Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,4,Mod(193,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.193");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.6567334422\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1534132224.8 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 107x^{4} + 210x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 193.2 | ||
Root | \(2.63019i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.193 |
Dual form | 384.4.d.f.193.7 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 3.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 5.67763i | − 0.507823i | −0.967227 | − | 0.253911i | \(-0.918283\pi\) | ||||
0.967227 | − | 0.253911i | \(-0.0817172\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 33.0917 | 1.78678 | 0.893391 | − | 0.449280i | \(-0.148320\pi\) | ||||
0.893391 | + | 0.449280i | \(0.148320\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 34.6274i | 0.949142i | 0.880217 | + | 0.474571i | \(0.157397\pi\) | ||||
−0.880217 | + | 0.474571i | \(0.842603\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 82.2421i | 1.75460i | 0.479939 | + | 0.877302i | \(0.340659\pi\) | ||||
−0.479939 | + | 0.877302i | \(0.659341\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −17.0329 | −0.293192 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 97.8823 | 1.39647 | 0.698233 | − | 0.715870i | \(-0.253970\pi\) | ||||
0.698233 | + | 0.715870i | \(0.253970\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 55.8823i | 0.674751i | 0.941370 | + | 0.337375i | \(0.109539\pi\) | ||||
−0.941370 | + | 0.337375i | \(0.890461\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 99.2750i | − 1.03160i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −130.418 | −1.18235 | −0.591176 | − | 0.806542i | \(-0.701336\pi\) | ||||
−0.591176 | + | 0.806542i | \(0.701336\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 92.7645 | 0.742116 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 147.451i | − 0.944173i | −0.881552 | − | 0.472086i | \(-0.843501\pi\) | ||||
0.881552 | − | 0.472086i | \(-0.156499\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −101.223 | −0.586459 | −0.293230 | − | 0.956042i | \(-0.594730\pi\) | ||||
−0.293230 | + | 0.956042i | \(0.594730\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 103.882 | 0.547987 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 187.882i | − 0.907368i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 184.439i | 0.819504i | 0.912197 | + | 0.409752i | \(0.134385\pi\) | ||||
−0.912197 | + | 0.409752i | \(0.865615\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 246.726 | 1.01302 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 237.411 | 0.904327 | 0.452164 | − | 0.891935i | \(-0.350652\pi\) | ||||
0.452164 | + | 0.891935i | \(0.350652\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 199.882i | 0.708878i | 0.935079 | + | 0.354439i | \(0.115328\pi\) | ||||
−0.935079 | + | 0.354439i | \(0.884672\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 51.0987i | 0.169274i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 334.813 | 1.03910 | 0.519548 | − | 0.854441i | \(-0.326100\pi\) | ||||
0.519548 | + | 0.854441i | \(0.326100\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 752.058 | 2.19259 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 293.647i | − 0.806250i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 102.030i | 0.264433i | 0.991221 | + | 0.132216i | \(0.0422094\pi\) | ||||
−0.991221 | + | 0.132216i | \(0.957791\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 196.602 | 0.481996 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 167.647 | 0.389568 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 105.961i | 0.233813i | 0.993143 | + | 0.116907i | \(0.0372978\pi\) | ||||
−0.993143 | + | 0.116907i | \(0.962702\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 717.803i | − 1.50664i | −0.657653 | − | 0.753321i | \(-0.728451\pi\) | ||||
0.657653 | − | 0.753321i | \(-0.271549\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −297.825 | −0.595594 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 466.940 | 0.891028 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 316.471i | − 0.577061i | −0.957471 | − | 0.288530i | \(-0.906833\pi\) | ||||
0.957471 | − | 0.288530i | \(-0.0931667\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 391.255i | 0.682632i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −800.045 | −1.33729 | −0.668647 | − | 0.743580i | \(-0.733126\pi\) | ||||
−0.668647 | + | 0.743580i | \(0.733126\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 301.058 | 0.482687 | 0.241344 | − | 0.970440i | \(-0.422412\pi\) | ||||
0.241344 | + | 0.970440i | \(0.422412\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 278.294i | − 0.428461i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1145.88i | 1.69591i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 42.8329 | 0.0610010 | 0.0305005 | − | 0.999535i | \(-0.490290\pi\) | ||||
0.0305005 | + | 0.999535i | \(0.490290\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 1236.67i | − 1.63544i | −0.575614 | − | 0.817721i | \(-0.695237\pi\) | ||||
0.575614 | − | 0.817721i | \(-0.304763\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 555.739i | − 0.709158i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −442.354 | −0.545119 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1325.29 | 1.57844 | 0.789218 | − | 0.614113i | \(-0.210486\pi\) | ||||
0.789218 | + | 0.614113i | \(0.210486\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2721.53i | 3.13509i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 303.670i | 0.338592i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 317.279 | 0.342654 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −505.765 | −0.529408 | −0.264704 | − | 0.964330i | \(-0.585274\pi\) | ||||
−0.264704 | + | 0.964330i | \(0.585274\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 311.647i | − 0.316381i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1281.97i | − 1.26298i | −0.775383 | − | 0.631491i | \(-0.782443\pi\) | ||||
0.775383 | − | 0.631491i | \(-0.217557\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −161.562 | −0.154555 | −0.0772775 | − | 0.997010i | \(-0.524623\pi\) | ||||
−0.0772775 | + | 0.997010i | \(0.524623\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −563.647 | −0.523869 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 481.726i | 0.435235i | 0.976034 | + | 0.217618i | \(0.0698286\pi\) | ||||
−0.976034 | + | 0.217618i | \(0.930171\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 286.637i | 0.251879i | 0.992038 | + | 0.125940i | \(0.0401945\pi\) | ||||
