Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(461,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.461");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.f (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: | \(7.71354883526\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 461.4 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.461 |
Dual form | 966.2.f.a.461.1 |
$q$-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 \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.73205i | 1.00000i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.73205 | 0.774597 | 0.387298 | − | 0.921954i | \(-0.373408\pi\) | ||||
0.387298 | + | 0.921954i | \(0.373408\pi\) | |||||||
\(6\) | −1.73205 | −0.707107 | ||||||||
\(7\) | 2.00000 | − | 1.73205i | 0.755929 | − | 0.654654i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 1.73205i | 0.547723i | ||||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | − | 1.73205i | − | 0.500000i | ||||||
\(13\) | 1.73205i | 0.480384i | 0.970725 | + | 0.240192i | \(0.0772105\pi\) | ||||
−0.970725 | + | 0.240192i | \(0.922790\pi\) | |||||||
\(14\) | 1.73205 | + | 2.00000i | 0.462910 | + | 0.534522i | ||||
\(15\) | 3.00000i | 0.774597i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.46410 | 0.840168 | 0.420084 | − | 0.907485i | \(-0.362001\pi\) | ||||
0.420084 | + | 0.907485i | \(0.362001\pi\) | |||||||
\(18\) | − | 3.00000i | − | 0.707107i | ||||||
\(19\) | 6.92820i | 1.58944i | 0.606977 | + | 0.794719i | \(0.292382\pi\) | ||||
−0.606977 | + | 0.794719i | \(0.707618\pi\) | |||||||
\(20\) | −1.73205 | −0.387298 | ||||||||
\(21\) | 3.00000 | + | 3.46410i | 0.654654 | + | 0.755929i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.00000i | − | 0.208514i | ||||||
\(24\) | 1.73205 | 0.353553 | ||||||||
\(25\) | −2.00000 | −0.400000 | ||||||||
\(26\) | −1.73205 | −0.339683 | ||||||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | −2.00000 | + | 1.73205i | −0.377964 | + | 0.327327i | ||||
\(29\) | 9.00000i | 1.67126i | 0.549294 | + | 0.835629i | \(0.314897\pi\) | ||||
−0.549294 | + | 0.835629i | \(0.685103\pi\) | |||||||
\(30\) | −3.00000 | −0.547723 | ||||||||
\(31\) | 10.3923i | 1.86651i | 0.359211 | + | 0.933257i | \(0.383046\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.46410i | 0.594089i | ||||||||
\(35\) | 3.46410 | − | 3.00000i | 0.585540 | − | 0.507093i | ||||
\(36\) | 3.00000 | 0.500000 | ||||||||
\(37\) | −5.00000 | −0.821995 | −0.410997 | − | 0.911636i | \(-0.634819\pi\) | ||||
−0.410997 | + | 0.911636i | \(0.634819\pi\) | |||||||
\(38\) | −6.92820 | −1.12390 | ||||||||
\(39\) | −3.00000 | −0.480384 | ||||||||
\(40\) | − | 1.73205i | − | 0.273861i | ||||||
\(41\) | 12.1244 | 1.89351 | 0.946753 | − | 0.321960i | \(-0.104342\pi\) | ||||
0.946753 | + | 0.321960i | \(0.104342\pi\) | |||||||
\(42\) | −3.46410 | + | 3.00000i | −0.534522 | + | 0.462910i | ||||
\(43\) | 1.00000 | 0.152499 | 0.0762493 | − | 0.997089i | \(-0.475706\pi\) | ||||
0.0762493 | + | 0.997089i | \(0.475706\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.19615 | −0.774597 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 8.66025 | 1.26323 | 0.631614 | − | 0.775283i | \(-0.282393\pi\) | ||||
0.631614 | + | 0.775283i | \(0.282393\pi\) | |||||||
\(48\) | 1.73205i | 0.250000i | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | − | 2.00000i | − | 0.282843i | ||||||
\(51\) | 6.00000i | 0.840168i | ||||||||
\(52\) | − | 1.73205i | − | 0.240192i | ||||||
\(53\) | − | 12.0000i | − | 1.64833i | −0.566352 | − | 0.824163i | \(-0.691646\pi\) | ||
0.566352 | − | 0.824163i | \(-0.308354\pi\) | |||||||
\(54\) | 5.19615 | 0.707107 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.73205 | − | 2.00000i | −0.231455 | − | 0.267261i | ||||
\(57\) | −12.0000 | −1.58944 | ||||||||
\(58\) | −9.00000 | −1.18176 | ||||||||
\(59\) | −3.46410 | −0.450988 | −0.225494 | − | 0.974245i | \(-0.572400\pi\) | ||||
−0.225494 | + | 0.974245i | \(0.572400\pi\) | |||||||
\(60\) | − | 3.00000i | − | 0.387298i | ||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | −10.3923 | −1.31982 | ||||||||
\(63\) | −6.00000 | + | 5.19615i | −0.755929 | + | 0.654654i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 3.00000i | 0.372104i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | −3.46410 | −0.420084 | ||||||||
\(69\) | 1.73205 | 0.208514 | ||||||||
\(70\) | 3.00000 | + | 3.46410i | 0.358569 | + | 0.414039i | ||||
\(71\) | − | 12.0000i | − | 1.42414i | −0.702109 | − | 0.712069i | \(-0.747758\pi\) | ||
0.702109 | − | 0.712069i | \(-0.252242\pi\) | |||||||
\(72\) | 3.00000i | 0.353553i | ||||||||
\(73\) | 6.92820i | 0.810885i | 0.914121 | + | 0.405442i | \(0.132883\pi\) | ||||
−0.914121 | + | 0.405442i | \(0.867117\pi\) | |||||||
\(74\) | − | 5.00000i | − | 0.581238i | ||||||
\(75\) | − | 3.46410i | − | 0.400000i | ||||||
\(76\) | − | 6.92820i | − | 0.794719i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 3.00000i | − | 0.339683i | ||||||
\(79\) | −10.0000 | −1.12509 | −0.562544 | − | 0.826767i | \(-0.690177\pi\) | ||||
−0.562544 | + | 0.826767i | \(0.690177\pi\) | |||||||
\(80\) | 1.73205 | 0.193649 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 12.1244i | 1.33891i | ||||||||
\(83\) | 3.46410 | 0.380235 | 0.190117 | − | 0.981761i | \(-0.439113\pi\) | ||||
0.190117 | + | 0.981761i | \(0.439113\pi\) | |||||||
\(84\) | −3.00000 | − | 3.46410i | −0.327327 | − | 0.377964i | ||||
\(85\) | 6.00000 | 0.650791 | ||||||||
\(86\) | 1.00000i | 0.107833i | ||||||||
\(87\) | −15.5885 | −1.67126 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.46410 | −0.367194 | −0.183597 | − | 0.983002i | \(-0.558774\pi\) | ||||
−0.183597 | + | 0.983002i | \(0.558774\pi\) | |||||||
\(90\) | − | 5.19615i | − | 0.547723i | ||||||
\(91\) | 3.00000 | + | 3.46410i | 0.314485 | + | 0.363137i | ||||
\(92\) | 1.00000i | 0.104257i | ||||||||
\(93\) | −18.0000 | −1.86651 | ||||||||
\(94\) | 8.66025i | 0.893237i | ||||||||
\(95\) | 12.0000i | 1.23117i | ||||||||
\(96\) | −1.73205 | −0.176777 | ||||||||
\(97\) | − | 12.1244i | − | 1.23104i | −0.788121 | − | 0.615521i | \(-0.788946\pi\) | ||
0.788121 | − | 0.615521i | \(-0.211054\pi\) | |||||||
\(98\) | 6.92820 | + | 1.00000i | 0.699854 | + | 0.101015i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.00000 | 0.200000 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | −6.00000 | −0.594089 | ||||||||
\(103\) | − | 5.19615i | − | 0.511992i | −0.966678 | − | 0.255996i | \(-0.917597\pi\) | ||
0.966678 | − | 0.255996i | \(-0.0824034\pi\) | |||||||
\(104\) | 1.73205 | 0.169842 | ||||||||
\(105\) | 5.19615 | + | 6.00000i | 0.507093 | + | 0.585540i | ||||
\(106\) | 12.0000 | 1.16554 | ||||||||
\(107\) | 18.0000i | 1.74013i | 0.492941 | + | 0.870063i | \(0.335922\pi\) | ||||
−0.492941 | + | 0.870063i | \(0.664078\pi\) | |||||||
\(108\) | 5.19615i | 0.500000i | ||||||||
\(109\) | −11.0000 | −1.05361 | −0.526804 | − | 0.849987i | \(-0.676610\pi\) | ||||
−0.526804 | + | 0.849987i | \(0.676610\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 8.66025i | − | 0.821995i | ||||||
\(112\) | 2.00000 | − | 1.73205i | 0.188982 | − | 0.163663i | ||||
\(113\) | − | 9.00000i | − | 0.846649i | −0.905978 | − | 0.423324i | \(-0.860863\pi\) | ||
0.905978 | − | 0.423324i | \(-0.139137\pi\) | |||||||
\(114\) | − | 12.0000i | − | 1.12390i | ||||||
\(115\) | − | 1.73205i | − | 0.161515i | ||||||
\(116\) | − | 9.00000i | − | 0.835629i | ||||||
