Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [196,2,Mod(195,196)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(196, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("196.195");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 196 = 2^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 196.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.56506787962\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1212153856.10 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 10x^{4} - 16x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 195.7 | ||
Root | \(1.07072 + 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 196.195 |
Dual form | 196.2.d.c.195.5 |
$q$-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 \(\left(\mathbb{Z}/196\mathbb{Z}\right)^\times\).
\(n\) | \(99\) | \(101\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.207107 | + | 1.39897i | 0.146447 | + | 0.989219i | ||||
\(3\) | −2.14144 | −1.23636 | −0.618182 | − | 0.786035i | \(-0.712130\pi\) | ||||
−0.618182 | + | 0.786035i | \(0.712130\pi\) | |||||||
\(4\) | −1.91421 | + | 0.579471i | −0.957107 | + | 0.289735i | ||||
\(5\) | − | 2.61313i | − | 1.16863i | −0.811529 | − | 0.584313i | \(-0.801364\pi\) | ||
0.811529 | − | 0.584313i | \(-0.198636\pi\) | |||||||
\(6\) | −0.443508 | − | 2.99581i | −0.181061 | − | 1.22303i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.20711 | − | 2.55791i | −0.426777 | − | 0.904357i | ||||
\(9\) | 1.58579 | 0.528595 | ||||||||
\(10\) | 3.65568 | − | 0.541196i | 1.15603 | − | 0.171141i | ||||
\(11\) | − | 3.95687i | − | 1.19304i | −0.802597 | − | 0.596521i | \(-0.796549\pi\) | ||
0.802597 | − | 0.596521i | \(-0.203451\pi\) | |||||||
\(12\) | 4.09918 | − | 1.24090i | 1.18333 | − | 0.358218i | ||||
\(13\) | − | 1.08239i | − | 0.300202i | −0.988671 | − | 0.150101i | \(-0.952040\pi\) | ||
0.988671 | − | 0.150101i | \(-0.0479598\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.59587i | 1.44485i | ||||||||
\(16\) | 3.32843 | − | 2.21846i | 0.832107 | − | 0.554615i | ||||
\(17\) | − | 0.317025i | − | 0.0768899i | −0.999261 | − | 0.0384450i | \(-0.987760\pi\) | ||
0.999261 | − | 0.0384450i | \(-0.0122404\pi\) | |||||||
\(18\) | 0.328427 | + | 2.21846i | 0.0774110 | + | 0.522896i | ||||
\(19\) | −5.16991 | −1.18606 | −0.593029 | − | 0.805181i | \(-0.702068\pi\) | ||||
−0.593029 | + | 0.805181i | \(0.702068\pi\) | |||||||
\(20\) | 1.51423 | + | 5.00208i | 0.338592 | + | 1.11850i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.53553 | − | 0.819496i | 1.18018 | − | 0.174717i | ||||
\(23\) | − | 2.31788i | − | 0.483312i | −0.970362 | − | 0.241656i | \(-0.922309\pi\) | ||
0.970362 | − | 0.241656i | \(-0.0776906\pi\) | |||||||
\(24\) | 2.58495 | + | 5.47762i | 0.527651 | + | 1.11811i | ||||
\(25\) | −1.82843 | −0.365685 | ||||||||
\(26\) | 1.51423 | − | 0.224171i | 0.296965 | − | 0.0439635i | ||||
\(27\) | 3.02846 | 0.582827 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.82843 | −1.26801 | −0.634004 | − | 0.773330i | \(-0.718590\pi\) | ||||
−0.634004 | + | 0.773330i | \(0.718590\pi\) | |||||||
\(30\) | −7.82843 | + | 1.15894i | −1.42927 | + | 0.211593i | ||||
\(31\) | −6.05692 | −1.08786 | −0.543928 | − | 0.839132i | \(-0.683063\pi\) | ||||
−0.543928 | + | 0.839132i | \(0.683063\pi\) | |||||||
\(32\) | 3.79289 | + | 4.19690i | 0.670495 | + | 0.741914i | ||||
\(33\) | 8.47343i | 1.47503i | ||||||||
\(34\) | 0.443508 | − | 0.0656581i | 0.0760610 | − | 0.0112603i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.03553 | + | 0.918917i | −0.505922 | + | 0.153153i | ||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | −1.07072 | − | 7.23252i | −0.173694 | − | 1.17327i | ||||
\(39\) | 2.31788i | 0.371158i | ||||||||
\(40\) | −6.68414 | + | 3.15432i | −1.05685 | + | 0.498742i | ||||
\(41\) | 2.29610i | 0.358591i | 0.983795 | + | 0.179295i | \(0.0573818\pi\) | ||||
−0.983795 | + | 0.179295i | \(0.942618\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.23486i | − | 1.10331i | −0.834074 | − | 0.551653i | \(-0.813997\pi\) | ||
0.834074 | − | 0.551653i | \(-0.186003\pi\) | |||||||
\(44\) | 2.29289 | + | 7.57430i | 0.345667 | + | 1.14187i | ||||
\(45\) | − | 4.14386i | − | 0.617730i | ||||||
\(46\) | 3.24264 | − | 0.480049i | 0.478101 | − | 0.0707794i | ||||
\(47\) | 4.28289 | 0.624724 | 0.312362 | − | 0.949963i | \(-0.398880\pi\) | ||||
0.312362 | + | 0.949963i | \(0.398880\pi\) | |||||||
\(48\) | −7.12764 | + | 4.75071i | −1.02879 | + | 0.685706i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.378680 | − | 2.55791i | −0.0535534 | − | 0.361743i | ||||
\(51\) | 0.678892i | 0.0950639i | ||||||||
\(52\) | 0.627215 | + | 2.07193i | 0.0869790 | + | 0.287325i | ||||
\(53\) | 10.4853 | 1.44026 | 0.720132 | − | 0.693837i | \(-0.244081\pi\) | ||||
0.720132 | + | 0.693837i | \(0.244081\pi\) | |||||||
\(54\) | 0.627215 | + | 4.23671i | 0.0853531 | + | 0.576544i | ||||
\(55\) | −10.3398 | −1.39422 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.0711 | 1.46640 | ||||||||
\(58\) | −1.41421 | − | 9.55274i | −0.185695 | − | 1.25434i | ||||
\(59\) | 11.2268 | 1.46161 | 0.730804 | − | 0.682587i | \(-0.239145\pi\) | ||||
0.730804 | + | 0.682587i | \(0.239145\pi\) | |||||||
\(60\) | −3.24264 | − | 10.7117i | −0.418623 | − | 1.38287i | ||||
\(61\) | − | 5.41196i | − | 0.692931i | −0.938063 | − | 0.346465i | \(-0.887382\pi\) | ||
0.938063 | − | 0.346465i | \(-0.112618\pi\) | |||||||
\(62\) | −1.25443 | − | 8.47343i | −0.159313 | − | 1.07613i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.08579 | + | 6.17534i | −0.635723 | + | 0.771917i | ||||
\(65\) | −2.82843 | −0.350823 | ||||||||
\(66\) | −11.8540 | + | 1.75490i | −1.45913 | + | 0.216014i | ||||
\(67\) | 3.27798i | 0.400469i | 0.979748 | + | 0.200235i | \(0.0641704\pi\) | ||||
−0.979748 | + | 0.200235i | \(0.935830\pi\) | |||||||
\(68\) | 0.183707 | + | 0.606854i | 0.0222777 | + | 0.0735919i | ||||
\(69\) | 4.96362i | 0.597550i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | −1.91421 | − | 4.05630i | −0.225592 | − | 0.478039i | ||||
\(73\) | 14.0167i | 1.64053i | 0.571983 | + | 0.820266i | \(0.306174\pi\) | ||||
−0.571983 | + | 0.820266i | \(0.693826\pi\) | |||||||
\(74\) | −0.828427 | − | 5.59587i | −0.0963027 | − | 0.650506i | ||||
\(75\) | 3.91548 | 0.452120 | ||||||||
\(76\) | 9.89630 | − | 2.99581i | 1.13518 | − | 0.343643i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.24264 | + | 0.480049i | −0.367157 | + | 0.0543549i | ||||
\(79\) | 7.91375i | 0.890366i | 0.895440 | + | 0.445183i | \(0.146861\pi\) | ||||
−0.895440 | + | 0.445183i | \(0.853139\pi\) | |||||||
\(80\) | −5.79712 | − | 8.69760i | −0.648138 | − | 0.972421i | ||||
\(81\) | −11.2426 | −1.24918 | ||||||||
\(82\) | −3.21217 | + | 0.475538i | −0.354725 | + | 0.0525144i | ||||
\(83\) | 9.45280 | 1.03758 | 0.518790 | − | 0.854902i | \(-0.326383\pi\) | ||||
0.518790 | + | 0.854902i | \(0.326383\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.828427 | −0.0898555 | ||||||||
\(86\) | 10.1213 | − | 1.49839i | 1.09141 | − | 0.161575i | ||||
\(87\) | 14.6227 | 1.56772 | ||||||||
\(88\) | −10.1213 | + | 4.77637i | −1.07894 | + | 0.509163i | ||||
\(89\) | − | 5.99162i | − | 0.635110i | −0.948240 | − | 0.317555i | \(-0.897138\pi\) | ||
0.948240 | − | 0.317555i | \(-0.102862\pi\) | |||||||
\(90\) | 5.79712 | − | 0.858221i | 0.611070 | − | 0.0904645i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.34315 | + | 4.43692i | 0.140033 | + | 0.462581i | ||||
\(93\) | 12.9706 | 1.34498 | ||||||||
\(94\) | 0.887016 | + | 5.99162i | 0.0914887 | + | 0.617988i | ||||
\(95\) | 13.5096i | 1.38606i | ||||||||
\(96\) | −8.12227 | − | 8.98743i | −0.828976 | − | 0.917276i | ||||
\(97\) | − | 9.23880i | − | 0.938058i | −0.883183 | − | 0.469029i | \(-0.844604\pi\) | ||
0.883183 | − | 0.469029i | \(-0.155396\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 6.27476i | − | 0.630637i | ||||||
\(100\) | 3.50000 | − | 1.05952i | 0.350000 | − | 0.105952i | ||||
\(101\) | − | 15.2304i | − | 1.51548i | −0.652555 | − | 0.757741i | \(-0.726303\pi\) | ||
0.652555 | − | 0.757741i | \(-0.273697\pi\) | |||||||
\(102\) | −0.949747 | + | 0.140603i | −0.0940390 | + | 0.0139218i | ||||
\(103\) | 12.1138 | 1.19361 | 0.596806 | − | 0.802385i | \(-0.296436\pi\) | ||||
0.596806 | + | 0.802385i | \(0.296436\pi\) | |||||||
\(104\) | −2.76866 | + | 1.30656i | −0.271489 | + | 0.128119i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.17157 | + | 14.6686i | 0.210922 | + | 1.42474i | ||||
\(107\) | − | 2.31788i | − | 0.224078i | −0.993704 | − | 0.112039i | \(-0.964262\pi\) | ||
0.993704 | − | 0.112039i | \(-0.0357382\pi\) | |||||||
\(108\) | −5.79712 | + | 1.75490i | −0.557828 | + | 0.168866i | ||||
\(109\) | −5.65685 | −0.541828 | −0.270914 | − | 0.962604i | \(-0.587326\pi\) | ||||
