Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,5,Mod(319,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.319");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.b (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: | \(39.6940658242\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.49787136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{28}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 319.2 | ||
Root | \(-0.228425 + 1.39564i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.319 |
Dual form | 384.5.b.c.319.3 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −5.19615 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 23.7490i | − 0.949961i | −0.879996 | − | 0.474980i | \(-0.842455\pi\) | ||||
0.879996 | − | 0.474980i | \(-0.157545\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.38251i | 0.191480i | 0.995406 | + | 0.0957399i | \(0.0305217\pi\) | ||||
−0.995406 | + | 0.0957399i | \(0.969478\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −112.001 | −0.925631 | −0.462816 | − | 0.886455i | \(-0.653161\pi\) | ||||
−0.462816 | + | 0.886455i | \(0.653161\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 56.5020i | − 0.334331i | −0.985929 | − | 0.167166i | \(-0.946539\pi\) | ||||
0.985929 | − | 0.167166i | \(-0.0534615\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 123.404i | 0.548460i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −79.9921 | −0.276789 | −0.138395 | − | 0.990377i | \(-0.544194\pi\) | ||||
−0.138395 | + | 0.990377i | \(0.544194\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −211.297 | −0.585309 | −0.292655 | − | 0.956218i | \(-0.594539\pi\) | ||||
−0.292655 | + | 0.956218i | \(0.594539\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 48.7530i | − 0.110551i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 217.355i | − 0.410880i | −0.978670 | − | 0.205440i | \(-0.934138\pi\) | ||||
0.978670 | − | 0.205440i | \(-0.0658625\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 60.9843 | 0.0975748 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −140.296 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 616.753i | − 0.733357i | −0.930348 | − | 0.366678i | \(-0.880495\pi\) | ||||
0.930348 | − | 0.366678i | \(-0.119505\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1111.81i | 1.15693i | 0.815707 | + | 0.578465i | \(0.196348\pi\) | ||||
−0.815707 | + | 0.578465i | \(0.803652\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 581.976 | 0.534414 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 222.825 | 0.181898 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 802.980i | − 0.586545i | −0.956029 | − | 0.293273i | \(-0.905256\pi\) | ||||
0.956029 | − | 0.293273i | \(-0.0947443\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 293.593i | 0.193026i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2411.93 | −1.43482 | −0.717409 | − | 0.696652i | \(-0.754672\pi\) | ||||
−0.717409 | + | 0.696652i | \(0.754672\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2130.38 | 1.15218 | 0.576090 | − | 0.817386i | \(-0.304578\pi\) | ||||
0.576090 | + | 0.817386i | \(0.304578\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 641.223i | − 0.316654i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3596.58i | 1.62815i | 0.580761 | + | 0.814074i | \(0.302755\pi\) | ||||
−0.580761 | + | 0.814074i | \(0.697245\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2312.97 | 0.963335 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 415.651 | 0.159804 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 833.725i | 0.296805i | 0.988927 | + | 0.148403i | \(0.0474131\pi\) | ||||
−0.988927 | + | 0.148403i | \(0.952587\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2659.92i | 0.879313i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1097.93 | 0.337928 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1309.43 | 0.376165 | 0.188083 | − | 0.982153i | \(-0.439773\pi\) | ||||
0.188083 | + | 0.982153i | \(0.439773\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4785.91i | 1.28619i | 0.765786 | + | 0.643095i | \(0.222350\pi\) | ||||
−0.765786 | + | 0.643095i | \(0.777650\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 253.328i | 0.0638266i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1341.87 | −0.317601 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4025.23 | −0.896688 | −0.448344 | − | 0.893861i | \(-0.647986\pi\) | ||||
−0.448344 | + | 0.893861i | \(0.647986\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1129.41i | 0.237221i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9487.13i | 1.88199i | 0.338416 | + | 0.940997i | \(0.390109\pi\) | ||||
−0.338416 | + | 0.940997i | \(0.609891\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −266.031 | −0.0499215 | −0.0249607 | − | 0.999688i | \(-0.507946\pi\) | ||||
−0.0249607 | + | 0.999688i | \(0.507946\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −316.883 | −0.0563348 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1050.85i | − 0.177240i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5756.11i | 0.922306i | 0.887321 | + | 0.461153i | \(0.152564\pi\) | ||||
−0.887321 | + | 0.461153i | \(0.847436\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7287.16 | −1.05780 | −0.528898 | − | 0.848685i | \(-0.677395\pi\) | ||||
−0.528898 | + | 0.848685i | \(0.677395\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1899.73i | 0.262939i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3204.74i | 0.423404i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1414.08 | −0.178523 | −0.0892614 | − | 0.996008i | \(-0.528451\pi\) | ||||
−0.0892614 | + | 0.996008i | \(0.528451\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 530.130 | 0.0640177 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 5777.13i | − 0.667953i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5018.09i | 0.556021i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3110.08 | −0.330543 | −0.165271 | − | 0.986248i | \(-0.552850\pi\) | ||||
−0.165271 | + | 0.986248i | \(0.552850\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3024.04 | −0.308544 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 488.501i | 0.0478876i | 0.999713 | + | 0.0239438i | \(0.00762227\pi\) | ||||
−0.999713 | + | 0.0239438i | \(0.992378\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 20097.0i | 1.89434i | 0.320739 | + | 0.947168i | \(0.396069\pi\) | ||||
−0.320739 | + | 0.947168i | \(0.603931\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1157.83 | −0.105019 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12383.0 | 1.08158 | 0.540790 | − | 0.841158i | \(-0.318126\pi\) | ||||
