Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [143,4,Mod(12,143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(143, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("143.12");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 143 = 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 143.b (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: | \(8.43727313082\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 12.6 | ||
Character | \(\chi\) | \(=\) | 143.12 |
Dual form | 143.4.b.a.12.31 |
$q$-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 \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 4.27424i | − | 1.51117i | −0.655049 | − | 0.755586i | \(-0.727352\pi\) | ||
0.655049 | − | 0.755586i | \(-0.272648\pi\) | |||||||
\(3\) | 4.33951 | 0.835140 | 0.417570 | − | 0.908645i | \(-0.362882\pi\) | ||||
0.417570 | + | 0.908645i | \(0.362882\pi\) | |||||||
\(4\) | −10.2691 | −1.28364 | ||||||||
\(5\) | 0.295728i | 0.0264507i | 0.999913 | + | 0.0132253i | \(0.00420988\pi\) | ||||
−0.999913 | + | 0.0132253i | \(0.995790\pi\) | |||||||
\(6\) | − | 18.5481i | − | 1.26204i | ||||||
\(7\) | − | 11.5737i | − | 0.624922i | −0.949931 | − | 0.312461i | \(-0.898847\pi\) | ||
0.949931 | − | 0.312461i | \(-0.101153\pi\) | |||||||
\(8\) | 9.69883i | 0.428632i | ||||||||
\(9\) | −8.16862 | −0.302542 | ||||||||
\(10\) | 1.26401 | 0.0399715 | ||||||||
\(11\) | − | 11.0000i | − | 0.301511i | ||||||
\(12\) | −44.5631 | −1.07202 | ||||||||
\(13\) | −1.44705 | − | 46.8498i | −0.0308722 | − | 0.999523i | ||||
\(14\) | −49.4689 | −0.944365 | ||||||||
\(15\) | 1.28331i | 0.0220900i | ||||||||
\(16\) | −40.6979 | −0.635905 | ||||||||
\(17\) | −39.7079 | −0.566505 | −0.283252 | − | 0.959045i | \(-0.591413\pi\) | ||||
−0.283252 | + | 0.959045i | \(0.591413\pi\) | |||||||
\(18\) | 34.9147i | 0.457192i | ||||||||
\(19\) | − | 68.1624i | − | 0.823028i | −0.911403 | − | 0.411514i | \(-0.865000\pi\) | ||
0.911403 | − | 0.411514i | \(-0.135000\pi\) | |||||||
\(20\) | − | 3.03687i | − | 0.0339532i | ||||||
\(21\) | − | 50.2243i | − | 0.521897i | ||||||
\(22\) | −47.0167 | −0.455636 | ||||||||
\(23\) | 83.5604 | 0.757545 | 0.378773 | − | 0.925490i | \(-0.376346\pi\) | ||||
0.378773 | + | 0.925490i | \(0.376346\pi\) | |||||||
\(24\) | 42.0882i | 0.357968i | ||||||||
\(25\) | 124.913 | 0.999300 | ||||||||
\(26\) | −200.247 | + | 6.18503i | −1.51045 | + | 0.0466533i | ||||
\(27\) | −152.615 | −1.08780 | ||||||||
\(28\) | 118.852i | 0.802176i | ||||||||
\(29\) | 198.255 | 1.26948 | 0.634742 | − | 0.772724i | \(-0.281107\pi\) | ||||
0.634742 | + | 0.772724i | \(0.281107\pi\) | |||||||
\(30\) | 5.48519 | 0.0333818 | ||||||||
\(31\) | 191.091i | 1.10713i | 0.832806 | + | 0.553565i | \(0.186733\pi\) | ||||
−0.832806 | + | 0.553565i | \(0.813267\pi\) | |||||||
\(32\) | 251.543i | 1.38959i | ||||||||
\(33\) | − | 47.7347i | − | 0.251804i | ||||||
\(34\) | 169.721i | 0.856086i | ||||||||
\(35\) | 3.42267 | 0.0165296 | ||||||||
\(36\) | 83.8847 | 0.388355 | ||||||||
\(37\) | 196.760i | 0.874246i | 0.899402 | + | 0.437123i | \(0.144003\pi\) | ||||
−0.899402 | + | 0.437123i | \(0.855997\pi\) | |||||||
\(38\) | −291.343 | −1.24374 | ||||||||
\(39\) | −6.27949 | − | 203.305i | −0.0257826 | − | 0.834742i | ||||
\(40\) | −2.86821 | −0.0113376 | ||||||||
\(41\) | 55.2695i | 0.210528i | 0.994444 | + | 0.105264i | \(0.0335688\pi\) | ||||
−0.994444 | + | 0.105264i | \(0.966431\pi\) | |||||||
\(42\) | −214.671 | −0.788677 | ||||||||
\(43\) | 240.921 | 0.854421 | 0.427210 | − | 0.904152i | \(-0.359496\pi\) | ||||
0.427210 | + | 0.904152i | \(0.359496\pi\) | |||||||
\(44\) | 112.960i | 0.387033i | ||||||||
\(45\) | − | 2.41569i | − | 0.00800243i | ||||||
\(46\) | − | 357.157i | − | 1.14478i | ||||||
\(47\) | − | 476.074i | − | 1.47750i | −0.673978 | − | 0.738751i | \(-0.735416\pi\) | ||
0.673978 | − | 0.738751i | \(-0.264584\pi\) | |||||||
\(48\) | −176.609 | −0.531070 | ||||||||
\(49\) | 209.049 | 0.609472 | ||||||||
\(50\) | − | 533.906i | − | 1.51012i | ||||||
\(51\) | −172.313 | −0.473111 | ||||||||
\(52\) | 14.8599 | + | 481.107i | 0.0396289 | + | 1.28303i | ||||
\(53\) | −39.3242 | −0.101917 | −0.0509585 | − | 0.998701i | \(-0.516228\pi\) | ||||
−0.0509585 | + | 0.998701i | \(0.516228\pi\) | |||||||
\(54\) | 652.312i | 1.64386i | ||||||||
\(55\) | 3.25300 | 0.00797518 | ||||||||
\(56\) | 112.252 | 0.267862 | ||||||||
\(57\) | − | 295.792i | − | 0.687344i | ||||||
\(58\) | − | 847.389i | − | 1.91841i | ||||||
\(59\) | − | 353.223i | − | 0.779419i | −0.920938 | − | 0.389710i | \(-0.872575\pi\) | ||
0.920938 | − | 0.389710i | \(-0.127425\pi\) | |||||||
\(60\) | − | 13.1785i | − | 0.0283557i | ||||||
\(61\) | 62.6336 | 0.131466 | 0.0657329 | − | 0.997837i | \(-0.479061\pi\) | ||||
0.0657329 | + | 0.997837i | \(0.479061\pi\) | |||||||
\(62\) | 816.771 | 1.67306 | ||||||||
\(63\) | 94.5414i | 0.189065i | ||||||||
\(64\) | 749.574 | 1.46401 | ||||||||
\(65\) | 13.8548 | − | 0.427932i | 0.0264381 | − | 0.000816592i | ||||
\(66\) | −204.029 | −0.380519 | ||||||||
\(67\) | 781.242i | 1.42454i | 0.701908 | + | 0.712268i | \(0.252332\pi\) | ||||
−0.701908 | + | 0.712268i | \(0.747668\pi\) | |||||||
\(68\) | 407.766 | 0.727189 | ||||||||
\(69\) | 362.611 | 0.632656 | ||||||||
\(70\) | − | 14.6293i | − | 0.0249791i | ||||||
\(71\) | − | 575.874i | − | 0.962586i | −0.876560 | − | 0.481293i | \(-0.840167\pi\) | ||
0.876560 | − | 0.481293i | \(-0.159833\pi\) | |||||||
\(72\) | − | 79.2261i | − | 0.129679i | ||||||
\(73\) | − | 526.139i | − | 0.843560i | −0.906698 | − | 0.421780i | \(-0.861405\pi\) | ||
0.906698 | − | 0.421780i | \(-0.138595\pi\) | |||||||
\(74\) | 840.998 | 1.32114 | ||||||||
\(75\) | 542.060 | 0.834555 | ||||||||
\(76\) | 699.969i | 1.05647i | ||||||||
\(77\) | −127.311 | −0.188421 | ||||||||
\(78\) | −868.976 | + | 26.8400i | −1.26144 | + | 0.0389620i | ||||
\(79\) | 886.680 | 1.26278 | 0.631388 | − | 0.775467i | \(-0.282486\pi\) | ||||
0.631388 | + | 0.775467i | \(0.282486\pi\) | |||||||
\(80\) | − | 12.0355i | − | 0.0168201i | ||||||
\(81\) | −441.721 | −0.605927 | ||||||||
\(82\) | 236.235 | 0.318144 | ||||||||
\(83\) | − | 111.859i | − | 0.147929i | −0.997261 | − | 0.0739647i | \(-0.976435\pi\) | ||
0.997261 | − | 0.0739647i | \(-0.0235652\pi\) | |||||||
\(84\) | 515.760i | 0.669929i | ||||||||
\(85\) | − | 11.7427i | − | 0.0149844i | ||||||
\(86\) | − | 1029.75i | − | 1.29118i | ||||||
\(87\) | 860.330 | 1.06020 | ||||||||
\(88\) | 106.687 | 0.129237 | ||||||||
\(89\) | − | 433.213i | − | 0.515960i | −0.966150 | − | 0.257980i | \(-0.916943\pi\) | ||
0.966150 | − | 0.257980i | \(-0.0830569\pi\) | |||||||
\(90\) | −10.3252 | −0.0120931 | ||||||||
\(91\) | −542.227 | + | 16.7477i | −0.624624 | + | 0.0192927i | ||||
\(92\) | −858.093 | −0.972417 | ||||||||
\(93\) | 829.244i | 0.924608i | ||||||||
\(94\) | −2034.86 | −2.23276 | ||||||||
\(95\) | 20.1575 | 0.0217697 | ||||||||
\(96\) | 1091.58i | 1.16051i | ||||||||
\(97\) | 1029.26i | 1.07738i | 0.842505 | + | 0.538689i | \(0.181080\pi\) | ||||
−0.842505 | + | 0.538689i | \(0.818920\pi\) | |||||||
\(98\) | − | 893.526i | − | 0.921017i | ||||||
\(99\) | 89.8548i | 0.0912197i | ||||||||
\(100\) | −1282.74 | −1.28274 | ||||||||
\(101\) | 1182.09 | 1.16458 | 0.582290 | − | 0.812981i | \(-0.302157\pi\) | ||||
0.582290 | + | 0.812981i | \(0.302157\pi\) | |||||||
\(102\) | 736.507i | 0.714952i | ||||||||
\(103\) | −1425.70 | −1.36387 | −0.681934 | − | 0.731414i | \(-0.738861\pi\) | ||||
−0.681934 | + | 0.731414i | \(0.738861\pi\) | |||||||
\(104\) | 454.389 | − | 14.0347i | 0.428428 | − | 0.0132328i | ||||
\(105\) | 14.8527 | 0.0138045 | ||||||||
\(106\) | 168.081i | 0.154014i | ||||||||
\(107\) | −1691.61 | −1.52835 | −0.764176 | − | 0.645008i | \(-0.776854\pi\) | ||||
