163\) | −2736.42 | −1.31493 | −0.657463 | − | 0.753487i | \(-0.728370\pi\) | ||||
−0.657463 | + | 0.753487i | \(0.728370\pi\) | |||||||
\(164\) | −13.6640 | −0.00650599 | ||||||||
\(165\) | 1047.28 | + | 657.472i | 0.494124 | + | 0.310207i | ||||
\(166\) | 788.315i | 0.368585i | ||||||||
\(167\) | −24.6732 | −0.0114328 | −0.00571638 | − | 0.999984i | \(-0.501820\pi\) | ||||
−0.00571638 | + | 0.999984i | \(0.501820\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2680.03 | −1.21986 | ||||||||
\(170\) | − | 1079.10i | − | 0.486843i | ||||||
\(171\) | −1929.33 | + | 930.997i | −0.862806 | + | 0.416346i | ||||
\(172\) | −13.8602 | −0.00614437 | ||||||||
\(173\) | 1403.61 | 0.616847 | 0.308424 | − | 0.951249i | \(-0.400199\pi\) | ||||
0.308424 | + | 0.951249i | \(0.400199\pi\) | |||||||
\(174\) | −45.3965 | + | 72.3116i | −0.0197787 | + | 0.0315053i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 2812.06i | − | 1.20436i | ||||||
\(177\) | 2040.84 | − | 3250.83i | 0.866661 | − | 1.38049i | ||||
\(178\) | − | 1552.71i | − | 0.653825i | ||||||
\(179\) | − | 1714.52i | − | 0.715919i | −0.933737 | − | 0.357959i | \(-0.883473\pi\) | ||
0.933737 | − | 0.357959i | \(-0.116527\pi\) | |||||||
\(180\) | 15.3685 | + | 31.8486i | 0.00636388 | + | 0.0131881i | ||||
\(181\) | 2046.41i | 0.840377i | 0.907437 | + | 0.420189i | \(0.138036\pi\) | ||||
−0.907437 | + | 0.420189i | \(0.861964\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1570.85 | − | 986.164i | −0.634538 | − | 0.398357i | ||||
\(184\) | 4653.34 | 1.86440 | ||||||||
\(185\) | 911.397 | 0.362201 | ||||||||
\(186\) | 1532.49 | − | 2441.09i | 0.604128 | − | 0.962307i | ||||
\(187\) | 2883.73i | 1.12770i | ||||||||
\(188\) | −34.9315 | −0.0135513 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1268.34 | −0.484290 | ||||||||
\(191\) | 3373.11i | 1.27785i | 0.769268 | + | 0.638926i | \(0.220621\pi\) | ||||
−0.769268 | + | 0.638926i | \(0.779379\pi\) | |||||||
\(192\) | −1370.56 | + | 2183.15i | −0.515166 | + | 0.820602i | ||||
\(193\) | −424.928 | −0.158482 | −0.0792409 | − | 0.996855i | \(-0.525250\pi\) | ||||
−0.0792409 | + | 0.996855i | \(0.525250\pi\) | |||||||
\(194\) | −118.994 | −0.0440374 | ||||||||
\(195\) | −1712.03 | − | 1074.79i | −0.628722 | − | 0.394706i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4420.59i | 1.59875i | 0.600832 | + | 0.799375i | \(0.294836\pi\) | ||||
−0.600832 | + | 0.799375i | \(0.705164\pi\) | |||||||
\(198\) | −1438.51 | − | 2981.07i | −0.516316 | − | 1.06998i | ||||
\(199\) | 1577.80i | 0.562046i | 0.959701 | + | 0.281023i | \(0.0906737\pi\) | ||||
−0.959701 | + | 0.281023i | \(0.909326\pi\) | |||||||
\(200\) | 2093.88i | 0.740299i | ||||||||
\(201\) | 1992.40 | − | 3173.67i | 0.699171 | − | 1.11370i | ||||
\(202\) | 3626.36i | 1.26312i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −43.8483 | + | 69.8454i | −0.0150490 | + | 0.0239714i | ||||
\(205\) | 323.743 | 0.110298 | ||||||||
\(206\) | −887.946 | −0.300321 | ||||||||
\(207\) | 5078.13 | − | 2450.44i | 1.70509 | − | 0.822790i | ||||
\(208\) | 4596.98i | 1.53242i | ||||||||
\(209\) | 3389.44 | 1.12178 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 911.064 | 0.297252 | 0.148626 | − | 0.988893i | \(-0.452515\pi\) | ||||
0.148626 | + | 0.988893i | \(0.452515\pi\) | |||||||
\(212\) | − | 23.6623i | − | 0.00766574i | ||||||
\(213\) | −1359.47 | − | 853.465i | −0.437322 | − | 0.274547i | ||||
\(214\) | −2570.42 | −0.821078 | ||||||||
\(215\) | 328.391 | 0.104168 | ||||||||
\(216\) | −346.340 | + | 3106.95i | −0.109099 | + | 0.978708i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4564.55i | 1.41812i | ||||||||
\(219\) | 3640.05 | + | 2285.19i | 1.12316 | + | 0.705109i | ||||
\(220\) | − | 55.9514i | − | 0.0171466i | ||||||
\(221\) | − | 4714.15i | − | 1.43488i | ||||||
\(222\) | −2066.20 | − | 1297.14i | −0.624659 | − | 0.392155i | ||||
\(223\) | 3070.23i | 0.921964i | 0.887410 | + | 0.460982i | \(0.152503\pi\) | ||||
−0.887410 | + | 0.460982i | \(0.847497\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1102.63 | + | 2285.02i | 0.326706 | + | 0.677044i | ||||
\(226\) | 2467.47 | 0.726255 | ||||||||
\(227\) | −3352.67 | −0.980284 | −0.490142 | − | 0.871643i | \(-0.663055\pi\) | ||||
−0.490142 | + | 0.871643i | \(0.663055\pi\) | |||||||
\(228\) | 82.0940 | + | 51.5378i | 0.0238456 | + | 0.0149701i | ||||
\(229\) | − | 4353.50i | − | 1.25628i | −0.778102 | − | 0.628138i | \(-0.783817\pi\) | ||
0.778102 | − | 0.628138i | \(-0.216183\pi\) | |||||||
\(230\) | 3338.35 | 0.957061 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −127.588 | −0.0361060 | ||||||||
\(233\) | 3683.52i | 1.03569i | 0.855475 | + | 0.517844i | \(0.173265\pi\) | ||||
−0.855475 | + | 0.517844i | \(0.826735\pi\) | |||||||
\(234\) | 2351.59 | + | 4873.27i | 0.656958 | + | 1.36143i | ||||
\(235\) | 827.633 | 0.229740 | ||||||||
\(236\) | −173.677 | −0.0479043 | ||||||||
\(237\) | 1290.78 | − | 2056.07i | 0.353777 | − | 0.563527i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 4537.46i | − | 1.22805i | −0.789287 | − | 0.614025i | \(-0.789549\pi\) | ||
0.789287 | − | 0.614025i | \(-0.210451\pi\) | |||||||
\(240\) | −1013.08 | + | 1613.72i | −0.272475 | + | 0.434021i | ||||
\(241\) | − | 2221.10i | − | 0.593666i | −0.954929 | − | 0.296833i | \(-0.904069\pi\) | ||
0.954929 | − | 0.296833i | \(-0.0959305\pi\) | |||||||
\(242\) | 1417.57i | 0.376549i | ||||||||
\(243\) | 1258.16 | + | 3572.95i | 0.332143 | + | 0.943229i | ||||
\(244\) | 83.9234i | 0.0220190i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −733.948 | − | 460.766i | −0.190223 | − | 0.119420i | ||||
\(247\) | −5540.86 | −1.42735 | ||||||||
\(248\) | 4307.12 | 1.10283 | ||||||||
\(249\) | −758.947 | + | 1208.92i | −0.193158 | + | 0.307679i | ||||
\(250\) | 3500.40i | 0.885539i | ||||||||
\(251\) | −652.142 | −0.163995 | −0.0819976 | − | 0.996633i | \(-0.526130\pi\) | ||||
−0.0819976 | + | 0.996633i | \(0.526130\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8921.22 | −2.21689 | ||||||||
\(254\) | − | 3967.82i | − | 0.980169i | ||||||
\(255\) | 1038.90 | − | 1654.85i | 0.255131 | − | 0.406395i | ||||
\(256\) | 360.828 | 0.0880927 | ||||||||
\(257\) | −6873.84 | −1.66840 | −0.834199 | − | 0.551464i | \(-0.814069\pi\) | ||||
−0.834199 | + | 0.551464i | \(0.814069\pi\) | |||||||
\(258\) | −744.485 | − | 467.381i | −0.179650 | − | 0.112782i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 91.4659i | 0.0218172i | ||||||||
\(261\) | −139.235 | + | 67.1878i | −0.0330209 | + | 0.0159342i | ||||
\(262\) | 2525.03i | 0.595407i | ||||||||
\(263\) | 3285.60i | 0.770337i | 0.922846 | + | 0.385169i | \(0.125857\pi\) | ||||
−0.922846 | + | 0.385169i | \(0.874143\pi\) | |||||||
\(264\) | 2629.94 | − | 4189.20i | 0.613112 | − | 0.976618i | ||||
