Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,5,Mod(511,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.511");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.g (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(79.3881316484\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 511.2 | ||
Root | \(-1.32288 - 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.511 |
Dual form | 768.5.g.c.511.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − 5.19615i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 23.7490 | 0.949961 | 0.474980 | − | 0.879996i | \(-0.342455\pi\) | ||||
0.474980 | + | 0.879996i | \(0.342455\pi\) | |||||||
\(6\) | 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 | ||||||||
\(11\) | 112.001i | 0.925631i | 0.886455 | + | 0.462816i | \(0.153161\pi\) | ||||
−0.886455 | + | 0.462816i | \(0.846839\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −56.5020 | −0.334331 | −0.167166 | − | 0.985929i | \(-0.553461\pi\) | ||||
−0.167166 | + | 0.985929i | \(0.553461\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | − 211.297i | − 0.585309i | −0.956218 | − | 0.292655i | \(-0.905461\pi\) | ||||
0.956218 | − | 0.292655i | \(-0.0945386\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 48.7530 | 0.110551 | ||||||||
\(22\) | 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 | ||||||||
\(27\) | 140.296i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −616.753 | −0.733357 | −0.366678 | − | 0.930348i | \(-0.619505\pi\) | ||||
−0.366678 | + | 0.930348i | \(0.619505\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 1111.81i | − 1.15693i | −0.815707 | − | 0.578465i | \(-0.803652\pi\) | ||||
0.815707 | − | 0.578465i | \(-0.196348\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 581.976 | 0.534414 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 222.825i | 0.181898i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 802.980 | 0.586545 | 0.293273 | − | 0.956029i | \(-0.405256\pi\) | ||||
0.293273 | + | 0.956029i | \(0.405256\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 293.593i | 0.193026i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2411.93 | 1.43482 | 0.717409 | − | 0.696652i | \(-0.245328\pi\) | ||||
0.717409 | + | 0.696652i | \(0.245328\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 2130.38i | − 1.15218i | −0.817386 | − | 0.576090i | \(-0.804578\pi\) | ||||
0.817386 | − | 0.576090i | \(-0.195422\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −641.223 | −0.316654 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 3596.58i | − 1.62815i | −0.580761 | − | 0.814074i | \(-0.697245\pi\) | ||||
0.580761 | − | 0.814074i | \(-0.302755\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2312.97 | 0.963335 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 415.651i | 0.159804i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −833.725 | −0.296805 | −0.148403 | − | 0.988927i | \(-0.547413\pi\) | ||||
−0.148403 | + | 0.988927i | \(0.547413\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2659.92i | 0.879313i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1097.93 | −0.337928 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 1309.43i | − 0.376165i | −0.982153 | − | 0.188083i | \(-0.939773\pi\) | ||||
0.982153 | − | 0.188083i | \(-0.0602272\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4785.91 | 1.28619 | 0.643095 | − | 0.765786i | \(-0.277650\pi\) | ||||
0.643095 | + | 0.765786i | \(0.277650\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 253.328i | − 0.0638266i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1341.87 | −0.317601 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 4025.23i | − 0.896688i | −0.893861 | − | 0.448344i | \(-0.852014\pi\) | ||||
0.893861 | − | 0.448344i | \(-0.147986\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1129.41 | −0.237221 | ||||||||
\(70\) | 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 | \(-0.492054\pi\) | ||||
0.0249607 | + | 0.999688i | \(0.492054\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 316.883i | 0.0563348i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1050.85 | −0.177240 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 5756.11i | − 0.922306i | −0.887321 | − | 0.461153i | \(-0.847436\pi\) | ||||
0.887321 | − | 0.461153i | \(-0.152564\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 7287.16i | − 1.05780i | −0.848685 | − | 0.528898i | \(-0.822605\pi\) | ||||
0.848685 | − | 0.528898i | \(-0.177395\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1899.73 | −0.262939 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3204.74i | 0.423404i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1414.08 | 0.178523 | 0.0892614 | − | 0.996008i | \(-0.471549\pi\) | ||||
0.0892614 | + | 0.996008i | \(0.471549\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 530.130i | − 0.0640177i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5777.13 | −0.667953 | ||||||||
\(94\) | 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 | ||||||||
\(99\) | − 3024.04i | − 0.308544i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −488.501 | −0.0478876 | −0.0239438 | − | 0.999713i | \(-0.507622\pi\) | ||||
−0.0239438 | + | 0.999713i | \(0.507622\pi\) | |||||||
\(102\) | 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 | ||||||||
\(107\) | − 12383.0i | − 1.08158i | −0.841158 | − | 0.540790i | \(-0.818126\pi\) | ||||
0.841158 | − | 0.540790i | \(-0.181874\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15542.1 | 1.30814 | 0.654072 | − | 0.756433i | \(-0.273059\pi\) | ||||