−0.764176 | + | 0.645008i | \(0.776854\pi\) | |||||||
\(108\) | 1567.22 | 1.39635 | ||||||||
\(109\) | 1202.17i | 1.05639i | 0.849122 | + | 0.528196i | \(0.177131\pi\) | ||||
−0.849122 | + | 0.528196i | \(0.822869\pi\) | |||||||
\(110\) | − | 13.9041i | − | 0.0120519i | ||||||
\(111\) | 853.842i | 0.730118i | ||||||||
\(112\) | 471.027i | 0.397391i | ||||||||
\(113\) | 382.151 | 0.318139 | 0.159070 | − | 0.987267i | \(-0.449151\pi\) | ||||
0.159070 | + | 0.987267i | \(0.449151\pi\) | |||||||
\(114\) | −1264.29 | −1.03869 | ||||||||
\(115\) | 24.7111i | 0.0200376i | ||||||||
\(116\) | −2035.91 | −1.62956 | ||||||||
\(117\) | 11.8204 | + | 382.698i | 0.00934013 | + | 0.302397i | ||||
\(118\) | −1509.76 | −1.17784 | ||||||||
\(119\) | 459.568i | 0.354021i | ||||||||
\(120\) | −12.4466 | −0.00946849 | ||||||||
\(121\) | −121.000 | −0.0909091 | ||||||||
\(122\) | − | 267.711i | − | 0.198667i | ||||||
\(123\) | 239.843i | 0.175820i | ||||||||
\(124\) | − | 1962.34i | − | 1.42116i | ||||||
\(125\) | 73.9060i | 0.0528829i | ||||||||
\(126\) | 404.093 | 0.285710 | ||||||||
\(127\) | −1181.10 | −0.825244 | −0.412622 | − | 0.910902i | \(-0.635387\pi\) | ||||
−0.412622 | + | 0.910902i | \(0.635387\pi\) | |||||||
\(128\) | − | 1191.51i | − | 0.822779i | ||||||
\(129\) | 1045.48 | 0.713561 | ||||||||
\(130\) | −1.82909 | − | 59.2187i | −0.00123401 | − | 0.0399525i | ||||
\(131\) | 2140.49 | 1.42760 | 0.713801 | − | 0.700349i | \(-0.246972\pi\) | ||||
0.713801 | + | 0.700349i | \(0.246972\pi\) | |||||||
\(132\) | 490.194i | 0.323226i | ||||||||
\(133\) | −788.893 | −0.514329 | ||||||||
\(134\) | 3339.22 | 2.15272 | ||||||||
\(135\) | − | 45.1324i | − | 0.0287732i | ||||||
\(136\) | − | 385.120i | − | 0.242822i | ||||||
\(137\) | − | 843.457i | − | 0.525996i | −0.964796 | − | 0.262998i | \(-0.915289\pi\) | ||
0.964796 | − | 0.262998i | \(-0.0847112\pi\) | |||||||
\(138\) | − | 1549.89i | − | 0.956052i | ||||||
\(139\) | 2046.42 | 1.24874 | 0.624371 | − | 0.781128i | \(-0.285355\pi\) | ||||
0.624371 | + | 0.781128i | \(0.285355\pi\) | |||||||
\(140\) | −35.1479 | −0.0212181 | ||||||||
\(141\) | − | 2065.93i | − | 1.23392i | ||||||
\(142\) | −2461.42 | −1.45463 | ||||||||
\(143\) | −515.348 | + | 15.9175i | −0.301368 | + | 0.00930833i | ||||
\(144\) | 332.446 | 0.192388 | ||||||||
\(145\) | 58.6295i | 0.0335787i | ||||||||
\(146\) | −2248.84 | −1.27476 | ||||||||
\(147\) | 907.171 | 0.508994 | ||||||||
\(148\) | − | 2020.55i | − | 1.12222i | ||||||
\(149\) | 717.397i | 0.394439i | 0.980359 | + | 0.197220i | \(0.0631912\pi\) | ||||
−0.980359 | + | 0.197220i | \(0.936809\pi\) | |||||||
\(150\) | − | 2316.89i | − | 1.26116i | ||||||
\(151\) | 2010.44i | 1.08349i | 0.840542 | + | 0.541747i | \(0.182237\pi\) | ||||
−0.840542 | + | 0.541747i | \(0.817763\pi\) | |||||||
\(152\) | 661.096 | 0.352776 | ||||||||
\(153\) | 324.359 | 0.171391 | ||||||||
\(154\) | 544.158i | 0.284737i | ||||||||
\(155\) | −56.5110 | −0.0292844 | ||||||||
\(156\) | 64.4849 | + | 2087.77i | 0.0330957 | + | 1.07151i | ||||
\(157\) | 390.900 | 0.198709 | 0.0993543 | − | 0.995052i | \(-0.468322\pi\) | ||||
0.0993543 | + | 0.995052i | \(0.468322\pi\) | |||||||
\(158\) | − | 3789.88i | − | 1.90827i | ||||||
\(159\) | −170.648 | −0.0851149 | ||||||||
\(160\) | −74.3884 | −0.0367557 | ||||||||
\(161\) | − | 967.104i | − | 0.473407i | ||||||
\(162\) | 1888.02i | 0.915660i | ||||||||
\(163\) | − | 607.427i | − | 0.291885i | −0.989293 | − | 0.145943i | \(-0.953378\pi\) | ||
0.989293 | − | 0.145943i | \(-0.0466215\pi\) | |||||||
\(164\) | − | 567.570i | − | 0.270243i | ||||||
\(165\) | 14.1165 | 0.00666039 | ||||||||
\(166\) | −478.113 | −0.223547 | ||||||||
\(167\) | 3446.58i | 1.59703i | 0.601975 | + | 0.798515i | \(0.294381\pi\) | ||||
−0.601975 | + | 0.798515i | \(0.705619\pi\) | |||||||
\(168\) | 487.117 | 0.223702 | ||||||||
\(169\) | −2192.81 | + | 135.588i | −0.998094 | + | 0.0617150i | ||||
\(170\) | −50.1912 | −0.0226441 | ||||||||
\(171\) | 556.793i | 0.249000i | ||||||||
\(172\) | −2474.05 | −1.09677 | ||||||||
\(173\) | 66.7622 | 0.0293401 | 0.0146700 | − | 0.999892i | \(-0.495330\pi\) | ||||
0.0146700 | + | 0.999892i | \(0.495330\pi\) | |||||||
\(174\) | − | 3677.26i | − | 1.60214i | ||||||
\(175\) | − | 1445.70i | − | 0.624485i | ||||||
\(176\) | 447.677i | 0.191733i | ||||||||
\(177\) | − | 1532.82i | − | 0.650924i | ||||||
\(178\) | −1851.66 | −0.779705 | ||||||||
\(179\) | 2614.66 | 1.09178 | 0.545891 | − | 0.837856i | \(-0.316191\pi\) | ||||
0.545891 | + | 0.837856i | \(0.316191\pi\) | |||||||
\(180\) | 24.8070i | 0.0102723i | ||||||||
\(181\) | −3968.01 | −1.62950 | −0.814750 | − | 0.579812i | \(-0.803126\pi\) | ||||
−0.814750 | + | 0.579812i | \(0.803126\pi\) | |||||||
\(182\) | 71.5839 | + | 2317.61i | 0.0291547 | + | 0.943915i | ||||
\(183\) | 271.799 | 0.109792 | ||||||||
\(184\) | 810.438i | 0.324708i | ||||||||
\(185\) | −58.1873 | −0.0231244 | ||||||||
\(186\) | 3544.39 | 1.39724 | ||||||||
\(187\) | 436.787i | 0.170808i | ||||||||
\(188\) | 4888.87i | 1.89658i | ||||||||
\(189\) | 1766.32i | 0.679793i | ||||||||
\(190\) | − | 86.1581i | − | 0.0328977i | ||||||
\(191\) | −950.221 | −0.359977 | −0.179988 | − | 0.983669i | \(-0.557606\pi\) | ||||
−0.179988 | + | 0.983669i | \(0.557606\pi\) | |||||||
\(192\) | 3252.79 | 1.22265 | ||||||||
\(193\) | 903.572i | 0.336997i | 0.985702 | + | 0.168499i | \(0.0538919\pi\) | ||||
−0.985702 | + | 0.168499i | \(0.946108\pi\) | |||||||
\(194\) | 4399.31 | 1.62810 | ||||||||
\(195\) | 60.1230 | − | 1.85702i | 0.0220795 | − | 0.000681968i | ||||
\(196\) | −2146.75 | −0.782344 | ||||||||
\(197\) | − | 3014.55i | − | 1.09024i | −0.838358 | − | 0.545121i | \(-0.816484\pi\) | ||
0.838358 | − | 0.545121i | \(-0.183516\pi\) | |||||||
\(198\) | 384.061 | 0.137849 | ||||||||
\(199\) | 2400.72 | 0.855189 | 0.427594 | − | 0.903971i | \(-0.359361\pi\) | ||||
0.427594 | + | 0.903971i | \(0.359361\pi\) | |||||||
\(200\) | 1211.51i | 0.428332i | ||||||||
\(201\) | 3390.21i | 1.18969i | ||||||||
\(202\) | − | 5052.55i | − | 1.75988i | ||||||
\(203\) | − | 2294.55i | − | 0.793328i | ||||||
\(204\) | 1769.51 | 0.607305 | ||||||||
\(205\) | −16.3447 | −0.00556861 | ||||||||
\(206\) | 6093.79i | 2.06104i | ||||||||
\(207\) | −682.573 | −0.229189 | ||||||||
\(208\) | 58.8919 | + | 1906.69i | 0.0196318 | + | 0.635602i | ||||
\(209\) | −749.787 | −0.248152 | ||||||||
\(210\) | − | 63.4841i | − | 0.0208610i | ||||||
\(211\) | 832.376 | 0.271579 | 0.135789 | − | 0.990738i | \(-0.456643\pi\) | ||||
0.135789 | + | 0.990738i | \(0.456643\pi\) | |||||||
\(212\) | 403.826 | 0.130825 | ||||||||
\(213\) | − | 2499.01i | − | 0.803894i | ||||||
\(214\) | 7230.33i | 2.30960i | ||||||||
\(215\) | 71.2470i | 0.0226000i | ||||||||
\(216\) | − | 1480.18i | − | 0.466268i | ||||||
\(217\) | 2211.64 | 0.691870 | ||||||||
\(218\) | 5138.35 | 1.59639 | ||||||||
\(219\) | − | 2283.19i | − | 0.704490i | ||||||
\(220\) | −33.4055 | −0.0102373 | ||||||||
\(221\) | 57.4592 | + | 1860.31i | 0.0174893 | + | 0.566235i | ||||
\(222\) | 3649.52 | 1.10333 | ||||||||
\(223\) | − | 426.781i | − | 0.128159i | −0.997945 | − | 0.0640794i | \(-0.979589\pi\) | ||
0.997945 | − | 0.0640794i | \(-0.0204111\pi\) | |||||||
\(224\) | 2911.29 | 0.868389 | ||||||||
\(225\) | −1020.36 | −0.302330 | ||||||||
\(226\) | − | 1633.40i | − | 0.480763i | ||||||
\(227\) | − | 2730.32i | − | 0.798316i | −0.916882 | − | 0.399158i | \(-0.869302\pi\) | ||
0.916882 | − | 0.399158i | \(-0.130698\pi\) | |||||||
\(228\) | 3037.53i | 0.882303i | ||||||||
\(229\) | − | 877.843i | − | 0.253317i | −0.991946 | − | 0.126658i | \(-0.959575\pi\) | ||
0.991946 | − | 0.126658i | \(-0.0404252\pi\) | |||||||
\(230\) | 105.621 | 0.0302802 | ||||||||
\(231\) | −552.468 | −0.157358 | ||||||||
