Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,5,Mod(29,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.29");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.20219778503\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 110x^{6} + 2705x^{4} + 17000x^{2} + 25600 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{2}\cdot 5^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 29.1 | ||
Root | \(-8.83726i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.29 |
Dual form | 60.5.b.a.29.2 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −8.97294 | − | 0.697422i | −0.996993 | − | 0.0774913i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 9.58741 | + | 23.0886i | 0.383496 | + | 0.923542i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 67.4301i | − | 1.37612i | −0.725652 | − | 0.688062i | \(-0.758462\pi\) | ||
0.725652 | − | 0.688062i | \(-0.241538\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 80.0272 | + | 12.5158i | 0.987990 | + | 0.154517i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 155.791i | − | 1.28753i | −0.765225 | − | 0.643763i | \(-0.777372\pi\) | ||
0.765225 | − | 0.643763i | \(-0.222628\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 206.475i | − | 1.22174i | −0.791729 | − | 0.610872i | \(-0.790819\pi\) | ||
0.791729 | − | 0.610872i | \(-0.209181\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −69.9247 | − | 213.859i | −0.310777 | − | 0.950483i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −119.476 | −0.413413 | −0.206707 | − | 0.978403i | \(-0.566275\pi\) | ||||
−0.206707 | + | 0.978403i | \(0.566275\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 492.163 | 1.36333 | 0.681667 | − | 0.731663i | \(-0.261256\pi\) | ||||
0.681667 | + | 0.731663i | \(0.261256\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −47.0272 | + | 605.046i | −0.106638 | + | 1.37199i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 353.261 | 0.667790 | 0.333895 | − | 0.942610i | \(-0.391637\pi\) | ||||
0.333895 | + | 0.942610i | \(0.391637\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −441.163 | + | 442.719i | −0.705861 | + | 0.708350i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −709.350 | − | 168.117i | −0.973046 | − | 0.230613i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 917.942i | − | 1.09149i | −0.837952 | − | 0.545744i | \(-0.816247\pi\) | ||
0.837952 | − | 0.545744i | \(-0.183753\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −632.163 | −0.657818 | −0.328909 | − | 0.944362i | \(-0.606681\pi\) | ||||
−0.328909 | + | 0.944362i | \(0.606681\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −108.652 | + | 1397.90i | −0.0997720 | + | 1.28365i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1556.86 | − | 646.480i | 1.27091 | − | 0.527739i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1755.93i | 1.28264i | 0.767274 | + | 0.641320i | \(0.221613\pi\) | ||||
−0.767274 | + | 0.641320i | \(0.778387\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −144.000 | + | 1852.69i | −0.0946746 | + | 1.21807i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1449.21i | − | 0.862111i | −0.902326 | − | 0.431055i | \(-0.858141\pi\) | ||
0.902326 | − | 0.431055i | \(-0.141859\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 627.316i | − | 0.339273i | −0.985507 | − | 0.169637i | \(-0.945741\pi\) | ||
0.985507 | − | 0.169637i | \(-0.0542594\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 478.281 | + | 1967.71i | 0.236188 | + | 0.971707i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3701.53 | −1.67566 | −0.837829 | − | 0.545932i | \(-0.816176\pi\) | ||||
−0.837829 | + | 0.545932i | \(0.816176\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2145.82 | −0.893718 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1072.05 | + | 83.3255i | 0.412170 | + | 0.0320359i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3662.42 | 1.30382 | 0.651909 | − | 0.758297i | \(-0.273969\pi\) | ||||
0.651909 | + | 0.758297i | \(0.273969\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3596.98 | − | 1493.63i | 1.18908 | − | 0.493761i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4416.15 | − | 343.245i | −1.35923 | − | 0.105646i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 1424.52i | − | 0.409226i | −0.978843 | − | 0.204613i | \(-0.934406\pi\) | ||
0.978843 | − | 0.204613i | \(-0.0655936\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1737.14 | 0.466848 | 0.233424 | − | 0.972375i | \(-0.425007\pi\) | ||||
0.233424 | + | 0.972375i | \(0.425007\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 843.944 | − | 5396.24i | 0.212634 | − | 1.35960i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4767.21 | − | 1979.56i | 1.12833 | − | 0.468534i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 6456.19i | − | 1.43822i | −0.694894 | − | 0.719112i | \(-0.744549\pi\) | ||
0.694894 | − | 0.719112i | \(-0.255451\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3169.79 | − | 246.372i | −0.665782 | − | 0.0517479i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2436.64i | 0.483365i | 0.970355 | + | 0.241683i | \(0.0776993\pi\) | ||||
−0.970355 | + | 0.241683i | \(0.922301\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2691.70i | 0.505104i | 0.967583 | + | 0.252552i | \(0.0812699\pi\) | ||||
−0.967583 | + | 0.252552i | \(0.918730\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4267.29 | − | 3664.81i | 0.758630 | − | 0.651522i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10505.0 | −1.77179 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3216.49 | 0.515381 | 0.257690 | − | 0.966228i | \(-0.417039\pi\) | ||||
0.257690 | + | 0.966228i | \(0.417039\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6247.71 | + | 2003.22i | 0.952249 | + | 0.305322i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1517.02 | −0.220208 | −0.110104 | − | 0.993920i | \(-0.535118\pi\) | ||||
−0.110104 | + | 0.993920i | \(0.535118\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1145.47 | − | 2758.54i | −0.158542 | − | 0.381805i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −640.193 | + | 8236.64i | −0.0845809 | + | 1.08821i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7466.75i | 0.942652i | 0.881959 | + | 0.471326i | \(0.156224\pi\) | ||||
−0.881959 | + | 0.471326i | \(0.843776\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13922.6 | −1.68127 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5672.36 | + | 440.884i | 0.655840 | + | 0.0509752i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4718.57 | + | 11363.3i | 0.522833 | + | 1.25910i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10716.1i | 1.13892i | 0.822018 | + | 0.569462i | \(0.192848\pi\) | ||||
−0.822018 | + | 0.569462i | \(0.807152\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1949.85 | − | 12467.5i | 0.198944 | − | 1.27206i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 3399.39i | − | 0.333241i | −0.986021 | − | 0.166620i | \(-0.946715\pi\) | ||
0.986021 | − | 0.166620i | \(-0.0532855\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8880.69i | 0.837090i | 0.908196 | + | 0.418545i | \(0.137460\pi\) | ||||
−0.908196 | + | 0.418545i | \(0.862540\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −14420.5 | + | 4715.03i | −1.30798 | + | 0.427667i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4732.46 | −0.413351 | −0.206676 | − | 0.978410i | \(-0.566264\pi\) | ||||
−0.206676 | + | 0.978410i | \(0.566264\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10138.4 | 0.853333 | 0.426666 | − | 0.904409i | \(-0.359688\pi\) | ||||