\(265\) | 560.633i | 0.129960i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1494.87 | − | 2381.16i | 0.342638 | − | 0.545785i | ||||
\(268\) | −169.555 | −0.0386464 | ||||||||
\(269\) | 1257.58 | 0.285040 | 0.142520 | − | 0.989792i | \(-0.454479\pi\) | ||||
0.142520 | + | 0.989792i | \(0.454479\pi\) | |||||||
\(270\) | −248.467 | + | 2228.95i | −0.0560046 | + | 0.502406i | ||||
\(271\) | − | 370.755i | − | 0.0831061i | −0.999136 | − | 0.0415530i | \(-0.986769\pi\) | ||
0.999136 | − | 0.0415530i | \(-0.0132306\pi\) | |||||||
\(272\) | −4443.46 | −0.990530 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8716.43 | 1.92182 | ||||||||
\(275\) | − | 4014.31i | − | 0.880263i | ||||||
\(276\) | −216.076 | − | 135.651i | −0.0471242 | − | 0.0295841i | ||||
\(277\) | −1540.16 | −0.334078 | −0.167039 | − | 0.985950i | \(-0.553421\pi\) | ||||
−0.167039 | + | 0.985950i | \(0.553421\pi\) | |||||||
\(278\) | 1871.50 | 0.403760 | ||||||||
\(279\) | 4700.29 | − | 2268.12i | 1.00860 | − | 0.486698i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 3782.78i | − | 0.803066i | −0.915845 | − | 0.401533i | \(-0.868478\pi\) | ||
0.915845 | − | 0.401533i | \(-0.131522\pi\) | |||||||
\(282\) | −1876.30 | − | 1177.93i | −0.396214 | − | 0.248739i | ||||
\(283\) | − | 9263.07i | − | 1.94570i | −0.231441 | − | 0.972849i | \(-0.574344\pi\) | ||
0.231441 | − | 0.972849i | \(-0.425656\pi\) | |||||||
\(284\) | 72.6306i | 0.0151755i | ||||||||
\(285\) | −1945.06 | − | 1221.09i | −0.404264 | − | 0.253793i | ||||
\(286\) | − | 8561.34i | − | 1.77008i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 258.651 | − | 124.812i | 0.0529207 | − | 0.0255368i | ||||
\(289\) | −356.285 | −0.0725187 | ||||||||
\(290\) | −91.5330 | −0.0185345 | ||||||||
\(291\) | −182.482 | − | 114.561i | −0.0367605 | − | 0.0230779i | ||||
\(292\) | − | 194.472i | − | 0.0389746i | ||||||
\(293\) | −7316.39 | −1.45880 | −0.729399 | − | 0.684089i | \(-0.760200\pi\) | ||||
−0.729399 | + | 0.684089i | \(0.760200\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4114.94 | 0.812140 | ||||||||
\(296\) | − | 3645.66i | − | 0.715877i | ||||||
\(297\) | 663.991 | − | 5956.53i | 0.129726 | − | 1.16375i | ||||
\(298\) | −1134.89 | −0.220612 | ||||||||
\(299\) | 14583.9 | 2.82076 | ||||||||
\(300\) | 61.0393 | − | 97.2287i | 0.0117470 | − | 0.0187117i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2023.50i | 0.385561i | ||||||||
\(303\) | −3491.27 | + | 5561.20i | −0.661941 | + | 1.05440i | ||||
\(304\) | 5222.69i | 0.985335i | ||||||||
\(305\) | − | 1988.40i | − | 0.373297i | ||||||
\(306\) | −4710.52 | + | 2273.05i | −0.880008 | + | 0.424647i | ||||
\(307\) | − | 4347.69i | − | 0.808260i | −0.914701 | − | 0.404130i | \(-0.867574\pi\) | ||
0.914701 | − | 0.404130i | \(-0.132426\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1361.71 | − | 854.867i | −0.250695 | − | 0.157384i | ||||
\(310\) | 3089.96 | 0.566123 | ||||||||
\(311\) | −4550.35 | −0.829667 | −0.414833 | − | 0.909897i | \(-0.636160\pi\) | ||||
−0.414833 | + | 0.909897i | \(0.636160\pi\) | |||||||
\(312\) | −4299.26 | + | 6848.24i | −0.780121 | + | 1.24265i | ||||
\(313\) | − | 8447.73i | − | 1.52554i | −0.646670 | − | 0.762770i | \(-0.723839\pi\) | ||
0.646670 | − | 0.762770i | \(-0.276161\pi\) | |||||||
\(314\) | −4585.17 | −0.824063 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −109.846 | −0.0195549 | ||||||||
\(317\) | − | 3333.54i | − | 0.590632i | −0.955400 | − | 0.295316i | \(-0.904575\pi\) | ||
0.955400 | − | 0.295316i | \(-0.0954249\pi\) | |||||||
\(318\) | 797.919 | − | 1271.00i | 0.140708 | − | 0.224132i | ||||
\(319\) | 244.608 | 0.0429323 | ||||||||
\(320\) | −2763.47 | −0.482758 | ||||||||
\(321\) | −3941.86 | − | 2474.67i | −0.685400 | − | 0.430288i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5355.81i | − | 0.922617i | ||||||
\(324\) | 106.654 | − | 134.174i | 0.0182876 | − | 0.0230065i | ||||
\(325\) | 6562.36i | 1.12004i | ||||||||
\(326\) | 7852.67i | 1.33411i | ||||||||
\(327\) | −4394.50 | + | 6999.94i | −0.743169 | + | 1.18379i | ||||
\(328\) | − | 1295.00i | − | 0.218001i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1886.74 | − | 3005.36i | 0.314732 | − | 0.501333i | ||||
\(331\) | −7496.89 | −1.24491 | −0.622457 | − | 0.782654i | \(-0.713865\pi\) | ||||
−0.622457 | + | 0.782654i | \(0.713865\pi\) | |||||||
\(332\) | 64.5870 | 0.0106767 | ||||||||
\(333\) | −1919.80 | − | 3978.46i | −0.315929 | − | 0.654709i | ||||
\(334\) | 70.8045i | 0.0115996i | ||||||||
\(335\) | 4017.28 | 0.655186 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5107.78 | 0.825633 | 0.412817 | − | 0.910814i | \(-0.364545\pi\) | ||||
0.412817 | + | 0.910814i | \(0.364545\pi\) | |||||||
\(338\) | 7690.84i | 1.23765i | ||||||||
\(339\) | 3783.98 | + | 2375.55i | 0.606246 | + | 0.380596i | ||||
\(340\) | −88.4113 | −0.0141023 | ||||||||
\(341\) | −8257.45 | −1.31134 | ||||||||
\(342\) | 2671.67 | + | 5536.59i | 0.422420 | + | 0.875393i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 1313.59i | − | 0.205884i | ||||||
\(345\) | 5119.51 | + | 3213.98i | 0.798913 | + | 0.501550i | ||||
\(346\) | − | 4027.93i | − | 0.625846i | ||||||
\(347\) | − | 2966.35i | − | 0.458910i | −0.973319 | − | 0.229455i | \(-0.926306\pi\) | ||
0.973319 | − | 0.229455i | \(-0.0736944\pi\) | |||||||
\(348\) | 5.92452 | + | 3.71936i | 0.000912608 | + | 0.000572927i | ||||
\(349\) | − | 2869.90i | − | 0.440178i | −0.975480 | − | 0.220089i | \(-0.929365\pi\) | ||
0.975480 | − | 0.220089i | \(-0.0706348\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1085.45 | + | 9737.37i | −0.165063 | + | 1.48075i | ||||
\(352\) | −454.397 | −0.0688052 | ||||||||
\(353\) | −12653.2 | −1.90783 | −0.953913 | − | 0.300083i | \(-0.902986\pi\) | ||||
−0.953913 | + | 0.300083i | \(0.902986\pi\) | |||||||
\(354\) | −9328.87 | − | 5856.58i | −1.40063 | − | 0.879304i | ||||
\(355\) | − | 1720.84i | − | 0.257275i | ||||||
\(356\) | −127.215 | −0.0189392 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4920.15 | −0.726363 | ||||||||
\(359\) | 6591.26i | 0.969006i | 0.874790 | + | 0.484503i | \(0.161000\pi\) | ||||
−0.874790 | + | 0.484503i | \(0.839000\pi\) | |||||||
\(360\) | −3018.42 | + | 1456.53i | −0.441902 | + | 0.213239i | ||||
\(361\) | 563.957 | 0.0822214 | ||||||||
\(362\) | 5872.55 | 0.852637 | ||||||||
\(363\) | −1364.76 | + | 2173.91i | −0.197331 | + | 0.314327i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4607.62i | 0.660751i | ||||||||
\(366\) | −2829.98 | + | 4507.85i | −0.404168 | + | 0.643795i | ||||
\(367\) | 10286.0i | 1.46301i | 0.681836 | + | 0.731505i | \(0.261182\pi\) | ||||
−0.681836 | + | 0.731505i | \(0.738818\pi\) | |||||||
\(368\) | − | 13746.4i | − | 1.94724i | ||||||
\(369\) | −681.943 | − | 1413.21i | −0.0962074 | − | 0.199373i | ||||
\(370\) | − | 2615.43i | − | 0.367485i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −199.999 | − | 125.558i | −0.0278750 | − | 0.0174996i | ||||
