Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [129,2,Mod(128,129)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(129, 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("129.128");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 129 = 3 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 129.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: | \(1.03007018607\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 6x^{10} + 29x^{8} + 88x^{6} + 261x^{4} + 486x^{2} + 729 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 128.11 | ||
Root | \(0.583090 - 1.63095i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 129.128 |
Dual form | 129.2.d.a.128.12 |
$q$-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 \(\left(\mathbb{Z}/129\mathbb{Z}\right)^\times\).
\(n\) | \(44\) | \(46\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.26382 | 1.60076 | 0.800382 | − | 0.599491i | \(-0.204630\pi\) | ||||
0.800382 | + | 0.599491i | \(0.204630\pi\) | |||||||
\(3\) | −0.583090 | − | 1.63095i | −0.336647 | − | 0.941631i | ||||
\(4\) | 3.12489 | 1.56244 | ||||||||
\(5\) | −1.38036 | −0.617315 | −0.308658 | − | 0.951173i | \(-0.599880\pi\) | ||||
−0.308658 | + | 0.951173i | \(0.599880\pi\) | |||||||
\(6\) | −1.32001 | − | 3.69218i | −0.538893 | − | 1.50733i | ||||
\(7\) | 0.790787i | 0.298889i | 0.988770 | + | 0.149445i | \(0.0477486\pi\) | ||||
−0.988770 | + | 0.149445i | \(0.952251\pi\) | |||||||
\(8\) | 2.54654 | 0.900338 | ||||||||
\(9\) | −2.32001 | + | 1.90198i | −0.773337 | + | 0.633995i | ||||
\(10\) | −3.12489 | −0.988176 | ||||||||
\(11\) | 4.15328i | 1.25226i | 0.779718 | + | 0.626131i | \(0.215363\pi\) | ||||
−0.779718 | + | 0.626131i | \(0.784637\pi\) | |||||||
\(12\) | −1.82209 | − | 5.09654i | −0.525992 | − | 1.47124i | ||||
\(13\) | 3.64002 | 1.00956 | 0.504780 | − | 0.863248i | \(-0.331573\pi\) | ||||
0.504780 | + | 0.863248i | \(0.331573\pi\) | |||||||
\(14\) | 1.79020i | 0.478451i | ||||||||
\(15\) | 0.804874 | + | 2.25130i | 0.207817 | + | 0.581283i | ||||
\(16\) | −0.484862 | −0.121215 | ||||||||
\(17\) | 1.44088i | 0.349466i | 0.984616 | + | 0.174733i | \(0.0559062\pi\) | ||||
−0.984616 | + | 0.174733i | \(0.944094\pi\) | |||||||
\(18\) | −5.25209 | + | 4.30575i | −1.23793 | + | 1.01488i | ||||
\(19\) | − | 6.14039i | − | 1.40870i | −0.709852 | − | 0.704351i | \(-0.751238\pi\) | ||
0.709852 | − | 0.704351i | \(-0.248762\pi\) | |||||||
\(20\) | −4.31346 | −0.964520 | ||||||||
\(21\) | 1.28974 | − | 0.461100i | 0.281443 | − | 0.100620i | ||||
\(22\) | 9.40229i | 2.00458i | ||||||||
\(23\) | − | 5.94348i | − | 1.23930i | −0.784877 | − | 0.619651i | \(-0.787274\pi\) | ||
0.784877 | − | 0.619651i | \(-0.212726\pi\) | |||||||
\(24\) | −1.48486 | − | 4.15328i | −0.303096 | − | 0.847786i | ||||
\(25\) | −3.09461 | −0.618922 | ||||||||
\(26\) | 8.24036 | 1.61607 | ||||||||
\(27\) | 4.45482 | + | 2.67480i | 0.857331 | + | 0.514766i | ||||
\(28\) | 2.47112i | 0.466997i | ||||||||
\(29\) | −4.59618 | −0.853489 | −0.426745 | − | 0.904372i | \(-0.640340\pi\) | ||||
−0.426745 | + | 0.904372i | \(0.640340\pi\) | |||||||
\(30\) | 1.82209 | + | 5.09654i | 0.332667 | + | 0.930497i | ||||
\(31\) | −1.15516 | −0.207473 | −0.103737 | − | 0.994605i | \(-0.533080\pi\) | ||||
−0.103737 | + | 0.994605i | \(0.533080\pi\) | |||||||
\(32\) | −6.19072 | −1.09437 | ||||||||
\(33\) | 6.77381 | − | 2.42174i | 1.17917 | − | 0.421571i | ||||
\(34\) | 3.26190i | 0.559412i | ||||||||
\(35\) | − | 1.09157i | − | 0.184509i | ||||||
\(36\) | −7.24977 | + | 5.94348i | −1.20830 | + | 0.990581i | ||||
\(37\) | 10.1931i | 1.67573i | 0.545876 | + | 0.837866i | \(0.316197\pi\) | ||||
−0.545876 | + | 0.837866i | \(0.683803\pi\) | |||||||
\(38\) | − | 13.9007i | − | 2.25500i | ||||||
\(39\) | −2.12246 | − | 5.93671i | −0.339866 | − | 0.950634i | ||||
\(40\) | −3.51514 | −0.555792 | ||||||||
\(41\) | − | 8.82525i | − | 1.37827i | −0.724632 | − | 0.689137i | \(-0.757990\pi\) | ||
0.724632 | − | 0.689137i | \(-0.242010\pi\) | |||||||
\(42\) | 2.91973 | − | 1.04385i | 0.450524 | − | 0.161069i | ||||
\(43\) | 5.15516 | − | 4.05269i | 0.786155 | − | 0.618030i | ||||
\(44\) | 12.9785i | 1.95659i | ||||||||
\(45\) | 3.20245 | − | 2.62542i | 0.477393 | − | 0.391375i | ||||
\(46\) | − | 13.4550i | − | 1.98383i | ||||||
\(47\) | − | 5.37060i | − | 0.783382i | −0.920097 | − | 0.391691i | \(-0.871890\pi\) | ||
0.920097 | − | 0.391691i | \(-0.128110\pi\) | |||||||
\(48\) | 0.282718 | + | 0.790787i | 0.0408069 | + | 0.114140i | ||||
\(49\) | 6.37466 | 0.910665 | ||||||||
\(50\) | −7.00564 | −0.990747 | ||||||||
\(51\) | 2.35001 | − | 0.840166i | 0.329068 | − | 0.117647i | ||||
\(52\) | 11.3747 | 1.57738 | ||||||||
\(53\) | 5.02128i | 0.689726i | 0.938653 | + | 0.344863i | \(0.112075\pi\) | ||||
−0.938653 | + | 0.344863i | \(0.887925\pi\) | |||||||
\(54\) | 10.0849 | + | 6.05527i | 1.37238 | + | 0.824018i | ||||
\(55\) | − | 5.73302i | − | 0.773041i | ||||||
\(56\) | 2.01377i | 0.269101i | ||||||||
\(57\) | −10.0147 | + | 3.58040i | −1.32648 | + | 0.474235i | ||||
\(58\) | −10.4049 | −1.36623 | ||||||||
\(59\) | 3.80397i | 0.495235i | 0.968858 | + | 0.247617i | \(0.0796476\pi\) | ||||
−0.968858 | + | 0.247617i | \(0.920352\pi\) | |||||||
\(60\) | 2.51514 | + | 7.03505i | 0.324703 | + | 0.908222i | ||||
\(61\) | 4.84348i | 0.620144i | 0.950713 | + | 0.310072i | \(0.100353\pi\) | ||||
−0.950713 | + | 0.310072i | \(0.899647\pi\) | |||||||
\(62\) | −2.61508 | −0.332115 | ||||||||
\(63\) | −1.50406 | − | 1.83463i | −0.189494 | − | 0.231142i | ||||
\(64\) | −13.0450 | −1.63062 | ||||||||
\(65\) | −5.02454 | −0.623217 | ||||||||
\(66\) | 15.3347 | − | 5.48238i | 1.88757 | − | 0.674835i | ||||
\(67\) | −0.515138 | −0.0629341 | −0.0314671 | − | 0.999505i | \(-0.510018\pi\) | ||||
−0.0314671 | + | 0.999505i | \(0.510018\pi\) | |||||||
\(68\) | 4.50260i | 0.546020i | ||||||||
\(69\) | −9.69354 | + | 3.46559i | −1.16697 | + | 0.417208i | ||||
\(70\) | − | 2.47112i | − | 0.295355i | ||||||
\(71\) | 15.4602 | 1.83479 | 0.917393 | − | 0.397983i | \(-0.130290\pi\) | ||||
0.917393 | + | 0.397983i | \(0.130290\pi\) | |||||||
\(72\) | −5.90800 | + | 4.84348i | −0.696265 | + | 0.570809i | ||||
\(73\) | 11.8734i | 1.38968i | 0.719166 | + | 0.694839i | \(0.244524\pi\) | ||||
−0.719166 | + | 0.694839i | \(0.755476\pi\) | |||||||
\(74\) | 23.0753i | 2.68245i | ||||||||
\(75\) | 1.80444 | + | 5.04716i | 0.208358 | + | 0.582796i | ||||
\(76\) | − | 19.1880i | − | 2.20102i | ||||||
\(77\) | −3.28436 | −0.374288 | ||||||||
\(78\) | −4.80487 | − | 13.4396i | −0.544045 | − | 1.52174i | ||||
\(79\) | 7.60975 | 0.856163 | 0.428082 | − | 0.903740i | \(-0.359190\pi\) | ||||
0.428082 | + | 0.903740i | \(0.359190\pi\) | |||||||
\(80\) | 0.669284 | 0.0748282 | ||||||||
\(81\) | 1.76491 | − | 8.82525i | 0.196101 | − | 0.980584i | ||||
\(82\) | − | 19.9788i | − | 2.20629i | ||||||
\(83\) | − | 7.95725i | − | 0.873422i | −0.899602 | − | 0.436711i | \(-0.856143\pi\) | ||
0.899602 | − | 0.436711i | \(-0.143857\pi\) | |||||||
\(84\) | 4.03028 | − | 1.44088i | 0.439739 | − | 0.157213i | ||||
\(85\) | − | 1.98894i | − | 0.215731i | ||||||
\(86\) | 11.6704 | − | 9.17457i | 1.25845 | − | 0.989319i | ||||
\(87\) | 2.67999 | + | 7.49615i | 0.287325 | + | 0.803672i | ||||
\(88\) | 10.5765i | 1.12746i | ||||||||
\(89\) | 0.419798 | 0.0444985 | 0.0222492 | − | 0.999752i | \(-0.492917\pi\) | ||||
0.0222492 | + | 0.999752i | \(0.492917\pi\) | |||||||
\(90\) | 7.24977 | − | 5.94348i | 0.764193 | − | 0.626498i | ||||
\(91\) | 2.87848i | 0.301747i | ||||||||
\(92\) | − | 18.5727i | − | 1.93634i | ||||||
\(93\) | 0.673563 | + | 1.88401i | 0.0698453 | + | 0.195363i | ||||
\(94\) | − | 12.1581i | − | 1.25401i | ||||||
\(95\) | 8.47594i | 0.869613i | ||||||||
\(96\) | 3.60975 | + | 10.0968i | 0.368418 | + | 1.03050i | ||||
\(97\) | −11.4995 | −1.16760 | −0.583801 | − | 0.811897i | \(-0.698435\pi\) | ||||
−0.583801 | + | 0.811897i | \(0.698435\pi\) | |||||||
\(98\) | 14.4311 | 1.45776 | ||||||||
\(99\) | −7.89948 | − | 9.63567i | −0.793928 | − | 0.968421i | ||||
\(100\) | −9.67030 | −0.967030 | ||||||||
\(101\) | − | 6.16705i | − | 0.613645i | −0.951767 | − | 0.306822i | \(-0.900734\pi\) | ||
0.951767 | − | 0.306822i | \(-0.0992658\pi\) | |||||||
\(102\) | 5.32001 | − | 1.90198i | 0.526760 | − | 0.188325i | ||||
\(103\) | −1.54541 | −0.152274 | −0.0761371 | − | 0.997097i | \(-0.524259\pi\) | ||||
−0.0761371 | + | 0.997097i | \(0.524259\pi\) | |||||||
\(104\) | 9.26946 | 0.908946 | ||||||||
\(105\) | −1.78030 | + | 0.636483i | −0.173739 | + | 0.0621144i | ||||
\(106\) | 11.3673i | 1.10409i | ||||||||
\(107\) | 16.5589i | 1.60081i | 0.599458 | + | 0.800406i | \(0.295383\pi\) | ||||