0.426666 | + | 0.904409i | \(0.359688\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1224.63 | − | 15755.9i | 0.0993934 | − | 1.27878i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5594.72 | 0.438149 | 0.219074 | − | 0.975708i | \(-0.429696\pi\) | ||||
0.219074 | + | 0.975708i | \(0.429696\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3386.86 | + | 8156.29i | 0.256095 | + | 0.616733i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2584.21 | − | 16523.6i | 0.188780 | − | 1.20707i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8056.30i | 0.568908i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9629.69 | −0.657721 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1010.71 | + | 13003.7i | −0.0668061 | + | 0.859518i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −14451.4 | − | 5941.30i | −0.924887 | − | 0.380243i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3557.28i | 0.220552i | 0.993901 | + | 0.110276i | \(0.0351735\pi\) | ||||
−0.993901 | + | 0.110276i | \(0.964827\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −437.504 | + | 5628.87i | −0.0262907 | + | 0.338253i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 31645.8i | 1.84406i | 0.387124 | + | 0.922028i | \(0.373469\pi\) | ||||
−0.387124 | + | 0.922028i | \(0.626531\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 33186.6i | − | 1.87612i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2919.26 | − | 17989.7i | −0.160179 | − | 0.987088i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19253.1 | 1.02579 | 0.512897 | − | 0.858450i | \(-0.328572\pi\) | ||||
0.512897 | + | 0.858450i | \(0.328572\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10124.2 | 0.523998 | 0.261999 | − | 0.965068i | \(-0.415618\pi\) | ||||
0.261999 | + | 0.965068i | \(0.415618\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 33213.6 | + | 2581.53i | 1.67062 | + | 0.129849i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −32166.8 | −1.57303 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 21194.0 | − | 8800.68i | 1.00804 | − | 0.418582i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 19254.3 | + | 1496.54i | 0.891030 | + | 0.0692553i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 25686.3i | − | 1.15699i | −0.815686 | − | 0.578495i | \(-0.803640\pi\) | ||
0.815686 | − | 0.578495i | \(-0.196360\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19518.2 | −0.856024 | −0.428012 | − | 0.903773i | \(-0.640786\pi\) | ||||
−0.428012 | + | 0.903773i | \(0.640786\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9561.36 | − | 1495.35i | −0.408448 | − | 0.0638792i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6060.81 | − | 14595.7i | −0.252271 | − | 0.607523i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 30918.8i | − | 1.25436i | −0.778874 | − | 0.627181i | \(-0.784209\pi\) | ||
0.778874 | − | 0.627181i | \(-0.215791\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −32862.7 | − | 2554.25i | −1.29990 | − | 0.101035i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 23820.4i | − | 0.918962i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2799.63i | − | 0.105372i | −0.998611 | − | 0.0526861i | \(-0.983222\pi\) | ||
0.998611 | − | 0.0526861i | \(-0.0167783\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −33317.2 | + | 10893.6i | −1.22377 | + | 0.400133i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 47351.4 | 1.69785 | 0.848925 | − | 0.528513i | \(-0.177250\pi\) | ||||
0.848925 | + | 0.528513i | \(0.177250\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14070.8 | −0.492659 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 39386.4 | + | 6159.84i | 1.34696 | + | 0.210658i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 33731.6 | 1.12705 | 0.563526 | − | 0.826098i | \(-0.309444\pi\) | ||||
0.563526 | + | 0.826098i | \(0.309444\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 29852.6 | + | 29747.7i | 0.974778 | + | 0.971353i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −993.489 | + | 12782.1i | −0.0317115 | + | 0.407996i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 33394.2i | 1.04223i | 0.853486 | + | 0.521116i | \(0.174484\pi\) | ||||
−0.853486 | + | 0.521116i | \(0.825516\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −29913.7 | −0.913088 | −0.456544 | − | 0.889701i | \(-0.650913\pi\) | ||||
−0.456544 | + | 0.889701i | \(0.650913\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15587.3 | − | 1211.52i | −0.465445 | − | 0.0361767i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −40542.0 | + | 16834.9i | −1.18457 | + | 0.491888i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18613.3i | 0.532280i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11336.1 | + | 47831.5i | −0.317352 | + | 1.33903i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 68732.1i | − | 1.88405i | −0.335539 | − | 0.942026i | \(-0.608918\pi\) | ||
0.335539 | − | 0.942026i | \(-0.391082\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 68685.9i | 1.84397i | 0.387230 | + | 0.921983i | \(0.373432\pi\) | ||||
−0.387230 | + | 0.921983i | \(0.626568\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −44156.4 | + | 14437.7i | −1.16125 | + | 0.379690i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 41628.9 | 1.07266 | 0.536330 | − | 0.844008i | \(-0.319810\pi\) | ||||
0.536330 | + | 0.844008i | \(0.319810\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8360.65 | −0.211122 | −0.105561 | − | 0.994413i | \(-0.533664\pi\) | ||||
−0.105561 | + | 0.994413i | \(0.533664\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4502.68 | + | 57931.0i | −0.111450 | + | 1.43390i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −61896.9 | −1.50202 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 33460.1 | − | 13894.1i | 0.796196 | − | 0.330616i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 28270.5 | + | 4421.36i | 0.659770 | + | 0.103185i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 76674.4i | − | 1.75533i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −38745.9 | −0.870283 | −0.435142 | − | 0.900362i | \(-0.643302\pi\) | ||||
−0.435142 | + | 0.900362i | \(0.643302\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1699.37 | − | 21863.9i | 0.0374566 | − | 0.481912i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14483.8 | − | 6014.33i | 0.313333 | − | 0.130110i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 42626.8i | 0.905239i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1877.25 | − | 24152.5i | 0.0391412 | − | 0.503585i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 24668.9i | 0.505085i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 839.566i | 0.0168828i | 0.999964 | + | 0.00844141i | \(0.00268702\pi\) | ||||
−0.999964 | + | 0.00844141i | \(0.997313\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −40846.1 | + | 29908.0i | −0.806836 | + | 0.590776i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 41746.0 | 0.810147 | 0.405073 | − | 0.914284i | \(-0.367246\pi\) | ||||
0.405073 | + | 0.914284i | \(0.367246\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 67230.2 | 1.28202 | 0.641008 | − | 0.767534i | \(-0.278516\pi\) | ||||
0.641008 | + | 0.767534i | \(0.278516\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 94260.4 | + | 7326.39i | 1.76647 | + | 0.137299i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 61606.5 | 1.13479 | 0.567394 | − | 0.823446i | \(-0.307952\pi\) | ||||
