Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [126,3,Mod(19,126)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(126, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("126.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 126.n (of order \(6\), degree \(2\), 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: | \(3.43325133094\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 73.1 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 126.73 |
Dual form | 126.3.n.a.19.1 |
$q$-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 \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 1.22474i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | + | 1.73205i | −0.250000 | + | 0.433013i | ||||
\(5\) | 1.24264 | − | 0.717439i | 0.248528 | − | 0.143488i | −0.370562 | − | 0.928808i | \(-0.620835\pi\) |
0.619090 | + | 0.785320i | \(0.287502\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.74264 | − | 6.77962i | 0.248949 | − | 0.968517i | ||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.75736 | − | 1.01461i | −0.175736 | − | 0.101461i | ||||
\(11\) | 3.00000 | − | 5.19615i | 0.272727 | − | 0.472377i | −0.696832 | − | 0.717234i | \(-0.745408\pi\) |
0.969559 | + | 0.244857i | \(0.0787410\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 21.3280i | − | 1.64061i | −0.571924 | − | 0.820306i | \(-0.693803\pi\) | ||
0.571924 | − | 0.820306i | \(-0.306197\pi\) | |||||||
\(14\) | −9.53553 | + | 2.65962i | −0.681110 | + | 0.189973i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | 7.75736 | + | 4.47871i | 0.456315 | + | 0.263454i | 0.710494 | − | 0.703704i | \(-0.248472\pi\) |
−0.254178 | + | 0.967157i | \(0.581805\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.25736 | + | 3.61269i | −0.329335 | + | 0.190141i | −0.655546 | − | 0.755156i | \(-0.727561\pi\) |
0.326211 | + | 0.945297i | \(0.394228\pi\) | |||||||
\(20\) | 2.86976i | 0.143488i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.48528 | −0.385695 | ||||||||
\(23\) | −18.7279 | − | 32.4377i | −0.814257 | − | 1.41034i | −0.909860 | − | 0.414916i | \(-0.863811\pi\) |
0.0956024 | − | 0.995420i | \(-0.469522\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.4706 | + | 19.8676i | −0.458823 | + | 0.794704i | ||||
\(26\) | −26.1213 | + | 15.0812i | −1.00467 | + | 0.580044i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 10.0000 | + | 9.79796i | 0.357143 | + | 0.349927i | ||||
\(29\) | 33.9411 | 1.17038 | 0.585192 | − | 0.810895i | \(-0.301019\pi\) | ||||
0.585192 | + | 0.810895i | \(0.301019\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 38.2279 | + | 22.0709i | 1.23316 | + | 0.711965i | 0.967687 | − | 0.252154i | \(-0.0811390\pi\) |
0.265472 | + | 0.964119i | \(0.414472\pi\) | |||||||
\(32\) | −2.82843 | + | 4.89898i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 12.6677i | − | 0.372580i | ||||||
\(35\) | −2.69848 | − | 9.67487i | −0.0770996 | − | 0.276425i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 13.9853 | + | 24.2232i | 0.377981 | + | 0.654682i | 0.990768 | − | 0.135566i | \(-0.0432853\pi\) |
−0.612788 | + | 0.790248i | \(0.709952\pi\) | |||||||
\(38\) | 8.84924 | + | 5.10911i | 0.232875 | + | 0.134450i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.51472 | − | 2.02922i | 0.0878680 | − | 0.0507306i | ||||
\(41\) | 54.8313i | 1.33735i | 0.743556 | + | 0.668674i | \(0.233138\pi\) | ||||
−0.743556 | + | 0.668674i | \(0.766862\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.48528 | −0.0345414 | −0.0172707 | − | 0.999851i | \(-0.505498\pi\) | ||||
−0.0172707 | + | 0.999851i | \(0.505498\pi\) | |||||||
\(44\) | 6.00000 | + | 10.3923i | 0.136364 | + | 0.236189i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −26.4853 | + | 45.8739i | −0.575767 | + | 0.997258i | ||||
\(47\) | 37.2426 | − | 21.5020i | 0.792397 | − | 0.457490i | −0.0484090 | − | 0.998828i | \(-0.515415\pi\) |
0.840806 | + | 0.541337i | \(0.182082\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −42.9264 | − | 23.6289i | −0.876049 | − | 0.482222i | ||||
\(50\) | 32.4437 | 0.648873 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 36.9411 | + | 21.3280i | 0.710406 | + | 0.410153i | ||||
\(53\) | −42.7279 | + | 74.0069i | −0.806187 | + | 1.39636i | 0.109299 | + | 0.994009i | \(0.465139\pi\) |
−0.915487 | + | 0.402348i | \(0.868194\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 8.60927i | − | 0.156532i | ||||||
\(56\) | 4.92893 | − | 19.1757i | 0.0880166 | − | 0.342422i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −24.0000 | − | 41.5692i | −0.413793 | − | 0.716711i | ||||
\(59\) | 35.6985 | + | 20.6105i | 0.605059 | + | 0.349331i | 0.771029 | − | 0.636800i | \(-0.219742\pi\) |
−0.165970 | + | 0.986131i | \(0.553076\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.02944 | + | 0.594346i | −0.0168760 | + | 0.00974337i | −0.508414 | − | 0.861113i | \(-0.669768\pi\) |
0.491538 | + | 0.870856i | \(0.336435\pi\) | |||||||
\(62\) | − | 62.4259i | − | 1.00687i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | −15.3015 | − | 26.5030i | −0.235408 | − | 0.407738i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.19848 | + | 3.80789i | −0.0328132 | + | 0.0568341i | −0.881966 | − | 0.471314i | \(-0.843780\pi\) |
0.849152 | + | 0.528148i | \(0.177113\pi\) | |||||||
\(68\) | −15.5147 | + | 8.95743i | −0.228158 | + | 0.131727i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −9.94113 | + | 10.1461i | −0.142016 | + | 0.144945i | ||||
\(71\) | −137.397 | −1.93517 | −0.967584 | − | 0.252548i | \(-0.918731\pi\) | ||||
−0.967584 | + | 0.252548i | \(0.918731\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 68.3528 | + | 39.4635i | 0.936340 | + | 0.540596i | 0.888811 | − | 0.458274i | \(-0.151532\pi\) |
0.0475288 | + | 0.998870i | \(0.484865\pi\) | |||||||
\(74\) | 19.7782 | − | 34.2568i | 0.267273 | − | 0.462930i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 14.4508i | − | 0.190141i | ||||||
\(77\) | −30.0000 | − | 29.3939i | −0.389610 | − | 0.381739i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −49.1690 | − | 85.1633i | −0.622393 | − | 1.07802i | −0.989039 | − | 0.147656i | \(-0.952827\pi\) |
0.366646 | − | 0.930361i | \(-0.380506\pi\) | |||||||
\(80\) | −4.97056 | − | 2.86976i | −0.0621320 | − | 0.0358719i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 67.1543 | − | 38.7716i | 0.818955 | − | 0.472824i | ||||
\(83\) | − | 110.401i | − | 1.33013i | −0.746784 | − | 0.665067i | \(-0.768403\pi\) | ||
0.746784 | − | 0.665067i | \(-0.231597\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.8528 | 0.151210 | ||||||||
\(86\) | 1.05025 | + | 1.81909i | 0.0122122 | + | 0.0211522i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.48528 | − | 14.6969i | 0.0964237 | − | 0.167011i | ||||
\(89\) | 18.0000 | − | 10.3923i | 0.202247 | − | 0.116767i | −0.395456 | − | 0.918485i | \(-0.629413\pi\) |
0.597703 | + | 0.801717i | \(0.296080\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −144.595 | − | 37.1670i | −1.58896 | − | 0.408428i | ||||
\(92\) | 74.9117 | 0.814257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −52.6690 | − | 30.4085i | −0.560309 | − | 0.323495i | ||||
\(95\) | −5.18377 | + | 8.97855i | −0.0545660 | + | 0.0945110i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.9867i | − | 0.113264i | −0.998395 | − | 0.0566322i | \(-0.981964\pi\) | ||
0.998395 | − | 0.0566322i | \(-0.0180362\pi\) | |||||||
\(98\) | 1.41421 | + | 69.2820i | 0.0144308 | + | 0.706960i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −22.9411 | − | 39.7352i | −0.229411 | − | 0.397352i | ||||
\(101\) | 92.8234 | + | 53.5916i | 0.919043 | + | 0.530610i | 0.883330 | − | 0.468752i | \(-0.155296\pi\) |
0.0357136 | + | 0.999362i | \(0.488630\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 91.1102 | − | 52.6025i | 0.884565 | − | 0.510704i | 0.0124040 | − | 0.999923i | \(-0.496052\pi\) |
0.872161 | + | 0.489219i | \(0.162718\pi\) | |||||||
\(104\) | − | 60.3246i | − | 0.580044i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 120.853 | 1.14012 | ||||||||
\(107\) | 59.2721 | + | 102.662i | 0.553945 | + | 0.959460i | 0.997985 | + | 0.0634534i | \(0.0202114\pi\) |
−0.444040 | + | 0.896007i | \(0.646455\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −55.5294 | + | 96.1798i | −0.509444 | + | 0.882384i | 0.490496 | + | 0.871444i | \(0.336816\pi\) |
−0.999940 | + | 0.0109400i | \(0.996518\pi\) | |||||||
\(110\) | −10.5442 | + | 6.08767i | −0.0958560 | + | 0.0553425i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −26.9706 | + | 7.52255i | −0.240809 | + | 0.0671656i | ||||
\(113\) | −101.397 | −0.897318 | −0.448659 | − | 0.893703i | \(-0.648098\pi\) | ||||
