Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [294,4,Mod(67,294)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(294, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("294.67");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 294 = 2 \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 294.e (of order \(3\), degree \(2\), not 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: | \(17.3465615417\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 294.79 |
Dual form | 294.4.e.d.67.1 |
$q$-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 \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(199\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.73205i | −0.353553 | + | 0.612372i | ||||
\(3\) | 1.50000 | + | 2.59808i | 0.288675 | + | 0.500000i | ||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.00000 | − | 1.73205i | 0.0894427 | − | 0.154919i | −0.817833 | − | 0.575456i | \(-0.804825\pi\) |
0.907276 | + | 0.420536i | \(0.138158\pi\) | |||||||
\(6\) | −6.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | 2.00000 | + | 3.46410i | 0.0632456 | + | 0.109545i | ||||
\(11\) | 4.00000 | + | 6.92820i | 0.109640 | + | 0.189903i | 0.915625 | − | 0.402034i | \(-0.131697\pi\) |
−0.805984 | + | 0.591937i | \(0.798363\pi\) | |||||||
\(12\) | 6.00000 | − | 10.3923i | 0.144338 | − | 0.250000i | ||||
\(13\) | 42.0000 | 0.896054 | 0.448027 | − | 0.894020i | \(-0.352127\pi\) | ||||
0.448027 | + | 0.894020i | \(0.352127\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.00000 | 0.103280 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.00000 | − | 1.73205i | −0.0142668 | − | 0.0247108i | 0.858804 | − | 0.512305i | \(-0.171208\pi\) |
−0.873071 | + | 0.487594i | \(0.837875\pi\) | |||||||
\(18\) | −9.00000 | − | 15.5885i | −0.117851 | − | 0.204124i | ||||
\(19\) | −62.0000 | + | 107.387i | −0.748620 | + | 1.29665i | 0.199865 | + | 0.979824i | \(0.435950\pi\) |
−0.948484 | + | 0.316824i | \(0.897384\pi\) | |||||||
\(20\) | −8.00000 | −0.0894427 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −16.0000 | −0.155055 | ||||||||
\(23\) | −38.0000 | + | 65.8179i | −0.344502 | + | 0.596695i | −0.985263 | − | 0.171045i | \(-0.945286\pi\) |
0.640761 | + | 0.767740i | \(0.278619\pi\) | |||||||
\(24\) | 12.0000 | + | 20.7846i | 0.102062 | + | 0.176777i | ||||
\(25\) | 60.5000 | + | 104.789i | 0.484000 | + | 0.838313i | ||||
\(26\) | −42.0000 | + | 72.7461i | −0.316803 | + | 0.548719i | ||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 254.000 | 1.62644 | 0.813218 | − | 0.581960i | \(-0.197714\pi\) | ||||
0.813218 | + | 0.581960i | \(0.197714\pi\) | |||||||
\(30\) | −6.00000 | + | 10.3923i | −0.0365148 | + | 0.0632456i | ||||
\(31\) | −36.0000 | − | 62.3538i | −0.208574 | − | 0.361261i | 0.742692 | − | 0.669634i | \(-0.233549\pi\) |
−0.951266 | + | 0.308373i | \(0.900216\pi\) | |||||||
\(32\) | −16.0000 | − | 27.7128i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −12.0000 | + | 20.7846i | −0.0633010 | + | 0.109640i | ||||
\(34\) | 4.00000 | 0.0201763 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | −199.000 | + | 344.678i | −0.884200 | + | 1.53148i | −0.0375721 | + | 0.999294i | \(0.511962\pi\) |
−0.846628 | + | 0.532185i | \(0.821371\pi\) | |||||||
\(38\) | −124.000 | − | 214.774i | −0.529354 | − | 0.916868i | ||||
\(39\) | 63.0000 | + | 109.119i | 0.258669 | + | 0.448027i | ||||
\(40\) | 8.00000 | − | 13.8564i | 0.0316228 | − | 0.0547723i | ||||
\(41\) | −462.000 | −1.75981 | −0.879906 | − | 0.475148i | \(-0.842394\pi\) | ||||
−0.879906 | + | 0.475148i | \(0.842394\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 212.000 | 0.751853 | 0.375927 | − | 0.926649i | \(-0.377324\pi\) | ||||
0.375927 | + | 0.926649i | \(0.377324\pi\) | |||||||
\(44\) | 16.0000 | − | 27.7128i | 0.0548202 | − | 0.0949514i | ||||
\(45\) | 9.00000 | + | 15.5885i | 0.0298142 | + | 0.0516398i | ||||
\(46\) | −76.0000 | − | 131.636i | −0.243600 | − | 0.421927i | ||||
\(47\) | −132.000 | + | 228.631i | −0.409663 | + | 0.709558i | −0.994852 | − | 0.101339i | \(-0.967687\pi\) |
0.585189 | + | 0.810897i | \(0.301021\pi\) | |||||||
\(48\) | −48.0000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −242.000 | −0.684479 | ||||||||
\(51\) | 3.00000 | − | 5.19615i | 0.00823694 | − | 0.0142668i | ||||
\(52\) | −84.0000 | − | 145.492i | −0.224014 | − | 0.388003i | ||||
\(53\) | 81.0000 | + | 140.296i | 0.209928 | + | 0.363607i | 0.951692 | − | 0.307055i | \(-0.0993436\pi\) |
−0.741763 | + | 0.670662i | \(0.766010\pi\) | |||||||
\(54\) | 27.0000 | − | 46.7654i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 16.0000 | 0.0392262 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −372.000 | −0.864432 | ||||||||
\(58\) | −254.000 | + | 439.941i | −0.575032 | + | 0.995984i | ||||
\(59\) | −386.000 | − | 668.572i | −0.851744 | − | 1.47526i | −0.879633 | − | 0.475654i | \(-0.842212\pi\) |
0.0278883 | − | 0.999611i | \(-0.491122\pi\) | |||||||
\(60\) | −12.0000 | − | 20.7846i | −0.0258199 | − | 0.0447214i | ||||
\(61\) | 15.0000 | − | 25.9808i | 0.0314845 | − | 0.0545327i | −0.849854 | − | 0.527018i | \(-0.823310\pi\) |
0.881338 | + | 0.472486i | \(0.156643\pi\) | |||||||
\(62\) | 144.000 | 0.294968 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 42.0000 | − | 72.7461i | 0.0801455 | − | 0.138816i | ||||
\(66\) | −24.0000 | − | 41.5692i | −0.0447605 | − | 0.0775275i | ||||
\(67\) | 382.000 | + | 661.643i | 0.696548 | + | 1.20646i | 0.969656 | + | 0.244473i | \(0.0786151\pi\) |
−0.273108 | + | 0.961983i | \(0.588052\pi\) | |||||||
\(68\) | −4.00000 | + | 6.92820i | −0.00713340 | + | 0.0123554i | ||||
\(69\) | −228.000 | −0.397797 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −236.000 | −0.394480 | −0.197240 | − | 0.980355i | \(-0.563198\pi\) | ||||
−0.197240 | + | 0.980355i | \(0.563198\pi\) | |||||||
\(72\) | −36.0000 | + | 62.3538i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 209.000 | + | 361.999i | 0.335090 | + | 0.580394i | 0.983502 | − | 0.180896i | \(-0.0578998\pi\) |
−0.648412 | + | 0.761290i | \(0.724566\pi\) | |||||||
\(74\) | −398.000 | − | 689.356i | −0.625224 | − | 1.08292i | ||||
\(75\) | −181.500 | + | 314.367i | −0.279438 | + | 0.484000i | ||||
\(76\) | 496.000 | 0.748620 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −252.000 | −0.365813 | ||||||||
\(79\) | −276.000 | + | 478.046i | −0.393069 | + | 0.680815i | −0.992853 | − | 0.119347i | \(-0.961920\pi\) |
0.599784 | + | 0.800162i | \(0.295253\pi\) | |||||||
\(80\) | 16.0000 | + | 27.7128i | 0.0223607 | + | 0.0387298i | ||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 462.000 | − | 800.207i | 0.622187 | − | 1.07766i | ||||
\(83\) | −1036.00 | −1.37007 | −0.685035 | − | 0.728510i | \(-0.740213\pi\) | ||||
−0.685035 | + | 0.728510i | \(0.740213\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | −0.00510425 | ||||||||
\(86\) | −212.000 | + | 367.195i | −0.265820 | + | 0.460414i | ||||
\(87\) | 381.000 | + | 659.911i | 0.469511 | + | 0.813218i | ||||
\(88\) | 32.0000 | + | 55.4256i | 0.0387638 | + | 0.0671408i | ||||
\(89\) | 15.0000 | − | 25.9808i | 0.0178651 | − | 0.0309433i | −0.856955 | − | 0.515392i | \(-0.827646\pi\) |
0.874820 | + | 0.484449i | \(0.160980\pi\) | |||||||
\(90\) | −36.0000 | −0.0421637 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 304.000 | 0.344502 | ||||||||
\(93\) | 108.000 | − | 187.061i | 0.120420 | − | 0.208574i | ||||
\(94\) | −264.000 | − | 457.261i | −0.289676 | − | 0.501733i | ||||
\(95\) | 124.000 | + | 214.774i | 0.133917 | + | 0.231951i | ||||
\(96\) | 48.0000 | − | 83.1384i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | 1190.00 | 1.24563 | 0.622815 | − | 0.782369i | \(-0.285989\pi\) | ||||
0.622815 | + | 0.782369i | \(0.285989\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −72.0000 | −0.0730937 | ||||||||
\(100\) | 242.000 | − | 419.156i | 0.242000 | − | 0.419156i | ||||
\(101\) | 685.000 | + | 1186.45i | 0.674852 | + | 1.16888i | 0.976512 | + | 0.215462i | \(0.0691259\pi\) |
−0.301660 | + | 0.953416i | \(0.597541\pi\) | |||||||
\(102\) | 6.00000 | + | 10.3923i | 0.00582440 | + | 0.0100882i | ||||
\(103\) | 232.000 | − | 401.836i | 0.221938 | − | 0.384408i | −0.733458 | − | 0.679735i | \(-0.762095\pi\) |
0.955396 | + | 0.295326i | \(0.0954283\pi\) | |||||||
\(104\) | 336.000 | 0.316803 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −324.000 | −0.296884 | ||||||||
\(107\) | 1068.00 | − | 1849.83i | 0.964930 | − | 1.67131i | 0.255125 | − | 0.966908i | \(-0.417883\pi\) |
0.709804 | − | 0.704399i | \(-0.248783\pi\) | |||||||
\(108\) | 54.0000 | + | 93.5307i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | 613.000 | + | 1061.75i | 0.538667 | + | 0.932999i | 0.998976 | + | 0.0452405i | \(0.0144054\pi\) |
−0.460309 | + | 0.887759i | \(0.652261\pi\) | |||||||
\(110\) | −16.0000 | + | 27.7128i | −0.0138685 | + | 0.0240210i | ||||
\(111\) | −1194.00 | −1.02099 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 338.000 | 0.281384 | 0.140692 | − | 0.990053i | \(-0.455067\pi\) | ||||
0.140692 | + | 0.990053i | \(0.455067\pi\) | |||||||
\(114\) | 372.000 | − | 644.323i | 0.305623 | − | 0.529354i | ||||
