Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,4,Mod(599,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1150.599");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.b (of order \(2\), degree \(1\), 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: | \(67.8521965066\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 136x^{6} + 5308x^{4} + 58833x^{2} + 116964 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 599.5 | ||
Root | \(-6.57209i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.599 |
Dual form | 1150.4.b.n.599.4 |
$q$-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 \(\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000i | 0.707107i | ||||||||
\(3\) | − 7.57209i | − 1.45725i | −0.684914 | − | 0.728624i | \(-0.740160\pi\) | ||||
0.684914 | − | 0.728624i | \(-0.259840\pi\) | |||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 15.1442 | 1.03043 | ||||||||
\(7\) | 35.4229i | 1.91266i | 0.292294 | + | 0.956328i | \(0.405581\pi\) | ||||
−0.292294 | + | 0.956328i | \(0.594419\pi\) | |||||||
\(8\) | − 8.00000i | − 0.353553i | ||||||||
\(9\) | −30.3365 | −1.12357 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −16.6298 | −0.455826 | −0.227913 | − | 0.973682i | \(-0.573190\pi\) | ||||
−0.227913 | + | 0.973682i | \(0.573190\pi\) | |||||||
\(12\) | 30.2883i | 0.728624i | ||||||||
\(13\) | − 79.9132i | − 1.70492i | −0.522795 | − | 0.852459i | \(-0.675111\pi\) | ||||
0.522795 | − | 0.852459i | \(-0.324889\pi\) | |||||||
\(14\) | −70.8458 | −1.35245 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 46.8219i | 0.667999i | 0.942573 | + | 0.333999i | \(0.108398\pi\) | ||||
−0.942573 | + | 0.333999i | \(0.891602\pi\) | |||||||
\(18\) | − 60.6730i | − 0.794486i | ||||||||
\(19\) | 110.653 | 1.33608 | 0.668042 | − | 0.744123i | \(-0.267132\pi\) | ||||
0.668042 | + | 0.744123i | \(0.267132\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 268.225 | 2.78722 | ||||||||
\(22\) | − 33.2597i | − 0.322318i | ||||||||
\(23\) | − 23.0000i | − 0.208514i | ||||||||
\(24\) | −60.5767 | −0.515215 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 159.826 | 1.20556 | ||||||||
\(27\) | 25.2641i | 0.180077i | ||||||||
\(28\) | − 141.692i | − 0.956328i | ||||||||
\(29\) | 0.836422 | 0.00535585 | 0.00267793 | − | 0.999996i | \(-0.499148\pi\) | ||||
0.00267793 | + | 0.999996i | \(0.499148\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −119.836 | −0.694295 | −0.347147 | − | 0.937811i | \(-0.612850\pi\) | ||||
−0.347147 | + | 0.937811i | \(0.612850\pi\) | |||||||
\(32\) | 32.0000i | 0.176777i | ||||||||
\(33\) | 125.923i | 0.664252i | ||||||||
\(34\) | −93.6438 | −0.472346 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 121.346 | 0.561787 | ||||||||
\(37\) | − 368.201i | − 1.63600i | −0.575221 | − | 0.817998i | \(-0.695084\pi\) | ||||
0.575221 | − | 0.817998i | \(-0.304916\pi\) | |||||||
\(38\) | 221.307i | 0.944755i | ||||||||
\(39\) | −605.109 | −2.48449 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −95.7927 | −0.364886 | −0.182443 | − | 0.983216i | \(-0.558400\pi\) | ||||
−0.182443 | + | 0.983216i | \(0.558400\pi\) | |||||||
\(42\) | 536.450i | 1.97086i | ||||||||
\(43\) | 331.961i | 1.17729i | 0.808390 | + | 0.588647i | \(0.200339\pi\) | ||||
−0.808390 | + | 0.588647i | \(0.799661\pi\) | |||||||
\(44\) | 66.5193 | 0.227913 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | 535.037i | 1.66049i | 0.557397 | + | 0.830246i | \(0.311800\pi\) | ||||
−0.557397 | + | 0.830246i | \(0.688200\pi\) | |||||||
\(48\) | − 121.153i | − 0.364312i | ||||||||
\(49\) | −911.782 | −2.65826 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 354.539 | 0.973440 | ||||||||
\(52\) | 319.653i | 0.852459i | ||||||||
\(53\) | 409.345i | 1.06090i | 0.847715 | + | 0.530452i | \(0.177978\pi\) | ||||
−0.847715 | + | 0.530452i | \(0.822022\pi\) | |||||||
\(54\) | −50.5282 | −0.127334 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 283.383 | 0.676226 | ||||||||
\(57\) | − 837.876i | − 1.94701i | ||||||||
\(58\) | 1.67284i | 0.00378716i | ||||||||
\(59\) | 352.950 | 0.778817 | 0.389408 | − | 0.921065i | \(-0.372679\pi\) | ||||
0.389408 | + | 0.921065i | \(0.372679\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −507.223 | −1.06464 | −0.532322 | − | 0.846542i | \(-0.678680\pi\) | ||||
−0.532322 | + | 0.846542i | \(0.678680\pi\) | |||||||
\(62\) | − 239.672i | − 0.490941i | ||||||||
\(63\) | − 1074.61i | − 2.14901i | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −251.845 | −0.469697 | ||||||||
\(67\) | 820.056i | 1.49531i | 0.664087 | + | 0.747655i | \(0.268820\pi\) | ||||
−0.664087 | + | 0.747655i | \(0.731180\pi\) | |||||||
\(68\) | − 187.288i | − 0.333999i | ||||||||
\(69\) | −174.158 | −0.303857 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −733.770 | −1.22651 | −0.613257 | − | 0.789884i | \(-0.710141\pi\) | ||||
−0.613257 | + | 0.789884i | \(0.710141\pi\) | |||||||
\(72\) | 242.692i | 0.397243i | ||||||||
\(73\) | − 91.4599i | − 0.146638i | −0.997309 | − | 0.0733190i | \(-0.976641\pi\) | ||||
0.997309 | − | 0.0733190i | \(-0.0233591\pi\) | |||||||
\(74\) | 736.402 | 1.15682 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −442.613 | −0.668042 | ||||||||
\(77\) | − 589.077i | − 0.871838i | ||||||||
\(78\) | − 1210.22i | − 1.75680i | ||||||||
\(79\) | −329.381 | −0.469092 | −0.234546 | − | 0.972105i | \(-0.575360\pi\) | ||||
−0.234546 | + | 0.972105i | \(0.575360\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −627.783 | −0.861156 | ||||||||
\(82\) | − 191.585i | − 0.258013i | ||||||||
\(83\) | − 753.834i | − 0.996916i | −0.866914 | − | 0.498458i | \(-0.833900\pi\) | ||||
0.866914 | − | 0.498458i | \(-0.166100\pi\) | |||||||
\(84\) | −1072.90 | −1.39361 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −663.922 | −0.832472 | ||||||||
\(87\) | − 6.33346i | − 0.00780481i | ||||||||
\(88\) | 133.039i | 0.161159i | ||||||||
\(89\) | 1050.14 | 1.25073 | 0.625365 | − | 0.780332i | \(-0.284950\pi\) | ||||
0.625365 | + | 0.780332i | \(0.284950\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2830.76 | 3.26092 | ||||||||
\(92\) | 92.0000i | 0.104257i | ||||||||
\(93\) | 907.407i | 1.01176i | ||||||||
\(94\) | −1070.07 | −1.17415 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 242.307 | 0.257608 | ||||||||
\(97\) | 271.928i | 0.284641i | 0.989821 | + | 0.142320i | \(0.0454563\pi\) | ||||
−0.989821 | + | 0.142320i | \(0.954544\pi\) | |||||||
\(98\) | − 1823.56i | − 1.87967i | ||||||||
\(99\) | 504.491 | 0.512154 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1658.68 | 1.63410 | 0.817052 | − | 0.576563i | \(-0.195607\pi\) | ||||
0.817052 | + | 0.576563i | \(0.195607\pi\) | |||||||
\(102\) | 709.079i | 0.688326i | ||||||||
\(103\) | 1735.52i | 1.66025i | 0.557580 | + | 0.830123i | \(0.311730\pi\) | ||||
−0.557580 | + | 0.830123i | \(0.688270\pi\) | |||||||
\(104\) | −639.305 | −0.602779 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −818.691 | −0.750172 | ||||||||
\(107\) | 1629.88i | 1.47258i | 0.676664 | + | 0.736292i | \(0.263425\pi\) | ||||
−0.676664 | + | 0.736292i | \(0.736575\pi\) | |||||||