−0.448659 | + | 0.893703i | \(0.648098\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −46.5442 | − | 26.8723i | −0.404732 | − | 0.233672i | ||||
\(116\) | −33.9411 | + | 58.7878i | −0.292596 | + | 0.506791i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 58.2954i | − | 0.494029i | ||||||
\(119\) | 43.8823 | − | 44.7871i | 0.368758 | − | 0.376362i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 42.5000 | + | 73.6122i | 0.351240 | + | 0.608365i | ||||
\(122\) | 1.45584 | + | 0.840532i | 0.0119331 | + | 0.00688961i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −76.4558 | + | 44.1418i | −0.616579 | + | 0.355982i | ||||
\(125\) | 68.7897i | 0.550317i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 82.5736 | 0.650186 | 0.325093 | − | 0.945682i | \(-0.394604\pi\) | ||||
0.325093 | + | 0.945682i | \(0.394604\pi\) | |||||||
\(128\) | −5.65685 | − | 9.79796i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −21.6396 | + | 37.4809i | −0.166459 | + | 0.288315i | ||||
\(131\) | 52.4558 | − | 30.2854i | 0.400426 | − | 0.231186i | −0.286242 | − | 0.958157i | \(-0.592406\pi\) |
0.686668 | + | 0.726971i | \(0.259073\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.5883 | + | 48.7181i | 0.102168 | + | 0.366302i | ||||
\(134\) | 6.21825 | 0.0464049 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 21.9411 | + | 12.6677i | 0.161332 | + | 0.0931450i | ||||
\(137\) | 33.5147 | − | 58.0492i | 0.244633 | − | 0.423717i | −0.717395 | − | 0.696666i | \(-0.754666\pi\) |
0.962028 | + | 0.272949i | \(0.0879992\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 91.5525i | 0.658651i | 0.944216 | + | 0.329326i | \(0.106821\pi\) | ||||
−0.944216 | + | 0.329326i | \(0.893179\pi\) | |||||||
\(140\) | 19.4558 | + | 5.00095i | 0.138970 | + | 0.0357211i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 97.1543 | + | 168.276i | 0.684185 | + | 1.18504i | ||||
\(143\) | −110.823 | − | 63.9839i | −0.774989 | − | 0.447440i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 42.1766 | − | 24.3507i | 0.290873 | − | 0.167936i | ||||
\(146\) | − | 111.620i | − | 0.764518i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −55.9411 | −0.377981 | ||||||||
\(149\) | 40.5442 | + | 70.2245i | 0.272108 | + | 0.471306i | 0.969402 | − | 0.245480i | \(-0.0789457\pi\) |
−0.697293 | + | 0.716786i | \(0.745612\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 25.6030 | − | 44.3457i | 0.169556 | − | 0.293680i | −0.768708 | − | 0.639600i | \(-0.779100\pi\) |
0.938264 | + | 0.345920i | \(0.112433\pi\) | |||||||
\(152\) | −17.6985 | + | 10.2182i | −0.116437 | + | 0.0672252i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −14.7868 | + | 57.5270i | −0.0960182 | + | 0.373552i | ||||
\(155\) | 63.3381 | 0.408633 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 162.000 | + | 93.5307i | 1.03185 | + | 0.595737i | 0.917513 | − | 0.397705i | \(-0.130193\pi\) |
0.114334 | + | 0.993442i | \(0.463527\pi\) | |||||||
\(158\) | −69.5355 | + | 120.439i | −0.440098 | + | 0.762273i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 8.11689i | 0.0507306i | ||||||||
\(161\) | −252.551 | + | 70.4409i | −1.56864 | + | 0.437521i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −41.9706 | − | 72.6951i | −0.257488 | − | 0.445982i | 0.708080 | − | 0.706132i | \(-0.249561\pi\) |
−0.965568 | + | 0.260149i | \(0.916228\pi\) | |||||||
\(164\) | −94.9706 | − | 54.8313i | −0.579089 | − | 0.334337i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −135.213 | + | 78.0654i | −0.814537 | + | 0.470273i | ||||
\(167\) | 127.620i | 0.764190i | 0.924123 | + | 0.382095i | \(0.124797\pi\) | ||||
−0.924123 | + | 0.382095i | \(0.875203\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −285.882 | −1.69161 | ||||||||
\(170\) | −9.08831 | − | 15.7414i | −0.0534607 | − | 0.0925966i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.48528 | − | 2.57258i | 0.00863536 | − | 0.0149569i | ||||
\(173\) | 123.816 | − | 71.4853i | 0.715701 | − | 0.413210i | −0.0974675 | − | 0.995239i | \(-0.531074\pi\) |
0.813168 | + | 0.582029i | \(0.197741\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 114.706 | + | 112.388i | 0.655461 | + | 0.642218i | ||||
\(176\) | −24.0000 | −0.136364 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −25.4558 | − | 14.6969i | −0.143010 | − | 0.0825671i | ||||
\(179\) | 84.6396 | − | 146.600i | 0.472847 | − | 0.818995i | −0.526670 | − | 0.850070i | \(-0.676560\pi\) |
0.999517 | + | 0.0310748i | \(0.00989300\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 209.969i | − | 1.16005i | −0.814600 | − | 0.580024i | \(-0.803043\pi\) | ||
0.814600 | − | 0.580024i | \(-0.196957\pi\) | |||||||
\(182\) | 56.7244 | + | 203.374i | 0.311672 | + | 1.11744i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −52.9706 | − | 91.7477i | −0.287883 | − | 0.498629i | ||||
\(185\) | 34.7574 | + | 20.0672i | 0.187878 | + | 0.108471i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 46.5442 | − | 26.8723i | 0.248899 | − | 0.143702i | ||||
\(188\) | 86.0082i | 0.457490i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 14.6619 | 0.0771679 | ||||||||
\(191\) | 33.3015 | + | 57.6799i | 0.174353 | + | 0.301989i | 0.939937 | − | 0.341347i | \(-0.110883\pi\) |
−0.765584 | + | 0.643336i | \(0.777550\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.89697 | − | 8.48180i | 0.0253729 | − | 0.0439472i | −0.853060 | − | 0.521813i | \(-0.825256\pi\) |
0.878433 | + | 0.477865i | \(0.158589\pi\) | |||||||
\(194\) | −13.4558 | + | 7.76874i | −0.0693600 | + | 0.0400450i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 83.8528 | − | 50.7218i | 0.427820 | − | 0.258785i | ||||
\(197\) | 267.161 | 1.35615 | 0.678075 | − | 0.734993i | \(-0.262815\pi\) | ||||
0.678075 | + | 0.734993i | \(0.262815\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −113.397 | − | 65.4698i | −0.569834 | − | 0.328994i | 0.187249 | − | 0.982312i | \(-0.440043\pi\) |
−0.757083 | + | 0.653319i | \(0.773376\pi\) | |||||||
\(200\) | −32.4437 | + | 56.1941i | −0.162218 | + | 0.280970i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 151.580i | − | 0.750396i | ||||||
\(203\) | 59.1472 | − | 230.108i | 0.291365 | − | 1.13354i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 39.3381 | + | 68.1356i | 0.191893 | + | 0.332369i | ||||
\(206\) | −128.849 | − | 74.3911i | −0.625482 | − | 0.361122i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −73.8823 | + | 42.6559i | −0.355203 | + | 0.205077i | ||||
\(209\) | 43.3523i | 0.207427i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.0883 | −0.109423 | −0.0547116 | − | 0.998502i | \(-0.517424\pi\) | ||||
−0.0547116 | + | 0.998502i | \(0.517424\pi\) | |||||||
\(212\) | −85.4558 | − | 148.014i | −0.403094 | − | 0.698179i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 83.8234 | − | 145.186i | 0.391698 | − | 0.678441i | ||||
\(215\) | −1.84567 | + | 1.06560i | −0.00858452 | + | 0.00495627i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 216.250 | − | 220.709i | 0.996543 | − | 1.01709i | ||||
\(218\) | 157.061 | 0.720463 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 14.9117 | + | 8.60927i | 0.0677804 | + | 0.0391330i | ||||
\(221\) | 95.5219 | − | 165.449i | 0.432226 | − | 0.748637i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 228.631i | 1.02525i | 0.858613 | + | 0.512625i | \(0.171327\pi\) | ||||
−0.858613 | + | 0.512625i | \(0.828673\pi\) | |||||||
\(224\) | 28.2843 | + | 27.7128i | 0.126269 | + | 0.123718i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 71.6985 | + | 124.185i | 0.317250 | + | 0.549493i | ||||
\(227\) | −56.8234 | − | 32.8070i | −0.250323 | − | 0.144524i | 0.369589 | − | 0.929195i | \(-0.379498\pi\) |
−0.619912 | + | 0.784671i | \(0.712832\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 80.9558 | − | 46.7399i | 0.353519 | − | 0.204104i | −0.312715 | − | 0.949847i | \(-0.601239\pi\) |
0.666234 | + | 0.745743i | \(0.267905\pi\) | |||||||
\(230\) | 76.0063i | 0.330462i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 96.0000 | 0.413793 | ||||||||
\(233\) | −118.757 | − | 205.694i | −0.509688 | − | 0.882806i | −0.999937 | − | 0.0112234i | \(-0.996427\pi\) |
0.490249 | − | 0.871583i | \(-0.336906\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 30.8528 | − | 53.4386i | 0.131289 | − | 0.227398i | ||||
\(236\) | −71.3970 | + | 41.2211i | −0.302530 | + | 0.174666i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −85.8823 | − | 22.0753i | −0.360850 | − | 0.0927533i | ||||
\(239\) | −366.853 | −1.53495 | −0.767475 | − | 0.641079i | \(-0.778487\pi\) | ||||
−0.767475 | + | 0.641079i | \(0.778487\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −364.617 | − | 210.512i | −1.51293 | − | 0.873493i | −0.999885 | − | 0.0151343i | \(-0.995182\pi\) |