\(115\) | 76.0000 | + | 131.636i | 0.0616264 | + | 0.106740i | ||||
\(116\) | −508.000 | − | 879.882i | −0.406609 | − | 0.704267i | ||||
\(117\) | −189.000 | + | 327.358i | −0.149342 | + | 0.258669i | ||||
\(118\) | 1544.00 | 1.20455 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 48.0000 | 0.0365148 | ||||||||
\(121\) | 633.500 | − | 1097.25i | 0.475958 | − | 0.824383i | ||||
\(122\) | 30.0000 | + | 51.9615i | 0.0222629 | + | 0.0385605i | ||||
\(123\) | −693.000 | − | 1200.31i | −0.508014 | − | 0.879906i | ||||
\(124\) | −144.000 | + | 249.415i | −0.104287 | + | 0.180630i | ||||
\(125\) | 492.000 | 0.352047 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2088.00 | 1.45890 | 0.729449 | − | 0.684035i | \(-0.239777\pi\) | ||||
0.729449 | + | 0.684035i | \(0.239777\pi\) | |||||||
\(128\) | −64.0000 | + | 110.851i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 318.000 | + | 550.792i | 0.217041 | + | 0.375927i | ||||
\(130\) | 84.0000 | + | 145.492i | 0.0566714 | + | 0.0981578i | ||||
\(131\) | −146.000 | + | 252.879i | −0.0973747 | + | 0.168658i | −0.910597 | − | 0.413295i | \(-0.864378\pi\) |
0.813223 | + | 0.581953i | \(0.197711\pi\) | |||||||
\(132\) | 96.0000 | 0.0633010 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1528.00 | −0.985068 | ||||||||
\(135\) | −27.0000 | + | 46.7654i | −0.0172133 | + | 0.0298142i | ||||
\(136\) | −8.00000 | − | 13.8564i | −0.00504408 | − | 0.00873660i | ||||
\(137\) | −409.000 | − | 708.409i | −0.255060 | − | 0.441777i | 0.709852 | − | 0.704351i | \(-0.248762\pi\) |
−0.964912 | + | 0.262574i | \(0.915429\pi\) | |||||||
\(138\) | 228.000 | − | 394.908i | 0.140642 | − | 0.243600i | ||||
\(139\) | 2156.00 | 1.31561 | 0.657804 | − | 0.753189i | \(-0.271485\pi\) | ||||
0.657804 | + | 0.753189i | \(0.271485\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −792.000 | −0.473039 | ||||||||
\(142\) | 236.000 | − | 408.764i | 0.139470 | − | 0.241568i | ||||
\(143\) | 168.000 | + | 290.985i | 0.0982438 | + | 0.170163i | ||||
\(144\) | −72.0000 | − | 124.708i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 254.000 | − | 439.941i | 0.145473 | − | 0.251966i | ||||
\(146\) | −836.000 | −0.473889 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1592.00 | 0.884200 | ||||||||
\(149\) | 1425.00 | − | 2468.17i | 0.783494 | − | 1.35705i | −0.146401 | − | 0.989225i | \(-0.546769\pi\) |
0.929895 | − | 0.367825i | \(-0.119898\pi\) | |||||||
\(150\) | −363.000 | − | 628.734i | −0.197592 | − | 0.342240i | ||||
\(151\) | −836.000 | − | 1447.99i | −0.450548 | − | 0.780372i | 0.547872 | − | 0.836562i | \(-0.315438\pi\) |
−0.998420 | + | 0.0561903i | \(0.982105\pi\) | |||||||
\(152\) | −496.000 | + | 859.097i | −0.264677 | + | 0.458434i | ||||
\(153\) | 18.0000 | 0.00951120 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −144.000 | −0.0746217 | ||||||||
\(156\) | 252.000 | − | 436.477i | 0.129334 | − | 0.224014i | ||||
\(157\) | 223.000 | + | 386.247i | 0.113359 | + | 0.196343i | 0.917123 | − | 0.398605i | \(-0.130506\pi\) |
−0.803764 | + | 0.594949i | \(0.797172\pi\) | |||||||
\(158\) | −552.000 | − | 956.092i | −0.277942 | − | 0.481409i | ||||
\(159\) | −243.000 | + | 420.888i | −0.121202 | + | 0.209928i | ||||
\(160\) | −64.0000 | −0.0316228 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | −1354.00 | + | 2345.20i | −0.650635 | + | 1.12693i | 0.332334 | + | 0.943162i | \(0.392164\pi\) |
−0.982969 | + | 0.183771i | \(0.941170\pi\) | |||||||
\(164\) | 924.000 | + | 1600.41i | 0.439953 | + | 0.762021i | ||||
\(165\) | 24.0000 | + | 41.5692i | 0.0113236 | + | 0.0196131i | ||||
\(166\) | 1036.00 | − | 1794.40i | 0.484393 | − | 0.838993i | ||||
\(167\) | −896.000 | −0.415177 | −0.207589 | − | 0.978216i | \(-0.566561\pi\) | ||||
−0.207589 | + | 0.978216i | \(0.566561\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −433.000 | −0.197087 | ||||||||
\(170\) | 4.00000 | − | 6.92820i | 0.00180462 | − | 0.00312570i | ||||
\(171\) | −558.000 | − | 966.484i | −0.249540 | − | 0.432216i | ||||
\(172\) | −424.000 | − | 734.390i | −0.187963 | − | 0.325562i | ||||
\(173\) | 2017.00 | − | 3493.55i | 0.886414 | − | 1.53531i | 0.0423302 | − | 0.999104i | \(-0.486522\pi\) |
0.844084 | − | 0.536211i | \(-0.180145\pi\) | |||||||
\(174\) | −1524.00 | −0.663989 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −128.000 | −0.0548202 | ||||||||
\(177\) | 1158.00 | − | 2005.71i | 0.491755 | − | 0.851744i | ||||
\(178\) | 30.0000 | + | 51.9615i | 0.0126326 | + | 0.0218802i | ||||
\(179\) | 1740.00 | + | 3013.77i | 0.726557 | + | 1.25843i | 0.958330 | + | 0.285664i | \(0.0922140\pi\) |
−0.231773 | + | 0.972770i | \(0.574453\pi\) | |||||||
\(180\) | 36.0000 | − | 62.3538i | 0.0149071 | − | 0.0258199i | ||||
\(181\) | 2898.00 | 1.19009 | 0.595046 | − | 0.803692i | \(-0.297134\pi\) | ||||
0.595046 | + | 0.803692i | \(0.297134\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 90.0000 | 0.0363551 | ||||||||
\(184\) | −304.000 | + | 526.543i | −0.121800 | + | 0.210964i | ||||
\(185\) | 398.000 | + | 689.356i | 0.158170 | + | 0.273959i | ||||
\(186\) | 216.000 | + | 374.123i | 0.0851499 | + | 0.147484i | ||||
\(187\) | 8.00000 | − | 13.8564i | 0.00312844 | − | 0.00541861i | ||||
\(188\) | 1056.00 | 0.409663 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −496.000 | −0.189387 | ||||||||
\(191\) | −1326.00 | + | 2296.70i | −0.502335 | + | 0.870070i | 0.497661 | + | 0.867371i | \(0.334192\pi\) |
−0.999996 | + | 0.00269837i | \(0.999141\pi\) | |||||||
\(192\) | 96.0000 | + | 166.277i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | −73.0000 | − | 126.440i | −0.0272262 | − | 0.0471571i | 0.852091 | − | 0.523393i | \(-0.175334\pi\) |
−0.879317 | + | 0.476236i | \(0.842001\pi\) | |||||||
\(194\) | −1190.00 | + | 2061.14i | −0.440397 | + | 0.762790i | ||||
\(195\) | 252.000 | 0.0925441 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2546.00 | −0.920787 | −0.460393 | − | 0.887715i | \(-0.652292\pi\) | ||||
−0.460393 | + | 0.887715i | \(0.652292\pi\) | |||||||
\(198\) | 72.0000 | − | 124.708i | 0.0258425 | − | 0.0447605i | ||||
\(199\) | −1268.00 | − | 2196.24i | −0.451689 | − | 0.782349i | 0.546802 | − | 0.837262i | \(-0.315845\pi\) |
−0.998491 | + | 0.0549134i | \(0.982512\pi\) | |||||||
\(200\) | 484.000 | + | 838.313i | 0.171120 | + | 0.296388i | ||||
\(201\) | −1146.00 | + | 1984.93i | −0.402152 | + | 0.696548i | ||||
\(202\) | −2740.00 | −0.954385 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −24.0000 | −0.00823694 | ||||||||
\(205\) | −462.000 | + | 800.207i | −0.157402 | + | 0.272629i | ||||
\(206\) | 464.000 | + | 803.672i | 0.156934 | + | 0.271818i | ||||
\(207\) | −342.000 | − | 592.361i | −0.114834 | − | 0.198898i | ||||
\(208\) | −336.000 | + | 581.969i | −0.112007 | + | 0.194001i | ||||
\(209\) | −992.000 | −0.328316 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1300.00 | −0.424150 | −0.212075 | − | 0.977253i | \(-0.568022\pi\) | ||||
−0.212075 | + | 0.977253i | \(0.568022\pi\) | |||||||
\(212\) | 324.000 | − | 561.184i | 0.104964 | − | 0.181803i | ||||
\(213\) | −354.000 | − | 613.146i | −0.113876 | − | 0.197240i | ||||
\(214\) | 2136.00 | + | 3699.66i | 0.682308 | + | 1.18179i | ||||
\(215\) | 212.000 | − | 367.195i | 0.0672478 | − | 0.116477i | ||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2452.00 | −0.761791 | ||||||||
\(219\) | −627.000 | + | 1086.00i | −0.193465 | + | 0.335090i | ||||
\(220\) | −32.0000 | − | 55.4256i | −0.00980654 | − | 0.0169854i | ||||
\(221\) | −42.0000 | − | 72.7461i | −0.0127838 | − | 0.0221422i | ||||
\(222\) | 1194.00 | − | 2068.07i | 0.360973 | − | 0.625224i | ||||
\(223\) | −2576.00 | −0.773550 | −0.386775 | − | 0.922174i | \(-0.626411\pi\) | ||||
−0.386775 | + | 0.922174i | \(0.626411\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1089.00 | −0.322667 | ||||||||
\(226\) | −338.000 | + | 585.433i | −0.0994842 | + | 0.172312i | ||||
\(227\) | −918.000 | − | 1590.02i | −0.268413 | − | 0.464905i | 0.700039 | − | 0.714105i | \(-0.253166\pi\) |
−0.968452 | + | 0.249199i | \(0.919833\pi\) | |||||||
\(228\) | 744.000 | + | 1288.65i | 0.216108 | + | 0.374310i | ||||
\(229\) | −937.000 | + | 1622.93i | −0.270387 | + | 0.468325i | −0.968961 | − | 0.247213i | \(-0.920485\pi\) |
0.698574 | + | 0.715538i | \(0.253818\pi\) | |||||||
\(230\) | −304.000 | −0.0871529 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2032.00 | 0.575032 | ||||||||
\(233\) | −1865.00 | + | 3230.27i | −0.524379 | + | 0.908250i | 0.475219 | + | 0.879868i | \(0.342369\pi\) |
−0.999597 | + | 0.0283826i | \(0.990964\pi\) | |||||||
\(234\) | −378.000 | − | 654.715i | −0.105601 | − | 0.182906i | ||||
\(235\) | 264.000 | + | 457.261i | 0.0732828 | + | 0.126930i | ||||
\(236\) | −1544.00 | + | 2674.29i | −0.425872 | + | 0.737632i | ||||
\(237\) | −1656.00 | −0.453877 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2004.00 | 0.542377 | 0.271188 | − | 0.962526i | \(-0.412583\pi\) | ||||
0.271188 | + | 0.962526i | \(0.412583\pi\) | |||||||
\(240\) | −48.0000 | + | 83.1384i | −0.0129099 | + | 0.0223607i | ||||
\(241\) | −323.000 | − | 559.452i | −0.0863330 | − | 0.149533i | 0.819625 | − | 0.572900i | \(-0.194182\pi\) |