\(108\) | − 101.056i | − 0.0900385i | ||||||||
\(109\) | 432.151 | 0.379748 | 0.189874 | − | 0.981808i | \(-0.439192\pi\) | ||||
0.189874 | + | 0.981808i | \(0.439192\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2788.05 | −2.38405 | ||||||||
\(112\) | 566.766i | 0.478164i | ||||||||
\(113\) | − 240.115i | − 0.199895i | −0.994993 | − | 0.0999476i | \(-0.968132\pi\) | ||||
0.994993 | − | 0.0999476i | \(-0.0318675\pi\) | |||||||
\(114\) | 1675.75 | 1.37674 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.34569 | −0.00267793 | ||||||||
\(117\) | 2424.28i | 1.91560i | ||||||||
\(118\) | 705.900i | 0.550707i | ||||||||
\(119\) | −1658.57 | −1.27765 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1054.45 | −0.792223 | ||||||||
\(122\) | − 1014.45i | − 0.752817i | ||||||||
\(123\) | 725.350i | 0.531729i | ||||||||
\(124\) | 479.343 | 0.347147 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2149.21 | 1.51958 | ||||||||
\(127\) | 210.993i | 0.147422i | 0.997280 | + | 0.0737110i | \(0.0234842\pi\) | ||||
−0.997280 | + | 0.0737110i | \(0.976516\pi\) | |||||||
\(128\) | − 128.000i | − 0.0883883i | ||||||||
\(129\) | 2513.64 | 1.71561 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −746.178 | −0.497663 | −0.248832 | − | 0.968547i | \(-0.580047\pi\) | ||||
−0.248832 | + | 0.968547i | \(0.580047\pi\) | |||||||
\(132\) | − 503.690i | − 0.332126i | ||||||||
\(133\) | 3919.66i | 2.55547i | ||||||||
\(134\) | −1640.11 | −1.05734 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 374.575 | 0.236173 | ||||||||
\(137\) | 2420.07i | 1.50920i | 0.656184 | + | 0.754601i | \(0.272170\pi\) | ||||
−0.656184 | + | 0.754601i | \(0.727830\pi\) | |||||||
\(138\) | − 348.316i | − 0.214860i | ||||||||
\(139\) | −924.030 | −0.563850 | −0.281925 | − | 0.959436i | \(-0.590973\pi\) | ||||
−0.281925 | + | 0.959436i | \(0.590973\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4051.34 | 2.41975 | ||||||||
\(142\) | − 1467.54i | − 0.867276i | ||||||||
\(143\) | 1328.94i | 0.777145i | ||||||||
\(144\) | −485.384 | −0.280893 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 182.920 | 0.103689 | ||||||||
\(147\) | 6904.09i | 3.87374i | ||||||||
\(148\) | 1472.80i | 0.817998i | ||||||||
\(149\) | −430.614 | −0.236760 | −0.118380 | − | 0.992968i | \(-0.537770\pi\) | ||||
−0.118380 | + | 0.992968i | \(0.537770\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −25.4118 | −0.0136953 | −0.00684763 | − | 0.999977i | \(-0.502180\pi\) | ||||
−0.00684763 | + | 0.999977i | \(0.502180\pi\) | |||||||
\(152\) | − 885.226i | − 0.472377i | ||||||||
\(153\) | − 1420.41i | − 0.750546i | ||||||||
\(154\) | 1178.15 | 0.616483 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2420.44 | 1.24224 | ||||||||
\(157\) | 1580.29i | 0.803317i | 0.915790 | + | 0.401658i | \(0.131566\pi\) | ||||
−0.915790 | + | 0.401658i | \(0.868434\pi\) | |||||||
\(158\) | − 658.762i | − 0.331698i | ||||||||
\(159\) | 3099.60 | 1.54600 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 814.727 | 0.398817 | ||||||||
\(162\) | − 1255.57i | − 0.608930i | ||||||||
\(163\) | 458.739i | 0.220437i | 0.993907 | + | 0.110218i | \(0.0351550\pi\) | ||||
−0.993907 | + | 0.110218i | \(0.964845\pi\) | |||||||
\(164\) | 383.171 | 0.182443 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1507.67 | 0.704926 | ||||||||
\(167\) | 561.275i | 0.260076i | 0.991509 | + | 0.130038i | \(0.0415100\pi\) | ||||
−0.991509 | + | 0.130038i | \(0.958490\pi\) | |||||||
\(168\) | − 2145.80i | − 0.985430i | ||||||||
\(169\) | −4189.11 | −1.90674 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3356.83 | −1.50119 | ||||||||
\(172\) | − 1327.84i | − 0.588647i | ||||||||
\(173\) | 1573.95i | 0.691705i | 0.938289 | + | 0.345852i | \(0.112410\pi\) | ||||
−0.938289 | + | 0.345852i | \(0.887590\pi\) | |||||||
\(174\) | 12.6669 | 0.00551883 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −266.077 | −0.113956 | ||||||||
\(177\) | − 2672.57i | − 1.13493i | ||||||||
\(178\) | 2100.29i | 0.884400i | ||||||||
\(179\) | −2215.59 | −0.925145 | −0.462572 | − | 0.886581i | \(-0.653073\pi\) | ||||
−0.462572 | + | 0.886581i | \(0.653073\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 873.497 | 0.358710 | 0.179355 | − | 0.983784i | \(-0.442599\pi\) | ||||
0.179355 | + | 0.983784i | \(0.442599\pi\) | |||||||
\(182\) | 5661.51i | 2.30582i | ||||||||
\(183\) | 3840.74i | 1.55145i | ||||||||
\(184\) | −184.000 | −0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1814.81 | −0.715422 | ||||||||
\(187\) | − 778.641i | − 0.304491i | ||||||||
\(188\) | − 2140.15i | − 0.830246i | ||||||||
\(189\) | −894.928 | −0.344425 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2497.74 | −0.946230 | −0.473115 | − | 0.881001i | \(-0.656870\pi\) | ||||
−0.473115 | + | 0.881001i | \(0.656870\pi\) | |||||||
\(192\) | 484.613i | 0.182156i | ||||||||
\(193\) | 909.155i | 0.339080i | 0.985523 | + | 0.169540i | \(0.0542282\pi\) | ||||
−0.985523 | + | 0.169540i | \(0.945772\pi\) | |||||||
\(194\) | −543.857 | −0.201271 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3647.13 | 1.32913 | ||||||||
\(197\) | − 608.627i | − 0.220116i | −0.993925 | − | 0.110058i | \(-0.964896\pi\) | ||||
0.993925 | − | 0.110058i | \(-0.0351037\pi\) | |||||||
\(198\) | 1008.98i | 0.362147i | ||||||||
\(199\) | 2304.98 | 0.821083 | 0.410542 | − | 0.911842i | \(-0.365340\pi\) | ||||
0.410542 | + | 0.911842i | \(0.365340\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6209.54 | 2.17904 | ||||||||
\(202\) | 3317.36i | 1.15549i | ||||||||
\(203\) | 29.6285i | 0.0102439i | ||||||||
\(204\) | −1418.16 | −0.486720 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3471.03 | −1.17397 | ||||||||
\(207\) | 697.739i | 0.234281i | ||||||||
\(208\) | − 1278.61i | − 0.426229i | ||||||||
\(209\) | −1840.15 | −0.609022 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4373.37 | −1.42690 | −0.713448 | − | 0.700708i | \(-0.752868\pi\) | ||||
−0.713448 | + | 0.700708i | \(0.752868\pi\) | |||||||
\(212\) | − 1637.38i | − 0.530452i | ||||||||
\(213\) | 5556.17i | 1.78733i | ||||||||
\(214\) | −3259.76 | −1.04127 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 202.113 | 0.0636668 | ||||||||
\(217\) | − 4244.93i | − 1.32795i | ||||||||
\(218\) | 864.303i | 0.268523i | ||||||||
\(219\) | −692.542 | −0.213688 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3741.69 | 1.13888 | ||||||||
\(222\) | − 5576.10i | − 1.68578i | ||||||||
\(223\) | 5439.50i | 1.63343i | 0.577038 | + | 0.816717i | \(0.304208\pi\) | ||||
−0.577038 | + | 0.816717i | \(0.695792\pi\) | |||||||
\(224\) | −1133.53 | −0.338113 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 480.231 | 0.141347 | ||||||||
\(227\) | − 216.498i | − 0.0633017i | −0.999499 | − | 0.0316508i | \(-0.989924\pi\) | ||||
0.999499 | − | 0.0316508i | \(-0.0100765\pi\) | |||||||
\(228\) | 3351.51i | 0.973504i | ||||||||
\(229\) | 924.664 | 0.266828 | 0.133414 | − | 0.991060i | \(-0.457406\pi\) | ||||
0.133414 | + | 0.991060i | \(0.457406\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4460.54 | −1.27049 | ||||||||
\(232\) | − 6.69138i | − 0.00189358i | ||||||||
