Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,3,Mod(145,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.145");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.be (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: | \(24.8502001097\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 228) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.145 |
Dual form | 912.3.be.a.673.1 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.50000 | + | 0.866025i | −0.500000 | + | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.00000 | − | 5.19615i | −0.600000 | − | 1.03923i | −0.992820 | − | 0.119615i | \(-0.961834\pi\) |
0.392820 | − | 0.919615i | \(-0.371499\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.00000 | 0.714286 | 0.357143 | − | 0.934050i | \(-0.383751\pi\) | ||||
0.357143 | + | 0.934050i | \(0.383751\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −16.5000 | − | 9.52628i | −1.26923 | − | 0.732791i | −0.294388 | − | 0.955686i | \(-0.595116\pi\) |
−0.974842 | + | 0.222895i | \(0.928449\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.00000 | + | 5.19615i | 0.600000 | + | 0.346410i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.00000 | − | 5.19615i | −0.176471 | − | 0.305656i | 0.764199 | − | 0.644981i | \(-0.223135\pi\) |
−0.940669 | + | 0.339325i | \(0.889801\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 13.0000 | − | 13.8564i | 0.684211 | − | 0.729285i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.50000 | + | 4.33013i | −0.357143 | + | 0.206197i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −12.0000 | + | 20.7846i | −0.521739 | + | 0.903679i | 0.477941 | + | 0.878392i | \(0.341383\pi\) |
−0.999680 | + | 0.0252868i | \(0.991950\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.50000 | + | 9.52628i | −0.220000 | + | 0.381051i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 27.0000 | + | 15.5885i | 0.931034 | + | 0.537533i | 0.887139 | − | 0.461503i | \(-0.152690\pi\) |
0.0438959 | + | 0.999036i | \(0.486023\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 29.4449i | 0.949834i | 0.880031 | + | 0.474917i | \(0.157522\pi\) | ||||
−0.880031 | + | 0.474917i | \(0.842478\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −15.0000 | − | 25.9808i | −0.428571 | − | 0.742307i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 60.6218i | − | 1.63843i | −0.573489 | − | 0.819213i | \(-0.694410\pi\) | ||
0.573489 | − | 0.819213i | \(-0.305590\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 33.0000 | 0.846154 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −36.0000 | + | 20.7846i | −0.878049 | + | 0.506942i | −0.870015 | − | 0.493026i | \(-0.835891\pi\) |
−0.00803422 | + | 0.999968i | \(0.502557\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.5000 | − | 21.6506i | −0.290698 | − | 0.503503i | 0.683277 | − | 0.730159i | \(-0.260554\pi\) |
−0.973975 | + | 0.226656i | \(0.927221\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −18.0000 | −0.400000 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −21.0000 | + | 36.3731i | −0.446809 | + | 0.773895i | −0.998176 | − | 0.0603673i | \(-0.980773\pi\) |
0.551368 | + | 0.834262i | \(0.314106\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −24.0000 | −0.489796 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.00000 | + | 5.19615i | 0.176471 | + | 0.101885i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 54.0000 | + | 31.1769i | 1.01887 | + | 0.588244i | 0.913776 | − | 0.406219i | \(-0.133153\pi\) |
0.105092 | + | 0.994462i | \(0.466486\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.50000 | + | 32.0429i | −0.131579 | + | 0.562157i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −63.0000 | + | 36.3731i | −1.06780 | + | 0.616493i | −0.927579 | − | 0.373628i | \(-0.878114\pi\) |
−0.140218 | + | 0.990121i | \(0.544780\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −21.5000 | + | 37.2391i | −0.352459 | + | 0.610477i | −0.986680 | − | 0.162675i | \(-0.947988\pi\) |
0.634221 | + | 0.773152i | \(0.281321\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.50000 | − | 12.9904i | 0.119048 | − | 0.206197i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 114.315i | 1.75870i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −49.5000 | − | 28.5788i | −0.738806 | − | 0.426550i | 0.0828290 | − | 0.996564i | \(-0.473604\pi\) |
−0.821635 | + | 0.570014i | \(0.806938\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 41.5692i | − | 0.602452i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −54.0000 | + | 31.1769i | −0.760563 | + | 0.439111i | −0.829498 | − | 0.558510i | \(-0.811373\pi\) |
0.0689346 | + | 0.997621i | \(0.478040\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.50000 | − | 9.52628i | −0.0753425 | − | 0.130497i | 0.825893 | − | 0.563827i | \(-0.190672\pi\) |
−0.901235 | + | 0.433330i | \(0.857338\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 19.0526i | − | 0.254034i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.50000 | + | 0.866025i | −0.0189873 | + | 0.0109623i | −0.509464 | − | 0.860492i | \(-0.670156\pi\) |
0.490476 | + | 0.871455i | \(0.336823\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −126.000 | −1.51807 | −0.759036 | − | 0.651048i | \(-0.774329\pi\) | ||||
−0.759036 | + | 0.651048i | \(0.774329\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −18.0000 | + | 31.1769i | −0.211765 | + | 0.366787i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −54.0000 | −0.620690 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.00000 | − | 5.19615i | −0.101124 | − | 0.0583837i | 0.448585 | − | 0.893740i | \(-0.351928\pi\) |
−0.549709 | + | 0.835356i | \(0.685261\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −82.5000 | − | 47.6314i | −0.906593 | − | 0.523422i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −25.5000 | − | 44.1673i | −0.274194 | − | 0.474917i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −111.000 | − | 25.9808i | −1.16842 | − | 0.273482i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −114.000 | + | 65.8179i | −1.17526 | + | 0.678535i | −0.954913 | − | 0.296887i | \(-0.904052\pi\) |
−0.220345 | + | 0.975422i | \(0.570718\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −78.0000 | + | 135.100i | −0.772277 | + | 1.33762i | 0.164035 | + | 0.986455i | \(0.447549\pi\) |
−0.936312 | + | 0.351169i | \(0.885784\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 36.3731i | − | 0.353137i | −0.984288 | − | 0.176568i | \(-0.943500\pi\) | ||
0.984288 | − | 0.176568i | \(-0.0564996\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 45.0000 | + | 25.9808i | 0.428571 | + | 0.247436i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 90.0000 | − | 51.9615i | 0.825688 | − | 0.476711i | −0.0266859 | − | 0.999644i | \(-0.508495\pi\) |
0.852374 | + | 0.522933i | \(0.175162\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 52.5000 | + | 90.9327i | 0.472973 | + | 0.819213i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 155.885i | − | 1.37951i | −0.724043 | − | 0.689755i | \(-0.757718\pi\) | ||
