Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(439,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.439");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.s (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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.49787136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 439.4 | ||
Root | \(0.228425 + 1.39564i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.439 |
Dual form | 930.2.s.b.769.2 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0.866025 | + | 0.500000i | 0.500000 | + | 0.288675i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −0.133975 | − | 2.23205i | −0.0599153 | − | 0.998203i | ||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | 2.29129 | + | 1.32288i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 2.23205 | − | 0.133975i | 0.705836 | − | 0.0423665i | ||||
\(11\) | −2.32288 | − | 4.02334i | −0.700373 | − | 1.21308i | −0.968335 | − | 0.249653i | \(-0.919684\pi\) |
0.267962 | − | 0.963429i | \(-0.413650\pi\) | |||||||
\(12\) | −0.866025 | − | 0.500000i | −0.250000 | − | 0.144338i | ||||
\(13\) | 4.58258 | − | 2.64575i | 1.27098 | − | 0.733799i | 0.295806 | − | 0.955248i | \(-0.404412\pi\) |
0.975172 | + | 0.221449i | \(0.0710785\pi\) | |||||||
\(14\) | −1.32288 | + | 2.29129i | −0.353553 | + | 0.612372i | ||||
\(15\) | 1.00000 | − | 2.00000i | 0.258199 | − | 0.516398i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.19615 | − | 3.00000i | −1.26025 | − | 0.727607i | −0.287129 | − | 0.957892i | \(-0.592701\pi\) |
−0.973123 | + | 0.230285i | \(0.926034\pi\) | |||||||
\(18\) | −0.866025 | + | 0.500000i | −0.204124 | + | 0.117851i | ||||
\(19\) | 2.64575 | − | 4.58258i | 0.606977 | − | 1.05131i | −0.384759 | − | 0.923017i | \(-0.625715\pi\) |
0.991736 | − | 0.128298i | \(-0.0409513\pi\) | |||||||
\(20\) | 0.133975 | + | 2.23205i | 0.0299576 | + | 0.499102i | ||||
\(21\) | 1.32288 | + | 2.29129i | 0.288675 | + | 0.500000i | ||||
\(22\) | 4.02334 | − | 2.32288i | 0.857779 | − | 0.495239i | ||||
\(23\) | − | 1.29150i | − | 0.269297i | −0.990893 | − | 0.134648i | \(-0.957009\pi\) | ||
0.990893 | − | 0.134648i | \(-0.0429905\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | −4.96410 | + | 0.598076i | −0.992820 | + | 0.119615i | ||||
\(26\) | 2.64575 | + | 4.58258i | 0.518875 | + | 0.898717i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −2.29129 | − | 1.32288i | −0.433013 | − | 0.250000i | ||||
\(29\) | 2.64575 | 0.491304 | 0.245652 | − | 0.969358i | \(-0.420998\pi\) | ||||
0.245652 | + | 0.969358i | \(0.420998\pi\) | |||||||
\(30\) | 2.00000 | + | 1.00000i | 0.365148 | + | 0.182574i | ||||
\(31\) | −4.14575 | + | 3.71655i | −0.744599 | + | 0.667512i | ||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − | 4.64575i | − | 0.808721i | ||||||
\(34\) | 3.00000 | − | 5.19615i | 0.514496 | − | 0.891133i | ||||
\(35\) | 2.64575 | − | 5.29150i | 0.447214 | − | 0.894427i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 3.46410 | + | 2.00000i | 0.569495 | + | 0.328798i | 0.756948 | − | 0.653476i | \(-0.226690\pi\) |
−0.187453 | + | 0.982274i | \(0.560023\pi\) | |||||||
\(38\) | 4.58258 | + | 2.64575i | 0.743392 | + | 0.429198i | ||||
\(39\) | 5.29150 | 0.847319 | ||||||||
\(40\) | −2.23205 | + | 0.133975i | −0.352918 | + | 0.0211832i | ||||
\(41\) | 3.64575 | + | 6.31463i | 0.569371 | + | 0.986179i | 0.996628 | + | 0.0820490i | \(0.0261464\pi\) |
−0.427258 | + | 0.904130i | \(0.640520\pi\) | |||||||
\(42\) | −2.29129 | + | 1.32288i | −0.353553 | + | 0.204124i | ||||
\(43\) | −0.613577 | − | 0.354249i | −0.0935696 | − | 0.0540224i | 0.452485 | − | 0.891772i | \(-0.350538\pi\) |
−0.546055 | + | 0.837750i | \(0.683871\pi\) | |||||||
\(44\) | 2.32288 | + | 4.02334i | 0.350187 | + | 0.606541i | ||||
\(45\) | 1.86603 | − | 1.23205i | 0.278171 | − | 0.183663i | ||||
\(46\) | 1.29150 | 0.190422 | ||||||||
\(47\) | − | 1.29150i | − | 0.188385i | −0.995554 | − | 0.0941925i | \(-0.969973\pi\) | ||
0.995554 | − | 0.0941925i | \(-0.0300269\pi\) | |||||||
\(48\) | 0.866025 | + | 0.500000i | 0.125000 | + | 0.0721688i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.598076 | − | 4.96410i | −0.0845807 | − | 0.702030i | ||||
\(51\) | −3.00000 | − | 5.19615i | −0.420084 | − | 0.727607i | ||||
\(52\) | −4.58258 | + | 2.64575i | −0.635489 | + | 0.366900i | ||||
\(53\) | 7.18065 | − | 4.14575i | 0.986338 | − | 0.569463i | 0.0821606 | − | 0.996619i | \(-0.473818\pi\) |
0.904178 | + | 0.427156i | \(0.140485\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −8.66909 | + | 5.72380i | −1.16894 | + | 0.771797i | ||||
\(56\) | 1.32288 | − | 2.29129i | 0.176777 | − | 0.306186i | ||||
\(57\) | 4.58258 | − | 2.64575i | 0.606977 | − | 0.350438i | ||||
\(58\) | 2.64575i | 0.347404i | ||||||||
\(59\) | 2.32288 | − | 4.02334i | 0.302413 | − | 0.523794i | −0.674269 | − | 0.738486i | \(-0.735541\pi\) |
0.976682 | + | 0.214692i | \(0.0688746\pi\) | |||||||
\(60\) | −1.00000 | + | 2.00000i | −0.129099 | + | 0.258199i | ||||
\(61\) | 10.0000 | 1.28037 | 0.640184 | − | 0.768221i | \(-0.278858\pi\) | ||||
0.640184 | + | 0.768221i | \(0.278858\pi\) | |||||||
\(62\) | −3.71655 | − | 4.14575i | −0.472002 | − | 0.526511i | ||||
\(63\) | 2.64575i | 0.333333i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −6.51940 | − | 9.87408i | −0.808632 | − | 1.22473i | ||||
\(66\) | 4.64575 | 0.571852 | ||||||||
\(67\) | 0.613577 | − | 0.354249i | 0.0749603 | − | 0.0432784i | −0.462051 | − | 0.886853i | \(-0.652886\pi\) |
0.537012 | + | 0.843575i | \(0.319553\pi\) | |||||||
\(68\) | 5.19615 | + | 3.00000i | 0.630126 | + | 0.363803i | ||||
\(69\) | 0.645751 | − | 1.11847i | 0.0777393 | − | 0.134648i | ||||
\(70\) | 5.29150 | + | 2.64575i | 0.632456 | + | 0.316228i | ||||
\(71\) | 7.29150 | + | 12.6293i | 0.865342 | + | 1.49882i | 0.866707 | + | 0.498818i | \(0.166232\pi\) |
−0.00136488 | + | 0.999999i | \(0.500434\pi\) | |||||||
\(72\) | 0.866025 | − | 0.500000i | 0.102062 | − | 0.0589256i | ||||
\(73\) | 12.6293 | − | 7.29150i | 1.47814 | − | 0.853406i | 0.478448 | − | 0.878116i | \(-0.341200\pi\) |
0.999695 | + | 0.0247103i | \(0.00786632\pi\) | |||||||
\(74\) | −2.00000 | + | 3.46410i | −0.232495 | + | 0.402694i | ||||
\(75\) | −4.59808 | − | 1.96410i | −0.530940 | − | 0.226795i | ||||
\(76\) | −2.64575 | + | 4.58258i | −0.303488 | + | 0.525657i | ||||
\(77\) | − | 12.2915i | − | 1.40075i | ||||||
\(78\) | 5.29150i | 0.599145i | ||||||||
\(79\) | −3.29150 | + | 5.70105i | −0.370323 | + | 0.641418i | −0.989615 | − | 0.143742i | \(-0.954086\pi\) |
0.619292 | + | 0.785161i | \(0.287420\pi\) | |||||||
\(80\) | −0.133975 | − | 2.23205i | −0.0149788 | − | 0.249551i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −6.31463 | + | 3.64575i | −0.697334 | + | 0.402606i | ||||
\(83\) | −10.0312 | + | 5.79150i | −1.10106 | + | 0.635700i | −0.936500 | − | 0.350666i | \(-0.885955\pi\) |
−0.164564 | + | 0.986366i | \(0.552622\pi\) | |||||||
\(84\) | −1.32288 | − | 2.29129i | −0.144338 | − | 0.250000i | ||||
\(85\) | −6.00000 | + | 12.0000i | −0.650791 | + | 1.30158i | ||||
\(86\) | 0.354249 | − | 0.613577i | 0.0381996 | − | 0.0661637i | ||||
\(87\) | 2.29129 | + | 1.32288i | 0.245652 | + | 0.141827i | ||||
\(88\) | −4.02334 | + | 2.32288i | −0.428889 | + | 0.247619i | ||||
\(89\) | −7.29150 | −0.772898 | −0.386449 | − | 0.922311i | \(-0.626298\pi\) | ||||
−0.386449 | + | 0.922311i | \(0.626298\pi\) | |||||||
\(90\) | 1.23205 | + | 1.86603i | 0.129870 | + | 0.196696i | ||||
\(91\) | 14.0000 | 1.46760 | ||||||||
\(92\) | 1.29150i | 0.134648i | ||||||||
\(93\) | −5.44860 | + | 1.14575i | −0.564994 | + | 0.118809i | ||||
\(94\) | 1.29150 | 0.133208 | ||||||||
\(95\) | −10.5830 | − | 5.29150i | −1.08579 | − | 0.542897i | ||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | 15.2288i | 1.54625i | 0.634256 | + | 0.773123i | \(0.281306\pi\) | ||||
−0.634256 | + | 0.773123i | \(0.718694\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.32288 | − | 4.02334i | 0.233458 | − | 0.404361i | ||||
\(100\) | 4.96410 | − | 0.598076i | 0.496410 | − | 0.0598076i | ||||
\(101\) | 1.35425 | 0.134753 | 0.0673764 | − | 0.997728i | \(-0.478537\pi\) | ||||
0.0673764 | + | 0.997728i | \(0.478537\pi\) | |||||||
\(102\) | 5.19615 | − | 3.00000i | 0.514496 | − | 0.297044i | ||||
\(103\) | −1.17281 | + | 0.677124i | −0.115561 | + | 0.0667190i | −0.556666 | − | 0.830736i | \(-0.687920\pi\) |
0.441106 | + | 0.897455i | \(0.354586\pi\) | |||||||
\(104\) | −2.64575 | − | 4.58258i | −0.259437 | − | 0.449359i | ||||
\(105\) | 4.93704 | − | 3.25970i | 0.481806 | − | 0.318114i | ||||
\(106\) | 4.14575 | + | 7.18065i | 0.402671 | + | 0.697447i | ||||
\(107\) | −4.33013 | − | 2.50000i | −0.418609 | − | 0.241684i | 0.275873 | − | 0.961194i | \(-0.411033\pi\) |
−0.694482 | + | 0.719510i | \(0.744366\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | −17.2915 | −1.65623 | −0.828113 | − | 0.560562i | \(-0.810585\pi\) | ||||
−0.828113 | + | 0.560562i | \(0.810585\pi\) | |||||||
\(110\) | −5.72380 | − | 8.66909i | −0.545743 | − | 0.826565i | ||||
\(111\) | 2.00000 | + | 3.46410i | 0.189832 | + | 0.328798i | ||||
\(112\) | 2.29129 | + | 1.32288i | 0.216506 | + | 0.125000i | ||||
\(113\) | −2.34563 | + | 1.35425i | −0.220658 | + | 0.127397i | −0.606255 | − | 0.795270i | \(-0.707329\pi\) |
0.385597 | + | 0.922667i | \(0.373996\pi\) | |||||||
\(114\) | 2.64575 | + | 4.58258i | 0.247797 | + | 0.429198i | ||||
\(115\) | −2.88270 | + | 0.173029i | −0.268813 | + | 0.0161350i | ||||
\(116\) | −2.64575 | −0.245652 | ||||||||
\(117\) | 4.58258 | + | 2.64575i | 0.423659 | + | 0.244600i | ||||
\(118\) | 4.02334 | + | 2.32288i | 0.370378 | + | 0.213838i | ||||
