Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(246,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.246");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.c (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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 11x^{6} + 36x^{4} + 31x^{2} + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 246.6 | ||
Root | \(1.07305i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.246 |
Dual form | 637.2.c.f.246.3 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.07305i | 0.758764i | 0.925240 | + | 0.379382i | \(0.123863\pi\) | ||||
−0.925240 | + | 0.379382i | \(0.876137\pi\) | |||||||
\(3\) | −2.43140 | −1.40377 | −0.701886 | − | 0.712289i | \(-0.747658\pi\) | ||||
−0.701886 | + | 0.712289i | \(0.747658\pi\) | |||||||
\(4\) | 0.848553 | 0.424277 | ||||||||
\(5\) | − | 0.625432i | − | 0.279702i | −0.990173 | − | 0.139851i | \(-0.955338\pi\) | ||
0.990173 | − | 0.139851i | \(-0.0446623\pi\) | |||||||
\(6\) | − | 2.60903i | − | 1.06513i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.05665i | 1.08069i | ||||||||
\(9\) | 2.91173 | 0.970576 | ||||||||
\(10\) | 0.671123 | 0.212228 | ||||||||
\(11\) | − | 0.708521i | − | 0.213627i | −0.994279 | − | 0.106814i | \(-0.965935\pi\) | ||
0.994279 | − | 0.106814i | \(-0.0340648\pi\) | |||||||
\(12\) | −2.06318 | −0.595588 | ||||||||
\(13\) | 0.848553 | − | 3.50428i | 0.235346 | − | 0.971912i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.52068i | 0.392637i | ||||||||
\(16\) | −1.58285 | −0.395713 | ||||||||
\(17\) | 3.34313 | 0.810829 | 0.405414 | − | 0.914133i | \(-0.367127\pi\) | ||||
0.405414 | + | 0.914133i | \(0.367127\pi\) | |||||||
\(18\) | 3.12445i | 0.736439i | ||||||||
\(19\) | 5.20276i | 1.19360i | 0.802392 | + | 0.596798i | \(0.203561\pi\) | ||||
−0.802392 | + | 0.596798i | \(0.796439\pi\) | |||||||
\(20\) | − | 0.530712i | − | 0.118671i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.760282 | 0.162093 | ||||||||
\(23\) | 4.43140 | 0.924012 | 0.462006 | − | 0.886877i | \(-0.347130\pi\) | ||||
0.462006 | + | 0.886877i | \(0.347130\pi\) | |||||||
\(24\) | − | 7.43196i | − | 1.51704i | ||||||
\(25\) | 4.60883 | 0.921767 | ||||||||
\(26\) | 3.76028 | + | 0.910544i | 0.737452 | + | 0.178572i | ||||
\(27\) | 0.214623 | 0.0413042 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.59711 | −1.22505 | −0.612526 | − | 0.790450i | \(-0.709847\pi\) | ||||
−0.612526 | + | 0.790450i | \(0.709847\pi\) | |||||||
\(30\) | −1.63177 | −0.297919 | ||||||||
\(31\) | 4.39061i | 0.788576i | 0.918987 | + | 0.394288i | \(0.129009\pi\) | ||||
−0.918987 | + | 0.394288i | \(0.870991\pi\) | |||||||
\(32\) | 4.41482i | 0.780437i | ||||||||
\(33\) | 1.72270i | 0.299884i | ||||||||
\(34\) | 3.58737i | 0.615228i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.47076 | 0.411793 | ||||||||
\(37\) | 0.423409i | 0.0696080i | 0.999394 | + | 0.0348040i | \(0.0110807\pi\) | ||||
−0.999394 | + | 0.0348040i | \(0.988919\pi\) | |||||||
\(38\) | −5.58285 | −0.905658 | ||||||||
\(39\) | −2.06318 | + | 8.52032i | −0.330373 | + | 1.36434i | ||||
\(40\) | 1.91173 | 0.302271 | ||||||||
\(41\) | 5.01604i | 0.783374i | 0.920099 | + | 0.391687i | \(0.128108\pi\) | ||||
−0.920099 | + | 0.391687i | \(0.871892\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.2059 | 1.70889 | 0.854445 | − | 0.519542i | \(-0.173897\pi\) | ||||
0.854445 | + | 0.519542i | \(0.173897\pi\) | |||||||
\(44\) | − | 0.601218i | − | 0.0906370i | ||||||
\(45\) | − | 1.82109i | − | 0.271472i | ||||||
\(46\) | 4.75514i | 0.701107i | ||||||||
\(47\) | 8.07269i | 1.17752i | 0.808307 | + | 0.588762i | \(0.200384\pi\) | ||||
−0.808307 | + | 0.588762i | \(0.799616\pi\) | |||||||
\(48\) | 3.84855 | 0.555491 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.94553i | 0.699404i | ||||||||
\(51\) | −8.12851 | −1.13822 | ||||||||
\(52\) | 0.720042 | − | 2.97356i | 0.0998519 | − | 0.412359i | ||||
\(53\) | −0.697106 | −0.0957549 | −0.0478774 | − | 0.998853i | \(-0.515246\pi\) | ||||
−0.0478774 | + | 0.998853i | \(0.515246\pi\) | |||||||
\(54\) | 0.230302i | 0.0313401i | ||||||||
\(55\) | −0.443132 | −0.0597519 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 12.6500i | − | 1.67554i | ||||||
\(58\) | − | 7.07906i | − | 0.929526i | ||||||
\(59\) | 9.86319i | 1.28408i | 0.766672 | + | 0.642039i | \(0.221911\pi\) | ||||
−0.766672 | + | 0.642039i | \(0.778089\pi\) | |||||||
\(60\) | 1.29038i | 0.166587i | ||||||||
\(61\) | 4.69711 | 0.601403 | 0.300701 | − | 0.953718i | \(-0.402779\pi\) | ||||
0.300701 | + | 0.953718i | \(0.402779\pi\) | |||||||
\(62\) | −4.71136 | −0.598344 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.90305 | −0.987881 | ||||||||
\(65\) | −2.19169 | − | 0.530712i | −0.271845 | − | 0.0658267i | ||||
\(66\) | −1.84855 | −0.227541 | ||||||||
\(67\) | − | 10.4208i | − | 1.27311i | −0.771233 | − | 0.636553i | \(-0.780360\pi\) | ||
0.771233 | − | 0.636553i | \(-0.219640\pi\) | |||||||
\(68\) | 2.83683 | 0.344016 | ||||||||
\(69\) | −10.7745 | −1.29710 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.0876i | 1.67189i | 0.548812 | + | 0.835946i | \(0.315080\pi\) | ||||
−0.548812 | + | 0.835946i | \(0.684920\pi\) | |||||||
\(72\) | 8.90015i | 1.04889i | ||||||||
\(73\) | − | 5.08383i | − | 0.595017i | −0.954719 | − | 0.297509i | \(-0.903844\pi\) | ||
0.954719 | − | 0.297509i | \(-0.0961557\pi\) | |||||||
\(74\) | −0.454341 | −0.0528161 | ||||||||
\(75\) | −11.2059 | −1.29395 | ||||||||
\(76\) | 4.41482i | 0.506415i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −9.14277 | − | 2.21390i | −1.03521 | − | 0.250675i | ||||
\(79\) | −3.91173 | −0.440104 | −0.220052 | − | 0.975488i | \(-0.570623\pi\) | ||||
−0.220052 | + | 0.975488i | \(0.570623\pi\) | |||||||
\(80\) | 0.989966i | 0.110682i | ||||||||
\(81\) | −9.25702 | −1.02856 | ||||||||
\(82\) | −5.38249 | −0.594396 | ||||||||
\(83\) | − | 10.2035i | − | 1.11998i | −0.828499 | − | 0.559990i | \(-0.810805\pi\) | ||
0.828499 | − | 0.559990i | \(-0.189195\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 2.09090i | − | 0.226790i | ||||||
\(86\) | 12.0246i | 1.29665i | ||||||||
\(87\) | 16.0402 | 1.71969 | ||||||||
\(88\) | 2.16570 | 0.230865 | ||||||||
\(89\) | − | 13.3791i | − | 1.41818i | −0.705117 | − | 0.709090i | \(-0.749106\pi\) | ||
0.705117 | − | 0.709090i | \(-0.250894\pi\) | |||||||
\(90\) | 1.95413 | 0.205983 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.76028 | 0.392036 | ||||||||
\(93\) | − | 10.6753i | − | 1.10698i | ||||||
\(94\) | −8.66244 | −0.893463 | ||||||||
\(95\) | 3.25397 | 0.333851 | ||||||||
\(96\) | − | 10.7342i | − | 1.09556i | ||||||
\(97\) | 0.202023i | 0.0205123i | 0.999947 | + | 0.0102562i | \(0.00326470\pi\) | ||||
−0.999947 | + | 0.0102562i | \(0.996735\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 2.06302i | − | 0.207341i | ||||||
\(100\) | 3.91084 | 0.391084 | ||||||||
\(101\) | 17.3345 | 1.72484 | 0.862421 | − | 0.506191i | \(-0.168947\pi\) | ||||
0.862421 | + | 0.506191i | \(0.168947\pi\) | |||||||
\(102\) | − | 8.72234i | − | 0.863640i | ||||||
\(103\) | 10.8148 | 1.06561 | 0.532806 | − | 0.846237i | \(-0.321138\pi\) | ||||
0.532806 | + | 0.846237i | \(0.321138\pi\) | |||||||
\(104\) | 10.7114 | + | 2.59373i | 1.05034 | + | 0.254336i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 0.748033i | − | 0.0726554i | ||||||
\(107\) | −6.11678 | −0.591332 | −0.295666 | − | 0.955291i | \(-0.595542\pi\) | ||||
−0.295666 | + | 0.955291i | \(0.595542\pi\) | |||||||
\(108\) | 0.182119 | 0.0175244 | ||||||||
\(109\) | − | 11.3992i | − | 1.09184i | −0.837837 | − | 0.545921i | \(-0.816180\pi\) | ||
0.837837 | − | 0.545921i | \(-0.183820\pi\) | |||||||