−0.905958 | + | 0.423367i | \(0.860848\pi\) | |||||||
\(242\) | 1267.00 | + | 2194.51i | 0.336553 | + | 0.582927i | ||||
\(243\) | 121.500 | − | 210.444i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −120.000 | −0.0314845 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2772.00 | 0.718440 | ||||||||
\(247\) | −2604.00 | + | 4510.26i | −0.670804 | + | 1.16187i | ||||
\(248\) | −288.000 | − | 498.831i | −0.0737420 | − | 0.127725i | ||||
\(249\) | −1554.00 | − | 2691.61i | −0.395505 | − | 0.685035i | ||||
\(250\) | −492.000 | + | 852.169i | −0.124467 | + | 0.215584i | ||||
\(251\) | −1260.00 | −0.316855 | −0.158427 | − | 0.987371i | \(-0.550642\pi\) | ||||
−0.158427 | + | 0.987371i | \(0.550642\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −608.000 | −0.151086 | ||||||||
\(254\) | −2088.00 | + | 3616.52i | −0.515798 | + | 0.893389i | ||||
\(255\) | −6.00000 | − | 10.3923i | −0.00147347 | − | 0.00255212i | ||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 2955.00 | − | 5118.21i | 0.717229 | − | 1.24228i | −0.244865 | − | 0.969557i | \(-0.578744\pi\) |
0.962094 | − | 0.272720i | \(-0.0879232\pi\) | |||||||
\(258\) | −1272.00 | −0.306943 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −336.000 | −0.0801455 | ||||||||
\(261\) | −1143.00 | + | 1979.73i | −0.271073 | + | 0.469511i | ||||
\(262\) | −292.000 | − | 505.759i | −0.0688543 | − | 0.119259i | ||||
\(263\) | −1494.00 | − | 2587.68i | −0.350281 | − | 0.606705i | 0.636017 | − | 0.771675i | \(-0.280581\pi\) |
−0.986299 | + | 0.164970i | \(0.947247\pi\) | |||||||
\(264\) | −96.0000 | + | 166.277i | −0.0223803 | + | 0.0387638i | ||||
\(265\) | 324.000 | 0.0751063 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 90.0000 | 0.0206289 | ||||||||
\(268\) | 1528.00 | − | 2646.57i | 0.348274 | − | 0.603228i | ||||
\(269\) | −659.000 | − | 1141.42i | −0.149368 | − | 0.258713i | 0.781626 | − | 0.623747i | \(-0.214391\pi\) |
−0.930994 | + | 0.365035i | \(0.881057\pi\) | |||||||
\(270\) | −54.0000 | − | 93.5307i | −0.0121716 | − | 0.0210819i | ||||
\(271\) | −2820.00 | + | 4884.38i | −0.632114 | + | 1.09485i | 0.355005 | + | 0.934864i | \(0.384479\pi\) |
−0.987119 | + | 0.159989i | \(0.948854\pi\) | |||||||
\(272\) | 32.0000 | 0.00713340 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1636.00 | 0.360709 | ||||||||
\(275\) | −484.000 | + | 838.313i | −0.106132 | + | 0.183826i | ||||
\(276\) | 456.000 | + | 789.815i | 0.0994492 | + | 0.172251i | ||||
\(277\) | −3223.00 | − | 5582.40i | −0.699102 | − | 1.21088i | −0.968778 | − | 0.247929i | \(-0.920250\pi\) |
0.269676 | − | 0.962951i | \(-0.413083\pi\) | |||||||
\(278\) | −2156.00 | + | 3734.30i | −0.465138 | + | 0.805642i | ||||
\(279\) | 648.000 | 0.139049 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4930.00 | 1.04662 | 0.523308 | − | 0.852144i | \(-0.324698\pi\) | ||||
0.523308 | + | 0.852144i | \(0.324698\pi\) | |||||||
\(282\) | 792.000 | − | 1371.78i | 0.167244 | − | 0.289676i | ||||
\(283\) | −3130.00 | − | 5421.32i | −0.657453 | − | 1.13874i | −0.981273 | − | 0.192623i | \(-0.938301\pi\) |
0.323820 | − | 0.946119i | \(-0.395033\pi\) | |||||||
\(284\) | 472.000 | + | 817.528i | 0.0986199 | + | 0.170815i | ||||
\(285\) | −372.000 | + | 644.323i | −0.0773171 | + | 0.133917i | ||||
\(286\) | −672.000 | −0.138938 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | 2454.50 | − | 4251.32i | 0.499593 | − | 0.865320i | ||||
\(290\) | 508.000 | + | 879.882i | 0.102865 | + | 0.178167i | ||||
\(291\) | 1785.00 | + | 3091.71i | 0.359583 | + | 0.622815i | ||||
\(292\) | 836.000 | − | 1447.99i | 0.167545 | − | 0.290197i | ||||
\(293\) | 2310.00 | 0.460586 | 0.230293 | − | 0.973121i | \(-0.426032\pi\) | ||||
0.230293 | + | 0.973121i | \(0.426032\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1544.00 | −0.304729 | ||||||||
\(296\) | −1592.00 | + | 2757.42i | −0.312612 | + | 0.541460i | ||||
\(297\) | −108.000 | − | 187.061i | −0.0211003 | − | 0.0365468i | ||||
\(298\) | 2850.00 | + | 4936.34i | 0.554014 | + | 0.959580i | ||||
\(299\) | −1596.00 | + | 2764.35i | −0.308693 | + | 0.534671i | ||||
\(300\) | 1452.00 | 0.279438 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3344.00 | 0.637171 | ||||||||
\(303\) | −2055.00 | + | 3559.36i | −0.389626 | + | 0.674852i | ||||
\(304\) | −992.000 | − | 1718.19i | −0.187155 | − | 0.324162i | ||||
\(305\) | −30.0000 | − | 51.9615i | −0.00563211 | − | 0.00975511i | ||||
\(306\) | −18.0000 | + | 31.1769i | −0.00336272 | + | 0.00582440i | ||||
\(307\) | −196.000 | −0.0364375 | −0.0182187 | − | 0.999834i | \(-0.505800\pi\) | ||||
−0.0182187 | + | 0.999834i | \(0.505800\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1392.00 | 0.256272 | ||||||||
\(310\) | 144.000 | − | 249.415i | 0.0263827 | − | 0.0456963i | ||||
\(311\) | −3368.00 | − | 5833.55i | −0.614089 | − | 1.06363i | −0.990544 | − | 0.137199i | \(-0.956190\pi\) |
0.376454 | − | 0.926435i | \(-0.377143\pi\) | |||||||
\(312\) | 504.000 | + | 872.954i | 0.0914531 | + | 0.158401i | ||||
\(313\) | 197.000 | − | 341.214i | 0.0355754 | − | 0.0616184i | −0.847690 | − | 0.530493i | \(-0.822007\pi\) |
0.883265 | + | 0.468874i | \(0.155340\pi\) | |||||||
\(314\) | −892.000 | −0.160314 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2208.00 | 0.393069 | ||||||||
\(317\) | 3357.00 | − | 5814.49i | 0.594788 | − | 1.03020i | −0.398788 | − | 0.917043i | \(-0.630569\pi\) |
0.993577 | − | 0.113161i | \(-0.0360975\pi\) | |||||||
\(318\) | −486.000 | − | 841.777i | −0.0857029 | − | 0.148442i | ||||
\(319\) | 1016.00 | + | 1759.76i | 0.178323 | + | 0.308865i | ||||
\(320\) | 64.0000 | − | 110.851i | 0.0111803 | − | 0.0193649i | ||||
\(321\) | 6408.00 | 1.11420 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 248.000 | 0.0427216 | ||||||||
\(324\) | −162.000 | + | 280.592i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 2541.00 | + | 4401.14i | 0.433690 | + | 0.751173i | ||||
\(326\) | −2708.00 | − | 4690.39i | −0.460068 | − | 0.796862i | ||||
\(327\) | −1839.00 | + | 3185.24i | −0.311000 | + | 0.538667i | ||||
\(328\) | −3696.00 | −0.622187 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −96.0000 | −0.0160140 | ||||||||
\(331\) | −346.000 | + | 599.290i | −0.0574558 | + | 0.0995164i | −0.893323 | − | 0.449416i | \(-0.851632\pi\) |
0.835867 | + | 0.548932i | \(0.184966\pi\) | |||||||
\(332\) | 2072.00 | + | 3588.81i | 0.342517 | + | 0.593258i | ||||
\(333\) | −1791.00 | − | 3102.10i | −0.294733 | − | 0.510493i | ||||
\(334\) | 896.000 | − | 1551.92i | 0.146787 | − | 0.254243i | ||||
\(335\) | 1528.00 | 0.249205 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1566.00 | −0.253132 | −0.126566 | − | 0.991958i | \(-0.540396\pi\) | ||||
−0.126566 | + | 0.991958i | \(0.540396\pi\) | |||||||
\(338\) | 433.000 | − | 749.978i | 0.0696808 | − | 0.120691i | ||||
\(339\) | 507.000 | + | 878.150i | 0.0812285 | + | 0.140692i | ||||
\(340\) | 8.00000 | + | 13.8564i | 0.00127606 | + | 0.00221020i | ||||
\(341\) | 288.000 | − | 498.831i | 0.0457363 | − | 0.0792176i | ||||
\(342\) | 2232.00 | 0.352903 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1696.00 | 0.265820 | ||||||||
\(345\) | −228.000 | + | 394.908i | −0.0355800 | + | 0.0616264i | ||||
\(346\) | 4034.00 | + | 6987.09i | 0.626790 | + | 1.08563i | ||||
\(347\) | 2664.00 | + | 4614.18i | 0.412135 | + | 0.713840i | 0.995123 | − | 0.0986415i | \(-0.0314497\pi\) |
−0.582988 | + | 0.812481i | \(0.698116\pi\) | |||||||
\(348\) | 1524.00 | − | 2639.65i | 0.234756 | − | 0.406609i | ||||
\(349\) | −11326.0 | −1.73715 | −0.868577 | − | 0.495554i | \(-0.834965\pi\) | ||||
−0.868577 | + | 0.495554i | \(0.834965\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1134.00 | −0.172446 | ||||||||
\(352\) | 128.000 | − | 221.703i | 0.0193819 | − | 0.0335704i | ||||
\(353\) | −1065.00 | − | 1844.63i | −0.160579 | − | 0.278130i | 0.774498 | − | 0.632577i | \(-0.218003\pi\) |
−0.935076 | + | 0.354446i | \(0.884669\pi\) | |||||||
\(354\) | 2316.00 | + | 4011.43i | 0.347723 | + | 0.602274i | ||||
\(355\) | −236.000 | + | 408.764i | −0.0352833 | + | 0.0611125i | ||||
\(356\) | −120.000 | −0.0178651 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6960.00 | −1.02751 | ||||||||
\(359\) | −1522.00 | + | 2636.18i | −0.223755 | + | 0.387555i | −0.955945 | − | 0.293545i | \(-0.905165\pi\) |
0.732190 | + | 0.681100i | \(0.238498\pi\) | |||||||
\(360\) | 72.0000 | + | 124.708i | 0.0105409 | + | 0.0182574i | ||||
\(361\) | −4258.50 | − | 7375.94i | −0.620863 | − | 1.07537i | ||||
\(362\) | −2898.00 | + | 5019.48i | −0.420761 | + | 0.728780i | ||||
\(363\) | 3801.00 | 0.549589 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 836.000 | 0.119886 | ||||||||
\(366\) | −90.0000 | + | 155.885i | −0.0128535 | + | 0.0222629i | ||||
\(367\) | 6208.00 | + | 10752.6i | 0.882984 | + | 1.52937i | 0.848008 | + | 0.529984i | \(0.177802\pi\) |
0.0349760 | + | 0.999388i | \(0.488865\pi\) | |||||||
\(368\) | −608.000 | − | 1053.09i | −0.0861255 | − | 0.149174i | ||||
\(369\) | 2079.00 | − | 3600.93i | 0.293302 | − | 0.508014i | ||||
\(370\) | −1592.00 | −0.223687 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −864.000 | −0.120420 | ||||||||