−0.992038 | + | 0.125940i | \(0.959805\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 553.318 | 0.473141 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1397.29 | −1.16324 | −0.581621 | − | 0.813460i | \(-0.697581\pi\) | ||||
−0.581621 | + | 0.813460i | \(0.697581\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 740.468i | 0.600426i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 740.179i | − 0.584868i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3239.09 | 2.49518 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 131.942 | 0.0991300 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 712.234i | − 0.522113i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1236.39i | − 0.884686i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −443.829 | −0.310106 | −0.155053 | − | 0.987906i | \(-0.549555\pi\) | ||||
−0.155053 | + | 0.987906i | \(0.549555\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 599.647 | 0.409271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 1365.57i | − 0.910765i | −0.890296 | − | 0.455382i | \(-0.849503\pi\) | ||||
0.890296 | − | 0.455382i | \(-0.150497\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1849.24i | 1.20563i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 153.296 | 0.0977305 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1223.06 | −0.762721 | −0.381360 | − | 0.924426i | \(-0.624544\pi\) | ||||
−0.381360 | + | 0.924426i | \(0.624544\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2176.70i | 1.32824i | 0.747625 | + | 0.664121i | \(0.231194\pi\) | ||||
−0.747625 | + | 0.664121i | \(0.768806\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 1004.44i | − 0.599922i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2847.83 | −1.66537 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −837.174 | −0.479473 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 2256.17i | − 1.26589i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2875.88i | 1.58122i | 0.612320 | + | 0.790610i | \(0.290236\pi\) | ||||
−0.612320 | + | 0.790610i | \(0.709764\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2330.03 | −1.25573 | −0.627863 | − | 0.778323i | \(-0.716070\pi\) | ||||
−0.627863 | + | 0.778323i | \(0.716070\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −880.940 | −0.465489 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 574.708i | 0.297817i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2447.31i | 1.24405i | 0.782996 | + | 0.622027i | \(0.213690\pi\) | ||||
−0.782996 | + | 0.622027i | \(0.786310\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 306.091 | 0.152670 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4315.76 | −2.11261 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1436.82i | 0.690432i | 0.938523 | + | 0.345216i | \(0.112194\pi\) | ||||
−0.938523 | + | 0.345216i | \(0.887806\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 589.805i | − 0.278280i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1769.42 | −0.819889 | −0.409945 | − | 0.912110i | \(-0.634452\pi\) | ||||
−0.409945 | + | 0.912110i | \(0.634452\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4566.76 | −2.07863 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 502.940i | − 0.224917i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 3897.86i | − 1.71300i | −0.516148 | − | 0.856499i | \(-0.672635\pi\) | ||||
0.516148 | − | 0.856499i | \(-0.327365\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3069.73 | 1.32600 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 317.884 | 0.134992 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 4146.74i | − 1.73152i | −0.500460 | − | 0.865760i | \(-0.666836\pi\) | ||||
0.500460 | − | 0.865760i | \(-0.333164\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 1104.22i | − 0.453457i | −0.973958 | − | 0.226728i | \(-0.927197\pi\) | ||||
0.973958 | − | 0.226728i | \(-0.0728030\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2153.41 | −0.869860 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1047.18 | 0.416163 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3389.41i | 1.32544i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 893.475i | 0.343866i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 35.0686 | 0.0132852 | 0.00664260 | − | 0.999978i | \(-0.497886\pi\) | ||||
0.00664260 | + | 0.999978i | \(0.497886\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 615.884 | 0.229701 | 0.114851 | − | 0.993383i | \(-0.463361\pi\) | ||||
0.114851 | + | 0.993383i | \(0.463361\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 1400.82i | − 0.514435i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 589.638i | − 0.213249i | −0.994299 | − | 0.106624i | \(-0.965996\pi\) | ||||
0.994299 | − | 0.106624i | \(-0.0340042\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4813.82 | 1.71479 | 0.857394 | − | 0.514661i | \(-0.172082\pi\) | ||||
0.857394 | + | 0.514661i | \(0.172082\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −949.413 | −0.333166 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 4879.41i | − 1.68703i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 1347.93i | − 0.459238i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1173.77 | 0.394118 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1935.06 | −0.640434 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3294.35i | 1.07484i | 0.843313 | + | 0.537422i | \(0.180602\pi\) | ||||
−0.843313 | + | 0.537422i | \(0.819398\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2400.13i | 0.772087i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1134.86 | 0.359984 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3349.65 | −1.04787 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 903.174i | − 0.278680i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8050.04i | 2.45025i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1572.78 | −0.472294 | −0.236147 | − | 0.971717i | \(-0.575885\pi\) | ||||
−0.236147 | + | 0.971717i | \(0.575885\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −834.881 | −0.247372 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1492.51i | 0.436394i | 0.975905 | + | 0.218197i | \(0.0700176\pi\) | ||||
−0.975905 | + | 0.218197i | \(0.929982\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 6163.31i | − 1.77853i | −0.457393 | − | 0.889265i | \(-0.651217\pi\) | ||||
0.457393 | − | 0.889265i | \(-0.348783\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3437.64 | 0.979134 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2540.35 | 0.714266 | 0.357133 | − | 0.934054i | \(-0.383754\pi\) | ||||
