Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,6,Mod(383,384)]
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, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.383");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(61.5873868082\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 306 x^{18} + 37827 x^{16} + 2442168 x^{14} + 88368509 x^{12} + 1774000974 x^{10} + \cdots + 2870280625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{88}\cdot 3^{14}\cdot 41^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 383.3 | ||
Root | \(-0.671758i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.383 |
Dual form | 384.6.c.a.383.4 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −15.1145 | − | 3.81453i | −0.969598 | − | 0.244702i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 40.5648i | 0.725645i | 0.931858 | + | 0.362822i | \(0.118187\pi\) | ||||
−0.931858 | + | 0.362822i | \(0.881813\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 81.4905i | 0.628582i | 0.949327 | + | 0.314291i | \(0.101767\pi\) | ||||
−0.949327 | + | 0.314291i | \(0.898233\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 213.899 | + | 115.310i | 0.880242 | + | 0.474525i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 499.309 | 1.24419 | 0.622097 | − | 0.782940i | \(-0.286281\pi\) | ||||
0.622097 | + | 0.782940i | \(0.286281\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −262.278 | −0.430431 | −0.215216 | − | 0.976567i | \(-0.569045\pi\) | ||||
−0.215216 | + | 0.976567i | \(0.569045\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 154.735 | − | 613.118i | 0.177567 | − | 0.703584i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 565.287i | − | 0.474402i | −0.971461 | − | 0.237201i | \(-0.923770\pi\) | ||
0.971461 | − | 0.237201i | \(-0.0762300\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2137.81i | 1.35858i | 0.733872 | + | 0.679288i | \(0.237711\pi\) | ||||
−0.733872 | + | 0.679288i | \(0.762289\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 310.848 | − | 1231.69i | 0.153815 | − | 0.609472i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3650.06 | 1.43873 | 0.719367 | − | 0.694630i | \(-0.244432\pi\) | ||||
0.719367 | + | 0.694630i | \(0.244432\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1479.50 | 0.473440 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2793.13 | − | 2558.77i | −0.737364 | − | 0.675496i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7310.25i | − | 1.61413i | −0.590466 | − | 0.807063i | \(-0.701056\pi\) | ||
0.590466 | − | 0.807063i | \(-0.298944\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2216.91i | − | 0.414328i | −0.978306 | − | 0.207164i | \(-0.933577\pi\) | ||
0.978306 | − | 0.207164i | \(-0.0664234\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7546.83 | − | 1904.63i | −1.20637 | − | 0.304457i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3305.64 | −0.456127 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10097.4 | −1.21256 | −0.606280 | − | 0.795251i | \(-0.707339\pi\) | ||||
−0.606280 | + | 0.795251i | \(0.707339\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3964.21 | + | 1000.47i | 0.417345 | + | 0.105327i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2865.65i | − | 0.266234i | −0.991100 | − | 0.133117i | \(-0.957501\pi\) | ||
0.991100 | − | 0.133117i | \(-0.0424987\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8282.13i | 0.683079i | 0.939867 | + | 0.341539i | \(0.110948\pi\) | ||||
−0.939867 | + | 0.341539i | \(0.889052\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4677.51 | + | 8676.75i | −0.344337 | + | 0.638743i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3920.49 | 0.258878 | 0.129439 | − | 0.991587i | \(-0.458682\pi\) | ||||
0.129439 | + | 0.991587i | \(0.458682\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10166.3 | 0.604884 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2156.30 | + | 8544.05i | −0.116087 | + | 0.459979i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1497.09i | 0.0732080i | 0.999330 | + | 0.0366040i | \(0.0116540\pi\) | ||||
−0.999330 | + | 0.0366040i | \(0.988346\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 20254.4i | 0.902843i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8154.71 | − | 32311.9i | 0.332446 | − | 1.31727i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6360.57 | −0.237885 | −0.118942 | − | 0.992901i | \(-0.537950\pi\) | ||||
−0.118942 | + | 0.992901i | \(0.537950\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5095.51 | 0.175333 | 0.0876664 | − | 0.996150i | \(-0.472059\pi\) | ||||
0.0876664 | + | 0.996150i | \(0.472059\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9396.64 | + | 17430.7i | −0.298278 | + | 0.553304i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 10639.2i | − | 0.312340i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 58778.9i | 1.59969i | 0.600209 | + | 0.799843i | \(0.295084\pi\) | ||||
−0.600209 | + | 0.799843i | \(0.704916\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −55169.0 | − | 13923.2i | −1.39499 | − | 0.352061i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 24686.6 | 0.581185 | 0.290593 | − | 0.956847i | \(-0.406148\pi\) | ||||
0.290593 | + | 0.956847i | \(0.406148\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 34838.3 | 0.765157 | 0.382578 | − | 0.923923i | \(-0.375036\pi\) | ||||
0.382578 | + | 0.923923i | \(0.375036\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −22362.0 | − | 5643.59i | −0.459047 | − | 0.115852i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 40689.0i | 0.782078i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 37197.4i | − | 0.670572i | −0.942116 | − | 0.335286i | \(-0.891167\pi\) | ||
0.942116 | − | 0.335286i | \(-0.108833\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 32456.4 | + | 49329.2i | 0.549652 | + | 0.835394i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 77701.0 | 1.23803 | 0.619015 | − | 0.785379i | \(-0.287532\pi\) | ||||
0.619015 | + | 0.785379i | \(0.287532\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 22930.7 | 0.344247 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −27885.1 | + | 110491.i | −0.394980 | + | 1.56505i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 38427.8i | 0.514245i | 0.966379 | + | 0.257123i | \(0.0827745\pi\) | ||||
−0.966379 | + | 0.257123i | \(0.917226\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 21373.2i | − | 0.270561i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8456.48 | + | 33507.6i | −0.101387 | + | 0.401732i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −86719.6 | −0.985844 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 148735. | 1.60503 | 0.802515 | − | 0.596632i | \(-0.203495\pi\) | ||||
0.802515 | + | 0.596632i | \(0.203495\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 106802. | + | 57575.2i | 1.09519 | + | 0.590401i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 43258.7i | 0.421959i | 0.977490 | + | 0.210980i | \(0.0676654\pi\) | ||||
−0.977490 | + | 0.210980i | \(0.932335\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 177132.i | 1.64514i | 0.568662 | + | 0.822571i | \(0.307461\pi\) | ||||
−0.568662 | + | 0.822571i | \(0.692539\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 49963.3 | + | 12609.5i | 0.442260 | + | 0.111615i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 108837. | 0.919006 | 0.459503 | − | 0.888176i | \(-0.348027\pi\) | ||||
