Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2394,2,Mod(1063,2394)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2394, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2394.1063");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2394.e (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: | \(19.1161862439\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 44x^{14} + 708x^{12} + 5378x^{10} + 20592x^{8} + 38856x^{6} + 33265x^{4} + 10216x^{2} + 900 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 266) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1063.7 | ||
Root | \(-0.584675i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2394.1063 |
Dual form | 2394.2.e.c.1063.10 |
$q$-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 \(\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times\).
\(n\) | \(533\) | \(1009\) | \(1711\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.74394i | 1.22713i | 0.789645 | + | 0.613564i | \(0.210265\pi\) | ||||
−0.789645 | + | 0.613564i | \(0.789735\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.24817 | − | 1.39489i | −0.849729 | − | 0.527220i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.74394 | 0.867710 | ||||||||
\(11\) | 1.52921 | 0.461074 | 0.230537 | − | 0.973064i | \(-0.425952\pi\) | ||||
0.230537 | + | 0.973064i | \(0.425952\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.33820 | −1.48055 | −0.740275 | − | 0.672305i | \(-0.765305\pi\) | ||||
−0.740275 | + | 0.672305i | \(0.765305\pi\) | |||||||
\(14\) | −1.39489 | + | 2.24817i | −0.372801 | + | 0.600849i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.78979i | 0.676623i | 0.941034 | + | 0.338311i | \(0.109856\pi\) | ||||
−0.941034 | + | 0.338311i | \(0.890144\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.01815 | − | 1.68953i | 0.921826 | − | 0.387605i | ||||
\(20\) | − | 2.74394i | − | 0.613564i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 1.52921i | − | 0.326028i | ||||||
\(23\) | −6.49634 | −1.35458 | −0.677290 | − | 0.735716i | \(-0.736846\pi\) | ||||
−0.677290 | + | 0.735716i | \(0.736846\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.52921 | −0.505842 | ||||||||
\(26\) | 5.33820i | 1.04691i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.24817 | + | 1.39489i | 0.424864 | + | 0.263610i | ||||
\(29\) | − | 6.88592i | − | 1.27868i | −0.768923 | − | 0.639342i | \(-0.779207\pi\) | ||
0.768923 | − | 0.639342i | \(-0.220793\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.830650 | 0.149189 | 0.0745946 | − | 0.997214i | \(-0.476234\pi\) | ||||
0.0745946 | + | 0.997214i | \(0.476234\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.78979 | 0.478445 | ||||||||
\(35\) | 3.82751 | − | 6.16885i | 0.646966 | − | 1.04273i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.3238i | − | 1.69723i | −0.529011 | − | 0.848615i | \(-0.677437\pi\) | ||
0.529011 | − | 0.848615i | \(-0.322563\pi\) | |||||||
\(38\) | −1.68953 | − | 4.01815i | −0.274078 | − | 0.651829i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.74394 | −0.433855 | ||||||||
\(41\) | 11.7026 | 1.82764 | 0.913818 | − | 0.406125i | \(-0.133120\pi\) | ||||
0.913818 | + | 0.406125i | \(0.133120\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.668836 | 0.101997 | 0.0509983 | − | 0.998699i | \(-0.483760\pi\) | ||||
0.0509983 | + | 0.998699i | \(0.483760\pi\) | |||||||
\(44\) | −1.52921 | −0.230537 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.49634i | 0.957833i | ||||||||
\(47\) | 4.83118i | 0.704700i | 0.935868 | + | 0.352350i | \(0.114617\pi\) | ||||
−0.935868 | + | 0.352350i | \(0.885383\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.10854 | + | 6.27192i | 0.444078 | + | 0.895988i | ||||
\(50\) | 2.52921i | 0.357684i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.33820 | 0.740275 | ||||||||
\(53\) | − | 2.02555i | − | 0.278231i | −0.990276 | − | 0.139115i | \(-0.955574\pi\) | ||
0.990276 | − | 0.139115i | \(-0.0444259\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.19606i | 0.565796i | ||||||||
\(56\) | 1.39489 | − | 2.24817i | 0.186401 | − | 0.300424i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.88592 | −0.904166 | ||||||||
\(59\) | 5.53373 | 0.720430 | 0.360215 | − | 0.932869i | \(-0.382703\pi\) | ||||
0.360215 | + | 0.932869i | \(0.382703\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 7.03169i | − | 0.900316i | −0.892949 | − | 0.450158i | \(-0.851368\pi\) | ||
0.892949 | − | 0.450158i | \(-0.148632\pi\) | |||||||
\(62\) | − | 0.830650i | − | 0.105493i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 14.6477i | − | 1.81682i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.43792i | 0.420009i | 0.977700 | + | 0.210005i | \(0.0673479\pi\) | ||||
−0.977700 | + | 0.210005i | \(0.932652\pi\) | |||||||
\(68\) | − | 2.78979i | − | 0.338311i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.16885 | − | 3.82751i | −0.737318 | − | 0.457474i | ||||
\(71\) | 11.4635i | 1.36046i | 0.732997 | + | 0.680232i | \(0.238121\pi\) | ||||
−0.732997 | + | 0.680232i | \(0.761879\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 12.5438i | − | 1.46814i | −0.679071 | − | 0.734072i | \(-0.737617\pi\) | ||
0.679071 | − | 0.734072i | \(-0.262383\pi\) | |||||||
\(74\) | −10.3238 | −1.20012 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.01815 | + | 1.68953i | −0.460913 | + | 0.193802i | ||||
\(77\) | −3.43792 | − | 2.13308i | −0.391788 | − | 0.243087i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 4.32385i | − | 0.486471i | −0.969967 | − | 0.243235i | \(-0.921791\pi\) | ||
0.969967 | − | 0.243235i | \(-0.0782087\pi\) | |||||||
\(80\) | 2.74394i | 0.306782i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 11.7026i | − | 1.29233i | ||||||
\(83\) | − | 14.4465i | − | 1.58571i | −0.609410 | − | 0.792856i | \(-0.708594\pi\) | ||
0.609410 | − | 0.792856i | \(-0.291406\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.65501 | −0.830302 | ||||||||
\(86\) | − | 0.668836i | − | 0.0721225i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.52921i | 0.163014i | ||||||||
\(89\) | 6.14458 | 0.651325 | 0.325662 | − | 0.945486i | \(-0.394413\pi\) | ||||
0.325662 | + | 0.945486i | \(0.394413\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0012 | + | 7.44622i | 1.25807 | + | 0.780576i | ||||
\(92\) | 6.49634 | 0.677290 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.83118 | 0.498298 | ||||||||
\(95\) | 4.63597 | + | 11.0256i | 0.475640 | + | 1.13120i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.31393 | 0.539548 | 0.269774 | − | 0.962924i | \(-0.413051\pi\) | ||||
0.269774 | + | 0.962924i | \(0.413051\pi\) | |||||||
\(98\) | 6.27192 | − | 3.10854i | 0.633559 | − | 0.314010i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.52921 | 0.252921 | ||||||||
\(101\) | − | 8.95863i | − | 0.891417i | −0.895178 | − | 0.445709i | \(-0.852952\pi\) | ||
0.895178 | − | 0.445709i | \(-0.147048\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.7288 | 1.25420 | 0.627101 | − | 0.778938i | \(-0.284241\pi\) | ||||
0.627101 | + | 0.778938i | \(0.284241\pi\) | |||||||
\(104\) | − | 5.33820i | − | 0.523453i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.02555 | −0.196739 | ||||||||
\(107\) | 1.15867i | 0.112013i | 0.998430 | + | 0.0560064i | \(0.0178367\pi\) | ||||
−0.998430 | + | 0.0560064i | \(0.982163\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 2.02555i | − | 0.194013i | −0.995284 | − | 0.0970063i | \(-0.969073\pi\) | ||