\(232\) | 1922.84i | 0.544141i | ||||||||
\(233\) | −4594.32 | −1.29178 | −0.645888 | − | 0.763432i | \(-0.723513\pi\) | ||||
−0.645888 | + | 0.763432i | \(0.723513\pi\) | |||||||
\(234\) | 1635.75 | − | 50.5232i | 0.456974 | − | 0.0141145i | ||||
\(235\) | 140.788 | 0.0390809 | ||||||||
\(236\) | 3627.30i | 1.00050i | ||||||||
\(237\) | 3847.76 | 1.05459 | ||||||||
\(238\) | 1964.31 | 0.534987 | ||||||||
\(239\) | − | 3058.65i | − | 0.827813i | −0.910319 | − | 0.413907i | \(-0.864164\pi\) | ||
0.910319 | − | 0.413907i | \(-0.135836\pi\) | |||||||
\(240\) | − | 52.2282i | − | 0.0140472i | ||||||
\(241\) | 246.112i | 0.0657820i | 0.999459 | + | 0.0328910i | \(0.0104714\pi\) | ||||
−0.999459 | + | 0.0328910i | \(0.989529\pi\) | |||||||
\(242\) | 517.183i | 0.137379i | ||||||||
\(243\) | 2203.74 | 0.581770 | ||||||||
\(244\) | −643.193 | −0.168755 | ||||||||
\(245\) | 61.8215i | 0.0161210i | ||||||||
\(246\) | 1025.15 | 0.265695 | ||||||||
\(247\) | −3193.40 | + | 98.6344i | −0.822636 | + | 0.0254087i | ||||
\(248\) | −1853.36 | −0.474551 | ||||||||
\(249\) | − | 485.414i | − | 0.123542i | ||||||
\(250\) | 315.892 | 0.0799151 | ||||||||
\(251\) | −5506.45 | −1.38472 | −0.692359 | − | 0.721553i | \(-0.743429\pi\) | ||||
−0.692359 | + | 0.721553i | \(0.743429\pi\) | |||||||
\(252\) | − | 970.858i | − | 0.242692i | ||||||
\(253\) | − | 919.164i | − | 0.228408i | ||||||
\(254\) | 5048.32i | 1.24709i | ||||||||
\(255\) | − | 50.9577i | − | 0.0125141i | ||||||
\(256\) | 903.783 | 0.220650 | ||||||||
\(257\) | −1094.53 | −0.265660 | −0.132830 | − | 0.991139i | \(-0.542407\pi\) | ||||
−0.132830 | + | 0.991139i | \(0.542407\pi\) | |||||||
\(258\) | − | 4468.63i | − | 1.07831i | ||||||
\(259\) | 2277.24 | 0.546336 | ||||||||
\(260\) | −142.277 | + | 4.39449i | −0.0339370 | + | 0.00104821i | ||||
\(261\) | −1619.47 | −0.384071 | ||||||||
\(262\) | − | 9148.98i | − | 2.15735i | ||||||
\(263\) | −1468.52 | −0.344307 | −0.172153 | − | 0.985070i | \(-0.555072\pi\) | ||||
−0.172153 | + | 0.985070i | \(0.555072\pi\) | |||||||
\(264\) | 462.970 | 0.107931 | ||||||||
\(265\) | − | 11.6293i | − | 0.00269577i | ||||||
\(266\) | 3371.92i | 0.777239i | ||||||||
\(267\) | − | 1879.93i | − | 0.430899i | ||||||
\(268\) | − | 8022.68i | − | 1.82859i | ||||||
\(269\) | −6900.60 | −1.56408 | −0.782039 | − | 0.623229i | \(-0.785820\pi\) | ||||
−0.782039 | + | 0.623229i | \(0.785820\pi\) | |||||||
\(270\) | −192.907 | −0.0434812 | ||||||||
\(271\) | 554.284i | 0.124245i | 0.998069 | + | 0.0621224i | \(0.0197869\pi\) | ||||
−0.998069 | + | 0.0621224i | \(0.980213\pi\) | |||||||
\(272\) | 1616.03 | 0.360243 | ||||||||
\(273\) | −2353.00 | + | 72.6770i | −0.521649 | + | 0.0161121i | ||||
\(274\) | −3605.14 | −0.794870 | ||||||||
\(275\) | − | 1374.04i | − | 0.301300i | ||||||
\(276\) | −3723.70 | −0.812104 | ||||||||
\(277\) | −8531.36 | −1.85054 | −0.925270 | − | 0.379310i | \(-0.876162\pi\) | ||||
−0.925270 | + | 0.379310i | \(0.876162\pi\) | |||||||
\(278\) | − | 8746.89i | − | 1.88706i | ||||||
\(279\) | − | 1560.95i | − | 0.334953i | ||||||
\(280\) | 33.1959i | 0.00708512i | ||||||||
\(281\) | 261.071i | 0.0554242i | 0.999616 | + | 0.0277121i | \(0.00882216\pi\) | ||||
−0.999616 | + | 0.0277121i | \(0.991178\pi\) | |||||||
\(282\) | −8830.29 | −1.86467 | ||||||||
\(283\) | 5786.71 | 1.21549 | 0.607746 | − | 0.794131i | \(-0.292074\pi\) | ||||
0.607746 | + | 0.794131i | \(0.292074\pi\) | |||||||
\(284\) | 5913.72i | 1.23562i | ||||||||
\(285\) | 87.4738 | 0.0181807 | ||||||||
\(286\) | 68.0354 | + | 2202.72i | 0.0140665 | + | 0.455418i | ||||
\(287\) | 639.674 | 0.131564 | ||||||||
\(288\) | − | 2054.76i | − | 0.420410i | ||||||
\(289\) | −3336.28 | −0.679072 | ||||||||
\(290\) | 250.596 | 0.0507432 | ||||||||
\(291\) | 4466.49i | 0.899761i | ||||||||
\(292\) | 5402.99i | 1.08283i | ||||||||
\(293\) | − | 4466.22i | − | 0.890509i | −0.895404 | − | 0.445255i | \(-0.853113\pi\) | ||
0.895404 | − | 0.445255i | \(-0.146887\pi\) | |||||||
\(294\) | − | 3877.47i | − | 0.769178i | ||||||
\(295\) | 104.458 | 0.0206162 | ||||||||
\(296\) | −1908.34 | −0.374730 | ||||||||
\(297\) | 1678.76i | 0.327985i | ||||||||
\(298\) | 3066.33 | 0.596065 | ||||||||
\(299\) | −120.916 | − | 3914.79i | −0.0233871 | − | 0.757184i | ||||
\(300\) | −5566.48 | −1.07127 | ||||||||
\(301\) | − | 2788.35i | − | 0.533947i | ||||||
\(302\) | 8593.12 | 1.63735 | ||||||||
\(303\) | 5129.70 | 0.972587 | ||||||||
\(304\) | 2774.07i | 0.523368i | ||||||||
\(305\) | 18.5225i | 0.00347736i | ||||||||
\(306\) | − | 1386.39i | − | 0.259002i | ||||||
\(307\) | − | 2578.45i | − | 0.479348i | −0.970853 | − | 0.239674i | \(-0.922959\pi\) | ||
0.970853 | − | 0.239674i | \(-0.0770405\pi\) | |||||||
\(308\) | 1307.37 | 0.241865 | ||||||||
\(309\) | −6186.84 | −1.13902 | ||||||||
\(310\) | 241.542i | 0.0442537i | ||||||||
\(311\) | 4244.93 | 0.773981 | 0.386990 | − | 0.922084i | \(-0.373515\pi\) | ||||
0.386990 | + | 0.922084i | \(0.373515\pi\) | |||||||
\(312\) | 1971.83 | − | 60.9037i | 0.357797 | − | 0.0110513i | ||||
\(313\) | 5516.53 | 0.996207 | 0.498103 | − | 0.867118i | \(-0.334030\pi\) | ||||
0.498103 | + | 0.867118i | \(0.334030\pi\) | |||||||
\(314\) | − | 1670.80i | − | 0.300283i | ||||||
\(315\) | −27.9585 | −0.00500090 | ||||||||
\(316\) | −9105.44 | −1.62095 | ||||||||
\(317\) | 8229.05i | 1.45801i | 0.684508 | + | 0.729005i | \(0.260017\pi\) | ||||
−0.684508 | + | 0.729005i | \(0.739983\pi\) | |||||||
\(318\) | 729.391i | 0.128623i | ||||||||
\(319\) | − | 2180.80i | − | 0.382764i | ||||||
\(320\) | 221.670i | 0.0387241i | ||||||||
\(321\) | −7340.75 | −1.27639 | ||||||||
\(322\) | −4133.64 | −0.715399 | ||||||||
\(323\) | 2706.59i | 0.466249i | ||||||||
\(324\) | 4536.09 | 0.777793 | ||||||||
\(325\) | −180.754 | − | 5852.13i | −0.0308506 | − | 0.998824i | ||||
\(326\) | −2596.29 | −0.441089 | ||||||||
\(327\) | 5216.82i | 0.882235i | ||||||||
\(328\) | −536.050 | −0.0902390 | ||||||||
\(329\) | −5509.95 | −0.923324 | ||||||||
\(330\) | − | 60.3371i | − | 0.0100650i | ||||||
\(331\) | 9065.84i | 1.50545i | 0.658336 | + | 0.752724i | \(0.271261\pi\) | ||||
−0.658336 | + | 0.752724i | \(0.728739\pi\) | |||||||
\(332\) | 1148.70i | 0.189888i | ||||||||
\(333\) | − | 1607.26i | − | 0.264496i | ||||||
\(334\) | 14731.5 | 2.41339 | ||||||||
\(335\) | −231.035 | −0.0376799 | ||||||||
\(336\) | 2044.03i | 0.331877i | ||||||||
\(337\) | −1819.38 | −0.294089 | −0.147045 | − | 0.989130i | \(-0.546976\pi\) | ||||
−0.147045 | + | 0.989130i | \(0.546976\pi\) | |||||||
\(338\) | 579.535 | + | 9372.61i | 0.0932620 | + | 1.50829i | ||||
\(339\) | 1658.35 | 0.265691 | ||||||||
\(340\) | 120.588i | 0.0192347i | ||||||||
\(341\) | 2102.01 | 0.333812 | ||||||||
\(342\) | 2379.87 | 0.376282 | ||||||||
\(343\) | − | 6389.26i | − | 1.00580i | ||||||
\(344\) | 2336.65i | 0.366232i | ||||||||
\(345\) | 107.234i | 0.0167342i | ||||||||
\(346\) | − | 285.358i | − | 0.0443379i | ||||||
\(347\) | 6353.91 | 0.982985 | 0.491492 | − | 0.870882i | \(-0.336452\pi\) | ||||
0.491492 | + | 0.870882i | \(0.336452\pi\) | |||||||
\(348\) | −8834.84 | −1.36091 | ||||||||
\(349\) | 3814.24i | 0.585019i | 0.956263 | + | 0.292509i | \(0.0944903\pi\) | ||||
−0.956263 | + | 0.292509i | \(0.905510\pi\) | |||||||
\(350\) | −6179.28 | −0.943705 | ||||||||
\(351\) | 220.841 | + | 7149.97i | 0.0335829 | + | 1.08729i | ||||
\(352\) | 2766.98 | 0.418978 | ||||||||
\(353\) | 10332.2i | 1.55786i | 0.627110 | + | 0.778931i | \(0.284238\pi\) | ||||
−0.627110 | + | 0.778931i | \(0.715762\pi\) | |||||||
\(354\) | −6551.63 | −0.983659 | ||||||||
\(355\) | 170.302 | 0.0254611 | ||||||||
\(356\) | 4448.72i | 0.662308i | ||||||||
\(357\) | 1994.30i | 0.295657i | ||||||||
\(358\) | − | 11175.7i | − | 1.64987i | ||||||