\(119\) | −7.93725 | − | 13.7477i | −0.727607 | − | 1.26025i | ||||
\(120\) | −2.00000 | − | 1.00000i | −0.182574 | − | 0.0912871i | ||||
\(121\) | −5.29150 | + | 9.16515i | −0.481046 | + | 0.833196i | ||||
\(122\) | 10.0000i | 0.905357i | ||||||||
\(123\) | 7.29150i | 0.657453i | ||||||||
\(124\) | 4.14575 | − | 3.71655i | 0.372299 | − | 0.333756i | ||||
\(125\) | 2.00000 | + | 11.0000i | 0.178885 | + | 0.983870i | ||||
\(126\) | −2.64575 | −0.235702 | ||||||||
\(127\) | 11.4564 | + | 6.61438i | 1.01659 | + | 0.586931i | 0.913116 | − | 0.407700i | \(-0.133669\pi\) |
0.103479 | + | 0.994632i | \(0.467003\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −0.354249 | − | 0.613577i | −0.0311899 | − | 0.0540224i | ||||
\(130\) | 9.87408 | − | 6.51940i | 0.866014 | − | 0.571789i | ||||
\(131\) | −6.64575 | + | 11.5108i | −0.580642 | + | 1.00570i | 0.414761 | + | 0.909930i | \(0.363865\pi\) |
−0.995403 | + | 0.0957712i | \(0.969468\pi\) | |||||||
\(132\) | 4.64575i | 0.404361i | ||||||||
\(133\) | 12.1244 | − | 7.00000i | 1.05131 | − | 0.606977i | ||||
\(134\) | 0.354249 | + | 0.613577i | 0.0306024 | + | 0.0530050i | ||||
\(135\) | 2.23205 | − | 0.133975i | 0.192104 | − | 0.0115307i | ||||
\(136\) | −3.00000 | + | 5.19615i | −0.257248 | + | 0.445566i | ||||
\(137\) | 9.16515 | − | 5.29150i | 0.783032 | − | 0.452084i | −0.0544719 | − | 0.998515i | \(-0.517348\pi\) |
0.837504 | + | 0.546432i | \(0.184014\pi\) | |||||||
\(138\) | 1.11847 | + | 0.645751i | 0.0952108 | + | 0.0549700i | ||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | −2.64575 | + | 5.29150i | −0.223607 | + | 0.447214i | ||||
\(141\) | 0.645751 | − | 1.11847i | 0.0543821 | − | 0.0941925i | ||||
\(142\) | −12.6293 | + | 7.29150i | −1.05982 | + | 0.611889i | ||||
\(143\) | −21.2895 | − | 12.2915i | −1.78032 | − | 1.02787i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | −0.354463 | − | 5.90545i | −0.0294366 | − | 0.490421i | ||||
\(146\) | 7.29150 | + | 12.6293i | 0.603449 | + | 1.04520i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.46410 | − | 2.00000i | −0.284747 | − | 0.164399i | ||||
\(149\) | −6.67712 | + | 11.5651i | −0.547011 | + | 0.947451i | 0.451466 | + | 0.892288i | \(0.350901\pi\) |
−0.998477 | + | 0.0551631i | \(0.982432\pi\) | |||||||
\(150\) | 1.96410 | − | 4.59808i | 0.160368 | − | 0.375431i | ||||
\(151\) | −22.2915 | −1.81406 | −0.907028 | − | 0.421069i | \(-0.861655\pi\) | ||||
−0.907028 | + | 0.421069i | \(0.861655\pi\) | |||||||
\(152\) | −4.58258 | − | 2.64575i | −0.371696 | − | 0.214599i | ||||
\(153\) | − | 6.00000i | − | 0.485071i | ||||||
\(154\) | 12.2915 | 0.990478 | ||||||||
\(155\) | 8.85095 | + | 8.75560i | 0.710926 | + | 0.703267i | ||||
\(156\) | −5.29150 | −0.423659 | ||||||||
\(157\) | − | 9.29150i | − | 0.741543i | −0.928724 | − | 0.370771i | \(-0.879093\pi\) | ||
0.928724 | − | 0.370771i | \(-0.120907\pi\) | |||||||
\(158\) | −5.70105 | − | 3.29150i | −0.453551 | − | 0.261858i | ||||
\(159\) | 8.29150 | 0.657559 | ||||||||
\(160\) | 2.23205 | − | 0.133975i | 0.176459 | − | 0.0105916i | ||||
\(161\) | 1.70850 | − | 2.95920i | 0.134648 | − | 0.233218i | ||||
\(162\) | −0.866025 | − | 0.500000i | −0.0680414 | − | 0.0392837i | ||||
\(163\) | − | 10.0000i | − | 0.783260i | −0.920123 | − | 0.391630i | \(-0.871911\pi\) | ||
0.920123 | − | 0.391630i | \(-0.128089\pi\) | |||||||
\(164\) | −3.64575 | − | 6.31463i | −0.284685 | − | 0.493089i | ||||
\(165\) | −10.3696 | + | 0.622413i | −0.807269 | + | 0.0484548i | ||||
\(166\) | −5.79150 | − | 10.0312i | −0.449508 | − | 0.778570i | ||||
\(167\) | −8.55157 | − | 4.93725i | −0.661741 | − | 0.382056i | 0.131199 | − | 0.991356i | \(-0.458117\pi\) |
−0.792940 | + | 0.609300i | \(0.791451\pi\) | |||||||
\(168\) | 2.29129 | − | 1.32288i | 0.176777 | − | 0.102062i | ||||
\(169\) | 7.50000 | − | 12.9904i | 0.576923 | − | 0.999260i | ||||
\(170\) | −12.0000 | − | 6.00000i | −0.920358 | − | 0.460179i | ||||
\(171\) | 5.29150 | 0.404651 | ||||||||
\(172\) | 0.613577 | + | 0.354249i | 0.0467848 | + | 0.0270112i | ||||
\(173\) | 3.71655 | − | 2.14575i | 0.282564 | − | 0.163138i | −0.352020 | − | 0.935993i | \(-0.614505\pi\) |
0.634584 | + | 0.772854i | \(0.281172\pi\) | |||||||
\(174\) | −1.32288 | + | 2.29129i | −0.100287 | + | 0.173702i | ||||
\(175\) | −12.1654 | − | 5.19652i | −0.919615 | − | 0.392820i | ||||
\(176\) | −2.32288 | − | 4.02334i | −0.175093 | − | 0.303271i | ||||
\(177\) | 4.02334 | − | 2.32288i | 0.302413 | − | 0.174598i | ||||
\(178\) | − | 7.29150i | − | 0.546521i | ||||||
\(179\) | 11.6144 | − | 20.1167i | 0.868099 | − | 1.50359i | 0.00416298 | − | 0.999991i | \(-0.498675\pi\) |
0.863936 | − | 0.503601i | \(-0.167992\pi\) | |||||||
\(180\) | −1.86603 | + | 1.23205i | −0.139085 | + | 0.0918316i | ||||
\(181\) | 5.64575 | + | 9.77873i | 0.419645 | + | 0.726847i | 0.995904 | − | 0.0904205i | \(-0.0288211\pi\) |
−0.576258 | + | 0.817268i | \(0.695488\pi\) | |||||||
\(182\) | 14.0000i | 1.03775i | ||||||||
\(183\) | 8.66025 | + | 5.00000i | 0.640184 | + | 0.369611i | ||||
\(184\) | −1.29150 | −0.0952108 | ||||||||
\(185\) | 4.00000 | − | 8.00000i | 0.294086 | − | 0.588172i | ||||
\(186\) | −1.14575 | − | 5.44860i | −0.0840106 | − | 0.399511i | ||||
\(187\) | 27.8745i | 2.03839i | ||||||||
\(188\) | 1.29150i | 0.0941925i | ||||||||
\(189\) | −1.32288 | + | 2.29129i | −0.0962250 | + | 0.166667i | ||||
\(190\) | 5.29150 | − | 10.5830i | 0.383886 | − | 0.767772i | ||||
\(191\) | −4.00000 | − | 6.92820i | −0.289430 | − | 0.501307i | 0.684244 | − | 0.729253i | \(-0.260132\pi\) |
−0.973674 | + | 0.227946i | \(0.926799\pi\) | |||||||
\(192\) | −0.866025 | − | 0.500000i | −0.0625000 | − | 0.0360844i | ||||
\(193\) | −13.2972 | − | 7.67712i | −0.957151 | − | 0.552612i | −0.0618561 | − | 0.998085i | \(-0.519702\pi\) |
−0.895295 | + | 0.445474i | \(0.853035\pi\) | |||||||
\(194\) | −15.2288 | −1.09336 | ||||||||
\(195\) | −0.708927 | − | 11.8109i | −0.0507673 | − | 0.845796i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.5983 | − | 9.58301i | 1.18258 | − | 0.682761i | 0.225967 | − | 0.974135i | \(-0.427446\pi\) |
0.956609 | + | 0.291374i | \(0.0941124\pi\) | |||||||
\(198\) | 4.02334 | + | 2.32288i | 0.285926 | + | 0.165080i | ||||
\(199\) | 2.85425 | + | 4.94370i | 0.202332 | + | 0.350450i | 0.949279 | − | 0.314434i | \(-0.101815\pi\) |
−0.746947 | + | 0.664883i | \(0.768481\pi\) | |||||||
\(200\) | 0.598076 | + | 4.96410i | 0.0422904 | + | 0.351015i | ||||
\(201\) | 0.708497 | 0.0499736 | ||||||||
\(202\) | 1.35425i | 0.0952846i | ||||||||
\(203\) | 6.06218 | + | 3.50000i | 0.425481 | + | 0.245652i | ||||
\(204\) | 3.00000 | + | 5.19615i | 0.210042 | + | 0.363803i | ||||
\(205\) | 13.6061 | − | 8.98350i | 0.950293 | − | 0.627435i | ||||
\(206\) | −0.677124 | − | 1.17281i | −0.0471775 | − | 0.0817138i | ||||
\(207\) | 1.11847 | − | 0.645751i | 0.0777393 | − | 0.0448828i | ||||
\(208\) | 4.58258 | − | 2.64575i | 0.317744 | − | 0.183450i | ||||
\(209\) | −24.5830 | −1.70044 | ||||||||
\(210\) | 3.25970 | + | 4.93704i | 0.224941 | + | 0.340688i | ||||
\(211\) | −2.29150 | + | 3.96900i | −0.157754 | + | 0.273237i | −0.934058 | − | 0.357121i | \(-0.883758\pi\) |
0.776305 | + | 0.630358i | \(0.217092\pi\) | |||||||
\(212\) | −7.18065 | + | 4.14575i | −0.493169 | + | 0.284731i | ||||
\(213\) | 14.5830i | 0.999211i | ||||||||
\(214\) | 2.50000 | − | 4.33013i | 0.170896 | − | 0.296001i | ||||
\(215\) | −0.708497 | + | 1.41699i | −0.0483191 | + | 0.0966382i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −14.4156 | + | 3.03137i | −0.978598 | + | 0.205783i | ||||
\(218\) | − | 17.2915i | − | 1.17113i | ||||||
\(219\) | 14.5830 | 0.985428 | ||||||||
\(220\) | 8.66909 | − | 5.72380i | 0.584470 | − | 0.385899i | ||||
\(221\) | −31.7490 | −2.13567 | ||||||||
\(222\) | −3.46410 | + | 2.00000i | −0.232495 | + | 0.134231i | ||||
\(223\) | 18.4933 | + | 10.6771i | 1.23840 | + | 0.714993i | 0.968768 | − | 0.247969i | \(-0.0797631\pi\) |
0.269636 | + | 0.962962i | \(0.413096\pi\) | |||||||
\(224\) | −1.32288 | + | 2.29129i | −0.0883883 | + | 0.153093i | ||||
\(225\) | −3.00000 | − | 4.00000i | −0.200000 | − | 0.266667i | ||||
\(226\) | −1.35425 | − | 2.34563i | −0.0900833 | − | 0.156029i | ||||
\(227\) | 12.9904 | − | 7.50000i | 0.862202 | − | 0.497792i | −0.00254715 | − | 0.999997i | \(-0.500811\pi\) |
0.864749 | + | 0.502204i | \(0.167477\pi\) | |||||||
\(228\) | −4.58258 | + | 2.64575i | −0.303488 | + | 0.175219i | ||||
\(229\) | 12.5830 | − | 21.7944i | 0.831508 | − | 1.44021i | −0.0653335 | − | 0.997863i | \(-0.520811\pi\) |
0.896842 | − | 0.442351i | \(-0.145856\pi\) | |||||||
\(230\) | −0.173029 | − | 2.88270i | −0.0114092 | − | 0.190080i | ||||
\(231\) | 6.14575 | − | 10.6448i | 0.404361 | − | 0.700373i | ||||
\(232\) | − | 2.64575i | − | 0.173702i | ||||||
\(233\) | − | 3.29150i | − | 0.215634i | −0.994171 | − | 0.107817i | \(-0.965614\pi\) | ||
0.994171 | − | 0.107817i | \(-0.0343860\pi\) | |||||||
\(234\) | −2.64575 | + | 4.58258i | −0.172958 | + | 0.299572i | ||||
\(235\) | −2.88270 | + | 0.173029i | −0.188047 | + | 0.0112871i | ||||
\(236\) | −2.32288 | + | 4.02334i | −0.151206 | + | 0.261897i | ||||
\(237\) | −5.70105 | + | 3.29150i | −0.370323 | + | 0.213806i | ||||
\(238\) | 13.7477 | − | 7.93725i | 0.891133 | − | 0.514496i | ||||
\(239\) | 1.70850 | + | 2.95920i | 0.110514 | + | 0.191415i | 0.915977 | − | 0.401230i | \(-0.131417\pi\) |
−0.805464 | + | 0.592645i | \(0.798084\pi\) | |||||||
\(240\) | 1.00000 | − | 2.00000i | 0.0645497 | − | 0.129099i | ||||
\(241\) | −10.5000 | + | 18.1865i | −0.676364 | + | 1.17150i | 0.299704 | + | 0.954032i | \(0.403112\pi\) |
−0.976068 | + | 0.217465i | \(0.930221\pi\) | |||||||