\(117\) | − | 5.19615i | − | 0.480384i | ||||||
\(118\) | − | 3.46410i | − | 0.318896i | ||||||
\(119\) | 6.92820 | − | 6.00000i | 0.635107 | − | 0.550019i | ||||
\(120\) | 3.00000 | 0.273861 | ||||||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 21.0000i | 1.89351i | ||||||||
\(124\) | − | 10.3923i | − | 0.933257i | ||||||
\(125\) | −12.1244 | −1.08444 | ||||||||
\(126\) | −5.19615 | − | 6.00000i | −0.462910 | − | 0.534522i | ||||
\(127\) | 17.0000 | 1.50851 | 0.754253 | − | 0.656584i | \(-0.227999\pi\) | ||||
0.754253 | + | 0.656584i | \(0.227999\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 1.73205i | 0.152499i | ||||||||
\(130\) | −3.00000 | −0.263117 | ||||||||
\(131\) | −13.8564 | −1.21064 | −0.605320 | − | 0.795982i | \(-0.706955\pi\) | ||||
−0.605320 | + | 0.795982i | \(0.706955\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.0000 | + | 13.8564i | 1.04053 | + | 1.20150i | ||||
\(134\) | − | 4.00000i | − | 0.345547i | ||||||
\(135\) | − | 9.00000i | − | 0.774597i | ||||||
\(136\) | − | 3.46410i | − | 0.297044i | ||||||
\(137\) | − | 15.0000i | − | 1.28154i | −0.767734 | − | 0.640768i | \(-0.778616\pi\) | ||
0.767734 | − | 0.640768i | \(-0.221384\pi\) | |||||||
\(138\) | 1.73205i | 0.147442i | ||||||||
\(139\) | − | 5.19615i | − | 0.440732i | −0.975417 | − | 0.220366i | \(-0.929275\pi\) | ||
0.975417 | − | 0.220366i | \(-0.0707252\pi\) | |||||||
\(140\) | −3.46410 | + | 3.00000i | −0.292770 | + | 0.253546i | ||||
\(141\) | 15.0000i | 1.26323i | ||||||||
\(142\) | 12.0000 | 1.00702 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | 15.5885i | 1.29455i | ||||||||
\(146\) | −6.92820 | −0.573382 | ||||||||
\(147\) | 12.0000 | + | 1.73205i | 0.989743 | + | 0.142857i | ||||
\(148\) | 5.00000 | 0.410997 | ||||||||
\(149\) | − | 18.0000i | − | 1.47462i | −0.675556 | − | 0.737309i | \(-0.736096\pi\) | ||
0.675556 | − | 0.737309i | \(-0.263904\pi\) | |||||||
\(150\) | 3.46410 | 0.282843 | ||||||||
\(151\) | 19.0000 | 1.54620 | 0.773099 | − | 0.634285i | \(-0.218706\pi\) | ||||
0.773099 | + | 0.634285i | \(0.218706\pi\) | |||||||
\(152\) | 6.92820 | 0.561951 | ||||||||
\(153\) | −10.3923 | −0.840168 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.0000i | 1.44579i | ||||||||
\(156\) | 3.00000 | 0.240192 | ||||||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | − | 10.0000i | − | 0.795557i | ||||||
\(159\) | 20.7846 | 1.64833 | ||||||||
\(160\) | 1.73205i | 0.136931i | ||||||||
\(161\) | −1.73205 | − | 2.00000i | −0.136505 | − | 0.157622i | ||||
\(162\) | 9.00000i | 0.707107i | ||||||||
\(163\) | 14.0000 | 1.09656 | 0.548282 | − | 0.836293i | \(-0.315282\pi\) | ||||
0.548282 | + | 0.836293i | \(0.315282\pi\) | |||||||
\(164\) | −12.1244 | −0.946753 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.46410i | 0.268866i | ||||||||
\(167\) | 17.3205 | 1.34030 | 0.670151 | − | 0.742225i | \(-0.266230\pi\) | ||||
0.670151 | + | 0.742225i | \(0.266230\pi\) | |||||||
\(168\) | 3.46410 | − | 3.00000i | 0.267261 | − | 0.231455i | ||||
\(169\) | 10.0000 | 0.769231 | ||||||||
\(170\) | 6.00000i | 0.460179i | ||||||||
\(171\) | − | 20.7846i | − | 1.58944i | ||||||
\(172\) | −1.00000 | −0.0762493 | ||||||||
\(173\) | −3.46410 | −0.263371 | −0.131685 | − | 0.991292i | \(-0.542039\pi\) | ||||
−0.131685 | + | 0.991292i | \(0.542039\pi\) | |||||||
\(174\) | − | 15.5885i | − | 1.18176i | ||||||
\(175\) | −4.00000 | + | 3.46410i | −0.302372 | + | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 6.00000i | − | 0.450988i | ||||||
\(178\) | − | 3.46410i | − | 0.259645i | ||||||
\(179\) | 21.0000i | 1.56961i | 0.619740 | + | 0.784807i | \(0.287238\pi\) | ||||
−0.619740 | + | 0.784807i | \(0.712762\pi\) | |||||||
\(180\) | 5.19615 | 0.387298 | ||||||||
\(181\) | − | 17.3205i | − | 1.28742i | −0.765268 | − | 0.643712i | \(-0.777394\pi\) | ||
0.765268 | − | 0.643712i | \(-0.222606\pi\) | |||||||
\(182\) | −3.46410 | + | 3.00000i | −0.256776 | + | 0.222375i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −8.66025 | −0.636715 | ||||||||
\(186\) | − | 18.0000i | − | 1.31982i | ||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −8.66025 | −0.631614 | ||||||||
\(189\) | −9.00000 | − | 10.3923i | −0.654654 | − | 0.755929i | ||||
\(190\) | −12.0000 | −0.870572 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | − | 1.73205i | − | 0.125000i | ||||||
\(193\) | −5.00000 | −0.359908 | −0.179954 | − | 0.983675i | \(-0.557595\pi\) | ||||
−0.179954 | + | 0.983675i | \(0.557595\pi\) | |||||||
\(194\) | 12.1244 | 0.870478 | ||||||||
\(195\) | −5.19615 | −0.372104 | ||||||||
\(196\) | −1.00000 | + | 6.92820i | −0.0714286 | + | 0.494872i | ||||
\(197\) | − | 15.0000i | − | 1.06871i | −0.845262 | − | 0.534353i | \(-0.820555\pi\) | ||
0.845262 | − | 0.534353i | \(-0.179445\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.1244i | 0.859473i | 0.902954 | + | 0.429736i | \(0.141394\pi\) | ||||
−0.902954 | + | 0.429736i | \(0.858606\pi\) | |||||||
\(200\) | 2.00000i | 0.141421i | ||||||||
\(201\) | − | 6.92820i | − | 0.488678i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.5885 | + | 18.0000i | 1.09410 | + | 1.26335i | ||||
\(204\) | − | 6.00000i | − | 0.420084i | ||||||
\(205\) | 21.0000 | 1.46670 | ||||||||
\(206\) | 5.19615 | 0.362033 | ||||||||
\(207\) | 3.00000i | 0.208514i | ||||||||
\(208\) | 1.73205i | 0.120096i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −6.00000 | + | 5.19615i | −0.414039 | + | 0.358569i | ||||
\(211\) | −26.0000 | −1.78991 | −0.894957 | − | 0.446153i | \(-0.852794\pi\) | ||||
−0.894957 | + | 0.446153i | \(0.852794\pi\) | |||||||
\(212\) | 12.0000i | 0.824163i | ||||||||
\(213\) | 20.7846 | 1.42414 | ||||||||
\(214\) | −18.0000 | −1.23045 | ||||||||
\(215\) | 1.73205 | 0.118125 | ||||||||
\(216\) | −5.19615 | −0.353553 | ||||||||
\(217\) | 18.0000 | + | 20.7846i | 1.22192 | + | 1.41095i | ||||
\(218\) | − | 11.0000i | − | 0.745014i | ||||||
\(219\) | −12.0000 | −0.810885 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.00000i | 0.403604i | ||||||||
\(222\) | 8.66025 | 0.581238 | ||||||||
\(223\) | 6.92820i | 0.463947i | 0.972722 | + | 0.231973i | \(0.0745182\pi\) | ||||
−0.972722 | + | 0.231973i | \(0.925482\pi\) | |||||||
\(224\) | 1.73205 | + | 2.00000i | 0.115728 | + | 0.133631i | ||||
\(225\) | 6.00000 | 0.400000 | ||||||||
\(226\) | 9.00000 | 0.598671 | ||||||||
\(227\) | −15.5885 | −1.03464 | −0.517321 | − | 0.855791i | \(-0.673071\pi\) | ||||
−0.517321 | + | 0.855791i | \(0.673071\pi\) | |||||||
\(228\) | 12.0000 | 0.794719 | ||||||||
\(229\) | − | 24.2487i | − | 1.60240i | −0.598397 | − | 0.801200i | \(-0.704195\pi\) | ||
0.598397 | − | 0.801200i | \(-0.295805\pi\) | |||||||
\(230\) | 1.73205 | 0.114208 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.00000 | 0.590879 | ||||||||
\(233\) | − | 12.0000i | − | 0.786146i | −0.919507 | − | 0.393073i | \(-0.871412\pi\) | ||
0.919507 | − | 0.393073i | \(-0.128588\pi\) | |||||||
\(234\) | 5.19615 | 0.339683 | ||||||||
\(235\) | 15.0000 | 0.978492 | ||||||||
\(236\) | 3.46410 | 0.225494 | ||||||||
\(237\) | − | 17.3205i | − | 1.12509i | ||||||
\(238\) | 6.00000 | + | 6.92820i | 0.388922 | + | 0.449089i | ||||
\(239\) | − | 6.00000i | − | 0.388108i | −0.980991 | − | 0.194054i | \(-0.937836\pi\) | ||
0.980991 | − | 0.194054i | \(-0.0621637\pi\) | |||||||
\(240\) | 3.00000i | 0.193649i | ||||||||
\(241\) | 15.5885i | 1.00414i | 0.864827 | + | 0.502070i | \(0.167428\pi\) | ||||