0.724043 | − | 0.689755i | \(-0.242282\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 144.000 | 1.25217 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −49.5000 | + | 28.5788i | −0.423077 | + | 0.244264i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −15.0000 | − | 25.9808i | −0.126050 | − | 0.218326i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −121.000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 36.0000 | − | 62.3538i | 0.292683 | − | 0.506942i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −84.0000 | −0.672000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 36.0000 | + | 20.7846i | 0.283465 | + | 0.163658i | 0.634991 | − | 0.772520i | \(-0.281004\pi\) |
−0.351526 | + | 0.936178i | \(0.614337\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 37.5000 | + | 21.6506i | 0.290698 | + | 0.167834i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 24.0000 | + | 41.5692i | 0.183206 | + | 0.317322i | 0.942971 | − | 0.332876i | \(-0.108019\pi\) |
−0.759764 | + | 0.650198i | \(0.774686\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 65.0000 | − | 69.2820i | 0.488722 | − | 0.520918i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 27.0000 | − | 15.5885i | 0.200000 | − | 0.115470i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 66.0000 | − | 114.315i | 0.481752 | − | 0.834419i | −0.518029 | − | 0.855363i | \(-0.673334\pi\) |
0.999781 | + | 0.0209445i | \(0.00666734\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.500000 | − | 0.866025i | 0.00359712 | − | 0.00623040i | −0.864221 | − | 0.503112i | \(-0.832188\pi\) |
0.867818 | + | 0.496882i | \(0.165522\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 72.7461i | − | 0.515930i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 187.061i | − | 1.29008i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 36.0000 | − | 20.7846i | 0.244898 | − | 0.141392i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −90.0000 | − | 155.885i | −0.604027 | − | 1.04621i | −0.992204 | − | 0.124621i | \(-0.960229\pi\) |
0.388178 | − | 0.921585i | \(-0.373105\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 235.559i | 1.55999i | 0.625784 | + | 0.779996i | \(0.284779\pi\) | ||||
−0.625784 | + | 0.779996i | \(0.715221\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −18.0000 | −0.117647 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 153.000 | − | 88.3346i | 0.987097 | − | 0.569901i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 38.5000 | + | 66.6840i | 0.245223 | + | 0.424739i | 0.962194 | − | 0.272364i | \(-0.0878055\pi\) |
−0.716971 | + | 0.697103i | \(0.754472\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −108.000 | −0.679245 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −60.0000 | + | 103.923i | −0.372671 | + | 0.645485i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −145.000 | −0.889571 | −0.444785 | − | 0.895637i | \(-0.646720\pi\) | ||||
−0.444785 | + | 0.895637i | \(0.646720\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 261.000 | + | 150.688i | 1.56287 | + | 0.902326i | 0.996964 | + | 0.0778587i | \(0.0248083\pi\) |
0.565910 | + | 0.824467i | \(0.308525\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 97.0000 | + | 168.009i | 0.573964 | + | 0.994136i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.5000 | − | 54.5596i | −0.0964912 | − | 0.319062i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.00000 | + | 5.19615i | −0.0520231 | + | 0.0300356i | −0.525786 | − | 0.850617i | \(-0.676229\pi\) |
0.473763 | + | 0.880652i | \(0.342895\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −27.5000 | + | 47.6314i | −0.157143 | + | 0.272179i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 63.0000 | − | 109.119i | 0.355932 | − | 0.616493i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −66.0000 | − | 38.1051i | −0.364641 | − | 0.210526i | 0.306474 | − | 0.951879i | \(-0.400851\pi\) |
−0.671115 | + | 0.741354i | \(0.734184\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 74.4782i | − | 0.406985i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −315.000 | + | 181.865i | −1.70270 | + | 0.983056i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 25.9808i | 0.137464i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.0000 | 0.0942408 | 0.0471204 | − | 0.998889i | \(-0.484996\pi\) | ||||
0.0471204 | + | 0.998889i | \(0.484996\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 49.5000 | − | 28.5788i | 0.256477 | − | 0.148077i | −0.366250 | − | 0.930517i | \(-0.619358\pi\) |
0.622726 | + | 0.782440i | \(0.286025\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −99.0000 | − | 171.473i | −0.507692 | − | 0.879349i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −90.0000 | −0.456853 | −0.228426 | − | 0.973561i | \(-0.573358\pi\) | ||||
−0.228426 | + | 0.973561i | \(0.573358\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −111.500 | + | 193.124i | −0.560302 | + | 0.970471i | 0.437168 | + | 0.899380i | \(0.355981\pi\) |
−0.997470 | + | 0.0710910i | \(0.977352\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 99.0000 | 0.492537 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 135.000 | + | 77.9423i | 0.665025 | + | 0.383952i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 216.000 | + | 124.708i | 1.05366 | + | 0.608330i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 36.0000 | + | 62.3538i | 0.173913 | + | 0.301226i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 292.500 | − | 168.875i | 1.38626 | − | 0.800355i | 0.393365 | − | 0.919382i | \(-0.371311\pi\) |
0.992891 | + | 0.119027i | \(0.0379776\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 54.0000 | − | 93.5307i | 0.253521 | − | 0.439111i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −75.0000 | + | 129.904i | −0.348837 | + | 0.604204i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 147.224i | 0.678453i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.5000 | + | 9.52628i | 0.0753425 | + | 0.0434990i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 114.315i | 0.517264i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 370.500 | − | 213.908i | 1.66143 | − | 0.959230i | 0.689404 | − | 0.724377i | \(-0.257872\pi\) |
0.972031 | − | 0.234853i | \(-0.0754609\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 16.5000 | + | 28.5788i | 0.0733333 | + | 0.127017i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 176.669i | 0.778278i | 0.921179 | + | 0.389139i | \(0.127227\pi\) | ||||
−0.921179 | + | 0.389139i | \(0.872773\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 391.000 | 1.70742 | 0.853712 | − | 0.520746i | \(-0.174346\pi\) | ||||
0.853712 | + | 0.520746i | \(0.174346\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −72.0000 | − | 124.708i | −0.309013 | − | 0.535226i | 0.669134 | − | 0.743142i | \(-0.266665\pi\) |
−0.978147 | + | 0.207916i | \(0.933332\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 252.000 | 1.07234 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.50000 | − | 2.59808i | 0.00632911 | − | 0.0109623i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −450.000 | −1.88285 | −0.941423 | − | 0.337229i | \(-0.890510\pi\) | ||||
−0.941423 | + | 0.337229i | \(0.890510\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 67.5000 | + | 38.9711i | 0.280083 | + | 0.161706i | 0.633461 | − | 0.773775i | \(-0.281634\pi\) |
