Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,3,Mod(67,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("392.67");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.k (of order \(6\), 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: | \(10.6812263629\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 4 x^{10} + 3 x^{9} + 86 x^{8} - 163 x^{7} + 155 x^{6} - 166 x^{5} + 164 x^{4} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 275.2 | ||
Root | \(-0.407369 - 0.812545i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.275 |
Dual form | 392.3.k.l.67.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.19654 | − | 1.60259i | −0.598272 | − | 0.801293i | ||||
\(3\) | 2.66613 | + | 4.61787i | 0.888709 | + | 1.53929i | 0.841403 | + | 0.540409i | \(0.181730\pi\) |
0.0473064 | + | 0.998880i | \(0.484936\pi\) | |||||||
\(4\) | −1.13656 | + | 3.83513i | −0.284141 | + | 0.958782i | ||||
\(5\) | −1.86796 | − | 1.07847i | −0.373592 | − | 0.215693i | 0.301435 | − | 0.953487i | \(-0.402534\pi\) |
−0.675026 | + | 0.737794i | \(0.735868\pi\) | |||||||
\(6\) | 4.21039 | − | 9.79818i | 0.701732 | − | 1.63303i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 7.50608 | − | 2.76746i | 0.938259 | − | 0.345932i | ||||
\(9\) | −9.71647 | + | 16.8294i | −1.07961 | + | 1.86993i | ||||
\(10\) | 0.506759 | + | 4.28400i | 0.0506759 | + | 0.428400i | ||||
\(11\) | −2.62956 | − | 4.55453i | −0.239051 | − | 0.414048i | 0.721392 | − | 0.692527i | \(-0.243503\pi\) |
−0.960442 | + | 0.278480i | \(0.910170\pi\) | |||||||
\(12\) | −20.7403 | + | 4.97644i | −1.72836 | + | 0.414703i | ||||
\(13\) | 21.4116i | 1.64704i | 0.567285 | + | 0.823522i | \(0.307994\pi\) | ||||
−0.567285 | + | 0.823522i | \(0.692006\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 11.5013i | − | 0.766754i | ||||||
\(16\) | −13.4164 | − | 8.71774i | −0.838528 | − | 0.544859i | ||||
\(17\) | 0.463429 | + | 0.802683i | 0.0272606 | + | 0.0472167i | 0.879334 | − | 0.476206i | \(-0.157988\pi\) |
−0.852073 | + | 0.523423i | \(0.824655\pi\) | |||||||
\(18\) | 38.5968 | − | 4.56566i | 2.14426 | − | 0.253648i | ||||
\(19\) | −2.96505 | + | 5.13561i | −0.156055 | + | 0.270295i | −0.933443 | − | 0.358726i | \(-0.883211\pi\) |
0.777388 | + | 0.629022i | \(0.216544\pi\) | |||||||
\(20\) | 6.25911 | − | 5.93812i | 0.312956 | − | 0.296906i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.15264 | + | 9.66378i | −0.188756 | + | 0.439263i | ||||
\(23\) | 7.52507 | + | 4.34460i | 0.327177 | + | 0.188896i | 0.654587 | − | 0.755987i | \(-0.272843\pi\) |
−0.327410 | + | 0.944882i | \(0.606176\pi\) | |||||||
\(24\) | 32.7919 | + | 27.2837i | 1.36633 | + | 1.13682i | ||||
\(25\) | −10.1738 | − | 17.6216i | −0.406953 | − | 0.704863i | ||||
\(26\) | 34.3139 | − | 25.6199i | 1.31976 | − | 0.985380i | ||||
\(27\) | −55.6311 | −2.06041 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.42223i | 0.324904i | 0.986716 | + | 0.162452i | \(0.0519403\pi\) | ||||
−0.986716 | + | 0.162452i | \(0.948060\pi\) | |||||||
\(30\) | −18.4318 | + | 13.7618i | −0.614395 | + | 0.458728i | ||||
\(31\) | −29.8813 | + | 17.2520i | −0.963912 | + | 0.556515i | −0.897375 | − | 0.441269i | \(-0.854529\pi\) |
−0.0665375 | + | 0.997784i | \(0.521195\pi\) | |||||||
\(32\) | 2.08243 | + | 31.9322i | 0.0650759 | + | 0.997880i | ||||
\(33\) | 14.0215 | − | 24.2859i | 0.424893 | − | 0.735936i | ||||
\(34\) | 0.731855 | − | 1.70313i | 0.0215252 | − | 0.0500921i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −53.4996 | − | 56.3916i | −1.48610 | − | 1.56643i | ||||
\(37\) | −11.0853 | − | 6.40011i | −0.299603 | − | 0.172976i | 0.342662 | − | 0.939459i | \(-0.388672\pi\) |
−0.642265 | + | 0.766483i | \(0.722005\pi\) | |||||||
\(38\) | 11.7781 | − | 1.39324i | 0.309949 | − | 0.0366643i | ||||
\(39\) | −98.8758 | + | 57.0860i | −2.53528 | + | 1.46374i | ||||
\(40\) | −17.0056 | − | 2.92555i | −0.425141 | − | 0.0731387i | ||||
\(41\) | −43.1339 | −1.05205 | −0.526023 | − | 0.850470i | \(-0.676317\pi\) | ||||
−0.526023 | + | 0.850470i | \(0.676317\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −41.7382 | −0.970656 | −0.485328 | − | 0.874332i | \(-0.661300\pi\) | ||||
−0.485328 | + | 0.874332i | \(0.661300\pi\) | |||||||
\(44\) | 20.4559 | − | 4.90818i | 0.464906 | − | 0.111550i | ||||
\(45\) | 36.2999 | − | 20.9578i | 0.806665 | − | 0.465728i | ||||
\(46\) | −2.04148 | − | 17.2581i | −0.0443800 | − | 0.375175i | ||||
\(47\) | −39.8357 | − | 22.9991i | −0.847567 | − | 0.489343i | 0.0122620 | − | 0.999925i | \(-0.496097\pi\) |
−0.859829 | + | 0.510582i | \(0.829430\pi\) | |||||||
\(48\) | 4.48745 | − | 85.1980i | 0.0934885 | − | 1.77496i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −16.0667 | + | 37.3894i | −0.321333 | + | 0.747788i | ||||
\(51\) | −2.47112 | + | 4.28011i | −0.0484534 | + | 0.0839238i | ||||
\(52\) | −82.1161 | − | 24.3356i | −1.57916 | − | 0.467993i | ||||
\(53\) | 64.5031 | − | 37.2409i | 1.21704 | − | 0.702658i | 0.252756 | − | 0.967530i | \(-0.418663\pi\) |
0.964284 | + | 0.264872i | \(0.0853297\pi\) | |||||||
\(54\) | 66.5650 | + | 89.1536i | 1.23269 | + | 1.65099i | ||||
\(55\) | 11.3436i | 0.206246i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −31.6208 | −0.554751 | ||||||||
\(58\) | 15.0999 | − | 11.2741i | 0.260344 | − | 0.194381i | ||||
\(59\) | 26.8367 | + | 46.4825i | 0.454860 | + | 0.787840i | 0.998680 | − | 0.0513617i | \(-0.0163561\pi\) |
−0.543821 | + | 0.839201i | \(0.683023\pi\) | |||||||
\(60\) | 44.1090 | + | 13.0720i | 0.735150 | + | 0.217866i | ||||
\(61\) | 24.0893 | + | 13.9080i | 0.394907 | + | 0.228000i | 0.684284 | − | 0.729215i | \(-0.260115\pi\) |
−0.289377 | + | 0.957215i | \(0.593448\pi\) | |||||||
\(62\) | 63.4020 | + | 27.2446i | 1.02261 | + | 0.439429i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 48.6823 | − | 41.5455i | 0.760661 | − | 0.649149i | ||||
\(65\) | 23.0916 | − | 39.9959i | 0.355256 | − | 0.615322i | ||||
\(66\) | −55.6975 | + | 6.58853i | −0.843902 | + | 0.0998262i | ||||
\(67\) | 39.2453 | + | 67.9749i | 0.585751 | + | 1.01455i | 0.994781 | + | 0.102030i | \(0.0325338\pi\) |
−0.409030 | + | 0.912521i | \(0.634133\pi\) | |||||||
\(68\) | −3.60511 | + | 0.865011i | −0.0530164 | + | 0.0127207i | ||||
\(69\) | 46.3330i | 0.671493i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 74.5100i | 1.04944i | 0.851276 | + | 0.524719i | \(0.175829\pi\) | ||||
−0.851276 | + | 0.524719i | \(0.824171\pi\) | |||||||
\(72\) | −26.3578 | + | 153.213i | −0.366081 | + | 2.12796i | ||||
\(73\) | 16.8020 | + | 29.1020i | 0.230165 | + | 0.398657i | 0.957857 | − | 0.287247i | \(-0.0927401\pi\) |
−0.727692 | + | 0.685904i | \(0.759407\pi\) | |||||||
\(74\) | 3.00734 | + | 25.4232i | 0.0406397 | + | 0.343556i | ||||
\(75\) | 54.2494 | − | 93.9627i | 0.723325 | − | 1.25284i | ||||
\(76\) | −16.3258 | − | 17.2083i | −0.214813 | − | 0.226425i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 209.794 | + | 90.1511i | 2.68967 | + | 1.15578i | ||||
\(79\) | −26.1642 | − | 15.1059i | −0.331192 | − | 0.191214i | 0.325178 | − | 0.945653i | \(-0.394576\pi\) |
−0.656370 | + | 0.754439i | \(0.727909\pi\) | |||||||
\(80\) | 15.6596 | + | 30.7536i | 0.195745 | + | 0.384420i | ||||
\(81\) | −60.8713 | − | 105.432i | −0.751497 | − | 1.30163i | ||||
\(82\) | 51.6116 | + | 69.1258i | 0.629410 | + | 0.842997i | ||||
\(83\) | 72.9274 | 0.878644 | 0.439322 | − | 0.898330i | \(-0.355219\pi\) | ||||
0.439322 | + | 0.898330i | \(0.355219\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 1.99917i | − | 0.0235197i | ||||||
\(86\) | 49.9416 | + | 66.8891i | 0.580716 | + | 0.777780i | ||||
\(87\) | −43.5106 | + | 25.1209i | −0.500122 | + | 0.288745i | ||||
\(88\) | −32.3421 | − | 26.9094i | −0.367524 | − | 0.305789i | ||||
\(89\) | −27.4198 | + | 47.4925i | −0.308088 | + | 0.533624i | −0.977944 | − | 0.208867i | \(-0.933022\pi\) |
0.669856 | + | 0.742491i | \(0.266356\pi\) | |||||||
\(90\) | −77.0211 | − | 33.0968i | −0.855790 | − | 0.367743i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −25.2148 | + | 23.9217i | −0.274074 | + | 0.260018i | ||||
\(93\) | −159.335 | − | 91.9919i | −1.71328 | − | 0.989160i | ||||
\(94\) | 10.8070 | + | 91.3596i | 0.114969 | + | 0.971910i | ||||
\(95\) | 11.0772 | − | 6.39541i | 0.116602 | − | 0.0673201i | ||||
\(96\) | −141.907 | + | 94.7516i | −1.47819 | + | 0.986996i | ||||
\(97\) | 53.7125 | 0.553738 | 0.276869 | − | 0.960908i | \(-0.410703\pi\) | ||||
0.276869 | + | 0.960908i | \(0.410703\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 102.200 | 1.03232 | ||||||||
\(100\) | 79.1442 | − | 18.9899i | 0.791442 | − | 0.189899i | ||||
\(101\) | 78.2037 | − | 45.1509i | 0.774294 | − | 0.447039i | −0.0601103 | − | 0.998192i | \(-0.519145\pi\) |
0.834404 | + | 0.551153i | \(0.185812\pi\) | |||||||
\(102\) | 9.81606 | − | 1.16115i | 0.0962358 | − | 0.0113839i | ||||
\(103\) | 97.6980 | + | 56.4060i | 0.948525 | + | 0.547631i | 0.892622 | − | 0.450805i | \(-0.148863\pi\) |
0.0559023 | + | 0.998436i | \(0.482196\pi\) | |||||||
\(104\) | 59.2556 | + | 160.717i | 0.569766 | + | 1.54535i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −136.863 | − | 58.8114i | −1.29116 | − | 0.554825i | ||||
\(107\) | 71.9950 | − | 124.699i | 0.672851 | − | 1.16541i | −0.304241 | − | 0.952595i | \(-0.598403\pi\) |
0.977092 | − | 0.212817i | \(-0.0682637\pi\) | |||||||
\(108\) | 63.2283 | − | 213.352i | 0.585447 | − | 1.97548i | ||||
\(109\) | −57.7477 | + | 33.3406i | −0.529795 | + | 0.305877i | −0.740933 | − | 0.671579i | \(-0.765616\pi\) |
0.211138 | + | 0.977456i | \(0.432283\pi\) | |||||||
\(110\) | 18.1790 | − | 13.5731i | 0.165264 | − | 0.123391i | ||||