0.357133 | + | 0.934054i | \(0.383754\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 1900.95i | − 0.527677i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 128.499i | − 0.0352190i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1339.25 | 0.362465 | 0.181232 | − | 0.983440i | \(-0.441991\pi\) | ||||
0.181232 | + | 0.983440i | \(0.441991\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2542.71 | 0.679627 | 0.339814 | − | 0.940493i | \(-0.389636\pi\) | ||||
0.339814 | + | 0.940493i | \(0.389636\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 4269.91i | − 1.11345i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4595.87 | −1.18392 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3710.00 | −0.944223 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4701.45i | 1.18228i | 0.806568 | + | 0.591141i | \(0.201322\pi\) | ||||
−0.806568 | + | 0.591141i | \(0.798678\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 4516.05i | − 1.12222i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1667.22 | −0.409432 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −863.884 | −0.209679 | −0.104840 | − | 0.994489i | \(-0.533433\pi\) | ||||
−0.104840 | + | 0.994489i | \(0.533433\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6103.41i | 1.46428i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1327.06i | 0.314724i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7091.36 | −1.66263 | −0.831315 | − | 0.555801i | \(-0.812412\pi\) | ||||
−0.831315 | + | 0.555801i | \(0.812412\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 579.290 | 0.134285 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 3975.88i | − 0.911311i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 395.596i | 0.0896650i | 0.998995 | + | 0.0448325i | \(0.0142754\pi\) | ||||
−0.998995 | + | 0.0448325i | \(0.985725\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5532.21 | −1.24007 | −0.620033 | − | 0.784576i | \(-0.712881\pi\) | ||||
−0.620033 | + | 0.784576i | \(0.712881\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8164.58 | 1.81005 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3212.20i | 0.704373i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3830.31i | 0.830834i | 0.909631 | + | 0.415417i | \(0.136364\pi\) | ||||
−0.909631 | + | 0.415417i | \(0.863636\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 911.009 | 0.195486 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5283.17 | 1.12159 | 0.560797 | − | 0.827954i | \(-0.310495\pi\) | ||||
0.560797 | + | 0.827954i | \(0.310495\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4639.76i | 0.974577i | 0.873241 | + | 0.487288i | \(0.162014\pi\) | ||||
−0.873241 | + | 0.487288i | \(0.837986\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 951.836i | − 0.197831i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7856.33 | 1.61584 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4667.94 | 0.950119 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1517.29i | 0.305654i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6022.12i | 1.20074i | 0.799723 | + | 0.600369i | \(0.204980\pi\) | ||||
−0.799723 | + | 0.600369i | \(0.795020\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 601.609 | 0.118736 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −934.940 | −0.182662 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 10725.9i | − 2.07456i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6614.44i | 1.26661i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3845.92 | −0.729183 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4075.42 | −0.765107 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2998.82i | − 0.557497i | −0.960364 | − | 0.278749i | \(-0.910080\pi\) | ||||
0.960364 | − | 0.278749i | \(-0.0899196\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 484.685i | 0.0892323i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2403.97 | 0.438318 | 0.219159 | − | 0.975689i | \(-0.429669\pi\) | ||||
0.219159 | + | 0.975689i | \(0.429669\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5845.75 | 1.05566 | 0.527830 | − | 0.849350i | \(-0.323006\pi\) | ||||
0.527830 | + | 0.849350i | \(0.323006\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1690.94i | 0.302456i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 8917.38i | − 1.57997i | −0.613127 | − | 0.789984i | \(-0.710089\pi\) | ||||
0.613127 | − | 0.789984i | \(-0.289911\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5105.86 | 0.896154 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1445.18 | 0.251283 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5469.88i | 0.942267i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7629.15i | 1.30212i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 859.910 | 0.145422 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11079.5 | 1.85664 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 9011.29i | − 1.49639i | −0.663478 | − | 0.748196i | \(-0.730920\pi\) | ||||
0.663478 | − | 0.748196i | \(-0.269080\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 1659.96i | − 0.273168i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1796.81 | −0.293045 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4516.35 | 0.730033 | 0.365017 | − | 0.931001i | \(-0.381063\pi\) | ||||
0.365017 | + | 0.931001i | \(0.381063\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4191.88i | 0.671598i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 3505.10i | − 0.556633i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13536.4 | 2.13090 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2221.40 | 0.346656 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 3651.48i | − 0.564904i | −0.959281 | − | 0.282452i | \(-0.908852\pi\) | ||||
0.959281 | − | 0.282452i | \(-0.0911478\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 3250.36i | − 0.498532i | −0.968435 | − | 0.249266i | \(-0.919811\pi\) | ||||
0.968435 | − | 0.249266i | \(-0.0801894\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2220.54 | −0.337674 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 592.345 | 0.0893125 | 0.0446563 | − | 0.999002i | \(-0.485781\pi\) | ||||
0.0446563 | + | 0.999002i | \(0.485781\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4542.36i | 0.679108i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 9717.26i | − 1.44059i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3443.48 | 0.506239 | 0.253120 | − | 0.967435i | \(-0.418543\pi\) | ||||
0.253120 | + | 0.967435i | \(0.418543\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3736.17 | 0.544711 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 395.826i | − 0.0572327i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 1709.30i | − 0.245120i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3297.39 | −0.468998 | −0.234499 | − | 0.972116i | \(-0.575345\pi\) | ||||