\(110\) | − | 0.475505i | − | 0.0453376i | ||||||
\(111\) | − | 1.02948i | − | 0.0977137i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.923456 | −0.0868714 | −0.0434357 | − | 0.999056i | \(-0.513830\pi\) | ||||
−0.0434357 | + | 0.999056i | \(0.513830\pi\) | |||||||
\(114\) | 13.5742 | 1.27134 | ||||||||
\(115\) | − | 2.77154i | − | 0.258448i | ||||||
\(116\) | −5.59800 | −0.519761 | ||||||||
\(117\) | 2.47076 | − | 10.2035i | 0.228422 | − | 0.943314i | ||||
\(118\) | −10.5837 | −0.974312 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −4.64819 | −0.424319 | ||||||||
\(121\) | 10.4980 | 0.954363 | ||||||||
\(122\) | 5.04025i | 0.456323i | ||||||||
\(123\) | − | 12.1960i | − | 1.09968i | ||||||
\(124\) | 3.72566i | 0.334574i | ||||||||
\(125\) | − | 6.00967i | − | 0.537521i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.50972 | 0.755116 | 0.377558 | − | 0.925986i | \(-0.376764\pi\) | ||||
0.377558 | + | 0.925986i | \(0.376764\pi\) | |||||||
\(128\) | 0.349236i | 0.0308684i | ||||||||
\(129\) | −27.2462 | −2.39889 | ||||||||
\(130\) | 0.569483 | − | 2.35180i | 0.0499470 | − | 0.206267i | ||||
\(131\) | −7.00305 | −0.611859 | −0.305930 | − | 0.952054i | \(-0.598967\pi\) | ||||
−0.305930 | + | 0.952054i | \(0.598967\pi\) | |||||||
\(132\) | 1.46180i | 0.127234i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 11.1821 | 0.965988 | ||||||||
\(135\) | − | 0.134232i | − | 0.0115528i | ||||||
\(136\) | 10.2188i | 0.876255i | ||||||||
\(137\) | − | 6.21694i | − | 0.531149i | −0.964090 | − | 0.265575i | \(-0.914438\pi\) | ||
0.964090 | − | 0.265575i | \(-0.0855617\pi\) | |||||||
\(138\) | − | 11.5617i | − | 0.984195i | ||||||
\(139\) | 6.53140 | 0.553986 | 0.276993 | − | 0.960872i | \(-0.410662\pi\) | ||||
0.276993 | + | 0.960872i | \(0.410662\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 19.6280i | − | 1.65297i | ||||||
\(142\) | −15.1168 | −1.26857 | ||||||||
\(143\) | −2.48285 | − | 0.601218i | −0.207627 | − | 0.0502763i | ||||
\(144\) | −4.60883 | −0.384070 | ||||||||
\(145\) | 4.12604i | 0.342649i | ||||||||
\(146\) | 5.45523 | 0.451478 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.359285i | 0.0295330i | ||||||||
\(149\) | 3.69738i | 0.302901i | 0.988465 | + | 0.151451i | \(0.0483945\pi\) | ||||
−0.988465 | + | 0.151451i | \(0.951606\pi\) | |||||||
\(150\) | − | 12.0246i | − | 0.981804i | ||||||
\(151\) | − | 4.87774i | − | 0.396945i | −0.980106 | − | 0.198473i | \(-0.936402\pi\) | ||
0.980106 | − | 0.198473i | \(-0.0635981\pi\) | |||||||
\(152\) | −15.9030 | −1.28991 | ||||||||
\(153\) | 9.73430 | 0.786971 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.74603 | 0.220566 | ||||||||
\(156\) | −1.75071 | + | 7.22994i | −0.140169 | + | 0.578858i | ||||
\(157\) | −9.51968 | −0.759753 | −0.379876 | − | 0.925037i | \(-0.624033\pi\) | ||||
−0.379876 | + | 0.925037i | \(0.624033\pi\) | |||||||
\(158\) | − | 4.19750i | − | 0.333935i | ||||||
\(159\) | 1.69495 | 0.134418 | ||||||||
\(160\) | 2.76117 | 0.218290 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 9.93329i | − | 0.780433i | ||||||
\(163\) | − | 23.7089i | − | 1.85702i | −0.371305 | − | 0.928511i | \(-0.621090\pi\) | ||
0.371305 | − | 0.928511i | \(-0.378910\pi\) | |||||||
\(164\) | 4.25637i | 0.332367i | ||||||||
\(165\) | 1.07743 | 0.0838780 | ||||||||
\(166\) | 10.9489 | 0.849801 | ||||||||
\(167\) | 1.13193i | 0.0875914i | 0.999041 | + | 0.0437957i | \(0.0139451\pi\) | ||||
−0.999041 | + | 0.0437957i | \(0.986055\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5599 | − | 5.94713i | −0.889224 | − | 0.457472i | ||||
\(170\) | 2.24365 | 0.172080 | ||||||||
\(171\) | 15.1490i | 1.15848i | ||||||||
\(172\) | 9.50884 | 0.725042 | ||||||||
\(173\) | −11.9892 | −0.911519 | −0.455760 | − | 0.890103i | \(-0.650632\pi\) | ||||
−0.455760 | + | 0.890103i | \(0.650632\pi\) | |||||||
\(174\) | 17.2121i | 1.30484i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.12148i | 0.0845350i | ||||||||
\(177\) | − | 23.9814i | − | 1.80255i | ||||||
\(178\) | 14.3565 | 1.07607 | ||||||||
\(179\) | −9.47076 | −0.707878 | −0.353939 | − | 0.935269i | \(-0.615158\pi\) | ||||
−0.353939 | + | 0.935269i | \(0.615158\pi\) | |||||||
\(180\) | − | 1.54529i | − | 0.115179i | ||||||
\(181\) | −11.4314 | −0.849690 | −0.424845 | − | 0.905266i | \(-0.639671\pi\) | ||||
−0.424845 | + | 0.905266i | \(0.639671\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.4206 | −0.844233 | ||||||||
\(184\) | 13.5453i | 0.998571i | ||||||||
\(185\) | 0.264813 | 0.0194695 | ||||||||
\(186\) | 11.4552 | 0.839938 | ||||||||
\(187\) | − | 2.36868i | − | 0.173215i | ||||||
\(188\) | 6.85011i | 0.499595i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.49169i | 0.253314i | ||||||||
\(191\) | 15.6875 | 1.13511 | 0.567555 | − | 0.823335i | \(-0.307889\pi\) | ||||
0.567555 | + | 0.823335i | \(0.307889\pi\) | |||||||
\(192\) | 19.2155 | 1.38676 | ||||||||
\(193\) | 23.0071i | 1.65609i | 0.560662 | + | 0.828045i | \(0.310547\pi\) | ||||
−0.560662 | + | 0.828045i | \(0.689453\pi\) | |||||||
\(194\) | −0.216782 | −0.0155640 | ||||||||
\(195\) | 5.32888 | + | 1.29038i | 0.381609 | + | 0.0924057i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.2035i | 0.726970i | 0.931600 | + | 0.363485i | \(0.118413\pi\) | ||||
−0.931600 | + | 0.363485i | \(0.881587\pi\) | |||||||
\(198\) | 2.21373 | 0.157323 | ||||||||
\(199\) | −11.9235 | −0.845231 | −0.422616 | − | 0.906309i | \(-0.638888\pi\) | ||||
−0.422616 | + | 0.906309i | \(0.638888\pi\) | |||||||
\(200\) | 14.0876i | 0.996145i | ||||||||
\(201\) | 25.3372i | 1.78715i | ||||||||
\(202\) | 18.6008i | 1.30875i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.89747 | −0.482920 | ||||||||
\(205\) | 3.13719 | 0.219111 | ||||||||
\(206\) | 11.6049i | 0.808548i | ||||||||
\(207\) | 12.9030 | 0.896824 | ||||||||
\(208\) | −1.34313 | + | 5.54675i | −0.0931296 | + | 0.384598i | ||||
\(209\) | 3.68627 | 0.254984 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.5893 | −1.07321 | −0.536606 | − | 0.843833i | \(-0.680294\pi\) | ||||
−0.536606 | + | 0.843833i | \(0.680294\pi\) | |||||||
\(212\) | −0.591531 | −0.0406265 | ||||||||
\(213\) | − | 34.2527i | − | 2.34696i | ||||||
\(214\) | − | 6.56365i | − | 0.448682i | ||||||
\(215\) | − | 7.00855i | − | 0.477979i | ||||||
\(216\) | 0.656028i | 0.0446370i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 12.2319 | 0.828451 | ||||||||
\(219\) | 12.3608i | 0.835269i | ||||||||
\(220\) | −0.376021 | −0.0253513 | ||||||||
\(221\) | 2.83683 | − | 11.7153i | 0.190826 | − | 0.788054i | ||||
\(222\) | 1.10469 | 0.0741417 | ||||||||
\(223\) | − | 6.76662i | − | 0.453126i | −0.973996 | − | 0.226563i | \(-0.927251\pi\) | ||
0.973996 | − | 0.226563i | \(-0.0727490\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.4197 | 0.894645 | ||||||||
\(226\) | − | 0.990919i | − | 0.0659149i | ||||||
\(227\) | 16.8245i | 1.11668i | 0.829612 | + | 0.558340i | \(0.188562\pi\) | ||||
−0.829612 | + | 0.558340i | \(0.811438\pi\) | |||||||
\(228\) | − | 10.7342i | − | 0.710891i | ||||||
\(229\) | − | 11.0257i | − | 0.728599i | −0.931282 | − | 0.364300i | \(-0.881308\pi\) | ||
0.931282 | − | 0.364300i | \(-0.118692\pi\) | |||||||
\(230\) | 2.97402 | 0.196101 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 20.1651i | − | 1.32390i | ||||||
\(233\) | −17.3549 | −1.13695 | −0.568477 | − | 0.822699i | \(-0.692467\pi\) | ||||
−0.568477 | + | 0.822699i | \(0.692467\pi\) | |||||||
\(234\) | 10.9489 | + | 2.65126i | 0.715753 | + | 0.173318i | ||||
\(235\) | 5.04892 | 0.329355 | ||||||||
\(236\) | 8.36944i | 0.544804i | ||||||||
\(237\) | 9.51100 | 0.617806 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.7223i | 1.27573i | 0.770148 | + | 0.637865i | \(0.220182\pi\) | ||||