−0.599458 | + | 0.800406i | \(0.704617\pi\) | |||||||
\(108\) | 13.9208 | + | 8.35844i | 1.33953 | + | 0.804292i | ||||
\(109\) | −5.57947 | −0.534416 | −0.267208 | − | 0.963639i | \(-0.586101\pi\) | ||||
−0.267208 | + | 0.963639i | \(0.586101\pi\) | |||||||
\(110\) | − | 12.9785i | − | 1.23746i | ||||||
\(111\) | 16.6244 | − | 5.94348i | 1.57792 | − | 0.564131i | ||||
\(112\) | − | 0.383422i | − | 0.0362300i | ||||||
\(113\) | 3.11198 | 0.292750 | 0.146375 | − | 0.989229i | \(-0.453239\pi\) | ||||
0.146375 | + | 0.989229i | \(0.453239\pi\) | |||||||
\(114\) | −22.6714 | + | 8.10538i | −2.12338 | + | 0.759139i | ||||
\(115\) | 8.20414i | 0.765040i | ||||||||
\(116\) | −14.3625 | −1.33353 | ||||||||
\(117\) | −8.44490 | + | 6.92327i | −0.780731 | + | 0.640056i | ||||
\(118\) | 8.61151i | 0.792753i | ||||||||
\(119\) | −1.13943 | −0.104452 | ||||||||
\(120\) | 2.04964 | + | 5.73302i | 0.187106 | + | 0.523351i | ||||
\(121\) | −6.24977 | −0.568161 | ||||||||
\(122\) | 10.9648i | 0.992703i | ||||||||
\(123\) | −14.3936 | + | 5.14592i | −1.29782 | + | 0.463992i | ||||
\(124\) | −3.60975 | −0.324165 | ||||||||
\(125\) | 11.1735 | 0.999385 | ||||||||
\(126\) | −3.40493 | − | 4.15328i | −0.303335 | − | 0.370004i | ||||
\(127\) | 10.2947 | 0.913509 | 0.456755 | − | 0.889593i | \(-0.349012\pi\) | ||||
0.456755 | + | 0.889593i | \(0.349012\pi\) | |||||||
\(128\) | −17.1500 | −1.51586 | ||||||||
\(129\) | −9.61567 | − | 6.04474i | −0.846613 | − | 0.532210i | ||||
\(130\) | −11.3747 | −0.997623 | ||||||||
\(131\) | −21.1454 | −1.84749 | −0.923743 | − | 0.383013i | \(-0.874887\pi\) | ||||
−0.923743 | + | 0.383013i | \(0.874887\pi\) | |||||||
\(132\) | 21.1674 | − | 7.56766i | 1.84238 | − | 0.658680i | ||||
\(133\) | 4.85574 | 0.421046 | ||||||||
\(134\) | −1.16618 | −0.100743 | ||||||||
\(135\) | −6.14925 | − | 3.69218i | −0.529244 | − | 0.317773i | ||||
\(136\) | 3.66927i | 0.314637i | ||||||||
\(137\) | −11.9198 | −1.01838 | −0.509191 | − | 0.860654i | \(-0.670055\pi\) | ||||
−0.509191 | + | 0.860654i | \(0.670055\pi\) | |||||||
\(138\) | −21.9444 | + | 7.84547i | −1.86803 | + | 0.667851i | ||||
\(139\) | −14.6850 | −1.24556 | −0.622782 | − | 0.782396i | \(-0.713998\pi\) | ||||
−0.622782 | + | 0.782396i | \(0.713998\pi\) | |||||||
\(140\) | − | 3.41103i | − | 0.288285i | ||||||
\(141\) | −8.75919 | + | 3.13154i | −0.737657 | + | 0.263724i | ||||
\(142\) | 34.9991 | 2.93706 | ||||||||
\(143\) | 15.1181i | 1.26424i | ||||||||
\(144\) | 1.12489 | − | 0.922200i | 0.0937405 | − | 0.0768500i | ||||
\(145\) | 6.34438 | 0.526872 | ||||||||
\(146\) | 26.8793i | 2.22454i | ||||||||
\(147\) | −3.71700 | − | 10.3968i | −0.306573 | − | 0.857510i | ||||
\(148\) | 31.8522i | 2.61824i | ||||||||
\(149\) | 6.08687 | 0.498656 | 0.249328 | − | 0.968419i | \(-0.419790\pi\) | ||||
0.249328 | + | 0.968419i | \(0.419790\pi\) | |||||||
\(150\) | 4.08492 | + | 11.4259i | 0.333532 | + | 0.932918i | ||||
\(151\) | − | 13.9611i | − | 1.13614i | −0.822981 | − | 0.568069i | \(-0.807691\pi\) | ||
0.822981 | − | 0.568069i | \(-0.192309\pi\) | |||||||
\(152\) | − | 15.6367i | − | 1.26831i | ||||||
\(153\) | −2.74054 | − | 3.34287i | −0.221560 | − | 0.270255i | ||||
\(154\) | −7.43521 | −0.599146 | ||||||||
\(155\) | 1.59454 | 0.128076 | ||||||||
\(156\) | −6.63245 | − | 18.5515i | −0.531021 | − | 1.48531i | ||||
\(157\) | 2.85454i | 0.227817i | 0.993491 | + | 0.113909i | \(0.0363371\pi\) | ||||
−0.993491 | + | 0.113909i | \(0.963663\pi\) | |||||||
\(158\) | 17.2271 | 1.37051 | ||||||||
\(159\) | 8.18948 | − | 2.92786i | 0.649468 | − | 0.232195i | ||||
\(160\) | 8.54541 | 0.675574 | ||||||||
\(161\) | 4.70003 | 0.370414 | ||||||||
\(162\) | 3.99544 | − | 19.9788i | 0.313911 | − | 1.56968i | ||||
\(163\) | 3.64533i | 0.285524i | 0.989757 | + | 0.142762i | \(0.0455984\pi\) | ||||
−0.989757 | + | 0.142762i | \(0.954402\pi\) | |||||||
\(164\) | − | 27.5779i | − | 2.15347i | ||||||
\(165\) | −9.35029 | + | 3.34287i | −0.727919 | + | 0.260242i | ||||
\(166\) | − | 18.0138i | − | 1.39814i | ||||||
\(167\) | − | 12.5750i | − | 0.973084i | −0.873657 | − | 0.486542i | \(-0.838258\pi\) | ||
0.873657 | − | 0.486542i | \(-0.161742\pi\) | |||||||
\(168\) | 3.28436 | − | 1.17421i | 0.253394 | − | 0.0905922i | ||||
\(169\) | 0.249771 | 0.0192131 | ||||||||
\(170\) | − | 4.50260i | − | 0.345334i | ||||||
\(171\) | 11.6789 | + | 14.2458i | 0.893110 | + | 1.08940i | ||||
\(172\) | 16.1093 | − | 12.6642i | 1.22832 | − | 0.965636i | ||||
\(173\) | 19.4949i | 1.48217i | 0.671411 | + | 0.741085i | \(0.265689\pi\) | ||||
−0.671411 | + | 0.741085i | \(0.734311\pi\) | |||||||
\(174\) | 6.06701 | + | 16.9699i | 0.459939 | + | 1.28649i | ||||
\(175\) | − | 2.44718i | − | 0.184989i | ||||||
\(176\) | − | 2.01377i | − | 0.151794i | ||||||
\(177\) | 6.20409 | − | 2.21806i | 0.466328 | − | 0.166719i | ||||
\(178\) | 0.950346 | 0.0712315 | ||||||||
\(179\) | −3.67949 | −0.275018 | −0.137509 | − | 0.990501i | \(-0.543910\pi\) | ||||
−0.137509 | + | 0.990501i | \(0.543910\pi\) | |||||||
\(180\) | 10.0073 | − | 8.20414i | 0.745899 | − | 0.611501i | ||||
\(181\) | 10.8751 | 0.808341 | 0.404170 | − | 0.914684i | \(-0.367560\pi\) | ||||
0.404170 | + | 0.914684i | \(0.367560\pi\) | |||||||
\(182\) | 6.51637i | 0.483025i | ||||||||
\(183\) | 7.89948 | − | 2.82418i | 0.583947 | − | 0.208770i | ||||
\(184\) | − | 15.1353i | − | 1.11579i | ||||||
\(185\) | − | 14.0701i | − | 1.03445i | ||||||
\(186\) | 1.52483 | + | 4.26507i | 0.111806 | + | 0.312730i | ||||
\(187\) | −5.98440 | −0.437623 | ||||||||
\(188\) | − | 16.7825i | − | 1.22399i | ||||||
\(189\) | −2.11520 | + | 3.52281i | −0.153858 | + | 0.256247i | ||||
\(190\) | 19.1880i | 1.39204i | ||||||||
\(191\) | 4.28023 | 0.309707 | 0.154853 | − | 0.987937i | \(-0.450510\pi\) | ||||
0.154853 | + | 0.987937i | \(0.450510\pi\) | |||||||
\(192\) | 7.60639 | + | 21.2757i | 0.548944 | + | 1.53544i | ||||
\(193\) | −14.2342 | −1.02460 | −0.512299 | − | 0.858807i | \(-0.671206\pi\) | ||||
−0.512299 | + | 0.858807i | \(0.671206\pi\) | |||||||
\(194\) | −26.0329 | −1.86905 | ||||||||
\(195\) | 2.92976 | + | 8.19478i | 0.209804 | + | 0.586841i | ||||
\(196\) | 19.9201 | 1.42286 | ||||||||
\(197\) | − | 19.9700i | − | 1.42280i | −0.702787 | − | 0.711401i | \(-0.748061\pi\) | ||
0.702787 | − | 0.711401i | \(-0.251939\pi\) | |||||||
\(198\) | −17.8830 | − | 21.8134i | −1.27089 | − | 1.55021i | ||||
\(199\) | − | 9.37835i | − | 0.664814i | −0.943136 | − | 0.332407i | \(-0.892139\pi\) | ||
0.943136 | − | 0.332407i | \(-0.107861\pi\) | |||||||
\(200\) | −7.88054 | −0.557239 | ||||||||
\(201\) | 0.300372 | + | 0.840166i | 0.0211866 | + | 0.0592607i | ||||
\(202\) | − | 13.9611i | − | 0.982300i | ||||||
\(203\) | − | 3.63460i | − | 0.255099i | ||||||
\(204\) | 7.34353 | − | 2.62542i | 0.514150 | − | 0.183816i | ||||
\(205\) | 12.1820i | 0.850829i | ||||||||
\(206\) | −3.49854 | −0.243755 | ||||||||
\(207\) | 11.3044 | + | 13.7890i | 0.785711 | + | 0.958398i | ||||
\(208\) | −1.76491 | −0.122374 | ||||||||
\(209\) | 25.5028 | 1.76406 | ||||||||
\(210\) | −4.03028 | + | 1.44088i | −0.278115 | + | 0.0994305i | ||||
\(211\) | 8.22808i | 0.566445i | 0.959054 | + | 0.283222i | \(0.0914034\pi\) | ||||
−0.959054 | + | 0.283222i | \(0.908597\pi\) | |||||||
\(212\) | 15.6909i | 1.07766i | ||||||||
\(213\) | −9.01468 | − | 25.2148i | −0.617676 | − | 1.72769i | ||||
\(214\) | 37.4865i | 2.56252i | ||||||||
\(215\) | −7.11597 | + | 5.59417i | −0.485305 | + | 0.381519i | ||||
\(216\) | 11.3444 | + | 6.81148i | 0.771887 | + | 0.463463i | ||||
\(217\) | − | 0.913486i | − | 0.0620115i | ||||||
\(218\) | −12.6309 | −0.855474 | ||||||||
\(219\) | 19.3650 | − | 6.92327i | 1.30856 | − | 0.467831i | ||||
\(220\) | − | 17.9150i | − | 1.20783i | ||||||
\(221\) | 5.24485i | 0.352807i | ||||||||
\(222\) | 37.6347 | − | 13.4550i | 2.52588 | − | 0.903039i | ||||
\(223\) | − | 4.15145i | − | 0.278002i | −0.990292 | − | 0.139001i | \(-0.955611\pi\) | ||
0.990292 | − | 0.139001i | \(-0.0443891\pi\) | |||||||
\(224\) | − | 4.89554i | − | 0.327097i | ||||||
\(225\) | 7.17953 | − | 5.88590i | 0.478635 | − | 0.392393i | ||||
\(226\) | 7.04496 | 0.468623 | ||||||||
\(227\) | 21.4635 | 1.42458 | 0.712290 | − | 0.701885i | \(-0.247658\pi\) | ||||
0.712290 | + | 0.701885i | \(0.247658\pi\) | |||||||
\(228\) | −31.2947 | + | 11.1883i | −2.07254 | + | 0.740966i | ||||
\(229\) | 15.8439 | 1.04700 | 0.523498 | − | 0.852027i | \(-0.324627\pi\) | ||||
0.523498 | + | 0.852027i | \(0.324627\pi\) | |||||||
\(230\) | 18.5727i | 1.22465i | ||||||||
\(231\) | 1.91508 | + | 5.35664i | 0.126003 | + | 0.352441i | ||||
\(232\) | −11.7044 | −0.768429 | ||||||||