\(242\) | −9.16515 | − | 5.29150i | −0.589158 | − | 0.340151i | ||||
\(243\) | −0.866025 | + | 0.500000i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | −10.0000 | −0.640184 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.29150 | −0.464889 | ||||||||
\(247\) | − | 28.0000i | − | 1.78160i | ||||||
\(248\) | 3.71655 | + | 4.14575i | 0.236001 | + | 0.263255i | ||||
\(249\) | −11.5830 | −0.734043 | ||||||||
\(250\) | −11.0000 | + | 2.00000i | −0.695701 | + | 0.126491i | ||||
\(251\) | −10.6458 | + | 18.4390i | −0.671954 | + | 1.16386i | 0.305395 | + | 0.952226i | \(0.401211\pi\) |
−0.977349 | + | 0.211633i | \(0.932122\pi\) | |||||||
\(252\) | − | 2.64575i | − | 0.166667i | ||||||
\(253\) | −5.19615 | + | 3.00000i | −0.326679 | + | 0.188608i | ||||
\(254\) | −6.61438 | + | 11.4564i | −0.415023 | + | 0.718841i | ||||
\(255\) | −11.1962 | + | 7.39230i | −0.701130 | + | 0.462924i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.58258 | + | 2.64575i | −0.285853 | + | 0.165037i | −0.636070 | − | 0.771631i | \(-0.719441\pi\) |
0.350217 | + | 0.936669i | \(0.386108\pi\) | |||||||
\(258\) | 0.613577 | − | 0.354249i | 0.0381996 | − | 0.0220546i | ||||
\(259\) | 5.29150 | + | 9.16515i | 0.328798 | + | 0.569495i | ||||
\(260\) | 6.51940 | + | 9.87408i | 0.404316 | + | 0.612364i | ||||
\(261\) | 1.32288 | + | 2.29129i | 0.0818839 | + | 0.141827i | ||||
\(262\) | −11.5108 | − | 6.64575i | −0.711138 | − | 0.410576i | ||||
\(263\) | 19.1660i | 1.18183i | 0.806735 | + | 0.590913i | \(0.201233\pi\) | ||||
−0.806735 | + | 0.590913i | \(0.798767\pi\) | |||||||
\(264\) | −4.64575 | −0.285926 | ||||||||
\(265\) | −10.2156 | − | 15.4722i | −0.627536 | − | 0.950447i | ||||
\(266\) | 7.00000 | + | 12.1244i | 0.429198 | + | 0.743392i | ||||
\(267\) | −6.31463 | − | 3.64575i | −0.386449 | − | 0.223116i | ||||
\(268\) | −0.613577 | + | 0.354249i | −0.0374802 | + | 0.0216392i | ||||
\(269\) | 4.00000 | + | 6.92820i | 0.243884 | + | 0.422420i | 0.961817 | − | 0.273692i | \(-0.0882449\pi\) |
−0.717933 | + | 0.696112i | \(0.754912\pi\) | |||||||
\(270\) | 0.133975 | + | 2.23205i | 0.00815343 | + | 0.135838i | ||||
\(271\) | −11.7085 | −0.711241 | −0.355620 | − | 0.934631i | \(-0.615730\pi\) | ||||
−0.355620 | + | 0.934631i | \(0.615730\pi\) | |||||||
\(272\) | −5.19615 | − | 3.00000i | −0.315063 | − | 0.181902i | ||||
\(273\) | 12.1244 | + | 7.00000i | 0.733799 | + | 0.423659i | ||||
\(274\) | 5.29150 | + | 9.16515i | 0.319671 | + | 0.553687i | ||||
\(275\) | 13.9373 | + | 18.5830i | 0.840448 | + | 1.12060i | ||||
\(276\) | −0.645751 | + | 1.11847i | −0.0388697 | + | 0.0673242i | ||||
\(277\) | − | 2.00000i | − | 0.120168i | −0.998193 | − | 0.0600842i | \(-0.980863\pi\) | ||
0.998193 | − | 0.0600842i | \(-0.0191369\pi\) | |||||||
\(278\) | − | 4.00000i | − | 0.239904i | ||||||
\(279\) | −5.29150 | − | 1.73205i | −0.316794 | − | 0.103695i | ||||
\(280\) | −5.29150 | − | 2.64575i | −0.316228 | − | 0.158114i | ||||
\(281\) | −2.58301 | −0.154089 | −0.0770446 | − | 0.997028i | \(-0.524548\pi\) | ||||
−0.0770446 | + | 0.997028i | \(0.524548\pi\) | |||||||
\(282\) | 1.11847 | + | 0.645751i | 0.0666042 | + | 0.0384539i | ||||
\(283\) | 29.2915i | 1.74120i | 0.491992 | + | 0.870600i | \(0.336269\pi\) | ||||
−0.491992 | + | 0.870600i | \(0.663731\pi\) | |||||||
\(284\) | −7.29150 | − | 12.6293i | −0.432671 | − | 0.749408i | ||||
\(285\) | −6.51940 | − | 9.87408i | −0.386176 | − | 0.584890i | ||||
\(286\) | 12.2915 | − | 21.2895i | 0.726812 | − | 1.25887i | ||||
\(287\) | 19.2915i | 1.13874i | ||||||||
\(288\) | −0.866025 | + | 0.500000i | −0.0510310 | + | 0.0294628i | ||||
\(289\) | 9.50000 | + | 16.4545i | 0.558824 | + | 0.967911i | ||||
\(290\) | 5.90545 | − | 0.354463i | 0.346780 | − | 0.0208148i | ||||
\(291\) | −7.61438 | + | 13.1885i | −0.446363 | + | 0.773123i | ||||
\(292\) | −12.6293 | + | 7.29150i | −0.739071 | + | 0.426703i | ||||
\(293\) | −21.0371 | − | 12.1458i | −1.22900 | − | 0.709562i | −0.262178 | − | 0.965020i | \(-0.584441\pi\) |
−0.966820 | + | 0.255457i | \(0.917774\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.29150 | − | 4.64575i | −0.540972 | − | 0.270486i | ||||
\(296\) | 2.00000 | − | 3.46410i | 0.116248 | − | 0.201347i | ||||
\(297\) | 4.02334 | − | 2.32288i | 0.233458 | − | 0.134787i | ||||
\(298\) | −11.5651 | − | 6.67712i | −0.669949 | − | 0.386795i | ||||
\(299\) | −3.41699 | − | 5.91841i | −0.197610 | − | 0.342270i | ||||
\(300\) | 4.59808 | + | 1.96410i | 0.265470 | + | 0.113397i | ||||
\(301\) | −0.937254 | − | 1.62337i | −0.0540224 | − | 0.0935696i | ||||
\(302\) | − | 22.2915i | − | 1.28273i | ||||||
\(303\) | 1.17281 | + | 0.677124i | 0.0673764 | + | 0.0388998i | ||||
\(304\) | 2.64575 | − | 4.58258i | 0.151744 | − | 0.262829i | ||||
\(305\) | −1.33975 | − | 22.3205i | −0.0767136 | − | 1.27807i | ||||
\(306\) | 6.00000 | 0.342997 | ||||||||
\(307\) | 15.4798 | + | 8.93725i | 0.883478 | + | 0.510076i | 0.871803 | − | 0.489856i | \(-0.162951\pi\) |
0.0116741 | + | 0.999932i | \(0.496284\pi\) | |||||||
\(308\) | 12.2915i | 0.700373i | ||||||||
\(309\) | −1.35425 | −0.0770405 | ||||||||
\(310\) | −8.75560 | + | 8.85095i | −0.497285 | + | 0.502700i | ||||
\(311\) | 19.8745 | 1.12698 | 0.563490 | − | 0.826123i | \(-0.309458\pi\) | ||||
0.563490 | + | 0.826123i | \(0.309458\pi\) | |||||||
\(312\) | − | 5.29150i | − | 0.299572i | ||||||
\(313\) | 1.67771 | + | 0.968627i | 0.0948298 | + | 0.0547500i | 0.546665 | − | 0.837351i | \(-0.315897\pi\) |
−0.451835 | + | 0.892101i | \(0.649230\pi\) | |||||||
\(314\) | 9.29150 | 0.524350 | ||||||||
\(315\) | 5.90545 | − | 0.354463i | 0.332734 | − | 0.0199718i | ||||
\(316\) | 3.29150 | − | 5.70105i | 0.185161 | − | 0.320709i | ||||
\(317\) | −4.94370 | − | 2.85425i | −0.277666 | − | 0.160311i | 0.354700 | − | 0.934980i | \(-0.384583\pi\) |
−0.632366 | + | 0.774669i | \(0.717916\pi\) | |||||||
\(318\) | 8.29150i | 0.464964i | ||||||||
\(319\) | −6.14575 | − | 10.6448i | −0.344096 | − | 0.595992i | ||||
\(320\) | 0.133975 | + | 2.23205i | 0.00748941 | + | 0.124775i | ||||
\(321\) | −2.50000 | − | 4.33013i | −0.139536 | − | 0.241684i | ||||
\(322\) | 2.95920 | + | 1.70850i | 0.164910 | + | 0.0952108i | ||||
\(323\) | −27.4955 | + | 15.8745i | −1.52989 | + | 0.883281i | ||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | −21.1660 | + | 15.8745i | −1.17408 | + | 0.880559i | ||||
\(326\) | 10.0000 | 0.553849 | ||||||||
\(327\) | −14.9749 | − | 8.64575i | −0.828113 | − | 0.478111i | ||||
\(328\) | 6.31463 | − | 3.64575i | 0.348667 | − | 0.201303i | ||||
\(329\) | 1.70850 | − | 2.95920i | 0.0941925 | − | 0.163146i | ||||
\(330\) | −0.622413 | − | 10.3696i | −0.0342627 | − | 0.570825i | ||||
\(331\) | 11.5830 | + | 20.0624i | 0.636660 | + | 1.10273i | 0.986161 | + | 0.165791i | \(0.0530177\pi\) |
−0.349501 | + | 0.936936i | \(0.613649\pi\) | |||||||
\(332\) | 10.0312 | − | 5.79150i | 0.550532 | − | 0.317850i | ||||
\(333\) | 4.00000i | 0.219199i | ||||||||
\(334\) | 4.93725 | − | 8.55157i | 0.270155 | − | 0.467921i | ||||
\(335\) | −0.872905 | − | 1.32207i | −0.0476919 | − | 0.0722326i | ||||
\(336\) | 1.32288 | + | 2.29129i | 0.0721688 | + | 0.125000i | ||||
\(337\) | − | 23.1033i | − | 1.25852i | −0.777197 | − | 0.629258i | \(-0.783359\pi\) | ||
0.777197 | − | 0.629258i | \(-0.216641\pi\) | |||||||
\(338\) | 12.9904 | + | 7.50000i | 0.706584 | + | 0.407946i | ||||
\(339\) | −2.70850 | −0.147105 | ||||||||
\(340\) | 6.00000 | − | 12.0000i | 0.325396 | − | 0.650791i | ||||
\(341\) | 24.5830 | + | 8.04668i | 1.33124 | + | 0.435752i | ||||
\(342\) | 5.29150i | 0.286132i | ||||||||
\(343\) | − | 18.5203i | − | 1.00000i | ||||||
\(344\) | −0.354249 | + | 0.613577i | −0.0190998 | + | 0.0330818i | ||||
\(345\) | −2.58301 | − | 1.29150i | −0.139064 | − | 0.0695322i | ||||
\(346\) | 2.14575 | + | 3.71655i | 0.115356 | + | 0.199803i | ||||
\(347\) | 15.2273 | + | 8.79150i | 0.817446 | + | 0.471953i | 0.849535 | − | 0.527532i | \(-0.176883\pi\) |
−0.0320890 | + | 0.999485i | \(0.510216\pi\) | |||||||
\(348\) | −2.29129 | − | 1.32288i | −0.122826 | − | 0.0709136i | ||||
\(349\) | −5.29150 | −0.283248 | −0.141624 | − | 0.989921i | \(-0.545232\pi\) | ||||
−0.141624 | + | 0.989921i | \(0.545232\pi\) | |||||||
\(350\) | 5.19652 | − | 12.1654i | 0.277766 | − | 0.650266i | ||||
\(351\) | 2.64575 | + | 4.58258i | 0.141220 | + | 0.244600i | ||||
\(352\) | 4.02334 | − | 2.32288i | 0.214445 | − | 0.123810i | ||||
\(353\) | 28.8313 | + | 16.6458i | 1.53453 | + | 0.885964i | 0.999144 | + | 0.0413591i | \(0.0131688\pi\) |
0.535390 | + | 0.844605i | \(0.320165\pi\) | |||||||
\(354\) | 2.32288 | + | 4.02334i | 0.123459 | + | 0.213838i | ||||
\(355\) | 27.2123 | − | 17.9670i | 1.44428 | − | 0.953590i | ||||
\(356\) | 7.29150 | 0.386449 | ||||||||
\(357\) | − | 15.8745i | − | 0.840168i | ||||||
\(358\) | 20.1167 | + | 11.6144i | 1.06320 | + | 0.613839i | ||||
\(359\) | 9.00000 | + | 15.5885i | 0.475002 | + | 0.822727i | 0.999590 | − | 0.0286287i | \(-0.00911406\pi\) |
−0.524588 | + | 0.851356i | \(0.675781\pi\) | |||||||
\(360\) | −1.23205 | − | 1.86603i | −0.0649348 | − | 0.0983482i | ||||
\(361\) | −4.50000 | − | 7.79423i | −0.236842 | − | 0.410223i | ||||
\(362\) | −9.77873 | + | 5.64575i | −0.513959 | + | 0.296734i | ||||
\(363\) | −9.16515 | + | 5.29150i | −0.481046 | + | 0.277732i | ||||
\(364\) | −14.0000 | −0.733799 | ||||||||
\(365\) | −17.9670 | − | 27.2123i | −0.940436 | − | 1.42435i | ||||
\(366\) | −5.00000 | + | 8.66025i | −0.261354 | + | 0.452679i | ||||
\(367\) | −15.9847 | + | 9.22876i | −0.834393 | + | 0.481737i | −0.855355 | − | 0.518043i | \(-0.826661\pi\) |
0.0209612 | + | 0.999780i | \(0.493327\pi\) | |||||||
