Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [42,3,Mod(19,42)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(42, 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("42.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 42 = 2 \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 42.g (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: | \(1.14441711031\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 42.19 |
Dual form | 42.3.g.a.31.2 |
$q$-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 \(\left(\mathbb{Z}/42\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(31\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||
\(3\) | 1.50000 | − | 0.866025i | 0.500000 | − | 0.288675i | ||||
\(4\) | −1.00000 | − | 1.73205i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.24264 | − | 0.717439i | −0.248528 | − | 0.143488i | 0.370562 | − | 0.928808i | \(-0.379165\pi\) |
−0.619090 | + | 0.785320i | \(0.712498\pi\) | |||||||
\(6\) | − | 2.44949i | − | 0.408248i | ||||||
\(7\) | 1.74264 | + | 6.77962i | 0.248949 | + | 0.968517i | ||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.166667 | − | 0.288675i | ||||
\(10\) | −1.75736 | + | 1.01461i | −0.175736 | + | 0.101461i | ||||
\(11\) | −3.00000 | − | 5.19615i | −0.272727 | − | 0.472377i | 0.696832 | − | 0.717234i | \(-0.254592\pi\) |
−0.969559 | + | 0.244857i | \(0.921259\pi\) | |||||||
\(12\) | −3.00000 | − | 1.73205i | −0.250000 | − | 0.144338i | ||||
\(13\) | 21.3280i | 1.64061i | 0.571924 | + | 0.820306i | \(0.306197\pi\) | ||||
−0.571924 | + | 0.820306i | \(0.693803\pi\) | |||||||
\(14\) | 9.53553 | + | 2.65962i | 0.681110 | + | 0.189973i | ||||
\(15\) | −2.48528 | −0.165685 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | −7.75736 | + | 4.47871i | −0.456315 | + | 0.263454i | −0.710494 | − | 0.703704i | \(-0.751528\pi\) |
0.254178 | + | 0.967157i | \(0.418195\pi\) | |||||||
\(18\) | −2.12132 | − | 3.67423i | −0.117851 | − | 0.204124i | ||||
\(19\) | −6.25736 | − | 3.61269i | −0.329335 | − | 0.190141i | 0.326211 | − | 0.945297i | \(-0.394228\pi\) |
−0.655546 | + | 0.755156i | \(0.727561\pi\) | |||||||
\(20\) | 2.86976i | 0.143488i | ||||||||
\(21\) | 8.48528 | + | 8.66025i | 0.404061 | + | 0.412393i | ||||
\(22\) | −8.48528 | −0.385695 | ||||||||
\(23\) | 18.7279 | − | 32.4377i | 0.814257 | − | 1.41034i | −0.0956024 | − | 0.995420i | \(-0.530478\pi\) |
0.909860 | − | 0.414916i | \(-0.136189\pi\) | |||||||
\(24\) | −4.24264 | + | 2.44949i | −0.176777 | + | 0.102062i | ||||
\(25\) | −11.4706 | − | 19.8676i | −0.458823 | − | 0.794704i | ||||
\(26\) | 26.1213 | + | 15.0812i | 1.00467 | + | 0.580044i | ||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | 10.0000 | − | 9.79796i | 0.357143 | − | 0.349927i | ||||
\(29\) | −33.9411 | −1.17038 | −0.585192 | − | 0.810895i | \(-0.698981\pi\) | ||||
−0.585192 | + | 0.810895i | \(0.698981\pi\) | |||||||
\(30\) | −1.75736 | + | 3.04384i | −0.0585786 | + | 0.101461i | ||||
\(31\) | 38.2279 | − | 22.0709i | 1.23316 | − | 0.711965i | 0.265472 | − | 0.964119i | \(-0.414472\pi\) |
0.967687 | + | 0.252154i | \(0.0811390\pi\) | |||||||
\(32\) | 2.82843 | + | 4.89898i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −9.00000 | − | 5.19615i | −0.272727 | − | 0.157459i | ||||
\(34\) | 12.6677i | 0.372580i | ||||||||
\(35\) | 2.69848 | − | 9.67487i | 0.0770996 | − | 0.276425i | ||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | 13.9853 | − | 24.2232i | 0.377981 | − | 0.654682i | −0.612788 | − | 0.790248i | \(-0.709952\pi\) |
0.990768 | + | 0.135566i | \(0.0432853\pi\) | |||||||
\(38\) | −8.84924 | + | 5.10911i | −0.232875 | + | 0.134450i | ||||
\(39\) | 18.4706 | + | 31.9920i | 0.473604 | + | 0.820306i | ||||
\(40\) | 3.51472 | + | 2.02922i | 0.0878680 | + | 0.0507306i | ||||
\(41\) | 54.8313i | 1.33735i | 0.743556 | + | 0.668674i | \(0.233138\pi\) | ||||
−0.743556 | + | 0.668674i | \(0.766862\pi\) | |||||||
\(42\) | 16.6066 | − | 4.26858i | 0.395395 | − | 0.101633i | ||||
\(43\) | −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 | ||||
\(45\) | −3.72792 | + | 2.15232i | −0.0828427 | + | 0.0478293i | ||||
\(46\) | −26.4853 | − | 45.8739i | −0.575767 | − | 0.997258i | ||||
\(47\) | −37.2426 | − | 21.5020i | −0.792397 | − | 0.457490i | 0.0484090 | − | 0.998828i | \(-0.484585\pi\) |
−0.840806 | + | 0.541337i | \(0.817918\pi\) | |||||||
\(48\) | 6.92820i | 0.144338i | ||||||||
\(49\) | −42.9264 | + | 23.6289i | −0.876049 | + | 0.482222i | ||||
\(50\) | −32.4437 | −0.648873 | ||||||||
\(51\) | −7.75736 | + | 13.4361i | −0.152105 | + | 0.263454i | ||||
\(52\) | 36.9411 | − | 21.3280i | 0.710406 | − | 0.410153i | ||||
\(53\) | 42.7279 | + | 74.0069i | 0.806187 | + | 1.39636i | 0.915487 | + | 0.402348i | \(0.131806\pi\) |
−0.109299 | + | 0.994009i | \(0.534861\pi\) | |||||||
\(54\) | −6.36396 | − | 3.67423i | −0.117851 | − | 0.0680414i | ||||
\(55\) | 8.60927i | 0.156532i | ||||||||
\(56\) | −4.92893 | − | 19.1757i | −0.0880166 | − | 0.342422i | ||||
\(57\) | −12.5147 | −0.219556 | ||||||||
\(58\) | −24.0000 | + | 41.5692i | −0.413793 | + | 0.716711i | ||||
\(59\) | −35.6985 | + | 20.6105i | −0.605059 | + | 0.349331i | −0.771029 | − | 0.636800i | \(-0.780258\pi\) |
0.165970 | + | 0.986131i | \(0.446924\pi\) | |||||||
\(60\) | 2.48528 | + | 4.30463i | 0.0414214 | + | 0.0717439i | ||||
\(61\) | −1.02944 | − | 0.594346i | −0.0168760 | − | 0.00974337i | 0.491538 | − | 0.870856i | \(-0.336435\pi\) |
−0.508414 | + | 0.861113i | \(0.669768\pi\) | |||||||
\(62\) | − | 62.4259i | − | 1.00687i | ||||||
\(63\) | 20.2279 | + | 5.64191i | 0.321078 | + | 0.0895542i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 15.3015 | − | 26.5030i | 0.235408 | − | 0.407738i | ||||
\(66\) | −12.7279 | + | 7.34847i | −0.192847 | + | 0.111340i | ||||
\(67\) | −2.19848 | − | 3.80789i | −0.0328132 | − | 0.0568341i | 0.849152 | − | 0.528148i | \(-0.177113\pi\) |
−0.881966 | + | 0.471314i | \(0.843780\pi\) | |||||||
\(68\) | 15.5147 | + | 8.95743i | 0.228158 | + | 0.131727i | ||||
\(69\) | − | 64.8754i | − | 0.940224i | ||||||
\(70\) | −9.94113 | − | 10.1461i | −0.142016 | − | 0.144945i | ||||
\(71\) | 137.397 | 1.93517 | 0.967584 | − | 0.252548i | \(-0.0812687\pi\) | ||||
0.967584 | + | 0.252548i | \(0.0812687\pi\) | |||||||
\(72\) | −4.24264 | + | 7.34847i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 68.3528 | − | 39.4635i | 0.936340 | − | 0.540596i | 0.0475288 | − | 0.998870i | \(-0.484865\pi\) |
0.888811 | + | 0.458274i | \(0.151532\pi\) | |||||||
\(74\) | −19.7782 | − | 34.2568i | −0.267273 | − | 0.462930i | ||||
\(75\) | −34.4117 | − | 19.8676i | −0.458823 | − | 0.264901i | ||||
\(76\) | 14.4508i | 0.190141i | ||||||||
\(77\) | 30.0000 | − | 29.3939i | 0.389610 | − | 0.381739i | ||||
\(78\) | 52.2426 | 0.669777 | ||||||||
\(79\) | −49.1690 | + | 85.1633i | −0.622393 | + | 1.07802i | 0.366646 | + | 0.930361i | \(0.380506\pi\) |
−0.989039 | + | 0.147656i | \(0.952827\pi\) | |||||||
\(80\) | 4.97056 | − | 2.86976i | 0.0621320 | − | 0.0358719i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 67.1543 | + | 38.7716i | 0.818955 | + | 0.472824i | ||||
\(83\) | − | 110.401i | − | 1.33013i | −0.746784 | − | 0.665067i | \(-0.768403\pi\) | ||
0.746784 | − | 0.665067i | \(-0.231597\pi\) | |||||||
\(84\) | 6.51472 | − | 23.3572i | 0.0775562 | − | 0.278062i | ||||
\(85\) | 12.8528 | 0.151210 | ||||||||
\(86\) | −1.05025 | + | 1.81909i | −0.0122122 | + | 0.0211522i | ||||
\(87\) | −50.9117 | + | 29.3939i | −0.585192 | + | 0.337861i | ||||
\(88\) | 8.48528 | + | 14.6969i | 0.0964237 | + | 0.167011i | ||||
\(89\) | −18.0000 | − | 10.3923i | −0.202247 | − | 0.116767i | 0.395456 | − | 0.918485i | \(-0.370587\pi\) |
−0.597703 | + | 0.801717i | \(0.703920\pi\) | |||||||
\(90\) | 6.08767i | 0.0676408i | ||||||||
\(91\) | −144.595 | + | 37.1670i | −1.58896 | + | 0.408428i | ||||
\(92\) | −74.9117 | −0.814257 | ||||||||
\(93\) | 38.2279 | − | 66.2127i | 0.411053 | − | 0.711965i | ||||
\(94\) | −52.6690 | + | 30.4085i | −0.560309 | + | 0.323495i | ||||
\(95\) | 5.18377 | + | 8.97855i | 0.0545660 | + | 0.0945110i | ||||
\(96\) | 8.48528 | + | 4.89898i | 0.0883883 | + | 0.0510310i | ||||
\(97\) | 10.9867i | 0.113264i | 0.998395 | + | 0.0566322i | \(0.0180362\pi\) | ||||
−0.998395 | + | 0.0566322i | \(0.981964\pi\) | |||||||
\(98\) | −1.41421 | + | 69.2820i | −0.0144308 | + | 0.706960i | ||||
\(99\) | −18.0000 | −0.181818 | ||||||||
\(100\) | −22.9411 | + | 39.7352i | −0.229411 | + | 0.397352i | ||||
\(101\) | −92.8234 | + | 53.5916i | −0.919043 | + | 0.530610i | −0.883330 | − | 0.468752i | \(-0.844704\pi\) |
−0.0357136 | + | 0.999362i | \(0.511370\pi\) | |||||||
\(102\) | 10.9706 | + | 19.0016i | 0.107555 | + | 0.186290i | ||||
\(103\) | 91.1102 | + | 52.6025i | 0.884565 | + | 0.510704i | 0.872161 | − | 0.489219i | \(-0.162718\pi\) |
0.0124040 | + | 0.999923i | \(0.496052\pi\) | |||||||
\(104\) | − | 60.3246i | − | 0.580044i | ||||||
\(105\) | −4.33095 | − | 16.8493i | −0.0412472 | − | 0.160469i | ||||
\(106\) | 120.853 | 1.14012 | ||||||||
\(107\) | −59.2721 | + | 102.662i | −0.553945 | + | 0.959460i | 0.444040 | + | 0.896007i | \(0.353545\pi\) |
−0.997985 | + | 0.0634534i | \(0.979789\pi\) | |||||||
\(108\) | −9.00000 | + | 5.19615i | −0.0833333 | + | 0.0481125i | ||||
\(109\) | −55.5294 | − | 96.1798i | −0.509444 | − | 0.882384i | −0.999940 | − | 0.0109400i | \(-0.996518\pi\) |
0.490496 | − | 0.871444i | \(-0.336816\pi\) | |||||||
\(110\) | 10.5442 | + | 6.08767i | 0.0958560 | + | 0.0553425i | ||||
\(111\) | − | 48.4464i | − | 0.436454i | ||||||
\(112\) | −26.9706 | − | 7.52255i | −0.240809 | − | 0.0671656i | ||||
\(113\) | 101.397 | 0.897318 | 0.448659 | − | 0.893703i | \(-0.351902\pi\) | ||||
0.448659 | + | 0.893703i | \(0.351902\pi\) | |||||||