0.567394 | + | 0.823446i | \(0.307952\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −35488.1 | − | 85463.0i | −0.642609 | − | 1.54754i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −28861.4 | − | 2243.25i | −0.513831 | − | 0.0399375i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17444.5i | 0.305395i | 0.988273 | + | 0.152697i | \(0.0487960\pi\) | ||||
−0.988273 | + | 0.152697i | \(0.951204\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −95187.1 | −1.63887 | −0.819434 | − | 0.573173i | \(-0.805712\pi\) | ||||
−0.819434 | + | 0.573173i | \(0.805712\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −54663.2 | − | 22332.0i | −0.925726 | − | 0.378195i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −20572.8 | − | 49543.8i | −0.342737 | − | 0.825386i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 101619.i | − | 1.66564i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13612.1 | + | 1058.00i | 0.219546 | + | 0.0170642i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 72970.0i | 1.15824i | 0.815244 | + | 0.579118i | \(0.196603\pi\) | ||||
−0.815244 | + | 0.579118i | \(0.803397\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 55034.7i | − | 0.859797i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8354.36 | + | 25551.1i | 0.128479 | + | 0.392942i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −102989. | −1.55928 | −0.779639 | − | 0.626229i | \(-0.784598\pi\) | ||||
−0.779639 | + | 0.626229i | \(0.784598\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 118403. | 1.76507 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11488.8 | − | 73460.3i | 0.168653 | − | 1.07838i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −31029.3 | −0.448602 | −0.224301 | − | 0.974520i | \(-0.572010\pi\) | ||||
−0.224301 | + | 0.974520i | \(0.572010\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 35113.1 | + | 84560.1i | 0.500009 | + | 1.20413i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5207.47 | − | 66998.6i | 0.0730473 | − | 0.939817i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 67187.7i | 0.928507i | 0.885702 | + | 0.464254i | \(0.153677\pi\) | ||||
−0.885702 | + | 0.464254i | \(0.846323\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31478.7 | 0.428626 | 0.214313 | − | 0.976765i | \(-0.431249\pi\) | ||||
0.214313 | + | 0.976765i | \(0.431249\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 124927. | + | 9709.93i | 1.67622 | + | 0.130284i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 68971.4 | + | 68729.1i | 0.912019 | + | 0.908814i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 917.662i | 0.0119598i | 0.999982 | + | 0.00597989i | \(0.00190347\pi\) | ||||
−0.999982 | + | 0.00597989i | \(0.998097\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −50590.3 | − | 7912.06i | −0.649918 | − | 0.101644i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 42100.9i | − | 0.533185i | −0.963809 | − | 0.266593i | \(-0.914102\pi\) | ||
0.963809 | − | 0.266593i | \(-0.0858979\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 32677.1i | − | 0.408010i | −0.978970 | − | 0.204005i | \(-0.934604\pi\) | ||
0.978970 | − | 0.204005i | \(-0.0653959\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −34414.4 | − | 105253.i | −0.423692 | − | 1.29582i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −97720.2 | −1.18637 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −69246.4 | −0.829090 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7473.66 | − | 96155.2i | 0.0882567 | − | 1.13550i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 42688.7 | 0.497254 | 0.248627 | − | 0.968599i | \(-0.420021\pi\) | ||||
0.248627 | + | 0.968599i | \(0.420021\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 32890.0 | − | 13657.4i | 0.377938 | − | 0.156937i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −26191.0 | + | 110510.i | −0.296920 | + | 1.25282i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 72939.5i | − | 0.815869i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −42300.0 | −0.466882 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2370.81 | + | 30502.5i | −0.0258233 | + | 0.332239i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16654.7 | + | 40108.1i | 0.179035 | + | 0.431154i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 153819.i | 1.63205i | 0.578018 | + | 0.816024i | \(0.303827\pi\) | ||||
−0.578018 | + | 0.816024i | \(0.696173\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6193.59 | − | 79685.9i | 0.0648672 | − | 0.834573i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 83923.2i | 0.867684i | 0.900989 | + | 0.433842i | \(0.142842\pi\) | ||||
−0.900989 | + | 0.433842i | \(0.857158\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 53435.9i | 0.545437i | 0.962094 | + | 0.272718i | \(0.0879227\pi\) | ||||
−0.962094 | + | 0.272718i | \(0.912077\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 132683. | − | 32250.5i | 1.33719 | − | 0.325024i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −82643.2 | −0.822410 | −0.411205 | − | 0.911543i | \(-0.634892\pi\) | ||||
−0.411205 | + | 0.911543i | \(0.634892\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −143007. | −1.40532 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 42464.1 | + | 3300.52i | 0.412108 | + | 0.0320311i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −58801.9 | −0.563620 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 91410.3 | + | 91089.1i | 0.865423 | + | 0.862382i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −90971.7 | − | 7070.77i | −0.850767 | − | 0.0661259i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 249594.i | 2.30591i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13288.6 | −0.121289 | −0.0606446 | − | 0.998159i | \(-0.519316\pi\) | ||||
−0.0606446 | + | 0.998159i | \(0.519316\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −21977.0 | + | 140522.i | −0.198189 | + | 1.26724i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 149064. | − | 61898.1i | 1.32826 | − | 0.551553i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 64665.3i | − | 0.569392i | −0.958618 | − | 0.284696i | \(-0.908107\pi\) | ||
0.958618 | − | 0.284696i | \(-0.0918927\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −50201.1 | − | 3901.88i | −0.436831 | − | 0.0339527i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 98485.1i | 0.846957i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17207.1i | − | 0.146258i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −24701.7 | − | 75547.9i | −0.207534 | − | 0.634723i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −115966. | −0.963104 | −0.481552 | − | 0.876418i | \(-0.659927\pi\) | ||||
−0.481552 | + | 0.876418i | \(0.659927\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −98097.2 | −0.805389 | −0.402694 | − | 0.915334i | \(-0.631926\pi\) | ||||
−0.402694 | + | 0.915334i | \(0.631926\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −34711.8 | + | 146463.i | −0.281750 | + | 1.18881i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 188093. | 1.50947 | 0.754735 | − | 0.656030i | \(-0.227766\pi\) | ||||
0.754735 | + | 0.656030i | \(0.227766\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −56258.6 | + | 23361.1i | −0.446408 | + | 0.185369i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5618.64 | − | 72288.7i | 0.0440854 | − | 0.567197i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 84492.4i | − | 0.655585i | −0.944750 | − | 0.327792i | \(-0.893695\pi\) | ||
0.944750 | − | 0.327792i | \(-0.106305\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 111904. | 0.858677 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 86406.6 | + | 6715.96i | 0.655743 | + | 0.0509677i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −62147.5 | + | 25806.4i | −0.466485 | + | 0.193706i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 88794.7i | 0.659257i | 0.944111 | + | 0.329629i | \(0.106924\pi\) | ||||