−0.770148 | + | 0.637865i | \(0.779818\pi\) | |||||||
\(240\) | − | 2.40701i | − | 0.155372i | ||||||
\(241\) | − | 2.78413i | − | 0.179341i | −0.995971 | − | 0.0896706i | \(-0.971419\pi\) | ||
0.995971 | − | 0.0896706i | \(-0.0285814\pi\) | |||||||
\(242\) | 11.2649i | 0.724137i | ||||||||
\(243\) | 21.8637 | 1.40256 | ||||||||
\(244\) | 3.98574 | 0.255161 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 13.0870 | 0.834397 | ||||||||
\(247\) | 18.2319 | + | 4.41482i | 1.16007 | + | 0.280908i | ||||
\(248\) | −13.4206 | −0.852207 | ||||||||
\(249\) | 24.8088i | 1.57220i | ||||||||
\(250\) | 6.44871 | 0.407852 | ||||||||
\(251\) | −23.5608 | −1.48714 | −0.743572 | − | 0.668655i | \(-0.766870\pi\) | ||||
−0.743572 | + | 0.668655i | \(0.766870\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 3.13974i | − | 0.197394i | ||||||
\(254\) | 9.13140i | 0.572955i | ||||||||
\(255\) | 5.08383i | 0.318362i | ||||||||
\(256\) | −16.1808 | −1.01130 | ||||||||
\(257\) | 3.43229 | 0.214101 | 0.107050 | − | 0.994254i | \(-0.465859\pi\) | ||||
0.107050 | + | 0.994254i | \(0.465859\pi\) | |||||||
\(258\) | − | 29.2367i | − | 1.82019i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.85976 | − | 0.450337i | −0.115338 | − | 0.0279287i | ||||
\(261\) | −19.2090 | −1.18901 | ||||||||
\(262\) | − | 7.51465i | − | 0.464257i | ||||||
\(263\) | −21.4491 | −1.32261 | −0.661303 | − | 0.750119i | \(-0.729996\pi\) | ||||
−0.661303 | + | 0.750119i | \(0.729996\pi\) | |||||||
\(264\) | −5.26570 | −0.324082 | ||||||||
\(265\) | 0.435992i | 0.0267828i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 32.5300i | 1.99080i | ||||||||
\(268\) | − | 8.84262i | − | 0.540149i | ||||||
\(269\) | 14.6569 | 0.893645 | 0.446822 | − | 0.894623i | \(-0.352556\pi\) | ||||
0.446822 | + | 0.894623i | \(0.352556\pi\) | |||||||
\(270\) | 0.144038 | 0.00876589 | ||||||||
\(271\) | 2.04366i | 0.124143i | 0.998072 | + | 0.0620717i | \(0.0197707\pi\) | ||||
−0.998072 | + | 0.0620717i | \(0.980229\pi\) | |||||||
\(272\) | −5.29168 | −0.320856 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.67112 | 0.403017 | ||||||||
\(275\) | − | 3.26546i | − | 0.196914i | ||||||
\(276\) | −9.14277 | −0.550330 | ||||||||
\(277\) | 5.43356 | 0.326471 | 0.163236 | − | 0.986587i | \(-0.447807\pi\) | ||||
0.163236 | + | 0.986587i | \(0.447807\pi\) | |||||||
\(278\) | 7.00855i | 0.420345i | ||||||||
\(279\) | 12.7843i | 0.765373i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 20.2356i | − | 1.20715i | −0.797305 | − | 0.603577i | \(-0.793742\pi\) | ||
0.797305 | − | 0.603577i | \(-0.206258\pi\) | |||||||
\(282\) | 21.0619 | 1.25422 | ||||||||
\(283\) | −1.73519 | −0.103146 | −0.0515731 | − | 0.998669i | \(-0.516424\pi\) | ||||
−0.0515731 | + | 0.998669i | \(0.516424\pi\) | |||||||
\(284\) | 11.9541i | 0.709345i | ||||||||
\(285\) | −7.91173 | −0.468650 | ||||||||
\(286\) | 0.645140 | − | 2.66424i | 0.0381479 | − | 0.157540i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 12.8548i | 0.757474i | ||||||||
\(289\) | −5.82346 | −0.342556 | ||||||||
\(290\) | −4.42747 | −0.259990 | ||||||||
\(291\) | − | 0.491200i | − | 0.0287947i | ||||||
\(292\) | − | 4.31390i | − | 0.252452i | ||||||
\(293\) | − | 27.2441i | − | 1.59162i | −0.605547 | − | 0.795810i | \(-0.707046\pi\) | ||
0.605547 | − | 0.795810i | \(-0.292954\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.16875 | 0.359159 | ||||||||
\(296\) | −1.29421 | −0.0752247 | ||||||||
\(297\) | − | 0.152065i | − | 0.00882369i | ||||||
\(298\) | −3.96750 | −0.229831 | ||||||||
\(299\) | 3.76028 | − | 15.5289i | 0.217463 | − | 0.898058i | ||||
\(300\) | −9.50884 | −0.548993 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5.23409 | 0.301188 | ||||||||
\(303\) | −42.1471 | −2.42129 | ||||||||
\(304\) | − | 8.23520i | − | 0.472321i | ||||||
\(305\) | − | 2.93772i | − | 0.168213i | ||||||
\(306\) | 10.4454i | 0.597126i | ||||||||
\(307\) | − | 12.7138i | − | 0.725612i | −0.931865 | − | 0.362806i | \(-0.881819\pi\) | ||
0.931865 | − | 0.362806i | \(-0.118181\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −26.2951 | −1.49588 | ||||||||
\(310\) | 2.94664i | 0.167358i | ||||||||
\(311\) | −9.61879 | −0.545431 | −0.272716 | − | 0.962095i | \(-0.587922\pi\) | ||||
−0.272716 | + | 0.962095i | \(0.587922\pi\) | |||||||
\(312\) | −26.0437 | − | 6.30641i | −1.47443 | − | 0.357030i | ||||
\(313\) | −9.02547 | −0.510149 | −0.255075 | − | 0.966921i | \(-0.582100\pi\) | ||||
−0.255075 | + | 0.966921i | \(0.582100\pi\) | |||||||
\(314\) | − | 10.2151i | − | 0.576473i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.31931 | −0.186726 | ||||||||
\(317\) | 24.6262i | 1.38314i | 0.722307 | + | 0.691572i | \(0.243082\pi\) | ||||
−0.722307 | + | 0.691572i | \(0.756918\pi\) | |||||||
\(318\) | 1.81877i | 0.101992i | ||||||||
\(319\) | 4.67419i | 0.261704i | ||||||||
\(320\) | 4.94282i | 0.276312i | ||||||||
\(321\) | 14.8724 | 0.830095 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.3935i | 0.967802i | ||||||||
\(324\) | −7.85507 | −0.436393 | ||||||||
\(325\) | 3.91084 | − | 16.1506i | 0.216934 | − | 0.895876i | ||||
\(326\) | 25.4409 | 1.40904 | ||||||||
\(327\) | 27.7160i | 1.53270i | ||||||||
\(328\) | −15.3323 | −0.846584 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.15614i | 0.0636436i | ||||||||
\(331\) | 13.1718i | 0.723989i | 0.932180 | + | 0.361994i | \(0.117904\pi\) | ||||
−0.932180 | + | 0.361994i | \(0.882096\pi\) | |||||||
\(332\) | − | 8.65821i | − | 0.475181i | ||||||
\(333\) | 1.23285i | 0.0675599i | ||||||||
\(334\) | −1.21462 | −0.0664612 | ||||||||
\(335\) | −6.51752 | −0.356090 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.0307 | 0.927720 | 0.463860 | − | 0.885909i | \(-0.346464\pi\) | ||||
0.463860 | + | 0.885909i | \(0.346464\pi\) | |||||||
\(338\) | 6.38160 | − | 12.4044i | 0.347113 | − | 0.674712i | ||||
\(339\) | 2.24529 | 0.121948 | ||||||||
\(340\) | − | 1.77424i | − | 0.0962218i | ||||||
\(341\) | 3.11084 | 0.168461 | ||||||||
\(342\) | −16.2558 | −0.879010 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 34.2527i | 1.84678i | ||||||||
\(345\) | 6.73874i | 0.362802i | ||||||||
\(346\) | − | 12.8650i | − | 0.691628i | ||||||
\(347\) | 0.459917 | 0.0246897 | 0.0123448 | − | 0.999924i | \(-0.496070\pi\) | ||||
0.0123448 | + | 0.999924i | \(0.496070\pi\) | |||||||
\(348\) | 13.6110 | 0.729626 | ||||||||
\(349\) | 6.87822i | 0.368183i | 0.982909 | + | 0.184091i | \(0.0589342\pi\) | ||||
−0.982909 | + | 0.184091i | \(0.941066\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.182119 | − | 0.752098i | 0.00972078 | − | 0.0401440i | ||||
\(352\) | 3.12799 | 0.166723 | ||||||||
\(353\) | 1.53326i | 0.0816073i | 0.999167 | + | 0.0408036i | \(0.0129918\pi\) | ||||
−0.999167 | + | 0.0408036i | \(0.987008\pi\) | |||||||
\(354\) | 25.7334 | 1.36771 | ||||||||
\(355\) | 8.81084 | 0.467631 | ||||||||
\(356\) | − | 11.3529i | − | 0.601701i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 10.1626i | − | 0.537112i | ||||||
\(359\) | 27.2068i | 1.43592i | 0.696085 | + | 0.717959i | \(0.254923\pi\) | ||||
−0.696085 | + | 0.717959i | \(0.745077\pi\) | |||||||
\(360\) | 5.56644 | 0.293377 | ||||||||
\(361\) | −8.06875 | −0.424671 | ||||||||
\(362\) | − | 12.2665i | − | 0.644714i | ||||||
\(363\) | −25.5249 | −1.33971 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.17959 | −0.166427 | ||||||||
\(366\) | − | 12.2549i | − | 0.640574i | ||||||
\(367\) | 26.9814 | 1.40842 | 0.704208 | − | 0.709994i | \(-0.251302\pi\) | ||||
0.704208 | + | 0.709994i | \(0.251302\pi\) | |||||||
\(368\) | −7.01426 | −0.365643 | ||||||||
\(369\) | 14.6053i | 0.760324i | ||||||||