−0.234499 | + | 0.972116i | \(0.575345\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2136.70 | −0.301442 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3376.35i | 0.472483i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 50.1819i | 0.00696601i | 0.999994 | + | 0.00348300i | \(0.00110868\pi\) | ||||
−0.999994 | + | 0.00348300i | \(0.998891\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3709.16 | −0.510774 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12126.7 | 1.65665 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 6769.28i | − 0.917453i | −0.888578 | − | 0.458726i | \(-0.848306\pi\) | ||||
0.888578 | − | 0.458726i | \(-0.151694\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1331.49i | 0.179040i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4208.46 | −0.561468 | −0.280734 | − | 0.959786i | \(-0.590578\pi\) | ||||
−0.280734 | + | 0.959786i | \(0.590578\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6505.88 | 0.861221 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 1798.94i | − 0.236293i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2490.47i | 0.324607i | 0.986741 | + | 0.162303i | \(0.0518923\pi\) | ||||
−0.986741 | + | 0.162303i | \(0.948108\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12765.6 | −1.65112 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4096.70 | −0.525830 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 243.190i | − 0.0309777i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7905.51i | 0.999411i | 0.866195 | + | 0.499706i | \(0.166558\pi\) | ||||
−0.866195 | + | 0.499706i | \(0.833442\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5547.71 | 0.696072 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10389.4 | −1.29382 | −0.646911 | − | 0.762566i | \(-0.723939\pi\) | ||||
−0.646911 | + | 0.762566i | \(0.723939\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 8324.81i | − 1.02900i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 459.888i | − 0.0564248i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6386.66 | −0.777826 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13448.1 | −1.62583 | −0.812917 | − | 0.582379i | \(-0.802122\pi\) | ||||
−0.812917 | + | 0.582379i | \(0.802122\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3669.17i | 0.440357i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3506.44i | 0.417773i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7021.33 | −0.830515 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6530.11 | 0.766860 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5191.34i | 0.605283i | 0.953105 | + | 0.302641i | \(0.0978684\pi\) | ||||
−0.953105 | + | 0.302641i | \(0.902132\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 5061.52i | − 0.585946i | −0.956121 | − | 0.292973i | \(-0.905355\pi\) | ||||
0.956121 | − | 0.292973i | \(-0.0946447\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3013.32 | −0.346365 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9080.00 | 1.03634 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 23753.3i | − 2.69204i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8543.49i | 0.961501i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3005.64 | 0.335909 | 0.167954 | − | 0.985795i | \(-0.446284\pi\) | ||||
0.167954 | + | 0.985795i | \(0.446284\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5895.88 | 0.654360 | 0.327180 | − | 0.944962i | \(-0.393902\pi\) | ||||
0.327180 | + | 0.944962i | \(0.393902\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2511.52i | 0.276824i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 7288.07i | − 0.797794i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11556.8 | −1.25644 | −0.628218 | − | 0.778038i | \(-0.716215\pi\) | ||||
−0.628218 | + | 0.778038i | \(0.716215\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6768.52 | −0.730863 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14007.8i | 1.50233i | 0.660117 | + | 0.751163i | \(0.270507\pi\) | ||||
−0.660117 | + | 0.751163i | \(0.729493\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 7524.53i | − 0.801566i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8627.65 | 0.912917 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3783.06 | 0.397625 | 0.198813 | − | 0.980038i | \(-0.436291\pi\) | ||||
0.198813 | + | 0.980038i | \(0.436291\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8220.94i | 0.858335i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6990.08i | 0.724994i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15451.8 | 1.59207 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1545.53 | −0.158198 | −0.0790992 | − | 0.996867i | \(-0.525204\pi\) | ||||
−0.0790992 | + | 0.996867i | \(0.525204\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2642.82i | 0.268750i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12730.2i | 1.28613i | 0.765811 | + | 0.643065i | \(0.222338\pi\) | ||||
−0.765811 | + | 0.643065i | \(0.777662\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19656.4 | 1.97303 | 0.986513 | − | 0.163682i | \(-0.0523370\pi\) | ||||
0.986513 | + | 0.163682i | \(0.0523370\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1724.12 | 0.171945 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6016.26i | 0.596144i | 0.954543 | + | 0.298072i | \(0.0963436\pi\) | ||||
−0.954543 | + | 0.298072i | \(0.903656\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 10472.6i | − 1.03108i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7341.92 | 0.718255 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6921.41 | −0.672826 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5183.89i | 0.500743i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 918.272i | − 0.0881442i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13890.6 | −1.32501 | −0.662505 | − | 0.749057i | \(-0.730507\pi\) | ||||
−0.662505 | + | 0.749057i | \(0.730507\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15168.7 | −1.43791 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12947.3i | 1.21971i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2871.54i | 0.268846i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9314.23 | 0.866669 | 0.433335 | − | 0.901233i | \(-0.357337\pi\) | ||||
0.433335 | + | 0.901233i | \(0.357337\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4310.46 | 0.398621 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 7253.34i | − 0.666677i | −0.942807 | − | 0.333339i | \(-0.891825\pi\) | ||||
0.942807 | − | 0.333339i | \(-0.108175\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 14432.9i | − 1.31851i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1769.42 | −0.160665 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −26474.8 | −2.38945 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 16208.2i | − 1.45407i | −0.686602 | − | 0.727034i | \(-0.740898\pi\) | ||||