0.459503 | + | 0.888176i | \(0.348027\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −242786. | −1.95730 | −0.978651 | − | 0.205530i | \(-0.934108\pi\) | ||||
−0.978651 | + | 0.205530i | \(0.934108\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 152617. | + | 38516.6i | 1.17570 | + | 0.296716i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 111435.i | 0.820964i | 0.911869 | + | 0.410482i | \(0.134640\pi\) | ||||
−0.911869 | + | 0.410482i | \(0.865360\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 148064.i | 1.04401i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −56101.0 | − | 30243.2i | −0.378883 | − | 0.204250i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 46065.5 | 0.298201 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 88258.9 | 0.548018 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10931.1 | + | 43313.0i | −0.0651480 | + | 0.258140i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 186780.i | 1.06919i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 310454.i | 1.70800i | 0.520272 | + | 0.854001i | \(0.325831\pi\) | ||||
−0.520272 | + | 0.854001i | \(0.674169\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 31592.4 | − | 125181.i | 0.167151 | − | 0.662312i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −126488. | −0.643980 | −0.321990 | − | 0.946743i | \(-0.604352\pi\) | ||||
−0.321990 | + | 0.946743i | \(0.604352\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −174211. | −0.853977 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 103796. | − | 113303.i | 0.490170 | − | 0.535064i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 407875.i | − | 1.85663i | −0.371795 | − | 0.928315i | \(-0.621258\pi\) | ||
0.371795 | − | 0.928315i | \(-0.378742\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 345151.i | 1.51521i | 0.652714 | + | 0.757604i | \(0.273630\pi\) | ||||
−0.652714 | + | 0.757604i | \(0.726370\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −59256.4 | − | 14954.8i | −0.251008 | − | 0.0633481i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −130958. | −0.535540 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 296539. | 1.17128 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −153659. | − | 38779.6i | −0.586495 | − | 0.148016i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 255290.i | − | 0.942036i | −0.882124 | − | 0.471018i | \(-0.843887\pi\) | ||
0.882124 | − | 0.471018i | \(-0.156113\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 39203.8i | − | 0.139922i | −0.997550 | − | 0.0699610i | \(-0.977713\pi\) | ||
0.997550 | − | 0.0699610i | \(-0.0222875\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 65183.0 | − | 120914.i | 0.225116 | − | 0.417589i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 89928.6 | 0.300655 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 90738.1 | 0.293792 | 0.146896 | − | 0.989152i | \(-0.453072\pi\) | ||||
0.146896 | + | 0.989152i | \(0.453072\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5710.69 | − | 22627.8i | 0.0179141 | − | 0.0709824i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 297445.i | 0.904362i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 82660.0i | 0.243684i | 0.992550 | + | 0.121842i | \(0.0388801\pi\) | ||||
−0.992550 | + | 0.121842i | \(0.961120\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 77260.8 | − | 306136.i | 0.220927 | − | 0.875395i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1354.48 | 0.00375821 | 0.00187910 | − | 0.999998i | \(-0.499402\pi\) | ||||
0.00187910 | + | 0.999998i | \(0.499402\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −302503. | −0.814729 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −246510. | + | 457274.i | −0.644679 | + | 1.19588i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 752693.i | 1.91207i | 0.293260 | + | 0.956033i | \(0.405260\pi\) | ||||
−0.293260 | + | 0.956033i | \(0.594740\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 120565.i | 0.297596i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 96137.2 | + | 24262.6i | 0.230652 | + | 0.0582108i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −145447. | −0.339292 | −0.169646 | − | 0.985505i | \(-0.554262\pi\) | ||||
−0.169646 | + | 0.985505i | \(0.554262\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −816899. | −1.85341 | −0.926706 | − | 0.375787i | \(-0.877372\pi\) | ||||
−0.926706 | + | 0.375787i | \(0.877372\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −77016.4 | − | 19437.0i | −0.170002 | − | 0.0429043i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 409597.i | − | 0.879888i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 282253.i | − | 0.590248i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 208516. | − | 227614.i | 0.424605 | − | 0.463494i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 570025. | 1.13060 | 0.565302 | − | 0.824884i | \(-0.308760\pi\) | ||||
0.565302 | + | 0.824884i | \(0.308760\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −402670. | −0.778138 | −0.389069 | − | 0.921209i | \(-0.627203\pi\) | ||||
−0.389069 | + | 0.921209i | \(0.627203\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −40583.7 | + | 160807.i | −0.0764302 | + | 0.302844i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 697392.i | − | 1.28030i | −0.768250 | − | 0.640150i | \(-0.778872\pi\) | ||
0.768250 | − | 0.640150i | \(-0.221128\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 17654.7i | − | 0.0316029i | −0.999875 | − | 0.0158015i | \(-0.994970\pi\) | ||
0.999875 | − | 0.0158015i | \(-0.00502997\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 224214. | − | 888417.i | 0.391446 | − | 1.55105i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 595716. | 1.01461 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 116245. | 0.193191 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 780743. | + | 420887.i | 1.26643 | + | 0.682715i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.06743e6i | 1.69033i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 705719.i | − | 1.09125i | −0.838028 | − | 0.545627i | \(-0.816292\pi\) | ||
0.838028 | − | 0.545627i | \(-0.183708\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −373126. | − | 94167.5i | −0.563516 | − | 0.142217i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −335963. | −0.495673 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 180658. | 0.260439 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −526566. | − | 132892.i | −0.741895 | − | 0.187235i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 148262.i | 0.204197i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 514390.i | − | 0.692676i | −0.938110 | − | 0.346338i | \(-0.887425\pi\) | ||
0.938110 | − | 0.346338i | \(-0.112575\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 316463. | + | 170601.i | 0.416742 | + | 0.224659i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 689433. | 0.888030 | 0.444015 | − | 0.896019i | \(-0.353554\pi\) | ||||
0.444015 | + | 0.896019i | \(0.353554\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.16383e6 | 1.46656 | 0.733280 | − | 0.679927i | \(-0.237989\pi\) | ||||
0.733280 | + | 0.679927i | \(0.237989\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 155209. | − | 614996.i | 0.191376 | − | 0.758302i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 918501.i | 1.10838i | 0.832389 | + | 0.554192i | \(0.186973\pi\) | ||||