\(370\) | 0.284159i | 0.0147727i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 9.05859i | − | 0.469666i | ||||||
\(373\) | 3.97238 | 0.205682 | 0.102841 | − | 0.994698i | \(-0.467207\pi\) | ||||
0.102841 | + | 0.994698i | \(0.467207\pi\) | |||||||
\(374\) | 2.54172 | 0.131429 | ||||||||
\(375\) | 14.6119i | 0.754558i | ||||||||
\(376\) | −24.6754 | −1.27254 | ||||||||
\(377\) | −5.59800 | + | 23.1181i | −0.288311 | + | 1.19064i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 11.4059i | − | 0.585884i | −0.956130 | − | 0.292942i | \(-0.905366\pi\) | ||
0.956130 | − | 0.292942i | \(-0.0946343\pi\) | |||||||
\(380\) | 2.76117 | 0.141645 | ||||||||
\(381\) | −20.6906 | −1.06001 | ||||||||
\(382\) | 16.8336i | 0.861281i | ||||||||
\(383\) | − | 23.7920i | − | 1.21571i | −0.794047 | − | 0.607856i | \(-0.792030\pi\) | ||
0.794047 | − | 0.607856i | \(-0.207970\pi\) | |||||||
\(384\) | − | 0.849134i | − | 0.0433322i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −24.6879 | −1.25658 | ||||||||
\(387\) | 32.6287 | 1.65861 | ||||||||
\(388\) | 0.171427i | 0.00870290i | ||||||||
\(389\) | 28.4110 | 1.44049 | 0.720247 | − | 0.693717i | \(-0.244028\pi\) | ||||
0.720247 | + | 0.693717i | \(0.244028\pi\) | |||||||
\(390\) | −1.38464 | + | 5.71818i | −0.0701142 | + | 0.289551i | ||||
\(391\) | 14.8148 | 0.749216 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.0272 | 0.858911 | ||||||||
\(394\) | −10.9489 | −0.551599 | ||||||||
\(395\) | 2.44652i | 0.123098i | ||||||||
\(396\) | − | 1.75058i | − | 0.0879701i | ||||||
\(397\) | 9.85912i | 0.494815i | 0.968912 | + | 0.247408i | \(0.0795786\pi\) | ||||
−0.968912 | + | 0.247408i | \(0.920421\pi\) | |||||||
\(398\) | − | 12.7945i | − | 0.641332i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.29510 | −0.364755 | ||||||||
\(401\) | − | 12.6194i | − | 0.630184i | −0.949061 | − | 0.315092i | \(-0.897965\pi\) | ||
0.949061 | − | 0.315092i | \(-0.102035\pi\) | |||||||
\(402\) | −27.1883 | −1.35603 | ||||||||
\(403\) | 15.3859 | + | 3.72566i | 0.766426 | + | 0.185588i | ||||
\(404\) | 14.7092 | 0.731810 | ||||||||
\(405\) | 5.78964i | 0.287689i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.299994 | 0.0148701 | ||||||||
\(408\) | − | 24.8460i | − | 1.23006i | ||||||
\(409\) | − | 18.0573i | − | 0.892878i | −0.894814 | − | 0.446439i | \(-0.852692\pi\) | ||
0.894814 | − | 0.446439i | \(-0.147308\pi\) | |||||||
\(410\) | 3.36638i | 0.166254i | ||||||||
\(411\) | 15.1159i | 0.745613i | ||||||||
\(412\) | 9.17691 | 0.452114 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 13.8457i | 0.680478i | ||||||||
\(415\) | −6.38160 | −0.313260 | ||||||||
\(416\) | 15.4708 | + | 3.74621i | 0.758516 | + | 0.183673i | ||||
\(417\) | −15.8805 | −0.777671 | ||||||||
\(418\) | 3.95557i | 0.193473i | ||||||||
\(419\) | 14.2805 | 0.697647 | 0.348823 | − | 0.937188i | \(-0.386581\pi\) | ||||
0.348823 | + | 0.937188i | \(0.386581\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.27439i | 0.208321i | 0.994561 | + | 0.104160i | \(0.0332155\pi\) | ||||
−0.994561 | + | 0.104160i | \(0.966784\pi\) | |||||||
\(422\) | − | 16.7282i | − | 0.814316i | ||||||
\(423\) | 23.5055i | 1.14288i | ||||||||
\(424\) | − | 2.13081i | − | 0.103481i | ||||||
\(425\) | 15.4080 | 0.747395 | ||||||||
\(426\) | 36.7550 | 1.78079 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5.19042 | −0.250888 | ||||||||
\(429\) | 6.03682 | + | 1.46180i | 0.291461 | + | 0.0705765i | ||||
\(430\) | 7.52056 | 0.362674 | ||||||||
\(431\) | 14.6067i | 0.703580i | 0.936079 | + | 0.351790i | \(0.114427\pi\) | ||||
−0.936079 | + | 0.351790i | \(0.885573\pi\) | |||||||
\(432\) | −0.339716 | −0.0163446 | ||||||||
\(433\) | 28.0099 | 1.34607 | 0.673035 | − | 0.739611i | \(-0.264991\pi\) | ||||
0.673035 | + | 0.739611i | \(0.264991\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 10.0321i | − | 0.481001i | ||||||
\(436\) | − | 9.67279i | − | 0.463243i | ||||||
\(437\) | 23.0556i | 1.10290i | ||||||||
\(438\) | −13.2639 | −0.633772 | ||||||||
\(439\) | −17.0774 | −0.815061 | −0.407531 | − | 0.913192i | \(-0.633610\pi\) | ||||
−0.407531 | + | 0.913192i | \(0.633610\pi\) | |||||||
\(440\) | − | 1.35450i | − | 0.0645733i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.5711 | + | 3.04407i | 0.597947 | + | 0.144792i | ||||
\(443\) | 13.8157 | 0.656402 | 0.328201 | − | 0.944608i | \(-0.393558\pi\) | ||||
0.328201 | + | 0.944608i | \(0.393558\pi\) | |||||||
\(444\) | − | 0.873567i | − | 0.0414576i | ||||||
\(445\) | −8.36771 | −0.396668 | ||||||||
\(446\) | 7.26096 | 0.343816 | ||||||||
\(447\) | − | 8.98984i | − | 0.425205i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 32.6410i | − | 1.54042i | −0.637789 | − | 0.770211i | \(-0.720151\pi\) | ||
0.637789 | − | 0.770211i | \(-0.279849\pi\) | |||||||
\(450\) | 14.4001i | 0.678825i | ||||||||
\(451\) | 3.55397 | 0.167350 | ||||||||
\(452\) | −0.783601 | −0.0368575 | ||||||||
\(453\) | 11.8598i | 0.557220i | ||||||||
\(454\) | −18.0536 | −0.847298 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 38.6667 | 1.81074 | ||||||||
\(457\) | − | 3.17034i | − | 0.148302i | −0.997247 | − | 0.0741511i | \(-0.976375\pi\) | ||
0.997247 | − | 0.0741511i | \(-0.0236247\pi\) | |||||||
\(458\) | 11.8312 | 0.552835 | ||||||||
\(459\) | 0.717513 | 0.0334906 | ||||||||
\(460\) | − | 2.35180i | − | 0.109653i | ||||||
\(461\) | − | 0.202023i | − | 0.00940915i | −0.999989 | − | 0.00470458i | \(-0.998502\pi\) | ||
0.999989 | − | 0.00470458i | \(-0.00149752\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.2121i | 0.799912i | 0.916534 | + | 0.399956i | \(0.130975\pi\) | ||||
−0.916534 | + | 0.399956i | \(0.869025\pi\) | |||||||
\(464\) | 10.4422 | 0.484769 | ||||||||
\(465\) | −6.67670 | −0.309625 | ||||||||
\(466\) | − | 18.6227i | − | 0.862681i | ||||||
\(467\) | 0.191169 | 0.00884625 | 0.00442312 | − | 0.999990i | \(-0.498592\pi\) | ||||
0.00442312 | + | 0.999990i | \(0.498592\pi\) | |||||||
\(468\) | 2.09657 | − | 8.65821i | 0.0969139 | − | 0.400226i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5.41777i | 0.249903i | ||||||||
\(471\) | 23.1462 | 1.06652 | ||||||||
\(472\) | −30.1483 | −1.38769 | ||||||||
\(473\) | − | 7.93965i | − | 0.365065i | ||||||
\(474\) | 10.2058i | 0.468769i | ||||||||
\(475\) | 23.9787i | 1.10022i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.02978 | −0.0929374 | ||||||||
\(478\) | −21.1631 | −0.967978 | ||||||||
\(479\) | − | 21.4785i | − | 0.981377i | −0.871335 | − | 0.490688i | \(-0.836745\pi\) | ||
0.871335 | − | 0.490688i | \(-0.163255\pi\) | |||||||
\(480\) | −6.71352 | −0.306429 | ||||||||
\(481\) | 1.48374 | + | 0.359285i | 0.0676528 | + | 0.0163820i | ||||
\(482\) | 2.98752 | 0.136078 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.90811 | 0.404914 | ||||||||
\(485\) | 0.126352 | 0.00573733 | ||||||||
\(486\) | 23.4609i | 1.06421i | ||||||||
\(487\) | 19.0484i | 0.863167i | 0.902073 | + | 0.431584i | \(0.142045\pi\) | ||||
−0.902073 | + | 0.431584i | \(0.857955\pi\) | |||||||
\(488\) | 14.3574i | 0.649930i | ||||||||
\(489\) | 57.6458i | 2.60684i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −35.7559 | −1.61364 | −0.806821 | − | 0.590796i | \(-0.798814\pi\) | ||||
−0.806821 | + | 0.590796i | \(0.798814\pi\) | |||||||
\(492\) | − | 10.3490i | − | 0.466568i | ||||||
\(493\) | −22.0550 | −0.993308 | ||||||||
\(494\) | −4.73735 | + | 19.5639i | −0.213143 | + | 0.880220i | ||||
\(495\) | −1.29028 | −0.0579937 | ||||||||
\(496\) | − | 6.94968i | − | 0.312050i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −26.6213 | −1.19293 | ||||||||
\(499\) | 17.6891i | 0.791875i | 0.918277 | + | 0.395937i | \(0.129580\pi\) | ||||
−0.918277 | + | 0.395937i | \(0.870420\pi\) | |||||||