−0.353378 | + | 0.935481i | \(0.614967\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5000 | + | 7.79423i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 72.0000 | + | 124.708i | 0.293878 | + | 0.509011i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −346.500 | + | 104.789i | −1.40283 | + | 0.424247i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 189.000 | − | 109.119i | 0.759036 | − | 0.438230i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.0000 | + | 36.3731i | −0.0836653 | + | 0.144913i | −0.904822 | − | 0.425791i | \(-0.859996\pi\) |
0.821156 | + | 0.570703i | \(0.193329\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 62.3538i | − | 0.244525i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 414.000 | + | 239.023i | 1.61089 | + | 0.930051i | 0.989163 | + | 0.146820i | \(0.0469039\pi\) |
0.621732 | + | 0.783230i | \(0.286429\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 303.109i | − | 1.17030i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 81.0000 | − | 46.7654i | 0.310345 | − | 0.179178i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 78.0000 | + | 135.100i | 0.296578 | + | 0.513688i | 0.975351 | − | 0.220660i | \(-0.0708212\pi\) |
−0.678773 | + | 0.734348i | \(0.737488\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 374.123i | − | 1.41178i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.0000 | 0.0674157 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −459.000 | + | 265.004i | −1.70632 | + | 0.985144i | −0.767295 | + | 0.641294i | \(0.778398\pi\) |
−0.939025 | + | 0.343850i | \(0.888269\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −257.000 | − | 445.137i | −0.948339 | − | 1.64257i | −0.748923 | − | 0.662657i | \(-0.769429\pi\) |
−0.199417 | − | 0.979915i | \(-0.563905\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 165.000 | 0.604396 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 238.000 | 0.859206 | 0.429603 | − | 0.903018i | \(-0.358654\pi\) | ||||
0.429603 | + | 0.903018i | \(0.358654\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 76.5000 | + | 44.1673i | 0.274194 | + | 0.158306i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −225.000 | − | 129.904i | −0.800712 | − | 0.462291i | 0.0430082 | − | 0.999075i | \(-0.486306\pi\) |
−0.843720 | + | 0.536784i | \(0.819639\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −113.000 | − | 195.722i | −0.399293 | − | 0.691596i | 0.594346 | − | 0.804210i | \(-0.297411\pi\) |
−0.993639 | + | 0.112613i | \(0.964078\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 189.000 | − | 57.1577i | 0.663158 | − | 0.200553i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −180.000 | + | 103.923i | −0.627178 | + | 0.362101i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 126.500 | − | 219.104i | 0.437716 | − | 0.758147i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 114.000 | − | 197.454i | 0.391753 | − | 0.678535i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 31.1769i | − | 0.106406i | −0.998584 | − | 0.0532029i | \(-0.983057\pi\) | ||
0.998584 | − | 0.0532029i | \(-0.0169430\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 378.000 | + | 218.238i | 1.28136 | + | 0.739791i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 396.000 | − | 228.631i | 1.32441 | − | 0.764651i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −62.5000 | − | 108.253i | −0.207641 | − | 0.359645i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 270.200i | − | 0.891749i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 258.000 | 0.845902 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −54.0000 | + | 31.1769i | −0.175896 | + | 0.101553i | −0.585363 | − | 0.810771i | \(-0.699048\pi\) |
0.409467 | + | 0.912325i | \(0.365715\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 31.5000 | + | 54.5596i | 0.101942 | + | 0.176568i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 534.000 | 1.71704 | 0.858521 | − | 0.512779i | \(-0.171384\pi\) | ||||
0.858521 | + | 0.512779i | \(0.171384\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −269.000 | + | 465.922i | −0.859425 | + | 1.48857i | 0.0130534 | + | 0.999915i | \(0.495845\pi\) |
−0.872478 | + | 0.488653i | \(0.837488\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −90.0000 | −0.285714 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 81.0000 | + | 46.7654i | 0.255521 | + | 0.147525i | 0.622289 | − | 0.782787i | \(-0.286203\pi\) |
−0.366769 | + | 0.930312i | \(0.619536\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −111.000 | − | 25.9808i | −0.343653 | − | 0.0804358i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 181.500 | − | 104.789i | 0.558462 | − | 0.322428i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −90.0000 | + | 155.885i | −0.275229 | + | 0.476711i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −105.000 | + | 181.865i | −0.319149 | + | 0.552782i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 278.860i | − | 0.842478i | −0.906950 | − | 0.421239i | \(-0.861595\pi\) | ||
0.906950 | − | 0.421239i | \(-0.138405\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −157.500 | − | 90.9327i | −0.472973 | − | 0.273071i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 342.946i | 1.02372i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 418.500 | − | 241.621i | 1.24184 | − | 0.716977i | 0.272371 | − | 0.962192i | \(-0.412192\pi\) |
0.969469 | + | 0.245216i | \(0.0788588\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 135.000 | + | 233.827i | 0.398230 | + | 0.689755i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −365.000 | −1.06414 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −216.000 | + | 124.708i | −0.626087 | + | 0.361471i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −267.000 | − | 462.458i | −0.769452 | − | 1.33273i | −0.937860 | − | 0.347013i | \(-0.887196\pi\) |
0.168408 | − | 0.985717i | \(-0.446137\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −187.000 | −0.535817 | −0.267908 | − | 0.963444i | \(-0.586332\pi\) | ||||
−0.267908 | + | 0.963444i | \(0.586332\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 49.5000 | − | 85.7365i | 0.141026 | − | 0.244264i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 438.000 | 1.24079 | 0.620397 | − | 0.784288i | \(-0.286972\pi\) | ||||
0.620397 | + | 0.784288i | \(0.286972\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 324.000 | + | 187.061i | 0.912676 | + | 0.526934i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 45.0000 | + | 25.9808i | 0.126050 | + | 0.0727752i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −168.000 | − | 290.985i | −0.467967 | − | 0.810542i | 0.531363 | − | 0.847144i | \(-0.321680\pi\) |
−0.999330 | + | 0.0366021i | \(0.988347\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −23.0000 | − | 360.267i | −0.0637119 | − | 0.997968i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 181.500 | − | 104.789i | 0.500000 | − | 0.288675i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −33.0000 | + | 57.1577i | −0.0904110 | + | 0.156596i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 50.5000 | − | 87.4686i | 0.137602 | − | 0.238334i | −0.788986 | − | 0.614411i | \(-0.789394\pi\) |