0.654072 | + | 0.756433i | \(0.273059\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | − 5161.98i | − 0.390319i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1525.55 | 0.111444 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 750.527i | − 0.0529996i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2096.69 | 0.143206 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 12532.8i | − 0.828393i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −16291.5 | −1.04265 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 4724.04i | − 0.292891i | −0.989219 | − | 0.146445i | \(-0.953217\pi\) | ||||
0.989219 | − | 0.146445i | \(-0.0467833\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11069.8 | −0.665212 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 9632.86i | − 0.561323i | −0.959807 | − | 0.280661i | \(-0.909446\pi\) | ||||
0.959807 | − | 0.280661i | \(-0.0905538\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1982.49 | 0.112075 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3331.89i | 0.182820i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16407.6 | −0.874185 | −0.437093 | − | 0.899417i | \(-0.643992\pi\) | ||||
−0.437093 | + | 0.899417i | \(0.643992\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 25544.1i | − 1.32209i | −0.750346 | − | 0.661046i | \(-0.770113\pi\) | ||||
0.750346 | − | 0.661046i | \(-0.229887\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18688.4 | −0.940012 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 6328.30i | − 0.309467i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14647.3 | −0.696660 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 12018.5i | − 0.556182i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18716.6 | 0.843054 | 0.421527 | − | 0.906816i | \(-0.361494\pi\) | ||||
0.421527 | + | 0.906816i | \(0.361494\pi\) | |||||||
\(150\) | 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 | ||||||||
\(155\) | − 26404.4i | − 1.09904i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 23963.1 | 0.972172 | 0.486086 | − | 0.873911i | \(-0.338424\pi\) | ||||
0.486086 | + | 0.873911i | \(0.338424\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4332.16i | 0.171360i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2039.34 | 0.0786752 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 24424.8i | − 0.919297i | −0.888101 | − | 0.459648i | \(-0.847975\pi\) | ||||
0.888101 | − | 0.459648i | \(-0.152025\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13821.4 | 0.507672 | ||||||||
\(166\) | 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 | ||||||||
\(171\) | 5705.01i | 0.195103i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18621.0 | −0.622171 | −0.311085 | − | 0.950382i | \(-0.600693\pi\) | ||||
−0.311085 | + | 0.950382i | \(0.600693\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 572.185i | − 0.0186836i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6804.00 | −0.217179 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 50739.3i | − 1.58357i | −0.610797 | − | 0.791787i | \(-0.709151\pi\) | ||||
0.610797 | − | 0.791787i | \(-0.290849\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −58050.5 | −1.77194 | −0.885970 | − | 0.463742i | \(-0.846506\pi\) | ||||
−0.885970 | + | 0.463742i | \(0.846506\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 24868.3i | − 0.742582i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 19070.0 | 0.557195 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 8959.23i | − 0.256205i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1316.33 | −0.0368503 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21285.6i | 0.583471i | 0.956499 | + | 0.291736i | \(0.0942327\pi\) | ||||
−0.956499 | + | 0.291736i | \(0.905767\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26074.3 | −0.700001 | −0.350001 | − | 0.936749i | \(-0.613819\pi\) | ||||
−0.350001 | + | 0.936749i | \(0.613819\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6972.54i | 0.183367i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4731.26 | 0.121911 | 0.0609557 | − | 0.998140i | \(-0.480585\pi\) | ||||
0.0609557 | + | 0.998140i | \(0.480585\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | − 5786.69i | − 0.140423i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 57280.9 | 1.36302 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5868.59i | 0.136960i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 23665.5 | 0.541780 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 48656.4i | − 1.09289i | −0.837496 | − | 0.546444i | \(-0.815981\pi\) | ||||
0.837496 | − | 0.546444i | \(-0.184019\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 49296.6 | 1.08657 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 50594.5i | − 1.09453i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10431.6 | 0.221529 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 1382.34i | − 0.0288222i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4519.71 | 0.0925393 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 73299.7i | 1.47398i | 0.675902 | + | 0.736992i | \(0.263754\pi\) | ||||
−0.675902 | + | 0.736992i | \(0.736246\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1646.57 | 0.0325249 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14996.0i | 0.291020i | 0.989357 | + | 0.145510i | \(0.0464823\pi\) | ||||
−0.989357 | + | 0.145510i | \(0.953518\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −74694.9 | −1.42436 | −0.712181 | − | 0.701996i | \(-0.752292\pi\) | ||||
−0.712181 | + | 0.701996i | \(0.752292\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5460.40i | 0.102329i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 69476.6 | 1.27975 | 0.639877 | − | 0.768477i | \(-0.278985\pi\) | ||||