−0.832389 | + | 0.554192i | \(0.813027\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 159034.i | 0.187854i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −141891. | + | 562222.i | −0.164090 | + | 0.650185i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.74289e6 | −1.97367 | −0.986836 | − | 0.161722i | \(-0.948295\pi\) | ||||
−0.986836 | + | 0.161722i | \(0.948295\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −819192. | −0.908538 | −0.454269 | − | 0.890865i | \(-0.650100\pi\) | ||||
−0.454269 | + | 0.890865i | \(0.650100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −302396. | − | 869394.i | −0.328519 | − | 0.944497i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 412393.i | 0.438931i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 560699.i | − | 0.584774i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.17442e6 | − | 296393.i | −1.20039 | − | 0.302949i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 594929. | 0.596047 | 0.298024 | − | 0.954559i | \(-0.403673\pi\) | ||||
0.298024 | + | 0.954559i | \(0.403673\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.82251e6 | 1.79006 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −346587. | − | 87469.9i | −0.333782 | − | 0.0842380i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.60886e6i | 1.51944i | 0.650248 | + | 0.759722i | \(0.274665\pi\) | ||||
−0.650248 | + | 0.759722i | \(0.725335\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 822839.i | − | 0.762194i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 842942. | − | 1.56365e6i | 0.765943 | − | 1.42082i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.44015e6 | −1.28386 | −0.641929 | − | 0.766764i | \(-0.721866\pi\) | ||||
−0.641929 | + | 0.766764i | \(0.721866\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −60729.1 | −0.0531230 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 146584. | − | 580819.i | 0.125837 | − | 0.498611i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.85670e6i | 1.56445i | 0.622996 | + | 0.782225i | \(0.285915\pi\) | ||||
−0.622996 | + | 0.782225i | \(0.714085\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 210714.i | − | 0.174289i | −0.996196 | − | 0.0871447i | \(-0.972226\pi\) | ||
0.996196 | − | 0.0871447i | \(-0.0277742\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −81528.6 | + | 323046.i | −0.0662069 | + | 0.262336i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 738728. | 0.589051 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 366298. | 0.286837 | 0.143419 | − | 0.989662i | \(-0.454190\pi\) | ||||
0.143419 | + | 0.989662i | \(0.454190\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 255632. | − | 474195.i | 0.196609 | − | 0.364709i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 962614.i | − | 0.727254i | −0.931545 | − | 0.363627i | \(-0.881538\pi\) | ||
0.931545 | − | 0.363627i | \(-0.118462\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1.59949e6i | − | 1.18717i | −0.804770 | − | 0.593587i | \(-0.797711\pi\) | ||
0.804770 | − | 0.593587i | \(-0.202289\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.31073e6 | + | 330794.i | 0.955873 | + | 0.241238i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 233524. | 0.167350 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.10031e6 | 0.774943 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.24806e6 | − | 567352.i | −1.55623 | − | 0.392754i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 451436.i | 0.307204i | 0.988133 | + | 0.153602i | \(0.0490874\pi\) | ||||
−0.988133 | + | 0.153602i | \(0.950913\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 258015.i | − | 0.172620i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.39464e6 | − | 1.27762e6i | −0.917424 | − | 0.840448i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −957331. | −0.619276 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −674915. | −0.429371 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 165012. | − | 653836.i | 0.103254 | − | 0.409131i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 206698.i | 0.127229i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.49010e6i | 1.50790i | 0.656934 | + | 0.753948i | \(0.271853\pi\) | ||||
−0.656934 | + | 0.753948i | \(0.728147\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 675674. | − | 2.67727e6i | 0.402569 | − | 1.59513i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −752051. | −0.440906 | −0.220453 | − | 0.975398i | \(-0.570754\pi\) | ||||
−0.220453 | + | 0.975398i | \(0.570754\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.30499e6 | −1.32987 | −0.664934 | − | 0.746902i | \(-0.731540\pi\) | ||||
−0.664934 | + | 0.746902i | \(0.731540\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −707073. | − | 381173.i | −0.401502 | − | 0.216444i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.11295e6i | 0.622054i | 0.950401 | + | 0.311027i | \(0.100673\pi\) | ||||
−0.950401 | + | 0.311027i | \(0.899327\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 3.65008e6i | − | 2.00828i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.64503e6 | − | 415163.i | −0.891067 | − | 0.224883i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.20847e6 | 0.644511 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −388040. | −0.203783 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.66960e6 | + | 926114.i | 1.89780 | + | 0.478955i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 319483.i | 0.162726i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 2.51218e6i | − | 1.26032i | −0.776465 | − | 0.630160i | \(-0.782989\pi\) | ||
0.776465 | − | 0.630160i | \(-0.217011\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.15981e6 | − | 1.16432e6i | −1.06735 | − | 0.575391i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.38435e6 | −1.16080 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −39468.6 | −0.0189311 | −0.00946556 | − | 0.999955i | \(-0.503013\pi\) | ||||
−0.00946556 | + | 0.999955i | \(0.503013\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 425070. | − | 1.68428e6i | 0.200892 | − | 0.796005i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.10693e6i | − | 0.515505i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.19807e6i | 1.00880i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 564793. | − | 2.23792e6i | 0.255471 | − | 1.01227i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −602701. | −0.268707 | −0.134353 | − | 0.990933i | \(-0.542896\pi\) | ||||
−0.134353 | + | 0.990933i | \(0.542896\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.47666e6 | 1.52791 | 0.763956 | − | 0.645268i | \(-0.223254\pi\) | ||||
0.763956 | + | 0.645268i | \(0.223254\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 732577. | + | 671111.i | 0.317384 | + | 0.290754i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.70548e6i | 1.58273i | 0.611341 | + | 0.791367i | \(0.290630\pi\) | ||||
−0.611341 | + | 0.791367i | \(0.709370\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.00140e6i | 0.421734i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −696259. | − | 175718.i | −0.289135 | − | 0.0729703i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.00364e6 | 0.411001 | 0.205501 | − | 0.978657i | \(-0.434118\pi\) | ||||
