Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [304,5,Mod(65,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("304.65");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.r (of order \(6\), degree \(2\), 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: | \(31.4244687775\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.2 | ||
Character | \(\chi\) | \(=\) | 304.145 |
Dual form | 304.5.r.d.65.2 |
$q$-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 \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −13.5253 | + | 7.80881i | −1.50281 | + | 0.867646i | −0.502812 | + | 0.864396i | \(0.667701\pi\) |
−0.999995 | + | 0.00325055i | \(0.998965\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 14.4872 | + | 25.0925i | 0.579486 | + | 1.00370i | 0.995538 | + | 0.0943585i | \(0.0300800\pi\) |
−0.416052 | + | 0.909341i | \(0.636587\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 26.1842 | 0.534372 | 0.267186 | − | 0.963645i | \(-0.413906\pi\) | ||||
0.267186 | + | 0.963645i | \(0.413906\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.4552 | − | 141.085i | 1.00562 | − | 1.74178i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −151.830 | −1.25479 | −0.627395 | − | 0.778701i | \(-0.715879\pi\) | ||||
−0.627395 | + | 0.778701i | \(0.715879\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 25.6769 | + | 14.8246i | 0.151935 | + | 0.0877195i | 0.574040 | − | 0.818827i | \(-0.305375\pi\) |
−0.422105 | + | 0.906547i | \(0.638709\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −391.885 | − | 226.255i | −1.74171 | − | 1.00558i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 14.4596 | + | 25.0447i | 0.0500331 | + | 0.0866599i | 0.889957 | − | 0.456044i | \(-0.150734\pi\) |
−0.839924 | + | 0.542704i | \(0.817401\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −348.126 | − | 95.5488i | −0.964337 | − | 0.264678i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −354.148 | + | 204.468i | −0.803058 | + | 0.463646i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −116.619 | + | 201.990i | −0.220452 | + | 0.381835i | −0.954945 | − | 0.296782i | \(-0.904087\pi\) |
0.734493 | + | 0.678616i | \(0.237420\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −107.255 | + | 185.771i | −0.171608 | + | 0.297234i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1279.25i | 1.75480i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1408.94 | − | 813.453i | −1.67532 | − | 0.967245i | −0.964581 | − | 0.263788i | \(-0.915028\pi\) |
−0.710737 | − | 0.703457i | \(-0.751639\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 382.463i | − | 0.397985i | −0.980001 | − | 0.198992i | \(-0.936233\pi\) | ||
0.980001 | − | 0.198992i | \(-0.0637669\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2053.54 | − | 1185.61i | 1.88571 | − | 1.08871i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 379.335 | + | 657.027i | 0.309661 | + | 0.536349i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1725.42i | 1.26035i | 0.776453 | + | 0.630176i | \(0.217017\pi\) | ||||
−0.776453 | + | 0.630176i | \(0.782983\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −463.050 | −0.304438 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2538.96 | − | 1465.87i | 1.51039 | − | 0.872024i | 0.510463 | − | 0.859900i | \(-0.329474\pi\) |
0.999927 | − | 0.0121237i | \(-0.00385920\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 264.444 | + | 458.031i | 0.143020 | + | 0.247718i | 0.928633 | − | 0.371001i | \(-0.120985\pi\) |
−0.785612 | + | 0.618719i | \(0.787652\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4720.21 | 2.33097 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1897.52 | − | 3286.61i | 0.858996 | − | 1.48783i | −0.0138908 | − | 0.999904i | \(-0.504422\pi\) |
0.872887 | − | 0.487922i | \(-0.162245\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1715.39 | −0.714447 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −391.139 | − | 225.824i | −0.150380 | − | 0.0868221i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2502.11 | − | 1444.59i | −0.890746 | − | 0.514273i | −0.0165599 | − | 0.999863i | \(-0.505271\pi\) |
−0.874187 | + | 0.485590i | \(0.838605\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2199.58 | − | 3809.78i | −0.727134 | − | 1.25943i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5454.61 | − | 1426.13i | 1.67886 | − | 0.438943i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 384.650 | − | 222.078i | 0.110500 | − | 0.0637971i | −0.443732 | − | 0.896160i | \(-0.646346\pi\) |
0.554231 | + | 0.832363i | \(0.313012\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2706.99 | − | 4688.64i | 0.727489 | − | 1.26005i | −0.230453 | − | 0.973084i | \(-0.574021\pi\) |
0.957941 | − | 0.286964i | \(-0.0926460\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2132.84 | − | 3694.19i | 0.537375 | − | 0.930760i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 859.064i | 0.203329i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2699.23 | + | 1558.40i | 0.601299 | + | 0.347160i | 0.769552 | − | 0.638584i | \(-0.220479\pi\) |
−0.168254 | + | 0.985744i | \(0.553813\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 3642.63i | − | 0.765098i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 380.479 | − | 219.670i | 0.0754769 | − | 0.0435766i | −0.461787 | − | 0.886991i | \(-0.652791\pi\) |
0.537263 | + | 0.843414i | \(0.319458\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1622.43 | + | 2810.13i | 0.304453 | + | 0.527327i | 0.977139 | − | 0.212600i | \(-0.0681932\pi\) |
−0.672687 | + | 0.739927i | \(0.734860\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 3350.14i | − | 0.595580i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3975.54 | −0.670525 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2331.93 | − | 1346.34i | 0.373646 | − | 0.215725i | −0.301404 | − | 0.953497i | \(-0.597455\pi\) |
0.675050 | + | 0.737772i | \(0.264122\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3391.52 | − | 5874.29i | −0.516922 | − | 0.895335i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9939.75 | 1.44284 | 0.721422 | − | 0.692496i | \(-0.243489\pi\) | ||||
0.721422 | + | 0.692496i | \(0.243489\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −418.956 | + | 725.653i | −0.0579870 | + | 0.100436i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 25408.4 | 3.35691 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3521.51 | − | 2033.14i | −0.444578 | − | 0.256677i | 0.260959 | − | 0.965350i | \(-0.415961\pi\) |
−0.705538 | + | 0.708672i | \(0.749294\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 672.331 | + | 388.170i | 0.0811896 | + | 0.0468748i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2986.59 | + | 5172.92i | 0.345310 | + | 0.598094i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2645.79 | − | 10119.6i | −0.293162 | − | 1.12128i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13922.1 | + | 8037.95i | −1.47966 | + | 0.854283i | −0.999735 | − | 0.0230249i | \(-0.992670\pi\) |
−0.479927 | + | 0.877308i | \(0.659337\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12367.3 | + | 21420.8i | −1.26184 | + | 2.18557i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2300.27 | + | 3984.19i | −0.225495 | + | 0.390568i | −0.956468 | − | 0.291838i | \(-0.905733\pi\) |
0.730973 | + | 0.682406i | \(0.239067\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7603.38i | 0.716691i | 0.933589 | + | 0.358346i | \(0.116659\pi\) | ||||
−0.933589 | + | 0.358346i | \(0.883341\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10261.2 | − | 5924.31i | −0.930722 | − | 0.537352i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 22180.9i | − | 1.93736i | −0.248307 | − | 0.968681i | \(-0.579874\pi\) | ||