0.639877 | + | 0.768477i | \(0.278985\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 85415.2i | − 1.54668i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −29909.6 | −0.532494 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 87478.2i | 1.53145i | 0.643166 | + | 0.765727i | \(0.277620\pi\) | ||||
−0.643166 | + | 0.765727i | \(0.722380\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 74951.4 | 1.29046 | 0.645232 | − | 0.763987i | \(-0.276761\pi\) | ||||
0.645232 | + | 0.763987i | \(0.276761\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 3788.00i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 54930.7 | 0.915131 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11938.7i | 0.195687i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −37865.2 | −0.610719 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 43677.8i | − 0.693287i | −0.937997 | − | 0.346643i | \(-0.887321\pi\) | ||||
0.937997 | − | 0.346643i | \(-0.112679\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24344.1 | 0.380323 | ||||||||
\(254\) | 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 | ||||||||
\(259\) | 7533.97i | 0.112312i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16652.3 | 0.244452 | ||||||||
\(262\) | 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 | ||||||||
\(267\) | − 7347.77i | − 0.103070i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −41077.9 | −0.567681 | −0.283840 | − | 0.958872i | \(-0.591609\pi\) | ||||
−0.283840 | + | 0.958872i | \(0.591609\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 46419.1i | 0.632060i | 0.948749 | + | 0.316030i | \(0.102350\pi\) | ||||
−0.948749 | + | 0.316030i | \(0.897650\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2754.64 | −0.0369606 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 6830.32i | − 0.0903183i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −150297. | −1.95881 | −0.979405 | − | 0.201907i | \(-0.935286\pi\) | ||||
−0.979405 | + | 0.201907i | \(0.935286\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 30018.8i | 0.385643i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 117793. | 1.49179 | 0.745895 | − | 0.666063i | \(-0.232022\pi\) | ||||
0.745895 | + | 0.666063i | \(0.232022\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 41243.6i | 0.514973i | 0.966282 | + | 0.257486i | \(0.0828942\pi\) | ||||
−0.966282 | + | 0.257486i | \(0.917106\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −26074.7 | −0.321019 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22629.9i | 0.274739i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −77122.3 | −0.923388 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16160.4i | 0.190839i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 71937.8 | 0.837957 | 0.418979 | − | 0.907996i | \(-0.362388\pi\) | ||||
0.418979 | + | 0.907996i | \(0.362388\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 31097.7i | − 0.357342i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −15713.4 | −0.178138 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12281.0i | 0.137370i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19988.3 | 0.220619 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2538.33i | 0.0276479i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 113661. | 1.22183 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 54572.7i | − 0.579027i | −0.957174 | − | 0.289514i | \(-0.906506\pi\) | ||||
0.957174 | − | 0.289514i | \(-0.0934936\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 104427. | 1.09370 | ||||||||
\(310\) | 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 | \(-0.675756\pi\) | ||||
−0.524521 | + | 0.851397i | \(0.675756\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 6016.29i | − 0.0606328i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −39779.2 | −0.395857 | −0.197928 | − | 0.980217i | \(-0.563421\pi\) | ||||
−0.197928 | + | 0.980217i | \(0.563421\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 69077.2i | − 0.678818i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −64344.0 | −0.624450 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16902.1i | 0.162007i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3445.73 | 0.0326223 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 80758.9i | − 0.755257i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 33744.9 | 0.311758 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 87804.6i | 0.801422i | 0.916204 | + | 0.400711i | \(0.131237\pi\) | ||||
−0.916204 | + | 0.400711i | \(0.868763\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −21680.5 | −0.195515 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | − 60554.1i | − 0.526919i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 124524. | 1.07089 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 44228.9i | 0.375939i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −26822.4 | −0.225351 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 159188.i | 1.32206i | 0.750359 | + | 0.661031i | \(0.229881\pi\) | ||||
−0.750359 | + | 0.661031i | \(0.770119\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17396.8 | 0.142830 | 0.0714149 | − | 0.997447i | \(-0.477249\pi\) | ||||
0.0714149 | + | 0.997447i | \(0.477249\pi\) | |||||||
\(350\) | 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.i | 1.78782i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3899.85 | −0.0305993 | ||||||||
\(358\) | 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 | ||||||||