\(359\) | − | 5905.08i | − | 0.868128i | −0.900882 | − | 0.434064i | \(-0.857079\pi\) | ||
0.900882 | − | 0.434064i | \(-0.142921\pi\) | |||||||
\(360\) | 23.4293 | 0.00343010 | ||||||||
\(361\) | 2212.88 | 0.322624 | ||||||||
\(362\) | 16960.2i | 2.46246i | ||||||||
\(363\) | −525.081 | −0.0759218 | ||||||||
\(364\) | 5568.20 | − | 171.985i | 0.801794 | − | 0.0247650i | ||||
\(365\) | 155.594 | 0.0223127 | ||||||||
\(366\) | − | 1161.74i | − | 0.165915i | ||||||
\(367\) | 13851.8 | 1.97018 | 0.985090 | − | 0.172038i | \(-0.0550351\pi\) | ||||
0.985090 | + | 0.172038i | \(0.0550351\pi\) | |||||||
\(368\) | −3400.73 | −0.481727 | ||||||||
\(369\) | − | 451.476i | − | 0.0636935i | ||||||
\(370\) | 248.707i | 0.0349450i | ||||||||
\(371\) | 455.128i | 0.0636902i | ||||||||
\(372\) | − | 8515.62i | − | 1.18687i | ||||||
\(373\) | −11878.0 | −1.64885 | −0.824424 | − | 0.565972i | \(-0.808501\pi\) | ||||
−0.824424 | + | 0.565972i | \(0.808501\pi\) | |||||||
\(374\) | 1866.93 | 0.258120 | ||||||||
\(375\) | 320.716i | 0.0441646i | ||||||||
\(376\) | 4617.37 | 0.633304 | ||||||||
\(377\) | −286.884 | − | 9288.21i | −0.0391918 | − | 1.26888i | ||||
\(378\) | 7549.68 | 1.02728 | ||||||||
\(379\) | 4585.38i | 0.621464i | 0.950497 | + | 0.310732i | \(0.100574\pi\) | ||||
−0.950497 | + | 0.310732i | \(0.899426\pi\) | |||||||
\(380\) | −207.000 | −0.0279445 | ||||||||
\(381\) | −5125.42 | −0.689194 | ||||||||
\(382\) | 4061.47i | 0.543987i | ||||||||
\(383\) | 2738.17i | 0.365311i | 0.983177 | + | 0.182655i | \(0.0584692\pi\) | ||||
−0.983177 | + | 0.182655i | \(0.941531\pi\) | |||||||
\(384\) | − | 5170.58i | − | 0.687136i | ||||||
\(385\) | − | 37.6494i | − | 0.00498387i | ||||||
\(386\) | 3862.08 | 0.509261 | ||||||||
\(387\) | −1967.99 | −0.258498 | ||||||||
\(388\) | − | 10569.6i | − | 1.38297i | ||||||
\(389\) | 73.0815 | 0.00952540 | 0.00476270 | − | 0.999989i | \(-0.498484\pi\) | ||||
0.00476270 | + | 0.999989i | \(0.498484\pi\) | |||||||
\(390\) | −7.93734 | − | 256.980i | −0.00103057 | − | 0.0333659i | ||||
\(391\) | −3318.01 | −0.429153 | ||||||||
\(392\) | 2027.53i | 0.261239i | ||||||||
\(393\) | 9288.70 | 1.19225 | ||||||||
\(394\) | −12884.9 | −1.64754 | ||||||||
\(395\) | 262.216i | 0.0334013i | ||||||||
\(396\) | − | 922.731i | − | 0.117093i | ||||||
\(397\) | 3133.25i | 0.396104i | 0.980191 | + | 0.198052i | \(0.0634616\pi\) | ||||
−0.980191 | + | 0.198052i | \(0.936538\pi\) | |||||||
\(398\) | − | 10261.3i | − | 1.29234i | ||||||
\(399\) | −3423.41 | −0.429536 | ||||||||
\(400\) | −5083.68 | −0.635460 | ||||||||
\(401\) | − | 9195.25i | − | 1.14511i | −0.819867 | − | 0.572555i | \(-0.805952\pi\) | ||
0.819867 | − | 0.572555i | \(-0.194048\pi\) | |||||||
\(402\) | 14490.6 | 1.79782 | ||||||||
\(403\) | 8952.60 | − | 276.519i | 1.10660 | − | 0.0341796i | ||||
\(404\) | −12139.1 | −1.49490 | ||||||||
\(405\) | − | 130.629i | − | 0.0160272i | ||||||
\(406\) | −9807.45 | −1.19886 | ||||||||
\(407\) | 2164.36 | 0.263595 | ||||||||
\(408\) | − | 1671.23i | − | 0.202790i | ||||||
\(409\) | − | 218.502i | − | 0.0264162i | −0.999913 | − | 0.0132081i | \(-0.995796\pi\) | ||
0.999913 | − | 0.0132081i | \(-0.00420439\pi\) | |||||||
\(410\) | 69.8613i | 0.00841513i | ||||||||
\(411\) | − | 3660.19i | − | 0.439280i | ||||||
\(412\) | 14640.7 | 1.75072 | ||||||||
\(413\) | −4088.11 | −0.487077 | ||||||||
\(414\) | 2917.48i | 0.346344i | ||||||||
\(415\) | 33.0798 | 0.00391283 | ||||||||
\(416\) | 11784.8 | − | 363.996i | 1.38893 | − | 0.0428999i | ||||
\(417\) | 8880.47 | 1.04287 | ||||||||
\(418\) | 3204.77i | 0.375001i | ||||||||
\(419\) | 15977.6 | 1.86290 | 0.931450 | − | 0.363869i | \(-0.118544\pi\) | ||||
0.931450 | + | 0.363869i | \(0.118544\pi\) | |||||||
\(420\) | −152.525 | −0.0177201 | ||||||||
\(421\) | 4043.12i | 0.468051i | 0.972230 | + | 0.234025i | \(0.0751899\pi\) | ||||
−0.972230 | + | 0.234025i | \(0.924810\pi\) | |||||||
\(422\) | − | 3557.78i | − | 0.410403i | ||||||
\(423\) | 3888.87i | 0.447006i | ||||||||
\(424\) | − | 381.399i | − | 0.0436848i | ||||||
\(425\) | −4960.01 | −0.566108 | ||||||||
\(426\) | −10681.4 | −1.21482 | ||||||||
\(427\) | − | 724.904i | − | 0.0821559i | ||||||
\(428\) | 17371.3 | 1.96186 | ||||||||
\(429\) | −2236.36 | + | 69.0743i | −0.251684 | + | 0.00777375i | ||||
\(430\) | 304.527 | 0.0341525 | ||||||||
\(431\) | 14547.9i | 1.62587i | 0.582358 | + | 0.812933i | \(0.302130\pi\) | ||||
−0.582358 | + | 0.812933i | \(0.697870\pi\) | |||||||
\(432\) | 6211.10 | 0.691740 | ||||||||
\(433\) | 5626.97 | 0.624515 | 0.312258 | − | 0.949997i | \(-0.398915\pi\) | ||||
0.312258 | + | 0.949997i | \(0.398915\pi\) | |||||||
\(434\) | − | 9453.08i | − | 1.04554i | ||||||
\(435\) | 254.423i | 0.0280429i | ||||||||
\(436\) | − | 12345.2i | − | 1.35603i | ||||||
\(437\) | − | 5695.68i | − | 0.623481i | ||||||
\(438\) | −9758.89 | −1.06461 | ||||||||
\(439\) | −4393.73 | −0.477679 | −0.238840 | − | 0.971059i | \(-0.576767\pi\) | ||||
−0.238840 | + | 0.971059i | \(0.576767\pi\) | |||||||
\(440\) | 31.5503i | 0.00341842i | ||||||||
\(441\) | −1707.64 | −0.184391 | ||||||||
\(442\) | 7951.40 | − | 245.595i | 0.855678 | − | 0.0264293i | ||||
\(443\) | 10180.2 | 1.09182 | 0.545912 | − | 0.837843i | \(-0.316183\pi\) | ||||
0.545912 | + | 0.837843i | \(0.316183\pi\) | |||||||
\(444\) | − | 8768.21i | − | 0.937210i | ||||||
\(445\) | 128.113 | 0.0136475 | ||||||||
\(446\) | −1824.17 | −0.193670 | ||||||||
\(447\) | 3113.15i | 0.329412i | ||||||||
\(448\) | − | 8675.36i | − | 0.914893i | ||||||
\(449\) | 4141.65i | 0.435316i | 0.976025 | + | 0.217658i | \(0.0698417\pi\) | ||||
−0.976025 | + | 0.217658i | \(0.930158\pi\) | |||||||
\(450\) | 4361.28i | 0.456873i | ||||||||
\(451\) | 607.965 | 0.0634766 | ||||||||
\(452\) | −3924.36 | −0.408377 | ||||||||
\(453\) | 8724.34i | 0.904869i | ||||||||
\(454\) | −11670.0 | −1.20639 | ||||||||
\(455\) | −4.95277 | − | 160.351i | −0.000510306 | − | 0.0165217i | ||||
\(456\) | 2868.84 | 0.294617 | ||||||||
\(457\) | 12713.7i | 1.30136i | 0.759352 | + | 0.650680i | \(0.225516\pi\) | ||||
−0.759352 | + | 0.650680i | \(0.774484\pi\) | |||||||
\(458\) | −3752.11 | −0.382805 | ||||||||
\(459\) | 6060.01 | 0.616246 | ||||||||
\(460\) | − | 253.762i | − | 0.0257211i | ||||||
\(461\) | − | 17549.9i | − | 1.77306i | −0.462673 | − | 0.886529i | \(-0.653110\pi\) | ||
0.462673 | − | 0.886529i | \(-0.346890\pi\) | |||||||
\(462\) | 2361.38i | 0.237795i | ||||||||
\(463\) | − | 10960.0i | − | 1.10012i | −0.835125 | − | 0.550060i | \(-0.814605\pi\) | ||
0.835125 | − | 0.550060i | \(-0.185395\pi\) | |||||||
\(464\) | −8068.57 | −0.807271 | ||||||||
\(465\) | −245.230 | −0.0244565 | ||||||||
\(466\) | 19637.2i | 1.95210i | ||||||||
\(467\) | −7368.99 | −0.730184 | −0.365092 | − | 0.930971i | \(-0.618963\pi\) | ||||
−0.365092 | + | 0.930971i | \(0.618963\pi\) | |||||||
\(468\) | −121.385 | − | 3929.98i | −0.0119894 | − | 0.388170i | ||||
\(469\) | 9041.88 | 0.890224 | ||||||||
\(470\) | − | 601.763i | − | 0.0590580i | ||||||
\(471\) | 1696.32 | 0.165949 | ||||||||
\(472\) | 3425.85 | 0.334084 | ||||||||
\(473\) | − | 2650.13i | − | 0.257618i | ||||||
\(474\) | − | 16446.3i | − | 1.59367i | ||||||
\(475\) | − | 8514.34i | − | 0.822452i | ||||||
\(476\) | − | 4719.37i | − | 0.454437i | ||||||
\(477\) | 321.225 | 0.0308341 | ||||||||
\(478\) | −13073.4 | −1.25097 | ||||||||
\(479\) | − | 10106.7i | − | 0.964065i | −0.876153 | − | 0.482032i | \(-0.839899\pi\) | ||
0.876153 | − | 0.482032i | \(-0.160101\pi\) | |||||||
\(480\) | −322.809 | −0.0306962 | ||||||||
\(481\) | 9218.16 | − | 284.721i | 0.873829 | − | 0.0269899i | ||||
\(482\) | 1051.94 | 0.0994079 | ||||||||
\(483\) | − | 4196.76i | − | 0.395361i | ||||||
\(484\) | 1242.57 | 0.116695 | ||||||||
\(485\) | −304.381 | −0.0284974 | ||||||||