0.540790 | + | 0.841158i | \(0.318126\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15542.1i | 1.30814i | 0.756433 | + | 0.654072i | \(0.226941\pi\) | ||||
−0.756433 | + | 0.654072i | \(0.773059\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4172.41i | 0.338642i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11653.6 | 0.912651 | 0.456325 | − | 0.889813i | \(-0.349165\pi\) | ||||
0.456325 | + | 0.889813i | \(0.349165\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5161.98 | −0.390319 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 1525.55i | − 0.111444i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 750.527i | − 0.0529996i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2096.69 | −0.143206 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12532.8 | 0.828393 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 16291.5i | − 1.04265i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4724.04i | 0.292891i | 0.989219 | + | 0.146445i | \(0.0467833\pi\) | ||||
−0.989219 | + | 0.146445i | \(0.953217\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11069.8 | −0.665212 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9632.86 | −0.561323 | −0.280661 | − | 0.959807i | \(-0.590554\pi\) | ||||
−0.280661 | + | 0.959807i | \(0.590554\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1982.49i | − 0.112075i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3331.89i | 0.182820i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16407.6 | 0.874185 | 0.437093 | − | 0.899417i | \(-0.356008\pi\) | ||||
0.437093 | + | 0.899417i | \(0.356008\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 25544.1 | 1.32209 | 0.661046 | − | 0.750346i | \(-0.270113\pi\) | ||||
0.661046 | + | 0.750346i | \(0.270113\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 18688.4i | − 0.940012i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6328.30i | 0.309467i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14647.3 | −0.696660 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12018.5 | −0.556182 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 18716.6i | − 0.843054i | −0.906816 | − | 0.421527i | \(-0.861494\pi\) | ||||
0.906816 | − | 0.421527i | \(-0.138506\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 28860.0i | − 1.26574i | −0.774260 | − | 0.632868i | \(-0.781878\pi\) | ||||
0.774260 | − | 0.632868i | \(-0.218122\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2159.79 | −0.0922631 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 26404.4 | 1.09904 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 23963.1i | 0.972172i | 0.873911 | + | 0.486086i | \(0.161576\pi\) | ||||
−0.873911 | + | 0.486086i | \(0.838424\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 4332.16i | − 0.171360i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2039.34 | 0.0786752 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −24424.8 | −0.919297 | −0.459648 | − | 0.888101i | \(-0.652025\pi\) | ||||
−0.459648 | + | 0.888101i | \(0.652025\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 13821.4i | − 0.507672i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 3088.40i | − 0.110739i | −0.998466 | − | 0.0553696i | \(-0.982366\pi\) | ||||
0.998466 | − | 0.0553696i | \(-0.0176337\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25368.5 | 0.888223 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5705.01 | −0.195103 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 18621.0i | − 0.622171i | −0.950382 | − | 0.311085i | \(-0.899307\pi\) | ||||
0.950382 | − | 0.311085i | \(-0.100693\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 572.185i | 0.0186836i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6804.00 | −0.217179 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −50739.3 | −1.58357 | −0.791787 | − | 0.610797i | \(-0.790849\pi\) | ||||
−0.791787 | + | 0.610797i | \(0.790849\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 58050.5i | 1.77194i | 0.463742 | + | 0.885970i | \(0.346506\pi\) | ||||
−0.463742 | + | 0.885970i | \(0.653494\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 24868.3i | − 0.742582i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −19070.0 | −0.557195 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8959.23 | 0.256205 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 1316.33i | − 0.0368503i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 21285.6i | − 0.583471i | −0.956499 | − | 0.291736i | \(-0.905767\pi\) | ||||
0.956499 | − | 0.291736i | \(-0.0942327\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26074.3 | −0.700001 | −0.350001 | − | 0.936749i | \(-0.613819\pi\) | ||||
−0.350001 | + | 0.936749i | \(0.613819\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6972.54 | 0.183367 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 4731.26i | − 0.121911i | −0.998140 | − | 0.0609557i | \(-0.980585\pi\) | ||||
0.998140 | − | 0.0609557i | \(-0.0194149\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 38561.7i | − 0.973756i | −0.873470 | − | 0.486878i | \(-0.838136\pi\) | ||||
0.873470 | − | 0.486878i | \(-0.161864\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 20915.7 | 0.517703 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5786.69 | 0.140423 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 57280.9i | 1.36302i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 5868.59i | − 0.136960i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 23665.5 | 0.541780 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −48656.4 | −1.09289 | −0.546444 | − | 0.837496i | \(-0.684019\pi\) | ||||
−0.546444 | + | 0.837496i | \(0.684019\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 49296.6i | − 1.08657i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 50594.5i | − 1.09453i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10431.6 | −0.221529 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1382.34 | 0.0288222 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4519.71i | 0.0925393i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 73299.7i | − 1.47398i | −0.675902 | − | 0.736992i | \(-0.736246\pi\) | ||||
0.675902 | − | 0.736992i | \(-0.263754\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1646.57 | 0.0325249 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14996.0 | 0.291020 | 0.145510 | − | 0.989357i | \(-0.453518\pi\) | ||||
0.145510 | + | 0.989357i | \(0.453518\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 74694.9i | 1.42436i | 0.701996 | + | 0.712181i | \(0.252292\pi\) | ||||
−0.701996 | + | 0.712181i | \(0.747708\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5460.40i | 0.102329i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −69476.6 | −1.27975 | −0.639877 | − | 0.768477i | \(-0.721015\pi\) | ||||