\(363\) | − 10894.7i | − 0.0826803i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6317.99 | 0.0474234 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 89484.6i | − 0.664379i | −0.943213 | − | 0.332190i | \(-0.892213\pi\) | ||||
0.943213 | − | 0.332190i | \(-0.107787\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −65122.1 | −0.478273 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 7822.44i | − 0.0568322i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −168536. | −1.21137 | −0.605684 | − | 0.795705i | \(-0.707100\pi\) | ||||
−0.605684 | + | 0.795705i | \(0.707100\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 84652.9i | 0.601976i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 34847.8 | 0.245184 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 126865.i | 0.883208i | 0.897210 | + | 0.441604i | \(0.145590\pi\) | ||||
−0.897210 | + | 0.441604i | \(0.854410\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −24546.8 | −0.169101 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 257277.i | − 1.75389i | −0.480587 | − | 0.876947i | \(-0.659576\pi\) | ||||
0.480587 | − | 0.876947i | \(-0.340424\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24956.8 | −0.168371 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 57520.3i | 0.384060i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −150562. | −0.994983 | −0.497492 | − | 0.867469i | \(-0.665745\pi\) | ||||
−0.497492 | + | 0.867469i | \(0.665745\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17386.7i | 0.113727i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −50053.8 | −0.324080 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 136702.i | − 0.876155i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 185402. | 1.17634 | 0.588171 | − | 0.808736i | \(-0.299848\pi\) | ||||
0.588171 | + | 0.808736i | \(0.299848\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 62819.4i | 0.386798i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17313.0 | 0.105551 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 89934.9i | 0.542925i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −60544.6 | −0.361934 | −0.180967 | − | 0.983489i | \(-0.557923\pi\) | ||||
−0.180967 | + | 0.983489i | \(0.557923\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 85256.3i | 0.504711i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12285.7 | 0.0720280 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 173063.i | − 1.00486i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −132731. | −0.763310 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 307306.i | 1.75042i | 0.483741 | + | 0.875211i | \(0.339277\pi\) | ||||
−0.483741 | + | 0.875211i | \(0.660723\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 172189. | 0.971496 | 0.485748 | − | 0.874099i | \(-0.338547\pi\) | ||||
0.485748 | + | 0.874099i | \(0.338547\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 97107.7i | 0.542716i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4878.26 | 0.0270077 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 44903.9i | 0.246279i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −32882.8 | −0.178671 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 28153.8i | − 0.151559i | −0.997125 | − | 0.0757797i | \(-0.975855\pi\) | ||||
0.997125 | − | 0.0757797i | \(-0.0241446\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −322037. | −1.71763 | −0.858815 | − | 0.512285i | \(-0.828799\pi\) | ||||
−0.858815 | + | 0.512285i | \(0.828799\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 76109.5i | 0.402217i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −45926.4 | −0.240492 | ||||||||
\(438\) | 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.i | 1.16016i | 0.814558 | + | 0.580082i | \(0.196980\pi\) | ||||
−0.814558 | + | 0.580082i | \(0.803020\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 33583.0 | 0.169590 | ||||||||
\(446\) | 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.i | 1.32811i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −149961. | −0.730773 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 12590.1i | − 0.0608143i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −340590. | −1.63079 | −0.815397 | − | 0.578902i | \(-0.803481\pi\) | ||||
−0.815397 | + | 0.578902i | \(0.803481\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 11222.6i | − 0.0532681i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −178561. | −0.840204 | −0.420102 | − | 0.907477i | \(-0.638006\pi\) | ||||
−0.420102 | + | 0.907477i | \(0.638006\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4179.11i | 0.0194950i | 0.999952 | + | 0.00974748i | \(0.00310277\pi\) | ||||
−0.999952 | + | 0.00974748i | \(0.996897\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −137201. | −0.634529 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 160583.i | − 0.736318i | −0.929763 | − | 0.368159i | \(-0.879988\pi\) | ||||
0.929763 | − | 0.368159i | \(-0.120012\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 37766.8 | 0.171698 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 124516.i | − 0.561284i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 238606. | 1.06649 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12885.8i | 0.0571114i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 22510.6 | 0.0989350 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 153260.i | 0.667970i | 0.942578 | + | 0.333985i | \(0.108393\pi\) | ||||
−0.942578 | + | 0.333985i | \(0.891607\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −45370.0 | −0.196100 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 10596.7i | − 0.0454231i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −73861.3 | −0.314003 | ||||||||