0.686602 | − | 0.727034i | \(-0.259102\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5308.25i | 0.473363i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2182.04 | −0.193425 | −0.0967123 | − | 0.995312i | \(-0.530833\pi\) | ||||
−0.0967123 | + | 0.995312i | \(0.530833\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7278.58 | −0.641371 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13700.3i | 1.20010i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1795.97i | 0.156395i | 0.996938 | + | 0.0781974i | \(0.0249164\pi\) | ||||
−0.996938 | + | 0.0781974i | \(0.975084\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9962.51 | 0.862457 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1508.82 | −0.129856 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 917.288i | 0.0784865i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11593.7i | 0.986249i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11693.6 | −0.989000 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20946.1 | −1.76135 | −0.880676 | − | 0.473718i | \(-0.842912\pi\) | ||||
−0.880676 | + | 0.473718i | \(0.842912\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 5363.64i | − 0.448443i | −0.974538 | − | 0.224221i | \(-0.928016\pi\) | ||||
0.974538 | − | 0.224221i | \(-0.0719838\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 9209.19i | − 0.765566i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9907.96 | −0.818970 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4841.96 | 0.397958 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 953.652i | − 0.0779378i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19525.2i | 1.58674i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2735.06 | 0.221022 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12440.2 | −0.999693 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 26041.8i | 2.08108i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 3431.20i | − 0.272678i | −0.990662 | − | 0.136339i | \(-0.956466\pi\) | ||||
0.990662 | − | 0.136339i | \(-0.0435337\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3312.65 | −0.261803 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1627.42 | 0.127910 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 19449.0i | − 1.52026i | −0.649773 | − | 0.760128i | \(-0.725136\pi\) | ||||
0.649773 | − | 0.760128i | \(-0.274864\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6460.22i | 0.502214i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8239.91 | 0.637082 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1417.41 | 0.108996 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 3141.54i | − 0.240272i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 9898.44i | − 0.752981i | −0.926420 | − | 0.376491i | \(-0.877131\pi\) | ||||
0.926420 | − | 0.376491i | \(-0.122869\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16438.7 | −1.24380 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10168.2 | 0.765246 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 13809.8i | − 1.03378i | −0.856053 | − | 0.516888i | \(-0.827091\pi\) | ||||
0.856053 | − | 0.516888i | \(-0.172909\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7933.32i | 0.590721i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2680.42 | 0.198531 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −123.053 | −0.00906615 | −0.00453308 | − | 0.999990i | \(-0.501443\pi\) | ||||
−0.00453308 | + | 0.999990i | \(0.501443\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2540.72i | 0.186210i | 0.995656 | + | 0.0931049i | \(0.0296792\pi\) | ||||
−0.995656 | + | 0.0931049i | \(0.970321\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 105.206i | − 0.00767022i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12098.2 | −0.877443 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15618.2 | −1.12685 | −0.563427 | − | 0.826166i | \(-0.690517\pi\) | ||||
−0.563427 | + | 0.826166i | \(0.690517\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 1847.65i | − 0.132618i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 40923.3i | − 2.92218i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3533.04 | −0.250984 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4202.46 | −0.297009 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 1809.56i | − 0.127238i | −0.997974 | − | 0.0636188i | \(-0.979736\pi\) | ||||
0.997974 | − | 0.0636188i | \(-0.0202642\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 5656.58i | − 0.395714i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1768.91 | −0.123119 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 898.229 | 0.0622021 | 0.0311010 | − | 0.999516i | \(-0.490099\pi\) | ||||
0.0311010 | + | 0.999516i | \(0.490099\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 18390.3i | − 1.26711i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 14441.5i | − 0.990033i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22990.9 | −1.56825 | −0.784125 | − | 0.620603i | \(-0.786888\pi\) | ||||
−0.784125 | + | 0.620603i | \(0.786888\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26893.7 | −1.82532 | −0.912661 | − | 0.408717i | \(-0.865976\pi\) | ||||
−0.912661 | + | 0.408717i | \(0.865976\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2848.24i | 0.192354i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 749.118i | − 0.0503405i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6306.93 | −0.421730 | −0.210865 | − | 0.977515i | \(-0.567628\pi\) | ||||
−0.210865 | + | 0.977515i | \(0.567628\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14638.2 | −0.974008 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 27535.7i | 1.82320i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 2612.97i | − 0.172164i | −0.996288 | − | 0.0860822i | \(-0.972565\pi\) | ||||
0.996288 | − | 0.0860822i | \(-0.0274348\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4043.80 | −0.265141 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2803.88 | −0.182949 | −0.0914747 | − | 0.995807i | \(-0.529158\pi\) | ||||
−0.0914747 | + | 0.995807i | \(0.529158\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 10547.1i | − 0.684849i | −0.939545 | − | 0.342425i | \(-0.888752\pi\) | ||||
0.939545 | − | 0.342425i | \(-0.111248\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 3521.30i | − 0.227544i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 43856.2 | 2.82032 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4575.82 | 0.292852 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5805.17i | 0.369755i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18053.3i | 1.14441i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14161.4 | 0.893431 | 0.446716 | − | 0.894676i | \(-0.352594\pi\) | ||||
