Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,3,Mod(161,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.i (of order \(4\), 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: | \(10.4632421514\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + \cdots + 1048576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{23} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 161.3 | ||
Root | \(1.28499 + 1.53258i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.161 |
Dual form | 384.3.i.c.353.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −2.17774 | − | 2.06336i | −0.725914 | − | 0.687785i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.17955 | − | 3.17955i | −0.635909 | − | 0.635909i | 0.313634 | − | 0.949544i | \(-0.398453\pi\) |
−0.949544 | + | 0.313634i | \(0.898453\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.03979i | 0.862827i | 0.902154 | + | 0.431414i | \(0.141985\pi\) | ||||
−0.902154 | + | 0.431414i | \(0.858015\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.485128 | + | 8.98692i | 0.0539031 | + | 0.998546i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.0097 | + | 13.0097i | 1.18270 | + | 1.18270i | 0.979042 | + | 0.203657i | \(0.0652828\pi\) |
0.203657 | + | 0.979042i | \(0.434717\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.39520 | − | 6.39520i | −0.491939 | − | 0.491939i | 0.416978 | − | 0.908917i | \(-0.363089\pi\) |
−0.908917 | + | 0.416978i | \(0.863089\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.363700 | + | 13.4848i | 0.0242466 | + | 0.898985i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.39848i | − | 0.258734i | −0.991597 | − | 0.129367i | \(-0.958705\pi\) | ||
0.991597 | − | 0.129367i | \(-0.0412945\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.21075 | − | 3.21075i | −0.168987 | − | 0.168987i | 0.617547 | − | 0.786534i | \(-0.288126\pi\) |
−0.786534 | + | 0.617547i | \(0.788126\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.4622 | − | 13.1531i | 0.593440 | − | 0.626339i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 34.0396 | 1.47998 | 0.739992 | − | 0.672616i | \(-0.234829\pi\) | ||||
0.739992 | + | 0.672616i | \(0.234829\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 4.78097i | − | 0.191239i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 17.4867 | − | 20.5722i | 0.647656 | − | 0.761933i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 27.9597 | − | 27.9597i | 0.964128 | − | 0.964128i | −0.0352510 | − | 0.999378i | \(-0.511223\pi\) |
0.999378 | + | 0.0352510i | \(0.0112231\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.90993 | 0.255159 | 0.127580 | − | 0.991828i | \(-0.459279\pi\) | ||||
0.127580 | + | 0.991828i | \(0.459279\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.48814 | − | 55.1754i | −0.0450952 | − | 1.67198i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 19.2038 | − | 19.2038i | 0.548680 | − | 0.548680i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −20.0443 | + | 20.0443i | −0.541736 | + | 0.541736i | −0.924038 | − | 0.382301i | \(-0.875132\pi\) |
0.382301 | + | 0.924038i | \(0.375132\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.731530 | + | 27.1227i | 0.0187572 | + | 0.695453i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 45.1067 | 1.10016 | 0.550081 | − | 0.835111i | \(-0.314597\pi\) | ||||
0.550081 | + | 0.835111i | \(0.314597\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −36.0095 | + | 36.0095i | −0.837431 | + | 0.837431i | −0.988520 | − | 0.151089i | \(-0.951722\pi\) |
0.151089 | + | 0.988520i | \(0.451722\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 27.0318 | − | 30.1168i | 0.600707 | − | 0.669262i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 5.08935i | − | 0.108284i | −0.998533 | − | 0.0541421i | \(-0.982758\pi\) | ||
0.998533 | − | 0.0541421i | \(-0.0172424\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.5209 | 0.255529 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.07563 | + | 9.57876i | −0.177953 | + | 0.187819i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 20.7687 | + | 20.7687i | 0.391863 | + | 0.391863i | 0.875351 | − | 0.483488i | \(-0.160630\pi\) |
−0.483488 | + | 0.875351i | \(0.660630\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 82.7299i | − | 1.50418i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.367268 | + | 13.6171i | 0.00644331 | + | 0.238896i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 39.0656 | + | 39.0656i | 0.662129 | + | 0.662129i | 0.955881 | − | 0.293753i | \(-0.0949043\pi\) |
−0.293753 | + | 0.955881i | \(0.594904\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 49.8322 | + | 49.8322i | 0.816921 | + | 0.816921i | 0.985661 | − | 0.168739i | \(-0.0539696\pi\) |
−0.168739 | + | 0.985661i | \(0.553970\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −54.2791 | + | 2.93007i | −0.861573 | + | 0.0465090i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 40.6677i | 0.625657i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 44.9162 | + | 44.9162i | 0.670390 | + | 0.670390i | 0.957806 | − | 0.287416i | \(-0.0927961\pi\) |
−0.287416 | + | 0.957806i | \(0.592796\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −74.1295 | − | 70.2358i | −1.07434 | − | 1.01791i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 46.6947 | 0.657672 | 0.328836 | − | 0.944387i | \(-0.393344\pi\) | ||||
0.328836 | + | 0.944387i | \(0.393344\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 97.3523i | − | 1.33359i | −0.745240 | − | 0.666797i | \(-0.767665\pi\) | ||