−0.864827 | + | 0.502070i | \(0.832572\pi\) | |||||||
\(242\) | 11.0000i | 0.707107i | ||||||||
\(243\) | 15.5885i | 1.00000i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.73205 | − | 12.0000i | 0.110657 | − | 0.766652i | ||||
\(246\) | −21.0000 | −1.33891 | ||||||||
\(247\) | −12.0000 | −0.763542 | ||||||||
\(248\) | 10.3923 | 0.659912 | ||||||||
\(249\) | 6.00000i | 0.380235i | ||||||||
\(250\) | − | 12.1244i | − | 0.766812i | ||||||
\(251\) | 22.5167 | 1.42124 | 0.710620 | − | 0.703577i | \(-0.248415\pi\) | ||||
0.710620 | + | 0.703577i | \(0.248415\pi\) | |||||||
\(252\) | 6.00000 | − | 5.19615i | 0.377964 | − | 0.327327i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 17.0000i | 1.06667i | ||||||||
\(255\) | 10.3923i | 0.650791i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.92820 | −0.432169 | −0.216085 | − | 0.976375i | \(-0.569329\pi\) | ||||
−0.216085 | + | 0.976375i | \(0.569329\pi\) | |||||||
\(258\) | −1.73205 | −0.107833 | ||||||||
\(259\) | −10.0000 | + | 8.66025i | −0.621370 | + | 0.538122i | ||||
\(260\) | − | 3.00000i | − | 0.186052i | ||||||
\(261\) | − | 27.0000i | − | 1.67126i | ||||||
\(262\) | − | 13.8564i | − | 0.856052i | ||||||
\(263\) | 27.0000i | 1.66489i | 0.554107 | + | 0.832446i | \(0.313060\pi\) | ||||
−0.554107 | + | 0.832446i | \(0.686940\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 20.7846i | − | 1.27679i | ||||||
\(266\) | −13.8564 | + | 12.0000i | −0.849591 | + | 0.735767i | ||||
\(267\) | − | 6.00000i | − | 0.367194i | ||||||
\(268\) | 4.00000 | 0.244339 | ||||||||
\(269\) | −13.8564 | −0.844840 | −0.422420 | − | 0.906400i | \(-0.638819\pi\) | ||||
−0.422420 | + | 0.906400i | \(0.638819\pi\) | |||||||
\(270\) | 9.00000 | 0.547723 | ||||||||
\(271\) | − | 20.7846i | − | 1.26258i | −0.775549 | − | 0.631288i | \(-0.782527\pi\) | ||
0.775549 | − | 0.631288i | \(-0.217473\pi\) | |||||||
\(272\) | 3.46410 | 0.210042 | ||||||||
\(273\) | −6.00000 | + | 5.19615i | −0.363137 | + | 0.314485i | ||||
\(274\) | 15.0000 | 0.906183 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.73205 | −0.104257 | ||||||||
\(277\) | −10.0000 | −0.600842 | −0.300421 | − | 0.953807i | \(-0.597127\pi\) | ||||
−0.300421 | + | 0.953807i | \(0.597127\pi\) | |||||||
\(278\) | 5.19615 | 0.311645 | ||||||||
\(279\) | − | 31.1769i | − | 1.86651i | ||||||
\(280\) | −3.00000 | − | 3.46410i | −0.179284 | − | 0.207020i | ||||
\(281\) | − | 9.00000i | − | 0.536895i | −0.963294 | − | 0.268447i | \(-0.913489\pi\) | ||
0.963294 | − | 0.268447i | \(-0.0865106\pi\) | |||||||
\(282\) | −15.0000 | −0.893237 | ||||||||
\(283\) | 3.46410i | 0.205919i | 0.994686 | + | 0.102960i | \(0.0328313\pi\) | ||||
−0.994686 | + | 0.102960i | \(0.967169\pi\) | |||||||
\(284\) | 12.0000i | 0.712069i | ||||||||
\(285\) | −20.7846 | −1.23117 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.2487 | − | 21.0000i | 1.43136 | − | 1.23959i | ||||
\(288\) | − | 3.00000i | − | 0.176777i | ||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | −15.5885 | −0.915386 | ||||||||
\(291\) | 21.0000 | 1.23104 | ||||||||
\(292\) | − | 6.92820i | − | 0.405442i | ||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | −1.73205 | + | 12.0000i | −0.101015 | + | 0.699854i | ||||
\(295\) | −6.00000 | −0.349334 | ||||||||
\(296\) | 5.00000i | 0.290619i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 18.0000 | 1.04271 | ||||||||
\(299\) | 1.73205 | 0.100167 | ||||||||
\(300\) | 3.46410i | 0.200000i | ||||||||
\(301\) | 2.00000 | − | 1.73205i | 0.115278 | − | 0.0998337i | ||||
\(302\) | 19.0000i | 1.09333i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.92820i | 0.397360i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 10.3923i | − | 0.594089i | ||||||
\(307\) | − | 1.73205i | − | 0.0988534i | −0.998778 | − | 0.0494267i | \(-0.984261\pi\) | ||
0.998778 | − | 0.0494267i | \(-0.0157394\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.00000 | 0.511992 | ||||||||
\(310\) | −18.0000 | −1.02233 | ||||||||
\(311\) | 10.3923 | 0.589294 | 0.294647 | − | 0.955606i | \(-0.404798\pi\) | ||||
0.294647 | + | 0.955606i | \(0.404798\pi\) | |||||||
\(312\) | 3.00000i | 0.169842i | ||||||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10.3923 | + | 9.00000i | −0.585540 | + | 0.507093i | ||||
\(316\) | 10.0000 | 0.562544 | ||||||||
\(317\) | 3.00000i | 0.168497i | 0.996445 | + | 0.0842484i | \(0.0268489\pi\) | ||||
−0.996445 | + | 0.0842484i | \(0.973151\pi\) | |||||||
\(318\) | 20.7846i | 1.16554i | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.73205 | −0.0968246 | ||||||||
\(321\) | −31.1769 | −1.74013 | ||||||||
\(322\) | 2.00000 | − | 1.73205i | 0.111456 | − | 0.0965234i | ||||
\(323\) | 24.0000i | 1.33540i | ||||||||
\(324\) | −9.00000 | −0.500000 | ||||||||
\(325\) | − | 3.46410i | − | 0.192154i | ||||||
\(326\) | 14.0000i | 0.775388i | ||||||||
\(327\) | − | 19.0526i | − | 1.05361i | ||||||
\(328\) | − | 12.1244i | − | 0.669456i | ||||||
\(329\) | 17.3205 | − | 15.0000i | 0.954911 | − | 0.826977i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0000 | 0.549650 | 0.274825 | − | 0.961494i | \(-0.411380\pi\) | ||||
0.274825 | + | 0.961494i | \(0.411380\pi\) | |||||||
\(332\) | −3.46410 | −0.190117 | ||||||||
\(333\) | 15.0000 | 0.821995 | ||||||||
\(334\) | 17.3205i | 0.947736i | ||||||||
\(335\) | −6.92820 | −0.378528 | ||||||||
\(336\) | 3.00000 | + | 3.46410i | 0.163663 | + | 0.188982i | ||||
\(337\) | 4.00000 | 0.217894 | 0.108947 | − | 0.994048i | \(-0.465252\pi\) | ||||
0.108947 | + | 0.994048i | \(0.465252\pi\) | |||||||
\(338\) | 10.0000i | 0.543928i | ||||||||
\(339\) | 15.5885 | 0.846649 | ||||||||
\(340\) | −6.00000 | −0.325396 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 20.7846 | 1.12390 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | − | 1.00000i | − | 0.0539164i | ||||||
\(345\) | 3.00000 | 0.161515 | ||||||||
\(346\) | − | 3.46410i | − | 0.186231i | ||||||
\(347\) | − | 9.00000i | − | 0.483145i | −0.970383 | − | 0.241573i | \(-0.922337\pi\) | ||
0.970383 | − | 0.241573i | \(-0.0776632\pi\) | |||||||
\(348\) | 15.5885 | 0.835629 | ||||||||
\(349\) | 13.8564i | 0.741716i | 0.928689 | + | 0.370858i | \(0.120936\pi\) | ||||
−0.928689 | + | 0.370858i | \(0.879064\pi\) | |||||||
\(350\) | −3.46410 | − | 4.00000i | −0.185164 | − | 0.213809i | ||||
\(351\) | 9.00000 | 0.480384 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.19615 | 0.276563 | 0.138282 | − | 0.990393i | \(-0.455842\pi\) | ||||
0.138282 | + | 0.990393i | \(0.455842\pi\) | |||||||
\(354\) | 6.00000 | 0.318896 | ||||||||
\(355\) | − | 20.7846i | − | 1.10313i | ||||||
\(356\) | 3.46410 | 0.183597 | ||||||||
\(357\) | 10.3923 | + | 12.0000i | 0.550019 | + | 0.635107i | ||||
\(358\) | −21.0000 | −1.10988 | ||||||||
\(359\) | − | 15.0000i | − | 0.791670i | −0.918322 | − | 0.395835i | \(-0.870455\pi\) | ||
0.918322 | − | 0.395835i | \(-0.129545\pi\) | |||||||
\(360\) | 5.19615i | 0.273861i | ||||||||
\(361\) | −29.0000 | −1.52632 | ||||||||
\(362\) | 17.3205 | 0.910346 | ||||||||
\(363\) | 19.0526i | 1.00000i | ||||||||
\(364\) | −3.00000 | − | 3.46410i | −0.157243 | − | 0.181568i | ||||
\(365\) | 12.0000i | 0.628109i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.73205i | − | 0.0904123i | −0.998978 | − | 0.0452062i | \(-0.985606\pi\) | ||
0.998978 | − | 0.0452062i | \(-0.0143945\pi\) | |||||||
\(368\) | − | 1.00000i | − | 0.0521286i | ||||||
\(369\) | −36.3731 | −1.89351 | ||||||||