\(373\) | 4411.01 | 0.612314 | 0.306157 | − | 0.951981i | \(-0.400957\pi\) | ||||
0.306157 | + | 0.951981i | \(0.400957\pi\) | |||||||
\(374\) | 8275.42 | 1.14415 | ||||||||
\(375\) | −3370.00 | + | 5368.03i | −0.464069 | + | 0.739210i | ||||
\(376\) | − | 3310.60i | − | 0.454072i | ||||||
\(377\) | −399.870 | −0.0546269 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3838.27 | 0.520207 | 0.260103 | − | 0.965581i | \(-0.416243\pi\) | ||||
0.260103 | + | 0.965581i | \(0.416243\pi\) | |||||||
\(380\) | 103.916i | 0.0140283i | ||||||||
\(381\) | 3820.00 | − | 6084.83i | 0.513660 | − | 0.818202i | ||||
\(382\) | 9679.78 | 1.29649 | ||||||||
\(383\) | −2126.75 | −0.283739 | −0.141869 | − | 0.989885i | \(-0.545311\pi\) | ||||
−0.141869 | + | 0.989885i | \(0.545311\pi\) | |||||||
\(384\) | 6639.45 | + | 4168.19i | 0.882339 | + | 0.553924i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1219.41i | 0.160794i | ||||||||
\(387\) | −691.733 | − | 1433.50i | −0.0908598 | − | 0.188292i | ||||
\(388\) | 9.74922i | 0.00127562i | ||||||||
\(389\) | 7218.57i | 0.940864i | 0.882436 | + | 0.470432i | \(0.155902\pi\) | ||||
−0.882436 | + | 0.470432i | \(0.844098\pi\) | |||||||
\(390\) | −3084.33 | + | 4912.98i | −0.400464 | + | 0.637894i | ||||
\(391\) | 14096.8i | 1.82329i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2430.96 | + | 3872.24i | −0.312025 | + | 0.497020i | ||||
\(394\) | 12685.7 | 1.62207 | ||||||||
\(395\) | 2602.60 | 0.331521 | ||||||||
\(396\) | −244.240 | + | 117.858i | −0.0309938 | + | 0.0149560i | ||||
\(397\) | 115.449i | 0.0145950i | 0.999973 | + | 0.00729750i | \(0.00232289\pi\) | ||||
−0.999973 | + | 0.00729750i | \(0.997677\pi\) | |||||||
\(398\) | 4527.79 | 0.570245 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6185.54 | 0.773192 | ||||||||
\(401\) | − | 8905.68i | − | 1.10905i | −0.832168 | − | 0.554524i | \(-0.812900\pi\) | ||
0.832168 | − | 0.554524i | \(-0.187100\pi\) | |||||||
\(402\) | −9107.46 | − | 5717.58i | −1.12995 | − | 0.709370i | ||||
\(403\) | 13498.8 | 1.66854 | ||||||||
\(404\) | 297.110 | 0.0365885 | ||||||||
\(405\) | −2526.95 | + | 3178.99i | −0.310037 | + | 0.390037i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6989.33i | 0.851224i | ||||||||
\(408\) | −6619.53 | − | 4155.68i | −0.803225 | − | 0.504257i | ||||
\(409\) | 6752.61i | 0.816370i | 0.912899 | + | 0.408185i | \(0.133838\pi\) | ||||
−0.912899 | + | 0.408185i | \(0.866162\pi\) | |||||||
\(410\) | − | 929.041i | − | 0.111908i | ||||||
\(411\) | 13367.0 | + | 8391.70i | 1.60425 | + | 1.00713i | ||||
\(412\) | 72.7499i | 0.00869934i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −7032.00 | − | 14572.6i | −0.834793 | − | 1.72997i | ||||
\(415\) | −1530.26 | −0.181007 | ||||||||
\(416\) | 742.820 | 0.0875475 | ||||||||
\(417\) | 2870.04 | + | 1801.78i | 0.337041 | + | 0.211591i | ||||
\(418\) | − | 9726.65i | − | 1.13815i | ||||||
\(419\) | 888.062 | 0.103543 | 0.0517717 | − | 0.998659i | \(-0.483513\pi\) | ||||
0.0517717 | + | 0.998659i | \(0.483513\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14976.0 | −1.73369 | −0.866847 | − | 0.498574i | \(-0.833857\pi\) | ||||
−0.866847 | + | 0.498574i | \(0.833857\pi\) | |||||||
\(422\) | − | 2614.47i | − | 0.301589i | ||||||
\(423\) | −1743.35 | − | 3612.81i | −0.200390 | − | 0.415273i | ||||
\(424\) | 2242.58 | 0.256861 | ||||||||
\(425\) | −6343.20 | −0.723977 | ||||||||
\(426\) | −2449.18 | + | 3901.27i | −0.278552 | + | 0.443702i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 210.596i | 0.0237840i | ||||||||
\(429\) | 8242.39 | − | 13129.2i | 0.927614 | − | 1.47758i | ||||
\(430\) | − | 942.379i | − | 0.105687i | ||||||
\(431\) | − | 1095.38i | − | 0.122419i | −0.998125 | − | 0.0612095i | \(-0.980504\pi\) | ||
0.998125 | − | 0.0612095i | \(-0.0194958\pi\) | |||||||
\(432\) | 9178.23 | + | 1023.12i | 1.02219 | + | 0.113947i | ||||
\(433\) | − | 12688.2i | − | 1.40822i | −0.710093 | − | 0.704108i | \(-0.751347\pi\) | ||
0.710093 | − | 0.704108i | \(-0.248653\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −140.370 | − | 88.1230i | −0.0154718 | − | 0.00971304i | ||||
\(436\) | 373.976 | 0.0410784 | ||||||||
\(437\) | 16568.9 | 1.81373 | ||||||||
\(438\) | 6557.78 | − | 10445.8i | 0.715395 | − | 1.13954i | ||||
\(439\) | 13445.2i | 1.46175i | 0.682513 | + | 0.730873i | \(0.260887\pi\) | ||||
−0.682513 | + | 0.730873i | \(0.739113\pi\) | |||||||
\(440\) | 5302.74 | 0.574541 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −13528.1 | −1.45581 | ||||||||
\(443\) | − | 2276.97i | − | 0.244204i | −0.992518 | − | 0.122102i | \(-0.961037\pi\) | ||
0.992518 | − | 0.122102i | \(-0.0389634\pi\) | |||||||
\(444\) | −106.276 | + | 169.285i | −0.0113595 | + | 0.0180944i | ||||
\(445\) | 3014.10 | 0.321083 | ||||||||
\(446\) | 8810.61 | 0.935414 | ||||||||
\(447\) | −1740.40 | − | 1092.61i | −0.184157 | − | 0.115612i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 1685.89i | − | 0.177198i | −0.996067 | − | 0.0885991i | \(-0.971761\pi\) | ||
0.996067 | − | 0.0885991i | \(-0.0282390\pi\) | |||||||
\(450\) | 6557.30 | − | 3164.22i | 0.686921 | − | 0.331472i | ||||
\(451\) | 2482.72i | 0.259217i | ||||||||
\(452\) | − | 202.161i | − | 0.0210373i | ||||||
\(453\) | −1948.12 | + | 3103.13i | −0.202054 | + | 0.321849i | ||||
\(454\) | 9621.12i | 0.994585i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4884.45 | + | 7780.38i | −0.501613 | + | 0.799013i | ||||
\(457\) | −2083.59 | −0.213275 | −0.106637 | − | 0.994298i | \(-0.534008\pi\) | ||||
−0.106637 | + | 0.994298i | \(0.534008\pi\) | |||||||
\(458\) | −12493.2 | −1.27460 | ||||||||
\(459\) | −9412.17 | − | 1049.20i | −0.957130 | − | 0.106694i | ||||
\(460\) | − | 273.512i | − | 0.0277230i | ||||||
\(461\) | 14128.1 | 1.42736 | 0.713679 | − | 0.700473i | \(-0.247028\pi\) | ||||
0.713679 | + | 0.700473i | \(0.247028\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16141.5 | 1.62021 | 0.810106 | − | 0.586283i | \(-0.199409\pi\) | ||||
0.810106 | + | 0.586283i | \(0.199409\pi\) | |||||||
\(464\) | 376.909i | 0.0377103i | ||||||||
\(465\) | 4738.60 | + | 2974.85i | 0.472575 | + | 0.296678i | ||||
\(466\) | 10570.6 | 1.05080 | ||||||||
\(467\) | −6249.38 | −0.619244 | −0.309622 | − | 0.950860i | \(-0.600203\pi\) | ||||
−0.309622 | + | 0.950860i | \(0.600203\pi\) | |||||||
\(468\) | 399.269 | − | 192.667i | 0.0394364 | − | 0.0190300i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 2375.05i | − | 0.233091i | ||||||
\(471\) | −7031.56 | − | 4414.35i | −0.687892 | − | 0.431852i | ||||
\(472\) | − | 16460.1i | − | 1.60516i | ||||||
\(473\) | 2518.36i | 0.244809i | ||||||||
\(474\) | −5900.27 | − | 3704.14i | −0.571748 | − | 0.358938i | ||||
\(475\) | 7455.58i | 0.720180i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2447.29 | − | 1180.94i | 0.234914 | − | 0.113357i | ||||