−0.270914 | + | 0.962604i | \(0.587326\pi\) | |||||||
\(110\) | −2.14144 | − | 14.4650i | −0.204179 | − | 1.37919i | ||||
\(111\) | 8.56578 | 0.813028 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.24264 | −0.399114 | −0.199557 | − | 0.979886i | \(-0.563950\pi\) | ||||
−0.199557 | + | 0.979886i | \(0.563950\pi\) | |||||||
\(114\) | 2.29289 | + | 15.4881i | 0.214749 | + | 1.45059i | ||||
\(115\) | −6.05692 | −0.564811 | ||||||||
\(116\) | 13.0711 | − | 3.95687i | 1.21362 | − | 0.367387i | ||||
\(117\) | − | 1.71644i | − | 0.158685i | ||||||
\(118\) | 2.32515 | + | 15.7060i | 0.214048 | + | 1.44585i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 14.3137 | − | 6.75481i | 1.30666 | − | 0.616627i | ||||
\(121\) | −4.65685 | −0.423350 | ||||||||
\(122\) | 7.57115 | − | 1.12085i | 0.685460 | − | 0.101477i | ||||
\(123\) | − | 4.91697i | − | 0.443349i | ||||||
\(124\) | 11.5942 | − | 3.50981i | 1.04119 | − | 0.315190i | ||||
\(125\) | − | 8.28772i | − | 0.741276i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.2316i | − | 0.907911i | −0.891024 | − | 0.453955i | \(-0.850013\pi\) | ||
0.891024 | − | 0.453955i | \(-0.149987\pi\) | |||||||
\(128\) | −9.69239 | − | 5.83589i | −0.856694 | − | 0.515825i | ||||
\(129\) | 15.4930i | 1.36409i | ||||||||
\(130\) | −0.585786 | − | 3.95687i | −0.0513769 | − | 0.347041i | ||||
\(131\) | 0.367414 | 0.0321011 | 0.0160505 | − | 0.999871i | \(-0.494891\pi\) | ||||
0.0160505 | + | 0.999871i | \(0.494891\pi\) | |||||||
\(132\) | −4.91010 | − | 16.2200i | −0.427370 | − | 1.41177i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.58579 | + | 0.678892i | −0.396152 | + | 0.0586474i | ||||
\(135\) | − | 7.91375i | − | 0.681107i | ||||||
\(136\) | −0.810922 | + | 0.382683i | −0.0695360 | + | 0.0328148i | ||||
\(137\) | −8.24264 | −0.704216 | −0.352108 | − | 0.935959i | \(-0.614535\pi\) | ||||
−0.352108 | + | 0.935959i | \(0.614535\pi\) | |||||||
\(138\) | −6.94394 | + | 1.02800i | −0.591107 | + | 0.0875091i | ||||
\(139\) | −22.8211 | −1.93566 | −0.967829 | − | 0.251610i | \(-0.919040\pi\) | ||||
−0.967829 | + | 0.251610i | \(0.919040\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.17157 | −0.772386 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.28289 | −0.358153 | ||||||||
\(144\) | 5.27817 | − | 3.51801i | 0.439848 | − | 0.293167i | ||||
\(145\) | 17.8435i | 1.48183i | ||||||||
\(146\) | −19.6089 | + | 2.90295i | −1.62284 | + | 0.240250i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.65685 | − | 2.31788i | 0.629390 | − | 0.190529i | ||||
\(149\) | 4.82843 | 0.395560 | 0.197780 | − | 0.980246i | \(-0.436627\pi\) | ||||
0.197780 | + | 0.980246i | \(0.436627\pi\) | |||||||
\(150\) | 0.810922 | + | 5.47762i | 0.0662115 | + | 0.447246i | ||||
\(151\) | − | 21.4234i | − | 1.74341i | −0.490032 | − | 0.871704i | \(-0.663015\pi\) | ||
0.490032 | − | 0.871704i | \(-0.336985\pi\) | |||||||
\(152\) | 6.24063 | + | 13.2241i | 0.506182 | + | 1.07262i | ||||
\(153\) | − | 0.502734i | − | 0.0406437i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.8275i | 1.27130i | ||||||||
\(156\) | −1.34315 | − | 4.43692i | −0.107538 | − | 0.355238i | ||||
\(157\) | − | 19.1886i | − | 1.53141i | −0.643189 | − | 0.765707i | \(-0.722389\pi\) | ||
0.643189 | − | 0.765707i | \(-0.277611\pi\) | |||||||
\(158\) | −11.0711 | + | 1.63899i | −0.880767 | + | 0.130391i | ||||
\(159\) | −22.4537 | −1.78069 | ||||||||
\(160\) | 10.9670 | − | 9.91131i | 0.867019 | − | 0.783558i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.32843 | − | 15.7281i | −0.182939 | − | 1.23571i | ||||
\(163\) | 15.1486i | 1.18653i | 0.805007 | + | 0.593265i | \(0.202161\pi\) | ||||
−0.805007 | + | 0.593265i | \(0.797839\pi\) | |||||||
\(164\) | −1.33052 | − | 4.39523i | −0.103896 | − | 0.343210i | ||||
\(165\) | 22.1421 | 1.72376 | ||||||||
\(166\) | 1.95774 | + | 13.2241i | 0.151950 | + | 1.02639i | ||||
\(167\) | 7.83095 | 0.605977 | 0.302989 | − | 0.952994i | \(-0.402016\pi\) | ||||
0.302989 | + | 0.952994i | \(0.402016\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.8284 | 0.909879 | ||||||||
\(170\) | −0.171573 | − | 1.15894i | −0.0131590 | − | 0.0888868i | ||||
\(171\) | −8.19837 | −0.626945 | ||||||||
\(172\) | 4.19239 | + | 13.8491i | 0.319667 | + | 1.05598i | ||||
\(173\) | − | 6.57128i | − | 0.499605i | −0.968297 | − | 0.249802i | \(-0.919634\pi\) | ||
0.968297 | − | 0.249802i | \(-0.0803657\pi\) | |||||||
\(174\) | 3.02846 | + | 20.4567i | 0.229587 | + | 1.55082i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8.77817 | − | 13.1702i | −0.661680 | − | 0.992739i | ||||
\(177\) | −24.0416 | −1.80708 | ||||||||
\(178\) | 8.38207 | − | 1.24090i | 0.628263 | − | 0.0930098i | ||||
\(179\) | 13.5096i | 1.00976i | 0.863191 | + | 0.504878i | \(0.168463\pi\) | ||||
−0.863191 | + | 0.504878i | \(0.831537\pi\) | |||||||
\(180\) | 2.40125 | + | 7.93223i | 0.178978 | + | 0.591234i | ||||
\(181\) | 21.9874i | 1.63431i | 0.576418 | + | 0.817155i | \(0.304450\pi\) | ||||
−0.576418 | + | 0.817155i | \(0.695550\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.5894i | 0.856714i | ||||||||
\(184\) | −5.92893 | + | 2.79793i | −0.437087 | + | 0.206266i | ||||
\(185\) | 10.4525i | 0.768483i | ||||||||
\(186\) | 2.68629 | + | 18.1454i | 0.196968 | + | 1.33048i | ||||
\(187\) | −1.25443 | −0.0917330 | ||||||||
\(188\) | −8.19837 | + | 2.48181i | −0.597927 | + | 0.181005i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −18.8995 | + | 2.79793i | −1.37111 | + | 0.202983i | ||||
\(191\) | − | 6.55596i | − | 0.474373i | −0.971464 | − | 0.237186i | \(-0.923775\pi\) | ||
0.971464 | − | 0.237186i | \(-0.0762252\pi\) | |||||||
\(192\) | 10.8909 | − | 13.2241i | 0.785985 | − | 0.954370i | ||||
\(193\) | 14.5858 | 1.04991 | 0.524954 | − | 0.851131i | \(-0.324083\pi\) | ||||
0.524954 | + | 0.851131i | \(0.324083\pi\) | |||||||
\(194\) | 12.9248 | − | 1.91342i | 0.927944 | − | 0.137375i | ||||
\(195\) | 6.05692 | 0.433745 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 8.77817 | − | 1.29954i | 0.623838 | − | 0.0923546i | ||||
\(199\) | −17.1316 | −1.21442 | −0.607212 | − | 0.794540i | \(-0.707712\pi\) | ||||
−0.607212 | + | 0.794540i | \(0.707712\pi\) | |||||||
\(200\) | 2.20711 | + | 4.67695i | 0.156066 | + | 0.330710i | ||||
\(201\) | − | 7.01962i | − | 0.495126i | ||||||
\(202\) | 21.3068 | − | 3.15432i | 1.49914 | − | 0.221937i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.393398 | − | 1.29954i | −0.0275434 | − | 0.0909863i | ||||
\(205\) | 6.00000 | 0.419058 | ||||||||
\(206\) | 2.50886 | + | 16.9469i | 0.174800 | + | 1.18074i | ||||
\(207\) | − | 3.67567i | − | 0.255477i | ||||||
\(208\) | −2.40125 | − | 3.60266i | −0.166496 | − | 0.249800i | ||||
\(209\) | 20.4567i | 1.41502i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.4697i | 0.996136i | 0.867138 | + | 0.498068i | \(0.165957\pi\) | ||||
−0.867138 | + | 0.498068i | \(0.834043\pi\) | |||||||
\(212\) | −20.0711 | + | 6.07591i | −1.37849 | + | 0.417296i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.24264 | − | 0.480049i | 0.221662 | − | 0.0328155i | ||||
\(215\) | −18.9056 | −1.28935 | ||||||||
\(216\) | −3.65568 | − | 7.74652i | −0.248737 | − | 0.527084i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.17157 | − | 7.91375i | −0.0793489 | − | 0.535987i | ||||
\(219\) | − | 30.0160i | − | 2.02829i | ||||||
\(220\) | 19.7926 | − | 5.99162i | 1.33442 | − | 0.403955i | ||||
\(221\) | −0.343146 | −0.0230825 | ||||||||
\(222\) | 1.77403 | + | 11.9832i | 0.119065 | + | 0.804262i | ||||
\(223\) | 7.83095 | 0.524399 | 0.262200 | − | 0.965014i | \(-0.415552\pi\) | ||||
0.262200 | + | 0.965014i | \(0.415552\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.89949 | −0.193300 | ||||||||
\(226\) | −0.878680 | − | 5.93531i | −0.0584489 | − | 0.394811i | ||||
\(227\) | −9.97240 | −0.661891 | −0.330946 | − | 0.943650i | \(-0.607368\pi\) | ||||
−0.330946 | + | 0.943650i | \(0.607368\pi\) | |||||||
\(228\) | −21.1924 | + | 6.41536i | −1.40350 | + | 0.424868i | ||||
\(229\) | 1.34502i | 0.0888817i | 0.999012 | + | 0.0444409i | \(0.0141506\pi\) | ||||
−0.999012 | + | 0.0444409i | \(0.985849\pi\) | |||||||
\(230\) | −1.25443 | − | 8.47343i | −0.0827146 | − | 0.558721i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.24264 | + | 17.4665i | 0.541156 | + | 1.14673i | ||||
\(233\) | 16.2426 | 1.06409 | 0.532045 | − | 0.846716i | \(-0.321424\pi\) | ||||
0.532045 | + | 0.846716i | \(0.321424\pi\) | |||||||
\(234\) | 2.40125 | − | 0.355487i | 0.156974 | − | 0.0232389i | ||||
\(235\) | − | 11.1917i | − | 0.730068i | ||||||
\(236\) | −21.4905 | + | 6.50562i | −1.39892 | + | 0.423480i | ||||
\(237\) | − | 16.9469i | − | 1.10082i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.2316i | − | 0.661829i | −0.943661 | − | 0.330915i | \(-0.892643\pi\) | ||
