Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,3,Mod(127,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.c (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: | \(3.48774738381\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.2 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 128.127 |
Dual form | 128.3.c.a.127.3 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 0.828427i | − 0.276142i | −0.990422 | − | 0.138071i | \(-0.955910\pi\) | ||||
0.990422 | − | 0.138071i | \(-0.0440903\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.65685 | 0.731371 | 0.365685 | − | 0.930739i | \(-0.380835\pi\) | ||||
0.365685 | + | 0.930739i | \(0.380835\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.65685i | 1.37955i | 0.724024 | + | 0.689775i | \(0.242291\pi\) | ||||
−0.724024 | + | 0.689775i | \(0.757709\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.31371 | 0.923745 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 18.4853i | − 1.68048i | −0.542215 | − | 0.840240i | \(-0.682414\pi\) | ||||
0.542215 | − | 0.840240i | \(-0.317586\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 11.6569 | 0.896681 | 0.448341 | − | 0.893863i | \(-0.352015\pi\) | ||||
0.448341 | + | 0.893863i | \(0.352015\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 3.02944i | − 0.201962i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 9.31371 | 0.547865 | 0.273933 | − | 0.961749i | \(-0.411675\pi\) | ||||
0.273933 | + | 0.961749i | \(0.411675\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 15.1716i | 0.798504i | 0.916841 | + | 0.399252i | \(0.130730\pi\) | ||||
−0.916841 | + | 0.399252i | \(0.869270\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.00000 | 0.380952 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 22.3431i | 0.971441i | 0.874114 | + | 0.485721i | \(0.161443\pi\) | ||||
−0.874114 | + | 0.485721i | \(0.838557\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.6274 | −0.465097 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 14.3431i | − 0.531228i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −28.3431 | −0.977350 | −0.488675 | − | 0.872466i | \(-0.662520\pi\) | ||||
−0.488675 | + | 0.872466i | \(0.662520\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 45.2548i | − 1.45983i | −0.683536 | − | 0.729917i | \(-0.739559\pi\) | ||||
0.683536 | − | 0.729917i | \(-0.260441\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −15.3137 | −0.464052 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 35.3137i | 1.00896i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −49.5980 | −1.34049 | −0.670243 | − | 0.742142i | \(-0.733810\pi\) | ||||
−0.670243 | + | 0.742142i | \(0.733810\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 9.65685i | − 0.247612i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −20.6274 | −0.503108 | −0.251554 | − | 0.967843i | \(-0.580942\pi\) | ||||
−0.251554 | + | 0.967843i | \(0.580942\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 46.0833i | 1.07170i | 0.844312 | + | 0.535852i | \(0.180009\pi\) | ||||
−0.844312 | + | 0.535852i | \(0.819991\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 30.4020 | 0.675600 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 12.6863i | − 0.269921i | −0.990851 | − | 0.134961i | \(-0.956909\pi\) | ||||
0.990851 | − | 0.134961i | \(-0.0430908\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −44.2548 | −0.903160 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 7.71573i | − 0.151289i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 27.6569 | 0.521827 | 0.260914 | − | 0.965362i | \(-0.415976\pi\) | ||||
0.260914 | + | 0.965362i | \(0.415976\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 67.5980i | − 1.22905i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.5685 | 0.220501 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 9.11270i | − 0.154453i | −0.997014 | − | 0.0772263i | \(-0.975394\pi\) | ||||
0.997014 | − | 0.0772263i | \(-0.0246064\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −113.598 | −1.86226 | −0.931131 | − | 0.364685i | \(-0.881177\pi\) | ||||
−0.931131 | + | 0.364685i | \(0.881177\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 80.2843i | 1.27435i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 42.6274 | 0.655806 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 45.5147i | − 0.679324i | −0.940548 | − | 0.339662i | \(-0.889687\pi\) | ||||
0.940548 | − | 0.339662i | \(-0.110313\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 18.5097 | 0.268256 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.2843i | 0.229356i | 0.993403 | + | 0.114678i | \(0.0365836\pi\) | ||||
−0.993403 | + | 0.114678i | \(0.963416\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.9411 | −0.163577 | −0.0817885 | − | 0.996650i | \(-0.526063\pi\) | ||||
−0.0817885 | + | 0.996650i | \(0.526063\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.63247i | 0.128433i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 178.510 | 2.31831 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 70.0589i | 0.886821i | 0.896319 | + | 0.443411i | \(0.146232\pi\) | ||||
−0.896319 | + | 0.443411i | \(0.853768\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 62.9411 | 0.777051 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 94.6518i | − 1.14038i | −0.821512 | − | 0.570192i | \(-0.806869\pi\) | ||||
0.821512 | − | 0.570192i | \(-0.193131\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 34.0589 | 0.400693 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 23.4802i | 0.269888i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 110.569 | 1.24234 | 0.621172 | − | 0.783675i | \(-0.286657\pi\) | ||||
0.621172 | + | 0.783675i | \(0.286657\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 112.569i | 1.23702i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −37.4903 | −0.403122 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 55.4802i | 0.584002i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −25.4315 | −0.262180 | −0.131090 | − | 0.991370i | \(-0.541848\pi\) | ||||
−0.131090 | + | 0.991370i | \(0.541848\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 153.681i | − 1.55234i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −33.5980 | −0.332653 | −0.166327 | − | 0.986071i | \(-0.553191\pi\) | ||||
−0.166327 | + | 0.986071i | \(0.553191\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 99.5980i | − 0.966971i | −0.875352 | − | 0.483485i | \(-0.839371\pi\) | ||||
0.875352 | − | 0.483485i | \(-0.160629\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 29.2548 | 0.278617 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 114.485i | − 1.06996i | −0.844866 | − | 0.534978i | \(-0.820320\pi\) | ||||