0.926588 | + | 0.376077i | \(0.122727\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 124.708i | 0.337961i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 270.000 | + | 155.885i | 0.727763 | + | 0.420174i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 547.328i | − | 1.46737i | −0.679491 | − | 0.733684i | \(-0.737799\pi\) | ||
0.679491 | − | 0.733684i | \(-0.262201\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 126.000 | − | 72.7461i | 0.336000 | − | 0.193990i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −297.000 | − | 514.419i | −0.787798 | − | 1.36451i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 46.7654i | 0.123391i | 0.998095 | + | 0.0616957i | \(0.0196508\pi\) | ||||
−0.998095 | + | 0.0616957i | \(0.980349\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −72.0000 | −0.188976 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −342.000 | + | 197.454i | −0.892950 | + | 0.515545i | −0.874906 | − | 0.484292i | \(-0.839077\pi\) |
−0.0180440 | + | 0.999837i | \(0.505744\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −75.0000 | −0.193798 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 228.000 | − | 394.908i | 0.586118 | − | 1.01519i | −0.408617 | − | 0.912706i | \(-0.633989\pi\) |
0.994735 | − | 0.102481i | \(-0.0326779\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 144.000 | 0.368286 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −72.0000 | − | 41.5692i | −0.183206 | − | 0.105774i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.00000 | + | 5.19615i | 0.0227848 | + | 0.0131548i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −116.500 | − | 201.784i | −0.293451 | − | 0.508272i | 0.681172 | − | 0.732123i | \(-0.261470\pi\) |
−0.974623 | + | 0.223851i | \(0.928137\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −37.5000 | + | 160.215i | −0.0939850 | + | 0.401541i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 63.0000 | − | 36.3731i | 0.157107 | − | 0.0907059i | −0.419385 | − | 0.907808i | \(-0.637754\pi\) |
0.576492 | + | 0.817102i | \(0.304421\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 280.500 | − | 485.840i | 0.696030 | − | 1.20556i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −27.0000 | + | 46.7654i | −0.0666667 | + | 0.115470i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −210.000 | − | 121.244i | −0.513447 | − | 0.296439i | 0.220802 | − | 0.975319i | \(-0.429132\pi\) |
−0.734250 | + | 0.678880i | \(0.762466\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 228.631i | 0.556279i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −315.000 | + | 181.865i | −0.762712 | + | 0.440352i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 378.000 | + | 654.715i | 0.910843 | + | 1.57763i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.73205i | 0.00415360i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −84.0000 | −0.200477 | −0.100239 | − | 0.994963i | \(-0.531961\pi\) | ||||
−0.100239 | + | 0.994963i | \(0.531961\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −678.000 | + | 391.443i | −1.61045 | + | 0.929794i | −0.621186 | + | 0.783663i | \(0.713349\pi\) |
−0.989265 | + | 0.146131i | \(0.953318\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 63.0000 | + | 109.119i | 0.148936 | + | 0.257965i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 66.0000 | 0.155294 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −107.500 | + | 186.195i | −0.251756 | + | 0.436055i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 333.000 | + | 192.258i | 0.772622 | + | 0.446073i | 0.833809 | − | 0.552053i | \(-0.186155\pi\) |
−0.0611873 | + | 0.998126i | \(0.519489\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 253.500 | + | 146.358i | 0.585450 | + | 0.338010i | 0.763296 | − | 0.646048i | \(-0.223580\pi\) |
−0.177846 | + | 0.984058i | \(0.556913\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 162.000 | + | 280.592i | 0.372414 | + | 0.645040i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 132.000 | + | 436.477i | 0.302059 | + | 0.998803i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 97.5000 | − | 56.2917i | 0.222096 | − | 0.128227i | −0.384825 | − | 0.922990i | \(-0.625738\pi\) |
0.606920 | + | 0.794763i | \(0.292405\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −36.0000 | + | 62.3538i | −0.0816327 | + | 0.141392i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 93.0000 | − | 161.081i | 0.209932 | − | 0.363613i | −0.741761 | − | 0.670665i | \(-0.766009\pi\) |
0.951693 | + | 0.307051i | \(0.0993423\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 62.3538i | 0.140121i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 270.000 | + | 155.885i | 0.604027 | + | 0.348735i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 135.100i | − | 0.300891i | −0.988618 | − | 0.150445i | \(-0.951929\pi\) | ||
0.988618 | − | 0.150445i | \(-0.0480708\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −204.000 | − | 353.338i | −0.450331 | − | 0.779996i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 571.577i | 1.25621i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −565.000 | −1.23632 | −0.618162 | − | 0.786051i | \(-0.712122\pi\) | ||||
−0.618162 | + | 0.786051i | \(0.712122\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 27.0000 | − | 15.5885i | 0.0588235 | − | 0.0339618i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 69.0000 | + | 119.512i | 0.149675 | + | 0.259244i | 0.931107 | − | 0.364746i | \(-0.118844\pi\) |
−0.781433 | + | 0.623990i | \(0.785511\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 139.000 | 0.300216 | 0.150108 | − | 0.988670i | \(-0.452038\pi\) | ||||
0.150108 | + | 0.988670i | \(0.452038\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −153.000 | + | 265.004i | −0.329032 | + | 0.569901i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −888.000 | −1.90150 | −0.950749 | − | 0.309960i | \(-0.899684\pi\) | ||||
−0.950749 | + | 0.309960i | \(0.899684\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −247.500 | − | 142.894i | −0.527719 | − | 0.304678i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −115.500 | − | 66.6840i | −0.245223 | − | 0.141580i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 60.5000 | + | 200.052i | 0.127368 | + | 0.421162i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 162.000 | − | 93.5307i | 0.339623 | − | 0.196081i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −348.000 | + | 602.754i | −0.726514 | + | 1.25836i | 0.231834 | + | 0.972755i | \(0.425527\pi\) |
−0.958348 | + | 0.285603i | \(0.907806\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −577.500 | + | 1000.26i | −1.20062 | + | 2.07954i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 207.846i | − | 0.430323i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 684.000 | + | 394.908i | 1.41031 | + | 0.814242i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 214.774i | 0.441015i | 0.975385 | + | 0.220507i | \(0.0707713\pi\) | ||||
−0.975385 | + | 0.220507i | \(0.929229\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 217.500 | − | 125.574i | 0.444785 | − | 0.256797i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −468.000 | − | 810.600i | −0.953157 | − | 1.65092i | −0.738531 | − | 0.674220i | \(-0.764480\pi\) |