−0.639877 | + | 0.768477i | \(0.721015\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 85415.2 | 1.54668 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 29909.6i | − 0.532494i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 87478.2i | − 1.53145i | −0.643166 | − | 0.765727i | \(-0.722380\pi\) | ||||
0.643166 | − | 0.765727i | \(-0.277620\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 74951.4 | 1.29046 | 0.645232 | − | 0.763987i | \(-0.276761\pi\) | ||||
0.645232 | + | 0.763987i | \(0.276761\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3788.00 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 54930.7i | − 0.915131i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11938.7i | 0.195687i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 37865.2 | 0.610719 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 43677.8 | 0.693287 | 0.346643 | − | 0.937997i | \(-0.387321\pi\) | ||||
0.346643 | + | 0.937997i | \(0.387321\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24344.1i | 0.380323i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 9871.31i | − 0.151808i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1164.55 | −0.0176316 | −0.00881581 | − | 0.999961i | \(-0.502806\pi\) | ||||
−0.00881581 | + | 0.999961i | \(0.502806\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7533.97 | 0.112312 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 16652.3i | − 0.244452i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 35001.0i | − 0.506021i | −0.967464 | − | 0.253010i | \(-0.918579\pi\) | ||||
0.967464 | − | 0.253010i | \(-0.0814207\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19800.2 | 0.281953 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7347.77 | 0.103070 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 41077.9i | − 0.567681i | −0.958872 | − | 0.283840i | \(-0.908391\pi\) | ||||
0.958872 | − | 0.283840i | \(-0.0916085\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 46419.1i | − 0.632060i | −0.948749 | − | 0.316030i | \(-0.897650\pi\) | ||||
0.948749 | − | 0.316030i | \(-0.102350\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2754.64 | −0.0369606 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6830.32 | −0.0903183 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 150297.i | 1.95881i | 0.201907 | + | 0.979405i | \(0.435286\pi\) | ||||
−0.201907 | + | 0.979405i | \(0.564714\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 30018.8i | 0.385643i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −117793. | −1.49179 | −0.745895 | − | 0.666063i | \(-0.767978\pi\) | ||||
−0.745895 | + | 0.666063i | \(0.767978\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −41243.6 | −0.514973 | −0.257486 | − | 0.966282i | \(-0.582894\pi\) | ||||
−0.257486 | + | 0.966282i | \(0.582894\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 26074.7i | − 0.321019i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 22629.9i | − 0.274739i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −77122.3 | −0.923388 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16160.4 | 0.190839 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 71937.8i | − 0.837957i | −0.907996 | − | 0.418979i | \(-0.862388\pi\) | ||||
0.907996 | − | 0.418979i | \(-0.137612\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 31097.7i | − 0.357342i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15713.4 | 0.178138 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12281.0 | −0.137370 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19988.3i | 0.220619i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 2538.33i | − 0.0276479i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 113661. | 1.22183 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −54572.7 | −0.579027 | −0.289514 | − | 0.957174i | \(-0.593494\pi\) | ||||
−0.289514 | + | 0.957174i | \(0.593494\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 104427.i | − 1.09370i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 60945.8i | 0.630119i | 0.949072 | + | 0.315060i | \(0.102025\pi\) | ||||
−0.949072 | + | 0.315060i | \(0.897975\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 102774. | 1.04904 | 0.524521 | − | 0.851397i | \(-0.324244\pi\) | ||||
0.524521 | + | 0.851397i | \(0.324244\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6016.29 | 0.0606328 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 39779.2i | − 0.395857i | −0.980217 | − | 0.197928i | \(-0.936579\pi\) | ||||
0.980217 | − | 0.197928i | \(-0.0634213\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 69077.2i | 0.678818i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −64344.0 | −0.624450 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16902.1 | 0.162007 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 3445.73i | − 0.0326223i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 80758.9i | − 0.755257i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −33744.9 | −0.311758 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −87804.6 | −0.801422 | −0.400711 | − | 0.916204i | \(-0.631237\pi\) | ||||
−0.400711 | + | 0.916204i | \(0.631237\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 21680.5i | − 0.195515i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 95595.3i | 0.851818i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −57972.0 | −0.510456 | −0.255228 | − | 0.966881i | \(-0.582151\pi\) | ||||
−0.255228 | + | 0.966881i | \(0.582151\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −60554.1 | −0.526919 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 124524.i | − 1.07089i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 44228.9i | 0.375939i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 26822.4 | 0.225351 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −159188. | −1.32206 | −0.661031 | − | 0.750359i | \(-0.729881\pi\) | ||||
−0.661031 | + | 0.750359i | \(0.729881\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17396.8i | 0.142830i | 0.997447 | + | 0.0714149i | \(0.0227514\pi\) | ||||
−0.997447 | + | 0.0714149i | \(0.977249\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7927.01i | 0.0643421i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 150532. | 1.20803 | 0.604017 | − | 0.796972i | \(-0.293566\pi\) | ||||
0.604017 | + | 0.796972i | \(0.293566\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 225310. | 1.78782 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3899.85i | 0.0305993i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24818.5i | 0.192569i | 0.995354 | + | 0.0962846i | \(0.0306959\pi\) | ||||