0.943661 | − | 0.330915i | \(-0.107357\pi\) | |||||||
\(240\) | 12.4142 | + | 18.6254i | 0.801334 | + | 1.20227i | ||||
\(241\) | − | 5.09494i | − | 0.328194i | −0.986444 | − | 0.164097i | \(-0.947529\pi\) | ||
0.986444 | − | 0.164097i | \(-0.0524710\pi\) | |||||||
\(242\) | −0.964466 | − | 6.51478i | −0.0619982 | − | 0.418786i | ||||
\(243\) | 14.9901 | 0.961616 | ||||||||
\(244\) | 3.13607 | + | 10.3596i | 0.200767 | + | 0.663209i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.87868 | − | 1.01834i | 0.438569 | − | 0.0649269i | ||||
\(247\) | 5.59587i | 0.356056i | ||||||||
\(248\) | 7.31135 | + | 15.4930i | 0.464271 | + | 0.983809i | ||||
\(249\) | −20.2426 | −1.28283 | ||||||||
\(250\) | 11.5942 | − | 1.71644i | 0.733284 | − | 0.108557i | ||||
\(251\) | −3.91548 | −0.247143 | −0.123571 | − | 0.992336i | \(-0.539435\pi\) | ||||
−0.123571 | + | 0.992336i | \(0.539435\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.17157 | −0.576612 | ||||||||
\(254\) | 14.3137 | − | 2.11904i | 0.898122 | − | 0.132960i | ||||
\(255\) | 1.77403 | 0.111094 | ||||||||
\(256\) | 6.15685 | − | 14.7680i | 0.384803 | − | 0.922999i | ||||
\(257\) | 19.0572i | 1.18876i | 0.804185 | + | 0.594379i | \(0.202602\pi\) | ||||
−0.804185 | + | 0.594379i | \(0.797398\pi\) | |||||||
\(258\) | −21.6743 | + | 3.20871i | −1.34938 | + | 0.199766i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5.41421 | − | 1.63899i | 0.335775 | − | 0.101646i | ||||
\(261\) | −10.8284 | −0.670263 | ||||||||
\(262\) | 0.0760939 | + | 0.514000i | 0.00470110 | + | 0.0317550i | ||||
\(263\) | − | 25.6614i | − | 1.58235i | −0.611588 | − | 0.791176i | \(-0.709469\pi\) | ||
0.611588 | − | 0.791176i | \(-0.290531\pi\) | |||||||
\(264\) | 21.6743 | − | 10.2283i | 1.33396 | − | 0.629510i | ||||
\(265\) | − | 27.3994i | − | 1.68313i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.8307i | 0.785227i | ||||||||
\(268\) | −1.89949 | − | 6.27476i | −0.116030 | − | 0.383292i | ||||
\(269\) | 5.04054i | 0.307327i | 0.988123 | + | 0.153664i | \(0.0491072\pi\) | ||||
−0.988123 | + | 0.153664i | \(0.950893\pi\) | |||||||
\(270\) | 11.0711 | − | 1.63899i | 0.673764 | − | 0.0997458i | ||||
\(271\) | 4.28289 | 0.260167 | 0.130084 | − | 0.991503i | \(-0.458475\pi\) | ||||
0.130084 | + | 0.991503i | \(0.458475\pi\) | |||||||
\(272\) | −0.703309 | − | 1.05520i | −0.0426443 | − | 0.0639806i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.70711 | − | 11.5312i | −0.103130 | − | 0.696624i | ||||
\(275\) | 7.23486i | 0.436278i | ||||||||
\(276\) | −2.87627 | − | 9.50143i | −0.173131 | − | 0.571919i | ||||
\(277\) | −4.14214 | −0.248877 | −0.124438 | − | 0.992227i | \(-0.539713\pi\) | ||||
−0.124438 | + | 0.992227i | \(0.539713\pi\) | |||||||
\(278\) | −4.72640 | − | 31.9259i | −0.283470 | − | 1.91479i | ||||
\(279\) | −9.60498 | −0.575035 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.3848 | 0.619504 | 0.309752 | − | 0.950817i | \(-0.399754\pi\) | ||||
0.309752 | + | 0.950817i | \(0.399754\pi\) | |||||||
\(282\) | −1.89949 | − | 12.8307i | −0.113113 | − | 0.764058i | ||||
\(283\) | 3.39587 | 0.201864 | 0.100932 | − | 0.994893i | \(-0.467818\pi\) | ||||
0.100932 | + | 0.994893i | \(0.467818\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 28.9301i | − | 1.71367i | ||||||
\(286\) | −0.887016 | − | 5.99162i | −0.0524503 | − | 0.354292i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 6.01472 | + | 6.65539i | 0.354421 | + | 0.392172i | ||||
\(289\) | 16.8995 | 0.994088 | ||||||||
\(290\) | −24.9625 | + | 3.69552i | −1.46585 | + | 0.217008i | ||||
\(291\) | 19.7844i | 1.15978i | ||||||||
\(292\) | −8.12227 | − | 26.8310i | −0.475320 | − | 1.57016i | ||||
\(293\) | − | 11.7975i | − | 0.689219i | −0.938746 | − | 0.344609i | \(-0.888011\pi\) | ||
0.938746 | − | 0.344609i | \(-0.111989\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 29.3371i | − | 1.70807i | ||||||
\(296\) | 4.82843 | + | 10.2316i | 0.280647 | + | 0.594702i | ||||
\(297\) | − | 11.9832i | − | 0.695338i | ||||||
\(298\) | 1.00000 | + | 6.75481i | 0.0579284 | + | 0.391295i | ||||
\(299\) | −2.50886 | −0.145091 | ||||||||
\(300\) | −7.49506 | + | 2.26890i | −0.432727 | + | 0.130995i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 29.9706 | − | 4.43692i | 1.72461 | − | 0.255316i | ||||
\(303\) | 32.6151i | 1.87369i | ||||||||
\(304\) | −17.2077 | + | 11.4692i | −0.986927 | + | 0.657806i | ||||
\(305\) | −14.1421 | −0.809776 | ||||||||
\(306\) | 0.703309 | − | 0.104120i | 0.0402055 | − | 0.00595213i | ||||
\(307\) | −3.91548 | −0.223468 | −0.111734 | − | 0.993738i | \(-0.535640\pi\) | ||||
−0.111734 | + | 0.993738i | \(0.535640\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.9411 | −1.47574 | ||||||||
\(310\) | −22.1421 | + | 3.27798i | −1.25759 | + | 0.186177i | ||||
\(311\) | 20.6796 | 1.17263 | 0.586317 | − | 0.810082i | \(-0.300577\pi\) | ||||
0.586317 | + | 0.810082i | \(0.300577\pi\) | |||||||
\(312\) | 5.92893 | − | 2.79793i | 0.335660 | − | 0.158402i | ||||
\(313\) | − | 12.7486i | − | 0.720594i | −0.932838 | − | 0.360297i | \(-0.882675\pi\) | ||
0.932838 | − | 0.360297i | \(-0.117325\pi\) | |||||||
\(314\) | 26.8442 | − | 3.97408i | 1.51490 | − | 0.224270i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.58579 | − | 15.1486i | −0.257971 | − | 0.852176i | ||||
\(317\) | −5.51472 | −0.309737 | −0.154869 | − | 0.987935i | \(-0.549495\pi\) | ||||
−0.154869 | + | 0.987935i | \(0.549495\pi\) | |||||||
\(318\) | −4.65030 | − | 31.4119i | −0.260776 | − | 1.76149i | ||||
\(319\) | 27.0192i | 1.51279i | ||||||||
\(320\) | 16.1369 | + | 13.2898i | 0.902082 | + | 0.742922i | ||||
\(321\) | 4.96362i | 0.277042i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.63899i | 0.0911959i | ||||||||
\(324\) | 21.5208 | − | 6.51478i | 1.19560 | − | 0.361932i | ||||
\(325\) | 1.97908i | 0.109779i | ||||||||
\(326\) | −21.1924 | + | 3.13738i | −1.17374 | + | 0.173763i | ||||
\(327\) | 12.1138 | 0.669897 | ||||||||
\(328\) | 5.87321 | − | 2.77164i | 0.324294 | − | 0.153038i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 4.58579 | + | 30.9761i | 0.252439 | + | 1.70518i | ||||
\(331\) | 15.1486i | 0.832643i | 0.909218 | + | 0.416321i | \(0.136681\pi\) | ||||
−0.909218 | + | 0.416321i | \(0.863319\pi\) | |||||||
\(332\) | −18.0947 | + | 5.47762i | −0.993074 | + | 0.300623i | ||||
\(333\) | −6.34315 | −0.347602 | ||||||||
\(334\) | 1.62184 | + | 10.9552i | 0.0887433 | + | 0.599444i | ||||
\(335\) | 8.56578 | 0.467999 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.8284 | 0.589862 | 0.294931 | − | 0.955519i | \(-0.404703\pi\) | ||||
0.294931 | + | 0.955519i | \(0.404703\pi\) | |||||||
\(338\) | 2.44975 | + | 16.5476i | 0.133249 | + | 0.900069i | ||||
\(339\) | 9.08538 | 0.493450 | ||||||||
\(340\) | 1.58579 | − | 0.480049i | 0.0860013 | − | 0.0260343i | ||||
\(341\) | 23.9665i | 1.29786i | ||||||||
\(342\) | −1.69794 | − | 11.4692i | −0.0918139 | − | 0.620185i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −18.5061 | + | 8.73324i | −0.997782 | + | 0.470865i | ||||
\(345\) | 12.9706 | 0.698312 | ||||||||
\(346\) | 9.19299 | − | 1.36096i | 0.494218 | − | 0.0731654i | ||||
\(347\) | − | 3.95687i | − | 0.212416i | −0.994344 | − | 0.106208i | \(-0.966129\pi\) | ||
0.994344 | − | 0.106208i | \(-0.0338710\pi\) | |||||||
\(348\) | −27.9910 | + | 8.47343i | −1.50047 | + | 0.454223i | ||||
\(349\) | 8.47343i | 0.453572i | 0.973945 | + | 0.226786i | \(0.0728218\pi\) | ||||
−0.973945 | + | 0.226786i | \(0.927178\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 3.27798i | − | 0.174966i | ||||||
\(352\) | 16.6066 | − | 15.0080i | 0.885135 | − | 0.799929i | ||||
\(353\) | 10.0586i | 0.535363i | 0.963507 | + | 0.267681i | \(0.0862575\pi\) | ||||
−0.963507 | + | 0.267681i | \(0.913743\pi\) | |||||||
\(354\) | −4.97918 | − | 33.6334i | −0.264641 | − | 1.78760i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.47197 | + | 11.4692i | 0.184014 | + | 0.607868i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.8995 | + | 2.79793i | −0.998869 | + | 0.147875i | ||||
\(359\) | − | 31.2573i | − | 1.64970i | −0.565353 | − | 0.824849i | \(-0.691260\pi\) | ||
0.565353 | − | 0.824849i | \(-0.308740\pi\) | |||||||
\(360\) | −10.5996 | + | 5.00208i | −0.558649 | + | 0.263633i | ||||
\(361\) | 7.72792 | 0.406733 | ||||||||
\(362\) | −30.7596 | + | 4.55374i | −1.61669 | + | 0.239339i | ||||
\(363\) | 9.97240 | 0.523415 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 36.6274 | 1.91717 | ||||||||
\(366\) | −16.2132 | + | 2.40025i | −0.847478 | + | 0.125463i | ||||
\(367\) | 12.8487 | 0.670695 | 0.335348 | − | 0.942094i | \(-0.391146\pi\) | ||||
0.335348 | + | 0.942094i | \(0.391146\pi\) | |||||||