\(111\) | − | 68.2540i | − | 0.614901i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.16467 | 0.0634042 | 0.0317021 | − | 0.999497i | \(-0.489907\pi\) | ||||
0.0317021 | + | 0.999497i | \(0.489907\pi\) | |||||||
\(114\) | 37.8357 | + | 50.6750i | 0.331892 | + | 0.444518i | ||||
\(115\) | −9.37101 | − | 16.2311i | −0.0814870 | − | 0.141140i | ||||
\(116\) | −36.1355 | − | 10.7090i | −0.311513 | − | 0.0923187i | ||||
\(117\) | −360.344 | − | 208.045i | −3.07986 | − | 1.77816i | ||||
\(118\) | 42.3810 | − | 98.6266i | 0.359161 | − | 0.835818i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −31.8294 | − | 86.3297i | −0.265245 | − | 0.719414i | ||||
\(121\) | 46.6709 | − | 80.8363i | 0.385710 | − | 0.668069i | ||||
\(122\) | −6.53521 | − | 55.2468i | −0.0535673 | − | 0.452842i | ||||
\(123\) | −115.000 | − | 199.187i | −0.934963 | − | 1.61940i | ||||
\(124\) | −32.2015 | − | 134.207i | −0.259690 | − | 1.08231i | ||||
\(125\) | 97.8118i | 0.782494i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 131.492i | 1.03537i | 0.855572 | + | 0.517684i | \(0.173206\pi\) | ||||
−0.855572 | + | 0.517684i | \(0.826794\pi\) | |||||||
\(128\) | −124.831 | − | 28.3066i | −0.975241 | − | 0.221145i | ||||
\(129\) | −111.279 | − | 192.742i | −0.862631 | − | 1.49412i | ||||
\(130\) | −91.7271 | + | 10.8505i | −0.705593 | + | 0.0834655i | ||||
\(131\) | −4.38060 | + | 7.58742i | −0.0334397 | + | 0.0579193i | −0.882261 | − | 0.470761i | \(-0.843980\pi\) |
0.848821 | + | 0.528680i | \(0.177313\pi\) | |||||||
\(132\) | 77.2032 | + | 81.3766i | 0.584873 | + | 0.616489i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 61.9769 | − | 144.229i | 0.462514 | − | 1.07634i | ||||
\(135\) | 103.916 | + | 59.9962i | 0.769752 | + | 0.444416i | ||||
\(136\) | 5.69993 | + | 4.74248i | 0.0419113 | + | 0.0348712i | ||||
\(137\) | 118.420 | + | 205.110i | 0.864381 | + | 1.49715i | 0.867660 | + | 0.497158i | \(0.165623\pi\) |
−0.00327850 | + | 0.999995i | \(0.501044\pi\) | |||||||
\(138\) | 74.2526 | − | 55.4395i | 0.538063 | − | 0.401735i | ||||
\(139\) | −172.122 | −1.23828 | −0.619142 | − | 0.785279i | \(-0.712520\pi\) | ||||
−0.619142 | + | 0.785279i | \(0.712520\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 245.274i | − | 1.73954i | ||||||
\(142\) | 119.409 | − | 89.1545i | 0.840907 | − | 0.627849i | ||||
\(143\) | 97.5195 | − | 56.3029i | 0.681955 | − | 0.393727i | ||||
\(144\) | 277.075 | − | 141.085i | 1.92413 | − | 0.979758i | ||||
\(145\) | 10.1616 | − | 17.6003i | 0.0700797 | − | 0.121382i | ||||
\(146\) | 26.5341 | − | 61.7485i | 0.181740 | − | 0.422935i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 37.1444 | − | 35.2395i | 0.250976 | − | 0.238105i | ||||
\(149\) | 199.798 | + | 115.354i | 1.34093 | + | 0.774186i | 0.986944 | − | 0.161066i | \(-0.0514931\pi\) |
0.353985 | + | 0.935251i | \(0.384826\pi\) | |||||||
\(150\) | −215.495 | + | 25.4912i | −1.43663 | + | 0.169941i | ||||
\(151\) | 128.077 | − | 73.9452i | 0.848190 | − | 0.489703i | −0.0118494 | − | 0.999930i | \(-0.503772\pi\) |
0.860040 | + | 0.510227i | \(0.170439\pi\) | |||||||
\(152\) | −8.04327 | + | 46.7540i | −0.0529163 | + | 0.307592i | ||||
\(153\) | −18.0116 | −0.117723 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 74.4227 | 0.480146 | ||||||||
\(156\) | −106.553 | − | 444.083i | −0.683034 | − | 2.84669i | ||||
\(157\) | 99.4450 | − | 57.4146i | 0.633407 | − | 0.365698i | −0.148663 | − | 0.988888i | \(-0.547497\pi\) |
0.782070 | + | 0.623190i | \(0.214164\pi\) | |||||||
\(158\) | 7.09810 | + | 60.0052i | 0.0449247 | + | 0.379780i | ||||
\(159\) | 343.947 | + | 198.578i | 2.16319 | + | 1.24892i | ||||
\(160\) | 30.5479 | − | 61.8938i | 0.190924 | − | 0.386836i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −96.1289 | + | 223.706i | −0.593388 | + | 1.38090i | ||||
\(163\) | −24.6545 | + | 42.7029i | −0.151255 | + | 0.261981i | −0.931689 | − | 0.363257i | \(-0.881665\pi\) |
0.780434 | + | 0.625238i | \(0.214998\pi\) | |||||||
\(164\) | 49.0245 | − | 165.424i | 0.298930 | − | 1.00868i | ||||
\(165\) | −52.3830 | + | 30.2433i | −0.317473 | + | 0.183293i | ||||
\(166\) | −87.2609 | − | 116.872i | −0.525668 | − | 0.704051i | ||||
\(167\) | 241.457i | 1.44585i | 0.690926 | + | 0.722926i | \(0.257203\pi\) | ||||
−0.690926 | + | 0.722926i | \(0.742797\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −289.455 | −1.71275 | ||||||||
\(170\) | −3.20385 | + | 2.39210i | −0.0188461 | + | 0.0140712i | ||||
\(171\) | −57.6196 | − | 99.8001i | −0.336957 | − | 0.583626i | ||||
\(172\) | 47.4382 | − | 160.071i | 0.275803 | − | 0.930648i | ||||
\(173\) | −47.1300 | − | 27.2105i | −0.272428 | − | 0.157286i | 0.357563 | − | 0.933889i | \(-0.383608\pi\) |
−0.629990 | + | 0.776603i | \(0.716941\pi\) | |||||||
\(174\) | 92.3207 | + | 39.6713i | 0.530579 | + | 0.227996i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.42590 | + | 84.0293i | −0.0251471 | + | 0.477439i | ||||
\(177\) | −143.100 | + | 247.857i | −0.808475 | + | 1.40032i | ||||
\(178\) | 108.920 | − | 12.8843i | 0.611909 | − | 0.0723836i | ||||
\(179\) | 63.5100 | + | 110.003i | 0.354805 | + | 0.614540i | 0.987084 | − | 0.160200i | \(-0.0512141\pi\) |
−0.632280 | + | 0.774740i | \(0.717881\pi\) | |||||||
\(180\) | 39.1186 | + | 163.035i | 0.217325 | + | 0.905748i | ||||
\(181\) | − | 212.704i | − | 1.17516i | −0.809165 | − | 0.587581i | \(-0.800080\pi\) | ||
0.809165 | − | 0.587581i | \(-0.199920\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 148.322i | 0.810502i | ||||||||
\(184\) | 68.5072 | + | 11.7856i | 0.372322 | + | 0.0640520i | ||||
\(185\) | 13.8046 | + | 23.9103i | 0.0746194 | + | 0.129245i | ||||
\(186\) | 43.2260 | + | 365.420i | 0.232398 | + | 1.96462i | ||||
\(187\) | 2.43723 | − | 4.22140i | 0.0130333 | − | 0.0225743i | ||||
\(188\) | 133.480 | − | 126.635i | 0.710002 | − | 0.673590i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −23.5035 | − | 10.0997i | −0.123703 | − | 0.0531565i | ||||
\(191\) | 35.1041 | + | 20.2674i | 0.183791 | + | 0.106112i | 0.589073 | − | 0.808080i | \(-0.299493\pi\) |
−0.405282 | + | 0.914192i | \(0.632826\pi\) | |||||||
\(192\) | 321.645 | + | 114.043i | 1.67523 | + | 0.593974i | ||||
\(193\) | −141.153 | − | 244.485i | −0.731364 | − | 1.26676i | −0.956300 | − | 0.292387i | \(-0.905551\pi\) |
0.224936 | − | 0.974374i | \(-0.427783\pi\) | |||||||
\(194\) | −64.2694 | − | 86.0790i | −0.331286 | − | 0.443706i | ||||
\(195\) | 246.261 | 1.26288 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 261.806i | − | 1.32896i | −0.747304 | − | 0.664482i | \(-0.768652\pi\) | ||
0.747304 | − | 0.664482i | \(-0.231348\pi\) | |||||||
\(198\) | −122.287 | − | 163.784i | −0.617610 | − | 0.827193i | ||||
\(199\) | −278.968 | + | 161.062i | −1.40185 | + | 0.809357i | −0.994582 | − | 0.103953i | \(-0.966851\pi\) |
−0.407265 | + | 0.913310i | \(0.633518\pi\) | |||||||
\(200\) | −125.132 | − | 104.113i | −0.625662 | − | 0.520566i | ||||
\(201\) | −209.266 | + | 362.460i | −1.04113 | + | 1.80328i | ||||
\(202\) | −165.932 | − | 71.3031i | −0.821448 | − | 0.352986i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −13.6062 | − | 14.3417i | −0.0666970 | − | 0.0703025i | ||||
\(205\) | 80.5723 | + | 46.5184i | 0.393036 | + | 0.226919i | ||||
\(206\) | −26.5046 | − | 224.062i | −0.128663 | − | 1.08768i | ||||
\(207\) | −146.234 | + | 84.4283i | −0.706445 | + | 0.407866i | ||||
\(208\) | 186.661 | − | 287.267i | 0.897406 | − | 1.38109i | ||||
\(209\) | 31.1870 | 0.149220 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 169.792 | 0.804702 | 0.402351 | − | 0.915485i | \(-0.368193\pi\) | ||||
0.402351 | + | 0.915485i | \(0.368193\pi\) | |||||||
\(212\) | 69.5117 | + | 289.704i | 0.327885 | + | 1.36653i | ||||
\(213\) | −344.077 | + | 198.653i | −1.61539 | + | 0.932644i | ||||
\(214\) | −285.986 | + | 33.8297i | −1.33638 | + | 0.158083i | ||||
\(215\) | 77.9652 | + | 45.0133i | 0.362629 | + | 0.209364i | ||||
\(216\) | −417.571 | + | 153.957i | −1.93320 | + | 0.712763i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 122.529 | + | 52.6521i | 0.562059 | + | 0.241523i | ||||
\(219\) | −89.5927 | + | 155.179i | −0.409099 | + | 0.708581i | ||||
\(220\) | −43.5040 | − | 12.8927i | −0.197745 | − | 0.0586031i | ||||
\(221\) | −17.1867 | + | 9.92275i | −0.0777679 | + | 0.0448993i | ||||
\(222\) | −109.383 | + | 81.6689i | −0.492716 | + | 0.367878i | ||||
\(223\) | − | 45.4626i | − | 0.203868i | −0.994791 | − | 0.101934i | \(-0.967497\pi\) | ||
0.994791 | − | 0.101934i | \(-0.0325031\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 395.414 | 1.75740 | ||||||||
\(226\) | −8.57285 | − | 11.4820i | −0.0379329 | − | 0.0508053i | ||||
\(227\) | 92.5653 | + | 160.328i | 0.407777 | + | 0.706290i | 0.994640 | − | 0.103396i | \(-0.0329708\pi\) |
−0.586864 | + | 0.809686i | \(0.699637\pi\) | |||||||
\(228\) | 35.9391 | − | 121.270i | 0.157627 | − | 0.531885i | ||||
\(229\) | 160.173 | + | 92.4759i | 0.699445 | + | 0.403825i | 0.807141 | − | 0.590359i | \(-0.201014\pi\) |
−0.107695 | + | 0.994184i | \(0.534347\pi\) | |||||||
\(230\) | −14.7988 | + | 34.4390i | −0.0643428 | + | 0.149735i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 26.0756 | + | 70.7239i | 0.112395 | + | 0.304845i | ||||
\(233\) | −48.3504 | + | 83.7453i | −0.207512 | + | 0.359422i | −0.950930 | − | 0.309405i | \(-0.899870\pi\) |
0.743418 | + | 0.668827i | \(0.233203\pi\) | |||||||
\(234\) | 97.7580 | + | 826.417i | 0.417769 | + | 3.53170i | ||||
\(235\) | 49.6076 | + | 85.9228i | 0.211096 | + | 0.365629i | ||||
\(236\) | −208.768 | + | 50.0919i | −0.884611 | + | 0.212254i | ||||
\(237\) | − | 161.097i | − | 0.679734i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 163.185i | 0.682782i | 0.939921 | + | 0.341391i | \(0.110898\pi\) | ||||
−0.939921 | + | 0.341391i | \(0.889102\pi\) | |||||||