−0.995354 | + | 0.0962846i | \(0.969304\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −85674.8 | −0.657413 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10894.7 | 0.0826803 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6317.99i | 0.0474234i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 89484.6i | 0.664379i | 0.943213 | + | 0.332190i | \(0.107787\pi\) | ||||
−0.943213 | + | 0.332190i | \(0.892213\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −65122.1 | −0.478273 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7822.44 | −0.0568322 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 168536.i | 1.21137i | 0.795705 | + | 0.605684i | \(0.207100\pi\) | ||||
−0.795705 | + | 0.605684i | \(0.792900\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 84652.9i | 0.601976i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −34847.8 | −0.245184 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −126865. | −0.883208 | −0.441604 | − | 0.897210i | \(-0.645590\pi\) | ||||
−0.441604 | + | 0.897210i | \(0.645590\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 24546.8i | − 0.169101i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 257277.i | 1.75389i | 0.480587 | + | 0.876947i | \(0.340424\pi\) | ||||
−0.480587 | + | 0.876947i | \(0.659576\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24956.8 | −0.168371 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 57520.3 | 0.384060 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 150562.i | 0.994983i | 0.867469 | + | 0.497492i | \(0.165745\pi\) | ||||
−0.867469 | + | 0.497492i | \(0.834255\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17386.7i | 0.113727i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 50053.8 | 0.324080 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 136702. | 0.876155 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 185402.i | 1.17634i | 0.808736 | + | 0.588171i | \(0.200152\pi\) | ||||
−0.808736 | + | 0.588171i | \(0.799848\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10301.3i | 0.0647064i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 167681. | 1.04279 | 0.521393 | − | 0.853317i | \(-0.325413\pi\) | ||||
0.521393 | + | 0.853317i | \(0.325413\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 62819.4 | 0.386798 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 17313.0i | − 0.105551i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 89934.9i | 0.542925i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 60544.6 | 0.361934 | 0.180967 | − | 0.983489i | \(-0.442077\pi\) | ||||
0.180967 | + | 0.983489i | \(0.442077\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −85256.3 | −0.504711 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12285.7i | 0.0720280i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 173063.i | 1.00486i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −132731. | −0.763310 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 307306. | 1.75042 | 0.875211 | − | 0.483741i | \(-0.160723\pi\) | ||||
0.875211 | + | 0.483741i | \(0.160723\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 172189.i | − 0.971496i | −0.874099 | − | 0.485748i | \(-0.838547\pi\) | ||||
0.874099 | − | 0.485748i | \(-0.161453\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 97107.7i | 0.542716i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4878.26 | −0.0270077 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −44903.9 | −0.246279 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 32882.8i | − 0.178671i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28153.8i | 0.151559i | 0.997125 | + | 0.0757797i | \(0.0241446\pi\) | ||||
−0.997125 | + | 0.0757797i | \(0.975855\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −322037. | −1.71763 | −0.858815 | − | 0.512285i | \(-0.828799\pi\) | ||||
−0.858815 | + | 0.512285i | \(0.828799\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 76109.5 | 0.402217 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 45926.4i | 0.240492i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 292438.i | 1.51742i | 0.651430 | + | 0.758709i | \(0.274170\pi\) | ||||
−0.651430 | + | 0.758709i | \(0.725830\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 62450.1 | 0.321112 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −227681. | −1.16016 | −0.580082 | − | 0.814558i | \(-0.696980\pi\) | ||||
−0.580082 | + | 0.814558i | \(0.696980\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 33583.0i | 0.169590i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 97254.5i | 0.486737i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 159097. | 0.789169 | 0.394585 | − | 0.918860i | \(-0.370889\pi\) | ||||
0.394585 | + | 0.918860i | \(0.370889\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 270139. | 1.32811 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 149961.i | 0.730773i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 12590.1i | − 0.0608143i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 340590. | 1.63079 | 0.815397 | − | 0.578902i | \(-0.196519\pi\) | ||||
0.815397 | + | 0.578902i | \(0.196519\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11222.6 | 0.0532681 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 178561.i | − 0.840204i | −0.907477 | − | 0.420102i | \(-0.861994\pi\) | ||||
0.907477 | − | 0.420102i | \(-0.138006\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 4179.11i | − 0.0194950i | −0.999952 | − | 0.00974748i | \(-0.996897\pi\) | ||||
0.999952 | − | 0.00974748i | \(-0.00310277\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −137201. | −0.634529 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −160583. | −0.736318 | −0.368159 | − | 0.929763i | \(-0.620012\pi\) | ||||
−0.368159 | + | 0.929763i | \(0.620012\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 37766.8i | − 0.171698i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 124516.i | − 0.561284i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −238606. | −1.06649 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12885.8 | −0.0571114 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 22510.6i | 0.0989350i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 153260.i | − 0.667970i | −0.942578 | − | 0.333985i | \(-0.891607\pi\) | ||||
0.942578 | − | 0.333985i | \(-0.108393\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −45370.0 | −0.196100 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10596.7 | −0.0454231 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 73861.3i | 0.314003i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 113347.i | 0.477917i | 0.971030 | + | 0.238958i | \(0.0768059\pi\) | ||||
−0.971030 | + | 0.238958i | \(0.923194\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 126915. | 0.530756 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −248336. | −1.03009 | −0.515046 | − | 0.857162i | \(-0.672225\pi\) | ||||