\(486\) | − | 9419.33i | − | 0.879155i | ||||||
\(487\) | 16640.4i | 1.54835i | 0.632969 | + | 0.774177i | \(0.281836\pi\) | ||||
−0.632969 | + | 0.774177i | \(0.718164\pi\) | |||||||
\(488\) | 607.473i | 0.0563504i | ||||||||
\(489\) | − | 2635.94i | − | 0.243765i | ||||||
\(490\) | 264.240 | 0.0243615 | ||||||||
\(491\) | 13448.1 | 1.23605 | 0.618027 | − | 0.786157i | \(-0.287932\pi\) | ||||
0.618027 | + | 0.786157i | \(0.287932\pi\) | |||||||
\(492\) | − | 2462.98i | − | 0.225690i | ||||||
\(493\) | −7872.29 | −0.719168 | ||||||||
\(494\) | 421.587 | + | 13649.4i | 0.0383970 | + | 1.24314i | ||||
\(495\) | −26.5726 | −0.00241282 | ||||||||
\(496\) | − | 7777.03i | − | 0.704030i | ||||||
\(497\) | −6665.00 | −0.601542 | ||||||||
\(498\) | −2074.78 | −0.186693 | ||||||||
\(499\) | 19287.6i | 1.73032i | 0.501496 | + | 0.865160i | \(0.332783\pi\) | ||||
−0.501496 | + | 0.865160i | \(0.667217\pi\) | |||||||
\(500\) | − | 758.951i | − | 0.0678827i | ||||||
\(501\) | 14956.5i | 1.33374i | ||||||||
\(502\) | 23535.9i | 2.09255i | ||||||||
\(503\) | −2212.03 | −0.196083 | −0.0980413 | − | 0.995182i | \(-0.531258\pi\) | ||||
−0.0980413 | + | 0.995182i | \(0.531258\pi\) | |||||||
\(504\) | −916.941 | −0.0810393 | ||||||||
\(505\) | 349.577i | 0.0308039i | ||||||||
\(506\) | −3928.73 | −0.345165 | ||||||||
\(507\) | −9515.74 | + | 588.386i | −0.833548 | + | 0.0515407i | ||||
\(508\) | 12128.9 | 1.05932 | ||||||||
\(509\) | 10398.3i | 0.905493i | 0.891639 | + | 0.452747i | \(0.149556\pi\) | ||||
−0.891639 | + | 0.452747i | \(0.850444\pi\) | |||||||
\(510\) | −217.806 | −0.0189110 | ||||||||
\(511\) | −6089.38 | −0.527159 | ||||||||
\(512\) | − | 13395.1i | − | 1.15622i | ||||||
\(513\) | 10402.6i | 0.895294i | ||||||||
\(514\) | 4678.27i | 0.401459i | ||||||||
\(515\) | − | 421.619i | − | 0.0360752i | ||||||
\(516\) | −10736.2 | −0.915957 | ||||||||
\(517\) | −5236.82 | −0.445484 | ||||||||
\(518\) | − | 9733.48i | − | 0.825608i | ||||||
\(519\) | 289.716 | 0.0245031 | ||||||||
\(520\) | 4.15044 | + | 134.375i | 0.000350017 | + | 0.0113322i | ||||
\(521\) | −20957.7 | −1.76233 | −0.881166 | − | 0.472807i | \(-0.843241\pi\) | ||||
−0.881166 | + | 0.472807i | \(0.843241\pi\) | |||||||
\(522\) | 6922.00i | 0.580398i | ||||||||
\(523\) | 21443.2 | 1.79282 | 0.896409 | − | 0.443228i | \(-0.146167\pi\) | ||||
0.896409 | + | 0.443228i | \(0.146167\pi\) | |||||||
\(524\) | −21981.0 | −1.83253 | ||||||||
\(525\) | − | 6273.65i | − | 0.521532i | ||||||
\(526\) | 6276.80i | 0.520307i | ||||||||
\(527\) | − | 7587.84i | − | 0.627194i | ||||||
\(528\) | 1942.70i | 0.160124i | ||||||||
\(529\) | −5184.67 | −0.426125 | ||||||||
\(530\) | −49.7062 | −0.00407378 | ||||||||
\(531\) | 2885.35i | 0.235807i | ||||||||
\(532\) | 8101.25 | 0.660214 | ||||||||
\(533\) | 2589.37 | − | 79.9777i | 0.210428 | − | 0.00649947i | ||||
\(534\) | −8035.29 | −0.651163 | ||||||||
\(535\) | − | 500.255i | − | 0.0404260i | ||||||
\(536\) | −7577.13 | −0.610601 | ||||||||
\(537\) | 11346.4 | 0.911790 | ||||||||
\(538\) | 29494.8i | 2.36359i | ||||||||
\(539\) | − | 2299.54i | − | 0.183763i | ||||||
\(540\) | 463.471i | 0.0369344i | ||||||||
\(541\) | 12626.1i | 1.00340i | 0.865042 | + | 0.501699i | \(0.167292\pi\) | ||||
−0.865042 | + | 0.501699i | \(0.832708\pi\) | |||||||
\(542\) | 2369.14 | 0.187755 | ||||||||
\(543\) | −17219.2 | −1.36086 | ||||||||
\(544\) | − | 9988.26i | − | 0.787212i | ||||||
\(545\) | −355.514 | −0.0279423 | ||||||||
\(546\) | 310.639 | + | 10057.3i | 0.0243482 | + | 0.788301i | ||||
\(547\) | 17202.2 | 1.34463 | 0.672317 | − | 0.740264i | \(-0.265299\pi\) | ||||
0.672317 | + | 0.740264i | \(0.265299\pi\) | |||||||
\(548\) | 8661.57i | 0.675190i | ||||||||
\(549\) | −511.630 | −0.0397739 | ||||||||
\(550\) | −5872.97 | −0.455317 | ||||||||
\(551\) | − | 13513.5i | − | 1.04482i | ||||||
\(552\) | 3516.91i | 0.271177i | ||||||||
\(553\) | − | 10262.2i | − | 0.789137i | ||||||
\(554\) | 36465.1i | 2.79648i | ||||||||
\(555\) | −252.505 | −0.0193121 | ||||||||
\(556\) | −21015.0 | −1.60294 | ||||||||
\(557\) | − | 21165.4i | − | 1.61007i | −0.593231 | − | 0.805033i | \(-0.702148\pi\) | ||
0.593231 | − | 0.805033i | \(-0.297852\pi\) | |||||||
\(558\) | −6671.89 | −0.506172 | ||||||||
\(559\) | −348.624 | − | 11287.1i | −0.0263779 | − | 0.854014i | ||||
\(560\) | −139.296 | −0.0105113 | ||||||||
\(561\) | 1895.44i | 0.142648i | ||||||||
\(562\) | 1115.88 | 0.0837555 | ||||||||
\(563\) | −12181.9 | −0.911908 | −0.455954 | − | 0.890003i | \(-0.650702\pi\) | ||||
−0.455954 | + | 0.890003i | \(0.650702\pi\) | |||||||
\(564\) | 21215.3i | 1.58391i | ||||||||
\(565\) | 113.013i | 0.00841500i | ||||||||
\(566\) | − | 24733.8i | − | 1.83682i | ||||||
\(567\) | 5112.35i | 0.378657i | ||||||||
\(568\) | 5585.30 | 0.412595 | ||||||||
\(569\) | 14988.3 | 1.10429 | 0.552147 | − | 0.833747i | \(-0.313809\pi\) | ||||
0.552147 | + | 0.833747i | \(0.313809\pi\) | |||||||
\(570\) | − | 373.884i | − | 0.0274742i | ||||||
\(571\) | −144.731 | −0.0106073 | −0.00530367 | − | 0.999986i | \(-0.501688\pi\) | ||||
−0.00530367 | + | 0.999986i | \(0.501688\pi\) | |||||||
\(572\) | 5292.18 | − | 163.459i | 0.386848 | − | 0.0119486i | ||||
\(573\) | −4123.50 | −0.300631 | ||||||||
\(574\) | − | 2734.12i | − | 0.198815i | ||||||
\(575\) | 10437.7 | 0.757015 | ||||||||
\(576\) | −6122.98 | −0.442924 | ||||||||
\(577\) | − | 8362.30i | − | 0.603340i | −0.953412 | − | 0.301670i | \(-0.902456\pi\) | ||
0.953412 | − | 0.301670i | \(-0.0975441\pi\) | |||||||
\(578\) | 14260.1i | 1.02620i | ||||||||
\(579\) | 3921.06i | 0.281440i | ||||||||
\(580\) | − | 602.074i | − | 0.0431030i | ||||||
\(581\) | −1294.63 | −0.0924444 | ||||||||
\(582\) | 19090.9 | 1.35969 | ||||||||
\(583\) | 432.566i | 0.0307291i | ||||||||
\(584\) | 5102.93 | 0.361577 | ||||||||
\(585\) | −113.175 | + | 3.49562i | −0.00799862 | + | 0.000247053i | ||||
\(586\) | −19089.7 | −1.34571 | ||||||||
\(587\) | − | 17166.0i | − | 1.20701i | −0.797359 | − | 0.603505i | \(-0.793770\pi\) | ||
0.797359 | − | 0.603505i | \(-0.206230\pi\) | |||||||
\(588\) | −9315.86 | −0.653367 | ||||||||
\(589\) | 13025.3 | 0.911199 | ||||||||
\(590\) | − | 446.478i | − | 0.0311546i | ||||||
\(591\) | − | 13081.7i | − | 0.910504i | ||||||
\(592\) | − | 8007.72i | − | 0.555938i | ||||||
\(593\) | − | 4113.76i | − | 0.284877i | −0.989804 | − | 0.142438i | \(-0.954506\pi\) | ||
0.989804 | − | 0.142438i | \(-0.0454943\pi\) | |||||||
\(594\) | 7175.43 | 0.495642 | ||||||||
\(595\) | −135.907 | −0.00936411 | ||||||||
\(596\) | − | 7367.04i | − | 0.506318i | ||||||
\(597\) | 10418.0 | 0.714202 | ||||||||
\(598\) | −16732.7 | + | 516.824i | −1.14424 | + | 0.0353420i | ||||
\(599\) | −14840.9 | −1.01233 | −0.506163 | − | 0.862438i | \(-0.668937\pi\) | ||||
−0.506163 | + | 0.862438i | \(0.668937\pi\) | |||||||
\(600\) | 5257.35i | 0.357717i | ||||||||
\(601\) | 9244.34 | 0.627429 | 0.313714 | − | 0.949517i | \(-0.398427\pi\) | ||||
0.313714 | + | 0.949517i | \(0.398427\pi\) | |||||||
\(602\) | −11918.1 | −0.806885 | ||||||||
\(603\) | − | 6381.67i | − | 0.430981i | ||||||
\(604\) | − | 20645.5i | − | 1.39082i | ||||||
\(605\) | − | 35.7830i | − | 0.00240461i | ||||||
\(606\) | − | 21925.6i | − | 1.46975i | ||||||
\(607\) | −19407.7 | −1.29775 | −0.648876 | − | 0.760894i | \(-0.724761\pi\) | ||||
−0.648876 | + | 0.760894i | \(0.724761\pi\) | |||||||
\(608\) | 17145.8 | 1.14368 | ||||||||
\(609\) | − | 9957.22i | − | 0.662540i | ||||||
\(610\) | 79.1696 | 0.00525489 | ||||||||
\(611\) | −22304.0 | + | 688.903i | −1.47680 | + | 0.0456138i | ||||
\(612\) | −3330.88 | −0.220005 | ||||||||
\(613\) | − | 11289.4i | − | 0.743842i | −0.928264 | − | 0.371921i | \(-0.878699\pi\) | ||
0.928264 | − | 0.371921i | \(-0.121301\pi\) | |||||||