\(373\) | 3721.00 | − | 6444.96i | 0.516531 | − | 0.894658i | −0.483285 | − | 0.875463i | \(-0.660556\pi\) |
0.999816 | − | 0.0191948i | \(-0.00611026\pi\) | |||||||
\(374\) | 16.0000 | + | 27.7128i | 0.00221214 | + | 0.00383154i | ||||
\(375\) | 738.000 | + | 1278.25i | 0.101627 | + | 0.176023i | ||||
\(376\) | −1056.00 | + | 1829.05i | −0.144838 | + | 0.250867i | ||||
\(377\) | 10668.0 | 1.45737 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 100.000 | 0.0135532 | 0.00677659 | − | 0.999977i | \(-0.497843\pi\) | ||||
0.00677659 | + | 0.999977i | \(0.497843\pi\) | |||||||
\(380\) | 496.000 | − | 859.097i | 0.0669586 | − | 0.115976i | ||||
\(381\) | 3132.00 | + | 5424.78i | 0.421148 | + | 0.729449i | ||||
\(382\) | −2652.00 | − | 4593.40i | −0.355205 | − | 0.615232i | ||||
\(383\) | 4040.00 | − | 6997.49i | 0.538993 | − | 0.933563i | −0.459965 | − | 0.887937i | \(-0.652138\pi\) |
0.998959 | − | 0.0456266i | \(-0.0145284\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 292.000 | 0.0385036 | ||||||||
\(387\) | −954.000 | + | 1652.38i | −0.125309 | + | 0.217041i | ||||
\(388\) | −2380.00 | − | 4122.28i | −0.311408 | − | 0.539374i | ||||
\(389\) | 2741.00 | + | 4747.55i | 0.357260 | + | 0.618793i | 0.987502 | − | 0.157606i | \(-0.0503776\pi\) |
−0.630242 | + | 0.776399i | \(0.717044\pi\) | |||||||
\(390\) | −252.000 | + | 436.477i | −0.0327193 | + | 0.0566714i | ||||
\(391\) | 152.000 | 0.0196598 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −876.000 | −0.112439 | ||||||||
\(394\) | 2546.00 | − | 4409.80i | 0.325547 | − | 0.563864i | ||||
\(395\) | 552.000 | + | 956.092i | 0.0703143 | + | 0.121788i | ||||
\(396\) | 144.000 | + | 249.415i | 0.0182734 | + | 0.0316505i | ||||
\(397\) | 5223.00 | − | 9046.50i | 0.660289 | − | 1.14365i | −0.320250 | − | 0.947333i | \(-0.603767\pi\) |
0.980540 | − | 0.196322i | \(-0.0628997\pi\) | |||||||
\(398\) | 5072.00 | 0.638785 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1936.00 | −0.242000 | ||||||||
\(401\) | 5667.00 | − | 9815.53i | 0.705727 | − | 1.22235i | −0.260702 | − | 0.965419i | \(-0.583954\pi\) |
0.966429 | − | 0.256935i | \(-0.0827128\pi\) | |||||||
\(402\) | −2292.00 | − | 3969.86i | −0.284365 | − | 0.492534i | ||||
\(403\) | −1512.00 | − | 2618.86i | −0.186894 | − | 0.323709i | ||||
\(404\) | 2740.00 | − | 4745.82i | 0.337426 | − | 0.584439i | ||||
\(405\) | −162.000 | −0.0198762 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3184.00 | −0.387776 | ||||||||
\(408\) | 24.0000 | − | 41.5692i | 0.00291220 | − | 0.00504408i | ||||
\(409\) | 4297.00 | + | 7442.62i | 0.519494 | + | 0.899790i | 0.999743 | + | 0.0226578i | \(0.00721280\pi\) |
−0.480249 | + | 0.877132i | \(0.659454\pi\) | |||||||
\(410\) | −924.000 | − | 1600.41i | −0.111300 | − | 0.192778i | ||||
\(411\) | 1227.00 | − | 2125.23i | 0.147259 | − | 0.255060i | ||||
\(412\) | −1856.00 | −0.221938 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1368.00 | 0.162400 | ||||||||
\(415\) | −1036.00 | + | 1794.40i | −0.122543 | + | 0.212250i | ||||
\(416\) | −672.000 | − | 1163.94i | −0.0792007 | − | 0.137180i | ||||
\(417\) | 3234.00 | + | 5601.45i | 0.379783 | + | 0.657804i | ||||
\(418\) | 992.000 | − | 1718.19i | 0.116077 | − | 0.201052i | ||||
\(419\) | −10500.0 | −1.22424 | −0.612122 | − | 0.790763i | \(-0.709684\pi\) | ||||
−0.612122 | + | 0.790763i | \(0.709684\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12066.0 | −1.39682 | −0.698410 | − | 0.715698i | \(-0.746109\pi\) | ||||
−0.698410 | + | 0.715698i | \(0.746109\pi\) | |||||||
\(422\) | 1300.00 | − | 2251.67i | 0.149960 | − | 0.259738i | ||||
\(423\) | −1188.00 | − | 2057.68i | −0.136554 | − | 0.236519i | ||||
\(424\) | 648.000 | + | 1122.37i | 0.0742209 | + | 0.128554i | ||||
\(425\) | 121.000 | − | 209.578i | 0.0138103 | − | 0.0239201i | ||||
\(426\) | 1416.00 | 0.161046 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −8544.00 | −0.964930 | ||||||||
\(429\) | −504.000 | + | 872.954i | −0.0567211 | + | 0.0982438i | ||||
\(430\) | 424.000 | + | 734.390i | 0.0475514 | + | 0.0823614i | ||||
\(431\) | −2166.00 | − | 3751.62i | −0.242071 | − | 0.419279i | 0.719233 | − | 0.694769i | \(-0.244493\pi\) |
−0.961304 | + | 0.275490i | \(0.911160\pi\) | |||||||
\(432\) | 216.000 | − | 374.123i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | 1918.00 | 0.212871 | 0.106436 | − | 0.994320i | \(-0.466056\pi\) | ||||
0.106436 | + | 0.994320i | \(0.466056\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1524.00 | 0.167977 | ||||||||
\(436\) | 2452.00 | − | 4246.99i | 0.269334 | − | 0.466500i | ||||
\(437\) | −4712.00 | − | 8161.42i | −0.515802 | − | 0.893395i | ||||
\(438\) | −1254.00 | − | 2171.99i | −0.136800 | − | 0.236945i | ||||
\(439\) | −3996.00 | + | 6921.28i | −0.434439 | + | 0.752470i | −0.997250 | − | 0.0741155i | \(-0.976387\pi\) |
0.562811 | + | 0.826586i | \(0.309720\pi\) | |||||||
\(440\) | 128.000 | 0.0138685 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 168.000 | 0.0180791 | ||||||||
\(443\) | −1592.00 | + | 2757.42i | −0.170741 | + | 0.295732i | −0.938679 | − | 0.344792i | \(-0.887949\pi\) |
0.767938 | + | 0.640524i | \(0.221283\pi\) | |||||||
\(444\) | 2388.00 | + | 4136.14i | 0.255247 | + | 0.442100i | ||||
\(445\) | −30.0000 | − | 51.9615i | −0.00319581 | − | 0.00553531i | ||||
\(446\) | 2576.00 | − | 4461.76i | 0.273491 | − | 0.473701i | ||||
\(447\) | 8550.00 | 0.904700 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11426.0 | 1.20095 | 0.600475 | − | 0.799644i | \(-0.294978\pi\) | ||||
0.600475 | + | 0.799644i | \(0.294978\pi\) | |||||||
\(450\) | 1089.00 | − | 1886.20i | 0.114080 | − | 0.197592i | ||||
\(451\) | −1848.00 | − | 3200.83i | −0.192947 | − | 0.334193i | ||||
\(452\) | −676.000 | − | 1170.87i | −0.0703459 | − | 0.121843i | ||||
\(453\) | 2508.00 | − | 4343.98i | 0.260124 | − | 0.450548i | ||||
\(454\) | 3672.00 | 0.379594 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2976.00 | −0.305623 | ||||||||
\(457\) | 8467.00 | − | 14665.3i | 0.866673 | − | 1.50112i | 0.00129662 | − | 0.999999i | \(-0.499587\pi\) |
0.865376 | − | 0.501122i | \(-0.167079\pi\) | |||||||
\(458\) | −1874.00 | − | 3245.86i | −0.191193 | − | 0.331156i | ||||
\(459\) | 27.0000 | + | 46.7654i | 0.00274565 | + | 0.00475560i | ||||
\(460\) | 304.000 | − | 526.543i | 0.0308132 | − | 0.0533700i | ||||
\(461\) | 17038.0 | 1.72134 | 0.860671 | − | 0.509161i | \(-0.170044\pi\) | ||||
0.860671 | + | 0.509161i | \(0.170044\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13592.0 | −1.36431 | −0.682153 | − | 0.731209i | \(-0.738956\pi\) | ||||
−0.682153 | + | 0.731209i | \(0.738956\pi\) | |||||||
\(464\) | −2032.00 | + | 3519.53i | −0.203304 | + | 0.352134i | ||||
\(465\) | −216.000 | − | 374.123i | −0.0215414 | − | 0.0373108i | ||||
\(466\) | −3730.00 | − | 6460.55i | −0.370792 | − | 0.642230i | ||||
\(467\) | 4306.00 | − | 7458.21i | 0.426676 | − | 0.739025i | −0.569899 | − | 0.821715i | \(-0.693018\pi\) |
0.996575 | + | 0.0826895i | \(0.0263510\pi\) | |||||||
\(468\) | 1512.00 | 0.149342 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1056.00 | −0.103638 | ||||||||
\(471\) | −669.000 | + | 1158.74i | −0.0654478 | + | 0.113359i | ||||
\(472\) | −3088.00 | − | 5348.57i | −0.301137 | − | 0.521585i | ||||
\(473\) | 848.000 | + | 1468.78i | 0.0824336 | + | 0.142779i | ||||
\(474\) | 1656.00 | − | 2868.28i | 0.160470 | − | 0.277942i | ||||
\(475\) | −15004.0 | −1.44933 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1458.00 | −0.139952 | ||||||||
\(478\) | −2004.00 | + | 3471.03i | −0.191759 | + | 0.332136i | ||||
\(479\) | 3716.00 | + | 6436.30i | 0.354464 | + | 0.613950i | 0.987026 | − | 0.160560i | \(-0.0513299\pi\) |
−0.632562 | + | 0.774510i | \(0.717997\pi\) | |||||||
\(480\) | −96.0000 | − | 166.277i | −0.00912871 | − | 0.0158114i | ||||
\(481\) | −8358.00 | + | 14476.5i | −0.792291 | + | 1.37229i | ||||
\(482\) | 1292.00 | 0.122093 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5068.00 | −0.475958 | ||||||||
\(485\) | 1190.00 | − | 2061.14i | 0.111413 | − | 0.192972i | ||||
\(486\) | 243.000 | + | 420.888i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | 3308.00 | + | 5729.62i | 0.307802 | + | 0.533129i | 0.977881 | − | 0.209160i | \(-0.0670731\pi\) |
−0.670079 | + | 0.742290i | \(0.733740\pi\) | |||||||
\(488\) | 120.000 | − | 207.846i | 0.0111314 | − | 0.0192802i | ||||
\(489\) | −8124.00 | −0.751288 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17040.0 | 1.56620 | 0.783100 | − | 0.621896i | \(-0.213637\pi\) | ||||
0.783100 | + | 0.621896i | \(0.213637\pi\) | |||||||
\(492\) | −2772.00 | + | 4801.24i | −0.254007 | + | 0.439953i | ||||
\(493\) | −254.000 | − | 439.941i | −0.0232040 | − | 0.0401906i | ||||
\(494\) | −5208.00 | − | 9020.52i | −0.474330 | − | 0.821564i | ||||
\(495\) | −72.0000 | + | 124.708i | −0.00653770 | + | 0.0113236i | ||||
\(496\) | 1152.00 | 0.104287 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 6216.00 | 0.559329 | ||||||||
\(499\) | 1474.00 | − | 2553.04i | 0.132235 | − | 0.229038i | −0.792303 | − | 0.610128i | \(-0.791118\pi\) |
0.924538 | + | 0.381090i | \(0.124451\pi\) | |||||||