\(233\) | − 2369.69i | − 0.666280i | −0.942877 | − | 0.333140i | \(-0.891892\pi\) | ||||
0.942877 | − | 0.333140i | \(-0.108108\pi\) | |||||||
\(234\) | −4848.57 | −1.35453 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1411.80 | −0.389408 | ||||||||
\(237\) | 2494.10i | 0.683584i | ||||||||
\(238\) | − 3317.14i | − 0.903437i | ||||||||
\(239\) | 2769.60 | 0.749583 | 0.374791 | − | 0.927109i | \(-0.377714\pi\) | ||||
0.374791 | + | 0.927109i | \(0.377714\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5334.10 | −1.42572 | −0.712862 | − | 0.701305i | \(-0.752601\pi\) | ||||
−0.712862 | + | 0.701305i | \(0.752601\pi\) | |||||||
\(242\) | − 2108.90i | − 0.560186i | ||||||||
\(243\) | 5435.76i | 1.43500i | ||||||||
\(244\) | 2028.89 | 0.532322 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1450.70 | −0.375989 | ||||||||
\(247\) | − 8842.66i | − 2.27791i | ||||||||
\(248\) | 958.686i | 0.245470i | ||||||||
\(249\) | −5708.10 | −1.45275 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4677.13 | 1.17617 | 0.588084 | − | 0.808800i | \(-0.299882\pi\) | ||||
0.588084 | + | 0.808800i | \(0.299882\pi\) | |||||||
\(252\) | 4298.42i | 1.07451i | ||||||||
\(253\) | 382.486i | 0.0950463i | ||||||||
\(254\) | −421.986 | −0.104243 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 2602.99i | 0.631789i | 0.948794 | + | 0.315895i | \(0.102305\pi\) | ||||
−0.948794 | + | 0.315895i | \(0.897695\pi\) | |||||||
\(258\) | 5027.28i | 1.21312i | ||||||||
\(259\) | 13042.7 | 3.12910 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −25.3741 | −0.00601769 | ||||||||
\(262\) | − 1492.36i | − 0.351901i | ||||||||
\(263\) | − 3411.30i | − 0.799809i | −0.916557 | − | 0.399904i | \(-0.869043\pi\) | ||||
0.916557 | − | 0.399904i | \(-0.130957\pi\) | |||||||
\(264\) | 1007.38 | 0.234848 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7839.32 | −1.80699 | ||||||||
\(267\) | − 7951.77i | − 1.82262i | ||||||||
\(268\) | − 3280.22i | − 0.747655i | ||||||||
\(269\) | −4366.56 | −0.989718 | −0.494859 | − | 0.868973i | \(-0.664780\pi\) | ||||
−0.494859 | + | 0.868973i | \(0.664780\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5682.45 | 1.27374 | 0.636872 | − | 0.770970i | \(-0.280228\pi\) | ||||
0.636872 | + | 0.770970i | \(0.280228\pi\) | |||||||
\(272\) | 749.150i | 0.167000i | ||||||||
\(273\) | − 21434.7i | − 4.75197i | ||||||||
\(274\) | −4840.14 | −1.06717 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 696.632 | 0.151929 | ||||||||
\(277\) | 1884.62i | 0.408794i | 0.978888 | + | 0.204397i | \(0.0655234\pi\) | ||||
−0.978888 | + | 0.204397i | \(0.934477\pi\) | |||||||
\(278\) | − 1848.06i | − 0.398702i | ||||||||
\(279\) | 3635.39 | 0.780091 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2706.42 | −0.574561 | −0.287281 | − | 0.957846i | \(-0.592751\pi\) | ||||
−0.287281 | + | 0.957846i | \(0.592751\pi\) | |||||||
\(282\) | 8102.69i | 1.71102i | ||||||||
\(283\) | − 5963.64i | − 1.25266i | −0.779560 | − | 0.626328i | \(-0.784557\pi\) | ||||
0.779560 | − | 0.626328i | \(-0.215443\pi\) | |||||||
\(284\) | 2935.08 | 0.613257 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2657.89 | −0.549525 | ||||||||
\(287\) | − 3393.26i | − 0.697901i | ||||||||
\(288\) | − 970.767i | − 0.198622i | ||||||||
\(289\) | 2720.71 | 0.553778 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2059.06 | 0.414792 | ||||||||
\(292\) | 365.840i | 0.0733190i | ||||||||
\(293\) | − 4735.85i | − 0.944272i | −0.881526 | − | 0.472136i | \(-0.843483\pi\) | ||||
0.881526 | − | 0.472136i | \(-0.156517\pi\) | |||||||
\(294\) | −13808.2 | −2.73915 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2945.61 | −0.578412 | ||||||||
\(297\) | − 420.138i | − 0.0820837i | ||||||||
\(298\) | − 861.227i | − 0.167415i | ||||||||
\(299\) | −1838.00 | −0.355500 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11759.0 | −2.25176 | ||||||||
\(302\) | − 50.8236i | − 0.00968401i | ||||||||
\(303\) | − 12559.6i | − 2.38130i | ||||||||
\(304\) | 1770.45 | 0.334021 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2840.82 | 0.530716 | ||||||||
\(307\) | 769.241i | 0.143006i | 0.997440 | + | 0.0715031i | \(0.0227796\pi\) | ||||
−0.997440 | + | 0.0715031i | \(0.977220\pi\) | |||||||
\(308\) | 2356.31i | 0.435919i | ||||||||
\(309\) | 13141.5 | 2.41939 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5592.71 | −1.01972 | −0.509861 | − | 0.860257i | \(-0.670303\pi\) | ||||
−0.509861 | + | 0.860257i | \(0.670303\pi\) | |||||||
\(312\) | 4840.87i | 0.878399i | ||||||||
\(313\) | 9777.19i | 1.76562i | 0.469729 | + | 0.882811i | \(0.344352\pi\) | ||||
−0.469729 | + | 0.882811i | \(0.655648\pi\) | |||||||
\(314\) | −3160.58 | −0.568031 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1317.52 | 0.234546 | ||||||||
\(317\) | − 1868.51i | − 0.331060i | −0.986205 | − | 0.165530i | \(-0.947066\pi\) | ||||
0.986205 | − | 0.165530i | \(-0.0529335\pi\) | |||||||
\(318\) | 6199.20i | 1.09319i | ||||||||
\(319\) | −13.9096 | −0.00244134 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12341.6 | 2.14592 | ||||||||
\(322\) | 1629.45i | 0.282006i | ||||||||
\(323\) | 5181.00i | 0.892503i | ||||||||
\(324\) | 2511.13 | 0.430578 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −917.477 | −0.155872 | ||||||||
\(327\) | − 3272.29i | − 0.553388i | ||||||||
\(328\) | 766.342i | 0.129007i | ||||||||
\(329\) | −18952.6 | −3.17595 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6966.91 | 1.15691 | 0.578454 | − | 0.815715i | \(-0.303656\pi\) | ||||
0.578454 | + | 0.815715i | \(0.303656\pi\) | |||||||
\(332\) | 3015.34i | 0.498458i | ||||||||
\(333\) | 11169.9i | 1.83816i | ||||||||
\(334\) | −1122.55 | −0.183902 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4291.60 | 0.696804 | ||||||||
\(337\) | 17.5487i | 0.00283661i | 0.999999 | + | 0.00141830i | \(0.000451460\pi\) | ||||
−0.999999 | + | 0.00141830i | \(0.999549\pi\) | |||||||
\(338\) | − 8378.23i | − 1.34827i | ||||||||
\(339\) | −1818.17 | −0.291297 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1992.85 | 0.316477 | ||||||||
\(342\) | − 6713.66i | − 1.06150i | ||||||||
\(343\) | − 20147.9i | − 3.17167i | ||||||||
\(344\) | 2655.69 | 0.416236 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3147.89 | −0.489109 | ||||||||
\(347\) | 9859.30i | 1.52529i | 0.646818 | + | 0.762644i | \(0.276099\pi\) | ||||
−0.646818 | + | 0.762644i | \(0.723901\pi\) | |||||||
\(348\) | 25.3338i | 0.00390240i | ||||||||
\(349\) | −7200.25 | −1.10436 | −0.552178 | − | 0.833726i | \(-0.686203\pi\) | ||||
−0.552178 | + | 0.833726i | \(0.686203\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2018.93 | 0.307016 | ||||||||
\(352\) | − 532.155i | − 0.0805794i | ||||||||
\(353\) | − 6054.58i | − 0.912897i | −0.889750 | − | 0.456449i | \(-0.849121\pi\) | ||||
0.889750 | − | 0.456449i | \(-0.150879\pi\) | |||||||
\(354\) | 5345.14 | 0.802516 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4200.57 | −0.625365 | ||||||||
\(357\) | 12558.8i | 1.86186i | ||||||||
\(358\) | − 4431.18i | − 0.654176i | ||||||||
\(359\) | −2734.26 | −0.401974 | −0.200987 | − | 0.979594i | \(-0.564415\pi\) | ||||