\(478\) | −13021.1 | −1.24597 | ||||||||
\(479\) | 10624.2 | 1.01343 | 0.506713 | − | 0.862115i | \(-0.330860\pi\) | ||||
0.506713 | + | 0.862115i | \(0.330860\pi\) | |||||||
\(480\) | 260.759 | + | 163.702i | 0.0247957 | + | 0.0155665i | ||||
\(481\) | − | 11425.7i | − | 1.08309i | ||||||
\(482\) | −6373.86 | −0.602327 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 116.142 | 0.0109074 | ||||||||
\(485\) | − | 230.989i | − | 0.0216261i | ||||||
\(486\) | 10253.2 | − | 3610.52i | 0.956989 | − | 0.336988i | ||||
\(487\) | −3970.15 | −0.369414 | −0.184707 | − | 0.982794i | \(-0.559134\pi\) | ||||
−0.184707 | + | 0.982794i | \(0.559134\pi\) | |||||||
\(488\) | −7953.76 | −0.737807 | ||||||||
\(489\) | −7560.13 | + | 12042.4i | −0.699143 | + | 1.11366i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 4184.69i | − | 0.384628i | −0.981333 | − | 0.192314i | \(-0.938401\pi\) | ||
0.981333 | − | 0.192314i | \(-0.0615993\pi\) | |||||||
\(492\) | −37.7508 | + | 60.1327i | −0.00345922 | + | 0.00551015i | ||||
\(493\) | − | 386.516i | − | 0.0353099i | ||||||
\(494\) | 15900.5i | 1.44818i | ||||||||
\(495\) | 5786.80 | − | 2792.41i | 0.525449 | − | 0.253555i | ||||
\(496\) | − | 12723.7i | − | 1.15183i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 3469.22 | + | 2177.94i | 0.312167 | + | 0.195976i | ||||
\(499\) | 18462.3 | 1.65628 | 0.828141 | − | 0.560520i | \(-0.189399\pi\) | ||||
0.828141 | + | 0.560520i | \(0.189399\pi\) | |||||||
\(500\) | 286.790 | 0.0256512 | ||||||||
\(501\) | −68.1668 | + | 108.582i | −0.00607877 | + | 0.00968280i | ||||
\(502\) | 1871.44i | 0.166388i | ||||||||
\(503\) | 11828.5 | 1.04853 | 0.524263 | − | 0.851557i | \(-0.324341\pi\) | ||||
0.524263 | + | 0.851557i | \(0.324341\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7039.44 | −0.620299 | ||||||||
\(506\) | 25601.1i | 2.24923i | ||||||||
\(507\) | −7404.33 | + | 11794.3i | −0.648595 | + | 1.03314i | ||||
\(508\) | −325.085 | −0.0283924 | ||||||||
\(509\) | −797.139 | −0.0694157 | −0.0347078 | − | 0.999398i | \(-0.511050\pi\) | ||||
−0.0347078 | + | 0.999398i | \(0.511050\pi\) | |||||||
\(510\) | −4748.91 | − | 2981.32i | −0.412324 | − | 0.258853i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11034.1i | 0.952425i | ||||||||
\(513\) | −1233.20 | + | 11062.8i | −0.106134 | + | 0.952110i | ||||
\(514\) | 19725.8i | 1.69274i | ||||||||
\(515\) | − | 1723.67i | − | 0.147483i | ||||||
\(516\) | −38.2927 | + | 60.9960i | −0.00326694 | + | 0.00520388i | ||||
\(517\) | 6346.96i | 0.539921i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3877.87 | − | 6177.01i | 0.327976 | − | 0.522429i | ||||
\(520\) | −8668.60 | −0.731044 | ||||||||
\(521\) | −8365.75 | −0.703475 | −0.351737 | − | 0.936099i | \(-0.614409\pi\) | ||||
−0.351737 | + | 0.936099i | \(0.614409\pi\) | |||||||
\(522\) | 192.808 | + | 399.562i | 0.0161666 | + | 0.0335026i | ||||
\(523\) | 3623.04i | 0.302915i | 0.988464 | + | 0.151457i | \(0.0483966\pi\) | ||||
−0.988464 | + | 0.151457i | \(0.951603\pi\) | |||||||
\(524\) | 206.877 | 0.0172470 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9428.65 | 0.781575 | ||||||||
\(527\) | 13048.0i | 1.07852i | ||||||||
\(528\) | −12375.3 | − | 7769.10i | −1.02001 | − | 0.640354i | ||||
\(529\) | −31443.4 | −2.58432 | ||||||||
\(530\) | 1608.84 | 0.131856 | ||||||||
\(531\) | −8667.85 | − | 17962.7i | −0.708386 | − | 1.46801i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 4058.60i | − | 0.329827i | ||||||
\(534\) | −6833.18 | − | 4289.81i | −0.553747 | − | 0.347637i | ||||
\(535\) | − | 4989.66i | − | 0.403219i | ||||||
\(536\) | − | 16069.4i | − | 1.29495i | ||||||
\(537\) | −7545.27 | − | 4736.85i | −0.606336 | − | 0.380652i | ||||
\(538\) | − | 3608.86i | − | 0.289199i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 182.619 | + | 20.3570i | 0.0145531 | + | 0.00162227i | ||||
\(541\) | 2220.96 | 0.176500 | 0.0882501 | − | 0.996098i | \(-0.471873\pi\) | ||||
0.0882501 | + | 0.996098i | \(0.471873\pi\) | |||||||
\(542\) | −1063.95 | −0.0843185 | ||||||||
\(543\) | 9005.83 | + | 5653.78i | 0.711744 | + | 0.446826i | ||||
\(544\) | 718.012i | 0.0565892i | ||||||||
\(545\) | −8860.62 | −0.696417 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10592.4 | 0.827969 | 0.413985 | − | 0.910284i | \(-0.364137\pi\) | ||||
0.413985 | + | 0.910284i | \(0.364137\pi\) | |||||||
\(548\) | − | 714.141i | − | 0.0556690i | ||||||
\(549\) | −8679.82 | + | 4188.43i | −0.674765 | + | 0.325607i | ||||
\(550\) | −11519.8 | −0.893104 | ||||||||
\(551\) | −454.298 | −0.0351248 | ||||||||
\(552\) | 12856.2 | − | 20478.4i | 0.991295 | − | 1.57902i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4419.79i | 0.338951i | ||||||||
\(555\) | 2517.99 | − | 4010.88i | 0.192582 | − | 0.306761i | ||||
\(556\) | − | 153.333i | − | 0.0116956i | ||||||
\(557\) | − | 989.584i | − | 0.0752783i | −0.999291 | − | 0.0376392i | \(-0.988016\pi\) | ||
0.999291 | − | 0.0376392i | \(-0.0119837\pi\) | |||||||
\(558\) | −6508.80 | − | 13488.4i | −0.493798 | − | 1.02331i | ||||
\(559\) | − | 4116.87i | − | 0.311494i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12690.7 | + | 7967.12i | 0.955086 | + | 0.599594i | ||||
\(562\) | −10855.4 | −0.814781 | ||||||||
\(563\) | −16789.7 | −1.25684 | −0.628422 | − | 0.777872i | \(-0.716299\pi\) | ||||
−0.628422 | + | 0.777872i | \(0.716299\pi\) | |||||||
\(564\) | −96.5080 | + | 153.726i | −0.00720518 | + | 0.0114770i | ||||
\(565\) | 4789.81i | 0.356653i | ||||||||
\(566\) | −26582.1 | −1.97408 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6883.50 | −0.508495 | ||||||||
\(569\) | − | 11077.7i | − | 0.816174i | −0.912943 | − | 0.408087i | \(-0.866196\pi\) | ||
0.912943 | − | 0.408087i | \(-0.133804\pi\) | |||||||
\(570\) | −3504.14 | + | 5581.71i | −0.257496 | + | 0.410161i | ||||
\(571\) | −4213.19 | −0.308785 | −0.154393 | − | 0.988010i | \(-0.549342\pi\) | ||||
−0.154393 | + | 0.988010i | \(0.549342\pi\) | |||||||
\(572\) | −701.434 | −0.0512735 | ||||||||
\(573\) | 14844.4 | + | 9319.17i | 1.08226 | + | 0.679431i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 19623.6i | − | 1.42323i | ||||||
\(576\) | 5821.06 | + | 12063.2i | 0.421083 | + | 0.872624i | ||||
\(577\) | 1676.34i | 0.120948i | 0.998170 | + | 0.0604738i | \(0.0192612\pi\) | ||||
−0.998170 | + | 0.0604738i | \(0.980739\pi\) | |||||||
\(578\) | 1022.43i | 0.0735767i | ||||||||
\(579\) | −1173.98 | + | 1870.02i | −0.0842644 | + | 0.134224i | ||||
\(580\) | 7.49934i | 0.000536885i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −328.754 | + | 523.668i | −0.0234146 | + | 0.0372968i | ||||
\(583\) | −4299.39 | −0.305424 | ||||||||
\(584\) | 18430.9 | 1.30595 | ||||||||
\(585\) | −9459.91 | + | 4564.86i | −0.668580 | + | 0.322622i | ||||
\(586\) | 20995.8i | 1.48008i | ||||||||