0.844866 | − | 0.534978i | \(-0.179680\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 70.4020 | 0.645890 | 0.322945 | − | 0.946418i | \(-0.395327\pi\) | ||||
0.322945 | + | 0.946418i | \(0.395327\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 41.0883i | 0.370165i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.5097 | 0.110705 | 0.0553525 | − | 0.998467i | \(-0.482372\pi\) | ||||
0.0553525 | + | 0.998467i | \(0.482372\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 81.7056i | 0.710484i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 96.9117 | 0.828305 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 89.9411i | 0.755808i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −220.706 | −1.82401 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 17.0883i | 0.138929i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −133.941 | −1.07153 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 57.3726i | − 0.451753i | −0.974156 | − | 0.225876i | \(-0.927475\pi\) | ||||
0.974156 | − | 0.225876i | \(-0.0725245\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 38.1766 | 0.295943 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 198.368i | 1.51426i | 0.653267 | + | 0.757128i | \(0.273398\pi\) | ||||
−0.653267 | + | 0.757128i | \(0.726602\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −146.510 | −1.10158 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 52.4508i | − 0.388524i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 53.8823 | 0.393301 | 0.196651 | − | 0.980474i | \(-0.436994\pi\) | ||||
0.196651 | + | 0.980474i | \(0.436994\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 103.456i | 0.744287i | 0.928175 | + | 0.372143i | \(0.121377\pi\) | ||||
−0.928175 | + | 0.372143i | \(0.878623\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.5097 | −0.0745367 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 215.480i | − 1.50685i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −103.647 | −0.714805 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 36.6619i | 0.249401i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.0883 | −0.101264 | −0.0506319 | − | 0.998717i | \(-0.516124\pi\) | ||||
−0.0506319 | + | 0.998717i | \(0.516124\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 158.676i | − 1.05084i | −0.850844 | − | 0.525418i | \(-0.823909\pi\) | ||||
0.850844 | − | 0.525418i | \(-0.176091\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 77.4315 | 0.506088 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 165.490i | − 1.06768i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −124.108 | −0.790495 | −0.395247 | − | 0.918575i | \(-0.629341\pi\) | ||||
−0.395247 | + | 0.918575i | \(0.629341\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 22.9117i | − 0.144099i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −215.765 | −1.34015 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 121.681i | 0.746511i | 0.927729 | + | 0.373255i | \(0.121758\pi\) | ||||
−0.927729 | + | 0.373255i | \(0.878242\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −56.0000 | −0.339394 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 330.794i | 1.98080i | 0.138224 | + | 0.990401i | \(0.455861\pi\) | ||||
−0.138224 | + | 0.990401i | \(0.544139\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −33.1177 | −0.195963 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 126.132i | 0.737614i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 27.6569 | 0.159866 | 0.0799331 | − | 0.996800i | \(-0.474529\pi\) | ||||
0.0799331 | + | 0.996800i | \(0.474529\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 112.284i | − 0.641624i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.54921 | −0.0426509 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 91.8579i | 0.513172i | 0.966521 | + | 0.256586i | \(0.0825978\pi\) | ||||
−0.966521 | + | 0.256586i | \(0.917402\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −84.1076 | −0.464683 | −0.232342 | − | 0.972634i | \(-0.574639\pi\) | ||||
−0.232342 | + | 0.972634i | \(0.574639\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 94.1076i | 0.514249i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −181.373 | −0.980392 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 172.167i | − 0.920677i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 138.510 | 0.732855 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 289.137i | − 1.51381i | −0.653527 | − | 0.756903i | \(-0.726711\pi\) | ||||
0.653527 | − | 0.756903i | \(-0.273289\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 225.078 | 1.16621 | 0.583104 | − | 0.812397i | \(-0.301838\pi\) | ||||
0.583104 | + | 0.812397i | \(0.301838\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 35.3137i | − 0.181096i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 238.167 | 1.20897 | 0.604484 | − | 0.796618i | \(-0.293380\pi\) | ||||
0.604484 | + | 0.796618i | \(0.293380\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 27.8335i | − 0.139867i | −0.997552 | − | 0.0699334i | \(-0.977721\pi\) | ||||
0.997552 | − | 0.0699334i | \(-0.0222787\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −37.7056 | −0.187590 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 273.706i | − 1.34830i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −75.4315 | −0.367958 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 185.754i | 0.897364i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 280.451 | 1.34187 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 42.7696i | − 0.202699i | −0.994851 | − | 0.101350i | \(-0.967684\pi\) | ||||
0.994851 | − | 0.101350i | \(-0.0323161\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.4903 | 0.0633349 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 168.520i | 0.783813i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 437.019 | 2.01391 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.89235i | 0.0451706i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 108.569 | 0.491260 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 301.255i | 1.35092i | 0.737397 | + | 0.675459i | \(0.236055\pi\) | ||||
−0.737397 | + | 0.675459i | \(0.763945\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −96.6670 | −0.429631 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 80.7797i | 0.355858i | 0.984043 | + | 0.177929i | \(0.0569397\pi\) | ||||
−0.984043 | + | 0.177929i | \(0.943060\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 195.186 | 0.852340 | 0.426170 | − | 0.904643i | \(-0.359863\pi\) | ||||
0.426170 | + | 0.904643i | \(0.359863\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 147.882i | − 0.640183i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −38.4508 | −0.165025 | −0.0825124 | − | 0.996590i | \(-0.526294\pi\) | ||||