\(614\) | −11020.9 | −0.724377 | ||||||||
\(615\) | −70.9281 | −0.00465057 | ||||||||
\(616\) | − | 1234.77i | − | 0.0807633i | ||||||
\(617\) | − | 11589.4i | − | 0.756193i | −0.925766 | − | 0.378097i | \(-0.876579\pi\) | ||
0.925766 | − | 0.378097i | \(-0.123421\pi\) | |||||||
\(618\) | 26444.1i | 1.72126i | ||||||||
\(619\) | 15574.1i | 1.01127i | 0.862747 | + | 0.505635i | \(0.168742\pi\) | ||||
−0.862747 | + | 0.505635i | \(0.831258\pi\) | |||||||
\(620\) | 580.319 | 0.0375906 | ||||||||
\(621\) | −12752.5 | −0.824061 | ||||||||
\(622\) | − | 18143.9i | − | 1.16962i | ||||||
\(623\) | −5013.89 | −0.322435 | ||||||||
\(624\) | 255.562 | + | 8274.11i | 0.0163953 | + | 0.530817i | ||||
\(625\) | 15592.2 | 0.997902 | ||||||||
\(626\) | − | 23579.0i | − | 1.50544i | ||||||
\(627\) | −3253.71 | −0.207242 | ||||||||
\(628\) | −4014.21 | −0.255071 | ||||||||
\(629\) | − | 7812.92i | − | 0.495264i | ||||||
\(630\) | 119.501i | 0.00755722i | ||||||||
\(631\) | − | 27292.4i | − | 1.72186i | −0.508725 | − | 0.860929i | \(-0.669883\pi\) | ||
0.508725 | − | 0.860929i | \(-0.330117\pi\) | |||||||
\(632\) | 8599.76i | 0.541266i | ||||||||
\(633\) | 3612.11 | 0.226806 | ||||||||
\(634\) | 35172.9 | 2.20331 | ||||||||
\(635\) | − | 349.285i | − | 0.0218283i | ||||||
\(636\) | 1752.41 | 0.109257 | ||||||||
\(637\) | −302.504 | − | 9793.91i | −0.0188158 | − | 0.609182i | ||||
\(638\) | −9321.28 | −0.578422 | ||||||||
\(639\) | 4704.09i | 0.291222i | ||||||||
\(640\) | 352.363 | 0.0217631 | ||||||||
\(641\) | −8093.08 | −0.498686 | −0.249343 | − | 0.968415i | \(-0.580215\pi\) | ||||
−0.249343 | + | 0.968415i | \(0.580215\pi\) | |||||||
\(642\) | 31376.1i | 1.92884i | ||||||||
\(643\) | 23867.9i | 1.46385i | 0.681384 | + | 0.731926i | \(0.261379\pi\) | ||||
−0.681384 | + | 0.731926i | \(0.738621\pi\) | |||||||
\(644\) | 9931.33i | 0.607685i | ||||||||
\(645\) | 309.177i | 0.0188742i | ||||||||
\(646\) | 11568.6 | 0.704583 | ||||||||
\(647\) | 18520.7 | 1.12538 | 0.562692 | − | 0.826667i | \(-0.309766\pi\) | ||||
0.562692 | + | 0.826667i | \(0.309766\pi\) | |||||||
\(648\) | − | 4284.18i | − | 0.259720i | ||||||
\(649\) | −3885.46 | −0.235004 | ||||||||
\(650\) | −25013.4 | + | 772.588i | −1.50940 | + | 0.0466206i | ||||
\(651\) | 9597.44 | 0.577808 | ||||||||
\(652\) | 6237.75i | 0.374676i | ||||||||
\(653\) | 7350.61 | 0.440508 | 0.220254 | − | 0.975443i | \(-0.429311\pi\) | ||||
0.220254 | + | 0.975443i | \(0.429311\pi\) | |||||||
\(654\) | 22297.9 | 1.33321 | ||||||||
\(655\) | 633.003i | 0.0377610i | ||||||||
\(656\) | − | 2249.36i | − | 0.133876i | ||||||
\(657\) | 4297.83i | 0.255212i | ||||||||
\(658\) | 23550.9i | 1.39530i | ||||||||
\(659\) | −6793.50 | −0.401574 | −0.200787 | − | 0.979635i | \(-0.564350\pi\) | ||||
−0.200787 | + | 0.979635i | \(0.564350\pi\) | |||||||
\(660\) | −144.964 | −0.00854956 | ||||||||
\(661\) | − | 2867.64i | − | 0.168742i | −0.996434 | − | 0.0843709i | \(-0.973112\pi\) | ||
0.996434 | − | 0.0843709i | \(-0.0268880\pi\) | |||||||
\(662\) | 38749.6 | 2.27499 | ||||||||
\(663\) | 249.345 | + | 8072.83i | 0.0146060 | + | 0.472885i | ||||
\(664\) | 1084.90 | 0.0634072 | ||||||||
\(665\) | − | 233.298i | − | 0.0136043i | ||||||
\(666\) | −6869.80 | −0.399699 | ||||||||
\(667\) | 16566.3 | 0.961691 | ||||||||
\(668\) | − | 35393.3i | − | 2.05001i | ||||||
\(669\) | − | 1852.02i | − | 0.107030i | ||||||
\(670\) | 987.499i | 0.0569409i | ||||||||
\(671\) | − | 688.970i | − | 0.0396384i | ||||||
\(672\) | 12633.6 | 0.725226 | ||||||||
\(673\) | 33234.8 | 1.90358 | 0.951788 | − | 0.306756i | \(-0.0992434\pi\) | ||||
0.951788 | + | 0.306756i | \(0.0992434\pi\) | |||||||
\(674\) | 7776.47i | 0.444419i | ||||||||
\(675\) | −19063.5 | −1.08704 | ||||||||
\(676\) | 22518.3 | − | 1392.37i | 1.28120 | − | 0.0792200i | ||||
\(677\) | −10422.3 | −0.591669 | −0.295835 | − | 0.955239i | \(-0.595598\pi\) | ||||
−0.295835 | + | 0.955239i | \(0.595598\pi\) | |||||||
\(678\) | − | 7088.18i | − | 0.401504i | ||||||
\(679\) | 11912.4 | 0.673277 | ||||||||
\(680\) | 113.891 | 0.00642281 | ||||||||
\(681\) | − | 11848.3i | − | 0.666705i | ||||||
\(682\) | − | 8984.48i | − | 0.504448i | ||||||
\(683\) | 31006.8i | 1.73710i | 0.495600 | + | 0.868551i | \(0.334948\pi\) | ||||
−0.495600 | + | 0.868551i | \(0.665052\pi\) | |||||||
\(684\) | − | 5717.79i | − | 0.319627i | ||||||
\(685\) | 249.434 | 0.0139129 | ||||||||
\(686\) | −27309.2 | −1.51993 | ||||||||
\(687\) | − | 3809.41i | − | 0.211555i | ||||||
\(688\) | −9804.99 | −0.543331 | ||||||||
\(689\) | 56.9040 | + | 1842.33i | 0.00314640 | + | 0.101868i | ||||
\(690\) | 458.345 | 0.0252882 | ||||||||
\(691\) | − | 5840.00i | − | 0.321511i | −0.986994 | − | 0.160755i | \(-0.948607\pi\) | ||
0.986994 | − | 0.160755i | \(-0.0513930\pi\) | |||||||
\(692\) | −685.590 | −0.0376622 | ||||||||
\(693\) | 1039.95 | 0.0570052 | ||||||||
\(694\) | − | 27158.1i | − | 1.48546i | ||||||
\(695\) | 605.183i | 0.0330301i | ||||||||
\(696\) | 8344.20i | 0.454434i | ||||||||
\(697\) | − | 2194.64i | − | 0.119265i | ||||||
\(698\) | 16303.0 | 0.884064 | ||||||||
\(699\) | −19937.1 | −1.07881 | ||||||||
\(700\) | 14846.1i | 0.801615i | ||||||||
\(701\) | −21174.3 | −1.14086 | −0.570431 | − | 0.821346i | \(-0.693224\pi\) | ||||
−0.570431 | + | 0.821346i | \(0.693224\pi\) | |||||||
\(702\) | 30560.7 | − | 943.927i | 1.64308 | − | 0.0507496i | ||||
\(703\) | 13411.6 | 0.719529 | ||||||||
\(704\) | − | 8245.31i | − | 0.441416i | ||||||
\(705\) | 610.953 | 0.0326380 | ||||||||
\(706\) | 44162.1 | 2.35420 | ||||||||
\(707\) | − | 13681.2i | − | 0.727772i | ||||||
\(708\) | 15740.7i | 0.835554i | ||||||||
\(709\) | 36423.9i | 1.92938i | 0.263391 | + | 0.964689i | \(0.415159\pi\) | ||||
−0.263391 | + | 0.964689i | \(0.584841\pi\) | |||||||
\(710\) | − | 727.911i | − | 0.0384761i | ||||||
\(711\) | −7242.95 | −0.382042 | ||||||||
\(712\) | 4201.66 | 0.221157 | ||||||||
\(713\) | 15967.7i | 0.838701i | ||||||||
\(714\) | 8524.13 | 0.446789 | ||||||||
\(715\) | −4.70725 | − | 152.403i | −0.000246212 | − | 0.00797138i | ||||
\(716\) | −26850.3 | −1.40146 | ||||||||
\(717\) | − | 13273.0i | − | 0.691340i | ||||||
\(718\) | −25239.7 | −1.31189 | ||||||||
\(719\) | 1016.87 | 0.0527440 | 0.0263720 | − | 0.999652i | \(-0.491605\pi\) | ||||
0.0263720 | + | 0.999652i | \(0.491605\pi\) | |||||||
\(720\) | 98.3135i | 0.00508879i | ||||||||
\(721\) | 16500.7i | 0.852311i | ||||||||
\(722\) | − | 9458.39i | − | 0.487541i | ||||||
\(723\) | 1068.01i | 0.0549371i | ||||||||
\(724\) | 40748.0 | 2.09170 | ||||||||
\(725\) | 24764.5 | 1.26860 | ||||||||
\(726\) | 2244.32i | 0.114731i | ||||||||
\(727\) | 12283.3 | 0.626633 | 0.313316 | − | 0.949649i | \(-0.398560\pi\) | ||||
0.313316 | + | 0.949649i | \(0.398560\pi\) | |||||||
\(728\) | −162.433 | − | 5258.97i | −0.00826949 | − | 0.267734i | ||||
\(729\) | 21489.6 | 1.09179 | ||||||||
\(730\) | − | 665.045i | − | 0.0337184i | ||||||
\(731\) | −9566.46 | −0.484033 | ||||||||
\(732\) | −2791.15 | −0.140934 | ||||||||
\(733\) | 33618.5i | 1.69404i | 0.531565 | + | 0.847018i | \(0.321604\pi\) | ||||
−0.531565 | + | 0.847018i | \(0.678396\pi\) | |||||||
\(734\) | − | 59205.8i | − | 2.97728i | ||||||
\(735\) | 268.275i | 0.0134633i | ||||||||
\(736\) | 21019.1i | 1.05268i | ||||||||
\(737\) | 8593.66 | 0.429514 | ||||||||
\(738\) | −1929.72 | −0.0962518 | ||||||||
\(739\) | − | 22942.0i | − | 1.14199i | −0.820952 | − | 0.570997i | \(-0.806557\pi\) | ||
0.820952 | − | 0.570997i | \(-0.193443\pi\) | |||||||
\(740\) | 597.533 | 0.0296835 | ||||||||
\(741\) | −13857.8 | + | 428.025i | −0.687016 | + | 0.0212198i | ||||
\(742\) | 1945.32 | 0.0962468 | ||||||||
\(743\) | 11157.6i | 0.550917i | 0.961313 | + | 0.275458i | \(0.0888297\pi\) | ||||