0.248307 | − | 0.968681i | \(-0.420126\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2667.96 | + | 1540.35i | −0.224557 | + | 0.129648i | −0.608059 | − | 0.793892i | \(-0.708051\pi\) |
0.383501 | + | 0.923540i | \(0.374718\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13473.5 | − | 23336.8i | −1.09354 | − | 1.89406i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14436.4i | 1.13058i | 0.824891 | + | 0.565292i | \(0.191237\pi\) | ||||
−0.824891 | + | 0.565292i | \(0.808763\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6757.92 | −0.510996 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4183.04 | − | 2415.08i | 0.305577 | − | 0.176425i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 378.613 | + | 655.777i | 0.0267363 | + | 0.0463086i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8411.25 | 0.574500 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −22893.4 | + | 39652.6i | −1.51322 | + | 2.62097i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11893.7 | 0.761194 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8245.29 | − | 4760.42i | −0.511209 | − | 0.295147i | 0.222122 | − | 0.975019i | \(-0.428702\pi\) |
−0.733330 | + | 0.679872i | \(0.762035\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7153.36 | − | 4129.99i | −0.429863 | − | 0.248182i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12953.1 | + | 22435.4i | 0.754797 | + | 1.30735i | 0.945475 | + | 0.325693i | \(0.105598\pi\) |
−0.190679 | + | 0.981652i | \(0.561069\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9115.40 | − | 2501.87i | −0.515314 | − | 0.141437i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −32099.4 | + | 18532.6i | −1.76129 | + | 1.01688i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14553.6 | − | 25207.6i | 0.775408 | − | 1.34305i | −0.159158 | − | 0.987253i | \(-0.550878\pi\) |
0.934565 | − | 0.355792i | \(-0.115789\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7423.68 | − | 12858.2i | 0.384229 | − | 0.665504i | −0.607433 | − | 0.794371i | \(-0.707801\pi\) |
0.991662 | + | 0.128867i | \(0.0411341\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 59269.6i | 2.98122i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3898.52 | − | 2250.81i | −0.190646 | − | 0.110070i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 47138.5i | − | 2.24202i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 23201.1 | − | 13395.1i | 1.07368 | − | 0.619887i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5125.65 | + | 8877.89i | 0.230875 | + | 0.399887i | 0.958066 | − | 0.286548i | \(-0.0925079\pi\) |
−0.727191 | + | 0.686435i | \(0.759175\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 16460.0i | − | 0.721896i | −0.932586 | − | 0.360948i | \(-0.882453\pi\) | ||
0.932586 | − | 0.360948i | \(-0.117547\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4711.23 | 0.201257 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9596.96 | − | 5540.80i | 0.399457 | − | 0.230627i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10562.8 | − | 18295.2i | −0.428527 | − | 0.742231i | 0.568215 | − | 0.822880i | \(-0.307634\pi\) |
−0.996743 | + | 0.0806490i | \(0.974301\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 45122.2 | 1.78483 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3053.58 | + | 5288.96i | −0.117803 | + | 0.204042i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2366.79 | −0.0890811 | −0.0445405 | − | 0.999008i | \(-0.514182\pi\) | ||||
−0.0445405 | + | 0.999008i | \(0.514182\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 59499.8 | + | 34352.2i | 2.18548 | + | 1.26179i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −37914.9 | − | 21890.2i | −1.35949 | − | 0.784904i | −0.369938 | − | 0.929056i | \(-0.620621\pi\) |
−0.989556 | + | 0.144152i | \(0.953954\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13841.0 | − | 23973.3i | −0.484611 | − | 0.839370i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −41837.1 | + | 41332.2i | −1.43077 | + | 1.41350i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13009.4 | − | 7510.96i | 0.434674 | − | 0.250959i | −0.266662 | − | 0.963790i | \(-0.585921\pi\) |
0.701336 | + | 0.712831i | \(0.252587\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2808.39 | + | 4864.27i | −0.0917025 | + | 0.158833i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3468.33 | + | 6007.32i | −0.110707 | + | 0.191750i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 27426.6i | − | 0.855984i | −0.903783 | − | 0.427992i | \(-0.859221\pi\) | ||
0.903783 | − | 0.427992i | \(-0.140779\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −46522.7 | − | 26859.9i | −1.42006 | − | 0.819874i | −0.423760 | − | 0.905774i | \(-0.639290\pi\) |
−0.996304 | + | 0.0859000i | \(0.972623\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 84553.4i | 2.52481i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −43295.1 | + | 24996.4i | −1.26501 | + | 0.730356i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2195.39 | − | 3802.53i | −0.0627811 | − | 0.108740i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 33496.1i | 0.937713i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 57805.6 | 1.58454 | 0.792271 | − | 0.610170i | \(-0.208899\pi\) | ||||
0.792271 | + | 0.610170i | \(0.208899\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 26896.3 | − | 15528.6i | 0.722068 | − | 0.416886i | −0.0934455 | − | 0.995624i | \(-0.529788\pi\) |
0.815513 | + | 0.578738i | \(0.196455\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6708.27 | − | 11619.1i | −0.176417 | − | 0.305564i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19725.7 | 0.508277 | 0.254139 | − | 0.967168i | \(-0.418208\pi\) | ||||
0.254139 | + | 0.967168i | \(0.418208\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −35403.2 | + | 61320.2i | −0.893998 | + | 1.54845i | −0.0589584 | + | 0.998260i | \(0.518778\pi\) |
−0.835040 | + | 0.550190i | \(0.814555\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −48677.1 | −1.20485 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −36892.1 | − | 21299.6i | −0.895243 | − | 0.516869i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 73564.7 | + | 42472.6i | 1.75050 | + | 1.01065i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 18998.5 | + | 32906.3i | 0.443382 | + | 0.767961i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 52855.8 | + | 14507.1i | 1.21004 | + | 0.332116i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1039.66 | + | 600.246i | −0.0233521 | + | 0.0134823i | −0.511631 | − | 0.859206i | \(-0.670958\pi\) |
0.488279 | + | 0.872688i | \(0.337625\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3430.72 | + | 5942.18i | −0.0756181 | + | 0.130974i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7662.09 | + | 13271.1i | −0.165756 | + | 0.287098i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 10014.5i | − | 0.212672i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −43887.5 | − | 25338.5i | −0.915067 | − | 0.528314i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 857.429i | 0.0175555i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −59249.9 | + | 34207.9i | −1.19146 | + | 0.687887i | −0.958637 | − | 0.284633i | \(-0.908128\pi\) |
−0.232819 | + | 0.972520i | \(0.574795\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 17473.0 | + | 30264.1i | 0.345145 | + | 0.597809i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 90560.9i | − | 1.75747i | −0.477306 | − | 0.878737i | \(-0.658387\pi\) | ||
0.477306 | − | 0.878737i | \(-0.341613\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −39212.6 | −0.747747 | −0.373874 | − | 0.927480i | \(-0.621971\pi\) | ||||
−0.373874 | + | 0.927480i | \(0.621971\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 53770.3 | − | 31044.3i | 1.00767 | − | 0.581778i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20451.0 | − | 35422.2i | −0.376707 | − | 0.652475i | 0.613874 | − | 0.789404i | \(-0.289610\pi\) |