\(368\) | −5.14214 | − | 7.71491i | −0.268052 | − | 0.402167i | ||||
\(369\) | 3.64113i | 0.189549i | ||||||||
\(370\) | −14.6227 | + | 2.16478i | −0.760198 | + | 0.112542i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −24.8284 | + | 7.51606i | −1.28729 | + | 0.389690i | ||||
\(373\) | −20.1421 | −1.04292 | −0.521460 | − | 0.853276i | \(-0.674612\pi\) | ||||
−0.521460 | + | 0.853276i | \(0.674612\pi\) | |||||||
\(374\) | −0.259801 | − | 1.75490i | −0.0134340 | − | 0.0907440i | ||||
\(375\) | 17.7477i | 0.916487i | ||||||||
\(376\) | −5.16991 | − | 10.9552i | −0.266618 | − | 0.564973i | ||||
\(377\) | 7.39104i | 0.380658i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 21.7046i | − | 1.11489i | −0.830214 | − | 0.557444i | \(-0.811782\pi\) | ||
0.830214 | − | 0.557444i | \(-0.188218\pi\) | |||||||
\(380\) | −7.82843 | − | 25.8603i | −0.401590 | − | 1.32660i | ||||
\(381\) | 21.9105i | 1.12251i | ||||||||
\(382\) | 9.17157 | − | 1.35778i | 0.469258 | − | 0.0694703i | ||||
\(383\) | 31.0194 | 1.58502 | 0.792509 | − | 0.609860i | \(-0.208774\pi\) | ||||
0.792509 | + | 0.609860i | \(0.208774\pi\) | |||||||
\(384\) | 20.7557 | + | 12.4972i | 1.05919 | + | 0.637747i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.02082 | + | 20.4050i | 0.153755 | + | 1.03859i | ||||
\(387\) | − | 11.4729i | − | 0.583202i | ||||||
\(388\) | 5.35361 | + | 17.6850i | 0.271788 | + | 0.897821i | ||||
\(389\) | 14.1421 | 0.717035 | 0.358517 | − | 0.933523i | \(-0.383282\pi\) | ||||
0.358517 | + | 0.933523i | \(0.383282\pi\) | |||||||
\(390\) | 1.25443 | + | 8.47343i | 0.0635205 | + | 0.429069i | ||||
\(391\) | −0.734828 | −0.0371618 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.786797 | −0.0396886 | ||||||||
\(394\) | 0.414214 | + | 2.79793i | 0.0208678 | + | 0.140958i | ||||
\(395\) | 20.6796 | 1.04050 | ||||||||
\(396\) | 3.63604 | + | 12.0112i | 0.182718 | + | 0.603587i | ||||
\(397\) | − | 16.1271i | − | 0.809396i | −0.914450 | − | 0.404698i | \(-0.867377\pi\) | ||
0.914450 | − | 0.404698i | \(-0.132623\pi\) | |||||||
\(398\) | −3.54806 | − | 23.9665i | −0.177848 | − | 1.20133i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.08579 | + | 4.05630i | −0.304289 | + | 0.202815i | ||||
\(401\) | −12.8284 | −0.640621 | −0.320311 | − | 0.947313i | \(-0.603787\pi\) | ||||
−0.320311 | + | 0.947313i | \(0.603787\pi\) | |||||||
\(402\) | 9.82021 | − | 1.45381i | 0.489788 | − | 0.0725095i | ||||
\(403\) | 6.55596i | 0.326576i | ||||||||
\(404\) | 8.82558 | + | 29.1543i | 0.439089 | + | 1.45048i | ||||
\(405\) | 29.3784i | 1.45983i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.8275i | 0.784540i | ||||||||
\(408\) | 1.73654 | − | 0.819496i | 0.0859717 | − | 0.0405711i | ||||
\(409\) | − | 13.8310i | − | 0.683899i | −0.939718 | − | 0.341949i | \(-0.888913\pi\) | ||
0.939718 | − | 0.341949i | \(-0.111087\pi\) | |||||||
\(410\) | 1.24264 | + | 8.39380i | 0.0613696 | + | 0.414540i | ||||
\(411\) | 17.6512 | 0.870668 | ||||||||
\(412\) | −23.1885 | + | 7.01962i | −1.14241 | + | 0.345832i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5.14214 | − | 0.761256i | 0.252722 | − | 0.0374137i | ||||
\(415\) | − | 24.7013i | − | 1.21254i | ||||||
\(416\) | 4.54269 | − | 4.10540i | 0.222724 | − | 0.201284i | ||||
\(417\) | 48.8701 | 2.39318 | ||||||||
\(418\) | −28.6182 | + | 4.23671i | −1.39976 | + | 0.207224i | ||||
\(419\) | −17.2837 | −0.844366 | −0.422183 | − | 0.906511i | \(-0.638736\pi\) | ||||
−0.422183 | + | 0.906511i | \(0.638736\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.4853 | −0.511021 | −0.255511 | − | 0.966806i | \(-0.582244\pi\) | ||||
−0.255511 | + | 0.966806i | \(0.582244\pi\) | |||||||
\(422\) | −20.2426 | + | 2.99678i | −0.985396 | + | 0.145881i | ||||
\(423\) | 6.79175 | 0.330226 | ||||||||
\(424\) | −12.6569 | − | 26.8204i | −0.614671 | − | 1.30251i | ||||
\(425\) | 0.579658i | 0.0281175i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.34315 | + | 4.43692i | 0.0649234 | + | 0.214467i | ||||
\(429\) | 9.17157 | 0.442808 | ||||||||
\(430\) | −3.91548 | − | 26.4483i | −0.188821 | − | 1.27545i | ||||
\(431\) | − | 0.960099i | − | 0.0462463i | −0.999733 | − | 0.0231232i | \(-0.992639\pi\) | ||
0.999733 | − | 0.0231232i | \(-0.00736099\pi\) | |||||||
\(432\) | 10.0800 | − | 6.71852i | 0.484975 | − | 0.323245i | ||||
\(433\) | 26.1857i | 1.25840i | 0.777243 | + | 0.629201i | \(0.216618\pi\) | ||||
−0.777243 | + | 0.629201i | \(0.783382\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 38.2110i | − | 1.83208i | ||||||
\(436\) | 10.8284 | − | 3.27798i | 0.518588 | − | 0.156987i | ||||
\(437\) | 11.9832i | 0.573236i | ||||||||
\(438\) | 41.9914 | − | 6.21652i | 2.00643 | − | 0.297037i | ||||
\(439\) | −22.4537 | −1.07165 | −0.535827 | − | 0.844328i | \(-0.680000\pi\) | ||||
−0.535827 | + | 0.844328i | \(0.680000\pi\) | |||||||
\(440\) | 12.4813 | + | 26.4483i | 0.595021 | + | 1.26087i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.0710678 | − | 0.480049i | −0.00338035 | − | 0.0228336i | ||||
\(443\) | 28.3770i | 1.34823i | 0.738625 | + | 0.674116i | \(0.235475\pi\) | ||||
−0.738625 | + | 0.674116i | \(0.764525\pi\) | |||||||
\(444\) | −16.3967 | + | 4.96362i | −0.778154 | + | 0.235563i | ||||
\(445\) | −15.6569 | −0.742206 | ||||||||
\(446\) | 1.62184 | + | 10.9552i | 0.0767965 | + | 0.518746i | ||||
\(447\) | −10.3398 | −0.489056 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.2843 | −0.768502 | −0.384251 | − | 0.923229i | \(-0.625540\pi\) | ||||
−0.384251 | + | 0.923229i | \(0.625540\pi\) | |||||||
\(450\) | −0.600505 | − | 4.05630i | −0.0283081 | − | 0.191216i | ||||
\(451\) | 9.08538 | 0.427814 | ||||||||
\(452\) | 8.12132 | − | 2.45849i | 0.381995 | − | 0.115637i | ||||
\(453\) | 45.8770i | 2.15549i | ||||||||
\(454\) | −2.06535 | − | 13.9510i | −0.0969317 | − | 0.654755i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13.3640 | − | 28.3188i | −0.625825 | − | 1.32615i | ||||
\(457\) | 0.727922 | 0.0340508 | 0.0170254 | − | 0.999855i | \(-0.494580\pi\) | ||||
0.0170254 | + | 0.999855i | \(0.494580\pi\) | |||||||
\(458\) | −1.88164 | + | 0.278564i | −0.0879235 | + | 0.0130164i | ||||
\(459\) | − | 0.960099i | − | 0.0448136i | ||||||
\(460\) | 11.5942 | − | 3.50981i | 0.540584 | − | 0.163646i | ||||
\(461\) | − | 29.7499i | − | 1.38559i | −0.721135 | − | 0.692794i | \(-0.756379\pi\) | ||
0.721135 | − | 0.692794i | \(-0.243621\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.9330i | 1.62347i | 0.584024 | + | 0.811737i | \(0.301477\pi\) | ||||
−0.584024 | + | 0.811737i | \(0.698523\pi\) | |||||||
\(464\) | −22.7279 | + | 15.1486i | −1.05512 | + | 0.703256i | ||||
\(465\) | − | 33.8937i | − | 1.57178i | ||||||
\(466\) | 3.36396 | + | 22.7229i | 0.155832 | + | 1.05262i | ||||
\(467\) | −24.0755 | −1.11408 | −0.557041 | − | 0.830485i | \(-0.688063\pi\) | ||||
−0.557041 | + | 0.830485i | \(0.688063\pi\) | |||||||
\(468\) | 0.994629 | + | 3.28564i | 0.0459767 | + | 0.151879i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 15.6569 | − | 2.31788i | 0.722197 | − | 0.106916i | ||||
\(471\) | 41.0913i | 1.89339i | ||||||||
\(472\) | −13.5520 | − | 28.7172i | −0.623780 | − | 1.32182i | ||||
\(473\) | −28.6274 | −1.31629 | ||||||||
\(474\) | 23.7081 | − | 3.50981i | 1.08895 | − | 0.161211i | ||||
\(475\) | 9.45280 | 0.433724 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.6274 | 0.761317 | ||||||||
\(478\) | 14.3137 | − | 2.11904i | 0.654694 | − | 0.0969226i | ||||
\(479\) | −32.7935 | −1.49837 | −0.749186 | − | 0.662360i | \(-0.769555\pi\) | ||||
−0.749186 | + | 0.662360i | \(0.769555\pi\) | |||||||
\(480\) | −23.4853 | + | 21.2245i | −1.07195 | + | 0.968762i | ||||
\(481\) | 4.32957i | 0.197411i | ||||||||
\(482\) | 7.12764 | − | 1.05520i | 0.324655 | − | 0.0480628i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.91421 | − | 2.69851i | 0.405192 | − | 0.122660i | ||||
\(485\) | −24.1421 | −1.09624 | ||||||||
\(486\) | 3.10455 | + | 20.9707i | 0.140825 | + | 0.951249i | ||||
\(487\) | 19.5032i | 0.883773i | 0.897071 | + | 0.441886i | \(0.145691\pi\) | ||||
−0.897071 | + | 0.441886i | \(0.854309\pi\) | |||||||
\(488\) | −13.8433 | + | 6.53281i | −0.626657 | + | 0.295727i | ||||
\(489\) | − | 32.4399i | − | 1.46698i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 14.4697i | − | 0.653009i | −0.945196 | − | 0.326504i | \(-0.894129\pi\) | ||
0.945196 | − | 0.326504i | \(-0.105871\pi\) | |||||||
\(492\) | 2.84924 | + | 9.41214i | 0.128454 | + | 0.424332i | ||||
\(493\) | 2.16478i | 0.0974970i | ||||||||
\(494\) | −7.82843 | + | 1.15894i | −0.352218 | + | 0.0521433i | ||||
\(495\) | −16.3967 | −0.736978 | ||||||||
\(496\) | −20.1600 | + | 13.4370i | −0.905212 | + | 0.603341i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.19239 | − | 28.3188i | −0.187865 | − | 1.26899i | ||||