−0.0825124 | + | 0.996590i | \(0.526294\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 46.3919i | − 0.197412i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 58.0387 | 0.244889 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 188.215i | 0.787512i | 0.919215 | + | 0.393756i | \(0.128824\pi\) | ||||
−0.919215 | + | 0.393756i | \(0.871176\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −267.706 | −1.11081 | −0.555406 | − | 0.831579i | \(-0.687437\pi\) | ||||
−0.555406 | + | 0.831579i | \(0.687437\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 181.230i | − 0.745804i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −161.833 | −0.660545 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 176.853i | 0.716003i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −78.4121 | −0.314908 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 158.652i | 0.632079i | 0.948746 | + | 0.316039i | \(0.102353\pi\) | ||||
−0.948746 | + | 0.316039i | \(0.897647\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 413.019 | 1.63249 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 28.2153i | − 0.110648i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 338.000 | 1.31518 | 0.657588 | − | 0.753378i | \(-0.271577\pi\) | ||||
0.657588 | + | 0.753378i | \(0.271577\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 478.960i | − 1.84927i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −235.637 | −0.902822 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 21.2061i | − 0.0806314i | −0.999187 | − | 0.0403157i | \(-0.987164\pi\) | ||||
0.999187 | − | 0.0403157i | \(-0.0128364\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 101.137 | 0.381649 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 91.5980i | − 0.343064i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −403.637 | −1.50051 | −0.750254 | − | 0.661150i | \(-0.770069\pi\) | ||||
−0.750254 | + | 0.661150i | \(0.770069\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 50.1766i | 0.185154i | 0.995706 | + | 0.0925768i | \(0.0295104\pi\) | ||||
−0.995706 | + | 0.0925768i | \(0.970490\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 93.2548 | 0.341593 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 214.936i | 0.781586i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 229.696 | 0.829226 | 0.414613 | − | 0.909998i | \(-0.363917\pi\) | ||||
0.414613 | + | 0.909998i | \(0.363917\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 376.235i | − 1.34851i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 86.8040 | 0.308911 | 0.154456 | − | 0.988000i | \(-0.450638\pi\) | ||||
0.154456 | + | 0.988000i | \(0.450638\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 389.848i | 1.37755i | 0.724973 | + | 0.688777i | \(0.241852\pi\) | ||||
−0.724973 | + | 0.688777i | \(0.758148\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 45.9613 | 0.161268 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 199.196i | − 0.694063i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −202.255 | −0.699844 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.0681i | 0.0723990i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 243.657 | 0.831593 | 0.415797 | − | 0.909458i | \(-0.363503\pi\) | ||||
0.415797 | + | 0.909458i | \(0.363503\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 33.3238i | − 0.112962i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −265.137 | −0.892717 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 260.451i | 0.871073i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −445.019 | −1.47847 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 27.8335i | 0.0918597i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −415.411 | −1.36200 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 276.240i | − 0.899804i | −0.893078 | − | 0.449902i | \(-0.851459\pi\) | ||||
0.893078 | − | 0.449902i | \(-0.148541\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −82.5097 | −0.267022 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 552.715i | − 1.77722i | −0.458665 | − | 0.888609i | \(-0.651672\pi\) | ||||
0.458665 | − | 0.888609i | \(-0.348328\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −372.627 | −1.19050 | −0.595251 | − | 0.803539i | \(-0.702948\pi\) | ||||
−0.595251 | + | 0.803539i | \(0.702948\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 293.588i | 0.932025i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 131.657 | 0.415321 | 0.207661 | − | 0.978201i | \(-0.433415\pi\) | ||||
0.207661 | + | 0.978201i | \(0.433415\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 523.931i | 1.64242i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −94.8427 | −0.295460 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 141.304i | 0.437472i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −135.539 | −0.417043 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 58.3229i | − 0.178358i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 122.510 | 0.372370 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 329.161i | 0.994446i | 0.867623 | + | 0.497223i | \(0.165647\pi\) | ||||
−0.867623 | + | 0.497223i | \(0.834353\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −412.343 | −1.23827 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 166.441i | − 0.496838i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 574.784 | 1.70559 | 0.852795 | − | 0.522246i | \(-0.174906\pi\) | ||||
0.852795 | + | 0.522246i | \(0.174906\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 10.3633i | − 0.0305703i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −836.548 | −2.45322 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 45.8234i | 0.133596i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 67.6872 | 0.196195 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 480.406i | − 1.38446i | −0.721679 | − | 0.692228i | \(-0.756629\pi\) | ||||
0.721679 | − | 0.692228i | \(-0.243371\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 547.186 | 1.56787 | 0.783934 | − | 0.620844i | \(-0.213210\pi\) | ||||
0.783934 | + | 0.620844i | \(0.213210\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 167.196i | − 0.476342i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −624.274 | −1.76848 | −0.884241 | − | 0.467031i | \(-0.845324\pi\) | ||||
−0.884241 | + | 0.467031i | \(0.845324\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 59.5492i | 0.167744i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 74.5097 | 0.208711 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 280.617i | − 0.781664i | −0.920462 | − | 0.390832i | \(-0.872187\pi\) | ||||
0.920462 | − | 0.390832i | \(-0.127813\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 130.823 | 0.362392 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 182.839i | 0.503687i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −43.6670 | −0.119635 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 103.196i | − 0.281188i | −0.990067 | − | 0.140594i | \(-0.955099\pi\) | ||||