−0.513049 | − | 0.858359i | \(-0.671484\pi\) | |||||||
\(242\) | 60.1041 | − | 104.103i | 0.248364 | − | 0.430179i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 2.37738i | − | 0.00974337i | ||||||
\(245\) | −70.2944 | + | 1.43488i | −0.286916 | + | 0.00585664i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 77.0513 | + | 133.457i | 0.311949 | + | 0.540311i | ||||
\(248\) | 108.125 | + | 62.4259i | 0.435987 | + | 0.251717i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 84.2498 | − | 48.6416i | 0.336999 | − | 0.194567i | ||||
\(251\) | 146.621i | 0.584148i | 0.956396 | + | 0.292074i | \(0.0943454\pi\) | ||||
−0.956396 | + | 0.292074i | \(0.905655\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −224.735 | −0.888281 | ||||||||
\(254\) | −58.3883 | − | 101.132i | −0.229875 | − | 0.398156i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −21.7279 | + | 12.5446i | −0.0845444 | + | 0.0488118i | −0.541676 | − | 0.840587i | \(-0.682210\pi\) |
0.457132 | + | 0.889399i | \(0.348877\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 188.595 | − | 52.6025i | 0.728168 | − | 0.203098i | ||||
\(260\) | 61.2061 | 0.235408 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −74.1838 | − | 42.8300i | −0.283144 | − | 0.163473i | ||||
\(263\) | −45.3381 | + | 78.5279i | −0.172388 | + | 0.298585i | −0.939254 | − | 0.343222i | \(-0.888482\pi\) |
0.766866 | + | 0.641807i | \(0.221815\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 122.619i | 0.462712i | ||||||||
\(266\) | 50.0589 | − | 51.0911i | 0.188191 | − | 0.192072i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.39697 | − | 7.61577i | −0.0164066 | − | 0.0284171i | ||||
\(269\) | 59.2355 | + | 34.1996i | 0.220206 | + | 0.127136i | 0.606046 | − | 0.795430i | \(-0.292755\pi\) |
−0.385839 | + | 0.922566i | \(0.626088\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −106.971 | + | 61.7595i | −0.394725 | + | 0.227895i | −0.684206 | − | 0.729289i | \(-0.739851\pi\) |
0.289480 | + | 0.957184i | \(0.406518\pi\) | |||||||
\(272\) | − | 35.8297i | − | 0.131727i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −94.7939 | −0.345963 | ||||||||
\(275\) | 68.8234 | + | 119.206i | 0.250267 | + | 0.433475i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 136.441 | − | 236.323i | 0.492567 | − | 0.853151i | −0.507396 | − | 0.861713i | \(-0.669392\pi\) |
0.999963 | + | 0.00856145i | \(0.00272523\pi\) | |||||||
\(278\) | 112.128 | − | 64.7374i | 0.403340 | − | 0.232868i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.63247 | − | 27.3647i | −0.0272588 | − | 0.0977309i | ||||
\(281\) | −133.103 | −0.473675 | −0.236837 | − | 0.971549i | \(-0.576111\pi\) | ||||
−0.236837 | + | 0.971549i | \(0.576111\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −111.507 | − | 64.3787i | −0.394018 | − | 0.227486i | 0.289882 | − | 0.957063i | \(-0.406384\pi\) |
−0.683900 | + | 0.729576i | \(0.739717\pi\) | |||||||
\(284\) | 137.397 | − | 237.979i | 0.483792 | − | 0.837953i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 180.974i | 0.632776i | ||||||||
\(287\) | 371.735 | + | 95.5512i | 1.29524 | + | 0.332931i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −104.382 | − | 180.795i | −0.361184 | − | 0.625589i | ||||
\(290\) | −59.6468 | − | 34.4371i | −0.205678 | − | 0.118749i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −136.706 | + | 78.9270i | −0.468170 | + | 0.270298i | ||||
\(293\) | 308.984i | 1.05455i | 0.849694 | + | 0.527276i | \(0.176787\pi\) | ||||
−0.849694 | + | 0.527276i | \(0.823213\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 59.1472 | 0.200499 | ||||||||
\(296\) | 39.5563 | + | 68.5136i | 0.133636 | + | 0.231465i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 57.3381 | − | 99.3125i | 0.192410 | − | 0.333263i | ||||
\(299\) | −691.831 | + | 399.429i | −2.31381 | + | 1.33588i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.58831 | + | 10.0696i | −0.00859904 | + | 0.0334539i | ||||
\(302\) | −72.4163 | −0.239789 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 25.0294 | + | 14.4508i | 0.0823337 | + | 0.0475354i | ||||
\(305\) | −0.852814 | + | 1.47712i | −0.00279611 | + | 0.00484301i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 606.090i | 1.97423i | 0.160003 | + | 0.987117i | \(0.448850\pi\) | ||||
−0.160003 | + | 0.987117i | \(0.551150\pi\) | |||||||
\(308\) | 80.9117 | − | 22.5676i | 0.262700 | − | 0.0732716i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −44.7868 | − | 77.5730i | −0.144474 | − | 0.250236i | ||||
\(311\) | 176.044 | + | 101.639i | 0.566057 | + | 0.326813i | 0.755573 | − | 0.655064i | \(-0.227359\pi\) |
−0.189516 | + | 0.981878i | \(0.560692\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −351.294 | + | 202.820i | −1.12234 | + | 0.647986i | −0.941999 | − | 0.335617i | \(-0.891055\pi\) |
−0.180346 | + | 0.983603i | \(0.557722\pi\) | |||||||
\(314\) | − | 264.545i | − | 0.842500i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 196.676 | 0.622393 | ||||||||
\(317\) | −13.0294 | − | 22.5676i | −0.0411023 | − | 0.0711913i | 0.844742 | − | 0.535173i | \(-0.179754\pi\) |
−0.885845 | + | 0.463982i | \(0.846420\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 101.823 | − | 176.363i | 0.319196 | − | 0.552863i | ||||
\(320\) | 9.94113 | − | 5.73951i | 0.0310660 | − | 0.0179360i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 264.853 | + | 259.502i | 0.822524 | + | 0.805906i | ||||
\(323\) | −64.7208 | −0.200374 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 423.735 | + | 244.644i | 1.30380 | + | 0.752750i | ||||
\(326\) | −59.3553 | + | 102.806i | −0.182072 | + | 0.315357i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 155.086i | 0.472824i | ||||||||
\(329\) | −80.8751 | − | 289.961i | −0.245821 | − | 0.881341i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 54.3162 | + | 94.0785i | 0.164097 | + | 0.284225i | 0.936334 | − | 0.351110i | \(-0.114196\pi\) |
−0.772237 | + | 0.635335i | \(0.780862\pi\) | |||||||
\(332\) | 191.220 | + | 110.401i | 0.575965 | + | 0.332533i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 156.302 | − | 90.2407i | 0.467969 | − | 0.270182i | ||||
\(335\) | 6.30911i | 0.0188332i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 441.735 | 1.31079 | 0.655393 | − | 0.755288i | \(-0.272503\pi\) | ||||
0.655393 | + | 0.755288i | \(0.272503\pi\) | |||||||
\(338\) | 202.149 | + | 350.133i | 0.598075 | + | 1.03590i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −12.8528 | + | 22.2617i | −0.0378024 | + | 0.0654757i | ||||
\(341\) | 229.368 | − | 132.425i | 0.672632 | − | 0.388344i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −235.000 | + | 249.848i | −0.685131 | + | 0.728420i | ||||
\(344\) | −4.20101 | −0.0122122 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −175.103 | − | 101.096i | −0.506077 | − | 0.292184i | ||||
\(347\) | 17.0955 | − | 29.6102i | 0.0492664 | − | 0.0853320i | −0.840341 | − | 0.542059i | \(-0.817645\pi\) |
0.889607 | + | 0.456727i | \(0.150978\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 221.787i | 0.635493i | 0.948176 | + | 0.317746i | \(0.102926\pi\) | ||||
−0.948176 | + | 0.317746i | \(0.897074\pi\) | |||||||
\(350\) | 56.5376 | − | 219.956i | 0.161536 | − | 0.628444i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.9706 | + | 29.3939i | 0.0482118 | + | 0.0835053i | ||||
\(353\) | −387.448 | − | 223.693i | −1.09759 | − | 0.633692i | −0.162000 | − | 0.986791i | \(-0.551794\pi\) |
−0.935586 | + | 0.353099i | \(0.885128\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −170.735 | + | 98.5739i | −0.480944 | + | 0.277673i | ||||
\(356\) | 41.5692i | 0.116767i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −239.397 | −0.668707 | ||||||||
\(359\) | 145.882 | + | 252.675i | 0.406357 | + | 0.703831i | 0.994478 | − | 0.104941i | \(-0.0334655\pi\) |
−0.588121 | + | 0.808773i | \(0.700132\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −154.397 | + | 267.423i | −0.427692 | + | 0.740785i | ||||
\(362\) | −257.158 | + | 148.470i | −0.710381 | + | 0.410139i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 208.971 | − | 213.280i | 0.574095 | − | 0.585933i | ||||
\(365\) | 113.251 | 0.310276 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −363.169 | − | 209.676i | −0.989561 | − | 0.571324i | −0.0844183 | − | 0.996430i | \(-0.526903\pi\) |
−0.905143 | + | 0.425107i | \(0.860237\pi\) | |||||||
\(368\) | −74.9117 | + | 129.751i | −0.203564 | + | 0.352584i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 56.7585i | − | 0.153401i | ||||||
\(371\) | 427.279 | + | 418.646i | 1.15170 | + | 1.12843i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.6909 | − | 27.1775i | −0.0420668 | − | 0.0728618i | 0.844225 | − | 0.535988i | \(-0.180061\pi\) |