\(233\) | 6.05364 | 0.396587 | 0.198294 | − | 0.980143i | \(-0.436460\pi\) | ||||
0.198294 | + | 0.980143i | \(0.436460\pi\) | |||||||
\(234\) | −19.1177 | + | 15.6730i | −1.24977 | + | 1.02458i | ||||
\(235\) | 7.41335i | 0.483594i | ||||||||
\(236\) | 11.8870i | 0.773776i | ||||||||
\(237\) | −4.43717 | − | 12.4111i | −0.288225 | − | 0.806190i | ||||
\(238\) | −2.57947 | −0.167202 | ||||||||
\(239\) | 10.0968i | 0.653106i | 0.945179 | + | 0.326553i | \(0.105887\pi\) | ||||
−0.945179 | + | 0.326553i | \(0.894113\pi\) | |||||||
\(240\) | −0.390253 | − | 1.09157i | −0.0251907 | − | 0.0704605i | ||||
\(241\) | − | 18.8046i | − | 1.21131i | −0.795727 | − | 0.605655i | \(-0.792911\pi\) | ||
0.795727 | − | 0.605655i | \(-0.207089\pi\) | |||||||
\(242\) | −14.1484 | −0.909491 | ||||||||
\(243\) | −15.4227 | + | 2.26744i | −0.989365 | + | 0.145456i | ||||
\(244\) | 15.1353i | 0.968939i | ||||||||
\(245\) | −8.79931 | −0.562168 | ||||||||
\(246\) | −32.5845 | + | 11.6494i | −2.07751 | + | 0.742741i | ||||
\(247\) | − | 22.3512i | − | 1.42217i | ||||||
\(248\) | −2.94166 | −0.186796 | ||||||||
\(249\) | −12.9779 | + | 4.63980i | −0.822441 | + | 0.294035i | ||||
\(250\) | 25.2947 | 1.59978 | ||||||||
\(251\) | − | 8.43231i | − | 0.532243i | −0.963940 | − | 0.266121i | \(-0.914258\pi\) | ||
0.963940 | − | 0.266121i | \(-0.0857422\pi\) | |||||||
\(252\) | −4.70003 | − | 5.73302i | −0.296074 | − | 0.361147i | ||||
\(253\) | 24.6850 | 1.55193 | ||||||||
\(254\) | 23.3054 | 1.46231 | ||||||||
\(255\) | −3.24386 | + | 1.15973i | −0.203139 | + | 0.0726251i | ||||
\(256\) | −12.7346 | −0.795915 | ||||||||
\(257\) | −20.0564 | −1.25108 | −0.625541 | − | 0.780191i | \(-0.715122\pi\) | ||||
−0.625541 | + | 0.780191i | \(0.715122\pi\) | |||||||
\(258\) | −21.7682 | − | 13.6842i | −1.35523 | − | 0.851941i | ||||
\(259\) | −8.06055 | −0.500858 | ||||||||
\(260\) | −15.7011 | −0.973741 | ||||||||
\(261\) | 10.6632 | − | 8.74187i | 0.660035 | − | 0.541108i | ||||
\(262\) | −47.8695 | −2.95739 | ||||||||
\(263\) | 9.75780 | 0.601692 | 0.300846 | − | 0.953673i | \(-0.402731\pi\) | ||||
0.300846 | + | 0.953673i | \(0.402731\pi\) | |||||||
\(264\) | 17.2498 | − | 6.16705i | 1.06165 | − | 0.379556i | ||||
\(265\) | − | 6.93117i | − | 0.425779i | ||||||
\(266\) | 10.9925 | 0.673995 | ||||||||
\(267\) | −0.244780 | − | 0.684670i | −0.0149803 | − | 0.0419011i | ||||
\(268\) | −1.60975 | −0.0983310 | ||||||||
\(269\) | 10.2225i | 0.623278i | 0.950201 | + | 0.311639i | \(0.100878\pi\) | ||||
−0.950201 | + | 0.311639i | \(0.899122\pi\) | |||||||
\(270\) | −13.9208 | − | 8.35844i | −0.847194 | − | 0.508679i | ||||
\(271\) | −1.73463 | −0.105371 | −0.0526857 | − | 0.998611i | \(-0.516778\pi\) | ||||
−0.0526857 | + | 0.998611i | \(0.516778\pi\) | |||||||
\(272\) | − | 0.698630i | − | 0.0423607i | ||||||
\(273\) | 4.69467 | − | 1.67841i | 0.284134 | − | 0.101582i | ||||
\(274\) | −26.9844 | −1.63019 | ||||||||
\(275\) | − | 12.8528i | − | 0.775053i | ||||||
\(276\) | −30.2912 | + | 10.8296i | −1.82332 | + | 0.651863i | ||||
\(277\) | 26.5026i | 1.59239i | 0.605042 | + | 0.796194i | \(0.293156\pi\) | ||||
−0.605042 | + | 0.796194i | \(0.706844\pi\) | |||||||
\(278\) | −33.2442 | −1.99385 | ||||||||
\(279\) | 2.67999 | − | 2.19710i | 0.160447 | − | 0.131537i | ||||
\(280\) | − | 2.77972i | − | 0.166120i | ||||||
\(281\) | 4.79771i | 0.286208i | 0.989708 | + | 0.143104i | \(0.0457083\pi\) | ||||
−0.989708 | + | 0.143104i | \(0.954292\pi\) | |||||||
\(282\) | −19.8292 | + | 7.08925i | −1.18081 | + | 0.422159i | ||||
\(283\) | −12.1249 | −0.720750 | −0.360375 | − | 0.932808i | \(-0.617351\pi\) | ||||
−0.360375 | + | 0.932808i | \(0.617351\pi\) | |||||||
\(284\) | 48.3113 | 2.86675 | ||||||||
\(285\) | 13.8239 | − | 4.94224i | 0.818854 | − | 0.292753i | ||||
\(286\) | 34.2246i | 2.02374i | ||||||||
\(287\) | 6.97889 | 0.411951 | ||||||||
\(288\) | 14.3625 | − | 11.7747i | 0.846321 | − | 0.693828i | ||||
\(289\) | 14.9239 | 0.877874 | ||||||||
\(290\) | 14.3625 | 0.843397 | ||||||||
\(291\) | 6.70527 | + | 18.7552i | 0.393070 | + | 1.09945i | ||||
\(292\) | 37.1030i | 2.17129i | ||||||||
\(293\) | 17.8741i | 1.04421i | 0.852880 | + | 0.522107i | \(0.174854\pi\) | ||||
−0.852880 | + | 0.522107i | \(0.825146\pi\) | |||||||
\(294\) | −8.41462 | − | 23.5364i | −0.490751 | − | 1.37267i | ||||
\(295\) | − | 5.25084i | − | 0.305716i | ||||||
\(296\) | 25.9571i | 1.50872i | ||||||||
\(297\) | −11.1092 | + | 18.5021i | −0.644622 | + | 1.07360i | ||||
\(298\) | 13.7796 | 0.798230 | ||||||||
\(299\) | − | 21.6344i | − | 1.25115i | ||||||
\(300\) | 5.63866 | + | 15.7718i | 0.325548 | + | 0.910585i | ||||
\(301\) | 3.20482 | + | 4.07663i | 0.184722 | + | 0.234973i | ||||
\(302\) | − | 31.6054i | − | 1.81869i | ||||||
\(303\) | −10.0582 | + | 3.59595i | −0.577827 | + | 0.206582i | ||||
\(304\) | 2.97724i | 0.170756i | ||||||||
\(305\) | − | 6.68574i | − | 0.382824i | ||||||
\(306\) | −6.20409 | − | 7.56766i | −0.354664 | − | 0.432614i | ||||
\(307\) | −12.1854 | −0.695460 | −0.347730 | − | 0.937595i | \(-0.613047\pi\) | ||||
−0.347730 | + | 0.937595i | \(0.613047\pi\) | |||||||
\(308\) | −10.2633 | −0.584803 | ||||||||
\(309\) | 0.901116 | + | 2.52050i | 0.0512627 | + | 0.143386i | ||||
\(310\) | 3.60975 | 0.205020 | ||||||||
\(311\) | 4.15328i | 0.235511i | 0.993043 | + | 0.117756i | \(0.0375699\pi\) | ||||
−0.993043 | + | 0.117756i | \(0.962430\pi\) | |||||||
\(312\) | −5.40493 | − | 15.1181i | −0.305994 | − | 0.855891i | ||||
\(313\) | − | 5.61032i | − | 0.317114i | −0.987350 | − | 0.158557i | \(-0.949316\pi\) | ||
0.987350 | − | 0.158557i | \(-0.0506842\pi\) | |||||||
\(314\) | 6.46217i | 0.364681i | ||||||||
\(315\) | 2.07615 | + | 2.53245i | 0.116978 | + | 0.142688i | ||||
\(316\) | 23.7796 | 1.33771 | ||||||||
\(317\) | 20.7122i | 1.16331i | 0.813434 | + | 0.581657i | \(0.197595\pi\) | ||||
−0.813434 | + | 0.581657i | \(0.802405\pi\) | |||||||
\(318\) | 18.5395 | − | 6.62815i | 1.03964 | − | 0.371688i | ||||
\(319\) | − | 19.0892i | − | 1.06879i | ||||||
\(320\) | 18.0067 | 1.00661 | ||||||||
\(321\) | 27.0068 | − | 9.65535i | 1.50737 | − | 0.538909i | ||||
\(322\) | 10.6400 | 0.592945 | ||||||||
\(323\) | 8.84759 | 0.492293 | ||||||||
\(324\) | 5.51514 | − | 27.5779i | 0.306397 | − | 1.53211i | ||||
\(325\) | −11.2645 | −0.624839 | ||||||||
\(326\) | 8.25237i | 0.457056i | ||||||||
\(327\) | 3.25333 | + | 9.09985i | 0.179910 | + | 0.503223i | ||||
\(328\) | − | 22.4739i | − | 1.24091i | ||||||
\(329\) | 4.24700 | 0.234145 | ||||||||
\(330\) | −21.1674 | + | 7.56766i | −1.16523 | + | 0.416586i | ||||
\(331\) | − | 7.62320i | − | 0.419009i | −0.977808 | − | 0.209505i | \(-0.932815\pi\) | ||
0.977808 | − | 0.209505i | \(-0.0671851\pi\) | |||||||
\(332\) | − | 24.8655i | − | 1.36467i | ||||||
\(333\) | −19.3871 | − | 23.6481i | −1.06241 | − | 1.29591i | ||||
\(334\) | − | 28.4676i | − | 1.55768i | ||||||
\(335\) | 0.711075 | 0.0388502 | ||||||||
\(336\) | −0.625344 | + | 0.223570i | −0.0341153 | + | 0.0121967i | ||||
\(337\) | 19.8898 | 1.08347 | 0.541733 | − | 0.840551i | \(-0.317768\pi\) | ||||
0.541733 | + | 0.840551i | \(0.317768\pi\) | |||||||
\(338\) | 0.565436 | 0.0307557 | ||||||||
\(339\) | −1.81456 | − | 5.07548i | −0.0985535 | − | 0.275662i | ||||
\(340\) | − | 6.21520i | − | 0.337067i | ||||||
\(341\) | − | 4.79771i | − | 0.259811i | ||||||
\(342\) | 26.4390 | + | 32.2499i | 1.42966 | + | 1.74387i | ||||
\(343\) | 10.5765i | 0.571077i | ||||||||
\(344\) | 13.1278 | − | 10.3203i | 0.707805 | − | 0.556435i | ||||
\(345\) | 13.3806 | − | 4.78375i | 0.720385 | − | 0.257549i | ||||
\(346\) | 44.1330i | 2.37260i | ||||||||
\(347\) | −27.8502 | −1.49508 | −0.747538 | − | 0.664219i | \(-0.768764\pi\) | ||||
−0.747538 | + | 0.664219i | \(0.768764\pi\) | |||||||
\(348\) | 8.37466 | + | 23.4246i | 0.448929 | + | 1.25569i | ||||
\(349\) | − | 23.3395i | − | 1.24933i | −0.780892 | − | 0.624666i | \(-0.785235\pi\) | ||
0.780892 | − | 0.624666i | \(-0.214765\pi\) | |||||||
\(350\) | − | 5.53997i | − | 0.296124i | ||||||
\(351\) | 16.2157 | + | 9.73634i | 0.865528 | + | 0.519687i | ||||
\(352\) | − | 25.7118i | − | 1.37044i | ||||||
\(353\) | 27.2828i | 1.45212i | 0.687633 | + | 0.726058i | \(0.258650\pi\) | ||||
−0.687633 | + | 0.726058i | \(0.741350\pi\) | |||||||
\(354\) | 14.0450 | − | 5.02128i | 0.746481 | − | 0.266878i | ||||
\(355\) | −21.3406 | −1.13264 | ||||||||
\(356\) | 1.31182 | 0.0695263 | ||||||||
\(357\) | 0.664392 | + | 1.85836i | 0.0351633 | + | 0.0983549i | ||||
\(358\) | −8.32970 | −0.440238 | ||||||||
\(359\) | 0.627085i | 0.0330963i | 0.999863 | + | 0.0165481i | \(0.00526768\pi\) | ||||
−0.999863 | + | 0.0165481i | \(0.994732\pi\) | |||||||