\(500\) | − | 5.09953i | − | 0.228058i | ||||||
\(501\) | − | 2.75218i | − | 0.122958i | ||||||
\(502\) | − | 25.2820i | − | 1.12839i | ||||||
\(503\) | 11.3305 | 0.505203 | 0.252601 | − | 0.967570i | \(-0.418714\pi\) | ||||
0.252601 | + | 0.967570i | \(0.418714\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 10.8415i | − | 0.482441i | ||||||
\(506\) | 3.36912 | 0.149776 | ||||||||
\(507\) | 28.1068 | + | 14.4599i | 1.24827 | + | 0.642186i | ||||
\(508\) | 7.22095 | 0.320378 | ||||||||
\(509\) | − | 19.3514i | − | 0.857735i | −0.903367 | − | 0.428868i | \(-0.858913\pi\) | ||
0.903367 | − | 0.428868i | \(-0.141087\pi\) | |||||||
\(510\) | −5.45523 | −0.241562 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 16.6645i | − | 0.736472i | ||||||
\(513\) | 1.11663i | 0.0493005i | ||||||||
\(514\) | 3.68304i | 0.162452i | ||||||||
\(515\) | − | 6.76391i | − | 0.298053i | ||||||
\(516\) | −23.1198 | −1.01779 | ||||||||
\(517\) | 5.71967 | 0.251551 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 29.1505 | 1.27957 | ||||||||
\(520\) | 1.62220 | − | 6.69923i | 0.0711383 | − | 0.293781i | ||||
\(521\) | −7.71099 | −0.337825 | −0.168912 | − | 0.985631i | \(-0.554025\pi\) | ||||
−0.168912 | + | 0.985631i | \(0.554025\pi\) | |||||||
\(522\) | − | 20.6123i | − | 0.902176i | ||||||
\(523\) | −35.0501 | −1.53263 | −0.766317 | − | 0.642462i | \(-0.777913\pi\) | ||||
−0.766317 | + | 0.642462i | \(0.777913\pi\) | |||||||
\(524\) | −5.94246 | −0.259597 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 23.0160i | − | 1.00355i | ||||||
\(527\) | 14.6784i | 0.639401i | ||||||||
\(528\) | − | 2.72678i | − | 0.118668i | ||||||
\(529\) | −3.36265 | −0.146202 | ||||||||
\(530\) | −0.467844 | −0.0203218 | ||||||||
\(531\) | 28.7189i | 1.24630i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.5776 | + | 4.25637i | 0.761370 | + | 0.184364i | ||||
\(534\) | −34.9065 | −1.51055 | ||||||||
\(535\) | 3.82563i | 0.165396i | ||||||||
\(536\) | 31.8529 | 1.37583 | ||||||||
\(537\) | 23.0272 | 0.993699 | ||||||||
\(538\) | 15.7276i | 0.678066i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | − | 0.113903i | − | 0.00490160i | ||||||
\(541\) | − | 12.1335i | − | 0.521659i | −0.965385 | − | 0.260829i | \(-0.916004\pi\) | ||
0.965385 | − | 0.260829i | \(-0.0839960\pi\) | |||||||
\(542\) | −2.19296 | −0.0941956 | ||||||||
\(543\) | 27.7944 | 1.19277 | ||||||||
\(544\) | 14.7593i | 0.632801i | ||||||||
\(545\) | −7.12940 | −0.305390 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.12546 | −0.219149 | −0.109575 | − | 0.993979i | \(-0.534949\pi\) | ||||
−0.109575 | + | 0.993979i | \(0.534949\pi\) | |||||||
\(548\) | − | 5.27541i | − | 0.225354i | ||||||
\(549\) | 13.6767 | 0.583707 | ||||||||
\(550\) | 3.50401 | 0.149412 | ||||||||
\(551\) | − | 34.3232i | − | 1.46222i | ||||||
\(552\) | − | 32.9340i | − | 1.40177i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 5.83051i | 0.247715i | ||||||||
\(555\) | −0.643868 | −0.0273307 | ||||||||
\(556\) | 5.54224 | 0.235043 | ||||||||
\(557\) | − | 37.5586i | − | 1.59141i | −0.605685 | − | 0.795705i | \(-0.707101\pi\) | ||
0.605685 | − | 0.795705i | \(-0.292899\pi\) | |||||||
\(558\) | −13.7182 | −0.580738 | ||||||||
\(559\) | 9.50884 | − | 39.2687i | 0.402181 | − | 1.66089i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.75922i | 0.243154i | ||||||||
\(562\) | 21.7139 | 0.915945 | ||||||||
\(563\) | −28.7009 | −1.20960 | −0.604799 | − | 0.796378i | \(-0.706747\pi\) | ||||
−0.604799 | + | 0.796378i | \(0.706747\pi\) | |||||||
\(564\) | − | 16.6554i | − | 0.701318i | ||||||
\(565\) | 0.577559i | 0.0242981i | ||||||||
\(566\) | − | 1.86195i | − | 0.0782636i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −43.0610 | −1.80680 | ||||||||
\(569\) | −17.9483 | −0.752434 | −0.376217 | − | 0.926532i | \(-0.622775\pi\) | ||||
−0.376217 | + | 0.926532i | \(0.622775\pi\) | |||||||
\(570\) | − | 8.48972i | − | 0.355595i | ||||||
\(571\) | −17.8274 | −0.746053 | −0.373027 | − | 0.927821i | \(-0.621680\pi\) | ||||
−0.373027 | + | 0.927821i | \(0.621680\pi\) | |||||||
\(572\) | −2.10683 | − | 0.510165i | −0.0880911 | − | 0.0213311i | ||||
\(573\) | −38.1428 | −1.59344 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.4236 | 0.851724 | ||||||||
\(576\) | −23.0115 | −0.958814 | ||||||||
\(577\) | 33.0570i | 1.37618i | 0.725624 | + | 0.688091i | \(0.241551\pi\) | ||||
−0.725624 | + | 0.688091i | \(0.758449\pi\) | |||||||
\(578\) | − | 6.24889i | − | 0.259920i | ||||||
\(579\) | − | 55.9396i | − | 2.32477i | ||||||
\(580\) | 3.50117i | 0.145378i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.527085 | 0.0218484 | ||||||||
\(583\) | 0.493914i | 0.0204558i | ||||||||
\(584\) | 15.5395 | 0.643029 | ||||||||
\(585\) | −6.38160 | − | 1.54529i | −0.263847 | − | 0.0638899i | ||||
\(586\) | 29.2345 | 1.20766 | ||||||||
\(587\) | 14.7295i | 0.607953i | 0.952680 | + | 0.303976i | \(0.0983144\pi\) | ||||
−0.952680 | + | 0.303976i | \(0.901686\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.8433 | −0.941241 | ||||||||
\(590\) | 6.61941i | 0.272517i | ||||||||
\(591\) | − | 24.8088i | − | 1.02050i | ||||||
\(592\) | − | 0.670193i | − | 0.0275448i | ||||||
\(593\) | 9.20987i | 0.378204i | 0.981957 | + | 0.189102i | \(0.0605577\pi\) | ||||
−0.981957 | + | 0.189102i | \(0.939442\pi\) | |||||||
\(594\) | 0.163174 | 0.00669510 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.13743i | 0.128514i | ||||||||
\(597\) | 28.9907 | 1.18651 | ||||||||
\(598\) | 16.6633 | + | 4.03499i | 0.681414 | + | 0.165003i | ||||
\(599\) | −10.5745 | −0.432064 | −0.216032 | − | 0.976386i | \(-0.569312\pi\) | ||||
−0.216032 | + | 0.976386i | \(0.569312\pi\) | |||||||
\(600\) | − | 34.2527i | − | 1.39836i | ||||||
\(601\) | 4.08916 | 0.166800 | 0.0834001 | − | 0.996516i | \(-0.473422\pi\) | ||||
0.0834001 | + | 0.996516i | \(0.473422\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 30.3426i | − | 1.23565i | ||||||
\(604\) | − | 4.13902i | − | 0.168414i | ||||||
\(605\) | − | 6.56578i | − | 0.266937i | ||||||
\(606\) | − | 45.2261i | − | 1.83719i | ||||||
\(607\) | 3.60706 | 0.146406 | 0.0732030 | − | 0.997317i | \(-0.476678\pi\) | ||||
0.0732030 | + | 0.997317i | \(0.476678\pi\) | |||||||
\(608\) | −22.9693 | −0.931527 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.15233 | 0.127634 | ||||||||
\(611\) | 28.2890 | + | 6.85011i | 1.14445 | + | 0.277126i | ||||
\(612\) | 8.26007 | 0.333893 | ||||||||
\(613\) | − | 38.4845i | − | 1.55437i | −0.629271 | − | 0.777186i | \(-0.716646\pi\) | ||
0.629271 | − | 0.777186i | \(-0.283354\pi\) | |||||||
\(614\) | 13.6426 | 0.550569 | ||||||||
\(615\) | −7.62778 | −0.307582 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 3.09503i | − | 0.124601i | −0.998057 | − | 0.0623007i | \(-0.980156\pi\) | ||
0.998057 | − | 0.0623007i | \(-0.0198438\pi\) | |||||||
\(618\) | − | 28.2161i | − | 1.13502i | ||||||
\(619\) | − | 12.2692i | − | 0.493142i | −0.969125 | − | 0.246571i | \(-0.920696\pi\) | ||
0.969125 | − | 0.246571i | \(-0.0793039\pi\) | |||||||
\(620\) | 2.33015 | 0.0935810 | ||||||||
\(621\) | 0.951081 | 0.0381655 | ||||||||
\(622\) | − | 10.3215i | − | 0.413854i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3.26570 | − | 13.4864i | 0.130733 | − | 0.539888i | ||||
\(625\) | 19.2855 | 0.771421 | ||||||||
\(626\) | − | 9.68482i | − | 0.387083i | ||||||
\(627\) | −8.96281 | −0.357940 | ||||||||
\(628\) | −8.07795 | −0.322345 | ||||||||
\(629\) | 1.41551i | 0.0564402i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.31780i | 0.211698i | 0.994382 | + | 0.105849i | \(0.0337561\pi\) | ||||
−0.994382 | + | 0.105849i | \(0.966244\pi\) | |||||||
\(632\) | − | 11.9568i | − | 0.475616i | ||||||