−0.200987 | + | 0.979594i | \(0.564415\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5385.16 | 0.785123 | ||||||||
\(362\) | 1746.99i | 0.253646i | ||||||||
\(363\) | 7984.37i | 1.15447i | ||||||||
\(364\) | −11323.0 | −1.63046 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7681.47 | −1.09704 | ||||||||
\(367\) | 2465.50i | 0.350676i | 0.984508 | + | 0.175338i | \(0.0561018\pi\) | ||||
−0.984508 | + | 0.175338i | \(0.943898\pi\) | |||||||
\(368\) | − 368.000i | − 0.0521286i | ||||||||
\(369\) | 2906.01 | 0.409976 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14500.2 | −2.02915 | ||||||||
\(372\) | − 3629.63i | − 0.505880i | ||||||||
\(373\) | 5704.45i | 0.791863i | 0.918280 | + | 0.395932i | \(0.129578\pi\) | ||||
−0.918280 | + | 0.395932i | \(0.870422\pi\) | |||||||
\(374\) | 1557.28 | 0.215308 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4280.29 | 0.587073 | ||||||||
\(377\) | − 66.8411i | − 0.00913128i | ||||||||
\(378\) | − 1789.86i | − 0.243546i | ||||||||
\(379\) | −10231.9 | −1.38675 | −0.693376 | − | 0.720576i | \(-0.743878\pi\) | ||||
−0.693376 | + | 0.720576i | \(0.743878\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1597.66 | 0.214830 | ||||||||
\(382\) | − 4995.47i | − 0.669086i | ||||||||
\(383\) | 6321.34i | 0.843356i | 0.906746 | + | 0.421678i | \(0.138559\pi\) | ||||
−0.906746 | + | 0.421678i | \(0.861441\pi\) | |||||||
\(384\) | −969.227 | −0.128804 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1818.31 | −0.239766 | ||||||||
\(387\) | − 10070.5i | − 1.32278i | ||||||||
\(388\) | − 1087.71i | − 0.142320i | ||||||||
\(389\) | 925.594 | 0.120641 | 0.0603207 | − | 0.998179i | \(-0.480788\pi\) | ||||
0.0603207 | + | 0.998179i | \(0.480788\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1076.90 | 0.139287 | ||||||||
\(392\) | 7294.25i | 0.939835i | ||||||||
\(393\) | 5650.13i | 0.725219i | ||||||||
\(394\) | 1217.25 | 0.155646 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2017.96 | −0.256077 | ||||||||
\(397\) | 2706.75i | 0.342187i | 0.985255 | + | 0.171093i | \(0.0547299\pi\) | ||||
−0.985255 | + | 0.171093i | \(0.945270\pi\) | |||||||
\(398\) | 4609.96i | 0.580594i | ||||||||
\(399\) | 29680.0 | 3.72396 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14095.3 | −1.75532 | −0.877661 | − | 0.479281i | \(-0.840897\pi\) | ||||
−0.877661 | + | 0.479281i | \(0.840897\pi\) | |||||||
\(402\) | 12419.1i | 1.54081i | ||||||||
\(403\) | 9576.45i | 1.18372i | ||||||||
\(404\) | −6634.71 | −0.817052 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −59.2570 | −0.00724353 | ||||||||
\(407\) | 6123.12i | 0.745729i | ||||||||
\(408\) | − 2836.32i | − 0.344163i | ||||||||
\(409\) | 10846.0 | 1.31125 | 0.655625 | − | 0.755087i | \(-0.272405\pi\) | ||||
0.655625 | + | 0.755087i | \(0.272405\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18325.0 | 2.19928 | ||||||||
\(412\) | − 6942.06i | − 0.830123i | ||||||||
\(413\) | 12502.5i | 1.48961i | ||||||||
\(414\) | −1395.48 | −0.165662 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2557.22 | 0.301390 | ||||||||
\(417\) | 6996.84i | 0.821670i | ||||||||
\(418\) | − 3680.29i | − 0.430644i | ||||||||
\(419\) | 5626.55 | 0.656026 | 0.328013 | − | 0.944673i | \(-0.393621\pi\) | ||||
0.328013 | + | 0.944673i | \(0.393621\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7109.09 | −0.822983 | −0.411491 | − | 0.911414i | \(-0.634992\pi\) | ||||
−0.411491 | + | 0.911414i | \(0.634992\pi\) | |||||||
\(422\) | − 8746.74i | − 1.00897i | ||||||||
\(423\) | − 16231.1i | − 1.86568i | ||||||||
\(424\) | 3274.76 | 0.375086 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −11112.3 | −1.26384 | ||||||||
\(427\) | − 17967.3i | − 2.03630i | ||||||||
\(428\) | − 6519.52i | − 0.736292i | ||||||||
\(429\) | 10062.9 | 1.13249 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4464.14 | 0.498909 | 0.249455 | − | 0.968387i | \(-0.419749\pi\) | ||||
0.249455 | + | 0.968387i | \(0.419749\pi\) | |||||||
\(432\) | 404.226i | 0.0450192i | ||||||||
\(433\) | 11009.4i | 1.22189i | 0.791672 | + | 0.610947i | \(0.209211\pi\) | ||||
−0.791672 | + | 0.610947i | \(0.790789\pi\) | |||||||
\(434\) | 8489.86 | 0.939001 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1728.61 | −0.189874 | ||||||||
\(437\) | − 2545.03i | − 0.278593i | ||||||||
\(438\) | − 1385.08i | − 0.151100i | ||||||||
\(439\) | 3052.70 | 0.331885 | 0.165943 | − | 0.986135i | \(-0.446933\pi\) | ||||
0.165943 | + | 0.986135i | \(0.446933\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 27660.2 | 2.98675 | ||||||||
\(442\) | 7483.37i | 0.805312i | ||||||||
\(443\) | − 4465.82i | − 0.478956i | −0.970902 | − | 0.239478i | \(-0.923024\pi\) | ||||
0.970902 | − | 0.239478i | \(-0.0769764\pi\) | |||||||
\(444\) | 11152.2 | 1.19203 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −10879.0 | −1.15501 | ||||||||
\(447\) | 3260.64i | 0.345018i | ||||||||
\(448\) | − 2267.07i | − 0.239082i | ||||||||
\(449\) | −9040.14 | −0.950179 | −0.475090 | − | 0.879937i | \(-0.657584\pi\) | ||||
−0.475090 | + | 0.879937i | \(0.657584\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1593.02 | 0.166324 | ||||||||
\(452\) | 960.462i | 0.0999476i | ||||||||
\(453\) | 192.420i | 0.0199574i | ||||||||
\(454\) | 432.996 | 0.0447610 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6703.01 | −0.688371 | ||||||||
\(457\) | − 7756.88i | − 0.793986i | −0.917822 | − | 0.396993i | \(-0.870054\pi\) | ||||
0.917822 | − | 0.396993i | \(-0.129946\pi\) | |||||||
\(458\) | 1849.33i | 0.188676i | ||||||||
\(459\) | −1182.91 | −0.120291 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7064.19 | 0.713692 | 0.356846 | − | 0.934163i | \(-0.383852\pi\) | ||||
0.356846 | + | 0.934163i | \(0.383852\pi\) | |||||||
\(462\) | − 8921.08i | − 0.898369i | ||||||||
\(463\) | 12599.7i | 1.26470i | 0.774682 | + | 0.632350i | \(0.217910\pi\) | ||||
−0.774682 | + | 0.632350i | \(0.782090\pi\) | |||||||
\(464\) | 13.3828 | 0.00133896 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4739.37 | 0.471131 | ||||||||
\(467\) | − 14746.0i | − 1.46117i | −0.682824 | − | 0.730583i | \(-0.739249\pi\) | ||||
0.682824 | − | 0.730583i | \(-0.260751\pi\) | |||||||
\(468\) | − 9697.14i | − 0.957800i | ||||||||
\(469\) | −29048.8 | −2.86002 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11966.1 | 1.17063 | ||||||||
\(472\) | − 2823.60i | − 0.275353i | ||||||||
\(473\) | − 5520.46i | − 0.536641i | ||||||||
\(474\) | −4988.20 | −0.483367 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6634.27 | 0.638826 | ||||||||
\(477\) | − 12418.1i | − 1.19200i | ||||||||
\(478\) | 5539.19i | 0.530035i | ||||||||
\(479\) | 17411.2 | 1.66084 | 0.830418 | − | 0.557141i | \(-0.188102\pi\) | ||||
0.830418 | + | 0.557141i | \(0.188102\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −29424.1 | −2.78924 | ||||||||
\(482\) | − 10668.2i | − 1.00814i | ||||||||
\(483\) | − 6169.18i | − 0.581175i | ||||||||
\(484\) | 4217.79 | 0.396111 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −10871.5 | −1.01470 | ||||||||