−0.515046 | + | 0.857162i | \(0.672225\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 49335.4i | 0.202985i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 71817.9i | 0.293104i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −89013.1 | −0.360364 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −378612. | −1.52052 | −0.760262 | − | 0.649617i | \(-0.774929\pi\) | ||||
−0.760262 | + | 0.649617i | \(0.774929\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16047.8i | 0.0639353i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 255639.i | 1.01040i | 0.863004 | + | 0.505198i | \(0.168580\pi\) | ||||
−0.863004 | + | 0.505198i | \(0.831420\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11601.4 | 0.0454913 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −131819. | −0.512816 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 204106.i | 0.787809i | 0.919151 | + | 0.393904i | \(0.128876\pi\) | ||||
−0.919151 | + | 0.393904i | \(0.871124\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 2496.04i | − 0.00955895i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 29644.1 | 0.112643 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 477284. | 1.79954 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 402822.i | − 1.50707i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 96757.3i | 0.359211i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −295131. | −1.08727 | −0.543637 | − | 0.839320i | \(-0.682953\pi\) | ||||
−0.543637 | + | 0.839320i | \(0.682953\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −212950. | −0.778527 | −0.389263 | − | 0.921127i | \(-0.627270\pi\) | ||||
−0.389263 | + | 0.921127i | \(0.627270\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 2973.16i | − 0.0107870i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 88936.0i | − 0.320226i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 232598. | 0.831178 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 35354.6 | 0.125388 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 136279.i | 0.479704i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 294084.i | − 1.02746i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 263649. | 0.914277 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −259056. | −0.891694 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 387756.i | − 1.32484i | −0.749132 | − | 0.662421i | \(-0.769529\pi\) | ||||
0.749132 | − | 0.662421i | \(-0.230471\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 301639.i | − 1.02303i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 369108. | 1.24268 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 241227. | 0.806215 | 0.403107 | − | 0.915153i | \(-0.367930\pi\) | ||||
0.403107 | + | 0.915153i | \(0.367930\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 129220.i | 0.428730i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 130318.i | 0.429240i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −54006.8 | −0.176603 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 99090.6 | 0.321697 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 86454.9i | − 0.278663i | −0.990246 | − | 0.139331i | \(-0.955505\pi\) | ||||
0.990246 | − | 0.139331i | \(-0.0444954\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 120371.i | − 0.385210i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −46553.5 | −0.147920 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −99585.2 | −0.314179 | −0.157090 | − | 0.987584i | \(-0.550211\pi\) | ||||
−0.157090 | + | 0.987584i | \(0.550211\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 276762.i | − 0.866982i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6839.85i | 0.0212755i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −524085. | −1.61874 | −0.809371 | − | 0.587298i | \(-0.800192\pi\) | ||||
−0.809371 | + | 0.587298i | \(0.800192\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32749.2 | −0.100445 | −0.0502225 | − | 0.998738i | \(-0.515993\pi\) | ||||
−0.0502225 | + | 0.998738i | \(0.515993\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 110603.i | 0.336867i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 13255.3i | − 0.0400915i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −140276. | −0.421338 | −0.210669 | − | 0.977557i | \(-0.567564\pi\) | ||||
−0.210669 | + | 0.977557i | \(0.567564\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 135486. | 0.404146 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 68371.8i | − 0.202547i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 93378.4i | − 0.274732i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −36230.4 | −0.105867 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 303094. | 0.879634 | 0.439817 | − | 0.898087i | \(-0.355043\pi\) | ||||
0.439817 | + | 0.898087i | \(0.355043\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 234921.i | − 0.677161i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24584.4i | 0.0703856i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 117438. | 0.333963 | 0.166981 | − | 0.985960i | \(-0.446598\pi\) | ||||
0.166981 | + | 0.985960i | \(0.446598\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17824.3 | −0.0503475 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 200373.i | 0.562198i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 537187.i | − 1.49717i | −0.663037 | − | 0.748587i | \(-0.730733\pi\) | ||||
0.663037 | − | 0.748587i | \(-0.269267\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 382705. | 1.05953 | 0.529767 | − | 0.848143i | \(-0.322279\pi\) | ||||
0.529767 | + | 0.848143i | \(0.322279\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −108681. | −0.298896 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 49794.2i | 0.136040i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 578934.i | − 1.57127i | −0.618688 | − | 0.785637i | \(-0.712336\pi\) | ||||
0.618688 | − | 0.785637i | \(-0.287664\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −30068.5 | −0.0810732 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 203214. | 0.544341 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 287542.i | − 0.765209i | −0.923912 | − | 0.382605i | \(-0.875027\pi\) | ||||
0.923912 | − | 0.382605i | \(-0.124973\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 297641.i | − 0.786940i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −400806. | −1.05284 | −0.526422 | − | 0.850223i | \(-0.676467\pi\) | ||||
−0.526422 | + | 0.850223i | \(0.676467\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 233469. | 0.609323 | 0.304661 | − | 0.952461i | \(-0.401457\pi\) | ||||