−0.214626 | − | 0.976696i | \(-0.568853\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 187.061i | − | 0.379435i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −270.000 | + | 155.885i | −0.543260 | + | 0.313651i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −263.500 | − | 456.395i | −0.528056 | − | 0.914620i | −0.999465 | − | 0.0327053i | \(-0.989588\pi\) |
0.471409 | − | 0.881915i | \(-0.343746\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −522.000 | −1.04192 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −195.000 | + | 337.750i | −0.387674 | + | 0.671471i | −0.992136 | − | 0.125163i | \(-0.960055\pi\) |
0.604462 | + | 0.796634i | \(0.293388\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 936.000 | 1.85347 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −291.000 | − | 168.009i | −0.573964 | − | 0.331379i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 513.000 | + | 296.181i | 1.00786 | + | 0.581887i | 0.910564 | − | 0.413368i | \(-0.135648\pi\) |
0.0972946 | + | 0.995256i | \(0.468981\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.5000 | − | 47.6314i | −0.0538160 | − | 0.0932121i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 72.0000 | + | 67.5500i | 0.140351 | + | 0.131676i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −189.000 | + | 109.119i | −0.366990 | + | 0.211882i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.00000 | − | 15.5885i | 0.0173410 | − | 0.0300356i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 103.923i | − | 0.199468i | −0.995014 | − | 0.0997342i | \(-0.968201\pi\) | ||
0.995014 | − | 0.0997342i | \(-0.0317993\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −118.500 | − | 68.4160i | −0.226577 | − | 0.130815i | 0.382415 | − | 0.923991i | \(-0.375093\pi\) |
−0.608992 | + | 0.793176i | \(0.708426\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 95.2628i | − | 0.181453i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 153.000 | − | 88.3346i | 0.290323 | − | 0.167618i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.5000 | − | 40.7032i | −0.0444234 | − | 0.0769437i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 218.238i | 0.410995i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 792.000 | 1.48593 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 99.5000 | − | 172.339i | 0.183919 | − | 0.318556i | −0.759293 | − | 0.650749i | \(-0.774455\pi\) |
0.943212 | + | 0.332192i | \(0.107788\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 132.000 | 0.243094 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −540.000 | − | 311.769i | −0.990826 | − | 0.572053i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −532.500 | − | 307.439i | −0.973492 | − | 0.562046i | −0.0731928 | − | 0.997318i | \(-0.523319\pi\) |
−0.900299 | + | 0.435272i | \(0.856652\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 64.5000 | + | 111.717i | 0.117486 | + | 0.203492i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 567.000 | − | 171.473i | 1.02904 | − | 0.311203i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.50000 | + | 4.33013i | −0.0135624 | + | 0.00783025i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 315.000 | − | 545.596i | 0.567568 | − | 0.983056i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −360.000 | + | 623.538i | −0.646320 | + | 1.11946i | 0.337675 | + | 0.941263i | \(0.390359\pi\) |
−0.983995 | + | 0.178196i | \(0.942974\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 476.314i | 0.852082i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 374.123i | − | 0.664517i | −0.943188 | − | 0.332258i | \(-0.892189\pi\) | ||
0.943188 | − | 0.332258i | \(-0.107811\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −810.000 | + | 467.654i | −1.43363 | + | 0.827706i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −22.5000 | − | 38.9711i | −0.0396825 | − | 0.0687322i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 290.985i | − | 0.511396i | −0.966757 | − | 0.255698i | \(-0.917695\pi\) | ||
0.966757 | − | 0.255698i | \(-0.0823053\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −95.0000 | −0.166375 | −0.0831874 | − | 0.996534i | \(-0.526510\pi\) | ||||
−0.0831874 | + | 0.996534i | \(0.526510\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −27.0000 | + | 15.5885i | −0.0471204 | + | 0.0272050i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −132.000 | − | 228.631i | −0.229565 | − | 0.397619i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 874.000 | 1.51473 | 0.757366 | − | 0.652991i | \(-0.226486\pi\) | ||||
0.757366 | + | 0.652991i | \(0.226486\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −49.5000 | + | 85.7365i | −0.0854922 | + | 0.148077i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −630.000 | −1.08434 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 297.000 | + | 171.473i | 0.507692 | + | 0.293116i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −327.000 | − | 566.381i | −0.557070 | − | 0.964873i | −0.997739 | − | 0.0672038i | \(-0.978592\pi\) |
0.440669 | − | 0.897669i | \(-0.354741\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 408.000 | + | 382.783i | 0.692699 | + | 0.649887i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 135.000 | − | 77.9423i | 0.228426 | − | 0.131882i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 471.000 | − | 815.796i | 0.794266 | − | 1.37571i | −0.129037 | − | 0.991640i | \(-0.541189\pi\) |
0.923304 | − | 0.384070i | \(-0.125478\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −90.0000 | + | 155.885i | −0.151261 | + | 0.261991i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 386.247i | − | 0.646980i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −324.000 | − | 187.061i | −0.540902 | − | 0.312290i | 0.204543 | − | 0.978858i | \(-0.434429\pi\) |
−0.745444 | + | 0.666568i | \(0.767763\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 646.055i | − | 1.07497i | −0.843274 | − | 0.537483i | \(-0.819375\pi\) | ||
0.843274 | − | 0.537483i | \(-0.180625\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −148.500 | + | 85.7365i | −0.246269 | + | 0.142183i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 363.000 | + | 628.734i | 0.600000 | + | 1.03923i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 358.535i | − | 0.590666i | −0.955394 | − | 0.295333i | \(-0.904569\pi\) | ||
0.955394 | − | 0.295333i | \(-0.0954307\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −270.000 | −0.443350 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 693.000 | − | 400.104i | 1.13421 | − | 0.654834i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −383.000 | − | 663.375i | −0.624796 | − | 1.08218i | −0.988580 | − | 0.150695i | \(-0.951849\pi\) |
0.363784 | − | 0.931483i | \(-0.381485\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −432.000 | −0.702439 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 270.000 | − | 467.654i | 0.437601 | − | 0.757948i | −0.559903 | − | 0.828558i | \(-0.689161\pi\) |
0.997504 | + | 0.0706107i | \(0.0224948\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −97.0000 | −0.156704 | −0.0783522 | − | 0.996926i | \(-0.524966\pi\) | ||||