\(240\) | −100.266 | + | 154.307i | −0.417773 | + | 0.642945i | ||||
\(241\) | 102.745 | + | 177.960i | 0.426330 | + | 0.738424i | 0.996544 | − | 0.0830718i | \(-0.0264731\pi\) |
−0.570214 | + | 0.821496i | \(0.693140\pi\) | |||||||
\(242\) | −185.391 | + | 21.9301i | −0.766078 | + | 0.0906204i | ||||
\(243\) | 74.2413 | − | 128.590i | 0.305520 | − | 0.529176i | ||||
\(244\) | −80.7180 | + | 76.5784i | −0.330812 | + | 0.313846i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −181.611 | + | 422.634i | −0.738254 | + | 1.71802i | ||||
\(247\) | −109.962 | − | 63.4863i | −0.445188 | − | 0.257030i | ||||
\(248\) | −176.547 | + | 212.190i | −0.711883 | + | 0.855604i | ||||
\(249\) | 194.434 | + | 336.769i | 0.780859 | + | 1.35249i | ||||
\(250\) | 156.752 | − | 117.036i | 0.627007 | − | 0.468145i | ||||
\(251\) | 159.299 | 0.634658 | 0.317329 | − | 0.948316i | \(-0.397214\pi\) | ||||
0.317329 | + | 0.948316i | \(0.397214\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 45.6975i | − | 0.180622i | ||||||
\(254\) | 210.727 | − | 157.336i | 0.829633 | − | 0.619431i | ||||
\(255\) | 9.23191 | − | 5.33005i | 0.0362036 | − | 0.0209021i | ||||
\(256\) | 104.002 | + | 233.922i | 0.406257 | + | 0.913759i | ||||
\(257\) | 107.889 | − | 186.868i | 0.419800 | − | 0.727114i | −0.576119 | − | 0.817366i | \(-0.695434\pi\) |
0.995919 | + | 0.0902512i | \(0.0287670\pi\) | |||||||
\(258\) | −175.734 | + | 408.959i | −0.681140 | + | 1.58511i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 127.144 | + | 134.017i | 0.489017 | + | 0.515452i | ||||
\(261\) | −158.571 | − | 91.5507i | −0.607550 | − | 0.350769i | ||||
\(262\) | 17.4011 | − | 2.05840i | 0.0664163 | − | 0.00785647i | ||||
\(263\) | 285.059 | − | 164.579i | 1.08387 | − | 0.625775i | 0.151935 | − | 0.988391i | \(-0.451450\pi\) |
0.931939 | + | 0.362616i | \(0.118116\pi\) | |||||||
\(264\) | 38.0360 | − | 221.096i | 0.144076 | − | 0.837483i | ||||
\(265\) | −160.652 | −0.606234 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −292.419 | −1.09520 | ||||||||
\(268\) | −305.298 | + | 73.2531i | −1.13917 | + | 0.273332i | ||||
\(269\) | 253.803 | − | 146.533i | 0.943507 | − | 0.544734i | 0.0524492 | − | 0.998624i | \(-0.483297\pi\) |
0.891058 | + | 0.453889i | \(0.149964\pi\) | |||||||
\(270\) | −28.1916 | − | 238.323i | −0.104413 | − | 0.882679i | ||||
\(271\) | 23.2529 | + | 13.4251i | 0.0858042 | + | 0.0495391i | 0.542288 | − | 0.840193i | \(-0.317558\pi\) |
−0.456484 | + | 0.889732i | \(0.650891\pi\) | |||||||
\(272\) | 0.780014 | − | 14.8092i | 0.00286770 | − | 0.0544456i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 187.011 | − | 435.202i | 0.682523 | − | 1.58833i | ||||
\(275\) | −53.5053 | + | 92.6739i | −0.194565 | + | 0.336996i | ||||
\(276\) | −177.693 | − | 52.6605i | −0.643816 | − | 0.190799i | ||||
\(277\) | 289.925 | − | 167.389i | 1.04666 | − | 0.604291i | 0.124949 | − | 0.992163i | \(-0.460123\pi\) |
0.921713 | + | 0.387872i | \(0.126790\pi\) | |||||||
\(278\) | 205.951 | + | 275.840i | 0.740831 | + | 0.992229i | ||||
\(279\) | − | 670.513i | − | 2.40327i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −123.357 | −0.438994 | −0.219497 | − | 0.975613i | \(-0.570442\pi\) | ||||
−0.219497 | + | 0.975613i | \(0.570442\pi\) | |||||||
\(282\) | −393.073 | + | 293.482i | −1.39388 | + | 1.04072i | ||||
\(283\) | −0.309453 | − | 0.535988i | −0.00109347 | − | 0.00189395i | 0.865478 | − | 0.500947i | \(-0.167015\pi\) |
−0.866572 | + | 0.499053i | \(0.833681\pi\) | |||||||
\(284\) | −285.756 | − | 84.6855i | −1.00618 | − | 0.298188i | ||||
\(285\) | 59.0663 | + | 34.1019i | 0.207250 | + | 0.119656i | ||||
\(286\) | −206.917 | − | 88.9145i | −0.723485 | − | 0.310890i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −557.634 | − | 275.222i | −1.93623 | − | 0.955631i | ||||
\(289\) | 144.070 | − | 249.537i | 0.498514 | − | 0.863451i | ||||
\(290\) | −40.3648 | + | 4.77480i | −0.139189 | + | 0.0164648i | ||||
\(291\) | 143.204 | + | 248.037i | 0.492112 | + | 0.852362i | ||||
\(292\) | −130.707 | + | 31.3617i | −0.447625 | + | 0.107403i | ||||
\(293\) | − | 28.2794i | − | 0.0965169i | −0.998835 | − | 0.0482584i | \(-0.984633\pi\) | ||
0.998835 | − | 0.0482584i | \(-0.0153671\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 115.770i | − | 0.392440i | ||||||
\(296\) | −100.919 | − | 17.3615i | −0.340943 | − | 0.0586538i | ||||
\(297\) | 146.285 | + | 253.373i | 0.492542 | + | 0.853108i | ||||
\(298\) | −54.2034 | − | 458.220i | −0.181891 | − | 1.53765i | ||||
\(299\) | −93.0247 | + | 161.123i | −0.311119 | + | 0.538874i | ||||
\(300\) | 298.701 | + | 314.848i | 0.995671 | + | 1.04949i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −271.753 | − | 116.775i | −0.899844 | − | 0.386674i | ||||
\(303\) | 417.002 | + | 240.756i | 1.37624 | + | 0.794575i | ||||
\(304\) | 84.5514 | − | 43.0531i | 0.278130 | − | 0.141622i | ||||
\(305\) | −29.9986 | − | 51.9591i | −0.0983560 | − | 0.170358i | ||||
\(306\) | 21.5517 | + | 28.8651i | 0.0704303 | + | 0.0943305i | ||||
\(307\) | −400.893 | −1.30584 | −0.652921 | − | 0.757426i | \(-0.726457\pi\) | ||||
−0.652921 | + | 0.757426i | \(0.726457\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 601.542i | 1.94674i | ||||||||
\(310\) | −89.0500 | − | 119.269i | −0.287258 | − | 0.384738i | ||||
\(311\) | 140.492 | − | 81.1132i | 0.451743 | − | 0.260814i | −0.256823 | − | 0.966459i | \(-0.582676\pi\) |
0.708566 | + | 0.705644i | \(0.249342\pi\) | |||||||
\(312\) | −584.186 | + | 702.126i | −1.87239 | + | 2.25040i | ||||
\(313\) | −133.123 | + | 230.576i | −0.425313 | + | 0.736664i | −0.996450 | − | 0.0841913i | \(-0.973169\pi\) |
0.571137 | + | 0.820855i | \(0.306503\pi\) | |||||||
\(314\) | −211.002 | − | 90.6700i | −0.671981 | − | 0.288758i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 87.6704 | − | 83.1742i | 0.277438 | − | 0.263210i | ||||
\(317\) | −374.864 | − | 216.428i | −1.18254 | − | 0.682737i | −0.225936 | − | 0.974142i | \(-0.572544\pi\) |
−0.956600 | + | 0.291405i | \(0.905877\pi\) | |||||||
\(318\) | −93.3096 | − | 788.812i | −0.293426 | − | 2.48054i | ||||
\(319\) | 42.9138 | − | 24.7763i | 0.134526 | − | 0.0776686i | ||||
\(320\) | −135.742 | + | 25.1030i | −0.424194 | + | 0.0784470i | ||||
\(321\) | 767.792 | 2.39187 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.49636 | −0.0170166 | ||||||||
\(324\) | 473.530 | − | 113.619i | 1.46151 | − | 0.350675i | ||||
\(325\) | 377.305 | − | 217.837i | 1.16094 | − | 0.670269i | ||||
\(326\) | 97.9353 | − | 11.5849i | 0.300415 | − | 0.0355365i | ||||
\(327\) | −307.925 | − | 177.781i | −0.941668 | − | 0.543672i | ||||
\(328\) | −323.766 | + | 119.371i | −0.987092 | + | 0.363937i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 111.146 | + | 47.7608i | 0.336807 | + | 0.144730i | ||||
\(331\) | −40.6264 | + | 70.3671i | −0.122738 | + | 0.212589i | −0.920847 | − | 0.389925i | \(-0.872501\pi\) |
0.798108 | + | 0.602514i | \(0.205834\pi\) | |||||||
\(332\) | −82.8867 | + | 279.686i | −0.249659 | + | 0.842428i | ||||
\(333\) | 215.420 | − | 124.373i | 0.646907 | − | 0.373492i | ||||
\(334\) | 386.956 | − | 288.914i | 1.15855 | − | 0.865012i | ||||
\(335\) | − | 169.299i | − | 0.505370i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −69.4941 | −0.206214 | −0.103107 | − | 0.994670i | \(-0.532878\pi\) | ||||
−0.103107 | + | 0.994670i | \(0.532878\pi\) | |||||||
\(338\) | 346.346 | + | 463.877i | 1.02469 | + | 1.37242i | ||||
\(339\) | 19.1019 | + | 33.0855i | 0.0563479 | + | 0.0975974i | ||||
\(340\) | 7.66708 | + | 2.27219i | 0.0225502 | + | 0.00668291i | ||||
\(341\) | 157.149 | + | 90.7300i | 0.460848 | + | 0.266071i | ||||
\(342\) | −90.9938 | + | 211.756i | −0.266064 | + | 0.619168i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −313.290 | + | 115.509i | −0.910727 | + | 0.335781i | ||||
\(345\) | 49.9686 | − | 86.5481i | 0.144836 | − | 0.250864i | ||||
\(346\) | 12.7859 | + | 108.089i | 0.0369536 | + | 0.312395i | ||||
\(347\) | 174.677 | + | 302.549i | 0.503391 | + | 0.871899i | 0.999992 | + | 0.00392020i | \(0.00124784\pi\) |
−0.496601 | + | 0.867979i | \(0.665419\pi\) | |||||||
\(348\) | −46.8891 | − | 195.420i | −0.134739 | − | 0.561552i | ||||
\(349\) | 165.836i | 0.475174i | 0.971366 | + | 0.237587i | \(0.0763566\pi\) | ||||
−0.971366 | + | 0.237587i | \(0.923643\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 1191.15i | − | 3.39358i | ||||||
\(352\) | 139.960 | − | 93.4519i | 0.397614 | − | 0.265488i | ||||
\(353\) | −235.858 | − | 408.519i | −0.668154 | − | 1.15728i | −0.978420 | − | 0.206627i | \(-0.933751\pi\) |
0.310266 | − | 0.950650i | \(-0.399582\pi\) | |||||||
\(354\) | 568.437 | − | 67.2412i | 1.60576 | − | 0.189947i | ||||
\(355\) | 80.3566 | − | 139.182i | 0.226356 | − | 0.392061i | ||||
\(356\) | −150.976 | − | 159.137i | −0.424089 | − | 0.447014i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 100.296 | − | 233.403i | 0.280157 | − | 0.651964i | ||||
\(359\) | −568.967 | − | 328.493i | −1.58487 | − | 0.915022i | −0.994134 | − | 0.108154i | \(-0.965506\pi\) |
−0.590731 | − | 0.806869i | \(-0.701161\pi\) | |||||||
\(360\) | 214.470 | − | 257.769i | 0.595750 | − | 0.716025i | ||||
\(361\) | 162.917 | + | 282.180i | 0.451294 | + | 0.781663i | ||||
\(362\) | −340.877 | + | 254.510i | −0.941649 | + | 0.703067i | ||||
\(363\) | 497.722 | 1.37113 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 72.4817i | − | 0.198580i | ||||||
\(366\) | 237.699 | − | 177.474i | 0.649450 | − | 0.484901i | ||||
\(367\) | −307.850 | + | 177.737i | −0.838829 | + | 0.484298i | −0.856866 | − | 0.515539i | \(-0.827592\pi\) |
0.0180371 | + | 0.999837i | \(0.494258\pi\) | |||||||
\(368\) | −63.0845 | − | 123.891i | −0.171425 | − | 0.336659i | ||||