\(487\) | − 1320.34i | − 0.122855i | −0.998112 | − | 0.0614276i | \(-0.980435\pi\) | ||||
0.998112 | − | 0.0614276i | \(-0.0195653\pi\) | |||||||
\(488\) | 4057.78i | 0.376408i | ||||||||
\(489\) | 3473.61 | 0.321231 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17115.8 | 1.57317 | 0.786583 | − | 0.617485i | \(-0.211848\pi\) | ||||
0.786583 | + | 0.617485i | \(0.211848\pi\) | |||||||
\(492\) | − 2901.40i | − 0.265864i | ||||||||
\(493\) | 39.1629i | 0.00357770i | ||||||||
\(494\) | 17685.3 | 1.61073 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1917.37 | −0.173574 | ||||||||
\(497\) | − 25992.3i | − 2.34590i | ||||||||
\(498\) | − 11416.2i | − 1.02725i | ||||||||
\(499\) | −17540.6 | −1.57360 | −0.786798 | − | 0.617210i | \(-0.788263\pi\) | ||||
−0.786798 | + | 0.617210i | \(0.788263\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4250.02 | 0.378996 | ||||||||
\(502\) | 9354.27i | 0.831676i | ||||||||
\(503\) | − 4934.98i | − 0.437455i | −0.975786 | − | 0.218727i | \(-0.929809\pi\) | ||||
0.975786 | − | 0.218727i | \(-0.0701905\pi\) | |||||||
\(504\) | −8596.85 | −0.759790 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −764.972 | −0.0672079 | ||||||||
\(507\) | 31720.3i | 2.77860i | ||||||||
\(508\) | − 843.972i | − 0.0737110i | ||||||||
\(509\) | −11927.3 | −1.03865 | −0.519323 | − | 0.854578i | \(-0.673816\pi\) | ||||
−0.519323 | + | 0.854578i | \(0.673816\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3239.78 | 0.280468 | ||||||||
\(512\) | 512.000i | 0.0441942i | ||||||||
\(513\) | 2795.56i | 0.240598i | ||||||||
\(514\) | −5205.97 | −0.446743 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −10054.6 | −0.857804 | ||||||||
\(517\) | − 8897.57i | − 0.756895i | ||||||||
\(518\) | 26085.5i | 2.21261i | ||||||||
\(519\) | 11918.1 | 1.00799 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9592.76 | −0.806653 | −0.403327 | − | 0.915056i | \(-0.632146\pi\) | ||||
−0.403327 | + | 0.915056i | \(0.632146\pi\) | |||||||
\(522\) | − 50.7482i | − 0.00425515i | ||||||||
\(523\) | 6525.20i | 0.545558i | 0.962077 | + | 0.272779i | \(0.0879428\pi\) | ||||
−0.962077 | + | 0.272779i | \(0.912057\pi\) | |||||||
\(524\) | 2984.71 | 0.248832 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6822.60 | 0.565550 | ||||||||
\(527\) | − 5610.94i | − 0.463788i | ||||||||
\(528\) | 2014.76i | 0.166063i | ||||||||
\(529\) | −529.000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10707.3 | −0.875058 | ||||||||
\(532\) | − 15678.6i | − 1.27774i | ||||||||
\(533\) | 7655.10i | 0.622100i | ||||||||
\(534\) | 15903.5 | 1.28879 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6560.45 | 0.528672 | ||||||||
\(537\) | 16776.6i | 1.34817i | ||||||||
\(538\) | − 8733.13i | − 0.699836i | ||||||||
\(539\) | 15162.8 | 1.21170 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5634.05 | 0.447739 | 0.223870 | − | 0.974619i | \(-0.428131\pi\) | ||||
0.223870 | + | 0.974619i | \(0.428131\pi\) | |||||||
\(542\) | 11364.9i | 0.900673i | ||||||||
\(543\) | − 6614.19i | − 0.522729i | ||||||||
\(544\) | −1498.30 | −0.118087 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 42869.5 | 3.36015 | ||||||||
\(547\) | − 6093.08i | − 0.476273i | −0.971232 | − | 0.238136i | \(-0.923463\pi\) | ||||
0.971232 | − | 0.238136i | \(-0.0765365\pi\) | |||||||
\(548\) | − 9680.29i | − 0.754601i | ||||||||
\(549\) | 15387.4 | 1.19620 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 92.5529 | 0.00715587 | ||||||||
\(552\) | 1393.26i | 0.107430i | ||||||||
\(553\) | − 11667.6i | − 0.897212i | ||||||||
\(554\) | −3769.24 | −0.289061 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3696.12 | 0.281925 | ||||||||
\(557\) | − 21461.9i | − 1.63262i | −0.577612 | − | 0.816311i | \(-0.696015\pi\) | ||||
0.577612 | − | 0.816311i | \(-0.303985\pi\) | |||||||
\(558\) | 7270.79i | 0.551608i | ||||||||
\(559\) | 26528.1 | 2.00719 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5895.93 | −0.443719 | ||||||||
\(562\) | − 5412.85i | − 0.406276i | ||||||||
\(563\) | − 11038.5i | − 0.826316i | −0.910659 | − | 0.413158i | \(-0.864426\pi\) | ||||
0.910659 | − | 0.413158i | \(-0.135574\pi\) | |||||||
\(564\) | −16205.4 | −1.20988 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11927.3 | 0.885761 | ||||||||
\(567\) | − 22237.9i | − 1.64710i | ||||||||
\(568\) | 5870.16i | 0.433638i | ||||||||
\(569\) | 19210.3 | 1.41535 | 0.707677 | − | 0.706536i | \(-0.249743\pi\) | ||||
0.707677 | + | 0.706536i | \(0.249743\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11967.0 | −0.877066 | −0.438533 | − | 0.898715i | \(-0.644502\pi\) | ||||
−0.438533 | + | 0.898715i | \(0.644502\pi\) | |||||||
\(572\) | − 5315.77i | − 0.388573i | ||||||||
\(573\) | 18913.1i | 1.37889i | ||||||||
\(574\) | 6786.51 | 0.493490 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1941.53 | 0.140447 | ||||||||
\(577\) | 14982.3i | 1.08097i | 0.841352 | + | 0.540487i | \(0.181760\pi\) | ||||
−0.841352 | + | 0.540487i | \(0.818240\pi\) | |||||||
\(578\) | 5441.42i | 0.391580i | ||||||||
\(579\) | 6884.20 | 0.494124 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26703.0 | 1.90676 | ||||||||
\(582\) | 4118.13i | 0.293302i | ||||||||
\(583\) | − 6807.35i | − 0.483587i | ||||||||
\(584\) | −731.679 | −0.0518444 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9471.71 | 0.667701 | ||||||||
\(587\) | − 24002.9i | − 1.68774i | −0.536547 | − | 0.843871i | \(-0.680271\pi\) | ||||
0.536547 | − | 0.843871i | \(-0.319729\pi\) | |||||||
\(588\) | − 27616.4i | − 1.93687i | ||||||||
\(589\) | −13260.2 | −0.927637 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4608.58 | −0.320764 | ||||||||
\(592\) | − 5891.21i | − 0.408999i | ||||||||
\(593\) | 5124.67i | 0.354882i | 0.984131 | + | 0.177441i | \(0.0567819\pi\) | ||||
−0.984131 | + | 0.177441i | \(0.943218\pi\) | |||||||
\(594\) | 840.276 | 0.0580420 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1722.45 | 0.118380 | ||||||||
\(597\) | − 17453.5i | − 1.19652i | ||||||||
\(598\) | − 3676.01i | − 0.251376i | ||||||||
\(599\) | 23776.8 | 1.62186 | 0.810928 | − | 0.585146i | \(-0.198963\pi\) | ||||
0.810928 | + | 0.585146i | \(0.198963\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25435.3 | −1.72633 | −0.863166 | − | 0.504920i | \(-0.831522\pi\) | ||||
−0.863166 | + | 0.504920i | \(0.831522\pi\) | |||||||
\(602\) | − 23518.1i | − 1.59223i | ||||||||
\(603\) | − 24877.6i | − 1.68009i | ||||||||
\(604\) | 101.647 | 0.00684763 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 25119.3 | 1.68383 | ||||||||
\(607\) | 7445.94i | 0.497894i | 0.968517 | + | 0.248947i | \(0.0800844\pi\) | ||||
−0.968517 | + | 0.248947i | \(0.919916\pi\) | |||||||
\(608\) | 3540.91i | 0.236189i | ||||||||
\(609\) | 224.349 | 0.0149279 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 42756.5 | 2.83100 | ||||||||
\(612\) | 5681.65i | 0.375273i | ||||||||
\(613\) | − 12874.4i | − 0.848275i | −0.905598 | − | 0.424138i | \(-0.860577\pi\) | ||||
0.905598 | − | 0.424138i | \(-0.139423\pi\) | |||||||
\(614\) | −1538.48 | −0.101121 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4712.62 | −0.308241 | ||||||||