0.990067 | − | 0.140594i | \(-0.0449012\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −171.490 | −0.464743 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 267.078i | 0.719887i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 177.147 | 0.474925 | 0.237463 | − | 0.971397i | \(-0.423684\pi\) | ||||
0.237463 | + | 0.971397i | \(0.423684\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 110.960i | 0.295895i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −330.392 | −0.876371 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 356.759i | − 0.941318i | −0.882315 | − | 0.470659i | \(-0.844016\pi\) | ||||
0.882315 | − | 0.470659i | \(-0.155984\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −47.5290 | −0.124748 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 106.039i | 0.276863i | 0.990372 | + | 0.138432i | \(0.0442061\pi\) | ||||
−0.990372 | + | 0.138432i | \(0.955794\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 652.784 | 1.69554 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 383.123i | 0.989981i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 520.912 | 1.33910 | 0.669552 | − | 0.742765i | \(-0.266486\pi\) | ||||
0.669552 | + | 0.742765i | \(0.266486\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 208.098i | 0.532219i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 164.333 | 0.418150 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 256.195i | 0.648595i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 80.4407 | 0.202621 | 0.101311 | − | 0.994855i | \(-0.467696\pi\) | ||||
0.101311 | + | 0.994855i | \(0.467696\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 121.373i | 0.304192i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.82338 | 0.00953460 | 0.00476730 | − | 0.999989i | \(-0.498483\pi\) | ||||
0.00476730 | + | 0.999989i | \(0.498483\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 527.529i | − 1.30900i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 230.167 | 0.568312 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 916.833i | 2.25266i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 378.902 | 0.926410 | 0.463205 | − | 0.886251i | \(-0.346699\pi\) | ||||
0.463205 | + | 0.886251i | \(0.346699\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 44.6375i | − 0.108607i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 88.0000 | 0.213075 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 346.128i | − 0.834043i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 85.7056 | 0.205529 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 603.907i | − 1.44130i | −0.693297 | − | 0.720652i | \(-0.743842\pi\) | ||||
0.693297 | − | 0.720652i | \(-0.256158\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 184.676 | 0.438661 | 0.219330 | − | 0.975651i | \(-0.429613\pi\) | ||||
0.219330 | + | 0.975651i | \(0.429613\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 105.470i | − 0.249338i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −108.294 | −0.254810 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 1097.00i | − 2.56908i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −178.510 | −0.416106 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 162.843i | − 0.377825i | −0.981994 | − | 0.188913i | \(-0.939504\pi\) | ||||
0.981994 | − | 0.188913i | \(-0.0604963\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 205.862 | 0.475432 | 0.237716 | − | 0.971335i | \(-0.423601\pi\) | ||||
0.237716 | + | 0.971335i | \(0.423601\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 85.8638i | 0.197388i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −338.981 | −0.775699 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 197.872i | 0.450734i | 0.974274 | + | 0.225367i | \(0.0723581\pi\) | ||||
−0.974274 | + | 0.225367i | \(0.927642\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −367.922 | −0.834290 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 26.1522i | − 0.0590344i | −0.999564 | − | 0.0295172i | \(-0.990603\pi\) | ||||
0.999564 | − | 0.0295172i | \(-0.00939698\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 404.333 | 0.908614 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.4996i | 0.0279632i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 321.078 | 0.715096 | 0.357548 | − | 0.933895i | \(-0.383613\pi\) | ||||
0.357548 | + | 0.933895i | \(0.383613\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 381.304i | 0.845463i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −131.452 | −0.290180 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 411.647i | 0.904718i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 357.882 | 0.783112 | 0.391556 | − | 0.920154i | \(-0.371937\pi\) | ||||
0.391556 | + | 0.920154i | \(0.371937\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 133.588i | − 0.291041i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 240.912 | 0.522585 | 0.261293 | − | 0.965260i | \(-0.415851\pi\) | ||||
0.261293 | + | 0.965260i | \(0.415851\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 176.098i | 0.380340i | 0.981751 | + | 0.190170i | \(0.0609040\pi\) | ||||
−0.981751 | + | 0.190170i | \(0.939096\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −137.097 | −0.294832 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 749.092i | 1.60405i | 0.597289 | + | 0.802026i | \(0.296245\pi\) | ||||
−0.597289 | + | 0.802026i | \(0.703755\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 439.529 | 0.937162 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 102.814i | 0.218289i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 851.862 | 1.80098 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 176.406i | − 0.371381i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 229.931 | 0.482036 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 120.235i | 0.251014i | 0.992093 | + | 0.125507i | \(0.0400557\pi\) | ||||
−0.992093 | + | 0.125507i | \(0.959944\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −578.156 | −1.20199 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 178.745i | 0.370073i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −92.9991 | −0.191751 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 624.284i | 1.28190i | 0.767584 | + | 0.640949i | \(0.221459\pi\) | ||||
−0.767584 | + | 0.640949i | \(0.778541\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 100.804 | 0.206143 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 279.602i | − 0.569455i | −0.958609 | − | 0.284727i | \(-0.908097\pi\) | ||||