\(114\) | −8.84924 | + | 15.3273i | −0.0776249 | + | 0.134450i | ||||
\(115\) | −46.5442 | + | 26.8723i | −0.404732 | + | 0.233672i | ||||
\(116\) | 33.9411 | + | 58.7878i | 0.292596 | + | 0.506791i | ||||
\(117\) | 55.4117 | + | 31.9920i | 0.473604 | + | 0.273435i | ||||
\(118\) | 58.2954i | 0.494029i | ||||||||
\(119\) | −43.8823 | − | 44.7871i | −0.368758 | − | 0.376362i | ||||
\(120\) | 7.02944 | 0.0585786 | ||||||||
\(121\) | 42.5000 | − | 73.6122i | 0.351240 | − | 0.608365i | ||||
\(122\) | −1.45584 | + | 0.840532i | −0.0119331 | + | 0.00688961i | ||||
\(123\) | 47.4853 | + | 82.2469i | 0.386059 | + | 0.668674i | ||||
\(124\) | −76.4558 | − | 44.1418i | −0.616579 | − | 0.355982i | ||||
\(125\) | 68.7897i | 0.550317i | ||||||||
\(126\) | 21.2132 | − | 20.7846i | 0.168359 | − | 0.164957i | ||||
\(127\) | 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 | ||||
\(129\) | −2.22792 | + | 1.28629i | −0.0172707 | + | 0.00997125i | ||||
\(130\) | −21.6396 | − | 37.4809i | −0.166459 | − | 0.288315i | ||||
\(131\) | −52.4558 | − | 30.2854i | −0.400426 | − | 0.231186i | 0.286242 | − | 0.958157i | \(-0.407594\pi\) |
−0.686668 | + | 0.726971i | \(0.740927\pi\) | |||||||
\(132\) | 20.7846i | 0.157459i | ||||||||
\(133\) | 13.5883 | − | 48.7181i | 0.102168 | − | 0.366302i | ||||
\(134\) | −6.21825 | −0.0464049 | ||||||||
\(135\) | −3.72792 | + | 6.45695i | −0.0276142 | + | 0.0478293i | ||||
\(136\) | 21.9411 | − | 12.6677i | 0.161332 | − | 0.0931450i | ||||
\(137\) | −33.5147 | − | 58.0492i | −0.244633 | − | 0.423717i | 0.717395 | − | 0.696666i | \(-0.245334\pi\) |
−0.962028 | + | 0.272949i | \(0.912001\pi\) | |||||||
\(138\) | −79.4558 | − | 45.8739i | −0.575767 | − | 0.332419i | ||||
\(139\) | − | 91.5525i | − | 0.658651i | −0.944216 | − | 0.329326i | \(-0.893179\pi\) | ||
0.944216 | − | 0.329326i | \(-0.106821\pi\) | |||||||
\(140\) | −19.4558 | + | 5.00095i | −0.138970 | + | 0.0357211i | ||||
\(141\) | −74.4853 | −0.528264 | ||||||||
\(142\) | 97.1543 | − | 168.276i | 0.684185 | − | 1.18504i | ||||
\(143\) | 110.823 | − | 63.9839i | 0.774989 | − | 0.447440i | ||||
\(144\) | 6.00000 | + | 10.3923i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 42.1766 | + | 24.3507i | 0.290873 | + | 0.167936i | ||||
\(146\) | − | 111.620i | − | 0.764518i | ||||||
\(147\) | −43.9264 | + | 72.6187i | −0.298819 | + | 0.494005i | ||||
\(148\) | −55.9411 | −0.377981 | ||||||||
\(149\) | −40.5442 | + | 70.2245i | −0.272108 | + | 0.471306i | −0.969402 | − | 0.245480i | \(-0.921054\pi\) |
0.697293 | + | 0.716786i | \(0.254388\pi\) | |||||||
\(150\) | −48.6655 | + | 28.0970i | −0.324437 | + | 0.187314i | ||||
\(151\) | 25.6030 | + | 44.3457i | 0.169556 | + | 0.293680i | 0.938264 | − | 0.345920i | \(-0.112433\pi\) |
−0.768708 | + | 0.639600i | \(0.779100\pi\) | |||||||
\(152\) | 17.6985 | + | 10.2182i | 0.116437 | + | 0.0672252i | ||||
\(153\) | 26.8723i | 0.175636i | ||||||||
\(154\) | −14.7868 | − | 57.5270i | −0.0960182 | − | 0.373552i | ||||
\(155\) | −63.3381 | −0.408633 | ||||||||
\(156\) | 36.9411 | − | 63.9839i | 0.236802 | − | 0.410153i | ||||
\(157\) | 162.000 | − | 93.5307i | 1.03185 | − | 0.595737i | 0.114334 | − | 0.993442i | \(-0.463527\pi\) |
0.917513 | + | 0.397705i | \(0.130193\pi\) | |||||||
\(158\) | 69.5355 | + | 120.439i | 0.440098 | + | 0.762273i | ||||
\(159\) | 128.184 | + | 74.0069i | 0.806187 | + | 0.465452i | ||||
\(160\) | − | 8.11689i | − | 0.0507306i | ||||||
\(161\) | 252.551 | + | 70.4409i | 1.56864 | + | 0.437521i | ||||
\(162\) | −12.7279 | −0.0785674 | ||||||||
\(163\) | −41.9706 | + | 72.6951i | −0.257488 | + | 0.445982i | −0.965568 | − | 0.260149i | \(-0.916228\pi\) |
0.708080 | + | 0.706132i | \(0.249561\pi\) | |||||||
\(164\) | 94.9706 | − | 54.8313i | 0.579089 | − | 0.334337i | ||||
\(165\) | 7.45584 | + | 12.9139i | 0.0451869 | + | 0.0782661i | ||||
\(166\) | −135.213 | − | 78.0654i | −0.814537 | − | 0.470273i | ||||
\(167\) | 127.620i | 0.764190i | 0.924123 | + | 0.382095i | \(0.124797\pi\) | ||||
−0.924123 | + | 0.382095i | \(0.875203\pi\) | |||||||
\(168\) | −24.0000 | − | 24.4949i | −0.142857 | − | 0.145803i | ||||
\(169\) | −285.882 | −1.69161 | ||||||||
\(170\) | 9.08831 | − | 15.7414i | 0.0534607 | − | 0.0925966i | ||||
\(171\) | −18.7721 | + | 10.8381i | −0.109778 | + | 0.0633805i | ||||
\(172\) | 1.48528 | + | 2.57258i | 0.00863536 | + | 0.0149569i | ||||
\(173\) | −123.816 | − | 71.4853i | −0.715701 | − | 0.413210i | 0.0974675 | − | 0.995239i | \(-0.468926\pi\) |
−0.813168 | + | 0.582029i | \(0.802259\pi\) | |||||||
\(174\) | 83.1384i | 0.477807i | ||||||||
\(175\) | 114.706 | − | 112.388i | 0.655461 | − | 0.642218i | ||||
\(176\) | 24.0000 | 0.136364 | ||||||||
\(177\) | −35.6985 | + | 61.8316i | −0.201686 | + | 0.349331i | ||||
\(178\) | −25.4558 | + | 14.6969i | −0.143010 | + | 0.0825671i | ||||
\(179\) | −84.6396 | − | 146.600i | −0.472847 | − | 0.818995i | 0.526670 | − | 0.850070i | \(-0.323440\pi\) |
−0.999517 | + | 0.0310748i | \(0.990107\pi\) | |||||||
\(180\) | 7.45584 | + | 4.30463i | 0.0414214 | + | 0.0239146i | ||||
\(181\) | 209.969i | 1.16005i | 0.814600 | + | 0.580024i | \(0.196957\pi\) | ||||
−0.814600 | + | 0.580024i | \(0.803043\pi\) | |||||||
\(182\) | −56.7244 | + | 203.374i | −0.311672 | + | 1.11744i | ||||
\(183\) | −2.05887 | −0.0112507 | ||||||||
\(184\) | −52.9706 | + | 91.7477i | −0.287883 | + | 0.498629i | ||||
\(185\) | −34.7574 | + | 20.0672i | −0.187878 | + | 0.108471i | ||||
\(186\) | −54.0624 | − | 93.6389i | −0.290658 | − | 0.503435i | ||||
\(187\) | 46.5442 | + | 26.8723i | 0.248899 | + | 0.143702i | ||||
\(188\) | 86.0082i | 0.457490i | ||||||||
\(189\) | 35.2279 | − | 9.05503i | 0.186391 | − | 0.0479102i | ||||
\(190\) | 14.6619 | 0.0771679 | ||||||||
\(191\) | −33.3015 | + | 57.6799i | −0.174353 | + | 0.301989i | −0.939937 | − | 0.341347i | \(-0.889117\pi\) |
0.765584 | + | 0.643336i | \(0.222450\pi\) | |||||||
\(192\) | 12.0000 | − | 6.92820i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | 4.89697 | + | 8.48180i | 0.0253729 | + | 0.0439472i | 0.878433 | − | 0.477865i | \(-0.158589\pi\) |
−0.853060 | + | 0.521813i | \(0.825256\pi\) | |||||||
\(194\) | 13.4558 | + | 7.76874i | 0.0693600 | + | 0.0400450i | ||||
\(195\) | − | 53.0060i | − | 0.271826i | ||||||
\(196\) | 83.8528 | + | 50.7218i | 0.427820 | + | 0.258785i | ||||
\(197\) | −267.161 | −1.35615 | −0.678075 | − | 0.734993i | \(-0.737185\pi\) | ||||
−0.678075 | + | 0.734993i | \(0.737185\pi\) | |||||||
\(198\) | −12.7279 | + | 22.0454i | −0.0642824 | + | 0.111340i | ||||
\(199\) | −113.397 | + | 65.4698i | −0.569834 | + | 0.328994i | −0.757083 | − | 0.653319i | \(-0.773376\pi\) |
0.187249 | + | 0.982312i | \(0.440043\pi\) | |||||||
\(200\) | 32.4437 | + | 56.1941i | 0.162218 | + | 0.280970i | ||||
\(201\) | −6.59545 | − | 3.80789i | −0.0328132 | − | 0.0189447i | ||||
\(202\) | 151.580i | 0.750396i | ||||||||
\(203\) | −59.1472 | − | 230.108i | −0.291365 | − | 1.13354i | ||||
\(204\) | 31.0294 | 0.152105 | ||||||||
\(205\) | 39.3381 | − | 68.1356i | 0.191893 | − | 0.332369i | ||||
\(206\) | 128.849 | − | 74.3911i | 0.625482 | − | 0.361122i | ||||
\(207\) | −56.1838 | − | 97.3131i | −0.271419 | − | 0.470112i | ||||
\(208\) | −73.8823 | − | 42.6559i | −0.355203 | − | 0.205077i | ||||
\(209\) | 43.3523i | 0.207427i | ||||||||
\(210\) | −23.6985 | − | 6.60991i | −0.112850 | − | 0.0314758i | ||||
\(211\) | −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 | ||||
\(213\) | 206.095 | − | 118.989i | 0.967584 | − | 0.558635i | ||||
\(214\) | 83.8234 | + | 145.186i | 0.391698 | + | 0.678441i | ||||
\(215\) | 1.84567 | + | 1.06560i | 0.00858452 | + | 0.00495627i | ||||
\(216\) | 14.6969i | 0.0680414i | ||||||||
\(217\) | 216.250 | + | 220.709i | 0.996543 | + | 1.01709i | ||||
\(218\) | −157.061 | −0.720463 | ||||||||
\(219\) | 68.3528 | − | 118.391i | 0.312113 | − | 0.540596i | ||||
\(220\) | 14.9117 | − | 8.60927i | 0.0677804 | − | 0.0391330i | ||||
\(221\) | −95.5219 | − | 165.449i | −0.432226 | − | 0.748637i | ||||
\(222\) | −59.3345 | − | 34.2568i | −0.267273 | − | 0.154310i | ||||
\(223\) | − | 228.631i | − | 1.02525i | −0.858613 | − | 0.512625i | \(-0.828673\pi\) | ||
0.858613 | − | 0.512625i | \(-0.171327\pi\) | |||||||
\(224\) | −28.2843 | + | 27.7128i | −0.126269 | + | 0.123718i | ||||
\(225\) | −68.8234 | −0.305882 | ||||||||
\(226\) | 71.6985 | − | 124.185i | 0.317250 | − | 0.549493i | ||||
\(227\) | 56.8234 | − | 32.8070i | 0.250323 | − | 0.144524i | −0.369589 | − | 0.929195i | \(-0.620502\pi\) |
0.619912 | + | 0.784671i | \(0.287168\pi\) | |||||||
\(228\) | 12.5147 | + | 21.6761i | 0.0548891 | + | 0.0950707i | ||||
\(229\) | 80.9558 | + | 46.7399i | 0.353519 | + | 0.204104i | 0.666234 | − | 0.745743i | \(-0.267905\pi\) |
−0.312715 | + | 0.949847i | \(0.601239\pi\) | |||||||
\(230\) | 76.0063i | 0.330462i | ||||||||
\(231\) | 19.5442 | − | 70.0716i | 0.0846067 | − | 0.303340i | ||||
\(232\) | 96.0000 | 0.413793 | ||||||||
\(233\) | 118.757 | − | 205.694i | 0.509688 | − | 0.882806i | −0.490249 | − | 0.871583i | \(-0.663094\pi\) |
0.999937 | − | 0.0112234i | \(-0.00357259\pi\) | |||||||
\(234\) | 78.3640 | − | 45.2435i | 0.334889 | − | 0.193348i | ||||
\(235\) | 30.8528 | + | 53.4386i | 0.131289 | + | 0.227398i | ||||
\(236\) | 71.3970 | + | 41.2211i | 0.302530 | + | 0.174666i | ||||
\(237\) | 170.327i | 0.718678i | ||||||||
\(238\) | −85.8823 | + | 22.0753i | −0.360850 | + | 0.0927533i | ||||
\(239\) | 366.853 | 1.53495 | 0.767475 | − | 0.641079i | \(-0.221513\pi\) | ||||
0.767475 | + | 0.641079i | \(0.221513\pi\) | |||||||
\(240\) | 4.97056 | − | 8.60927i | 0.0207107 | − | 0.0358719i | ||||
\(241\) | −364.617 | + | 210.512i | −1.51293 | + | 0.873493i | −0.513049 | + | 0.858359i | \(0.671484\pi\) |