\(587\) | −22687.3 | −1.59524 | −0.797620 | − | 0.603161i | \(-0.793908\pi\) | ||||
−0.797620 | + | 0.603161i | \(0.793908\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15336.1 | 1.07286 | ||||||||
\(590\) | − | 11808.6i | − | 0.823988i | ||||||
\(591\) | 19454.1 | + | 12213.1i | 1.35404 | + | 0.850052i | ||||
\(592\) | −10769.6 | −0.747685 | ||||||||
\(593\) | 17961.5 | 1.24383 | 0.621916 | − | 0.783084i | \(-0.286355\pi\) | ||||
0.621916 | + | 0.783084i | \(0.286355\pi\) | |||||||
\(594\) | −17093.4 | − | 1905.45i | −1.18072 | − | 0.131619i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 92.9820i | 0.00639042i | ||||||||
\(597\) | 6943.57 | + | 4359.11i | 0.476016 | + | 0.298838i | ||||
\(598\) | − | 41851.2i | − | 2.86191i | ||||||
\(599\) | 6899.45i | 0.470624i | 0.971920 | + | 0.235312i | \(0.0756112\pi\) | ||||
−0.971920 | + | 0.235312i | \(0.924389\pi\) | |||||||
\(600\) | 9214.76 | + | 5784.94i | 0.626985 | + | 0.393615i | ||||
\(601\) | − | 19792.8i | − | 1.34337i | −0.740838 | − | 0.671684i | \(-0.765571\pi\) | ||
0.740838 | − | 0.671684i | \(-0.234429\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8462.13 | − | 17536.3i | −0.571484 | − | 1.18430i | ||||
\(604\) | 165.786 | 0.0111685 | ||||||||
\(605\) | −2751.76 | −0.184918 | ||||||||
\(606\) | 15958.9 | + | 10018.9i | 1.06978 | + | 0.671597i | ||||
\(607\) | − | 17838.2i | − | 1.19280i | −0.802688 | − | 0.596399i | \(-0.796598\pi\) | ||
0.802688 | − | 0.596399i | \(-0.203402\pi\) | |||||||
\(608\) | 843.928 | 0.0562924 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5706.09 | −0.378743 | ||||||||
\(611\) | − | 10375.6i | − | 0.686993i | ||||||
\(612\) | 186.232 | + | 385.935i | 0.0123007 | + | 0.0254910i | ||||
\(613\) | 6785.09 | 0.447059 | 0.223530 | − | 0.974697i | \(-0.428242\pi\) | ||||
0.223530 | + | 0.974697i | \(0.428242\pi\) | |||||||
\(614\) | −12476.5 | −0.820052 | ||||||||
\(615\) | 894.431 | − | 1424.73i | 0.0586454 | − | 0.0934155i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 3472.07i | − | 0.226549i | −0.993564 | − | 0.113274i | \(-0.963866\pi\) | ||
0.993564 | − | 0.113274i | \(-0.0361339\pi\) | |||||||
\(618\) | −2453.20 | + | 3907.67i | −0.159680 | + | 0.254352i | ||||
\(619\) | − | 7359.94i | − | 0.477901i | −0.971032 | − | 0.238951i | \(-0.923197\pi\) | ||
0.971032 | − | 0.238951i | \(-0.0768034\pi\) | |||||||
\(620\) | − | 253.162i | − | 0.0163988i | ||||||
\(621\) | 3245.85 | − | 29117.8i | 0.209745 | − | 1.88158i | ||||
\(622\) | 13058.1i | 0.841770i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 20230.4 | + | 12700.5i | 1.29786 | + | 0.814784i | ||||
\(625\) | 4951.14 | 0.316873 | ||||||||
\(626\) | −24242.4 | −1.54780 | ||||||||
\(627\) | 9364.29 | − | 14916.3i | 0.596449 | − | 0.950077i | ||||
\(628\) | 375.665i | 0.0238705i | ||||||||
\(629\) | 11044.2 | 0.700094 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14566.0 | −0.918957 | −0.459479 | − | 0.888189i | \(-0.651964\pi\) | ||||
−0.459479 | + | 0.888189i | \(0.651964\pi\) | |||||||
\(632\) | − | 10410.6i | − | 0.655239i | ||||||
\(633\) | 2517.07 | − | 4009.41i | 0.158048 | − | 0.251753i | ||||
\(634\) | −9566.23 | −0.599248 | ||||||||
\(635\) | 7702.26 | 0.481346 | ||||||||
\(636\) | −104.133 | − | 65.3739i | −0.00649238 | − | 0.00407585i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 701.949i | − | 0.0435586i | ||||||
\(639\) | −7511.86 | + | 3624.84i | −0.465046 | + | 0.224407i | ||||
\(640\) | 8404.31i | 0.519077i | ||||||||
\(641\) | − | 2089.00i | − | 0.128722i | −0.997927 | − | 0.0643609i | \(-0.979499\pi\) | ||
0.997927 | − | 0.0643609i | \(-0.0205009\pi\) | |||||||
\(642\) | −7101.52 | + | 11311.9i | −0.436565 | + | 0.695399i | ||||
\(643\) | 9732.76i | 0.596925i | 0.954421 | + | 0.298462i | \(0.0964737\pi\) | ||||
−0.954421 | + | 0.298462i | \(0.903526\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 907.272 | − | 1445.18i | 0.0553857 | − | 0.0882232i | ||||
\(646\) | −15369.5 | −0.936077 | ||||||||
\(647\) | 18491.0 | 1.12358 | 0.561790 | − | 0.827280i | \(-0.310113\pi\) | ||||
0.561790 | + | 0.827280i | \(0.310113\pi\) | |||||||
\(648\) | 12716.2 | + | 10108.0i | 0.770894 | + | 0.612777i | ||||
\(649\) | 31556.7i | 1.90864i | ||||||||
\(650\) | 18831.9 | 1.13638 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 643.373 | 0.0386449 | ||||||||
\(653\) | − | 5592.68i | − | 0.335158i | −0.985859 | − | 0.167579i | \(-0.946405\pi\) | ||
0.985859 | − | 0.167579i | \(-0.0535950\pi\) | |||||||
\(654\) | 20087.7 | + | 12610.8i | 1.20105 | + | 0.754011i | ||||
\(655\) | −4901.54 | −0.292395 | ||||||||
\(656\) | −3825.55 | −0.227687 | ||||||||
\(657\) | 20113.3 | − | 9705.65i | 1.19436 | − | 0.576337i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9543.49i | 0.564130i | 0.959395 | + | 0.282065i | \(0.0910193\pi\) | ||||
−0.959395 | + | 0.282065i | \(0.908981\pi\) | |||||||
\(660\) | −246.231 | − | 154.581i | −0.0145220 | − | 0.00911678i | ||||
\(661\) | − | 6778.91i | − | 0.398894i | −0.979909 | − | 0.199447i | \(-0.936085\pi\) | ||
0.979909 | − | 0.199447i | \(-0.0639146\pi\) | |||||||
\(662\) | 21513.7i | 1.26307i | ||||||||
\(663\) | −20746.0 | − | 13024.2i | −1.21525 | − | 0.762921i | ||||
\(664\) | 6121.18i | 0.357753i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −11416.9 | + | 5509.22i | −0.664260 | + | 0.320538i | ||||
\(667\) | 1195.74 | 0.0694141 | ||||||||
\(668\) | 5.80105 | 0.000336002 | ||||||||
\(669\) | 13511.5 | + | 8482.38i | 0.780843 | + | 0.490206i | ||||
\(670\) | − | 11528.3i | − | 0.664744i | ||||||
\(671\) | 15248.7 | 0.877300 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25094.5 | −1.43733 | −0.718663 | − | 0.695359i | \(-0.755246\pi\) | ||||
−0.718663 | + | 0.695359i | \(0.755246\pi\) | |||||||
\(674\) | − | 14657.7i | − | 0.837678i | ||||||
\(675\) | 13102.3 | + | 1460.55i | 0.747120 | + | 0.0832836i | ||||
\(676\) | 630.114 | 0.0358508 | ||||||||
\(677\) | 26332.2 | 1.49487 | 0.747435 | − | 0.664335i | \(-0.231285\pi\) | ||||
0.747435 | + | 0.664335i | \(0.231285\pi\) | |||||||
\(678\) | 6817.08 | − | 10858.8i | 0.386148 | − | 0.615090i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 8379.10i | − | 0.472535i | ||||||
\(681\) | −9262.69 | + | 14754.4i | −0.521214 | + | 0.830236i | ||||
\(682\) | 23696.3i | 1.33047i | ||||||||
\(683\) | − | 2346.73i | − | 0.131472i | −0.997837 | − | 0.0657359i | \(-0.979061\pi\) | ||
0.997837 | − | 0.0657359i | \(-0.0209395\pi\) | |||||||
\(684\) | 453.615 | − | 218.891i | 0.0253573 | − | 0.0122361i | ||||
\(685\) | 16920.2i | 0.943777i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19158.9 | − | 12027.8i | −1.06398 | − | 0.667959i | ||||
\(688\) | −3880.47 | −0.215031 | ||||||||
\(689\) | 7028.38 | 0.388621 | ||||||||
\(690\) | 9223.12 | − | 14691.4i | 0.508867 | − | 0.810568i | ||||