−0.886292 | + | 0.463127i | \(0.846728\pi\) | |||||||
\(374\) | −65.8234 | − | 38.0031i | −0.175998 | − | 0.101613i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 105.338 | − | 60.8170i | 0.280155 | − | 0.161747i | ||||
\(377\) | − | 723.895i | − | 1.92015i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 206.779 | 0.545590 | 0.272795 | − | 0.962072i | \(-0.412052\pi\) | ||||
0.272795 | + | 0.962072i | \(0.412052\pi\) | |||||||
\(380\) | −10.3675 | − | 17.9571i | −0.0272830 | − | 0.0472555i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 47.0955 | − | 81.5717i | 0.123287 | − | 0.213539i | ||||
\(383\) | 431.772 | − | 249.283i | 1.12734 | − | 0.650871i | 0.184076 | − | 0.982912i | \(-0.441071\pi\) |
0.943265 | + | 0.332041i | \(0.107737\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −58.3675 | − | 15.0029i | −0.151604 | − | 0.0389685i | ||||
\(386\) | −13.8507 | −0.0358827 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 19.0294 | + | 10.9867i | 0.0490449 | + | 0.0283161i | ||||
\(389\) | −324.213 | + | 561.554i | −0.833453 | + | 1.44358i | 0.0618308 | + | 0.998087i | \(0.480306\pi\) |
−0.895284 | + | 0.445496i | \(0.853027\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 335.508i | − | 0.858077i | ||||||
\(392\) | −121.414 | − | 66.8325i | −0.309730 | − | 0.170491i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −188.912 | − | 327.205i | −0.479471 | − | 0.830469i | ||||
\(395\) | −122.199 | − | 70.5516i | −0.309364 | − | 0.178612i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 65.6026 | − | 37.8757i | 0.165246 | − | 0.0954047i | −0.415096 | − | 0.909777i | \(-0.636252\pi\) |
0.580342 | + | 0.814373i | \(0.302919\pi\) | |||||||
\(398\) | 185.176i | 0.465268i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 91.7645 | 0.229411 | ||||||||
\(401\) | −282.125 | − | 488.655i | −0.703553 | − | 1.21859i | −0.967211 | − | 0.253974i | \(-0.918262\pi\) |
0.263658 | − | 0.964616i | \(-0.415071\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 470.727 | − | 815.324i | 1.16806 | − | 2.02314i | ||||
\(404\) | −185.647 | + | 107.183i | −0.459522 | + | 0.265305i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −323.647 | + | 90.2706i | −0.797159 | + | 0.222341i | ||||
\(407\) | 167.823 | 0.412342 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −309.559 | − | 178.724i | −0.756868 | − | 0.436978i | 0.0713023 | − | 0.997455i | \(-0.477284\pi\) |
−0.828170 | + | 0.560477i | \(0.810618\pi\) | |||||||
\(410\) | 55.6325 | − | 96.3583i | 0.135689 | − | 0.235020i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 210.410i | 0.510704i | ||||||||
\(413\) | 201.941 | − | 206.105i | 0.488962 | − | 0.499044i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −79.2061 | − | 137.189i | −0.190858 | − | 0.330576i | ||||
\(416\) | 104.485 | + | 60.3246i | 0.251167 | + | 0.145011i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 53.0955 | − | 30.6547i | 0.127023 | − | 0.0733365i | ||||
\(419\) | 502.175i | 1.19851i | 0.800559 | + | 0.599254i | \(0.204536\pi\) | ||||
−0.800559 | + | 0.599254i | \(0.795464\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.7939 | 0.0802706 | 0.0401353 | − | 0.999194i | \(-0.487221\pi\) | ||||
0.0401353 | + | 0.999194i | \(0.487221\pi\) | |||||||
\(422\) | 16.3259 | + | 28.2773i | 0.0386870 | + | 0.0670078i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −120.853 | + | 209.323i | −0.285030 | + | 0.493687i | ||||
\(425\) | −177.963 | + | 102.747i | −0.418735 | + | 0.241757i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.23550 | + | 8.01492i | 0.00523536 | + | 0.0187703i | ||||
\(428\) | −237.088 | −0.553945 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.61017 | + | 1.50698i | 0.00607017 | + | 0.00350461i | ||||
\(431\) | 251.860 | − | 436.234i | 0.584362 | − | 1.01214i | −0.410593 | − | 0.911819i | \(-0.634678\pi\) |
0.994955 | − | 0.100326i | \(-0.0319884\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 837.548i | − | 1.93429i | −0.254224 | − | 0.967145i | \(-0.581820\pi\) | ||
0.254224 | − | 0.967145i | \(-0.418180\pi\) | |||||||
\(434\) | −423.224 | − | 108.786i | −0.975170 | − | 0.250659i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −111.059 | − | 192.360i | −0.254722 | − | 0.441192i | ||||
\(437\) | 234.375 | + | 135.316i | 0.536326 | + | 0.309648i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −164.558 | + | 95.0079i | −0.374848 | + | 0.216419i | −0.675575 | − | 0.737292i | \(-0.736104\pi\) |
0.300726 | + | 0.953711i | \(0.402771\pi\) | |||||||
\(440\) | − | 24.3507i | − | 0.0553425i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −270.177 | −0.611259 | ||||||||
\(443\) | −84.7279 | − | 146.753i | −0.191259 | − | 0.331271i | 0.754408 | − | 0.656405i | \(-0.227924\pi\) |
−0.945668 | + | 0.325134i | \(0.894591\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.9117 | − | 25.8278i | 0.0335094 | − | 0.0580400i | ||||
\(446\) | 280.014 | − | 161.666i | 0.627835 | − | 0.362481i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 13.9411 | − | 54.2369i | 0.0311186 | − | 0.121065i | ||||
\(449\) | −18.1035 | −0.0403195 | −0.0201598 | − | 0.999797i | \(-0.506417\pi\) | ||||
−0.0201598 | + | 0.999797i | \(0.506417\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 284.912 | + | 164.494i | 0.631733 | + | 0.364731i | ||||
\(452\) | 101.397 | − | 175.625i | 0.224330 | − | 0.388550i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 92.7922i | 0.204388i | ||||||||
\(455\) | −206.345 | + | 57.5532i | −0.453506 | + | 0.126491i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 164.412 | + | 284.769i | 0.359763 | + | 0.623128i | 0.987921 | − | 0.154958i | \(-0.0495242\pi\) |
−0.628158 | + | 0.778086i | \(0.716191\pi\) | |||||||
\(458\) | −114.489 | − | 66.1002i | −0.249976 | − | 0.144324i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 93.0883 | − | 53.7446i | 0.202366 | − | 0.116836i | ||||
\(461\) | − | 794.331i | − | 1.72306i | −0.507706 | − | 0.861530i | \(-0.669506\pi\) | ||
0.507706 | − | 0.861530i | \(-0.330494\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −403.396 | −0.871266 | −0.435633 | − | 0.900124i | \(-0.643475\pi\) | ||||
−0.435633 | + | 0.900124i | \(0.643475\pi\) | |||||||
\(464\) | −67.8823 | − | 117.576i | −0.146298 | − | 0.253395i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −167.948 | + | 290.895i | −0.360404 | + | 0.624238i | ||||
\(467\) | 2.44870 | − | 1.41376i | 0.00524347 | − | 0.00302732i | −0.497376 | − | 0.867535i | \(-0.665703\pi\) |
0.502619 | + | 0.864508i | \(0.332370\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.9848 | + | 21.5407i | 0.0468760 | + | 0.0459289i | ||||
\(470\) | −87.2649 | −0.185670 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 100.971 | + | 58.2954i | 0.213921 | + | 0.123507i | ||||
\(473\) | −4.45584 | + | 7.71775i | −0.00942039 | + | 0.0163166i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 165.758i | − | 0.348965i | ||||||
\(476\) | 33.6913 | + | 120.793i | 0.0707801 | + | 0.253768i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 259.404 | + | 449.301i | 0.542686 | + | 0.939960i | ||||
\(479\) | −328.669 | − | 189.757i | −0.686157 | − | 0.396153i | 0.116014 | − | 0.993248i | \(-0.462988\pi\) |
−0.802171 | + | 0.597095i | \(0.796322\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 516.632 | − | 298.278i | 1.07408 | − | 0.620120i | ||||
\(482\) | 595.418i | 1.23531i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −170.000 | −0.351240 | ||||||||
\(485\) | −7.88225 | − | 13.6525i | −0.0162521 | − | 0.0281494i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −287.757 | + | 498.410i | −0.590877 | + | 1.02343i | 0.403238 | + | 0.915095i | \(0.367885\pi\) |
−0.994115 | + | 0.108333i | \(0.965449\pi\) | |||||||
\(488\) | −2.91169 | + | 1.68106i | −0.00596657 | + | 0.00344480i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 51.4630 | + | 85.0781i | 0.105027 | + | 0.173629i | ||||
\(491\) | −238.441 | −0.485623 | −0.242811 | − | 0.970074i | \(-0.578070\pi\) | ||||
−0.242811 | + | 0.970074i | \(0.578070\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 263.294 | + | 152.013i | 0.534064 | + | 0.308342i | ||||
\(494\) | 108.967 | − | 188.736i | 0.220581 | − | 0.382057i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 176.567i | − | 0.355982i | ||||||
\(497\) | −239.434 | + | 931.499i | −0.481758 | + | 1.87424i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 143.287 | + | 248.180i | 0.287148 | + | 0.497355i | 0.973128 | − | 0.230266i | \(-0.0739595\pi\) |
−0.685980 | + | 0.727620i | \(0.740626\pi\) | |||||||
\(500\) | −119.147 | − | 68.7897i | −0.238294 | − | 0.137579i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 179.574 | − | 103.677i | 0.357716 | − | 0.206528i | ||||