−0.944111 | + | 0.329629i | \(0.893076\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 18138.1 | − | 115976.i | 0.133210 | − | 0.851757i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 246957.i | − | 1.79421i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 148706.i | − | 1.06883i | −0.845222 | − | 0.534416i | \(-0.820532\pi\) | ||
0.845222 | − | 0.534416i | \(-0.179468\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 125527. | + | 63389.6i | 0.892640 | + | 0.450770i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −189532. | −1.33352 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 204699. | 1.42508 | 0.712538 | − | 0.701634i | \(-0.247546\pi\) | ||||
0.712538 | + | 0.701634i | \(0.247546\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2480.93 | − | 31919.3i | 0.0170909 | − | 0.219889i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17100.8 | −0.116579 | −0.0582893 | − | 0.998300i | \(-0.518565\pi\) | ||||
−0.0582893 | + | 0.998300i | \(0.518565\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −100715. | − | 242545.i | −0.679477 | − | 1.63633i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7851.39 | − | 50202.3i | 0.0524233 | − | 0.335198i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 212163.i | − | 1.40207i | −0.713126 | − | 0.701036i | \(-0.752721\pi\) | ||
0.713126 | − | 0.701036i | \(-0.247279\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −42206.4 | −0.276073 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 22070.5 | − | 283956.i | 0.142898 | − | 1.83851i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 30837.8 | + | 74264.1i | 0.197647 | + | 0.475976i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 99063.8i | − | 0.628542i | −0.949333 | − | 0.314271i | \(-0.898240\pi\) | ||
0.949333 | − | 0.314271i | \(-0.101760\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −23145.1 | + | 297781.i | −0.145383 | + | 1.87047i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11025.4i | 0.0685658i | 0.999412 | + | 0.0342829i | \(0.0109147\pi\) | ||||
−0.999412 | + | 0.0342829i | \(0.989085\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 130526.i | 0.803686i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13647.9 | + | 163456.i | 0.0832065 | + | 0.996532i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 273558. | 1.65143 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 103902. | 0.621122 | 0.310561 | − | 0.950553i | \(-0.399483\pi\) | ||||
0.310561 | + | 0.950553i | \(0.399483\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −172757. | − | 13427.5i | −1.02271 | − | 0.0794901i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −96055.3 | −0.563146 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14544.2 | − | 35025.7i | −0.0844491 | − | 0.203372i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −90843.5 | − | 7060.81i | −0.522422 | − | 0.0406053i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 116135.i | 0.661509i | 0.943717 | + | 0.330755i | \(0.107303\pi\) | ||||
−0.943717 | + | 0.330755i | \(0.892697\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 288576. | 1.62816 | 0.814078 | − | 0.580756i | \(-0.197243\pi\) | ||||
0.814078 | + | 0.580756i | \(0.197243\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −296223. | − | 46327.8i | −1.65553 | − | 0.258917i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 52708.6 | − | 52894.5i | 0.291812 | − | 0.292841i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 117136.i | − | 0.642441i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 288631. | + | 22433.8i | 1.56830 | + | 0.121896i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 42439.1i | − | 0.228461i | −0.993454 | − | 0.114230i | \(-0.963560\pi\) | ||
0.993454 | − | 0.114230i | \(-0.0364402\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 95739.7i | 0.510642i | 0.966856 | + | 0.255321i | \(0.0821811\pi\) | ||||
−0.966856 | + | 0.255321i | \(0.917819\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −196310. | + | 64186.9i | −1.03744 | + | 0.339209i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 173862. | 0.910420 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 45614.7 | 0.236688 | 0.118344 | − | 0.992973i | \(-0.462241\pi\) | ||||
0.118344 | + | 0.992973i | \(0.462241\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −171724. | − | 26856.7i | −0.882984 | − | 0.138094i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30310.8 | 0.154451 | 0.0772253 | − | 0.997014i | \(-0.475394\pi\) | ||||
0.0772253 | + | 0.997014i | \(0.475394\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −172396. | + | 71586.7i | −0.870579 | + | 0.361503i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17914.2 | + | 230482.i | −0.0896567 | + | 1.15351i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 133743.i | − | 0.663406i | −0.943384 | − | 0.331703i | \(-0.892377\pi\) | ||
0.943384 | − | 0.331703i | \(-0.107623\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −225773. | −1.10999 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 175136. | + | 13612.4i | 0.853450 | + | 0.0663344i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −133482. | − | 321453.i | −0.644762 | − | 1.55273i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 95910.3i | − | 0.459233i | −0.973281 | − | 0.229616i | \(-0.926253\pi\) | ||
0.973281 | − | 0.229616i | \(-0.0737472\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 84750.6 | + | 20086.0i | 0.402270 | + | 0.0953383i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19465.2i | 0.0915920i | 0.998951 | + | 0.0457960i | \(0.0145824\pi\) | ||||
−0.998951 | + | 0.0457960i | \(0.985418\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 152228.i | 0.710120i | 0.934843 | + | 0.355060i | \(0.115540\pi\) | ||||
−0.934843 | + | 0.355060i | \(0.884460\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 44203.9 | + | 135194.i | 0.204435 | + | 0.625245i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 225192. | 1.03257 | 0.516284 | − | 0.856418i | \(-0.327315\pi\) | ||||
0.516284 | + | 0.856418i | \(0.327315\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −435341. | −1.97917 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21563.4 | + | 277432.i | −0.0972021 | + | 1.25059i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −97729.9 | −0.436823 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −217124. | + | 217890.i | −0.962324 | + | 0.965717i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 293093. | + | 45838.3i | 1.28816 | + | 0.201461i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 419939.i | − | 1.83027i | −0.403148 | − | 0.915135i | \(-0.632084\pi\) | ||
0.403148 | − | 0.915135i | \(-0.367916\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 362556. | 1.56706 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −16612.9 | + | 213739.i | −0.0712116 | + | 0.916199i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −247420. | + | 102740.i | −1.05184 | + | 0.436773i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 45776.8i | 0.193013i | 0.995332 | + | 0.0965067i | \(0.0307669\pi\) | ||||
−0.995332 | + | 0.0965067i | \(0.969233\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1952.53 | + | 25120.9i | −0.00816543 | + | 0.105055i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 142734.i | 0.592057i | 0.955179 | + | 0.296028i | \(0.0956623\pi\) | ||||
