Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(37,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.cj (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 4x^{14} + 6x^{12} + 8x^{10} + 20x^{8} + 32x^{6} + 96x^{4} + 256x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 37.2 | ||
Root | \(-1.01214 - 0.987711i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.37 |
Dual form | 504.2.cj.d.109.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.01214 | + | 0.987711i | −0.715691 | + | 0.698417i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.0488544 | − | 1.99940i | 0.0244272 | − | 0.999702i | ||||
\(5\) | 2.26303 | + | 1.30656i | 1.01206 | + | 0.584313i | 0.911794 | − | 0.410648i | \(-0.134697\pi\) |
0.100265 | + | 0.994961i | \(0.468031\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.62132 | + | 0.358719i | 0.990766 | + | 0.135583i | ||||
\(8\) | 1.92538 | + | 2.07193i | 0.680726 | + | 0.732538i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.58101 | + | 0.912798i | −1.13242 | + | 0.288652i | ||||
\(11\) | 1.87476 | − | 1.08239i | 0.565261 | − | 0.326354i | −0.189993 | − | 0.981785i | \(-0.560847\pi\) |
0.755254 | + | 0.655432i | \(0.227513\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.50490i | − | 1.80413i | −0.431596 | − | 0.902067i | \(-0.642049\pi\) | ||
0.431596 | − | 0.902067i | \(-0.357951\pi\) | |||||||
\(14\) | −3.00745 | + | 2.22603i | −0.803776 | + | 0.594932i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.99523 | − | 0.195359i | −0.998807 | − | 0.0488398i | ||||
\(17\) | 0.797521 | + | 1.38135i | 0.193427 | + | 0.335026i | 0.946384 | − | 0.323045i | \(-0.104706\pi\) |
−0.752957 | + | 0.658070i | \(0.771373\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.27620 | − | 0.736813i | −0.292780 | − | 0.169036i | 0.346415 | − | 0.938081i | \(-0.387399\pi\) |
−0.639195 | + | 0.769045i | \(0.720732\pi\) | |||||||
\(20\) | 2.72291 | − | 4.46088i | 0.608860 | − | 0.997484i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.828427 | + | 2.94725i | −0.176621 | + | 0.628356i | ||||
\(23\) | −1.92538 | + | 3.33486i | −0.401470 | + | 0.695367i | −0.993904 | − | 0.110252i | \(-0.964834\pi\) |
0.592433 | + | 0.805620i | \(0.298167\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.914214 | + | 1.58346i | 0.182843 | + | 0.316693i | ||||
\(26\) | 6.42496 | + | 6.58387i | 1.26004 | + | 1.29120i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.845288 | − | 5.22355i | 0.159744 | − | 0.987158i | ||||
\(29\) | − | 7.39104i | − | 1.37248i | −0.727375 | − | 0.686240i | \(-0.759260\pi\) | ||
0.727375 | − | 0.686240i | \(-0.240740\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.79289 | + | 3.10538i | 0.322013 | + | 0.557743i | 0.980903 | − | 0.194496i | \(-0.0623071\pi\) |
−0.658890 | + | 0.752239i | \(0.728974\pi\) | |||||||
\(32\) | 4.23669 | − | 3.74840i | 0.748947 | − | 0.662629i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.17157 | − | 0.610396i | −0.372422 | − | 0.104682i | ||||
\(35\) | 5.46345 | + | 4.23671i | 0.923491 | + | 0.716135i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.69064 | + | 3.86285i | 1.09994 | + | 0.635048i | 0.936204 | − | 0.351457i | \(-0.114314\pi\) |
0.163731 | + | 0.986505i | \(0.447647\pi\) | |||||||
\(38\) | 2.01945 | − | 0.514756i | 0.327598 | − | 0.0835045i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.65010 | + | 7.20448i | 0.260904 | + | 1.13913i | ||||
\(41\) | 7.70154 | 1.20278 | 0.601389 | − | 0.798956i | \(-0.294614\pi\) | ||||
0.601389 | + | 0.798956i | \(0.294614\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.69442i | 0.410895i | 0.978668 | + | 0.205447i | \(0.0658649\pi\) | ||||
−0.978668 | + | 0.205447i | \(0.934135\pi\) | |||||||
\(44\) | −2.07255 | − | 3.80128i | −0.312448 | − | 0.573064i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.34512 | − | 5.27707i | −0.198328 | − | 0.778062i | ||||
\(47\) | −5.77615 | + | 10.0046i | −0.842539 | + | 1.45932i | 0.0452029 | + | 0.998978i | \(0.485607\pi\) |
−0.887742 | + | 0.460342i | \(0.847727\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.74264 | + | 1.88064i | 0.963234 | + | 0.268662i | ||||
\(50\) | −2.48932 | − | 0.699709i | −0.352043 | − | 0.0989538i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −13.0059 | − | 0.317793i | −1.80360 | − | 0.0440700i | ||||
\(53\) | −8.66386 | + | 5.00208i | −1.19007 | + | 0.687089i | −0.958323 | − | 0.285687i | \(-0.907778\pi\) |
−0.231749 | + | 0.972776i | \(0.574445\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.65685 | 0.762770 | ||||||||
\(56\) | 4.30381 | + | 6.12186i | 0.575121 | + | 0.818069i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.30021 | + | 7.48076i | 0.958564 | + | 0.982272i | ||||
\(59\) | −8.11475 | + | 4.68506i | −1.05645 | + | 0.609942i | −0.924448 | − | 0.381307i | \(-0.875474\pi\) |
−0.132003 | + | 0.991249i | \(0.542141\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.60963 | − | 2.08402i | −0.462166 | − | 0.266832i | 0.250789 | − | 0.968042i | \(-0.419310\pi\) |
−0.712955 | + | 0.701210i | \(0.752643\pi\) | |||||||
\(62\) | −4.88188 | − | 1.37222i | −0.619999 | − | 0.174272i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.585786 | + | 7.97852i | −0.0732233 | + | 0.997316i | ||||
\(65\) | 8.49906 | − | 14.7208i | 1.05418 | − | 1.82589i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.99062 | − | 5.76809i | 1.22055 | − | 0.704684i | 0.255513 | − | 0.966806i | \(-0.417756\pi\) |
0.965035 | + | 0.262122i | \(0.0844222\pi\) | |||||||
\(68\) | 2.80083 | − | 1.52708i | 0.339651 | − | 0.185186i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −9.71442 | + | 1.10816i | −1.16110 | + | 0.132450i | ||||
\(71\) | −14.7424 | −1.74960 | −0.874800 | − | 0.484484i | \(-0.839007\pi\) | ||||
−0.874800 | + | 0.484484i | \(0.839007\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.50000 | + | 2.59808i | 0.175562 | + | 0.304082i | 0.940356 | − | 0.340193i | \(-0.110493\pi\) |
−0.764794 | + | 0.644275i | \(0.777159\pi\) | |||||||
\(74\) | −10.5872 | + | 2.69868i | −1.23074 | + | 0.313715i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.53553 | + | 2.51564i | −0.176138 | + | 0.288563i | ||||
\(77\) | 5.30262 | − | 2.16478i | 0.604289 | − | 0.246700i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.62132 | + | 6.27231i | −0.407430 | + | 0.705690i | −0.994601 | − | 0.103773i | \(-0.966908\pi\) |
0.587171 | + | 0.809463i | \(0.300242\pi\) | |||||||
\(80\) | −8.78608 | − | 5.66212i | −0.982314 | − | 0.633044i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.79504 | + | 7.60689i | −0.860818 | + | 0.840041i | ||||
\(83\) | − | 7.20533i | − | 0.790887i | −0.918490 | − | 0.395444i | \(-0.870591\pi\) | ||
0.918490 | − | 0.395444i | \(-0.129409\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.16804i | 0.452088i | ||||||||
\(86\) | −2.66131 | − | 2.72713i | −0.286976 | − | 0.294074i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.85227 | + | 1.80035i | 0.623854 | + | 0.191918i | ||||
\(89\) | 3.85077 | − | 6.66973i | 0.408181 | − | 0.706990i | −0.586505 | − | 0.809945i | \(-0.699497\pi\) |
0.994686 | + | 0.102956i | \(0.0328300\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.33343 | − | 17.0514i | 0.244610 | − | 1.78747i | ||||
\(92\) | 6.57368 | + | 4.01254i | 0.685353 | + | 0.418337i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.03537 | − | 15.8312i | −0.416217 | − | 1.63287i | ||||
\(95\) | −1.92538 | − | 3.33486i | −0.197540 | − | 0.342150i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.828427 | 0.0841140 | 0.0420570 | − | 0.999115i | \(-0.486609\pi\) | ||||
0.0420570 | + | 0.999115i | \(0.486609\pi\) | |||||||
\(98\) | −8.68202 | + | 4.75631i | −0.877017 | + | 0.480460i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.21065 | − | 1.75052i | 0.321065 | − | 0.175052i | ||||
\(101\) | −3.74952 | + | 2.16478i | −0.373091 | + | 0.215404i | −0.674808 | − | 0.737993i | \(-0.735774\pi\) |
0.301717 | + | 0.953398i | \(0.402440\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.20711 | − | 9.01897i | 0.513071 | − | 0.888666i | −0.486814 | − | 0.873506i | \(-0.661841\pi\) |
0.999885 | − | 0.0151600i | \(-0.00482576\pi\) | |||||||
\(104\) | 13.4777 | − | 12.5244i | 1.32160 | − | 1.22812i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.82843 | − | 13.6202i | 0.371850 | − | 1.32291i | ||||
\(107\) | 2.81214 | + | 1.62359i | 0.271860 | + | 0.156958i | 0.629732 | − | 0.776812i | \(-0.283165\pi\) |
−0.357873 | + | 0.933770i | \(0.616498\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.24304 | + | 5.33647i | −0.885323 | + | 0.511141i | −0.872410 | − | 0.488775i | \(-0.837444\pi\) |
−0.0129129 | + | 0.999917i | \(0.504110\pi\) | |||||||
\(110\) | −5.72553 | + | 5.58734i | −0.545908 | + | 0.532732i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −10.4027 | − | 1.94526i | −0.982962 | − | 0.183810i | ||||
\(113\) | 9.29658 | 0.874549 | 0.437274 | − | 0.899328i | \(-0.355944\pi\) | ||||