\(503\) | 25.4374i | 0.0505714i | 0.999680 | + | 0.0252857i | \(0.00804954\pi\) | ||||
−0.999680 | + | 0.0252857i | \(0.991950\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 153.795 | 0.304544 | ||||||||
\(506\) | 158.912 | + | 275.243i | 0.314055 | + | 0.543959i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −82.5736 | + | 143.022i | −0.162546 | + | 0.281539i | ||||
\(509\) | 697.889 | − | 402.926i | 1.37110 | − | 0.791603i | 0.380031 | − | 0.924974i | \(-0.375913\pi\) |
0.991066 | + | 0.133370i | \(0.0425800\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 386.662 | − | 394.635i | 0.756677 | − | 0.772280i | ||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 30.7279 | + | 17.7408i | 0.0597819 | + | 0.0345151i | ||||
\(515\) | 75.4781 | − | 130.732i | 0.146559 | − | 0.253848i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 258.025i | − | 0.499080i | ||||||
\(518\) | −197.782 | − | 193.786i | −0.381818 | − | 0.374104i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −43.2792 | − | 74.9618i | −0.0832293 | − | 0.144157i | ||||
\(521\) | 661.706 | + | 382.036i | 1.27007 | + | 0.733274i | 0.975001 | − | 0.222202i | \(-0.0713244\pi\) |
0.295068 | + | 0.955476i | \(0.404658\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −153.096 | + | 88.3900i | −0.292726 | + | 0.169006i | −0.639171 | − | 0.769065i | \(-0.720722\pi\) |
0.346444 | + | 0.938071i | \(0.387389\pi\) | |||||||
\(524\) | 121.142i | 0.231186i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 128.235 | 0.243794 | ||||||||
\(527\) | 197.698 | + | 342.424i | 0.375139 | + | 0.649761i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −436.970 | + | 756.854i | −0.826030 | + | 1.43073i | ||||
\(530\) | 150.177 | − | 86.7045i | 0.283352 | − | 0.163593i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −97.9706 | − | 25.1825i | −0.184155 | − | 0.0473355i | ||||
\(533\) | 1169.44 | 2.19407 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 147.308 | + | 85.0482i | 0.275342 | + | 0.158969i | ||||
\(536\) | −6.21825 | + | 10.7703i | −0.0116012 | + | 0.0200939i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 96.7312i | − | 0.179798i | ||||||
\(539\) | −251.558 | + | 152.166i | −0.466713 | + | 0.282311i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.58831 | − | 14.8754i | −0.0158749 | − | 0.0274961i | 0.857979 | − | 0.513685i | \(-0.171720\pi\) |
−0.873854 | + | 0.486189i | \(0.838387\pi\) | |||||||
\(542\) | 151.279 | + | 87.3411i | 0.279113 | + | 0.161146i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −43.8823 | + | 25.3354i | −0.0806659 | + | 0.0465725i | ||||
\(545\) | 159.356i | 0.292396i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 212.676 | 0.388805 | 0.194402 | − | 0.980922i | \(-0.437723\pi\) | ||||
0.194402 | + | 0.980922i | \(0.437723\pi\) | |||||||
\(548\) | 67.0294 | + | 116.098i | 0.122316 | + | 0.211858i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 97.3310 | − | 168.582i | 0.176965 | − | 0.306513i | ||||
\(551\) | −212.382 | + | 122.619i | −0.385448 | + | 0.222538i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −663.058 | + | 184.938i | −1.19902 | + | 0.334427i | ||||
\(554\) | −385.914 | −0.696595 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −158.574 | − | 91.5525i | −0.285204 | − | 0.164663i | ||||
\(557\) | −440.823 | + | 763.528i | −0.791424 | + | 1.37079i | 0.133661 | + | 0.991027i | \(0.457327\pi\) |
−0.925085 | + | 0.379760i | \(0.876007\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.6780i | 0.0566691i | ||||||||
\(560\) | −28.1177 | + | 28.6976i | −0.0502103 | + | 0.0512456i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 94.1177 | + | 163.017i | 0.167469 | + | 0.290065i | ||||
\(563\) | −664.301 | − | 383.534i | −1.17993 | − | 0.681233i | −0.223932 | − | 0.974605i | \(-0.571889\pi\) |
−0.955998 | + | 0.293372i | \(0.905223\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −126.000 | + | 72.7461i | −0.223009 | + | 0.128754i | ||||
\(566\) | 182.090i | 0.321714i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −388.617 | −0.684185 | ||||||||
\(569\) | −14.6468 | − | 25.3689i | −0.0257412 | − | 0.0445851i | 0.852868 | − | 0.522127i | \(-0.174861\pi\) |
−0.878609 | + | 0.477542i | \(0.841528\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −482.521 | + | 835.752i | −0.845046 | + | 1.46366i | 0.0405347 | + | 0.999178i | \(0.487094\pi\) |
−0.885581 | + | 0.464485i | \(0.846239\pi\) | |||||||
\(572\) | 221.647 | − | 127.968i | 0.387494 | − | 0.223720i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −145.831 | − | 522.846i | −0.254060 | − | 0.910881i | ||||
\(575\) | 859.279 | 1.49440 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 227.883 | + | 131.568i | 0.394944 | + | 0.228021i | 0.684300 | − | 0.729201i | \(-0.260108\pi\) |
−0.289356 | + | 0.957222i | \(0.593441\pi\) | |||||||
\(578\) | −147.619 | + | 255.683i | −0.255396 | + | 0.442359i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 97.4027i | 0.167936i | ||||||||
\(581\) | −748.477 | − | 192.389i | −1.28826 | − | 0.331135i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 256.368 | + | 444.042i | 0.439738 | + | 0.761649i | ||||
\(584\) | 193.331 | + | 111.620i | 0.331046 | + | 0.191130i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 378.426 | − | 218.485i | 0.645779 | − | 0.372841i | ||||
\(587\) | − | 436.477i | − | 0.743572i | −0.928318 | − | 0.371786i | \(-0.878746\pi\) | ||
0.928318 | − | 0.371786i | \(-0.121254\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −318.941 | −0.541496 | ||||||||
\(590\) | −41.8234 | − | 72.4402i | −0.0708871 | − | 0.122780i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 55.9411 | − | 96.8929i | 0.0944951 | − | 0.163670i | ||||
\(593\) | −603.603 | + | 348.490i | −1.01788 | + | 0.587673i | −0.913489 | − | 0.406863i | \(-0.866623\pi\) |
−0.104391 | + | 0.994536i | \(0.533289\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.3978 | − | 87.1372i | 0.0376434 | − | 0.146449i | ||||
\(596\) | −162.177 | −0.272108 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 978.396 | + | 564.877i | 1.63611 | + | 0.944611i | ||||
\(599\) | 199.206 | − | 345.035i | 0.332564 | − | 0.576018i | −0.650450 | − | 0.759549i | \(-0.725419\pi\) |
0.983014 | + | 0.183531i | \(0.0587528\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.1691i | 0.0601816i | 0.999547 | + | 0.0300908i | \(0.00957964\pi\) | ||||
−0.999547 | + | 0.0300908i | \(0.990420\pi\) | |||||||
\(602\) | 14.1630 | − | 3.95029i | 0.0235265 | − | 0.00656194i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 51.2061 | + | 88.6915i | 0.0847782 | + | 0.146840i | ||||
\(605\) | 105.624 | + | 60.9823i | 0.174586 | + | 0.100797i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.3457 | − | 15.7880i | 0.0450505 | − | 0.0260099i | −0.477306 | − | 0.878737i | \(-0.658387\pi\) |
0.522356 | + | 0.852727i | \(0.325053\pi\) | |||||||
\(608\) | − | 40.8729i | − | 0.0672252i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.41212 | 0.00395430 | ||||||||
\(611\) | −458.595 | − | 794.310i | −0.750565 | − | 1.30002i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 204.632 | − | 354.434i | 0.333821 | − | 0.578195i | −0.649436 | − | 0.760416i | \(-0.724995\pi\) |
0.983258 | + | 0.182220i | \(0.0583285\pi\) | |||||||
\(614\) | 742.305 | − | 428.570i | 1.20897 | − | 0.697997i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −84.8528 | − | 83.1384i | −0.137748 | − | 0.134965i | ||||
\(617\) | −1227.38 | −1.98927 | −0.994636 | − | 0.103436i | \(-0.967016\pi\) | ||||
−0.994636 | + | 0.103436i | \(0.967016\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 412.022 | + | 237.881i | 0.665625 | + | 0.384299i | 0.794417 | − | 0.607373i | \(-0.207777\pi\) |
−0.128792 | + | 0.991672i | \(0.541110\pi\) | |||||||
\(620\) | −63.3381 | + | 109.705i | −0.102158 | + | 0.176943i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 287.478i | − | 0.462184i | ||||||
\(623\) | −39.0883 | − | 140.143i | −0.0627421 | − | 0.224949i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −237.412 | − | 411.209i | −0.379859 | − | 0.657935i | ||||
\(626\) | 496.805 | + | 286.830i | 0.793618 | + | 0.458195i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −324.000 | + | 187.061i | −0.515924 | + | 0.297869i | ||||
\(629\) | 250.544i | 0.398322i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −54.9420 | −0.0870713 | −0.0435357 | − | 0.999052i | \(-0.513862\pi\) | ||||
−0.0435357 | + | 0.999052i | \(0.513862\pi\) | |||||||
\(632\) | −139.071 | − | 240.878i | −0.220049 | − | 0.381136i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −18.4264 | + | 31.9155i | −0.0290637 | + | 0.0503399i | ||||