0.446716 | + | 0.894676i | \(0.352594\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9883.04 | 0.620562 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2519.90i | 0.157479i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 61850.8i | 3.84713i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7200.40 | 0.445764 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5622.61 | 0.346458 | 0.173229 | − | 0.984882i | \(-0.444580\pi\) | ||||
0.173229 | + | 0.984882i | \(0.444580\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 29438.7i | − 1.80552i | −0.430146 | − | 0.902759i | \(-0.641538\pi\) | ||||
0.430146 | − | 0.902759i | \(-0.358462\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 3404.57i | − 0.207837i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4607.39 | 0.279962 | 0.139981 | − | 0.990154i | \(-0.455296\pi\) | ||||
0.139981 | + | 0.990154i | \(0.455296\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3669.17 | −0.221922 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10048.9i | 0.604991i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 16634.1i | − 0.996850i | −0.866933 | − | 0.498425i | \(-0.833912\pi\) | ||||
0.866933 | − | 0.498425i | \(-0.166088\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7753.19 | −0.462507 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2709.52 | −0.160896 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 20619.9i | − 1.21887i | −0.792835 | − | 0.609437i | \(-0.791396\pi\) | ||||
0.792835 | − | 0.609437i | \(-0.208604\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 881.112i | 0.0518476i | 0.999664 | + | 0.0259238i | \(0.00825273\pi\) | ||||
−0.999664 | + | 0.0259238i | \(0.991747\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 24150.1 | 1.41465 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10499.3 | 0.612248 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19230.4i | 1.11635i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4718.35i | 0.272679i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24855.6 | 1.43002 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8943.86 | 0.512274 | 0.256137 | − | 0.966641i | \(-0.417550\pi\) | ||||
0.256137 | + | 0.966641i | \(0.417550\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2504.64i | 0.142820i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21748.7i | 1.23467i | 0.786702 | + | 0.617333i | \(0.211787\pi\) | ||||
−0.786702 | + | 0.617333i | \(0.788213\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16736.6 | −0.945937 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4477.53 | 0.251952 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7922.37i | 0.443838i | 0.975065 | + | 0.221919i | \(0.0712320\pi\) | ||||
−0.975065 | + | 0.221919i | \(0.928768\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6944.06i | 0.387327i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18489.9 | −1.02683 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8391.18 | −0.463975 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 177.517i | 0.00977288i | 0.999988 | + | 0.00488644i | \(0.00155541\pi\) | ||||
−0.999988 | + | 0.00488644i | \(0.998445\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 10312.9i | − 0.565303i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12358.5 | 0.674511 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23238.3 | 1.26286 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 7621.05i | − 0.412382i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 767.980i | 0.0413783i | 0.999786 | + | 0.0206891i | \(0.00658603\pi\) | ||||
−0.999786 | + | 0.0206891i | \(0.993414\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10306.9 | −0.552961 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5702.84 | −0.304654 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 42422.7i | − 2.25667i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 31634.2i | − 1.67566i | −0.545928 | − | 0.837832i | \(-0.683823\pi\) | ||||
0.545928 | − | 0.837832i | \(-0.316177\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −385.496 | −0.0203337 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13201.4 | 0.693401 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16168.9i | 0.845712i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 4017.76i | − 0.209269i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17351.7 | −0.900011 | −0.450005 | − | 0.893026i | \(-0.648578\pi\) | ||||
−0.450005 | + | 0.893026i | \(0.648578\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5346.35 | −0.276156 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 7628.12i | − 0.392383i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 13678.2i | − 0.700686i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16364.6 | 0.834842 | 0.417421 | − | 0.908713i | \(-0.362934\pi\) | ||||
0.417421 | + | 0.908713i | \(0.362934\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19564.9i | 0.989925i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 23552.7i | − 1.18682i | −0.804900 | − | 0.593410i | \(-0.797781\pi\) | ||||
0.804900 | − | 0.593410i | \(-0.202219\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12809.7 | −0.642849 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10958.6 | 0.547713 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3519.05i | 0.175169i | 0.996157 | + | 0.0875847i | \(0.0279149\pi\) | ||||
−0.996157 | + | 0.0875847i | \(0.972085\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13787.6i | 0.683537i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20752.4 | −1.02467 | −0.512336 | − | 0.858785i | \(-0.671220\pi\) | ||||
−0.512336 | + | 0.858785i | \(0.671220\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16328.2 | 0.802979 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11130.0i | 0.545148i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15941.1i | 0.777671i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3679.08 | 0.178764 | 0.0893818 | − | 0.995997i | \(-0.471511\pi\) | ||||
0.0893818 | + | 0.995997i | \(0.471511\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14104.3 | 0.682591 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13229.0i | 0.637687i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 527.275i | 0.0253159i | 0.999920 | + | 0.0126579i | \(0.00402926\pi\) | ||||
−0.999920 | + | 0.0126579i | \(0.995971\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13548.2 | −0.647914 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3231.54 | 0.153933 | 0.0769666 | − | 0.997034i | \(-0.475477\pi\) | ||||