0.437274 | + | 0.899328i | \(0.355944\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.71442 | + | 5.03127i | −0.812624 | + | 0.469169i | ||||
\(116\) | −14.7777 | − | 0.361085i | −1.37207 | − | 0.0335259i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.58579 | − | 12.7570i | 0.330098 | − | 1.17437i | ||||
\(119\) | 1.59504 | + | 3.90704i | 0.146217 | + | 0.358157i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.15685 | + | 5.46783i | −0.286987 | + | 0.497076i | ||||
\(122\) | 5.71186 | − | 1.45595i | 0.517128 | − | 0.131816i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.29650 | − | 3.43300i | 0.565443 | − | 0.308293i | ||||
\(125\) | − | 8.28772i | − | 0.741276i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.0711 | −0.893663 | −0.446831 | − | 0.894618i | \(-0.647448\pi\) | ||||
−0.446831 | + | 0.894618i | \(0.647448\pi\) | |||||||
\(128\) | −7.28758 | − | 8.65397i | −0.644137 | − | 0.764910i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.93766 | + | 23.2941i | 0.520767 | + | 2.04303i | ||||
\(131\) | 4.52607 | + | 2.61313i | 0.395444 | + | 0.228310i | 0.684516 | − | 0.728997i | \(-0.260013\pi\) |
−0.289072 | + | 0.957307i | \(0.593347\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.08101 | − | 2.38922i | −0.267158 | − | 0.207172i | ||||
\(134\) | −4.41470 | + | 15.7060i | −0.381372 | + | 1.35679i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.32652 | + | 4.31203i | −0.113748 | + | 0.369753i | ||||
\(137\) | −7.70154 | − | 13.3395i | −0.657987 | − | 1.13967i | −0.981136 | − | 0.193319i | \(-0.938075\pi\) |
0.323149 | − | 0.946348i | \(-0.395258\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.7042i | 1.33201i | 0.745945 | + | 0.666007i | \(0.231998\pi\) | ||||
−0.745945 | + | 0.666007i | \(0.768002\pi\) | |||||||
\(140\) | 8.73781 | − | 10.7166i | 0.738480 | − | 0.905722i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 14.9214 | − | 14.5612i | 1.25217 | − | 1.22195i | ||||
\(143\) | −7.04085 | − | 12.1951i | −0.588786 | − | 1.01981i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.65685 | − | 16.7262i | 0.801958 | − | 1.38903i | ||||
\(146\) | −4.08436 | − | 1.14805i | −0.338024 | − | 0.0950133i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.05025 | − | 13.1886i | 0.661727 | − | 1.08409i | ||||
\(149\) | −9.05213 | − | 5.22625i | −0.741580 | − | 0.428151i | 0.0810637 | − | 0.996709i | \(-0.474168\pi\) |
−0.822643 | + | 0.568558i | \(0.807502\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.41421 | − | 7.64564i | −0.359224 | − | 0.622194i | 0.628608 | − | 0.777723i | \(-0.283625\pi\) |
−0.987831 | + | 0.155529i | \(0.950292\pi\) | |||||||
\(152\) | −0.930546 | − | 4.06284i | −0.0754773 | − | 0.329540i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.22881 | + | 7.42852i | −0.260185 | + | 0.598607i | ||||
\(155\) | 9.37011i | 0.752625i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.21926 | − | 4.16804i | 0.576160 | − | 0.332646i | −0.183446 | − | 0.983030i | \(-0.558725\pi\) |
0.759606 | + | 0.650384i | \(0.225392\pi\) | |||||||
\(158\) | −2.52995 | − | 9.92527i | −0.201272 | − | 0.789612i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 14.4853 | − | 2.94725i | 1.14516 | − | 0.233001i | ||||
\(161\) | −6.24333 | + | 8.05107i | −0.492043 | + | 0.634514i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.71442 | − | 5.03127i | −0.682566 | − | 0.394080i | 0.118255 | − | 0.992983i | \(-0.462270\pi\) |
−0.800821 | + | 0.598904i | \(0.795603\pi\) | |||||||
\(164\) | 0.376254 | − | 15.3985i | 0.0293805 | − | 1.20242i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.11678 | + | 7.29280i | 0.552369 | + | 0.566031i | ||||
\(167\) | 14.7424 | 1.14080 | 0.570400 | − | 0.821367i | \(-0.306788\pi\) | ||||
0.570400 | + | 0.821367i | \(0.306788\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −29.3137 | −2.25490 | ||||||||
\(170\) | −4.11682 | − | 4.21864i | −0.315746 | − | 0.323555i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.38723 | + | 0.131634i | 0.410772 | + | 0.0100370i | ||||
\(173\) | −5.23600 | − | 3.02301i | −0.398086 | − | 0.229835i | 0.287572 | − | 0.957759i | \(-0.407152\pi\) |
−0.685658 | + | 0.727924i | \(0.740485\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.82843 | + | 4.47871i | 0.138216 | + | 0.338559i | ||||
\(176\) | −7.70154 | + | 3.95815i | −0.580525 | + | 0.298357i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.69025 | + | 10.5541i | 0.201642 | + | 0.791067i | ||||
\(179\) | −19.0416 | + | 10.9937i | −1.42324 | + | 0.821708i | −0.996574 | − | 0.0827020i | \(-0.973645\pi\) |
−0.426665 | + | 0.904410i | \(0.640312\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.77844i | − | 0.355179i | −0.984105 | − | 0.177589i | \(-0.943170\pi\) | ||
0.984105 | − | 0.177589i | \(-0.0568299\pi\) | |||||||
\(182\) | 14.4801 | + | 19.5632i | 1.07334 | + | 1.45012i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.6167 | + | 2.43164i | −0.782674 | + | 0.179263i | ||||
\(185\) | 10.0941 | + | 17.4835i | 0.742133 | + | 1.28541i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.99032 | + | 1.72646i | 0.218674 | + | 0.126251i | ||||
\(188\) | 19.7210 | + | 12.0376i | 1.43830 | + | 0.877934i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.24264 | + | 1.47363i | 0.380341 | + | 0.106908i | ||||
\(191\) | −8.96624 | + | 15.5300i | −0.648774 | + | 1.12371i | 0.334642 | + | 0.942345i | \(0.391385\pi\) |
−0.983416 | + | 0.181364i | \(0.941949\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.15685 | − | 8.93193i | −0.371198 | − | 0.642935i | 0.618552 | − | 0.785744i | \(-0.287720\pi\) |
−0.989750 | + | 0.142809i | \(0.954386\pi\) | |||||||
\(194\) | −0.838484 | + | 0.818246i | −0.0601997 | + | 0.0587467i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.08956 | − | 13.3894i | 0.292111 | − | 0.956384i | ||||
\(197\) | 19.5600i | 1.39359i | 0.717270 | + | 0.696796i | \(0.245392\pi\) | ||||
−0.717270 | + | 0.696796i | \(0.754608\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.414214 | + | 0.717439i | 0.0293628 | + | 0.0508579i | 0.880333 | − | 0.474355i | \(-0.157319\pi\) |
−0.850971 | + | 0.525213i | \(0.823986\pi\) | |||||||
\(200\) | −1.52061 | + | 4.94296i | −0.107524 | + | 0.349520i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.65685 | − | 5.89450i | 0.116576 | − | 0.414736i | ||||
\(203\) | 2.65131 | − | 19.3743i | 0.186085 | − | 1.35981i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.4288 | + | 10.0625i | 1.21728 | + | 0.702799i | ||||
\(206\) | 3.63782 | + | 14.2716i | 0.253459 | + | 0.994348i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.27079 | + | 25.9885i | −0.0881136 | + | 1.80198i | ||||
\(209\) | −3.19008 | −0.220663 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.1251i | 1.38547i | 0.721193 | + | 0.692734i | \(0.243594\pi\) | ||||
−0.721193 | + | 0.692734i | \(0.756406\pi\) | |||||||
\(212\) | 9.57791 | + | 17.5669i | 0.657814 | + | 1.20650i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.44991 | + | 1.13428i | −0.304190 | + | 0.0775378i | ||||
\(215\) | −3.52043 | + | 6.09756i | −0.240091 | + | 0.415850i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.58579 | + | 8.78335i | 0.243419 | + | 0.596252i | ||||
\(218\) | 4.08436 | − | 14.5307i | 0.276628 | − | 0.984144i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.276362 | − | 11.3103i | 0.0186323 | − | 0.762542i | ||||
\(221\) | 8.98552 | − | 5.18779i | 0.604431 | − | 0.348969i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.1421 | −1.08096 | −0.540479 | − | 0.841358i | \(-0.681757\pi\) | ||||
−0.540479 | + | 0.841358i | \(0.681757\pi\) | |||||||
\(224\) | 12.4503 | − | 8.30597i | 0.831873 | − | 0.554966i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.40944 | + | 9.18233i | −0.625907 | + | 0.610800i | ||||
\(227\) | 13.8999 | − | 8.02509i | 0.922566 | − | 0.532644i | 0.0381132 | − | 0.999273i | \(-0.487865\pi\) |
0.884453 | + | 0.466630i | \(0.154532\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.9099 | − | 8.03089i | −0.919192 | − | 0.530696i | −0.0358151 | − | 0.999358i | \(-0.511403\pi\) |
−0.883377 | + | 0.468662i | \(0.844736\pi\) | |||||||
\(230\) | 3.85077 | − | 13.6997i | 0.253912 | − | 0.903330i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 15.3137 | − | 14.2306i | 1.00539 | − | 0.934284i | ||||
\(233\) | 6.24333 | − | 10.8138i | 0.409014 | − | 0.708433i | −0.585765 | − | 0.810481i | \(-0.699206\pi\) |
0.994780 | + | 0.102047i | \(0.0325393\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −26.1433 | + | 15.0938i | −1.70540 | + | 0.984612i | ||||
\(236\) | 8.97087 | + | 16.4536i | 0.583954 | + | 1.07104i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.47343 | − | 2.37903i | −0.354790 | − | 0.154210i | ||||
\(239\) | −4.51146 | −0.291822 | −0.145911 | − | 0.989298i | \(-0.546611\pi\) | ||||