0.958609 | − | 0.284727i | \(-0.0919030\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −263.980 | −0.535456 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 561.990i | − 1.13533i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −157.255 | −0.316408 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 260.759i | 0.522564i | 0.965263 | + | 0.261282i | \(0.0841453\pi\) | ||||
−0.965263 | + | 0.261282i | \(0.915855\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 274.039 | 0.546983 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 735.813i | − 1.46285i | −0.681922 | − | 0.731425i | \(-0.738856\pi\) | ||||
0.681922 | − | 0.731425i | \(-0.261144\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −122.863 | −0.243293 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 27.4356i | 0.0541137i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −508.108 | −0.998247 | −0.499123 | − | 0.866531i | \(-0.666345\pi\) | ||||
−0.499123 | + | 0.866531i | \(0.666345\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 115.314i | − 0.225663i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 217.608 | 0.424187 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 364.215i | − 0.707214i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −234.510 | −0.453597 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 22.9117i | − 0.0441458i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −973.724 | −1.86895 | −0.934476 | − | 0.356026i | \(-0.884131\pi\) | ||||
−0.934476 | + | 0.356026i | \(0.884131\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 65.8192i | − 0.125849i | −0.998018 | − | 0.0629247i | \(-0.979957\pi\) | ||||
0.998018 | − | 0.0629247i | \(-0.0200428\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −93.0193 | −0.177180 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 421.490i | − 0.799792i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 29.7838 | 0.0563022 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 75.7603i | − 0.142675i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −240.451 | −0.451127 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 418.656i | − 0.782535i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 76.0975 | 0.141709 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 818.063i | 1.51774i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −524.108 | −0.968776 | −0.484388 | − | 0.874853i | \(-0.660958\pi\) | ||||
−0.484388 | + | 0.874853i | \(0.660958\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 69.6771i | 0.128319i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 257.450 | 0.472385 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 552.642i | 1.01031i | 0.863027 | + | 0.505157i | \(0.168565\pi\) | ||||
−0.863027 | + | 0.505157i | \(0.831435\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −944.420 | −1.72026 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 430.010i | − 0.780418i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −676.548 | −1.22341 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 150.254i | 0.270728i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 374.638 | 0.672599 | 0.336299 | − | 0.941755i | \(-0.390825\pi\) | ||||
0.336299 | + | 0.941755i | \(0.390825\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 537.186i | 0.960976i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −142.627 | −0.254238 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 479.220i | − 0.851191i | −0.904914 | − | 0.425595i | \(-0.860065\pi\) | ||||
0.904914 | − | 0.425595i | \(-0.139935\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 45.7460 | 0.0809664 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 607.813i | 1.07198i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −696.705 | −1.22444 | −0.612219 | − | 0.790689i | \(-0.709723\pi\) | ||||
−0.612219 | + | 0.790689i | \(0.709723\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 307.103i | 0.537833i | 0.963164 | + | 0.268916i | \(0.0866656\pi\) | ||||
−0.963164 | + | 0.268916i | \(0.913334\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −239.529 | −0.418026 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 259.793i | − 0.451814i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −714.313 | −1.23798 | −0.618989 | − | 0.785400i | \(-0.712457\pi\) | ||||
−0.618989 | + | 0.785400i | \(0.712457\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 186.461i | − 0.322040i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 914.039 | 1.57322 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 511.245i | − 0.876921i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 354.392 | 0.605798 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 533.279i | 0.908482i | 0.890879 | + | 0.454241i | \(0.150090\pi\) | ||||
−0.890879 | + | 0.454241i | \(0.849910\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 686.587 | 1.16568 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 197.304i | − 0.333847i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.4517 | 0.0496655 | 0.0248328 | − | 0.999692i | \(-0.492095\pi\) | ||||
0.0248328 | + | 0.999692i | \(0.492095\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 328.902i | 0.552776i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −23.0580 | −0.0386231 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 699.265i | − 1.16739i | −0.811974 | − | 0.583694i | \(-0.801607\pi\) | ||||
0.811974 | − | 0.583694i | \(-0.198393\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 473.549 | 0.787935 | 0.393968 | − | 0.919124i | \(-0.371102\pi\) | ||||
0.393968 | + | 0.919124i | \(0.371102\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 378.396i | − 0.627523i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −807.088 | −1.33403 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 696.431i | − 1.14733i | −0.819089 | − | 0.573666i | \(-0.805521\pi\) | ||||
0.819089 | − | 0.573666i | \(-0.194479\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −226.745 | −0.372324 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 147.882i | − 0.242033i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −828.343 | −1.35129 | −0.675647 | − | 0.737225i | \(-0.736136\pi\) | ||||
−0.675647 | + | 0.737225i | \(0.736136\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 62.4895i | 0.101609i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 885.862 | 1.43576 | 0.717878 | − | 0.696168i | \(-0.245113\pi\) | ||||
0.717878 | + | 0.696168i | \(0.245113\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1217.40i | 1.96672i | 0.181679 | + | 0.983358i | \(0.441847\pi\) | ||||
−0.181679 | + | 0.983358i | \(0.558153\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 320.471 | 0.516056 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1067.74i | 1.71388i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −199.118 | −0.318588 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 232.333i | − 0.370547i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −461.941 | −0.734406 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 261.677i | 0.414702i | 0.978267 | + | 0.207351i | \(0.0664842\pi\) | ||||