\(369\) | 419.109 | − | 725.918i | 1.13580 | − | 1.96726i | ||||
\(370\) | 21.8004 | − | 50.7327i | 0.0589201 | − | 0.137116i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 533.895 | − | 506.514i | 1.43520 | − | 1.36160i | ||||
\(373\) | 273.662 | + | 157.999i | 0.733680 | + | 0.423590i | 0.819767 | − | 0.572698i | \(-0.194103\pi\) |
−0.0860872 | + | 0.996288i | \(0.527436\pi\) | |||||||
\(374\) | −9.68141 | + | 1.14523i | −0.0258861 | + | 0.00306210i | ||||
\(375\) | −451.682 | + | 260.779i | −1.20449 | + | 0.695410i | ||||
\(376\) | −362.659 | − | 62.3896i | −0.964518 | − | 0.165930i | ||||
\(377\) | −201.745 | −0.535132 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −178.404 | −0.470723 | −0.235361 | − | 0.971908i | \(-0.575627\pi\) | ||||
−0.235361 | + | 0.971908i | \(0.575627\pi\) | |||||||
\(380\) | 11.9373 | + | 49.7512i | 0.0314140 | + | 0.130924i | ||||
\(381\) | −607.211 | + | 350.574i | −1.59373 | + | 0.920140i | ||||
\(382\) | −9.52341 | − | 80.5082i | −0.0249304 | − | 0.210754i | ||||
\(383\) | −604.832 | − | 349.200i | −1.57920 | − | 0.911750i | −0.994972 | − | 0.100158i | \(-0.968065\pi\) |
−0.584225 | − | 0.811591i | \(-0.698602\pi\) | |||||||
\(384\) | −202.099 | − | 651.921i | −0.526299 | − | 1.69771i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −222.912 | + | 518.747i | −0.577491 | + | 1.34390i | ||||
\(387\) | 405.548 | − | 702.430i | 1.04793 | − | 1.81506i | ||||
\(388\) | −61.0478 | + | 205.995i | −0.157340 | + | 0.530914i | ||||
\(389\) | 151.865 | − | 87.6790i | 0.390397 | − | 0.225396i | −0.291935 | − | 0.956438i | \(-0.594299\pi\) |
0.682332 | + | 0.731042i | \(0.260966\pi\) | |||||||
\(390\) | −294.662 | − | 394.655i | −0.755544 | − | 1.01193i | ||||
\(391\) | 8.05366i | 0.0205976i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −46.7170 | −0.118873 | ||||||||
\(394\) | −419.567 | + | 313.263i | −1.06489 | + | 0.795083i | ||||
\(395\) | 32.5824 | + | 56.4344i | 0.0824871 | + | 0.142872i | ||||
\(396\) | −116.157 | + | 391.950i | −0.293325 | + | 0.989773i | ||||
\(397\) | 334.033 | + | 192.854i | 0.841393 | + | 0.485778i | 0.857737 | − | 0.514088i | \(-0.171870\pi\) |
−0.0163447 | + | 0.999866i | \(0.505203\pi\) | |||||||
\(398\) | 591.913 | + | 254.352i | 1.48722 | + | 0.639075i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −17.1239 | + | 325.112i | −0.0428098 | + | 0.812779i | ||||
\(401\) | −263.548 | + | 456.479i | −0.657228 | + | 1.13835i | 0.324103 | + | 0.946022i | \(0.394938\pi\) |
−0.981330 | + | 0.192330i | \(0.938396\pi\) | |||||||
\(402\) | 831.269 | − | 98.3319i | 2.06783 | − | 0.244607i | ||||
\(403\) | −369.392 | − | 639.805i | −0.916605 | − | 1.58761i | ||||
\(404\) | 84.2761 | + | 351.238i | 0.208604 | + | 0.869402i | ||||
\(405\) | 262.590i | 0.648371i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 67.3178i | 0.165400i | ||||||||
\(408\) | −6.70340 | + | 38.9656i | −0.0164299 | + | 0.0955039i | ||||
\(409\) | −211.872 | − | 366.973i | −0.518025 | − | 0.897245i | −0.999781 | − | 0.0209399i | \(-0.993334\pi\) |
0.481756 | − | 0.876305i | \(-0.339999\pi\) | |||||||
\(410\) | −21.8585 | − | 184.785i | −0.0533134 | − | 0.450696i | ||||
\(411\) | −631.447 | + | 1093.70i | −1.53637 | + | 2.66107i | ||||
\(412\) | −327.364 | + | 310.576i | −0.794574 | + | 0.753824i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 310.279 | + | 133.331i | 0.749467 | + | 0.322055i | ||||
\(415\) | −136.225 | − | 78.6498i | −0.328254 | − | 0.189517i | ||||
\(416\) | −683.718 | + | 44.5881i | −1.64355 | + | 0.107183i | ||||
\(417\) | −458.898 | − | 794.834i | −1.10047 | − | 1.90608i | ||||
\(418\) | −37.3167 | − | 49.9799i | −0.0892743 | − | 0.119569i | ||||
\(419\) | −295.598 | −0.705485 | −0.352742 | − | 0.935721i | \(-0.614751\pi\) | ||||
−0.352742 | + | 0.935721i | \(0.614751\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 126.260i | 0.299904i | 0.988693 | + | 0.149952i | \(0.0479119\pi\) | ||||
−0.988693 | + | 0.149952i | \(0.952088\pi\) | |||||||
\(422\) | −203.164 | − | 272.107i | −0.481431 | − | 0.644802i | ||||
\(423\) | 774.124 | − | 446.941i | 1.83008 | − | 1.05660i | ||||
\(424\) | 381.102 | − | 458.043i | 0.898827 | − | 1.08029i | ||||
\(425\) | 9.42970 | − | 16.3327i | 0.0221875 | − | 0.0384299i | ||||
\(426\) | 730.063 | + | 313.716i | 1.71376 | + | 0.736424i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 396.410 | + | 417.839i | 0.926192 | + | 0.976259i | ||||
\(429\) | 519.999 | + | 300.221i | 1.21212 | + | 0.699817i | ||||
\(430\) | −21.1512 | − | 178.806i | −0.0491889 | − | 0.415829i | ||||
\(431\) | −220.198 | + | 127.131i | −0.510900 | + | 0.294968i | −0.733204 | − | 0.680009i | \(-0.761976\pi\) |
0.222303 | + | 0.974978i | \(0.428642\pi\) | |||||||
\(432\) | 746.371 | + | 484.977i | 1.72771 | + | 1.12263i | ||||
\(433\) | −546.301 | −1.26167 | −0.630833 | − | 0.775919i | \(-0.717287\pi\) | ||||
−0.630833 | + | 0.775919i | \(0.717287\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 108.368 | 0.249122 | ||||||||
\(436\) | −62.2317 | − | 259.364i | −0.142733 | − | 0.594871i | ||||
\(437\) | −44.6244 | + | 25.7639i | −0.102115 | + | 0.0589563i | ||||
\(438\) | 355.890 | − | 42.0987i | 0.812534 | − | 0.0961156i | ||||
\(439\) | −236.715 | − | 136.667i | −0.539214 | − | 0.311315i | 0.205546 | − | 0.978647i | \(-0.434103\pi\) |
−0.744760 | + | 0.667332i | \(0.767436\pi\) | |||||||
\(440\) | 31.3928 | + | 85.1456i | 0.0713473 | + | 0.193513i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 36.4667 | + | 15.6702i | 0.0825039 | + | 0.0354529i | ||||
\(443\) | −237.385 | + | 411.163i | −0.535858 | + | 0.928133i | 0.463263 | + | 0.886221i | \(0.346678\pi\) |
−0.999121 | + | 0.0419124i | \(0.986655\pi\) | |||||||
\(444\) | 261.763 | + | 77.5751i | 0.589556 | + | 0.174719i | ||||
\(445\) | 102.438 | − | 59.1427i | 0.230198 | − | 0.132905i | ||||
\(446\) | −72.8578 | + | 54.3981i | −0.163358 | + | 0.121969i | ||||
\(447\) | 1230.19i | 2.75210i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 782.101 | 1.74187 | 0.870936 | − | 0.491396i | \(-0.163513\pi\) | ||||
0.870936 | + | 0.491396i | \(0.163513\pi\) | |||||||
\(450\) | −473.131 | − | 633.686i | −1.05140 | − | 1.40819i | ||||
\(451\) | 113.423 | + | 196.454i | 0.251492 | + | 0.435597i | ||||
\(452\) | −8.14311 | + | 27.4774i | −0.0180157 | + | 0.0607908i | ||||
\(453\) | 682.938 | + | 394.294i | 1.50759 | + | 0.870407i | ||||
\(454\) | 146.181 | − | 340.183i | 0.321984 | − | 0.749302i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −237.348 | + | 87.5092i | −0.520500 | + | 0.191906i | ||||
\(457\) | 94.7793 | − | 164.163i | 0.207395 | − | 0.359218i | −0.743498 | − | 0.668738i | \(-0.766835\pi\) |
0.950893 | + | 0.309520i | \(0.100168\pi\) | |||||||
\(458\) | −43.4534 | − | 367.343i | −0.0948765 | − | 0.802058i | ||||
\(459\) | −25.7811 | − | 44.6541i | −0.0561679 | − | 0.0972857i | ||||
\(460\) | 72.8990 | − | 17.4914i | 0.158476 | − | 0.0380247i | ||||
\(461\) | − | 202.533i | − | 0.439335i | −0.975575 | − | 0.219667i | \(-0.929503\pi\) | ||
0.975575 | − | 0.219667i | \(-0.0704972\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 652.927i | 1.41021i | 0.709103 | + | 0.705105i | \(0.249100\pi\) | ||||
−0.709103 | + | 0.705105i | \(0.750900\pi\) | |||||||
\(464\) | 82.1406 | − | 126.413i | 0.177027 | − | 0.272441i | ||||
\(465\) | 198.420 | + | 343.674i | 0.426710 | + | 0.739084i | ||||
\(466\) | 192.062 | − | 22.7193i | 0.412151 | − | 0.0487539i | ||||
\(467\) | 272.725 | − | 472.373i | 0.583993 | − | 1.01150i | −0.411008 | − | 0.911632i | \(-0.634823\pi\) |
0.995000 | − | 0.0998730i | \(-0.0318437\pi\) | |||||||
\(468\) | 1207.43 | − | 1145.51i | 2.57998 | − | 2.44767i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 78.3411 | − | 182.311i | 0.166683 | − | 0.387895i | ||||
\(471\) | 530.266 | + | 306.149i | 1.12583 | + | 0.649998i | ||||
\(472\) | 330.077 | + | 274.632i | 0.699316 | + | 0.581847i | ||||
\(473\) | 109.753 | + | 190.098i | 0.232036 | + | 0.401898i | ||||
\(474\) | −258.172 | + | 192.760i | −0.544666 | + | 0.406666i | ||||
\(475\) | 120.663 | 0.254028 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1447.40i | 3.03438i | ||||||||
\(478\) | 261.518 | − | 195.258i | 0.547108 | − | 0.408489i | ||||
\(479\) | −94.3079 | + | 54.4487i | −0.196885 | + | 0.113672i | −0.595202 | − | 0.803576i | \(-0.702928\pi\) |
0.398317 | + | 0.917248i | \(0.369595\pi\) | |||||||
\(480\) | 367.262 | − | 23.9507i | 0.765129 | − | 0.0498972i | ||||
\(481\) | 137.036 | − | 237.354i | 0.284899 | − | 0.493459i | ||||
\(482\) | 162.257 | − | 377.596i | 0.336633 | − | 0.783394i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 256.973 | + | 270.865i | 0.530937 | + | 0.559637i | ||||
\(485\) | −100.333 | − | 57.9272i | −0.206872 | − | 0.119437i | ||||
\(486\) | −294.909 | + | 34.8852i | −0.606809 | + | 0.0717802i | ||||
\(487\) | −371.831 | + | 214.677i | −0.763513 | + | 0.440814i | −0.830556 | − | 0.556936i | \(-0.811977\pi\) |
0.0670428 | + | 0.997750i | \(0.478644\pi\) | |||||||
\(488\) | 219.306 | + | 37.7281i | 0.449398 | + | 0.0773117i | ||||
\(489\) | −262.929 | −0.537686 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 453.887 | 0.924413 | 0.462206 | − | 0.886772i | \(-0.347058\pi\) | ||||
0.462206 | + | 0.886772i | \(0.347058\pi\) | |||||||
\(492\) | 894.612 | − | 214.653i | 1.81832 | − | 0.436287i | ||||
\(493\) | −7.56306 | + | 4.36654i | −0.0153409 | + | 0.00885707i | ||||
\(494\) | 29.8315 | + | 252.187i | 0.0603877 | + | 0.510500i | ||||
\(495\) | −190.905 | − | 110.219i | −0.385667 | − | 0.222665i | ||||
\(496\) | 551.299 | + | 29.0374i | 1.11149 | + | 0.0585431i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 307.053 | − | 714.556i | 0.616572 | − | 1.43485i | ||||