−0.145911 | + | 0.989298i | \(0.546611\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.58579 | + | 2.74666i | 0.102149 | + | 0.176928i | 0.912570 | − | 0.408920i | \(-0.134095\pi\) |
−0.810421 | + | 0.585849i | \(0.800761\pi\) | |||||||
\(242\) | −2.20546 | − | 8.65227i | −0.141772 | − | 0.556189i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.34315 | + | 7.11529i | −0.278041 | + | 0.455510i | ||||
\(245\) | 12.8017 | + | 13.0656i | 0.817867 | + | 0.834732i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.79289 | + | 8.30153i | −0.304964 | + | 0.528214i | ||||
\(248\) | −2.98212 | + | 9.69380i | −0.189365 | + | 0.615557i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.18587 | + | 8.38833i | 0.517720 | + | 0.530525i | ||||
\(251\) | − | 5.04054i | − | 0.318156i | −0.987266 | − | 0.159078i | \(-0.949148\pi\) | ||
0.987266 | − | 0.159078i | \(-0.0508522\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.33609i | 0.524085i | ||||||||
\(254\) | 10.1933 | − | 9.94730i | 0.639586 | − | 0.624149i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.9237 | + | 1.56101i | 0.995229 | + | 0.0975631i | ||||
\(257\) | −6.90402 | + | 11.9581i | −0.430661 | + | 0.745926i | −0.996930 | − | 0.0782937i | \(-0.975053\pi\) |
0.566269 | + | 0.824220i | \(0.308386\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.1526 | + | 12.5258i | 1.00368 | + | 0.778317i | ||||
\(260\) | −29.0176 | − | 17.7122i | −1.79960 | − | 1.09847i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.16203 | + | 1.82560i | −0.442471 | + | 0.112786i | ||||
\(263\) | 5.44581 | + | 9.43242i | 0.335803 | + | 0.581628i | 0.983639 | − | 0.180152i | \(-0.0576590\pi\) |
−0.647836 | + | 0.761780i | \(0.724326\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −26.1421 | −1.60590 | ||||||||
\(266\) | 5.47827 | − | 0.624926i | 0.335895 | − | 0.0383167i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −11.0446 | − | 20.2571i | −0.674659 | − | 1.23740i | ||||
\(269\) | 18.1043 | − | 10.4525i | 1.10384 | − | 0.637300i | 0.166611 | − | 0.986023i | \(-0.446718\pi\) |
0.937226 | + | 0.348722i | \(0.113384\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0711 | − | 20.9077i | 0.733265 | − | 1.27005i | −0.222215 | − | 0.974998i | \(-0.571329\pi\) |
0.955480 | − | 0.295055i | \(-0.0953379\pi\) | |||||||
\(272\) | −2.91642 | − | 5.67459i | −0.176834 | − | 0.344073i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 20.9706 | + | 5.89450i | 1.26688 | + | 0.356100i | ||||
\(275\) | 3.42786 | + | 1.97908i | 0.206708 | + | 0.119343i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.74788 | + | 4.47324i | −0.465525 | + | 0.268771i | −0.714365 | − | 0.699774i | \(-0.753284\pi\) |
0.248840 | + | 0.968545i | \(0.419951\pi\) | |||||||
\(278\) | −15.5112 | − | 15.8949i | −0.930301 | − | 0.953311i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.74106 | + | 19.4772i | 0.104048 | + | 1.16398i | ||||
\(281\) | 4.78512 | 0.285457 | 0.142728 | − | 0.989762i | \(-0.454413\pi\) | ||||
0.142728 | + | 0.989762i | \(0.454413\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.8195 | − | 12.0202i | 1.23759 | − | 0.714524i | 0.268990 | − | 0.963143i | \(-0.413310\pi\) |
0.968601 | + | 0.248619i | \(0.0799768\pi\) | |||||||
\(284\) | −0.720231 | + | 29.4760i | −0.0427378 | + | 1.74908i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 19.1716 | + | 5.38883i | 1.13364 | + | 0.318648i | ||||
\(287\) | 20.1882 | + | 2.76269i | 1.19167 | + | 0.163077i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.22792 | − | 12.5191i | 0.425172 | − | 0.736419i | ||||
\(290\) | 6.74652 | + | 26.4674i | 0.396170 | + | 1.55422i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.26788 | − | 2.87218i | 0.308280 | − | 0.168081i | ||||
\(293\) | − | 10.8239i | − | 0.632340i | −0.948703 | − | 0.316170i | \(-0.897603\pi\) | ||
0.948703 | − | 0.316170i | \(-0.102397\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.4853 | −1.42559 | ||||||||
\(296\) | 4.87852 | + | 21.3000i | 0.283558 | + | 1.23804i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.3241 | − | 3.65119i | 0.829770 | − | 0.211508i | ||||
\(299\) | 21.6930 | + | 12.5244i | 1.25454 | + | 0.724307i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.966540 | + | 7.06293i | −0.0557104 | + | 0.407101i | ||||
\(302\) | 12.0195 | + | 3.37849i | 0.691644 | + | 0.194410i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.95475 | + | 3.19305i | 0.284175 | + | 0.183134i | ||||
\(305\) | −5.44581 | − | 9.43242i | −0.311826 | − | 0.540099i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 10.3154i | − | 0.588730i | −0.955693 | − | 0.294365i | \(-0.904892\pi\) | ||
0.955693 | − | 0.294365i | \(-0.0951081\pi\) | |||||||
\(308\) | −4.06922 | − | 10.7078i | −0.231865 | − | 0.610135i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.25496 | − | 9.48386i | −0.525646 | − | 0.538647i | ||||
\(311\) | −16.9981 | − | 29.4416i | −0.963875 | − | 1.66948i | −0.712608 | − | 0.701563i | \(-0.752486\pi\) |
−0.251267 | − | 0.967918i | \(-0.580847\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.98528 | + | 5.17066i | −0.168738 | + | 0.292263i | −0.937976 | − | 0.346699i | \(-0.887303\pi\) |
0.769238 | + | 0.638962i | \(0.220636\pi\) | |||||||
\(314\) | −3.19008 | + | 11.3492i | −0.180027 | + | 0.640472i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.3640 | + | 7.54691i | 0.695527 | + | 0.424547i | ||||
\(317\) | −8.73048 | − | 5.04054i | −0.490352 | − | 0.283105i | 0.234368 | − | 0.972148i | \(-0.424698\pi\) |
−0.724721 | + | 0.689043i | \(0.758031\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.00000 | − | 13.8564i | −0.447914 | − | 0.775810i | ||||
\(320\) | −11.7501 | + | 17.2903i | −0.656851 | + | 0.966557i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.63301 | − | 14.3154i | −0.0910041 | − | 0.797767i | ||||
\(323\) | − | 2.35049i | − | 0.130785i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.3003 | − | 5.94687i | 0.571356 | − | 0.329873i | ||||
\(326\) | 13.7897 | − | 3.51498i | 0.763738 | − | 0.194677i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 14.8284 | + | 15.9570i | 0.818763 | + | 0.881081i | ||||
\(329\) | −18.7300 | + | 24.1532i | −1.03262 | + | 1.33161i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.88583 | + | 2.82083i | 0.268549 | + | 0.155047i | 0.628228 | − | 0.778029i | \(-0.283780\pi\) |
−0.359679 | + | 0.933076i | \(0.617114\pi\) | |||||||
\(332\) | −14.4064 | − | 0.352012i | −0.790651 | − | 0.0193192i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −14.9214 | + | 14.5612i | −0.816461 | + | 0.796755i | ||||
\(335\) | 30.1455 | 1.64702 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.6569 | 0.689463 | 0.344731 | − | 0.938701i | \(-0.387970\pi\) | ||||
0.344731 | + | 0.938701i | \(0.387970\pi\) | |||||||
\(338\) | 29.6696 | − | 28.9535i | 1.61381 | − | 1.57486i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.33360 | + | 0.203627i | 0.451953 | + | 0.0110432i | ||||
\(341\) | 6.72248 | + | 3.88123i | 0.364043 | + | 0.210180i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.0000 | + | 7.34847i | 0.917914 | + | 0.396780i | ||||
\(344\) | −5.58264 | + | 5.18779i | −0.300996 | + | 0.279707i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.28542 | − | 2.11195i | 0.445427 | − | 0.113539i | ||||
\(347\) | 11.5426 | − | 6.66413i | 0.619640 | − | 0.357749i | −0.157089 | − | 0.987584i | \(-0.550211\pi\) |
0.776729 | + | 0.629835i | \(0.216878\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.2931i | 1.30038i | 0.759771 | + | 0.650191i | \(0.225311\pi\) | ||||
−0.759771 | + | 0.650191i | \(0.774689\pi\) | |||||||
\(350\) | −6.27430 | − | 2.72713i | −0.335375 | − | 0.145771i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.88553 | − | 11.6131i | 0.207099 | − | 0.618980i | ||||
\(353\) | 6.24333 | + | 10.8138i | 0.332299 | + | 0.575559i | 0.982962 | − | 0.183808i | \(-0.0588424\pi\) |
−0.650663 | + | 0.759366i | \(0.725509\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −33.3625 | − | 19.2619i | −1.77070 | − | 1.02231i | ||||
\(356\) | −13.1474 | − | 8.02509i | −0.696808 | − | 0.425329i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.41421 | − | 29.9348i | 0.444705 | − | 1.58210i | ||||
\(359\) | −1.59504 | + | 2.76269i | −0.0841830 | + | 0.145809i | −0.905043 | − | 0.425320i | \(-0.860161\pi\) |
0.820860 | + | 0.571130i | \(0.193495\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.41421 | − | 14.5738i | −0.442853 | − | 0.767044i | ||||
\(362\) | 4.71972 | + | 4.83645i | 0.248063 | + | 0.254198i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −33.9787 | − | 5.49851i | −1.78097 | − | 0.288200i | ||||
\(365\) | 7.83938i | 0.410332i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.6924 | + | 27.1800i | 0.819136 | + | 1.41879i | 0.906320 | + | 0.422593i | \(0.138880\pi\) |
−0.0871836 | + | 0.996192i | \(0.527787\pi\) | |||||||