0.995284 | − | 0.0970063i | \(-0.0309267\pi\) | |||||||
\(110\) | 4.19606 | 0.400079 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.24817 | − | 1.39489i | −0.212432 | − | 0.131805i | ||||
\(113\) | − | 10.5966i | − | 0.996844i | −0.866935 | − | 0.498422i | \(-0.833913\pi\) | ||
0.866935 | − | 0.498422i | \(-0.166087\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 17.8256i | − | 1.66224i | ||||||
\(116\) | 6.88592i | 0.639342i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 5.53373i | − | 0.509421i | ||||||
\(119\) | 3.89146 | − | 6.27192i | 0.356729 | − | 0.574946i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.66152 | −0.787411 | ||||||||
\(122\) | −7.03169 | −0.636620 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.830650 | −0.0745946 | ||||||||
\(125\) | 6.77970i | 0.606395i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 19.2353i | − | 1.70686i | −0.521209 | − | 0.853429i | \(-0.674519\pi\) | ||
0.521209 | − | 0.853429i | \(-0.325481\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −14.6477 | −1.28469 | ||||||||
\(131\) | 8.95863i | 0.782719i | 0.920238 | + | 0.391360i | \(0.127995\pi\) | ||||
−0.920238 | + | 0.391360i | \(0.872005\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.3902 | − | 1.80653i | −0.987655 | − | 0.156646i | ||||
\(134\) | 3.43792 | 0.296991 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.78979 | −0.239222 | ||||||||
\(137\) | 0.769087 | 0.0657075 | 0.0328538 | − | 0.999460i | \(-0.489540\pi\) | ||||
0.0328538 | + | 0.999460i | \(0.489540\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.60077i | − | 0.390232i | −0.980780 | − | 0.195116i | \(-0.937492\pi\) | ||
0.980780 | − | 0.195116i | \(-0.0625084\pi\) | |||||||
\(140\) | −3.82751 | + | 6.16885i | −0.323483 | + | 0.521363i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 11.4635 | 0.961993 | ||||||||
\(143\) | −8.16322 | −0.682643 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.8946 | 1.56911 | ||||||||
\(146\) | −12.5438 | −1.03814 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.3238i | 0.848615i | ||||||||
\(149\) | 1.65501 | 0.135584 | 0.0677919 | − | 0.997699i | \(-0.478405\pi\) | ||||
0.0677919 | + | 0.997699i | \(0.478405\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.72075i | 0.302790i | 0.988473 | + | 0.151395i | \(0.0483765\pi\) | ||||
−0.988473 | + | 0.151395i | \(0.951623\pi\) | |||||||
\(152\) | 1.68953 | + | 4.01815i | 0.137039 | + | 0.325915i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.13308 | + | 3.43792i | −0.171889 | + | 0.277036i | ||||
\(155\) | 2.27925i | 0.183074i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 21.8613i | − | 1.74472i | −0.488860 | − | 0.872362i | \(-0.662587\pi\) | ||
0.488860 | − | 0.872362i | \(-0.337413\pi\) | |||||||
\(158\) | −4.32385 | −0.343987 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.74394 | 0.216928 | ||||||||
\(161\) | 14.6049 | + | 9.06171i | 1.15103 | + | 0.714162i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.52921 | −0.746385 | −0.373193 | − | 0.927754i | \(-0.621737\pi\) | ||||
−0.373193 | + | 0.927754i | \(0.621737\pi\) | |||||||
\(164\) | −11.7026 | −0.913818 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.4465 | −1.12127 | ||||||||
\(167\) | −16.4636 | −1.27399 | −0.636997 | − | 0.770866i | \(-0.719824\pi\) | ||||
−0.636997 | + | 0.770866i | \(0.719824\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.4963 | 1.19203 | ||||||||
\(170\) | 7.65501i | 0.587112i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.668836 | −0.0509983 | ||||||||
\(173\) | 7.59670 | 0.577567 | 0.288783 | − | 0.957394i | \(-0.406749\pi\) | ||||
0.288783 | + | 0.957394i | \(0.406749\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.68609 | + | 3.52798i | 0.429828 | + | 0.266690i | ||||
\(176\) | 1.52921 | 0.115268 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 6.14458i | − | 0.460556i | ||||||
\(179\) | − | 20.6477i | − | 1.54328i | −0.636059 | − | 0.771641i | \(-0.719436\pi\) | ||
0.636059 | − | 0.771641i | \(-0.280564\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.20564 | −0.535591 | −0.267795 | − | 0.963476i | \(-0.586295\pi\) | ||||
−0.267795 | + | 0.963476i | \(0.586295\pi\) | |||||||
\(182\) | 7.44622 | − | 12.0012i | 0.551950 | − | 0.889586i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 6.49634i | − | 0.478917i | ||||||
\(185\) | 28.3280 | 2.08272 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.26617i | 0.311973i | ||||||||
\(188\) | − | 4.83118i | − | 0.352350i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 11.0256 | − | 4.63597i | 0.799878 | − | 0.336329i | ||||
\(191\) | −16.5474 | −1.19733 | −0.598665 | − | 0.800999i | \(-0.704302\pi\) | ||||
−0.598665 | + | 0.800999i | \(0.704302\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 24.3684i | − | 1.75408i | −0.480419 | − | 0.877039i | \(-0.659515\pi\) | ||
0.480419 | − | 0.877039i | \(-0.340485\pi\) | |||||||
\(194\) | − | 5.31393i | − | 0.381518i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.10854 | − | 6.27192i | −0.222039 | − | 0.447994i | ||||
\(197\) | 6.99268 | 0.498208 | 0.249104 | − | 0.968477i | \(-0.419864\pi\) | ||||
0.249104 | + | 0.968477i | \(0.419864\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.0719i | 1.42286i | 0.702756 | + | 0.711431i | \(0.251953\pi\) | ||||
−0.702756 | + | 0.711431i | \(0.748047\pi\) | |||||||
\(200\) | − | 2.52921i | − | 0.178842i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.95863 | −0.630327 | ||||||||
\(203\) | −9.60513 | + | 15.4807i | −0.674148 | + | 1.08653i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 32.1112i | 2.24274i | ||||||||
\(206\) | − | 12.7288i | − | 0.886854i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.33820 | −0.370137 | ||||||||
\(209\) | 6.14458 | − | 2.58364i | 0.425030 | − | 0.178714i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.48902i | 0.515566i | 0.966203 | + | 0.257783i | \(0.0829919\pi\) | ||||
−0.966203 | + | 0.257783i | \(0.917008\pi\) | |||||||
\(212\) | 2.02555i | 0.139115i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.15867 | 0.0792050 | ||||||||
\(215\) | 1.83525i | 0.125163i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.86744 | − | 1.15867i | −0.126770 | − | 0.0786556i | ||||
\(218\) | −2.02555 | −0.137188 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 4.19606i | − | 0.282898i | ||||||
\(221\) | − | 14.8924i | − | 1.00177i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.5806 | 0.909426 | 0.454713 | − | 0.890638i | \(-0.349742\pi\) | ||||
0.454713 | + | 0.890638i | \(0.349742\pi\) | |||||||
\(224\) | −1.39489 | + | 2.24817i | −0.0932003 | + | 0.150212i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.5966 | −0.704875 | ||||||||
\(227\) | 23.9027 | 1.58648 | 0.793240 | − | 0.608909i | \(-0.208393\pi\) | ||||
0.793240 | + | 0.608909i | \(0.208393\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.0816i | 0.996622i | 0.866998 | + | 0.498311i | \(0.166046\pi\) | ||||
−0.866998 | + | 0.498311i | \(0.833954\pi\) | |||||||
\(230\) | −17.8256 | −1.17538 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.88592 | 0.452083 | ||||||||
\(233\) | −12.1258 | −0.794388 | −0.397194 | − | 0.917735i | \(-0.630016\pi\) | ||||
−0.397194 | + | 0.917735i | \(0.630016\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.2565 | −0.864756 | ||||||||