\(360\) | 8.15516 | − | 6.68574i | 0.429815 | − | 0.352369i | ||||
\(361\) | −18.7044 | −0.984440 | ||||||||
\(362\) | 24.6193 | 1.29396 | ||||||||
\(363\) | 3.64418 | + | 10.1931i | 0.191270 | + | 0.534998i | ||||
\(364\) | 8.99493i | 0.471462i | ||||||||
\(365\) | − | 16.3896i | − | 0.857869i | ||||||
\(366\) | 17.8830 | − | 6.39345i | 0.934760 | − | 0.334191i | ||||
\(367\) | −16.2909 | −0.850380 | −0.425190 | − | 0.905104i | \(-0.639793\pi\) | ||||
−0.425190 | + | 0.905104i | \(0.639793\pi\) | |||||||
\(368\) | 2.88177i | 0.150223i | ||||||||
\(369\) | 16.7855 | + | 20.4747i | 0.873818 | + | 1.06587i | ||||
\(370\) | − | 31.8522i | − | 1.65592i | ||||||
\(371\) | −3.97077 | −0.206152 | ||||||||
\(372\) | 2.10481 | + | 5.88733i | 0.109129 | + | 0.305244i | ||||
\(373\) | − | 7.53605i | − | 0.390202i | −0.980783 | − | 0.195101i | \(-0.937497\pi\) | ||
0.980783 | − | 0.195101i | \(-0.0625035\pi\) | |||||||
\(374\) | −13.5476 | −0.700531 | ||||||||
\(375\) | −6.51514 | − | 18.2234i | −0.336440 | − | 0.941052i | ||||
\(376\) | − | 13.6764i | − | 0.705309i | ||||||
\(377\) | −16.7302 | −0.861650 | ||||||||
\(378\) | −4.78843 | + | 7.97502i | −0.246290 | + | 0.410191i | ||||
\(379\) | −29.0440 | −1.49189 | −0.745946 | − | 0.666006i | \(-0.768002\pi\) | ||||
−0.745946 | + | 0.666006i | \(0.768002\pi\) | |||||||
\(380\) | 26.4863i | 1.35872i | ||||||||
\(381\) | −6.00275 | − | 16.7902i | −0.307530 | − | 0.860188i | ||||
\(382\) | 9.68968 | 0.495767 | ||||||||
\(383\) | −8.98467 | −0.459095 | −0.229548 | − | 0.973297i | \(-0.573725\pi\) | ||||
−0.229548 | + | 0.973297i | \(0.573725\pi\) | |||||||
\(384\) | 10.0000 | + | 27.9708i | 0.510310 | + | 1.42738i | ||||
\(385\) | 4.53360 | 0.231054 | ||||||||
\(386\) | −32.2236 | −1.64014 | ||||||||
\(387\) | −4.25188 | + | 19.2073i | −0.216135 | + | 0.976363i | ||||
\(388\) | −35.9348 | −1.82431 | ||||||||
\(389\) | 27.6542 | 1.40212 | 0.701062 | − | 0.713101i | \(-0.252710\pi\) | ||||
0.701062 | + | 0.713101i | \(0.252710\pi\) | |||||||
\(390\) | 6.63245 | + | 18.5515i | 0.335847 | + | 0.939393i | ||||
\(391\) | 8.56387 | 0.433094 | ||||||||
\(392\) | 16.2333 | 0.819906 | ||||||||
\(393\) | 12.3297 | + | 34.4872i | 0.621951 | + | 1.73965i | ||||
\(394\) | − | 45.2084i | − | 2.27757i | ||||||
\(395\) | −10.5042 | −0.528523 | ||||||||
\(396\) | −24.6850 | − | 30.1104i | −1.24047 | − | 1.51310i | ||||
\(397\) | −4.28383 | −0.214999 | −0.107500 | − | 0.994205i | \(-0.534284\pi\) | ||||
−0.107500 | + | 0.994205i | \(0.534284\pi\) | |||||||
\(398\) | − | 21.2309i | − | 1.06421i | ||||||
\(399\) | −2.83133 | − | 7.91948i | −0.141744 | − | 0.396470i | ||||
\(400\) | 1.50046 | 0.0750229 | ||||||||
\(401\) | − | 13.1043i | − | 0.654397i | −0.944956 | − | 0.327198i | \(-0.893895\pi\) | ||
0.944956 | − | 0.327198i | \(-0.106105\pi\) | |||||||
\(402\) | 0.679988 | + | 1.90198i | 0.0339147 | + | 0.0948624i | ||||
\(403\) | −4.20482 | −0.209457 | ||||||||
\(404\) | − | 19.2713i | − | 0.958785i | ||||||
\(405\) | −2.43621 | + | 12.1820i | −0.121056 | + | 0.605329i | ||||
\(406\) | − | 8.22808i | − | 0.408353i | ||||||
\(407\) | −42.3348 | −2.09846 | ||||||||
\(408\) | 5.98440 | − | 2.13951i | 0.296272 | − | 0.105922i | ||||
\(409\) | 0.913486i | 0.0451690i | 0.999745 | + | 0.0225845i | \(0.00718948\pi\) | ||||
−0.999745 | + | 0.0225845i | \(0.992811\pi\) | |||||||
\(410\) | 27.5779i | 1.36198i | ||||||||
\(411\) | 6.95035 | + | 19.4407i | 0.342835 | + | 0.958939i | ||||
\(412\) | −4.82924 | −0.237920 | ||||||||
\(413\) | −3.00813 | −0.148020 | ||||||||
\(414\) | 25.5912 | + | 31.2157i | 1.25774 | + | 1.53417i | ||||
\(415\) | 10.9839i | 0.539177i | ||||||||
\(416\) | −22.5344 | −1.10484 | ||||||||
\(417\) | 8.56267 | + | 23.9505i | 0.419316 | + | 1.17286i | ||||
\(418\) | 57.7337 | 2.82385 | ||||||||
\(419\) | 19.6345 | 0.959208 | 0.479604 | − | 0.877485i | \(-0.340780\pi\) | ||||
0.479604 | + | 0.877485i | \(0.340780\pi\) | |||||||
\(420\) | −5.56323 | + | 1.98894i | −0.271458 | + | 0.0970502i | ||||
\(421\) | − | 1.89018i | − | 0.0921217i | −0.998939 | − | 0.0460609i | \(-0.985333\pi\) | ||
0.998939 | − | 0.0460609i | \(-0.0146668\pi\) | |||||||
\(422\) | 18.6269i | 0.906744i | ||||||||
\(423\) | 10.2148 | + | 12.4599i | 0.496660 | + | 0.605819i | ||||
\(424\) | 12.7869i | 0.620987i | ||||||||
\(425\) | − | 4.45898i | − | 0.216292i | ||||||
\(426\) | −20.4076 | − | 57.0818i | −0.988752 | − | 2.76562i | ||||
\(427\) | −3.83016 | −0.185354 | ||||||||
\(428\) | 51.7448i | 2.50118i | ||||||||
\(429\) | 24.6568 | − | 8.81519i | 1.19044 | − | 0.425601i | ||||
\(430\) | −16.1093 | + | 12.6642i | −0.776859 | + | 0.610722i | ||||
\(431\) | − | 38.4169i | − | 1.85048i | −0.379384 | − | 0.925239i | \(-0.623864\pi\) | ||
0.379384 | − | 0.925239i | \(-0.376136\pi\) | |||||||
\(432\) | −2.15997 | − | 1.29691i | −0.103922 | − | 0.0623976i | ||||
\(433\) | − | 23.8456i | − | 1.14595i | −0.819574 | − | 0.572973i | \(-0.805790\pi\) | ||
0.819574 | − | 0.572973i | \(-0.194210\pi\) | |||||||
\(434\) | − | 2.06797i | − | 0.0992657i | ||||||
\(435\) | −3.69935 | − | 10.3474i | −0.177370 | − | 0.496119i | ||||
\(436\) | −17.4352 | −0.834995 | ||||||||
\(437\) | −36.4953 | −1.74581 | ||||||||
\(438\) | 43.8388 | − | 15.6730i | 2.09470 | − | 0.748887i | ||||
\(439\) | −1.71526 | −0.0818647 | −0.0409323 | − | 0.999162i | \(-0.513033\pi\) | ||||
−0.0409323 | + | 0.999162i | \(0.513033\pi\) | |||||||
\(440\) | − | 14.5994i | − | 0.695998i | ||||||
\(441\) | −14.7893 | + | 12.1245i | −0.704251 | + | 0.577357i | ||||
\(442\) | 11.8734i | 0.564761i | ||||||||
\(443\) | − | 30.7374i | − | 1.46038i | −0.683244 | − | 0.730190i | \(-0.739432\pi\) | ||
0.683244 | − | 0.730190i | \(-0.260568\pi\) | |||||||
\(444\) | 51.9494 | − | 18.5727i | 2.46541 | − | 0.881422i | ||||
\(445\) | −0.579471 | −0.0274696 | ||||||||
\(446\) | − | 9.39814i | − | 0.445015i | ||||||
\(447\) | −3.54920 | − | 9.92740i | −0.167871 | − | 0.469550i | ||||
\(448\) | − | 10.3158i | − | 0.487375i | ||||||
\(449\) | −34.7969 | −1.64217 | −0.821084 | − | 0.570808i | \(-0.806630\pi\) | ||||
−0.821084 | + | 0.570808i | \(0.806630\pi\) | |||||||
\(450\) | 16.2532 | − | 13.3246i | 0.766182 | − | 0.628129i | ||||
\(451\) | 36.6538 | 1.72596 | ||||||||
\(452\) | 9.72457 | 0.457405 | ||||||||
\(453\) | −22.7699 | + | 8.14058i | −1.06982 | + | 0.382478i | ||||
\(454\) | 48.5895 | 2.28042 | ||||||||
\(455\) | − | 3.97334i | − | 0.186273i | ||||||
\(456\) | −25.5028 | + | 9.11763i | −1.19428 | + | 0.426972i | ||||
\(457\) | − | 4.33736i | − | 0.202893i | −0.994841 | − | 0.101446i | \(-0.967653\pi\) | ||
0.994841 | − | 0.101446i | \(-0.0323471\pi\) | |||||||
\(458\) | 35.8678 | 1.67599 | ||||||||
\(459\) | −3.85408 | + | 6.41889i | −0.179893 | + | 0.299608i | ||||
\(460\) | 25.6370i | 1.19533i | ||||||||
\(461\) | − | 16.0297i | − | 0.746576i | −0.927715 | − | 0.373288i | \(-0.878230\pi\) | ||
0.927715 | − | 0.373288i | \(-0.121770\pi\) | |||||||
\(462\) | 4.33540 | + | 12.1265i | 0.201701 | + | 0.564175i | ||||
\(463\) | 9.09369i | 0.422619i | 0.977419 | + | 0.211310i | \(0.0677729\pi\) | ||||
−0.977419 | + | 0.211310i | \(0.932227\pi\) | |||||||
\(464\) | 2.22851 | 0.103456 | ||||||||
\(465\) | −0.929759 | − | 2.60061i | −0.0431165 | − | 0.120601i | ||||
\(466\) | 13.7044 | 0.634842 | ||||||||
\(467\) | 8.32602 | 0.385282 | 0.192641 | − | 0.981269i | \(-0.438295\pi\) | ||||
0.192641 | + | 0.981269i | \(0.438295\pi\) | |||||||
\(468\) | −26.3893 | + | 21.6344i | −1.21985 | + | 1.00005i | ||||
\(469\) | − | 0.407364i | − | 0.0188103i | ||||||
\(470\) | 16.7825i | 0.774119i | ||||||||
\(471\) | 4.65562 | − | 1.66445i | 0.214520 | − | 0.0766940i | ||||
\(472\) | 9.68696i | 0.445878i | ||||||||
\(473\) | 16.8320 | + | 21.4109i | 0.773935 | + | 0.984472i | ||||
\(474\) | −10.0450 | − | 28.0966i | −0.461380 | − | 1.29052i | ||||
\(475\) | 19.0021i | 0.871876i | ||||||||
\(476\) | −3.56060 | −0.163200 | ||||||||
\(477\) | −9.55041 | − | 11.6494i | −0.437283 | − | 0.533391i | ||||
\(478\) | 22.8573i | 1.04547i | ||||||||
\(479\) | 39.2307i | 1.79250i | 0.443552 | + | 0.896249i | \(0.353718\pi\) | ||||
−0.443552 | + | 0.896249i | \(0.646282\pi\) | |||||||
\(480\) | −4.98275 | − | 13.9372i | −0.227430 | − | 0.636142i | ||||
\(481\) | 37.1030i | 1.69175i | ||||||||
\(482\) | − | 42.5702i | − | 1.93902i | ||||||
\(483\) | −2.74054 | − | 7.66552i | −0.124699 | − | 0.348793i | ||||
\(484\) | −19.5298 | −0.887719 | ||||||||
\(485\) | 15.8735 | 0.720778 | ||||||||
\(486\) | −34.9142 | + | 5.13307i | −1.58374 | + | 0.232841i | ||||
\(487\) | −19.0984 | −0.865431 | −0.432715 | − | 0.901531i | \(-0.642444\pi\) | ||||