\(368\) | 8.34385 | − | 12.9474i | 0.434953 | − | 0.674930i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −27.4853 | − | 7.72569i | −1.42889 | − | 0.401640i | ||||
\(371\) | −24.5051 | + | 10.0042i | −1.27224 | + | 0.519390i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.5099 | − | 11.8414i | −1.06196 | − | 0.613123i | −0.135986 | − | 0.990711i | \(-0.543420\pi\) |
−0.925974 | + | 0.377588i | \(0.876754\pi\) | |||||||
\(374\) | −4.73186 | + | 1.20615i | −0.244679 | + | 0.0623685i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −31.8501 | + | 7.29491i | −1.64255 | + | 0.376206i | ||||
\(377\) | −48.0779 | −2.47614 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 16.2099i | − | 0.832646i | −0.909217 | − | 0.416323i | \(-0.863319\pi\) | ||
0.909217 | − | 0.416323i | \(-0.136681\pi\) | |||||||
\(380\) | −6.76180 | + | 3.68670i | −0.346873 | + | 0.189124i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.26404 | − | 24.5746i | −0.320496 | − | 1.25734i | ||||
\(383\) | 15.0727 | − | 26.1067i | 0.770181 | − | 1.33399i | −0.167283 | − | 0.985909i | \(-0.553499\pi\) |
0.937464 | − | 0.348083i | \(-0.113167\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.8284 | + | 2.02922i | 0.755727 | + | 0.103419i | ||||
\(386\) | 14.0416 | + | 3.94689i | 0.714700 | + | 0.200891i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.0404723 | − | 1.65636i | 0.00205467 | − | 0.0840889i | ||||
\(389\) | −7.88731 | + | 4.55374i | −0.399902 | + | 0.230884i | −0.686442 | − | 0.727185i | \(-0.740828\pi\) |
0.286539 | + | 0.958068i | \(0.407495\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.14214 | −0.310621 | ||||||||
\(392\) | 9.08563 | + | 17.5912i | 0.458894 | + | 0.888491i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −19.3196 | − | 19.7974i | −0.973308 | − | 0.997381i | ||||
\(395\) | −16.3903 | + | 9.46297i | −0.824687 | + | 0.476133i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.4051 | − | 8.89412i | −0.773158 | − | 0.446383i | 0.0608420 | − | 0.998147i | \(-0.480621\pi\) |
−0.834000 | + | 0.551764i | \(0.813955\pi\) | |||||||
\(398\) | −1.12786 | − | 0.317025i | −0.0565347 | − | 0.0158910i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.34315 | − | 6.50490i | −0.167157 | − | 0.325245i | ||||
\(401\) | −5.30898 | + | 9.19542i | −0.265118 | + | 0.459197i | −0.967594 | − | 0.252509i | \(-0.918744\pi\) |
0.702477 | + | 0.711707i | \(0.252077\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.2002 | − | 11.6626i | 1.00624 | − | 0.580955i | ||||
\(404\) | 4.14510 | + | 7.60255i | 0.206226 | + | 0.378241i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 16.4527 | + | 22.2282i | 0.816533 | + | 1.10317i | ||||
\(407\) | 16.7245 | 0.829000 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.4706 | + | 25.0637i | 0.715523 | + | 1.23932i | 0.962757 | + | 0.270367i | \(0.0871450\pi\) |
−0.247234 | + | 0.968956i | \(0.579522\pi\) | |||||||
\(410\) | −27.5793 | + | 7.02995i | −1.36205 | + | 0.347185i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −17.7782 | − | 10.8517i | −0.875868 | − | 0.534626i | ||||
\(413\) | −22.9520 | + | 9.37011i | −1.12939 | + | 0.461073i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.41421 | − | 16.3059i | 0.462126 | − | 0.800425i | ||||
\(416\) | −24.3829 | − | 27.5592i | −1.19547 | − | 1.35120i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.22881 | − | 3.15088i | 0.157926 | − | 0.154115i | ||||
\(419\) | − | 18.7402i | − | 0.915520i | −0.889076 | − | 0.457760i | \(-0.848652\pi\) | ||
0.889076 | − | 0.457760i | \(-0.151348\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.610396i | 0.0297489i | 0.999889 | + | 0.0148744i | \(0.00473485\pi\) | ||||
−0.999889 | + | 0.0148744i | \(0.995265\pi\) | |||||||
\(422\) | −19.8778 | − | 20.3694i | −0.967635 | − | 0.991567i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −27.0452 | − | 8.31998i | −1.31343 | − | 0.404054i | ||||
\(425\) | −1.45821 | + | 2.52569i | −0.0707335 | + | 0.122514i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.71442 | − | 6.75773i | −0.421720 | − | 0.327030i | ||||
\(428\) | 3.38359 | − | 5.54328i | 0.163552 | − | 0.267944i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.45946 | − | 9.64874i | −0.118606 | − | 0.465304i | ||||
\(431\) | 3.52043 | + | 6.09756i | 0.169573 | + | 0.293709i | 0.938270 | − | 0.345904i | \(-0.112428\pi\) |
−0.768697 | + | 0.639613i | \(0.779094\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.7990 | 1.57622 | 0.788109 | − | 0.615535i | \(-0.211060\pi\) | ||||
0.788109 | + | 0.615535i | \(0.211060\pi\) | |||||||
\(434\) | −12.3047 | − | 5.34826i | −0.590646 | − | 0.256724i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.2182 | + | 18.7413i | 0.489363 | + | 0.897544i | ||||
\(437\) | 4.91434 | − | 2.83730i | 0.235085 | − | 0.135726i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.757359 | + | 1.31178i | −0.0361468 | + | 0.0626081i | −0.883533 | − | 0.468369i | \(-0.844842\pi\) |
0.847386 | + | 0.530977i | \(0.178175\pi\) | |||||||
\(440\) | 10.8916 | + | 11.7206i | 0.519238 | + | 0.558758i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.97056 | + | 14.1259i | −0.188860 | + | 0.671899i | ||||
\(443\) | −32.1650 | − | 18.5704i | −1.52820 | − | 0.882308i | −0.999437 | − | 0.0335407i | \(-0.989322\pi\) |
−0.528766 | − | 0.848768i | \(-0.677345\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.4288 | − | 10.0625i | 0.826206 | − | 0.477010i | ||||
\(446\) | 16.3381 | − | 15.9438i | 0.773631 | − | 0.754959i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.39759 | + | 20.7041i | −0.207766 | + | 0.978178i | ||||
\(449\) | 1.59504 | 0.0752746 | 0.0376373 | − | 0.999291i | \(-0.488017\pi\) | ||||
0.0376373 | + | 0.999291i | \(0.488017\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.4385 | − | 8.33609i | 0.679884 | − | 0.392531i | ||||
\(452\) | 0.454179 | − | 18.5876i | 0.0213628 | − | 0.874288i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.14214 | + | 21.8516i | −0.288265 | + | 1.02554i | ||||
\(455\) | 27.5594 | − | 35.5392i | 1.29200 | − | 1.66610i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.2279 | + | 36.7678i | −0.993000 | + | 1.71993i | −0.394212 | + | 0.919019i | \(0.628983\pi\) |
−0.598788 | + | 0.800908i | \(0.704351\pi\) | |||||||
\(458\) | 22.0110 | − | 5.61058i | 1.02850 | − | 0.262165i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9.63381 | + | 17.6694i | 0.449179 | + | 0.823842i | ||||
\(461\) | 39.1200i | 1.82200i | 0.412408 | + | 0.910999i | \(0.364688\pi\) | ||||
−0.412408 | + | 0.910999i | \(0.635312\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.2132 | 0.846439 | 0.423220 | − | 0.906027i | \(-0.360900\pi\) | ||||
0.423220 | + | 0.906027i | \(0.360900\pi\) | |||||||
\(464\) | −1.44391 | + | 29.5289i | −0.0670317 | + | 1.37084i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.36175 | + | 17.1117i | 0.202054 | + | 0.792682i | ||||
\(467\) | −29.1920 | − | 16.8540i | −1.35084 | − | 0.779910i | −0.362476 | − | 0.931993i | \(-0.618069\pi\) |
−0.988368 | + | 0.152083i | \(0.951402\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.2577 | − | 11.5362i | 1.30482 | − | 0.532691i | ||||
\(470\) | 11.5523 | − | 41.0990i | 0.532868 | − | 1.89576i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −25.3311 | − | 7.79267i | −1.16596 | − | 0.358687i | ||||
\(473\) | 2.91642 | + | 5.05138i | 0.134097 | + | 0.232263i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 2.69442i | − | 0.123628i | ||||||
\(476\) | 7.88967 | − | 2.99825i | 0.361622 | − | 0.137425i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.56623 | − | 4.45602i | 0.208854 | − | 0.203813i | ||||
\(479\) | −14.4120 | − | 24.9624i | −0.658503 | − | 1.14056i | −0.981003 | − | 0.193992i | \(-0.937857\pi\) |
0.322500 | − | 0.946569i | \(-0.395477\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.1274 | − | 43.5220i | 1.14571 | − | 1.98443i | ||||
\(482\) | −4.31795 | − | 1.21371i | −0.196677 | − | 0.0552829i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.7782 | + | 6.57895i | 0.489917 | + | 0.299043i | ||||
\(485\) | 1.87476 | + | 1.08239i | 0.0851284 | + | 0.0491489i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.13604 | + | 8.89588i | 0.232736 | + | 0.403111i | 0.958612 | − | 0.284715i | \(-0.0918988\pi\) |
−0.725876 | + | 0.687825i | \(0.758565\pi\) | |||||||
\(488\) | −2.63198 | − | 11.4914i | −0.119144 | − | 0.520193i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −25.8621 | − | 0.579916i | −1.16833 | − | 0.0261979i | ||||
\(491\) | 7.39104i | 0.333553i | 0.985995 | + | 0.166776i | \(0.0533358\pi\) | ||||
−0.985995 | + | 0.166776i | \(0.946664\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.2096 | − | 5.89450i | 0.459816 | − | 0.265475i | ||||
\(494\) | −3.34844 | − | 13.1363i | −0.150653 | − | 0.591030i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.55635 | − | 12.7570i | −0.294389 | − | 0.572805i | ||||