−0.990581 | + | 0.136929i | \(0.956277\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 109959. | 1.99111 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −21026.6 | + | 36419.2i | −0.374345 | + | 0.648385i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −87676.6 | −1.53493 | −0.767464 | − | 0.641092i | \(-0.778482\pi\) | ||||
−0.767464 | + | 0.641092i | \(0.778482\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 35152.4 | + | 20295.3i | 0.605231 | + | 0.349430i | 0.771097 | − | 0.636718i | \(-0.219709\pi\) |
−0.165866 | + | 0.986148i | \(0.553042\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2005.90 | + | 1158.11i | 0.0339701 | + | 0.0196127i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −24851.1 | − | 43043.3i | −0.414012 | − | 0.717090i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7522.33 | − | 7614.22i | −0.123299 | − | 0.124805i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −134438. | + | 77617.7i | −2.16832 | + | 1.25188i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13850.9 | + | 23990.4i | −0.219851 | + | 0.380794i | −0.954762 | − | 0.297370i | \(-0.903891\pi\) |
0.734911 | + | 0.678164i | \(0.237224\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17706.3 | − | 30668.1i | 0.276621 | − | 0.479122i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 13086.2i | − | 0.201249i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −74472.0 | − | 42996.4i | −1.12753 | − | 0.650978i | −0.184215 | − | 0.982886i | \(-0.558974\pi\) |
−0.943312 | + | 0.331908i | \(0.892308\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 45178.8i | 0.673496i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −229531. | + | 132520.i | −3.36947 | + | 1.94536i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12692.5 | + | 21984.1i | 0.183500 | + | 0.317831i | 0.943070 | − | 0.332594i | \(-0.107924\pi\) |
−0.759570 | + | 0.650425i | \(0.774591\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 83712.1i | − | 1.19206i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 63505.7 | 0.890821 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −34445.2 | + | 19887.0i | −0.476019 | + | 0.274830i | −0.718756 | − | 0.695262i | \(-0.755288\pi\) |
0.242737 | + | 0.970092i | \(0.421955\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5496.61 | + | 9520.41i | 0.0748439 | + | 0.129633i | 0.901018 | − | 0.433781i | \(-0.142821\pi\) |
−0.826174 | + | 0.563414i | \(0.809487\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12124.6 | −0.162683 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16284.5 | − | 28205.6i | 0.215332 | − | 0.372966i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 75853.3 | 0.988587 | 0.494294 | − | 0.869295i | \(-0.335427\pi\) | ||||
0.494294 | + | 0.869295i | \(0.335427\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −53959.7 | − | 31153.6i | −0.693204 | − | 0.400221i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −94497.4 | − | 54558.1i | −1.19676 | − | 0.690950i | −0.236929 | − | 0.971527i | \(-0.576141\pi\) |
−0.959831 | + | 0.280577i | \(0.909474\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16943.2 | + | 29346.5i | 0.211555 | + | 0.366423i | 0.952201 | − | 0.305471i | \(-0.0988141\pi\) |
−0.740647 | + | 0.671895i | \(0.765481\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 114807. | + | 116209.i | 1.41344 | + | 1.43071i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 66480.8 | − | 38382.7i | 0.807109 | − | 0.465985i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 41342.3 | − | 71607.0i | 0.494993 | − | 0.857354i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 125534. | − | 217431.i | 1.48243 | − | 2.56765i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 109192.i | − | 1.27191i | −0.771725 | − | 0.635956i | \(-0.780606\pi\) | ||
0.771725 | − | 0.635956i | \(-0.219394\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11145.0 | + | 6434.55i | 0.128066 | + | 0.0739391i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 194227.i | − | 2.20190i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5988.85 | + | 3457.67i | −0.0669886 | + | 0.0386759i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6924.27 | + | 11993.2i | 0.0764259 | + | 0.132374i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 71849.6i | − | 0.782599i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 156866. | 1.68628 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −130929. | + | 75591.9i | −1.38918 | + | 0.802044i | −0.993223 | − | 0.116224i | \(-0.962921\pi\) |
−0.395958 | + | 0.918268i | \(0.629588\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −59373.4 | − | 102838.i | −0.621835 | − | 1.07705i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 63635.6 | 0.657929 | 0.328965 | − | 0.944342i | \(-0.393300\pi\) | ||||
0.328965 | + | 0.944342i | \(0.393300\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 62756.5 | − | 108697.i | 0.640575 | − | 1.10951i | −0.344730 | − | 0.938702i | \(-0.612029\pi\) |
0.985305 | − | 0.170806i | \(-0.0546372\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 123595. | 1.24560 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 68452.4 | + | 39521.0i | 0.681193 | + | 0.393287i | 0.800305 | − | 0.599594i | \(-0.204671\pi\) |
−0.119111 | + | 0.992881i | \(0.538004\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 213919. | + | 123506.i | 2.10217 | + | 1.21369i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 173206. | + | 300002.i | 1.68095 | + | 2.91148i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2640.75 | − | 10100.3i | −0.0253118 | − | 0.0968121i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5507.96 | + | 3180.02i | −0.0521464 | + | 0.0301067i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 24056.6 | − | 41667.3i | 0.224977 | − | 0.389672i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 49685.2 | − | 86057.2i | 0.459024 | − | 0.795052i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 51095.1i | 0.466363i | 0.972433 | + | 0.233181i | \(0.0749135\pi\) | ||||
−0.972433 | + | 0.233181i | \(0.925086\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 243430. | + | 140544.i | 2.19526 | + | 1.26743i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 90307.2i | 0.804698i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 50433.4 | − | 29117.8i | 0.444078 | − | 0.256388i | −0.261248 | − | 0.965272i | \(-0.584134\pi\) |
0.705326 | + | 0.708883i | \(0.250801\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −112731. | − | 195257.i | −0.980947 | − | 1.69905i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 58069.3i | 0.499388i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −107784. | −0.916152 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 91402.7 | − | 52771.4i | 0.767928 | − | 0.443364i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −53216.5 | − | 92173.7i | −0.441965 | − | 0.765505i | 0.555871 | − | 0.831269i | \(-0.312385\pi\) |
−0.997835 | + | 0.0657637i | \(0.979052\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 86665.4 | 0.711533 | 0.355767 | − | 0.934575i | \(-0.384220\pi\) | ||||
0.355767 | + | 0.934575i | \(0.384220\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18964.3 | + | 32847.1i | −0.153930 | + | 0.266614i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −93586.9 | −0.751045 | −0.375522 | − | 0.926813i | \(-0.622537\pi\) | ||||
−0.375522 | + | 0.926813i | \(0.622537\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11024.1 | + | 6364.78i | 0.0874756 | + | 0.0505041i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10241.7 | − | 5913.03i | −0.0803590 | − | 0.0463953i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −45001.8 | − | 77945.4i | −0.349173 | − | 0.604786i | 0.636929 | − | 0.770922i | \(-0.280204\pi\) |