−0.955179 | + | 0.296028i | \(0.904338\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 109672.i | 0.451236i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 306550. | − | 74511.6i | 1.25110 | − | 0.304098i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 164303. | 0.665171 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 79974.9 | 0.321183 | 0.160592 | − | 0.987021i | \(-0.448660\pi\) | ||||
0.160592 | + | 0.987021i | \(0.448660\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −424881. | − | 33023.9i | −1.69275 | − | 0.131569i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 140135. | 0.553872 | 0.276936 | − | 0.960888i | \(-0.410681\pi\) | ||||
0.276936 | + | 0.960888i | \(0.410681\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 78487.0 | − | 32591.3i | 0.307762 | − | 0.127797i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 126257. | + | 9813.31i | 0.491178 | + | 0.0381768i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 369825.i | 1.42745i | 0.700427 | + | 0.713724i | \(0.252993\pi\) | ||||
−0.700427 | + | 0.713724i | \(0.747007\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 181502. | 0.695086 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −349116. | − | 82740.8i | −1.32659 | − | 0.314402i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −205042. | + | 85142.8i | −0.773088 | + | 0.321021i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 576663.i | 2.15745i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −302671. | − | 23525.1i | −1.12366 | − | 0.0873368i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 60637.1i | − | 0.223390i | −0.993743 | − | 0.111695i | \(-0.964372\pi\) | ||
0.993743 | − | 0.111695i | \(-0.0356279\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 296749.i | − | 1.08489i | −0.840091 | − | 0.542445i | \(-0.817499\pi\) | ||
0.840091 | − | 0.542445i | \(-0.182501\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −247119. | − | 287744.i | −0.896575 | − | 1.04397i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 75528.6 | 0.271951 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −155048. | −0.554056 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17829.0 | − | 114000.i | 0.0632322 | − | 0.404312i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −299225. | −1.05328 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −45372.0 | − | 109266.i | −0.158519 | − | 0.381747i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 23289.8 | − | 299644.i | 0.0807639 | − | 1.03910i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 334298.i | 1.15068i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 239602. | 0.818645 | 0.409323 | − | 0.912390i | \(-0.365765\pi\) | ||||
0.409323 | + | 0.912390i | \(0.365765\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 268414. | + | 20862.4i | 0.910342 | + | 0.0707564i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 97201.4 | + | 234082.i | 0.327250 | + | 0.788089i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 388724.i | − | 1.29917i | −0.760288 | − | 0.649586i | \(-0.774942\pi\) | ||
0.760288 | − | 0.649586i | \(-0.225058\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 139019. | + | 21741.8i | 0.461242 | + | 0.0721358i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 451777.i | − | 1.48806i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 216888.i | − | 0.709228i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 375522. | − | 122783.i | 1.21913 | − | 0.398614i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 568369. | 1.83198 | 0.915988 | − | 0.401206i | \(-0.131409\pi\) | ||||
0.915988 | + | 0.401206i | \(0.131409\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −129525. | −0.414505 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12981.3 | − | 167016.i | 0.0412471 | − | 0.530679i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −195184. | −0.615782 | −0.307891 | − | 0.951422i | \(-0.599623\pi\) | ||||
−0.307891 | + | 0.951422i | \(0.599623\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 53638.8 | + | 129174.i | 0.168028 | + | 0.404649i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 135077. | − | 421283.i | 0.420161 | − | 1.31041i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 159125.i | 0.491490i | 0.969334 | + | 0.245745i | \(0.0790327\pi\) | ||||
−0.969334 | + | 0.245745i | \(0.920967\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 482080. | 1.47859 | 0.739294 | − | 0.673383i | \(-0.235160\pi\) | ||||
0.739294 | + | 0.673383i | \(0.235160\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −47935.3 | + | 616729.i | −0.145998 | + | 1.87839i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −155846. | + | 156395.i | −0.471367 | + | 0.473029i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 319133.i | − | 0.958560i | −0.877662 | − | 0.479280i | \(-0.840898\pi\) | ||
0.877662 | − | 0.479280i | \(-0.159102\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 47903.0 | − | 616314.i | 0.142891 | − | 1.83842i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 102293.i | 0.303034i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 570571.i | − | 1.67870i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 406282. | − | 98752.9i | 1.18718 | − | 0.288561i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −357229. | −1.03674 | −0.518371 | − | 0.855156i | \(-0.673461\pi\) | ||||
−0.518371 | + | 0.855156i | \(0.673461\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −311128. | −0.896825 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −373533. | − | 29032.9i | −1.06944 | − | 0.0831219i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −306233. | −0.870848 | −0.435424 | − | 0.900226i | \(-0.643402\pi\) | ||||
−0.435424 | + | 0.900226i | \(0.643402\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −186008. | + | 77239.1i | −0.525411 | + | 0.218174i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 75019.6 | + | 5830.90i | 0.210487 | + | 0.0163601i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 27985.3i | − | 0.0779967i | −0.999239 | − | 0.0389984i | \(-0.987583\pi\) | ||
0.999239 | − | 0.0389984i | \(-0.0124167\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −200646. | −0.555497 | −0.277748 | − | 0.960654i | \(-0.589588\pi\) | ||||
−0.277748 | + | 0.960654i | \(0.589588\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 80804.6 | − | 516671.i | 0.222229 | − | 1.42095i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −92323.8 | − | 222336.i | −0.252234 | − | 0.607433i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 104545.i | 0.283742i | 0.989885 | + | 0.141871i | \(0.0453119\pi\) | ||||
−0.989885 | + | 0.141871i | \(0.954688\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 555397. | + | 43168.2i | 1.49751 | + | 0.116394i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 764273.i | 2.04723i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 263612.i | 0.701526i | 0.936464 | + | 0.350763i | \(0.114078\pi\) | ||||
−0.936464 | + | 0.350763i | \(0.885922\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −309926. | + | 101335.i | −0.819421 | + | 0.267924i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −343423. | −0.902110 | −0.451055 | − | 0.892496i | \(-0.648952\pi\) | ||||
−0.451055 | + | 0.892496i | \(0.648952\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 269937. | 0.704501 | 0.352250 | − | 0.935906i | \(-0.385417\pi\) | ||||