−0.999885 | + | 0.0151343i | \(0.995182\pi\) | |||||||
\(242\) | −60.1041 | − | 104.103i | −0.248364 | − | 0.430179i | ||||
\(243\) | −13.5000 | − | 7.79423i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 2.37738i | 0.00974337i | ||||||||
\(245\) | 70.2944 | + | 1.43488i | 0.286916 | + | 0.00585664i | ||||
\(246\) | 134.309 | 0.545970 | ||||||||
\(247\) | 77.0513 | − | 133.457i | 0.311949 | − | 0.540311i | ||||
\(248\) | −108.125 | + | 62.4259i | −0.435987 | + | 0.251717i | ||||
\(249\) | −95.6102 | − | 165.602i | −0.383977 | − | 0.665067i | ||||
\(250\) | 84.2498 | + | 48.6416i | 0.336999 | + | 0.194567i | ||||
\(251\) | 146.621i | 0.584148i | 0.956396 | + | 0.292074i | \(0.0943454\pi\) | ||||
−0.956396 | + | 0.292074i | \(0.905655\pi\) | |||||||
\(252\) | −10.4558 | − | 40.6777i | −0.0414914 | − | 0.161419i | ||||
\(253\) | −224.735 | −0.888281 | ||||||||
\(254\) | 58.3883 | − | 101.132i | 0.229875 | − | 0.398156i | ||||
\(255\) | 19.2792 | − | 11.1309i | 0.0756048 | − | 0.0436504i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 21.7279 | + | 12.5446i | 0.0845444 | + | 0.0488118i | 0.541676 | − | 0.840587i | \(-0.317790\pi\) |
−0.457132 | + | 0.889399i | \(0.651123\pi\) | |||||||
\(258\) | 3.63818i | 0.0141015i | ||||||||
\(259\) | 188.595 | + | 52.6025i | 0.728168 | + | 0.203098i | ||||
\(260\) | −61.2061 | −0.235408 | ||||||||
\(261\) | −50.9117 | + | 88.1816i | −0.195064 | + | 0.337861i | ||||
\(262\) | −74.1838 | + | 42.8300i | −0.283144 | + | 0.163473i | ||||
\(263\) | 45.3381 | + | 78.5279i | 0.172388 | + | 0.298585i | 0.939254 | − | 0.343222i | \(-0.111518\pi\) |
−0.766866 | + | 0.641807i | \(0.778185\pi\) | |||||||
\(264\) | 25.4558 | + | 14.6969i | 0.0964237 | + | 0.0556702i | ||||
\(265\) | − | 122.619i | − | 0.462712i | ||||||
\(266\) | −50.0589 | − | 51.0911i | −0.188191 | − | 0.192072i | ||||
\(267\) | −36.0000 | −0.134831 | ||||||||
\(268\) | −4.39697 | + | 7.61577i | −0.0164066 | + | 0.0284171i | ||||
\(269\) | −59.2355 | + | 34.1996i | −0.220206 | + | 0.127136i | −0.606046 | − | 0.795430i | \(-0.707245\pi\) |
0.385839 | + | 0.922566i | \(0.373912\pi\) | |||||||
\(270\) | 5.27208 | + | 9.13151i | 0.0195262 | + | 0.0338204i | ||||
\(271\) | −106.971 | − | 61.7595i | −0.394725 | − | 0.227895i | 0.289480 | − | 0.957184i | \(-0.406518\pi\) |
−0.684206 | + | 0.729289i | \(0.739851\pi\) | |||||||
\(272\) | − | 35.8297i | − | 0.131727i | ||||||
\(273\) | −184.706 | + | 180.974i | −0.676577 | + | 0.662908i | ||||
\(274\) | −94.7939 | −0.345963 | ||||||||
\(275\) | −68.8234 | + | 119.206i | −0.250267 | + | 0.433475i | ||||
\(276\) | −112.368 | + | 64.8754i | −0.407129 | + | 0.235056i | ||||
\(277\) | 136.441 | + | 236.323i | 0.492567 | + | 0.853151i | 0.999963 | − | 0.00856145i | \(-0.00272523\pi\) |
−0.507396 | + | 0.861713i | \(0.669392\pi\) | |||||||
\(278\) | −112.128 | − | 64.7374i | −0.403340 | − | 0.232868i | ||||
\(279\) | − | 132.425i | − | 0.474643i | ||||||
\(280\) | −7.63247 | + | 27.3647i | −0.0272588 | + | 0.0977309i | ||||
\(281\) | 133.103 | 0.473675 | 0.236837 | − | 0.971549i | \(-0.423889\pi\) | ||||
0.236837 | + | 0.971549i | \(0.423889\pi\) | |||||||
\(282\) | −52.6690 | + | 91.2255i | −0.186770 | + | 0.323495i | ||||
\(283\) | −111.507 | + | 64.3787i | −0.394018 | + | 0.227486i | −0.683900 | − | 0.729576i | \(-0.739717\pi\) |
0.289882 | + | 0.957063i | \(0.406384\pi\) | |||||||
\(284\) | −137.397 | − | 237.979i | −0.483792 | − | 0.837953i | ||||
\(285\) | 15.5513 | + | 8.97855i | 0.0545660 | + | 0.0315037i | ||||
\(286\) | − | 180.974i | − | 0.632776i | ||||||
\(287\) | −371.735 | + | 95.5512i | −1.29524 | + | 0.332931i | ||||
\(288\) | 16.9706 | 0.0589256 | ||||||||
\(289\) | −104.382 | + | 180.795i | −0.361184 | + | 0.625589i | ||||
\(290\) | 59.6468 | − | 34.4371i | 0.205678 | − | 0.118749i | ||||
\(291\) | 9.51472 | + | 16.4800i | 0.0326966 | + | 0.0566322i | ||||
\(292\) | −136.706 | − | 78.9270i | −0.468170 | − | 0.270298i | ||||
\(293\) | 308.984i | 1.05455i | 0.849694 | + | 0.527276i | \(0.176787\pi\) | ||||
−0.849694 | + | 0.527276i | \(0.823213\pi\) | |||||||
\(294\) | 57.8787 | + | 105.148i | 0.196866 | + | 0.357646i | ||||
\(295\) | 59.1472 | 0.200499 | ||||||||
\(296\) | −39.5563 | + | 68.5136i | −0.133636 | + | 0.231465i | ||||
\(297\) | −27.0000 | + | 15.5885i | −0.0909091 | + | 0.0524864i | ||||
\(298\) | 57.3381 | + | 99.3125i | 0.192410 | + | 0.333263i | ||||
\(299\) | 691.831 | + | 399.429i | 2.31381 | + | 1.33588i | ||||
\(300\) | 79.4704i | 0.264901i | ||||||||
\(301\) | −2.58831 | − | 10.0696i | −0.00859904 | − | 0.0334539i | ||||
\(302\) | 72.4163 | 0.239789 | ||||||||
\(303\) | −92.8234 | + | 160.775i | −0.306348 | + | 0.530610i | ||||
\(304\) | 25.0294 | − | 14.4508i | 0.0823337 | − | 0.0475354i | ||||
\(305\) | 0.852814 | + | 1.47712i | 0.00279611 | + | 0.00484301i | ||||
\(306\) | 32.9117 | + | 19.0016i | 0.107555 | + | 0.0620966i | ||||
\(307\) | − | 606.090i | − | 1.97423i | −0.160003 | − | 0.987117i | \(-0.551150\pi\) | ||
0.160003 | − | 0.987117i | \(-0.448850\pi\) | |||||||
\(308\) | −80.9117 | − | 22.5676i | −0.262700 | − | 0.0732716i | ||||
\(309\) | 182.220 | 0.589710 | ||||||||
\(310\) | −44.7868 | + | 77.5730i | −0.144474 | + | 0.250236i | ||||
\(311\) | −176.044 | + | 101.639i | −0.566057 | + | 0.326813i | −0.755573 | − | 0.655064i | \(-0.772641\pi\) |
0.189516 | + | 0.981878i | \(0.439308\pi\) | |||||||
\(312\) | −52.2426 | − | 90.4869i | −0.167444 | − | 0.290022i | ||||
\(313\) | −351.294 | − | 202.820i | −1.12234 | − | 0.647986i | −0.180346 | − | 0.983603i | \(-0.557722\pi\) |
−0.941999 | + | 0.335617i | \(0.891055\pi\) | |||||||
\(314\) | − | 264.545i | − | 0.842500i | ||||||
\(315\) | −21.0883 | − | 21.5232i | −0.0669470 | − | 0.0683275i | ||||
\(316\) | 196.676 | 0.622393 | ||||||||
\(317\) | 13.0294 | − | 22.5676i | 0.0411023 | − | 0.0711913i | −0.844742 | − | 0.535173i | \(-0.820246\pi\) |
0.885845 | + | 0.463982i | \(0.153580\pi\) | |||||||
\(318\) | 181.279 | − | 104.662i | 0.570060 | − | 0.329125i | ||||
\(319\) | 101.823 | + | 176.363i | 0.319196 | + | 0.552863i | ||||
\(320\) | −9.94113 | − | 5.73951i | −0.0310660 | − | 0.0179360i | ||||
\(321\) | 205.325i | 0.639640i | ||||||||
\(322\) | 264.853 | − | 259.502i | 0.822524 | − | 0.805906i | ||||
\(323\) | 64.7208 | 0.200374 | ||||||||
\(324\) | −9.00000 | + | 15.5885i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 423.735 | − | 244.644i | 1.30380 | − | 0.752750i | ||||
\(326\) | 59.3553 | + | 102.806i | 0.182072 | + | 0.315357i | ||||
\(327\) | −166.588 | − | 96.1798i | −0.509444 | − | 0.294128i | ||||
\(328\) | − | 155.086i | − | 0.472824i | ||||||
\(329\) | 80.8751 | − | 289.961i | 0.245821 | − | 0.881341i | ||||
\(330\) | 21.0883 | 0.0639040 | ||||||||
\(331\) | 54.3162 | − | 94.0785i | 0.164097 | − | 0.284225i | −0.772237 | − | 0.635335i | \(-0.780862\pi\) |
0.936334 | + | 0.351110i | \(0.114196\pi\) | |||||||
\(332\) | −191.220 | + | 110.401i | −0.575965 | + | 0.332533i | ||||
\(333\) | −41.9558 | − | 72.6697i | −0.125994 | − | 0.218227i | ||||
\(334\) | 156.302 | + | 90.2407i | 0.467969 | + | 0.270182i | ||||
\(335\) | 6.30911i | 0.0188332i | ||||||||
\(336\) | −46.9706 | + | 12.0734i | −0.139793 | + | 0.0359326i | ||||
\(337\) | 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 | ||||
\(339\) | 152.095 | − | 87.8124i | 0.448659 | − | 0.259033i | ||||
\(340\) | −12.8528 | − | 22.2617i | −0.0378024 | − | 0.0654757i | ||||
\(341\) | −229.368 | − | 132.425i | −0.672632 | − | 0.388344i | ||||
\(342\) | 30.6547i | 0.0896336i | ||||||||
\(343\) | −235.000 | − | 249.848i | −0.685131 | − | 0.728420i | ||||
\(344\) | 4.20101 | 0.0122122 | ||||||||
\(345\) | −46.5442 | + | 80.6168i | −0.134911 | + | 0.233672i | ||||
\(346\) | −175.103 | + | 101.096i | −0.506077 | + | 0.292184i | ||||
\(347\) | −17.0955 | − | 29.6102i | −0.0492664 | − | 0.0853320i | 0.840341 | − | 0.542059i | \(-0.182355\pi\) |
−0.889607 | + | 0.456727i | \(0.849022\pi\) | |||||||
\(348\) | 101.823 | + | 58.7878i | 0.292596 | + | 0.168930i | ||||
\(349\) | − | 221.787i | − | 0.635493i | −0.948176 | − | 0.317746i | \(-0.897074\pi\) | ||
0.948176 | − | 0.317746i | \(-0.102926\pi\) | |||||||
\(350\) | −56.5376 | − | 219.956i | −0.161536 | − | 0.628444i | ||||
\(351\) | 110.823 | 0.315736 | ||||||||
\(352\) | 16.9706 | − | 29.3939i | 0.0482118 | − | 0.0835053i | ||||
\(353\) | 387.448 | − | 223.693i | 1.09759 | − | 0.633692i | 0.162000 | − | 0.986791i | \(-0.448206\pi\) |
0.935586 | + | 0.353099i | \(0.114872\pi\) | |||||||
\(354\) | 50.4853 | + | 87.4431i | 0.142614 | + | 0.247014i | ||||
\(355\) | −170.735 | − | 98.5739i | −0.480944 | − | 0.277673i | ||||
\(356\) | 41.5692i | 0.116767i | ||||||||
\(357\) | −104.610 | − | 29.1776i | −0.293026 | − | 0.0817299i | ||||
\(358\) | −239.397 | −0.668707 | ||||||||
\(359\) | −145.882 | + | 252.675i | −0.406357 | + | 0.703831i | −0.994478 | − | 0.104941i | \(-0.966534\pi\) |
0.588121 | + | 0.808773i | \(0.299868\pi\) | |||||||
\(360\) | 10.5442 | − | 6.08767i | 0.0292893 | − | 0.0169102i | ||||
\(361\) | −154.397 | − | 267.423i | −0.427692 | − | 0.740785i | ||||
\(362\) | 257.158 | + | 148.470i | 0.710381 | + | 0.410139i | ||||
\(363\) | − | 147.224i | − | 0.405577i | ||||||
\(364\) | 208.971 | + | 213.280i | 0.574095 | + | 0.585933i | ||||
\(365\) | −113.251 | −0.310276 | ||||||||
\(366\) | −1.45584 | + | 2.52160i | −0.00397772 | + | 0.00688961i | ||||
\(367\) | −363.169 | + | 209.676i | −0.989561 | + | 0.571324i | −0.905143 | − | 0.425107i | \(-0.860237\pi\) |
−0.0844183 | + | 0.996430i | \(0.526903\pi\) | |||||||
\(368\) | 74.9117 | + | 129.751i | 0.203564 | + | 0.352584i | ||||
\(369\) | 142.456 | + | 82.2469i | 0.386059 | + | 0.222891i | ||||
\(370\) | 56.7585i | 0.153401i | ||||||||