\(499\) | − | 12.5495i | − | 0.561793i | −0.959738 | − | 0.280897i | \(-0.909368\pi\) | ||
0.959738 | − | 0.280897i | \(-0.0906318\pi\) | |||||||
\(500\) | 4.80249 | + | 15.8645i | 0.214774 | + | 0.709480i | ||||
\(501\) | −16.7696 | −0.749208 | ||||||||
\(502\) | −0.810922 | − | 5.47762i | −0.0361932 | − | 0.244478i | ||||
\(503\) | −7.83095 | −0.349165 | −0.174582 | − | 0.984643i | \(-0.555858\pi\) | ||||
−0.174582 | + | 0.984643i | \(0.555858\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −39.7990 | −1.77103 | ||||||||
\(506\) | −1.89949 | − | 12.8307i | −0.0844428 | − | 0.570395i | ||||
\(507\) | −25.3299 | −1.12494 | ||||||||
\(508\) | 5.92893 | + | 19.5855i | 0.263054 | + | 0.868967i | ||||
\(509\) | − | 6.57128i | − | 0.291267i | −0.989339 | − | 0.145633i | \(-0.953478\pi\) | ||
0.989339 | − | 0.145633i | \(-0.0465220\pi\) | |||||||
\(510\) | 0.367414 | + | 2.48181i | 0.0162694 | + | 0.109896i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 21.9350 | + | 5.55468i | 0.969400 | + | 0.245485i | ||||
\(513\) | −15.6569 | −0.691267 | ||||||||
\(514\) | −26.6604 | + | 3.94689i | −1.17594 | + | 0.174090i | ||||
\(515\) | − | 31.6550i | − | 1.39489i | ||||||
\(516\) | −8.97777 | − | 29.6570i | −0.395224 | − | 1.30558i | ||||
\(517\) | − | 16.9469i | − | 0.745322i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.0720i | 0.617693i | ||||||||
\(520\) | 3.41421 | + | 7.23486i | 0.149723 | + | 0.317269i | ||||
\(521\) | 12.0376i | 0.527378i | 0.964608 | + | 0.263689i | \(0.0849393\pi\) | ||||
−0.964608 | + | 0.263689i | \(0.915061\pi\) | |||||||
\(522\) | −2.24264 | − | 15.1486i | −0.0981577 | − | 0.663036i | ||||
\(523\) | −7.46354 | −0.326358 | −0.163179 | − | 0.986597i | \(-0.552175\pi\) | ||||
−0.163179 | + | 0.986597i | \(0.552175\pi\) | |||||||
\(524\) | −0.703309 | + | 0.212906i | −0.0307242 | + | 0.00930083i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 35.8995 | − | 5.31466i | 1.56529 | − | 0.231730i | ||||
\(527\) | 1.92020i | 0.0836451i | ||||||||
\(528\) | 18.7980 | + | 28.2032i | 0.818077 | + | 1.22739i | ||||
\(529\) | 17.6274 | 0.766409 | ||||||||
\(530\) | 38.3308 | − | 5.67459i | 1.66498 | − | 0.246489i | ||||
\(531\) | 17.8033 | 0.772600 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.48528 | 0.107649 | ||||||||
\(534\) | −17.9497 | + | 2.65733i | −0.776762 | + | 0.114994i | ||||
\(535\) | −6.05692 | −0.261864 | ||||||||
\(536\) | 8.38478 | − | 3.95687i | 0.362167 | − | 0.170911i | ||||
\(537\) | − | 28.9301i | − | 1.24843i | ||||||
\(538\) | −7.05155 | + | 1.04393i | −0.304014 | + | 0.0450070i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.58579 | + | 15.1486i | 0.197341 | + | 0.651892i | ||||
\(541\) | 45.3137 | 1.94819 | 0.974094 | − | 0.226142i | \(-0.0726115\pi\) | ||||
0.974094 | + | 0.226142i | \(0.0726115\pi\) | |||||||
\(542\) | 0.887016 | + | 5.99162i | 0.0381006 | + | 0.257362i | ||||
\(543\) | − | 47.0848i | − | 2.02060i | ||||||
\(544\) | 1.33052 | − | 1.20244i | 0.0570457 | − | 0.0515543i | ||||
\(545\) | 14.7821i | 0.633194i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.6981i | 1.18429i | 0.805833 | + | 0.592143i | \(0.201718\pi\) | ||||
−0.805833 | + | 0.592143i | \(0.798282\pi\) | |||||||
\(548\) | 15.7782 | − | 4.77637i | 0.674010 | − | 0.204036i | ||||
\(549\) | − | 8.58221i | − | 0.366280i | ||||||
\(550\) | −10.1213 | + | 1.49839i | −0.431575 | + | 0.0638915i | ||||
\(551\) | 35.3023 | 1.50393 | ||||||||
\(552\) | 12.6965 | − | 5.99162i | 0.540398 | − | 0.255020i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −0.857864 | − | 5.79471i | −0.0364472 | − | 0.246194i | ||||
\(555\) | − | 22.3835i | − | 0.950125i | ||||||
\(556\) | 43.6844 | − | 13.2241i | 1.85263 | − | 0.560829i | ||||
\(557\) | −19.6569 | −0.832888 | −0.416444 | − | 0.909161i | \(-0.636724\pi\) | ||||
−0.416444 | + | 0.909161i | \(0.636724\pi\) | |||||||
\(558\) | −1.98926 | − | 13.4370i | −0.0842120 | − | 0.568836i | ||||
\(559\) | −7.83095 | −0.331214 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.68629 | 0.113415 | ||||||||
\(562\) | 2.15076 | + | 14.5280i | 0.0907242 | + | 0.612825i | ||||
\(563\) | −21.0470 | −0.887027 | −0.443513 | − | 0.896268i | \(-0.646268\pi\) | ||||
−0.443513 | + | 0.896268i | \(0.646268\pi\) | |||||||
\(564\) | 17.5563 | − | 5.31466i | 0.739256 | − | 0.223788i | ||||
\(565\) | 11.0866i | 0.466415i | ||||||||
\(566\) | 0.703309 | + | 4.75071i | 0.0295623 | + | 0.199687i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.8284 | 0.789329 | 0.394664 | − | 0.918825i | \(-0.370861\pi\) | ||||
0.394664 | + | 0.918825i | \(0.370861\pi\) | |||||||
\(570\) | 40.4722 | − | 5.99162i | 1.69520 | − | 0.250961i | ||||
\(571\) | − | 9.95043i | − | 0.416412i | −0.978085 | − | 0.208206i | \(-0.933237\pi\) | ||
0.978085 | − | 0.208206i | \(-0.0667625\pi\) | |||||||
\(572\) | 8.19837 | − | 2.48181i | 0.342791 | − | 0.103770i | ||||
\(573\) | 14.0392i | 0.586497i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.23808i | 0.176740i | ||||||||
\(576\) | −8.06497 | + | 9.79276i | −0.336040 | + | 0.408032i | ||||
\(577\) | 0.842290i | 0.0350650i | 0.999846 | + | 0.0175325i | \(0.00558105\pi\) | ||||
−0.999846 | + | 0.0175325i | \(0.994419\pi\) | |||||||
\(578\) | 3.50000 | + | 23.6418i | 0.145581 | + | 0.983370i | ||||
\(579\) | −31.2347 | −1.29807 | ||||||||
\(580\) | −10.3398 | − | 34.1563i | −0.429337 | − | 1.41827i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −27.6777 | + | 4.09748i | −1.14728 | + | 0.169846i | ||||
\(583\) | − | 41.4889i | − | 1.71830i | ||||||
\(584\) | 35.8534 | − | 16.9197i | 1.48363 | − | 0.700141i | ||||
\(585\) | −4.48528 | −0.185444 | ||||||||
\(586\) | 16.5043 | − | 2.44335i | 0.681788 | − | 0.100934i | ||||
\(587\) | 22.8211 | 0.941926 | 0.470963 | − | 0.882153i | \(-0.343906\pi\) | ||||
0.470963 | + | 0.882153i | \(0.343906\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31.3137 | 1.29026 | ||||||||
\(590\) | 41.0416 | − | 6.07591i | 1.68966 | − | 0.250141i | ||||
\(591\) | −4.28289 | −0.176175 | ||||||||
\(592\) | −13.3137 | + | 8.87385i | −0.547190 | + | 0.364713i | ||||
\(593\) | − | 37.4579i | − | 1.53821i | −0.639121 | − | 0.769106i | \(-0.720702\pi\) | ||
0.639121 | − | 0.769106i | \(-0.279298\pi\) | |||||||
\(594\) | 16.7641 | − | 2.48181i | 0.687841 | − | 0.101830i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.24264 | + | 2.79793i | −0.378593 | + | 0.114608i | ||||
\(597\) | 36.6863 | 1.50147 | ||||||||
\(598\) | −0.519602 | − | 3.50981i | −0.0212481 | − | 0.143527i | ||||
\(599\) | 32.2174i | 1.31637i | 0.752857 | + | 0.658184i | \(0.228675\pi\) | ||||
−0.752857 | + | 0.658184i | \(0.771325\pi\) | |||||||
\(600\) | −4.72640 | − | 10.0154i | −0.192954 | − | 0.408878i | ||||
\(601\) | − | 25.5516i | − | 1.04227i | −0.853474 | − | 0.521136i | \(-0.825509\pi\) | ||
0.853474 | − | 0.521136i | \(-0.174491\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.19818i | 0.211686i | ||||||||
\(604\) | 12.4142 | + | 41.0089i | 0.505127 | + | 1.66863i | ||||
\(605\) | 12.1689i | 0.494738i | ||||||||
\(606\) | −45.6274 | + | 6.75481i | −1.85349 | + | 0.274395i | ||||
\(607\) | 12.1138 | 0.491686 | 0.245843 | − | 0.969310i | \(-0.420935\pi\) | ||||
0.245843 | + | 0.969310i | \(0.420935\pi\) | |||||||
\(608\) | −19.6089 | − | 21.6976i | −0.795246 | − | 0.879953i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.92893 | − | 19.7844i | −0.118589 | − | 0.801046i | ||||
\(611\) | − | 4.63577i | − | 0.187543i | ||||||
\(612\) | 0.291320 | + | 0.962341i | 0.0117759 | + | 0.0389003i | ||||
\(613\) | −8.68629 | −0.350836 | −0.175418 | − | 0.984494i | \(-0.556128\pi\) | ||||
−0.175418 | + | 0.984494i | \(0.556128\pi\) | |||||||
\(614\) | −0.810922 | − | 5.47762i | −0.0327261 | − | 0.221059i | ||||
\(615\) | −12.8487 | −0.518108 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.4558 | −1.42740 | −0.713699 | − | 0.700452i | \(-0.752982\pi\) | ||||
−0.713699 | + | 0.700452i | \(0.752982\pi\) | |||||||
\(618\) | −5.37258 | − | 36.2908i | −0.216117 | − | 1.45983i | ||||
\(619\) | 13.5205 | 0.543433 | 0.271717 | − | 0.962377i | \(-0.412409\pi\) | ||||
0.271717 | + | 0.962377i | \(0.412409\pi\) | |||||||
\(620\) | −9.17157 | − | 30.2972i | −0.368339 | − | 1.21677i | ||||
\(621\) | − | 7.01962i | − | 0.281688i | ||||||
\(622\) | 4.28289 | + | 28.9301i | 0.171728 | + | 1.15999i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.14214 | + | 7.71491i | 0.205850 | + | 0.308843i | ||||
\(625\) | −30.7990 | −1.23196 | ||||||||
\(626\) | 17.8349 | − | 2.64032i | 0.712825 | − | 0.105529i | ||||
\(627\) | − | 43.8068i | − | 1.74948i | ||||||
\(628\) | 11.1192 | + | 36.7310i | 0.443705 | + | 1.46573i | ||||