0.352250 | + | 0.935906i | \(0.385417\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −250586. | − | 59389.0i | −0.649790 | − | 0.154001i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 503483. | 1.29721 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1375.00 | − | 390623.i | −0.00352000 | − | 0.999994i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −53474.4 | + | 687994.i | −0.136022 | + | 1.75005i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 209793.i | − | 0.530260i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 543880. | 1.36598 | 0.682990 | − | 0.730428i | \(-0.260679\pi\) | ||||
0.682990 | + | 0.730428i | \(0.260679\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 347664. | + | 27022.2i | 0.867666 | + | 0.0674394i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −82132.6 | + | 34105.1i | −0.203689 | + | 0.0845809i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 443057.i | 1.09189i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −30496.7 | + | 194998.i | −0.0746880 | + | 0.477560i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 647339.i | 1.57549i | 0.616001 | + | 0.787745i | \(0.288752\pi\) | ||||
−0.616001 | + | 0.787745i | \(0.711248\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 647221.i | 1.56542i | 0.622387 | + | 0.782710i | \(0.286163\pi\) | ||||
−0.622387 | + | 0.782710i | \(0.713837\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −134157. | + | 43864.9i | −0.322473 | + | 0.105438i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −334797. | −0.799784 | −0.399892 | − | 0.916562i | \(-0.630952\pi\) | ||||
−0.399892 | + | 0.916562i | \(0.630952\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −221926. | −0.526889 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 29728.9 | − | 382488.i | 0.0701482 | − | 0.902517i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 45027.6 | 0.105597 | 0.0527986 | − | 0.998605i | \(-0.483186\pi\) | ||||
0.0527986 | + | 0.998605i | \(0.483186\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −730657. | + | 303402.i | −1.70306 | + | 0.707189i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −33688.9 | + | 215409.i | −0.0780470 | + | 0.499038i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 428579.i | 0.986870i | 0.869783 | + | 0.493435i | \(0.164259\pi\) | ||||
−0.869783 | + | 0.493435i | \(0.835741\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −570406. | −1.30551 | −0.652757 | − | 0.757568i | \(-0.726388\pi\) | ||||
−0.652757 | + | 0.757568i | \(0.726388\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 17204.6 | − | 221352.i | 0.0391397 | − | 0.503566i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 766231. | − | 318174.i | 1.73267 | − | 0.719483i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 324273.i | − | 0.728885i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 585.532 | − | 7533.37i | 0.00130827 | − | 0.0168321i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 270630.i | − | 0.601079i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 196875.i | 0.434670i | 0.976097 | + | 0.217335i | \(0.0697364\pi\) | ||||
−0.976097 | + | 0.217335i | \(0.930264\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 387368. | − | 239876.i | 0.850190 | − | 0.526477i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −74588.7 | −0.162741 | −0.0813703 | − | 0.996684i | \(-0.525930\pi\) | ||||
−0.0813703 | + | 0.996684i | \(0.525930\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 722590. | 1.56730 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −374585. | − | 29114.6i | −0.807711 | − | 0.0627793i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 331599. | 0.710839 | 0.355420 | − | 0.934707i | \(-0.384338\pi\) | ||||
0.355420 | + | 0.934707i | \(0.384338\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 184587. | + | 444527.i | 0.393388 | + | 0.947364i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −603253. | − | 46887.8i | −1.27816 | − | 0.0993452i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 756198.i | − | 1.59293i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −321604. | −0.673544 | −0.336772 | − | 0.941586i | \(-0.609335\pi\) | ||||
−0.336772 | + | 0.941586i | \(0.609335\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −840683. | − | 131479.i | −1.75052 | − | 0.273772i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 97064.5 | + | 233752.i | 0.200951 | + | 0.483934i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 173146.i | 0.356408i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −552791. | − | 42965.7i | −1.13138 | − | 0.0879362i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 918547.i | − | 1.86924i | −0.355647 | − | 0.934620i | \(-0.615739\pi\) | ||
0.355647 | − | 0.934620i | \(-0.384261\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 864206.i | 1.74867i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 258829. | + | 791604.i | 0.520756 | + | 1.59269i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −229221. | −0.458581 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 456638. | 0.908405 | 0.454202 | − | 0.890899i | \(-0.349924\pi\) | ||||
0.454202 | + | 0.890899i | \(0.349924\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 257407. | + | 40257.1i | 0.509191 | + | 0.0796348i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −223319. | −0.439285 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −308396. | − | 742686.i | −0.603250 | − | 1.45276i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12166.1 | − | 156528.i | 0.0236654 | − | 0.304476i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 167509.i | 0.324027i | 0.986789 | + | 0.162014i | \(0.0517989\pi\) | ||||
−0.986789 | + | 0.162014i | \(0.948201\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 598826. | 1.15194 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 854108. | + | 66385.6i | 1.63394 | + | 0.126998i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 406390. | + | 404962.i | 0.773156 | + | 0.770439i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 38860.6i | − | 0.0735259i | −0.999324 | − | 0.0367629i | \(-0.988295\pi\) | ||
0.999324 | − | 0.0367629i | \(-0.0117046\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 474915. | + | 238507.i | 0.893636 | + | 0.448793i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 74949.4i | 0.140260i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 740222.i | − | 1.37770i | −0.724905 | − | 0.688849i | \(-0.758116\pi\) | ||
0.724905 | − | 0.688849i | \(-0.241884\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 150046. | + | 458901.i | 0.277747 | + | 0.849463i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.00581e6 | −1.85175 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −705765. | −1.29232 | −0.646162 | − | 0.763201i | \(-0.723627\pi\) | ||||
−0.646162 | + | 0.763201i | \(0.723627\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −70871.5 | + | 911824.i | −0.129073 | + | 1.66064i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 504628. | 0.914100 | 0.457050 | − | 0.889441i | \(-0.348906\pi\) | ||||
0.457050 | + | 0.889441i | \(0.348906\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 593061. | − | 246265.i | 1.06853 | − | 0.443702i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −121403. | − | 18986.7i | −0.217564 | − | 0.0340259i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 319110.i | 0.568823i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −413475. | −0.733111 | −0.366555 | − | 0.930396i | \(-0.619463\pi\) | ||||
−0.366555 | + | 0.930396i | \(0.619463\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 50890.9 | − | 654756.i | 0.0897532 | − | 1.15475i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −187129. | − | 450647.i | −0.328282 | − | 0.790575i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 803866.i | − | 1.40279i | −0.712774 | − | 0.701394i | \(-0.752561\pi\) | ||