\(236\) | −5.53373 | −0.360215 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.27192 | − | 3.89146i | −0.406548 | − | 0.252246i | ||||
\(239\) | −9.55476 | −0.618046 | −0.309023 | − | 0.951055i | \(-0.600002\pi\) | ||||
−0.309023 | + | 0.951055i | \(0.600002\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.77104 | −0.564992 | −0.282496 | − | 0.959268i | \(-0.591162\pi\) | ||||
−0.282496 | + | 0.959268i | \(0.591162\pi\) | |||||||
\(242\) | 8.66152i | 0.556784i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.03169i | 0.450158i | ||||||||
\(245\) | −17.2098 | + | 8.52966i | −1.09949 | + | 0.544940i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.4496 | + | 9.01904i | −1.36481 | + | 0.573868i | ||||
\(248\) | 0.830650i | 0.0527463i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.77970 | 0.428786 | ||||||||
\(251\) | 2.10882i | 0.133108i | 0.997783 | + | 0.0665538i | \(0.0212004\pi\) | ||||
−0.997783 | + | 0.0665538i | \(0.978800\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.93426 | −0.624562 | ||||||||
\(254\) | −19.2353 | −1.20693 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −22.7700 | −1.42036 | −0.710178 | − | 0.704022i | \(-0.751385\pi\) | ||||
−0.710178 | + | 0.704022i | \(0.751385\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.4007 | + | 23.2098i | −0.894814 | + | 1.44218i | ||||
\(260\) | 14.6477i | 0.908411i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.95863 | 0.553466 | ||||||||
\(263\) | −22.3027 | −1.37524 | −0.687622 | − | 0.726069i | \(-0.741345\pi\) | ||||
−0.687622 | + | 0.726069i | \(0.741345\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.55799 | 0.341425 | ||||||||
\(266\) | −1.80653 | + | 11.3902i | −0.110766 | + | 0.698377i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 3.43792i | − | 0.210005i | ||||||
\(269\) | −3.88304 | −0.236753 | −0.118377 | − | 0.992969i | \(-0.537769\pi\) | ||||
−0.118377 | + | 0.992969i | \(0.537769\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.7969i | 1.20257i | 0.799033 | + | 0.601287i | \(0.205345\pi\) | ||||
−0.799033 | + | 0.601287i | \(0.794655\pi\) | |||||||
\(272\) | 2.78979i | 0.169156i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 0.769087i | − | 0.0464622i | ||||||
\(275\) | −3.86769 | −0.233230 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.7061 | 1.30419 | 0.652097 | − | 0.758136i | \(-0.273890\pi\) | ||||
0.652097 | + | 0.758136i | \(0.273890\pi\) | |||||||
\(278\) | −4.60077 | −0.275936 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.16885 | + | 3.82751i | 0.368659 | + | 0.228737i | ||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 0.703721i | − | 0.0418319i | −0.999781 | − | 0.0209159i | \(-0.993342\pi\) | ||
0.999781 | − | 0.0209159i | \(-0.00665824\pi\) | |||||||
\(284\) | − | 11.4635i | − | 0.680232i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.16322i | 0.482701i | ||||||||
\(287\) | −26.3094 | − | 16.3238i | −1.55299 | − | 0.963566i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.21709 | 0.542182 | ||||||||
\(290\) | − | 18.8946i | − | 1.10953i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.5438i | 0.734072i | ||||||||
\(293\) | 11.5650 | 0.675636 | 0.337818 | − | 0.941211i | \(-0.390311\pi\) | ||||
0.337818 | + | 0.941211i | \(0.390311\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.1842i | 0.884059i | ||||||||
\(296\) | 10.3238 | 0.600061 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 1.65501i | − | 0.0958722i | ||||||
\(299\) | 34.6787 | 2.00552 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.50366 | − | 0.932956i | −0.0866694 | − | 0.0537747i | ||||
\(302\) | 3.72075 | 0.214105 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.01815 | − | 1.68953i | 0.230456 | − | 0.0969012i | ||||
\(305\) | 19.2945 | 1.10480 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.4686 | −1.05406 | −0.527030 | − | 0.849847i | \(-0.676694\pi\) | ||||
−0.527030 | + | 0.849847i | \(0.676694\pi\) | |||||||
\(308\) | 3.43792 | + | 2.13308i | 0.195894 | + | 0.121544i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.27925 | 0.129453 | ||||||||
\(311\) | 4.80842i | 0.272661i | 0.990663 | + | 0.136330i | \(0.0435308\pi\) | ||||
−0.990663 | + | 0.136330i | \(0.956469\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.4521i | 0.703837i | 0.936031 | + | 0.351918i | \(0.114471\pi\) | ||||
−0.936031 | + | 0.351918i | \(0.885529\pi\) | |||||||
\(314\) | −21.8613 | −1.23371 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.32385i | 0.243235i | ||||||||
\(317\) | 30.0767i | 1.68927i | 0.535340 | + | 0.844637i | \(0.320183\pi\) | ||||
−0.535340 | + | 0.844637i | \(0.679817\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 10.5300i | − | 0.589568i | ||||||
\(320\) | − | 2.74394i | − | 0.153391i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 9.06171 | − | 14.6049i | 0.504989 | − | 0.813898i | ||||
\(323\) | 4.71343 | + | 11.2098i | 0.262262 | + | 0.623728i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.5014 | 0.748924 | ||||||||
\(326\) | 9.52921i | 0.527774i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.7026i | 0.646167i | ||||||||
\(329\) | 6.73898 | − | 10.8613i | 0.371532 | − | 0.598804i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 10.8413i | − | 0.595893i | −0.954582 | − | 0.297947i | \(-0.903698\pi\) | ||
0.954582 | − | 0.297947i | \(-0.0963018\pi\) | |||||||
\(332\) | 14.4465i | 0.792856i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 16.4636i | 0.900850i | ||||||||
\(335\) | −9.43346 | −0.515405 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 8.27925i | − | 0.451000i | −0.974243 | − | 0.225500i | \(-0.927598\pi\) | ||
0.974243 | − | 0.225500i | \(-0.0724015\pi\) | |||||||
\(338\) | − | 15.4963i | − | 0.842890i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.65501 | 0.415151 | ||||||||
\(341\) | 1.27024 | 0.0687872 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.76012 | − | 18.4364i | 0.0950377 | − | 0.995474i | ||||
\(344\) | 0.668836i | 0.0360612i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 7.59670i | − | 0.408401i | ||||||
\(347\) | −1.32465 | −0.0711112 | −0.0355556 | − | 0.999368i | \(-0.511320\pi\) | ||||
−0.0355556 | + | 0.999368i | \(0.511320\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 5.15328i | − | 0.275849i | −0.990443 | − | 0.137924i | \(-0.955957\pi\) | ||
0.990443 | − | 0.137924i | \(-0.0440431\pi\) | |||||||
\(350\) | 3.52798 | − | 5.68609i | 0.188578 | − | 0.303935i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 1.52921i | − | 0.0815071i | ||||||
\(353\) | − | 20.5237i | − | 1.09236i | −0.837666 | − | 0.546182i | \(-0.816081\pi\) | ||
0.837666 | − | 0.546182i | \(-0.183919\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −31.4551 | −1.66946 | ||||||||
\(356\) | −6.14458 | −0.325662 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.6477 | −1.09126 | ||||||||
\(359\) | 16.2171 | 0.855905 | 0.427953 | − | 0.903801i | \(-0.359235\pi\) | ||||
0.427953 | + | 0.903801i | \(0.359235\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.2910 | − | 13.5776i | 0.699525 | − | 0.714608i | ||||
\(362\) | 7.20564i | 0.378720i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12.0012 | − | 7.44622i | −0.629033 | − | 0.390288i | ||||
\(365\) | 34.4195 | 1.80160 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 28.7403i | − | 1.50023i | −0.661306 | − | 0.750116i | \(-0.729998\pi\) | ||