−0.978267 | + | 0.207351i | \(0.933516\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −35.4315 | −0.0559739 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 209.803i | − 0.330399i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −515.872 | −0.809846 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 135.383i | 0.211866i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 923.588 | 1.44085 | 0.720427 | − | 0.693530i | \(-0.243946\pi\) | ||||
0.720427 | + | 0.693530i | \(0.243946\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 416.260i | − 0.647372i | −0.946165 | − | 0.323686i | \(-0.895078\pi\) | ||||
0.946165 | − | 0.323686i | \(-0.104922\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 139.606 | 0.216444 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 745.283i | − 1.15191i | −0.817483 | − | 0.575953i | \(-0.804631\pi\) | ||||
0.817483 | − | 0.575953i | \(-0.195369\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −168.451 | −0.259554 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 362.039i | − 0.556127i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 928.441 | 1.42181 | 0.710904 | − | 0.703289i | \(-0.248286\pi\) | ||||
0.710904 | + | 0.703289i | \(0.248286\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 725.401i | 1.10748i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −99.2750 | −0.151104 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 1085.71i | − 1.64751i | −0.566945 | − | 0.823756i | \(-0.691875\pi\) | ||||
0.566945 | − | 0.823756i | \(-0.308125\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 251.421 | 0.380365 | 0.190183 | − | 0.981749i | \(-0.439092\pi\) | ||||
0.190183 | + | 0.981749i | \(0.439092\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 89.9411i | − 0.135658i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −535.765 | −0.805661 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 633.275i | − 0.949438i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 249.568 | 0.373046 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2099.89i | 3.12949i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 173.001 | 0.257059 | 0.128530 | − | 0.991706i | \(-0.458974\pi\) | ||||
0.128530 | + | 0.991706i | \(0.458974\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 166.774i | 0.247072i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 856.441 | 1.26505 | 0.632526 | − | 0.774539i | \(-0.282018\pi\) | ||||
0.632526 | + | 0.774539i | \(0.282018\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 245.588i | − 0.361691i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 66.9201 | 0.0982673 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 762.201i | 1.11596i | 0.829854 | + | 0.557980i | \(0.188424\pi\) | ||||
−0.829854 | + | 0.557980i | \(0.811576\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 197.040 | 0.287649 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 161.697i | − 0.235367i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 322.392 | 0.467913 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 217.161i | − 0.314271i | −0.987577 | − | 0.157136i | \(-0.949774\pi\) | ||||
0.987577 | − | 0.157136i | \(-0.0502260\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1484.08 | 2.14153 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 378.323i | 0.544350i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −192.118 | −0.275635 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 31.8537i | 0.0455704i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −663.088 | −0.945918 | −0.472959 | − | 0.881085i | \(-0.656814\pi\) | ||||
−0.472959 | + | 0.881085i | \(0.656814\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 752.479i | − 1.07038i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −38.4323 | −0.0545139 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 324.451i | − 0.458912i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −912.656 | −1.28724 | −0.643622 | − | 0.765344i | \(-0.722569\pi\) | ||||
−0.643622 | + | 0.765344i | \(0.722569\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 582.449i | 0.819197i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1011.14 | 1.41814 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 787.980i | − 1.10207i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 155.923 | 0.217465 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 105.275i | 0.146419i | 0.997317 | + | 0.0732093i | \(0.0233241\pi\) | ||||
−0.997317 | + | 0.0732093i | \(0.976676\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 961.803 | 1.33398 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 221.775i | 0.306742i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 329.558 | 0.454562 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 518.246i | − 0.712855i | −0.934323 | − | 0.356428i | \(-0.883995\pi\) | ||||
0.934323 | − | 0.356428i | \(-0.116005\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 416.334 | 0.571103 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 429.206i | 0.587149i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −469.911 | −0.641079 | −0.320539 | − | 0.947235i | \(-0.603864\pi\) | ||||
−0.320539 | + | 0.947235i | \(0.603864\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 134.067i | 0.182404i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −841.352 | −1.14159 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 334.278i | − 0.452339i | −0.974088 | − | 0.226169i | \(-0.927380\pi\) | ||||
0.974088 | − | 0.226169i | \(-0.0726203\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 146.510 | 0.197719 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 937.852i | 1.26225i | 0.775681 | + | 0.631125i | \(0.217407\pi\) | ||||
−0.775681 | + | 0.631125i | \(0.782593\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −55.1758 | −0.0740614 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 786.908i | − 1.05342i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1105.57 | 1.47606 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 1193.67i | − 1.58943i | −0.606980 | − | 0.794717i | \(-0.707619\pi\) | ||||
0.606980 | − | 0.794717i | \(-0.292381\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 131.431 | 0.174544 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 580.256i | − 0.768551i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 129.383 | 0.170915 | 0.0854575 | − | 0.996342i | \(-0.472765\pi\) | ||||
0.0854575 | + | 0.996342i | \(0.472765\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 342.156i | − 0.450799i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1055.45 | 1.38693 | 0.693463 | − | 0.720493i | \(-0.256084\pi\) | ||||