\(633\) | 37.9039 | 1.50655 | ||||||||
\(634\) | −26.4253 | −1.04948 | ||||||||
\(635\) | − | 5.32225i | − | 0.211207i | ||||||
\(636\) | 1.43825 | 0.0570304 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.01566 | −0.198572 | ||||||||
\(639\) | 41.0193i | 1.62270i | ||||||||
\(640\) | 0.218423 | 0.00863394 | ||||||||
\(641\) | −12.1904 | −0.481493 | −0.240746 | − | 0.970588i | \(-0.577392\pi\) | ||||
−0.240746 | + | 0.970588i | \(0.577392\pi\) | |||||||
\(642\) | 15.9589i | 0.629847i | ||||||||
\(643\) | − | 18.9733i | − | 0.748235i | −0.927381 | − | 0.374117i | \(-0.877946\pi\) | ||
0.927381 | − | 0.374117i | \(-0.122054\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.0406i | 0.670974i | ||||||||
\(646\) | −18.6642 | −0.734334 | ||||||||
\(647\) | −19.7117 | −0.774948 | −0.387474 | − | 0.921881i | \(-0.626652\pi\) | ||||
−0.387474 | + | 0.921881i | \(0.626652\pi\) | |||||||
\(648\) | − | 28.2955i | − | 1.11155i | ||||||
\(649\) | 6.98827 | 0.274314 | ||||||||
\(650\) | 17.3305 | + | 4.19655i | 0.679759 | + | 0.164602i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 20.1182i | − | 0.787891i | ||||||
\(653\) | −20.3973 | −0.798206 | −0.399103 | − | 0.916906i | \(-0.630678\pi\) | ||||
−0.399103 | + | 0.916906i | \(0.630678\pi\) | |||||||
\(654\) | −29.7408 | −1.16296 | ||||||||
\(655\) | 4.37993i | 0.171138i | ||||||||
\(656\) | − | 7.93965i | − | 0.309991i | ||||||
\(657\) | − | 14.8027i | − | 0.577510i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.6628 | 1.27236 | 0.636181 | − | 0.771540i | \(-0.280513\pi\) | ||||
0.636181 | + | 0.771540i | \(0.280513\pi\) | |||||||
\(660\) | 0.914258 | 0.0355875 | ||||||||
\(661\) | 9.73692i | 0.378722i | 0.981908 | + | 0.189361i | \(0.0606417\pi\) | ||||
−0.981908 | + | 0.189361i | \(0.939358\pi\) | |||||||
\(662\) | −14.1341 | −0.549337 | ||||||||
\(663\) | −6.89747 | + | 28.4846i | −0.267876 | + | 1.10625i | ||||
\(664\) | 31.1886 | 1.21035 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.32292 | −0.0512620 | ||||||||
\(667\) | −29.2345 | −1.13196 | ||||||||
\(668\) | 0.960502i | 0.0371630i | ||||||||
\(669\) | 16.4524i | 0.636086i | ||||||||
\(670\) | − | 6.99365i | − | 0.270188i | ||||||
\(671\) | − | 3.32800i | − | 0.128476i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.4512 | −1.52073 | −0.760367 | − | 0.649494i | \(-0.774981\pi\) | ||||
−0.760367 | + | 0.649494i | \(0.774981\pi\) | |||||||
\(674\) | 18.2748i | 0.703921i | ||||||||
\(675\) | 0.989161 | 0.0380728 | ||||||||
\(676\) | −9.80920 | − | 5.04646i | −0.377277 | − | 0.194094i | ||||
\(677\) | −48.6339 | −1.86915 | −0.934576 | − | 0.355764i | \(-0.884221\pi\) | ||||
−0.934576 | + | 0.355764i | \(0.884221\pi\) | |||||||
\(678\) | 2.40932i | 0.0925296i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.39117 | 0.245090 | ||||||||
\(681\) | − | 40.9072i | − | 1.56757i | ||||||
\(682\) | 3.33810i | 0.127822i | ||||||||
\(683\) | − | 5.70773i | − | 0.218400i | −0.994020 | − | 0.109200i | \(-0.965171\pi\) | ||
0.994020 | − | 0.109200i | \(-0.0348289\pi\) | |||||||
\(684\) | 12.8548i | 0.491514i | ||||||||
\(685\) | −3.88828 | −0.148563 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.8080i | 1.02279i | ||||||||
\(688\) | −17.7373 | −0.676230 | ||||||||
\(689\) | −0.591531 | + | 2.44285i | −0.0225356 | + | 0.0930653i | ||||
\(690\) | −7.23104 | −0.275281 | ||||||||
\(691\) | − | 41.7732i | − | 1.58913i | −0.607182 | − | 0.794563i | \(-0.707700\pi\) | ||
0.607182 | − | 0.794563i | \(-0.292300\pi\) | |||||||
\(692\) | −10.1734 | −0.386736 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.493517i | 0.0187336i | ||||||||
\(695\) | − | 4.08495i | − | 0.154951i | ||||||
\(696\) | 49.0295i | 1.85846i | ||||||||
\(697\) | 16.7693i | 0.635182i | ||||||||
\(698\) | −7.38071 | −0.279364 | ||||||||
\(699\) | 42.1967 | 1.59603 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.4361 | 0.847399 | 0.423700 | − | 0.905803i | \(-0.360731\pi\) | ||||
0.423700 | + | 0.905803i | \(0.360731\pi\) | |||||||
\(702\) | 0.807042 | + | 0.195424i | 0.0304598 | + | 0.00737579i | ||||
\(703\) | −2.20290 | −0.0830838 | ||||||||
\(704\) | 5.59948i | 0.211038i | ||||||||
\(705\) | −12.2760 | −0.462340 | ||||||||
\(706\) | −1.64527 | −0.0619207 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 20.3495i | − | 0.764780i | ||||||
\(709\) | 28.7468i | 1.07961i | 0.841790 | + | 0.539804i | \(0.181502\pi\) | ||||
−0.841790 | + | 0.539804i | \(0.818498\pi\) | |||||||
\(710\) | 9.45452i | 0.354822i | ||||||||
\(711\) | −11.3899 | −0.427154 | ||||||||
\(712\) | 40.8953 | 1.53261 | ||||||||
\(713\) | 19.4566i | 0.728654i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.376021 | + | 1.55286i | −0.0140624 | + | 0.0580735i | ||||
\(716\) | −8.03644 | −0.300336 | ||||||||
\(717\) | − | 47.9529i | − | 1.79083i | ||||||
\(718\) | −29.1944 | −1.08952 | ||||||||
\(719\) | 4.20899 | 0.156969 | 0.0784844 | − | 0.996915i | \(-0.474992\pi\) | ||||
0.0784844 | + | 0.996915i | \(0.474992\pi\) | |||||||
\(720\) | 2.88251i | 0.107425i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 8.65821i | − | 0.322225i | ||||||
\(723\) | 6.76934i | 0.251754i | ||||||||
\(724\) | −9.70015 | −0.360503 | ||||||||
\(725\) | −30.4050 | −1.12921 | ||||||||
\(726\) | − | 27.3896i | − | 1.01652i | ||||||
\(727\) | −43.4680 | −1.61214 | −0.806070 | − | 0.591820i | \(-0.798409\pi\) | ||||
−0.806070 | + | 0.591820i | \(0.798409\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.3884 | −0.940312 | ||||||||
\(730\) | − | 3.41187i | − | 0.126279i | ||||||
\(731\) | 37.4630 | 1.38562 | ||||||||
\(732\) | −9.69096 | −0.358188 | ||||||||
\(733\) | − | 9.09421i | − | 0.335902i | −0.985795 | − | 0.167951i | \(-0.946285\pi\) | ||
0.985795 | − | 0.167951i | \(-0.0537151\pi\) | |||||||
\(734\) | 28.9525i | 1.06866i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 19.5639i | 0.721133i | ||||||||
\(737\) | −7.38337 | −0.271970 | ||||||||
\(738\) | −15.6723 | −0.576907 | ||||||||
\(739\) | 9.60867i | 0.353461i | 0.984259 | + | 0.176730i | \(0.0565520\pi\) | ||||
−0.984259 | + | 0.176730i | \(0.943448\pi\) | |||||||
\(740\) | 0.224708 | 0.00826044 | ||||||||
\(741\) | −44.3292 | − | 10.7342i | −1.62847 | − | 0.394331i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 32.1771i | − | 1.18046i | −0.807234 | − | 0.590231i | \(-0.799036\pi\) | ||
0.807234 | − | 0.590231i | \(-0.200964\pi\) | |||||||
\(744\) | 32.6308 | 1.19630 | ||||||||
\(745\) | 2.31246 | 0.0847220 | ||||||||
\(746\) | 4.26258i | 0.156064i | ||||||||
\(747\) | − | 29.7098i | − | 1.08703i | ||||||
\(748\) | − | 2.00995i | − | 0.0734911i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −15.6794 | −0.572531 | ||||||||
\(751\) | −7.79784 | −0.284547 | −0.142274 | − | 0.989827i | \(-0.545441\pi\) | ||||
−0.142274 | + | 0.989827i | \(0.545441\pi\) | |||||||
\(752\) | − | 12.7779i | − | 0.465961i | ||||||
\(753\) | 57.2858 | 2.08761 | ||||||||
\(754\) | −24.8070 | − | 6.00696i | −0.903417 | − | 0.218760i | ||||
\(755\) | −3.05070 | −0.111026 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.9970 | 0.654110 | 0.327055 | − | 0.945005i | \(-0.393944\pi\) | ||||
0.327055 | + | 0.945005i | \(0.393944\pi\) | |||||||
\(758\) | 12.2392 | 0.444548 | ||||||||
\(759\) | 7.63399i | 0.277096i | ||||||||
\(760\) | 9.94627i | 0.360789i | ||||||||
\(761\) | 40.6790i | 1.47461i | 0.675559 | + | 0.737306i | \(0.263902\pi\) | ||||
−0.675559 | + | 0.737306i | \(0.736098\pi\) | |||||||
\(762\) | − | 22.2021i | − | 0.804299i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 13.3117 | 0.481601 | ||||||||
\(765\) | − | 6.08814i | − | 0.220117i | ||||||
\(766\) | 25.5301 | 0.922439 | ||||||||
\(767\) | 34.5633 | + | 8.36944i | 1.24801 | + | 0.302203i | ||||