−0.432715 | + | 0.901531i | \(0.642444\pi\) | |||||||
\(488\) | 12.3341i | 0.558339i | ||||||||
\(489\) | 5.94536 | − | 2.12555i | 0.268858 | − | 0.0961209i | ||||
\(490\) | −19.9201 | −0.899897 | ||||||||
\(491\) | −4.49233 | −0.202736 | −0.101368 | − | 0.994849i | \(-0.532322\pi\) | ||||
−0.101368 | + | 0.994849i | \(0.532322\pi\) | |||||||
\(492\) | −44.9783 | + | 16.0804i | −2.02778 | + | 0.724961i | ||||
\(493\) | − | 6.62257i | − | 0.298265i | ||||||
\(494\) | − | 50.5990i | − | 2.27656i | ||||||
\(495\) | 10.9041 | + | 13.3007i | 0.490104 | + | 0.597821i | ||||
\(496\) | 0.560094 | 0.0251490 | ||||||||
\(497\) | 12.2257i | 0.548398i | ||||||||
\(498\) | −29.3796 | + | 10.5037i | −1.31653 | + | 0.470681i | ||||
\(499\) | 41.7606i | 1.86946i | 0.355356 | + | 0.934731i | \(0.384360\pi\) | ||||
−0.355356 | + | 0.934731i | \(0.615640\pi\) | |||||||
\(500\) | 34.9158 | 1.56148 | ||||||||
\(501\) | −20.5093 | + | 7.33237i | −0.916286 | + | 0.327586i | ||||
\(502\) | − | 19.0892i | − | 0.851995i | ||||||
\(503\) | 3.35290 | 0.149499 | 0.0747493 | − | 0.997202i | \(-0.476184\pi\) | ||||
0.0747493 | + | 0.997202i | \(0.476184\pi\) | |||||||
\(504\) | −3.83016 | − | 4.67197i | −0.170609 | − | 0.208106i | ||||
\(505\) | 8.51275i | 0.378812i | ||||||||
\(506\) | 55.8824 | 2.48427 | ||||||||
\(507\) | −0.145639 | − | 0.407364i | −0.00646805 | − | 0.0180917i | ||||
\(508\) | 32.1698 | 1.42731 | ||||||||
\(509\) | − | 30.9784i | − | 1.37309i | −0.727087 | − | 0.686546i | \(-0.759126\pi\) | ||
0.727087 | − | 0.686546i | \(-0.240874\pi\) | |||||||
\(510\) | −7.34353 | + | 2.62542i | −0.325177 | + | 0.116256i | ||||
\(511\) | −9.38934 | −0.415360 | ||||||||
\(512\) | 5.47108 | 0.241790 | ||||||||
\(513\) | 16.4243 | − | 27.3543i | 0.725151 | − | 1.20772i | ||||
\(514\) | −45.4040 | −2.00269 | ||||||||
\(515\) | 2.13323 | 0.0940012 | ||||||||
\(516\) | −30.0479 | − | 18.8891i | −1.32278 | − | 0.831547i | ||||
\(517\) | 22.3056 | 0.981000 | ||||||||
\(518\) | −18.2476 | −0.801756 | ||||||||
\(519\) | 31.7953 | − | 11.3673i | 1.39566 | − | 0.498969i | ||||
\(520\) | −12.7952 | −0.561106 | ||||||||
\(521\) | 13.6912 | 0.599822 | 0.299911 | − | 0.953967i | \(-0.403043\pi\) | ||||
0.299911 | + | 0.953967i | \(0.403043\pi\) | |||||||
\(522\) | 24.1396 | − | 19.7900i | 1.05656 | − | 0.866186i | ||||
\(523\) | 22.4499i | 0.981666i | 0.871254 | + | 0.490833i | \(0.163308\pi\) | ||||
−0.871254 | + | 0.490833i | \(0.836692\pi\) | |||||||
\(524\) | −66.0771 | −2.88659 | ||||||||
\(525\) | −3.99123 | + | 1.42692i | −0.174191 | + | 0.0622761i | ||||
\(526\) | 22.0899 | 0.963166 | ||||||||
\(527\) | − | 1.66445i | − | 0.0725048i | ||||||
\(528\) | −3.28436 | + | 1.17421i | −0.142934 | + | 0.0511009i | ||||
\(529\) | −12.3250 | −0.535870 | ||||||||
\(530\) | − | 15.6909i | − | 0.681571i | ||||||
\(531\) | −7.23509 | − | 8.82525i | −0.313976 | − | 0.382983i | ||||
\(532\) | 15.1736 | 0.657860 | ||||||||
\(533\) | − | 32.1241i | − | 1.39145i | ||||||
\(534\) | −0.554138 | − | 1.54997i | −0.0239799 | − | 0.0670738i | ||||
\(535\) | − | 22.8573i | − | 0.988206i | ||||||
\(536\) | −1.31182 | −0.0566620 | ||||||||
\(537\) | 2.14547 | + | 6.00107i | 0.0925840 | + | 0.258965i | ||||
\(538\) | 23.1419i | 0.997720i | ||||||||
\(539\) | 26.4758i | 1.14039i | ||||||||
\(540\) | −19.2157 | − | 11.5377i | −0.826913 | − | 0.496502i | ||||
\(541\) | 24.2947 | 1.04451 | 0.522256 | − | 0.852789i | \(-0.325091\pi\) | ||||
0.522256 | + | 0.852789i | \(0.325091\pi\) | |||||||
\(542\) | −3.92690 | −0.168675 | ||||||||
\(543\) | −6.34117 | − | 17.7368i | −0.272126 | − | 0.761159i | ||||
\(544\) | − | 8.92011i | − | 0.382447i | ||||||
\(545\) | 7.70167 | 0.329903 | ||||||||
\(546\) | 10.6279 | − | 3.79963i | 0.454832 | − | 0.162609i | ||||
\(547\) | −31.9726 | −1.36705 | −0.683525 | − | 0.729927i | \(-0.739554\pi\) | ||||
−0.683525 | + | 0.729927i | \(0.739554\pi\) | |||||||
\(548\) | −37.2482 | −1.59116 | ||||||||
\(549\) | −9.21222 | − | 11.2369i | −0.393168 | − | 0.479580i | ||||
\(550\) | − | 29.0964i | − | 1.24068i | ||||||
\(551\) | 28.2223i | 1.20231i | ||||||||
\(552\) | −24.6850 | + | 8.82525i | −1.05066 | + | 0.375628i | ||||
\(553\) | 6.01769i | 0.255898i | ||||||||
\(554\) | 59.9971i | 2.54903i | ||||||||
\(555\) | −22.9477 | + | 8.20414i | −0.974075 | + | 0.348246i | ||||
\(556\) | −45.8889 | −1.94612 | ||||||||
\(557\) | 15.6473i | 0.662998i | 0.943456 | + | 0.331499i | \(0.107554\pi\) | ||||
−0.943456 | + | 0.331499i | \(0.892446\pi\) | |||||||
\(558\) | 6.06701 | − | 4.97384i | 0.256837 | − | 0.210559i | ||||
\(559\) | 18.7649 | − | 14.7519i | 0.793671 | − | 0.623939i | ||||
\(560\) | 0.529261i | 0.0223653i | ||||||||
\(561\) | 3.48945 | + | 9.76028i | 0.147325 | + | 0.412079i | ||||
\(562\) | 10.8612i | 0.458151i | ||||||||
\(563\) | 13.0764i | 0.551103i | 0.961286 | + | 0.275551i | \(0.0888605\pi\) | ||||
−0.961286 | + | 0.275551i | \(0.911140\pi\) | |||||||
\(564\) | −27.3715 | + | 9.78571i | −1.15255 | + | 0.412053i | ||||
\(565\) | −4.29564 | −0.180719 | ||||||||
\(566\) | −27.4486 | −1.15375 | ||||||||
\(567\) | 6.97889 | + | 1.39567i | 0.293086 | + | 0.0586125i | ||||
\(568\) | 39.3700 | 1.65193 | ||||||||
\(569\) | 3.28528i | 0.137726i | 0.997626 | + | 0.0688631i | \(0.0219372\pi\) | ||||
−0.997626 | + | 0.0688631i | \(0.978063\pi\) | |||||||
\(570\) | 31.2947 | − | 11.1883i | 1.31079 | − | 0.468628i | ||||
\(571\) | − | 9.40229i | − | 0.393474i | −0.980456 | − | 0.196737i | \(-0.936966\pi\) | ||
0.980456 | − | 0.196737i | \(-0.0630345\pi\) | |||||||
\(572\) | 47.2422i | 1.97529i | ||||||||
\(573\) | −2.49576 | − | 6.98085i | −0.104262 | − | 0.291629i | ||||
\(574\) | 15.7990 | 0.659436 | ||||||||
\(575\) | 18.3928i | 0.767031i | ||||||||
\(576\) | 30.2645 | − | 24.8113i | 1.26102 | − | 1.03380i | ||||
\(577\) | − | 11.6759i | − | 0.486074i | −0.970017 | − | 0.243037i | \(-0.921856\pi\) | ||
0.970017 | − | 0.243037i | \(-0.0781436\pi\) | |||||||
\(578\) | 33.7849 | 1.40527 | ||||||||
\(579\) | 8.29981 | + | 23.2153i | 0.344928 | + | 0.964793i | ||||
\(580\) | 19.8255 | 0.823207 | ||||||||
\(581\) | 6.29249 | 0.261057 | ||||||||
\(582\) | 15.1795 | + | 42.4584i | 0.629212 | + | 1.75996i | ||||
\(583\) | −20.8548 | −0.863718 | ||||||||
\(584\) | 30.2361i | 1.25118i | ||||||||
\(585\) | 11.6570 | − | 9.55660i | 0.481957 | − | 0.395117i | ||||
\(586\) | 40.4637i | 1.67154i | ||||||||
\(587\) | 9.96549 | 0.411320 | 0.205660 | − | 0.978624i | \(-0.434066\pi\) | ||||
0.205660 | + | 0.978624i | \(0.434066\pi\) | |||||||
\(588\) | −11.6152 | − | 32.4887i | −0.479003 | − | 1.33981i | ||||
\(589\) | 7.09314i | 0.292268i | ||||||||
\(590\) | − | 11.8870i | − | 0.489379i | ||||||
\(591\) | −32.5701 | + | 11.6443i | −1.33975 | + | 0.478982i | ||||
\(592\) | − | 4.94224i | − | 0.203125i | ||||||
\(593\) | 7.66844 | 0.314905 | 0.157453 | − | 0.987527i | \(-0.449672\pi\) | ||||
0.157453 | + | 0.987527i | \(0.449672\pi\) | |||||||
\(594\) | −25.1493 | + | 41.8855i | −1.03189 | + | 1.71858i | ||||
\(595\) | 1.57283 | 0.0644796 | ||||||||
\(596\) | 19.0208 | 0.779121 | ||||||||
\(597\) | −15.2956 | + | 5.46842i | −0.626009 | + | 0.223808i | ||||
\(598\) | − | 48.9765i | − | 2.00280i | ||||||
\(599\) | − | 31.9548i | − | 1.30564i | −0.757515 | − | 0.652818i | \(-0.773587\pi\) | ||
0.757515 | − | 0.652818i | \(-0.226413\pi\) | |||||||
\(600\) | 4.59507 | + | 12.8528i | 0.187593 | + | 0.524713i | ||||
\(601\) | − | 21.1530i | − | 0.862849i | −0.902149 | − | 0.431424i | \(-0.858011\pi\) | ||
0.902149 | − | 0.431424i | \(-0.141989\pi\) | |||||||
\(602\) | 7.25513 | + | 9.22877i | 0.295697 | + | 0.376137i | ||||
\(603\) | 1.19513 | − | 0.979785i | 0.0486693 | − | 0.0398999i | ||||
\(604\) | − | 43.6269i | − | 1.77515i | ||||||
\(605\) | 8.62693 | 0.350734 | ||||||||
\(606\) | −22.7699 | + | 8.14058i | −0.924964 | + | 0.330689i | ||||
\(607\) | 9.30353i | 0.377619i | 0.982014 | + | 0.188809i | \(0.0604628\pi\) | ||||
−0.982014 | + | 0.188809i | \(0.939537\pi\) | |||||||
\(608\) | 38.0134i | 1.54165i | ||||||||
\(609\) | −5.92786 | + | 2.11930i | −0.240209 | + | 0.0858783i | ||||
\(610\) | − | 15.1353i | − | 0.612811i | ||||||
\(611\) | − | 19.5491i | − | 0.790872i | ||||||
\(612\) | −8.56387 | − | 10.4461i | −0.346174 | − | 0.422258i | ||||
\(613\) | 20.8898 | 0.843731 | 0.421865 | − | 0.906658i | \(-0.361375\pi\) | ||||
0.421865 | + | 0.906658i | \(0.361375\pi\) | |||||||
\(614\) | −27.5856 | −1.11327 | ||||||||
\(615\) | 19.8683 | − | 7.10321i | 0.801167 | − | 0.286429i | ||||
\(616\) | −8.36376 | −0.336985 | ||||||||
\(617\) | − | 40.0920i | − | 1.61404i | −0.590523 | − | 0.807021i | \(-0.701079\pi\) | ||
0.590523 | − | 0.807021i | \(-0.298921\pi\) | |||||||