\(497\) | −38.6445 | − | 5.28838i | −1.73344 | − | 0.237216i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.49546 | + | 4.90486i | 0.380309 | + | 0.219572i | 0.677953 | − | 0.735106i | \(-0.262867\pi\) |
−0.297644 | + | 0.954677i | \(0.596201\pi\) | |||||||
\(500\) | −16.5705 | − | 0.404892i | −0.741055 | − | 0.0181073i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.97860 | + | 5.10173i | 0.222206 | + | 0.227702i | ||||
\(503\) | 24.9733 | 1.11351 | 0.556753 | − | 0.830678i | \(-0.312047\pi\) | ||||
0.556753 | + | 0.830678i | \(0.312047\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.3137 | −0.503453 | ||||||||
\(506\) | −8.23364 | − | 8.43729i | −0.366030 | − | 0.375083i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.492016 | + | 20.1361i | −0.0218297 | + | 0.893396i | ||||
\(509\) | 14.2881 | + | 8.24926i | 0.633310 | + | 0.365642i | 0.782033 | − | 0.623237i | \(-0.214183\pi\) |
−0.148723 | + | 0.988879i | \(0.547516\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.00000 | + | 7.34847i | 0.132712 | + | 0.325077i | ||||
\(512\) | −17.6588 | + | 14.1480i | −0.780416 | + | 0.625260i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.82332 | − | 18.9225i | −0.212748 | − | 0.834634i | ||||
\(515\) | 23.5677 | − | 13.6068i | 1.03852 | − | 0.599588i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.0083i | 1.09986i | ||||||||
\(518\) | −28.7206 | + | 3.27626i | −1.26191 | + | 0.143951i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 46.8644 | − | 10.7338i | 2.05514 | − | 0.470706i | ||||
\(521\) | 14.7424 | + | 25.5346i | 0.645876 | + | 1.11869i | 0.984098 | + | 0.177624i | \(0.0568410\pi\) |
−0.338223 | + | 0.941066i | \(0.609826\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.7623 | + | 11.4098i | 0.864144 | + | 0.498914i | 0.865398 | − | 0.501085i | \(-0.167066\pi\) |
−0.00125385 | + | 0.999999i | \(0.500399\pi\) | |||||||
\(524\) | 5.44581 | − | 8.92177i | 0.237901 | − | 0.389749i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.8284 | − | 4.16804i | −0.646550 | − | 0.181735i | ||||
\(527\) | −2.85974 | + | 4.95321i | −0.124572 | + | 0.215765i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.08579 | + | 7.07679i | 0.177643 | + | 0.307687i | ||||
\(530\) | 26.4595 | − | 25.8209i | 1.14933 | − | 1.12159i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.92753 | + | 6.04346i | −0.213636 | + | 0.262017i | ||||
\(533\) | − | 50.0977i | − | 2.16997i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.24264 | + | 7.34847i | 0.183425 | + | 0.317702i | ||||
\(536\) | 31.1869 | + | 9.59407i | 1.34707 | + | 0.414401i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.00000 | + | 28.4612i | −0.344904 | + | 1.22705i | ||||
\(539\) | 14.6764 | − | 3.77244i | 0.632158 | − | 0.162491i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.8815 | − | 21.2935i | −1.58566 | − | 0.915480i | −0.994011 | − | 0.109283i | \(-0.965145\pi\) |
−0.591647 | − | 0.806197i | \(-0.701522\pi\) | |||||||
\(542\) | 8.43316 | + | 33.0842i | 0.362235 | + | 1.42109i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.55668 | + | 2.86291i | 0.366865 | + | 0.122746i | ||||
\(545\) | −27.8897 | −1.19467 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.6722i | 0.712851i | 0.934324 | + | 0.356425i | \(0.116005\pi\) | ||||
−0.934324 | + | 0.356425i | \(0.883995\pi\) | |||||||
\(548\) | −27.0472 | + | 14.7468i | −1.15540 | + | 0.629952i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.42423 | + | 1.38263i | −0.231290 | + | 0.0589556i | ||||
\(551\) | −5.44581 | + | 9.43242i | −0.231999 | + | 0.401835i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.7426 | + | 15.1427i | −0.499348 | + | 0.643933i | ||||
\(554\) | 3.42367 | − | 12.1802i | 0.145458 | − | 0.517488i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 31.3991 | + | 0.767220i | 1.33162 | + | 0.0325374i | ||||
\(557\) | −11.7034 | + | 6.75699i | −0.495891 | + | 0.286303i | −0.727015 | − | 0.686622i | \(-0.759093\pi\) |
0.231124 | + | 0.972924i | \(0.425760\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.5269 | 0.741309 | ||||||||
\(560\) | −21.0000 | − | 17.9940i | −0.887413 | − | 0.760384i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.84321 | + | 4.72632i | −0.204299 | + | 0.199368i | ||||
\(563\) | −23.8894 | + | 13.7925i | −1.00682 | + | 0.581286i | −0.910258 | − | 0.414041i | \(-0.864117\pi\) |
−0.0965588 | + | 0.995327i | \(0.530784\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.0385 | + | 12.1466i | 0.885095 | + | 0.511010i | ||||
\(566\) | −9.19982 | + | 32.7297i | −0.386697 | + | 1.37573i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −28.3848 | − | 30.5452i | −1.19100 | − | 1.28165i | ||||
\(569\) | 14.7424 | − | 25.5346i | 0.618033 | − | 1.07046i | −0.371811 | − | 0.928308i | \(-0.621263\pi\) |
0.989844 | − | 0.142156i | \(-0.0454036\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.4767 | + | 16.4410i | −1.19171 | + | 0.688036i | −0.958695 | − | 0.284437i | \(-0.908193\pi\) |
−0.233018 | + | 0.972472i | \(0.574860\pi\) | |||||||
\(572\) | −24.7269 | + | 13.4817i | −1.03388 | + | 0.563699i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −23.1620 | + | 17.1439i | −0.966764 | + | 0.715572i | ||||
\(575\) | −7.04085 | −0.293624 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.67157 | + | 15.0196i | 0.361002 | + | 0.625274i | 0.988126 | − | 0.153645i | \(-0.0491013\pi\) |
−0.627124 | + | 0.778920i | \(0.715768\pi\) | |||||||
\(578\) | 5.04961 | + | 19.8102i | 0.210036 | + | 0.823996i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −32.9706 | − | 20.1251i | −1.36903 | − | 0.835649i | ||||
\(581\) | 2.58469 | − | 18.8875i | 0.107231 | − | 0.783584i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.8284 | + | 18.7554i | −0.448468 | + | 0.776769i | ||||
\(584\) | −2.49495 | + | 8.11019i | −0.103242 | + | 0.335602i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.6909 | + | 10.9553i | 0.441637 | + | 0.452560i | ||||
\(587\) | 20.5336i | 0.847512i | 0.905776 | + | 0.423756i | \(0.139289\pi\) | ||||
−0.905776 | + | 0.423756i | \(0.860711\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 5.28411i | − | 0.217728i | ||||||
\(590\) | 24.7825 | − | 24.1844i | 1.02028 | − | 0.995655i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −25.9760 | − | 16.7400i | −1.06761 | − | 0.688011i | ||||
\(593\) | 11.5523 | − | 20.0092i | 0.474396 | − | 0.821679i | −0.525174 | − | 0.850995i | \(-0.676000\pi\) |
0.999570 | + | 0.0293163i | \(0.00933299\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.49516 | + | 10.9258i | −0.0612955 | + | 0.447913i | ||||
\(596\) | −10.8916 | + | 17.8435i | −0.446138 | + | 0.730900i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −34.3268 | + | 8.74989i | −1.40373 | + | 0.357810i | ||||
\(599\) | −0.660688 | − | 1.14434i | −0.0269950 | − | 0.0467567i | 0.852212 | − | 0.523196i | \(-0.175260\pi\) |
−0.879207 | + | 0.476439i | \(0.841927\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.7990 | −0.522082 | −0.261041 | − | 0.965328i | \(-0.584066\pi\) | ||||
−0.261041 | + | 0.965328i | \(0.584066\pi\) | |||||||
\(602\) | −5.99786 | − | 8.10334i | −0.244455 | − | 0.330267i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15.5024 | + | 8.45227i | −0.630783 | + | 0.343918i | ||||
\(605\) | −14.2881 | + | 8.24926i | −0.580895 | + | 0.335380i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.96447 | − | 10.3308i | 0.242090 | − | 0.419313i | −0.719219 | − | 0.694783i | \(-0.755500\pi\) |
0.961309 | + | 0.275471i | \(0.0888337\pi\) | |||||||
\(608\) | −8.16872 | + | 1.66205i | −0.331285 | + | 0.0674050i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 14.8284 | + | 4.16804i | 0.600385 | + | 0.168759i | ||||
\(611\) | 65.0789 | + | 37.5733i | 2.63281 | + | 1.52005i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.8289 | − | 6.25206i | 0.437375 | − | 0.252519i | −0.265109 | − | 0.964219i | \(-0.585408\pi\) |
0.702483 | + | 0.711700i | \(0.252074\pi\) | |||||||
\(614\) | 10.1886 | + | 10.4406i | 0.411179 | + | 0.421349i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 14.6949 | + | 6.81861i | 0.592073 | + | 0.274730i | ||||
\(617\) | −3.19008 | −0.128428 | −0.0642139 | − | 0.997936i | \(-0.520454\pi\) | ||||
−0.0642139 | + | 0.997936i | \(0.520454\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.32375 | − | 3.07367i | 0.213980 | − | 0.123541i | −0.389180 | − | 0.921162i | \(-0.627242\pi\) |
0.603160 | + | 0.797621i | \(0.293908\pi\) | |||||||
\(620\) | 18.7346 | + | 0.457771i | 0.752401 | + | 0.0183845i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 46.2843 | + | 13.0098i | 1.85583 | + | 0.521645i | ||||
\(623\) | 12.4867 | − | 16.1021i | 0.500268 | − | 0.645119i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.3995 | − | 26.6727i | 0.615980 | − | 1.06691i | ||||
\(626\) | −2.08559 | − | 8.18203i | −0.0833571 | − | 0.327020i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.98091 | − | 14.6378i | −0.318473 | − | 0.584114i | ||||