\(371\) | −427.279 | + | 418.646i | −1.15170 | + | 1.12843i | ||||
\(372\) | −152.912 | −0.411053 | ||||||||
\(373\) | −15.6909 | + | 27.1775i | −0.0420668 | + | 0.0728618i | −0.886292 | − | 0.463127i | \(-0.846728\pi\) |
0.844225 | + | 0.535988i | \(0.180061\pi\) | |||||||
\(374\) | 65.8234 | − | 38.0031i | 0.175998 | − | 0.101613i | ||||
\(375\) | 59.5736 | + | 103.184i | 0.158863 | + | 0.275159i | ||||
\(376\) | 105.338 | + | 60.8170i | 0.280155 | + | 0.161747i | ||||
\(377\) | − | 723.895i | − | 1.92015i | ||||||
\(378\) | 13.8198 | − | 49.5481i | 0.0365603 | − | 0.131080i | ||||
\(379\) | 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 | ||||
\(381\) | 123.860 | − | 71.5108i | 0.325093 | − | 0.187692i | ||||
\(382\) | 47.0955 | + | 81.5717i | 0.123287 | + | 0.213539i | ||||
\(383\) | −431.772 | − | 249.283i | −1.12734 | − | 0.650871i | −0.184076 | − | 0.982912i | \(-0.558929\pi\) |
−0.943265 | + | 0.332041i | \(0.892263\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | −58.3675 | + | 15.0029i | −0.151604 | + | 0.0389685i | ||||
\(386\) | 13.8507 | 0.0358827 | ||||||||
\(387\) | −2.22792 | + | 3.85887i | −0.00575690 | + | 0.00997125i | ||||
\(388\) | 19.0294 | − | 10.9867i | 0.0490449 | − | 0.0283161i | ||||
\(389\) | 324.213 | + | 561.554i | 0.833453 | + | 1.44358i | 0.895284 | + | 0.445496i | \(0.146973\pi\) |
−0.0618308 | + | 0.998087i | \(0.519694\pi\) | |||||||
\(390\) | −64.9188 | − | 37.4809i | −0.166459 | − | 0.0961049i | ||||
\(391\) | 335.508i | 0.858077i | ||||||||
\(392\) | 121.414 | − | 66.8325i | 0.309730 | − | 0.170491i | ||||
\(393\) | −104.912 | −0.266951 | ||||||||
\(394\) | −188.912 | + | 327.205i | −0.479471 | + | 0.830469i | ||||
\(395\) | 122.199 | − | 70.5516i | 0.309364 | − | 0.178612i | ||||
\(396\) | 18.0000 | + | 31.1769i | 0.0454545 | + | 0.0787296i | ||||
\(397\) | 65.6026 | + | 37.8757i | 0.165246 | + | 0.0954047i | 0.580342 | − | 0.814373i | \(-0.302919\pi\) |
−0.415096 | + | 0.909777i | \(0.636252\pi\) | |||||||
\(398\) | 185.176i | 0.465268i | ||||||||
\(399\) | −21.8087 | − | 84.8450i | −0.0546583 | − | 0.212644i | ||||
\(400\) | 91.7645 | 0.229411 | ||||||||
\(401\) | 282.125 | − | 488.655i | 0.703553 | − | 1.21859i | −0.263658 | − | 0.964616i | \(-0.584929\pi\) |
0.967211 | − | 0.253974i | \(-0.0817377\pi\) | |||||||
\(402\) | −9.32738 | + | 5.38517i | −0.0232024 | + | 0.0133959i | ||||
\(403\) | 470.727 | + | 815.324i | 1.16806 | + | 2.02314i | ||||
\(404\) | 185.647 | + | 107.183i | 0.459522 | + | 0.265305i | ||||
\(405\) | 12.9139i | 0.0318862i | ||||||||
\(406\) | −323.647 | − | 90.2706i | −0.797159 | − | 0.222341i | ||||
\(407\) | −167.823 | −0.412342 | ||||||||
\(408\) | 21.9411 | − | 38.0031i | 0.0537773 | − | 0.0931450i | ||||
\(409\) | −309.559 | + | 178.724i | −0.756868 | + | 0.436978i | −0.828170 | − | 0.560477i | \(-0.810618\pi\) |
0.0713023 | + | 0.997455i | \(0.477284\pi\) | |||||||
\(410\) | −55.6325 | − | 96.3583i | −0.135689 | − | 0.235020i | ||||
\(411\) | −100.544 | − | 58.0492i | −0.244633 | − | 0.141239i | ||||
\(412\) | − | 210.410i | − | 0.510704i | ||||||
\(413\) | −201.941 | − | 206.105i | −0.488962 | − | 0.499044i | ||||
\(414\) | −158.912 | −0.383845 | ||||||||
\(415\) | −79.2061 | + | 137.189i | −0.190858 | + | 0.330576i | ||||
\(416\) | −104.485 | + | 60.3246i | −0.251167 | + | 0.145011i | ||||
\(417\) | −79.2868 | − | 137.329i | −0.190136 | − | 0.329326i | ||||
\(418\) | 53.0955 | + | 30.6547i | 0.127023 | + | 0.0733365i | ||||
\(419\) | 502.175i | 1.19851i | 0.800559 | + | 0.599254i | \(0.204536\pi\) | ||||
−0.800559 | + | 0.599254i | \(0.795464\pi\) | |||||||
\(420\) | −24.8528 | + | 24.3507i | −0.0591734 | + | 0.0579778i | ||||
\(421\) | 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 | ||||
\(423\) | −111.728 | + | 64.5061i | −0.264132 | + | 0.152497i | ||||
\(424\) | −120.853 | − | 209.323i | −0.285030 | − | 0.493687i | ||||
\(425\) | 177.963 | + | 102.747i | 0.418735 | + | 0.241757i | ||||
\(426\) | − | 336.552i | − | 0.790029i | ||||||
\(427\) | 2.23550 | − | 8.01492i | 0.00523536 | − | 0.0187703i | ||||
\(428\) | 237.088 | 0.553945 | ||||||||
\(429\) | 110.823 | − | 191.952i | 0.258330 | − | 0.447440i | ||||
\(430\) | 2.61017 | − | 1.50698i | 0.00607017 | − | 0.00350461i | ||||
\(431\) | −251.860 | − | 436.234i | −0.584362 | − | 1.01214i | −0.994955 | − | 0.100326i | \(-0.968012\pi\) |
0.410593 | − | 0.911819i | \(-0.365322\pi\) | |||||||
\(432\) | 18.0000 | + | 10.3923i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | 837.548i | 1.93429i | 0.254224 | + | 0.967145i | \(0.418180\pi\) | ||||
−0.254224 | + | 0.967145i | \(0.581820\pi\) | |||||||
\(434\) | 423.224 | − | 108.786i | 0.975170 | − | 0.250659i | ||||
\(435\) | 84.3532 | 0.193916 | ||||||||
\(436\) | −111.059 | + | 192.360i | −0.254722 | + | 0.441192i | ||||
\(437\) | −234.375 | + | 135.316i | −0.536326 | + | 0.309648i | ||||
\(438\) | −96.6655 | − | 167.430i | −0.220697 | − | 0.382259i | ||||
\(439\) | −164.558 | − | 95.0079i | −0.374848 | − | 0.216419i | 0.300726 | − | 0.953711i | \(-0.402771\pi\) |
−0.675575 | + | 0.737292i | \(0.736104\pi\) | |||||||
\(440\) | − | 24.3507i | − | 0.0553425i | ||||||
\(441\) | −3.00000 | + | 146.969i | −0.00680272 | + | 0.333264i | ||||
\(442\) | −270.177 | −0.611259 | ||||||||
\(443\) | 84.7279 | − | 146.753i | 0.191259 | − | 0.331271i | −0.754408 | − | 0.656405i | \(-0.772076\pi\) |
0.945668 | + | 0.325134i | \(0.105409\pi\) | |||||||
\(444\) | −83.9117 | + | 48.4464i | −0.188990 | + | 0.109114i | ||||
\(445\) | 14.9117 | + | 25.8278i | 0.0335094 | + | 0.0580400i | ||||
\(446\) | −280.014 | − | 161.666i | −0.627835 | − | 0.362481i | ||||
\(447\) | 140.449i | 0.314204i | ||||||||
\(448\) | 13.9411 | + | 54.2369i | 0.0311186 | + | 0.121065i | ||||
\(449\) | 18.1035 | 0.0403195 | 0.0201598 | − | 0.999797i | \(-0.493583\pi\) | ||||
0.0201598 | + | 0.999797i | \(0.493583\pi\) | |||||||
\(450\) | −48.6655 | + | 84.2911i | −0.108146 | + | 0.187314i | ||||
\(451\) | 284.912 | − | 164.494i | 0.631733 | − | 0.364731i | ||||
\(452\) | −101.397 | − | 175.625i | −0.224330 | − | 0.388550i | ||||
\(453\) | 76.8091 | + | 44.3457i | 0.169556 | + | 0.0978935i | ||||
\(454\) | − | 92.7922i | − | 0.204388i | ||||||
\(455\) | 206.345 | + | 57.5532i | 0.453506 | + | 0.126491i | ||||
\(456\) | 35.3970 | 0.0776249 | ||||||||
\(457\) | 164.412 | − | 284.769i | 0.359763 | − | 0.623128i | −0.628158 | − | 0.778086i | \(-0.716191\pi\) |
0.987921 | + | 0.154958i | \(0.0495242\pi\) | |||||||
\(458\) | 114.489 | − | 66.1002i | 0.249976 | − | 0.144324i | ||||
\(459\) | 23.2721 | + | 40.3084i | 0.0507017 | + | 0.0878179i | ||||
\(460\) | 93.0883 | + | 53.7446i | 0.202366 | + | 0.116836i | ||||
\(461\) | − | 794.331i | − | 1.72306i | −0.507706 | − | 0.861530i | \(-0.669506\pi\) | ||
0.507706 | − | 0.861530i | \(-0.330494\pi\) | |||||||
\(462\) | −72.0000 | − | 73.4847i | −0.155844 | − | 0.159058i | ||||
\(463\) | −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 | ||||
\(465\) | −95.0071 | + | 54.8524i | −0.204316 | + | 0.117962i | ||||
\(466\) | −167.948 | − | 290.895i | −0.360404 | − | 0.624238i | ||||
\(467\) | −2.44870 | − | 1.41376i | −0.00524347 | − | 0.00302732i | 0.497376 | − | 0.867535i | \(-0.334297\pi\) |
−0.502619 | + | 0.864508i | \(0.667630\pi\) | |||||||
\(468\) | − | 127.968i | − | 0.273435i | ||||||
\(469\) | 21.9848 | − | 21.5407i | 0.0468760 | − | 0.0459289i | ||||
\(470\) | 87.2649 | 0.185670 | ||||||||
\(471\) | 162.000 | − | 280.592i | 0.343949 | − | 0.595737i | ||||
\(472\) | 100.971 | − | 58.2954i | 0.213921 | − | 0.123507i | ||||
\(473\) | 4.45584 | + | 7.71775i | 0.00942039 | + | 0.0163166i | ||||
\(474\) | 208.607 | + | 120.439i | 0.440098 | + | 0.254091i | ||||
\(475\) | 165.758i | 0.348965i | ||||||||
\(476\) | −33.6913 | + | 120.793i | −0.0707801 | + | 0.253768i | ||||
\(477\) | 256.368 | 0.537458 | ||||||||
\(478\) | 259.404 | − | 449.301i | 0.542686 | − | 0.939960i | ||||
\(479\) | 328.669 | − | 189.757i | 0.686157 | − | 0.396153i | −0.116014 | − | 0.993248i | \(-0.537012\pi\) |
0.802171 | + | 0.597095i | \(0.203678\pi\) | |||||||
\(480\) | −7.02944 | − | 12.1753i | −0.0146447 | − | 0.0253653i | ||||
\(481\) | 516.632 | + | 298.278i | 1.07408 | + | 0.620120i | ||||
\(482\) | 595.418i | 1.23531i | ||||||||
\(483\) | 439.831 | − | 113.055i | 0.910622 | − | 0.234067i | ||||
\(484\) | −170.000 | −0.351240 | ||||||||
\(485\) | 7.88225 | − | 13.6525i | 0.0162521 | − | 0.0281494i | ||||
\(486\) | −19.0919 | + | 11.0227i | −0.0392837 | + | 0.0226805i | ||||
\(487\) | −287.757 | − | 498.410i | −0.590877 | − | 1.02343i | −0.994115 | − | 0.108333i | \(-0.965449\pi\) |
0.403238 | − | 0.915095i | \(-0.367885\pi\) | |||||||
\(488\) | 2.91169 | + | 1.68106i | 0.00596657 | + | 0.00344480i | ||||
\(489\) | 145.390i | 0.297322i | ||||||||
\(490\) | 51.4630 | − | 85.0781i | 0.105027 | − | 0.173629i | ||||
\(491\) | 238.441 | 0.485623 | 0.242811 | − | 0.970074i | \(-0.421930\pi\) | ||||
0.242811 | + | 0.970074i | \(0.421930\pi\) | |||||||
\(492\) | 94.9706 | − | 164.494i | 0.193030 | − | 0.334337i | ||||
\(493\) | 263.294 | − | 152.013i | 0.534064 | − | 0.308342i | ||||
\(494\) | −108.967 | − | 188.736i | −0.220581 | − | 0.382057i | ||||
\(495\) | 22.3675 | + | 12.9139i | 0.0451869 | + | 0.0260887i | ||||
\(496\) | 176.567i | 0.355982i | ||||||||
\(497\) | 239.434 | + | 931.499i | 0.481758 | + | 1.87424i | ||||
\(498\) | −270.426 | −0.543025 | ||||||||
\(499\) | 143.287 | − | 248.180i | 0.287148 | − | 0.497355i | −0.685980 | − | 0.727620i | \(-0.740626\pi\) |
0.973128 | + | 0.230266i | \(0.0739595\pi\) | |||||||
\(500\) | 119.147 | − | 68.7897i | 0.238294 | − | 0.137579i | ||||
\(501\) | 110.522 | + | 191.429i | 0.220603 | + | 0.382095i | ||||