\(500\) | −984.000 | − | 1704.34i | −0.0880116 | − | 0.152441i | ||||
\(501\) | −1344.00 | − | 2327.88i | −0.119851 | − | 0.207589i | ||||
\(502\) | 1260.00 | − | 2182.38i | 0.112025 | − | 0.194033i | ||||
\(503\) | −17304.0 | −1.53389 | −0.766946 | − | 0.641712i | \(-0.778224\pi\) | ||||
−0.766946 | + | 0.641712i | \(0.778224\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2740.00 | 0.241442 | ||||||||
\(506\) | 608.000 | − | 1053.09i | 0.0534168 | − | 0.0925206i | ||||
\(507\) | −649.500 | − | 1124.97i | −0.0568941 | − | 0.0985435i | ||||
\(508\) | −4176.00 | − | 7233.04i | −0.364724 | − | 0.631721i | ||||
\(509\) | 2325.00 | − | 4027.02i | 0.202463 | − | 0.350677i | −0.746858 | − | 0.664983i | \(-0.768439\pi\) |
0.949322 | + | 0.314307i | \(0.101772\pi\) | |||||||
\(510\) | 24.0000 | 0.00208380 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 1674.00 | − | 2899.45i | 0.144072 | − | 0.249540i | ||||
\(514\) | 5910.00 | + | 10236.4i | 0.507157 | + | 0.878422i | ||||
\(515\) | −464.000 | − | 803.672i | −0.0397015 | − | 0.0687651i | ||||
\(516\) | 1272.00 | − | 2203.17i | 0.108521 | − | 0.187963i | ||||
\(517\) | −2112.00 | −0.179663 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12102.0 | 1.02354 | ||||||||
\(520\) | 336.000 | − | 581.969i | 0.0283357 | − | 0.0490789i | ||||
\(521\) | 8427.00 | + | 14596.0i | 0.708625 | + | 1.22737i | 0.965367 | + | 0.260894i | \(0.0840175\pi\) |
−0.256742 | + | 0.966480i | \(0.582649\pi\) | |||||||
\(522\) | −2286.00 | − | 3959.47i | −0.191677 | − | 0.331995i | ||||
\(523\) | −62.0000 | + | 107.387i | −0.00518369 | + | 0.00897842i | −0.868606 | − | 0.495504i | \(-0.834983\pi\) |
0.863422 | + | 0.504482i | \(0.168317\pi\) | |||||||
\(524\) | 1168.00 | 0.0973747 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5976.00 | 0.495373 | ||||||||
\(527\) | −72.0000 | + | 124.708i | −0.00595136 | + | 0.0103081i | ||||
\(528\) | −192.000 | − | 332.554i | −0.0158252 | − | 0.0274101i | ||||
\(529\) | 3195.50 | + | 5534.77i | 0.262637 | + | 0.454900i | ||||
\(530\) | −324.000 | + | 561.184i | −0.0265541 | + | 0.0459930i | ||||
\(531\) | 6948.00 | 0.567830 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −19404.0 | −1.57689 | ||||||||
\(534\) | −90.0000 | + | 155.885i | −0.00729341 | + | 0.0126326i | ||||
\(535\) | −2136.00 | − | 3699.66i | −0.172612 | − | 0.298972i | ||||
\(536\) | 3056.00 | + | 5293.15i | 0.246267 | + | 0.426547i | ||||
\(537\) | −5220.00 | + | 9041.31i | −0.419478 | + | 0.726557i | ||||
\(538\) | 2636.00 | 0.211238 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 216.000 | 0.0172133 | ||||||||
\(541\) | −2691.00 | + | 4660.95i | −0.213854 | + | 0.370406i | −0.952918 | − | 0.303230i | \(-0.901935\pi\) |
0.739063 | + | 0.673636i | \(0.235268\pi\) | |||||||
\(542\) | −5640.00 | − | 9768.77i | −0.446972 | − | 0.774178i | ||||
\(543\) | 4347.00 | + | 7529.22i | 0.343550 | + | 0.595046i | ||||
\(544\) | −32.0000 | + | 55.4256i | −0.00252204 | + | 0.00436830i | ||||
\(545\) | 2452.00 | 0.192720 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17460.0 | 1.36478 | 0.682391 | − | 0.730987i | \(-0.260940\pi\) | ||||
0.682391 | + | 0.730987i | \(0.260940\pi\) | |||||||
\(548\) | −1636.00 | + | 2833.64i | −0.127530 | + | 0.220888i | ||||
\(549\) | 135.000 | + | 233.827i | 0.0104948 | + | 0.0181776i | ||||
\(550\) | −968.000 | − | 1676.63i | −0.0750467 | − | 0.129985i | ||||
\(551\) | −15748.0 | + | 27276.3i | −1.21758 | + | 2.10891i | ||||
\(552\) | −1824.00 | −0.140642 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 12892.0 | 0.988680 | ||||||||
\(555\) | −1194.00 | + | 2068.07i | −0.0913198 | + | 0.158170i | ||||
\(556\) | −4312.00 | − | 7468.60i | −0.328902 | − | 0.569675i | ||||
\(557\) | 4757.00 | + | 8239.37i | 0.361868 | + | 0.626774i | 0.988268 | − | 0.152728i | \(-0.0488057\pi\) |
−0.626400 | + | 0.779502i | \(0.715472\pi\) | |||||||
\(558\) | −648.000 | + | 1122.37i | −0.0491613 | + | 0.0851499i | ||||
\(559\) | 8904.00 | 0.673701 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 48.0000 | 0.00361241 | ||||||||
\(562\) | −4930.00 | + | 8539.01i | −0.370035 | + | 0.640919i | ||||
\(563\) | 1994.00 | + | 3453.71i | 0.149267 | + | 0.258537i | 0.930957 | − | 0.365130i | \(-0.118975\pi\) |
−0.781690 | + | 0.623667i | \(0.785642\pi\) | |||||||
\(564\) | 1584.00 | + | 2743.57i | 0.118260 | + | 0.204832i | ||||
\(565\) | 338.000 | − | 585.433i | 0.0251677 | − | 0.0435918i | ||||
\(566\) | 12520.0 | 0.929779 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1888.00 | −0.139470 | ||||||||
\(569\) | −5673.00 | + | 9825.92i | −0.417969 | + | 0.723944i | −0.995735 | − | 0.0922585i | \(-0.970591\pi\) |
0.577766 | + | 0.816203i | \(0.303925\pi\) | |||||||
\(570\) | −744.000 | − | 1288.65i | −0.0546715 | − | 0.0946937i | ||||
\(571\) | 4218.00 | + | 7305.79i | 0.309138 | + | 0.535443i | 0.978174 | − | 0.207787i | \(-0.0666262\pi\) |
−0.669036 | + | 0.743230i | \(0.733293\pi\) | |||||||
\(572\) | 672.000 | − | 1163.94i | 0.0491219 | − | 0.0850816i | ||||
\(573\) | −7956.00 | −0.580047 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9196.00 | −0.666956 | ||||||||
\(576\) | −288.000 | + | 498.831i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 1049.00 | + | 1816.92i | 0.0756853 | + | 0.131091i | 0.901384 | − | 0.433020i | \(-0.142552\pi\) |
−0.825699 | + | 0.564111i | \(0.809219\pi\) | |||||||
\(578\) | 4909.00 | + | 8502.64i | 0.353266 | + | 0.611874i | ||||
\(579\) | 219.000 | − | 379.319i | 0.0157190 | − | 0.0272262i | ||||
\(580\) | −2032.00 | −0.145473 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −7140.00 | −0.508527 | ||||||||
\(583\) | −648.000 | + | 1122.37i | −0.0460333 | + | 0.0797320i | ||||
\(584\) | 1672.00 | + | 2895.99i | 0.118472 | + | 0.205200i | ||||
\(585\) | 378.000 | + | 654.715i | 0.0267152 | + | 0.0462720i | ||||
\(586\) | −2310.00 | + | 4001.04i | −0.162842 | + | 0.282050i | ||||
\(587\) | −9436.00 | −0.663484 | −0.331742 | − | 0.943370i | \(-0.607636\pi\) | ||||
−0.331742 | + | 0.943370i | \(0.607636\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8928.00 | 0.624570 | ||||||||
\(590\) | 1544.00 | − | 2674.29i | 0.107738 | − | 0.186608i | ||||
\(591\) | −3819.00 | − | 6614.70i | −0.265808 | − | 0.460393i | ||||
\(592\) | −3184.00 | − | 5514.85i | −0.221050 | − | 0.382870i | ||||
\(593\) | −657.000 | + | 1137.96i | −0.0454971 | + | 0.0788032i | −0.887877 | − | 0.460081i | \(-0.847820\pi\) |
0.842380 | + | 0.538884i | \(0.181154\pi\) | |||||||
\(594\) | 432.000 | 0.0298404 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11400.0 | −0.783494 | ||||||||
\(597\) | 3804.00 | − | 6588.72i | 0.260783 | − | 0.451689i | ||||
\(598\) | −3192.00 | − | 5528.71i | −0.218279 | − | 0.378070i | ||||
\(599\) | 4470.00 | + | 7742.27i | 0.304907 | + | 0.528114i | 0.977241 | − | 0.212134i | \(-0.0680413\pi\) |
−0.672334 | + | 0.740248i | \(0.734708\pi\) | |||||||
\(600\) | −1452.00 | + | 2514.94i | −0.0987961 | + | 0.171120i | ||||
\(601\) | −16058.0 | −1.08988 | −0.544941 | − | 0.838474i | \(-0.683448\pi\) | ||||
−0.544941 | + | 0.838474i | \(0.683448\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6876.00 | −0.464365 | ||||||||
\(604\) | −3344.00 | + | 5791.98i | −0.225274 | + | 0.390186i | ||||
\(605\) | −1267.00 | − | 2194.51i | −0.0851419 | − | 0.147470i | ||||
\(606\) | −4110.00 | − | 7118.73i | −0.275507 | − | 0.477192i | ||||
\(607\) | 1968.00 | − | 3408.68i | 0.131596 | − | 0.227931i | −0.792696 | − | 0.609617i | \(-0.791323\pi\) |
0.924292 | + | 0.381686i | \(0.124657\pi\) | |||||||
\(608\) | 3968.00 | 0.264677 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 120.000 | 0.00796501 | ||||||||
\(611\) | −5544.00 | + | 9602.49i | −0.367081 | + | 0.635802i | ||||
\(612\) | −36.0000 | − | 62.3538i | −0.00237780 | − | 0.00411847i | ||||
\(613\) | −87.0000 | − | 150.688i | −0.00573230 | − | 0.00992863i | 0.863145 | − | 0.504956i | \(-0.168491\pi\) |
−0.868877 | + | 0.495027i | \(0.835158\pi\) | |||||||
\(614\) | 196.000 | − | 339.482i | 0.0128826 | − | 0.0223133i | ||||
\(615\) | −2772.00 | −0.181753 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16018.0 | 1.04515 | 0.522577 | − | 0.852592i | \(-0.324971\pi\) | ||||
0.522577 | + | 0.852592i | \(0.324971\pi\) | |||||||
\(618\) | −1392.00 | + | 2411.01i | −0.0906059 | + | 0.156934i | ||||
\(619\) | −1534.00 | − | 2656.97i | −0.0996069 | − | 0.172524i | 0.811915 | − | 0.583776i | \(-0.198425\pi\) |
−0.911522 | + | 0.411251i | \(0.865092\pi\) | |||||||
\(620\) | 288.000 | + | 498.831i | 0.0186554 | + | 0.0323121i | ||||
\(621\) | 1026.00 | − | 1777.08i | 0.0662995 | − | 0.114834i | ||||
\(622\) | 13472.0 | 0.868453 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2016.00 | −0.129334 | ||||||||
\(625\) | −7070.50 | + | 12246.5i | −0.452512 | + | 0.783774i | ||||
\(626\) | 394.000 | + | 682.428i | 0.0251556 | + | 0.0435708i | ||||
\(627\) | −1488.00 | − | 2577.29i | −0.0947767 | − | 0.164158i | ||||
\(628\) | 892.000 | − | 1544.99i | 0.0566794 | − | 0.0981716i | ||||
\(629\) | 796.000 | 0.0504588 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24656.0 | 1.55553 | 0.777765 | − | 0.628555i | \(-0.216353\pi\) | ||||