\(691\) | 11233.2i | 0.618421i | 0.950994 | + | 0.309211i | \(0.100065\pi\) | ||||
−0.950994 | + | 0.309211i | \(0.899935\pi\) | |||||||
\(692\) | −330.010 | −0.0181288 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8512.50 | −0.465605 | ||||||||
\(695\) | 3632.93i | 0.198280i | ||||||||
\(696\) | −352.499 | + | 561.491i | −0.0191975 | + | 0.0305794i | ||||
\(697\) | 3923.06 | 0.213194 | ||||||||
\(698\) | −8235.72 | −0.446600 | ||||||||
\(699\) | 16210.4 | + | 10176.8i | 0.877160 | + | 0.550673i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17277.2i | 0.930887i | 0.885078 | + | 0.465443i | \(0.154105\pi\) | ||||
−0.885078 | + | 0.465443i | \(0.845895\pi\) | |||||||
\(702\) | 27943.2 | + | 3114.91i | 1.50235 | + | 0.167471i | ||||
\(703\) | − | 12980.9i | − | 0.696422i | ||||||
\(704\) | − | 21192.5i | − | 1.13455i | ||||||
\(705\) | 2286.57 | − | 3642.25i | 0.122152 | − | 0.194574i | ||||
\(706\) | 36310.8i | 1.93566i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −479.832 | + | 764.319i | −0.0254706 | + | 0.0405718i | ||||
\(709\) | 18839.1 | 0.997910 | 0.498955 | − | 0.866628i | \(-0.333717\pi\) | ||||
0.498955 | + | 0.866628i | \(0.333717\pi\) | |||||||
\(710\) | −4938.28 | −0.261029 | ||||||||
\(711\) | −5482.20 | − | 11360.9i | −0.289168 | − | 0.599252i | ||||
\(712\) | − | 12056.6i | − | 0.634609i | ||||||
\(713\) | −40365.7 | −2.12020 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16619.1 | 0.869259 | ||||||||
\(716\) | 403.110i | 0.0210404i | ||||||||
\(717\) | −19968.5 | − | 12536.0i | −1.04008 | − | 0.652951i | ||||
\(718\) | 18914.9 | 0.983142 | ||||||||
\(719\) | −10519.4 | −0.545630 | −0.272815 | − | 0.962067i | \(-0.587955\pi\) | ||||
−0.272815 | + | 0.962067i | \(0.587955\pi\) | |||||||
\(720\) | 4302.74 | + | 8916.71i | 0.222714 | + | 0.461536i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 1618.38i | − | 0.0834209i | ||||||
\(723\) | −9774.61 | − | 6136.41i | −0.502796 | − | 0.315651i | ||||
\(724\) | − | 481.141i | − | 0.0246982i | ||||||
\(725\) | 538.051i | 0.0275624i | ||||||||
\(726\) | 6238.44 | + | 3916.44i | 0.318912 | + | 0.200210i | ||||
\(727\) | − | 1692.44i | − | 0.0863401i | −0.999068 | − | 0.0431700i | \(-0.986254\pi\) | ||
0.999068 | − | 0.0431700i | \(-0.0137457\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19199.8 | + | 4334.38i | 0.975453 | + | 0.220209i | ||||
\(730\) | 13222.5 | 0.670390 | ||||||||
\(731\) | 3979.38 | 0.201344 | ||||||||
\(732\) | 369.330 | + | 231.862i | 0.0186487 | + | 0.0117075i | ||||
\(733\) | 30431.1i | 1.53342i | 0.641991 | + | 0.766712i | \(0.278108\pi\) | ||||
−0.641991 | + | 0.766712i | \(0.721892\pi\) | |||||||
\(734\) | 29517.6 | 1.48435 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2221.27 | −0.111246 | ||||||||
\(737\) | 30807.7i | 1.53978i | ||||||||
\(738\) | −4055.48 | + | 1956.96i | −0.202282 | + | 0.0976109i | ||||
\(739\) | 4913.38 | 0.244576 | 0.122288 | − | 0.992495i | \(-0.460977\pi\) | ||||
0.122288 | + | 0.992495i | \(0.460977\pi\) | |||||||
\(740\) | −214.283 | −0.0106449 | ||||||||
\(741\) | −15308.2 | + | 24384.2i | −0.758920 | + | 1.20887i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27101.5i | 1.33816i | 0.743188 | + | 0.669082i | \(0.233313\pi\) | ||||
−0.743188 | + | 0.669082i | \(0.766687\pi\) | |||||||
\(744\) | 11899.6 | − | 18954.8i | 0.586373 | − | 0.934026i | ||||
\(745\) | − | 2203.03i | − | 0.108339i | ||||||
\(746\) | − | 12658.2i | − | 0.621247i | ||||||
\(747\) | 3223.40 | + | 6679.95i | 0.157882 | + | 0.327184i | ||||
\(748\) | − | 678.009i | − | 0.0331423i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 15404.6 | + | 9670.84i | 0.749994 | + | 0.470839i | ||||
\(751\) | 16616.9 | 0.807403 | 0.403701 | − | 0.914891i | \(-0.367723\pi\) | ||||
0.403701 | + | 0.914891i | \(0.367723\pi\) | |||||||
\(752\) | −9779.84 | −0.474247 | ||||||||
\(753\) | −1801.72 | + | 2869.94i | −0.0871959 | + | 0.138893i | ||||
\(754\) | 1147.50i | 0.0554239i | ||||||||
\(755\) | −3927.98 | −0.189343 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29748.9 | −1.42833 | −0.714163 | − | 0.699980i | \(-0.753192\pi\) | ||||
−0.714163 | + | 0.699980i | \(0.753192\pi\) | |||||||
\(758\) | − | 11014.6i | − | 0.527796i | ||||||
\(759\) | −24647.4 | + | 39260.5i | −1.17871 | + | 1.87756i | ||||
\(760\) | −9848.51 | −0.470057 | ||||||||
\(761\) | −4756.16 | −0.226558 | −0.113279 | − | 0.993563i | \(-0.536135\pi\) | ||||
−0.113279 | + | 0.993563i | \(0.536135\pi\) | |||||||
\(762\) | −17461.6 | − | 10962.2i | −0.830139 | − | 0.521153i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 793.069i | − | 0.0375553i | ||||||
\(765\) | −4412.41 | − | 9143.98i | −0.208538 | − | 0.432159i | ||||
\(766\) | 6103.12i | 0.287878i | ||||||||
\(767\) | − | 51587.0i | − | 2.42855i | ||||||
\(768\) | 996.888 | − | 1587.93i | 0.0468387 | − | 0.0746088i | ||||
\(769\) | − | 9226.71i | − | 0.432671i | −0.976319 | − | 0.216335i | \(-0.930590\pi\) | ||
0.976319 | − | 0.216335i | \(-0.0694104\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18990.9 | + | 30250.4i | −0.887083 | + | 1.41302i | ||||
\(772\) | 99.9070 | 0.00465768 | ||||||||
\(773\) | −4745.02 | −0.220785 | −0.110392 | − | 0.993888i | \(-0.535211\pi\) | ||||
−0.110392 | + | 0.993888i | \(0.535211\pi\) | |||||||
\(774\) | −4113.70 | + | 1985.06i | −0.191039 | + | 0.0921853i | ||||
\(775\) | − | 18163.5i | − | 0.841873i | ||||||
\(776\) | −923.973 | −0.0427432 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20715.1 | 0.954590 | ||||||||
\(779\) | − | 4611.03i | − | 0.212076i | ||||||
\(780\) | 402.523 | + | 252.700i | 0.0184777 | + | 0.0116002i | ||||
\(781\) | 13196.8 | 0.604633 | ||||||||
\(782\) | 40453.5 | 1.84989 | ||||||||
\(783\) | −88.9968 | + | 798.372i | −0.00406192 | + | 0.0364387i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 8900.65i | − | 0.404685i | ||||||
\(786\) | 11112.1 | + | 6976.09i | 0.504271 | + | 0.316576i | ||||
\(787\) | − | 17586.8i | − | 0.796573i | −0.917261 | − | 0.398286i | \(-0.869605\pi\) | ||
0.917261 | − | 0.398286i | \(-0.130395\pi\) | |||||||
\(788\) | − | 1039.35i | − | 0.0469863i | ||||||
\(789\) | 14459.3 | + | 9077.39i | 0.652425 | + | 0.409586i | ||||
\(790\) | − | 7468.65i | − | 0.336358i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −11169.9 | − | 23147.7i | −0.501141 | − | 1.03853i | ||||
\(793\) | −24927.6 | −1.11627 | ||||||||
\(794\) | 331.302 | 0.0148079 | ||||||||
\(795\) | 2467.23 | + | 1548.91i | 0.110068 | + | 0.0690994i | ||||
\(796\) | − | 370.964i | − | 0.0165182i | ||||||
\(797\) | 14578.6 | 0.647930 | 0.323965 | − | 0.946069i | \(-0.394984\pi\) | ||||
0.323965 | + | 0.946069i | \(0.394984\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10029.1 | 0.444061 | ||||||||
\(800\) | − | 999.513i | − | 0.0441726i | ||||||
\(801\) | −6349.00 | − | 13157.2i | −0.280064 | − | 0.580385i | ||||