0.0769666 | + | 0.997034i | \(0.475477\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9485.29i | 0.450053i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5001.65i | 0.236386i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8714.48 | −0.410250 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13681.7 | 0.641581 | 0.320791 | − | 0.947150i | \(-0.396051\pi\) | ||||
0.320791 | + | 0.947150i | \(0.396051\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2591.65i | 0.121058i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9216.63i | 0.428847i | 0.976741 | + | 0.214424i | \(0.0687873\pi\) | ||||
−0.976741 | + | 0.214424i | \(0.931213\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9389.92 | −0.435221 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 18310.2 | 0.845400 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13267.1i | 0.610196i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 27703.5i | − 1.26928i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3981.18 | 0.181706 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13894.9 | 0.631759 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33169.0i | 1.50235i | 0.660104 | + | 0.751174i | \(0.270512\pi\) | ||||
−0.660104 | + | 0.751174i | \(0.729488\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21274.1i | 0.959920i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −46238.8 | −2.07846 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 59033.6 | 2.64356 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 1737.87i | − 0.0775294i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 23781.9i | − 1.05696i | −0.848945 | − | 0.528481i | \(-0.822762\pi\) | ||||
0.848945 | − | 0.528481i | \(-0.177238\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32772.3 | 1.45106 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11927.6 | −0.526145 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10424.9i | 0.458139i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24503.3i | 1.07283i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1186.79 | 0.0517681 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29842.4 | −1.29691 | −0.648456 | − | 0.761252i | \(-0.724585\pi\) | ||||
−0.648456 | + | 0.761252i | \(0.724585\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 19074.5i | − 0.825888i | −0.910756 | − | 0.412944i | \(-0.864500\pi\) | ||||
0.910756 | − | 0.412944i | \(-0.135500\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16596.6i | 0.715952i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8157.74 | 0.350617 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11169.9 | −0.478316 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 24493.7i | − 1.04503i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7493.97i | 0.318564i | 0.987233 | + | 0.159282i | \(0.0509180\pi\) | ||||
−0.987233 | + | 0.159282i | \(0.949082\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1780.90 | 0.0754294 | 0.0377147 | − | 0.999289i | \(-0.487992\pi\) | ||||
0.0377147 | + | 0.999289i | \(0.487992\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9636.59 | 0.406670 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10860.1i | 0.456640i | 0.973586 | + | 0.228320i | \(0.0733232\pi\) | ||||
−0.973586 | + | 0.228320i | \(0.926677\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 34105.1i | − 1.42885i | −0.699711 | − | 0.714426i | \(-0.746688\pi\) | ||||
0.699711 | − | 0.714426i | \(-0.253312\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11490.9 | 0.479682 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 73613.1 | 3.06188 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10046.1i | 0.416358i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 2733.03i | − 0.112864i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32688.9 | 1.34511 | 0.672555 | − | 0.740047i | \(-0.265197\pi\) | ||||
0.672555 | + | 0.740047i | \(0.265197\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2647.12 | 0.108537 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 15849.5i | − 0.647552i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25928.4i | 1.05558i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4366.18 | 0.177124 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13919.3 | 0.562672 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 24054.3i | − 0.968943i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 17391.2i | − 0.698080i | −0.937108 | − | 0.349040i | \(-0.886508\pi\) | ||||
0.937108 | − | 0.349040i | \(-0.113492\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2855.51 | −0.114218 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4182.34 | −0.166705 | −0.0833525 | − | 0.996520i | \(-0.526563\pi\) | ||||
−0.0833525 | + | 0.996520i | \(0.526563\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20585.0i | 0.817639i | 0.912615 | + | 0.408820i | \(0.134059\pi\) | ||||
−0.912615 | + | 0.408820i | \(0.865941\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 23569.0i | − 0.932903i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14159.7 | 0.558518 | 0.279259 | − | 0.960216i | \(-0.409911\pi\) | ||||
0.279259 | + | 0.960216i | \(0.409911\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22130.6 | −0.869900 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 14003.8i | − 0.548552i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1483.19i | 0.0578986i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26027.2 | 1.01251 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4551.88 | 0.176469 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 40914.1i | − 1.58074i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 5156.38i | − 0.198539i | −0.995061 | − | 0.0992695i | \(-0.968349\pi\) | ||||
0.995061 | − | 0.0992695i | \(-0.0316506\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18066.4 | 0.693246 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 841.065 | 0.0321637 | 0.0160818 | − | 0.999871i | \(-0.494881\pi\) | ||||
0.0160818 | + | 0.999871i | \(0.494881\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 7845.99i | − 0.299024i | −0.988760 | − | 0.149512i | \(-0.952230\pi\) | ||||
0.988760 | − | 0.149512i | \(-0.0477703\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 1804.83i | − 0.0685521i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 38781.9 | 1.46806 | 0.734029 | − | 0.679118i | \(-0.237637\pi\) | ||||