0.661306 | − | 0.750116i | \(-0.270002\pi\) | |||||||
\(368\) | −6.49634 | −0.338645 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 28.3280i | − | 1.47270i | ||||||
\(371\) | −2.82543 | + | 4.55378i | −0.146689 | + | 0.236421i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 6.88592i | − | 0.356540i | −0.983982 | − | 0.178270i | \(-0.942950\pi\) | ||
0.983982 | − | 0.178270i | \(-0.0570500\pi\) | |||||||
\(374\) | 4.26617 | 0.220598 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.83118 | −0.249149 | ||||||||
\(377\) | 36.7584i | 1.89315i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.56208i | 0.439804i | 0.975522 | + | 0.219902i | \(0.0705738\pi\) | ||||
−0.975522 | + | 0.219902i | \(0.929426\pi\) | |||||||
\(380\) | −4.63597 | − | 11.0256i | −0.237820 | − | 0.565599i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.5474i | 0.846641i | ||||||||
\(383\) | 0.0485251 | 0.00247952 | 0.00123976 | − | 0.999999i | \(-0.499605\pi\) | ||||
0.00123976 | + | 0.999999i | \(0.499605\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.85306 | − | 9.43346i | 0.298299 | − | 0.480773i | ||||
\(386\) | −24.3684 | −1.24032 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.31393 | −0.269774 | ||||||||
\(389\) | −2.94158 | −0.149144 | −0.0745721 | − | 0.997216i | \(-0.523759\pi\) | ||||
−0.0745721 | + | 0.997216i | \(0.523759\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 18.1234i | − | 0.916540i | ||||||
\(392\) | −6.27192 | + | 3.10854i | −0.316780 | + | 0.157005i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 6.99268i | − | 0.352286i | ||||||
\(395\) | 11.8644 | 0.596962 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.1275i | 1.31130i | 0.755064 | + | 0.655651i | \(0.227606\pi\) | ||||
−0.755064 | + | 0.655651i | \(0.772394\pi\) | |||||||
\(398\) | 20.0719 | 1.00612 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.52921 | −0.126460 | ||||||||
\(401\) | − | 8.31734i | − | 0.415348i | −0.978198 | − | 0.207674i | \(-0.933411\pi\) | ||
0.978198 | − | 0.207674i | \(-0.0665893\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.43417 | −0.220882 | ||||||||
\(404\) | 8.95863i | 0.445709i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 15.4807 | + | 9.60513i | 0.768296 | + | 0.476695i | ||||
\(407\) | − | 15.7873i | − | 0.782548i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.0822533 | 0.00406716 | 0.00203358 | − | 0.999998i | \(-0.499353\pi\) | ||||
0.00203358 | + | 0.999998i | \(0.499353\pi\) | |||||||
\(410\) | 32.1112 | 1.58586 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −12.7288 | −0.627101 | ||||||||
\(413\) | −12.4408 | − | 7.71896i | −0.612170 | − | 0.379825i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 39.6404 | 1.94587 | ||||||||
\(416\) | 5.33820i | 0.261727i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.58364 | − | 6.14458i | −0.126370 | − | 0.300541i | ||||
\(419\) | 20.4384i | 0.998480i | 0.866464 | + | 0.499240i | \(0.166387\pi\) | ||||
−0.866464 | + | 0.499240i | \(0.833613\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 11.2098i | − | 0.546331i | −0.961967 | − | 0.273165i | \(-0.911929\pi\) | ||
0.961967 | − | 0.273165i | \(-0.0880706\pi\) | |||||||
\(422\) | 7.48902 | 0.364560 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.02555 | 0.0983694 | ||||||||
\(425\) | − | 7.05596i | − | 0.342264i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.80846 | + | 15.8084i | −0.474665 | + | 0.765024i | ||||
\(428\) | − | 1.15867i | − | 0.0560064i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.83525 | 0.0885035 | ||||||||
\(431\) | − | 15.6916i | − | 0.755839i | −0.925838 | − | 0.377920i | \(-0.876640\pi\) | ||
0.925838 | − | 0.377920i | \(-0.123360\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.1026 | 1.44664 | 0.723319 | − | 0.690514i | \(-0.242615\pi\) | ||||
0.723319 | + | 0.690514i | \(0.242615\pi\) | |||||||
\(434\) | −1.15867 | + | 1.86744i | −0.0556179 | + | 0.0896402i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.02555i | 0.0970063i | ||||||||
\(437\) | −26.1032 | + | 10.9758i | −1.24869 | + | 0.525042i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.1452 | −1.53420 | −0.767102 | − | 0.641525i | \(-0.778302\pi\) | ||||
−0.767102 | + | 0.641525i | \(0.778302\pi\) | |||||||
\(440\) | −4.19606 | −0.200039 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.8924 | −0.708361 | ||||||||
\(443\) | 29.3165 | 1.39287 | 0.696435 | − | 0.717620i | \(-0.254768\pi\) | ||||
0.696435 | + | 0.717620i | \(0.254768\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.8604i | 0.799258i | ||||||||
\(446\) | − | 13.5806i | − | 0.643061i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.24817 | + | 1.39489i | 0.106216 | + | 0.0659025i | ||||
\(449\) | 14.3173i | 0.675677i | 0.941204 | + | 0.337838i | \(0.109696\pi\) | ||||
−0.941204 | + | 0.337838i | \(0.890304\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.8957 | 0.842675 | ||||||||
\(452\) | 10.5966i | 0.498422i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 23.9027i | − | 1.12181i | ||||||
\(455\) | −20.4320 | + | 32.9305i | −0.957866 | + | 1.54381i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.5564 | −1.42937 | −0.714684 | − | 0.699447i | \(-0.753430\pi\) | ||||
−0.714684 | + | 0.699447i | \(0.753430\pi\) | |||||||
\(458\) | 15.0816 | 0.704718 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 17.8256i | 0.831122i | ||||||||
\(461\) | − | 5.25748i | − | 0.244865i | −0.992477 | − | 0.122433i | \(-0.960930\pi\) | ||
0.992477 | − | 0.122433i | \(-0.0390695\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.4926 | 0.627054 | 0.313527 | − | 0.949579i | \(-0.398489\pi\) | ||||
0.313527 | + | 0.949579i | \(0.398489\pi\) | |||||||
\(464\) | − | 6.88592i | − | 0.319671i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.1258i | 0.561717i | ||||||||
\(467\) | 26.7842i | 1.23943i | 0.784829 | + | 0.619713i | \(0.212751\pi\) | ||||
−0.784829 | + | 0.619713i | \(0.787249\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.79554 | − | 7.72904i | 0.221437 | − | 0.356894i | ||||
\(470\) | 13.2565i | 0.611475i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.53373i | 0.254710i | ||||||||
\(473\) | 1.02279 | 0.0470280 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.1627 | + | 4.27317i | −0.466298 | + | 0.196067i | ||||
\(476\) | −3.89146 | + | 6.27192i | −0.178365 | + | 0.287473i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.55476i | 0.437025i | ||||||||
\(479\) | − | 20.1864i | − | 0.922340i | −0.887312 | − | 0.461170i | \(-0.847430\pi\) | ||
0.887312 | − | 0.461170i | \(-0.152570\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 55.1107i | 2.51283i | ||||||||
\(482\) | 8.77104i | 0.399510i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.66152 | 0.393705 | ||||||||
\(485\) | 14.5811i | 0.662094i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 24.0576i | − | 1.09015i | −0.838386 | − | 0.545077i | \(-0.816500\pi\) | ||
0.838386 | − | 0.545077i | \(-0.183500\pi\) | |||||||
\(488\) | 7.03169 | 0.318310 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8.52966 | + | 17.2098i | 0.385331 | + | 0.777458i | ||||
\(491\) | 1.32465 | 0.0597808 | 0.0298904 | − | 0.999553i | \(-0.490484\pi\) | ||||
0.0298904 | + | 0.999553i | \(0.490484\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.2103 | 0.865187 | ||||||||