\(486\) | 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.i | 1.03009i | 0.857162 | + | 0.515046i | \(0.172225\pi\) | ||||
−0.857162 | + | 0.515046i | \(0.827775\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 49335.4 | 0.202985 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 71817.9i | − 0.293104i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −89013.1 | −0.360364 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 378612.i | − 1.52052i | −0.649617 | − | 0.760262i | \(-0.725071\pi\) | ||||
0.649617 | − | 0.760262i | \(-0.274929\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16047.8 | −0.0639353 | ||||||||
\(502\) | 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.i | 0.512816i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 204106. | 0.787809 | 0.393904 | − | 0.919151i | \(-0.371124\pi\) | ||||
0.393904 | + | 0.919151i | \(0.371124\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2496.04i | 0.00955895i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 29644.1 | 0.112643 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 477284.i | 1.79954i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 402822. | 1.50707 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 96757.3i | 0.359211i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 295131. | 1.08727 | 0.543637 | − | 0.839320i | \(-0.317047\pi\) | ||||
0.543637 | + | 0.839320i | \(0.317047\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 212950.i | 0.778527i | 0.921127 | + | 0.389263i | \(0.127270\pi\) | ||||
−0.921127 | + | 0.389263i | \(0.872730\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2973.16 | −0.0107870 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 88936.0i | 0.320226i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 232598. | 0.831178 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 35354.6i | 0.125388i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −136279. | −0.479704 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 294084.i | − 1.02746i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −263649. | −0.914277 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 259056.i | 0.891694i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −387756. | −1.32484 | −0.662421 | − | 0.749132i | \(-0.730471\pi\) | ||||
−0.662421 | + | 0.749132i | \(0.730471\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 301639.i | 1.02303i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 369108. | 1.24268 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 241227.i | 0.806215i | 0.915153 | + | 0.403107i | \(0.132070\pi\) | ||||
−0.915153 | + | 0.403107i | \(0.867930\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −129220. | −0.428730 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 130318.i | 0.429240i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 54006.8 | 0.176603 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 99090.6i | − 0.321697i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −86454.9 | −0.278663 | −0.139331 | − | 0.990246i | \(-0.544495\pi\) | ||||
−0.139331 | + | 0.990246i | \(0.544495\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 120371.i | 0.385210i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −46553.5 | −0.147920 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 99585.2i | − 0.314179i | −0.987584 | − | 0.157090i | \(-0.949789\pi\) | ||||
0.987584 | − | 0.157090i | \(-0.0502112\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 276762. | 0.866982 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6839.85i | 0.0212755i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 524085. | 1.61874 | 0.809371 | − | 0.587298i | \(-0.199808\pi\) | ||||
0.809371 | + | 0.587298i | \(0.199808\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32749.2i | 0.100445i | 0.998738 | + | 0.0502225i | \(0.0159931\pi\) | ||||
−0.998738 | + | 0.0502225i | \(0.984007\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 110603. | 0.336867 | ||||||||
\(574\) | 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.i | 0.404146i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 68371.8 | 0.202547 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 93378.4i | − 0.274732i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 36230.4 | 0.105867 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 303094.i | − 0.879634i | −0.898087 | − | 0.439817i | \(-0.855043\pi\) | ||||
0.898087 | − | 0.439817i | \(-0.144957\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −234921. | −0.677161 | ||||||||
\(590\) | 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 | ||||||||
\(595\) | − 17824.3i | − 0.0503475i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −200373. | −0.562198 | ||||||||
\(598\) | 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 | \(-0.677721\pi\) | ||||
−0.529767 | + | 0.848143i | \(0.677721\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 108681.i | 0.298896i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 49794.2 | 0.136040 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 578934.i | 1.57127i | 0.618688 | + | 0.785637i | \(0.287664\pi\) | ||||
−0.618688 | + | 0.785637i | \(0.712336\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −30068.5 | −0.0810732 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 203214.i | 0.544341i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 287542. | 0.765209 | 0.382605 | − | 0.923912i | \(-0.375027\pi\) | ||||
0.382605 | + | 0.923912i | \(0.375027\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 297641.i | − 0.786940i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 400806. | 1.05284 | 0.526422 | − | 0.850223i | \(-0.323533\pi\) | ||||