0.205501 | + | 0.978657i | \(0.434118\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.09411e6 | −0.845730 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.33399e6 | − | 336666.i | −0.531358 | − | 0.134101i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.41321e6i | 0.555232i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.82819e6i | − | 1.09608i | −0.836451 | − | 0.548042i | \(-0.815373\pi\) | ||
0.836451 | − | 0.548042i | \(-0.184627\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 330437. | − | 612960.i | 0.126335 | − | 0.234351i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −121999. | −0.0460172 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.58345e6 | 0.589296 | 0.294648 | − | 0.955606i | \(-0.404798\pi\) | ||||
0.294648 | + | 0.955606i | \(0.404798\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 712479. | − | 2.82310e6i | 0.261634 | − | 1.03669i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.91732e6i | 0.694770i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.10073e6i | − | 0.393624i | −0.980441 | − | 0.196812i | \(-0.936941\pi\) | ||
0.980441 | − | 0.196812i | \(-0.0630588\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.18424e6 | − | 4.69237e6i | 0.417951 | − | 1.65608i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 729536. | 0.254126 | 0.127063 | − | 0.991895i | \(-0.459445\pi\) | ||||
0.127063 | + | 0.991895i | \(0.459445\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.65054e6 | −0.567511 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −955009. | + | 1.77154e6i | −0.324138 | + | 0.601275i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 1.70809e6i | − | 0.572319i | −0.958182 | − | 0.286159i | \(-0.907621\pi\) | ||
0.958182 | − | 0.286159i | \(-0.0923787\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.06333e6i | − | 0.682538i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.91181e6 | + | 482493.i | 0.624402 | + | 0.157583i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.50890e6 | 0.486597 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.33954e6 | −1.38187 | −0.690935 | − | 0.722917i | \(-0.742801\pi\) | ||||
−0.690935 | + | 0.722917i | \(0.742801\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.63312e6 | + | 664532.i | 0.828015 | + | 0.208970i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 3.02307e6i | − | 0.938832i | −0.882977 | − | 0.469416i | \(-0.844464\pi\) | ||
0.882977 | − | 0.469416i | \(-0.155536\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 581448.i | 0.178340i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.00103e6 | + | 1.31659e6i | −0.606199 | + | 0.398852i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.04171e6 | −1.50866 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.62103e6 | 1.07035 | 0.535173 | − | 0.844743i | \(-0.320246\pi\) | ||||
0.535173 | + | 0.844743i | \(0.320246\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.55585e6 | + | 6.16484e6i | −0.454321 | + | 1.80019i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 518327.i | − | 0.149530i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.15192e6i | 0.898371i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.31659e6 | − | 5.21680e6i | 0.370775 | − | 1.46914i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.48851e6 | 0.970744 | 0.485372 | − | 0.874308i | \(-0.338684\pi\) | ||||
0.485372 | + | 0.874308i | \(0.338684\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −870260. | −0.239301 | −0.119650 | − | 0.992816i | \(-0.538177\pi\) | ||||
−0.119650 | + | 0.992816i | \(0.538177\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 838588. | + | 452070.i | 0.227876 | + | 0.122844i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 836342.i | − | 0.224601i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 415236.i | 0.110211i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.97937e6 | + | 499542.i | 0.519258 | + | 0.131048i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.04631e6 | 0.530614 | 0.265307 | − | 0.964164i | \(-0.414527\pi\) | ||||
0.265307 | + | 0.964164i | \(0.414527\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3382.30 | 0.000866946 | 0.000433473 | − | 1.00000i | \(-0.499862\pi\) | ||||
0.000433473 | 1.00000i | \(0.499862\pi\) | ||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.48204e6 | − | 1.13115e6i | −1.13567 | − | 0.286615i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.80312e6i | 1.95463i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.09542e6i | 1.50953i | 0.655993 | + | 0.754767i | \(0.272250\pi\) | ||||
−0.655993 | + | 0.754767i | \(0.727750\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.17456e6 | + | 1.17227e6i | 0.532445 | + | 0.287033i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.51063e6 | 0.849915 | 0.424957 | − | 0.905213i | \(-0.360289\pi\) | ||||
0.424957 | + | 0.905213i | \(0.360289\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.55881e6 | −0.373159 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −973809. | + | 3.85858e6i | −0.230518 | + | 0.913396i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.42542e6i | 0.801859i | 0.916109 | + | 0.400929i | \(0.131313\pi\) | ||||
−0.916109 | + | 0.400929i | \(0.868687\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1.43085e6i | − | 0.331247i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −149544. | + | 592548.i | −0.0342392 | + | 0.135668i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 866998. | 0.196331 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.02677e6 | 1.12590 | 0.562948 | − | 0.826492i | \(-0.309667\pi\) | ||||
0.562948 | + | 0.826492i | \(0.309667\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.44644e6 | + | 1.57892e6i | −0.320457 | + | 0.349807i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.17924e6i | 0.915894i | 0.888979 | + | 0.457947i | \(0.151415\pi\) | ||||
−0.888979 | + | 0.457947i | \(0.848585\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.01723e6i | 0.654118i | 0.945004 | + | 0.327059i | \(0.106058\pi\) | ||||
−0.945004 | + | 0.327059i | \(0.893942\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.35923e6 | − | 343035.i | −0.291515 | − | 0.0735709i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.42968e6 | 1.36426 | 0.682130 | − | 0.731231i | \(-0.261054\pi\) | ||||
0.682130 | + | 0.731231i | \(0.261054\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.78993e6 | −1.00553 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.37146e6 | − | 346123.i | −0.284860 | − | 0.0718915i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.13535e6i | 0.849883i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.16288e6i | 0.643204i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −172629. | + | 320226.i | −0.0347390 | + | 0.0644407i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.05852e6 | −1.00736 | −0.503680 | − | 0.863890i | \(-0.668021\pi\) | ||||
−0.503680 | + | 0.863890i | \(0.668021\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.64832e6 | 0.521924 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.13461e6 | − | 4.49575e6i | 0.221299 | − | 0.876868i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.03339e6i | 1.16468i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.19956e6i | 1.18451i | 0.805751 | + | 0.592255i | \(0.201762\pi\) | ||||