0.712774 | − | 0.701394i | \(-0.247439\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −38382.4 | + | 493823.i | −0.0666268 | + | 0.857211i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 582961.i | − | 1.00663i | −0.864103 | − | 0.503315i | \(-0.832113\pi\) | ||
0.864103 | − | 0.503315i | \(-0.167887\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 683636.i | − | 1.17429i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −57143.3 | − | 235095.i | −0.0976432 | − | 0.401717i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −294127. | −0.499970 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −655679. | −1.10876 | −0.554381 | − | 0.832263i | \(-0.687045\pi\) | ||||
−0.554381 | + | 0.832263i | \(0.687045\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 924112. | + | 71826.6i | 1.55459 | + | 0.120831i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 102465. | 0.171481 | 0.0857404 | − | 0.996318i | \(-0.472674\pi\) | ||||
0.0857404 | + | 0.996318i | \(0.472674\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 278887. | − | 279871.i | 0.464328 | − | 0.465966i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.06242e6 | − | 82576.7i | −1.75976 | − | 0.136778i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 713247.i | − | 1.17534i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 379606. | 0.622345 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −154321. | + | 651142.i | −0.251711 | + | 1.06207i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 713869. | − | 296431.i | 1.15846 | − | 0.481043i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.01738e6i | 1.64261i | 0.570488 | + | 0.821306i | \(0.306754\pi\) | ||||
−0.570488 | + | 0.821306i | \(0.693246\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 278424. | + | 21640.5i | 0.447253 | + | 0.0347627i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 377252.i | − | 0.602947i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 358676.i | − | 0.570369i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −256094. | − | 783241.i | −0.405196 | − | 1.23926i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 952098. | 1.49887 | 0.749437 | − | 0.662076i | \(-0.230324\pi\) | ||||
0.749437 | + | 0.662076i | \(0.230324\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 442246. | 0.692739 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −93452.6 | + | 597543.i | −0.145655 | + | 0.931331i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 419341. | 0.650334 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 549979. | − | 228376.i | 0.848701 | − | 0.352419i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 46858.2 | − | 602871.i | 0.0719512 | − | 0.925715i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 273009.i | − | 0.417138i | −0.978008 | − | 0.208569i | \(-0.933119\pi\) | ||
0.978008 | − | 0.208569i | \(-0.0668806\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −164169. | −0.249603 | −0.124801 | − | 0.992182i | \(-0.539829\pi\) | ||||
−0.124801 | + | 0.992182i | \(0.539829\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −282456. | − | 21953.9i | −0.427337 | − | 0.0332148i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 64639.5 | − | 26841.2i | 0.0973157 | − | 0.0404099i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 308742.i | − | 0.462542i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.11419e6 | − | 174253.i | −1.66108 | − | 0.259784i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 306236.i | 0.454329i | 0.973856 | + | 0.227165i | \(0.0729455\pi\) | ||||
−0.973856 | + | 0.227165i | \(0.927054\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 514884.i | − | 0.760169i | −0.924952 | − | 0.380084i | \(-0.875895\pi\) | ||
0.924952 | − | 0.380084i | \(-0.124105\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −570943. | − | 664804.i | −0.838851 | − | 0.976755i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −732893. | −1.07159 | −0.535796 | − | 0.844347i | \(-0.679988\pi\) | ||||
−0.535796 | + | 0.844347i | \(0.679988\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −739391. | −1.07588 | −0.537942 | − | 0.842982i | \(-0.680798\pi\) | ||||
−0.537942 | + | 0.842982i | \(0.680798\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 639.997 | − | 8234.12i | 0.000926779 | − | 0.0119238i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 256374. | 0.369475 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 453977. | + | 1.09327e6i | 0.651119 | + | 1.56804i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 448425. | + | 106277.i | 0.640087 | + | 0.151701i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 360957.i | 0.512780i | 0.966573 | + | 0.256390i | \(0.0825331\pi\) | ||||
−0.966573 | + | 0.256390i | \(0.917467\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −135336. | −0.191348 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −29362.1 | + | 377768.i | −0.0413172 | + | 0.531582i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −134903. | − | 324875.i | −0.188933 | − | 0.454992i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 649331.i | 0.905106i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22789.7 | + | 293210.i | −0.0316173 | + | 0.406783i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 620303.i | 0.856534i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.10949e6i | 1.52484i | 0.647083 | + | 0.762419i | \(0.275989\pi\) | ||||
−0.647083 | + | 0.762419i | \(0.724011\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 235392. | + | 968433.i | 0.322003 | + | 1.32476i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3132.46 | −0.00426505 | −0.00213253 | − | 0.999998i | \(-0.500679\pi\) | ||||
−0.00213253 | + | 0.999998i | \(0.500679\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 696854. | 0.944399 | 0.472200 | − | 0.881492i | \(-0.343460\pi\) | ||||
0.472200 | + | 0.881492i | \(0.343460\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 876837. | + | 68152.2i | 1.18280 | + | 0.0919334i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −248786. | −0.334045 | −0.167022 | − | 0.985953i | \(-0.553415\pi\) | ||||
−0.167022 | + | 0.985953i | \(0.553415\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 323398. | + | 778813.i | 0.432221 | + | 1.04088i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 621343. | + | 48293.9i | 0.826596 | + | 0.0642472i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 501099.i | − | 0.663565i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.33304e6 | −1.75714 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −134121. | + | 857582.i | −0.175983 | + | 1.12525i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −400622. | + | 974456.i | −0.523262 | + | 1.27276i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 579821.i | − | 0.753867i | −0.926240 | − | 0.376933i | \(-0.876979\pi\) | ||
0.926240 | − | 0.376933i | \(-0.123021\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −383043. | − | 29772.1i | −0.495759 | − | 0.0385328i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 597254.i | − | 0.769498i | −0.923021 | − | 0.384749i | \(-0.874288\pi\) | ||
0.923021 | − | 0.384749i | \(-0.125712\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52207.6i | 0.0669595i | 0.999439 | + | 0.0334797i | \(0.0106589\pi\) | ||||
−0.999439 | + | 0.0334797i | \(0.989341\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −304645. | + | 99609.0i | −0.388963 | + | 0.127178i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 69800.2 | 0.0887176 | 0.0443588 | − | 0.999016i | \(-0.485876\pi\) | ||||