\(370\) | − | 8.66025i | − | 0.450225i | ||||||
\(371\) | −20.7846 | − | 24.0000i | −1.07908 | − | 1.24602i | ||||
\(372\) | 18.0000 | 0.933257 | ||||||||
\(373\) | −10.0000 | −0.517780 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 21.0000i | − | 1.08444i | ||||||
\(376\) | − | 8.66025i | − | 0.446619i | ||||||
\(377\) | −15.5885 | −0.802846 | ||||||||
\(378\) | 10.3923 | − | 9.00000i | 0.534522 | − | 0.462910i | ||||
\(379\) | −11.0000 | −0.565032 | −0.282516 | − | 0.959263i | \(-0.591169\pi\) | ||||
−0.282516 | + | 0.959263i | \(0.591169\pi\) | |||||||
\(380\) | − | 12.0000i | − | 0.615587i | ||||||
\(381\) | 29.4449i | 1.50851i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −27.7128 | −1.41606 | −0.708029 | − | 0.706183i | \(-0.750416\pi\) | ||||
−0.708029 | + | 0.706183i | \(0.750416\pi\) | |||||||
\(384\) | 1.73205 | 0.0883883 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 5.00000i | − | 0.254493i | ||||||
\(387\) | −3.00000 | −0.152499 | ||||||||
\(388\) | 12.1244i | 0.615521i | ||||||||
\(389\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(390\) | − | 5.19615i | − | 0.263117i | ||||||
\(391\) | − | 3.46410i | − | 0.175187i | ||||||
\(392\) | −6.92820 | − | 1.00000i | −0.349927 | − | 0.0505076i | ||||
\(393\) | − | 24.0000i | − | 1.21064i | ||||||
\(394\) | 15.0000 | 0.755689 | ||||||||
\(395\) | −17.3205 | −0.871489 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 13.8564i | − | 0.695433i | −0.937600 | − | 0.347717i | \(-0.886957\pi\) | ||
0.937600 | − | 0.347717i | \(-0.113043\pi\) | |||||||
\(398\) | −12.1244 | −0.607739 | ||||||||
\(399\) | −24.0000 | + | 20.7846i | −1.20150 | + | 1.04053i | ||||
\(400\) | −2.00000 | −0.100000 | ||||||||
\(401\) | 18.0000i | 0.898877i | 0.893311 | + | 0.449439i | \(0.148376\pi\) | ||||
−0.893311 | + | 0.449439i | \(0.851624\pi\) | |||||||
\(402\) | 6.92820 | 0.345547 | ||||||||
\(403\) | −18.0000 | −0.896644 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.5885 | 0.774597 | ||||||||
\(406\) | −18.0000 | + | 15.5885i | −0.893325 | + | 0.773642i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 6.00000 | 0.297044 | ||||||||
\(409\) | 13.8564i | 0.685155i | 0.939490 | + | 0.342578i | \(0.111300\pi\) | ||||
−0.939490 | + | 0.342578i | \(0.888700\pi\) | |||||||
\(410\) | 21.0000i | 1.03712i | ||||||||
\(411\) | 25.9808 | 1.28154 | ||||||||
\(412\) | 5.19615i | 0.255996i | ||||||||
\(413\) | −6.92820 | + | 6.00000i | −0.340915 | + | 0.295241i | ||||
\(414\) | −3.00000 | −0.147442 | ||||||||
\(415\) | 6.00000 | 0.294528 | ||||||||
\(416\) | −1.73205 | −0.0849208 | ||||||||
\(417\) | 9.00000 | 0.440732 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.46410 | 0.169232 | 0.0846162 | − | 0.996414i | \(-0.473034\pi\) | ||||
0.0846162 | + | 0.996414i | \(0.473034\pi\) | |||||||
\(420\) | −5.19615 | − | 6.00000i | −0.253546 | − | 0.292770i | ||||
\(421\) | −19.0000 | −0.926003 | −0.463002 | − | 0.886357i | \(-0.653228\pi\) | ||||
−0.463002 | + | 0.886357i | \(0.653228\pi\) | |||||||
\(422\) | − | 26.0000i | − | 1.26566i | ||||||
\(423\) | −25.9808 | −1.26323 | ||||||||
\(424\) | −12.0000 | −0.582772 | ||||||||
\(425\) | −6.92820 | −0.336067 | ||||||||
\(426\) | 20.7846i | 1.00702i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 18.0000i | − | 0.870063i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.73205i | 0.0835269i | ||||||||
\(431\) | − | 27.0000i | − | 1.30054i | −0.759701 | − | 0.650272i | \(-0.774655\pi\) | ||
0.759701 | − | 0.650272i | \(-0.225345\pi\) | |||||||
\(432\) | − | 5.19615i | − | 0.250000i | ||||||
\(433\) | − | 19.0526i | − | 0.915608i | −0.889053 | − | 0.457804i | \(-0.848636\pi\) | ||
0.889053 | − | 0.457804i | \(-0.151364\pi\) | |||||||
\(434\) | −20.7846 | + | 18.0000i | −0.997693 | + | 0.864028i | ||||
\(435\) | −27.0000 | −1.29455 | ||||||||
\(436\) | 11.0000 | 0.526804 | ||||||||
\(437\) | 6.92820 | 0.331421 | ||||||||
\(438\) | − | 12.0000i | − | 0.573382i | ||||||
\(439\) | 27.7128i | 1.32266i | 0.750095 | + | 0.661330i | \(0.230008\pi\) | ||||
−0.750095 | + | 0.661330i | \(0.769992\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | + | 20.7846i | −0.142857 | + | 0.989743i | ||||
\(442\) | −6.00000 | −0.285391 | ||||||||
\(443\) | 9.00000i | 0.427603i | 0.976877 | + | 0.213801i | \(0.0685846\pi\) | ||||
−0.976877 | + | 0.213801i | \(0.931415\pi\) | |||||||
\(444\) | 8.66025i | 0.410997i | ||||||||
\(445\) | −6.00000 | −0.284427 | ||||||||
\(446\) | −6.92820 | −0.328060 | ||||||||
\(447\) | 31.1769 | 1.47462 | ||||||||
\(448\) | −2.00000 | + | 1.73205i | −0.0944911 | + | 0.0818317i | ||||
\(449\) | − | 24.0000i | − | 1.13263i | −0.824189 | − | 0.566315i | \(-0.808369\pi\) | ||
0.824189 | − | 0.566315i | \(-0.191631\pi\) | |||||||
\(450\) | 6.00000i | 0.282843i | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 9.00000i | 0.423324i | ||||||||
\(453\) | 32.9090i | 1.54620i | ||||||||
\(454\) | − | 15.5885i | − | 0.731603i | ||||||
\(455\) | 5.19615 | + | 6.00000i | 0.243599 | + | 0.281284i | ||||
\(456\) | 12.0000i | 0.561951i | ||||||||
\(457\) | 22.0000 | 1.02912 | 0.514558 | − | 0.857455i | \(-0.327956\pi\) | ||||
0.514558 | + | 0.857455i | \(0.327956\pi\) | |||||||
\(458\) | 24.2487 | 1.13307 | ||||||||
\(459\) | − | 18.0000i | − | 0.840168i | ||||||
\(460\) | 1.73205i | 0.0807573i | ||||||||
\(461\) | 31.1769 | 1.45205 | 0.726027 | − | 0.687666i | \(-0.241365\pi\) | ||||
0.726027 | + | 0.687666i | \(0.241365\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.0000 | 0.790057 | 0.395029 | − | 0.918669i | \(-0.370735\pi\) | ||||
0.395029 | + | 0.918669i | \(0.370735\pi\) | |||||||
\(464\) | 9.00000i | 0.417815i | ||||||||
\(465\) | −31.1769 | −1.44579 | ||||||||
\(466\) | 12.0000 | 0.555889 | ||||||||
\(467\) | 19.0526 | 0.881647 | 0.440824 | − | 0.897594i | \(-0.354686\pi\) | ||||
0.440824 | + | 0.897594i | \(0.354686\pi\) | |||||||
\(468\) | 5.19615i | 0.240192i | ||||||||
\(469\) | −8.00000 | + | 6.92820i | −0.369406 | + | 0.319915i | ||||
\(470\) | 15.0000i | 0.691898i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.46410i | 0.159448i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 17.3205 | 0.795557 | ||||||||
\(475\) | − | 13.8564i | − | 0.635776i | ||||||
\(476\) | −6.92820 | + | 6.00000i | −0.317554 | + | 0.275010i | ||||
\(477\) | 36.0000i | 1.64833i | ||||||||
\(478\) | 6.00000 | 0.274434 | ||||||||
\(479\) | 27.7128 | 1.26623 | 0.633115 | − | 0.774057i | \(-0.281776\pi\) | ||||
0.633115 | + | 0.774057i | \(0.281776\pi\) | |||||||
\(480\) | −3.00000 | −0.136931 | ||||||||
\(481\) | − | 8.66025i | − | 0.394874i | ||||||
\(482\) | −15.5885 | −0.710035 | ||||||||
\(483\) | 3.46410 | − | 3.00000i | 0.157622 | − | 0.136505i | ||||
\(484\) | −11.0000 | −0.500000 | ||||||||
\(485\) | − | 21.0000i | − | 0.953561i | ||||||
\(486\) | −15.5885 | −0.707107 | ||||||||
\(487\) | −29.0000 | −1.31412 | −0.657058 | − | 0.753840i | \(-0.728199\pi\) | ||||
−0.657058 | + | 0.753840i | \(0.728199\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.2487i | 1.09656i | ||||||||
\(490\) | 12.0000 | + | 1.73205i | 0.542105 | + | 0.0782461i | ||||
\(491\) | − | 36.0000i | − | 1.62466i | −0.583200 | − | 0.812329i | \(-0.698200\pi\) | ||
0.583200 | − | 0.812329i | \(-0.301800\pi\) | |||||||
\(492\) | − | 21.0000i | − | 0.946753i | ||||||
\(493\) | 31.1769i | 1.40414i | ||||||||
\(494\) | − | 12.0000i | − | 0.539906i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.3923i | 0.466628i | ||||||||