0.693463 | + | 0.720493i | \(0.256084\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 679.862i | 0.891038i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 283.156 | 0.370138 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 106.225i | − 0.138495i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −285.980 | −0.371885 | −0.185943 | − | 0.982561i | \(-0.559534\pi\) | ||||
−0.185943 | + | 0.982561i | \(0.559534\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 280.008i | − 0.363176i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −688.656 | −0.890887 | −0.445444 | − | 0.895310i | \(-0.646954\pi\) | ||||
−0.445444 | + | 0.895310i | \(0.646954\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 526.197i | 0.678964i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −396.784 | −0.510661 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 312.950i | − 0.401733i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 301.019 | 0.385428 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 406.530i | 0.519195i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −453.844 | −0.578145 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1535.27i | 1.95079i | 0.220472 | + | 0.975393i | \(0.429240\pi\) | ||||
−0.220472 | + | 0.975393i | \(0.570760\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −17.5677 | −0.0222657 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 120.804i | 0.152723i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1324.20 | −1.66986 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 83.7847i | − 0.105390i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −311.559 | −0.390915 | −0.195458 | − | 0.980712i | \(-0.562619\pi\) | ||||
−0.195458 | + | 0.980712i | \(0.562619\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 118.156i | − 0.147880i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 919.235 | 1.14761 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 220.735i | 0.274888i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −789.019 | −0.980148 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 334.384i | 0.414354i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −669.724 | −0.827842 | −0.413921 | − | 0.910313i | \(-0.635841\pi\) | ||||
−0.413921 | + | 0.910313i | \(0.635841\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.94531i | 0.00733084i | 0.999993 | + | 0.00366542i | \(0.00116674\pi\) | ||||
−0.999993 | + | 0.00366542i | \(0.998833\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 41.5677 | 0.0511288 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 444.971i | 0.545976i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −699.156 | −0.855760 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 935.862i | 1.14269i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −804.814 | −0.980285 | −0.490143 | − | 0.871642i | \(-0.663055\pi\) | ||||
−0.490143 | + | 0.871642i | \(0.663055\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 352.382i | 0.428167i | 0.976815 | + | 0.214084i | \(0.0686765\pi\) | ||||
−0.976815 | + | 0.214084i | \(0.931323\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 178.059 | 0.215829 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 51.5248i | − 0.0623033i | −0.999515 | − | 0.0311516i | \(-0.990083\pi\) | ||||
0.999515 | − | 0.0311516i | \(-0.00991748\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1243.17 | −1.49960 | −0.749798 | − | 0.661666i | \(-0.769850\pi\) | ||||
−0.749798 | + | 0.661666i | \(0.769850\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 190.286i | − 0.228984i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −412.177 | −0.494810 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1209.67i | 1.44870i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −649.097 | −0.775504 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1383.20i | − 1.64863i | −0.566128 | − | 0.824317i | \(-0.691559\pi\) | ||||
0.566128 | − | 0.824317i | \(-0.308441\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −37.6661 | −0.0447873 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 71.9108i | − 0.0853035i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −121.107 | −0.143322 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 2131.32i | − 2.51632i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 322.960 | 0.380401 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1108.17i | − 1.30220i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 886.167 | 1.03888 | 0.519441 | − | 0.854506i | \(-0.326140\pi\) | ||||
0.519441 | + | 0.854506i | \(0.326140\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 461.246i | 0.539470i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −409.647 | −0.478001 | −0.239000 | − | 0.971019i | \(-0.576820\pi\) | ||||
−0.239000 | + | 0.971019i | \(0.576820\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 506.494i | 0.589632i | 0.955554 | + | 0.294816i | \(0.0952583\pi\) | ||||
−0.955554 | + | 0.294816i | \(0.904742\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −165.019 | −0.191660 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1226.04i | − 1.42067i | −0.703863 | − | 0.710335i | \(-0.748543\pi\) | ||||
0.703863 | − | 0.710335i | \(-0.251457\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 101.137 | 0.116921 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 167.553i | 0.193257i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1295.06 | 1.49029 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 530.558i | − 0.609137i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −211.430 | −0.242188 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 1293.45i | − 1.47823i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1052.73 | −1.20038 | −0.600190 | − | 0.799857i | \(-0.704908\pi\) | ||||
−0.600190 | + | 0.799857i | \(0.704908\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 201.852i | − 0.229638i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −149.294 | −0.169459 | −0.0847296 | − | 0.996404i | \(-0.527003\pi\) | ||||
−0.0847296 | + | 0.996404i | \(0.527003\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1621.05i | 1.83585i | 0.396758 | + | 0.917923i | \(0.370135\pi\) | ||||
−0.396758 | + | 0.917923i | \(0.629865\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −27.6063 | −0.0311936 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 266.420i | 0.300361i | 0.988659 | + | 0.150181i | \(0.0479855\pi\) | ||||