−0.961313 | + | 0.275458i | \(0.911170\pi\) | |||||||
\(744\) | −8042.70 | −0.396317 | ||||||||
\(745\) | −212.154 | −0.0104332 | ||||||||
\(746\) | 50769.5i | 2.49169i | ||||||||
\(747\) | 913.735i | 0.0447548i | ||||||||
\(748\) | − | 4485.42i | − | 0.219256i | ||||||
\(749\) | 19578.2i | 0.955102i | ||||||||
\(750\) | 1370.82 | 0.0667403 | ||||||||
\(751\) | 8534.37 | 0.414678 | 0.207339 | − | 0.978269i | \(-0.433520\pi\) | ||||
0.207339 | + | 0.978269i | \(0.433520\pi\) | |||||||
\(752\) | 19375.2i | 0.939551i | ||||||||
\(753\) | −23895.3 | −1.15643 | ||||||||
\(754\) | −39700.0 | + | 1226.21i | −1.91749 | + | 0.0592255i | ||||
\(755\) | −594.544 | −0.0286591 | ||||||||
\(756\) | − | 18138.6i | − | 0.872611i | ||||||
\(757\) | −34403.9 | −1.65182 | −0.825912 | − | 0.563799i | \(-0.809339\pi\) | ||||
−0.825912 | + | 0.563799i | \(0.809339\pi\) | |||||||
\(758\) | 19599.0 | 0.939140 | ||||||||
\(759\) | − | 3988.72i | − | 0.190753i | ||||||
\(760\) | 195.504i | 0.00933117i | ||||||||
\(761\) | 9083.21i | 0.432676i | 0.976319 | + | 0.216338i | \(0.0694113\pi\) | ||||
−0.976319 | + | 0.216338i | \(0.930589\pi\) | |||||||
\(762\) | 21907.3i | 1.04149i | ||||||||
\(763\) | 13913.5 | 0.660163 | ||||||||
\(764\) | 9757.95 | 0.462082 | ||||||||
\(765\) | 95.9219i | 0.00453341i | ||||||||
\(766\) | 11703.6 | 0.552047 | ||||||||
\(767\) | −16548.4 | + | 511.131i | −0.779048 | + | 0.0240624i | ||||
\(768\) | 3921.98 | 0.184274 | ||||||||
\(769\) | 5495.59i | 0.257706i | 0.991664 | + | 0.128853i | \(0.0411296\pi\) | ||||
−0.991664 | + | 0.128853i | \(0.958870\pi\) | |||||||
\(770\) | −160.922 | −0.00753148 | ||||||||
\(771\) | −4749.72 | −0.221864 | ||||||||
\(772\) | − | 9278.90i | − | 0.432584i | ||||||
\(773\) | 7785.64i | 0.362264i | 0.983459 | + | 0.181132i | \(0.0579761\pi\) | ||||
−0.983459 | + | 0.181132i | \(0.942024\pi\) | |||||||
\(774\) | 8411.67i | 0.390635i | ||||||||
\(775\) | 23869.7i | 1.10636i | ||||||||
\(776\) | −9982.63 | −0.461798 | ||||||||
\(777\) | 9882.13 | 0.456267 | ||||||||
\(778\) | − | 312.368i | − | 0.0143945i | ||||||
\(779\) | 3767.30 | 0.173270 | ||||||||
\(780\) | −617.412 | + | 19.0700i | −0.0283422 | + | 0.000875403i | ||||
\(781\) | −6334.61 | −0.290231 | ||||||||
\(782\) | 14182.0i | 0.648524i | ||||||||
\(783\) | −30256.6 | −1.38095 | ||||||||
\(784\) | −8507.86 | −0.387567 | ||||||||
\(785\) | 115.600i | 0.00525598i | ||||||||
\(786\) | − | 39702.1i | − | 1.80169i | ||||||
\(787\) | − | 18657.7i | − | 0.845075i | −0.906345 | − | 0.422537i | \(-0.861140\pi\) | ||
0.906345 | − | 0.422537i | \(-0.138860\pi\) | |||||||
\(788\) | 30956.8i | 1.39948i | ||||||||
\(789\) | −6372.65 | −0.287544 | ||||||||
\(790\) | 1120.77 | 0.0504751 | ||||||||
\(791\) | − | 4422.91i | − | 0.198812i | ||||||
\(792\) | −871.487 | −0.0390997 | ||||||||
\(793\) | −90.6339 | − | 2934.37i | −0.00405864 | − | 0.131403i | ||||
\(794\) | 13392.3 | 0.598582 | ||||||||
\(795\) | − | 50.4653i | − | 0.00225135i | ||||||
\(796\) | −24653.3 | −1.09776 | ||||||||
\(797\) | 11130.4 | 0.494679 | 0.247340 | − | 0.968929i | \(-0.420444\pi\) | ||||
0.247340 | + | 0.968929i | \(0.420444\pi\) | |||||||
\(798\) | 14632.5i | 0.649104i | ||||||||
\(799\) | 18903.9i | 0.837012i | ||||||||
\(800\) | 31420.9i | 1.38862i | ||||||||
\(801\) | 3538.75i | 0.156099i | ||||||||
\(802\) | −39302.7 | −1.73046 | ||||||||
\(803\) | −5787.52 | −0.254343 | ||||||||
\(804\) | − | 34814.5i | − | 1.52713i | ||||||
\(805\) | 285.999 | 0.0125219 | ||||||||
\(806\) | −1181.91 | − | 38265.6i | −0.0516512 | − | 1.67227i | ||||
\(807\) | −29945.3 | −1.30622 | ||||||||
\(808\) | 11464.9i | 0.499176i | ||||||||
\(809\) | 30801.9 | 1.33861 | 0.669307 | − | 0.742986i | \(-0.266591\pi\) | ||||
0.669307 | + | 0.742986i | \(0.266591\pi\) | |||||||
\(810\) | −558.340 | −0.0242198 | ||||||||
\(811\) | − | 33447.1i | − | 1.44820i | −0.689697 | − | 0.724098i | \(-0.742256\pi\) | ||
0.689697 | − | 0.724098i | \(-0.257744\pi\) | |||||||
\(812\) | 23563.0i | 1.01835i | ||||||||
\(813\) | 2405.32i | 0.103762i | ||||||||
\(814\) | − | 9250.98i | − | 0.398338i | ||||||
\(815\) | 179.633 | 0.00772057 | ||||||||
\(816\) | 7012.78 | 0.300854 | ||||||||
\(817\) | − | 16421.8i | − | 0.703213i | ||||||
\(818\) | −933.931 | −0.0399195 | ||||||||
\(819\) | 4429.25 | − | 136.806i | 0.188975 | − | 0.00583686i | ||||
\(820\) | 167.846 | 0.00714810 | ||||||||
\(821\) | − | 3022.20i | − | 0.128472i | −0.997935 | − | 0.0642360i | \(-0.979539\pi\) | ||
0.997935 | − | 0.0642360i | \(-0.0204610\pi\) | |||||||
\(822\) | −15644.5 | −0.663828 | ||||||||
\(823\) | −16292.5 | −0.690060 | −0.345030 | − | 0.938592i | \(-0.612131\pi\) | ||||
−0.345030 | + | 0.938592i | \(0.612131\pi\) | |||||||
\(824\) | − | 13827.6i | − | 0.584597i | ||||||
\(825\) | − | 5962.66i | − | 0.251628i | ||||||
\(826\) | 17473.6i | 0.736057i | ||||||||
\(827\) | − | 11340.8i | − | 0.476856i | −0.971160 | − | 0.238428i | \(-0.923368\pi\) | ||
0.971160 | − | 0.238428i | \(-0.0766321\pi\) | |||||||
\(828\) | 7009.43 | 0.294196 | ||||||||
\(829\) | −9566.57 | −0.400797 | −0.200399 | − | 0.979714i | \(-0.564224\pi\) | ||||
−0.200399 | + | 0.979714i | \(0.564224\pi\) | |||||||
\(830\) | − | 141.391i | − | 0.00591296i | ||||||
\(831\) | −37021.9 | −1.54546 | ||||||||
\(832\) | −1084.67 | − | 35117.4i | −0.0451973 | − | 1.46331i | ||||
\(833\) | −8300.89 | −0.345269 | ||||||||
\(834\) | − | 37957.3i | − | 1.57596i | ||||||
\(835\) | −1019.25 | −0.0422425 | ||||||||
\(836\) | 7699.66 | 0.318539 | ||||||||
\(837\) | − | 29163.4i | − | 1.20434i | ||||||
\(838\) | − | 68292.0i | − | 2.81516i | ||||||
\(839\) | 21117.2i | 0.868946i | 0.900685 | + | 0.434473i | \(0.143065\pi\) | ||||
−0.900685 | + | 0.434473i | \(0.856935\pi\) | |||||||
\(840\) | 144.054i | 0.00591707i | ||||||||
\(841\) | 14916.0 | 0.611588 | ||||||||
\(842\) | 17281.3 | 0.707306 | ||||||||
\(843\) | 1132.92i | 0.0462869i | ||||||||
\(844\) | −8547.78 | −0.348610 | ||||||||
\(845\) | −40.0971 | − | 648.475i | −0.00163240 | − | 0.0264003i | ||||
\(846\) | 16622.0 | 0.675503 | ||||||||
\(847\) | 1400.42i | 0.0568111i | ||||||||
\(848\) | 1600.41 | 0.0648095 | ||||||||
\(849\) | 25111.5 | 1.01511 | ||||||||
\(850\) | 21200.3i | 0.855487i | ||||||||
\(851\) | 16441.3i | 0.662281i | ||||||||
\(852\) | 25662.7i | 1.03191i | ||||||||
\(853\) | 15065.9i | 0.604742i | 0.953190 | + | 0.302371i | \(0.0977782\pi\) | ||||
−0.953190 | + | 0.302371i | \(0.902222\pi\) | |||||||
\(854\) | −3098.42 | −0.124152 | ||||||||
\(855\) | −164.659 | −0.00658623 | ||||||||
\(856\) | − | 16406.6i | − | 0.655101i | ||||||
\(857\) | 24221.6 | 0.965454 | 0.482727 | − | 0.875771i | \(-0.339646\pi\) | ||||
0.482727 | + | 0.875771i | \(0.339646\pi\) | |||||||
\(858\) | 295.240 | + | 9558.74i | 0.0117475 | + | 0.380338i | ||||
\(859\) | −12928.4 | −0.513517 | −0.256758 | − | 0.966476i | \(-0.582654\pi\) | ||||
−0.256758 | + | 0.966476i | \(0.582654\pi\) | |||||||
\(860\) | − | 731.645i | − | 0.0290103i | ||||||
\(861\) | 2775.87 | 0.109874 | ||||||||
\(862\) | 62181.2 | 2.45696 | ||||||||
\(863\) | 1369.14i | 0.0540047i | 0.999635 | + | 0.0270024i | \(0.00859616\pi\) | ||||
−0.999635 | + | 0.0270024i | \(0.991404\pi\) | |||||||
\(864\) | − | 38389.2i | − | 1.51161i | ||||||
\(865\) | 19.7434i | 0.000776066i | ||||||||
\(866\) | − | 24051.0i | − | 0.943750i | ||||||
\(867\) | −14477.8 | −0.567120 | ||||||||
\(868\) | −22711.6 | −0.888114 | ||||||||
\(869\) | − | 9753.48i | − | 0.380741i | ||||||
\(870\) | 1087.47 | 0.0423777 | ||||||||
\(871\) | 36601.0 | − | 1130.49i | 1.42386 | − | 0.0439786i | ||||
\(872\) | −11659.6 | −0.452803 | ||||||||
\(873\) | − | 8407.65i | − | 0.325952i | ||||||
\(874\) | −24344.7 | −0.942187 | ||||||||
\(875\) | 855.368 | 0.0330477 | ||||||||
\(876\) | 23446.3i | 0.904313i | ||||||||