\(618\) | 2.03996 | + | 5.70595i | 0.0820594 | + | 0.229527i | ||||
\(619\) | 28.7181 | 1.15428 | 0.577139 | − | 0.816646i | \(-0.304169\pi\) | ||||
0.577139 | + | 0.816646i | \(0.304169\pi\) | |||||||
\(620\) | 4.98275 | 0.200112 | ||||||||
\(621\) | 15.8976 | − | 26.4772i | 0.637950 | − | 1.06249i | ||||
\(622\) | 9.40229i | 0.376998i | ||||||||
\(623\) | 0.331970i | 0.0133001i | ||||||||
\(624\) | 1.02910 | + | 2.87848i | 0.0411970 | + | 0.115232i | ||||
\(625\) | 0.0496535 | 0.00198614 | ||||||||
\(626\) | − | 12.7008i | − | 0.507625i | ||||||
\(627\) | −14.8704 | − | 41.5938i | −0.593867 | − | 1.66110i | ||||
\(628\) | 8.92011i | 0.355951i | ||||||||
\(629\) | −14.6871 | −0.585611 | ||||||||
\(630\) | 4.70003 | + | 5.73302i | 0.187254 | + | 0.228409i | ||||
\(631\) | 23.0432i | 0.917335i | 0.888608 | + | 0.458667i | \(0.151673\pi\) | ||||
−0.888608 | + | 0.458667i | \(0.848327\pi\) | |||||||
\(632\) | 19.3785 | 0.770836 | ||||||||
\(633\) | 13.4196 | − | 4.79771i | 0.533382 | − | 0.190692i | ||||
\(634\) | 46.8888i | 1.86219i | ||||||||
\(635\) | −14.2104 | −0.563923 | ||||||||
\(636\) | 25.5912 | − | 9.14923i | 1.01476 | − | 0.362791i | ||||
\(637\) | 23.2039 | 0.919372 | ||||||||
\(638\) | − | 43.2146i | − | 1.71088i | ||||||
\(639\) | −35.8678 | + | 29.4050i | −1.41891 | + | 1.16324i | ||||
\(640\) | 23.6732 | 0.935764 | ||||||||
\(641\) | 11.9349 | 0.471400 | 0.235700 | − | 0.971826i | \(-0.424262\pi\) | ||||
0.235700 | + | 0.971826i | \(0.424262\pi\) | |||||||
\(642\) | 61.1386 | − | 21.8580i | 2.41295 | − | 0.862666i | ||||
\(643\) | −23.3288 | −0.919997 | −0.459999 | − | 0.887920i | \(-0.652150\pi\) | ||||
−0.459999 | + | 0.887920i | \(0.652150\pi\) | |||||||
\(644\) | 14.6871 | 0.578751 | ||||||||
\(645\) | 13.2731 | + | 8.34391i | 0.522627 | + | 0.328541i | ||||
\(646\) | 20.0294 | 0.788045 | ||||||||
\(647\) | 24.7629 | 0.973529 | 0.486765 | − | 0.873533i | \(-0.338177\pi\) | ||||
0.486765 | + | 0.873533i | \(0.338177\pi\) | |||||||
\(648\) | 4.49441 | − | 22.4739i | 0.176557 | − | 0.882856i | ||||
\(649\) | −15.7990 | −0.620164 | ||||||||
\(650\) | −25.5007 | −1.00022 | ||||||||
\(651\) | −1.48985 | + | 0.532645i | −0.0583919 | + | 0.0208760i | ||||
\(652\) | 11.3912i | 0.446115i | ||||||||
\(653\) | 26.0682 | 1.02013 | 0.510064 | − | 0.860136i | \(-0.329622\pi\) | ||||
0.510064 | + | 0.860136i | \(0.329622\pi\) | |||||||
\(654\) | 7.36497 | + | 20.6004i | 0.287993 | + | 0.805541i | ||||
\(655\) | 29.1883 | 1.14048 | ||||||||
\(656\) | 4.27903i | 0.167068i | ||||||||
\(657\) | −22.5830 | − | 27.5465i | −0.881048 | − | 1.07469i | ||||
\(658\) | 9.61445 | 0.374810 | ||||||||
\(659\) | 10.5545i | 0.411144i | 0.978642 | + | 0.205572i | \(0.0659055\pi\) | ||||
−0.978642 | + | 0.205572i | \(0.934094\pi\) | |||||||
\(660\) | −29.2186 | + | 10.4461i | −1.13733 | + | 0.406613i | ||||
\(661\) | −48.3094 | −1.87902 | −0.939509 | − | 0.342524i | \(-0.888718\pi\) | ||||
−0.939509 | + | 0.342524i | \(0.888718\pi\) | |||||||
\(662\) | − | 17.2576i | − | 0.670734i | ||||||
\(663\) | 8.55411 | − | 3.05822i | 0.332214 | − | 0.118772i | ||||
\(664\) | − | 20.2635i | − | 0.786375i | ||||||
\(665\) | −6.70266 | −0.259918 | ||||||||
\(666\) | −43.8889 | − | 53.5350i | −1.70066 | − | 2.07444i | ||||
\(667\) | 27.3173i | 1.05773i | ||||||||
\(668\) | − | 39.2955i | − | 1.52039i | ||||||
\(669\) | −6.77082 | + | 2.42067i | −0.261775 | + | 0.0935885i | ||||
\(670\) | 1.60975 | 0.0621900 | ||||||||
\(671\) | −20.1163 | −0.776583 | ||||||||
\(672\) | −7.98439 | + | 2.85454i | −0.308005 | + | 0.110116i | ||||
\(673\) | − | 20.1763i | − | 0.777740i | −0.921293 | − | 0.388870i | \(-0.872866\pi\) | ||
0.921293 | − | 0.388870i | \(-0.127134\pi\) | |||||||
\(674\) | 45.0269 | 1.73437 | ||||||||
\(675\) | −13.7859 | − | 8.27746i | −0.530621 | − | 0.318600i | ||||
\(676\) | 0.780505 | 0.0300194 | ||||||||
\(677\) | 34.1094 | 1.31093 | 0.655466 | − | 0.755225i | \(-0.272472\pi\) | ||||
0.655466 | + | 0.755225i | \(0.272472\pi\) | |||||||
\(678\) | −4.10784 | − | 11.4900i | −0.157761 | − | 0.441270i | ||||
\(679\) | − | 9.09369i | − | 0.348984i | ||||||
\(680\) | − | 5.06491i | − | 0.194230i | ||||||
\(681\) | −12.5151 | − | 35.0059i | −0.479581 | − | 1.34143i | ||||
\(682\) | − | 10.8612i | − | 0.415896i | ||||||
\(683\) | 13.5793i | 0.519599i | 0.965663 | + | 0.259800i | \(0.0836565\pi\) | ||||
−0.965663 | + | 0.259800i | \(0.916344\pi\) | |||||||
\(684\) | 36.4953 | + | 44.5164i | 1.39543 | + | 1.70213i | ||||
\(685\) | 16.4537 | 0.628662 | ||||||||
\(686\) | 23.9433i | 0.914160i | ||||||||
\(687\) | −9.23843 | − | 25.8407i | −0.352468 | − | 0.985884i | ||||
\(688\) | −2.49954 | + | 1.96500i | −0.0952941 | + | 0.0749148i | ||||
\(689\) | 18.2776i | 0.696321i | ||||||||
\(690\) | 30.2912 | − | 10.8296i | 1.15317 | − | 0.412274i | ||||
\(691\) | − | 43.0220i | − | 1.63663i | −0.574768 | − | 0.818317i | \(-0.694908\pi\) | ||
0.574768 | − | 0.818317i | \(-0.305092\pi\) | |||||||
\(692\) | 60.9193i | 2.31581i | ||||||||
\(693\) | 7.61976 | − | 6.24681i | 0.289451 | − | 0.237297i | ||||
\(694\) | −63.0478 | −2.39326 | ||||||||
\(695\) | 20.2705 | 0.768905 | ||||||||
\(696\) | 6.82470 | + | 19.0892i | 0.258689 | + | 0.723576i | ||||
\(697\) | 12.7162 | 0.481659 | ||||||||
\(698\) | − | 52.8364i | − | 1.99989i | ||||||
\(699\) | −3.52982 | − | 9.87320i | −0.133510 | − | 0.373439i | ||||
\(700\) | − | 7.64715i | − | 0.289035i | ||||||
\(701\) | 22.2615i | 0.840806i | 0.907338 | + | 0.420403i | \(0.138111\pi\) | ||||
−0.907338 | + | 0.420403i | \(0.861889\pi\) | |||||||
\(702\) | 36.7093 | + | 22.0413i | 1.38551 | + | 0.831896i | ||||
\(703\) | 62.5895 | 2.36061 | ||||||||
\(704\) | − | 54.1794i | − | 2.04196i | ||||||
\(705\) | 12.0908 | − | 4.32265i | 0.455367 | − | 0.162801i | ||||
\(706\) | 61.7634i | 2.32449i | ||||||||
\(707\) | 4.87682 | 0.183412 | ||||||||
\(708\) | 19.3871 | − | 6.93117i | 0.728611 | − | 0.260489i | ||||
\(709\) | −8.11021 | −0.304585 | −0.152293 | − | 0.988335i | \(-0.548666\pi\) | ||||
−0.152293 | + | 0.988335i | \(0.548666\pi\) | |||||||
\(710\) | −48.3113 | −1.81309 | ||||||||
\(711\) | −17.6547 | + | 14.4736i | −0.662103 | + | 0.542803i | ||||
\(712\) | 1.06903 | 0.0400636 | ||||||||
\(713\) | 6.86568i | 0.257122i | ||||||||
\(714\) | 1.50406 | + | 4.20699i | 0.0562882 | + | 0.157443i | ||||
\(715\) | − | 20.8683i | − | 0.780432i | ||||||
\(716\) | −11.4980 | −0.429700 | ||||||||
\(717\) | 16.4673 | − | 5.88733i | 0.614984 | − | 0.219866i | ||||
\(718\) | 1.41961i | 0.0529793i | ||||||||
\(719\) | − | 2.88177i | − | 0.107472i | −0.998555 | − | 0.0537359i | \(-0.982887\pi\) | ||
0.998555 | − | 0.0537359i | \(-0.0171129\pi\) | |||||||
\(720\) | −1.55275 | + | 1.27297i | −0.0578674 | + | 0.0474407i | ||||
\(721\) | − | 1.22209i | − | 0.0455131i | ||||||
\(722\) | −42.3433 | −1.57586 | ||||||||
\(723\) | −30.6694 | + | 10.9648i | −1.14061 | + | 0.407784i | ||||
\(724\) | 33.9835 | 1.26299 | ||||||||
\(725\) | 14.2234 | 0.528243 | ||||||||
\(726\) | 8.24977 | + | 23.0753i | 0.306178 | + | 0.856405i | ||||
\(727\) | 23.1180i | 0.857399i | 0.903447 | + | 0.428700i | \(0.141028\pi\) | ||||
−0.903447 | + | 0.428700i | \(0.858972\pi\) | |||||||
\(728\) | 7.33017i | 0.271674i | ||||||||
\(729\) | 12.6909 | + | 23.8315i | 0.470033 | + | 0.882649i | ||||
\(730\) | − | 37.1030i | − | 1.37325i | ||||||
\(731\) | 5.83946 | + | 7.42799i | 0.215980 | + | 0.274734i | ||||
\(732\) | 24.6850 | − | 8.82525i | 0.912383 | − | 0.326191i | ||||
\(733\) | − | 32.3583i | − | 1.19518i | −0.801801 | − | 0.597591i | \(-0.796125\pi\) | ||
0.801801 | − | 0.597591i | \(-0.203875\pi\) | |||||||
\(734\) | −36.8798 | −1.36126 | ||||||||
\(735\) | 5.13079 | + | 14.3513i | 0.189252 | + | 0.529354i | ||||
\(736\) | 36.7944i | 1.35626i | ||||||||
\(737\) | − | 2.13951i | − | 0.0788100i | ||||||
\(738\) | 37.9994 | + | 46.3510i | 1.39878 | + | 1.70621i | ||||
\(739\) | 7.67408i | 0.282295i | 0.989989 | + | 0.141148i | \(0.0450793\pi\) | ||||
−0.989989 | + | 0.141148i | \(0.954921\pi\) | |||||||
\(740\) | − | 43.9675i | − | 1.61628i | ||||||
\(741\) | −36.4537 | + | 13.0327i | −1.33916 | + | 0.478770i | ||||
\(742\) | −8.98910 | −0.330000 | ||||||||
\(743\) | 34.3439 | 1.25995 | 0.629977 | − | 0.776613i | \(-0.283064\pi\) | ||||
0.629977 | + | 0.776613i | \(0.283064\pi\) | |||||||
\(744\) | 1.71526 | + | 4.79771i | 0.0628843 | + | 0.175893i | ||||
\(745\) | −8.40207 | −0.307828 | ||||||||
\(746\) | − | 17.0603i | − | 0.624621i | ||||||
\(747\) | 15.1346 | + | 18.4609i | 0.553745 | + | 0.675450i | ||||
\(748\) | −18.7006 | −0.683761 | ||||||||
\(749\) | −13.0946 | −0.478466 | ||||||||