\(629\) | 1.26810i | 0.0505625i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.4633i | 0.814630i | 0.913288 | + | 0.407315i | \(0.133535\pi\) | ||||
−0.913288 | + | 0.407315i | \(0.866465\pi\) | |||||||
\(632\) | 20.2426 | − | 9.55274i | 0.805209 | − | 0.379988i | ||||
\(633\) | − | 30.9861i | − | 1.23159i | ||||||
\(634\) | −1.14214 | − | 7.71491i | −0.0453600 | − | 0.306398i | ||||
\(635\) | −26.7365 | −1.06101 | ||||||||
\(636\) | 42.9811 | − | 13.0112i | 1.70431 | − | 0.515929i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −37.7990 | + | 5.59587i | −1.49648 | + | 0.221542i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −15.2499 | + | 25.3274i | −0.602806 | + | 1.00115i | ||||
\(641\) | 49.4558 | 1.95339 | 0.976694 | − | 0.214636i | \(-0.0688564\pi\) | ||||
0.976694 | + | 0.214636i | \(0.0688564\pi\) | |||||||
\(642\) | −6.94394 | + | 1.02800i | −0.274055 | + | 0.0405719i | ||||
\(643\) | 41.7267 | 1.64554 | 0.822769 | − | 0.568375i | \(-0.192428\pi\) | ||||
0.822769 | + | 0.568375i | \(0.192428\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 40.4853 | 1.59411 | ||||||||
\(646\) | −2.29289 | + | 0.339446i | −0.0902127 | + | 0.0133553i | ||||
\(647\) | −43.8681 | −1.72463 | −0.862317 | − | 0.506370i | \(-0.830987\pi\) | ||||
−0.862317 | + | 0.506370i | \(0.830987\pi\) | |||||||
\(648\) | 13.5711 | + | 28.7576i | 0.533122 | + | 1.12971i | ||||
\(649\) | − | 44.4231i | − | 1.74376i | ||||||
\(650\) | −2.76866 | + | 0.409880i | −0.108596 | + | 0.0160768i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.77817 | − | 28.9977i | −0.343780 | − | 1.13564i | ||||
\(653\) | −23.7990 | −0.931326 | −0.465663 | − | 0.884962i | \(-0.654184\pi\) | ||||
−0.465663 | + | 0.884962i | \(0.654184\pi\) | |||||||
\(654\) | 2.50886 | + | 16.9469i | 0.0981041 | + | 0.662675i | ||||
\(655\) | − | 0.960099i | − | 0.0375142i | ||||||
\(656\) | 5.09381 | + | 7.64240i | 0.198880 | + | 0.298386i | ||||
\(657\) | 22.2275i | 0.867177i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.2284i | 0.515306i | 0.966238 | + | 0.257653i | \(0.0829491\pi\) | ||||
−0.966238 | + | 0.257653i | \(0.917051\pi\) | |||||||
\(660\) | −42.3848 | + | 12.8307i | −1.64983 | + | 0.499435i | ||||
\(661\) | 37.6662i | 1.46504i | 0.680744 | + | 0.732522i | \(0.261657\pi\) | ||||
−0.680744 | + | 0.732522i | \(0.738343\pi\) | |||||||
\(662\) | −21.1924 | + | 3.13738i | −0.823666 | + | 0.121938i | ||||
\(663\) | 0.734828 | 0.0285383 | ||||||||
\(664\) | −11.4105 | − | 24.1794i | −0.442815 | − | 0.938342i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.31371 | − | 8.87385i | −0.0509052 | − | 0.343855i | ||||
\(667\) | 15.8275i | 0.612843i | ||||||||
\(668\) | −14.9901 | + | 4.53781i | −0.579985 | + | 0.175573i | ||||
\(669\) | −16.7696 | −0.648348 | ||||||||
\(670\) | 1.77403 | + | 11.9832i | 0.0685368 | + | 0.462953i | ||||
\(671\) | −21.4144 | −0.826696 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.3848 | 0.400304 | 0.200152 | − | 0.979765i | \(-0.435856\pi\) | ||||
0.200152 | + | 0.979765i | \(0.435856\pi\) | |||||||
\(674\) | 2.24264 | + | 15.1486i | 0.0863833 | + | 0.583502i | ||||
\(675\) | −5.53732 | −0.213132 | ||||||||
\(676\) | −22.6421 | + | 6.85423i | −0.870851 | + | 0.263624i | ||||
\(677\) | 28.8532i | 1.10892i | 0.832211 | + | 0.554459i | \(0.187075\pi\) | ||||
−0.832211 | + | 0.554459i | \(0.812925\pi\) | |||||||
\(678\) | 1.88164 | + | 12.7101i | 0.0722641 | + | 0.488130i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.00000 | + | 2.11904i | 0.0383482 | + | 0.0812615i | ||||
\(681\) | 21.3553 | 0.818338 | ||||||||
\(682\) | −33.5283 | + | 4.96362i | −1.28386 | + | 0.190067i | ||||
\(683\) | 32.2174i | 1.23276i | 0.787447 | + | 0.616382i | \(0.211402\pi\) | ||||
−0.787447 | + | 0.616382i | \(0.788598\pi\) | |||||||
\(684\) | 15.6934 | − | 4.75071i | 0.600053 | − | 0.181648i | ||||
\(685\) | 21.5391i | 0.822965i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 2.88030i | − | 0.109890i | ||||||
\(688\) | −16.0503 | − | 24.0807i | −0.611910 | − | 0.918068i | ||||
\(689\) | − | 11.3492i | − | 0.432370i | ||||||
\(690\) | 2.68629 | + | 18.1454i | 0.102265 | + | 0.690783i | ||||
\(691\) | 8.19837 | 0.311881 | 0.155940 | − | 0.987766i | \(-0.450159\pi\) | ||||
0.155940 | + | 0.987766i | \(0.450159\pi\) | |||||||
\(692\) | 3.80786 | + | 12.5788i | 0.144753 | + | 0.478175i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.53553 | − | 0.819496i | 0.210126 | − | 0.0311076i | ||||
\(695\) | 59.6343i | 2.26206i | ||||||||
\(696\) | −17.6512 | − | 37.4035i | −0.669066 | − | 1.41778i | ||||
\(697\) | 0.727922 | 0.0275720 | ||||||||
\(698\) | −11.8540 | + | 1.75490i | −0.448682 | + | 0.0664241i | ||||
\(699\) | −34.7827 | −1.31560 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.0000 | 0.604312 | 0.302156 | − | 0.953259i | \(-0.402294\pi\) | ||||
0.302156 | + | 0.953259i | \(0.402294\pi\) | |||||||
\(702\) | 4.58579 | − | 0.678892i | 0.173079 | − | 0.0256231i | ||||
\(703\) | 20.6796 | 0.779947 | ||||||||
\(704\) | 24.4350 | + | 20.1238i | 0.920930 | + | 0.758445i | ||||
\(705\) | 23.9665i | 0.902630i | ||||||||
\(706\) | −14.0716 | + | 2.08319i | −0.529591 | + | 0.0784021i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 46.0208 | − | 13.9314i | 1.72957 | − | 0.523575i | ||||
\(709\) | −46.6274 | −1.75113 | −0.875565 | − | 0.483101i | \(-0.839510\pi\) | ||||
−0.875565 | + | 0.483101i | \(0.839510\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.5495i | 0.470644i | ||||||||
\(712\) | −15.3260 | + | 7.23252i | −0.574366 | + | 0.271050i | ||||
\(713\) | 14.0392i | 0.525774i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.1917i | 0.418547i | ||||||||
\(716\) | −7.82843 | − | 25.8603i | −0.292562 | − | 0.966444i | ||||
\(717\) | 21.9105i | 0.818262i | ||||||||
\(718\) | 43.7279 | − | 6.47360i | 1.63191 | − | 0.241593i | ||||
\(719\) | −33.5283 | −1.25039 | −0.625197 | − | 0.780467i | \(-0.714981\pi\) | ||||
−0.625197 | + | 0.780467i | \(0.714981\pi\) | |||||||
\(720\) | −9.19299 | − | 13.7925i | −0.342603 | − | 0.514017i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.60051 | + | 10.8111i | 0.0595646 | + | 0.402348i | ||||
\(723\) | 10.9105i | 0.405767i | ||||||||
\(724\) | −12.7411 | − | 42.0886i | −0.473518 | − | 1.56421i | ||||
\(725\) | 12.4853 | 0.463692 | ||||||||
\(726\) | 2.06535 | + | 13.9510i | 0.0766524 | + | 0.517772i | ||||
\(727\) | 29.9802 | 1.11191 | 0.555953 | − | 0.831214i | \(-0.312354\pi\) | ||||
0.555953 | + | 0.831214i | \(0.312354\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.62742 | 0.0602747 | ||||||||
\(730\) | 7.58579 | + | 51.2405i | 0.280763 | + | 1.89650i | ||||
\(731\) | −2.29363 | −0.0848331 | ||||||||
\(732\) | −6.71573 | − | 22.1846i | −0.248220 | − | 0.819967i | ||||
\(733\) | 20.4567i | 0.755584i | 0.925890 | + | 0.377792i | \(0.123317\pi\) | ||||
−0.925890 | + | 0.377792i | \(0.876683\pi\) | |||||||
\(734\) | 2.66105 | + | 17.9749i | 0.0982210 | + | 0.663464i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.72792 | − | 8.79148i | 0.358576 | − | 0.324058i | ||||
\(737\) | 12.9706 | 0.477777 | ||||||||
\(738\) | −5.09381 | + | 0.754102i | −0.187506 | + | 0.0277589i | ||||
\(739\) | − | 12.4330i | − | 0.457357i | −0.973502 | − | 0.228678i | \(-0.926560\pi\) | ||
0.973502 | − | 0.228678i | \(-0.0734404\pi\) | |||||||
\(740\) | −6.05692 | − | 20.0083i | −0.222657 | − | 0.735521i | ||||
\(741\) | − | 11.9832i | − | 0.440215i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 45.1646i | − | 1.65693i | −0.560042 | − | 0.828464i | \(-0.689215\pi\) | ||
0.560042 | − | 0.828464i | \(-0.310785\pi\) | |||||||
\(744\) | −15.6569 | − | 33.1775i | −0.574008 | − | 1.21635i | ||||
\(745\) | − | 12.6173i | − | 0.462262i | ||||||
\(746\) | −4.17157 | − | 28.1782i | −0.152732 | − | 1.03168i | ||||
\(747\) | 14.9901 | 0.548460 | ||||||||
\(748\) | 2.40125 | − | 0.726905i | 0.0877982 | − | 0.0265783i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −24.8284 | + | 3.67567i | −0.906606 | + | 0.134216i | ||||
\(751\) | − | 37.2509i | − | 1.35930i | −0.733535 | − | 0.679652i | \(-0.762131\pi\) | ||
0.733535 | − | 0.679652i | \(-0.237869\pi\) | |||||||
\(752\) | 14.2553 | − | 9.50143i | 0.519837 | − | 0.346481i | ||||
\(753\) | 8.38478 | 0.305558 | ||||||||
\(754\) | −10.3398 | + | 1.53073i | −0.376554 | + | 0.0557460i | ||||
\(755\) | −55.9819 | −2.03739 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −44.2843 | −1.60954 | −0.804770 | − | 0.593587i | \(-0.797711\pi\) | ||||
−0.804770 | + | 0.593587i | \(0.797711\pi\) | |||||||
\(758\) | 30.3640 | − | 4.49516i | 1.10287 | − | 0.163272i | ||||
\(759\) | 19.6404 | 0.712902 | ||||||||
\(760\) | 34.5563 | − | 16.3075i | 1.25349 | − | 0.591537i | ||||
\(761\) | − | 0.0543929i | − | 0.00197174i | −1.00000 | 0.000985871i | \(-0.999686\pi\) | |||