\(368\) | − | 1.29150i | − | 0.0673242i | ||||||
\(369\) | −3.64575 | + | 6.31463i | −0.189790 | + | 0.328726i | ||||
\(370\) | 8.00000 | + | 4.00000i | 0.415900 | + | 0.207950i | ||||
\(371\) | 21.9373 | 1.13893 | ||||||||
\(372\) | 5.44860 | − | 1.14575i | 0.282497 | − | 0.0594044i | ||||
\(373\) | − | 27.1660i | − | 1.40660i | −0.710892 | − | 0.703301i | \(-0.751708\pi\) | ||
0.710892 | − | 0.703301i | \(-0.248292\pi\) | |||||||
\(374\) | −27.8745 | −1.44136 | ||||||||
\(375\) | −3.76795 | + | 10.5263i | −0.194576 | + | 0.543575i | ||||
\(376\) | −1.29150 | −0.0666042 | ||||||||
\(377\) | 12.1244 | − | 7.00000i | 0.624436 | − | 0.360518i | ||||
\(378\) | −2.29129 | − | 1.32288i | −0.117851 | − | 0.0680414i | ||||
\(379\) | −7.64575 | + | 13.2428i | −0.392736 | + | 0.680238i | −0.992809 | − | 0.119706i | \(-0.961805\pi\) |
0.600073 | + | 0.799945i | \(0.295138\pi\) | |||||||
\(380\) | 10.5830 | + | 5.29150i | 0.542897 | + | 0.271448i | ||||
\(381\) | 6.61438 | + | 11.4564i | 0.338865 | + | 0.586931i | ||||
\(382\) | 6.92820 | − | 4.00000i | 0.354478 | − | 0.204658i | ||||
\(383\) | −31.5731 | + | 18.2288i | −1.61331 | + | 0.931446i | −0.624716 | + | 0.780852i | \(0.714785\pi\) |
−0.988596 | + | 0.150594i | \(0.951881\pi\) | |||||||
\(384\) | 0.500000 | − | 0.866025i | 0.0255155 | − | 0.0441942i | ||||
\(385\) | −27.4353 | + | 1.64675i | −1.39823 | + | 0.0839261i | ||||
\(386\) | 7.67712 | − | 13.2972i | 0.390755 | − | 0.676808i | ||||
\(387\) | − | 0.708497i | − | 0.0360149i | ||||||
\(388\) | − | 15.2288i | − | 0.773123i | ||||||
\(389\) | −8.00000 | + | 13.8564i | −0.405616 | + | 0.702548i | −0.994393 | − | 0.105748i | \(-0.966276\pi\) |
0.588777 | + | 0.808296i | \(0.299610\pi\) | |||||||
\(390\) | 11.8109 | − | 0.708927i | 0.598068 | − | 0.0358979i | ||||
\(391\) | −3.87451 | + | 6.71084i | −0.195942 | + | 0.339382i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.5108 | + | 6.64575i | −0.580642 | + | 0.335234i | ||||
\(394\) | 9.58301 | + | 16.5983i | 0.482785 | + | 0.836208i | ||||
\(395\) | 13.1660 | + | 6.58301i | 0.662454 | + | 0.331227i | ||||
\(396\) | −2.32288 | + | 4.02334i | −0.116729 | + | 0.202180i | ||||
\(397\) | −4.47390 | − | 2.58301i | −0.224538 | − | 0.129637i | 0.383512 | − | 0.923536i | \(-0.374715\pi\) |
−0.608050 | + | 0.793899i | \(0.708048\pi\) | |||||||
\(398\) | −4.94370 | + | 2.85425i | −0.247805 | + | 0.143071i | ||||
\(399\) | 14.0000 | 0.700877 | ||||||||
\(400\) | −4.96410 | + | 0.598076i | −0.248205 | + | 0.0299038i | ||||
\(401\) | −22.0000 | −1.09863 | −0.549314 | − | 0.835616i | \(-0.685111\pi\) | ||||
−0.549314 | + | 0.835616i | \(0.685111\pi\) | |||||||
\(402\) | 0.708497i | 0.0353366i | ||||||||
\(403\) | −9.16515 | + | 28.0000i | −0.456549 | + | 1.39478i | ||||
\(404\) | −1.35425 | −0.0673764 | ||||||||
\(405\) | 2.00000 | + | 1.00000i | 0.0993808 | + | 0.0496904i | ||||
\(406\) | −3.50000 | + | 6.06218i | −0.173702 | + | 0.300861i | ||||
\(407\) | − | 18.5830i | − | 0.921125i | ||||||
\(408\) | −5.19615 | + | 3.00000i | −0.257248 | + | 0.148522i | ||||
\(409\) | 15.7915 | − | 27.3517i | 0.780840 | − | 1.35245i | −0.150614 | − | 0.988593i | \(-0.548125\pi\) |
0.931453 | − | 0.363861i | \(-0.118542\pi\) | |||||||
\(410\) | 8.98350 | + | 13.6061i | 0.443664 | + | 0.671959i | ||||
\(411\) | 10.5830 | 0.522021 | ||||||||
\(412\) | 1.17281 | − | 0.677124i | 0.0577804 | − | 0.0333595i | ||||
\(413\) | 10.6448 | − | 6.14575i | 0.523794 | − | 0.302413i | ||||
\(414\) | 0.645751 | + | 1.11847i | 0.0317369 | + | 0.0549700i | ||||
\(415\) | 14.2709 | + | 21.6142i | 0.700529 | + | 1.06100i | ||||
\(416\) | 2.64575 | + | 4.58258i | 0.129719 | + | 0.224679i | ||||
\(417\) | −3.46410 | − | 2.00000i | −0.169638 | − | 0.0979404i | ||||
\(418\) | − | 24.5830i | − | 1.20239i | ||||||
\(419\) | −1.93725 | −0.0946410 | −0.0473205 | − | 0.998880i | \(-0.515068\pi\) | ||||
−0.0473205 | + | 0.998880i | \(0.515068\pi\) | |||||||
\(420\) | −4.93704 | + | 3.25970i | −0.240903 | + | 0.159057i | ||||
\(421\) | −0.0627461 | − | 0.108679i | −0.00305806 | − | 0.00529671i | 0.864492 | − | 0.502646i | \(-0.167640\pi\) |
−0.867550 | + | 0.497349i | \(0.834307\pi\) | |||||||
\(422\) | −3.96900 | − | 2.29150i | −0.193208 | − | 0.111549i | ||||
\(423\) | 1.11847 | − | 0.645751i | 0.0543821 | − | 0.0313975i | ||||
\(424\) | −4.14575 | − | 7.18065i | −0.201335 | − | 0.348723i | ||||
\(425\) | 27.5885 | + | 11.7846i | 1.33824 | + | 0.571638i | ||||
\(426\) | −14.5830 | −0.706549 | ||||||||
\(427\) | 22.9129 | + | 13.2288i | 1.10883 | + | 0.640184i | ||||
\(428\) | 4.33013 | + | 2.50000i | 0.209305 | + | 0.120842i | ||||
\(429\) | −12.2915 | − | 21.2895i | −0.593439 | − | 1.02787i | ||||
\(430\) | −1.41699 | − | 0.708497i | −0.0683336 | − | 0.0341668i | ||||
\(431\) | 17.5203 | − | 30.3460i | 0.843921 | − | 1.46171i | −0.0426336 | − | 0.999091i | \(-0.513575\pi\) |
0.886555 | − | 0.462624i | \(-0.153092\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | − | 33.1660i | − | 1.59386i | −0.604074 | − | 0.796928i | \(-0.706457\pi\) | ||
0.604074 | − | 0.796928i | \(-0.293543\pi\) | |||||||
\(434\) | −3.03137 | − | 14.4156i | −0.145511 | − | 0.691973i | ||||
\(435\) | 2.64575 | − | 5.29150i | 0.126854 | − | 0.253708i | ||||
\(436\) | 17.2915 | 0.828113 | ||||||||
\(437\) | −5.91841 | − | 3.41699i | −0.283116 | − | 0.163457i | ||||
\(438\) | 14.5830i | 0.696803i | ||||||||
\(439\) | 13.4373 | + | 23.2740i | 0.641325 | + | 1.11081i | 0.985137 | + | 0.171769i | \(0.0549483\pi\) |
−0.343812 | + | 0.939038i | \(0.611718\pi\) | |||||||
\(440\) | 5.72380 | + | 8.66909i | 0.272872 | + | 0.413283i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 31.7490i | − | 1.51015i | ||||||
\(443\) | 6.92820 | − | 4.00000i | 0.329169 | − | 0.190046i | −0.326303 | − | 0.945265i | \(-0.605803\pi\) |
0.655472 | + | 0.755219i | \(0.272470\pi\) | |||||||
\(444\) | −2.00000 | − | 3.46410i | −0.0949158 | − | 0.164399i | ||||
\(445\) | 0.976876 | + | 16.2750i | 0.0463084 | + | 0.771509i | ||||
\(446\) | −10.6771 | + | 18.4933i | −0.505576 | + | 0.875684i | ||||
\(447\) | −11.5651 | + | 6.67712i | −0.547011 | + | 0.315817i | ||||
\(448\) | −2.29129 | − | 1.32288i | −0.108253 | − | 0.0625000i | ||||
\(449\) | 29.1660 | 1.37643 | 0.688215 | − | 0.725507i | \(-0.258395\pi\) | ||||
0.688215 | + | 0.725507i | \(0.258395\pi\) | |||||||
\(450\) | 4.00000 | − | 3.00000i | 0.188562 | − | 0.141421i | ||||
\(451\) | 16.9373 | − | 29.3362i | 0.797544 | − | 1.38139i | ||||
\(452\) | 2.34563 | − | 1.35425i | 0.110329 | − | 0.0636985i | ||||
\(453\) | −19.3050 | − | 11.1458i | −0.907028 | − | 0.523673i | ||||
\(454\) | 7.50000 | + | 12.9904i | 0.351992 | + | 0.609669i | ||||
\(455\) | −1.87564 | − | 31.2487i | −0.0879316 | − | 1.46496i | ||||
\(456\) | −2.64575 | − | 4.58258i | −0.123899 | − | 0.214599i | ||||
\(457\) | 25.1660i | 1.17722i | 0.808418 | + | 0.588608i | \(0.200324\pi\) | ||||
−0.808418 | + | 0.588608i | \(0.799676\pi\) | |||||||
\(458\) | 21.7944 | + | 12.5830i | 1.01839 | + | 0.587965i | ||||
\(459\) | 3.00000 | − | 5.19615i | 0.140028 | − | 0.242536i | ||||
\(460\) | 2.88270 | − | 0.173029i | 0.134407 | − | 0.00806750i | ||||
\(461\) | 9.22876 | 0.429826 | 0.214913 | − | 0.976633i | \(-0.431053\pi\) | ||||
0.214913 | + | 0.976633i | \(0.431053\pi\) | |||||||
\(462\) | 10.6448 | + | 6.14575i | 0.495239 | + | 0.285926i | ||||
\(463\) | − | 18.6458i | − | 0.866542i | −0.901264 | − | 0.433271i | \(-0.857359\pi\) | ||
0.901264 | − | 0.433271i | \(-0.142641\pi\) | |||||||
\(464\) | 2.64575 | 0.122826 | ||||||||
\(465\) | 3.28735 | + | 12.0081i | 0.152447 | + | 0.556860i | ||||
\(466\) | 3.29150 | 0.152476 | ||||||||
\(467\) | 36.7490i | 1.70054i | 0.526345 | + | 0.850271i | \(0.323562\pi\) | ||||
−0.526345 | + | 0.850271i | \(0.676438\pi\) | |||||||
\(468\) | −4.58258 | − | 2.64575i | −0.211830 | − | 0.122300i | ||||
\(469\) | 1.87451 | 0.0865567 | ||||||||
\(470\) | −0.173029 | − | 2.88270i | −0.00798121 | − | 0.132969i | ||||
\(471\) | 4.64575 | − | 8.04668i | 0.214065 | − | 0.370771i | ||||
\(472\) | −4.02334 | − | 2.32288i | −0.185189 | − | 0.106919i | ||||
\(473\) | 3.29150i | 0.151343i | ||||||||
\(474\) | −3.29150 | − | 5.70105i | −0.151184 | − | 0.261858i | ||||
\(475\) | −10.3930 | + | 24.3307i | −0.476866 | + | 1.11637i | ||||
\(476\) | 7.93725 | + | 13.7477i | 0.363803 | + | 0.630126i | ||||
\(477\) | 7.18065 | + | 4.14575i | 0.328779 | + | 0.189821i | ||||
\(478\) | −2.95920 | + | 1.70850i | −0.135351 | + | 0.0781449i | ||||
\(479\) | 16.2915 | − | 28.2177i | 0.744378 | − | 1.28930i | −0.206107 | − | 0.978529i | \(-0.566080\pi\) |
0.950485 | − | 0.310771i | \(-0.100587\pi\) | |||||||
\(480\) | 2.00000 | + | 1.00000i | 0.0912871 | + | 0.0456435i | ||||
\(481\) | 21.1660 | 0.965087 | ||||||||
\(482\) | −18.1865 | − | 10.5000i | −0.828374 | − | 0.478262i | ||||
\(483\) | 2.95920 | − | 1.70850i | 0.134648 | − | 0.0777393i | ||||
\(484\) | 5.29150 | − | 9.16515i | 0.240523 | − | 0.416598i | ||||
\(485\) | 33.9914 | − | 2.04027i | 1.54347 | − | 0.0926437i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | 7.99234 | − | 4.61438i | 0.362167 | − | 0.209097i | −0.307864 | − | 0.951430i | \(-0.599614\pi\) |
0.670031 | + | 0.742333i | \(0.266281\pi\) | |||||||
\(488\) | − | 10.0000i | − | 0.452679i | ||||||
\(489\) | 5.00000 | − | 8.66025i | 0.226108 | − | 0.391630i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.90588 | + | 15.4254i | 0.401917 | + | 0.696140i | 0.993957 | − | 0.109768i | \(-0.0350108\pi\) |
−0.592040 | + | 0.805908i | \(0.701677\pi\) | |||||||
\(492\) | − | 7.29150i | − | 0.328726i | ||||||
\(493\) | −13.7477 | − | 7.93725i | −0.619166 | − | 0.357476i | ||||