\(497\) | −20.7846 | − | 24.0000i | −0.932317 | − | 1.07655i | ||||
\(498\) | −6.00000 | −0.268866 | ||||||||
\(499\) | 4.00000 | 0.179065 | 0.0895323 | − | 0.995984i | \(-0.471463\pi\) | ||||
0.0895323 | + | 0.995984i | \(0.471463\pi\) | |||||||
\(500\) | 12.1244 | 0.542218 | ||||||||
\(501\) | 30.0000i | 1.34030i | ||||||||
\(502\) | 22.5167i | 1.00497i | ||||||||
\(503\) | 20.7846 | 0.926740 | 0.463370 | − | 0.886165i | \(-0.346640\pi\) | ||||
0.463370 | + | 0.886165i | \(0.346640\pi\) | |||||||
\(504\) | 5.19615 | + | 6.00000i | 0.231455 | + | 0.267261i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 17.3205i | 0.769231i | ||||||||
\(508\) | −17.0000 | −0.754253 | ||||||||
\(509\) | −24.2487 | −1.07481 | −0.537403 | − | 0.843326i | \(-0.680594\pi\) | ||||
−0.537403 | + | 0.843326i | \(0.680594\pi\) | |||||||
\(510\) | −10.3923 | −0.460179 | ||||||||
\(511\) | 12.0000 | + | 13.8564i | 0.530849 | + | 0.612971i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 36.0000 | 1.58944 | ||||||||
\(514\) | − | 6.92820i | − | 0.305590i | ||||||
\(515\) | − | 9.00000i | − | 0.396587i | ||||||
\(516\) | − | 1.73205i | − | 0.0762493i | ||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −8.66025 | − | 10.0000i | −0.380510 | − | 0.439375i | ||||
\(519\) | − | 6.00000i | − | 0.263371i | ||||||
\(520\) | 3.00000 | 0.131559 | ||||||||
\(521\) | −10.3923 | −0.455295 | −0.227648 | − | 0.973744i | \(-0.573103\pi\) | ||||
−0.227648 | + | 0.973744i | \(0.573103\pi\) | |||||||
\(522\) | 27.0000 | 1.18176 | ||||||||
\(523\) | 3.46410i | 0.151475i | 0.997128 | + | 0.0757373i | \(0.0241310\pi\) | ||||
−0.997128 | + | 0.0757373i | \(0.975869\pi\) | |||||||
\(524\) | 13.8564 | 0.605320 | ||||||||
\(525\) | −6.00000 | − | 6.92820i | −0.261861 | − | 0.302372i | ||||
\(526\) | −27.0000 | −1.17726 | ||||||||
\(527\) | 36.0000i | 1.56818i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 20.7846 | 0.902826 | ||||||||
\(531\) | 10.3923 | 0.450988 | ||||||||
\(532\) | −12.0000 | − | 13.8564i | −0.520266 | − | 0.600751i | ||||
\(533\) | 21.0000i | 0.909611i | ||||||||
\(534\) | 6.00000 | 0.259645 | ||||||||
\(535\) | 31.1769i | 1.34790i | ||||||||
\(536\) | 4.00000i | 0.172774i | ||||||||
\(537\) | −36.3731 | −1.56961 | ||||||||
\(538\) | − | 13.8564i | − | 0.597392i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 9.00000i | 0.387298i | ||||||||
\(541\) | 38.0000 | 1.63375 | 0.816874 | − | 0.576816i | \(-0.195705\pi\) | ||||
0.816874 | + | 0.576816i | \(0.195705\pi\) | |||||||
\(542\) | 20.7846 | 0.892775 | ||||||||
\(543\) | 30.0000 | 1.28742 | ||||||||
\(544\) | 3.46410i | 0.148522i | ||||||||
\(545\) | −19.0526 | −0.816122 | ||||||||
\(546\) | −5.19615 | − | 6.00000i | −0.222375 | − | 0.256776i | ||||
\(547\) | 26.0000 | 1.11168 | 0.555840 | − | 0.831289i | \(-0.312397\pi\) | ||||
0.555840 | + | 0.831289i | \(0.312397\pi\) | |||||||
\(548\) | 15.0000i | 0.640768i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −62.3538 | −2.65636 | ||||||||
\(552\) | − | 1.73205i | − | 0.0737210i | ||||||
\(553\) | −20.0000 | + | 17.3205i | −0.850487 | + | 0.736543i | ||||
\(554\) | − | 10.0000i | − | 0.424859i | ||||||
\(555\) | − | 15.0000i | − | 0.636715i | ||||||
\(556\) | 5.19615i | 0.220366i | ||||||||
\(557\) | 6.00000i | 0.254228i | 0.991888 | + | 0.127114i | \(0.0405714\pi\) | ||||
−0.991888 | + | 0.127114i | \(0.959429\pi\) | |||||||
\(558\) | 31.1769 | 1.31982 | ||||||||
\(559\) | 1.73205i | 0.0732579i | ||||||||
\(560\) | 3.46410 | − | 3.00000i | 0.146385 | − | 0.126773i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.00000 | 0.379642 | ||||||||
\(563\) | −32.9090 | −1.38695 | −0.693474 | − | 0.720482i | \(-0.743921\pi\) | ||||
−0.693474 | + | 0.720482i | \(0.743921\pi\) | |||||||
\(564\) | − | 15.0000i | − | 0.631614i | ||||||
\(565\) | − | 15.5885i | − | 0.655811i | ||||||
\(566\) | −3.46410 | −0.145607 | ||||||||
\(567\) | 18.0000 | − | 15.5885i | 0.755929 | − | 0.654654i | ||||
\(568\) | −12.0000 | −0.503509 | ||||||||
\(569\) | 9.00000i | 0.377300i | 0.982044 | + | 0.188650i | \(0.0604111\pi\) | ||||
−0.982044 | + | 0.188650i | \(0.939589\pi\) | |||||||
\(570\) | − | 20.7846i | − | 0.870572i | ||||||
\(571\) | −28.0000 | −1.17176 | −0.585882 | − | 0.810397i | \(-0.699252\pi\) | ||||
−0.585882 | + | 0.810397i | \(0.699252\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 21.0000 | + | 24.2487i | 0.876523 | + | 1.01212i | ||||
\(575\) | 2.00000i | 0.0834058i | ||||||||
\(576\) | 3.00000 | 0.125000 | ||||||||
\(577\) | − | 13.8564i | − | 0.576850i | −0.957503 | − | 0.288425i | \(-0.906868\pi\) | ||
0.957503 | − | 0.288425i | \(-0.0931316\pi\) | |||||||
\(578\) | − | 5.00000i | − | 0.207973i | ||||||
\(579\) | − | 8.66025i | − | 0.359908i | ||||||
\(580\) | − | 15.5885i | − | 0.647275i | ||||||
\(581\) | 6.92820 | − | 6.00000i | 0.287430 | − | 0.248922i | ||||
\(582\) | 21.0000i | 0.870478i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 6.92820 | 0.286691 | ||||||||
\(585\) | − | 9.00000i | − | 0.372104i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −38.1051 | −1.57277 | −0.786383 | − | 0.617739i | \(-0.788049\pi\) | ||||
−0.786383 | + | 0.617739i | \(0.788049\pi\) | |||||||
\(588\) | −12.0000 | − | 1.73205i | −0.494872 | − | 0.0714286i | ||||
\(589\) | −72.0000 | −2.96671 | ||||||||
\(590\) | − | 6.00000i | − | 0.247016i | ||||||
\(591\) | 25.9808 | 1.06871 | ||||||||
\(592\) | −5.00000 | −0.205499 | ||||||||
\(593\) | 5.19615 | 0.213380 | 0.106690 | − | 0.994292i | \(-0.465975\pi\) | ||||
0.106690 | + | 0.994292i | \(0.465975\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.0000 | − | 10.3923i | 0.491952 | − | 0.426043i | ||||
\(596\) | 18.0000i | 0.737309i | ||||||||
\(597\) | −21.0000 | −0.859473 | ||||||||
\(598\) | 1.73205i | 0.0708288i | ||||||||
\(599\) | − | 18.0000i | − | 0.735460i | −0.929933 | − | 0.367730i | \(-0.880135\pi\) | ||
0.929933 | − | 0.367730i | \(-0.119865\pi\) | |||||||
\(600\) | −3.46410 | −0.141421 | ||||||||
\(601\) | 24.2487i | 0.989126i | 0.869142 | + | 0.494563i | \(0.164672\pi\) | ||||
−0.869142 | + | 0.494563i | \(0.835328\pi\) | |||||||
\(602\) | 1.73205 | + | 2.00000i | 0.0705931 | + | 0.0815139i | ||||
\(603\) | 12.0000 | 0.488678 | ||||||||
\(604\) | −19.0000 | −0.773099 | ||||||||
\(605\) | 19.0526 | 0.774597 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.3205i | 0.703018i | 0.936185 | + | 0.351509i | \(0.114331\pi\) | ||||
−0.936185 | + | 0.351509i | \(0.885669\pi\) | |||||||
\(608\) | −6.92820 | −0.280976 | ||||||||
\(609\) | −31.1769 | + | 27.0000i | −1.26335 | + | 1.09410i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.0000i | 0.606835i | ||||||||
\(612\) | 10.3923 | 0.420084 | ||||||||
\(613\) | −31.0000 | −1.25208 | −0.626039 | − | 0.779792i | \(-0.715325\pi\) | ||||
−0.626039 | + | 0.779792i | \(0.715325\pi\) | |||||||
\(614\) | 1.73205 | 0.0698999 | ||||||||
\(615\) | 36.3731i | 1.46670i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.0000i | 0.724653i | 0.932051 | + | 0.362326i | \(0.118017\pi\) | ||||
−0.932051 | + | 0.362326i | \(0.881983\pi\) | |||||||
\(618\) | 9.00000i | 0.362033i | ||||||||
\(619\) | 6.92820i | 0.278468i | 0.990260 | + | 0.139234i | \(0.0444640\pi\) | ||||
−0.990260 | + | 0.139234i | \(0.955536\pi\) | |||||||
\(620\) | − | 18.0000i | − | 0.722897i | ||||||
\(621\) | −5.19615 | −0.208514 | ||||||||
\(622\) | 10.3923i | 0.416693i | ||||||||