\(494\) | 9.01904 | + | 21.4496i | 0.405786 | + | 0.965065i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.830650 | 0.0372973 | ||||||||
\(497\) | 15.9903 | − | 25.7718i | 0.717264 | − | 1.15603i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.8620 | 1.15774 | 0.578872 | − | 0.815419i | \(-0.303493\pi\) | ||||
0.578872 | + | 0.815419i | \(0.303493\pi\) | |||||||
\(500\) | − | 6.77970i | − | 0.303198i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.10882 | 0.0941213 | ||||||||
\(503\) | − | 19.9802i | − | 0.890875i | −0.895313 | − | 0.445437i | \(-0.853048\pi\) | ||
0.895313 | − | 0.445437i | \(-0.146952\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.5820 | 1.09388 | ||||||||
\(506\) | 9.93426i | 0.441632i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 19.2353i | 0.853429i | ||||||||
\(509\) | 25.3306 | 1.12276 | 0.561379 | − | 0.827559i | \(-0.310271\pi\) | ||||
0.561379 | + | 0.827559i | \(0.310271\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.4973 | + | 28.2007i | −0.774036 | + | 1.24752i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 22.7700i | 1.00434i | ||||||||
\(515\) | 34.9269i | 1.53907i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.38788i | 0.324919i | ||||||||
\(518\) | 23.2098 | + | 14.4007i | 1.01978 | + | 0.632729i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 14.6477 | 0.642344 | ||||||||
\(521\) | −15.1934 | −0.665635 | −0.332818 | − | 0.942991i | \(-0.607999\pi\) | ||||
−0.332818 | + | 0.942991i | \(0.607999\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.1839 | −0.663947 | −0.331974 | − | 0.943289i | \(-0.607715\pi\) | ||||
−0.331974 | + | 0.943289i | \(0.607715\pi\) | |||||||
\(524\) | − | 8.95863i | − | 0.391360i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.3027i | 0.972444i | ||||||||
\(527\) | 2.31734i | 0.100945i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.2025 | 0.834889 | ||||||||
\(530\) | − | 5.55799i | − | 0.241424i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 11.3902 | + | 1.80653i | 0.493827 | + | 0.0783232i | ||||
\(533\) | −62.4706 | −2.70590 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.17932 | −0.137454 | ||||||||
\(536\) | −3.43792 | −0.148496 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.88304i | 0.167410i | ||||||||
\(539\) | 4.75361 | + | 9.59107i | 0.204753 | + | 0.413117i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.3684 | 1.39163 | 0.695814 | − | 0.718222i | \(-0.255044\pi\) | ||||
0.695814 | + | 0.718222i | \(0.255044\pi\) | |||||||
\(542\) | 19.7969 | 0.850348 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.78979 | 0.119611 | ||||||||
\(545\) | 5.55799 | 0.238078 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.1022i | 1.37259i | 0.727323 | + | 0.686296i | \(0.240764\pi\) | ||||
−0.727323 | + | 0.686296i | \(0.759236\pi\) | |||||||
\(548\) | −0.769087 | −0.0328538 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.86769i | 0.164919i | ||||||||
\(551\) | −11.6340 | − | 27.6686i | −0.495624 | − | 1.17872i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.03131 | + | 9.72075i | −0.256477 | + | 0.413368i | ||||
\(554\) | − | 21.7061i | − | 0.922204i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.60077i | 0.195116i | ||||||||
\(557\) | 29.4122 | 1.24624 | 0.623118 | − | 0.782128i | \(-0.285866\pi\) | ||||
0.623118 | + | 0.782128i | \(0.285866\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.57038 | −0.151011 | ||||||||
\(560\) | 3.82751 | − | 6.16885i | 0.161742 | − | 0.260681i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.2394 | −0.768698 | −0.384349 | − | 0.923188i | \(-0.625574\pi\) | ||||
−0.384349 | + | 0.923188i | \(0.625574\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 29.0764 | 1.22325 | ||||||||
\(566\) | −0.703721 | −0.0295796 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.4635 | −0.480997 | ||||||||
\(569\) | 6.50741i | 0.272805i | 0.990654 | + | 0.136402i | \(0.0435540\pi\) | ||||
−0.990654 | + | 0.136402i | \(0.956446\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.2557 | 1.01507 | 0.507534 | − | 0.861632i | \(-0.330557\pi\) | ||||
0.507534 | + | 0.861632i | \(0.330557\pi\) | |||||||
\(572\) | 8.16322 | 0.341321 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −16.3238 | + | 26.3094i | −0.681344 | + | 1.09813i | ||||
\(575\) | 16.4306 | 0.685204 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.341005i | 0.0141962i | 0.999975 | + | 0.00709812i | \(0.00225942\pi\) | ||||
−0.999975 | + | 0.00709812i | \(0.997741\pi\) | |||||||
\(578\) | − | 9.21709i | − | 0.383380i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −18.8946 | −0.784554 | ||||||||
\(581\) | −20.1514 | + | 32.4782i | −0.836019 | + | 1.34742i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3.09749i | − | 0.128285i | ||||||
\(584\) | 12.5438 | 0.519068 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 11.5650i | − | 0.477747i | ||||||
\(587\) | 16.9385i | 0.699125i | 0.936913 | + | 0.349563i | \(0.113670\pi\) | ||||
−0.936913 | + | 0.349563i | \(0.886330\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.33767 | − | 1.40341i | 0.137526 | − | 0.0578264i | ||||
\(590\) | 15.1842 | 0.625124 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 10.3238i | − | 0.424307i | ||||||
\(593\) | − | 0.183387i | − | 0.00753082i | −0.999993 | − | 0.00376541i | \(-0.998801\pi\) | ||
0.999993 | − | 0.00376541i | \(-0.00119857\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.2098 | + | 10.6779i | 0.705532 | + | 0.437752i | ||||
\(596\) | −1.65501 | −0.0677919 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 34.6787i | − | 1.41812i | ||||||
\(599\) | − | 12.5365i | − | 0.512229i | −0.966647 | − | 0.256114i | \(-0.917558\pi\) | ||
0.966647 | − | 0.256114i | \(-0.0824423\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.0774 | −0.615021 | −0.307510 | − | 0.951545i | \(-0.599496\pi\) | ||||
−0.307510 | + | 0.951545i | \(0.599496\pi\) | |||||||
\(602\) | −0.932956 | + | 1.50366i | −0.0380244 | + | 0.0612845i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 3.72075i | − | 0.151395i | ||||||
\(605\) | − | 23.7667i | − | 0.966253i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.05236 | −0.0833028 | −0.0416514 | − | 0.999132i | \(-0.513262\pi\) | ||||
−0.0416514 | + | 0.999132i | \(0.513262\pi\) | |||||||
\(608\) | −1.68953 | − | 4.01815i | −0.0685195 | − | 0.162957i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 19.2945i | − | 0.781213i | ||||||
\(611\) | − | 25.7898i | − | 1.04334i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.8685 | −0.883262 | −0.441631 | − | 0.897197i | \(-0.645600\pi\) | ||||
−0.441631 | + | 0.897197i | \(0.645600\pi\) | |||||||
\(614\) | 18.4686i | 0.745333i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.13308 | − | 3.43792i | 0.0859444 | − | 0.138518i | ||||
\(617\) | 1.59740 | 0.0643089 | 0.0321544 | − | 0.999483i | \(-0.489763\pi\) | ||||
0.0321544 | + | 0.999483i | \(0.489763\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.3993i | 0.699336i | 0.936874 | + | 0.349668i | \(0.113706\pi\) | ||||
−0.936874 | + | 0.349668i | \(0.886294\pi\) | |||||||
\(620\) | − | 2.27925i | − | 0.0915371i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.80842 | 0.192800 | ||||||||
\(623\) | −13.8141 | − | 8.57104i | −0.553449 | − | 0.343392i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2491 | −1.24997 | ||||||||