\(494\) | 28.0000 | 1.25978 | ||||||||
\(495\) | −9.29150 | − | 4.64575i | −0.417622 | − | 0.208811i | ||||
\(496\) | −4.14575 | + | 3.71655i | −0.186150 | + | 0.166878i | ||||
\(497\) | 38.5830i | 1.73068i | ||||||||
\(498\) | − | 11.5830i | − | 0.519047i | ||||||
\(499\) | −18.2288 | + | 31.5731i | −0.816031 | + | 1.41341i | 0.0925539 | + | 0.995708i | \(0.470497\pi\) |
−0.908585 | + | 0.417700i | \(0.862836\pi\) | |||||||
\(500\) | −2.00000 | − | 11.0000i | −0.0894427 | − | 0.491935i | ||||
\(501\) | −4.93725 | − | 8.55157i | −0.220580 | − | 0.382056i | ||||
\(502\) | −18.4390 | − | 10.6458i | −0.822972 | − | 0.475143i | ||||
\(503\) | −6.92820 | − | 4.00000i | −0.308913 | − | 0.178351i | 0.337527 | − | 0.941316i | \(-0.390410\pi\) |
−0.646440 | + | 0.762965i | \(0.723743\pi\) | |||||||
\(504\) | 2.64575 | 0.117851 | ||||||||
\(505\) | −0.181435 | − | 3.02275i | −0.00807375 | − | 0.134511i | ||||
\(506\) | −3.00000 | − | 5.19615i | −0.133366 | − | 0.230997i | ||||
\(507\) | 12.9904 | − | 7.50000i | 0.576923 | − | 0.333087i | ||||
\(508\) | −11.4564 | − | 6.61438i | −0.508297 | − | 0.293466i | ||||
\(509\) | −1.32288 | − | 2.29129i | −0.0586354 | − | 0.101560i | 0.835218 | − | 0.549920i | \(-0.185342\pi\) |
−0.893853 | + | 0.448360i | \(0.852008\pi\) | |||||||
\(510\) | −7.39230 | − | 11.1962i | −0.327337 | − | 0.495774i | ||||
\(511\) | 38.5830 | 1.70681 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 4.58258 | + | 2.64575i | 0.202326 | + | 0.116813i | ||||
\(514\) | −2.64575 | − | 4.58258i | −0.116699 | − | 0.202129i | ||||
\(515\) | 1.66850 | + | 2.52706i | 0.0735230 | + | 0.111356i | ||||
\(516\) | 0.354249 | + | 0.613577i | 0.0155949 | + | 0.0270112i | ||||
\(517\) | −5.19615 | + | 3.00000i | −0.228527 | + | 0.131940i | ||||
\(518\) | −9.16515 | + | 5.29150i | −0.402694 | + | 0.232495i | ||||
\(519\) | 4.29150 | 0.188376 | ||||||||
\(520\) | −9.87408 | + | 6.51940i | −0.433007 | + | 0.285895i | ||||
\(521\) | −9.00000 | + | 15.5885i | −0.394297 | + | 0.682943i | −0.993011 | − | 0.118020i | \(-0.962345\pi\) |
0.598714 | + | 0.800963i | \(0.295679\pi\) | |||||||
\(522\) | −2.29129 | + | 1.32288i | −0.100287 | + | 0.0579007i | ||||
\(523\) | 1.87451i | 0.0819665i | 0.999160 | + | 0.0409833i | \(0.0130490\pi\) | ||||
−0.999160 | + | 0.0409833i | \(0.986951\pi\) | |||||||
\(524\) | 6.64575 | − | 11.5108i | 0.290321 | − | 0.502851i | ||||
\(525\) | −7.93725 | − | 10.5830i | −0.346410 | − | 0.461880i | ||||
\(526\) | −19.1660 | −0.835678 | ||||||||
\(527\) | 32.6916 | − | 6.87451i | 1.42407 | − | 0.299458i | ||||
\(528\) | − | 4.64575i | − | 0.202180i | ||||||
\(529\) | 21.3320 | 0.927479 | ||||||||
\(530\) | 15.4722 | − | 10.2156i | 0.672067 | − | 0.443735i | ||||
\(531\) | 4.64575 | 0.201608 | ||||||||
\(532\) | −12.1244 | + | 7.00000i | −0.525657 | + | 0.303488i | ||||
\(533\) | 33.4139 | + | 19.2915i | 1.44732 | + | 0.835608i | ||||
\(534\) | 3.64575 | − | 6.31463i | 0.157767 | − | 0.273261i | ||||
\(535\) | −5.00000 | + | 10.0000i | −0.216169 | + | 0.432338i | ||||
\(536\) | −0.354249 | − | 0.613577i | −0.0153012 | − | 0.0265025i | ||||
\(537\) | 20.1167 | − | 11.6144i | 0.868099 | − | 0.501197i | ||||
\(538\) | −6.92820 | + | 4.00000i | −0.298696 | + | 0.172452i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.23205 | + | 0.133975i | −0.0960522 | + | 0.00576535i | ||||
\(541\) | −1.93725 | + | 3.35542i | −0.0832891 | + | 0.144261i | −0.904661 | − | 0.426132i | \(-0.859876\pi\) |
0.821372 | + | 0.570393i | \(0.193209\pi\) | |||||||
\(542\) | − | 11.7085i | − | 0.502923i | ||||||
\(543\) | 11.2915i | 0.484565i | ||||||||
\(544\) | 3.00000 | − | 5.19615i | 0.128624 | − | 0.222783i | ||||
\(545\) | 2.31662 | + | 38.5955i | 0.0992332 | + | 1.65325i | ||||
\(546\) | −7.00000 | + | 12.1244i | −0.299572 | + | 0.518875i | ||||
\(547\) | −11.0059 | + | 6.35425i | −0.470578 | + | 0.271688i | −0.716481 | − | 0.697606i | \(-0.754249\pi\) |
0.245904 | + | 0.969294i | \(0.420915\pi\) | |||||||
\(548\) | −9.16515 | + | 5.29150i | −0.391516 | + | 0.226042i | ||||
\(549\) | 5.00000 | + | 8.66025i | 0.213395 | + | 0.369611i | ||||
\(550\) | −18.5830 | + | 13.9373i | −0.792382 | + | 0.594287i | ||||
\(551\) | 7.00000 | − | 12.1244i | 0.298210 | − | 0.516515i | ||||
\(552\) | −1.11847 | − | 0.645751i | −0.0476054 | − | 0.0274850i | ||||
\(553\) | −15.0836 | + | 8.70850i | −0.641418 | + | 0.370323i | ||||
\(554\) | 2.00000 | 0.0849719 | ||||||||
\(555\) | 7.46410 | − | 4.92820i | 0.316833 | − | 0.209191i | ||||
\(556\) | 4.00000 | 0.169638 | ||||||||
\(557\) | − | 6.29150i | − | 0.266580i | −0.991077 | − | 0.133290i | \(-0.957446\pi\) | ||
0.991077 | − | 0.133290i | \(-0.0425541\pi\) | |||||||
\(558\) | 1.73205 | − | 5.29150i | 0.0733236 | − | 0.224007i | ||||
\(559\) | −3.74902 | −0.158566 | ||||||||
\(560\) | 2.64575 | − | 5.29150i | 0.111803 | − | 0.223607i | ||||
\(561\) | −13.9373 | + | 24.1400i | −0.588431 | + | 1.01919i | ||||
\(562\) | − | 2.58301i | − | 0.108958i | ||||||
\(563\) | 7.28933 | − | 4.20850i | 0.307209 | − | 0.177367i | −0.338468 | − | 0.940978i | \(-0.609909\pi\) |
0.645677 | + | 0.763611i | \(0.276575\pi\) | |||||||
\(564\) | −0.645751 | + | 1.11847i | −0.0271910 | + | 0.0470963i | ||||
\(565\) | 3.33701 | + | 5.05412i | 0.140389 | + | 0.212629i | ||||
\(566\) | −29.2915 | −1.23121 | ||||||||
\(567\) | −2.29129 | + | 1.32288i | −0.0962250 | + | 0.0555556i | ||||
\(568\) | 12.6293 | − | 7.29150i | 0.529912 | − | 0.305945i | ||||
\(569\) | 3.00000 | + | 5.19615i | 0.125767 | + | 0.217834i | 0.922032 | − | 0.387113i | \(-0.126528\pi\) |
−0.796266 | + | 0.604947i | \(0.793194\pi\) | |||||||
\(570\) | 9.87408 | − | 6.51940i | 0.413580 | − | 0.273068i | ||||
\(571\) | 20.0000 | + | 34.6410i | 0.836974 | + | 1.44968i | 0.892413 | + | 0.451219i | \(0.149011\pi\) |
−0.0554391 | + | 0.998462i | \(0.517656\pi\) | |||||||
\(572\) | 21.2895 | + | 12.2915i | 0.890159 | + | 0.513934i | ||||
\(573\) | − | 8.00000i | − | 0.334205i | ||||||
\(574\) | −19.2915 | −0.805212 | ||||||||
\(575\) | 0.772417 | + | 6.41115i | 0.0322120 | + | 0.267363i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 24.0314 | + | 13.8745i | 1.00044 | + | 0.577603i | 0.908378 | − | 0.418150i | \(-0.137321\pi\) |
0.0920604 | + | 0.995753i | \(0.470655\pi\) | |||||||
\(578\) | −16.4545 | + | 9.50000i | −0.684416 | + | 0.395148i | ||||
\(579\) | −7.67712 | − | 13.2972i | −0.319050 | − | 0.552612i | ||||
\(580\) | 0.354463 | + | 5.90545i | 0.0147183 | + | 0.245211i | ||||
\(581\) | −30.6458 | −1.27140 | ||||||||
\(582\) | −13.1885 | − | 7.61438i | −0.546681 | − | 0.315626i | ||||
\(583\) | −33.3595 | − | 19.2601i | −1.38161 | − | 0.797673i | ||||
\(584\) | −7.29150 | − | 12.6293i | −0.301725 | − | 0.522602i | ||||
\(585\) | 5.29150 | − | 10.5830i | 0.218777 | − | 0.437553i | ||||
\(586\) | 12.1458 | − | 21.0371i | 0.501736 | − | 0.869033i | ||||
\(587\) | 3.00000i | 0.123823i | 0.998082 | + | 0.0619116i | \(0.0197197\pi\) | ||||
−0.998082 | + | 0.0619116i | \(0.980280\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.06275 | + | 28.8313i | 0.249811 | + | 1.18797i | ||||
\(590\) | 4.64575 | − | 9.29150i | 0.191263 | − | 0.382525i | ||||
\(591\) | 19.1660 | 0.788384 | ||||||||
\(592\) | 3.46410 | + | 2.00000i | 0.142374 | + | 0.0821995i | ||||
\(593\) | 28.4575i | 1.16861i | 0.811534 | + | 0.584305i | \(0.198633\pi\) | ||||
−0.811534 | + | 0.584305i | \(0.801367\pi\) | |||||||
\(594\) | 2.32288 | + | 4.02334i | 0.0953087 | + | 0.165080i | ||||
\(595\) | −29.6222 | + | 19.5582i | −1.21439 | + | 0.801808i | ||||
\(596\) | 6.67712 | − | 11.5651i | 0.273506 | − | 0.473726i | ||||
\(597\) | 5.70850i | 0.233633i | ||||||||
\(598\) | 5.91841 | − | 3.41699i | 0.242022 | − | 0.139731i | ||||
\(599\) | 3.64575 | + | 6.31463i | 0.148961 | + | 0.258009i | 0.930844 | − | 0.365417i | \(-0.119074\pi\) |
−0.781882 | + | 0.623426i | \(0.785740\pi\) | |||||||
\(600\) | −1.96410 | + | 4.59808i | −0.0801841 | + | 0.187716i | ||||
\(601\) | −17.5830 | + | 30.4547i | −0.717226 | + | 1.24227i | 0.244869 | + | 0.969556i | \(0.421255\pi\) |
−0.962095 | + | 0.272715i | \(0.912078\pi\) | |||||||
\(602\) | 1.62337 | − | 0.937254i | 0.0661637 | − | 0.0381996i | ||||
\(603\) | 0.613577 | + | 0.354249i | 0.0249868 | + | 0.0144261i | ||||
\(604\) | 22.2915 | 0.907028 | ||||||||
\(605\) | 21.1660 | + | 10.5830i | 0.860521 | + | 0.430260i | ||||
\(606\) | −0.677124 | + | 1.17281i | −0.0275063 | + | 0.0476423i | ||||
\(607\) | 23.1302 | − | 13.3542i | 0.938827 | − | 0.542032i | 0.0492348 | − | 0.998787i | \(-0.484322\pi\) |
0.889593 | + | 0.456755i | \(0.150988\pi\) | |||||||
\(608\) | 4.58258 | + | 2.64575i | 0.185848 | + | 0.107299i | ||||
\(609\) | 3.50000 | + | 6.06218i | 0.141827 | + | 0.245652i | ||||
\(610\) | 22.3205 | − | 1.33975i | 0.903731 | − | 0.0542447i | ||||
\(611\) | −3.41699 | − | 5.91841i | −0.138237 | − | 0.239433i | ||||
\(612\) | 6.00000i | 0.242536i | ||||||||
\(613\) | −23.6351 | − | 13.6458i | −0.954614 | − | 0.551147i | −0.0601029 | − | 0.998192i | \(-0.519143\pi\) |
−0.894511 | + | 0.447045i | \(0.852476\pi\) | |||||||
\(614\) | −8.93725 | + | 15.4798i | −0.360678 | + | 0.624713i | ||||
\(615\) | 16.2750 | − | 0.976876i | 0.656272 | − | 0.0393914i | ||||
\(616\) | −12.2915 | −0.495239 | ||||||||
\(617\) | −2.95920 | − | 1.70850i | −0.119133 | − | 0.0687815i | 0.439249 | − | 0.898365i | \(-0.355244\pi\) |
−0.558382 | + | 0.829584i | \(0.688578\pi\) | |||||||
\(618\) | − | 1.35425i | − | 0.0544759i | ||||||
\(619\) | −6.58301 | −0.264593 | −0.132297 | − | 0.991210i | \(-0.542235\pi\) | ||||
−0.132297 | + | 0.991210i | \(0.542235\pi\) | |||||||