−0.805751 | + | 0.592255i | \(0.798238\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 315309. | − | 1.24937e6i | 0.0596299 | − | 0.236275i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.31690e6 | 0.433714 | 0.216857 | − | 0.976203i | \(-0.430419\pi\) | ||||
0.216857 | + | 0.976203i | \(0.430419\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.13239e6 | −0.765744 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.33552e6 | + | 4.33239e6i | −0.428422 | + | 0.794720i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.01172e6i | 0.365323i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.84932e6i | 1.77074i | 0.464887 | + | 0.885370i | \(0.346095\pi\) | ||||
−0.464887 | + | 0.885370i | \(0.653905\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20472.3 | − | 5166.69i | −0.00364395 | − | 0.000919641i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.70258e6 | −1.18120 | −0.590598 | − | 0.806966i | \(-0.701108\pi\) | ||||
−0.590598 | + | 0.806966i | \(0.701108\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.75478e6 | −0.306192 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.57220e6 | + | 1.15391e6i | 0.789960 | + | 0.199366i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 3.85622e6i | − | 0.659732i | −0.944028 | − | 0.329866i | \(-0.892996\pi\) | ||
0.944028 | − | 0.329866i | \(-0.107004\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.83900e6i | 0.480964i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.47016e6 | − | 5.97117e6i | 0.917713 | − | 1.00177i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.18531e6 | −1.19379 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.95754e6 | 0.322095 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.87117e6 | − | 1.13766e7i | 0.467886 | − | 1.85394i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.16460e6i | 1.31777i | 0.752243 | + | 0.658886i | \(0.228972\pi\) | ||||
−0.752243 | + | 0.658886i | \(0.771028\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 2.95007e6i | − | 0.471605i | −0.971801 | − | 0.235802i | \(-0.924228\pi\) | ||
0.971801 | − | 0.235802i | \(-0.0757718\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 459899. | − | 1.82229e6i | 0.0728223 | − | 0.288548i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.25319e6 | −0.196558 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.88659e6 | 1.06995 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.36052e6 | − | 733435.i | −0.209396 | − | 0.112882i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 751598.i | 0.114596i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.41496e6i | 0.666872i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.19837e6 | + | 554813.i | 0.328977 | + | 0.0830254i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.07613e6 | 0.752594 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.20843e6 | −1.05888 | −0.529441 | − | 0.848347i | \(-0.677598\pi\) | ||||
−0.529441 | + | 0.848347i | \(0.677598\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.23471e7 | + | 3.11608e6i | 1.79707 | + | 0.453534i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 9.84857e6i | − | 1.42031i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.12166e6i | 0.160285i | 0.996783 | + | 0.0801427i | \(0.0255376\pi\) | ||||
−0.996783 | + | 0.0801427i | \(0.974462\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.08992e6 | + | 587562.i | 0.154335 | + | 0.0831999i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.56279e7 | 2.19291 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.03124e6 | 0.421509 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.56242e6 | + | 6.19087e6i | −0.215310 | + | 0.853138i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 1.22251e7i | − | 1.66961i | −0.550549 | − | 0.834803i | \(-0.685581\pi\) | ||
0.550549 | − | 0.834803i | \(-0.314419\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.17222e6i | − | 0.294018i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.07666e6 | + | 4.26613e6i | −0.144435 | + | 0.572304i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.55071e6 | −0.472111 | −0.236056 | − | 0.971740i | \(-0.575855\pi\) | ||||
−0.236056 | + | 0.971740i | \(0.575855\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.52032e6 | −0.595728 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.01986e6 | + | 2.64489e6i | −0.525114 | + | 0.345501i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 692500.i | 0.0896683i | 0.998994 | + | 0.0448341i | \(0.0142759\pi\) | ||||
−0.998994 | + | 0.0448341i | \(0.985724\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.28266e6i | 0.806406i | 0.915111 | + | 0.403203i | \(0.132103\pi\) | ||||
−0.915111 | + | 0.403203i | \(0.867897\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.61566e6 | − | 2.17437e6i | −1.09623 | − | 0.276661i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.40026e6 | 0.681154 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 57039.3 | 0.00713238 | 0.00356619 | − | 0.999994i | \(-0.498865\pi\) | ||||
0.00356619 | + | 0.999994i | \(0.498865\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.08618e6 | + | 1.53600e6i | 0.754481 | + | 0.190412i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.33190e6i | 0.778204i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 747512.i | 0.0910849i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.22681e6 | − | 2.27572e6i | 0.148213 | − | 0.274935i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.50165e6 | 0.539233 | 0.269616 | − | 0.962968i | \(-0.413103\pi\) | ||||
0.269616 | + | 0.962968i | \(0.413103\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.73933e6 | 0.562897 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.66022e6 | + | 1.05408e7i | −0.313292 | + | 1.24138i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 1.63168e7i | − | 1.90545i | −0.303832 | − | 0.952725i | \(-0.598266\pi\) | ||
0.303832 | − | 0.952725i | \(-0.401734\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.86864e6i | 0.216388i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −67344.2 | + | 266842.i | −0.00773330 | + | 0.0306421i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.53911e6 | −0.744650 | −0.372325 | − | 0.928103i | \(-0.621439\pi\) | ||||
−0.372325 | + | 0.928103i | \(0.621439\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.41684e6 | 0.385868 | 0.192934 | − | 0.981212i | \(-0.438200\pi\) | ||||
0.192934 | + | 0.981212i | \(0.438200\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.77778e6 | + | 1.25727e7i | −0.759091 | + | 1.40811i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.58020e6i | 0.397667i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.20758e7i | − | 1.33028i | −0.746720 | − | 0.665139i | \(-0.768372\pi\) | ||
0.746720 | − | 0.665139i | \(-0.231628\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.00398e6 | − | 2.27237e6i | −0.983764 | − | 0.248277i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.02826e6 | −0.111429 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.10117e6 | 0.440815 | 0.220407 | − | 0.975408i | \(-0.429261\pi\) | ||||
0.220407 | + | 0.975408i | \(0.429261\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.75698e6 | − | 443418.i | −0.187318 | − | 0.0472743i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.22186e7i | 1.29214i | 0.763278 | + | 0.646070i | \(0.223588\pi\) | ||||
−0.763278 | + | 0.646070i | \(0.776412\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 4.74806e6i | − | 0.498069i | −0.968495 | − | 0.249035i | \(-0.919887\pi\) | ||