\(629\) | 12.3228i | 0.491342i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.82843 | −0.192217 | −0.0961083 | − | 0.995371i | \(-0.530640\pi\) | ||||
−0.0961083 | + | 0.995371i | \(0.530640\pi\) | |||||||
\(632\) | −19.9682 | + | 4.57349i | −0.794293 | + | 0.181924i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.8151 | − | 3.52145i | 0.548666 | − | 0.139855i | ||||
\(635\) | −22.7912 | − | 13.1585i | −0.904440 | − | 0.522179i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.2334 | − | 43.8602i | 0.484703 | − | 1.73780i | ||||
\(638\) | 21.7832 | + | 6.12293i | 0.862407 | + | 0.242409i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5.18507 | − | 29.1059i | −0.204958 | − | 1.15051i | ||||
\(641\) | −0.797521 | − | 1.38135i | −0.0315002 | − | 0.0545599i | 0.849846 | − | 0.527032i | \(-0.176695\pi\) |
−0.881346 | + | 0.472472i | \(0.843362\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 8.58892i | − | 0.338714i | −0.985555 | − | 0.169357i | \(-0.945831\pi\) | ||
0.985555 | − | 0.169357i | \(-0.0541691\pi\) | |||||||
\(644\) | 15.7923 | + | 12.8763i | 0.622305 | + | 0.507396i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.32161 | + | 2.37903i | 0.0913424 | + | 0.0936016i | ||||
\(647\) | 0.660688 | + | 1.14434i | 0.0259743 | + | 0.0449888i | 0.878720 | − | 0.477337i | \(-0.158398\pi\) |
−0.852746 | + | 0.522326i | \(0.825065\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.1421 | + | 17.5667i | −0.398114 | + | 0.689553i | ||||
\(650\) | −4.55153 | + | 16.1928i | −0.178526 | + | 0.635132i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.4853 | + | 17.1778i | −0.410635 | + | 0.672736i | ||||
\(653\) | 20.3007 | + | 11.7206i | 0.794427 | + | 0.458663i | 0.841519 | − | 0.540228i | \(-0.181662\pi\) |
−0.0470917 | + | 0.998891i | \(0.514995\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.82843 | + | 11.8272i | 0.266809 | + | 0.462126i | ||||
\(656\) | −30.7694 | − | 1.50457i | −1.20134 | − | 0.0587435i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.89903 | − | 42.9463i | −0.190984 | − | 1.67422i | ||||
\(659\) | − | 8.10201i | − | 0.315610i | −0.987470 | − | 0.157805i | \(-0.949558\pi\) | ||
0.987470 | − | 0.157805i | \(-0.0504417\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.68096 | + | 5.58931i | −0.376546 | + | 0.217399i | −0.676314 | − | 0.736613i | \(-0.736424\pi\) |
0.299769 | + | 0.954012i | \(0.403091\pi\) | |||||||
\(662\) | −7.73131 | + | 1.97071i | −0.300486 | + | 0.0765937i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.9289 | − | 13.8730i | 0.579355 | − | 0.538378i | ||||
\(665\) | −3.85077 | − | 9.43242i | −0.149326 | − | 0.365774i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.6481 | + | 14.2306i | 0.954378 | + | 0.551011i | ||||
\(668\) | 0.720231 | − | 29.4760i | 0.0278666 | − | 1.14046i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −30.5114 | + | 29.7750i | −1.17876 | + | 1.15031i | ||||
\(671\) | −9.02291 | −0.348326 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.62742 | 0.294015 | 0.147008 | − | 0.989135i | \(-0.453036\pi\) | ||||
0.147008 | + | 0.989135i | \(0.453036\pi\) | |||||||
\(674\) | −12.8105 | + | 12.5013i | −0.493442 | + | 0.481533i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.43210 | + | 58.6099i | −0.0550809 | + | 2.25423i | ||||
\(677\) | −0.776550 | − | 0.448342i | −0.0298453 | − | 0.0172312i | 0.485003 | − | 0.874512i | \(-0.338818\pi\) |
−0.514848 | + | 0.857281i | \(0.672152\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.17157 | + | 0.297173i | 0.0833373 | + | 0.0114045i | ||||
\(680\) | −8.63589 | + | 8.02509i | −0.331171 | + | 0.307748i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10.6376 | + | 2.71152i | −0.407336 | + | 0.103830i | ||||
\(683\) | 25.4425 | − | 14.6892i | 0.973529 | − | 0.562067i | 0.0732188 | − | 0.997316i | \(-0.476673\pi\) |
0.900310 | + | 0.435249i | \(0.143340\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 40.2502i | − | 1.53788i | ||||||
\(686\) | −24.4645 | + | 9.35341i | −0.934061 | + | 0.357115i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.526379 | − | 10.7648i | 0.0200680 | − | 0.410404i | ||||
\(689\) | 32.5380 | + | 56.3575i | 1.23960 | + | 2.14705i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.0863 | − | 18.5250i | −1.22062 | − | 0.704726i | −0.255571 | − | 0.966790i | \(-0.582263\pi\) |
−0.965050 | + | 0.262064i | \(0.915597\pi\) | |||||||
\(692\) | −6.30001 | + | 10.3212i | −0.239490 | + | 0.392353i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.10051 | + | 18.1458i | −0.193613 | + | 0.688805i | ||||
\(695\) | −20.5185 | + | 35.5392i | −0.778313 | + | 1.34808i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.14214 | + | 10.6385i | 0.232650 | + | 0.402962i | ||||
\(698\) | −23.9946 | − | 24.5881i | −0.908209 | − | 0.930671i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.04408 | − | 3.43696i | 0.341834 | − | 0.129905i | ||||
\(701\) | − | 7.83938i | − | 0.296089i | −0.988981 | − | 0.148045i | \(-0.952702\pi\) | ||
0.988981 | − | 0.148045i | \(-0.0472979\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.69239 | − | 9.85951i | −0.214692 | − | 0.371858i | ||||
\(704\) | 7.53768 | + | 15.5919i | 0.284087 | + | 0.587640i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.0000 | − | 4.77844i | −0.639803 | − | 0.179839i | ||||
\(707\) | −10.6052 | + | 4.32957i | −0.398851 | + | 0.162830i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.8192 | + | 7.97852i | 0.518991 | + | 0.299640i | 0.736522 | − | 0.676414i | \(-0.236467\pi\) |
−0.217531 | + | 0.976054i | \(0.569800\pi\) | |||||||
\(710\) | 52.7927 | − | 13.4568i | 1.98127 | − | 0.505026i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 21.2334 | − | 4.86327i | 0.795756 | − | 0.182259i | ||||
\(713\) | −13.8080 | −0.517115 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 36.7973i | − | 1.37614i | ||||||
\(716\) | 21.0506 | + | 38.6090i | 0.786697 | + | 1.44289i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.11434 | − | 4.37167i | −0.0415867 | − | 0.163149i | ||||
\(719\) | −7.04085 | + | 12.1951i | −0.262579 | + | 0.454801i | −0.966927 | − | 0.255055i | \(-0.917907\pi\) |
0.704347 | + | 0.709856i | \(0.251240\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.8848 | − | 21.7737i | 0.628822 | − | 0.810896i | ||||
\(722\) | 22.9111 | + | 6.43996i | 0.852663 | + | 0.239671i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.55403 | − | 0.233448i | −0.355073 | − | 0.00867602i | ||||
\(725\) | 11.7034 | − | 6.75699i | 0.434655 | − | 0.250948i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.8995 | 0.404240 | 0.202120 | − | 0.979361i | \(-0.435217\pi\) | ||||
0.202120 | + | 0.979361i | \(0.435217\pi\) | |||||||
\(728\) | 39.8221 | − | 27.9958i | 1.47591 | − | 1.03759i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7.74304 | − | 7.93455i | −0.286583 | − | 0.293671i | ||||
\(731\) | −3.72192 | + | 2.14885i | −0.137660 | + | 0.0794782i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.4526 | + | 11.2310i | 0.718499 | + | 0.414825i | 0.814200 | − | 0.580585i | \(-0.197176\pi\) |
−0.0957011 | + | 0.995410i | \(0.530509\pi\) | |||||||
\(734\) | −42.7289 | − | 12.0104i | −1.57715 | − | 0.443313i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.34315 | + | 21.3459i | 0.160090 | + | 0.786820i | ||||
\(737\) | 12.4867 | − | 21.6275i | 0.459952 | − | 0.796660i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.7147 | + | 9.07290i | −0.578075 | + | 0.333752i | −0.760368 | − | 0.649492i | \(-0.774981\pi\) |
0.182293 | + | 0.983244i | \(0.441648\pi\) | |||||||
\(740\) | 35.4497 | − | 19.3280i | 1.30316 | − | 0.710513i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14.9214 | − | 34.3296i | 0.547780 | − | 1.26028i | ||||
\(743\) | −26.2947 | −0.964659 | −0.482329 | − | 0.875990i | \(-0.660209\pi\) | ||||
−0.482329 | + | 0.875990i | \(0.660209\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.6569 | − | 23.6544i | −0.500348 | − | 0.866629i | ||||
\(746\) | 32.4547 | − | 8.27268i | 1.18825 | − | 0.302884i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.59798 | − | 5.89450i | 0.131555 | − | 0.215524i | ||||
\(749\) | 6.78910 | + | 5.26471i | 0.248068 | + | 0.192368i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.8640 | − | 29.2092i | 0.615375 | − | 1.06586i | −0.374944 | − | 0.927047i | \(-0.622338\pi\) |
0.990319 | − | 0.138813i | \(-0.0443286\pi\) | |||||||
\(752\) | 25.0315 | − | 38.8422i | 0.912806 | − | 1.41643i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 48.6616 | − | 47.4871i | 1.77215 | − | 1.72938i | ||||
\(755\) | − | 23.0698i | − | 0.839596i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.2931i | 0.882949i | 0.897274 | + | 0.441475i | \(0.145544\pi\) | ||||
−0.897274 | + | 0.441475i | \(0.854456\pi\) | |||||||
\(758\) | 16.0107 | + | 16.4067i | 0.581534 | + | 0.595917i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.20250 | − | 10.4102i | 0.116167 | − | 0.377616i | ||||