\(626\) | 12.4521 | 0.497688 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 21.8613i | 0.872362i | ||||||||
\(629\) | 28.8013 | 1.14838 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.5382 | −0.618565 | −0.309282 | − | 0.950970i | \(-0.600089\pi\) | ||||
−0.309282 | + | 0.950970i | \(0.600089\pi\) | |||||||
\(632\) | 4.32385 | 0.171993 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 30.0767 | 1.19450 | ||||||||
\(635\) | 52.7806 | 2.09453 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.5940 | − | 33.4807i | −0.657479 | − | 1.32655i | ||||
\(638\) | −10.5300 | −0.416887 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.74394 | −0.108464 | ||||||||
\(641\) | − | 3.72075i | − | 0.146961i | −0.997297 | − | 0.0734803i | \(-0.976589\pi\) | ||
0.997297 | − | 0.0734803i | \(-0.0234106\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.9990i | 0.591504i | 0.955265 | + | 0.295752i | \(0.0955701\pi\) | ||||
−0.955265 | + | 0.295752i | \(0.904430\pi\) | |||||||
\(644\) | −14.6049 | − | 9.06171i | −0.575513 | − | 0.357081i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.2098 | − | 4.71343i | 0.441042 | − | 0.185447i | ||||
\(647\) | − | 10.5953i | − | 0.416545i | −0.978071 | − | 0.208272i | \(-0.933216\pi\) | ||
0.978071 | − | 0.208272i | \(-0.0667840\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.46223 | 0.332171 | ||||||||
\(650\) | − | 13.5014i | − | 0.529569i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.52921 | 0.373193 | ||||||||
\(653\) | 20.5129 | 0.802733 | 0.401366 | − | 0.915918i | \(-0.368535\pi\) | ||||
0.401366 | + | 0.915918i | \(0.368535\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −24.5820 | −0.960497 | ||||||||
\(656\) | 11.7026 | 0.456909 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −10.8613 | − | 6.73898i | −0.423418 | − | 0.262713i | ||||
\(659\) | − | 44.7154i | − | 1.74186i | −0.491404 | − | 0.870932i | \(-0.663516\pi\) | ||
0.491404 | − | 0.870932i | \(-0.336484\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.2948 | 0.828272 | 0.414136 | − | 0.910215i | \(-0.364084\pi\) | ||||
0.414136 | + | 0.910215i | \(0.364084\pi\) | |||||||
\(662\) | −10.8413 | −0.421360 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.4465 | 0.560634 | ||||||||
\(665\) | 4.95702 | − | 31.2540i | 0.192225 | − | 1.21198i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 44.7333i | 1.73208i | ||||||||
\(668\) | 16.4636 | 0.636997 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.43346i | 0.364446i | ||||||||
\(671\) | − | 10.7529i | − | 0.415112i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 34.3815i | − | 1.32531i | −0.748926 | − | 0.662654i | \(-0.769430\pi\) | ||
0.748926 | − | 0.662654i | \(-0.230570\pi\) | |||||||
\(674\) | −8.27925 | −0.318905 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15.4963 | −0.596013 | ||||||||
\(677\) | −13.2476 | −0.509145 | −0.254573 | − | 0.967054i | \(-0.581935\pi\) | ||||
−0.254573 | + | 0.967054i | \(0.581935\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.9466 | − | 7.41237i | −0.458470 | − | 0.284461i | ||||
\(680\) | − | 7.65501i | − | 0.293556i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 1.27024i | − | 0.0486399i | ||||||
\(683\) | − | 40.0892i | − | 1.53397i | −0.641665 | − | 0.766985i | \(-0.721756\pi\) | ||
0.641665 | − | 0.766985i | \(-0.278244\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.11033i | 0.0806315i | ||||||||
\(686\) | −18.4364 | − | 1.76012i | −0.703906 | − | 0.0672018i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.668836 | 0.0254991 | ||||||||
\(689\) | 10.8128i | 0.411934i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.88304i | 0.147718i | 0.997269 | + | 0.0738589i | \(0.0235314\pi\) | ||||
−0.997269 | + | 0.0738589i | \(0.976469\pi\) | |||||||
\(692\) | −7.59670 | −0.288783 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.32465i | 0.0502832i | ||||||||
\(695\) | 12.6242 | 0.478865 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.6477i | 1.23662i | ||||||||
\(698\) | −5.15328 | −0.195054 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.68609 | − | 3.52798i | −0.214914 | − | 0.133345i | ||||
\(701\) | −42.4651 | −1.60389 | −0.801943 | − | 0.597401i | \(-0.796200\pi\) | ||||
−0.801943 | + | 0.597401i | \(0.796200\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.4424 | − | 41.4827i | −0.657854 | − | 1.56455i | ||||
\(704\) | −1.52921 | −0.0576342 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20.5237 | −0.772418 | ||||||||
\(707\) | −12.4963 | + | 20.1405i | −0.469973 | + | 0.757463i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.49259 | 0.356502 | 0.178251 | − | 0.983985i | \(-0.442956\pi\) | ||||
0.178251 | + | 0.983985i | \(0.442956\pi\) | |||||||
\(710\) | 31.4551i | 1.18049i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.14458i | 0.230278i | ||||||||
\(713\) | −5.39619 | −0.202089 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 22.3994i | − | 0.837690i | ||||||
\(716\) | 20.6477i | 0.771641i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 16.2171i | − | 0.605216i | ||||||
\(719\) | 40.2152i | 1.49977i | 0.661567 | + | 0.749886i | \(0.269892\pi\) | ||||
−0.661567 | + | 0.749886i | \(0.730108\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28.6164 | − | 17.7553i | −1.06573 | − | 0.661240i | ||||
\(722\) | −13.5776 | − | 13.2910i | −0.505304 | − | 0.494639i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.20564 | 0.267795 | ||||||||
\(725\) | 17.4159i | 0.646812i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.8327i | 0.587203i | 0.955928 | + | 0.293601i | \(0.0948538\pi\) | ||||
−0.955928 | + | 0.293601i | \(0.905146\pi\) | |||||||
\(728\) | −7.44622 | + | 12.0012i | −0.275975 | + | 0.444793i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − | 34.4195i | − | 1.27392i | ||||||
\(731\) | 1.86591i | 0.0690132i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 20.8446i | − | 0.769913i | −0.922935 | − | 0.384956i | \(-0.874216\pi\) | ||
0.922935 | − | 0.384956i | \(-0.125784\pi\) | |||||||
\(734\) | −28.7403 | −1.06082 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.49634i | 0.239458i | ||||||||
\(737\) | 5.25730i | 0.193655i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.9992 | −1.28747 | −0.643733 | − | 0.765250i | \(-0.722615\pi\) | ||||
−0.643733 | + | 0.765250i | \(0.722615\pi\) | |||||||
\(740\) | −28.3280 | −1.04136 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.55378 | + | 2.82543i | 0.167175 | + | 0.103725i | ||||
\(743\) | 41.8985i | 1.53711i | 0.639786 | + | 0.768553i | \(0.279023\pi\) | ||||
−0.639786 | + | 0.768553i | \(0.720977\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.54125i | 0.166378i | ||||||||
\(746\) | −6.88592 | −0.252112 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 4.26617i | − | 0.155987i | ||||||
\(749\) | 1.61622 | − | 2.60488i | 0.0590554 | − | 0.0951804i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 47.0226i | − | 1.71588i | −0.513749 | − | 0.857940i | \(-0.671744\pi\) | ||
0.513749 | − | 0.857940i | \(-0.328256\pi\) | |||||||
\(752\) | 4.83118i | 0.176175i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 36.7584 | 1.33866 | ||||||||
\(755\) | −10.2095 | −0.371562 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.1859 | 0.442903 | 0.221451 | − | 0.975171i | \(-0.428921\pi\) | ||||