\(499\) | −166.698 | + | 288.730i | −0.334064 | + | 0.578617i | −0.983305 | − | 0.181967i | \(-0.941754\pi\) |
0.649240 | + | 0.760583i | \(0.275087\pi\) | |||||||
\(500\) | −375.121 | − | 111.169i | −0.750242 | − | 0.222339i | ||||
\(501\) | −1115.02 | + | 643.755i | −2.22558 | + | 1.28494i | ||||
\(502\) | −190.608 | − | 255.291i | −0.379698 | − | 0.508547i | ||||
\(503\) | 580.170i | 1.15342i | 0.816949 | + | 0.576710i | \(0.195664\pi\) | ||||
−0.816949 | + | 0.576710i | \(0.804336\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −194.775 | −0.385693 | ||||||||
\(506\) | −73.2341 | + | 54.6790i | −0.144731 | + | 0.108061i | ||||
\(507\) | −771.724 | − | 1336.67i | −1.52214 | − | 2.63642i | ||||
\(508\) | −504.288 | − | 149.449i | −0.992692 | − | 0.294190i | ||||
\(509\) | −266.271 | − | 153.732i | −0.523126 | − | 0.302027i | 0.215087 | − | 0.976595i | \(-0.430997\pi\) |
−0.738213 | + | 0.674568i | \(0.764330\pi\) | |||||||
\(510\) | −19.5882 | − | 8.41730i | −0.0384083 | − | 0.0165045i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 250.438 | − | 446.570i | 0.489136 | − | 0.872207i | ||||
\(513\) | 164.949 | − | 285.700i | 0.321538 | − | 0.556919i | ||||
\(514\) | −428.566 | + | 50.6956i | −0.833786 | + | 0.0986296i | ||||
\(515\) | −121.664 | − | 210.728i | −0.236241 | − | 0.409181i | ||||
\(516\) | 865.665 | − | 207.708i | 1.67765 | − | 0.402534i | ||||
\(517\) | 241.910i | 0.467911i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 290.187i | − | 0.559127i | ||||||
\(520\) | 62.6406 | − | 364.118i | 0.120463 | − | 0.700226i | ||||
\(521\) | 360.480 | + | 624.369i | 0.691899 | + | 1.19840i | 0.971215 | + | 0.238205i | \(0.0765591\pi\) |
−0.279316 | + | 0.960199i | \(0.590108\pi\) | |||||||
\(522\) | 43.0187 | + | 363.667i | 0.0824113 | + | 0.696681i | ||||
\(523\) | −134.988 | + | 233.807i | −0.258104 | + | 0.447049i | −0.965734 | − | 0.259534i | \(-0.916431\pi\) |
0.707630 | + | 0.706583i | \(0.249764\pi\) | |||||||
\(524\) | −24.1199 | − | 25.4238i | −0.0460304 | − | 0.0485186i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −604.837 | − | 259.905i | −1.14988 | − | 0.494117i | ||||
\(527\) | −27.6957 | − | 15.9901i | −0.0525536 | − | 0.0303418i | ||||
\(528\) | −399.836 | + | 203.595i | −0.757266 | + | 0.385596i | ||||
\(529\) | −226.749 | − | 392.741i | −0.428637 | − | 0.742421i | ||||
\(530\) | 192.227 | + | 257.459i | 0.362693 | + | 0.485771i | ||||
\(531\) | −1043.03 | −1.96428 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 923.564i | − | 1.73277i | ||||||
\(534\) | 349.892 | + | 468.626i | 0.655229 | + | 0.877578i | ||||
\(535\) | −268.967 | + | 155.288i | −0.502743 | + | 0.290259i | ||||
\(536\) | 482.696 | + | 401.615i | 0.900553 | + | 0.749282i | ||||
\(537\) | −338.652 | + | 586.562i | −0.630636 | + | 1.09229i | ||||
\(538\) | −538.520 | − | 231.408i | −1.00097 | − | 0.430127i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −348.201 | + | 330.344i | −0.644817 | + | 0.611748i | ||||
\(541\) | 785.695 | + | 453.621i | 1.45230 | + | 0.838486i | 0.998612 | − | 0.0526734i | \(-0.0167742\pi\) |
0.453689 | + | 0.891160i | \(0.350108\pi\) | |||||||
\(542\) | −6.30831 | − | 53.3286i | −0.0116389 | − | 0.0983922i | ||||
\(543\) | 982.241 | − | 567.097i | 1.80891 | − | 1.04438i | ||||
\(544\) | −24.6664 | + | 16.4698i | −0.0453426 | + | 0.0302754i | ||||
\(545\) | 143.827 | 0.263903 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −557.327 | −1.01888 | −0.509439 | − | 0.860506i | \(-0.670147\pi\) | ||||
−0.509439 | + | 0.860506i | \(0.670147\pi\) | |||||||
\(548\) | −921.215 | + | 221.036i | −1.68105 | + | 0.403351i | ||||
\(549\) | −468.127 | + | 270.273i | −0.852690 | + | 0.492301i | ||||
\(550\) | 212.539 | − | 25.1415i | 0.386435 | − | 0.0457119i | ||||
\(551\) | −48.3889 | − | 27.9374i | −0.0878202 | − | 0.0507030i | ||||
\(552\) | 128.225 | + | 347.779i | 0.232291 | + | 0.630035i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −615.163 | − | 264.343i | −1.11040 | − | 0.477153i | ||||
\(555\) | −73.6096 | + | 127.496i | −0.132630 | + | 0.229722i | ||||
\(556\) | 195.627 | − | 660.108i | 0.351847 | − | 1.18725i | ||||
\(557\) | −741.896 | + | 428.334i | −1.33195 | + | 0.769002i | −0.985598 | − | 0.169103i | \(-0.945913\pi\) |
−0.346352 | + | 0.938105i | \(0.612580\pi\) | |||||||
\(558\) | −1074.55 | + | 802.298i | −1.92572 | + | 1.43781i | ||||
\(559\) | − | 893.680i | − | 1.59871i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 25.9918 | 0.0463313 | ||||||||
\(562\) | 147.602 | + | 197.691i | 0.262638 | + | 0.351763i | ||||
\(563\) | 6.84436 | + | 11.8548i | 0.0121569 | + | 0.0210564i | 0.872040 | − | 0.489435i | \(-0.162797\pi\) |
−0.859883 | + | 0.510491i | \(0.829464\pi\) | |||||||
\(564\) | 940.659 | + | 278.770i | 1.66784 | + | 0.494273i | ||||
\(565\) | −13.3833 | − | 7.72686i | −0.0236873 | − | 0.0136759i | ||||
\(566\) | −0.488693 | + | 1.13726i | −0.000863416 | + | 0.00200929i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 206.204 | + | 559.278i | 0.363034 | + | 0.984644i | ||||
\(569\) | 545.991 | − | 945.684i | 0.959563 | − | 1.66201i | 0.235999 | − | 0.971753i | \(-0.424164\pi\) |
0.723563 | − | 0.690258i | \(-0.242503\pi\) | |||||||
\(570\) | −16.0241 | − | 135.463i | −0.0281125 | − | 0.237655i | ||||
\(571\) | −359.549 | − | 622.757i | −0.629683 | − | 1.09064i | −0.987615 | − | 0.156895i | \(-0.949852\pi\) |
0.357932 | − | 0.933747i | \(-0.383482\pi\) | |||||||
\(572\) | 105.092 | + | 437.992i | 0.183727 | + | 0.765720i | ||||
\(573\) | 216.142i | 0.377210i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 176.805i | − | 0.307486i | ||||||
\(576\) | 226.166 | + | 1222.97i | 0.392650 | + | 2.12321i | ||||
\(577\) | −515.560 | − | 892.976i | −0.893518 | − | 1.54762i | −0.835628 | − | 0.549296i | \(-0.814896\pi\) |
−0.0578905 | − | 0.998323i | \(-0.518437\pi\) | |||||||
\(578\) | −572.292 | + | 67.6971i | −0.990124 | + | 0.117123i | ||||
\(579\) | 752.665 | − | 1303.65i | 1.29994 | − | 2.25156i | ||||
\(580\) | 55.9503 | + | 58.9748i | 0.0964660 | + | 0.101681i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 226.151 | − | 526.285i | 0.388575 | − | 0.904270i | ||||
\(583\) | −339.229 | − | 195.854i | −0.581868 | − | 0.335942i | ||||
\(584\) | 206.656 | + | 171.943i | 0.353863 | + | 0.294423i | ||||
\(585\) | 448.738 | + | 777.238i | 0.767074 | + | 1.32861i | ||||
\(586\) | −45.3202 | + | 33.8376i | −0.0773383 | + | 0.0577434i | ||||
\(587\) | 671.907 | 1.14464 | 0.572322 | − | 0.820029i | \(-0.306043\pi\) | ||||
0.572322 | + | 0.820029i | \(0.306043\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 204.612i | − | 0.347388i | ||||||
\(590\) | −185.531 | + | 138.524i | −0.314460 | + | 0.234786i | ||||
\(591\) | 1208.99 | − | 698.008i | 2.04566 | − | 1.18106i | ||||
\(592\) | 92.9309 | + | 182.506i | 0.156978 | + | 0.308286i | ||||
\(593\) | 176.999 | − | 306.572i | 0.298481 | − | 0.516984i | −0.677308 | − | 0.735700i | \(-0.736853\pi\) |
0.975789 | + | 0.218716i | \(0.0701867\pi\) | |||||||
\(594\) | 231.016 | − | 537.606i | 0.388915 | − | 0.905061i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −669.480 | + | 635.146i | −1.12329 | + | 1.06568i | ||||
\(597\) | −1487.53 | − | 858.824i | −2.49167 | − | 1.43857i | ||||
\(598\) | 369.522 | − | 43.7113i | 0.617930 | − | 0.0730958i | ||||
\(599\) | 983.923 | − | 568.068i | 1.64261 | − | 0.948361i | 0.662708 | − | 0.748878i | \(-0.269407\pi\) |
0.979901 | − | 0.199484i | \(-0.0639265\pi\) | |||||||
\(600\) | 147.162 | − | 855.424i | 0.245270 | − | 1.42571i | ||||
\(601\) | 6.80783 | 0.0113275 | 0.00566375 | − | 0.999984i | \(-0.498197\pi\) | ||||
0.00566375 | + | 0.999984i | \(0.498197\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1525.30 | −2.52953 | ||||||||
\(604\) | 138.022 | + | 575.234i | 0.228513 | + | 0.952375i | ||||
\(605\) | −174.358 | + | 100.666i | −0.288196 | + | 0.166390i | ||||
\(606\) | −113.129 | − | 956.357i | −0.186681 | − | 1.57815i | ||||
\(607\) | 386.628 | + | 223.220i | 0.636948 | + | 0.367742i | 0.783438 | − | 0.621470i | \(-0.213464\pi\) |
−0.146490 | + | 0.989212i | \(0.546798\pi\) | |||||||
\(608\) | −170.166 | − | 83.9859i | −0.279878 | − | 0.138135i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −47.3743 | + | 110.247i | −0.0776627 | + | 0.180732i | ||||
\(611\) | 492.447 | − | 852.944i | 0.805970 | − | 1.39598i | ||||
\(612\) | 20.4713 | − | 69.0768i | 0.0334499 | − | 0.112871i | ||||
\(613\) | −555.650 | + | 320.805i | −0.906443 | + | 0.523335i | −0.879285 | − | 0.476296i | \(-0.841979\pi\) |
−0.0271583 | + | 0.999631i | \(0.508646\pi\) | |||||||
\(614\) | 479.687 | + | 642.466i | 0.781249 | + | 1.04636i | ||||
\(615\) | 496.096i | 0.806661i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −502.890 | −0.815057 | −0.407528 | − | 0.913193i | \(-0.633609\pi\) | ||||
−0.407528 | + | 0.913193i | \(0.633609\pi\) | |||||||
\(618\) | 964.023 | − | 719.772i | 1.55991 | − | 1.16468i | ||||
\(619\) | 216.495 | + | 374.980i | 0.349749 | + | 0.605783i | 0.986205 | − | 0.165530i | \(-0.0529336\pi\) |
−0.636456 | + | 0.771313i | \(0.719600\pi\) | |||||||
\(620\) | −84.5861 | + | 285.421i | −0.136429 | + | 0.460356i | ||||
\(621\) | −418.627 | − | 241.695i | −0.674118 | − | 0.389202i | ||||
\(622\) | −298.096 | − | 128.095i | −0.479254 | − | 0.205941i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1824.22 | + | 96.0833i | 2.92343 | + | 0.153980i | ||||
\(625\) | −148.859 | + | 257.831i | −0.238174 | + | 0.412530i | ||||
\(626\) | 528.805 | − | 62.5530i | 0.844736 | − | 0.0999250i | ||||
\(627\) | 83.1486 | + | 144.018i | 0.132613 | + | 0.229693i | ||||
\(628\) | 107.167 | + | 446.640i | 0.170648 | + | 0.711210i | ||||