\(623\) | −6.92820 | + | 6.00000i | −0.277573 | + | 0.240385i | ||||
\(624\) | −3.00000 | −0.120096 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −17.3205 | −0.690614 | ||||||||
\(630\) | −9.00000 | − | 10.3923i | −0.358569 | − | 0.414039i | ||||
\(631\) | −28.0000 | −1.11466 | −0.557331 | − | 0.830290i | \(-0.688175\pi\) | ||||
−0.557331 | + | 0.830290i | \(0.688175\pi\) | |||||||
\(632\) | 10.0000i | 0.397779i | ||||||||
\(633\) | − | 45.0333i | − | 1.78991i | ||||||
\(634\) | −3.00000 | −0.119145 | ||||||||
\(635\) | 29.4449 | 1.16848 | ||||||||
\(636\) | −20.7846 | −0.824163 | ||||||||
\(637\) | 12.0000 | + | 1.73205i | 0.475457 | + | 0.0686264i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 36.0000i | 1.42414i | ||||||||
\(640\) | − | 1.73205i | − | 0.0684653i | ||||||
\(641\) | − | 27.0000i | − | 1.06644i | −0.845978 | − | 0.533218i | \(-0.820983\pi\) | ||
0.845978 | − | 0.533218i | \(-0.179017\pi\) | |||||||
\(642\) | − | 31.1769i | − | 1.23045i | ||||||
\(643\) | − | 38.1051i | − | 1.50272i | −0.659893 | − | 0.751360i | \(-0.729398\pi\) | ||
0.659893 | − | 0.751360i | \(-0.270602\pi\) | |||||||
\(644\) | 1.73205 | + | 2.00000i | 0.0682524 | + | 0.0788110i | ||||
\(645\) | 3.00000i | 0.118125i | ||||||||
\(646\) | −24.0000 | −0.944267 | ||||||||
\(647\) | 17.3205 | 0.680939 | 0.340470 | − | 0.940255i | \(-0.389414\pi\) | ||||
0.340470 | + | 0.940255i | \(0.389414\pi\) | |||||||
\(648\) | − | 9.00000i | − | 0.353553i | ||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 3.46410 | 0.135873 | ||||||||
\(651\) | −36.0000 | + | 31.1769i | −1.41095 | + | 1.22192i | ||||
\(652\) | −14.0000 | −0.548282 | ||||||||
\(653\) | − | 21.0000i | − | 0.821794i | −0.911682 | − | 0.410897i | \(-0.865216\pi\) | ||
0.911682 | − | 0.410897i | \(-0.134784\pi\) | |||||||
\(654\) | 19.0526 | 0.745014 | ||||||||
\(655\) | −24.0000 | −0.937758 | ||||||||
\(656\) | 12.1244 | 0.473377 | ||||||||
\(657\) | − | 20.7846i | − | 0.810885i | ||||||
\(658\) | 15.0000 | + | 17.3205i | 0.584761 | + | 0.675224i | ||||
\(659\) | 6.00000i | 0.233727i | 0.993148 | + | 0.116863i | \(0.0372840\pi\) | ||||
−0.993148 | + | 0.116863i | \(0.962716\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 6.92820i | − | 0.269476i | −0.990881 | − | 0.134738i | \(-0.956981\pi\) | ||
0.990881 | − | 0.134738i | \(-0.0430193\pi\) | |||||||
\(662\) | 10.0000i | 0.388661i | ||||||||
\(663\) | −10.3923 | −0.403604 | ||||||||
\(664\) | − | 3.46410i | − | 0.134433i | ||||||
\(665\) | 20.7846 | + | 24.0000i | 0.805993 | + | 0.930680i | ||||
\(666\) | 15.0000i | 0.581238i | ||||||||
\(667\) | 9.00000 | 0.348481 | ||||||||
\(668\) | −17.3205 | −0.670151 | ||||||||
\(669\) | −12.0000 | −0.463947 | ||||||||
\(670\) | − | 6.92820i | − | 0.267660i | ||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −3.46410 | + | 3.00000i | −0.133631 | + | 0.115728i | ||||
\(673\) | 25.0000 | 0.963679 | 0.481840 | − | 0.876259i | \(-0.339969\pi\) | ||||
0.481840 | + | 0.876259i | \(0.339969\pi\) | |||||||
\(674\) | 4.00000i | 0.154074i | ||||||||
\(675\) | 10.3923i | 0.400000i | ||||||||
\(676\) | −10.0000 | −0.384615 | ||||||||
\(677\) | 27.7128 | 1.06509 | 0.532545 | − | 0.846402i | \(-0.321236\pi\) | ||||
0.532545 | + | 0.846402i | \(0.321236\pi\) | |||||||
\(678\) | 15.5885i | 0.598671i | ||||||||
\(679\) | −21.0000 | − | 24.2487i | −0.805906 | − | 0.930580i | ||||
\(680\) | − | 6.00000i | − | 0.230089i | ||||||
\(681\) | − | 27.0000i | − | 1.03464i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.0000i | 0.459167i | 0.973289 | + | 0.229584i | \(0.0737364\pi\) | ||||
−0.973289 | + | 0.229584i | \(0.926264\pi\) | |||||||
\(684\) | 20.7846i | 0.794719i | ||||||||
\(685\) | − | 25.9808i | − | 0.992674i | ||||||
\(686\) | 15.5885 | − | 10.0000i | 0.595170 | − | 0.381802i | ||||
\(687\) | 42.0000 | 1.60240 | ||||||||
\(688\) | 1.00000 | 0.0381246 | ||||||||
\(689\) | 20.7846 | 0.791831 | ||||||||
\(690\) | 3.00000i | 0.114208i | ||||||||
\(691\) | 43.3013i | 1.64726i | 0.567129 | + | 0.823629i | \(0.308054\pi\) | ||||
−0.567129 | + | 0.823629i | \(0.691946\pi\) | |||||||
\(692\) | 3.46410 | 0.131685 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.00000 | 0.341635 | ||||||||
\(695\) | − | 9.00000i | − | 0.341389i | ||||||
\(696\) | 15.5885i | 0.590879i | ||||||||
\(697\) | 42.0000 | 1.59086 | ||||||||
\(698\) | −13.8564 | −0.524473 | ||||||||
\(699\) | 20.7846 | 0.786146 | ||||||||
\(700\) | 4.00000 | − | 3.46410i | 0.151186 | − | 0.130931i | ||||
\(701\) | 6.00000i | 0.226617i | 0.993560 | + | 0.113308i | \(0.0361448\pi\) | ||||
−0.993560 | + | 0.113308i | \(0.963855\pi\) | |||||||
\(702\) | 9.00000i | 0.339683i | ||||||||
\(703\) | − | 34.6410i | − | 1.30651i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 25.9808i | 0.978492i | ||||||||
\(706\) | 5.19615i | 0.195560i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 6.00000i | 0.225494i | ||||||||
\(709\) | 22.0000 | 0.826227 | 0.413114 | − | 0.910679i | \(-0.364441\pi\) | ||||
0.413114 | + | 0.910679i | \(0.364441\pi\) | |||||||
\(710\) | 20.7846 | 0.780033 | ||||||||
\(711\) | 30.0000 | 1.12509 | ||||||||
\(712\) | 3.46410i | 0.129823i | ||||||||
\(713\) | 10.3923 | 0.389195 | ||||||||
\(714\) | −12.0000 | + | 10.3923i | −0.449089 | + | 0.388922i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 21.0000i | − | 0.784807i | ||||||
\(717\) | 10.3923 | 0.388108 | ||||||||
\(718\) | 15.0000 | 0.559795 | ||||||||
\(719\) | −12.1244 | −0.452162 | −0.226081 | − | 0.974108i | \(-0.572591\pi\) | ||||
−0.226081 | + | 0.974108i | \(0.572591\pi\) | |||||||
\(720\) | −5.19615 | −0.193649 | ||||||||
\(721\) | −9.00000 | − | 10.3923i | −0.335178 | − | 0.387030i | ||||
\(722\) | − | 29.0000i | − | 1.07927i | ||||||
\(723\) | −27.0000 | −1.00414 | ||||||||
\(724\) | 17.3205i | 0.643712i | ||||||||
\(725\) | − | 18.0000i | − | 0.668503i | ||||||
\(726\) | −19.0526 | −0.707107 | ||||||||
\(727\) | − | 31.1769i | − | 1.15629i | −0.815935 | − | 0.578144i | \(-0.803777\pi\) | ||
0.815935 | − | 0.578144i | \(-0.196223\pi\) | |||||||
\(728\) | 3.46410 | − | 3.00000i | 0.128388 | − | 0.111187i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | −12.0000 | −0.444140 | ||||||||
\(731\) | 3.46410 | 0.128124 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 3.46410i | − | 0.127950i | −0.997952 | − | 0.0639748i | \(-0.979622\pi\) | ||
0.997952 | − | 0.0639748i | \(-0.0203777\pi\) | |||||||
\(734\) | 1.73205 | 0.0639312 | ||||||||
\(735\) | 20.7846 | + | 3.00000i | 0.766652 | + | 0.110657i | ||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | − | 36.3731i | − | 1.33891i | ||||||
\(739\) | 20.0000 | 0.735712 | 0.367856 | − | 0.929883i | \(-0.380092\pi\) | ||||
0.367856 | + | 0.929883i | \(0.380092\pi\) | |||||||
\(740\) | 8.66025 | 0.318357 | ||||||||
\(741\) | − | 20.7846i | − | 0.763542i | ||||||
\(742\) | 24.0000 | − | 20.7846i | 0.881068 | − | 0.763027i | ||||
\(743\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(744\) | 18.0000i | 0.659912i | ||||||||
\(745\) | − | 31.1769i | − | 1.14223i | ||||||
\(746\) | − | 10.0000i | − | 0.366126i | ||||||
\(747\) | −10.3923 | −0.380235 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 31.1769 | + | 36.0000i | 1.13918 | + | 1.31541i | ||||
\(750\) | 21.0000 | 0.766812 | ||||||||
\(751\) | −14.0000 | −0.510867 | −0.255434 | − | 0.966827i | \(-0.582218\pi\) | ||||
−0.255434 | + | 0.966827i | \(0.582218\pi\) | |||||||