0.304661 | + | 0.952461i | \(0.401457\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 30494.1i | 0.0790738i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 13267.6i | − 0.0341835i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −348791. | −0.892904 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −122970. | −0.312797 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 64232.1i | 0.162349i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 499538.i | − 1.25461i | −0.778773 | − | 0.627306i | \(-0.784157\pi\) | ||||
0.778773 | − | 0.627306i | \(-0.215843\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 252826. | 0.630979 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 112191. | 0.278235 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 130687.i | − 0.322073i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 256152.i | 0.627331i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 405774. | 0.987571 | 0.493786 | − | 0.869584i | \(-0.335613\pi\) | ||||
0.493786 | + | 0.869584i | \(0.335613\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 550571. | 1.33165 | 0.665827 | − | 0.746106i | \(-0.268079\pi\) | ||||
0.665827 | + | 0.746106i | \(0.268079\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 262897.i | 0.631925i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 428220.i | − 1.02296i | −0.859295 | − | 0.511480i | \(-0.829097\pi\) | ||||
0.859295 | − | 0.511480i | \(-0.170903\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −146658. | −0.348190 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 54204.0 | 0.127900 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 802147.i | 1.88117i | 0.339561 | + | 0.940584i | \(0.389721\pi\) | ||||
−0.339561 | + | 0.940584i | \(0.610279\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 228771.i | 0.533234i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7182.85 | −0.0166405 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −662958. | −1.52656 | −0.763282 | − | 0.646065i | \(-0.776414\pi\) | ||||
−0.763282 | + | 0.646065i | \(0.776414\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 231396.i | − 0.529607i | −0.964302 | − | 0.264804i | \(-0.914693\pi\) | ||||
0.964302 | − | 0.264804i | \(-0.0853071\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 23485.1i | − 0.0534276i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −47082.2 | −0.106467 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −134055. | −0.301321 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 380877.i | 0.851005i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 536029.i | − 1.19054i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 311867. | 0.688557 | 0.344278 | − | 0.938868i | \(-0.388124\pi\) | ||||
0.344278 | + | 0.938868i | \(0.388124\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8555.85 | −0.0187783 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 655173.i | 1.42948i | 0.699389 | + | 0.714741i | \(0.253455\pi\) | ||||
−0.699389 | + | 0.714741i | \(0.746545\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 29180.3i | − 0.0632923i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −77921.4 | −0.168021 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 358002. | 0.767439 | 0.383719 | − | 0.923450i | \(-0.374643\pi\) | ||||
0.383719 | + | 0.923450i | \(0.374643\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 389664.i | − 0.830442i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 388126.i | − 0.822355i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 47107.1 | 0.0992312 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −826006. | −1.72992 | −0.864962 | − | 0.501838i | \(-0.832657\pi\) | ||||
−0.864962 | + | 0.501838i | \(0.832657\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 28373.1i | − 0.0590799i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 606648.i | − 1.25593i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 192935. | 0.397142 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 361011. | 0.738866 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 229057.i | − 0.466130i | −0.972461 | − | 0.233065i | \(-0.925124\pi\) | ||||
0.972461 | − | 0.233065i | \(-0.0748756\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 169667.i | 0.343310i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −443831. | −0.892974 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4583.37 | −0.00916950 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 6312.88i | − 0.0125584i | −0.999980 | − | 0.00627921i | \(-0.998001\pi\) | ||||
0.999980 | − | 0.00627921i | \(-0.00199875\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 155415.i | 0.307435i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 241658. | 0.475359 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 150291. | 0.293982 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 454550.i | 0.884185i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 179483.i | − 0.347189i | −0.984817 | − | 0.173594i | \(-0.944462\pi\) | ||||
0.984817 | − | 0.173594i | \(-0.0555382\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −188560. | −0.362727 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −389459. | −0.745049 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 37612.2i | − 0.0715571i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 310931.i | − 0.588295i | −0.955760 | − | 0.294147i | \(-0.904964\pi\) | ||||
0.955760 | − | 0.294147i | \(-0.0950357\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −170414. | −0.318911 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 602271.i | − 1.12094i | −0.828173 | − | 0.560472i | \(-0.810620\pi\) | ||||
0.828173 | − | 0.560472i | \(-0.189380\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 285428.i | 0.528351i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 450832. | 0.830002 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 64180.3 | 0.117520 | 0.0587602 | − | 0.998272i | \(-0.481285\pi\) | ||||
0.0587602 | + | 0.998272i | \(0.481285\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 62035.2i | − 0.112980i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 525793.i | 0.952440i | 0.879326 | + | 0.476220i | \(0.157993\pi\) | ||||
−0.879326 | + | 0.476220i | \(0.842007\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −444502. | −0.800868 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −196753. | −0.352599 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 116184.i | 0.207101i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 405381.i | − 0.718759i | −0.933191 | − | 0.359380i | \(-0.882988\pi\) | ||||
0.933191 | − | 0.359380i | \(-0.117012\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −226956. | −0.400269 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −685398. | −1.20240 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 5071.58i | − 0.00885016i | −0.999990 | − | 0.00442508i | \(-0.998591\pi\) | ||||