\(629\) | − | 11.8640i | − | 0.0188617i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 238.957i | − | 0.378695i | −0.981910 | − | 0.189348i | \(-0.939363\pi\) | ||
0.981910 | − | 0.189348i | \(-0.0606373\pi\) | |||||||
\(632\) | −238.195 | − | 40.9777i | −0.376891 | − | 0.0648381i | ||||
\(633\) | 452.687 | + | 784.078i | 0.715146 | + | 1.23867i | ||||
\(634\) | 101.697 | + | 859.717i | 0.160405 | + | 1.35602i | ||||
\(635\) | 141.809 | − | 245.621i | 0.223322 | − | 0.386805i | ||||
\(636\) | −1152.49 | + | 1093.38i | −1.81209 | + | 1.71916i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −91.0543 | − | 39.1271i | −0.142718 | − | 0.0613277i | ||||
\(639\) | −1253.96 | − | 723.974i | −1.96238 | − | 1.13298i | ||||
\(640\) | 202.651 | + | 187.501i | 0.316642 | + | 0.292971i | ||||
\(641\) | 3.98065 | + | 6.89469i | 0.00621006 | + | 0.0107561i | 0.869114 | − | 0.494612i | \(-0.164690\pi\) |
−0.862904 | + | 0.505368i | \(0.831357\pi\) | |||||||
\(642\) | −918.696 | − | 1230.45i | −1.43099 | − | 1.91659i | ||||
\(643\) | 584.919 | 0.909672 | 0.454836 | − | 0.890575i | \(-0.349698\pi\) | ||||
0.454836 | + | 0.890575i | \(0.349698\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 480.044i | 0.744255i | ||||||||
\(646\) | 6.57664 | + | 8.80839i | 0.0101806 | + | 0.0136353i | ||||
\(647\) | −290.707 | + | 167.840i | −0.449316 | + | 0.259413i | −0.707541 | − | 0.706672i | \(-0.750196\pi\) |
0.258225 | + | 0.966085i | \(0.416862\pi\) | |||||||
\(648\) | −748.683 | − | 622.923i | −1.15538 | − | 0.961300i | ||||
\(649\) | 141.137 | − | 244.457i | 0.217469 | − | 0.376667i | ||||
\(650\) | −800.566 | − | 344.012i | −1.23164 | − | 0.529250i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −135.750 | − | 143.088i | −0.208205 | − | 0.219460i | ||||
\(653\) | −42.0252 | − | 24.2632i | −0.0643571 | − | 0.0371566i | 0.467476 | − | 0.884006i | \(-0.345163\pi\) |
−0.531833 | + | 0.846849i | \(0.678497\pi\) | |||||||
\(654\) | 83.5372 | + | 706.199i | 0.127733 | + | 1.07982i | ||||
\(655\) | 16.3656 | − | 9.44866i | 0.0249856 | − | 0.0144254i | ||||
\(656\) | 578.703 | + | 376.030i | 0.882170 | + | 0.573217i | ||||
\(657\) | −653.026 | −0.993951 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1224.65 | 1.85835 | 0.929176 | − | 0.369638i | \(-0.120518\pi\) | ||||
0.929176 | + | 0.369638i | \(0.120518\pi\) | |||||||
\(660\) | −56.4505 | − | 235.269i | −0.0855311 | − | 0.356468i | ||||
\(661\) | 725.765 | − | 419.021i | 1.09798 | − | 0.633919i | 0.162291 | − | 0.986743i | \(-0.448112\pi\) |
0.935690 | + | 0.352823i | \(0.114778\pi\) | |||||||
\(662\) | 161.381 | − | 19.0899i | 0.243777 | − | 0.0288367i | ||||
\(663\) | −91.6439 | − | 52.9106i | −0.138226 | − | 0.0798049i | ||||
\(664\) | 547.399 | − | 201.824i | 0.824396 | − | 0.303951i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −457.078 | − | 196.412i | −0.686303 | − | 0.294912i | ||||
\(667\) | −40.9358 | + | 70.9029i | −0.0613730 | + | 0.106301i | ||||
\(668\) | −926.019 | − | 274.432i | −1.38626 | − | 0.410826i | ||||
\(669\) | 209.940 | − | 121.209i | 0.313812 | − | 0.181180i | ||||
\(670\) | −271.316 | + | 202.574i | −0.404950 | + | 0.302349i | ||||
\(671\) | − | 146.287i | − | 0.218014i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 147.714 | 0.219486 | 0.109743 | − | 0.993960i | \(-0.464997\pi\) | ||||
0.109743 | + | 0.993960i | \(0.464997\pi\) | |||||||
\(674\) | 83.1528 | + | 111.370i | 0.123372 | + | 0.165238i | ||||
\(675\) | 565.980 | + | 980.307i | 0.838490 | + | 1.45231i | ||||
\(676\) | 328.984 | − | 1110.10i | 0.486663 | − | 1.64216i | ||||
\(677\) | −725.024 | − | 418.593i | −1.07094 | − | 0.618305i | −0.142499 | − | 0.989795i | \(-0.545514\pi\) |
−0.928437 | + | 0.371490i | \(0.878847\pi\) | |||||||
\(678\) | 30.1661 | − | 70.2007i | 0.0444927 | − | 0.103541i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −5.53263 | − | 15.0059i | −0.00813622 | − | 0.0220676i | ||||
\(681\) | −493.582 | + | 854.909i | −0.724790 | + | 1.25537i | ||||
\(682\) | −42.6331 | − | 360.407i | −0.0625118 | − | 0.528457i | ||||
\(683\) | 32.2189 | + | 55.8047i | 0.0471725 | + | 0.0817053i | 0.888648 | − | 0.458591i | \(-0.151646\pi\) |
−0.841475 | + | 0.540296i | \(0.818312\pi\) | |||||||
\(684\) | 448.235 | − | 107.549i | 0.655314 | − | 0.157236i | ||||
\(685\) | − | 510.849i | − | 0.745765i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 986.210i | 1.43553i | ||||||||
\(688\) | 559.978 | + | 363.863i | 0.813922 | + | 0.528871i | ||||
\(689\) | 797.385 | + | 1381.11i | 1.15731 | + | 2.00452i | ||||
\(690\) | −198.490 | + | 23.4797i | −0.287667 | + | 0.0340285i | ||||
\(691\) | −263.374 | + | 456.177i | −0.381149 | + | 0.660169i | −0.991227 | − | 0.132172i | \(-0.957805\pi\) |
0.610078 | + | 0.792341i | \(0.291138\pi\) | |||||||
\(692\) | 157.922 | − | 149.823i | 0.228211 | − | 0.216508i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 275.852 | − | 641.948i | 0.397482 | − | 0.924997i | ||||
\(695\) | 321.516 | + | 185.627i | 0.462613 | + | 0.267090i | ||||
\(696\) | −257.073 | + | 308.973i | −0.369358 | + | 0.443926i | ||||
\(697\) | −19.9895 | − | 34.6229i | −0.0286794 | − | 0.0496741i | ||||
\(698\) | 265.766 | − | 198.430i | 0.380754 | − | 0.284284i | ||||
\(699\) | −515.633 | −0.737672 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 695.486i | − | 0.992134i | −0.868284 | − | 0.496067i | \(-0.834777\pi\) | ||
0.868284 | − | 0.496067i | \(-0.165223\pi\) | |||||||
\(702\) | −1908.92 | + | 1425.26i | −2.71926 | + | 2.03029i | ||||
\(703\) | 65.7370 | − | 37.9532i | 0.0935092 | − | 0.0539875i | ||||
\(704\) | −317.233 | − | 112.479i | −0.450615 | − | 0.159771i | ||||
\(705\) | −264.520 | + | 458.162i | −0.375206 | + | 0.649876i | ||||
\(706\) | −372.471 | + | 866.794i | −0.527580 | + | 1.22775i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −787.920 | − | 830.513i | −1.11288 | − | 1.17304i | ||||
\(709\) | 803.161 | + | 463.705i | 1.13281 | + | 0.654027i | 0.944640 | − | 0.328110i | \(-0.106412\pi\) |
0.188168 | + | 0.982137i | \(0.439745\pi\) | |||||||
\(710\) | −319.201 | + | 37.7587i | −0.449578 | + | 0.0531812i | ||||
\(711\) | 508.447 | − | 293.552i | 0.715115 | − | 0.412872i | ||||
\(712\) | −74.3816 | + | 432.366i | −0.104469 | + | 0.607255i | ||||
\(713\) | −299.812 | −0.420493 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −242.883 | −0.339697 | ||||||||
\(716\) | −494.057 | + | 118.544i | −0.690024 | + | 0.165564i | ||||
\(717\) | −753.566 | + | 435.071i | −1.05100 | + | 0.606794i | ||||
\(718\) | 154.355 | + | 1304.87i | 0.214979 | + | 1.81737i | ||||
\(719\) | −1150.37 | − | 664.169i | −1.59996 | − | 0.923739i | −0.991493 | − | 0.130163i | \(-0.958450\pi\) |
−0.608471 | − | 0.793576i | \(-0.708217\pi\) | |||||||
\(720\) | −669.720 | − | 35.2747i | −0.930167 | − | 0.0489927i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 257.281 | − | 598.730i | 0.356345 | − | 0.829266i | ||||
\(723\) | −547.865 | + | 948.929i | −0.757766 | + | 1.31249i | ||||
\(724\) | 815.749 | + | 241.752i | 1.12673 | + | 0.333912i | ||||
\(725\) | 166.034 | − | 95.8600i | 0.229013 | − | 0.132221i | ||||
\(726\) | −595.546 | − | 797.642i | −0.820311 | − | 1.09868i | ||||
\(727\) | 539.401i | 0.741954i | 0.928642 | + | 0.370977i | \(0.120977\pi\) | ||||
−0.928642 | + | 0.370977i | \(0.879023\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −303.936 | −0.416922 | ||||||||
\(730\) | −116.158 | + | 86.7276i | −0.159121 | + | 0.118805i | ||||
\(731\) | −19.3427 | − | 33.5026i | −0.0264606 | − | 0.0458311i | ||||
\(732\) | −568.834 | − | 168.577i | −0.777095 | − | 0.230297i | ||||
\(733\) | −382.859 | − | 221.044i | −0.522318 | − | 0.301561i | 0.215564 | − | 0.976490i | \(-0.430841\pi\) |
−0.737883 | + | 0.674929i | \(0.764174\pi\) | |||||||
\(734\) | 653.196 | + | 280.686i | 0.889913 | + | 0.382406i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −123.062 | + | 249.339i | −0.167204 | + | 0.338776i | ||||
\(737\) | 206.396 | − | 357.488i | 0.280048 | − | 0.485058i | ||||
\(738\) | −1664.83 | + | 196.935i | −2.25587 | + | 0.266849i | ||||
\(739\) | 574.116 | + | 994.398i | 0.776882 | + | 1.34560i | 0.933730 | + | 0.357977i | \(0.116533\pi\) |
−0.156848 | + | 0.987623i | \(0.550133\pi\) | |||||||
\(740\) | −107.389 | + | 25.7669i | −0.145120 | + | 0.0348201i | ||||
\(741\) | − | 677.050i | − | 0.913698i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 588.688i | − | 0.792313i | −0.918183 | − | 0.396156i | \(-0.870344\pi\) | ||
0.918183 | − | 0.396156i | \(-0.129656\pi\) | |||||||
\(744\) | −1450.56 | − | 249.546i | −1.94968 | − | 0.335411i | ||||
\(745\) | −248.810 | − | 430.952i | −0.333973 | − | 0.578459i | ||||
\(746\) | −74.2420 | − | 627.621i | −0.0995202 | − | 0.841314i | ||||
\(747\) | −708.597 | + | 1227.33i | −0.948590 | + | 1.64301i | ||||
\(748\) | 13.4196 | + | 14.1450i | 0.0179406 | + | 0.0189104i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 958.378 | + | 411.826i | 1.27784 | + | 0.549101i | ||||
\(751\) | −708.754 | − | 409.199i | −0.943747 | − | 0.544873i | −0.0526140 | − | 0.998615i | \(-0.516755\pi\) |
−0.891133 | + | 0.453742i | \(0.850089\pi\) | |||||||
\(752\) | 333.952 | + | 655.844i | 0.444086 | + | 0.872133i | ||||
\(753\) | 424.712 | + | 735.622i | 0.564026 | + | 0.976922i | ||||
\(754\) | 241.396 | + | 323.313i | 0.320154 | + | 0.428797i | ||||
\(755\) | −318.989 | −0.422503 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 105.101i | 0.138838i | 0.997588 | + | 0.0694192i | \(0.0221146\pi\) | ||||
−0.997588 | + | 0.0694192i | \(0.977885\pi\) | |||||||
\(758\) | 213.468 | + | 285.908i | 0.281620 | + | 0.377187i | ||||
\(759\) | 211.025 | − | 121.835i | 0.278030 | − | 0.160521i | ||||