\(752\) | 8.66025 | 0.315807 | ||||||||
\(753\) | 39.0000i | 1.42124i | ||||||||
\(754\) | − | 15.5885i | − | 0.567698i | ||||||
\(755\) | 32.9090 | 1.19768 | ||||||||
\(756\) | 9.00000 | + | 10.3923i | 0.327327 | + | 0.377964i | ||||
\(757\) | 10.0000 | 0.363456 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(758\) | − | 11.0000i | − | 0.399538i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12.0000 | 0.435286 | ||||||||
\(761\) | −27.7128 | −1.00459 | −0.502294 | − | 0.864697i | \(-0.667511\pi\) | ||||
−0.502294 | + | 0.864697i | \(0.667511\pi\) | |||||||
\(762\) | −29.4449 | −1.06667 | ||||||||
\(763\) | −22.0000 | + | 19.0526i | −0.796453 | + | 0.689749i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18.0000 | −0.650791 | ||||||||
\(766\) | − | 27.7128i | − | 1.00130i | ||||||
\(767\) | − | 6.00000i | − | 0.216647i | ||||||
\(768\) | 1.73205i | 0.0625000i | ||||||||
\(769\) | 8.66025i | 0.312297i | 0.987734 | + | 0.156148i | \(0.0499078\pi\) | ||||
−0.987734 | + | 0.156148i | \(0.950092\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 12.0000i | − | 0.432169i | ||||||
\(772\) | 5.00000 | 0.179954 | ||||||||
\(773\) | 1.73205 | 0.0622975 | 0.0311488 | − | 0.999515i | \(-0.490083\pi\) | ||||
0.0311488 | + | 0.999515i | \(0.490083\pi\) | |||||||
\(774\) | − | 3.00000i | − | 0.107833i | ||||||
\(775\) | − | 20.7846i | − | 0.746605i | ||||||
\(776\) | −12.1244 | −0.435239 | ||||||||
\(777\) | −15.0000 | − | 17.3205i | −0.538122 | − | 0.621370i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 84.0000i | 3.00961i | ||||||||
\(780\) | 5.19615 | 0.186052 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 3.46410 | 0.123876 | ||||||||
\(783\) | 46.7654 | 1.67126 | ||||||||
\(784\) | 1.00000 | − | 6.92820i | 0.0357143 | − | 0.247436i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 24.0000 | 0.856052 | ||||||||
\(787\) | − | 17.3205i | − | 0.617409i | −0.951158 | − | 0.308705i | \(-0.900105\pi\) | ||
0.951158 | − | 0.308705i | \(-0.0998955\pi\) | |||||||
\(788\) | 15.0000i | 0.534353i | ||||||||
\(789\) | −46.7654 | −1.66489 | ||||||||
\(790\) | − | 17.3205i | − | 0.616236i | ||||||
\(791\) | −15.5885 | − | 18.0000i | −0.554262 | − | 0.640006i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 13.8564 | 0.491745 | ||||||||
\(795\) | 36.0000 | 1.27679 | ||||||||
\(796\) | − | 12.1244i | − | 0.429736i | ||||||
\(797\) | −15.5885 | −0.552171 | −0.276086 | − | 0.961133i | \(-0.589037\pi\) | ||||
−0.276086 | + | 0.961133i | \(0.589037\pi\) | |||||||
\(798\) | −20.7846 | − | 24.0000i | −0.735767 | − | 0.849591i | ||||
\(799\) | 30.0000 | 1.06132 | ||||||||
\(800\) | − | 2.00000i | − | 0.0707107i | ||||||
\(801\) | 10.3923 | 0.367194 | ||||||||
\(802\) | −18.0000 | −0.635602 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 6.92820i | 0.244339i | ||||||||
\(805\) | −3.00000 | − | 3.46410i | −0.105736 | − | 0.122094i | ||||
\(806\) | − | 18.0000i | − | 0.634023i | ||||||
\(807\) | − | 24.0000i | − | 0.844840i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 48.0000i | − | 1.68759i | −0.536666 | − | 0.843795i | \(-0.680316\pi\) | ||
0.536666 | − | 0.843795i | \(-0.319684\pi\) | |||||||
\(810\) | 15.5885i | 0.547723i | ||||||||
\(811\) | − | 1.73205i | − | 0.0608205i | −0.999538 | − | 0.0304103i | \(-0.990319\pi\) | ||
0.999538 | − | 0.0304103i | \(-0.00968138\pi\) | |||||||
\(812\) | −15.5885 | − | 18.0000i | −0.547048 | − | 0.631676i | ||||
\(813\) | 36.0000 | 1.26258 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.2487 | 0.849395 | ||||||||
\(816\) | 6.00000i | 0.210042i | ||||||||
\(817\) | 6.92820i | 0.242387i | ||||||||
\(818\) | −13.8564 | −0.484478 | ||||||||
\(819\) | −9.00000 | − | 10.3923i | −0.314485 | − | 0.363137i | ||||
\(820\) | −21.0000 | −0.733352 | ||||||||
\(821\) | − | 6.00000i | − | 0.209401i | −0.994504 | − | 0.104701i | \(-0.966612\pi\) | ||
0.994504 | − | 0.104701i | \(-0.0333885\pi\) | |||||||
\(822\) | 25.9808i | 0.906183i | ||||||||
\(823\) | −31.0000 | −1.08059 | −0.540296 | − | 0.841475i | \(-0.681688\pi\) | ||||
−0.540296 | + | 0.841475i | \(0.681688\pi\) | |||||||
\(824\) | −5.19615 | −0.181017 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.00000 | − | 6.92820i | −0.208767 | − | 0.241063i | ||||
\(827\) | − | 30.0000i | − | 1.04320i | −0.853189 | − | 0.521601i | \(-0.825335\pi\) | ||
0.853189 | − | 0.521601i | \(-0.174665\pi\) | |||||||
\(828\) | − | 3.00000i | − | 0.104257i | ||||||
\(829\) | − | 6.92820i | − | 0.240626i | −0.992736 | − | 0.120313i | \(-0.961610\pi\) | ||
0.992736 | − | 0.120313i | \(-0.0383899\pi\) | |||||||
\(830\) | 6.00000i | 0.208263i | ||||||||
\(831\) | − | 17.3205i | − | 0.600842i | ||||||
\(832\) | − | 1.73205i | − | 0.0600481i | ||||||
\(833\) | 3.46410 | − | 24.0000i | 0.120024 | − | 0.831551i | ||||
\(834\) | 9.00000i | 0.311645i | ||||||||
\(835\) | 30.0000 | 1.03819 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 54.0000 | 1.86651 | ||||||||
\(838\) | 3.46410i | 0.119665i | ||||||||
\(839\) | 45.0333 | 1.55472 | 0.777361 | − | 0.629054i | \(-0.216558\pi\) | ||||
0.777361 | + | 0.629054i | \(0.216558\pi\) | |||||||
\(840\) | 6.00000 | − | 5.19615i | 0.207020 | − | 0.179284i | ||||
\(841\) | −52.0000 | −1.79310 | ||||||||
\(842\) | − | 19.0000i | − | 0.654783i | ||||||
\(843\) | 15.5885 | 0.536895 | ||||||||
\(844\) | 26.0000 | 0.894957 | ||||||||
\(845\) | 17.3205 | 0.595844 | ||||||||
\(846\) | − | 25.9808i | − | 0.893237i | ||||||
\(847\) | 22.0000 | − | 19.0526i | 0.755929 | − | 0.654654i | ||||
\(848\) | − | 12.0000i | − | 0.412082i | ||||||
\(849\) | −6.00000 | −0.205919 | ||||||||
\(850\) | − | 6.92820i | − | 0.237635i | ||||||
\(851\) | 5.00000i | 0.171398i | ||||||||
\(852\) | −20.7846 | −0.712069 | ||||||||
\(853\) | 22.5167i | 0.770956i | 0.922717 | + | 0.385478i | \(0.125963\pi\) | ||||
−0.922717 | + | 0.385478i | \(0.874037\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 36.0000i | − | 1.23117i | ||||||
\(856\) | 18.0000 | 0.615227 | ||||||||
\(857\) | 50.2295 | 1.71581 | 0.857903 | − | 0.513812i | \(-0.171767\pi\) | ||||
0.857903 | + | 0.513812i | \(0.171767\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 8.66025i | − | 0.295484i | −0.989026 | − | 0.147742i | \(-0.952799\pi\) | ||
0.989026 | − | 0.147742i | \(-0.0472005\pi\) | |||||||
\(860\) | −1.73205 | −0.0590624 | ||||||||
\(861\) | 36.3731 | + | 42.0000i | 1.23959 | + | 1.43136i | ||||
\(862\) | 27.0000 | 0.919624 | ||||||||
\(863\) | 48.0000i | 1.63394i | 0.576681 | + | 0.816970i | \(0.304348\pi\) | ||||
−0.576681 | + | 0.816970i | \(0.695652\pi\) | |||||||
\(864\) | 5.19615 | 0.176777 | ||||||||
\(865\) | −6.00000 | −0.204006 | ||||||||
\(866\) | 19.0526 | 0.647432 | ||||||||
\(867\) | − | 8.66025i | − | 0.294118i | ||||||
\(868\) | −18.0000 | − | 20.7846i | −0.610960 | − | 0.705476i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | − | 27.0000i | − | 0.915386i | ||||||
\(871\) | − | 6.92820i | − | 0.234753i | ||||||
\(872\) | 11.0000i | 0.372507i | ||||||||
\(873\) | 36.3731i | 1.23104i | ||||||||
\(874\) | 6.92820i | 0.234350i | ||||||||
\(875\) | −24.2487 | + | 21.0000i | −0.819756 | + | 0.709930i | ||||
\(876\) | 12.0000 | 0.405442 | ||||||||
\(877\) | 32.0000 | 1.08056 | 0.540282 | − | 0.841484i | \(-0.318318\pi\) | ||||
0.540282 | + | 0.841484i | \(0.318318\pi\) | |||||||
\(878\) | −27.7128 | −0.935262 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.46410 | −0.116709 | −0.0583543 | − | 0.998296i | \(-0.518585\pi\) | ||||