0.526422 | + | 0.850223i | \(0.323533\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 233469.i | − 0.609323i | −0.952461 | − | 0.304661i | \(-0.901457\pi\) | ||||
0.952461 | − | 0.304661i | \(-0.0985433\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 30494.1 | 0.0790738 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13267.6i | 0.0341835i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −348791. | −0.892904 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 122970.i | − 0.312797i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −64232.1 | −0.162349 | ||||||||
\(630\) | 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.i | − 0.278235i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −130687. | −0.322073 | ||||||||
\(638\) | 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.i | 1.33165i | 0.746106 | + | 0.665827i | \(0.231921\pi\) | ||||
−0.746106 | + | 0.665827i | \(0.768079\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −262897. | −0.631925 | ||||||||
\(646\) | 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 | ||||||||
\(651\) | − 54204.0i | − 0.127900i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 802147. | 1.88117 | 0.940584 | − | 0.339561i | \(-0.110279\pi\) | ||||
0.940584 | + | 0.339561i | \(0.110279\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 228771.i | − 0.533234i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7182.85 | −0.0166405 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 662958.i | − 1.52656i | −0.646065 | − | 0.763282i | \(-0.723586\pi\) | ||||
0.646065 | − | 0.763282i | \(-0.276414\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 231396. | 0.529607 | 0.264804 | − | 0.964302i | \(-0.414693\pi\) | ||||
0.264804 | + | 0.964302i | \(0.414693\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 23485.1i | − 0.0534276i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 47082.2 | 0.106467 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 134055.i | 0.301321i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 380877. | 0.851005 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | − 8555.85i | − 0.0187783i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −655173. | −1.42948 | −0.714741 | − | 0.699389i | \(-0.753455\pi\) | ||||
−0.714741 | + | 0.699389i | \(0.753455\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 29180.3i | − 0.0632923i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 77921.4 | 0.168021 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 358002.i | − 0.767439i | −0.923450 | − | 0.383719i | \(-0.874643\pi\) | ||||
0.923450 | − | 0.383719i | \(-0.125357\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −389664. | −0.830442 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 388126.i | 0.822355i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 47107.1 | 0.0992312 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 826006.i | − 1.72992i | −0.501838 | − | 0.864962i | \(-0.667343\pi\) | ||||
0.501838 | − | 0.864962i | \(-0.332657\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 28373.1 | 0.0590799 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 606648.i | − 1.25593i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −192935. | −0.397142 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 361011.i | − 0.738866i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −229057. | −0.466130 | −0.233065 | − | 0.972461i | \(-0.574876\pi\) | ||||
−0.233065 | + | 0.972461i | \(0.574876\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 169667.i | − 0.343310i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −443831. | −0.892974 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 4583.37i | − 0.00916950i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6312.88 | 0.0125584 | 0.00627921 | − | 0.999980i | \(-0.498001\pi\) | ||||
0.00627921 | + | 0.999980i | \(0.498001\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 155415.i | 0.307435i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −241658. | −0.475359 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 150291.i | − 0.293982i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 454550. | 0.884185 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 179483.i | 0.347189i | 0.984817 | + | 0.173594i | \(0.0555382\pi\) | ||||
−0.984817 | + | 0.173594i | \(0.944462\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −188560. | −0.362727 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 389459.i | − 0.745049i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 37612.2 | 0.0715571 | ||||||||
\(726\) | 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.i | 0.318911i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −602271. | −1.12094 | −0.560472 | − | 0.828173i | \(-0.689380\pi\) | ||||
−0.560472 | + | 0.828173i | \(0.689380\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 285428.i | − 0.528351i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 450832. | 0.830002 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 64180.3i | 0.117520i | 0.998272 | + | 0.0587602i | \(0.0187147\pi\) | ||||
−0.998272 | + | 0.0587602i | \(0.981285\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 62035.2 | 0.112980 | ||||||||
\(742\) | 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.i | 0.352599i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 116184. | 0.207101 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 405381.i | 0.718759i | 0.933191 | + | 0.359380i | \(0.117012\pi\) | ||||