\(750\) | −14.7491 | − | 41.2545i | −0.538561 | − | 1.50640i | ||||
\(751\) | − | 36.1147i | − | 1.31785i | −0.752211 | − | 0.658923i | \(-0.771012\pi\) | ||
0.752211 | − | 0.658923i | \(-0.228988\pi\) | |||||||
\(752\) | 2.60400i | 0.0949581i | ||||||||
\(753\) | −13.7527 | + | 4.91680i | −0.501176 | + | 0.179178i | ||||
\(754\) | −37.8742 | −1.37930 | ||||||||
\(755\) | 19.2713i | 0.701356i | ||||||||
\(756\) | −6.60975 | + | 11.0084i | −0.240394 | + | 0.400371i | ||||
\(757\) | 46.4814i | 1.68940i | 0.535244 | + | 0.844698i | \(0.320220\pi\) | ||||
−0.535244 | + | 0.844698i | \(0.679780\pi\) | |||||||
\(758\) | −65.7505 | −2.38817 | ||||||||
\(759\) | −14.3936 | − | 40.2600i | −0.522453 | − | 1.46135i | ||||
\(760\) | 21.5843i | 0.782945i | ||||||||
\(761\) | −41.1600 | −1.49205 | −0.746025 | − | 0.665918i | \(-0.768040\pi\) | ||||
−0.746025 | + | 0.665918i | \(0.768040\pi\) | |||||||
\(762\) | −13.5892 | − | 38.0100i | −0.492283 | − | 1.37696i | ||||
\(763\) | − | 4.41217i | − | 0.159731i | ||||||
\(764\) | 13.3752 | 0.483899 | ||||||||
\(765\) | 3.78293 | + | 4.61436i | 0.136772 | + | 0.166833i | ||||
\(766\) | −20.3397 | −0.734903 | ||||||||
\(767\) | 13.8465i | 0.499969i | ||||||||
\(768\) | 7.42544 | + | 20.7696i | 0.267942 | + | 0.749458i | ||||
\(769\) | 14.3756 | 0.518396 | 0.259198 | − | 0.965824i | \(-0.416542\pi\) | ||||
0.259198 | + | 0.965824i | \(0.416542\pi\) | |||||||
\(770\) | 10.2633 | 0.369862 | ||||||||
\(771\) | 11.6947 | + | 32.7110i | 0.421173 | + | 1.17806i | ||||
\(772\) | −44.4802 | −1.60088 | ||||||||
\(773\) | −17.9885 | −0.647003 | −0.323501 | − | 0.946228i | \(-0.604860\pi\) | ||||
−0.323501 | + | 0.946228i | \(0.604860\pi\) | |||||||
\(774\) | −9.62549 | + | 43.4820i | −0.345981 | + | 1.56293i | ||||
\(775\) | 3.57477 | 0.128410 | ||||||||
\(776\) | −29.2840 | −1.05124 | ||||||||
\(777\) | 4.70003 | + | 13.1464i | 0.168613 | + | 0.471624i | ||||
\(778\) | 62.6041 | 2.24447 | ||||||||
\(779\) | −54.1905 | −1.94158 | ||||||||
\(780\) | 9.15516 | + | 25.6078i | 0.327807 | + | 0.916905i | ||||
\(781\) | 64.2105i | 2.29763i | ||||||||
\(782\) | 19.3871 | 0.693281 | ||||||||
\(783\) | −20.4752 | − | 12.2939i | −0.731723 | − | 0.439347i | ||||
\(784\) | −3.09083 | −0.110387 | ||||||||
\(785\) | − | 3.94029i | − | 0.140635i | ||||||
\(786\) | 27.9122 | + | 78.0729i | 0.995596 | + | 2.78477i | ||||
\(787\) | −2.57947 | −0.0919482 | −0.0459741 | − | 0.998943i | \(-0.514639\pi\) | ||||
−0.0459741 | + | 0.998943i | \(0.514639\pi\) | |||||||
\(788\) | − | 62.4039i | − | 2.22305i | ||||||
\(789\) | −5.68968 | − | 15.9145i | −0.202558 | − | 0.566571i | ||||
\(790\) | −23.7796 | −0.846040 | ||||||||
\(791\) | 2.46091i | 0.0874999i | ||||||||
\(792\) | −20.1163 | − | 24.5376i | −0.714803 | − | 0.871906i | ||||
\(793\) | 17.6304i | 0.626073i | ||||||||
\(794\) | −9.69782 | −0.344163 | ||||||||
\(795\) | −11.3044 | + | 4.04150i | −0.400926 | + | 0.143337i | ||||
\(796\) | − | 29.3063i | − | 1.03873i | ||||||
\(797\) | 47.7714i | 1.69215i | 0.533063 | + | 0.846076i | \(0.321041\pi\) | ||||
−0.533063 | + | 0.846076i | \(0.678959\pi\) | |||||||
\(798\) | −6.40963 | − | 17.9283i | −0.226898 | − | 0.634654i | ||||
\(799\) | 7.73841 | 0.273765 | ||||||||
\(800\) | 19.1579 | 0.677333 | ||||||||
\(801\) | −0.973935 | + | 0.798448i | −0.0344123 | + | 0.0282118i | ||||
\(802\) | − | 29.6658i | − | 1.04753i | ||||||
\(803\) | −49.3136 | −1.74024 | ||||||||
\(804\) | 0.938628 | + | 2.62542i | 0.0331029 | + | 0.0925915i | ||||
\(805\) | −6.48773 | −0.228662 | ||||||||
\(806\) | −9.51895 | −0.335291 | ||||||||
\(807\) | 16.6724 | − | 5.96065i | 0.586897 | − | 0.209825i | ||||
\(808\) | − | 15.7046i | − | 0.552487i | ||||||
\(809\) | 22.4918i | 0.790771i | 0.918515 | + | 0.395386i | \(0.129389\pi\) | ||||
−0.918515 | + | 0.395386i | \(0.870611\pi\) | |||||||
\(810\) | −5.51514 | + | 27.5779i | −0.193782 | + | 0.968989i | ||||
\(811\) | 20.5481i | 0.721542i | 0.932654 | + | 0.360771i | \(0.117486\pi\) | ||||
−0.932654 | + | 0.360771i | \(0.882514\pi\) | |||||||
\(812\) | − | 11.3577i | − | 0.398577i | ||||||
\(813\) | 1.01145 | + | 2.82910i | 0.0354730 | + | 0.0992210i | ||||
\(814\) | −95.8383 | −3.35913 | ||||||||
\(815\) | − | 5.03186i | − | 0.176258i | ||||||
\(816\) | −1.13943 | + | 0.407364i | −0.0398881 | + | 0.0142606i | ||||
\(817\) | −24.8851 | − | 31.6547i | −0.870619 | − | 1.10746i | ||||
\(818\) | 2.06797i | 0.0723049i | ||||||||
\(819\) | −5.47483 | − | 6.67811i | −0.191306 | − | 0.233352i | ||||
\(820\) | 38.0674i | 1.32937i | ||||||||
\(821\) | − | 29.4659i | − | 1.02837i | −0.857680 | − | 0.514184i | \(-0.828095\pi\) | ||
0.857680 | − | 0.514184i | \(-0.171905\pi\) | |||||||
\(822\) | 15.7343 | + | 44.0103i | 0.548798 | + | 1.53503i | ||||
\(823\) | −17.9239 | −0.624786 | −0.312393 | − | 0.949953i | \(-0.601131\pi\) | ||||
−0.312393 | + | 0.949953i | \(0.601131\pi\) | |||||||
\(824\) | −3.93546 | −0.137098 | ||||||||
\(825\) | −20.9623 | + | 7.49434i | −0.729813 | + | 0.260919i | ||||
\(826\) | −6.80986 | −0.236945 | ||||||||
\(827\) | − | 16.0839i | − | 0.559291i | −0.960103 | − | 0.279646i | \(-0.909783\pi\) | ||
0.960103 | − | 0.279646i | \(-0.0902170\pi\) | |||||||
\(828\) | 35.3250 | + | 43.0889i | 1.22763 | + | 1.49744i | ||||
\(829\) | − | 46.9875i | − | 1.63194i | −0.578091 | − | 0.815972i | \(-0.696202\pi\) | ||
0.578091 | − | 0.815972i | \(-0.303798\pi\) | |||||||
\(830\) | 24.8655i | 0.863094i | ||||||||
\(831\) | 43.2245 | − | 15.4534i | 1.49944 | − | 0.536073i | ||||
\(832\) | −47.4839 | −1.64621 | ||||||||
\(833\) | 9.18514i | 0.318246i | ||||||||
\(834\) | 19.3843 | + | 54.2197i | 0.671225 | + | 1.87747i | ||||
\(835\) | 17.3580i | 0.600700i | ||||||||
\(836\) | 79.6932 | 2.75625 | ||||||||
\(837\) | −5.14604 | − | 3.08983i | −0.177873 | − | 0.106800i | ||||
\(838\) | 44.4490 | 1.53546 | ||||||||
\(839\) | 10.4024 | 0.359131 | 0.179566 | − | 0.983746i | \(-0.442531\pi\) | ||||
0.179566 | + | 0.983746i | \(0.442531\pi\) | |||||||
\(840\) | −4.53360 | + | 1.62083i | −0.156424 | + | 0.0559240i | ||||
\(841\) | −7.87511 | −0.271556 | ||||||||
\(842\) | − | 4.27903i | − | 0.147465i | ||||||
\(843\) | 7.82484 | − | 2.79750i | 0.269502 | − | 0.0963510i | ||||
\(844\) | 25.7118i | 0.885037i | ||||||||
\(845\) | −0.344773 | −0.0118606 | ||||||||
\(846\) | 23.1245 | + | 28.2069i | 0.795036 | + | 0.969772i | ||||
\(847\) | − | 4.94224i | − | 0.169817i | ||||||
\(848\) | − | 2.43463i | − | 0.0836055i | ||||||
\(849\) | 7.06990 | + | 19.7751i | 0.242638 | + | 0.678680i | ||||
\(850\) | − | 10.0943i | − | 0.346232i | ||||||
\(851\) | 60.5824 | 2.07674 | ||||||||
\(852\) | −28.1698 | − | 78.7934i | −0.965083 | − | 2.69942i | ||||
\(853\) | −0.280047 | −0.00958862 | −0.00479431 | − | 0.999989i | \(-0.501526\pi\) | ||||
−0.00479431 | + | 0.999989i | \(0.501526\pi\) | |||||||
\(854\) | −8.67079 | −0.296708 | ||||||||
\(855\) | −16.1211 | − | 19.6643i | −0.551330 | − | 0.672504i | ||||
\(856\) | 42.1680i | 1.44127i | ||||||||
\(857\) | 2.54303i | 0.0868683i | 0.999056 | + | 0.0434341i | \(0.0138299\pi\) | ||||
−0.999056 | + | 0.0434341i | \(0.986170\pi\) | |||||||
\(858\) | 55.8186 | − | 19.9560i | 1.90562 | − | 0.681287i | ||||
\(859\) | − | 2.47112i | − | 0.0843135i | −0.999111 | − | 0.0421567i | \(-0.986577\pi\) | ||
0.999111 | − | 0.0421567i | \(-0.0134229\pi\) | |||||||
\(860\) | −22.2366 | + | 17.4811i | −0.758262 | + | 0.596102i | ||||
\(861\) | −4.06932 | − | 11.3822i | −0.138682 | − | 0.387906i | ||||
\(862\) | − | 86.9690i | − | 2.96218i | ||||||
\(863\) | 33.7475 | 1.14878 | 0.574390 | − | 0.818582i | \(-0.305239\pi\) | ||||
0.574390 | + | 0.818582i | \(0.305239\pi\) | |||||||
\(864\) | −27.5786 | − | 16.5589i | −0.938241 | − | 0.563346i | ||||
\(865\) | − | 26.9100i | − | 0.914966i | ||||||
\(866\) | − | 53.9821i | − | 1.83439i | ||||||
\(867\) | −8.70195 | − | 24.3401i | −0.295534 | − | 0.826633i | ||||
\(868\) | − | 2.85454i | − | 0.0968894i | ||||||
\(869\) | 31.6054i | 1.07214i | ||||||||
\(870\) | −8.37466 | − | 23.4246i | −0.283927 | − | 0.794169i | ||||
\(871\) | −1.87511 | −0.0635358 | ||||||||
\(872\) | −14.2083 | −0.481155 | ||||||||
\(873\) | 26.6791 | − | 21.8720i | 0.902950 | − | 0.740253i | ||||
\(874\) | −82.6188 | −2.79462 | ||||||||
\(875\) | 8.83583i | 0.298706i | ||||||||
\(876\) | 60.5133 | − | 21.6344i | 2.04456 | − | 0.730959i | ||||
\(877\) | 16.1661 | 0.545889 | 0.272945 | − | 0.962030i | \(-0.412002\pi\) | ||||
0.272945 | + | 0.962030i | \(0.412002\pi\) | |||||||
\(878\) | −3.88303 | −0.131046 | ||||||||
\(879\) | 29.1518 | − | 10.4222i | 0.983265 | − | 0.351532i | ||||
\(880\) | 2.77972i | 0.0937045i | ||||||||