−0.986103 | + | 0.166136i | \(0.946871\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 112062. | + | 66526.0i | 0.859891 | + | 0.510478i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −113764. | + | 65681.9i | −0.863362 | + | 0.498463i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −47008.7 | + | 81421.5i | −0.352852 | + | 0.611158i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16656.8 | − | 28850.4i | 0.123668 | − | 0.214200i | −0.797543 | − | 0.603262i | \(-0.793867\pi\) |
0.921212 | + | 0.389062i | \(0.127201\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 477611.i | − | 3.50770i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −65515.7 | − | 37825.5i | −0.475990 | − | 0.274813i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 89569.8i | 0.643789i | 0.946775 | + | 0.321895i | \(0.104320\pi\) | ||||
−0.946775 | + | 0.321895i | \(0.895680\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −160865. | + | 92875.4i | −1.14393 | + | 0.660447i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −24118.2 | − | 41774.0i | −0.169693 | − | 0.293916i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33228.0i | 0.231327i | 0.993288 | + | 0.115663i | \(0.0368994\pi\) | ||||
−0.993288 | + | 0.115663i | \(0.963101\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 148693. | 1.02433 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 122413. | − | 70675.3i | 0.834508 | − | 0.481804i | −0.0208855 | − | 0.999782i | \(-0.506649\pi\) |
0.855394 | + | 0.517978i | \(0.173315\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −57594.3 | − | 99756.2i | −0.388560 | − | 0.673005i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 86161.4 | 0.575295 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 45995.4 | − | 79666.4i | 0.303959 | − | 0.526473i | −0.673070 | − | 0.739579i | \(-0.735025\pi\) |
0.977029 | + | 0.213106i | \(0.0683580\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6745.06 | −0.0441197 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −350387. | − | 202296.i | −2.26863 | − | 1.30979i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 67565.9 | + | 39009.2i | 0.433045 | + | 0.250019i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −57126.4 | − | 98945.8i | −0.362456 | − | 0.627793i | 0.625908 | − | 0.779897i | \(-0.284728\pi\) |
−0.988364 | + | 0.152104i | \(0.951395\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 142825. | − | 37342.0i | 0.897135 | − | 0.234559i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −210749. | + | 121676.i | −1.31062 | + | 0.756687i | −0.982199 | − | 0.187845i | \(-0.939850\pi\) |
−0.328421 | + | 0.944531i | \(0.606517\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5669.86 | − | 9820.49i | 0.0349110 | − | 0.0604677i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 98267.0 | − | 170203.i | 0.599098 | − | 1.03767i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 261970.i | − | 1.58148i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 36346.9 | + | 20984.9i | 0.217280 | + | 0.125447i | 0.604690 | − | 0.796461i | \(-0.293297\pi\) |
−0.387410 | + | 0.921908i | \(0.626630\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 454586.i | 2.69112i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10071.8 | − | 5814.93i | 0.0590480 | − | 0.0340914i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 143999. | + | 249413.i | 0.836108 | + | 1.44818i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 231881.i | 1.33350i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −213970. | −1.21878 | −0.609390 | − | 0.792871i | \(-0.708586\pi\) | ||||
−0.609390 | + | 0.792871i | \(0.708586\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −160145. | + | 92459.6i | −0.903542 | + | 0.521660i | −0.878348 | − | 0.478022i | \(-0.841354\pi\) |
−0.0251947 | + | 0.999683i | \(0.508021\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −309126. | − | 535422.i | −1.72765 | − | 2.99237i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6203.45 | −0.0343444 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 70880.3 | − | 122768.i | 0.388750 | − | 0.673334i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 70304.7 | 0.382006 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −262233. | − | 151400.i | −1.41167 | − | 0.815028i | −0.416124 | − | 0.909308i | \(-0.636612\pi\) |
−0.995546 | + | 0.0942797i | \(0.969945\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 97747.5 | + | 56434.5i | 0.521350 | + | 0.301002i | 0.737487 | − | 0.675361i | \(-0.236012\pi\) |
−0.216137 | + | 0.976363i | \(0.569346\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 368096. | + | 637560.i | 1.94528 | + | 3.36932i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 59898.1 | − | 59175.2i | 0.313654 | − | 0.309868i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 122771. | − | 70881.7i | 0.637038 | − | 0.367794i | −0.146435 | − | 0.989220i | \(-0.546780\pi\) |
0.783473 | + | 0.621426i | \(0.213446\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −139727. | + | 242014.i | −0.718462 | + | 1.24441i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21949.9 | − | 38018.3i | 0.111847 | − | 0.193725i | −0.804668 | − | 0.593725i | \(-0.797657\pi\) |
0.916515 | + | 0.400000i | \(0.130990\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 117818.i | − | 0.594964i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −138652. | − | 80050.6i | −0.693921 | − | 0.400635i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 341964.i | 1.69624i | 0.529803 | + | 0.848121i | \(0.322266\pi\) | ||||
−0.529803 | + | 0.848121i | \(0.677734\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −385490. | + | 222563.i | −1.89522 | + | 1.09421i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 128533. | + | 222625.i | 0.626351 | + | 1.08487i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 22493.9i | 0.108653i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −310982. | −1.48903 | −0.744514 | − | 0.667606i | \(-0.767319\pi\) | ||||
−0.744514 | + | 0.667606i | \(0.767319\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −32038.4 | + | 18497.4i | −0.152070 | + | 0.0877979i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8617.64 | + | 14926.2i | 0.0405496 | + | 0.0702340i | 0.885588 | − | 0.464472i | \(-0.153756\pi\) |
−0.845038 | + | 0.534706i | \(0.820422\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −41988.4 | −0.195870 | −0.0979350 | − | 0.995193i | \(-0.531224\pi\) | ||||
−0.0979350 | + | 0.995193i | \(0.531224\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −86534.2 | + | 149882.i | −0.400205 | + | 0.693175i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −127467. | −0.584471 | −0.292235 | − | 0.956346i | \(-0.594399\pi\) | ||||
−0.292235 | + | 0.956346i | \(0.594399\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 70677.2 | + | 40805.5i | 0.321317 | + | 0.185513i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 285728. | + | 164965.i | 1.28799 | + | 0.743620i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −40150.5 | − | 69542.7i | −0.179460 | − | 0.310834i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 55088.5 | − | 54423.6i | 0.244159 | − | 0.241213i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −407619. | + | 235339.i | −1.79150 | + | 1.03433i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 199847. | − | 346146.i | 0.871019 | − | 1.50865i | 0.0100742 | − | 0.999949i | \(-0.496793\pi\) |
0.860944 | − | 0.508699i | \(-0.169873\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25578.7 | + | 44303.5i | −0.110557 | + | 0.191491i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 95379.5i | − | 0.408847i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −403384. | − | 232894.i | −1.71489 | − | 0.990091i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 148836.i | 0.627551i | 0.949497 | + | 0.313776i | \(0.101594\pi\) | ||||