\(617\) | 19247.2i | 1.25585i | 0.778272 | + | 0.627927i | \(0.216096\pi\) | ||||
−0.778272 | + | 0.627927i | \(0.783904\pi\) | |||||||
\(618\) | 26282.9i | 1.71077i | ||||||||
\(619\) | 14496.4 | 0.941293 | 0.470647 | − | 0.882322i | \(-0.344021\pi\) | ||||
0.470647 | + | 0.882322i | \(0.344021\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 581.074 | 0.0375486 | ||||||||
\(622\) | − 11185.4i | − 0.721052i | ||||||||
\(623\) | 37199.1i | 2.39222i | ||||||||
\(624\) | −9681.75 | −0.621122 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −19554.4 | −1.24848 | ||||||||
\(627\) | 13933.7i | 0.887496i | ||||||||
\(628\) | − 6321.15i | − 0.401658i | ||||||||
\(629\) | 17239.9 | 1.09284 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18030.9 | −1.13756 | −0.568779 | − | 0.822490i | \(-0.692584\pi\) | ||||
−0.568779 | + | 0.822490i | \(0.692584\pi\) | |||||||
\(632\) | 2635.05i | 0.165849i | ||||||||
\(633\) | 33115.5i | 2.07934i | ||||||||
\(634\) | 3737.03 | 0.234095 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −12398.4 | −0.773000 | ||||||||
\(637\) | 72863.4i | 4.53211i | ||||||||
\(638\) | − 27.8191i | − 0.00172628i | ||||||||
\(639\) | 22260.0 | 1.37808 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11776.4 | 0.725646 | 0.362823 | − | 0.931858i | \(-0.381813\pi\) | ||||
0.362823 | + | 0.931858i | \(0.381813\pi\) | |||||||
\(642\) | 24683.2i | 1.51740i | ||||||||
\(643\) | 20207.4i | 1.23935i | 0.784858 | + | 0.619676i | \(0.212736\pi\) | ||||
−0.784858 | + | 0.619676i | \(0.787264\pi\) | |||||||
\(644\) | −3258.91 | −0.199408 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10362.0 | −0.631095 | ||||||||
\(647\) | − 21452.8i | − 1.30355i | −0.758412 | − | 0.651776i | \(-0.774024\pi\) | ||||
0.758412 | − | 0.651776i | \(-0.225976\pi\) | |||||||
\(648\) | 5022.26i | 0.304465i | ||||||||
\(649\) | −5869.50 | −0.355005 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −32143.0 | −1.93515 | ||||||||
\(652\) | − 1834.95i | − 0.110218i | ||||||||
\(653\) | − 15095.2i | − 0.904624i | −0.891860 | − | 0.452312i | \(-0.850599\pi\) | ||||
0.891860 | − | 0.452312i | \(-0.149401\pi\) | |||||||
\(654\) | 6544.57 | 0.391304 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1532.68 | −0.0912214 | ||||||||
\(657\) | 2774.57i | 0.164759i | ||||||||
\(658\) | − 37905.1i | − 2.24574i | ||||||||
\(659\) | −6964.68 | −0.411693 | −0.205846 | − | 0.978584i | \(-0.565995\pi\) | ||||
−0.205846 | + | 0.978584i | \(0.565995\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17380.4 | −1.02272 | −0.511361 | − | 0.859366i | \(-0.670858\pi\) | ||||
−0.511361 | + | 0.859366i | \(0.670858\pi\) | |||||||
\(662\) | 13933.8i | 0.818057i | ||||||||
\(663\) | − 28332.4i | − 1.65964i | ||||||||
\(664\) | −6030.67 | −0.352463 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −22339.8 | −1.29978 | ||||||||
\(667\) | − 19.2377i | − 0.00111677i | ||||||||
\(668\) | − 2245.10i | − 0.130038i | ||||||||
\(669\) | 41188.3 | 2.38032 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8435.04 | 0.485292 | ||||||||
\(672\) | 8583.21i | 0.492715i | ||||||||
\(673\) | 12383.2i | 0.709271i | 0.935005 | + | 0.354635i | \(0.115395\pi\) | ||||
−0.935005 | + | 0.354635i | \(0.884605\pi\) | |||||||
\(674\) | −35.0973 | −0.00200578 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16756.5 | 0.953371 | ||||||||
\(677\) | 8375.74i | 0.475489i | 0.971328 | + | 0.237744i | \(0.0764080\pi\) | ||||
−0.971328 | + | 0.237744i | \(0.923592\pi\) | |||||||
\(678\) | − 3636.35i | − 0.205978i | ||||||||
\(679\) | −9632.49 | −0.544420 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1639.34 | −0.0922463 | ||||||||
\(682\) | 3985.70i | 0.223783i | ||||||||
\(683\) | − 4434.66i | − 0.248444i | −0.992254 | − | 0.124222i | \(-0.960356\pi\) | ||||
0.992254 | − | 0.124222i | \(-0.0396436\pi\) | |||||||
\(684\) | 13427.3 | 0.750595 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 40295.8 | 2.24271 | ||||||||
\(687\) | − 7001.64i | − 0.388834i | ||||||||
\(688\) | 5311.38i | 0.294323i | ||||||||
\(689\) | 32712.1 | 1.80875 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11032.8 | 0.607389 | 0.303694 | − | 0.952770i | \(-0.401780\pi\) | ||||
0.303694 | + | 0.952770i | \(0.401780\pi\) | |||||||
\(692\) | − 6295.79i | − 0.345852i | ||||||||
\(693\) | 17870.5i | 0.979574i | ||||||||
\(694\) | −19718.6 | −1.07854 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −50.6677 | −0.00275942 | ||||||||
\(697\) | − 4485.20i | − 0.243743i | ||||||||
\(698\) | − 14400.5i | − 0.780898i | ||||||||
\(699\) | −17943.5 | −0.970936 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3708.40 | 0.199806 | 0.0999032 | − | 0.994997i | \(-0.468147\pi\) | ||||
0.0999032 | + | 0.994997i | \(0.468147\pi\) | |||||||
\(702\) | 4037.87i | 0.217093i | ||||||||
\(703\) | − 40742.6i | − 2.18583i | ||||||||
\(704\) | 1064.31 | 0.0569782 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12109.2 | 0.645516 | ||||||||
\(707\) | 58755.2i | 3.12548i | ||||||||
\(708\) | 10690.3i | 0.567465i | ||||||||
\(709\) | 6315.04 | 0.334508 | 0.167254 | − | 0.985914i | \(-0.446510\pi\) | ||||
0.167254 | + | 0.985914i | \(0.446510\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9992.26 | 0.527059 | ||||||||
\(712\) | − 8401.15i | − 0.442200i | ||||||||
\(713\) | 2756.22i | 0.144770i | ||||||||
\(714\) | −25117.6 | −1.31653 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8862.36 | 0.462572 | ||||||||
\(717\) | − 20971.6i | − 1.09233i | ||||||||
\(718\) | − 5468.52i | − 0.284239i | ||||||||
\(719\) | −24736.9 | −1.28307 | −0.641536 | − | 0.767093i | \(-0.721703\pi\) | ||||
−0.641536 | + | 0.767093i | \(0.721703\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −61477.0 | −3.17548 | ||||||||
\(722\) | 10770.3i | 0.555165i | ||||||||
\(723\) | 40390.2i | 2.07763i | ||||||||
\(724\) | −3493.99 | −0.179355 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −15968.7 | −0.816330 | ||||||||
\(727\) | − 33283.6i | − 1.69797i | −0.528420 | − | 0.848983i | \(-0.677215\pi\) | ||||
0.528420 | − | 0.848983i | \(-0.322785\pi\) | |||||||
\(728\) | − 22646.0i | − 1.15291i | ||||||||
\(729\) | 24209.9 | 1.22999 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15543.1 | −0.786430 | ||||||||
\(732\) | − 15362.9i | − 0.775725i | ||||||||
\(733\) | − 33636.5i | − 1.69494i | −0.530841 | − | 0.847471i | \(-0.678124\pi\) | ||||
0.530841 | − | 0.847471i | \(-0.321876\pi\) | |||||||
\(734\) | −4931.00 | −0.247965 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | − 13637.4i | − 0.681601i | ||||||||
\(738\) | 5812.03i | 0.289897i | ||||||||
\(739\) | −36575.5 | −1.82064 | −0.910319 | − | 0.413907i | \(-0.864164\pi\) | ||||
−0.910319 | + | 0.413907i | \(0.864164\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −66957.3 | −3.31949 | ||||||||
\(742\) | − 29000.4i | − 1.43482i | ||||||||
\(743\) | − 17704.7i | − 0.874190i | −0.899415 | − | 0.437095i | \(-0.856007\pi\) | ||||
0.899415 | − | 0.437095i | \(-0.143993\pi\) | |||||||
\(744\) | 7259.25 | 0.357711 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −11408.9 | −0.559932 | ||||||||