\(761\) | −3.98760 | + | 6.90673i | −0.144550 | + | 0.250369i | −0.929205 | − | 0.369564i | \(-0.879507\pi\) |
0.784655 | + | 0.619933i | \(0.212840\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26.1433 | + | 10.6729i | −0.946450 | + | 0.386386i | ||||
\(764\) | 30.6126 | + | 18.6858i | 1.10753 | + | 0.676030i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.5302 | + | 41.3112i | 0.380471 | + | 1.49263i | ||||
\(767\) | 30.4758 | + | 52.7857i | 1.10042 | + | 1.90598i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.1716 | 0.583162 | 0.291581 | − | 0.956546i | \(-0.405819\pi\) | ||||
0.291581 | + | 0.956546i | \(0.405819\pi\) | |||||||
\(770\) | −17.0127 | + | 12.5923i | −0.613096 | + | 0.453796i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −18.1105 | + | 9.87427i | −0.651810 | + | 0.355383i | ||||
\(773\) | 39.6364 | − | 22.8841i | 1.42562 | − | 0.823083i | 0.428851 | − | 0.903375i | \(-0.358919\pi\) |
0.996771 | + | 0.0802922i | \(0.0255853\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.27817 | + | 5.67796i | −0.117756 | + | 0.203959i | ||||
\(776\) | 1.59504 | + | 1.71644i | 0.0572586 | + | 0.0616167i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.48528 | − | 12.3994i | 0.124953 | − | 0.444540i | ||||
\(779\) | −9.82868 | − | 5.67459i | −0.352149 | − | 0.203313i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.6384 | + | 15.9570i | −0.988980 | + | 0.570988i | ||||
\(782\) | 6.21670 | − | 6.06665i | 0.222309 | − | 0.216943i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −26.5710 | − | 8.83081i | −0.948963 | − | 0.315386i | ||||
\(785\) | 21.7832 | 0.777477 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.71442 | − | 5.03127i | 0.310636 | − | 0.179346i | −0.336575 | − | 0.941657i | \(-0.609269\pi\) |
0.647211 | + | 0.762311i | \(0.275935\pi\) | |||||||
\(788\) | 39.1083 | + | 0.955591i | 1.39318 | + | 0.0340415i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.24264 | − | 25.7668i | 0.257682 | − | 0.916740i | ||||
\(791\) | 24.3693 | + | 3.33486i | 0.866473 | + | 0.118574i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.5563 | + | 23.4803i | −0.481400 | + | 0.833809i | ||||
\(794\) | 24.3769 | − | 6.21366i | 0.865104 | − | 0.220514i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.45469 | − | 0.793130i | 0.0515600 | − | 0.0281117i | ||||
\(797\) | 41.3617i | 1.46511i | 0.680710 | + | 0.732553i | \(0.261671\pi\) | ||||
−0.680710 | + | 0.732553i | \(0.738329\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.4264 | −0.651879 | ||||||||
\(800\) | 9.80869 | + | 3.28181i | 0.346790 | + | 0.116029i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.70899 | − | 14.5508i | −0.130969 | − | 0.513806i | ||||
\(803\) | 5.62427 | + | 3.24718i | 0.198476 | + | 0.114590i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −24.6481 | + | 10.0625i | −0.868731 | + | 0.354658i | ||||
\(806\) | −8.92616 | + | 31.7561i | −0.314411 | + | 1.11856i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.7045 | − | 3.60069i | −0.411764 | − | 0.126672i | ||||
\(809\) | 9.43341 | + | 16.3392i | 0.331661 | + | 0.574454i | 0.982838 | − | 0.184472i | \(-0.0590576\pi\) |
−0.651177 | + | 0.758926i | \(0.725724\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 16.6722i | − | 0.585439i | −0.956198 | − | 0.292720i | \(-0.905440\pi\) | ||
0.956198 | − | 0.292720i | \(-0.0945602\pi\) | |||||||
\(812\) | −38.6075 | − | 6.24755i | −1.35486 | − | 0.219246i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −16.9275 | + | 16.5189i | −0.593308 | + | 0.578988i | ||||
\(815\) | −13.1474 | − | 22.7719i | −0.460532 | − | 0.797664i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.98528 | − | 3.43861i | 0.0694562 | − | 0.120302i | ||||
\(818\) | −39.4020 | − | 11.0753i | −1.37766 | − | 0.387238i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 20.9706 | − | 34.3557i | 0.732324 | − | 1.19975i | ||||
\(821\) | −0.709933 | − | 0.409880i | −0.0247768 | − | 0.0143049i | 0.487560 | − | 0.873089i | \(-0.337887\pi\) |
−0.512337 | + | 0.858784i | \(0.671220\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.89949 | + | 11.9503i | 0.240501 | + | 0.416560i | 0.960857 | − | 0.277044i | \(-0.0893548\pi\) |
−0.720356 | + | 0.693605i | \(0.756022\pi\) | |||||||
\(824\) | 28.7124 | − | 6.57623i | 1.00024 | − | 0.229094i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.9757 | − | 32.1538i | 0.486276 | − | 1.11877i | ||||
\(827\) | − | 16.2359i | − | 0.564577i | −0.959330 | − | 0.282288i | \(-0.908906\pi\) | ||
0.959330 | − | 0.282288i | \(-0.0910935\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −47.7104 | + | 27.5456i | −1.65705 | + | 0.956698i | −0.682983 | + | 0.730434i | \(0.739318\pi\) |
−0.974066 | + | 0.226263i | \(0.927349\pi\) | |||||||
\(830\) | 6.57701 | + | 25.8024i | 0.228291 | + | 0.895613i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 51.8995 | + | 3.81048i | 1.79929 | + | 0.132105i | ||||
\(833\) | 2.77958 | + | 10.8138i | 0.0963069 | + | 0.374675i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 33.3625 | + | 19.2619i | 1.15456 | + | 0.666584i | ||||
\(836\) | −0.155850 | + | 6.37826i | −0.00539017 | + | 0.220597i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 18.5099 | + | 18.9677i | 0.639415 | + | 0.655229i | ||||
\(839\) | −23.1046 | −0.797660 | −0.398830 | − | 0.917025i | \(-0.630584\pi\) | ||||
−0.398830 | + | 0.917025i | \(0.630584\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.6274 | −0.883704 | ||||||||
\(842\) | −0.602895 | − | 0.617806i | −0.0207771 | − | 0.0212910i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 40.2382 | + | 0.983199i | 1.38506 | + | 0.0338431i | ||||
\(845\) | −66.3379 | − | 38.3002i | −2.28209 | − | 1.31757i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.2365 | + | 13.2005i | −0.351732 | + | 0.453575i | ||||
\(848\) | 35.5913 | − | 18.2919i | 1.22221 | − | 0.628146i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.01874 | − | 3.99664i | −0.0349425 | − | 0.137084i | ||||
\(851\) | −25.7641 | + | 14.8749i | −0.883183 | + | 0.509906i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.01057i | 0.240037i | 0.992772 | + | 0.120019i | \(0.0382954\pi\) | ||||
−0.992772 | + | 0.120019i | \(0.961705\pi\) | |||||||
\(854\) | 15.4949 | − | 1.76756i | 0.530225 | − | 0.0604845i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.05049 | + | 8.95258i | 0.0700842 | + | 0.305993i | ||||
\(857\) | −2.91642 | − | 5.05138i | −0.0996229 | − | 0.172552i | 0.811906 | − | 0.583789i | \(-0.198430\pi\) |
−0.911529 | + | 0.411237i | \(0.865097\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.21926 | + | 4.16804i | 0.246318 | + | 0.142212i | 0.618077 | − | 0.786117i | \(-0.287912\pi\) |
−0.371759 | + | 0.928329i | \(0.621245\pi\) | |||||||
\(860\) | 12.0195 | + | 7.33664i | 0.409861 | + | 0.250177i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.58579 | − | 2.69442i | −0.326493 | − | 0.0917722i | ||||
\(863\) | −17.6588 | + | 30.5860i | −0.601113 | + | 1.04116i | 0.391540 | + | 0.920161i | \(0.371942\pi\) |
−0.992653 | + | 0.120997i | \(0.961391\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.89949 | − | 13.6823i | −0.268591 | − | 0.465213i | ||||
\(866\) | −33.1972 | + | 32.3959i | −1.12809 | + | 1.10086i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 17.7366 | − | 6.74033i | 0.602021 | − | 0.228782i | ||||
\(869\) | 15.6788i | 0.531865i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37.5208 | − | 64.9880i | −1.27134 | − | 2.20203i | ||||
\(872\) | −28.8532 | − | 8.87617i | −0.977093 | − | 0.300585i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.17157 | + | 7.72569i | −0.0734545 | + | 0.261325i | ||||
\(875\) | 2.97297 | − | 21.7248i | 0.100505 | − | 0.734431i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.0288 | + | 13.8730i | 0.811395 | + | 0.468459i | 0.847440 | − | 0.530891i | \(-0.178143\pi\) |
−0.0360454 | + | 0.999350i | \(0.511476\pi\) | |||||||
\(878\) | −0.529111 | − | 2.07576i | −0.0178566 | − | 0.0700536i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −22.6004 | − | 1.10512i | −0.761860 | − | 0.0372536i | ||||
\(881\) | −23.3783 | −0.787634 | −0.393817 | − | 0.919189i | \(-0.628846\pi\) | ||||
−0.393817 | + | 0.919189i | \(0.628846\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.0418i | 0.405240i | 0.979257 | + | 0.202620i | \(0.0649457\pi\) | ||||
−0.979257 | + | 0.202620i | \(0.935054\pi\) | |||||||
\(884\) | −9.93350 | − | 18.2191i | −0.334100 | − | 0.612775i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 50.8977 | − | 12.9738i | 1.70994 | − | 0.435863i | ||||
\(887\) | 9.29658 | − | 16.1021i | 0.312149 | − | 0.540657i | −0.666679 | − | 0.745345i | \(-0.732285\pi\) |
0.978827 | + | 0.204688i | \(0.0656180\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26.3995 | − | 3.61269i | −0.885411 | − | 0.121166i | ||||