0.968495 | − | 0.249035i | \(-0.0801133\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.01951e7 | − | 9.33968e6i | −1.06087 | − | 0.971858i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.13150e6 | −0.323246 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.95327e6 | −0.302415 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.07173e6 | − | 1.61337e7i | 0.413628 | − | 1.63894i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.70790e6i | 0.575241i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 8.28679e6i | − | 0.828539i | −0.910154 | − | 0.414269i | \(-0.864037\pi\) | ||
0.910154 | − | 0.414269i | \(-0.135963\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.69198e6 | + | 1.06666e7i | −0.267032 | + | 1.05808i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.25935e7 | −1.23940 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.66640e6 | −0.260361 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.28043e6 | + | 2.84660e6i | 0.511584 | + | 0.275787i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1.29886e7i | − | 1.24858i | −0.781193 | − | 0.624289i | \(-0.785389\pi\) | ||
0.781193 | − | 0.624289i | \(-0.214611\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.08387e7i | 1.03383i | 0.856038 | + | 0.516914i | \(0.172919\pi\) | ||||
−0.856038 | + | 0.516914i | \(0.827081\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.07792e6 | + | 1.28154e6i | 0.480603 | + | 0.121292i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.26979e6 | 0.682749 | 0.341375 | − | 0.939927i | \(-0.389107\pi\) | ||||
0.341375 | + | 0.939927i | \(0.389107\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.17589e6 | −0.295975 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.73056e6 | − | 689123.i | −0.252522 | − | 0.0637300i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 1.41342e7i | − | 1.29714i | −0.761154 | − | 0.648571i | \(-0.775367\pi\) | ||
0.761154 | − | 0.648571i | \(-0.224633\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 5.13097e6i | − | 0.467301i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.45188e6 | + | 4.01720e6i | 0.673523 | + | 0.363086i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.84668e6 | −0.345042 | −0.172521 | − | 0.985006i | \(-0.555191\pi\) | ||||
−0.172521 | + | 0.985006i | \(0.555191\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.41825e7 | 1.26255 | 0.631274 | − | 0.775560i | \(-0.282532\pi\) | ||||
0.631274 | + | 0.775560i | \(0.282532\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 565551. | − | 2.24092e6i | 0.0499675 | − | 0.197989i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 7.06682e6i | − | 0.619684i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 2.66828e7i | − | 2.32230i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.96215e6 | + | 7.77476e6i | −0.169499 | + | 0.671617i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.54424e6 | 0.218148 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.88309e7 | −1.60263 | −0.801315 | − | 0.598243i | \(-0.795866\pi\) | ||||
−0.801315 | + | 0.598243i | \(0.795866\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.13244e6 | − | 3.78571e6i | −0.349097 | − | 0.319807i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.13428e6i | 0.178970i | 0.995988 | + | 0.0894850i | \(0.0285221\pi\) | ||||
−0.995988 | + | 0.0894850i | \(0.971478\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.21205e7i | 1.00889i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.04205e7 | − | 2.62986e6i | −0.861032 | − | 0.217303i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.35008e7 | −1.10741 | −0.553704 | − | 0.832714i | \(-0.686786\pi\) | ||||
−0.553704 | + | 0.832714i | \(0.686786\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.65453e7 | 1.34725 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.75907e7 | − | 4.43945e6i | −1.42197 | − | 0.358870i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 392654.i | − | 0.0315110i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.61029e6i | 0.685998i | 0.939336 | + | 0.342999i | \(0.111443\pi\) | ||||
−0.939336 | + | 0.342999i | \(0.888557\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.69183e6 | + | 8.70333e6i | −0.371116 | + | 0.688418i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.40010e7 | −1.09950 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.61992e6 | −0.126302 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.50365e6 | − | 1.38827e7i | 0.271224 | − | 1.07469i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.35843e7i | − | 1.04410i | −0.852915 | − | 0.522050i | \(-0.825168\pi\) | ||
0.852915 | − | 0.522050i | \(-0.174832\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 2.15862e7i | − | 1.64736i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 606639. | − | 2.40372e6i | 0.0459682 | − | 0.182143i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.52518e6 | −0.265236 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.58912e7 | −1.18725 | −0.593623 | − | 0.804743i | \(-0.702303\pi\) | ||||
−0.593623 | + | 0.804743i | \(0.702303\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.28922e6 | − | 7.95648e6i | 0.318203 | − | 0.590265i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 8.09187e6i | − | 0.596108i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 5.31228e6i | − | 0.388612i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.63430e7 | + | 6.64830e6i | 1.91367 | + | 0.482962i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.32529e6 | −0.456308 | −0.228154 | − | 0.973625i | \(-0.573269\pi\) | ||||
−0.228154 | + | 0.973625i | \(0.573269\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.44346e7 | −1.03411 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.23817e7 | + | 3.12483e6i | 0.880917 | + | 0.222321i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 1.08155e7i | − | 0.764191i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.91829e7i | 1.34610i | 0.739596 | + | 0.673051i | \(0.235017\pi\) | ||||
−0.739596 | + | 0.673051i | \(0.764983\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.25425e6 | + | 1.42940e7i | 0.0874109 | + | 0.996172i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.68178e6 | 0.324054 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.15672e6 | 0.148264 | 0.0741318 | − | 0.997248i | \(-0.476381\pi\) | ||||
0.0741318 | + | 0.997248i | \(0.476381\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.57308e6 | − | 6.23314e6i | 0.107407 | − | 0.425587i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.93489e7i | 1.99032i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.62944e6i | 0.581262i | 0.956835 | + | 0.290631i | \(0.0938651\pi\) | ||||
−0.956835 | + | 0.290631i | \(0.906135\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.13880e6 | + | 8.47472e6i | −0.143095 | + | 0.566996i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.75125e7 | 1.82834 | 0.914171 | − | 0.405328i | \(-0.132843\pi\) | ||||
0.914171 | + | 0.405328i | \(0.132843\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.03558e7 | 0.683583 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.66202e7 | + | 8.95968e6i | 1.08977 | + | 0.587477i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.86922e6i | 0.577671i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 2.11517e7i | − | 1.36850i | −0.729247 | − | 0.684250i | \(-0.760129\pi\) | ||