\(635\) | 102.609 | − | 59.2415i | 0.161589 | − | 0.0932937i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −503.956 | + | 915.533i | −0.791139 | + | 1.43726i | ||||
\(638\) | −288.000 | −0.451411 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −14.0589 | − | 8.11689i | −0.0219670 | − | 0.0126826i | ||||
\(641\) | −114.551 | + | 198.409i | −0.178707 | + | 0.309530i | −0.941438 | − | 0.337186i | \(-0.890525\pi\) |
0.762731 | + | 0.646716i | \(0.223858\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 854.640i | − | 1.32914i | −0.747224 | − | 0.664572i | \(-0.768614\pi\) | ||
0.747224 | − | 0.664572i | \(-0.231386\pi\) | |||||||
\(644\) | 130.544 | − | 507.873i | 0.202708 | − | 0.788622i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 45.7645 | + | 79.2664i | 0.0708429 | + | 0.122703i | ||||
\(647\) | −868.632 | − | 501.505i | −1.34255 | − | 0.775124i | −0.355372 | − | 0.934725i | \(-0.615646\pi\) |
−0.987182 | + | 0.159601i | \(0.948979\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 214.191 | − | 123.663i | 0.330032 | − | 0.190544i | ||||
\(650\) | − | 691.957i | − | 1.06455i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 167.882 | 0.257488 | ||||||||
\(653\) | 635.382 | + | 1100.51i | 0.973020 | + | 1.68532i | 0.686321 | + | 0.727299i | \(0.259224\pi\) |
0.286698 | + | 0.958021i | \(0.407442\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 43.4558 | − | 75.2677i | 0.0663448 | − | 0.114913i | ||||
\(656\) | 189.941 | − | 109.663i | 0.289544 | − | 0.167169i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −297.941 | + | 304.085i | −0.452798 | + | 0.462135i | ||||
\(659\) | 783.308 | 1.18863 | 0.594315 | − | 0.804232i | \(-0.297423\pi\) | ||||
0.594315 | + | 0.804232i | \(0.297423\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 72.5589 | + | 41.8919i | 0.109771 | + | 0.0633765i | 0.553881 | − | 0.832596i | \(-0.313146\pi\) |
−0.444109 | + | 0.895973i | \(0.646480\pi\) | |||||||
\(662\) | 76.8148 | − | 133.047i | 0.116034 | − | 0.200977i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 312.262i | − | 0.470273i | ||||||
\(665\) | 51.8377 | + | 50.7903i | 0.0779514 | + | 0.0763764i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −635.647 | − | 1100.97i | −0.952994 | − | 1.65063i | ||||
\(668\) | −221.044 | − | 127.620i | −0.330904 | − | 0.191047i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.72706 | − | 4.46122i | 0.0115329 | − | 0.00665853i | ||||
\(671\) | 7.13215i | 0.0106291i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 415.676 | 0.617647 | 0.308823 | − | 0.951119i | \(-0.400065\pi\) | ||||
0.308823 | + | 0.951119i | \(0.400065\pi\) | |||||||
\(674\) | −312.354 | − | 541.013i | −0.463433 | − | 0.802690i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 285.882 | − | 495.163i | 0.422903 | − | 0.732489i | ||||
\(677\) | −685.279 | + | 395.646i | −1.01223 | + | 0.584411i | −0.911844 | − | 0.410538i | \(-0.865341\pi\) |
−0.100386 | + | 0.994949i | \(0.532008\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −74.4853 | − | 19.1458i | −0.109698 | − | 0.0281970i | ||||
\(680\) | 36.3532 | 0.0534607 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −324.375 | − | 187.278i | −0.475623 | − | 0.274601i | ||||
\(683\) | −164.080 | + | 284.195i | −0.240235 | + | 0.416099i | −0.960781 | − | 0.277308i | \(-0.910558\pi\) |
0.720546 | + | 0.693407i | \(0.243891\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 96.1791i | − | 0.140407i | ||||||
\(686\) | 472.170 | + | 111.146i | 0.688295 | + | 0.162020i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.97056 | + | 5.14517i | 0.00431768 | + | 0.00747844i | ||||
\(689\) | 1578.42 | + | 911.300i | 2.29088 | + | 1.32264i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 875.182 | − | 505.287i | 1.26654 | − | 0.731240i | 0.292212 | − | 0.956353i | \(-0.405609\pi\) |
0.974333 | + | 0.225113i | \(0.0722753\pi\) | |||||||
\(692\) | 285.941i | 0.413210i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −48.3532 | −0.0696733 | ||||||||
\(695\) | 65.6833 | + | 113.767i | 0.0945084 | + | 0.163693i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −245.574 | + | 425.346i | −0.352329 | + | 0.610252i | ||||
\(698\) | 271.632 | − | 156.827i | 0.389158 | − | 0.224681i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −309.368 | + | 86.2879i | −0.441954 | + | 0.123268i | ||||
\(701\) | 0.103464 | 0.000147594 | 7.37972e−5 | − | 1.00000i | \(-0.499977\pi\) | ||||
7.37972e−5 | 1.00000i | \(0.499977\pi\) | ||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −175.022 | − | 101.049i | −0.248964 | − | 0.143740i | ||||
\(704\) | 24.0000 | − | 41.5692i | 0.0340909 | − | 0.0590472i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 632.700i | 0.896175i | ||||||||
\(707\) | 525.088 | − | 535.916i | 0.742699 | − | 0.758014i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −602.588 | − | 1043.71i | −0.849912 | − | 1.47209i | −0.881286 | − | 0.472584i | \(-0.843321\pi\) |
0.0313734 | − | 0.999508i | \(-0.490012\pi\) | |||||||
\(710\) | 241.456 | + | 139.405i | 0.340079 | + | 0.196345i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 50.9117 | − | 29.3939i | 0.0715052 | − | 0.0412835i | ||||
\(713\) | − | 1653.37i | − | 2.31889i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −183.618 | −0.256809 | ||||||||
\(716\) | 169.279 | + | 293.200i | 0.236423 | + | 0.409498i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 206.309 | − | 357.337i | 0.287338 | − | 0.497684i | ||||
\(719\) | −850.925 | + | 491.282i | −1.18348 | + | 0.683285i | −0.956818 | − | 0.290688i | \(-0.906116\pi\) |
−0.226666 | + | 0.973973i | \(0.572783\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −197.852 | − | 709.359i | −0.274414 | − | 0.983855i | ||||
\(722\) | 436.701 | 0.604848 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 363.676 | + | 209.969i | 0.502315 | + | 0.290012i | ||||
\(725\) | −389.324 | + | 674.329i | −0.536998 | + | 0.930108i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 630.440i | − | 0.867181i | −0.901110 | − | 0.433590i | \(-0.857247\pi\) | ||
0.901110 | − | 0.433590i | \(-0.142753\pi\) | |||||||
\(728\) | −408.978 | − | 105.124i | −0.561783 | − | 0.144401i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −80.0803 | − | 138.703i | −0.109699 | − | 0.190004i | ||||
\(731\) | −11.5219 | − | 6.65215i | −0.0157618 | − | 0.00910007i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 258.486 | − | 149.237i | 0.352641 | − | 0.203597i | −0.313207 | − | 0.949685i | \(-0.601403\pi\) |
0.665848 | + | 0.746088i | \(0.268070\pi\) | |||||||
\(734\) | 593.053i | 0.807974i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 211.882 | 0.287883 | ||||||||
\(737\) | 13.1909 | + | 22.8473i | 0.0178981 | + | 0.0310004i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −172.684 | + | 299.097i | −0.233672 | + | 0.404732i | −0.958886 | − | 0.283792i | \(-0.908408\pi\) |
0.725214 | + | 0.688524i | \(0.241741\pi\) | |||||||
\(740\) | −69.5147 | + | 40.1343i | −0.0939388 | + | 0.0542356i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 210.603 | − | 819.336i | 0.283832 | − | 1.10423i | ||||
\(743\) | −683.616 | −0.920076 | −0.460038 | − | 0.887899i | \(-0.652164\pi\) | ||||
−0.460038 | + | 0.887899i | \(0.652164\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 100.764 | + | 58.1759i | 0.135253 | + | 0.0780885i | ||||
\(746\) | −22.1903 | + | 38.4347i | −0.0297457 | + | 0.0515211i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 107.489i | 0.143702i | ||||||||
\(749\) | 799.301 | − | 222.939i | 1.06716 | − | 0.297648i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 289.169 | + | 500.855i | 0.385045 | + | 0.666918i | 0.991775 | − | 0.127990i | \(-0.0408525\pi\) |
−0.606730 | + | 0.794908i | \(0.707519\pi\) | |||||||
\(752\) | −148.971 | − | 86.0082i | −0.198099 | − | 0.114373i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −886.587 | + | 511.871i | −1.17584 | + | 0.678874i | ||||
\(755\) | − | 73.4744i | − | 0.0973171i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1204.82 | 1.59158 | 0.795788 | − | 0.605576i | \(-0.207057\pi\) | ||||
0.795788 | + | 0.605576i | \(0.207057\pi\) | |||||||
\(758\) | −146.215 | − | 253.251i | −0.192895 | − | 0.334105i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −14.6619 | + | 25.3952i | −0.0192920 | + | 0.0334147i | ||||
\(761\) | 202.669 | − | 117.011i | 0.266319 | − | 0.153760i | −0.360894 | − | 0.932607i | \(-0.617529\pi\) |
0.627214 | + | 0.778847i | \(0.284195\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 555.294 | + | 544.075i | 0.727778 | + | 0.713074i | ||||
\(764\) | −133.206 | −0.174353 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −610.617 | − | 352.540i | −0.797151 | − | 0.460235i | ||||