0.999990 | − | 0.00442508i | \(-0.00140855\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 126496.i | − 0.219580i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29104.4 | −0.0502561 | −0.0251280 | − | 0.999684i | \(-0.507999\pi\) | ||||
−0.0251280 | + | 0.999684i | \(0.507999\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −145823. | −0.250483 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 51292.8i | 0.0876463i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 73985.4i | − 0.125764i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −235095. | −0.397548 | −0.198774 | − | 0.980045i | \(-0.563696\pi\) | ||||
−0.198774 | + | 0.980045i | \(0.563696\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6051.19 | 0.0101796 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 89776.8i | − 0.150247i | −0.997174 | − | 0.0751234i | \(-0.976065\pi\) | ||||
0.997174 | − | 0.0751234i | \(-0.0239351\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 67802.8i | 0.112887i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −39147.7 | −0.0648431 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 509632. | 0.839812 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1.06257e6i | − 1.74203i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 86528.0i | 0.141135i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 569099. | 0.923525 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −406715. | −0.656660 | −0.328330 | − | 0.944563i | \(-0.606486\pi\) | ||||
−0.328330 | + | 0.944563i | \(0.606486\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 181870.i | 0.292151i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 109340.i | 0.174754i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 270414. | 0.430013 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −102885. | −0.162786 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.02634e6i | 1.61576i | 0.589350 | + | 0.807878i | \(0.299384\pi\) | ||||
−0.589350 | + | 0.807878i | \(0.700616\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 287698.i | − 0.450654i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −38180.1 | −0.0595076 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 29795.9 | 0.0462089 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 48432.3i | − 0.0747383i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 213447.i | 0.327751i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 245306. | 0.374810 | 0.187405 | − | 0.982283i | \(-0.439992\pi\) | ||||
0.187405 | + | 0.982283i | \(0.439992\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.26760e6 | 1.92726 | 0.963628 | − | 0.267246i | \(-0.0861137\pi\) | ||||
0.963628 | + | 0.267246i | \(0.0861137\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 241201.i | 0.364920i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 580065.i | 0.873296i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −450142. | −0.674382 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 14313.5 | 0.0213392 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 163484.i | 0.242542i | 0.992619 | + | 0.121271i | \(0.0386971\pi\) | ||||
−0.992619 | + | 0.121271i | \(0.961303\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 913000.i | 1.34794i | 0.738758 | + | 0.673971i | \(0.235413\pi\) | ||||
−0.738758 | + | 0.673971i | \(0.764587\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 35491.4 | 0.0521453 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 378235. | 0.553032 | 0.276516 | − | 0.961009i | \(-0.410820\pi\) | ||||
0.276516 | + | 0.961009i | \(0.410820\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 70195.3i | 0.102141i | 0.998695 | + | 0.0510704i | \(0.0162633\pi\) | ||||
−0.998695 | + | 0.0510704i | \(0.983737\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 780969.i | − 1.13092i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −185019. | −0.266641 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −73346.5 | −0.105198 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 155982.i | − 0.222651i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 410513.i | 0.583180i | 0.956543 | + | 0.291590i | \(0.0941843\pi\) | ||||
−0.956543 | + | 0.291590i | \(0.905816\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 326897. | 0.462188 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 612072. | 0.861286 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 602478.i | − 0.843777i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 19672.2i | − 0.0274211i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 214308. | 0.297320 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −174532. | −0.240999 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 577725.i | − 0.794005i | −0.917817 | − | 0.397003i | \(-0.870050\pi\) | ||||
0.917817 | − | 0.397003i | \(-0.129950\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 135488.i | 0.185340i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −388294. | −0.528687 | −0.264344 | − | 0.964429i | \(-0.585155\pi\) | ||||
−0.264344 | + | 0.964429i | \(0.585155\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 124443. | 0.168650 | 0.0843248 | − | 0.996438i | \(-0.473127\pi\) | ||||
0.0843248 | + | 0.996438i | \(0.473127\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 117589.i | 0.158620i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 652166.i | 0.875662i | 0.899057 | + | 0.437831i | \(0.144253\pi\) | ||||
−0.899057 | + | 0.437831i | \(0.855747\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −442229. | −0.591038 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 400739. | 0.533118 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 644693.i | − 0.853716i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 227434.i | 0.299791i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −83972.1 | −0.110181 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 152855. | 0.199647 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 75235.9i | − 0.0978196i | −0.998803 | − | 0.0489098i | \(-0.984425\pi\) | ||||
0.998803 | − | 0.0489098i | \(-0.0155747\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 373800.i | 0.483795i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −916209. | −1.18044 | −0.590218 | − | 0.807244i | \(-0.700958\pi\) | ||||
−0.590218 | + | 0.807244i | \(0.700958\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.14981e6 | −1.47471 | −0.737354 | − | 0.675506i | \(-0.763925\pi\) | ||||
−0.737354 | + | 0.675506i | \(0.763925\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 161588.i | 0.206311i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.01630e6i | 1.29174i | 0.763448 | + | 0.645870i | \(0.223505\pi\) | ||||