−0.949497 | + | 0.313776i | \(0.898406\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 32011.5 | − | 18481.9i | 0.133872 | − | 0.0772908i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −40416.6 | − | 70003.6i | −0.167647 | − | 0.290374i | 0.769945 | − | 0.638110i | \(-0.220284\pi\) |
−0.937592 | + | 0.347737i | \(0.886950\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 47048.8i | − | 0.193577i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −716669. | −2.92488 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9962.55 | − | 5751.88i | 0.0403327 | − | 0.0232861i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 177011. | + | 306591.i | 0.710883 | + | 1.23129i | 0.964526 | + | 0.263987i | \(0.0850378\pi\) |
−0.253643 | + | 0.967298i | \(0.581629\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 683746. | 2.72408 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −112647. | + | 195110.i | −0.445229 | + | 0.771160i | −0.998068 | − | 0.0621282i | \(-0.980211\pi\) |
0.552839 | + | 0.833288i | \(0.313545\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −133298. | −0.522684 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 374405. | + | 216163.i | 1.45655 | + | 0.840941i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26520.7 | + | 15311.7i | 0.102365 | + | 0.0591002i | 0.550308 | − | 0.834962i | \(-0.314510\pi\) |
−0.447944 | + | 0.894062i | \(0.647844\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 42482.0 | + | 73581.0i | 0.162691 | + | 0.281789i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 122230. | − | 445338.i | 0.464456 | − | 1.69221i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −190788. | + | 110151.i | −0.719343 | + | 0.415313i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −288100. | + | 499004.i | −1.07786 | + | 1.86691i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −117303. | + | 203175.i | −0.435488 | + | 0.754287i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 258518.i | 0.952390i | 0.879340 | + | 0.476195i | \(0.157984\pi\) | ||||
−0.879340 | + | 0.476195i | \(0.842016\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −378631. | − | 218603.i | −1.38424 | − | 0.799194i | −0.391586 | − | 0.920142i | \(-0.628073\pi\) |
−0.992659 | + | 0.120948i | \(0.961407\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 87720.8i | − | 0.318261i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9578.69 | − | 5530.26i | 0.0344893 | − | 0.0199124i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 112720. | + | 195237.i | 0.402802 | + | 0.697673i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 72357.6i | − | 0.256623i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 86923.8 | 0.305974 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 556573. | − | 321338.i | 1.94453 | − | 1.12267i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 214169. | + | 370952.i | 0.742691 | + | 1.28638i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 260447. | 0.896481 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −141527. | + | 245131.i | −0.483552 | + | 0.837537i | −0.999822 | − | 0.0188890i | \(-0.993987\pi\) |
0.516269 | + | 0.856426i | \(0.327320\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 838976. | 2.84544 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −77302.4 | − | 44630.5i | −0.260255 | − | 0.150259i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −44577.7 | − | 25736.9i | −0.148985 | − | 0.0860166i | 0.423654 | − | 0.905824i | \(-0.360747\pi\) |
−0.572639 | + | 0.819807i | \(0.694080\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −440996. | − | 763828.i | −1.46315 | − | 2.53426i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 412764. | + | 417807.i | 1.35956 | + | 1.37617i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 61059.7 | − | 35252.8i | 0.199666 | − | 0.115277i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 390385. | − | 676167.i | 1.26738 | − | 2.19517i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 114117. | − | 197657.i | 0.367825 | − | 0.637092i | −0.621400 | − | 0.783494i | \(-0.713436\pi\) |
0.989225 | + | 0.146401i | \(0.0467691\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15681.1i | 0.0501826i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 59386.5 | + | 34286.8i | 0.188696 | + | 0.108944i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 506715.i | − | 1.59863i | −0.600914 | − | 0.799313i | \(-0.705197\pi\) | ||
0.600914 | − | 0.799313i | \(-0.294803\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −362246. | + | 209143.i | −1.13477 | + | 0.655158i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −88804.4 | − | 153814.i | −0.276228 | − | 0.478442i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 596850.i | − | 1.84349i | −0.387797 | − | 0.921745i | \(-0.626764\pi\) | ||
0.387797 | − | 0.921745i | \(-0.373236\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −266256. | −0.816635 | −0.408317 | − | 0.912840i | \(-0.633884\pi\) | ||||
−0.408317 | + | 0.912840i | \(0.633884\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −781837. | + | 451394.i | −2.38126 | + | 1.37482i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −25016.0 | − | 43329.0i | −0.0756628 | − | 0.131052i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 459755. | 1.38094 | 0.690470 | − | 0.723361i | \(-0.257404\pi\) | ||||
0.690470 | + | 0.723361i | \(0.257404\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −242520. | + | 420056.i | −0.723419 | + | 1.25300i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 260265. | 0.771015 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 379894. | + | 219332.i | 1.11770 | + | 0.645305i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 121201. | + | 69975.2i | 0.354155 | + | 0.204471i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 75602.9 | + | 130948.i | 0.219413 | + | 0.380034i | 0.954629 | − | 0.297799i | \(-0.0962525\pi\) |
−0.735216 | + | 0.677833i | \(0.762919\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36543.9 | + | 133145.i | −0.105338 | + | 0.383791i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −266796. | + | 154035.i | −0.763842 | + | 0.441005i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −85790.0 | + | 148593.i | −0.243965 | + | 0.422559i | −0.961840 | − | 0.273612i | \(-0.911781\pi\) |
0.717875 | + | 0.696172i | \(0.245115\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10970.0 | + | 19000.7i | −0.0309866 | + | 0.0536704i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 1.10583e6i | − | 3.10270i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19875.7 | + | 11475.2i | 0.0553947 | + | 0.0319821i | 0.527442 | − | 0.849591i | \(-0.323151\pi\) |
−0.472047 | + | 0.881573i | \(0.656485\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 107019.i | − | 0.296287i | −0.988966 | − | 0.148144i | \(-0.952670\pi\) | ||
0.988966 | − | 0.148144i | \(-0.0473298\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 439733. | − | 253880.i | 1.20936 | − | 0.698222i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 121855. | + | 211059.i | 0.332915 | + | 0.576625i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 264918.i | 0.719010i | 0.933143 | + | 0.359505i | \(0.117054\pi\) | ||||
−0.933143 | + | 0.359505i | \(0.882946\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 665300. | 1.79384 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 97445.2 | − | 56260.0i | 0.261023 | − | 0.150701i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 267953. | + | 464108.i | 0.713079 | + | 1.23509i | 0.963696 | + | 0.267003i | \(0.0860335\pi\) |
−0.250616 | + | 0.968087i | \(0.580633\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.32664e6 | −3.50755 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −92145.4 | + | 159601.i | −0.242049 | + | 0.419241i | −0.961298 | − | 0.275511i | \(-0.911153\pi\) |