\(768\) | 39.3422 | 1.41964 | ||||||||
\(769\) | 39.3098i | 1.41755i | 0.705435 | + | 0.708774i | \(0.250752\pi\) | ||||
−0.705435 | + | 0.708774i | \(0.749248\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.34529 | −0.300548 | ||||||||
\(772\) | 19.5228i | 0.702640i | ||||||||
\(773\) | 13.4736i | 0.484611i | 0.970200 | + | 0.242306i | \(0.0779036\pi\) | ||||
−0.970200 | + | 0.242306i | \(0.922096\pi\) | |||||||
\(774\) | 35.0124i | 1.25849i | ||||||||
\(775\) | 20.2356i | 0.726884i | ||||||||
\(776\) | −0.617515 | −0.0221675 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 30.4866i | 1.09300i | ||||||||
\(779\) | −26.0973 | −0.935032 | ||||||||
\(780\) | 4.52183 | + | 1.09495i | 0.161908 | + | 0.0392056i | ||||
\(781\) | 9.98137 | 0.357161 | ||||||||
\(782\) | 15.8971i | 0.568478i | ||||||||
\(783\) | −1.41589 | −0.0505998 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.95391i | 0.212504i | ||||||||
\(786\) | 18.2712i | 0.651711i | ||||||||
\(787\) | − | 39.8291i | − | 1.41975i | −0.704326 | − | 0.709877i | \(-0.748751\pi\) | ||
0.704326 | − | 0.709877i | \(-0.251249\pi\) | |||||||
\(788\) | 8.65821i | 0.308436i | ||||||||
\(789\) | 52.1514 | 1.85664 | ||||||||
\(790\) | −2.62525 | −0.0934022 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 6.30594 | 0.224072 | ||||||||
\(793\) | 3.98574 | − | 16.4600i | 0.141538 | − | 0.584510i | ||||
\(794\) | −10.5794 | −0.375448 | ||||||||
\(795\) | − | 1.06007i | − | 0.0375969i | ||||||
\(796\) | −10.1177 | −0.358612 | ||||||||
\(797\) | 21.2530 | 0.752821 | 0.376410 | − | 0.926453i | \(-0.377158\pi\) | ||||
0.376410 | + | 0.926453i | \(0.377158\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.9881i | 0.954770i | ||||||||
\(800\) | 20.3472i | 0.719382i | ||||||||
\(801\) | − | 38.9563i | − | 1.37645i | ||||||
\(802\) | 13.5413 | 0.478161 | ||||||||
\(803\) | −3.60200 | −0.127112 | ||||||||
\(804\) | 21.5000i | 0.758246i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.99784 | + | 16.5099i | −0.140818 | + | 0.581537i | ||||
\(807\) | −35.6368 | −1.25447 | ||||||||
\(808\) | 52.9854i | 1.86402i | ||||||||
\(809\) | 21.4175 | 0.753000 | 0.376500 | − | 0.926417i | \(-0.377128\pi\) | ||||
0.376500 | + | 0.926417i | \(0.377128\pi\) | |||||||
\(810\) | −6.21260 | −0.218288 | ||||||||
\(811\) | − | 11.0116i | − | 0.386669i | −0.981133 | − | 0.193335i | \(-0.938070\pi\) | ||
0.981133 | − | 0.193335i | \(-0.0619303\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 4.96896i | − | 0.174269i | ||||||
\(814\) | 0.321910i | 0.0112829i | ||||||||
\(815\) | −14.8283 | −0.519412 | ||||||||
\(816\) | 12.8662 | 0.450408 | ||||||||
\(817\) | 58.3019i | 2.03972i | ||||||||
\(818\) | 19.3765 | 0.677484 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.66207 | 0.0929636 | ||||||||
\(821\) | − | 38.6685i | − | 1.34954i | −0.738029 | − | 0.674769i | \(-0.764243\pi\) | ||
0.738029 | − | 0.674769i | \(-0.235757\pi\) | |||||||
\(822\) | −16.2202 | −0.565744 | ||||||||
\(823\) | 20.4566 | 0.713073 | 0.356537 | − | 0.934281i | \(-0.383957\pi\) | ||||
0.356537 | + | 0.934281i | \(0.383957\pi\) | |||||||
\(824\) | 33.0570i | 1.15160i | ||||||||
\(825\) | 7.93965i | 0.276423i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 27.3451i | − | 0.950881i | −0.879748 | − | 0.475440i | \(-0.842289\pi\) | ||
0.879748 | − | 0.475440i | \(-0.157711\pi\) | |||||||
\(828\) | 10.9489 | 0.380501 | ||||||||
\(829\) | 25.0086 | 0.868585 | 0.434292 | − | 0.900772i | \(-0.356998\pi\) | ||||
0.434292 | + | 0.900772i | \(0.356998\pi\) | |||||||
\(830\) | − | 6.84780i | − | 0.237691i | ||||||
\(831\) | −13.2112 | −0.458291 | ||||||||
\(832\) | −6.70616 | + | 27.6945i | −0.232494 | + | 0.960133i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | − | 17.0406i | − | 0.590069i | ||||||
\(835\) | 0.707945 | 0.0244994 | ||||||||
\(836\) | 3.12799 | 0.108184 | ||||||||
\(837\) | 0.942324i | 0.0325715i | ||||||||
\(838\) | 15.3237i | 0.529350i | ||||||||
\(839\) | − | 8.76981i | − | 0.302768i | −0.988475 | − | 0.151384i | \(-0.951627\pi\) | ||
0.988475 | − | 0.151384i | \(-0.0483729\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.5218 | 0.500753 | ||||||||
\(842\) | −4.58665 | −0.158066 | ||||||||
\(843\) | 49.2009i | 1.69457i | ||||||||
\(844\) | −13.2284 | −0.455339 | ||||||||
\(845\) | −3.71952 | + | 7.22994i | −0.127956 | + | 0.248717i | ||||
\(846\) | −25.2227 | −0.867174 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.10342 | 0.0378914 | ||||||||
\(849\) | 4.21894 | 0.144794 | ||||||||
\(850\) | 16.5336i | 0.567097i | ||||||||
\(851\) | 1.87630i | 0.0643186i | ||||||||
\(852\) | − | 29.0652i | − | 0.995758i | ||||||
\(853\) | − | 19.8232i | − | 0.678734i | −0.940654 | − | 0.339367i | \(-0.889787\pi\) | ||
0.940654 | − | 0.339367i | \(-0.110213\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.47469 | 0.324028 | ||||||||
\(856\) | − | 18.6969i | − | 0.639047i | ||||||
\(857\) | 2.67037 | 0.0912181 | 0.0456090 | − | 0.998959i | \(-0.485477\pi\) | ||||
0.0456090 | + | 0.998959i | \(0.485477\pi\) | |||||||
\(858\) | −1.56860 | + | 6.47784i | −0.0535510 | + | 0.221150i | ||||
\(859\) | −38.9597 | −1.32929 | −0.664644 | − | 0.747160i | \(-0.731417\pi\) | ||||
−0.664644 | + | 0.747160i | \(0.731417\pi\) | |||||||
\(860\) | − | 5.94713i | − | 0.202795i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15.6738 | −0.533851 | ||||||||
\(863\) | − | 24.7976i | − | 0.844121i | −0.906568 | − | 0.422060i | \(-0.861307\pi\) | ||
0.906568 | − | 0.422060i | \(-0.138693\pi\) | |||||||
\(864\) | 0.947521i | 0.0322353i | ||||||||
\(865\) | 7.49840i | 0.254953i | ||||||||
\(866\) | 30.0561i | 1.02135i | ||||||||
\(867\) | 14.1592 | 0.480871 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.77154i | 0.0940181i | ||||||||
\(870\) | 10.7650 | 0.364967 | ||||||||
\(871\) | −36.5175 | − | 8.84262i | −1.23735 | − | 0.299621i | ||||
\(872\) | 34.8433 | 1.17994 | ||||||||
\(873\) | 0.588237i | 0.0199088i | ||||||||
\(874\) | −24.7399 | −0.836839 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.4888i | 0.354385i | ||||||||
\(877\) | 1.97840i | 0.0668059i | 0.999442 | + | 0.0334029i | \(0.0106345\pi\) | ||||
−0.999442 | + | 0.0334029i | \(0.989366\pi\) | |||||||
\(878\) | − | 18.3250i | − | 0.618440i | ||||||
\(879\) | 66.2415i | 2.23427i | ||||||||
\(880\) | 0.701412 | 0.0236446 | ||||||||
\(881\) | −17.1466 | −0.577683 | −0.288841 | − | 0.957377i | \(-0.593270\pi\) | ||||
−0.288841 | + | 0.957377i | \(0.593270\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.2168 | 0.343822 | 0.171911 | − | 0.985112i | \(-0.445006\pi\) | ||||
0.171911 | + | 0.985112i | \(0.445006\pi\) | |||||||
\(884\) | 2.40720 | − | 9.94102i | 0.0809628 | − | 0.334353i | ||||
\(885\) | −14.9987 | −0.504177 | ||||||||
\(886\) | 14.8250i | 0.498055i | ||||||||
\(887\) | 50.9931 | 1.71218 | 0.856090 | − | 0.516826i | \(-0.172887\pi\) | ||||
0.856090 | + | 0.516826i | \(0.172887\pi\) | |||||||
\(888\) | 3.14676 | 0.105598 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 8.97901i | − | 0.300977i | ||||||
\(891\) | 6.55879i | 0.219728i | ||||||||
\(892\) | − | 5.74184i | − | 0.192251i | ||||||
\(893\) | −42.0003 | −1.40549 | ||||||||
\(894\) | 9.64659 | 0.322630 | ||||||||
\(895\) | 5.92331i | 0.197995i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.14277 | + | 37.7570i | −0.305268 | + | 1.26067i | ||||
\(898\) | 35.0255 | 1.16882 | ||||||||
\(899\) | − | 28.9653i | − | 0.966047i | ||||||
\(900\) | 11.3873 | 0.379577 | ||||||||
\(901\) | −2.33052 | −0.0776408 | ||||||||
\(902\) | 3.81360i | 0.126979i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 2.82268i | − | 0.0938811i | ||||||
\(905\) | 7.14957i | 0.237660i | ||||||||