0.734029 | + | 0.679118i | \(0.237637\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14687.1 | −0.554092 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2804.82i | 0.105460i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18710.1i | 0.701131i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23543.7 | −0.879305 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −32177.6 | −1.19775 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14925.5i | 0.553719i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9986.95i | 0.369271i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 19843.3 | 0.731278 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6269.33 | −0.230276 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36431.2i | 1.33371i | 0.745187 | + | 0.666856i | \(0.232360\pi\) | ||||
−0.745187 | + | 0.666856i | \(0.767640\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11537.8i | 0.420994i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51077.9 | −1.85762 | −0.928808 | − | 0.370562i | \(-0.879165\pi\) | ||||
−0.928808 | + | 0.370562i | \(0.879165\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42822.6 | 1.55227 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12226.3i | 0.441735i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 45188.9i | − 1.62734i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37080.1 | −1.33097 | −0.665484 | − | 0.746412i | \(-0.731775\pi\) | ||||
−0.665484 | + | 0.746412i | \(0.731775\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8996.46 | −0.321871 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 65797.3i | − 2.34642i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17109.4i | 0.608167i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1454.06 | 0.0515183 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38259.5 | 1.35119 | 0.675595 | − | 0.737273i | \(-0.263887\pi\) | ||||
0.675595 | + | 0.737273i | \(0.263887\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 42026.7i | 1.47945i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 7211.92i | − 0.253063i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19243.8 | 0.673091 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4413.55 | 0.153879 | 0.0769394 | − | 0.997036i | \(-0.475485\pi\) | ||||
0.0769394 | + | 0.997036i | \(0.475485\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 17537.3i | − 0.609486i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31511.2i | 1.09164i | 0.837902 | + | 0.545821i | \(0.183782\pi\) | ||||
−0.837902 | + | 0.545821i | \(0.816218\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30962.8 | −1.06923 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5072.82 | 0.174623 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 23561.3i | − 0.808490i | −0.914651 | − | 0.404245i | \(-0.867534\pi\) | ||||
0.914651 | − | 0.404245i | \(-0.132466\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24759.6i | 0.846925i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26752.1 | −0.912195 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35039.7 | 1.19103 | 0.595513 | − | 0.803346i | \(-0.296949\pi\) | ||||
0.595513 | + | 0.803346i | \(0.296949\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 199.107i | − 0.00674653i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 15317.6i | − 0.517395i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −40473.0 | −1.36282 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19544.9 | −0.656066 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 4335.53i | − 0.145078i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 3496.76i | − 0.116647i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7975.38 | 0.265223 | 0.132612 | − | 0.991168i | \(-0.457664\pi\) | ||||
0.132612 | + | 0.991168i | \(0.457664\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16409.6 | 0.544018 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21386.8i | 0.706834i | 0.935466 | + | 0.353417i | \(0.114980\pi\) | ||||
−0.935466 | + | 0.353417i | \(0.885020\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 72030.7i | 2.37328i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 22887.4 | 0.751779 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −40142.3 | −1.31450 | −0.657250 | − | 0.753673i | \(-0.728280\pi\) | ||||
−0.657250 | + | 0.753673i | \(0.728280\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45891.5i | 1.49816i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 2579.73i | − 0.0839597i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9205.44 | −0.298686 | −0.149343 | − | 0.988785i | \(-0.547716\pi\) | ||||
−0.149343 | + | 0.988785i | \(0.547716\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3347.75 | −0.108292 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 33238.6i | − 1.07193i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 26068.3i | − 0.838144i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22082.2 | 0.707834 | 0.353917 | − | 0.935277i | \(-0.384850\pi\) | ||||
0.353917 | + | 0.935277i | \(0.384850\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27033.9 | −0.863942 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 27331.1i | − 0.870808i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7207.66i | 0.228956i | 0.993426 | + | 0.114478i | \(0.0365195\pi\) | ||||
−0.993426 | + | 0.114478i | \(0.963480\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4979.87 | −0.157714 |
(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 | 384.4.d.f.193.2 | ✓ | 8 | |
3.2 | odd | 2 | 1152.4.d.p.577.6 | 8 | |||
4.3 | odd | 2 | inner | 384.4.d.f.193.6 | yes | 8 | |
8.3 | odd | 2 | inner | 384.4.d.f.193.3 | yes | 8 | |
8.5 | even | 2 | inner | 384.4.d.f.193.7 | yes | 8 | |
12.11 | even | 2 | 1152.4.d.p.577.5 | 8 | |||
16.3 | odd | 4 | 768.4.a.u.1.2 | 4 | |||
16.5 | even | 4 | 768.4.a.u.1.3 | 4 | |||
16.11 | odd | 4 | 768.4.a.v.1.3 | 4 | |||
16.13 | even | 4 | 768.4.a.v.1.2 | 4 | |||
24.5 | odd | 2 | 1152.4.d.p.577.4 | 8 | |||
24.11 | even | 2 | 1152.4.d.p.577.3 | 8 | |||
48.5 | odd | 4 | 2304.4.a.cb.1.2 | 4 | |||
48.11 | even | 4 | 2304.4.a.by.1.2 | 4 | |||
48.29 | odd | 4 | 2304.4.a.by.1.3 | 4 | |||
48.35 | even | 4 | 2304.4.a.cb.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.d.f.193.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
384.4.d.f.193.3 | yes | 8 | 8.3 | odd | 2 | inner | |
384.4.d.f.193.6 | yes | 8 | 4.3 | odd | 2 | inner | |
384.4.d.f.193.7 | yes | 8 | 8.5 | even | 2 | inner | |
768.4.a.u.1.2 | 4 | 16.3 | odd | 4 | |||
768.4.a.u.1.3 | 4 | 16.5 | even | 4 | |||
768.4.a.v.1.2 | 4 | 16.13 | even | 4 | |||
768.4.a.v.1.3 | 4 | 16.11 | odd | 4 | |||
1152.4.d.p.577.3 | 8 | 24.11 | even | 2 | |||
1152.4.d.p.577.4 | 8 | 24.5 | odd | 2 | |||
1152.4.d.p.577.5 | 8 | 12.11 | even | 2 | |||
1152.4.d.p.577.6 | 8 | 3.2 | odd | 2 | |||
2304.4.a.by.1.2 | 4 | 48.11 | even | 4 | |||
2304.4.a.by.1.3 | 4 | 48.29 | odd | 4 | |||
2304.4.a.cb.1.2 | 4 | 48.5 | odd | 4 | |||
2304.4.a.cb.1.3 | 4 | 48.35 | even | 4 |