0.719249 | + | 0.694753i | \(0.244486\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −400704. | −1.04578 | −0.522892 | − | 0.852399i | \(-0.675147\pi\) | ||||
−0.522892 | + | 0.852399i | \(0.675147\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −258395. | − | 149185.i | −0.670041 | − | 0.386849i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −92207.9 | − | 53236.2i | −0.237570 | − | 0.137161i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 239340. | + | 414548.i | 0.612709 | + | 1.06124i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −828172. | + | 216528.i | −2.10662 | + | 0.550781i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −43212.7 | + | 24948.9i | −0.109222 | + | 0.0630593i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −91315.6 | + | 158163.i | −0.229343 | + | 0.397235i | −0.957614 | − | 0.288056i | \(-0.906991\pi\) |
0.728270 | + | 0.685290i | \(0.240325\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9374.42 | − | 16237.0i | 0.0233958 | − | 0.0405226i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 275860.i | − | 0.684133i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −44045.9 | − | 25429.9i | −0.108549 | − | 0.0626709i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 71572.9i | − | 0.175286i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −141458. | + | 81670.6i | −0.344279 | + | 0.198770i | −0.662163 | − | 0.749360i | \(-0.730361\pi\) |
0.317884 | + | 0.948130i | \(0.397028\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −138596. | − | 240055.i | −0.335219 | − | 0.580616i | 0.648308 | − | 0.761378i | \(-0.275477\pi\) |
−0.983527 | + | 0.180762i | \(0.942144\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 239327.i | − | 0.575271i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −624788. | −1.49253 | −0.746267 | − | 0.665647i | \(-0.768156\pi\) | ||||
−0.746267 | + | 0.665647i | \(0.768156\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −58401.3 | + | 33718.0i | −0.138654 | + | 0.0800521i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 78201.4 | + | 135449.i | 0.184524 | + | 0.319605i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 32974.6 | 0.0773308 | 0.0386654 | − | 0.999252i | \(-0.487689\pi\) | ||||
0.0386654 | + | 0.999252i | \(0.487689\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −375306. | + | 650049.i | −0.874788 | + | 1.51518i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 528621. | 1.22465 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 245158. | + | 141542.i | 0.564514 | + | 0.325922i | 0.754955 | − | 0.655776i | \(-0.227659\pi\) |
−0.190441 | + | 0.981699i | \(0.560992\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −469830. | − | 271257.i | −1.07532 | − | 0.620837i | −0.145691 | − | 0.989330i | \(-0.546540\pi\) |
−0.929630 | + | 0.368493i | \(0.879874\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6695.51 | − | 11597.0i | −0.0152320 | − | 0.0263826i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −69278.0 | − | 264973.i | −0.156658 | − | 0.599181i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 328620. | − | 189729.i | 0.738655 | − | 0.426463i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 534247. | − | 925343.i | 1.19369 | − | 2.06752i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −411001. | + | 711874.i | −0.912846 | + | 1.58110i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 278225.i | − | 0.614279i | −0.951664 | − | 0.307140i | \(-0.900628\pi\) | ||
0.951664 | − | 0.307140i | \(-0.0993719\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −237647. | − | 137206.i | −0.521585 | − | 0.301137i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 107959.i | − | 0.235550i | −0.993040 | − | 0.117775i | \(-0.962424\pi\) | ||
0.993040 | − | 0.117775i | \(-0.0375761\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −364540. | + | 210468.i | −0.790690 | + | 0.456505i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 707173. | + | 1.22486e6i | 1.52487 | + | 2.64114i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 344624.i | − | 0.738761i | −0.929278 | − | 0.369381i | \(-0.879570\pi\) | ||
0.929278 | − | 0.369381i | \(-0.120430\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 843362. | 1.79735 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 530361. | − | 306204.i | 1.12372 | − | 0.648780i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −42831.0 | − | 74185.4i | −0.0902235 | − | 0.156272i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 143967. | 0.301513 | 0.150757 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150757 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −323828. | + | 560887.i | −0.674293 | + | 1.16791i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 430192. | 0.890621 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 73424.7 | + | 42391.8i | 0.151139 | + | 0.0872602i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 553211. | + | 319397.i | 1.13223 | + | 0.653696i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −371742. | − | 643876.i | −0.756494 | − | 1.31029i | −0.944628 | − | 0.328142i | \(-0.893577\pi\) |
0.188134 | − | 0.982143i | \(-0.439756\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 164862. | − | 600663.i | 0.333587 | − | 1.21540i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.48722e6 | + | 858648.i | −2.99225 | + | 1.72758i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −60230.8 | + | 104323.i | −0.120498 | + | 0.208709i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −167187. | + | 289576.i | −0.332590 | + | 0.576063i | −0.983019 | − | 0.183504i | \(-0.941256\pi\) |
0.650429 | + | 0.759567i | \(0.274589\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 438665.i | − | 0.867748i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 77254.0 | + | 44602.6i | 0.151964 | + | 0.0877367i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 130431.i | − | 0.255135i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.18585e6 | − | 684651.i | 2.30670 | − | 1.33177i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 166066. | + | 287634.i | 0.321234 | + | 0.556394i | 0.980743 | − | 0.195303i | \(-0.0625689\pi\) |
−0.659509 | + | 0.751697i | \(0.729236\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 199089.i | 0.382980i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −633927. | −1.21273 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 302232. | − | 174494.i | 0.574996 | − | 0.331974i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −88406.6 | − | 153125.i | −0.167269 | − | 0.289719i | 0.770190 | − | 0.637815i | \(-0.220162\pi\) |
−0.937459 | + | 0.348096i | \(0.886828\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 513253. | 0.965776 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7647.50 | + | 13245.9i | −0.0143115 | + | 0.0247882i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −534132. | −0.994124 | −0.497062 | − | 0.867715i | \(-0.665588\pi\) | ||||
−0.497062 | + | 0.867715i | \(0.665588\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 672234. | + | 388115.i | 1.24436 | + | 0.718432i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −409823. | − | 236612.i | −0.754504 | − | 0.435613i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −221075. | − | 382913.i | −0.404810 | − | 0.701151i | 0.589490 | − | 0.807776i | \(-0.299329\pi\) |
−0.994299 | + | 0.106625i | \(0.965996\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 161200. | + | 44243.9i | 0.293581 | + | 0.0805781i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18451.4 | + | 10652.9i | −0.0334235 | + | 0.0192971i | −0.516619 | − | 0.856216i | \(-0.672809\pi\) |