0.729247 | − | 0.684250i | \(-0.239871\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.99207e6 | − | 2.26937e6i | −0.577926 | − | 0.145854i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.59029e6 | 0.101534 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.55766e7 | 1.62219 | 0.811096 | − | 0.584913i | \(-0.198871\pi\) | ||||
0.811096 | + | 0.584913i | \(0.198871\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.75464e7 | − | 6.95201e6i | −1.73564 | − | 0.438032i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.87679e6i | 0.242667i | 0.992612 | + | 0.121333i | \(0.0387170\pi\) | ||||
−0.992612 | + | 0.121333i | \(0.961283\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1.97848e7i | − | 1.23032i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.90485e6 | + | 2.64413e6i | 0.303021 | + | 0.163354i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.66824e6 | 0.102393 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.92438e7 | 1.78327 | 0.891637 | − | 0.452750i | \(-0.149557\pi\) | ||||
0.891637 | + | 0.452750i | \(0.149557\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.13703e6 | − | 2.43171e7i | 0.371811 | − | 1.47325i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 3.45316e6i | − | 0.207859i | −0.994585 | − | 0.103929i | \(-0.966858\pi\) | ||
0.994585 | − | 0.103929i | \(-0.0331416\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3.27992e6i | − | 0.196160i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.13874e6 | + | 1.24368e7i | −0.186510 | + | 0.739022i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.12621e6 | 0.361700 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.23262e7 | 0.723107 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.87053e7 | + | 2.04185e7i | −1.09033 | + | 1.19020i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.68077e6i | 0.213189i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1.36417e7i | − | 0.785110i | −0.919728 | − | 0.392555i | \(-0.871591\pi\) | ||
0.919728 | − | 0.392555i | \(-0.128409\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.17671e7 | + | 5.49347e6i | 1.24483 | + | 0.314163i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.08087e6 | −0.516043 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.33644e6 | −0.0754687 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 917893. | + | 231653.i | 0.0515080 | + | 0.0129993i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.88629e6i | 0.439771i | 0.975526 | + | 0.219886i | \(0.0705684\pi\) | ||||
−0.975526 | + | 0.219886i | \(0.929432\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 2.21620e6i | − | 0.122812i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.43109e6 | + | 8.21966e6i | −0.244022 | + | 0.452660i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.73951e7 | 0.952003 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.20658e7 | −0.656246 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.08244e6 | − | 2.80632e7i | 0.382824 | − | 1.51689i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 7.30535e6i | − | 0.392437i | −0.980560 | − | 0.196218i | \(-0.937134\pi\) | ||
0.980560 | − | 0.196218i | \(-0.0628661\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.67815e7i | − | 0.895941i | −0.894048 | − | 0.447971i | \(-0.852147\pi\) | ||
0.894048 | − | 0.447971i | \(-0.147853\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −803775. | + | 3.18485e6i | −0.0426489 | + | 0.168991i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.35308e6 | −0.176828 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.77056e7 | −0.928015 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.46453e6 | − | 4.57170e6i | 0.128388 | − | 0.238159i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 3.03619e7i | − | 1.57207i | −0.618185 | − | 0.786033i | \(-0.712132\pi\) | ||
0.618185 | − | 0.786033i | \(-0.287868\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.48318e6i | 0.0763296i | 0.999271 | + | 0.0381648i | \(0.0121512\pi\) | ||||
−0.999271 | + | 0.0381648i | \(0.987849\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.11655e7 | − | 2.81790e6i | −0.571143 | − | 0.144142i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.47869e7 | −0.751819 | −0.375910 | − | 0.926656i | \(-0.622670\pi\) | ||||
−0.375910 | + | 0.926656i | \(0.622670\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.09627e7 | −0.554025 | −0.277013 | − | 0.960866i | \(-0.589344\pi\) | ||||
−0.277013 | + | 0.960866i | \(0.589344\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.53643e6 | − | 1.39725e6i | −0.278117 | − | 0.0701896i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 5.74687e6i | − | 0.286958i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 54944.1i | 0.00272712i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.67258e6 | + | 6.19213e6i | −0.279877 | + | 0.305511i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.22320e7 | 1.58082 | 0.790409 | − | 0.612580i | \(-0.209868\pi\) | ||||
0.790409 | + | 0.612580i | \(0.209868\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.29286e7 | −1.60540 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.67191e6 | + | 1.45495e7i | −0.177960 | + | 0.705144i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 1.22710e7i | − | 0.591204i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.19227e6i | 0.344475i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.10128e6 | + | 2.41755e7i | −0.290504 | + | 1.15108i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.68560e7 | −1.74455 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.55584e6 | 0.355558 | 0.177779 | − | 0.984070i | \(-0.443109\pi\) | ||||
0.177779 | + | 0.984070i | \(0.443109\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.85492e7 | − | 9.99960e6i | −0.867781 | − | 0.467808i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 9.11651e6i | − | 0.424010i | −0.977269 | − | 0.212005i | \(-0.932001\pi\) | ||
0.977269 | − | 0.212005i | \(-0.0679994\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1.22074e7i | − | 0.564471i | −0.959345 | − | 0.282235i | \(-0.908924\pi\) | ||
0.959345 | − | 0.282235i | \(-0.0910759\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.52960e6 | − | 890782.i | −0.162262 | − | 0.0409509i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.22980e7 | 1.47621 | 0.738106 | − | 0.674685i | \(-0.235721\pi\) | ||||
0.738106 | + | 0.674685i | \(0.235721\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.05328e7 | −1.38748 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.66306e7 | − | 4.19715e6i | −0.751383 | − | 0.189630i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.85730e7i | − | 0.834321i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.54164e7i | − | 0.688555i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.18142e7 | + | 1.71505e7i | 1.41281 | + | 0.761627i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.52208e7 | −0.672076 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.11768e7 | 0.490703 | 0.245352 | − | 0.969434i | \(-0.421097\pi\) | ||||
0.245352 | + | 0.969434i | \(0.421097\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.72202e6 | − | 6.82325e6i | 0.0751735 | − | 0.297865i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.55914e7i | − | 1.54492i | −0.635065 | − | 0.772459i | \(-0.719027\pi\) | ||