−0.763448 | + | 0.645870i | \(0.776495\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −44323.3 | −0.0560827 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −81649.0 | −0.102848 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 759945.i | − 0.952970i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.20501e6i | 1.50433i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 63814.0 | 0.0793105 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 685711. | 0.848442 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 66691.5i | − 0.0821525i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 103862.i | − 0.127375i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.37864e6 | 1.68327 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.00415e6 | 1.22063 | 0.610315 | − | 0.792159i | \(-0.291043\pi\) | ||||
0.610315 | + | 0.792159i | \(0.291043\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13189.5i | 0.0159625i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 231087.i | 0.278444i | 0.990261 | + | 0.139222i | \(0.0444602\pi\) | ||||
−0.990261 | + | 0.139222i | \(0.955540\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 816172. | 0.979129 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −590598. | −0.705424 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 90380.4i | − 0.107482i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 545658.i | 0.646084i | 0.946385 | + | 0.323042i | \(0.104706\pi\) | ||||
−0.946385 | + | 0.323042i | \(0.895294\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 283568. | 0.334302 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 536041. | 0.629209 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 48969.2i | − 0.0572320i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 542619.i | 0.631445i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −243550. | −0.282200 | −0.141100 | − | 0.989995i | \(-0.545064\pi\) | ||||
−0.141100 | + | 0.989995i | \(0.545064\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −488722. | −0.563849 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 316684.i | − 0.363800i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 212773.i | − 0.243385i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 479076. | 0.545664 | 0.272832 | − | 0.962062i | \(-0.412040\pi\) | ||||
0.272832 | + | 0.962062i | \(0.412040\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −534027. | −0.605665 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.25655e6i | 1.41906i | 0.704675 | + | 0.709530i | \(0.251093\pi\) | ||||
−0.704675 | + | 0.709530i | \(0.748907\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 524246.i | 0.589538i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −31261.5 | −0.0350063 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.22304e6 | −1.36377 | −0.681886 | − | 0.731459i | \(-0.738840\pi\) | ||||
−0.681886 | + | 0.731459i | \(0.738840\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15031.3i | 0.0166903i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 206699.i | 0.228548i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.12329e6 | −1.23682 | −0.618409 | − | 0.785856i | \(-0.712223\pi\) | ||||
−0.618409 | + | 0.785856i | \(0.712223\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −505512. | −0.554275 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 358936.i | − 0.391916i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 153944.i | 0.167389i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −312598. | −0.338485 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 334341. | 0.360526 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 619240.i | 0.664974i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 310108.i | 0.331635i | 0.986156 | + | 0.165818i | \(0.0530263\pi\) | ||||
−0.986156 | + | 0.165818i | \(0.946974\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −87825.7 | −0.0935350 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −459519. | −0.487376 | −0.243688 | − | 0.969854i | \(-0.578357\pi\) | ||||
−0.243688 | + | 0.969854i | \(0.578357\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 239668.i | 0.253154i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 17904.5i | 0.0188345i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −645770. | −0.676532 | −0.338266 | − | 0.941050i | \(-0.609840\pi\) | ||||
−0.338266 | + | 0.941050i | \(0.609840\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 158379. | 0.165246 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 419635.i | 0.436048i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 828941.i | 0.857860i | 0.903338 | + | 0.428930i | \(0.141109\pi\) | ||||
−0.903338 | + | 0.428930i | \(0.858891\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −112363. | −0.115811 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 175344. | 0.179993 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 463050.i | − 0.473407i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 460245.i | 0.468642i | 0.972159 | + | 0.234321i | \(0.0752867\pi\) | ||||
−0.972159 | + | 0.234321i | \(0.924713\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 456246. | 0.462701 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −915803. | −0.925030 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.82730e6i | 1.83831i | 0.393894 | + | 0.919156i | \(0.371128\pi\) | ||||
−0.393894 | + | 0.919156i | \(0.628872\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 112655.i | 0.112881i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 384.5.b.c.319.2 | ✓ | 8 | |
3.2 | odd | 2 | 1152.5.b.k.703.6 | 8 | |||
4.3 | odd | 2 | inner | 384.5.b.c.319.6 | yes | 8 | |
8.3 | odd | 2 | inner | 384.5.b.c.319.3 | yes | 8 | |
8.5 | even | 2 | inner | 384.5.b.c.319.7 | yes | 8 | |
12.11 | even | 2 | 1152.5.b.k.703.5 | 8 | |||
16.3 | odd | 4 | 768.5.g.g.511.3 | 4 | |||
16.5 | even | 4 | 768.5.g.c.511.4 | 4 | |||
16.11 | odd | 4 | 768.5.g.c.511.2 | 4 | |||
16.13 | even | 4 | 768.5.g.g.511.1 | 4 | |||
24.5 | odd | 2 | 1152.5.b.k.703.4 | 8 | |||
24.11 | even | 2 | 1152.5.b.k.703.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.5.b.c.319.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
384.5.b.c.319.3 | yes | 8 | 8.3 | odd | 2 | inner | |
384.5.b.c.319.6 | yes | 8 | 4.3 | odd | 2 | inner | |
384.5.b.c.319.7 | yes | 8 | 8.5 | even | 2 | inner | |
768.5.g.c.511.2 | 4 | 16.11 | odd | 4 | |||
768.5.g.c.511.4 | 4 | 16.5 | even | 4 | |||
768.5.g.g.511.1 | 4 | 16.13 | even | 4 | |||
768.5.g.g.511.3 | 4 | 16.3 | odd | 4 | |||
1152.5.b.k.703.3 | 8 | 24.11 | even | 2 | |||
1152.5.b.k.703.4 | 8 | 24.5 | odd | 2 | |||
1152.5.b.k.703.5 | 8 | 12.11 | even | 2 | |||
1152.5.b.k.703.6 | 8 | 3.2 | odd | 2 |