\(890\) | −7.70154 | + | 27.3994i | −0.258156 | + | 0.918429i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.788614 | + | 32.2746i | −0.0264048 | + | 1.08063i | ||||
\(893\) | 14.7430 | − | 8.51189i | 0.493357 | − | 0.284840i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −57.4558 | −1.92054 | ||||||||
\(896\) | −15.9987 | − | 25.2990i | −0.534480 | − | 0.845181i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.61440 | + | 1.57544i | −0.0538734 | + | 0.0525731i | ||||
\(899\) | 22.9520 | − | 13.2513i | 0.765492 | − | 0.441957i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.8192 | − | 7.97852i | −0.460385 | − | 0.265803i | ||||
\(902\) | −6.38016 | + | 22.6984i | −0.212436 | + | 0.755773i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 17.8995 | + | 19.2619i | 0.595328 | + | 0.640640i | ||||
\(905\) | 6.24333 | − | 10.8138i | 0.207535 | − | 0.359462i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.7532 | − | 21.2195i | 1.22037 | − | 0.704581i | 0.255373 | − | 0.966843i | \(-0.417802\pi\) |
0.964997 | + | 0.262262i | \(0.0844684\pi\) | |||||||
\(908\) | −15.3663 | − | 28.1835i | −0.509949 | − | 0.935302i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.20845 | + | 63.1913i | 0.238958 | + | 2.09477i | ||||
\(911\) | −28.8241 | −0.954985 | −0.477492 | − | 0.878636i | \(-0.658454\pi\) | ||||
−0.477492 | + | 0.878636i | \(0.658454\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.79899 | − | 13.5082i | −0.258109 | − | 0.447058i | ||||
\(914\) | −14.8304 | − | 58.1812i | −0.490545 | − | 1.92446i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.7365 | + | 27.4192i | −0.552991 | + | 0.905955i | ||||
\(917\) | 10.9269 | + | 8.47343i | 0.360838 | + | 0.279817i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.6213 | + | 18.3967i | −0.350365 | + | 0.606850i | −0.986313 | − | 0.164882i | \(-0.947276\pi\) |
0.635948 | + | 0.771732i | \(0.280609\pi\) | |||||||
\(920\) | −27.2031 | − | 8.36853i | −0.896858 | − | 0.275902i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −38.6392 | − | 39.5949i | −1.27251 | − | 1.30399i | ||||
\(923\) | 95.8978i | 3.15651i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.1259i | 0.464455i | ||||||||
\(926\) | −18.4343 | + | 17.9894i | −0.605789 | + | 0.591168i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −27.7045 | − | 31.3135i | −0.909446 | − | 1.02792i | ||||
\(929\) | 21.6464 | − | 37.4927i | 0.710196 | − | 1.23009i | −0.254588 | − | 0.967050i | \(-0.581940\pi\) |
0.964783 | − | 0.263045i | \(-0.0847269\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.21926 | − | 7.36813i | −0.236602 | − | 0.241481i | ||||
\(932\) | −21.3161 | − | 13.0112i | −0.698231 | − | 0.426197i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 46.1933 | − | 11.7746i | 1.51149 | − | 0.385278i | ||||
\(935\) | 4.51146 | + | 7.81407i | 0.147540 | + | 0.255548i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.1716 | −0.920325 | −0.460163 | − | 0.887835i | \(-0.652209\pi\) | ||||
−0.460163 | + | 0.887835i | \(0.652209\pi\) | |||||||
\(938\) | −17.2064 | + | 39.5867i | −0.561808 | + | 1.29255i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 28.9014 | + | 53.0083i | 0.942660 | + | 1.72894i | ||||
\(941\) | −8.66386 | + | 5.00208i | −0.282434 | + | 0.163063i | −0.634525 | − | 0.772903i | \(-0.718804\pi\) |
0.352091 | + | 0.935966i | \(0.385471\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.8284 | + | 25.6836i | −0.482880 | + | 0.836373i | ||||
\(944\) | 33.3356 | − | 17.1326i | 1.08498 | − | 0.557618i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.94113 | − | 2.23213i | −0.258188 | − | 0.0725728i | ||||
\(947\) | 41.0563 | + | 23.7038i | 1.33415 | + | 0.770271i | 0.985933 | − | 0.167143i | \(-0.0534541\pi\) |
0.348216 | + | 0.937414i | \(0.386787\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.9002 | − | 9.75735i | 0.548604 | − | 0.316737i | ||||
\(950\) | 2.66131 | + | 2.72713i | 0.0863441 | + | 0.0884797i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.02404 | + | 10.8274i | −0.162830 | + | 0.350917i | ||||
\(953\) | 49.6730 | 1.60907 | 0.804533 | − | 0.593908i | \(-0.202416\pi\) | ||||
0.804533 | + | 0.593908i | \(0.202416\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −40.5818 | + | 23.4299i | −1.31320 | + | 0.758174i | ||||
\(956\) | −0.220405 | + | 9.02022i | −0.00712839 | + | 0.291735i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 39.2426 | + | 11.0305i | 1.26787 | + | 0.356379i | ||||
\(959\) | −15.4031 | − | 37.7297i | −0.497391 | − | 1.21836i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.07107 | − | 15.7116i | 0.292615 | − | 0.506824i | ||||
\(962\) | 17.5547 | + | 68.8689i | 0.565985 | + | 2.22042i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.56916 | − | 3.03644i | 0.179371 | − | 0.0977971i | ||||
\(965\) | − | 26.9510i | − | 0.867584i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.58579 | −0.243942 | −0.121971 | − | 0.992534i | \(-0.538922\pi\) | ||||
−0.121971 | + | 0.992534i | \(0.538922\pi\) | |||||||
\(968\) | −17.4071 | + | 3.98690i | −0.559486 | + | 0.128144i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.96661 | + | 0.756187i | −0.0952521 | + | 0.0242797i | ||||
\(971\) | 7.65986 | + | 4.42242i | 0.245817 | + | 0.141922i | 0.617847 | − | 0.786298i | \(-0.288005\pi\) |
−0.372031 | + | 0.928220i | \(0.621338\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.63341 | + | 41.1658i | −0.180599 | + | 1.31971i | ||||
\(974\) | −13.9849 | − | 3.93095i | −0.448107 | − | 0.125956i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.0142 | + | 9.03131i | 0.448582 | + | 0.289085i | ||||
\(977\) | −10.8916 | − | 18.8648i | −0.348454 | − | 0.603540i | 0.637521 | − | 0.770433i | \(-0.279960\pi\) |
−0.985975 | + | 0.166893i | \(0.946627\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 16.6722i | − | 0.532845i | ||||||
\(980\) | 26.7489 | − | 24.9573i | 0.854462 | − | 0.797233i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.30021 | − | 7.48076i | −0.232959 | − | 0.238721i | ||||
\(983\) | −6.71051 | − | 11.6229i | −0.214032 | − | 0.370714i | 0.738941 | − | 0.673770i | \(-0.235326\pi\) |
−0.952973 | + | 0.303056i | \(0.901993\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.5563 | + | 44.2649i | −0.814293 | + | 1.41040i | ||||
\(986\) | −4.51146 | + | 16.0502i | −0.143674 | + | 0.511142i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 16.3640 | + | 9.98849i | 0.520607 | + | 0.317776i | ||||
\(989\) | −8.98552 | − | 5.18779i | −0.285723 | − | 0.164962i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.7635 | − | 44.6236i | −0.818403 | − | 1.41752i | −0.906858 | − | 0.421436i | \(-0.861526\pi\) |
0.0884551 | − | 0.996080i | \(-0.471807\pi\) | |||||||
\(992\) | 19.2361 | + | 6.43605i | 0.610748 | + | 0.204345i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 44.3371 | − | 32.8170i | 1.40629 | − | 1.04089i | ||||
\(995\) | 2.16478i | 0.0686283i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.30996 | + | 4.22041i | −0.231509 | + | 0.133662i | −0.611268 | − | 0.791424i | \(-0.709340\pi\) |
0.379759 | + | 0.925085i | \(0.376007\pi\) | |||||||
\(998\) | −13.4432 | + | 3.42666i | −0.425536 | + | 0.108469i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 504.2.cj.d.37.2 | ✓ | 16 | |
3.2 | odd | 2 | inner | 504.2.cj.d.37.7 | yes | 16 | |
4.3 | odd | 2 | 2016.2.cr.d.1297.7 | 16 | |||
7.4 | even | 3 | inner | 504.2.cj.d.109.3 | yes | 16 | |
8.3 | odd | 2 | 2016.2.cr.d.1297.2 | 16 | |||
8.5 | even | 2 | inner | 504.2.cj.d.37.3 | yes | 16 | |
12.11 | even | 2 | 2016.2.cr.d.1297.1 | 16 | |||
21.11 | odd | 6 | inner | 504.2.cj.d.109.6 | yes | 16 | |
24.5 | odd | 2 | inner | 504.2.cj.d.37.6 | yes | 16 | |
24.11 | even | 2 | 2016.2.cr.d.1297.8 | 16 | |||
28.11 | odd | 6 | 2016.2.cr.d.1873.1 | 16 | |||
56.11 | odd | 6 | 2016.2.cr.d.1873.8 | 16 | |||
56.53 | even | 6 | inner | 504.2.cj.d.109.2 | yes | 16 | |
84.11 | even | 6 | 2016.2.cr.d.1873.7 | 16 | |||
168.11 | even | 6 | 2016.2.cr.d.1873.2 | 16 | |||
168.53 | odd | 6 | inner | 504.2.cj.d.109.7 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.cj.d.37.2 | ✓ | 16 | 1.1 | even | 1 | trivial | |
504.2.cj.d.37.3 | yes | 16 | 8.5 | even | 2 | inner | |
504.2.cj.d.37.6 | yes | 16 | 24.5 | odd | 2 | inner | |
504.2.cj.d.37.7 | yes | 16 | 3.2 | odd | 2 | inner | |
504.2.cj.d.109.2 | yes | 16 | 56.53 | even | 6 | inner | |
504.2.cj.d.109.3 | yes | 16 | 7.4 | even | 3 | inner | |
504.2.cj.d.109.6 | yes | 16 | 21.11 | odd | 6 | inner | |
504.2.cj.d.109.7 | yes | 16 | 168.53 | odd | 6 | inner | |
2016.2.cr.d.1297.1 | 16 | 12.11 | even | 2 | |||
2016.2.cr.d.1297.2 | 16 | 8.3 | odd | 2 | |||
2016.2.cr.d.1297.7 | 16 | 4.3 | odd | 2 | |||
2016.2.cr.d.1297.8 | 16 | 24.11 | even | 2 | |||
2016.2.cr.d.1873.1 | 16 | 28.11 | odd | 6 | |||
2016.2.cr.d.1873.2 | 16 | 168.11 | even | 6 | |||
2016.2.cr.d.1873.7 | 16 | 84.11 | even | 6 | |||
2016.2.cr.d.1873.8 | 16 | 56.11 | odd | 6 |