\(502\) | 179.574 | + | 103.677i | 0.357716 | + | 0.206528i | ||||
\(503\) | 25.4374i | 0.0505714i | 0.999680 | + | 0.0252857i | \(0.00804954\pi\) | ||||
−0.999680 | + | 0.0252857i | \(0.991950\pi\) | |||||||
\(504\) | −57.2132 | − | 15.9577i | −0.113518 | − | 0.0316622i | ||||
\(505\) | 153.795 | 0.304544 | ||||||||
\(506\) | −158.912 | + | 275.243i | −0.314055 | + | 0.543959i | ||||
\(507\) | −428.823 | + | 247.581i | −0.845805 | + | 0.488326i | ||||
\(508\) | −82.5736 | − | 143.022i | −0.162546 | − | 0.281539i | ||||
\(509\) | −697.889 | − | 402.926i | −1.37110 | − | 0.791603i | −0.380031 | − | 0.924974i | \(-0.624087\pi\) |
−0.991066 | + | 0.133370i | \(0.957420\pi\) | |||||||
\(510\) | − | 31.4828i | − | 0.0617310i | ||||||
\(511\) | 386.662 | + | 394.635i | 0.756677 | + | 0.772280i | ||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | −18.7721 | + | 32.5142i | −0.0365927 | + | 0.0633805i | ||||
\(514\) | 30.7279 | − | 17.7408i | 0.0597819 | − | 0.0345151i | ||||
\(515\) | −75.4781 | − | 130.732i | −0.146559 | − | 0.253848i | ||||
\(516\) | 4.45584 | + | 2.57258i | 0.00863536 | + | 0.00498563i | ||||
\(517\) | 258.025i | 0.499080i | ||||||||
\(518\) | 197.782 | − | 193.786i | 0.381818 | − | 0.374104i | ||||
\(519\) | −247.632 | −0.477134 | ||||||||
\(520\) | −43.2792 | + | 74.9618i | −0.0832293 | + | 0.144157i | ||||
\(521\) | −661.706 | + | 382.036i | −1.27007 | + | 0.733274i | −0.975001 | − | 0.222202i | \(-0.928676\pi\) |
−0.295068 | + | 0.955476i | \(0.595342\pi\) | |||||||
\(522\) | 72.0000 | + | 124.708i | 0.137931 | + | 0.238904i | ||||
\(523\) | −153.096 | − | 88.3900i | −0.292726 | − | 0.169006i | 0.346444 | − | 0.938071i | \(-0.387389\pi\) |
−0.639171 | + | 0.769065i | \(0.720722\pi\) | |||||||
\(524\) | 121.142i | 0.231186i | ||||||||
\(525\) | 74.7275 | − | 267.920i | 0.142338 | − | 0.510324i | ||||
\(526\) | 128.235 | 0.243794 | ||||||||
\(527\) | −197.698 | + | 342.424i | −0.375139 | + | 0.649761i | ||||
\(528\) | 36.0000 | − | 20.7846i | 0.0681818 | − | 0.0393648i | ||||
\(529\) | −436.970 | − | 756.854i | −0.826030 | − | 1.43073i | ||||
\(530\) | −150.177 | − | 86.7045i | −0.283352 | − | 0.163593i | ||||
\(531\) | 123.663i | 0.232887i | ||||||||
\(532\) | −97.9706 | + | 25.1825i | −0.184155 | + | 0.0473355i | ||||
\(533\) | −1169.44 | −2.19407 | ||||||||
\(534\) | −25.4558 | + | 44.0908i | −0.0476701 | + | 0.0825671i | ||||
\(535\) | 147.308 | − | 85.0482i | 0.275342 | − | 0.158969i | ||||
\(536\) | 6.21825 | + | 10.7703i | 0.0116012 | + | 0.0200939i | ||||
\(537\) | −253.919 | − | 146.600i | −0.472847 | − | 0.272998i | ||||
\(538\) | 96.7312i | 0.179798i | ||||||||
\(539\) | 251.558 | + | 152.166i | 0.466713 | + | 0.282311i | ||||
\(540\) | 14.9117 | 0.0276142 | ||||||||
\(541\) | −8.58831 | + | 14.8754i | −0.0158749 | + | 0.0274961i | −0.873854 | − | 0.486189i | \(-0.838387\pi\) |
0.857979 | + | 0.513685i | \(0.171720\pi\) | |||||||
\(542\) | −151.279 | + | 87.3411i | −0.279113 | + | 0.161146i | ||||
\(543\) | 181.838 | + | 314.953i | 0.334877 | + | 0.580024i | ||||
\(544\) | −43.8823 | − | 25.3354i | −0.0806659 | − | 0.0465725i | ||||
\(545\) | 159.356i | 0.292396i | ||||||||
\(546\) | 91.0402 | + | 354.185i | 0.166740 | + | 0.648691i | ||||
\(547\) | 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 | ||||
\(549\) | −3.08831 | + | 1.78304i | −0.00562534 | + | 0.00324779i | ||||
\(550\) | 97.3310 | + | 168.582i | 0.176965 | + | 0.306513i | ||||
\(551\) | 212.382 | + | 122.619i | 0.385448 | + | 0.222538i | ||||
\(552\) | 183.495i | 0.332419i | ||||||||
\(553\) | −663.058 | − | 184.938i | −1.19902 | − | 0.334427i | ||||
\(554\) | 385.914 | 0.696595 | ||||||||
\(555\) | −34.7574 | + | 60.2015i | −0.0626259 | + | 0.108471i | ||||
\(556\) | −158.574 | + | 91.5525i | −0.285204 | + | 0.164663i | ||||
\(557\) | 440.823 | + | 763.528i | 0.791424 | + | 1.37079i | 0.925085 | + | 0.379760i | \(0.123993\pi\) |
−0.133661 | + | 0.991027i | \(0.542673\pi\) | |||||||
\(558\) | −162.187 | − | 93.6389i | −0.290658 | − | 0.167812i | ||||
\(559\) | − | 31.6780i | − | 0.0566691i | ||||||
\(560\) | 28.1177 | + | 28.6976i | 0.0502103 | + | 0.0512456i | ||||
\(561\) | 93.0883 | 0.165933 | ||||||||
\(562\) | 94.1177 | − | 163.017i | 0.167469 | − | 0.290065i | ||||
\(563\) | 664.301 | − | 383.534i | 1.17993 | − | 0.681233i | 0.223932 | − | 0.974605i | \(-0.428111\pi\) |
0.955998 | + | 0.293372i | \(0.0947774\pi\) | |||||||
\(564\) | 74.4853 | + | 129.012i | 0.132066 | + | 0.228745i | ||||
\(565\) | −126.000 | − | 72.7461i | −0.223009 | − | 0.128754i | ||||
\(566\) | 182.090i | 0.321714i | ||||||||
\(567\) | 45.0000 | − | 44.0908i | 0.0793651 | − | 0.0777616i | ||||
\(568\) | −388.617 | −0.684185 | ||||||||
\(569\) | 14.6468 | − | 25.3689i | 0.0257412 | − | 0.0445851i | −0.852868 | − | 0.522127i | \(-0.825139\pi\) |
0.878609 | + | 0.477542i | \(0.158472\pi\) | |||||||
\(570\) | 21.9929 | − | 12.6976i | 0.0385840 | − | 0.0222765i | ||||
\(571\) | −482.521 | − | 835.752i | −0.845046 | − | 1.46366i | −0.885581 | − | 0.464485i | \(-0.846239\pi\) |
0.0405347 | − | 0.999178i | \(-0.487094\pi\) | |||||||
\(572\) | −221.647 | − | 127.968i | −0.387494 | − | 0.223720i | ||||
\(573\) | 115.360i | 0.201326i | ||||||||
\(574\) | −145.831 | + | 522.846i | −0.254060 | + | 0.910881i | ||||
\(575\) | −859.279 | −1.49440 | ||||||||
\(576\) | 12.0000 | − | 20.7846i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 227.883 | − | 131.568i | 0.394944 | − | 0.228021i | −0.289356 | − | 0.957222i | \(-0.593441\pi\) |
0.684300 | + | 0.729201i | \(0.260108\pi\) | |||||||
\(578\) | 147.619 | + | 255.683i | 0.255396 | + | 0.442359i | ||||
\(579\) | 14.6909 | + | 8.48180i | 0.0253729 | + | 0.0146491i | ||||
\(580\) | − | 97.4027i | − | 0.167936i | ||||||
\(581\) | 748.477 | − | 192.389i | 1.28826 | − | 0.331135i | ||||
\(582\) | 26.9117 | 0.0462400 | ||||||||
\(583\) | 256.368 | − | 444.042i | 0.439738 | − | 0.761649i | ||||
\(584\) | −193.331 | + | 111.620i | −0.331046 | + | 0.191130i | ||||
\(585\) | −45.9045 | − | 79.5090i | −0.0784693 | − | 0.135913i | ||||
\(586\) | 378.426 | + | 218.485i | 0.645779 | + | 0.372841i | ||||
\(587\) | − | 436.477i | − | 0.743572i | −0.928318 | − | 0.371786i | \(-0.878746\pi\) | ||
0.928318 | − | 0.371786i | \(-0.121254\pi\) | |||||||
\(588\) | 169.706 | + | 3.46410i | 0.288615 | + | 0.00589133i | ||||
\(589\) | −318.941 | −0.541496 | ||||||||
\(590\) | 41.8234 | − | 72.4402i | 0.0708871 | − | 0.122780i | ||||
\(591\) | −400.742 | + | 231.369i | −0.678075 | + | 0.391487i | ||||
\(592\) | 55.9411 | + | 96.8929i | 0.0944951 | + | 0.163670i | ||||
\(593\) | 603.603 | + | 348.490i | 1.01788 | + | 0.587673i | 0.913489 | − | 0.406863i | \(-0.133377\pi\) |
0.104391 | + | 0.994536i | \(0.466711\pi\) | |||||||
\(594\) | 44.0908i | 0.0742270i | ||||||||
\(595\) | 22.3978 | + | 87.1372i | 0.0376434 | + | 0.146449i | ||||
\(596\) | 162.177 | 0.272108 | ||||||||
\(597\) | −113.397 | + | 196.409i | −0.189945 | + | 0.328994i | ||||
\(598\) | 978.396 | − | 564.877i | 1.63611 | − | 0.944611i | ||||
\(599\) | −199.206 | − | 345.035i | −0.332564 | − | 0.576018i | 0.650450 | − | 0.759549i | \(-0.274581\pi\) |
−0.983014 | + | 0.183531i | \(0.941247\pi\) | |||||||
\(600\) | 97.3310 | + | 56.1941i | 0.162218 | + | 0.0936568i | ||||
\(601\) | − | 36.1691i | − | 0.0601816i | −0.999547 | − | 0.0300908i | \(-0.990420\pi\) | ||
0.999547 | − | 0.0300908i | \(-0.00957964\pi\) | |||||||
\(602\) | −14.1630 | − | 3.95029i | −0.0235265 | − | 0.00656194i | ||||
\(603\) | −13.1909 | −0.0218755 | ||||||||
\(604\) | 51.2061 | − | 88.6915i | 0.0847782 | − | 0.146840i | ||||
\(605\) | −105.624 | + | 60.9823i | −0.174586 | + | 0.100797i | ||||
\(606\) | 131.272 | + | 227.370i | 0.216621 | + | 0.375198i | ||||
\(607\) | 27.3457 | + | 15.7880i | 0.0450505 | + | 0.0260099i | 0.522356 | − | 0.852727i | \(-0.325053\pi\) |
−0.477306 | + | 0.878737i | \(0.658387\pi\) | |||||||
\(608\) | − | 40.8729i | − | 0.0672252i | ||||||
\(609\) | −288.000 | − | 293.939i | −0.472906 | − | 0.482658i | ||||
\(610\) | 2.41212 | 0.00395430 | ||||||||
\(611\) | 458.595 | − | 794.310i | 0.750565 | − | 1.30002i | ||||
\(612\) | 46.5442 | − | 26.8723i | 0.0760525 | − | 0.0439090i | ||||
\(613\) | 204.632 | + | 354.434i | 0.333821 | + | 0.578195i | 0.983258 | − | 0.182220i | \(-0.0583285\pi\) |
−0.649436 | + | 0.760416i | \(0.724995\pi\) | |||||||
\(614\) | −742.305 | − | 428.570i | −1.20897 | − | 0.697997i | ||||
\(615\) | − | 136.271i | − | 0.221579i | ||||||
\(616\) | −84.8528 | + | 83.1384i | −0.137748 | + | 0.134965i | ||||
\(617\) | 1227.38 | 1.98927 | 0.994636 | − | 0.103436i | \(-0.0329837\pi\) | ||||
0.994636 | + | 0.103436i | \(0.0329837\pi\) | |||||||
\(618\) | 128.849 | − | 223.173i | 0.208494 | − | 0.361122i | ||||
\(619\) | 412.022 | − | 237.881i | 0.665625 | − | 0.384299i | −0.128792 | − | 0.991672i | \(-0.541110\pi\) |
0.794417 | + | 0.607373i | \(0.207777\pi\) | |||||||
\(620\) | 63.3381 | + | 109.705i | 0.102158 | + | 0.176943i | ||||
\(621\) | −168.551 | − | 97.3131i | −0.271419 | − | 0.156704i | ||||
\(622\) | 287.478i | 0.462184i | ||||||||
\(623\) | 39.0883 | − | 140.143i | 0.0627421 | − | 0.224949i | ||||
\(624\) | −147.765 | −0.236802 | ||||||||
\(625\) | −237.412 | + | 411.209i | −0.379859 | + | 0.657935i | ||||
\(626\) | −496.805 | + | 286.830i | −0.793618 | + | 0.458195i | ||||
\(627\) | 37.5442 | + | 65.0284i | 0.0598790 | + | 0.103714i | ||||
\(628\) | −324.000 | − | 187.061i | −0.515924 | − | 0.297869i | ||||
\(629\) | 250.544i | 0.398322i | ||||||||
\(630\) | −41.2721 | + | 10.6086i | −0.0655112 | + | 0.0168391i | ||||
\(631\) | −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 | ||||
\(633\) | −34.6325 | + | 19.9951i | −0.0547116 | + | 0.0315878i | ||||