\(767\) | 439.581 | − | 761.376i | 0.573117 | − | 0.992668i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1290.16i | 1.67771i | 0.544358 | + | 0.838853i | \(0.316774\pi\) | ||||
−0.544358 | + | 0.838853i | \(0.683226\pi\) | |||||||
\(770\) | 22.8974 | + | 82.0940i | 0.0297369 | + | 0.106616i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.79394 | + | 16.9636i | 0.0126864 | + | 0.0219736i | ||||
\(773\) | −345.646 | − | 199.559i | −0.447149 | − | 0.258161i | 0.259477 | − | 0.965749i | \(-0.416450\pi\) |
−0.706625 | + | 0.707588i | \(0.749783\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −876.992 | + | 506.331i | −1.13160 | + | 0.653331i | ||||
\(776\) | − | 31.0749i | − | 0.0400450i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 917.013 | 1.17868 | ||||||||
\(779\) | −198.088 | − | 343.099i | −0.254285 | − | 0.440435i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −412.191 | + | 713.936i | −0.527773 | + | 0.914130i | ||||
\(782\) | −410.912 | + | 237.240i | −0.525463 | + | 0.303376i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.00000 | + | 195.959i | 0.00510204 | + | 0.249948i | ||||
\(785\) | 268.410 | 0.341924 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1348.16 | − | 778.361i | −1.71304 | − | 0.989023i | −0.930401 | − | 0.366544i | \(-0.880541\pi\) |
−0.782637 | − | 0.622478i | \(-0.786126\pi\) | |||||||
\(788\) | −267.161 | + | 462.737i | −0.339037 | + | 0.587230i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 199.550i | 0.252595i | ||||||||
\(791\) | −176.698 | + | 687.433i | −0.223386 | + | 0.869068i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.6762 | + | 21.9558i | 0.0159851 | + | 0.0276870i | ||||
\(794\) | −92.7761 | − | 53.5643i | −0.116846 | − | 0.0674613i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 226.794 | − | 130.940i | 0.284917 | − | 0.164497i | ||||
\(797\) | − | 600.232i | − | 0.753114i | −0.926393 | − | 0.376557i | \(-0.877108\pi\) | ||
0.926393 | − | 0.376557i | \(-0.122892\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 385.206 | 0.482110 | ||||||||
\(800\) | −64.8873 | − | 112.388i | −0.0811091 | − | 0.140485i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −398.985 | + | 691.062i | −0.497487 | + | 0.861673i | ||||
\(803\) | 410.117 | − | 236.781i | 0.510731 | − | 0.294871i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −263.294 | + | 268.723i | −0.327073 | + | 0.333817i | ||||
\(806\) | −1331.42 | −1.65188 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 262.544 | + | 151.580i | 0.324931 | + | 0.187599i | ||||
\(809\) | −114.640 | + | 198.562i | −0.141705 | + | 0.245441i | −0.928139 | − | 0.372234i | \(-0.878592\pi\) |
0.786434 | + | 0.617675i | \(0.211925\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 529.955i | 0.653459i | 0.945118 | + | 0.326729i | \(0.105947\pi\) | ||||
−0.945118 | + | 0.326729i | \(0.894053\pi\) | |||||||
\(812\) | 339.411 | + | 332.554i | 0.417994 | + | 0.409549i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −118.669 | − | 205.541i | −0.145785 | − | 0.252507i | ||||
\(815\) | −104.309 | − | 60.2226i | −0.127986 | − | 0.0738928i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.29394 | − | 5.36586i | 0.0113757 | − | 0.00656776i | ||||
\(818\) | 505.508i | 0.617980i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −157.352 | −0.191893 | ||||||||
\(821\) | −151.669 | − | 262.698i | −0.184737 | − | 0.319974i | 0.758751 | − | 0.651381i | \(-0.225810\pi\) |
−0.943488 | + | 0.331407i | \(0.892477\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 564.955 | − | 978.531i | 0.686459 | − | 1.18898i | −0.286517 | − | 0.958075i | \(-0.592498\pi\) |
0.972976 | − | 0.230906i | \(-0.0741690\pi\) | |||||||
\(824\) | 257.698 | − | 148.782i | 0.312741 | − | 0.180561i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −395.220 | − | 101.588i | −0.478475 | − | 0.122988i | ||||
\(827\) | 161.604 | 0.195410 | 0.0977049 | − | 0.995215i | \(-0.468850\pi\) | ||||
0.0977049 | + | 0.995215i | \(0.468850\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1325.32 | + | 765.175i | 1.59870 | + | 0.923010i | 0.991738 | + | 0.128279i | \(0.0409454\pi\) |
0.606962 | + | 0.794731i | \(0.292388\pi\) | |||||||
\(830\) | −112.014 | + | 194.014i | −0.134957 | + | 0.233752i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 170.624i | − | 0.205077i | ||||||
\(833\) | −227.169 | − | 375.553i | −0.272711 | − | 0.450844i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 91.5593 | + | 158.585i | 0.109652 | + | 0.189923i | ||||
\(836\) | −75.0883 | − | 43.3523i | −0.0898186 | − | 0.0518568i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 615.037 | − | 355.092i | 0.733934 | − | 0.423737i | ||||
\(839\) | 218.629i | 0.260583i | 0.991476 | + | 0.130291i | \(0.0415913\pi\) | ||||
−0.991476 | + | 0.130291i | \(0.958409\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 311.000 | 0.369798 | ||||||||
\(842\) | −23.8959 | − | 41.3890i | −0.0283800 | − | 0.0491555i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 23.0883 | − | 39.9901i | 0.0273558 | − | 0.0473817i | ||||
\(845\) | −355.249 | + | 205.103i | −0.420413 | + | 0.242726i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 573.124 | − | 159.854i | 0.676652 | − | 0.188730i | ||||
\(848\) | 341.823 | 0.403094 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 251.677 | + | 145.306i | 0.296091 | + | 0.170948i | ||||
\(851\) | 523.831 | − | 907.301i | 0.615547 | − | 1.06616i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 762.730i | 0.894174i | 0.894491 | + | 0.447087i | \(0.147539\pi\) | ||||
−0.894491 | + | 0.447087i | \(0.852461\pi\) | |||||||
\(854\) | 8.23550 | − | 8.40532i | 0.00964344 | − | 0.00984230i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 167.647 | + | 290.373i | 0.195849 | + | 0.339220i | ||||
\(857\) | 795.015 | + | 459.002i | 0.927672 | + | 0.535592i | 0.886075 | − | 0.463543i | \(-0.153422\pi\) |
0.0415977 | + | 0.999134i | \(0.486755\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −761.367 | + | 439.575i | −0.886341 | + | 0.511729i | −0.872744 | − | 0.488179i | \(-0.837661\pi\) |
−0.0135969 | + | 0.999908i | \(0.504328\pi\) | |||||||
\(860\) | − | 4.26239i | − | 0.00495627i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −712.368 | −0.826412 | ||||||||
\(863\) | 175.294 | + | 303.619i | 0.203122 | + | 0.351818i | 0.949533 | − | 0.313668i | \(-0.101558\pi\) |
−0.746411 | + | 0.665486i | \(0.768224\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 102.573 | − | 177.661i | 0.118581 | − | 0.205389i | ||||
\(866\) | −1025.78 | + | 592.236i | −1.18451 | + | 0.683875i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 166.029 | + | 595.265i | 0.191278 | + | 0.685789i | ||||
\(869\) | −590.029 | −0.678974 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 81.2145 | + | 46.8892i | 0.0932428 | + | 0.0538338i | ||||
\(872\) | −157.061 | + | 272.038i | −0.180116 | + | 0.311970i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 382.732i | − | 0.437909i | ||||||
\(875\) | 466.368 | + | 119.876i | 0.532991 | + | 0.137001i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.77965 | − | 3.08245i | −0.00202925 | − | 0.00351477i | 0.865009 | − | 0.501756i | \(-0.167313\pi\) |
−0.867038 | + | 0.498242i | \(0.833979\pi\) | |||||||
\(878\) | 232.721 | + | 134.361i | 0.265058 | + | 0.153031i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −29.8234 | + | 17.2185i | −0.0338902 | + | 0.0195665i | ||||
\(881\) | 488.565i | 0.554557i | 0.960790 | + | 0.277279i | \(0.0894325\pi\) | ||||
−0.960790 | + | 0.277279i | \(0.910567\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1162.16 | −1.31615 | −0.658075 | − | 0.752953i | \(-0.728629\pi\) | ||||
−0.658075 | + | 0.752953i | \(0.728629\pi\) | |||||||
\(884\) | 191.044 | + | 330.897i | 0.216113 | + | 0.374318i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −119.823 | + | 207.540i | −0.135241 | + | 0.234244i | ||||
\(887\) | −75.2801 | + | 43.4630i | −0.0848704 | + | 0.0490000i | −0.541835 | − | 0.840485i | \(-0.682270\pi\) |
0.456964 | + | 0.889485i | \(0.348937\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 143.896 | − | 559.817i | 0.161863 | − | 0.629716i | ||||
\(890\) | −42.1766 | −0.0473895 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −396.000 | − | 228.631i | −0.443946 | − | 0.256312i | ||||
\(893\) | −155.360 | + | 269.092i | −0.173976 | + | 0.301335i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 242.895i | − | 0.271391i | ||||||
\(896\) | −76.2843 | + | 21.2770i | −0.0851387 | + | 0.0237466i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 12.8011 | + | 22.1721i | 0.0142551 | + | 0.0246906i | ||||