−0.933191 | + | 0.359380i | \(0.882988\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −226956. | −0.400269 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 685398.i | − 1.20240i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5071.58 | 0.00885016 | 0.00442508 | − | 0.999990i | \(-0.498591\pi\) | ||||
0.00442508 | + | 0.999990i | \(0.498591\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 126496.i | − 0.219580i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29104.4 | 0.0502561 | 0.0251280 | − | 0.999684i | \(-0.492001\pi\) | ||||
0.0251280 | + | 0.999684i | \(0.492001\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 145823.i | 0.250483i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 51292.8 | 0.0876463 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | 6051.19i | 0.0101796i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 89776.8 | 0.150247 | 0.0751234 | − | 0.997174i | \(-0.476065\pi\) | ||||
0.0751234 | + | 0.997174i | \(0.476065\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 67802.8i | 0.112887i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 39147.7 | 0.0648431 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 509632.i | − 0.839812i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.06257e6 | −1.74203 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 86528.0i | − 0.141135i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 569099. | 0.923525 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 406715.i | − 0.656660i | −0.944563 | − | 0.328330i | \(-0.893514\pi\) | ||||
0.944563 | − | 0.328330i | \(-0.106486\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −181870. | −0.292151 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 109340.i | 0.174754i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −270414. | −0.430013 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 102885.i | 0.162786i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.02634e6 | 1.61576 | 0.807878 | − | 0.589350i | \(-0.200616\pi\) | ||||
0.807878 | + | 0.589350i | \(0.200616\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 287698.i | 0.450654i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −38180.1 | −0.0595076 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 29795.9i | 0.0462089i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 48432.3 | 0.0747383 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 213447.i | 0.327751i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −245306. | −0.374810 | −0.187405 | − | 0.982283i | \(-0.560008\pi\) | ||||
−0.187405 | + | 0.982283i | \(0.560008\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1.26760e6i | − 1.92726i | −0.267246 | − | 0.963628i | \(-0.586114\pi\) | ||||
0.267246 | − | 0.963628i | \(-0.413886\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 241201. | 0.364920 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 580065.i | − 0.873296i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −450142. | −0.674382 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 14313.5i | 0.0213392i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −163484. | −0.242542 | −0.121271 | − | 0.992619i | \(-0.538697\pi\) | ||||
−0.121271 | + | 0.992619i | \(0.538697\pi\) | |||||||
\(822\) | 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.i | − 0.553032i | −0.961009 | − | 0.276516i | \(-0.910820\pi\) | ||||
0.961009 | − | 0.276516i | \(-0.0891799\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 70195.3 | 0.102141 | 0.0510704 | − | 0.998695i | \(-0.483737\pi\) | ||||
0.0510704 | + | 0.998695i | \(0.483737\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 780969.i | 1.13092i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −185019. | −0.266641 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 73346.5i | − 0.105198i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 155982. | 0.222651 | ||||||||
\(838\) | 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.i | − 0.861286i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −602478. | −0.843777 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19672.2i | 0.0274211i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 214308. | 0.297320 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 174532.i | − 0.240999i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 577725. | 0.794005 | 0.397003 | − | 0.917817i | \(-0.370050\pi\) | ||||
0.397003 | + | 0.917817i | \(0.370050\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 135488.i | 0.185340i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 388294. | 0.528687 | 0.264344 | − | 0.964429i | \(-0.414845\pi\) | ||||
0.264344 | + | 0.964429i | \(0.414845\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 124443.i | − 0.168650i | −0.996438 | − | 0.0843248i | \(-0.973127\pi\) | ||||
0.996438 | − | 0.0843248i | \(-0.0268733\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 117589. | 0.158620 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 652166.i | − 0.875662i | −0.899057 | − | 0.437831i | \(-0.855747\pi\) | ||||
0.899057 | − | 0.437831i | \(-0.144253\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −442229. | −0.591038 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 400739.i | 0.533118i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 644693. | 0.853716 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 227434.i | 0.299791i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 83972.1 | 0.110181 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 152855.i | − 0.199647i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −75235.9 | −0.0978196 | −0.0489098 | − | 0.998803i | \(-0.515575\pi\) | ||||