\(747\) | 22868.7i | 1.12011i | ||||||||
\(748\) | 3114.56i | 0.152246i | ||||||||
\(749\) | −57735.1 | −2.81655 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8858.37 | 0.430421 | 0.215211 | − | 0.976568i | \(-0.430956\pi\) | ||||
0.215211 | + | 0.976568i | \(0.430956\pi\) | |||||||
\(752\) | 8560.59i | 0.415123i | ||||||||
\(753\) | − 35415.7i | − 1.71397i | ||||||||
\(754\) | 133.682 | 0.00645679 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3579.71 | 0.172213 | ||||||||
\(757\) | − 7899.26i | − 0.379265i | −0.981855 | − | 0.189633i | \(-0.939270\pi\) | ||||
0.981855 | − | 0.189633i | \(-0.0607297\pi\) | |||||||
\(758\) | − 20463.9i | − 0.980582i | ||||||||
\(759\) | 2896.22 | 0.138506 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23437.4 | 1.11643 | 0.558216 | − | 0.829696i | \(-0.311486\pi\) | ||||
0.558216 | + | 0.829696i | \(0.311486\pi\) | |||||||
\(762\) | 3195.31i | 0.151908i | ||||||||
\(763\) | 15308.1i | 0.726329i | ||||||||
\(764\) | 9990.95 | 0.473115 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12642.7 | −0.596343 | ||||||||
\(767\) | − 28205.4i | − 1.32782i | ||||||||
\(768\) | − 1938.45i | − 0.0910780i | ||||||||
\(769\) | −31447.7 | −1.47468 | −0.737342 | − | 0.675519i | \(-0.763919\pi\) | ||||
−0.737342 | + | 0.675519i | \(0.763919\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19710.0 | 0.920674 | ||||||||
\(772\) | − 3636.62i | − 0.169540i | ||||||||
\(773\) | 2397.42i | 0.111551i | 0.998443 | + | 0.0557756i | \(0.0177632\pi\) | ||||
−0.998443 | + | 0.0557756i | \(0.982237\pi\) | |||||||
\(774\) | 20141.1 | 0.935343 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2175.43 | 0.100636 | ||||||||
\(777\) | − 98760.8i | − 4.55987i | ||||||||
\(778\) | 1851.19i | 0.0853063i | ||||||||
\(779\) | −10599.8 | −0.487518 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12202.5 | 0.559077 | ||||||||
\(782\) | 2153.81i | 0.0984911i | ||||||||
\(783\) | 21.1314i | 0 0.000964465i | ||||||||
\(784\) | −14588.5 | −0.664564 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −11300.3 | −0.512807 | ||||||||
\(787\) | 19407.0i | 0.879014i | 0.898239 | + | 0.439507i | \(0.144847\pi\) | ||||
−0.898239 | + | 0.439507i | \(0.855153\pi\) | |||||||
\(788\) | 2434.51i | 0.110058i | ||||||||
\(789\) | −25830.7 | −1.16552 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8505.58 | 0.382331 | ||||||||
\(792\) | − 4035.93i | − 0.181074i | ||||||||
\(793\) | 40533.8i | 1.81513i | ||||||||
\(794\) | −5413.51 | −0.241962 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9219.91 | −0.410542 | ||||||||
\(797\) | 28631.1i | 1.27248i | 0.771491 | + | 0.636240i | \(0.219511\pi\) | ||||
−0.771491 | + | 0.636240i | \(0.780489\pi\) | |||||||
\(798\) | 59360.0i | 2.63324i | ||||||||
\(799\) | −25051.4 | −1.10921 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −31857.6 | −1.40529 | ||||||||
\(802\) | − 28190.6i | − 1.24120i | ||||||||
\(803\) | 1520.96i | 0.0668414i | ||||||||
\(804\) | −24838.1 | −1.08952 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −19152.9 | −0.837013 | ||||||||
\(807\) | 33064.0i | 1.44227i | ||||||||
\(808\) | − 13269.4i | − 0.577743i | ||||||||
\(809\) | 9191.25 | 0.399440 | 0.199720 | − | 0.979853i | \(-0.435997\pi\) | ||||
0.199720 | + | 0.979853i | \(0.435997\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −567.477 | −0.0245706 | −0.0122853 | − | 0.999925i | \(-0.503911\pi\) | ||||
−0.0122853 | + | 0.999925i | \(0.503911\pi\) | |||||||
\(812\) | − 118.514i | − 0.00512195i | ||||||||
\(813\) | − 43028.0i | − 1.85616i | ||||||||
\(814\) | −12246.2 | −0.527310 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5672.63 | 0.243360 | ||||||||
\(817\) | 36732.6i | 1.57296i | ||||||||
\(818\) | 21692.0i | 0.927193i | ||||||||
\(819\) | −85875.2 | −3.66388 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6057.35 | −0.257494 | −0.128747 | − | 0.991677i | \(-0.541096\pi\) | ||||
−0.128747 | + | 0.991677i | \(0.541096\pi\) | |||||||
\(822\) | 36650.0i | 1.55513i | ||||||||
\(823\) | − 21327.0i | − 0.903294i | −0.892197 | − | 0.451647i | \(-0.850837\pi\) | ||||
0.892197 | − | 0.451647i | \(-0.149163\pi\) | |||||||
\(824\) | 13884.1 | 0.586986 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −25005.0 | −1.05331 | ||||||||
\(827\) | 27553.8i | 1.15857i | 0.815124 | + | 0.579286i | \(0.196668\pi\) | ||||
−0.815124 | + | 0.579286i | \(0.803332\pi\) | |||||||
\(828\) | − 2790.96i | − 0.117141i | ||||||||
\(829\) | −11181.6 | −0.468461 | −0.234231 | − | 0.972181i | \(-0.575257\pi\) | ||||
−0.234231 | + | 0.972181i | \(0.575257\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14270.5 | 0.595715 | ||||||||
\(832\) | 5114.44i | 0.213115i | ||||||||
\(833\) | − 42691.4i | − 1.77571i | ||||||||
\(834\) | −13993.7 | −0.581009 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7360.59 | 0.304511 | ||||||||
\(837\) | − 3027.54i | − 0.125026i | ||||||||
\(838\) | 11253.1i | 0.463881i | ||||||||
\(839\) | −9811.83 | −0.403745 | −0.201872 | − | 0.979412i | \(-0.564703\pi\) | ||||
−0.201872 | + | 0.979412i | \(0.564703\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24388.3 | −0.999971 | ||||||||
\(842\) | − 14218.2i | − 0.581937i | ||||||||
\(843\) | 20493.3i | 0.837279i | ||||||||
\(844\) | 17493.5 | 0.713448 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 32462.3 | 1.31924 | ||||||||
\(847\) | − 37351.6i | − 1.51525i | ||||||||
\(848\) | 6549.53i | 0.265226i | ||||||||
\(849\) | −45157.2 | −1.82543 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8468.62 | −0.341129 | ||||||||
\(852\) | − 22224.7i | − 0.893667i | ||||||||
\(853\) | − 24030.8i | − 0.964594i | −0.876008 | − | 0.482297i | \(-0.839803\pi\) | ||||
0.876008 | − | 0.482297i | \(-0.160197\pi\) | |||||||
\(854\) | 35934.6 | 1.43988 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13039.0 | 0.520637 | ||||||||
\(857\) | 16934.8i | 0.675008i | 0.941324 | + | 0.337504i | \(0.109583\pi\) | ||||
−0.941324 | + | 0.337504i | \(0.890417\pi\) | |||||||
\(858\) | 20125.7i | 0.800794i | ||||||||
\(859\) | 31057.0 | 1.23359 | 0.616793 | − | 0.787125i | \(-0.288432\pi\) | ||||
0.616793 | + | 0.787125i | \(0.288432\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −25694.0 | −1.01701 | ||||||||
\(862\) | 8928.27i | 0.352782i | ||||||||
\(863\) | − 16157.8i | − 0.637332i | −0.947867 | − | 0.318666i | \(-0.896765\pi\) | ||||
0.947867 | − | 0.318666i | \(-0.103235\pi\) | |||||||
\(864\) | −808.451 | −0.0318334 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −22018.9 | −0.864009 | ||||||||
\(867\) | − 20601.4i | − 0.806992i | ||||||||
\(868\) | 16979.7i | 0.663974i | ||||||||
\(869\) | 5477.55 | 0.213824 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 65533.3 | 2.54938 | ||||||||
\(872\) | − 3457.21i | − 0.134261i | ||||||||
\(873\) | − 8249.35i | − 0.319815i | ||||||||
\(874\) | 5090.05 | 0.196995 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2770.17 | 0.106844 | ||||||||
\(877\) | 32473.9i | 1.25036i | 0.780480 | + | 0.625180i | \(0.214975\pi\) | ||||
−0.780480 | + | 0.625180i | \(0.785025\pi\) | |||||||
\(878\) | 6105.41i | 0.234678i | ||||||||