−0.0583543 | + | 0.998296i | \(0.518585\pi\) | |||||||
\(882\) | −20.7846 | − | 3.00000i | −0.699854 | − | 0.101015i | ||||
\(883\) | 10.0000 | 0.336527 | 0.168263 | − | 0.985742i | \(-0.446184\pi\) | ||||
0.168263 | + | 0.985742i | \(0.446184\pi\) | |||||||
\(884\) | − | 6.00000i | − | 0.201802i | ||||||
\(885\) | − | 10.3923i | − | 0.349334i | ||||||
\(886\) | −9.00000 | −0.302361 | ||||||||
\(887\) | 51.9615 | 1.74470 | 0.872349 | − | 0.488884i | \(-0.162596\pi\) | ||||
0.872349 | + | 0.488884i | \(0.162596\pi\) | |||||||
\(888\) | −8.66025 | −0.290619 | ||||||||
\(889\) | 34.0000 | − | 29.4449i | 1.14032 | − | 0.987549i | ||||
\(890\) | − | 6.00000i | − | 0.201120i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 6.92820i | − | 0.231973i | ||||||
\(893\) | 60.0000i | 2.00782i | ||||||||
\(894\) | 31.1769i | 1.04271i | ||||||||
\(895\) | 36.3731i | 1.21582i | ||||||||
\(896\) | −1.73205 | − | 2.00000i | −0.0578638 | − | 0.0668153i | ||||
\(897\) | 3.00000i | 0.100167i | ||||||||
\(898\) | 24.0000 | 0.800890 | ||||||||
\(899\) | −93.5307 | −3.11942 | ||||||||
\(900\) | −6.00000 | −0.200000 | ||||||||
\(901\) | − | 41.5692i | − | 1.38487i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.00000 | + | 3.46410i | 0.0998337 | + | 0.115278i | ||||
\(904\) | −9.00000 | −0.299336 | ||||||||
\(905\) | − | 30.0000i | − | 0.997234i | ||||||
\(906\) | −32.9090 | −1.09333 | ||||||||
\(907\) | 37.0000 | 1.22856 | 0.614282 | − | 0.789086i | \(-0.289446\pi\) | ||||
0.614282 | + | 0.789086i | \(0.289446\pi\) | |||||||
\(908\) | 15.5885 | 0.517321 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.00000 | + | 5.19615i | −0.198898 | + | 0.172251i | ||||
\(911\) | 9.00000i | 0.298183i | 0.988823 | + | 0.149092i | \(0.0476349\pi\) | ||||
−0.988823 | + | 0.149092i | \(0.952365\pi\) | |||||||
\(912\) | −12.0000 | −0.397360 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 22.0000i | 0.727695i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24.2487i | 0.801200i | ||||||||
\(917\) | −27.7128 | + | 24.0000i | −0.915158 | + | 0.792550i | ||||
\(918\) | 18.0000 | 0.594089 | ||||||||
\(919\) | −26.0000 | −0.857661 | −0.428830 | − | 0.903385i | \(-0.641074\pi\) | ||||
−0.428830 | + | 0.903385i | \(0.641074\pi\) | |||||||
\(920\) | −1.73205 | −0.0571040 | ||||||||
\(921\) | 3.00000 | 0.0988534 | ||||||||
\(922\) | 31.1769i | 1.02676i | ||||||||
\(923\) | 20.7846 | 0.684134 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.0000 | 0.328798 | ||||||||
\(926\) | 17.0000i | 0.558655i | ||||||||
\(927\) | 15.5885i | 0.511992i | ||||||||
\(928\) | −9.00000 | −0.295439 | ||||||||
\(929\) | −50.2295 | −1.64798 | −0.823988 | − | 0.566608i | \(-0.808256\pi\) | ||||
−0.823988 | + | 0.566608i | \(0.808256\pi\) | |||||||
\(930\) | − | 31.1769i | − | 1.02233i | ||||||
\(931\) | 48.0000 | + | 6.92820i | 1.57314 | + | 0.227063i | ||||
\(932\) | 12.0000i | 0.393073i | ||||||||
\(933\) | 18.0000i | 0.589294i | ||||||||
\(934\) | 19.0526i | 0.623419i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.19615 | −0.169842 | ||||||||
\(937\) | 5.19615i | 0.169751i | 0.996392 | + | 0.0848755i | \(0.0270492\pi\) | ||||
−0.996392 | + | 0.0848755i | \(0.972951\pi\) | |||||||
\(938\) | −6.92820 | − | 8.00000i | −0.226214 | − | 0.261209i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −15.0000 | −0.489246 | ||||||||
\(941\) | 39.8372 | 1.29865 | 0.649327 | − | 0.760509i | \(-0.275051\pi\) | ||||
0.649327 | + | 0.760509i | \(0.275051\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 12.1244i | − | 0.394823i | ||||||
\(944\) | −3.46410 | −0.112747 | ||||||||
\(945\) | −15.5885 | − | 18.0000i | −0.507093 | − | 0.585540i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.0000i | 0.877382i | 0.898638 | + | 0.438691i | \(0.144558\pi\) | ||||
−0.898638 | + | 0.438691i | \(0.855442\pi\) | |||||||
\(948\) | 17.3205i | 0.562544i | ||||||||
\(949\) | −12.0000 | −0.389536 | ||||||||
\(950\) | 13.8564 | 0.449561 | ||||||||
\(951\) | −5.19615 | −0.168497 | ||||||||
\(952\) | −6.00000 | − | 6.92820i | −0.194461 | − | 0.224544i | ||||
\(953\) | 42.0000i | 1.36051i | 0.732974 | + | 0.680257i | \(0.238132\pi\) | ||||
−0.732974 | + | 0.680257i | \(0.761868\pi\) | |||||||
\(954\) | −36.0000 | −1.16554 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.00000i | 0.194054i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 27.7128i | 0.895360i | ||||||||
\(959\) | −25.9808 | − | 30.0000i | −0.838963 | − | 0.968751i | ||||
\(960\) | − | 3.00000i | − | 0.0968246i | ||||||
\(961\) | −77.0000 | −2.48387 | ||||||||
\(962\) | 8.66025 | 0.279218 | ||||||||
\(963\) | − | 54.0000i | − | 1.74013i | ||||||
\(964\) | − | 15.5885i | − | 0.502070i | ||||||
\(965\) | −8.66025 | −0.278783 | ||||||||
\(966\) | 3.00000 | + | 3.46410i | 0.0965234 | + | 0.111456i | ||||
\(967\) | 8.00000 | 0.257263 | 0.128631 | − | 0.991692i | \(-0.458942\pi\) | ||||
0.128631 | + | 0.991692i | \(0.458942\pi\) | |||||||
\(968\) | − | 11.0000i | − | 0.353553i | ||||||
\(969\) | −41.5692 | −1.33540 | ||||||||
\(970\) | 21.0000 | 0.674269 | ||||||||
\(971\) | −10.3923 | −0.333505 | −0.166752 | − | 0.985999i | \(-0.553328\pi\) | ||||
−0.166752 | + | 0.985999i | \(0.553328\pi\) | |||||||
\(972\) | − | 15.5885i | − | 0.500000i | ||||||
\(973\) | −9.00000 | − | 10.3923i | −0.288527 | − | 0.333162i | ||||
\(974\) | − | 29.0000i | − | 0.929220i | ||||||
\(975\) | 6.00000 | 0.192154 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 57.0000i | − | 1.82359i | −0.410644 | − | 0.911796i | \(-0.634696\pi\) | ||
0.410644 | − | 0.911796i | \(-0.365304\pi\) | |||||||
\(978\) | −24.2487 | −0.775388 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.73205 | + | 12.0000i | −0.0553283 | + | 0.383326i | ||||
\(981\) | 33.0000 | 1.05361 | ||||||||
\(982\) | 36.0000 | 1.14881 | ||||||||
\(983\) | 17.3205 | 0.552438 | 0.276219 | − | 0.961095i | \(-0.410918\pi\) | ||||
0.276219 | + | 0.961095i | \(0.410918\pi\) | |||||||
\(984\) | 21.0000 | 0.669456 | ||||||||
\(985\) | − | 25.9808i | − | 0.827816i | ||||||
\(986\) | −31.1769 | −0.992875 | ||||||||
\(987\) | 25.9808 | + | 30.0000i | 0.826977 | + | 0.954911i | ||||
\(988\) | 12.0000 | 0.381771 | ||||||||
\(989\) | − | 1.00000i | − | 0.0317982i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.00000 | −0.254128 | −0.127064 | − | 0.991894i | \(-0.540555\pi\) | ||||
−0.127064 | + | 0.991894i | \(0.540555\pi\) | |||||||
\(992\) | −10.3923 | −0.329956 | ||||||||
\(993\) | 17.3205i | 0.549650i | ||||||||
\(994\) | 24.0000 | − | 20.7846i | 0.761234 | − | 0.659248i | ||||
\(995\) | 21.0000i | 0.665745i | ||||||||
\(996\) | − | 6.00000i | − | 0.190117i | ||||||
\(997\) | − | 6.92820i | − | 0.219418i | −0.993964 | − | 0.109709i | \(-0.965008\pi\) | ||
0.993964 | − | 0.109709i | \(-0.0349920\pi\) | |||||||
\(998\) | 4.00000i | 0.126618i | ||||||||
\(999\) | 25.9808i | 0.821995i |
(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 | 966.2.f.a.461.4 | yes | 4 | |
3.2 | odd | 2 | inner | 966.2.f.a.461.2 | yes | 4 | |
7.6 | odd | 2 | inner | 966.2.f.a.461.3 | yes | 4 | |
21.20 | even | 2 | inner | 966.2.f.a.461.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.f.a.461.1 | ✓ | 4 | 21.20 | even | 2 | inner | |
966.2.f.a.461.2 | yes | 4 | 3.2 | odd | 2 | inner | |
966.2.f.a.461.3 | yes | 4 | 7.6 | odd | 2 | inner | |
966.2.f.a.461.4 | yes | 4 | 1.1 | even | 1 | trivial |