1.00000 | 0.000985871i | \(-0.000313813\pi\) | ||||||||
\(762\) | −30.6520 | + | 4.53781i | −1.11041 | + | 0.164387i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3.79899 | + | 12.5495i | 0.137443 | + | 0.454026i | ||||
\(765\) | −1.31371 | −0.0474972 | ||||||||
\(766\) | 6.42433 | + | 43.3951i | 0.232121 | + | 1.56793i | ||||
\(767\) | − | 12.1518i | − | 0.438777i | ||||||
\(768\) | −13.1846 | + | 31.6248i | −0.475757 | + | 1.14116i | ||||
\(769\) | − | 19.1342i | − | 0.689996i | −0.938603 | − | 0.344998i | \(-0.887880\pi\) | ||
0.938603 | − | 0.344998i | \(-0.112120\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 40.8100i | − | 1.46974i | ||||||
\(772\) | −27.9203 | + | 8.45204i | −1.00487 | + | 0.304195i | ||||
\(773\) | − | 49.4955i | − | 1.78023i | −0.455735 | − | 0.890116i | \(-0.650624\pi\) | ||
0.455735 | − | 0.890116i | \(-0.349376\pi\) | |||||||
\(774\) | 16.0503 | − | 2.37612i | 0.576914 | − | 0.0854080i | ||||
\(775\) | 11.0746 | 0.397813 | ||||||||
\(776\) | −23.6320 | + | 11.1522i | −0.848339 | + | 0.400341i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.92893 | + | 19.7844i | 0.105007 | + | 0.709304i | ||||
\(779\) | − | 11.8706i | − | 0.425309i | ||||||
\(780\) | −11.5942 | + | 3.50981i | −0.415140 | + | 0.125671i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −0.152188 | − | 1.02800i | −0.00544222 | − | 0.0367612i | ||||
\(783\) | −20.6796 | −0.739029 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −50.1421 | −1.78965 | ||||||||
\(786\) | −0.162951 | − | 1.10070i | −0.00581227 | − | 0.0392607i | ||||
\(787\) | 41.2071 | 1.46887 | 0.734436 | − | 0.678677i | \(-0.237447\pi\) | ||||
0.734436 | + | 0.678677i | \(0.237447\pi\) | |||||||
\(788\) | −3.82843 | + | 1.15894i | −0.136382 | + | 0.0412856i | ||||
\(789\) | 54.9526i | 1.95636i | ||||||||
\(790\) | 4.28289 | + | 28.9301i | 0.152378 | + | 1.02929i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −16.0503 | + | 7.57430i | −0.570321 | + | 0.269141i | ||||
\(793\) | −5.85786 | −0.208019 | ||||||||
\(794\) | 22.5613 | − | 3.34003i | 0.800669 | − | 0.118533i | ||||
\(795\) | 58.6742i | 2.08096i | ||||||||
\(796\) | 32.7935 | − | 9.92724i | 1.16233 | − | 0.351862i | ||||
\(797\) | − | 20.1940i | − | 0.715309i | −0.933854 | − | 0.357655i | \(-0.883576\pi\) | ||
0.933854 | − | 0.357655i | \(-0.116424\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.35778i | − | 0.0480350i | ||||||
\(800\) | −6.93503 | − | 7.67372i | −0.245190 | − | 0.271307i | ||||
\(801\) | − | 9.50143i | − | 0.335716i | ||||||
\(802\) | −2.65685 | − | 17.9465i | −0.0938168 | − | 0.633714i | ||||
\(803\) | 55.4623 | 1.95722 | ||||||||
\(804\) | 4.06766 | + | 13.4370i | 0.143455 | + | 0.473888i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.17157 | + | 1.35778i | −0.323055 | + | 0.0478259i | ||||
\(807\) | − | 10.7940i | − | 0.379968i | ||||||
\(808\) | −38.9580 | + | 18.3847i | −1.37054 | + | 0.646773i | ||||
\(809\) | −0.0416306 | −0.00146365 | −0.000731826 | − | 1.00000i | \(-0.500233\pi\) | ||||
−0.000731826 | 1.00000i | \(0.500233\pi\) | ||||||||
\(810\) | −41.0994 | + | 6.08447i | −1.44409 | + | 0.213787i | ||||
\(811\) | 39.4330 | 1.38468 | 0.692340 | − | 0.721571i | \(-0.256580\pi\) | ||||
0.692340 | + | 0.721571i | \(0.256580\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.17157 | −0.321661 | ||||||||
\(814\) | −22.1421 | + | 3.27798i | −0.776081 | + | 0.114893i | ||||
\(815\) | 39.5852 | 1.38661 | ||||||||
\(816\) | 1.50610 | + | 2.25964i | 0.0527239 | + | 0.0791033i | ||||
\(817\) | 37.4035i | 1.30858i | ||||||||
\(818\) | 19.3491 | − | 2.86449i | 0.676525 | − | 0.100155i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.4853 | + | 3.47682i | −0.401083 | + | 0.121416i | ||||
\(821\) | −18.0000 | −0.628204 | −0.314102 | − | 0.949389i | \(-0.601703\pi\) | ||||
−0.314102 | + | 0.949389i | \(0.601703\pi\) | |||||||
\(822\) | 3.65568 | + | 24.6934i | 0.127506 | + | 0.861281i | ||||
\(823\) | − | 17.1853i | − | 0.599041i | −0.954090 | − | 0.299521i | \(-0.903173\pi\) | ||
0.954090 | − | 0.299521i | \(-0.0968267\pi\) | |||||||
\(824\) | −14.6227 | − | 30.9861i | −0.509406 | − | 1.07945i | ||||
\(825\) | − | 15.4930i | − | 0.539399i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 45.1646i | − | 1.57053i | −0.619162 | − | 0.785264i | \(-0.712527\pi\) | ||
0.619162 | − | 0.785264i | \(-0.287473\pi\) | |||||||
\(828\) | 2.12994 | + | 7.03601i | 0.0740206 | + | 0.244518i | ||||
\(829\) | 47.2220i | 1.64009i | 0.572301 | + | 0.820044i | \(0.306051\pi\) | ||||
−0.572301 | + | 0.820044i | \(0.693949\pi\) | |||||||
\(830\) | 34.5563 | − | 5.11582i | 1.19947 | − | 0.177573i | ||||
\(831\) | 8.87016 | 0.307702 | ||||||||
\(832\) | 6.68414 | + | 5.50482i | 0.231731 | + | 0.190845i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 10.1213 | + | 68.3676i | 0.350473 | + | 2.36738i | ||||
\(835\) | − | 20.4633i | − | 0.708160i | ||||||
\(836\) | −11.8540 | − | 39.1584i | −0.409981 | − | 1.35432i | ||||
\(837\) | −18.3431 | −0.634032 | ||||||||
\(838\) | −3.57958 | − | 24.1794i | −0.123655 | − | 0.835263i | ||||
\(839\) | 42.3984 | 1.46376 | 0.731878 | − | 0.681435i | \(-0.238644\pi\) | ||||
0.731878 | + | 0.681435i | \(0.238644\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.6274 | 0.607842 | ||||||||
\(842\) | −2.17157 | − | 14.6686i | −0.0748373 | − | 0.505512i | ||||
\(843\) | −22.2384 | −0.765932 | ||||||||
\(844\) | −8.38478 | − | 27.6981i | −0.288616 | − | 0.953409i | ||||
\(845\) | − | 30.9092i | − | 1.06331i | ||||||
\(846\) | 1.40662 | + | 9.50143i | 0.0483605 | + | 0.326666i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 34.8995 | − | 23.2612i | 1.19845 | − | 0.798793i | ||||
\(849\) | −7.27208 | −0.249577 | ||||||||
\(850\) | −0.810922 | + | 0.120051i | −0.0278144 | + | 0.00411772i | ||||
\(851\) | 9.27153i | 0.317824i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.3002i | 1.31137i | 0.755033 | + | 0.655687i | \(0.227621\pi\) | ||||
−0.755033 | + | 0.655687i | \(0.772379\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 21.4234i | 0.732664i | ||||||||
\(856\) | −5.92893 | + | 2.79793i | −0.202647 | + | 0.0956314i | ||||
\(857\) | − | 3.45542i | − | 0.118035i | −0.998257 | − | 0.0590174i | \(-0.981203\pi\) | ||
0.998257 | − | 0.0590174i | \(-0.0187967\pi\) | |||||||
\(858\) | 1.89949 | + | 12.8307i | 0.0648477 | + | 0.438034i | ||||
\(859\) | 2.66105 | 0.0907937 | 0.0453969 | − | 0.998969i | \(-0.485545\pi\) | ||||
0.0453969 | + | 0.998969i | \(0.485545\pi\) | |||||||
\(860\) | 36.1893 | − | 10.9552i | 1.23405 | − | 0.373571i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.34315 | − | 0.198843i | 0.0457477 | − | 0.00677262i | ||||
\(863\) | − | 12.5495i | − | 0.427190i | −0.976922 | − | 0.213595i | \(-0.931483\pi\) | ||
0.976922 | − | 0.213595i | \(-0.0685174\pi\) | |||||||
\(864\) | 11.4866 | + | 12.7101i | 0.390783 | + | 0.432408i | ||||
\(865\) | −17.1716 | −0.583851 | ||||||||
\(866\) | −36.6328 | + | 5.42323i | −1.24483 | + | 0.184289i | ||||
\(867\) | −36.1893 | −1.22905 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 31.3137 | 1.06224 | ||||||||
\(870\) | 53.4558 | − | 7.91375i | 1.81232 | − | 0.268301i | ||||
\(871\) | 3.54806 | 0.120221 | ||||||||
\(872\) | 6.82843 | + | 14.4697i | 0.231240 | + | 0.490006i | ||||
\(873\) | − | 14.6508i | − | 0.495853i | ||||||
\(874\) | −16.7641 | + | 2.48181i | −0.567056 | + | 0.0839485i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 17.3934 | + | 57.4570i | 0.587668 | + | 1.94129i | ||||
\(877\) | 30.4264 | 1.02743 | 0.513713 | − | 0.857962i | \(-0.328269\pi\) | ||||
0.513713 | + | 0.857962i | \(0.328269\pi\) | |||||||
\(878\) | −4.65030 | − | 31.4119i | −0.156940 | − | 1.06010i | ||||
\(879\) | 25.2638i | 0.852125i | ||||||||
\(880\) | −34.4153 | + | 22.9385i | −1.16014 | + | 0.773256i | ||||
\(881\) | 26.1857i | 0.882217i | 0.897454 | + | 0.441109i | \(0.145415\pi\) | ||||
−0.897454 | + | 0.441109i | \(0.854585\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.7013i | 0.831266i | 0.909532 | + | 0.415633i | \(0.136440\pi\) | ||||
−0.909532 | + | 0.415633i | \(0.863560\pi\) | |||||||
\(884\) | 0.656854 | − | 0.198843i | 0.0220924 | − | 0.00668781i | ||||
\(885\) | 62.8238i | 2.11180i | ||||||||
\(886\) | −39.6985 | + | 5.87707i | −1.33370 | + | 0.197444i | ||||
\(887\) | −22.4537 | −0.753920 | −0.376960 | − | 0.926230i | \(-0.623031\pi\) | ||||
−0.376960 | + | 0.926230i | \(0.623031\pi\) | |||||||
\(888\) | −10.3398 | − | 21.9105i | −0.346981 | − | 0.735267i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −3.24264 | − | 21.9034i | −0.108694 | − | 0.734204i | ||||
\(891\) | 44.4857i | 1.49033i | ||||||||
\(892\) | −14.9901 | + | 4.53781i | −0.501906 | + | 0.151937i | ||||
\(893\) | −22.1421 | −0.740958 | ||||||||