−0.0783522 | + | 0.996926i | \(0.524966\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −108.000 | − | 62.3538i | −0.173913 | − | 0.100409i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −45.0000 | − | 25.9808i | −0.0722311 | − | 0.0417027i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 389.500 | + | 674.634i | 0.623200 | + | 1.07941i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −315.000 | + | 181.865i | −0.500795 | + | 0.289134i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −224.500 | + | 388.845i | −0.355784 | + | 0.616237i | −0.987252 | − | 0.159166i | \(-0.949120\pi\) |
0.631467 | + | 0.775402i | \(0.282453\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −292.500 | + | 506.625i | −0.462085 | + | 0.800355i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 249.415i | − | 0.392780i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 396.000 | + | 228.631i | 0.621664 | + | 0.358918i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 187.061i | 0.292741i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −513.000 | + | 296.181i | −0.800312 | + | 0.462060i | −0.843580 | − | 0.537003i | \(-0.819556\pi\) |
0.0432682 | + | 0.999063i | \(0.486223\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 461.500 | + | 799.341i | 0.717729 | + | 1.24314i | 0.961897 | + | 0.273411i | \(0.0881518\pi\) |
−0.244168 | + | 0.969733i | \(0.578515\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 259.808i | − | 0.402803i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −594.000 | −0.918083 | −0.459042 | − | 0.888415i | \(-0.651807\pi\) | ||||
−0.459042 | + | 0.888415i | \(0.651807\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −127.500 | − | 220.836i | −0.195853 | − | 0.339227i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 936.000 | 1.43338 | 0.716692 | − | 0.697390i | \(-0.245655\pi\) | ||||
0.716692 | + | 0.697390i | \(0.245655\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 144.000 | − | 249.415i | 0.219847 | − | 0.380787i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −33.0000 | −0.0502283 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 252.000 | + | 145.492i | 0.382398 | + | 0.220777i | 0.678861 | − | 0.734267i | \(-0.262474\pi\) |
−0.296463 | + | 0.955044i | \(0.595807\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −672.000 | − | 387.979i | −1.01664 | − | 0.586958i | −0.103512 | − | 0.994628i | \(-0.533008\pi\) |
−0.913129 | + | 0.407670i | \(0.866341\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −99.0000 | − | 171.473i | −0.149321 | − | 0.258632i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −555.000 | − | 129.904i | −0.834586 | − | 0.195344i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −648.000 | + | 374.123i | −0.971514 | + | 0.560904i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −370.500 | + | 641.725i | −0.553812 | + | 0.959230i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 961.288i | 1.42836i | 0.699961 | + | 0.714181i | \(0.253201\pi\) | ||||
−0.699961 | + | 0.714181i | \(0.746799\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −49.5000 | − | 28.5788i | −0.0733333 | − | 0.0423390i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 259.808i | − | 0.383763i | −0.981418 | − | 0.191882i | \(-0.938541\pi\) | ||
0.981418 | − | 0.191882i | \(-0.0614589\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −570.000 | + | 329.090i | −0.839470 | + | 0.484668i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −153.000 | − | 265.004i | −0.224670 | − | 0.389139i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1132.76i | 1.65851i | 0.558872 | + | 0.829254i | \(0.311234\pi\) | ||||
−0.558872 | + | 0.829254i | \(0.688766\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −792.000 | −1.15620 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −586.500 | + | 338.616i | −0.853712 | + | 0.492891i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −594.000 | − | 1028.84i | −0.862119 | − | 1.49323i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 58.0000 | 0.0839363 | 0.0419682 | − | 0.999119i | \(-0.486637\pi\) | ||||
0.0419682 | + | 0.999119i | \(0.486637\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.00000 | −0.00863309 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 216.000 | + | 124.708i | 0.309900 | + | 0.178921i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 216.000 | + | 124.708i | 0.309013 | + | 0.178409i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 171.000 | + | 296.181i | 0.243937 | + | 0.422512i | 0.961832 | − | 0.273640i | \(-0.0882276\pi\) |
−0.717895 | + | 0.696151i | \(0.754894\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −840.000 | − | 788.083i | −1.19488 | − | 1.12103i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −378.000 | + | 218.238i | −0.536170 | + | 0.309558i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −390.000 | + | 675.500i | −0.551627 | + | 0.955445i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −272.500 | + | 471.984i | −0.384344 | + | 0.665704i | −0.991678 | − | 0.128743i | \(-0.958906\pi\) |
0.607334 | + | 0.794447i | \(0.292239\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.19615i | 0.00730823i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −612.000 | − | 353.338i | −0.858345 | − | 0.495566i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 675.000 | − | 389.711i | 0.941423 | − | 0.543531i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −534.000 | − | 924.915i | −0.742698 | − | 1.28639i | −0.951262 | − | 0.308382i | \(-0.900212\pi\) |
0.208564 | − | 0.978009i | \(-0.433121\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 181.865i | − | 0.252240i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −135.000 | −0.186722 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −297.000 | + | 171.473i | −0.409655 | + | 0.236515i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −57.5000 | − | 99.5929i | −0.0790922 | − | 0.136992i | 0.823766 | − | 0.566929i | \(-0.191869\pi\) |
−0.902858 | + | 0.429938i | \(0.858535\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −75.0000 | + | 129.904i | −0.102599 | + | 0.177707i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −298.000 | −0.406548 | −0.203274 | − | 0.979122i | \(-0.565158\pi\) | ||||
−0.203274 | + | 0.979122i | \(0.565158\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −216.000 | − | 124.708i | −0.293878 | − | 0.169670i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 666.500 | + | 1154.41i | 0.901894 | + | 1.56213i | 0.825033 | + | 0.565085i | \(0.191157\pi\) |
0.0768619 | + | 0.997042i | \(0.475510\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 429.000 | − | 457.261i | 0.578947 | − | 0.617087i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 738.000 | − | 426.084i | 0.993271 | − | 0.573465i | 0.0870202 | − | 0.996207i | \(-0.472266\pi\) |
0.906250 | + | 0.422742i | \(0.138932\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −540.000 | + | 935.307i | −0.724832 | + | 1.25545i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −189.000 | + | 327.358i | −0.253012 | + | 0.438230i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 343.500 | + | 198.320i | 0.457390 | + | 0.264074i | 0.710946 | − | 0.703246i | \(-0.248267\pi\) |