\(881\) | − | 16.8803i | − | 0.568713i | −0.958719 | − | 0.284356i | \(-0.908220\pi\) | ||
0.958719 | − | 0.284356i | \(-0.0917799\pi\) | |||||||
\(882\) | −33.4803 | + | 27.4477i | −1.12734 | + | 0.924212i | ||||
\(883\) | 44.9229 | 1.51178 | 0.755889 | − | 0.654700i | \(-0.227205\pi\) | ||||
0.755889 | + | 0.654700i | \(0.227205\pi\) | |||||||
\(884\) | 16.3896i | 0.551241i | ||||||||
\(885\) | −8.56387 | + | 3.06171i | −0.287872 | + | 0.102918i | ||||
\(886\) | − | 69.5841i | − | 2.33772i | ||||||
\(887\) | −11.3609 | −0.381462 | −0.190731 | − | 0.981642i | \(-0.561086\pi\) | ||||
−0.190731 | + | 0.981642i | \(0.561086\pi\) | |||||||
\(888\) | 42.3348 | − | 15.1353i | 1.42066 | − | 0.507908i | ||||
\(889\) | 8.14093i | 0.273038i | ||||||||
\(890\) | −1.31182 | −0.0439723 | ||||||||
\(891\) | 36.6538 | + | 7.33017i | 1.22795 | + | 0.245570i | ||||
\(892\) | − | 12.9728i | − | 0.434362i | ||||||
\(893\) | −32.9776 | −1.10355 | ||||||||
\(894\) | −8.03474 | − | 22.4739i | −0.268722 | − | 0.751638i | ||||
\(895\) | 5.07901 | 0.169773 | ||||||||
\(896\) | − | 13.5620i | − | 0.453075i | ||||||
\(897\) | −35.2847 | + | 12.6148i | −1.17812 | + | 0.421197i | ||||
\(898\) | −78.7740 | −2.62872 | ||||||||
\(899\) | 5.30933 | 0.177076 | ||||||||
\(900\) | 22.4352 | − | 18.3928i | 0.747840 | − | 0.613092i | ||||
\(901\) | −7.23509 | −0.241036 | ||||||||
\(902\) | 82.9776 | 2.76285 | ||||||||
\(903\) | 4.78010 | − | 7.60395i | 0.159072 | − | 0.253043i | ||||
\(904\) | 7.92477 | 0.263574 | ||||||||
\(905\) | −15.0116 | −0.499001 | ||||||||
\(906\) | −51.5470 | + | 18.4288i | −1.71253 | + | 0.612257i | ||||
\(907\) | 38.7825 | 1.28775 | 0.643875 | − | 0.765131i | \(-0.277326\pi\) | ||||
0.643875 | + | 0.765131i | \(0.277326\pi\) | |||||||
\(908\) | 67.0709 | 2.22583 | ||||||||
\(909\) | 11.7296 | + | 14.3076i | 0.389048 | + | 0.474554i | ||||
\(910\) | − | 8.99493i | − | 0.298179i | ||||||
\(911\) | −23.7070 | −0.785449 | −0.392724 | − | 0.919656i | \(-0.628467\pi\) | ||||
−0.392724 | + | 0.919656i | \(0.628467\pi\) | |||||||
\(912\) | 4.85574 | − | 1.73600i | 0.160790 | − | 0.0574847i | ||||
\(913\) | 33.0487 | 1.09375 | ||||||||
\(914\) | − | 9.81900i | − | 0.324784i | ||||||
\(915\) | −10.9041 | + | 3.89839i | −0.360479 | + | 0.128877i | ||||
\(916\) | 49.5104 | 1.63587 | ||||||||
\(917\) | − | 16.7215i | − | 0.552194i | ||||||
\(918\) | −8.72494 | + | 14.5312i | −0.287966 | + | 0.479601i | ||||
\(919\) | 48.6950 | 1.60630 | 0.803149 | − | 0.595778i | \(-0.203156\pi\) | ||||
0.803149 | + | 0.595778i | \(0.203156\pi\) | |||||||
\(920\) | 20.8922i | 0.688794i | ||||||||
\(921\) | 7.10521 | + | 19.8739i | 0.234125 | + | 0.654866i | ||||
\(922\) | − | 36.2883i | − | 1.19509i | ||||||
\(923\) | 56.2754 | 1.85233 | ||||||||
\(924\) | 5.98440 | + | 16.7389i | 0.196872 | + | 0.550669i | ||||
\(925\) | − | 31.5436i | − | 1.03715i | ||||||
\(926\) | 20.5865i | 0.676514i | ||||||||
\(927\) | 3.58538 | − | 2.93935i | 0.117759 | − | 0.0965411i | ||||
\(928\) | 28.4537 | 0.934037 | ||||||||
\(929\) | 2.58626 | 0.0848523 | 0.0424262 | − | 0.999100i | \(-0.486491\pi\) | ||||
0.0424262 | + | 0.999100i | \(0.486491\pi\) | |||||||
\(930\) | −2.10481 | − | 5.88733i | −0.0690194 | − | 0.193053i | ||||
\(931\) | − | 39.1429i | − | 1.28286i | ||||||
\(932\) | 18.9169 | 0.619645 | ||||||||
\(933\) | 6.77381 | − | 2.42174i | 0.221765 | − | 0.0792842i | ||||
\(934\) | 18.8486 | 0.616746 | ||||||||
\(935\) | 8.26062 | 0.270151 | ||||||||
\(936\) | −21.5053 | + | 17.6304i | −0.702921 | + | 0.576267i | ||||
\(937\) | 46.6280i | 1.52327i | 0.648005 | + | 0.761636i | \(0.275603\pi\) | ||||
−0.648005 | + | 0.761636i | \(0.724397\pi\) | |||||||
\(938\) | − | 0.922200i | − | 0.0301109i | ||||||
\(939\) | −9.15017 | + | 3.27132i | −0.298605 | + | 0.106756i | ||||
\(940\) | 23.1659i | 0.755588i | ||||||||
\(941\) | − | 38.0240i | − | 1.23955i | −0.784781 | − | 0.619773i | \(-0.787225\pi\) | ||
0.784781 | − | 0.619773i | \(-0.212775\pi\) | |||||||
\(942\) | 10.5395 | − | 3.76803i | 0.343395 | − | 0.122769i | ||||
\(943\) | −52.4528 | −1.70810 | ||||||||
\(944\) | − | 1.84440i | − | 0.0600301i | ||||||
\(945\) | 2.91973 | − | 4.86275i | 0.0949788 | − | 0.158185i | ||||
\(946\) | 38.1046 | + | 48.4703i | 1.23889 | + | 1.57591i | ||||
\(947\) | − | 40.7364i | − | 1.32375i | −0.749612 | − | 0.661877i | \(-0.769760\pi\) | ||
0.749612 | − | 0.661877i | \(-0.230240\pi\) | |||||||
\(948\) | −13.8656 | − | 38.7834i | −0.450335 | − | 1.25963i | ||||
\(949\) | 43.2195i | 1.40296i | ||||||||
\(950\) | 43.0174i | 1.39567i | ||||||||
\(951\) | 33.7806 | − | 12.0771i | 1.09541 | − | 0.391627i | ||||
\(952\) | −2.90161 | −0.0940417 | ||||||||
\(953\) | 33.7229 | 1.09239 | 0.546196 | − | 0.837658i | \(-0.316076\pi\) | ||||
0.546196 | + | 0.837658i | \(0.316076\pi\) | |||||||
\(954\) | −21.6204 | − | 26.3722i | −0.699987 | − | 0.853833i | ||||
\(955\) | −5.90826 | −0.191187 | ||||||||
\(956\) | 31.5512i | 1.02044i | ||||||||
\(957\) | −31.1337 | + | 11.1308i | −1.00641 | + | 0.359806i | ||||
\(958\) | 88.8113i | 2.86936i | ||||||||
\(959\) | − | 9.42606i | − | 0.304383i | ||||||
\(960\) | −10.4995 | − | 29.3681i | −0.338871 | − | 0.947852i | ||||
\(961\) | −29.6656 | −0.956955 | ||||||||
\(962\) | 83.9947i | 2.70810i | ||||||||
\(963\) | −31.4948 | − | 38.4169i | −1.01491 | − | 1.23797i | ||||
\(964\) | − | 58.7622i | − | 1.89260i | ||||||
\(965\) | 19.6483 | 0.632500 | ||||||||
\(966\) | −6.20409 | − | 17.3534i | −0.199613 | − | 0.558336i | ||||
\(967\) | −20.3241 | −0.653579 | −0.326789 | − | 0.945097i | \(-0.605967\pi\) | ||||
−0.326789 | + | 0.945097i | \(0.605967\pi\) | |||||||
\(968\) | −15.9153 | −0.511537 | ||||||||
\(969\) | −5.15894 | − | 14.4300i | −0.165729 | − | 0.463558i | ||||
\(970\) | 35.9348 | 1.15380 | ||||||||
\(971\) | 14.4736i | 0.464481i | 0.972658 | + | 0.232240i | \(0.0746056\pi\) | ||||
−0.972658 | + | 0.232240i | \(0.925394\pi\) | |||||||
\(972\) | −48.1941 | + | 7.08548i | −1.54583 | + | 0.227267i | ||||
\(973\) | − | 11.6127i | − | 0.372286i | ||||||
\(974\) | −43.2353 | −1.38535 | ||||||||
\(975\) | 6.56819 | + | 18.3718i | 0.210350 | + | 0.588368i | ||||
\(976\) | − | 2.34842i | − | 0.0751710i | ||||||
\(977\) | 10.2661i | 0.328443i | 0.986424 | + | 0.164221i | \(0.0525112\pi\) | ||||
−0.986424 | + | 0.164221i | \(0.947489\pi\) | |||||||
\(978\) | 13.4592 | − | 4.81187i | 0.430378 | − | 0.153867i | ||||
\(979\) | 1.74354i | 0.0557237i | ||||||||
\(980\) | −27.4968 | −0.878355 | ||||||||
\(981\) | 12.9444 | − | 10.6121i | 0.413284 | − | 0.338817i | ||||
\(982\) | −10.1698 | −0.324533 | ||||||||
\(983\) | −1.68775 | −0.0538309 | −0.0269154 | − | 0.999638i | \(-0.508568\pi\) | ||||
−0.0269154 | + | 0.999638i | \(0.508568\pi\) | |||||||
\(984\) | −36.6538 | + | 13.1043i | −1.16848 | + | 0.417749i | ||||
\(985\) | 27.5657i | 0.878317i | ||||||||
\(986\) | − | 14.9923i | − | 0.477452i | ||||||
\(987\) | −2.47638 | − | 6.92665i | −0.0788241 | − | 0.220478i | ||||
\(988\) | − | 69.8448i | − | 2.22206i | ||||||
\(989\) | −24.0871 | − | 30.6396i | −0.765925 | − | 0.974283i | ||||
\(990\) | 24.6850 | + | 30.1104i | 0.784540 | + | 0.956970i | ||||
\(991\) | 45.2324i | 1.43685i | 0.695603 | + | 0.718427i | \(0.255137\pi\) | ||||
−0.695603 | + | 0.718427i | \(0.744863\pi\) | |||||||
\(992\) | 7.15128 | 0.227053 | ||||||||
\(993\) | −12.4331 | + | 4.44501i | −0.394552 | + | 0.141058i | ||||
\(994\) | 27.6768i | 0.877855i | ||||||||
\(995\) | 12.9455i | 0.410400i | ||||||||
\(996\) | −40.5545 | + | 14.4988i | −1.28502 | + | 0.459413i | ||||
\(997\) | 19.1641i | 0.606932i | 0.952842 | + | 0.303466i | \(0.0981439\pi\) | ||||
−0.952842 | + | 0.303466i | \(0.901856\pi\) | |||||||
\(998\) | 94.5386i | 2.99257i | ||||||||
\(999\) | −27.2645 | + | 45.4084i | −0.862609 | + | 1.43666i |
(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 | 129.2.d.a.128.11 | yes | 12 | |
3.2 | odd | 2 | inner | 129.2.d.a.128.1 | ✓ | 12 | |
4.3 | odd | 2 | 2064.2.l.h.257.8 | 12 | |||
12.11 | even | 2 | 2064.2.l.h.257.6 | 12 | |||
43.42 | odd | 2 | inner | 129.2.d.a.128.2 | yes | 12 | |
129.128 | even | 2 | inner | 129.2.d.a.128.12 | yes | 12 | |
172.171 | even | 2 | 2064.2.l.h.257.5 | 12 | |||
516.515 | odd | 2 | 2064.2.l.h.257.7 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
129.2.d.a.128.1 | ✓ | 12 | 3.2 | odd | 2 | inner | |
129.2.d.a.128.2 | yes | 12 | 43.42 | odd | 2 | inner | |
129.2.d.a.128.11 | yes | 12 | 1.1 | even | 1 | trivial | |
129.2.d.a.128.12 | yes | 12 | 129.128 | even | 2 | inner | |
2064.2.l.h.257.5 | 12 | 172.171 | even | 2 | |||
2064.2.l.h.257.6 | 12 | 12.11 | even | 2 | |||
2064.2.l.h.257.7 | 12 | 516.515 | odd | 2 | |||
2064.2.l.h.257.8 | 12 | 4.3 | odd | 2 |