0.777765 | + | 0.628555i | \(0.216353\pi\) | |||||||
\(632\) | −2208.00 | + | 3824.37i | −0.138971 | + | 0.240704i | ||||
\(633\) | −1950.00 | − | 3377.50i | −0.122442 | − | 0.212075i | ||||
\(634\) | 6714.00 | + | 11629.0i | 0.420579 | + | 0.728464i | ||||
\(635\) | 2088.00 | − | 3616.52i | 0.130488 | − | 0.226011i | ||||
\(636\) | 1944.00 | 0.121202 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4064.00 | −0.252187 | ||||||||
\(639\) | 1062.00 | − | 1839.44i | 0.0657466 | − | 0.113876i | ||||
\(640\) | 128.000 | + | 221.703i | 0.00790569 | + | 0.0136931i | ||||
\(641\) | −3797.00 | − | 6576.60i | −0.233966 | − | 0.405242i | 0.725005 | − | 0.688743i | \(-0.241837\pi\) |
−0.958972 | + | 0.283501i | \(0.908504\pi\) | |||||||
\(642\) | −6408.00 | + | 11099.0i | −0.393931 | + | 0.682308i | ||||
\(643\) | 3724.00 | 0.228398 | 0.114199 | − | 0.993458i | \(-0.463570\pi\) | ||||
0.114199 | + | 0.993458i | \(0.463570\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1272.00 | 0.0776511 | ||||||||
\(646\) | −248.000 | + | 429.549i | −0.0151044 | + | 0.0261616i | ||||
\(647\) | 1896.00 | + | 3283.97i | 0.115208 | + | 0.199546i | 0.917863 | − | 0.396898i | \(-0.129913\pi\) |
−0.802655 | + | 0.596444i | \(0.796580\pi\) | |||||||
\(648\) | −324.000 | − | 561.184i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 3088.00 | − | 5348.57i | 0.186771 | − | 0.323497i | ||||
\(650\) | −10164.0 | −0.613331 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10832.0 | 0.650635 | ||||||||
\(653\) | −12351.0 | + | 21392.6i | −0.740171 | + | 1.28201i | 0.212245 | + | 0.977216i | \(0.431922\pi\) |
−0.952417 | + | 0.304798i | \(0.901411\pi\) | |||||||
\(654\) | −3678.00 | − | 6370.48i | −0.219910 | − | 0.380895i | ||||
\(655\) | 292.000 | + | 505.759i | 0.0174189 | + | 0.0301704i | ||||
\(656\) | 3696.00 | − | 6401.66i | 0.219976 | − | 0.381010i | ||||
\(657\) | −3762.00 | −0.223394 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20144.0 | −1.19074 | −0.595371 | − | 0.803451i | \(-0.702995\pi\) | ||||
−0.595371 | + | 0.803451i | \(0.702995\pi\) | |||||||
\(660\) | 96.0000 | − | 166.277i | 0.00566181 | − | 0.00980654i | ||||
\(661\) | −1261.00 | − | 2184.12i | −0.0742015 | − | 0.128521i | 0.826537 | − | 0.562882i | \(-0.190307\pi\) |
−0.900739 | + | 0.434361i | \(0.856974\pi\) | |||||||
\(662\) | −692.000 | − | 1198.58i | −0.0406274 | − | 0.0703687i | ||||
\(663\) | 126.000 | − | 218.238i | 0.00738075 | − | 0.0127838i | ||||
\(664\) | −8288.00 | −0.484393 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7164.00 | 0.416816 | ||||||||
\(667\) | −9652.00 | + | 16717.8i | −0.560310 | + | 0.970486i | ||||
\(668\) | 1792.00 | + | 3103.84i | 0.103794 | + | 0.179777i | ||||
\(669\) | −3864.00 | − | 6692.64i | −0.223305 | − | 0.386775i | ||||
\(670\) | −1528.00 | + | 2646.57i | −0.0881071 | + | 0.152606i | ||||
\(671\) | 240.000 | 0.0138079 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10414.0 | −0.596479 | −0.298239 | − | 0.954491i | \(-0.596399\pi\) | ||||
−0.298239 | + | 0.954491i | \(0.596399\pi\) | |||||||
\(674\) | 1566.00 | − | 2712.39i | 0.0894956 | − | 0.155011i | ||||
\(675\) | −1633.50 | − | 2829.30i | −0.0931458 | − | 0.161333i | ||||
\(676\) | 866.000 | + | 1499.96i | 0.0492717 | + | 0.0853411i | ||||
\(677\) | −11115.0 | + | 19251.7i | −0.630996 | + | 1.09292i | 0.356353 | + | 0.934352i | \(0.384020\pi\) |
−0.987348 | + | 0.158565i | \(0.949313\pi\) | |||||||
\(678\) | −2028.00 | −0.114874 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −32.0000 | −0.00180462 | ||||||||
\(681\) | 2754.00 | − | 4770.07i | 0.154968 | − | 0.268413i | ||||
\(682\) | 576.000 | + | 997.661i | 0.0323404 | + | 0.0560153i | ||||
\(683\) | −9096.00 | − | 15754.7i | −0.509588 | − | 0.882633i | −0.999938 | − | 0.0111072i | \(-0.996464\pi\) |
0.490350 | − | 0.871526i | \(-0.336869\pi\) | |||||||
\(684\) | −2232.00 | + | 3865.94i | −0.124770 | + | 0.216108i | ||||
\(685\) | −1636.00 | −0.0912531 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5622.00 | −0.312216 | ||||||||
\(688\) | −1696.00 | + | 2937.56i | −0.0939817 | + | 0.162781i | ||||
\(689\) | 3402.00 | + | 5892.44i | 0.188107 | + | 0.325811i | ||||
\(690\) | −456.000 | − | 789.815i | −0.0251589 | − | 0.0435764i | ||||
\(691\) | 4054.00 | − | 7021.73i | 0.223186 | − | 0.386569i | −0.732588 | − | 0.680673i | \(-0.761688\pi\) |
0.955774 | + | 0.294103i | \(0.0950210\pi\) | |||||||
\(692\) | −16136.0 | −0.886414 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10656.0 | −0.582848 | ||||||||
\(695\) | 2156.00 | − | 3734.30i | 0.117672 | − | 0.203813i | ||||
\(696\) | 3048.00 | + | 5279.29i | 0.165997 | + | 0.287516i | ||||
\(697\) | 462.000 | + | 800.207i | 0.0251069 | + | 0.0434864i | ||||
\(698\) | 11326.0 | − | 19617.2i | 0.614177 | − | 1.06379i | ||||
\(699\) | −11190.0 | −0.605500 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5794.00 | −0.312177 | −0.156089 | − | 0.987743i | \(-0.549889\pi\) | ||||
−0.156089 | + | 0.987743i | \(0.549889\pi\) | |||||||
\(702\) | 1134.00 | − | 1964.15i | 0.0609688 | − | 0.105601i | ||||
\(703\) | −24676.0 | − | 42740.1i | −1.32386 | − | 2.29299i | ||||
\(704\) | 256.000 | + | 443.405i | 0.0137051 | + | 0.0237379i | ||||
\(705\) | −792.000 | + | 1371.78i | −0.0423099 | + | 0.0732828i | ||||
\(706\) | 4260.00 | 0.227092 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −9264.00 | −0.491755 | ||||||||
\(709\) | 977.000 | − | 1692.21i | 0.0517518 | − | 0.0896367i | −0.838989 | − | 0.544148i | \(-0.816853\pi\) |
0.890741 | + | 0.454512i | \(0.150186\pi\) | |||||||
\(710\) | −472.000 | − | 817.528i | −0.0249491 | − | 0.0432131i | ||||
\(711\) | −2484.00 | − | 4302.41i | −0.131023 | − | 0.226938i | ||||
\(712\) | 120.000 | − | 207.846i | 0.00631628 | − | 0.0109401i | ||||
\(713\) | 5472.00 | 0.287417 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 672.000 | 0.0351488 | ||||||||
\(716\) | 6960.00 | − | 12055.1i | 0.363279 | − | 0.629217i | ||||
\(717\) | 3006.00 | + | 5206.54i | 0.156571 | + | 0.271188i | ||||
\(718\) | −3044.00 | − | 5272.36i | −0.158219 | − | 0.274043i | ||||
\(719\) | −16008.0 | + | 27726.7i | −0.830317 | + | 1.43815i | 0.0674706 | + | 0.997721i | \(0.478507\pi\) |
−0.897787 | + | 0.440429i | \(0.854826\pi\) | |||||||
\(720\) | −288.000 | −0.0149071 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 17034.0 | 0.878033 | ||||||||
\(723\) | 969.000 | − | 1678.36i | 0.0498444 | − | 0.0863330i | ||||
\(724\) | −5796.00 | − | 10039.0i | −0.297523 | − | 0.515325i | ||||
\(725\) | 15367.0 | + | 26616.4i | 0.787195 | + | 1.36346i | ||||
\(726\) | −3801.00 | + | 6583.53i | −0.194309 | + | 0.336553i | ||||
\(727\) | 23072.0 | 1.17702 | 0.588510 | − | 0.808490i | \(-0.299715\pi\) | ||||
0.588510 | + | 0.808490i | \(0.299715\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −836.000 | + | 1447.99i | −0.0423860 | + | 0.0734146i | ||||
\(731\) | −212.000 | − | 367.195i | −0.0107265 | − | 0.0185789i | ||||
\(732\) | −180.000 | − | 311.769i | −0.00908879 | − | 0.0157422i | ||||
\(733\) | 15891.0 | − | 27524.0i | 0.800747 | − | 1.38693i | −0.118378 | − | 0.992969i | \(-0.537770\pi\) |
0.919125 | − | 0.393966i | \(-0.128897\pi\) | |||||||
\(734\) | −24832.0 | −1.24873 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2432.00 | 0.121800 | ||||||||
\(737\) | −3056.00 | + | 5293.15i | −0.152740 | + | 0.264553i | ||||
\(738\) | 4158.00 | + | 7201.87i | 0.207396 | + | 0.359220i | ||||
\(739\) | 12198.0 | + | 21127.6i | 0.607186 | + | 1.05168i | 0.991702 | + | 0.128559i | \(0.0410352\pi\) |
−0.384516 | + | 0.923119i | \(0.625631\pi\) | |||||||
\(740\) | 1592.00 | − | 2757.42i | 0.0790852 | − | 0.136980i | ||||
\(741\) | −15624.0 | −0.774578 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32604.0 | −1.60986 | −0.804929 | − | 0.593371i | \(-0.797797\pi\) | ||||
−0.804929 | + | 0.593371i | \(0.797797\pi\) | |||||||
\(744\) | 864.000 | − | 1496.49i | 0.0425750 | − | 0.0737420i | ||||
\(745\) | −2850.00 | − | 4936.34i | −0.140156 | − | 0.242757i | ||||
\(746\) | 7442.00 | + | 12889.9i | 0.365243 | + | 0.632619i | ||||
\(747\) | 4662.00 | − | 8074.82i | 0.228345 | − | 0.395505i | ||||
\(748\) | −64.0000 | −0.00312844 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2952.00 | −0.143722 | ||||||||
\(751\) | 3840.00 | − | 6651.08i | 0.186583 | − | 0.323171i | −0.757526 | − | 0.652805i | \(-0.773592\pi\) |
0.944109 | + | 0.329634i | \(0.106925\pi\) | |||||||
\(752\) | −2112.00 | − | 3658.09i | −0.102416 | − | 0.177389i | ||||
\(753\) | −1890.00 | − | 3273.58i | −0.0914680 | − | 0.158427i | ||||
\(754\) | −10668.0 | + | 18477.5i | −0.515259 | + | 0.892456i | ||||
\(755\) | −3344.00 | −0.161193 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 366.000 | 0.0175727 | 0.00878633 | − | 0.999961i | \(-0.497203\pi\) | ||||
0.00878633 | + | 0.999961i | \(0.497203\pi\) | |||||||
\(758\) | −100.000 | + | 173.205i | −0.00479177 | + | 0.00829959i | ||||
\(759\) | −912.000 | − | 1579.63i | −0.0436146 | − | 0.0755428i | ||||
\(760\) | 992.000 | + | 1718.19i | 0.0473469 | + | 0.0820072i | ||||