0.483195 | + | 0.875513i | \(0.339476\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −148512. | + | 257231.i | −0.267578 | + | 0.463458i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 809644. | − | 1.40235e6i | 1.45095 | − | 2.51312i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 580789.i | − | 1.03527i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 345107. | + | 199248.i | 0.611891 | + | 0.353275i | 0.773705 | − | 0.633546i | \(-0.218401\pi\) |
−0.161814 | + | 0.986821i | \(0.551735\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 432635.i | − | 0.763013i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 413021. | − | 238458.i | 0.724567 | − | 0.418329i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −200807. | − | 347808.i | −0.350419 | − | 0.606943i | 0.635904 | − | 0.771768i | \(-0.280627\pi\) |
−0.986323 | + | 0.164825i | \(0.947294\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 553060.i | 0.960038i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −383128. | −0.661568 | −0.330784 | − | 0.943706i | \(-0.607313\pi\) | ||||
−0.330784 | + | 0.943706i | \(0.607313\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −69858.5 | + | 40332.8i | −0.119997 | + | 0.0692803i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 68252.3 | + | 118216.i | 0.116626 | + | 0.202002i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13168.9 | 0.0223850 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 86027.4 | − | 149004.i | 0.145474 | − | 0.251968i | −0.784076 | − | 0.620665i | \(-0.786863\pi\) |
0.929550 | + | 0.368697i | \(0.120196\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.34301e6 | 2.25927 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 145779. | + | 84165.8i | 0.243971 | + | 0.140856i | 0.617000 | − | 0.786963i | \(-0.288348\pi\) |
−0.373030 | + | 0.927819i | \(0.621681\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 71050.7 | + | 41021.1i | 0.118295 | + | 0.0682974i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −352793. | − | 611055.i | −0.584356 | − | 1.01213i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.02394e6 | + | 267712.i | −1.68733 | + | 0.441157i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −57768.0 | + | 33352.4i | −0.0947077 | + | 0.0546795i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.04061e6 | − | 1.80238e6i | 1.69732 | − | 2.93984i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 306049. | − | 530092.i | 0.496651 | − | 0.860225i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 90783.2i | 0.146574i | 0.997311 | + | 0.0732868i | \(0.0233489\pi\) | ||||
−0.997311 | + | 0.0732868i | \(0.976651\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −343339. | − | 198227.i | −0.551530 | − | 0.318426i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 378007.i | 0.604153i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 139014. | − | 80259.9i | 0.221061 | − | 0.127630i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 653692. | + | 1.13223e6i | 1.03428 | + | 1.79143i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 250407.i | − | 0.394213i | −0.980382 | − | 0.197106i | \(-0.936846\pi\) | ||
0.980382 | − | 0.197106i | \(-0.0631544\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 109750. | 0.171913 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −573690. | + | 331220.i | −0.894153 | + | 0.516240i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −246333. | − | 426661.i | −0.382024 | − | 0.661685i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −176951. | −0.273062 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 310587. | − | 537953.i | 0.476910 | − | 0.826033i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 366214. | 0.559549 | 0.279775 | − | 0.960066i | \(-0.409740\pi\) | ||||
0.279775 | + | 0.960066i | \(0.409740\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −379096. | − | 218871.i | −0.576379 | − | 0.332772i | 0.183314 | − | 0.983054i | \(-0.441317\pi\) |
−0.759693 | + | 0.650282i | \(0.774651\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −148686. | − | 85844.0i | −0.224952 | − | 0.129876i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −34288.1 | − | 59388.8i | −0.0516212 | − | 0.0894106i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −48295.5 | − | 184720.i | −0.0723540 | − | 0.276738i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 109530. | − | 63237.0i | 0.163292 | − | 0.0942765i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 434018. | − | 751741.i | 0.643904 | − | 1.11527i | −0.340649 | − | 0.940190i | \(-0.610647\pi\) |
0.984553 | − | 0.175084i | \(-0.0560198\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 310831. | − | 538375.i | 0.458907 | − | 0.794850i | −0.539997 | − | 0.841667i | \(-0.681575\pi\) |
0.998903 | + | 0.0468175i | \(0.0149079\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 508651.i | 0.747329i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −543344. | − | 313700.i | −0.794445 | − | 0.458673i | 0.0470803 | − | 0.998891i | \(-0.485008\pi\) |
−0.841525 | + | 0.540218i | \(0.818342\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 644642.i | − | 0.938015i | −0.883194 | − | 0.469007i | \(-0.844612\pi\) | ||
0.883194 | − | 0.469007i | \(-0.155388\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.02594e6 | + | 592325.i | −1.48566 | + | 0.857744i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24803.8 | − | 42961.4i | −0.0357460 | − | 0.0619139i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 1.26851e6i | − | 1.81936i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 489265. | 0.698382 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 673952. | − | 389106.i | 0.957426 | − | 0.552770i | 0.0620460 | − | 0.998073i | \(-0.480237\pi\) |
0.895380 | + | 0.445303i | \(0.146904\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 969772. | + | 1.67969e6i | 1.37113 | + | 2.37486i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.70414e6 | 2.39800 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 401032. | − | 694608.i | 0.561650 | − | 0.972807i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 220242. | 0.306997 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −458322. | − | 264613.i | −0.635851 | − | 0.367109i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −348518. | − | 201217.i | −0.481246 | − | 0.277847i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 591661. | + | 1.02479e6i | 0.813158 | + | 1.40843i | 0.910643 | + | 0.413194i | \(0.135587\pi\) |
−0.0974854 | + | 0.995237i | \(0.531080\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.64323e6 | − | 451011.i | −2.24784 | − | 0.616957i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 732946. | − | 423166.i | 0.997953 | − | 0.576168i | 0.0903111 | − | 0.995914i | \(-0.471214\pi\) |
0.907642 | + | 0.419745i | \(0.137881\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −128900. | + | 223261.i | −0.174689 | + | 0.302570i | −0.940054 | − | 0.341027i | \(-0.889225\pi\) |
0.765365 | + | 0.643597i | \(0.222559\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −599447. | + | 1.03827e6i | −0.808620 | + | 1.40057i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 615296.i | 0.826157i | 0.910695 | + | 0.413079i | \(0.135547\pi\) | ||||
−0.910695 | + | 0.413079i | \(0.864453\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 376937. | + | 217625.i | 0.503775 | + | 0.290855i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.29134e6i | 1.71792i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −354056. | + | 204414.i | −0.468848 | + | 0.270689i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 46205.3 | + | 80030.0i | 0.0609054 | + | 0.105491i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.61893e6i | 3.43634i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 311426. | 0.406761 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 641044. | − | 370107.i | 0.833468 | − | 0.481203i | −0.0215707 | − | 0.999767i | \(-0.506867\pi\) |