\(879\) | −35860.3 | −1.37604 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15703.2 | −0.600517 | −0.300258 | − | 0.953858i | \(-0.597073\pi\) | ||||
−0.300258 | + | 0.953858i | \(0.597073\pi\) | |||||||
\(882\) | 55320.5i | 2.11195i | ||||||||
\(883\) | − 14330.4i | − 0.546155i | −0.961992 | − | 0.273078i | \(-0.911958\pi\) | ||||
0.961992 | − | 0.273078i | \(-0.0880416\pi\) | |||||||
\(884\) | −14966.7 | −0.569441 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8931.65 | 0.338673 | ||||||||
\(887\) | − 23238.2i | − 0.879664i | −0.898080 | − | 0.439832i | \(-0.855038\pi\) | ||||
0.898080 | − | 0.439832i | \(-0.144962\pi\) | |||||||
\(888\) | 22304.4i | 0.842890i | ||||||||
\(889\) | −7473.98 | −0.281968 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10439.9 | 0.392537 | ||||||||
\(892\) | − 21758.0i | − 0.816717i | ||||||||
\(893\) | 59203.6i | 2.21856i | ||||||||
\(894\) | −6521.29 | −0.243965 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4534.13 | 0.169057 | ||||||||
\(897\) | 13917.5i | 0.518052i | ||||||||
\(898\) | − 18080.3i | − 0.671878i | ||||||||
\(899\) | −100.233 | −0.00371854 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19166.3 | −0.708683 | ||||||||
\(902\) | 3186.03i | 0.117609i | ||||||||
\(903\) | 89040.4i | 3.28137i | ||||||||
\(904\) | −1920.92 | −0.0706736 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −384.841 | −0.0141120 | ||||||||
\(907\) | 3667.46i | 0.134263i | 0.997744 | + | 0.0671313i | \(0.0213846\pi\) | ||||
−0.997744 | + | 0.0671313i | \(0.978615\pi\) | |||||||
\(908\) | 865.992i | 0.0316508i | ||||||||
\(909\) | −50318.4 | −1.83604 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21457.9 | 0.780385 | 0.390192 | − | 0.920733i | \(-0.372409\pi\) | ||||
0.390192 | + | 0.920733i | \(0.372409\pi\) | |||||||
\(912\) | − 13406.0i | − 0.486752i | ||||||||
\(913\) | 12536.1i | 0.454420i | ||||||||
\(914\) | 15513.8 | 0.561433 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3698.66 | −0.133414 | ||||||||
\(917\) | − 26431.8i | − 0.951859i | ||||||||
\(918\) | − 2365.83i | − 0.0850587i | ||||||||
\(919\) | 11109.3 | 0.398762 | 0.199381 | − | 0.979922i | \(-0.436107\pi\) | ||||
0.199381 | + | 0.979922i | \(0.436107\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5824.76 | 0.208396 | ||||||||
\(922\) | 14128.4i | 0.504657i | ||||||||
\(923\) | 58637.9i | 2.09110i | ||||||||
\(924\) | 17842.2 | 0.635243 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −25199.3 | −0.894279 | ||||||||
\(927\) | − 52649.4i | − 1.86541i | ||||||||
\(928\) | 26.7655i | 0 0.000946790i | ||||||||
\(929\) | 20804.3 | 0.734732 | 0.367366 | − | 0.930076i | \(-0.380260\pi\) | ||||
0.367366 | + | 0.930076i | \(0.380260\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −100892. | −3.55166 | ||||||||
\(932\) | 9478.75i | 0.333140i | ||||||||
\(933\) | 42348.5i | 1.48599i | ||||||||
\(934\) | 29492.0 | 1.03320 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 19394.3 | 0.677267 | ||||||||
\(937\) | 35550.5i | 1.23947i | 0.784811 | + | 0.619735i | \(0.212760\pi\) | ||||
−0.784811 | + | 0.619735i | \(0.787240\pi\) | |||||||
\(938\) | − 58097.5i | − 2.02234i | ||||||||
\(939\) | 74033.7 | 2.57295 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 49674.4 | 1.72087 | 0.860436 | − | 0.509558i | \(-0.170191\pi\) | ||||
0.860436 | + | 0.509558i | \(0.170191\pi\) | |||||||
\(942\) | 23932.2i | 0.827762i | ||||||||
\(943\) | 2203.23i | 0.0760839i | ||||||||
\(944\) | 5647.20 | 0.194704 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11040.9 | 0.379462 | ||||||||
\(947\) | − 33466.2i | − 1.14837i | −0.818726 | − | 0.574184i | \(-0.805319\pi\) | ||||
0.818726 | − | 0.574184i | \(-0.194681\pi\) | |||||||
\(948\) | − 9976.41i | − 0.341792i | ||||||||
\(949\) | −7308.85 | −0.250006 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14148.5 | −0.482437 | ||||||||
\(952\) | 13268.5i | 0.451718i | ||||||||
\(953\) | − 17298.4i | − 0.587984i | −0.955808 | − | 0.293992i | \(-0.905016\pi\) | ||||
0.955808 | − | 0.293992i | \(-0.0949839\pi\) | |||||||
\(954\) | 24836.2 | 0.842874 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −11078.4 | −0.374791 | ||||||||
\(957\) | 105.324i | 0.00355763i | ||||||||
\(958\) | 34822.5i | 1.17439i | ||||||||
\(959\) | −85726.0 | −2.88659 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15430.4 | −0.517955 | ||||||||
\(962\) | − 58848.2i | − 1.97229i | ||||||||
\(963\) | − 49444.8i | − 1.65456i | ||||||||
\(964\) | 21336.4 | 0.712862 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 12338.4 | 0.410953 | ||||||||
\(967\) | 14869.7i | 0.494495i | 0.968952 | + | 0.247248i | \(0.0795261\pi\) | ||||
−0.968952 | + | 0.247248i | \(0.920474\pi\) | |||||||
\(968\) | 8435.59i | 0.280093i | ||||||||
\(969\) | 39231.0 | 1.30060 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26634.9 | 0.880283 | 0.440142 | − | 0.897928i | \(-0.354928\pi\) | ||||
0.440142 | + | 0.897928i | \(0.354928\pi\) | |||||||
\(972\) | − 21743.0i | − 0.717498i | ||||||||
\(973\) | − 32731.8i | − 1.07845i | ||||||||
\(974\) | 2640.69 | 0.0868717 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8115.57 | −0.266161 | ||||||||
\(977\) | − 40803.6i | − 1.33615i | −0.744092 | − | 0.668077i | \(-0.767118\pi\) | ||||
0.744092 | − | 0.668077i | \(-0.232882\pi\) | |||||||
\(978\) | 6947.22i | 0.227145i | ||||||||
\(979\) | −17463.7 | −0.570115 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13109.9 | −0.426675 | ||||||||
\(982\) | 34231.6i | 1.11240i | ||||||||
\(983\) | − 18615.8i | − 0.604021i | −0.953305 | − | 0.302011i | \(-0.902342\pi\) | ||||
0.953305 | − | 0.302011i | \(-0.0976578\pi\) | |||||||
\(984\) | 5802.80 | 0.187995 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −78.3257 | −0.00252982 | ||||||||
\(987\) | 143510.i | 4.62815i | ||||||||
\(988\) | 35370.6i | 1.13896i | ||||||||
\(989\) | 7635.11 | 0.245483 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46185.1 | 1.48044 | 0.740220 | − | 0.672364i | \(-0.234721\pi\) | ||||
0.740220 | + | 0.672364i | \(0.234721\pi\) | |||||||
\(992\) | − 3834.74i | − 0.122735i | ||||||||
\(993\) | − 52754.1i | − 1.68590i | ||||||||
\(994\) | 51984.5 | 1.65880 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 22832.4 | 0.726377 | ||||||||
\(997\) | − 16544.3i | − 0.525541i | −0.964858 | − | 0.262771i | \(-0.915364\pi\) | ||||
0.964858 | − | 0.262771i | \(-0.0846363\pi\) | |||||||
\(998\) | − 35081.2i | − 1.11270i | ||||||||
\(999\) | 9302.26 | 0.294605 |
(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 | 1150.4.b.n.599.5 | 8 | ||
5.2 | odd | 4 | 230.4.a.h.1.1 | ✓ | 4 | ||
5.3 | odd | 4 | 1150.4.a.p.1.4 | 4 | |||
5.4 | even | 2 | inner | 1150.4.b.n.599.4 | 8 | ||
15.2 | even | 4 | 2070.4.a.bj.1.1 | 4 | |||
20.7 | even | 4 | 1840.4.a.m.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.4.a.h.1.1 | ✓ | 4 | 5.2 | odd | 4 | ||
1150.4.a.p.1.4 | 4 | 5.3 | odd | 4 | |||
1150.4.b.n.599.4 | 8 | 5.4 | even | 2 | inner | ||
1150.4.b.n.599.5 | 8 | 1.1 | even | 1 | trivial | ||
1840.4.a.m.1.4 | 4 | 20.7 | even | 4 | |||
2070.4.a.bj.1.1 | 4 | 15.2 | even | 4 |