\(634\) | −18.4264 | − | 31.9155i | −0.0290637 | − | 0.0503399i | ||||
\(635\) | −102.609 | − | 59.2415i | −0.161589 | − | 0.0932937i | ||||
\(636\) | − | 296.028i | − | 0.465452i | ||||||
\(637\) | −503.956 | − | 915.533i | −0.791139 | − | 1.43726i | ||||
\(638\) | 288.000 | 0.451411 | ||||||||
\(639\) | 206.095 | − | 356.968i | 0.322528 | − | 0.558635i | ||||
\(640\) | −14.0589 | + | 8.11689i | −0.0219670 | + | 0.0126826i | ||||
\(641\) | 114.551 | + | 198.409i | 0.178707 | + | 0.309530i | 0.941438 | − | 0.337186i | \(-0.109475\pi\) |
−0.762731 | + | 0.646716i | \(0.776142\pi\) | |||||||
\(642\) | 251.470 | + | 145.186i | 0.391698 | + | 0.226147i | ||||
\(643\) | 854.640i | 1.32914i | 0.747224 | + | 0.664572i | \(0.231386\pi\) | ||||
−0.747224 | + | 0.664572i | \(0.768614\pi\) | |||||||
\(644\) | −130.544 | − | 507.873i | −0.202708 | − | 0.788622i | ||||
\(645\) | 3.69134 | 0.00572301 | ||||||||
\(646\) | 45.7645 | − | 79.2664i | 0.0708429 | − | 0.122703i | ||||
\(647\) | 868.632 | − | 501.505i | 1.34255 | − | 0.775124i | 0.355372 | − | 0.934725i | \(-0.384354\pi\) |
0.987182 | + | 0.159601i | \(0.0510207\pi\) | |||||||
\(648\) | 12.7279 | + | 22.0454i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | 214.191 | + | 123.663i | 0.330032 | + | 0.190544i | ||||
\(650\) | − | 691.957i | − | 1.06455i | ||||||
\(651\) | 515.514 | + | 143.786i | 0.791881 | + | 0.220869i | ||||
\(652\) | 167.882 | 0.257488 | ||||||||
\(653\) | −635.382 | + | 1100.51i | −0.973020 | + | 1.68532i | −0.286698 | + | 0.958021i | \(0.592558\pi\) |
−0.686321 | + | 0.727299i | \(0.740776\pi\) | |||||||
\(654\) | −235.591 | + | 136.019i | −0.360232 | + | 0.207980i | ||||
\(655\) | 43.4558 | + | 75.2677i | 0.0663448 | + | 0.114913i | ||||
\(656\) | −189.941 | − | 109.663i | −0.289544 | − | 0.167169i | ||||
\(657\) | − | 236.781i | − | 0.360397i | ||||||
\(658\) | −297.941 | − | 304.085i | −0.452798 | − | 0.462135i | ||||
\(659\) | −783.308 | −1.18863 | −0.594315 | − | 0.804232i | \(-0.702577\pi\) | ||||
−0.594315 | + | 0.804232i | \(0.702577\pi\) | |||||||
\(660\) | 14.9117 | − | 25.8278i | 0.0225935 | − | 0.0391330i | ||||
\(661\) | 72.5589 | − | 41.8919i | 0.109771 | − | 0.0633765i | −0.444109 | − | 0.895973i | \(-0.646480\pi\) |
0.553881 | + | 0.832596i | \(0.313146\pi\) | |||||||
\(662\) | −76.8148 | − | 133.047i | −0.116034 | − | 0.200977i | ||||
\(663\) | −286.566 | − | 165.449i | −0.432226 | − | 0.249546i | ||||
\(664\) | 312.262i | 0.470273i | ||||||||
\(665\) | −51.8377 | + | 50.7903i | −0.0779514 | + | 0.0763764i | ||||
\(666\) | −118.669 | −0.178182 | ||||||||
\(667\) | −635.647 | + | 1100.97i | −0.952994 | + | 1.65063i | ||||
\(668\) | 221.044 | − | 127.620i | 0.330904 | − | 0.191047i | ||||
\(669\) | −198.000 | − | 342.946i | −0.295964 | − | 0.512625i | ||||
\(670\) | 7.72706 | + | 4.46122i | 0.0115329 | + | 0.00665853i | ||||
\(671\) | 7.13215i | 0.0106291i | ||||||||
\(672\) | −18.4264 | + | 66.0641i | −0.0274202 | + | 0.0983097i | ||||
\(673\) | 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 | ||||
\(675\) | −103.235 | + | 59.6028i | −0.152941 | + | 0.0883004i | ||||
\(676\) | 285.882 | + | 495.163i | 0.422903 | + | 0.732489i | ||||
\(677\) | 685.279 | + | 395.646i | 1.01223 | + | 0.584411i | 0.911844 | − | 0.410538i | \(-0.134659\pi\) |
0.100386 | + | 0.994949i | \(0.467992\pi\) | |||||||
\(678\) | − | 248.371i | − | 0.366329i | ||||||
\(679\) | −74.4853 | + | 19.1458i | −0.109698 | + | 0.0281970i | ||||
\(680\) | −36.3532 | −0.0534607 | ||||||||
\(681\) | 56.8234 | − | 98.4210i | 0.0834411 | − | 0.144524i | ||||
\(682\) | −324.375 | + | 187.278i | −0.475623 | + | 0.274601i | ||||
\(683\) | 164.080 | + | 284.195i | 0.240235 | + | 0.416099i | 0.960781 | − | 0.277308i | \(-0.0894423\pi\) |
−0.720546 | + | 0.693407i | \(0.756109\pi\) | |||||||
\(684\) | 37.5442 | + | 21.6761i | 0.0548891 | + | 0.0316902i | ||||
\(685\) | 96.1791i | 0.140407i | ||||||||
\(686\) | −472.170 | + | 111.146i | −0.688295 | + | 0.162020i | ||||
\(687\) | 161.912 | 0.235679 | ||||||||
\(688\) | 2.97056 | − | 5.14517i | 0.00431768 | − | 0.00747844i | ||||
\(689\) | −1578.42 | + | 911.300i | −2.29088 | + | 1.32264i | ||||
\(690\) | 65.8234 | + | 114.009i | 0.0953962 | + | 0.165231i | ||||
\(691\) | 875.182 | + | 505.287i | 1.26654 | + | 0.731240i | 0.974333 | − | 0.225113i | \(-0.0722753\pi\) |
0.292212 | + | 0.956353i | \(0.405609\pi\) | |||||||
\(692\) | 285.941i | 0.413210i | ||||||||
\(693\) | −31.3675 | − | 122.033i | −0.0452634 | − | 0.176094i | ||||
\(694\) | −48.3532 | −0.0696733 | ||||||||
\(695\) | −65.6833 | + | 113.767i | −0.0945084 | + | 0.163693i | ||||
\(696\) | 144.000 | − | 83.1384i | 0.206897 | − | 0.119452i | ||||
\(697\) | −245.574 | − | 425.346i | −0.352329 | − | 0.610252i | ||||
\(698\) | −271.632 | − | 156.827i | −0.389158 | − | 0.224681i | ||||
\(699\) | − | 411.388i | − | 0.588537i | ||||||
\(700\) | −309.368 | − | 86.2879i | −0.441954 | − | 0.123268i | ||||
\(701\) | −0.103464 | −0.000147594 | −7.37972e−5 | − | 1.00000i | \(-0.500023\pi\) | ||||
−7.37972e−5 | 1.00000i | \(0.500023\pi\) | ||||||||
\(702\) | 78.3640 | − | 135.730i | 0.111630 | − | 0.193348i | ||||
\(703\) | −175.022 | + | 101.049i | −0.248964 | + | 0.143740i | ||||
\(704\) | −24.0000 | − | 41.5692i | −0.0340909 | − | 0.0590472i | ||||
\(705\) | 92.5584 | + | 53.4386i | 0.131289 | + | 0.0757995i | ||||
\(706\) | − | 632.700i | − | 0.896175i | ||||||
\(707\) | −525.088 | − | 535.916i | −0.742699 | − | 0.758014i | ||||
\(708\) | 142.794 | 0.201686 | ||||||||
\(709\) | −602.588 | + | 1043.71i | −0.849912 | + | 1.47209i | 0.0313734 | + | 0.999508i | \(0.490012\pi\) |
−0.881286 | + | 0.472584i | \(0.843321\pi\) | |||||||
\(710\) | −241.456 | + | 139.405i | −0.340079 | + | 0.196345i | ||||
\(711\) | 147.507 | + | 255.490i | 0.207464 | + | 0.359339i | ||||
\(712\) | 50.9117 | + | 29.3939i | 0.0715052 | + | 0.0412835i | ||||
\(713\) | − | 1653.37i | − | 2.31889i | ||||||
\(714\) | −109.706 | + | 107.489i | −0.153649 | + | 0.150545i | ||||
\(715\) | −183.618 | −0.256809 | ||||||||
\(716\) | −169.279 | + | 293.200i | −0.236423 | + | 0.409498i | ||||
\(717\) | 550.279 | − | 317.704i | 0.767475 | − | 0.443102i | ||||
\(718\) | 206.309 | + | 357.337i | 0.287338 | + | 0.497684i | ||||
\(719\) | 850.925 | + | 491.282i | 1.18348 | + | 0.683285i | 0.956818 | − | 0.290688i | \(-0.0938840\pi\) |
0.226666 | + | 0.973973i | \(0.427217\pi\) | |||||||
\(720\) | − | 17.2185i | − | 0.0239146i | ||||||
\(721\) | −197.852 | + | 709.359i | −0.274414 | + | 0.983855i | ||||
\(722\) | −436.701 | −0.604848 | ||||||||
\(723\) | −364.617 | + | 631.536i | −0.504312 | + | 0.873493i | ||||
\(724\) | 363.676 | − | 209.969i | 0.502315 | − | 0.290012i | ||||
\(725\) | 389.324 | + | 674.329i | 0.536998 | + | 0.930108i | ||||
\(726\) | −180.312 | − | 104.103i | −0.248364 | − | 0.143393i | ||||
\(727\) | 630.440i | 0.867181i | 0.901110 | + | 0.433590i | \(0.142753\pi\) | ||||
−0.901110 | + | 0.433590i | \(0.857247\pi\) | |||||||
\(728\) | 408.978 | − | 105.124i | 0.561783 | − | 0.144401i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | −80.0803 | + | 138.703i | −0.109699 | + | 0.190004i | ||||
\(731\) | 11.5219 | − | 6.65215i | 0.0157618 | − | 0.00910007i | ||||
\(732\) | 2.05887 | + | 3.56608i | 0.00281267 | + | 0.00487169i | ||||
\(733\) | 258.486 | + | 149.237i | 0.352641 | + | 0.203597i | 0.665848 | − | 0.746088i | \(-0.268070\pi\) |
−0.313207 | + | 0.949685i | \(0.601403\pi\) | |||||||
\(734\) | 593.053i | 0.807974i | ||||||||
\(735\) | 106.684 | − | 58.7244i | 0.145149 | − | 0.0798971i | ||||
\(736\) | 211.882 | 0.287883 | ||||||||
\(737\) | −13.1909 | + | 22.8473i | −0.0178981 | + | 0.0310004i | ||||
\(738\) | 201.463 | − | 116.315i | 0.272985 | − | 0.157608i | ||||
\(739\) | −172.684 | − | 299.097i | −0.233672 | − | 0.404732i | 0.725214 | − | 0.688524i | \(-0.241741\pi\) |
−0.958886 | + | 0.283792i | \(0.908408\pi\) | |||||||
\(740\) | 69.5147 | + | 40.1343i | 0.0939388 | + | 0.0542356i | ||||
\(741\) | − | 266.914i | − | 0.360207i | ||||||
\(742\) | 210.603 | + | 819.336i | 0.283832 | + | 1.10423i | ||||
\(743\) | 683.616 | 0.920076 | 0.460038 | − | 0.887899i | \(-0.347836\pi\) | ||||
0.460038 | + | 0.887899i | \(0.347836\pi\) | |||||||
\(744\) | −108.125 | + | 187.278i | −0.145329 | + | 0.251717i | ||||
\(745\) | 100.764 | − | 58.1759i | 0.135253 | − | 0.0780885i | ||||
\(746\) | 22.1903 | + | 38.4347i | 0.0297457 | + | 0.0515211i | ||||
\(747\) | −286.831 | − | 165.602i | −0.383977 | − | 0.221689i | ||||
\(748\) | − | 107.489i | − | 0.143702i | ||||||
\(749\) | −799.301 | − | 222.939i | −1.06716 | − | 0.297648i | ||||
\(750\) | 168.500 | 0.224666 | ||||||||
\(751\) | 289.169 | − | 500.855i | 0.385045 | − | 0.666918i | −0.606730 | − | 0.794908i | \(-0.707519\pi\) |
0.991775 | + | 0.127990i | \(0.0408525\pi\) | |||||||
\(752\) | 148.971 | − | 86.0082i | 0.198099 | − | 0.114373i | ||||
\(753\) | 126.978 | + | 219.932i | 0.168629 | + | 0.292074i | ||||
\(754\) | −886.587 | − | 511.871i | −1.17584 | − | 0.678874i | ||||
\(755\) | − | 73.4744i | − | 0.0973171i | ||||||
\(756\) | −50.9117 | − | 51.9615i | −0.0673435 | − | 0.0687322i | ||||
\(757\) | 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 | ||||
\(759\) | −337.103 | + | 194.626i | −0.444140 | + | 0.256425i | ||||
\(760\) | −14.6619 | − | 25.3952i | −0.0192920 | − | 0.0334147i | ||||
\(761\) | −202.669 | − | 117.011i | −0.266319 | − | 0.153760i | 0.360894 | − | 0.932607i | \(-0.382471\pi\) |
−0.627214 | + | 0.778847i | \(0.715805\pi\) | |||||||
\(762\) | − | 202.263i | − | 0.265437i | ||||||
\(763\) | 555.294 | − | 544.075i | 0.727778 | − | 0.713074i | ||||
\(764\) | 133.206 | 0.174353 | ||||||||
\(765\) | 19.2792 | − | 33.3926i | 0.0252016 | − | 0.0436504i | ||||