\(760\) | 65.4471 | − | 78.6600i | 0.0861146 | − | 0.103500i | ||||
\(761\) | 507.117 | − | 878.352i | 0.666382 | − | 1.15421i | −0.312527 | − | 0.949909i | \(-0.601175\pi\) |
0.978909 | − | 0.204299i | \(-0.0654913\pi\) | |||||||
\(762\) | 1288.38 | + | 553.631i | 1.69079 | + | 0.726550i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −117.626 | + | 111.594i | −0.153961 | + | 0.146065i | ||||
\(765\) | 33.6449 | + | 19.4249i | 0.0439803 | + | 0.0253920i | ||||
\(766\) | 164.085 | + | 1387.13i | 0.214211 | + | 1.81087i | ||||
\(767\) | −995.264 | + | 574.616i | −1.29761 | + | 0.749173i | ||||
\(768\) | −802.940 | + | 1103.93i | −1.04549 | + | 1.43741i | ||||
\(769\) | 1183.99 | 1.53964 | 0.769822 | − | 0.638258i | \(-0.220345\pi\) | ||||
0.769822 | + | 0.638258i | \(0.220345\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1150.58 | 1.49232 | ||||||||
\(772\) | 1098.06 | − | 263.469i | 1.42236 | − | 0.341281i | ||||
\(773\) | −280.862 | + | 162.156i | −0.363340 | + | 0.209774i | −0.670545 | − | 0.741869i | \(-0.733940\pi\) |
0.307205 | + | 0.951643i | \(0.400606\pi\) | |||||||
\(774\) | −1610.96 | + | 190.563i | −2.08134 | + | 0.246205i | ||||
\(775\) | 608.014 | + | 351.037i | 0.784534 | + | 0.452951i | ||||
\(776\) | 403.170 | − | 148.647i | 0.519550 | − | 0.191556i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −322.226 | − | 138.464i | −0.414172 | − | 0.177975i | ||||
\(779\) | 127.894 | − | 221.519i | 0.164177 | − | 0.284363i | ||||
\(780\) | −279.892 | + | 944.443i | −0.358835 | + | 1.21082i | ||||
\(781\) | 339.358 | − | 195.928i | 0.434517 | − | 0.250869i | ||||
\(782\) | 12.9067 | − | 9.63656i | 0.0165047 | − | 0.0123230i | ||||
\(783\) | − | 524.168i | − | 0.669436i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −247.679 | −0.315514 | ||||||||
\(786\) | 55.8989 | + | 74.8679i | 0.0711182 | + | 0.0952518i | ||||
\(787\) | 134.268 | + | 232.559i | 0.170607 | + | 0.295500i | 0.938632 | − | 0.344919i | \(-0.112094\pi\) |
−0.768025 | + | 0.640420i | \(0.778760\pi\) | |||||||
\(788\) | 1004.06 | + | 297.559i | 1.27419 | + | 0.377614i | ||||
\(789\) | 1520.01 | + | 877.576i | 1.92650 | + | 1.11226i | ||||
\(790\) | 51.4547 | − | 119.742i | 0.0651325 | − | 0.151573i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 767.121 | − | 282.834i | 0.968587 | − | 0.357114i | ||||
\(793\) | −297.792 | + | 515.791i | −0.375526 | + | 0.650429i | ||||
\(794\) | −90.6200 | − | 766.075i | −0.114131 | − | 0.964830i | ||||
\(795\) | −428.319 | − | 741.870i | −0.538766 | − | 0.933170i | ||||
\(796\) | −300.629 | − | 1252.93i | −0.377675 | − | 1.57404i | ||||
\(797\) | − | 1502.06i | − | 1.88465i | −0.334705 | − | 0.942323i | \(-0.608637\pi\) | ||
0.334705 | − | 0.942323i | \(-0.391363\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 42.6339i | − | 0.0533591i | ||||||
\(800\) | 541.509 | − | 361.568i | 0.676886 | − | 0.451960i | ||||
\(801\) | −532.848 | − | 922.919i | −0.665228 | − | 1.15221i | ||||
\(802\) | 1046.89 | − | 123.838i | 1.30535 | − | 0.154412i | ||||
\(803\) | 88.3638 | − | 153.051i | 0.110042 | − | 0.190599i | ||||
\(804\) | −1152.24 | − | 1214.52i | −1.43313 | − | 1.51060i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −583.349 | + | 1357.54i | −0.723758 | + | 1.68429i | ||||
\(807\) | 1353.34 | + | 781.354i | 1.67701 | + | 0.968220i | ||||
\(808\) | 462.049 | − | 555.332i | 0.571843 | − | 0.687292i | ||||
\(809\) | −35.3793 | − | 61.2788i | −0.0437322 | − | 0.0757464i | 0.843331 | − | 0.537395i | \(-0.180591\pi\) |
−0.887063 | + | 0.461648i | \(0.847258\pi\) | |||||||
\(810\) | 420.824 | − | 314.201i | 0.519535 | − | 0.387902i | ||||
\(811\) | −5.94522 | −0.00733072 | −0.00366536 | − | 0.999993i | \(-0.501167\pi\) | ||||
−0.00366536 | + | 0.999993i | \(0.501167\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 143.172i | 0.176103i | ||||||||
\(814\) | 107.883 | − | 80.5487i | 0.132534 | − | 0.0989541i | ||||
\(815\) | 92.1073 | − | 53.1782i | 0.113015 | − | 0.0652493i | ||||
\(816\) | 70.4666 | − | 35.8812i | 0.0863561 | − | 0.0439721i | ||||
\(817\) | 123.756 | − | 214.351i | 0.151476 | − | 0.262364i | ||||
\(818\) | −334.592 | + | 778.643i | −0.409037 | + | 0.951886i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −269.980 | + | 256.134i | −0.329244 | + | 0.312359i | ||||
\(821\) | −13.1159 | − | 7.57244i | −0.0159755 | − | 0.00922344i | 0.491991 | − | 0.870600i | \(-0.336269\pi\) |
−0.507966 | + | 0.861377i | \(0.669603\pi\) | |||||||
\(822\) | 2508.30 | − | 296.710i | 3.05146 | − | 0.360961i | ||||
\(823\) | −1284.10 | + | 741.378i | −1.56027 | + | 0.900824i | −0.563044 | + | 0.826427i | \(0.690370\pi\) |
−0.997229 | + | 0.0743964i | \(0.976297\pi\) | |||||||
\(824\) | 889.430 | + | 153.012i | 1.07941 | + | 0.185694i | ||||
\(825\) | −570.607 | −0.691645 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −74.3070 | −0.0898513 | −0.0449257 | − | 0.998990i | \(-0.514305\pi\) | ||||
−0.0449257 | + | 0.998990i | \(0.514305\pi\) | |||||||
\(828\) | −157.589 | − | 656.785i | −0.190325 | − | 0.793219i | ||||
\(829\) | −123.722 | + | 71.4311i | −0.149243 | + | 0.0861654i | −0.572762 | − | 0.819722i | \(-0.694128\pi\) |
0.423519 | + | 0.905887i | \(0.360795\pi\) | |||||||
\(830\) | 36.9567 | + | 312.421i | 0.0445261 | + | 0.376411i | ||||
\(831\) | 1545.96 | + | 892.558i | 1.86036 | + | 1.07408i | ||||
\(832\) | 889.555 | + | 1042.36i | 1.06918 | + | 1.25284i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −724.699 | + | 1686.48i | −0.868944 | + | 2.02216i | ||||
\(835\) | 260.403 | − | 451.032i | 0.311860 | − | 0.540158i | ||||
\(836\) | −35.4461 | + | 119.606i | −0.0423996 | + | 0.143070i | ||||
\(837\) | 1662.33 | − | 959.745i | 1.98605 | − | 1.14665i | ||||
\(838\) | 353.696 | + | 473.721i | 0.422072 | + | 0.565300i | ||||
\(839\) | − | 16.7454i | − | 0.0199588i | −0.999950 | − | 0.00997940i | \(-0.996823\pi\) | ||
0.999950 | − | 0.00997940i | \(-0.00317659\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 752.222 | 0.894437 | ||||||||
\(842\) | 202.342 | − | 151.075i | 0.240311 | − | 0.179424i | ||||
\(843\) | −328.886 | − | 569.648i | −0.390138 | − | 0.675739i | ||||
\(844\) | −192.980 | + | 651.175i | −0.228649 | + | 0.771534i | ||||
\(845\) | 540.690 | + | 312.168i | 0.639870 | + | 0.369429i | ||||
\(846\) | −1642.53 | − | 705.816i | −1.94153 | − | 0.834298i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1190.06 | − | 62.6814i | −1.40337 | − | 0.0739167i | ||||
\(849\) | 1.65008 | − | 2.85803i | 0.00194356 | − | 0.00336634i | ||||
\(850\) | −37.4576 | + | 4.43091i | −0.0440678 | + | 0.00521284i | ||||
\(851\) | −55.6118 | − | 96.3224i | −0.0653488 | − | 0.113187i | ||||
\(852\) | −370.795 | − | 1545.36i | −0.435205 | − | 1.81381i | ||||
\(853\) | 1299.38i | 1.52331i | 0.647984 | + | 0.761654i | \(0.275612\pi\) | ||||
−0.647984 | + | 0.761654i | \(0.724388\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 248.563i | 0.290717i | ||||||||
\(856\) | 195.301 | − | 1135.24i | 0.228155 | − | 1.32622i | ||||
\(857\) | −597.668 | − | 1035.19i | −0.697396 | − | 1.20792i | −0.969366 | − | 0.245619i | \(-0.921009\pi\) |
0.271971 | − | 0.962305i | \(-0.412325\pi\) | |||||||
\(858\) | −141.071 | − | 1192.57i | −0.164418 | − | 1.38994i | ||||
\(859\) | −170.885 | + | 295.981i | −0.198934 | + | 0.344564i | −0.948183 | − | 0.317724i | \(-0.897081\pi\) |
0.749249 | + | 0.662289i | \(0.230415\pi\) | |||||||
\(860\) | −261.244 | + | 247.846i | −0.303772 | + | 0.288193i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 467.216 | + | 200.768i | 0.542014 | + | 0.232909i | ||||
\(863\) | 844.362 | + | 487.493i | 0.978404 | + | 0.564882i | 0.901788 | − | 0.432179i | \(-0.142255\pi\) |
0.0766158 | + | 0.997061i | \(0.475589\pi\) | |||||||
\(864\) | −115.848 | − | 1776.42i | −0.134083 | − | 2.05604i | ||||
\(865\) | 58.6913 | + | 101.656i | 0.0678512 | + | 0.117522i | ||||
\(866\) | 653.674 | + | 875.495i | 0.754819 | + | 1.01096i | ||||
\(867\) | 1536.44 | 1.77213 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 158.887i | 0.182839i | ||||||||
\(870\) | −129.667 | − | 173.669i | −0.149043 | − | 0.199620i | ||||
\(871\) | −1455.45 | + | 840.304i | −1.67101 | + | 0.964758i | ||||
\(872\) | −341.190 | + | 410.072i | −0.391272 | + | 0.470266i | ||||
\(873\) | −521.896 | + | 903.951i | −0.597819 | + | 1.03545i | ||||
\(874\) | 94.6839 | + | 40.6868i | 0.108334 | + | 0.0465524i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −493.304 | − | 519.971i | −0.563133 | − | 0.593574i | ||||
\(877\) | −274.158 | − | 158.285i | −0.312609 | − | 0.180485i | 0.335484 | − | 0.942046i | \(-0.391100\pi\) |
−0.648093 | + | 0.761561i | \(0.724433\pi\) | |||||||
\(878\) | 64.2186 | + | 542.885i | 0.0731419 | + | 0.618320i | ||||
\(879\) | 130.591 | − | 75.3966i | 0.148567 | − | 0.0857754i | ||||
\(880\) | 98.8902 | − | 152.190i | 0.112375 | − | 0.172943i | ||||
\(881\) | 464.977 | 0.527783 | 0.263891 | − | 0.964552i | \(-0.414994\pi\) | ||||
0.263891 | + | 0.964552i | \(0.414994\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 69.4594 | 0.0786630 | 0.0393315 | − | 0.999226i | \(-0.487477\pi\) | ||||
0.0393315 | + | 0.999226i | \(0.487477\pi\) | |||||||
\(884\) | −18.5212 | − | 77.1911i | −0.0209516 | − | 0.0873202i | ||||
\(885\) | 534.610 | − | 308.657i | 0.604079 | − | 0.348765i | ||||
\(886\) | 942.966 | − | 111.545i | 1.06430 | − | 0.125897i | ||||
\(887\) | 9.46740 | + | 5.46601i | 0.0106735 | + | 0.00616235i | 0.505327 | − | 0.862928i | \(-0.331372\pi\) |
−0.494654 | + | 0.869090i | \(0.664705\pi\) | |||||||
\(888\) | −188.890 | − | 512.320i | −0.212714 | − | 0.576936i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −217.353 | − | 93.3991i | −0.244217 | − | 0.104943i | ||||