\(620\) | −8.85095 | − | 8.75560i | −0.355463 | − | 0.351634i | ||||
\(621\) | 1.29150 | 0.0518262 | ||||||||
\(622\) | 19.8745i | 0.796895i | ||||||||
\(623\) | −16.7069 | − | 9.64575i | −0.669349 | − | 0.386449i | ||||
\(624\) | 5.29150 | 0.211830 | ||||||||
\(625\) | 24.2846 | − | 5.93782i | 0.971384 | − | 0.237513i | ||||
\(626\) | −0.968627 | + | 1.67771i | −0.0387141 | + | 0.0670548i | ||||
\(627\) | −21.2895 | − | 12.2915i | −0.850221 | − | 0.490875i | ||||
\(628\) | 9.29150i | 0.370771i | ||||||||
\(629\) | −12.0000 | − | 20.7846i | −0.478471 | − | 0.828737i | ||||
\(630\) | 0.354463 | + | 5.90545i | 0.0141222 | + | 0.235279i | ||||
\(631\) | −2.43725 | − | 4.22145i | −0.0970255 | − | 0.168053i | 0.813427 | − | 0.581668i | \(-0.197600\pi\) |
−0.910452 | + | 0.413614i | \(0.864266\pi\) | |||||||
\(632\) | 5.70105 | + | 3.29150i | 0.226776 | + | 0.130929i | ||||
\(633\) | −3.96900 | + | 2.29150i | −0.157754 | + | 0.0910791i | ||||
\(634\) | 2.85425 | − | 4.94370i | 0.113357 | − | 0.196340i | ||||
\(635\) | 13.2288 | − | 26.4575i | 0.524967 | − | 1.04993i | ||||
\(636\) | −8.29150 | −0.328779 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 10.6448 | − | 6.14575i | 0.421430 | − | 0.243313i | ||||
\(639\) | −7.29150 | + | 12.6293i | −0.288447 | + | 0.499606i | ||||
\(640\) | −2.23205 | + | 0.133975i | −0.0882296 | + | 0.00529581i | ||||
\(641\) | −12.5203 | − | 21.6857i | −0.494521 | − | 0.856535i | 0.505460 | − | 0.862850i | \(-0.331323\pi\) |
−0.999980 | + | 0.00631566i | \(0.997990\pi\) | |||||||
\(642\) | 4.33013 | − | 2.50000i | 0.170896 | − | 0.0986671i | ||||
\(643\) | − | 7.87451i | − | 0.310540i | −0.987872 | − | 0.155270i | \(-0.950375\pi\) | ||
0.987872 | − | 0.155270i | \(-0.0496248\pi\) | |||||||
\(644\) | −1.70850 | + | 2.95920i | −0.0673242 | + | 0.116609i | ||||
\(645\) | −1.32207 | + | 0.872905i | −0.0520566 | + | 0.0343706i | ||||
\(646\) | −15.8745 | − | 27.4955i | −0.624574 | − | 1.08179i | ||||
\(647\) | 2.00000i | 0.0786281i | 0.999227 | + | 0.0393141i | \(0.0125173\pi\) | ||||
−0.999227 | + | 0.0393141i | \(0.987483\pi\) | |||||||
\(648\) | 0.866025 | + | 0.500000i | 0.0340207 | + | 0.0196419i | ||||
\(649\) | −21.5830 | −0.847207 | ||||||||
\(650\) | −15.8745 | − | 21.1660i | −0.622649 | − | 0.830199i | ||||
\(651\) | −14.0000 | − | 4.58258i | −0.548703 | − | 0.179605i | ||||
\(652\) | 10.0000i | 0.391630i | ||||||||
\(653\) | 30.8745i | 1.20821i | 0.796904 | + | 0.604106i | \(0.206470\pi\) | ||||
−0.796904 | + | 0.604106i | \(0.793530\pi\) | |||||||
\(654\) | 8.64575 | − | 14.9749i | 0.338076 | − | 0.585564i | ||||
\(655\) | 26.5830 | + | 13.2915i | 1.03868 | + | 0.519342i | ||||
\(656\) | 3.64575 | + | 6.31463i | 0.142343 | + | 0.246545i | ||||
\(657\) | 12.6293 | + | 7.29150i | 0.492714 | + | 0.284469i | ||||
\(658\) | 2.95920 | + | 1.70850i | 0.115362 | + | 0.0666042i | ||||
\(659\) | −49.9373 | −1.94528 | −0.972640 | − | 0.232319i | \(-0.925369\pi\) | ||||
−0.972640 | + | 0.232319i | \(0.925369\pi\) | |||||||
\(660\) | 10.3696 | − | 0.622413i | 0.403634 | − | 0.0242274i | ||||
\(661\) | −23.2288 | − | 40.2334i | −0.903494 | − | 1.56490i | −0.822926 | − | 0.568148i | \(-0.807660\pi\) |
−0.0805677 | − | 0.996749i | \(-0.525673\pi\) | |||||||
\(662\) | −20.0624 | + | 11.5830i | −0.779746 | + | 0.450186i | ||||
\(663\) | −27.4955 | − | 15.8745i | −1.06783 | − | 0.616515i | ||||
\(664\) | 5.79150 | + | 10.0312i | 0.224754 | + | 0.389285i | ||||
\(665\) | −17.2487 | − | 26.1244i | −0.668876 | − | 1.01306i | ||||
\(666\) | −4.00000 | −0.154997 | ||||||||
\(667\) | − | 3.41699i | − | 0.132307i | ||||||
\(668\) | 8.55157 | + | 4.93725i | 0.330870 | + | 0.191028i | ||||
\(669\) | 10.6771 | + | 18.4933i | 0.412801 | + | 0.714993i | ||||
\(670\) | 1.32207 | − | 0.872905i | 0.0510762 | − | 0.0337233i | ||||
\(671\) | −23.2288 | − | 40.2334i | −0.896736 | − | 1.55319i | ||||
\(672\) | −2.29129 | + | 1.32288i | −0.0883883 | + | 0.0510310i | ||||
\(673\) | 38.5557 | − | 22.2601i | 1.48621 | − | 0.858065i | 0.486335 | − | 0.873772i | \(-0.338333\pi\) |
0.999877 | + | 0.0157073i | \(0.00499998\pi\) | |||||||
\(674\) | 23.1033 | 0.889904 | ||||||||
\(675\) | −0.598076 | − | 4.96410i | −0.0230200 | − | 0.191068i | ||||
\(676\) | −7.50000 | + | 12.9904i | −0.288462 | + | 0.499630i | ||||
\(677\) | 17.0681 | − | 9.85425i | 0.655979 | − | 0.378730i | −0.134764 | − | 0.990878i | \(-0.543028\pi\) |
0.790743 | + | 0.612148i | \(0.209694\pi\) | |||||||
\(678\) | − | 2.70850i | − | 0.104019i | ||||||
\(679\) | −20.1458 | + | 34.8935i | −0.773123 | + | 1.33909i | ||||
\(680\) | 12.0000 | + | 6.00000i | 0.460179 | + | 0.230089i | ||||
\(681\) | 15.0000 | 0.574801 | ||||||||
\(682\) | −8.04668 | + | 24.5830i | −0.308123 | + | 0.941332i | ||||
\(683\) | − | 20.1660i | − | 0.771631i | −0.922576 | − | 0.385815i | \(-0.873920\pi\) | ||
0.922576 | − | 0.385815i | \(-0.126080\pi\) | |||||||
\(684\) | −5.29150 | −0.202326 | ||||||||
\(685\) | −13.0388 | − | 19.7482i | −0.498187 | − | 0.754538i | ||||
\(686\) | 18.5203 | 0.707107 | ||||||||
\(687\) | 21.7944 | − | 12.5830i | 0.831508 | − | 0.480072i | ||||
\(688\) | −0.613577 | − | 0.354249i | −0.0233924 | − | 0.0135056i | ||||
\(689\) | 21.9373 | − | 37.9964i | 0.835743 | − | 1.44755i | ||||
\(690\) | 1.29150 | − | 2.58301i | 0.0491667 | − | 0.0983333i | ||||
\(691\) | −20.5830 | − | 35.6508i | −0.783014 | − | 1.35622i | −0.930178 | − | 0.367109i | \(-0.880348\pi\) |
0.147164 | − | 0.989112i | \(-0.452986\pi\) | |||||||
\(692\) | −3.71655 | + | 2.14575i | −0.141282 | + | 0.0815692i | ||||
\(693\) | 10.6448 | − | 6.14575i | 0.404361 | − | 0.233458i | ||||
\(694\) | −8.79150 | + | 15.2273i | −0.333721 | + | 0.578022i | ||||
\(695\) | 0.535898 | + | 8.92820i | 0.0203278 | + | 0.338666i | ||||
\(696\) | 1.32288 | − | 2.29129i | 0.0501435 | − | 0.0868510i | ||||
\(697\) | − | 43.7490i | − | 1.65711i | ||||||
\(698\) | − | 5.29150i | − | 0.200286i | ||||||
\(699\) | 1.64575 | − | 2.85052i | 0.0622480 | − | 0.107817i | ||||
\(700\) | 12.1654 | + | 5.19652i | 0.459808 | + | 0.196410i | ||||
\(701\) | 24.6144 | − | 42.6334i | 0.929672 | − | 1.61024i | 0.145803 | − | 0.989314i | \(-0.453423\pi\) |
0.783869 | − | 0.620926i | \(-0.213243\pi\) | |||||||
\(702\) | −4.58258 | + | 2.64575i | −0.172958 | + | 0.0998574i | ||||
\(703\) | 18.3303 | − | 10.5830i | 0.691340 | − | 0.399146i | ||||
\(704\) | 2.32288 | + | 4.02334i | 0.0875467 | + | 0.151635i | ||||
\(705\) | −2.58301 | − | 1.29150i | −0.0972816 | − | 0.0486408i | ||||
\(706\) | −16.6458 | + | 28.8313i | −0.626471 | + | 1.08508i | ||||
\(707\) | 3.10297 | + | 1.79150i | 0.116699 | + | 0.0673764i | ||||
\(708\) | −4.02334 | + | 2.32288i | −0.151206 | + | 0.0872990i | ||||
\(709\) | −23.2915 | −0.874731 | −0.437365 | − | 0.899284i | \(-0.644088\pi\) | ||||
−0.437365 | + | 0.899284i | \(0.644088\pi\) | |||||||
\(710\) | 17.9670 | + | 27.2123i | 0.674290 | + | 1.02126i | ||||
\(711\) | −6.58301 | −0.246882 | ||||||||
\(712\) | 7.29150i | 0.273261i | ||||||||
\(713\) | 4.79993 | + | 5.35425i | 0.179759 | + | 0.200518i | ||||
\(714\) | 15.8745 | 0.594089 | ||||||||
\(715\) | −24.5830 | + | 49.1660i | −0.919352 | + | 1.83870i | ||||
\(716\) | −11.6144 | + | 20.1167i | −0.434050 | + | 0.751796i | ||||
\(717\) | 3.41699i | 0.127610i | ||||||||
\(718\) | −15.5885 | + | 9.00000i | −0.581756 | + | 0.335877i | ||||
\(719\) | −7.29150 | + | 12.6293i | −0.271927 | + | 0.470992i | −0.969355 | − | 0.245663i | \(-0.920994\pi\) |
0.697428 | + | 0.716655i | \(0.254328\pi\) | |||||||
\(720\) | 1.86603 | − | 1.23205i | 0.0695427 | − | 0.0459158i | ||||
\(721\) | −3.58301 | −0.133438 | ||||||||
\(722\) | 7.79423 | − | 4.50000i | 0.290071 | − | 0.167473i | ||||
\(723\) | −18.1865 | + | 10.5000i | −0.676364 | + | 0.390499i | ||||
\(724\) | −5.64575 | − | 9.77873i | −0.209823 | − | 0.363424i | ||||
\(725\) | −13.1338 | + | 1.58236i | −0.487776 | + | 0.0587674i | ||||
\(726\) | −5.29150 | − | 9.16515i | −0.196386 | − | 0.340151i | ||||
\(727\) | −21.8487 | − | 12.6144i | −0.810325 | − | 0.467841i | 0.0367437 | − | 0.999325i | \(-0.488301\pi\) |
−0.847069 | + | 0.531483i | \(0.821635\pi\) | |||||||
\(728\) | − | 14.0000i | − | 0.518875i | ||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 27.2123 | − | 17.9670i | 1.00717 | − | 0.664989i | ||||
\(731\) | 2.12549 | + | 3.68146i | 0.0786142 | + | 0.136164i | ||||
\(732\) | −8.66025 | − | 5.00000i | −0.320092 | − | 0.184805i | ||||
\(733\) | −10.5010 | + | 6.06275i | −0.387863 | + | 0.223933i | −0.681234 | − | 0.732066i | \(-0.738556\pi\) |
0.293371 | + | 0.955999i | \(0.405223\pi\) | |||||||
\(734\) | −9.22876 | − | 15.9847i | −0.340640 | − | 0.590005i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.29150 | 0.0476054 | ||||||||
\(737\) | −2.85052 | − | 1.64575i | −0.105000 | − | 0.0606220i | ||||
\(738\) | −6.31463 | − | 3.64575i | −0.232445 | − | 0.134202i | ||||
\(739\) | −19.6458 | − | 34.0274i | −0.722681 | − | 1.25172i | −0.959922 | − | 0.280269i | \(-0.909576\pi\) |
0.237241 | − | 0.971451i | \(-0.423757\pi\) | |||||||
\(740\) | −4.00000 | + | 8.00000i | −0.147043 | + | 0.294086i | ||||
\(741\) | 14.0000 | − | 24.2487i | 0.514303 | − | 0.890799i | ||||
\(742\) | 21.9373i | 0.805342i | ||||||||
\(743\) | 18.5830i | 0.681744i | 0.940110 | + | 0.340872i | \(0.110722\pi\) | ||||
−0.940110 | + | 0.340872i | \(0.889278\pi\) | |||||||
\(744\) | 1.14575 | + | 5.44860i | 0.0420053 | + | 0.199755i | ||||
\(745\) | 26.7085 | + | 13.3542i | 0.978524 | + | 0.489262i | ||||
\(746\) | 27.1660 | 0.994618 | ||||||||
\(747\) | −10.0312 | − | 5.79150i | −0.367022 | − | 0.211900i | ||||
\(748\) | − | 27.8745i | − | 1.01919i | ||||||
\(749\) | −6.61438 | − | 11.4564i | −0.241684 | − | 0.418609i | ||||