0.0443588 | + | 0.999016i | \(0.485876\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 239868. | 0.303507 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 312082. | − | 973334.i | 0.393109 | − | 1.22604i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.82176e6 | −2.28448 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −771023. | + | 320163.i | −0.962546 | + | 0.399692i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −50869.6 | + | 654481.i | −0.0632227 | + | 0.813416i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 580289.i | 0.718001i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −437573. | −0.539015 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 379555. | + | 29500.9i | 0.465478 | + | 0.0361793i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −286795. | − | 690664.i | −0.350166 | − | 0.843275i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 262086.i | 0.318588i | 0.987231 | + | 0.159294i | \(0.0509218\pi\) | ||||
−0.987231 | + | 0.159294i | \(0.949078\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 42546.2 | − | 272044.i | 0.0514912 | − | 0.329239i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 640805.i | 0.772128i | 0.922472 | + | 0.386064i | \(0.126166\pi\) | ||||
−0.922472 | + | 0.386064i | \(0.873834\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 236337.i | 0.283524i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −121469. | − | 371503.i | −0.145086 | − | 0.443731i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.13388e6 | 2.53765 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 868444. | 1.02828 | 0.514139 | − | 0.857707i | \(-0.328112\pi\) | ||||
0.514139 | + | 0.857707i | \(0.328112\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 107277. | − | 1.38021e6i | 0.126470 | − | 1.62714i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 503106. | 0.590549 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −777385. | − | 774653.i | −0.908558 | − | 0.905366i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −111149. | + | 710697.i | −0.129344 | + | 0.827037i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.52215e6i | 1.76370i | 0.471527 | + | 0.881852i | \(0.343703\pi\) | ||||
−0.471527 | + | 0.881852i | \(0.656297\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.05609e6 | −1.21843 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 58529.9 | − | 753038.i | 0.0672379 | − | 0.865075i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −429754. | + | 178453.i | −0.491583 | + | 0.204127i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 714034.i | 0.813279i | 0.913589 | + | 0.406640i | \(0.133300\pi\) | ||||
−0.913589 | + | 0.406640i | \(0.866700\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 37267.3 | − | 479477.i | 0.0422666 | − | 0.543796i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 153242.i | − | 0.173061i | −0.996249 | − | 0.0865306i | \(-0.972422\pi\) | ||
0.996249 | − | 0.0865306i | \(-0.0275780\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 511949.i | − | 0.575709i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.21305e6 | + | 196846.i | −1.35836 | + | 0.220426i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 329584. | 0.367507 | 0.183754 | − | 0.982972i | \(-0.441175\pi\) | ||||
0.183754 | + | 0.982972i | \(0.441175\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 555768. | 0.617108 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 741552. | + | 57637.1i | 0.819937 | + | 0.0637296i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.25777e6 | 1.38489 | 0.692445 | − | 0.721470i | \(-0.256533\pi\) | ||||
0.692445 | + | 0.721470i | \(0.256533\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.58693e6 | − | 658963.i | 1.74000 | − | 0.722527i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.28319e6 | + | 99736.0i | 1.40109 | + | 0.108900i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1.29824e6i | − | 1.41162i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −523891. | −0.567275 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −378725. | − | 59230.7i | −0.408387 | − | 0.0638696i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.58586e6 | + | 658520.i | −1.70298 | + | 0.707154i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 947106.i | − | 1.01285i | −0.862284 | − | 0.506426i | \(-0.830966\pi\) | ||
0.862284 | − | 0.506426i | \(-0.169034\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 527626. | + | 41009.7i | 0.561925 | + | 0.0436756i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 910287.i | 0.965472i | 0.875766 | + | 0.482736i | \(0.160357\pi\) | ||||
−0.875766 | + | 0.482736i | \(0.839643\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 682673.i | − | 0.721086i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −756691. | − | 881088.i | −0.795993 | − | 0.926851i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −989219. | −1.03634 | −0.518171 | − | 0.855277i | \(-0.673387\pi\) | ||||
−0.518171 | + | 0.855277i | \(0.673387\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.16325e6 | 1.21369 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 811352. | + | 126891.i | 0.843085 | + | 0.131854i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.06218e6 | −1.09923 | −0.549616 | − | 0.835417i | \(-0.685226\pi\) | ||||
−0.549616 | + | 0.835417i | \(0.685226\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 399113. | + | 961151.i | 0.411361 | + | 0.990648i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 174073. | − | 2.23960e6i | 0.178688 | − | 2.29898i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 221606.i | − | 0.226563i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −332884. | −0.338957 | −0.169479 | − | 0.985534i | \(-0.554208\pi\) | ||||
−0.169479 | + | 0.985534i | \(0.554208\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 119238. | + | 9267.74i | 0.120925 | + | 0.00939886i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −80157.0 | − | 193035.i | −0.0809646 | − | 0.194980i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1.10583e6i | − | 1.11249i | −0.831018 | − | 0.556245i | \(-0.812242\pi\) | ||
0.831018 | − | 0.556245i | \(-0.187758\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 295202. | − | 1.24557e6i | 0.295793 | − | 1.24807i |
(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 | 60.5.b.a.29.1 | ✓ | 8 | |
3.2 | odd | 2 | inner | 60.5.b.a.29.7 | yes | 8 | |
4.3 | odd | 2 | 240.5.c.e.209.8 | 8 | |||
5.2 | odd | 4 | 300.5.g.h.101.4 | 8 | |||
5.3 | odd | 4 | 300.5.g.h.101.5 | 8 | |||
5.4 | even | 2 | inner | 60.5.b.a.29.8 | yes | 8 | |
12.11 | even | 2 | 240.5.c.e.209.2 | 8 | |||
15.2 | even | 4 | 300.5.g.h.101.3 | 8 | |||
15.8 | even | 4 | 300.5.g.h.101.6 | 8 | |||
15.14 | odd | 2 | inner | 60.5.b.a.29.2 | yes | 8 | |
20.19 | odd | 2 | 240.5.c.e.209.1 | 8 | |||
60.59 | even | 2 | 240.5.c.e.209.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.5.b.a.29.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
60.5.b.a.29.2 | yes | 8 | 15.14 | odd | 2 | inner | |
60.5.b.a.29.7 | yes | 8 | 3.2 | odd | 2 | inner | |
60.5.b.a.29.8 | yes | 8 | 5.4 | even | 2 | inner | |
240.5.c.e.209.1 | 8 | 20.19 | odd | 2 | |||
240.5.c.e.209.2 | 8 | 12.11 | even | 2 | |||
240.5.c.e.209.7 | 8 | 60.59 | even | 2 | |||
240.5.c.e.209.8 | 8 | 4.3 | odd | 2 | |||
300.5.g.h.101.3 | 8 | 15.2 | even | 4 | |||
300.5.g.h.101.4 | 8 | 5.2 | odd | 4 | |||
300.5.g.h.101.5 | 8 | 5.3 | odd | 4 | |||
300.5.g.h.101.6 | 8 | 15.8 | even | 4 |