\(899\) | 1297.50 | + | 749.111i | 1.44327 | + | 0.833272i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −662.912 | + | 382.732i | −0.735751 | + | 0.424786i | ||||
\(902\) | − | 465.259i | − | 0.515808i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −286.794 | −0.317250 | ||||||||
\(905\) | −150.640 | − | 260.915i | −0.166453 | − | 0.288304i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 230.448 | − | 399.148i | 0.254077 | − | 0.440075i | −0.710567 | − | 0.703629i | \(-0.751562\pi\) |
0.964645 | + | 0.263554i | \(0.0848948\pi\) | |||||||
\(908\) | 113.647 | − | 65.6140i | 0.125162 | − | 0.0722621i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 216.396 | + | 212.024i | 0.237798 | + | 0.232993i | ||||
\(911\) | 1184.28 | 1.29998 | 0.649988 | − | 0.759944i | \(-0.274774\pi\) | ||||
0.649988 | + | 0.759944i | \(0.274774\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −573.661 | − | 331.203i | −0.628325 | − | 0.362764i | ||||
\(914\) | 232.513 | − | 402.725i | 0.254391 | − | 0.440618i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 186.960i | 0.204104i | ||||||||
\(917\) | −113.912 | − | 408.407i | −0.124222 | − | 0.445373i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 270.919 | + | 469.246i | 0.294798 | + | 0.510605i | 0.974938 | − | 0.222477i | \(-0.0714143\pi\) |
−0.680140 | + | 0.733082i | \(0.738081\pi\) | |||||||
\(920\) | −131.647 | − | 76.0063i | −0.143094 | − | 0.0826155i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −972.853 | + | 561.677i | −1.05515 | + | 0.609194i | ||||
\(923\) | 2930.40i | 3.17486i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −641.676 | −0.693704 | ||||||||
\(926\) | 285.244 | + | 494.057i | 0.308039 | + | 0.533539i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −96.0000 | + | 166.277i | −0.103448 | + | 0.179178i | ||||
\(929\) | 779.610 | − | 450.108i | 0.839193 | − | 0.484508i | −0.0177969 | − | 0.999842i | \(-0.505665\pi\) |
0.856990 | + | 0.515333i | \(0.172332\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 353.970 | − | 7.22538i | 0.380204 | − | 0.00776088i | ||||
\(932\) | 475.029 | 0.509688 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.46299 | − | 1.99936i | −0.00370769 | − | 0.00214064i | ||||
\(935\) | 38.5584 | − | 66.7852i | 0.0412390 | − | 0.0714280i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 233.964i | 0.249695i | 0.992176 | + | 0.124847i | \(0.0398441\pi\) | ||||
−0.992176 | + | 0.124847i | \(0.960156\pi\) | |||||||
\(938\) | 10.8362 | − | 42.1574i | 0.0115524 | − | 0.0449439i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 61.7056 | + | 106.877i | 0.0656443 | + | 0.113699i | ||||
\(941\) | −1132.49 | − | 653.845i | −1.20350 | − | 0.694840i | −0.242167 | − | 0.970234i | \(-0.577858\pi\) |
−0.961331 | + | 0.275394i | \(0.911192\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1778.60 | − | 1026.88i | 1.88611 | − | 1.08895i | ||||
\(944\) | − | 164.884i | − | 0.174666i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.6030 | 0.0133224 | ||||||||
\(947\) | −563.881 | − | 976.671i | −0.595440 | − | 1.03133i | −0.993485 | − | 0.113966i | \(-0.963645\pi\) |
0.398045 | − | 0.917366i | \(-0.369689\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 841.677 | − | 1457.83i | 0.886909 | − | 1.53617i | ||||
\(950\) | −203.012 | + | 117.209i | −0.213696 | + | 0.123378i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 124.118 | − | 126.677i | 0.130376 | − | 0.133064i | ||||
\(953\) | 91.4255 | 0.0959345 | 0.0479672 | − | 0.998849i | \(-0.484726\pi\) | ||||
0.0479672 | + | 0.998849i | \(0.484726\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 82.7636 | + | 47.7836i | 0.0866635 | + | 0.0500352i | ||||
\(956\) | 366.853 | − | 635.408i | 0.383737 | − | 0.664652i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 536.714i | 0.560245i | ||||||||
\(959\) | −335.147 | − | 328.376i | −0.349476 | − | 0.342415i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 493.749 | + | 855.199i | 0.513787 | + | 0.889905i | ||||
\(962\) | −730.628 | − | 421.828i | −0.759489 | − | 0.438491i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 729.235 | − | 421.024i | 0.756467 | − | 0.436747i | ||||
\(965\) | − | 14.0531i | − | 0.0145628i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1098.19 | −1.13567 | −0.567834 | − | 0.823143i | \(-0.692218\pi\) | ||||
−0.567834 | + | 0.823143i | \(0.692218\pi\) | |||||||
\(968\) | 120.208 | + | 208.207i | 0.124182 | + | 0.215089i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11.1472 | + | 19.3075i | −0.0114919 | + | 0.0199046i | ||||
\(971\) | −114.405 | + | 66.0517i | −0.117822 | + | 0.0680245i | −0.557753 | − | 0.830007i | \(-0.688336\pi\) |
0.439931 | + | 0.898032i | \(0.355003\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 620.691 | + | 159.543i | 0.637915 | + | 0.163970i | ||||
\(974\) | 813.899 | 0.835626 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.11775 | + | 2.37738i | 0.00421901 | + | 0.00243584i | ||||
\(977\) | 224.117 | − | 388.182i | 0.229393 | − | 0.397320i | −0.728235 | − | 0.685327i | \(-0.759659\pi\) |
0.957628 | + | 0.288007i | \(0.0929926\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 124.708i | − | 0.127383i | ||||||
\(980\) | 67.8091 | − | 123.188i | 0.0691930 | − | 0.125702i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 168.603 | + | 292.029i | 0.171694 | + | 0.297382i | ||||
\(983\) | −1426.14 | − | 823.382i | −1.45080 | − | 0.837621i | −0.452276 | − | 0.891878i | \(-0.649388\pi\) |
−0.998527 | + | 0.0542567i | \(0.982721\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 331.986 | − | 191.672i | 0.337041 | − | 0.194591i | ||||
\(986\) | − | 429.956i | − | 0.436061i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −308.205 | −0.311949 | ||||||||
\(989\) | 27.8162 | + | 48.1791i | 0.0281256 | + | 0.0487150i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 314.448 | − | 544.640i | 0.317304 | − | 0.549587i | −0.662621 | − | 0.748955i | \(-0.730556\pi\) |
0.979925 | + | 0.199369i | \(0.0638891\pi\) | |||||||
\(992\) | −216.250 | + | 124.852i | −0.217994 | + | 0.125859i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1310.15 | − | 365.424i | 1.31806 | − | 0.367630i | ||||
\(995\) | −187.882 | −0.188826 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −869.645 | − | 502.090i | −0.872262 | − | 0.503601i | −0.00416289 | − | 0.999991i | \(-0.501325\pi\) |
−0.868099 | + | 0.496390i | \(0.834658\pi\) | |||||||
\(998\) | 202.638 | − | 350.980i | 0.203044 | − | 0.351683i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 126.3.n.a.73.1 | 4 | ||
3.2 | odd | 2 | 42.3.g.a.31.2 | yes | 4 | ||
4.3 | odd | 2 | 1008.3.cg.h.577.2 | 4 | |||
7.2 | even | 3 | 882.3.n.e.19.1 | 4 | |||
7.3 | odd | 6 | 882.3.c.b.685.3 | 4 | |||
7.4 | even | 3 | 882.3.c.b.685.4 | 4 | |||
7.5 | odd | 6 | inner | 126.3.n.a.19.1 | 4 | ||
7.6 | odd | 2 | 882.3.n.e.325.1 | 4 | |||
12.11 | even | 2 | 336.3.bh.e.241.1 | 4 | |||
15.2 | even | 4 | 1050.3.q.a.199.2 | 8 | |||
15.8 | even | 4 | 1050.3.q.a.199.3 | 8 | |||
15.14 | odd | 2 | 1050.3.p.a.451.1 | 4 | |||
21.2 | odd | 6 | 294.3.g.a.19.2 | 4 | |||
21.5 | even | 6 | 42.3.g.a.19.2 | ✓ | 4 | ||
21.11 | odd | 6 | 294.3.c.a.97.1 | 4 | |||
21.17 | even | 6 | 294.3.c.a.97.2 | 4 | |||
21.20 | even | 2 | 294.3.g.a.31.2 | 4 | |||
28.19 | even | 6 | 1008.3.cg.h.145.2 | 4 | |||
84.11 | even | 6 | 2352.3.f.e.97.3 | 4 | |||
84.47 | odd | 6 | 336.3.bh.e.145.1 | 4 | |||
84.59 | odd | 6 | 2352.3.f.e.97.2 | 4 | |||
105.47 | odd | 12 | 1050.3.q.a.649.3 | 8 | |||
105.68 | odd | 12 | 1050.3.q.a.649.2 | 8 | |||
105.89 | even | 6 | 1050.3.p.a.901.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.3.g.a.19.2 | ✓ | 4 | 21.5 | even | 6 | ||
42.3.g.a.31.2 | yes | 4 | 3.2 | odd | 2 | ||
126.3.n.a.19.1 | 4 | 7.5 | odd | 6 | inner | ||
126.3.n.a.73.1 | 4 | 1.1 | even | 1 | trivial | ||
294.3.c.a.97.1 | 4 | 21.11 | odd | 6 | |||
294.3.c.a.97.2 | 4 | 21.17 | even | 6 | |||
294.3.g.a.19.2 | 4 | 21.2 | odd | 6 | |||
294.3.g.a.31.2 | 4 | 21.20 | even | 2 | |||
336.3.bh.e.145.1 | 4 | 84.47 | odd | 6 | |||
336.3.bh.e.241.1 | 4 | 12.11 | even | 2 | |||
882.3.c.b.685.3 | 4 | 7.3 | odd | 6 | |||
882.3.c.b.685.4 | 4 | 7.4 | even | 3 | |||
882.3.n.e.19.1 | 4 | 7.2 | even | 3 | |||
882.3.n.e.325.1 | 4 | 7.6 | odd | 2 | |||
1008.3.cg.h.145.2 | 4 | 28.19 | even | 6 | |||
1008.3.cg.h.577.2 | 4 | 4.3 | odd | 2 | |||
1050.3.p.a.451.1 | 4 | 15.14 | odd | 2 | |||
1050.3.p.a.901.1 | 4 | 105.89 | even | 6 | |||
1050.3.q.a.199.2 | 8 | 15.2 | even | 4 | |||
1050.3.q.a.199.3 | 8 | 15.8 | even | 4 | |||
1050.3.q.a.649.2 | 8 | 105.68 | odd | 12 | |||
1050.3.q.a.649.3 | 8 | 105.47 | odd | 12 | |||
2352.3.f.e.97.2 | 4 | 84.59 | odd | 6 | |||
2352.3.f.e.97.3 | 4 | 84.11 | even | 6 |