−0.0489098 | + | 0.998803i | \(0.515575\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | − 1.14981e6i | − 1.47471i | −0.675506 | − | 0.737354i | \(-0.736075\pi\) | ||||
0.675506 | − | 0.737354i | \(-0.263925\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −161588. | −0.206311 | ||||||||
\(886\) | 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 | ||||||||
\(891\) | 81649.0i | 0.102848i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −759945. | −0.952970 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 1.20501e6i | − 1.50433i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 63814.0 | 0.0793105 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 685711.i | 0.848442i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 66691.5 | 0.0821525 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 103862.i | − 0.127375i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.37864e6 | −1.68327 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1.00415e6i | − 1.22063i | −0.792159 | − | 0.610315i | \(-0.791043\pi\) | ||||
0.792159 | − | 0.610315i | \(-0.208957\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13189.5 | 0.0159625 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 231087.i | − 0.278444i | −0.990261 | − | 0.139222i | \(-0.955540\pi\) | ||||
0.990261 | − | 0.139222i | \(-0.0444602\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 816172. | 0.979129 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 590598.i | − 0.705424i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 90380.4 | 0.107482 | ||||||||
\(918\) | 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.i | − 0.629209i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −48969.2 | −0.0572320 | ||||||||
\(926\) | 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.i | − 0.563849i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 316684. | 0.363800 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 212773.i | − 0.243385i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −479076. | −0.545664 | −0.272832 | − | 0.962062i | \(-0.587960\pi\) | ||||
−0.272832 | + | 0.962062i | \(0.587960\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 534027.i | 0.605665i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.25655e6 | 1.41906 | 0.709530 | − | 0.704675i | \(-0.248907\pi\) | ||||
0.709530 | + | 0.704675i | \(0.248907\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 524246.i | − 0.589538i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −31261.5 | −0.0350063 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1.22304e6i | − 1.36377i | −0.731459 | − | 0.681886i | \(-0.761160\pi\) | ||||
0.731459 | − | 0.681886i | \(-0.238840\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15031.3 | −0.0166903 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 206699.i | 0.228548i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.12329e6 | 1.23682 | 0.618409 | − | 0.785856i | \(-0.287777\pi\) | ||||
0.618409 | + | 0.785856i | \(0.287777\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 505512.i | 0.554275i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −358936. | −0.391916 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 153944.i | − 0.167389i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −312598. | −0.338485 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 334341.i | 0.360526i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −619240. | −0.664974 | ||||||||
\(966\) | 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.i | 0.487376i | 0.969854 | + | 0.243688i | \(0.0783574\pi\) | ||||
−0.969854 | + | 0.243688i | \(0.921643\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 239668. | 0.253154 | ||||||||
\(974\) | 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.i | 0.165246i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −419635. | −0.436048 | ||||||||
\(982\) | 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.i | − 0.179993i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −463050. | −0.473407 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 460245.i | − 0.468642i | −0.972159 | − | 0.234321i | \(-0.924713\pi\) | ||||
0.972159 | − | 0.234321i | \(-0.0752867\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 456246. | 0.462701 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 915803.i | − 0.925030i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.82730e6 | −1.83831 | −0.919156 | − | 0.393894i | \(-0.871128\pi\) | ||||
−0.919156 | + | 0.393894i | \(0.871128\pi\) | |||||||
\(998\) | 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 | 768.5.g.c.511.2 | 4 | ||
4.3 | odd | 2 | inner | 768.5.g.c.511.4 | 4 | ||
8.3 | odd | 2 | 768.5.g.g.511.1 | 4 | |||
8.5 | even | 2 | 768.5.g.g.511.3 | 4 | |||
16.3 | odd | 4 | 384.5.b.c.319.2 | ✓ | 8 | ||
16.5 | even | 4 | 384.5.b.c.319.3 | yes | 8 | ||
16.11 | odd | 4 | 384.5.b.c.319.7 | yes | 8 | ||
16.13 | even | 4 | 384.5.b.c.319.6 | yes | 8 | ||
48.5 | odd | 4 | 1152.5.b.k.703.3 | 8 | |||
48.11 | even | 4 | 1152.5.b.k.703.4 | 8 | |||
48.29 | odd | 4 | 1152.5.b.k.703.5 | 8 | |||
48.35 | even | 4 | 1152.5.b.k.703.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.5.b.c.319.2 | ✓ | 8 | 16.3 | odd | 4 | ||
384.5.b.c.319.3 | yes | 8 | 16.5 | even | 4 | ||
384.5.b.c.319.6 | yes | 8 | 16.13 | even | 4 | ||
384.5.b.c.319.7 | yes | 8 | 16.11 | odd | 4 | ||
768.5.g.c.511.2 | 4 | 1.1 | even | 1 | trivial | ||
768.5.g.c.511.4 | 4 | 4.3 | odd | 2 | inner | ||
768.5.g.g.511.1 | 4 | 8.3 | odd | 2 | |||
768.5.g.g.511.3 | 4 | 8.5 | even | 2 | |||
1152.5.b.k.703.3 | 8 | 48.5 | odd | 4 | |||
1152.5.b.k.703.4 | 8 | 48.11 | even | 4 | |||
1152.5.b.k.703.5 | 8 | 48.29 | odd | 4 | |||
1152.5.b.k.703.6 | 8 | 48.35 | even | 4 |