\(906\) | −12.7262 | −0.422799 | ||||||||
\(907\) | 5.78538 | 0.192100 | 0.0960501 | − | 0.995376i | \(-0.469379\pi\) | ||||
0.0960501 | + | 0.995376i | \(0.469379\pi\) | |||||||
\(908\) | 14.2765i | 0.473782i | ||||||||
\(909\) | 50.4732 | 1.67409 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.70706 | −0.0565573 | −0.0282787 | − | 0.999600i | \(-0.509003\pi\) | ||||
−0.0282787 | + | 0.999600i | \(0.509003\pi\) | |||||||
\(912\) | 20.0231i | 0.663032i | ||||||||
\(913\) | −7.22940 | −0.239258 | ||||||||
\(914\) | 3.40195 | 0.112526 | ||||||||
\(915\) | 7.14279i | 0.236133i | ||||||||
\(916\) | − | 9.35590i | − | 0.309128i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.769931i | 0.0254115i | ||||||||
\(919\) | 37.2050 | 1.22728 | 0.613640 | − | 0.789586i | \(-0.289705\pi\) | ||||
0.613640 | + | 0.789586i | \(0.289705\pi\) | |||||||
\(920\) | 8.47164 | 0.279302 | ||||||||
\(921\) | 30.9123i | 1.01859i | ||||||||
\(922\) | 0.216782 | 0.00713933 | ||||||||
\(923\) | 49.3669 | + | 11.9541i | 1.62493 | + | 0.393474i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.95142i | 0.0641623i | ||||||||
\(926\) | −18.4695 | −0.606945 | ||||||||
\(927\) | 31.4897 | 1.03426 | ||||||||
\(928\) | − | 29.1251i | − | 0.956077i | ||||||
\(929\) | − | 19.9046i | − | 0.653048i | −0.945189 | − | 0.326524i | \(-0.894123\pi\) | ||
0.945189 | − | 0.326524i | \(-0.105877\pi\) | |||||||
\(930\) | − | 7.16447i | − | 0.234932i | ||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −14.7265 | −0.482383 | ||||||||
\(933\) | 23.3872 | 0.765661 | ||||||||
\(934\) | 0.205135i | 0.00671222i | ||||||||
\(935\) | −1.48145 | −0.0484485 | ||||||||
\(936\) | 31.1886 | + | 7.55225i | 1.01943 | + | 0.246853i | ||||
\(937\) | 7.16949 | 0.234217 | 0.117109 | − | 0.993119i | \(-0.462637\pi\) | ||||
0.117109 | + | 0.993119i | \(0.462637\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.9446 | 0.716134 | ||||||||
\(940\) | 4.28428 | 0.139738 | ||||||||
\(941\) | − | 3.06072i | − | 0.0997766i | −0.998755 | − | 0.0498883i | \(-0.984113\pi\) | ||
0.998755 | − | 0.0498883i | \(-0.0158865\pi\) | |||||||
\(942\) | 24.8371i | 0.809237i | ||||||||
\(943\) | 22.2281i | 0.723846i | ||||||||
\(944\) | − | 15.6120i | − | 0.508126i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.51968 | 0.276999 | ||||||||
\(947\) | − | 44.2056i | − | 1.43649i | −0.695791 | − | 0.718244i | \(-0.744946\pi\) | ||
0.695791 | − | 0.718244i | \(-0.255054\pi\) | |||||||
\(948\) | 8.07058 | 0.262120 | ||||||||
\(949\) | −17.8151 | − | 4.31390i | −0.578304 | − | 0.140035i | ||||
\(950\) | −25.7304 | −0.834806 | ||||||||
\(951\) | − | 59.8762i | − | 1.94162i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.7002 | 0.443791 | 0.221896 | − | 0.975070i | \(-0.428776\pi\) | ||||
0.221896 | + | 0.975070i | \(0.428776\pi\) | |||||||
\(954\) | − | 2.17807i | − | 0.0705176i | ||||||
\(955\) | − | 9.81149i | − | 0.317492i | ||||||
\(956\) | 16.7354i | 0.541262i | ||||||||
\(957\) | − | 11.3648i | − | 0.367373i | ||||||
\(958\) | 23.0476 | 0.744634 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | − | 12.0180i | − | 0.387879i | ||||||
\(961\) | 11.7226 | 0.378147 | ||||||||
\(962\) | −0.385532 | + | 1.59214i | −0.0124301 | + | 0.0513325i | ||||
\(963\) | −17.8104 | −0.573933 | ||||||||
\(964\) | − | 2.36248i | − | 0.0760903i | ||||||
\(965\) | 14.3894 | 0.463211 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.9429i | 1.41311i | 0.707659 | + | 0.706554i | \(0.249751\pi\) | ||||
−0.707659 | + | 0.706554i | \(0.750249\pi\) | |||||||
\(968\) | 32.0887i | 1.03137i | ||||||||
\(969\) | − | 42.2907i | − | 1.35857i | ||||||
\(970\) | 0.135582i | 0.00435329i | ||||||||
\(971\) | −21.3171 | −0.684098 | −0.342049 | − | 0.939682i | \(-0.611121\pi\) | ||||
−0.342049 | + | 0.939682i | \(0.611121\pi\) | |||||||
\(972\) | 18.5525 | 0.595072 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −20.4400 | −0.654941 | ||||||||
\(975\) | −9.50884 | + | 39.2687i | −0.304527 | + | 1.25761i | ||||
\(976\) | −7.43482 | −0.237983 | ||||||||
\(977\) | 16.4466i | 0.526173i | 0.964772 | + | 0.263087i | \(0.0847405\pi\) | ||||
−0.964772 | + | 0.263087i | \(0.915260\pi\) | |||||||
\(978\) | −61.8572 | −1.97797 | ||||||||
\(979\) | −9.47937 | −0.302962 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 33.1913i | − | 1.05972i | ||||||
\(982\) | − | 38.3681i | − | 1.22437i | ||||||
\(983\) | 11.7104i | 0.373504i | 0.982407 | + | 0.186752i | \(0.0597961\pi\) | ||||
−0.982407 | + | 0.186752i | \(0.940204\pi\) | |||||||
\(984\) | 37.2790 | 1.18841 | ||||||||
\(985\) | 6.38160 | 0.203335 | ||||||||
\(986\) | − | 23.6662i | − | 0.753687i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 15.4708 | + | 3.74621i | 0.492190 | + | 0.119183i | ||||
\(989\) | 49.6581 | 1.57903 | ||||||||
\(990\) | − | 1.38454i | − | 0.0440036i | ||||||
\(991\) | −31.3747 | −0.996650 | −0.498325 | − | 0.866990i | \(-0.666051\pi\) | ||||
−0.498325 | + | 0.866990i | \(0.666051\pi\) | |||||||
\(992\) | −19.3837 | −0.615434 | ||||||||
\(993\) | − | 32.0260i | − | 1.01632i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.45731i | 0.236413i | ||||||||
\(996\) | 21.0516i | 0.667046i | ||||||||
\(997\) | −4.69711 | −0.148759 | −0.0743794 | − | 0.997230i | \(-0.523698\pi\) | ||||
−0.0743794 | + | 0.997230i | \(0.523698\pi\) | |||||||
\(998\) | −18.9814 | −0.600847 | ||||||||
\(999\) | 0.0908732i | 0.00287510i |
(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 | 637.2.c.f.246.6 | 8 | ||
7.2 | even | 3 | 91.2.r.a.25.6 | yes | 16 | ||
7.3 | odd | 6 | 637.2.r.f.324.3 | 16 | |||
7.4 | even | 3 | 91.2.r.a.51.3 | yes | 16 | ||
7.5 | odd | 6 | 637.2.r.f.116.6 | 16 | |||
7.6 | odd | 2 | 637.2.c.e.246.6 | 8 | |||
13.5 | odd | 4 | 8281.2.a.ck.1.6 | 8 | |||
13.8 | odd | 4 | 8281.2.a.ck.1.3 | 8 | |||
13.12 | even | 2 | inner | 637.2.c.f.246.3 | 8 | ||
21.2 | odd | 6 | 819.2.dl.e.298.3 | 16 | |||
21.11 | odd | 6 | 819.2.dl.e.415.6 | 16 | |||
91.12 | odd | 6 | 637.2.r.f.116.3 | 16 | |||
91.18 | odd | 12 | 1183.2.e.i.170.3 | 16 | |||
91.25 | even | 6 | 91.2.r.a.51.6 | yes | 16 | ||
91.34 | even | 4 | 8281.2.a.cj.1.3 | 8 | |||
91.38 | odd | 6 | 637.2.r.f.324.6 | 16 | |||
91.44 | odd | 12 | 1183.2.e.i.508.3 | 16 | |||
91.51 | even | 6 | 91.2.r.a.25.3 | ✓ | 16 | ||
91.60 | odd | 12 | 1183.2.e.i.170.6 | 16 | |||
91.83 | even | 4 | 8281.2.a.cj.1.6 | 8 | |||
91.86 | odd | 12 | 1183.2.e.i.508.6 | 16 | |||
91.90 | odd | 2 | 637.2.c.e.246.3 | 8 | |||
273.116 | odd | 6 | 819.2.dl.e.415.3 | 16 | |||
273.233 | odd | 6 | 819.2.dl.e.298.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.r.a.25.3 | ✓ | 16 | 91.51 | even | 6 | ||
91.2.r.a.25.6 | yes | 16 | 7.2 | even | 3 | ||
91.2.r.a.51.3 | yes | 16 | 7.4 | even | 3 | ||
91.2.r.a.51.6 | yes | 16 | 91.25 | even | 6 | ||
637.2.c.e.246.3 | 8 | 91.90 | odd | 2 | |||
637.2.c.e.246.6 | 8 | 7.6 | odd | 2 | |||
637.2.c.f.246.3 | 8 | 13.12 | even | 2 | inner | ||
637.2.c.f.246.6 | 8 | 1.1 | even | 1 | trivial | ||
637.2.r.f.116.3 | 16 | 91.12 | odd | 6 | |||
637.2.r.f.116.6 | 16 | 7.5 | odd | 6 | |||
637.2.r.f.324.3 | 16 | 7.3 | odd | 6 | |||
637.2.r.f.324.6 | 16 | 91.38 | odd | 6 | |||
819.2.dl.e.298.3 | 16 | 21.2 | odd | 6 | |||
819.2.dl.e.298.6 | 16 | 273.233 | odd | 6 | |||
819.2.dl.e.415.3 | 16 | 273.116 | odd | 6 | |||
819.2.dl.e.415.6 | 16 | 21.11 | odd | 6 | |||
1183.2.e.i.170.3 | 16 | 91.18 | odd | 12 | |||
1183.2.e.i.170.6 | 16 | 91.60 | odd | 12 | |||
1183.2.e.i.508.3 | 16 | 91.44 | odd | 12 | |||
1183.2.e.i.508.6 | 16 | 91.86 | odd | 12 | |||
8281.2.a.cj.1.3 | 8 | 91.34 | even | 4 | |||
8281.2.a.cj.1.6 | 8 | 91.83 | even | 4 | |||
8281.2.a.ck.1.3 | 8 | 13.8 | odd | 4 | |||
8281.2.a.ck.1.6 | 8 | 13.5 | odd | 4 |