\(766\) | −610.617 | + | 352.540i | −0.797151 | + | 0.460235i | ||||
\(767\) | −439.581 | − | 761.376i | −0.573117 | − | 0.992668i | ||||
\(768\) | −24.0000 | − | 13.8564i | −0.0312500 | − | 0.0180422i | ||||
\(769\) | − | 1290.16i | − | 1.67771i | −0.544358 | − | 0.838853i | \(-0.683226\pi\) | ||
0.544358 | − | 0.838853i | \(-0.316774\pi\) | |||||||
\(770\) | −22.8974 | + | 82.0940i | −0.0297369 | + | 0.106616i | ||||
\(771\) | 43.4558 | 0.0563630 | ||||||||
\(772\) | 9.79394 | − | 16.9636i | 0.0126864 | − | 0.0219736i | ||||
\(773\) | 345.646 | − | 199.559i | 0.447149 | − | 0.258161i | −0.259477 | − | 0.965749i | \(-0.583550\pi\) |
0.706625 | + | 0.707588i | \(0.250217\pi\) | |||||||
\(774\) | 3.15076 | + | 5.45727i | 0.00407075 | + | 0.00705074i | ||||
\(775\) | −876.992 | − | 506.331i | −1.13160 | − | 0.653331i | ||||
\(776\) | − | 31.0749i | − | 0.0400450i | ||||||
\(777\) | 328.448 | − | 84.4247i | 0.422713 | − | 0.108655i | ||||
\(778\) | 917.013 | 1.17868 | ||||||||
\(779\) | 198.088 | − | 343.099i | 0.254285 | − | 0.440435i | ||||
\(780\) | −91.8091 | + | 53.0060i | −0.117704 | + | 0.0679564i | ||||
\(781\) | −412.191 | − | 713.936i | −0.527773 | − | 0.914130i | ||||
\(782\) | 410.912 | + | 237.240i | 0.525463 | + | 0.303376i | ||||
\(783\) | 176.363i | 0.225240i | ||||||||
\(784\) | 4.00000 | − | 195.959i | 0.00510204 | − | 0.249948i | ||||
\(785\) | −268.410 | −0.341924 | ||||||||
\(786\) | −74.1838 | + | 128.490i | −0.0943814 | + | 0.163473i | ||||
\(787\) | −1348.16 | + | 778.361i | −1.71304 | + | 0.989023i | −0.782637 | + | 0.622478i | \(0.786126\pi\) |
−0.930401 | + | 0.366544i | \(0.880541\pi\) | |||||||
\(788\) | 267.161 | + | 462.737i | 0.339037 | + | 0.587230i | ||||
\(789\) | 136.014 | + | 78.5279i | 0.172388 | + | 0.0995284i | ||||
\(790\) | − | 199.550i | − | 0.252595i | ||||||
\(791\) | 176.698 | + | 687.433i | 0.223386 | + | 0.869068i | ||||
\(792\) | 50.9117 | 0.0642824 | ||||||||
\(793\) | 12.6762 | − | 21.9558i | 0.0159851 | − | 0.0276870i | ||||
\(794\) | 92.7761 | − | 53.5643i | 0.116846 | − | 0.0674613i | ||||
\(795\) | −106.191 | − | 183.928i | −0.133573 | − | 0.231356i | ||||
\(796\) | 226.794 | + | 130.940i | 0.284917 | + | 0.164497i | ||||
\(797\) | − | 600.232i | − | 0.753114i | −0.926393 | − | 0.376557i | \(-0.877108\pi\) | ||
0.926393 | − | 0.376557i | \(-0.122892\pi\) | |||||||
\(798\) | −119.335 | − | 33.2844i | −0.149542 | − | 0.0417098i | ||||
\(799\) | 385.206 | 0.482110 | ||||||||
\(800\) | 64.8873 | − | 112.388i | 0.0811091 | − | 0.140485i | ||||
\(801\) | −54.0000 | + | 31.1769i | −0.0674157 | + | 0.0389225i | ||||
\(802\) | −398.985 | − | 691.062i | −0.497487 | − | 0.861673i | ||||
\(803\) | −410.117 | − | 236.781i | −0.510731 | − | 0.294871i | ||||
\(804\) | 15.2315i | 0.0189447i | ||||||||
\(805\) | −263.294 | − | 268.723i | −0.327073 | − | 0.333817i | ||||
\(806\) | 1331.42 | 1.65188 | ||||||||
\(807\) | −59.2355 | + | 102.599i | −0.0734021 | + | 0.127136i | ||||
\(808\) | 262.544 | − | 151.580i | 0.324931 | − | 0.187599i | ||||
\(809\) | 114.640 | + | 198.562i | 0.141705 | + | 0.245441i | 0.928139 | − | 0.372234i | \(-0.121408\pi\) |
−0.786434 | + | 0.617675i | \(0.788075\pi\) | |||||||
\(810\) | 15.8162 | + | 9.13151i | 0.0195262 | + | 0.0112735i | ||||
\(811\) | − | 529.955i | − | 0.653459i | −0.945118 | − | 0.326729i | \(-0.894053\pi\) | ||
0.945118 | − | 0.326729i | \(-0.105947\pi\) | |||||||
\(812\) | −339.411 | + | 332.554i | −0.417994 | + | 0.409549i | ||||
\(813\) | −213.941 | −0.263150 | ||||||||
\(814\) | −118.669 | + | 205.541i | −0.145785 | + | 0.252507i | ||||
\(815\) | 104.309 | − | 60.2226i | 0.127986 | − | 0.0738928i | ||||
\(816\) | −31.0294 | − | 53.7446i | −0.0380263 | − | 0.0658634i | ||||
\(817\) | 9.29394 | + | 5.36586i | 0.0113757 | + | 0.00656776i | ||||
\(818\) | 505.508i | 0.617980i | ||||||||
\(819\) | −120.331 | + | 431.420i | −0.146924 | + | 0.526765i | ||||
\(820\) | −157.352 | −0.191893 | ||||||||
\(821\) | 151.669 | − | 262.698i | 0.184737 | − | 0.319974i | −0.758751 | − | 0.651381i | \(-0.774190\pi\) |
0.943488 | + | 0.331407i | \(0.107523\pi\) | |||||||
\(822\) | −142.191 | + | 82.0940i | −0.172982 | + | 0.0998710i | ||||
\(823\) | 564.955 | + | 978.531i | 0.686459 | + | 1.18898i | 0.972976 | + | 0.230906i | \(0.0741690\pi\) |
−0.286517 | + | 0.958075i | \(0.592498\pi\) | |||||||
\(824\) | −257.698 | − | 148.782i | −0.312741 | − | 0.180561i | ||||
\(825\) | 238.411i | 0.288983i | ||||||||
\(826\) | −395.220 | + | 101.588i | −0.478475 | + | 0.122988i | ||||
\(827\) | −161.604 | −0.195410 | −0.0977049 | − | 0.995215i | \(-0.531150\pi\) | ||||
−0.0977049 | + | 0.995215i | \(0.531150\pi\) | |||||||
\(828\) | −112.368 | + | 194.626i | −0.135710 | + | 0.235056i | ||||
\(829\) | 1325.32 | − | 765.175i | 1.59870 | − | 0.923010i | 0.606962 | − | 0.794731i | \(-0.292388\pi\) |
0.991738 | − | 0.128279i | \(-0.0409454\pi\) | |||||||
\(830\) | 112.014 | + | 194.014i | 0.134957 | + | 0.233752i | ||||
\(831\) | 409.323 | + | 236.323i | 0.492567 | + | 0.284384i | ||||
\(832\) | 170.624i | 0.205077i | ||||||||
\(833\) | 227.169 | − | 375.553i | 0.272711 | − | 0.450844i | ||||
\(834\) | −224.257 | −0.268893 | ||||||||
\(835\) | 91.5593 | − | 158.585i | 0.109652 | − | 0.189923i | ||||
\(836\) | 75.0883 | − | 43.3523i | 0.0898186 | − | 0.0518568i | ||||
\(837\) | −114.684 | − | 198.638i | −0.137018 | − | 0.237322i | ||||
\(838\) | 615.037 | + | 355.092i | 0.733934 | + | 0.423737i | ||||
\(839\) | 218.629i | 0.260583i | 0.991476 | + | 0.130291i | \(0.0415913\pi\) | ||||
−0.991476 | + | 0.130291i | \(0.958409\pi\) | |||||||
\(840\) | 12.2498 | + | 47.6569i | 0.0145831 | + | 0.0567344i | ||||
\(841\) | 311.000 | 0.369798 | ||||||||
\(842\) | 23.8959 | − | 41.3890i | 0.0283800 | − | 0.0491555i | ||||
\(843\) | 199.654 | − | 115.270i | 0.236837 | − | 0.136738i | ||||
\(844\) | 23.0883 | + | 39.9901i | 0.0273558 | + | 0.0473817i | ||||
\(845\) | 355.249 | + | 205.103i | 0.420413 | + | 0.242726i | ||||
\(846\) | 182.451i | 0.215663i | ||||||||
\(847\) | 573.124 | + | 159.854i | 0.676652 | + | 0.188730i | ||||
\(848\) | −341.823 | −0.403094 | ||||||||
\(849\) | −111.507 | + | 193.136i | −0.131339 | + | 0.227486i | ||||
\(850\) | 251.677 | − | 145.306i | 0.296091 | − | 0.170948i | ||||
\(851\) | −523.831 | − | 907.301i | −0.615547 | − | 1.06616i | ||||
\(852\) | −412.191 | − | 237.979i | −0.483792 | − | 0.279318i | ||||
\(853\) | − | 762.730i | − | 0.894174i | −0.894491 | − | 0.447087i | \(-0.852461\pi\) | ||
0.894491 | − | 0.447087i | \(-0.147539\pi\) | |||||||
\(854\) | −8.23550 | − | 8.40532i | −0.00964344 | − | 0.00984230i | ||||
\(855\) | 31.1026 | 0.0363773 | ||||||||
\(856\) | 167.647 | − | 290.373i | 0.195849 | − | 0.339220i | ||||
\(857\) | −795.015 | + | 459.002i | −0.927672 | + | 0.535592i | −0.886075 | − | 0.463543i | \(-0.846578\pi\) |
−0.0415977 | + | 0.999134i | \(0.513245\pi\) | |||||||
\(858\) | −156.728 | − | 271.461i | −0.182667 | − | 0.316388i | ||||
\(859\) | −761.367 | − | 439.575i | −0.886341 | − | 0.511729i | −0.0135969 | − | 0.999908i | \(-0.504328\pi\) |
−0.872744 | + | 0.488179i | \(0.837661\pi\) | |||||||
\(860\) | − | 4.26239i | − | 0.00495627i | ||||||
\(861\) | −474.853 | + | 465.259i | −0.551513 | + | 0.540370i | ||||
\(862\) | −712.368 | −0.826412 | ||||||||
\(863\) | −175.294 | + | 303.619i | −0.203122 | + | 0.351818i | −0.949533 | − | 0.313668i | \(-0.898442\pi\) |
0.746411 | + | 0.665486i | \(0.231776\pi\) | |||||||
\(864\) | 25.4558 | − | 14.6969i | 0.0294628 | − | 0.0170103i | ||||
\(865\) | 102.573 | + | 177.661i | 0.118581 | + | 0.205389i | ||||
\(866\) | 1025.78 | + | 592.236i | 1.18451 | + | 0.683875i | ||||
\(867\) | 361.591i | 0.417060i | ||||||||
\(868\) | 166.029 | − | 595.265i | 0.191278 | − | 0.685789i | ||||
\(869\) | 590.029 | 0.678974 | ||||||||
\(870\) | 59.6468 | − | 103.311i | 0.0685595 | − | 0.118749i | ||||
\(871\) | 81.2145 | − | 46.8892i | 0.0932428 | − | 0.0538338i | ||||
\(872\) | 157.061 | + | 272.038i | 0.180116 | + | 0.311970i | ||||
\(873\) | 28.5442 | + | 16.4800i | 0.0326966 | + | 0.0188774i | ||||
\(874\) | 382.732i | 0.437909i | ||||||||
\(875\) | −466.368 | + | 119.876i | −0.532991 | + | 0.137001i | ||||
\(876\) | −273.411 | −0.312113 | ||||||||
\(877\) | −1.77965 | + | 3.08245i | −0.00202925 | + | 0.00351477i | −0.867038 | − | 0.498242i | \(-0.833979\pi\) |
0.865009 | + | 0.501756i | \(0.167313\pi\) | |||||||
\(878\) | −232.721 | + | 134.361i | −0.265058 | + | 0.153031i | ||||
\(879\) | 267.588 | + | 463.476i | 0.304423 | + | 0.527276i | ||||
\(880\) | −29.8234 | − | 17.2185i | −0.0338902 | − | 0.0195665i | ||||
\(881\) | 488.565i | 0.554557i | 0.960790 | + | 0.277279i | \(0.0894325\pi\) | ||||
−0.960790 | + | 0.277279i | \(0.910567\pi\) | |||||||
\(882\) | 177.879 | + | 107.597i | 0.201677 | + | 0.121992i | ||||
\(883\) | −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 | ||||
\(885\) | 88.7208 | − | 51.2230i | 0.100249 | − | 0.0578791i | ||||
\(886\) | −119.823 | − | 207.540i | −0.135241 | − | 0.234244i | ||||
\(887\) | 75.2801 | + | 43.4630i | 0.0848704 | + | 0.0490000i | 0.541835 | − | 0.840485i | \(-0.317730\pi\) |
−0.456964 | + | 0.889485i | \(0.651063\pi\) | |||||||
\(888\) | 137.027i | 0.154310i | ||||||||
\(889\) | 143.896 | + | 559.817i | 0.161863 | + | 0.629716i | ||||
\(890\) | 42.1766 | 0.0473895 | ||||||||
\(891\) | −27.0000 | + | 46.7654i | −0.0303030 | + | 0.0524864i | ||||
\(892\) | −396.000 | + | 228.631i | −0.443946 | + | 0.256312i | ||||
\(893\) | 155.360 | + | 269.092i | 0.173976 | + | 0.301335i | ||||
\(894\) | 172.014 | + | 99.3125i | 0.192410 | + | 0.111088i | ||||
\(895\) | 242.895i | 0.271391i | ||||||||
\(896\) | 76.2843 | + | 21.2770i | 0.0851387 | + | 0.0237466i | ||||
\(897\) | 1383.66 | 1.54254 | ||||||||