−0.253556 | + | 0.967321i | \(0.581600\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 72.7461i | − | 0.0966084i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1224.00 | − | 706.677i | 1.62119 | − | 0.935996i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −117.500 | − | 203.516i | −0.155218 | − | 0.268845i | 0.777920 | − | 0.628363i | \(-0.216275\pi\) |
−0.933138 | + | 0.359517i | \(0.882941\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1158.00 | −1.52168 | −0.760841 | − | 0.648938i | \(-0.775213\pi\) | ||||
−0.760841 | + | 0.648938i | \(0.775213\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 450.000 | − | 259.808i | 0.589777 | − | 0.340508i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 54.0000 | + | 93.5307i | 0.0705882 | + | 0.122262i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1386.00 | 1.80704 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −492.500 | + | 853.035i | −0.640442 | + | 1.10928i | 0.344892 | + | 0.938642i | \(0.387916\pi\) |
−0.985334 | + | 0.170636i | \(0.945418\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −828.000 | −1.07393 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −873.000 | − | 504.027i | −1.12937 | − | 0.652040i | −0.185591 | − | 0.982627i | \(-0.559420\pi\) |
−0.943775 | + | 0.330587i | \(0.892753\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −280.500 | − | 161.947i | −0.361935 | − | 0.208964i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 262.500 | + | 454.663i | 0.337838 | + | 0.585152i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −180.000 | + | 769.031i | −0.231065 | + | 0.987202i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −81.0000 | + | 140.296i | −0.103448 | + | 0.179178i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 231.000 | − | 400.104i | 0.294268 | − | 0.509686i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1404.69i | 1.78487i | 0.451175 | + | 0.892435i | \(0.351005\pi\) | ||||
−0.451175 | + | 0.892435i | \(0.648995\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −234.000 | − | 135.100i | −0.296578 | − | 0.171229i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 779.423i | − | 0.985364i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 709.500 | − | 409.630i | 0.894704 | − | 0.516557i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 324.000 | + | 561.184i | 0.407547 | + | 0.705892i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1267.86i | − | 1.59079i | −0.606090 | − | 0.795396i | \(-0.707263\pi\) | ||
0.606090 | − | 0.795396i | \(-0.292737\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 252.000 | 0.315394 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −27.0000 | + | 15.5885i | −0.0337079 | + | 0.0194612i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 720.000 | 0.894410 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 459.000 | − | 795.011i | 0.568773 | − | 0.985144i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −546.000 | −0.674907 | −0.337454 | − | 0.941342i | \(-0.609566\pi\) | ||||
−0.337454 | + | 0.941342i | \(0.609566\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −936.000 | − | 540.400i | −1.15413 | − | 0.666338i | −0.204240 | − | 0.978921i | \(-0.565472\pi\) |
−0.949890 | + | 0.312583i | \(0.898806\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 771.000 | + | 445.137i | 0.948339 | + | 0.547524i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 435.000 | + | 753.442i | 0.533742 | + | 0.924469i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −462.500 | − | 108.253i | −0.566095 | − | 0.132501i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −247.500 | + | 142.894i | −0.302198 | + | 0.174474i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −477.000 | + | 826.188i | −0.580999 | + | 1.00632i | 0.414363 | + | 0.910112i | \(0.364005\pi\) |
−0.995361 | + | 0.0962075i | \(0.969329\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −349.000 | + | 604.486i | −0.424058 | + | 0.734491i | −0.996332 | − | 0.0855722i | \(-0.972728\pi\) |
0.572274 | + | 0.820063i | \(0.306062\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 333.000 | + | 192.258i | 0.402660 | + | 0.232476i | 0.687631 | − | 0.726060i | \(-0.258651\pi\) |
−0.284971 | + | 0.958536i | \(0.591984\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 57.1577i | − | 0.0689477i | −0.999406 | − | 0.0344739i | \(-0.989024\pi\) | ||
0.999406 | − | 0.0344739i | \(-0.0109755\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −357.000 | + | 206.114i | −0.429603 | + | 0.248031i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 72.0000 | + | 124.708i | 0.0864346 | + | 0.149709i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 1808.26i | − | 2.16558i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −153.000 | −0.182796 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.00000 | − | 5.19615i | 0.0107271 | − | 0.00619327i | −0.494627 | − | 0.869105i | \(-0.664695\pi\) |
0.505354 | + | 0.862912i | \(0.331362\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 65.5000 | + | 113.449i | 0.0778835 | + | 0.134898i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 450.000 | 0.533808 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 582.000 | − | 1008.05i | 0.688757 | − | 1.19296i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −605.000 | −0.714286 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 339.000 | + | 195.722i | 0.399293 | + | 0.230532i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1260.00 | + | 727.461i | 1.48061 | + | 0.854831i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −794.500 | − | 1376.11i | −0.931419 | − | 1.61326i | −0.780899 | − | 0.624657i | \(-0.785239\pi\) |
−0.150519 | − | 0.988607i | \(-0.548095\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −234.000 | + | 249.415i | −0.273684 | + | 0.291714i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 747.000 | − | 431.281i | 0.871645 | − | 0.503245i | 0.00375064 | − | 0.999993i | \(-0.498806\pi\) |
0.867895 | + | 0.496748i | \(0.165473\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −461.500 | + | 799.341i | −0.537253 | + | 0.930549i | 0.461798 | + | 0.886985i | \(0.347204\pi\) |
−0.999051 | + | 0.0435637i | \(0.986129\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 180.000 | − | 311.769i | 0.209059 | − | 0.362101i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 197.454i | − | 0.228799i | −0.993435 | − | 0.114400i | \(-0.963506\pi\) | ||
0.993435 | − | 0.114400i | \(-0.0364944\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 54.0000 | + | 31.1769i | 0.0624277 | + | 0.0360427i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 438.209i | 0.505431i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 544.500 | + | 943.102i | 0.625144 | + | 1.08278i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 394.908i | 0.452357i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −420.000 | −0.480000 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 736.500 | − | 425.218i | 0.839795 | − | 0.484856i | −0.0173997 | − | 0.999849i | \(-0.505539\pi\) |