−0.988659 | + | 0.150181i | \(0.952014\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 554.039 | 0.623216 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 1163.48i | − 1.30582i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 192.471 | 0.215533 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 335.911i | 0.375319i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 215.765 | 0.240540 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1282.66i | 1.42677i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 257.588 | 0.285891 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 368.666i | 0.408268i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −307.569 | −0.339856 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1060.43i | 1.16917i | 0.811333 | + | 0.584584i | \(0.198742\pi\) | ||||
−0.811333 | + | 0.584584i | \(0.801258\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −279.324 | −0.307287 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 558.018i | 0.612534i | 0.951946 | + | 0.306267i | \(0.0990800\pi\) | ||||
−0.951946 | + | 0.306267i | \(0.900920\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1749.67 | −1.91639 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 344.138i | 0.376107i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1915.61 | −2.08899 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1271.68i | 1.38376i | 0.722013 | + | 0.691880i | \(0.243217\pi\) | ||||
−0.722013 | + | 0.691880i | \(0.756783\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −228.844 | −0.248474 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 189.823i | 0.205659i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 576.696 | 0.623456 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 828.029i | − 0.893235i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 439.040 | 0.472594 | 0.236297 | − | 0.971681i | \(-0.424066\pi\) | ||||
0.236297 | + | 0.971681i | \(0.424066\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 671.415i | − 0.721177i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −457.884 | −0.490765 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 629.588i | − 0.673356i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1009.43 | −1.07730 | −0.538651 | − | 0.842529i | \(-0.681066\pi\) | ||||
−0.538651 | + | 0.842529i | \(0.681066\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 308.695i | 0.328748i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1689.54 | 1.79547 | 0.897735 | − | 0.440536i | \(-0.145212\pi\) | ||||
0.897735 | + | 0.440536i | \(0.145212\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 460.881i | − 0.488740i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 506.510 | 0.535989 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 61.5635i | 0.0650090i | 0.999472 | + | 0.0325045i | \(0.0103483\pi\) | ||||
−0.999472 | + | 0.0325045i | \(0.989652\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −139.196 | −0.146676 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 109.068i | − 0.114688i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 873.960 | 0.917061 | 0.458531 | − | 0.888679i | \(-0.348376\pi\) | ||||
0.458531 | + | 0.888679i | \(0.348376\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1057.33i | − 1.10715i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 434.039 | 0.453541 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 520.333i | 0.542579i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1087.00 | −1.13111 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 951.797i | − 0.988367i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 823.078 | 0.852931 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 722.363i | 0.747015i | 0.927627 | + | 0.373507i | \(0.121845\pi\) | ||||
−0.927627 | + | 0.373507i | \(0.878155\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 117.060 | 0.120805 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 475.338i | 0.489535i | 0.969582 | + | 0.244767i | \(0.0787116\pi\) | ||||
−0.969582 | + | 0.244767i | \(0.921288\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −999.058 | −1.02678 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 112.284i | 0.115163i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 926.333 | 0.948140 | 0.474070 | − | 0.880487i | \(-0.342784\pi\) | ||||
0.474070 | + | 0.880487i | \(0.342784\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 2043.89i | − 2.08773i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 585.302 | 0.596638 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 248.991i | − 0.253297i | −0.991948 | − | 0.126648i | \(-0.959578\pi\) | ||||
0.991948 | − | 0.126648i | \(-0.0404220\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 870.940 | 0.884203 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 101.490i | − 0.102827i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1029.65 | −1.04110 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 680.902i | 0.687085i | 0.939137 | + | 0.343543i | \(0.111627\pi\) | ||||
−0.939137 | + | 0.343543i | \(0.888373\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 272.686 | 0.274609 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 101.783i | − 0.102294i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 146.950 | 0.147393 | 0.0736963 | − | 0.997281i | \(-0.476520\pi\) | ||||
0.0736963 | + | 0.997281i | \(0.476520\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 711.391i | 0.712103i |
(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 | 128.3.c.a.127.2 | ✓ | 4 | |
3.2 | odd | 2 | 1152.3.g.b.127.2 | 4 | |||
4.3 | odd | 2 | inner | 128.3.c.a.127.3 | yes | 4 | |
8.3 | odd | 2 | 128.3.c.b.127.2 | yes | 4 | ||
8.5 | even | 2 | 128.3.c.b.127.3 | yes | 4 | ||
12.11 | even | 2 | 1152.3.g.b.127.1 | 4 | |||
16.3 | odd | 4 | 256.3.d.e.127.1 | 4 | |||
16.5 | even | 4 | 256.3.d.e.127.2 | 4 | |||
16.11 | odd | 4 | 256.3.d.d.127.4 | 4 | |||
16.13 | even | 4 | 256.3.d.d.127.3 | 4 | |||
24.5 | odd | 2 | 1152.3.g.a.127.4 | 4 | |||
24.11 | even | 2 | 1152.3.g.a.127.3 | 4 | |||
48.5 | odd | 4 | 2304.3.b.j.127.2 | 4 | |||
48.11 | even | 4 | 2304.3.b.p.127.2 | 4 | |||
48.29 | odd | 4 | 2304.3.b.p.127.3 | 4 | |||
48.35 | even | 4 | 2304.3.b.j.127.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
128.3.c.a.127.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
128.3.c.a.127.3 | yes | 4 | 4.3 | odd | 2 | inner | |
128.3.c.b.127.2 | yes | 4 | 8.3 | odd | 2 | ||
128.3.c.b.127.3 | yes | 4 | 8.5 | even | 2 | ||
256.3.d.d.127.3 | 4 | 16.13 | even | 4 | |||
256.3.d.d.127.4 | 4 | 16.11 | odd | 4 | |||
256.3.d.e.127.1 | 4 | 16.3 | odd | 4 | |||
256.3.d.e.127.2 | 4 | 16.5 | even | 4 | |||
1152.3.g.a.127.3 | 4 | 24.11 | even | 2 | |||
1152.3.g.a.127.4 | 4 | 24.5 | odd | 2 | |||
1152.3.g.b.127.1 | 4 | 12.11 | even | 2 | |||
1152.3.g.b.127.2 | 4 | 3.2 | odd | 2 | |||
2304.3.b.j.127.2 | 4 | 48.5 | odd | 4 | |||
2304.3.b.j.127.3 | 4 | 48.35 | even | 4 | |||
2304.3.b.p.127.2 | 4 | 48.11 | even | 4 | |||
2304.3.b.p.127.3 | 4 | 48.29 | odd | 4 |