0.221451 | + | 0.975171i | \(0.428921\pi\) | |||||||
\(758\) | 8.56208 | 0.310989 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −11.0256 | + | 4.63597i | −0.399939 | + | 0.168164i | ||||
\(761\) | 43.1626i | 1.56464i | 0.622876 | + | 0.782321i | \(0.285964\pi\) | ||||
−0.622876 | + | 0.782321i | \(0.714036\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.82543 | + | 4.55378i | −0.102287 | + | 0.164858i | ||||
\(764\) | 16.5474 | 0.598665 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 0.0485251i | − | 0.00175328i | ||||||
\(767\) | −29.5401 | −1.06663 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 44.4328i | − | 1.60229i | −0.598472 | − | 0.801144i | \(-0.704225\pi\) | ||
0.598472 | − | 0.801144i | \(-0.295775\pi\) | |||||||
\(770\) | −9.43346 | − | 5.85306i | −0.339958 | − | 0.210929i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 24.3684i | 0.877039i | ||||||||
\(773\) | −39.0961 | −1.40619 | −0.703095 | − | 0.711096i | \(-0.748199\pi\) | ||||
−0.703095 | + | 0.711096i | \(0.748199\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.10089 | −0.0754661 | ||||||||
\(776\) | 5.31393i | 0.190759i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.94158i | 0.105461i | ||||||||
\(779\) | 47.0226 | − | 19.7718i | 1.68476 | − | 0.708400i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.5300i | 0.627274i | ||||||||
\(782\) | −18.1234 | −0.648092 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.10854 | + | 6.27192i | 0.111019 | + | 0.223997i | ||||
\(785\) | 59.9862 | 2.14100 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.65455 | −0.165917 | −0.0829584 | − | 0.996553i | \(-0.526437\pi\) | ||||
−0.0829584 | + | 0.996553i | \(0.526437\pi\) | |||||||
\(788\) | −6.99268 | −0.249104 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 11.8644i | − | 0.422116i | ||||||
\(791\) | −14.7811 | + | 23.8229i | −0.525556 | + | 0.847047i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 37.5366i | 1.33296i | ||||||||
\(794\) | 26.1275 | 0.927230 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 20.0719i | − | 0.711431i | ||||||
\(797\) | 23.9027 | 0.846678 | 0.423339 | − | 0.905971i | \(-0.360858\pi\) | ||||
0.423339 | + | 0.905971i | \(0.360858\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.4780 | −0.476816 | ||||||||
\(800\) | 2.52921i | 0.0894210i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.31734 | −0.293695 | ||||||||
\(803\) | − | 19.1821i | − | 0.676923i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −24.8648 | + | 40.0749i | −0.876368 | + | 1.41246i | ||||
\(806\) | 4.43417i | 0.156187i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.95863 | 0.315164 | ||||||||
\(809\) | −23.3657 | −0.821494 | −0.410747 | − | 0.911749i | \(-0.634732\pi\) | ||||
−0.410747 | + | 0.911749i | \(0.634732\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.7337 | 1.57081 | 0.785406 | − | 0.618981i | \(-0.212454\pi\) | ||||
0.785406 | + | 0.618981i | \(0.212454\pi\) | |||||||
\(812\) | 9.60513 | − | 15.4807i | 0.337074 | − | 0.543267i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −15.7873 | −0.553345 | ||||||||
\(815\) | − | 26.1476i | − | 0.915910i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.68748 | − | 1.13002i | 0.0940231 | − | 0.0395344i | ||||
\(818\) | − | 0.0822533i | − | 0.00287592i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 32.1112i | − | 1.12137i | ||||||
\(821\) | 15.4269 | 0.538401 | 0.269201 | − | 0.963084i | \(-0.413241\pi\) | ||||
0.269201 | + | 0.963084i | \(0.413241\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.0199 | 1.53444 | 0.767218 | − | 0.641386i | \(-0.221640\pi\) | ||||
0.767218 | + | 0.641386i | \(0.221640\pi\) | |||||||
\(824\) | 12.7288i | 0.443427i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.71896 | + | 12.4408i | −0.268577 | + | 0.432870i | ||||
\(827\) | 0.651261i | 0.0226466i | 0.999936 | + | 0.0113233i | \(0.00360439\pi\) | ||||
−0.999936 | + | 0.0113233i | \(0.996396\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.76653 | −0.339206 | −0.169603 | − | 0.985513i | \(-0.554248\pi\) | ||||
−0.169603 | + | 0.985513i | \(0.554248\pi\) | |||||||
\(830\) | − | 39.6404i | − | 1.37594i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.33820 | 0.185069 | ||||||||
\(833\) | −17.4973 | + | 8.67217i | −0.606246 | + | 0.300473i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 45.1753i | − | 1.56335i | ||||||
\(836\) | −6.14458 | + | 2.58364i | −0.212515 | + | 0.0893572i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 20.4384 | 0.706032 | ||||||||
\(839\) | −30.7589 | −1.06192 | −0.530958 | − | 0.847398i | \(-0.678168\pi\) | ||||
−0.530958 | + | 0.847398i | \(0.678168\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.4159 | −0.635032 | ||||||||
\(842\) | −11.2098 | −0.386314 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 7.48902i | − | 0.257783i | ||||||
\(845\) | 42.5210i | 1.46277i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19.4726 | + | 12.0819i | 0.669086 | + | 0.415139i | ||||
\(848\) | − | 2.02555i | − | 0.0695577i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7.05596 | −0.242017 | ||||||||
\(851\) | 67.0672i | 2.29904i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1.15311i | − | 0.0394817i | −0.999805 | − | 0.0197409i | \(-0.993716\pi\) | ||
0.999805 | − | 0.0197409i | \(-0.00628412\pi\) | |||||||
\(854\) | 15.8084 | + | 9.80846i | 0.540954 | + | 0.335639i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.15867 | −0.0396025 | ||||||||
\(857\) | 34.8849 | 1.19165 | 0.595823 | − | 0.803116i | \(-0.296826\pi\) | ||||
0.595823 | + | 0.803116i | \(0.296826\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 39.4425i | − | 1.34576i | −0.739751 | − | 0.672880i | \(-0.765057\pi\) | ||
0.739751 | − | 0.672880i | \(-0.234943\pi\) | |||||||
\(860\) | − | 1.83525i | − | 0.0625814i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15.6916 | −0.534459 | ||||||||
\(863\) | 45.6192i | 1.55290i | 0.630181 | + | 0.776448i | \(0.282981\pi\) | ||||
−0.630181 | + | 0.776448i | \(0.717019\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.8449i | 0.708748i | ||||||||
\(866\) | − | 30.1026i | − | 1.02293i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.86744 | + | 1.15867i | 0.0633852 | + | 0.0393278i | ||||
\(869\) | − | 6.61207i | − | 0.224299i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 18.3523i | − | 0.621844i | ||||||
\(872\) | 2.02555 | 0.0685938 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 10.9758 | + | 26.1032i | 0.371261 | + | 0.882955i | ||||
\(875\) | 9.45696 | − | 15.2419i | 0.319704 | − | 0.515271i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.4670i | 0.724890i | 0.932005 | + | 0.362445i | \(0.118058\pi\) | ||||
−0.932005 | + | 0.362445i | \(0.881942\pi\) | |||||||
\(878\) | 32.1452i | 1.08485i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.19606i | 0.141449i | ||||||||
\(881\) | − | 23.2218i | − | 0.782361i | −0.920314 | − | 0.391181i | \(-0.872067\pi\) | ||
0.920314 | − | 0.391181i | \(-0.127933\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −55.2588 | −1.85961 | −0.929803 | − | 0.368058i | \(-0.880023\pi\) | ||||
−0.929803 | + | 0.368058i | \(0.880023\pi\) | |||||||
\(884\) | 14.8924i | 0.500887i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 29.3165i | − | 0.984908i | ||||||
\(887\) | −16.7872 | −0.563661 | −0.281830 | − | 0.959464i | \(-0.590942\pi\) | ||||