\(750\) | −10.5263 | − | 3.76795i | −0.384365 | − | 0.137586i | ||||
\(751\) | −23.1458 | + | 40.0896i | −0.844600 | + | 1.46289i | 0.0413673 | + | 0.999144i | \(0.486829\pi\) |
−0.885968 | + | 0.463747i | \(0.846505\pi\) | |||||||
\(752\) | − | 1.29150i | − | 0.0470963i | ||||||
\(753\) | −18.4390 | + | 10.6458i | −0.671954 | + | 0.387953i | ||||
\(754\) | 7.00000 | + | 12.1244i | 0.254925 | + | 0.441543i | ||||
\(755\) | 2.98650 | + | 49.7558i | 0.108690 | + | 1.81080i | ||||
\(756\) | 1.32288 | − | 2.29129i | 0.0481125 | − | 0.0833333i | ||||
\(757\) | 32.8003 | − | 18.9373i | 1.19215 | − | 0.688286i | 0.233354 | − | 0.972392i | \(-0.425030\pi\) |
0.958793 | + | 0.284106i | \(0.0916967\pi\) | |||||||
\(758\) | −13.2428 | − | 7.64575i | −0.481001 | − | 0.277706i | ||||
\(759\) | −6.00000 | −0.217786 | ||||||||
\(760\) | −5.29150 | + | 10.5830i | −0.191943 | + | 0.383886i | ||||
\(761\) | −12.0000 | + | 20.7846i | −0.435000 | + | 0.753442i | −0.997296 | − | 0.0734946i | \(-0.976585\pi\) |
0.562296 | + | 0.826936i | \(0.309918\pi\) | |||||||
\(762\) | −11.4564 | + | 6.61438i | −0.415023 | + | 0.239614i | ||||
\(763\) | −39.6198 | − | 22.8745i | −1.43433 | − | 0.828113i | ||||
\(764\) | 4.00000 | + | 6.92820i | 0.144715 | + | 0.250654i | ||||
\(765\) | −13.3923 | + | 0.803848i | −0.484200 | + | 0.0290632i | ||||
\(766\) | −18.2288 | − | 31.5731i | −0.658632 | − | 1.14078i | ||||
\(767\) | − | 24.5830i | − | 0.887641i | ||||||
\(768\) | 0.866025 | + | 0.500000i | 0.0312500 | + | 0.0180422i | ||||
\(769\) | 13.7915 | − | 23.8876i | 0.497334 | − | 0.861408i | −0.502661 | − | 0.864484i | \(-0.667646\pi\) |
0.999995 | + | 0.00307535i | \(0.000978916\pi\) | |||||||
\(770\) | −1.64675 | − | 27.4353i | −0.0593447 | − | 0.988698i | ||||
\(771\) | −5.29150 | −0.190569 | ||||||||
\(772\) | 13.2972 | + | 7.67712i | 0.478576 | + | 0.276306i | ||||
\(773\) | 47.1660i | 1.69644i | 0.529641 | + | 0.848222i | \(0.322327\pi\) | ||||
−0.529641 | + | 0.848222i | \(0.677673\pi\) | |||||||
\(774\) | 0.708497 | 0.0254664 | ||||||||
\(775\) | 18.3572 | − | 20.9288i | 0.659408 | − | 0.751785i | ||||
\(776\) | 15.2288 | 0.546681 | ||||||||
\(777\) | 10.5830i | 0.379663i | ||||||||
\(778\) | −13.8564 | − | 8.00000i | −0.496776 | − | 0.286814i | ||||
\(779\) | 38.5830 | 1.38238 | ||||||||
\(780\) | 0.708927 | + | 11.8109i | 0.0253837 | + | 0.422898i | ||||
\(781\) | 33.8745 | − | 58.6724i | 1.21213 | − | 2.09946i | ||||
\(782\) | −6.71084 | − | 3.87451i | −0.239979 | − | 0.138552i | ||||
\(783\) | 2.64575i | 0.0945514i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.7391 | + | 1.24483i | −0.740210 | + | 0.0444297i | ||||
\(786\) | −6.64575 | − | 11.5108i | −0.237046 | − | 0.410576i | ||||
\(787\) | −12.7379 | − | 7.35425i | −0.454058 | − | 0.262151i | 0.255484 | − | 0.966813i | \(-0.417765\pi\) |
−0.709543 | + | 0.704663i | \(0.751098\pi\) | |||||||
\(788\) | −16.5983 | + | 9.58301i | −0.591288 | + | 0.341380i | ||||
\(789\) | −9.58301 | + | 16.5983i | −0.341164 | + | 0.590913i | ||||
\(790\) | −6.58301 | + | 13.1660i | −0.234213 | + | 0.468426i | ||||
\(791\) | −7.16601 | −0.254794 | ||||||||
\(792\) | −4.02334 | − | 2.32288i | −0.142963 | − | 0.0825398i | ||||
\(793\) | 45.8258 | − | 26.4575i | 1.62732 | − | 0.939534i | ||||
\(794\) | 2.58301 | − | 4.47390i | 0.0916674 | − | 0.158773i | ||||
\(795\) | −1.11085 | − | 18.5071i | −0.0393978 | − | 0.656378i | ||||
\(796\) | −2.85425 | − | 4.94370i | −0.101166 | − | 0.175225i | ||||
\(797\) | 18.2952 | − | 10.5627i | 0.648050 | − | 0.374152i | −0.139659 | − | 0.990200i | \(-0.544601\pi\) |
0.787709 | + | 0.616048i | \(0.211267\pi\) | |||||||
\(798\) | 14.0000i | 0.495595i | ||||||||
\(799\) | −3.87451 | + | 6.71084i | −0.137070 | + | 0.237413i | ||||
\(800\) | −0.598076 | − | 4.96410i | −0.0211452 | − | 0.175507i | ||||
\(801\) | −3.64575 | − | 6.31463i | −0.128816 | − | 0.223116i | ||||
\(802\) | − | 22.0000i | − | 0.776847i | ||||||
\(803\) | −58.6724 | − | 33.8745i | −2.07050 | − | 1.19541i | ||||
\(804\) | −0.708497 | −0.0249868 | ||||||||
\(805\) | −6.83399 | − | 3.41699i | −0.240866 | − | 0.120433i | ||||
\(806\) | −28.0000 | − | 9.16515i | −0.986258 | − | 0.322829i | ||||
\(807\) | 8.00000i | 0.281613i | ||||||||
\(808\) | − | 1.35425i | − | 0.0476423i | ||||||
\(809\) | −11.7085 | + | 20.2797i | −0.411649 | + | 0.712997i | −0.995070 | − | 0.0991729i | \(-0.968380\pi\) |
0.583421 | + | 0.812170i | \(0.301714\pi\) | |||||||
\(810\) | −1.00000 | + | 2.00000i | −0.0351364 | + | 0.0702728i | ||||
\(811\) | −2.64575 | − | 4.58258i | −0.0929049 | − | 0.160916i | 0.815827 | − | 0.578295i | \(-0.196282\pi\) |
−0.908732 | + | 0.417379i | \(0.862949\pi\) | |||||||
\(812\) | −6.06218 | − | 3.50000i | −0.212741 | − | 0.122826i | ||||
\(813\) | −10.1399 | − | 5.85425i | −0.355620 | − | 0.205317i | ||||
\(814\) | 18.5830 | 0.651334 | ||||||||
\(815\) | −22.3205 | + | 1.33975i | −0.781853 | + | 0.0469293i | ||||
\(816\) | −3.00000 | − | 5.19615i | −0.105021 | − | 0.181902i | ||||
\(817\) | −3.24674 | + | 1.87451i | −0.113589 | + | 0.0655807i | ||||
\(818\) | 27.3517 | + | 15.7915i | 0.956329 | + | 0.552137i | ||||
\(819\) | 7.00000 | + | 12.1244i | 0.244600 | + | 0.423659i | ||||
\(820\) | −13.6061 | + | 8.98350i | −0.475147 | + | 0.313717i | ||||
\(821\) | −9.10326 | −0.317706 | −0.158853 | − | 0.987302i | \(-0.550780\pi\) | ||||
−0.158853 | + | 0.987302i | \(0.550780\pi\) | |||||||
\(822\) | 10.5830i | 0.369125i | ||||||||
\(823\) | 19.6118 | + | 11.3229i | 0.683624 | + | 0.394691i | 0.801219 | − | 0.598371i | \(-0.204185\pi\) |
−0.117595 | + | 0.993062i | \(0.537518\pi\) | |||||||
\(824\) | 0.677124 | + | 1.17281i | 0.0235887 | + | 0.0408569i | ||||
\(825\) | 2.77851 | + | 23.0620i | 0.0967354 | + | 0.802915i | ||||
\(826\) | 6.14575 | + | 10.6448i | 0.213838 | + | 0.370378i | ||||
\(827\) | 29.9498 | − | 17.2915i | 1.04146 | − | 0.601284i | 0.121210 | − | 0.992627i | \(-0.461323\pi\) |
0.920245 | + | 0.391342i | \(0.127989\pi\) | |||||||
\(828\) | −1.11847 | + | 0.645751i | −0.0388697 | + | 0.0224414i | ||||
\(829\) | −45.7490 | −1.58893 | −0.794464 | − | 0.607311i | \(-0.792248\pi\) | ||||
−0.794464 | + | 0.607311i | \(0.792248\pi\) | |||||||
\(830\) | −21.6142 | + | 14.2709i | −0.750239 | + | 0.495348i | ||||
\(831\) | 1.00000 | − | 1.73205i | 0.0346896 | − | 0.0600842i | ||||
\(832\) | −4.58258 | + | 2.64575i | −0.158872 | + | 0.0917249i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.00000 | − | 3.46410i | 0.0692543 | − | 0.119952i | ||||
\(835\) | −9.87451 | + | 19.7490i | −0.341721 | + | 0.683443i | ||||
\(836\) | 24.5830 | 0.850221 | ||||||||
\(837\) | −3.71655 | − | 4.14575i | −0.128463 | − | 0.143298i | ||||
\(838\) | − | 1.93725i | − | 0.0669213i | ||||||
\(839\) | −42.0000 | −1.45000 | −0.725001 | − | 0.688748i | \(-0.758161\pi\) | ||||
−0.725001 | + | 0.688748i | \(0.758161\pi\) | |||||||
\(840\) | −3.25970 | − | 4.93704i | −0.112470 | − | 0.170344i | ||||
\(841\) | −22.0000 | −0.758621 | ||||||||
\(842\) | 0.108679 | − | 0.0627461i | 0.00374534 | − | 0.00216237i | ||||
\(843\) | −2.23695 | − | 1.29150i | −0.0770446 | − | 0.0444817i | ||||
\(844\) | 2.29150 | − | 3.96900i | 0.0788768 | − | 0.136619i | ||||
\(845\) | −30.0000 | − | 15.0000i | −1.03203 | − | 0.516016i | ||||
\(846\) | 0.645751 | + | 1.11847i | 0.0222014 | + | 0.0384539i | ||||
\(847\) | −24.2487 | + | 14.0000i | −0.833196 | + | 0.481046i | ||||
\(848\) | 7.18065 | − | 4.14575i | 0.246585 | − | 0.142366i | ||||
\(849\) | −14.6458 | + | 25.3672i | −0.502641 | + | 0.870600i | ||||
\(850\) | −11.7846 | + | 27.5885i | −0.404209 | + | 0.946276i | ||||
\(851\) | 2.58301 | − | 4.47390i | 0.0885443 | − | 0.153363i | ||||
\(852\) | − | 14.5830i | − | 0.499606i | ||||||
\(853\) | 12.4575i | 0.426537i | 0.976994 | + | 0.213269i | \(0.0684109\pi\) | ||||
−0.976994 | + | 0.213269i | \(0.931589\pi\) | |||||||
\(854\) | −13.2288 | + | 22.9129i | −0.452679 | + | 0.784063i | ||||
\(855\) | −0.708927 | − | 11.8109i | −0.0242448 | − | 0.403924i | ||||
\(856\) | −2.50000 | + | 4.33013i | −0.0854482 | + | 0.148001i | ||||
\(857\) | −46.6567 | + | 26.9373i | −1.59376 | + | 0.920159i | −0.601109 | + | 0.799167i | \(0.705274\pi\) |
−0.992654 | + | 0.120992i | \(0.961393\pi\) | |||||||
\(858\) | 21.2895 | − | 12.2915i | 0.726812 | − | 0.419625i | ||||
\(859\) | 9.64575 | + | 16.7069i | 0.329109 | + | 0.570033i | 0.982335 | − | 0.187129i | \(-0.0599184\pi\) |
−0.653226 | + | 0.757163i | \(0.726585\pi\) | |||||||
\(860\) | 0.708497 | − | 1.41699i | 0.0241596 | − | 0.0483191i | ||||
\(861\) | −9.64575 | + | 16.7069i | −0.328726 | + | 0.569371i | ||||
\(862\) | 30.3460 | + | 17.5203i | 1.03359 | + | 0.596742i | ||||
\(863\) | 30.9596 | − | 17.8745i | 1.05388 | − | 0.608455i | 0.130144 | − | 0.991495i | \(-0.458456\pi\) |
0.923732 | + | 0.383040i | \(0.125123\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −5.28735 | − | 8.00805i | −0.179775 | − | 0.272282i | ||||
\(866\) | 33.1660 | 1.12703 | ||||||||
\(867\) | 19.0000i | 0.645274i | ||||||||
\(868\) | 14.4156 | − | 3.03137i | 0.489299 | − | 0.102892i | ||||
\(869\) | 30.5830 | 1.03746 | ||||||||
\(870\) | 5.29150 | + | 2.64575i | 0.179399 | + | 0.0896994i | ||||
\(871\) | 1.87451 | − | 3.24674i | 0.0635153 | − | 0.110012i | ||||
\(872\) | 17.2915i | 0.585564i | ||||||||
\(873\) | −13.1885 | + | 7.61438i | −0.446363 | + | 0.257708i | ||||
\(874\) | 3.41699 | − | 5.91841i | 0.115582 | − | 0.200193i | ||||
\(875\) | −9.96906 | + | 27.8499i | −0.337016 | + | 0.941499i | ||||
\(876\) | −14.5830 | −0.492714 | ||||||||
\(877\) | 13.7477 | − | 7.93725i | 0.464228 | − | 0.268022i | −0.249593 | − | 0.968351i | \(-0.580297\pi\) |