\(761\) | 14687.0 | − | 25438.6i | 0.699610 | − | 1.21176i | −0.268992 | − | 0.963143i | \(-0.586690\pi\) |
0.968602 | − | 0.248618i | \(-0.0799763\pi\) | |||||||
\(762\) | −12528.0 | −0.595593 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 10608.0 | 0.502335 | ||||||||
\(765\) | 18.0000 | − | 31.1769i | 0.000850708 | − | 0.00147347i | ||||
\(766\) | 8080.00 | + | 13995.0i | 0.381126 | + | 0.660129i | ||||
\(767\) | −16212.0 | − | 28080.0i | −0.763209 | − | 1.32192i | ||||
\(768\) | 384.000 | − | 665.108i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | 38990.0 | 1.82837 | 0.914184 | − | 0.405299i | \(-0.132833\pi\) | ||||
0.914184 | + | 0.405299i | \(0.132833\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17730.0 | 0.828185 | ||||||||
\(772\) | −292.000 | + | 505.759i | −0.0136131 | + | 0.0235786i | ||||
\(773\) | −10235.0 | − | 17727.5i | −0.476232 | − | 0.824858i | 0.523397 | − | 0.852089i | \(-0.324664\pi\) |
−0.999629 | + | 0.0272308i | \(0.991331\pi\) | |||||||
\(774\) | −1908.00 | − | 3304.75i | −0.0886068 | − | 0.153471i | ||||
\(775\) | 4356.00 | − | 7544.81i | 0.201900 | − | 0.349700i | ||||
\(776\) | 9520.00 | 0.440397 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10964.0 | −0.505242 | ||||||||
\(779\) | 28644.0 | − | 49612.9i | 1.31743 | − | 2.28186i | ||||
\(780\) | −504.000 | − | 872.954i | −0.0231360 | − | 0.0400728i | ||||
\(781\) | −944.000 | − | 1635.06i | −0.0432509 | − | 0.0749128i | ||||
\(782\) | −152.000 | + | 263.272i | −0.00695078 | + | 0.0120391i | ||||
\(783\) | −6858.00 | −0.313008 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 892.000 | 0.0405565 | ||||||||
\(786\) | 876.000 | − | 1517.28i | 0.0397530 | − | 0.0688543i | ||||
\(787\) | 14958.0 | + | 25908.0i | 0.677503 | + | 1.17347i | 0.975730 | + | 0.218975i | \(0.0702714\pi\) |
−0.298227 | + | 0.954495i | \(0.596395\pi\) | |||||||
\(788\) | 5092.00 | + | 8819.60i | 0.230197 | + | 0.398712i | ||||
\(789\) | 4482.00 | − | 7763.05i | 0.202235 | − | 0.350281i | ||||
\(790\) | −2208.00 | −0.0994394 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −576.000 | −0.0258425 | ||||||||
\(793\) | 630.000 | − | 1091.19i | 0.0282118 | − | 0.0488643i | ||||
\(794\) | 10446.0 | + | 18093.0i | 0.466895 | + | 0.808686i | ||||
\(795\) | 486.000 | + | 841.777i | 0.0216813 | + | 0.0375531i | ||||
\(796\) | −5072.00 | + | 8784.96i | −0.225845 | + | 0.391174i | ||||
\(797\) | −4914.00 | −0.218398 | −0.109199 | − | 0.994020i | \(-0.534828\pi\) | ||||
−0.109199 | + | 0.994020i | \(0.534828\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 528.000 | 0.0233783 | ||||||||
\(800\) | 1936.00 | − | 3353.25i | 0.0855599 | − | 0.148194i | ||||
\(801\) | 135.000 | + | 233.827i | 0.00595504 | + | 0.0103144i | ||||
\(802\) | 11334.0 | + | 19631.1i | 0.499024 | + | 0.864335i | ||||
\(803\) | −1672.00 | + | 2895.99i | −0.0734790 | + | 0.127269i | ||||
\(804\) | 9168.00 | 0.402152 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6048.00 | 0.264307 | ||||||||
\(807\) | 1977.00 | − | 3424.26i | 0.0862375 | − | 0.149368i | ||||
\(808\) | 5480.00 | + | 9491.64i | 0.238596 | + | 0.413261i | ||||
\(809\) | −17125.0 | − | 29661.4i | −0.744231 | − | 1.28905i | −0.950553 | − | 0.310562i | \(-0.899483\pi\) |
0.206322 | − | 0.978484i | \(-0.433851\pi\) | |||||||
\(810\) | 162.000 | − | 280.592i | 0.00702728 | − | 0.0121716i | ||||
\(811\) | 41804.0 | 1.81003 | 0.905017 | − | 0.425376i | \(-0.139858\pi\) | ||||
0.905017 | + | 0.425376i | \(0.139858\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16920.0 | −0.729902 | ||||||||
\(814\) | 3184.00 | − | 5514.85i | 0.137100 | − | 0.237464i | ||||
\(815\) | 2708.00 | + | 4690.39i | 0.116389 | + | 0.201592i | ||||
\(816\) | 48.0000 | + | 83.1384i | 0.00205924 | + | 0.00356670i | ||||
\(817\) | −13144.0 | + | 22766.1i | −0.562852 | + | 0.974889i | ||||
\(818\) | −17188.0 | −0.734675 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3696.00 | 0.157402 | ||||||||
\(821\) | −15431.0 | + | 26727.3i | −0.655963 | + | 1.13616i | 0.325688 | + | 0.945477i | \(0.394404\pi\) |
−0.981651 | + | 0.190684i | \(0.938929\pi\) | |||||||
\(822\) | 2454.00 | + | 4250.45i | 0.104128 | + | 0.180355i | ||||
\(823\) | −5288.00 | − | 9159.08i | −0.223971 | − | 0.387929i | 0.732039 | − | 0.681262i | \(-0.238569\pi\) |
−0.956010 | + | 0.293333i | \(0.905235\pi\) | |||||||
\(824\) | 1856.00 | − | 3214.69i | 0.0784670 | − | 0.135909i | ||||
\(825\) | −2904.00 | −0.122551 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10680.0 | −0.449069 | −0.224534 | − | 0.974466i | \(-0.572086\pi\) | ||||
−0.224534 | + | 0.974466i | \(0.572086\pi\) | |||||||
\(828\) | −1368.00 | + | 2369.45i | −0.0574170 | + | 0.0994492i | ||||
\(829\) | −589.000 | − | 1020.18i | −0.0246765 | − | 0.0427409i | 0.853423 | − | 0.521218i | \(-0.174522\pi\) |
−0.878100 | + | 0.478477i | \(0.841189\pi\) | |||||||
\(830\) | −2072.00 | − | 3588.81i | −0.0866508 | − | 0.150084i | ||||
\(831\) | 9669.00 | − | 16747.2i | 0.403627 | − | 0.699102i | ||||
\(832\) | 2688.00 | 0.112007 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −12936.0 | −0.537095 | ||||||||
\(835\) | −896.000 | + | 1551.92i | −0.0371346 | + | 0.0643189i | ||||
\(836\) | 1984.00 | + | 3436.39i | 0.0820790 | + | 0.142165i | ||||
\(837\) | 972.000 | + | 1683.55i | 0.0401401 | + | 0.0695246i | ||||
\(838\) | 10500.0 | − | 18186.5i | 0.432836 | − | 0.749694i | ||||
\(839\) | 5600.00 | 0.230433 | 0.115217 | − | 0.993340i | \(-0.463244\pi\) | ||||
0.115217 | + | 0.993340i | \(0.463244\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 40127.0 | 1.64529 | ||||||||
\(842\) | 12066.0 | − | 20898.9i | 0.493850 | − | 0.855374i | ||||
\(843\) | 7395.00 | + | 12808.5i | 0.302132 | + | 0.523308i | ||||
\(844\) | 2600.00 | + | 4503.33i | 0.106038 | + | 0.183662i | ||||
\(845\) | −433.000 | + | 749.978i | −0.0176280 | + | 0.0305326i | ||||
\(846\) | 4752.00 | 0.193117 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2592.00 | −0.104964 | ||||||||
\(849\) | 9390.00 | − | 16264.0i | 0.379581 | − | 0.657453i | ||||
\(850\) | 242.000 | + | 419.156i | 0.00976533 | + | 0.0169140i | ||||
\(851\) | −15124.0 | − | 26195.5i | −0.609217 | − | 1.05520i | ||||
\(852\) | −1416.00 | + | 2452.58i | −0.0569382 | + | 0.0986199i | ||||
\(853\) | 826.000 | 0.0331556 | 0.0165778 | − | 0.999863i | \(-0.494723\pi\) | ||||
0.0165778 | + | 0.999863i | \(0.494723\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2232.00 | −0.0892781 | ||||||||
\(856\) | 8544.00 | − | 14798.6i | 0.341154 | − | 0.590896i | ||||
\(857\) | 22959.0 | + | 39766.2i | 0.915128 | + | 1.58505i | 0.806714 | + | 0.590942i | \(0.201244\pi\) |
0.108414 | + | 0.994106i | \(0.465423\pi\) | |||||||
\(858\) | −1008.00 | − | 1745.91i | −0.0401079 | − | 0.0694689i | ||||
\(859\) | 21190.0 | − | 36702.2i | 0.841669 | − | 1.45781i | −0.0468143 | − | 0.998904i | \(-0.514907\pi\) |
0.888483 | − | 0.458909i | \(-0.151760\pi\) | |||||||
\(860\) | −1696.00 | −0.0672478 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8664.00 | 0.342340 | ||||||||
\(863\) | 13262.0 | − | 22970.5i | 0.523110 | − | 0.906053i | −0.476529 | − | 0.879159i | \(-0.658105\pi\) |
0.999638 | − | 0.0268937i | \(-0.00856156\pi\) | |||||||
\(864\) | 432.000 | + | 748.246i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | −4034.00 | − | 6987.09i | −0.158567 | − | 0.274645i | ||||
\(866\) | −1918.00 | + | 3322.07i | −0.0752613 | + | 0.130356i | ||||
\(867\) | 14727.0 | 0.576880 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4416.00 | −0.172385 | ||||||||
\(870\) | −1524.00 | + | 2639.65i | −0.0593890 | + | 0.102865i | ||||
\(871\) | 16044.0 | + | 27789.0i | 0.624145 | + | 1.08105i | ||||
\(872\) | 4904.00 | + | 8493.98i | 0.190448 | + | 0.329865i | ||||
\(873\) | −5355.00 | + | 9275.13i | −0.207605 | + | 0.359583i | ||||
\(874\) | 18848.0 | 0.729454 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5016.00 | 0.193465 | ||||||||
\(877\) | −10307.0 | + | 17852.2i | −0.396856 | + | 0.687375i | −0.993336 | − | 0.115253i | \(-0.963232\pi\) |
0.596480 | + | 0.802628i | \(0.296565\pi\) | |||||||
\(878\) | −7992.00 | − | 13842.6i | −0.307195 | − | 0.532077i | ||||
\(879\) | 3465.00 | + | 6001.56i | 0.132960 | + | 0.230293i | ||||
\(880\) | −128.000 | + | 221.703i | −0.00490327 | + | 0.00849272i | ||||
\(881\) | 23730.0 | 0.907473 | 0.453737 | − | 0.891136i | \(-0.350091\pi\) | ||||
0.453737 | + | 0.891136i | \(0.350091\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9028.00 | −0.344073 | −0.172036 | − | 0.985091i | \(-0.555035\pi\) | ||||
−0.172036 | + | 0.985091i | \(0.555035\pi\) | |||||||
\(884\) | −168.000 | + | 290.985i | −0.00639191 | + | 0.0110711i | ||||
\(885\) | −2316.00 | − | 4011.43i | −0.0879678 | − | 0.152365i | ||||
\(886\) | −3184.00 | − | 5514.85i | −0.120732 | − | 0.209114i | ||||
\(887\) | 18600.0 | − | 32216.1i | 0.704089 | − | 1.21952i | −0.262930 | − | 0.964815i | \(-0.584689\pi\) |
0.967019 | − | 0.254703i | \(-0.0819777\pi\) | |||||||
\(888\) | −9552.00 | −0.360973 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 120.000 | 0.00451956 | ||||||||
\(891\) | 324.000 | − | 561.184i | 0.0121823 | − | 0.0211003i | ||||