\(802\) | −25556.5 | −1.12523 | ||||||||
\(803\) | −35335.0 | −1.55286 | ||||||||
\(804\) | −468.444 | + | 746.179i | −0.0205482 | + | 0.0327310i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 38737.3i | − | 1.69288i | ||||||
\(807\) | 3474.41 | − | 5534.35i | 0.151555 | − | 0.241410i | ||||
\(808\) | 28158.3i | 1.22600i | ||||||||
\(809\) | 45307.2i | 1.96899i | 0.175401 | + | 0.984497i | \(0.443878\pi\) | ||||
−0.175401 | + | 0.984497i | \(0.556122\pi\) | |||||||
\(810\) | 9122.70 | + | 7251.55i | 0.395727 | + | 0.314560i | ||||
\(811\) | − | 36799.2i | − | 1.59334i | −0.604417 | − | 0.796668i | \(-0.706594\pi\) | ||
0.604417 | − | 0.796668i | \(-0.293406\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1631.62 | − | 1024.31i | −0.0703854 | − | 0.0441873i | ||||
\(814\) | 20057.2 | 0.863642 | ||||||||
\(815\) | −15243.5 | −0.655160 | ||||||||
\(816\) | −12276.3 | + | 19554.8i | −0.526662 | + | 0.838914i | ||||
\(817\) | − | 4677.23i | − | 0.200288i | ||||||
\(818\) | 19377.9 | 0.828279 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −76.1168 | −0.00324160 | ||||||||
\(821\) | 3854.25i | 0.163842i | 0.996639 | + | 0.0819210i | \(0.0261055\pi\) | ||||
−0.996639 | + | 0.0819210i | \(0.973894\pi\) | |||||||
\(822\) | 24081.6 | − | 38359.3i | 1.02183 | − | 1.62766i | ||||
\(823\) | 26287.0 | 1.11338 | 0.556688 | − | 0.830722i | \(-0.312072\pi\) | ||||
0.556688 | + | 0.830722i | \(0.312072\pi\) | |||||||
\(824\) | −6894.80 | −0.291495 | ||||||||
\(825\) | −17666.2 | − | 11090.7i | −0.745525 | − | 0.468034i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17592.8i | 0.739735i | 0.929085 | + | 0.369868i | \(0.120597\pi\) | ||||
−0.929085 | + | 0.369868i | \(0.879403\pi\) | |||||||
\(828\) | −1193.94 | + | 576.136i | −0.0501116 | + | 0.0241813i | ||||
\(829\) | 29603.5i | 1.24025i | 0.784501 | + | 0.620127i | \(0.212919\pi\) | ||||
−0.784501 | + | 0.620127i | \(0.787081\pi\) | |||||||
\(830\) | 4391.38i | 0.183647i | ||||||||
\(831\) | −4255.14 | + | 6777.96i | −0.177628 | + | 0.282942i | ||||
\(832\) | 34644.2i | 1.44359i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 5170.55 | − | 8236.11i | 0.214678 | − | 0.341958i | ||||
\(835\) | −137.445 | −0.00569636 | ||||||||
\(836\) | −796.909 | −0.0329685 | ||||||||
\(837\) | 3004.34 | − | 26951.4i | 0.124068 | − | 1.11299i | ||||
\(838\) | − | 2548.46i | − | 0.105054i | ||||||
\(839\) | −29706.3 | −1.22238 | −0.611189 | − | 0.791485i | \(-0.709308\pi\) | ||||
−0.611189 | + | 0.791485i | \(0.709308\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24356.2 | 0.998656 | ||||||||
\(842\) | 42976.5i | 1.75899i | ||||||||
\(843\) | −16647.2 | − | 10451.0i | −0.680144 | − | 0.426988i | ||||
\(844\) | −214.205 | −0.00873606 | ||||||||
\(845\) | −14929.3 | −0.607793 | ||||||||
\(846\) | −10367.6 | + | 5002.88i | −0.421332 | + | 0.203313i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 6624.80i | − | 0.268274i | ||||||
\(849\) | −40764.9 | − | 25591.8i | −1.64788 | − | 1.03452i | ||||
\(850\) | 18203.0i | 0.734539i | ||||||||
\(851\) | 34166.6i | 1.37628i | ||||||||
\(852\) | 319.633 | + | 200.663i | 0.0128526 | + | 0.00806876i | ||||
\(853\) | − | 12651.1i | − | 0.507813i | −0.967229 | − | 0.253906i | \(-0.918284\pi\) | ||
0.967229 | − | 0.253906i | \(-0.0817155\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10747.5 | + | 5186.21i | −0.429892 | + | 0.207444i | ||||
\(856\) | −19959.1 | −0.796947 | ||||||||
\(857\) | 40877.8 | 1.62936 | 0.814678 | − | 0.579914i | \(-0.196914\pi\) | ||||
0.814678 | + | 0.579914i | \(0.196914\pi\) | |||||||
\(858\) | −37676.7 | − | 23653.1i | −1.49914 | − | 0.941146i | ||||
\(859\) | − | 39042.1i | − | 1.55076i | −0.631497 | − | 0.775378i | \(-0.717559\pi\) | ||
0.631497 | − | 0.775378i | \(-0.282441\pi\) | |||||||
\(860\) | −77.2096 | −0.00306142 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3143.40 | −0.124205 | ||||||||
\(863\) | 20896.4i | 0.824243i | 0.911129 | + | 0.412121i | \(0.135212\pi\) | ||||
−0.911129 | + | 0.412121i | \(0.864788\pi\) | |||||||
\(864\) | 165.325 | − | 1483.10i | 0.00650981 | − | 0.0583982i | ||||
\(865\) | 7818.94 | 0.307343 | ||||||||
\(866\) | −36411.3 | −1.42876 | ||||||||
\(867\) | −984.336 | + | 1567.94i | −0.0385580 | + | 0.0614186i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19958.8i | 0.779121i | ||||||||
\(870\) | −252.886 | + | 402.818i | −0.00985474 | + | 0.0156975i | ||||
\(871\) | − | 50362.6i | − | 1.95921i | ||||||
\(872\) | 35443.2i | 1.37644i | ||||||||
\(873\) | −1008.32 | + | 486.562i | −0.0390910 | + | 0.0188633i | ||||
\(874\) | − | 47547.7i | − | 1.84019i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −855.831 | − | 537.282i | −0.0330089 | − | 0.0207227i | ||||
\(877\) | −31551.7 | −1.21485 | −0.607427 | − | 0.794376i | \(-0.707798\pi\) | ||||
−0.607427 | + | 0.794376i | \(0.707798\pi\) | |||||||
\(878\) | 38583.7 | 1.48307 | ||||||||
\(879\) | −20213.6 | + | 32197.9i | −0.775639 | + | 1.23551i | ||||
\(880\) | − | 15664.8i | − | 0.600070i | ||||||
\(881\) | 43754.6 | 1.67325 | 0.836623 | − | 0.547779i | \(-0.184527\pi\) | ||||
0.836623 | + | 0.547779i | \(0.184527\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11781.7 | 0.449020 | 0.224510 | − | 0.974472i | \(-0.427922\pi\) | ||||
0.224510 | + | 0.974472i | \(0.427922\pi\) | |||||||
\(884\) | 1108.37i | 0.0421702i | ||||||||
\(885\) | 11368.7 | − | 18109.0i | 0.431813 | − | 0.687829i | ||||
\(886\) | −6534.20 | −0.247766 | ||||||||
\(887\) | 34715.7 | 1.31414 | 0.657068 | − | 0.753831i | \(-0.271796\pi\) | ||||
0.657068 | + | 0.753831i | \(0.271796\pi\) | |||||||
\(888\) | −16043.8 | − | 10072.2i | −0.606301 | − | 0.380630i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 8649.53i | − | 0.325767i | ||||||
\(891\) | −24379.0 | − | 19378.7i | −0.916642 | − | 0.728631i | ||||
\(892\) | − | 721.858i | − | 0.0270959i | ||||||
\(893\) | − | 11787.9i | − | 0.441732i | ||||||
\(894\) | −3135.45 | + | 4994.42i | −0.117299 | + | 0.186844i | ||||
\(895\) | − | 9550.91i | − | 0.356706i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 40292.0 | − | 64180.7i | 1.49979 | − | 2.38900i | ||||
\(898\) | −4837.98 | −0.179783 | ||||||||
\(899\) | 1106.77 | 0.0410600 | ||||||||
\(900\) | −259.246 | − | 537.243i | −0.00960170 | − | 0.0198979i | ||||
\(901\) | 6793.65i | 0.251198i | ||||||||
\(902\) | 7124.64 | 0.262998 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19159.6 | 0.704911 | ||||||||
\(905\) | 11399.7i | 0.418717i | ||||||||
\(906\) | 8905.01 | + | 5590.49i | 0.326544 | + | 0.205002i | ||||
\(907\) | −2983.50 | −0.109223 | −0.0546117 | − | 0.998508i | \(-0.517392\pi\) | ||||
−0.0546117 | + | 0.998508i | \(0.517392\pi\) | |||||||
\(908\) | 788.263 | 0.0288099 | ||||||||
\(909\) | 14828.1 | + | 30728.7i | 0.541053 | + | 1.12124i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 16802.5i | − | 0.611076i | −0.952180 | − | 0.305538i | \(-0.901164\pi\) | ||