0.857194 | + | 0.514993i | \(0.172205\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 27.0000 | + | 46.7654i | 0.0307167 | + | 0.0532029i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −402.000 | −0.456300 | −0.228150 | − | 0.973626i | \(-0.573268\pi\) | ||||
−0.228150 | + | 0.973626i | \(0.573268\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 630.500 | − | 1092.06i | 0.714043 | − | 1.23676i | −0.249284 | − | 0.968430i | \(-0.580195\pi\) |
0.963327 | − | 0.268329i | \(-0.0864713\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −756.000 | −0.854237 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −189.000 | − | 109.119i | −0.213078 | − | 0.123021i | 0.389663 | − | 0.920957i | \(-0.372591\pi\) |
−0.602741 | + | 0.797937i | \(0.705925\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 180.000 | + | 103.923i | 0.202475 | + | 0.116899i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 231.000 | + | 763.834i | 0.258679 | + | 0.855358i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −396.000 | + | 685.892i | −0.441472 | + | 0.764651i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −459.000 | + | 795.011i | −0.510567 | + | 0.884328i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 374.123i | − | 0.415231i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 187.500 | + | 108.253i | 0.207641 | + | 0.119882i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 457.261i | 0.505261i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −60.0000 | + | 34.6410i | −0.0661521 | + | 0.0381930i | −0.532711 | − | 0.846297i | \(-0.678827\pi\) |
0.466559 | + | 0.884490i | \(0.345493\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 234.000 | + | 405.300i | 0.257426 | + | 0.445874i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1184.72i | − | 1.30046i | −0.759736 | − | 0.650232i | \(-0.774672\pi\) | ||
0.759736 | − | 0.650232i | \(-0.225328\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −387.000 | + | 223.435i | −0.422951 | + | 0.244191i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 120.000 | + | 207.846i | 0.130862 | + | 0.226659i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −955.000 | −1.03917 | −0.519587 | − | 0.854418i | \(-0.673914\pi\) | ||||
−0.519587 | + | 0.854418i | \(0.673914\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 54.0000 | − | 93.5307i | 0.0586319 | − | 0.101553i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1188.00 | 1.28711 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 577.500 | + | 333.420i | 0.624324 | + | 0.360454i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −94.5000 | − | 54.5596i | −0.101942 | − | 0.0588561i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 537.000 | + | 930.111i | 0.578041 | + | 1.00120i | 0.995704 | + | 0.0925942i | \(0.0295159\pi\) |
−0.417663 | + | 0.908602i | \(0.637151\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −312.000 | + | 332.554i | −0.335124 | + | 0.357201i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −801.000 | + | 462.458i | −0.858521 | + | 0.495667i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 324.500 | − | 562.050i | 0.346318 | − | 0.599840i | −0.639274 | − | 0.768979i | \(-0.720765\pi\) |
0.985592 | + | 0.169138i | \(0.0540985\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 931.843i | − | 0.992378i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1188.00 | + | 685.892i | 1.26249 | + | 0.728897i | 0.973555 | − | 0.228453i | \(-0.0733666\pi\) |
0.288932 | + | 0.957350i | \(0.406700\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 997.661i | − | 1.05797i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 135.000 | − | 77.9423i | 0.142857 | − | 0.0824786i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −282.000 | − | 488.438i | −0.297782 | − | 0.515774i | 0.677846 | − | 0.735204i | \(-0.262914\pi\) |
−0.975628 | + | 0.219430i | \(0.929580\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 209.578i | 0.220841i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −162.000 | −0.170347 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1530.00 | − | 883.346i | 1.60546 | − | 0.926911i | 0.615087 | − | 0.788459i | \(-0.289121\pi\) |
0.990369 | − | 0.138452i | \(-0.0442126\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −54.0000 | − | 93.5307i | −0.0565445 | − | 0.0979380i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 330.000 | − | 571.577i | 0.344108 | − | 0.596013i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 94.0000 | 0.0978148 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −297.000 | − | 171.473i | −0.307772 | − | 0.177692i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −530.500 | − | 918.853i | −0.548604 | − | 0.950210i | −0.998371 | − | 0.0570638i | \(-0.981826\pi\) |
0.449767 | − | 0.893146i | \(-0.351507\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 189.000 | − | 57.1577i | 0.195046 | − | 0.0589863i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 477.000 | − | 275.396i | 0.491246 | − | 0.283621i | −0.233845 | − | 0.972274i | \(-0.575131\pi\) |
0.725091 | + | 0.688653i | \(0.241798\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.50000 | − | 4.33013i | 0.00256937 | − | 0.00445028i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −181.500 | + | 314.367i | −0.186154 | + | 0.322428i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 737.854i | 0.755224i | 0.925964 | + | 0.377612i | \(0.123255\pi\) | ||||
−0.925964 | + | 0.377612i | \(0.876745\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 311.769i | − | 0.317807i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 630.000 | − | 363.731i | 0.640895 | − | 0.370021i | −0.144064 | − | 0.989568i | \(-0.546017\pi\) |
0.784959 | + | 0.619547i | \(0.212684\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 270.000 | + | 467.654i | 0.274112 | + | 0.474775i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 363.731i | − | 0.368521i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 600.000 | 0.606673 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1042.50 | − | 601.888i | 1.05197 | − | 0.607354i | 0.128768 | − | 0.991675i | \(-0.458898\pi\) |
0.923200 | + | 0.384321i | \(0.125564\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 241.500 | + | 418.290i | 0.243202 | + | 0.421239i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1338.00 | 1.34472 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 104.500 | − | 180.999i | 0.104814 | − | 0.181544i | −0.808848 | − | 0.588018i | \(-0.799908\pi\) |
0.913662 | + | 0.406474i | \(0.133242\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 315.000 | 0.315315 |
(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 | 912.3.be.a.145.1 | 2 | ||
4.3 | odd | 2 | 228.3.l.a.145.1 | ✓ | 2 | ||
12.11 | even | 2 | 684.3.y.e.145.1 | 2 | |||
19.8 | odd | 6 | inner | 912.3.be.a.673.1 | 2 | ||
76.27 | even | 6 | 228.3.l.a.217.1 | yes | 2 | ||
228.179 | odd | 6 | 684.3.y.e.217.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
228.3.l.a.145.1 | ✓ | 2 | 4.3 | odd | 2 | ||
228.3.l.a.217.1 | yes | 2 | 76.27 | even | 6 | ||
684.3.y.e.145.1 | 2 | 12.11 | even | 2 | |||
684.3.y.e.217.1 | 2 | 228.179 | odd | 6 | |||
912.3.be.a.145.1 | 2 | 1.1 | even | 1 | trivial | ||
912.3.be.a.673.1 | 2 | 19.8 | odd | 6 | inner |