\(894\) | −2.14144 | − | 14.4650i | −0.0716206 | − | 0.483784i | ||||
\(895\) | 35.3023 | 1.18003 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.37258 | 0.179385 | ||||||||
\(898\) | −3.37258 | − | 22.7811i | −0.112545 | − | 0.760217i | ||||
\(899\) | 41.3592 | 1.37941 | ||||||||
\(900\) | 5.55025 | − | 1.68017i | 0.185008 | − | 0.0560058i | ||||
\(901\) | − | 3.32410i | − | 0.110742i | ||||||
\(902\) | 1.88164 | + | 12.7101i | 0.0626519 | + | 0.423201i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.12132 | + | 10.8523i | 0.170333 | + | 0.360942i | ||||
\(905\) | 57.4558 | 1.90990 | ||||||||
\(906\) | −64.1803 | + | 9.50143i | −2.13225 | + | 0.315664i | ||||
\(907\) | 33.9729i | 1.12805i | 0.825757 | + | 0.564025i | \(0.190748\pi\) | ||||
−0.825757 | + | 0.564025i | \(0.809252\pi\) | |||||||
\(908\) | 19.0893 | − | 5.77871i | 0.633501 | − | 0.191773i | ||||
\(909\) | − | 24.1522i | − | 0.801077i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 18.7078i | − | 0.619817i | −0.950766 | − | 0.309908i | \(-0.899702\pi\) | ||
0.950766 | − | 0.309908i | \(-0.100298\pi\) | |||||||
\(912\) | 36.8492 | − | 24.5607i | 1.22020 | − | 0.813287i | ||||
\(913\) | − | 37.4035i | − | 1.23788i | ||||||
\(914\) | 0.150758 | + | 1.01834i | 0.00498662 | + | 0.0336836i | ||||
\(915\) | 30.2846 | 1.00118 | ||||||||
\(916\) | −0.779403 | − | 2.57466i | −0.0257522 | − | 0.0850693i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.34315 | − | 0.198843i | 0.0443304 | − | 0.00656280i | ||||
\(919\) | 48.8403i | 1.61109i | 0.592533 | + | 0.805546i | \(0.298128\pi\) | ||||
−0.592533 | + | 0.805546i | \(0.701872\pi\) | |||||||
\(920\) | 7.31135 | + | 15.4930i | 0.241048 | + | 0.510791i | ||||
\(921\) | 8.38478 | 0.276288 | ||||||||
\(922\) | 41.6190 | − | 6.16140i | 1.37065 | − | 0.202915i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.31371 | 0.240473 | ||||||||
\(926\) | −48.8701 | + | 7.23486i | −1.60597 | + | 0.237752i | ||||
\(927\) | 19.2100 | 0.630938 | ||||||||
\(928\) | −25.8995 | − | 28.6582i | −0.850193 | − | 0.940752i | ||||
\(929\) | − | 29.8812i | − | 0.980369i | −0.871619 | − | 0.490185i | \(-0.836929\pi\) | ||
0.871619 | − | 0.490185i | \(-0.163071\pi\) | |||||||
\(930\) | 47.4162 | − | 7.01962i | 1.55484 | − | 0.230182i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −31.0919 | + | 9.41214i | −1.01845 | + | 0.308305i | ||||
\(933\) | −44.2843 | −1.44980 | ||||||||
\(934\) | −4.98620 | − | 33.6808i | −0.163153 | − | 1.10207i | ||||
\(935\) | 3.27798i | 0.107201i | ||||||||
\(936\) | −4.39050 | + | 2.07193i | −0.143508 | + | 0.0677231i | ||||
\(937\) | 29.8042i | 0.973662i | 0.873496 | + | 0.486831i | \(0.161847\pi\) | ||||
−0.873496 | + | 0.486831i | \(0.838153\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.3004i | 0.890916i | ||||||||
\(940\) | 6.48528 | + | 21.4234i | 0.211527 | + | 0.698753i | ||||
\(941\) | − | 24.7862i | − | 0.808008i | −0.914757 | − | 0.404004i | \(-0.867618\pi\) | ||
0.914757 | − | 0.404004i | \(-0.132382\pi\) | |||||||
\(942\) | −57.4853 | + | 8.51028i | −1.87297 | + | 0.277280i | ||||
\(943\) | 5.32209 | 0.173311 | ||||||||
\(944\) | 37.3677 | − | 24.9063i | 1.21621 | − | 0.810631i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.92893 | − | 40.0488i | −0.192766 | − | 1.30210i | ||||
\(947\) | 9.15505i | 0.297499i | 0.988875 | + | 0.148750i | \(0.0475249\pi\) | ||||
−0.988875 | + | 0.148750i | \(0.952475\pi\) | |||||||
\(948\) | 9.82021 | + | 32.4399i | 0.318946 | + | 1.05360i | ||||
\(949\) | 15.1716 | 0.492490 | ||||||||
\(950\) | 1.95774 | + | 13.2241i | 0.0635174 | + | 0.429048i | ||||
\(951\) | 11.8095 | 0.382948 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.3431 | 0.853338 | 0.426669 | − | 0.904408i | \(-0.359687\pi\) | ||||
0.426669 | + | 0.904408i | \(0.359687\pi\) | |||||||
\(954\) | 3.44365 | + | 23.2612i | 0.111492 | + | 0.753109i | ||||
\(955\) | −17.1316 | −0.554364 | ||||||||
\(956\) | 5.92893 | + | 19.5855i | 0.191755 | + | 0.633441i | ||||
\(957\) | − | 57.8602i | − | 1.87035i | ||||||
\(958\) | −6.79175 | − | 45.8770i | −0.219431 | − | 1.48222i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −34.5563 | − | 28.4594i | −1.11530 | − | 0.918522i | ||||
\(961\) | 5.68629 | 0.183429 | ||||||||
\(962\) | −6.05692 | + | 0.896683i | −0.195283 | + | 0.0289102i | ||||
\(963\) | − | 3.67567i | − | 0.118447i | ||||||
\(964\) | 2.95237 | + | 9.75279i | 0.0950893 | + | 0.314116i | ||||
\(965\) | − | 38.1145i | − | 1.22695i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 45.1646i | − | 1.45240i | −0.687486 | − | 0.726198i | \(-0.741286\pi\) | ||
0.687486 | − | 0.726198i | \(-0.258714\pi\) | |||||||
\(968\) | 5.62132 | + | 11.9118i | 0.180676 | + | 0.382860i | ||||
\(969\) | − | 3.50981i | − | 0.112751i | ||||||
\(970\) | −5.00000 | − | 33.7740i | −0.160540 | − | 1.08442i | ||||
\(971\) | −13.0009 | −0.417217 | −0.208609 | − | 0.977999i | \(-0.566894\pi\) | ||||
−0.208609 | + | 0.977999i | \(0.566894\pi\) | |||||||
\(972\) | −28.6943 | + | 8.68633i | −0.920369 | + | 0.278614i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −27.2843 | + | 4.03924i | −0.874244 | + | 0.129426i | ||||
\(975\) | − | 4.23808i | − | 0.135727i | ||||||
\(976\) | −12.0062 | − | 18.0133i | −0.384310 | − | 0.576592i | ||||
\(977\) | 17.6152 | 0.563561 | 0.281780 | − | 0.959479i | \(-0.409075\pi\) | ||||
0.281780 | + | 0.959479i | \(0.409075\pi\) | |||||||
\(978\) | 45.3823 | − | 6.71852i | 1.45117 | − | 0.214835i | ||||
\(979\) | −23.7081 | −0.757714 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.97056 | −0.286408 | ||||||||
\(982\) | 20.2426 | − | 2.99678i | 0.645969 | − | 0.0956310i | ||||
\(983\) | 9.60498 | 0.306351 | 0.153176 | − | 0.988199i | \(-0.451050\pi\) | ||||
0.153176 | + | 0.988199i | \(0.451050\pi\) | |||||||
\(984\) | −12.5772 | + | 5.93531i | −0.400945 | + | 0.189211i | ||||
\(985\) | − | 5.22625i | − | 0.166522i | ||||||
\(986\) | −3.02846 | + | 0.448342i | −0.0964458 | + | 0.0142781i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.24264 | − | 10.7117i | −0.103162 | − | 0.340784i | ||||
\(989\) | −16.7696 | −0.533241 | ||||||||
\(990\) | −3.39587 | − | 22.9385i | −0.107928 | − | 0.729033i | ||||
\(991\) | − | 25.6614i | − | 0.815163i | −0.913169 | − | 0.407581i | \(-0.866372\pi\) | ||
0.913169 | − | 0.407581i | \(-0.133628\pi\) | |||||||
\(992\) | −22.9733 | − | 25.4203i | −0.729402 | − | 0.807095i | ||||
\(993\) | − | 32.4399i | − | 1.02945i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 44.7669i | 1.41921i | ||||||||
\(996\) | 38.7487 | − | 11.7300i | 1.22780 | − | 0.371680i | ||||
\(997\) | 30.9092i | 0.978903i | 0.872030 | + | 0.489452i | \(0.162803\pi\) | ||||
−0.872030 | + | 0.489452i | \(0.837197\pi\) | |||||||
\(998\) | 17.5563 | − | 2.59909i | 0.555737 | − | 0.0822727i | ||||
\(999\) | −12.1138 | −0.383265 |
(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 | 196.2.d.c.195.7 | yes | 8 | |
3.2 | odd | 2 | 1764.2.b.k.1567.2 | 8 | |||
4.3 | odd | 2 | inner | 196.2.d.c.195.6 | yes | 8 | |
7.2 | even | 3 | 196.2.f.d.31.6 | 16 | |||
7.3 | odd | 6 | 196.2.f.d.19.1 | 16 | |||
7.4 | even | 3 | 196.2.f.d.19.2 | 16 | |||
7.5 | odd | 6 | 196.2.f.d.31.5 | 16 | |||
7.6 | odd | 2 | inner | 196.2.d.c.195.8 | yes | 8 | |
8.3 | odd | 2 | 3136.2.f.i.3135.4 | 8 | |||
8.5 | even | 2 | 3136.2.f.i.3135.6 | 8 | |||
12.11 | even | 2 | 1764.2.b.k.1567.4 | 8 | |||
21.20 | even | 2 | 1764.2.b.k.1567.1 | 8 | |||
28.3 | even | 6 | 196.2.f.d.19.6 | 16 | |||
28.11 | odd | 6 | 196.2.f.d.19.5 | 16 | |||
28.19 | even | 6 | 196.2.f.d.31.2 | 16 | |||
28.23 | odd | 6 | 196.2.f.d.31.1 | 16 | |||
28.27 | even | 2 | inner | 196.2.d.c.195.5 | ✓ | 8 | |
56.13 | odd | 2 | 3136.2.f.i.3135.3 | 8 | |||
56.27 | even | 2 | 3136.2.f.i.3135.5 | 8 | |||
84.83 | odd | 2 | 1764.2.b.k.1567.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
196.2.d.c.195.5 | ✓ | 8 | 28.27 | even | 2 | inner | |
196.2.d.c.195.6 | yes | 8 | 4.3 | odd | 2 | inner | |
196.2.d.c.195.7 | yes | 8 | 1.1 | even | 1 | trivial | |
196.2.d.c.195.8 | yes | 8 | 7.6 | odd | 2 | inner | |
196.2.f.d.19.1 | 16 | 7.3 | odd | 6 | |||
196.2.f.d.19.2 | 16 | 7.4 | even | 3 | |||
196.2.f.d.19.5 | 16 | 28.11 | odd | 6 | |||
196.2.f.d.19.6 | 16 | 28.3 | even | 6 | |||
196.2.f.d.31.1 | 16 | 28.23 | odd | 6 | |||
196.2.f.d.31.2 | 16 | 28.19 | even | 6 | |||
196.2.f.d.31.5 | 16 | 7.5 | odd | 6 | |||
196.2.f.d.31.6 | 16 | 7.2 | even | 3 | |||
1764.2.b.k.1567.1 | 8 | 21.20 | even | 2 | |||
1764.2.b.k.1567.2 | 8 | 3.2 | odd | 2 | |||
1764.2.b.k.1567.3 | 8 | 84.83 | odd | 2 | |||
1764.2.b.k.1567.4 | 8 | 12.11 | even | 2 | |||
3136.2.f.i.3135.3 | 8 | 56.13 | odd | 2 | |||
3136.2.f.i.3135.4 | 8 | 8.3 | odd | 2 | |||
3136.2.f.i.3135.5 | 8 | 56.27 | even | 2 | |||
3136.2.f.i.3135.6 | 8 | 8.5 | even | 2 |