−0.281830 | + | 0.959464i | \(0.590942\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26.8312 | + | 43.2443i | −0.899890 | + | 1.45037i | ||||
\(890\) | 16.8604 | 0.565161 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13.5806 | −0.454713 | ||||||||
\(893\) | 8.16242 | + | 19.4124i | 0.273145 | + | 0.649610i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 56.6560 | 1.89380 | ||||||||
\(896\) | 1.39489 | − | 2.24817i | 0.0466001 | − | 0.0751061i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14.3173 | 0.477776 | ||||||||
\(899\) | − | 5.71979i | − | 0.190766i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.65086 | 0.188257 | ||||||||
\(902\) | − | 17.8957i | − | 0.595861i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.5966 | 0.352437 | ||||||||
\(905\) | − | 19.7718i | − | 0.657238i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.5912i | 1.31461i | 0.753627 | + | 0.657303i | \(0.228303\pi\) | ||||
−0.753627 | + | 0.657303i | \(0.771697\pi\) | |||||||
\(908\) | −23.9027 | −0.793240 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 32.9305 | + | 20.4320i | 1.09164 | + | 0.677313i | ||||
\(911\) | − | 24.6031i | − | 0.815137i | −0.913175 | − | 0.407569i | \(-0.866377\pi\) | ||
0.913175 | − | 0.407569i | \(-0.133623\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 22.0917i | − | 0.731130i | ||||||
\(914\) | 30.5564i | 1.01072i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 15.0816i | − | 0.498311i | ||||||
\(917\) | 12.4963 | − | 20.1405i | 0.412666 | − | 0.665099i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.7300 | 0.683820 | 0.341910 | − | 0.939733i | \(-0.388926\pi\) | ||||
0.341910 | + | 0.939733i | \(0.388926\pi\) | |||||||
\(920\) | 17.8256 | 0.587692 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.25748 | −0.173146 | ||||||||
\(923\) | − | 61.1943i | − | 2.01423i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26.1112i | 0.858530i | ||||||||
\(926\) | − | 13.4926i | − | 0.443394i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.88592 | −0.226042 | ||||||||
\(929\) | 22.0690i | 0.724060i | 0.932166 | + | 0.362030i | \(0.117916\pi\) | ||||
−0.932166 | + | 0.362030i | \(0.882084\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23.0872 | + | 19.9495i | 0.756651 | + | 0.653818i | ||||
\(932\) | 12.1258 | 0.397194 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 26.7842 | 0.876406 | ||||||||
\(935\) | −11.7061 | −0.382831 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.6688i | 1.36126i | 0.732627 | + | 0.680630i | \(0.238294\pi\) | ||||
−0.732627 | + | 0.680630i | \(0.761706\pi\) | |||||||
\(938\) | −7.72904 | − | 4.79554i | −0.252362 | − | 0.156580i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 13.2565 | 0.432378 | ||||||||
\(941\) | −20.6014 | −0.671585 | −0.335792 | − | 0.941936i | \(-0.609004\pi\) | ||||
−0.335792 | + | 0.941936i | \(0.609004\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −76.0239 | −2.47568 | ||||||||
\(944\) | 5.53373 | 0.180107 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 1.02279i | − | 0.0332538i | ||||||
\(947\) | −35.2077 | −1.14410 | −0.572048 | − | 0.820220i | \(-0.693851\pi\) | ||||
−0.572048 | + | 0.820220i | \(0.693851\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 66.9615i | 2.17366i | ||||||||
\(950\) | 4.27317 | + | 10.1627i | 0.138640 | + | 0.329722i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.27192 | + | 3.89146i | 0.203274 | + | 0.126123i | ||||
\(953\) | − | 8.06412i | − | 0.261222i | −0.991434 | − | 0.130611i | \(-0.958306\pi\) | ||
0.991434 | − | 0.130611i | \(-0.0416940\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 45.4052i | − | 1.46928i | ||||||
\(956\) | 9.55476 | 0.309023 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −20.1864 | −0.652193 | ||||||||
\(959\) | −1.72904 | − | 1.07279i | −0.0558336 | − | 0.0346423i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3100 | −0.977743 | ||||||||
\(962\) | 55.1107 | 1.77684 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.77104 | 0.282496 | ||||||||
\(965\) | 66.8655 | 2.15248 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.9723 | 1.22111 | 0.610554 | − | 0.791974i | \(-0.290947\pi\) | ||||
0.610554 | + | 0.791974i | \(0.290947\pi\) | |||||||
\(968\) | − | 8.66152i | − | 0.278392i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 14.5811 | 0.468171 | ||||||||
\(971\) | −46.3048 | −1.48599 | −0.742996 | − | 0.669296i | \(-0.766596\pi\) | ||||
−0.742996 | + | 0.669296i | \(0.766596\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.41759 | + | 10.3433i | −0.205738 | + | 0.331592i | ||||
\(974\) | −24.0576 | −0.770856 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 7.03169i | − | 0.225079i | ||||||
\(977\) | 26.9780i | 0.863104i | 0.902088 | + | 0.431552i | \(0.142034\pi\) | ||||
−0.902088 | + | 0.431552i | \(0.857966\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.39635 | 0.300309 | ||||||||
\(980\) | 17.2098 | − | 8.52966i | 0.549746 | − | 0.272470i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 1.32465i | − | 0.0422714i | ||||||
\(983\) | −49.7145 | −1.58565 | −0.792824 | − | 0.609451i | \(-0.791390\pi\) | ||||
−0.792824 | + | 0.609451i | \(0.791390\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.1875i | 0.611365i | ||||||||
\(986\) | − | 19.2103i | − | 0.611779i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 21.4496 | − | 9.01904i | 0.682404 | − | 0.286934i | ||||
\(989\) | −4.34499 | −0.138163 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 42.3393i | − | 1.34495i | −0.740119 | − | 0.672476i | \(-0.765231\pi\) | ||
0.740119 | − | 0.672476i | \(-0.234769\pi\) | |||||||
\(992\) | − | 0.830650i | − | 0.0263732i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −25.7718 | − | 15.9903i | −0.817433 | − | 0.507182i | ||||
\(995\) | −55.0762 | −1.74603 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.3567i | 0.486352i | 0.969982 | + | 0.243176i | \(0.0781893\pi\) | ||||
−0.969982 | + | 0.243176i | \(0.921811\pi\) | |||||||
\(998\) | − | 25.8620i | − | 0.818648i | ||||||
\(999\) | 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 | 2394.2.e.c.1063.7 | 16 | ||
3.2 | odd | 2 | 266.2.d.a.265.12 | yes | 16 | ||
7.6 | odd | 2 | inner | 2394.2.e.c.1063.2 | 16 | ||
12.11 | even | 2 | 2128.2.m.f.1329.9 | 16 | |||
19.18 | odd | 2 | inner | 2394.2.e.c.1063.15 | 16 | ||
21.20 | even | 2 | 266.2.d.a.265.13 | yes | 16 | ||
57.56 | even | 2 | 266.2.d.a.265.5 | yes | 16 | ||
84.83 | odd | 2 | 2128.2.m.f.1329.8 | 16 | |||
133.132 | even | 2 | inner | 2394.2.e.c.1063.10 | 16 | ||
228.227 | odd | 2 | 2128.2.m.f.1329.7 | 16 | |||
399.398 | odd | 2 | 266.2.d.a.265.4 | ✓ | 16 | ||
1596.1595 | even | 2 | 2128.2.m.f.1329.10 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
266.2.d.a.265.4 | ✓ | 16 | 399.398 | odd | 2 | ||
266.2.d.a.265.5 | yes | 16 | 57.56 | even | 2 | ||
266.2.d.a.265.12 | yes | 16 | 3.2 | odd | 2 | ||
266.2.d.a.265.13 | yes | 16 | 21.20 | even | 2 | ||
2128.2.m.f.1329.7 | 16 | 228.227 | odd | 2 | |||
2128.2.m.f.1329.8 | 16 | 84.83 | odd | 2 | |||
2128.2.m.f.1329.9 | 16 | 12.11 | even | 2 | |||
2128.2.m.f.1329.10 | 16 | 1596.1595 | even | 2 | |||
2394.2.e.c.1063.2 | 16 | 7.6 | odd | 2 | inner | ||
2394.2.e.c.1063.7 | 16 | 1.1 | even | 1 | trivial | ||
2394.2.e.c.1063.10 | 16 | 133.132 | even | 2 | inner | ||
2394.2.e.c.1063.15 | 16 | 19.18 | odd | 2 | inner |