\(877\) | − | 21506.7i | − | 0.828085i | −0.910258 | − | 0.414042i | \(-0.864117\pi\) | ||
0.910258 | − | 0.414042i | \(-0.135883\pi\) | |||||||
\(878\) | 18779.8i | 0.721855i | ||||||||
\(879\) | − | 19381.2i | − | 0.743700i | ||||||
\(880\) | −132.391 | −0.00507146 | ||||||||
\(881\) | 5767.13 | 0.220544 | 0.110272 | − | 0.993901i | \(-0.464828\pi\) | ||||
0.110272 | + | 0.993901i | \(0.464828\pi\) | |||||||
\(882\) | 7298.87i | 0.278646i | ||||||||
\(883\) | −40233.2 | −1.53336 | −0.766680 | − | 0.642030i | \(-0.778092\pi\) | ||||
−0.766680 | + | 0.642030i | \(0.778092\pi\) | |||||||
\(884\) | −590.057 | − | 19103.8i | −0.0224500 | − | 0.726843i | ||||
\(885\) | 453.296 | 0.0172174 | ||||||||
\(886\) | − | 43512.8i | − | 1.64993i | ||||||
\(887\) | −31997.0 | −1.21122 | −0.605611 | − | 0.795761i | \(-0.707071\pi\) | ||||
−0.605611 | + | 0.795761i | \(0.707071\pi\) | |||||||
\(888\) | −8281.27 | −0.312952 | ||||||||
\(889\) | 13669.8i | 0.515714i | ||||||||
\(890\) | − | 547.586i | − | 0.0206237i | ||||||
\(891\) | 4858.93i | 0.182694i | ||||||||
\(892\) | 4382.68i | 0.164510i | ||||||||
\(893\) | −32450.4 | −1.21603 | ||||||||
\(894\) | 13306.4 | 0.497798 | ||||||||
\(895\) | 773.227i | 0.0288784i | ||||||||
\(896\) | −13790.2 | −0.514173 | ||||||||
\(897\) | −524.716 | − | 16988.3i | −0.0195315 | − | 0.632355i | ||||
\(898\) | 17702.4 | 0.657837 | ||||||||
\(899\) | 37884.8i | 1.40548i | ||||||||
\(900\) | 10478.2 | 0.388083 | ||||||||
\(901\) | 1561.48 | 0.0577364 | ||||||||
\(902\) | − | 2598.59i | − | 0.0959240i | ||||||
\(903\) | − | 12100.1i | − | 0.445920i | ||||||
\(904\) | 3706.42i | 0.136365i | ||||||||
\(905\) | − | 1173.45i | − | 0.0431014i | ||||||
\(906\) | 37290.0 | 1.36741 | ||||||||
\(907\) | −19192.1 | −0.702605 | −0.351302 | − | 0.936262i | \(-0.614261\pi\) | ||||
−0.351302 | + | 0.936262i | \(0.614261\pi\) | |||||||
\(908\) | 28038.0i | 1.02475i | ||||||||
\(909\) | −9656.06 | −0.352334 | ||||||||
\(910\) | −685.381 | + | 21.1693i | −0.0249672 | + | 0.000771161i | ||||
\(911\) | −3361.95 | −0.122268 | −0.0611341 | − | 0.998130i | \(-0.519472\pi\) | ||||
−0.0611341 | + | 0.998130i | \(0.519472\pi\) | |||||||
\(912\) | 12038.1i | 0.437085i | ||||||||
\(913\) | −1230.45 | −0.0446024 | ||||||||
\(914\) | 54341.4 | 1.96658 | ||||||||
\(915\) | 80.3786i | 0.00290408i | ||||||||
\(916\) | 9014.69i | 0.325168i | ||||||||
\(917\) | − | 24773.5i | − | 0.892140i | ||||||
\(918\) | − | 25901.9i | − | 0.931254i | ||||||
\(919\) | 25861.9 | 0.928298 | 0.464149 | − | 0.885757i | \(-0.346360\pi\) | ||||
0.464149 | + | 0.885757i | \(0.346360\pi\) | |||||||
\(920\) | −239.669 | −0.00858875 | ||||||||
\(921\) | − | 11189.2i | − | 0.400323i | ||||||
\(922\) | −75012.4 | −2.67940 | ||||||||
\(923\) | −26979.6 | + | 833.317i | −0.962127 | + | 0.0297172i | ||||
\(924\) | 5673.36 | 0.201991 | ||||||||
\(925\) | 24577.8i | 0.873634i | ||||||||
\(926\) | −46845.8 | −1.66247 | ||||||||
\(927\) | 11646.0 | 0.412627 | ||||||||
\(928\) | 49869.7i | 1.76407i | ||||||||
\(929\) | 41969.4i | 1.48221i | 0.671390 | + | 0.741104i | \(0.265698\pi\) | ||||
−0.671390 | + | 0.741104i | \(0.734302\pi\) | |||||||
\(930\) | 1048.17i | 0.0369580i | ||||||||
\(931\) | − | 14249.3i | − | 0.501613i | ||||||
\(932\) | 47179.7 | 1.65818 | ||||||||
\(933\) | 18420.9 | 0.646382 | ||||||||
\(934\) | 31496.8i | 1.10343i | ||||||||
\(935\) | −129.170 | −0.00451798 | ||||||||
\(936\) | −3711.73 | + | 114.644i | −0.129617 | + | 0.00400348i | ||||
\(937\) | 4940.31 | 0.172244 | 0.0861221 | − | 0.996285i | \(-0.472552\pi\) | ||||
0.0861221 | + | 0.996285i | \(0.472552\pi\) | |||||||
\(938\) | − | 38647.2i | − | 1.34528i | ||||||
\(939\) | 23939.1 | 0.831972 | ||||||||
\(940\) | −1445.77 | −0.0501659 | ||||||||
\(941\) | 39192.7i | 1.35775i | 0.734252 | + | 0.678877i | \(0.237533\pi\) | ||||
−0.734252 | + | 0.678877i | \(0.762467\pi\) | |||||||
\(942\) | − | 7250.47i | − | 0.250778i | ||||||
\(943\) | 4618.34i | 0.159484i | ||||||||
\(944\) | 14375.5i | 0.495637i | ||||||||
\(945\) | −522.350 | −0.0179810 | ||||||||
\(946\) | −11327.3 | −0.389305 | ||||||||
\(947\) | 36734.5i | 1.26052i | 0.776385 | + | 0.630259i | \(0.217051\pi\) | ||||
−0.776385 | + | 0.630259i | \(0.782949\pi\) | |||||||
\(948\) | −39513.2 | −1.35372 | ||||||||
\(949\) | −24649.5 | + | 761.348i | −0.843158 | + | 0.0260426i | ||||
\(950\) | −36392.4 | −1.24287 | ||||||||
\(951\) | 35710.1i | 1.21764i | ||||||||
\(952\) | −4457.27 | −0.151745 | ||||||||
\(953\) | −6994.80 | −0.237758 | −0.118879 | − | 0.992909i | \(-0.537930\pi\) | ||||
−0.118879 | + | 0.992909i | \(0.537930\pi\) | |||||||
\(954\) | − | 1372.99i | − | 0.0465956i | ||||||
\(955\) | − | 281.007i | − | 0.00952164i | ||||||
\(956\) | 31409.7i | 1.06262i | ||||||||
\(957\) | − | 9463.63i | − | 0.319661i | ||||||
\(958\) | −43198.5 | −1.45687 | ||||||||
\(959\) | −9761.94 | −0.328706 | ||||||||
\(960\) | 961.939i | 0.0323400i | ||||||||
\(961\) | −6724.94 | −0.225737 | ||||||||
\(962\) | −1216.97 | − | 39400.6i | −0.0407864 | − | 1.32051i | ||||
\(963\) | 13818.1 | 0.462390 | ||||||||
\(964\) | − | 2527.35i | − | 0.0844405i | ||||||
\(965\) | −267.211 | −0.00891381 | ||||||||
\(966\) | −17938.0 | −0.597458 | ||||||||
\(967\) | − | 16441.3i | − | 0.546758i | −0.961906 | − | 0.273379i | \(-0.911859\pi\) | ||
0.961906 | − | 0.273379i | \(-0.0881413\pi\) | |||||||
\(968\) | − | 1173.56i | − | 0.0389665i | ||||||
\(969\) | 11745.3i | 0.389383i | ||||||||
\(970\) | 1301.00i | 0.0430645i | ||||||||
\(971\) | −815.576 | −0.0269548 | −0.0134774 | − | 0.999909i | \(-0.504290\pi\) | ||||
−0.0134774 | + | 0.999909i | \(0.504290\pi\) | |||||||
\(972\) | −22630.5 | −0.746785 | ||||||||
\(973\) | − | 23684.7i | − | 0.780366i | ||||||
\(974\) | 71125.1 | 2.33983 | ||||||||
\(975\) | −784.387 | − | 25395.4i | −0.0257646 | − | 0.834158i | ||||
\(976\) | −2549.06 | −0.0835998 | ||||||||
\(977\) | 14340.9i | 0.469606i | 0.972043 | + | 0.234803i | \(0.0754444\pi\) | ||||
−0.972043 | + | 0.234803i | \(0.924556\pi\) | |||||||
\(978\) | −11266.6 | −0.368371 | ||||||||
\(979\) | −4765.34 | −0.155568 | ||||||||
\(980\) | − | 634.854i | − | 0.0206935i | ||||||
\(981\) | − | 9820.05i | − | 0.319602i | ||||||
\(982\) | − | 57480.3i | − | 1.86789i | ||||||
\(983\) | 5189.65i | 0.168387i | 0.996449 | + | 0.0841933i | \(0.0268313\pi\) | ||||
−0.996449 | + | 0.0841933i | \(0.973169\pi\) | |||||||
\(984\) | −2326.20 | −0.0753622 | ||||||||
\(985\) | 891.485 | 0.0288376 | ||||||||
\(986\) | 33648.0i | 1.08679i | ||||||||
\(987\) | −23910.5 | −0.771105 | ||||||||
\(988\) | 32793.4 | − | 1012.89i | 1.05597 | − | 0.0326157i | ||||
\(989\) | 20131.4 | 0.647262 | ||||||||
\(990\) | 113.578i | 0.00364619i | ||||||||
\(991\) | −9352.86 | −0.299802 | −0.149901 | − | 0.988701i | \(-0.547895\pi\) | ||||
−0.149901 | + | 0.988701i | \(0.547895\pi\) | |||||||
\(992\) | −48067.8 | −1.53846 | ||||||||
\(993\) | 39341.3i | 1.25726i | ||||||||
\(994\) | 28487.8i | 0.909033i | ||||||||
\(995\) | 709.959i | 0.0226203i | ||||||||
\(996\) | 4984.79i | 0.158583i | ||||||||
\(997\) | −43798.5 | −1.39129 | −0.695644 | − | 0.718387i | \(-0.744881\pi\) | ||||
−0.695644 | + | 0.718387i | \(0.744881\pi\) | |||||||
\(998\) | 82439.6 | 2.61481 | ||||||||
\(999\) | − | 30028.4i | − | 0.951008i |
(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 | 143.4.b.a.12.6 | ✓ | 36 | |
13.5 | odd | 4 | 1859.4.a.k.1.3 | 18 | |||
13.8 | odd | 4 | 1859.4.a.j.1.16 | 18 | |||
13.12 | even | 2 | inner | 143.4.b.a.12.31 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.4.b.a.12.6 | ✓ | 36 | 1.1 | even | 1 | trivial | |
143.4.b.a.12.31 | yes | 36 | 13.12 | even | 2 | inner | |
1859.4.a.j.1.16 | 18 | 13.8 | odd | 4 | |||
1859.4.a.k.1.3 | 18 | 13.5 | odd | 4 |