0.635065 | − | 0.772459i | \(-0.280973\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1.56424e7i | − | 0.675152i | −0.941298 | − | 0.337576i | \(-0.890393\pi\) | ||
0.941298 | − | 0.337576i | \(-0.109607\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −984206. | + | 3.89978e6i | −0.0422404 | + | 0.167372i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.40474e7 | −1.45303 | −0.726515 | − | 0.687150i | \(-0.758861\pi\) | ||||
−0.726515 | + | 0.687150i | \(0.758861\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.52991e7 | −1.07362 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.62058e7 | + | 2.46305e7i | 0.683873 | + | 1.03939i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.38125e6i | 0.351706i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 5.90004e6i | − | 0.246205i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.44696e7 | + | 3.65176e6i | 0.600449 | + | 0.151538i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.62062e7 | −0.668778 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 846286. | 0.0347300 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.02010e7 | + | 2.57448e6i | 0.416318 | + | 0.105068i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 3.31373e7i | − | 1.34492i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.54115e7i | 0.622052i | 0.950401 | + | 0.311026i | \(0.100673\pi\) | ||||
−0.950401 | + | 0.311026i | \(0.899327\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.98815e6 | + | 9.25299e6i | −0.200230 | + | 0.371426i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.35161e7 | 0.539580 | 0.269790 | − | 0.962919i | \(-0.413046\pi\) | ||||
0.269790 | + | 0.962919i | \(0.413046\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.87969e7 | 1.54035 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 788456. | − | 3.12415e6i | 0.0311333 | − | 0.123361i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 1.03076e7i | − | 0.404794i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.00733e7i | 1.56519i | 0.622533 | + | 0.782594i | \(0.286104\pi\) | ||||
−0.622533 | + | 0.782594i | \(0.713896\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.49856e6 | − | 3.76368e7i | 0.368985 | − | 1.46205i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.47474e6 | −0.250160 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.49390e7 | −0.574075 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.04250e7 | + | 3.78883e7i | −0.780661 | + | 1.44812i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.38484e7i | 0.526454i | 0.964734 | + | 0.263227i | \(0.0847868\pi\) | ||||
−0.964734 | + | 0.263227i | \(0.915213\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.17336e7i | 0.821782i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.13669e7 | + | 2.86872e6i | 0.427502 | + | 0.107891i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.14495e7 | 0.428310 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.64331e7 | −0.611464 | −0.305732 | − | 0.952118i | \(-0.598901\pi\) | ||||
−0.305732 | + | 0.952118i | \(0.598901\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.48389e7 | + | 8.79245e6i | 1.28944 | + | 0.325421i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1.22708e7i | − | 0.451752i | −0.974156 | − | 0.225876i | \(-0.927476\pi\) | ||
0.974156 | − | 0.225876i | \(-0.0725245\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.04598e7i | − | 0.383040i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.23310e6 | + | 8.45840e6i | 0.336332 | + | 0.308112i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.94103e6 | 0.179037 | 0.0895185 | − | 0.995985i | \(-0.471467\pi\) | ||||
0.0895185 | + | 0.995985i | \(0.471467\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.13733e6 | −0.329347 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.24538e6 | − | 1.68217e7i | 0.152218 | − | 0.603142i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 3.15735e7i | − | 1.12614i | −0.826410 | − | 0.563068i | \(-0.809621\pi\) | ||
0.826410 | − | 0.563068i | \(-0.190379\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.31229e7i | 0.820416i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.39233e7 | + | 5.51692e7i | −0.491431 | + | 1.94723i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.32379e7 | 1.16704 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.37144e7 | 0.828332 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.32802e7 | + | 1.25500e7i | 0.808948 | + | 0.436092i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1.63342e7i | − | 0.564651i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 3.69660e7i | − | 1.27127i | −0.771991 | − | 0.635634i | \(-0.780739\pi\) | ||
0.771991 | − | 0.635634i | \(-0.219261\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.82655e7 | − | 4.60975e6i | −0.624917 | − | 0.157713i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.40891e7 | −1.50066 | −0.750331 | − | 0.661062i | \(-0.770106\pi\) | ||||
−0.750331 | + | 0.661062i | \(0.770106\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.81266e7 | −0.952433 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.86505e6 | + | 1.48019e6i | 0.197588 | + | 0.0498662i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.62078e6i | 0.0543236i | 0.999631 | + | 0.0271618i | \(0.00864694\pi\) | ||||
−0.999631 | + | 0.0271618i | \(0.991353\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.91874e7i | 0.639821i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.19317e7 | − | 2.79956e7i | −1.72290 | − | 0.928789i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.23292e7 | −1.39719 | −0.698596 | − | 0.715516i | \(-0.746191\pi\) | ||||
−0.698596 | + | 0.715516i | \(0.746191\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.82895e7 | 0.929042 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.21868e6 | − | 4.82884e6i | 0.0398195 | − | 0.157779i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.02303e7i | 0.982769i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.76998e6i | 0.0572513i | 0.999590 | + | 0.0286256i | \(0.00911307\pi\) | ||||
−0.999590 | + | 0.0286256i | \(0.990887\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.58278e6 | + | 3.79705e7i | −0.308403 | + | 1.22200i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 716158. | 0.0229325 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −872512. | −0.0277993 | −0.0138996 | − | 0.999903i | \(-0.504425\pi\) | ||||
−0.0138996 | + | 0.999903i | \(0.504425\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.82032e7 | + | 2.58369e7i | 0.894099 | + | 0.819080i |
(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 | 384.6.c.a.383.3 | ✓ | 20 | |
3.2 | odd | 2 | 384.6.c.d.383.17 | yes | 20 | ||
4.3 | odd | 2 | 384.6.c.d.383.18 | yes | 20 | ||
8.3 | odd | 2 | 384.6.c.b.383.3 | yes | 20 | ||
8.5 | even | 2 | 384.6.c.c.383.18 | yes | 20 | ||
12.11 | even | 2 | inner | 384.6.c.a.383.4 | yes | 20 | |
24.5 | odd | 2 | 384.6.c.b.383.4 | yes | 20 | ||
24.11 | even | 2 | 384.6.c.c.383.17 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.6.c.a.383.3 | ✓ | 20 | 1.1 | even | 1 | trivial | |
384.6.c.a.383.4 | yes | 20 | 12.11 | even | 2 | inner | |
384.6.c.b.383.3 | yes | 20 | 8.3 | odd | 2 | ||
384.6.c.b.383.4 | yes | 20 | 24.5 | odd | 2 | ||
384.6.c.c.383.17 | yes | 20 | 24.11 | even | 2 | ||
384.6.c.c.383.18 | yes | 20 | 8.5 | even | 2 | ||
384.6.c.d.383.17 | yes | 20 | 3.2 | odd | 2 | ||
384.6.c.d.383.18 | yes | 20 | 4.3 | odd | 2 |