\(898\) | 12.8011 | − | 22.1721i | 0.0142551 | − | 0.0246906i | ||||
\(899\) | −1297.50 | + | 749.111i | −1.44327 | + | 0.833272i | ||||
\(900\) | 68.8234 | + | 119.206i | 0.0764704 | + | 0.132451i | ||||
\(901\) | −662.912 | − | 382.732i | −0.735751 | − | 0.424786i | ||||
\(902\) | − | 465.259i | − | 0.515808i | ||||||
\(903\) | −12.6030 | − | 12.8629i | −0.0139568 | − | 0.0142446i | ||||
\(904\) | −286.794 | −0.317250 | ||||||||
\(905\) | 150.640 | − | 260.915i | 0.166453 | − | 0.288304i | ||||
\(906\) | 108.624 | − | 62.7144i | 0.119895 | − | 0.0692211i | ||||
\(907\) | 230.448 | + | 399.148i | 0.254077 | + | 0.440075i | 0.964645 | − | 0.263554i | \(-0.0848948\pi\) |
−0.710567 | + | 0.703629i | \(0.751562\pi\) | |||||||
\(908\) | −113.647 | − | 65.6140i | −0.125162 | − | 0.0722621i | ||||
\(909\) | 321.550i | 0.353740i | ||||||||
\(910\) | 216.396 | − | 212.024i | 0.237798 | − | 0.232993i | ||||
\(911\) | −1184.28 | −1.29998 | −0.649988 | − | 0.759944i | \(-0.725226\pi\) | ||||
−0.649988 | + | 0.759944i | \(0.725226\pi\) | |||||||
\(912\) | 25.0294 | − | 43.3523i | 0.0274446 | − | 0.0475354i | ||||
\(913\) | −573.661 | + | 331.203i | −0.628325 | + | 0.362764i | ||||
\(914\) | −232.513 | − | 402.725i | −0.254391 | − | 0.440618i | ||||
\(915\) | 2.55844 | + | 1.47712i | 0.00279611 | + | 0.00161434i | ||||
\(916\) | − | 186.960i | − | 0.204104i | ||||||
\(917\) | 113.912 | − | 408.407i | 0.124222 | − | 0.445373i | ||||
\(918\) | 65.8234 | 0.0717030 | ||||||||
\(919\) | 270.919 | − | 469.246i | 0.294798 | − | 0.510605i | −0.680140 | − | 0.733082i | \(-0.738081\pi\) |
0.974938 | + | 0.222477i | \(0.0714143\pi\) | |||||||
\(920\) | 131.647 | − | 76.0063i | 0.143094 | − | 0.0826155i | ||||
\(921\) | −524.889 | − | 909.134i | −0.569912 | − | 0.987117i | ||||
\(922\) | −972.853 | − | 561.677i | −1.05515 | − | 0.609194i | ||||
\(923\) | 2930.40i | 3.17486i | ||||||||
\(924\) | −140.912 | + | 36.2201i | −0.152502 | + | 0.0391992i | ||||
\(925\) | −641.676 | −0.693704 | ||||||||
\(926\) | −285.244 | + | 494.057i | −0.308039 | + | 0.533539i | ||||
\(927\) | 273.331 | − | 157.807i | 0.294855 | − | 0.170235i | ||||
\(928\) | −96.0000 | − | 166.277i | −0.103448 | − | 0.179178i | ||||
\(929\) | −779.610 | − | 450.108i | −0.839193 | − | 0.484508i | 0.0177969 | − | 0.999842i | \(-0.494335\pi\) |
−0.856990 | + | 0.515333i | \(0.827668\pi\) | |||||||
\(930\) | 155.146i | 0.166824i | ||||||||
\(931\) | 353.970 | + | 7.22538i | 0.380204 | + | 0.00776088i | ||||
\(932\) | −475.029 | −0.509688 | ||||||||
\(933\) | −176.044 | + | 304.917i | −0.188686 | + | 0.326813i | ||||
\(934\) | −3.46299 | + | 1.99936i | −0.00370769 | + | 0.00214064i | ||||
\(935\) | −38.5584 | − | 66.7852i | −0.0412390 | − | 0.0714280i | ||||
\(936\) | −156.728 | − | 90.4869i | −0.167444 | − | 0.0966740i | ||||
\(937\) | − | 233.964i | − | 0.249695i | −0.992176 | − | 0.124847i | \(-0.960156\pi\) | ||
0.992176 | − | 0.124847i | \(-0.0398441\pi\) | |||||||
\(938\) | −10.8362 | − | 42.1574i | −0.0115524 | − | 0.0449439i | ||||
\(939\) | −702.588 | −0.748230 | ||||||||
\(940\) | 61.7056 | − | 106.877i | 0.0656443 | − | 0.113699i | ||||
\(941\) | 1132.49 | − | 653.845i | 1.20350 | − | 0.694840i | 0.242167 | − | 0.970234i | \(-0.422142\pi\) |
0.961331 | + | 0.275394i | \(0.0888083\pi\) | |||||||
\(942\) | −229.103 | − | 396.817i | −0.243209 | − | 0.421250i | ||||
\(943\) | 1778.60 | + | 1026.88i | 1.88611 | + | 1.08895i | ||||
\(944\) | − | 164.884i | − | 0.174666i | ||||||
\(945\) | −50.2721 | − | 14.0217i | −0.0531980 | − | 0.0148378i | ||||
\(946\) | 12.6030 | 0.0133224 | ||||||||
\(947\) | 563.881 | − | 976.671i | 0.595440 | − | 1.03133i | −0.398045 | − | 0.917366i | \(-0.630311\pi\) |
0.993485 | − | 0.113966i | \(-0.0363555\pi\) | |||||||
\(948\) | 295.014 | − | 170.327i | 0.311197 | − | 0.179669i | ||||
\(949\) | 841.677 | + | 1457.83i | 0.886909 | + | 1.53617i | ||||
\(950\) | 203.012 | + | 117.209i | 0.213696 | + | 0.123378i | ||||
\(951\) | − | 45.1353i | − | 0.0474609i | ||||||
\(952\) | 124.118 | + | 126.677i | 0.130376 | + | 0.133064i | ||||
\(953\) | −91.4255 | −0.0959345 | −0.0479672 | − | 0.998849i | \(-0.515274\pi\) | ||||
−0.0479672 | + | 0.998849i | \(0.515274\pi\) | |||||||
\(954\) | 181.279 | − | 313.985i | 0.190020 | − | 0.329125i | ||||
\(955\) | 82.7636 | − | 47.7836i | 0.0866635 | − | 0.0500352i | ||||
\(956\) | −366.853 | − | 635.408i | −0.383737 | − | 0.664652i | ||||
\(957\) | 305.470 | + | 176.363i | 0.319196 | + | 0.184288i | ||||
\(958\) | − | 536.714i | − | 0.560245i | ||||||
\(959\) | 335.147 | − | 328.376i | 0.349476 | − | 0.342415i | ||||
\(960\) | −19.8823 | −0.0207107 | ||||||||
\(961\) | 493.749 | − | 855.199i | 0.513787 | − | 0.889905i | ||||
\(962\) | 730.628 | − | 421.828i | 0.759489 | − | 0.438491i | ||||
\(963\) | 177.816 | + | 307.987i | 0.184648 | + | 0.319820i | ||||
\(964\) | 729.235 | + | 421.024i | 0.756467 | + | 0.436747i | ||||
\(965\) | − | 14.0531i | − | 0.0145628i | ||||||
\(966\) | 172.544 | − | 618.622i | 0.178617 | − | 0.640395i | ||||
\(967\) | −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 | ||||
\(969\) | 97.0812 | − | 56.0498i | 0.100187 | − | 0.0578430i | ||||
\(970\) | −11.1472 | − | 19.3075i | −0.0114919 | − | 0.0199046i | ||||
\(971\) | 114.405 | + | 66.0517i | 0.117822 | + | 0.0680245i | 0.557753 | − | 0.830007i | \(-0.311664\pi\) |
−0.439931 | + | 0.898032i | \(0.644997\pi\) | |||||||
\(972\) | 31.1769i | 0.0320750i | ||||||||
\(973\) | 620.691 | − | 159.543i | 0.637915 | − | 0.163970i | ||||
\(974\) | −813.899 | −0.835626 | ||||||||
\(975\) | 423.735 | − | 733.931i | 0.434601 | − | 0.752750i | ||||
\(976\) | 4.11775 | − | 2.37738i | 0.00421901 | − | 0.00243584i | ||||
\(977\) | −224.117 | − | 388.182i | −0.229393 | − | 0.397320i | 0.728235 | − | 0.685327i | \(-0.240341\pi\) |
−0.957628 | + | 0.288007i | \(0.907007\pi\) | |||||||
\(978\) | 178.066 | + | 102.806i | 0.182072 | + | 0.105119i | ||||
\(979\) | 124.708i | 0.127383i | ||||||||
\(980\) | −67.8091 | − | 123.188i | −0.0691930 | − | 0.125702i | ||||
\(981\) | −333.177 | −0.339630 | ||||||||
\(982\) | 168.603 | − | 292.029i | 0.171694 | − | 0.297382i | ||||
\(983\) | 1426.14 | − | 823.382i | 1.45080 | − | 0.837621i | 0.452276 | − | 0.891878i | \(-0.350612\pi\) |
0.998527 | + | 0.0542567i | \(0.0172789\pi\) | |||||||
\(984\) | −134.309 | − | 232.629i | −0.136493 | − | 0.236412i | ||||
\(985\) | 331.986 | + | 191.672i | 0.337041 | + | 0.194591i | ||||
\(986\) | − | 429.956i | − | 0.436061i | ||||||
\(987\) | −129.801 | − | 504.982i | −0.131511 | − | 0.511633i | ||||
\(988\) | −308.205 | −0.311949 | ||||||||
\(989\) | −27.8162 | + | 48.1791i | −0.0281256 | + | 0.0487150i | ||||
\(990\) | 31.6325 | − | 18.2630i | 0.0319520 | − | 0.0184475i | ||||
\(991\) | 314.448 | + | 544.640i | 0.317304 | + | 0.549587i | 0.979925 | − | 0.199369i | \(-0.0638891\pi\) |
−0.662621 | + | 0.748955i | \(0.730556\pi\) | |||||||
\(992\) | 216.250 | + | 124.852i | 0.217994 | + | 0.125859i | ||||
\(993\) | − | 188.157i | − | 0.189483i | ||||||
\(994\) | 1310.15 | + | 365.424i | 1.31806 | + | 0.367630i | ||||
\(995\) | 187.882 | 0.188826 | ||||||||
\(996\) | −191.220 | + | 331.203i | −0.191988 | + | 0.332533i | ||||
\(997\) | −869.645 | + | 502.090i | −0.872262 | + | 0.503601i | −0.868099 | − | 0.496390i | \(-0.834658\pi\) |
−0.00416289 | + | 0.999991i | \(0.501325\pi\) | |||||||
\(998\) | −202.638 | − | 350.980i | −0.203044 | − | 0.351683i | ||||
\(999\) | −125.868 | − | 72.6697i | −0.125994 | − | 0.0727424i |
(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 | 42.3.g.a.19.2 | ✓ | 4 | |
3.2 | odd | 2 | 126.3.n.a.19.1 | 4 | |||
4.3 | odd | 2 | 336.3.bh.e.145.1 | 4 | |||
5.2 | odd | 4 | 1050.3.q.a.649.3 | 8 | |||
5.3 | odd | 4 | 1050.3.q.a.649.2 | 8 | |||
5.4 | even | 2 | 1050.3.p.a.901.1 | 4 | |||
7.2 | even | 3 | 294.3.c.a.97.2 | 4 | |||
7.3 | odd | 6 | inner | 42.3.g.a.31.2 | yes | 4 | |
7.4 | even | 3 | 294.3.g.a.31.2 | 4 | |||
7.5 | odd | 6 | 294.3.c.a.97.1 | 4 | |||
7.6 | odd | 2 | 294.3.g.a.19.2 | 4 | |||
12.11 | even | 2 | 1008.3.cg.h.145.2 | 4 | |||
21.2 | odd | 6 | 882.3.c.b.685.3 | 4 | |||
21.5 | even | 6 | 882.3.c.b.685.4 | 4 | |||
21.11 | odd | 6 | 882.3.n.e.325.1 | 4 | |||
21.17 | even | 6 | 126.3.n.a.73.1 | 4 | |||
21.20 | even | 2 | 882.3.n.e.19.1 | 4 | |||
28.3 | even | 6 | 336.3.bh.e.241.1 | 4 | |||
28.19 | even | 6 | 2352.3.f.e.97.3 | 4 | |||
28.23 | odd | 6 | 2352.3.f.e.97.2 | 4 | |||
35.3 | even | 12 | 1050.3.q.a.199.3 | 8 | |||
35.17 | even | 12 | 1050.3.q.a.199.2 | 8 | |||
35.24 | odd | 6 | 1050.3.p.a.451.1 | 4 | |||
84.59 | odd | 6 | 1008.3.cg.h.577.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.3.g.a.19.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
42.3.g.a.31.2 | yes | 4 | 7.3 | odd | 6 | inner | |
126.3.n.a.19.1 | 4 | 3.2 | odd | 2 | |||
126.3.n.a.73.1 | 4 | 21.17 | even | 6 | |||
294.3.c.a.97.1 | 4 | 7.5 | odd | 6 | |||
294.3.c.a.97.2 | 4 | 7.2 | even | 3 | |||
294.3.g.a.19.2 | 4 | 7.6 | odd | 2 | |||
294.3.g.a.31.2 | 4 | 7.4 | even | 3 | |||
336.3.bh.e.145.1 | 4 | 4.3 | odd | 2 | |||
336.3.bh.e.241.1 | 4 | 28.3 | even | 6 | |||
882.3.c.b.685.3 | 4 | 21.2 | odd | 6 | |||
882.3.c.b.685.4 | 4 | 21.5 | even | 6 | |||
882.3.n.e.19.1 | 4 | 21.20 | even | 2 | |||
882.3.n.e.325.1 | 4 | 21.11 | odd | 6 | |||
1008.3.cg.h.145.2 | 4 | 12.11 | even | 2 | |||
1008.3.cg.h.577.2 | 4 | 84.59 | odd | 6 | |||
1050.3.p.a.451.1 | 4 | 35.24 | odd | 6 | |||
1050.3.p.a.901.1 | 4 | 5.4 | even | 2 | |||
1050.3.q.a.199.2 | 8 | 35.17 | even | 12 | |||
1050.3.q.a.199.3 | 8 | 35.3 | even | 12 | |||
1050.3.q.a.649.2 | 8 | 5.3 | odd | 4 | |||
1050.3.q.a.649.3 | 8 | 5.2 | odd | 4 | |||
2352.3.f.e.97.2 | 4 | 28.23 | odd | 6 | |||
2352.3.f.e.97.3 | 4 | 28.19 | even | 6 |