0.952180 | − | 0.305538i | \(-0.0988363\pi\) | |||||||
\(912\) | 22984.0 | + | 14429.2i | 0.834514 | + | 0.523900i | ||||
\(913\) | − | 11735.3i | − | 0.425391i | ||||||
\(914\) | 5979.27i | 0.216386i | ||||||||
\(915\) | −8750.56 | − | 5493.52i | −0.316158 | − | 0.198481i | ||||
\(916\) | 1023.57i | 0.0369212i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3010.88 | + | 27010.0i | −0.108250 | + | 0.971093i | ||||
\(919\) | 12904.7 | 0.463207 | 0.231604 | − | 0.972810i | \(-0.425603\pi\) | ||||
0.231604 | + | 0.972810i | \(0.425603\pi\) | |||||||
\(920\) | 25921.9 | 0.928934 | ||||||||
\(921\) | −19133.3 | − | 12011.7i | −0.684544 | − | 0.429750i | ||||
\(922\) | − | 40543.3i | − | 1.44818i | ||||||
\(923\) | −21573.3 | −0.769333 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15374.1 | −0.546482 | ||||||||
\(926\) | − | 46321.0i | − | 1.64385i | ||||||
\(927\) | −7524.19 | + | 3630.79i | −0.266588 | + | 0.128642i | ||||
\(928\) | 60.9042 | 0.00215440 | ||||||||
\(929\) | −24725.6 | −0.873221 | −0.436610 | − | 0.899651i | \(-0.643821\pi\) | ||||
−0.436610 | + | 0.899651i | \(0.643821\pi\) | |||||||
\(930\) | 8536.89 | − | 13598.3i | 0.301006 | − | 0.479469i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 866.050i | − | 0.0304382i | ||||||
\(933\) | −12571.6 | + | 20025.2i | −0.441132 | + | 0.702673i | ||||
\(934\) | 17933.8i | 0.628278i | ||||||||
\(935\) | 16064.1i | 0.561874i | ||||||||
\(936\) | 18259.8 | + | 37840.4i | 0.637650 | + | 1.32142i | ||||
\(937\) | − | 42100.7i | − | 1.46785i | −0.679233 | − | 0.733923i | \(-0.737687\pi\) | ||
0.679233 | − | 0.733923i | \(-0.262313\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −37176.8 | − | 23339.2i | −1.29203 | − | 0.811126i | ||||
\(940\) | −194.589 | −0.00675191 | ||||||||
\(941\) | −52185.3 | −1.80786 | −0.903928 | − | 0.427684i | \(-0.859330\pi\) | ||||
−0.903928 | + | 0.427684i | \(0.859330\pi\) | |||||||
\(942\) | −12667.8 | + | 20178.4i | −0.438152 | + | 0.697927i | ||||
\(943\) | 12136.5i | 0.419109i | ||||||||
\(944\) | −48624.8 | −1.67648 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7226.92 | 0.248380 | ||||||||
\(947\) | − | 20875.9i | − | 0.716340i | −0.933656 | − | 0.358170i | \(-0.883401\pi\) | ||
0.933656 | − | 0.358170i | \(-0.116599\pi\) | |||||||
\(948\) | −303.482 | + | 483.412i | −0.0103973 | + | 0.0165617i | ||||
\(949\) | 57763.5 | 1.97585 | ||||||||
\(950\) | 21395.2 | 0.730687 | ||||||||
\(951\) | −14670.2 | − | 9209.85i | −0.500226 | − | 0.314038i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 3810.33i | − | 0.129516i | −0.997901 | − | 0.0647579i | \(-0.979372\pi\) | ||
0.997901 | − | 0.0647579i | \(-0.0206275\pi\) | |||||||
\(954\) | −3388.92 | − | 7022.96i | −0.115011 | − | 0.238340i | ||||
\(955\) | 18790.2i | 0.636688i | ||||||||
\(956\) | 1066.83i | 0.0360916i | ||||||||
\(957\) | 675.798 | − | 1076.47i | 0.0228270 | − | 0.0363609i | ||||
\(958\) | − | 30488.1i | − | 1.02821i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −7634.85 | + | 12161.5i | −0.256681 | + | 0.408864i | ||||
\(961\) | −7571.30 | −0.254147 | ||||||||
\(962\) | −32788.3 | −1.09889 | ||||||||
\(963\) | −21781.0 | + | 10510.4i | −0.728851 | + | 0.351706i | ||||
\(964\) | 522.214i | 0.0174475i | ||||||||
\(965\) | −2367.10 | −0.0789634 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −141.303 | −0.00469905 | −0.00234953 | − | 0.999997i | \(-0.500748\pi\) | ||||
−0.00234953 | + | 0.999997i | \(0.500748\pi\) | |||||||
\(968\) | 11007.3i | 0.365483i | ||||||||
\(969\) | −23569.9 | − | 14796.9i | −0.781396 | − | 0.490553i | ||||
\(970\) | −662.866 | −0.0219416 | ||||||||
\(971\) | −24283.2 | −0.802560 | −0.401280 | − | 0.915955i | \(-0.631435\pi\) | ||||
−0.401280 | + | 0.915955i | \(0.631435\pi\) | |||||||
\(972\) | −295.811 | − | 840.054i | −0.00976148 | − | 0.0277209i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 11393.1i | 0.374803i | ||||||||
\(975\) | 28879.6 | + | 18130.4i | 0.948603 | + | 0.595524i | ||||
\(976\) | 23496.2i | 0.770589i | ||||||||
\(977\) | − | 31536.2i | − | 1.03268i | −0.856382 | − | 0.516342i | \(-0.827293\pi\) | ||
0.856382 | − | 0.516342i | \(-0.172707\pi\) | |||||||
\(978\) | 34558.0 | + | 21695.2i | 1.12990 | + | 0.709342i | ||||
\(979\) | 23114.6i | 0.754591i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18664.3 | + | 38678.6i | 0.607447 | + | 1.25883i | ||||
\(982\) | −12008.8 | −0.390239 | ||||||||
\(983\) | −16651.6 | −0.540290 | −0.270145 | − | 0.962820i | \(-0.587072\pi\) | ||||
−0.270145 | + | 0.962820i | \(0.587072\pi\) | |||||||
\(984\) | −5699.02 | − | 3577.79i | −0.184632 | − | 0.115910i | ||||
\(985\) | 24625.3i | 0.796576i | ||||||||
\(986\) | −1109.18 | −0.0358250 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1302.74 | 0.0419490 | ||||||||
\(989\) | 12310.8i | 0.395813i | ||||||||
\(990\) | −8013.35 | − | 16606.3i | −0.257254 | − | 0.533115i | ||||
\(991\) | −12620.6 | −0.404547 | −0.202274 | − | 0.979329i | \(-0.564833\pi\) | ||||
−0.202274 | + | 0.979329i | \(0.564833\pi\) | |||||||
\(992\) | −2056.00 | −0.0658045 | ||||||||
\(993\) | −20712.3 | + | 32992.3i | −0.661917 | + | 1.05436i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8789.27i | 0.280039i | ||||||||
\(996\) | 178.440 | − | 284.235i | 0.00567679 | − | 0.00904249i | ||||
\(997\) | 41721.5i | 1.32531i | 0.748925 | + | 0.662655i | \(0.230570\pi\) | ||||
−0.748925 | + | 0.662655i | \(0.769430\pi\) | |||||||
\(998\) | − | 52981.0i | − | 1.68044i | ||||||
\(999\) | −22812.4 | − | 2542.96i | −0.722474 | − | 0.0805362i |
(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 | 147.4.c.b.146.8 | yes | 24 | |
3.2 | odd | 2 | inner | 147.4.c.b.146.17 | yes | 24 | |
7.2 | even | 3 | 147.4.g.e.80.8 | 48 | |||
7.3 | odd | 6 | 147.4.g.e.68.18 | 48 | |||
7.4 | even | 3 | 147.4.g.e.68.17 | 48 | |||
7.5 | odd | 6 | 147.4.g.e.80.7 | 48 | |||
7.6 | odd | 2 | inner | 147.4.c.b.146.7 | ✓ | 24 | |
21.2 | odd | 6 | 147.4.g.e.80.18 | 48 | |||
21.5 | even | 6 | 147.4.g.e.80.17 | 48 | |||
21.11 | odd | 6 | 147.4.g.e.68.7 | 48 | |||
21.17 | even | 6 | 147.4.g.e.68.8 | 48 | |||
21.20 | even | 2 | inner | 147.4.c.b.146.18 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.4.c.b.146.7 | ✓ | 24 | 7.6 | odd | 2 | inner | |
147.4.c.b.146.8 | yes | 24 | 1.1 | even | 1 | trivial | |
147.4.c.b.146.17 | yes | 24 | 3.2 | odd | 2 | inner | |
147.4.c.b.146.18 | yes | 24 | 21.20 | even | 2 | inner | |
147.4.g.e.68.7 | 48 | 21.11 | odd | 6 | |||
147.4.g.e.68.8 | 48 | 21.17 | even | 6 | |||
147.4.g.e.68.17 | 48 | 7.4 | even | 3 | |||
147.4.g.e.68.18 | 48 | 7.3 | odd | 6 | |||
147.4.g.e.80.7 | 48 | 7.5 | odd | 6 | |||
147.4.g.e.80.8 | 48 | 7.2 | even | 3 | |||
147.4.g.e.80.17 | 48 | 21.5 | even | 6 | |||
147.4.g.e.80.18 | 48 | 21.2 | odd | 6 |