\(892\) | 5152.00 | + | 8923.53i | 0.193388 | + | 0.334957i | ||||
\(893\) | −16368.0 | − | 28350.2i | −0.613364 | − | 1.06238i | ||||
\(894\) | −8550.00 | + | 14809.0i | −0.319860 | + | 0.554014i | ||||
\(895\) | 6960.00 | 0.259941 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9576.00 | −0.356447 | ||||||||
\(898\) | −11426.0 | + | 19790.4i | −0.424600 | + | 0.735428i | ||||
\(899\) | −9144.00 | − | 15837.9i | −0.339232 | − | 0.587567i | ||||
\(900\) | 2178.00 | + | 3772.41i | 0.0806667 | + | 0.139719i | ||||
\(901\) | 162.000 | − | 280.592i | 0.00599001 | − | 0.0103750i | ||||
\(902\) | 7392.00 | 0.272868 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2704.00 | 0.0994842 | ||||||||
\(905\) | 2898.00 | − | 5019.48i | 0.106445 | − | 0.184368i | ||||
\(906\) | 5016.00 | + | 8687.97i | 0.183935 | + | 0.318585i | ||||
\(907\) | −11994.0 | − | 20774.2i | −0.439090 | − | 0.760525i | 0.558530 | − | 0.829484i | \(-0.311366\pi\) |
−0.997619 | + | 0.0689589i | \(0.978032\pi\) | |||||||
\(908\) | −3672.00 | + | 6360.09i | −0.134207 | + | 0.232453i | ||||
\(909\) | −12330.0 | −0.449901 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15276.0 | 0.555561 | 0.277781 | − | 0.960645i | \(-0.410401\pi\) | ||||
0.277781 | + | 0.960645i | \(0.410401\pi\) | |||||||
\(912\) | 2976.00 | − | 5154.58i | 0.108054 | − | 0.187155i | ||||
\(913\) | −4144.00 | − | 7177.62i | −0.150215 | − | 0.260180i | ||||
\(914\) | 16934.0 | + | 29330.5i | 0.612830 | + | 1.06145i | ||||
\(915\) | 90.0000 | − | 155.885i | 0.00325170 | − | 0.00563211i | ||||
\(916\) | 7496.00 | 0.270387 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −108.000 | −0.00388293 | ||||||||
\(919\) | 5380.00 | − | 9318.43i | 0.193112 | − | 0.334480i | −0.753168 | − | 0.657828i | \(-0.771475\pi\) |
0.946280 | + | 0.323349i | \(0.104809\pi\) | |||||||
\(920\) | 608.000 | + | 1053.09i | 0.0217882 | + | 0.0377383i | ||||
\(921\) | −294.000 | − | 509.223i | −0.0105186 | − | 0.0182187i | ||||
\(922\) | −17038.0 | + | 29510.7i | −0.608586 | + | 1.05410i | ||||
\(923\) | −9912.00 | −0.353475 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −48158.0 | −1.71181 | ||||||||
\(926\) | 13592.0 | − | 23542.0i | 0.482355 | − | 0.835464i | ||||
\(927\) | 2088.00 | + | 3616.52i | 0.0739794 | + | 0.128136i | ||||
\(928\) | −4064.00 | − | 7039.05i | −0.143758 | − | 0.248996i | ||||
\(929\) | −26445.0 | + | 45804.1i | −0.933942 | + | 1.61764i | −0.157433 | + | 0.987530i | \(0.550322\pi\) |
−0.776509 | + | 0.630106i | \(0.783012\pi\) | |||||||
\(930\) | 864.000 | 0.0304642 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 14920.0 | 0.524379 | ||||||||
\(933\) | 10104.0 | − | 17500.6i | 0.354545 | − | 0.614089i | ||||
\(934\) | 8612.00 | + | 14916.4i | 0.301706 | + | 0.522570i | ||||
\(935\) | −16.0000 | − | 27.7128i | −0.000559632 | − | 0.000969311i | ||||
\(936\) | −1512.00 | + | 2618.86i | −0.0528005 | + | 0.0914531i | ||||
\(937\) | 6118.00 | 0.213305 | 0.106652 | − | 0.994296i | \(-0.465987\pi\) | ||||
0.106652 | + | 0.994296i | \(0.465987\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1182.00 | 0.0410789 | ||||||||
\(940\) | 1056.00 | − | 1829.05i | 0.0366414 | − | 0.0634648i | ||||
\(941\) | −16115.0 | − | 27912.0i | −0.558272 | − | 0.966956i | −0.997641 | − | 0.0686488i | \(-0.978131\pi\) |
0.439369 | − | 0.898307i | \(-0.355202\pi\) | |||||||
\(942\) | −1338.00 | − | 2317.48i | −0.0462786 | − | 0.0801568i | ||||
\(943\) | 17556.0 | − | 30407.9i | 0.606259 | − | 1.05007i | ||||
\(944\) | 12352.0 | 0.425872 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3392.00 | −0.116579 | ||||||||
\(947\) | 9272.00 | − | 16059.6i | 0.318162 | − | 0.551073i | −0.661942 | − | 0.749555i | \(-0.730268\pi\) |
0.980105 | + | 0.198482i | \(0.0636010\pi\) | |||||||
\(948\) | 3312.00 | + | 5736.55i | 0.113469 | + | 0.196534i | ||||
\(949\) | 8778.00 | + | 15203.9i | 0.300259 | + | 0.520064i | ||||
\(950\) | 15004.0 | − | 25987.7i | 0.512415 | − | 0.887528i | ||||
\(951\) | 20142.0 | 0.686802 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25930.0 | 0.881380 | 0.440690 | − | 0.897659i | \(-0.354734\pi\) | ||||
0.440690 | + | 0.897659i | \(0.354734\pi\) | |||||||
\(954\) | 1458.00 | − | 2525.33i | 0.0494806 | − | 0.0857029i | ||||
\(955\) | 2652.00 | + | 4593.40i | 0.0898604 | + | 0.155643i | ||||
\(956\) | −4008.00 | − | 6942.06i | −0.135594 | − | 0.234856i | ||||
\(957\) | −3048.00 | + | 5279.29i | −0.102955 | + | 0.178323i | ||||
\(958\) | −14864.0 | −0.501288 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 384.000 | 0.0129099 | ||||||||
\(961\) | 12303.5 | − | 21310.3i | 0.412994 | − | 0.715326i | ||||
\(962\) | −16716.0 | − | 28953.0i | −0.560234 | − | 0.970354i | ||||
\(963\) | 9612.00 | + | 16648.5i | 0.321643 | + | 0.557102i | ||||
\(964\) | −1292.00 | + | 2237.81i | −0.0431665 | + | 0.0747666i | ||||
\(965\) | −292.000 | −0.00974074 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8192.00 | 0.272427 | 0.136214 | − | 0.990680i | \(-0.456507\pi\) | ||||
0.136214 | + | 0.990680i | \(0.456507\pi\) | |||||||
\(968\) | 5068.00 | − | 8778.03i | 0.168277 | − | 0.291464i | ||||
\(969\) | 372.000 | + | 644.323i | 0.0123327 | + | 0.0213608i | ||||
\(970\) | 2380.00 | + | 4122.28i | 0.0787806 | + | 0.136452i | ||||
\(971\) | −27222.0 | + | 47149.9i | −0.899686 | + | 1.55830i | −0.0717914 | + | 0.997420i | \(0.522872\pi\) |
−0.827895 | + | 0.560883i | \(0.810462\pi\) | |||||||
\(972\) | −972.000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −13232.0 | −0.435298 | ||||||||
\(975\) | −7623.00 | + | 13203.4i | −0.250391 | + | 0.433690i | ||||
\(976\) | 240.000 | + | 415.692i | 0.00787112 | + | 0.0136332i | ||||
\(977\) | 12723.0 | + | 22036.9i | 0.416627 | + | 0.721620i | 0.995598 | − | 0.0937289i | \(-0.0298787\pi\) |
−0.578970 | + | 0.815348i | \(0.696545\pi\) | |||||||
\(978\) | 8124.00 | − | 14071.2i | 0.265621 | − | 0.460068i | ||||
\(979\) | 240.000 | 0.00783497 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11034.0 | −0.359112 | ||||||||
\(982\) | −17040.0 | + | 29514.1i | −0.553735 | + | 0.959098i | ||||
\(983\) | 16596.0 | + | 28745.1i | 0.538484 | + | 0.932682i | 0.998986 | + | 0.0450235i | \(0.0143363\pi\) |
−0.460502 | + | 0.887659i | \(0.652330\pi\) | |||||||
\(984\) | −5544.00 | − | 9602.49i | −0.179610 | − | 0.311094i | ||||
\(985\) | −2546.00 | + | 4409.80i | −0.0823577 | + | 0.142648i | ||||
\(986\) | 1016.00 | 0.0328154 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 20832.0 | 0.670804 | ||||||||
\(989\) | −8056.00 | + | 13953.4i | −0.259015 | + | 0.448627i | ||||
\(990\) | −144.000 | − | 249.415i | −0.00462285 | − | 0.00800701i | ||||
\(991\) | −5512.00 | − | 9547.06i | −0.176685 | − | 0.306027i | 0.764058 | − | 0.645147i | \(-0.223204\pi\) |
−0.940743 | + | 0.339120i | \(0.889871\pi\) | |||||||
\(992\) | −1152.00 | + | 1995.32i | −0.0368710 | + | 0.0638625i | ||||
\(993\) | −2076.00 | −0.0663443 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5072.00 | −0.161601 | ||||||||
\(996\) | −6216.00 | + | 10766.4i | −0.197753 | + | 0.342517i | ||||
\(997\) | −20357.0 | − | 35259.4i | −0.646653 | − | 1.12004i | −0.983917 | − | 0.178625i | \(-0.942835\pi\) |
0.337265 | − | 0.941410i | \(-0.390498\pi\) | |||||||
\(998\) | 2948.00 | + | 5106.09i | 0.0935043 | + | 0.161954i | ||||
\(999\) | 5373.00 | − | 9306.31i | 0.170164 | − | 0.294733i |
(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 | 294.4.e.d.79.1 | 2 | ||
3.2 | odd | 2 | 882.4.g.r.667.1 | 2 | |||
7.2 | even | 3 | 294.4.a.h.1.1 | 1 | |||
7.3 | odd | 6 | 294.4.e.a.67.1 | 2 | |||
7.4 | even | 3 | inner | 294.4.e.d.67.1 | 2 | ||
7.5 | odd | 6 | 42.4.a.b.1.1 | ✓ | 1 | ||
7.6 | odd | 2 | 294.4.e.a.79.1 | 2 | |||
21.2 | odd | 6 | 882.4.a.d.1.1 | 1 | |||
21.5 | even | 6 | 126.4.a.c.1.1 | 1 | |||
21.11 | odd | 6 | 882.4.g.r.361.1 | 2 | |||
21.17 | even | 6 | 882.4.g.s.361.1 | 2 | |||
21.20 | even | 2 | 882.4.g.s.667.1 | 2 | |||
28.19 | even | 6 | 336.4.a.d.1.1 | 1 | |||
28.23 | odd | 6 | 2352.4.a.ba.1.1 | 1 | |||
35.12 | even | 12 | 1050.4.g.n.799.2 | 2 | |||
35.19 | odd | 6 | 1050.4.a.d.1.1 | 1 | |||
35.33 | even | 12 | 1050.4.g.n.799.1 | 2 | |||
56.5 | odd | 6 | 1344.4.a.f.1.1 | 1 | |||
56.19 | even | 6 | 1344.4.a.t.1.1 | 1 | |||
84.47 | odd | 6 | 1008.4.a.j.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.4.a.b.1.1 | ✓ | 1 | 7.5 | odd | 6 | ||
126.4.a.c.1.1 | 1 | 21.5 | even | 6 | |||
294.4.a.h.1.1 | 1 | 7.2 | even | 3 | |||
294.4.e.a.67.1 | 2 | 7.3 | odd | 6 | |||
294.4.e.a.79.1 | 2 | 7.6 | odd | 2 | |||
294.4.e.d.67.1 | 2 | 7.4 | even | 3 | inner | ||
294.4.e.d.79.1 | 2 | 1.1 | even | 1 | trivial | ||
336.4.a.d.1.1 | 1 | 28.19 | even | 6 | |||
882.4.a.d.1.1 | 1 | 21.2 | odd | 6 | |||
882.4.g.r.361.1 | 2 | 21.11 | odd | 6 | |||
882.4.g.r.667.1 | 2 | 3.2 | odd | 2 | |||
882.4.g.s.361.1 | 2 | 21.17 | even | 6 | |||
882.4.g.s.667.1 | 2 | 21.20 | even | 2 | |||
1008.4.a.j.1.1 | 1 | 84.47 | odd | 6 | |||
1050.4.a.d.1.1 | 1 | 35.19 | odd | 6 | |||
1050.4.g.n.799.1 | 2 | 35.33 | even | 12 | |||
1050.4.g.n.799.2 | 2 | 35.12 | even | 12 | |||
1344.4.a.f.1.1 | 1 | 56.5 | odd | 6 | |||
1344.4.a.t.1.1 | 1 | 56.19 | even | 6 | |||
2352.4.a.ba.1.1 | 1 | 28.23 | odd | 6 |