\(891\) | −320.129 | + | 554.479i | −0.359292 | + | 0.622311i | ||||
\(892\) | 174.355 | + | 51.6712i | 0.195465 | + | 0.0579274i | ||||
\(893\) | 236.229 | − | 136.387i | 0.264535 | − | 0.152729i | ||||
\(894\) | 1971.49 | − | 1471.98i | 2.20524 | − | 1.64651i | ||||
\(895\) | − | 273.974i | − | 0.306116i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −992.062 | −1.10598 | ||||||||
\(898\) | −935.818 | − | 1253.38i | −1.04211 | − | 1.39575i | ||||
\(899\) | −162.552 | − | 281.548i | −0.180814 | − | 0.313179i | ||||
\(900\) | −449.414 | + | 1516.47i | −0.499349 | + | 1.68496i | ||||
\(901\) | 59.7853 | + | 34.5170i | 0.0663543 | + | 0.0383097i | ||||
\(902\) | 179.119 | − | 416.837i | 0.198580 | − | 0.462125i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 53.7786 | − | 19.8279i | 0.0594896 | − | 0.0219336i | ||||
\(905\) | −229.395 | + | 397.323i | −0.253475 | + | 0.439031i | ||||
\(906\) | −185.275 | − | 1566.26i | −0.204497 | − | 1.72876i | ||||
\(907\) | 11.3588 | + | 19.6740i | 0.0125235 | + | 0.0216913i | 0.872219 | − | 0.489115i | \(-0.162680\pi\) |
−0.859696 | + | 0.510806i | \(0.829347\pi\) | |||||||
\(908\) | −720.085 | + | 172.777i | −0.793045 | + | 0.190283i | ||||
\(909\) | 1754.83i | 1.93051i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 721.866i | − | 0.792389i | −0.918167 | − | 0.396194i | \(-0.870331\pi\) | ||
0.918167 | − | 0.396194i | \(-0.129669\pi\) | |||||||
\(912\) | 424.238 | + | 275.662i | 0.465174 | + | 0.302261i | ||||
\(913\) | −191.767 | − | 332.150i | −0.210040 | − | 0.363800i | ||||
\(914\) | −376.492 | + | 44.5358i | −0.411917 | + | 0.0487262i | ||||
\(915\) | 159.960 | − | 277.059i | 0.174820 | − | 0.302797i | ||||
\(916\) | −536.704 | + | 509.179i | −0.585922 | + | 0.555873i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −40.7139 | + | 94.7470i | −0.0443506 | + | 0.103210i | ||||
\(919\) | −113.209 | − | 65.3612i | −0.123187 | − | 0.0711221i | 0.437140 | − | 0.899393i | \(-0.355991\pi\) |
−0.560327 | + | 0.828271i | \(0.689325\pi\) | |||||||
\(920\) | −115.258 | − | 95.8977i | −0.125281 | − | 0.104237i | ||||
\(921\) | −1068.83 | − | 1851.27i | −1.16051 | − | 2.01007i | ||||
\(922\) | −324.577 | + | 242.340i | −0.352036 | + | 0.262842i | ||||
\(923\) | −1595.38 | −1.72847 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 260.454i | 0.281572i | ||||||||
\(926\) | 1046.37 | − | 781.256i | 1.12999 | − | 0.843689i | ||||
\(927\) | −1898.56 | + | 1096.13i | −2.04807 | + | 1.18245i | ||||
\(928\) | −300.872 | + | 19.6211i | −0.324216 | + | 0.0211434i | ||||
\(929\) | −227.643 | + | 394.289i | −0.245041 | + | 0.424423i | −0.962143 | − | 0.272545i | \(-0.912135\pi\) |
0.717102 | + | 0.696968i | \(0.245468\pi\) | |||||||
\(930\) | 313.349 | − | 729.207i | 0.336934 | − | 0.784093i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −266.221 | − | 280.612i | −0.285645 | − | 0.301086i | ||||
\(933\) | 749.140 | + | 432.516i | 0.802937 | + | 0.463576i | ||||
\(934\) | −1083.35 | + | 128.150i | −1.15990 | + | 0.137206i | ||||
\(935\) | −9.10528 | + | 5.25694i | −0.00973827 | + | 0.00562239i | ||||
\(936\) | −3280.53 | − | 564.362i | −3.50483 | − | 0.602951i | ||||
\(937\) | 1242.79 | 1.32635 | 0.663176 | − | 0.748464i | \(-0.269208\pi\) | ||||
0.663176 | + | 0.748464i | \(0.269208\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1419.69 | −1.51192 | ||||||||
\(940\) | −385.907 | + | 92.5946i | −0.410540 | + | 0.0985049i | ||||
\(941\) | 984.767 | − | 568.556i | 1.04651 | − | 0.604204i | 0.124841 | − | 0.992177i | \(-0.460158\pi\) |
0.921671 | + | 0.387973i | \(0.126825\pi\) | |||||||
\(942\) | −143.856 | − | 1216.12i | −0.152713 | − | 1.29100i | ||||
\(943\) | −324.585 | − | 187.399i | −0.344205 | − | 0.198727i | ||||
\(944\) | 45.1698 | − | 857.586i | 0.0478493 | − | 0.908460i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 173.324 | − | 403.349i | 0.183217 | − | 0.426373i | ||||
\(947\) | −352.421 | + | 610.411i | −0.372145 | + | 0.644573i | −0.989895 | − | 0.141801i | \(-0.954711\pi\) |
0.617751 | + | 0.786374i | \(0.288044\pi\) | |||||||
\(948\) | 617.828 | + | 183.097i | 0.651717 | + | 0.193140i | ||||
\(949\) | −623.119 | + | 359.758i | −0.656606 | + | 0.379092i | ||||
\(950\) | −144.379 | − | 193.374i | −0.151978 | − | 0.203551i | ||||
\(951\) | − | 2308.09i | − | 2.42702i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 765.039 | 0.802769 | 0.401384 | − | 0.915910i | \(-0.368529\pi\) | ||||
0.401384 | + | 0.915910i | \(0.368529\pi\) | |||||||
\(954\) | 2319.58 | − | 1731.88i | 2.43143 | − | 1.81538i | ||||
\(955\) | −43.7153 | − | 75.7172i | −0.0457752 | − | 0.0792850i | ||||
\(956\) | −625.835 | − | 185.470i | −0.654639 | − | 0.194006i | ||||
\(957\) | 228.827 | + | 132.113i | 0.239109 | + | 0.138050i | ||||
\(958\) | 200.102 | + | 85.9863i | 0.208875 | + | 0.0897561i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −477.828 | − | 559.911i | −0.497737 | − | 0.583240i | ||||
\(961\) | 114.761 | − | 198.772i | 0.119418 | − | 0.206838i | ||||
\(962\) | −544.350 | + | 64.3919i | −0.565852 | + | 0.0669354i | ||||
\(963\) | 1399.07 | + | 2423.27i | 1.45283 | + | 2.51637i | ||||
\(964\) | −799.278 | + | 191.779i | −0.829126 | + | 0.198941i | ||||
\(965\) | 608.916i | 0.631001i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 771.494i | − | 0.797822i | −0.916990 | − | 0.398911i | \(-0.869388\pi\) | ||
0.916990 | − | 0.398911i | \(-0.130612\pi\) | |||||||
\(968\) | 126.604 | − | 735.923i | 0.130789 | − | 0.760251i | ||||
\(969\) | −14.6540 | − | 25.3815i | −0.0151228 | − | 0.0261935i | ||||
\(970\) | 27.2193 | + | 230.104i | 0.0280612 | + | 0.237221i | ||||
\(971\) | 458.754 | − | 794.586i | 0.472456 | − | 0.818317i | −0.527047 | − | 0.849836i | \(-0.676701\pi\) |
0.999503 | + | 0.0315186i | \(0.0100343\pi\) | |||||||
\(972\) | 408.778 | + | 430.875i | 0.420554 | + | 0.443287i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 788.949 | + | 339.021i | 0.810010 | + | 0.348071i | ||||
\(975\) | 2011.89 | + | 1161.56i | 2.06348 | + | 1.19135i | ||||
\(976\) | −201.947 | − | 396.600i | −0.206913 | − | 0.406353i | ||||
\(977\) | −133.301 | − | 230.883i | −0.136439 | − | 0.236319i | 0.789707 | − | 0.613484i | \(-0.210232\pi\) |
−0.926146 | + | 0.377165i | \(0.876899\pi\) | |||||||
\(978\) | 314.606 | + | 421.366i | 0.321683 | + | 0.430844i | ||||
\(979\) | 288.408 | 0.294594 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 1295.81i | − | 1.32091i | ||||||
\(982\) | −543.095 | − | 727.392i | −0.553050 | − | 0.740726i | ||||
\(983\) | 1601.95 | − | 924.884i | 1.62965 | − | 0.940879i | 0.645454 | − | 0.763799i | \(-0.276668\pi\) |
0.984197 | − | 0.177080i | \(-0.0566650\pi\) | |||||||
\(984\) | −1414.44 | − | 1176.85i | −1.43744 | − | 1.19599i | ||||
\(985\) | −282.349 | + | 489.043i | −0.286649 | + | 0.496490i | ||||
\(986\) | 16.0473 | + | 6.89571i | 0.0162751 | + | 0.00699362i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 368.457 | − | 349.560i | 0.372932 | − | 0.353806i | ||||
\(989\) | −314.083 | − | 181.336i | −0.317576 | − | 0.183353i | ||||
\(990\) | 51.7908 | + | 437.824i | 0.0523140 | + | 0.442247i | ||||
\(991\) | 303.420 | − | 175.180i | 0.306175 | − | 0.176770i | −0.339038 | − | 0.940773i | \(-0.610102\pi\) |
0.645214 | + | 0.764002i | \(0.276768\pi\) | |||||||
\(992\) | −613.118 | − | 918.248i | −0.618063 | − | 0.925654i | ||||
\(993\) | −433.261 | −0.436315 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 694.800 | 0.698291 | ||||||||
\(996\) | −1512.54 | + | 362.919i | −1.51861 | + | 0.364376i | ||||
\(997\) | 455.495 | − | 262.980i | 0.456866 | − | 0.263772i | −0.253860 | − | 0.967241i | \(-0.581700\pi\) |
0.710726 | + | 0.703469i | \(0.248367\pi\) | |||||||
\(998\) | 662.176 | − | 78.3296i | 0.663503 | − | 0.0784866i | ||||
\(999\) | 616.687 | + | 356.045i | 0.617305 | + | 0.356401i |
(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 | 392.3.k.l.275.2 | 12 | ||
7.2 | even | 3 | 392.3.g.i.99.4 | 6 | |||
7.3 | odd | 6 | 56.3.k.d.11.6 | yes | 12 | ||
7.4 | even | 3 | inner | 392.3.k.l.67.6 | 12 | ||
7.5 | odd | 6 | 392.3.g.j.99.4 | 6 | |||
7.6 | odd | 2 | 56.3.k.d.51.2 | yes | 12 | ||
8.3 | odd | 2 | inner | 392.3.k.l.275.6 | 12 | ||
28.3 | even | 6 | 224.3.o.d.207.5 | 12 | |||
28.19 | even | 6 | 1568.3.g.j.687.1 | 6 | |||
28.23 | odd | 6 | 1568.3.g.l.687.6 | 6 | |||
28.27 | even | 2 | 224.3.o.d.79.6 | 12 | |||
56.3 | even | 6 | 56.3.k.d.11.2 | ✓ | 12 | ||
56.5 | odd | 6 | 1568.3.g.j.687.2 | 6 | |||
56.11 | odd | 6 | inner | 392.3.k.l.67.2 | 12 | ||
56.13 | odd | 2 | 224.3.o.d.79.5 | 12 | |||
56.19 | even | 6 | 392.3.g.j.99.3 | 6 | |||
56.27 | even | 2 | 56.3.k.d.51.6 | yes | 12 | ||
56.37 | even | 6 | 1568.3.g.l.687.5 | 6 | |||
56.45 | odd | 6 | 224.3.o.d.207.6 | 12 | |||
56.51 | odd | 6 | 392.3.g.i.99.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.k.d.11.2 | ✓ | 12 | 56.3 | even | 6 | ||
56.3.k.d.11.6 | yes | 12 | 7.3 | odd | 6 | ||
56.3.k.d.51.2 | yes | 12 | 7.6 | odd | 2 | ||
56.3.k.d.51.6 | yes | 12 | 56.27 | even | 2 | ||
224.3.o.d.79.5 | 12 | 56.13 | odd | 2 | |||
224.3.o.d.79.6 | 12 | 28.27 | even | 2 | |||
224.3.o.d.207.5 | 12 | 28.3 | even | 6 | |||
224.3.o.d.207.6 | 12 | 56.45 | odd | 6 | |||
392.3.g.i.99.3 | 6 | 56.51 | odd | 6 | |||
392.3.g.i.99.4 | 6 | 7.2 | even | 3 | |||
392.3.g.j.99.3 | 6 | 56.19 | even | 6 | |||
392.3.g.j.99.4 | 6 | 7.5 | odd | 6 | |||
392.3.k.l.67.2 | 12 | 56.11 | odd | 6 | inner | ||
392.3.k.l.67.6 | 12 | 7.4 | even | 3 | inner | ||
392.3.k.l.275.2 | 12 | 1.1 | even | 1 | trivial | ||
392.3.k.l.275.6 | 12 | 8.3 | odd | 2 | inner | ||
1568.3.g.j.687.1 | 6 | 28.19 | even | 6 | |||
1568.3.g.j.687.2 | 6 | 56.5 | odd | 6 | |||
1568.3.g.l.687.5 | 6 | 56.37 | even | 6 | |||
1568.3.g.l.687.6 | 6 | 28.23 | odd | 6 |