0.855039 | + | 0.518564i | \(0.173533\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 852663. | + | 1.47686e6i | 1.10357 | + | 1.91144i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28024.1 | −0.0361061 | −0.0180530 | − | 0.999837i | \(-0.505747\pi\) | ||||
−0.0180530 | + | 0.999837i | \(0.505747\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 518628. | − | 898290.i | 0.665173 | − | 1.15211i | −0.314066 | − | 0.949401i | \(-0.601691\pi\) |
0.979238 | − | 0.202712i | \(-0.0649754\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −200985. | −0.256612 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −785062. | − | 453255.i | −0.997830 | − | 0.576097i | −0.0902243 | − | 0.995921i | \(-0.528758\pi\) |
−0.907605 | + | 0.419824i | \(0.862092\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −215896. | − | 124648.i | −0.273176 | − | 0.157718i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 514934. | + | 891892.i | 0.648629 | + | 1.12346i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −974608. | + | 962846.i | −1.22216 | + | 1.20741i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 688201. | − | 397333.i | 0.859150 | − | 0.496031i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 54000.5 | − | 93531.7i | 0.0671140 | − | 0.116245i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −311116. | + | 538869.i | −0.384949 | + | 0.666751i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 83552.8i | − | 0.102923i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −187305. | − | 108141.i | −0.229707 | − | 0.132621i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1.55649e6i | − | 1.90042i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 534950. | − | 308854.i | 0.650278 | − | 0.375438i | −0.138285 | − | 0.990392i | \(-0.544159\pi\) |
0.788563 | + | 0.614954i | \(0.210826\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 374738. | + | 649066.i | 0.453524 | + | 0.785526i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 728686.i | − | 0.878019i | −0.898482 | − | 0.439009i | \(-0.855329\pi\) | ||
0.898482 | − | 0.439009i | \(-0.144671\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.50915e6 | −1.81047 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.12165e6 | + | 1.22494e6i | −2.53415 | + | 1.46309i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 339166. | + | 587452.i | 0.403342 | + | 0.698609i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −545481. | −0.645875 | −0.322938 | − | 0.946420i | \(-0.604670\pi\) | ||||
−0.322938 | + | 0.946420i | \(0.604670\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.18057e6 | − | 2.04480e6i | 1.39178 | − | 2.41064i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13026.1 | 0.0152901 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −320533. | − | 185060.i | −0.374619 | − | 0.216286i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.07272e6 | + | 619335.i | 1.24832 | + | 0.720719i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −450263. | − | 779878.i | −0.521717 | − | 0.903640i | −0.999681 | − | 0.0252606i | \(-0.991958\pi\) |
0.477964 | − | 0.878379i | \(-0.341375\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 597170. | + | 163903.i | 0.688967 | + | 0.189098i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −860688. | + | 496918.i | −0.988741 | + | 0.570850i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 63610.0 | − | 110176.i | 0.0727616 | − | 0.126027i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 324708. | − | 562411.i | 0.369840 | − | 0.640582i | −0.619700 | − | 0.784839i | \(-0.712746\pi\) |
0.989540 | + | 0.144256i | \(0.0460790\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.96021e6i | 2.22317i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −460050. | − | 265610.i | −0.519548 | − | 0.299961i | 0.217202 | − | 0.976127i | \(-0.430307\pi\) |
−0.736750 | + | 0.676165i | \(0.763640\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 683795.i | 0.768958i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −840499. | + | 485262.i | −0.941182 | + | 0.543392i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −803821. | − | 1.39226e6i | −0.896313 | − | 1.55246i | −0.832172 | − | 0.554518i | \(-0.812903\pi\) |
−0.0641411 | − | 0.997941i | \(-0.520431\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 96207.3i | 0.106826i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.23445e6 | −1.36494 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −662976. | + | 382769.i | −0.729982 | + | 0.421455i | −0.818416 | − | 0.574627i | \(-0.805147\pi\) |
0.0884337 | + | 0.996082i | \(0.471814\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 837439. | + | 1.45049e6i | 0.918219 | + | 1.59040i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.85775e6 | −4.21222 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 381075. | − | 660042.i | 0.414356 | − | 0.717686i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 777243. | 0.841608 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.12938e6 | − | 1.80675e6i | −3.37447 | − | 1.94825i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 779302. | + | 449930.i | 0.836856 | + | 0.483159i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −67077.0 | − | 116181.i | −0.0717332 | − | 0.124246i | 0.827928 | − | 0.560835i | \(-0.189520\pi\) |
−0.899661 | + | 0.436589i | \(0.856186\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 114588. | + | 115988.i | 0.122037 | + | 0.123528i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −362961. | + | 209555.i | −0.384965 | + | 0.222260i | −0.679976 | − | 0.733234i | \(-0.738010\pi\) |
0.295011 | + | 0.955494i | \(0.404677\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 194383. | − | 336682.i | 0.205321 | − | 0.355626i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 49664.5 | − | 86021.4i | 0.0522440 | − | 0.0904893i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.26450e6i | 1.32474i | 0.749178 | + | 0.662369i | \(0.230449\pi\) | ||||
−0.749178 | + | 0.662369i | \(0.769551\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 534669. | + | 308691.i | 0.557853 | + | 0.322077i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 501878.i | 0.521507i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 632772. | − | 365331.i | 0.654848 | − | 0.378076i | −0.135463 | − | 0.990782i | \(-0.543252\pi\) |
0.790311 | + | 0.612706i | \(0.209919\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 285770. | + | 494967.i | 0.294539 | + | 0.510157i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.55193e6i | 1.59308i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −123357. | −0.126116 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −228836. | + | 132118.i | −0.233011 | + | 0.134529i | −0.611960 | − | 0.790888i | \(-0.709619\pi\) |
0.378949 | + | 0.925417i | \(0.376285\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −398993. | − | 691075.i | −0.404638 | − | 0.700853i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.05157e6 | −2.07224 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 263686. | − | 456717.i | 0.265275 | − | 0.459469i | −0.702361 | − | 0.711821i | \(-0.747871\pi\) |
0.967636 | + | 0.252352i | \(0.0812040\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.20724e6 | −2.21166 |
(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 | 304.5.r.d.145.2 | 40 | ||
4.3 | odd | 2 | 152.5.n.a.145.19 | yes | 40 | ||
19.8 | odd | 6 | inner | 304.5.r.d.65.2 | 40 | ||
76.27 | even | 6 | 152.5.n.a.65.19 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.5.n.a.65.19 | ✓ | 40 | 76.27 | even | 6 | ||
152.5.n.a.145.19 | yes | 40 | 4.3 | odd | 2 | ||
304.5.r.d.65.2 | 40 | 19.8 | odd | 6 | inner | ||
304.5.r.d.145.2 | 40 | 1.1 | even | 1 | trivial |