0.713820 | + | 0.700329i | \(0.246963\pi\) | |||||||
\(878\) | −23.2740 | + | 13.4373i | −0.785460 | + | 0.453485i | ||||
\(879\) | −12.1458 | − | 21.0371i | −0.409666 | − | 0.709562i | ||||
\(880\) | −8.66909 | + | 5.72380i | −0.292235 | + | 0.192949i | ||||
\(881\) | 12.0000 | + | 20.7846i | 0.404290 | + | 0.700251i | 0.994239 | − | 0.107190i | \(-0.0341852\pi\) |
−0.589948 | + | 0.807441i | \(0.700852\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 8.00000i | − | 0.269221i | −0.990899 | − | 0.134611i | \(-0.957022\pi\) | ||
0.990899 | − | 0.134611i | \(-0.0429784\pi\) | |||||||
\(884\) | 31.7490 | 1.06783 | ||||||||
\(885\) | −5.72380 | − | 8.66909i | −0.192403 | − | 0.291408i | ||||
\(886\) | 4.00000 | + | 6.92820i | 0.134383 | + | 0.232758i | ||||
\(887\) | 43.5888 | + | 25.1660i | 1.46357 | + | 0.844992i | 0.999174 | − | 0.0406363i | \(-0.0129385\pi\) |
0.464395 | + | 0.885628i | \(0.346272\pi\) | |||||||
\(888\) | 3.46410 | − | 2.00000i | 0.116248 | − | 0.0671156i | ||||
\(889\) | 17.5000 | + | 30.3109i | 0.586931 | + | 1.01659i | ||||
\(890\) | −16.2750 | + | 0.976876i | −0.545539 | + | 0.0327450i | ||||
\(891\) | 4.64575 | 0.155639 | ||||||||
\(892\) | −18.4933 | − | 10.6771i | −0.619202 | − | 0.357497i | ||||
\(893\) | −5.91841 | − | 3.41699i | −0.198052 | − | 0.114345i | ||||
\(894\) | −6.67712 | − | 11.5651i | −0.223316 | − | 0.386795i | ||||
\(895\) | −46.4575 | − | 23.2288i | −1.55290 | − | 0.776452i | ||||
\(896\) | 1.32288 | − | 2.29129i | 0.0441942 | − | 0.0765466i | ||||
\(897\) | − | 6.83399i | − | 0.228180i | ||||||
\(898\) | 29.1660i | 0.973282i | ||||||||
\(899\) | −10.9686 | + | 9.83307i | −0.365824 | + | 0.327951i | ||||
\(900\) | 3.00000 | + | 4.00000i | 0.100000 | + | 0.133333i | ||||
\(901\) | −49.7490 | −1.65738 | ||||||||
\(902\) | 29.3362 | + | 16.9373i | 0.976788 | + | 0.563949i | ||||
\(903\) | − | 1.87451i | − | 0.0623797i | ||||||
\(904\) | 1.35425 | + | 2.34563i | 0.0450416 | + | 0.0780144i | ||||
\(905\) | 21.0702 | − | 13.9117i | 0.700398 | − | 0.462441i | ||||
\(906\) | 11.1458 | − | 19.3050i | 0.370293 | − | 0.641366i | ||||
\(907\) | 36.5830i | 1.21472i | 0.794427 | + | 0.607359i | \(0.207771\pi\) | ||||
−0.794427 | + | 0.607359i | \(0.792229\pi\) | |||||||
\(908\) | −12.9904 | + | 7.50000i | −0.431101 | + | 0.248896i | ||||
\(909\) | 0.677124 | + | 1.17281i | 0.0224588 | + | 0.0388998i | ||||
\(910\) | 31.2487 | − | 1.87564i | 1.03588 | − | 0.0621770i | ||||
\(911\) | −14.3542 | + | 24.8623i | −0.475577 | + | 0.823724i | −0.999609 | − | 0.0279747i | \(-0.991094\pi\) |
0.524031 | + | 0.851699i | \(0.324428\pi\) | |||||||
\(912\) | 4.58258 | − | 2.64575i | 0.151744 | − | 0.0876096i | ||||
\(913\) | 46.6024 | + | 26.9059i | 1.54231 | + | 0.890455i | ||||
\(914\) | −25.1660 | −0.832418 | ||||||||
\(915\) | 10.0000 | − | 20.0000i | 0.330590 | − | 0.661180i | ||||
\(916\) | −12.5830 | + | 21.7944i | −0.415754 | + | 0.720107i | ||||
\(917\) | −30.4547 | + | 17.5830i | −1.00570 | + | 0.580642i | ||||
\(918\) | 5.19615 | + | 3.00000i | 0.171499 | + | 0.0990148i | ||||
\(919\) | −17.7288 | − | 30.7071i | −0.584818 | − | 1.01293i | −0.994898 | − | 0.100885i | \(-0.967833\pi\) |
0.410080 | − | 0.912049i | \(-0.365501\pi\) | |||||||
\(920\) | 0.173029 | + | 2.88270i | 0.00570458 | + | 0.0950398i | ||||
\(921\) | 8.93725 | + | 15.4798i | 0.294493 | + | 0.510076i | ||||
\(922\) | 9.22876i | 0.303933i | ||||||||
\(923\) | 66.8277 | + | 38.5830i | 2.19966 | + | 1.26998i | ||||
\(924\) | −6.14575 | + | 10.6448i | −0.202180 | + | 0.350187i | ||||
\(925\) | −18.3923 | − | 7.85641i | −0.604735 | − | 0.258317i | ||||
\(926\) | 18.6458 | 0.612737 | ||||||||
\(927\) | −1.17281 | − | 0.677124i | −0.0385203 | − | 0.0222397i | ||||
\(928\) | 2.64575i | 0.0868510i | ||||||||
\(929\) | 6.70850 | 0.220099 | 0.110049 | − | 0.993926i | \(-0.464899\pi\) | ||||
0.110049 | + | 0.993926i | \(0.464899\pi\) | |||||||
\(930\) | −12.0081 | + | 3.28735i | −0.393760 | + | 0.107796i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.29150i | 0.107817i | ||||||||
\(933\) | 17.2118 | + | 9.93725i | 0.563490 | + | 0.325331i | ||||
\(934\) | −36.7490 | −1.20246 | ||||||||
\(935\) | 62.2173 | − | 3.73448i | 2.03472 | − | 0.122130i | ||||
\(936\) | 2.64575 | − | 4.58258i | 0.0864791 | − | 0.149786i | ||||
\(937\) | −12.6293 | − | 7.29150i | −0.412580 | − | 0.238203i | 0.279318 | − | 0.960199i | \(-0.409892\pi\) |
−0.691898 | + | 0.721996i | \(0.743225\pi\) | |||||||
\(938\) | 1.87451i | 0.0612049i | ||||||||
\(939\) | 0.968627 | + | 1.67771i | 0.0316099 | + | 0.0547500i | ||||
\(940\) | 2.88270 | − | 0.173029i | 0.0940233 | − | 0.00564357i | ||||
\(941\) | −12.5516 | − | 21.7401i | −0.409172 | − | 0.708706i | 0.585626 | − | 0.810582i | \(-0.300849\pi\) |
−0.994797 | + | 0.101876i | \(0.967516\pi\) | |||||||
\(942\) | 8.04668 | + | 4.64575i | 0.262175 | + | 0.151367i | ||||
\(943\) | 8.15536 | − | 4.70850i | 0.265575 | − | 0.153330i | ||||
\(944\) | 2.32288 | − | 4.02334i | 0.0756032 | − | 0.130949i | ||||
\(945\) | 5.29150 | + | 2.64575i | 0.172133 | + | 0.0860663i | ||||
\(946\) | −3.29150 | −0.107016 | ||||||||
\(947\) | 3.46410 | + | 2.00000i | 0.112568 | + | 0.0649913i | 0.555227 | − | 0.831699i | \(-0.312631\pi\) |
−0.442659 | + | 0.896690i | \(0.645965\pi\) | |||||||
\(948\) | 5.70105 | − | 3.29150i | 0.185161 | − | 0.106903i | ||||
\(949\) | 38.5830 | − | 66.8277i | 1.25246 | − | 2.16932i | ||||
\(950\) | −24.3307 | − | 10.3930i | −0.789393 | − | 0.337195i | ||||
\(951\) | −2.85425 | − | 4.94370i | −0.0925554 | − | 0.160311i | ||||
\(952\) | −13.7477 | + | 7.93725i | −0.445566 | + | 0.257248i | ||||
\(953\) | − | 28.5830i | − | 0.925894i | −0.886386 | − | 0.462947i | \(-0.846792\pi\) | ||
0.886386 | − | 0.462947i | \(-0.153208\pi\) | |||||||
\(954\) | −4.14575 | + | 7.18065i | −0.134224 | + | 0.232482i | ||||
\(955\) | −14.9282 | + | 9.85641i | −0.483065 | + | 0.318946i | ||||
\(956\) | −1.70850 | − | 2.95920i | −0.0552568 | − | 0.0957075i | ||||
\(957\) | − | 12.2915i | − | 0.397328i | ||||||
\(958\) | 28.2177 | + | 16.2915i | 0.911673 | + | 0.526355i | ||||
\(959\) | 28.0000 | 0.904167 | ||||||||
\(960\) | −1.00000 | + | 2.00000i | −0.0322749 | + | 0.0645497i | ||||
\(961\) | 3.37451 | − | 30.8158i | 0.108855 | − | 0.994058i | ||||
\(962\) | 21.1660i | 0.682420i | ||||||||
\(963\) | − | 5.00000i | − | 0.161123i | ||||||
\(964\) | 10.5000 | − | 18.1865i | 0.338182 | − | 0.585749i | ||||
\(965\) | −15.3542 | + | 30.7085i | −0.494271 | + | 0.988542i | ||||
\(966\) | 1.70850 | + | 2.95920i | 0.0549700 | + | 0.0952108i | ||||
\(967\) | 22.9129 | + | 13.2288i | 0.736828 | + | 0.425408i | 0.820915 | − | 0.571050i | \(-0.193464\pi\) |
−0.0840866 | + | 0.996458i | \(0.526797\pi\) | |||||||
\(968\) | 9.16515 | + | 5.29150i | 0.294579 | + | 0.170075i | ||||
\(969\) | −31.7490 | −1.01993 | ||||||||
\(970\) | 2.04027 | + | 33.9914i | 0.0655090 | + | 1.09140i | ||||
\(971\) | −25.5516 | − | 44.2567i | −0.819991 | − | 1.42027i | −0.905688 | − | 0.423945i | \(-0.860645\pi\) |
0.0856972 | − | 0.996321i | \(-0.472688\pi\) | |||||||
\(972\) | 0.866025 | − | 0.500000i | 0.0277778 | − | 0.0160375i | ||||
\(973\) | −9.16515 | − | 5.29150i | −0.293821 | − | 0.169638i | ||||
\(974\) | 4.61438 | + | 7.99234i | 0.147854 | + | 0.256091i | ||||
\(975\) | −26.2676 | + | 3.16472i | −0.841235 | + | 0.101352i | ||||
\(976\) | 10.0000 | 0.320092 | ||||||||
\(977\) | 30.5830i | 0.978437i | 0.872161 | + | 0.489219i | \(0.162718\pi\) | ||||
−0.872161 | + | 0.489219i | \(0.837282\pi\) | |||||||
\(978\) | 8.66025 | + | 5.00000i | 0.276924 | + | 0.159882i | ||||
\(979\) | 16.9373 | + | 29.3362i | 0.541317 | + | 0.937589i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.64575 | − | 14.9749i | −0.276038 | − | 0.478111i | ||||
\(982\) | −15.4254 | + | 8.90588i | −0.492246 | + | 0.284198i | ||||
\(983\) | 7.54178 | − | 4.35425i | 0.240545 | − | 0.138879i | −0.374882 | − | 0.927073i | \(-0.622317\pi\) |
0.615427 | + | 0.788194i | \(0.288983\pi\) | |||||||
\(984\) | 7.29150 | 0.232445 | ||||||||
\(985\) | −23.6135 | − | 35.7643i | −0.752389 | − | 1.13954i | ||||
\(986\) | 7.93725 | − | 13.7477i | 0.252774 | − | 0.437817i | ||||
\(987\) | 2.95920 | − | 1.70850i | 0.0941925 | − | 0.0543821i | ||||
\(988\) | 28.0000i | 0.890799i | ||||||||
\(989\) | −0.457513 | + | 0.792436i | −0.0145481 | + | 0.0251980i | ||||
\(990\) | 4.64575 | − | 9.29150i | 0.147652 | − | 0.295303i | ||||
\(991\) | −2.58301 | −0.0820519 | −0.0410259 | − | 0.999158i | \(-0.513063\pi\) | ||||
−0.0410259 | + | 0.999158i | \(0.513063\pi\) | |||||||
\(992\) | −3.71655 | − | 4.14575i | −0.118001 | − | 0.131628i | ||||
\(993\) | 23.1660i | 0.735151i | ||||||||
\(994\) | −38.5830 | −1.22378 | ||||||||
\(995\) | 10.6522 | − | 7.03316i | 0.337697 | − | 0.222966i | ||||
\(996\) | 11.5830 | 0.367022 | ||||||||
\(997\) | 1.84073 | − | 1.06275i | 0.0582965 | − | 0.0336575i | −0.470568 | − | 0.882363i | \(-0.655951\pi\) |
0.528865 | + | 0.848706i | \(0.322618\pi\) | |||||||
\(998\) | −31.5731 | − | 18.2288i | −0.999430 | − | 0.577021i | ||||
\(999\) | −2.00000 | + | 3.46410i | −0.0632772 | + | 0.109599i |
(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 | 930.2.s.b.439.4 | yes | 8 | |
5.4 | even | 2 | inner | 930.2.s.b.439.1 | ✓ | 8 | |
31.25 | even | 3 | inner | 930.2.s.b.769.3 | yes | 8 | |
155.149 | even | 6 | inner | 930.2.s.b.769.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.s.b.439.1 | ✓ | 8 | 5.4 | even | 2 | inner | |
930.2.s.b.439.4 | yes | 8 | 1.1 | even | 1 | trivial | |
930.2.s.b.769.2 | yes | 8 | 155.149 | even | 6 | inner | |
930.2.s.b.769.3 | yes | 8 | 31.25 | even | 3 | inner |