0.745240 | − | 0.666797i | \(-0.232335\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.86483 | + | 10.4117i | −0.131531 | + | 0.138823i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −78.5758 | + | 78.5758i | −1.02047 | + | 1.02047i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 40.1637 | 0.508402 | 0.254201 | − | 0.967151i | \(-0.418188\pi\) | ||||
0.254201 | + | 0.967151i | \(0.418188\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −80.5293 | + | 8.71960i | −0.994189 | + | 0.107649i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 35.5451 | − | 35.5451i | 0.428254 | − | 0.428254i | −0.459779 | − | 0.888033i | \(-0.652071\pi\) |
0.888033 | + | 0.459779i | \(0.152071\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.9852 | + | 13.9852i | −0.164531 | + | 0.164531i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −118.580 | + | 3.19823i | −1.36299 | + | 0.0367613i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −69.6795 | −0.782916 | −0.391458 | − | 0.920196i | \(-0.628029\pi\) | ||||
−0.391458 | + | 0.920196i | \(0.628029\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 38.6257 | − | 38.6257i | 0.424458 | − | 0.424458i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −17.2258 | − | 16.3210i | −0.185224 | − | 0.175495i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 20.4174i | 0.214920i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 61.0939 | 0.629834 | 0.314917 | − | 0.949119i | \(-0.398023\pi\) | ||||
0.314917 | + | 0.949119i | \(0.398023\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −110.606 | + | 123.228i | −1.11723 | + | 1.24473i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 104.036 | + | 104.036i | 1.03006 | + | 1.03006i | 0.999534 | + | 0.0305280i | \(0.00971886\pi\) |
0.0305280 | + | 0.999534i | \(0.490281\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 57.2961i | 0.556272i | 0.960542 | + | 0.278136i | \(0.0897167\pi\) | ||||
−0.960542 | + | 0.278136i | \(0.910283\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −81.4452 | + | 2.19667i | −0.775668 | + | 0.0209207i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −92.4468 | − | 92.4468i | −0.863989 | − | 0.863989i | 0.127810 | − | 0.991799i | \(-0.459205\pi\) |
−0.991799 | + | 0.127810i | \(0.959205\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −75.3749 | − | 75.3749i | −0.691513 | − | 0.691513i | 0.271052 | − | 0.962565i | \(-0.412629\pi\) |
−0.962565 | + | 0.271052i | \(0.912629\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 85.0096 | − | 2.29281i | 0.765853 | − | 0.0206559i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 112.254i | 0.993401i | 0.867922 | + | 0.496701i | \(0.165455\pi\) | ||||
−0.867922 | + | 0.496701i | \(0.834545\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −108.231 | − | 108.231i | −0.941135 | − | 0.941135i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 54.3707 | − | 60.5756i | 0.464706 | − | 0.517740i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 26.5659 | 0.223243 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 217.504i | 1.79756i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −98.2307 | − | 93.0711i | −0.798624 | − | 0.756676i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −94.6900 | + | 94.6900i | −0.757520 | + | 0.757520i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −93.6335 | −0.737272 | −0.368636 | − | 0.929574i | \(-0.620175\pi\) | ||||
−0.368636 | + | 0.929574i | \(0.620175\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 152.720 | − | 4.11903i | 1.18388 | − | 0.0319305i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 81.5208 | − | 81.5208i | 0.622296 | − | 0.622296i | −0.323822 | − | 0.946118i | \(-0.604968\pi\) |
0.946118 | + | 0.323822i | \(0.104968\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.3922 | − | 19.3922i | 0.145806 | − | 0.145806i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −121.010 | + | 9.81037i | −0.896371 | + | 0.0726694i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 24.5510 | 0.179205 | 0.0896023 | − | 0.995978i | \(-0.471440\pi\) | ||||
0.0896023 | + | 0.995978i | \(0.471440\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.06917 | − | 3.06917i | 0.0220804 | − | 0.0220804i | −0.695980 | − | 0.718061i | \(-0.745030\pi\) |
0.718061 | + | 0.695980i | \(0.245030\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.5011 | + | 11.0833i | −0.0744762 | + | 0.0786050i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 166.399i | − | 1.16363i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −177.798 | −1.22620 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −27.2674 | − | 25.8351i | −0.185492 | − | 0.175749i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.86344 | + | 5.86344i | 0.0393519 | + | 0.0393519i | 0.726509 | − | 0.687157i | \(-0.241142\pi\) |
−0.687157 | + | 0.726509i | \(0.741142\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 179.561i | 1.18914i | 0.804043 | + | 0.594571i | \(0.202678\pi\) | ||||
−0.804043 | + | 0.594571i | \(0.797322\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 39.5288 | − | 2.13382i | 0.258358 | − | 0.0139466i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −25.1500 | − | 25.1500i | −0.162258 | − | 0.162258i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.8689 | + | 14.8689i | 0.0947067 | + | 0.0947067i | 0.752873 | − | 0.658166i | \(-0.228668\pi\) |
−0.658166 | + | 0.752873i | \(0.728668\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.37568 | − | 88.0822i | −0.0149414 | − | 0.553976i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 205.592i | 1.27697i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 66.1190 | + | 66.1190i | 0.405638 | + | 0.405638i | 0.880214 | − | 0.474577i | \(-0.157399\pi\) |
−0.474577 | + | 0.880214i | \(0.657399\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −170.701 | + | 180.164i | −1.03455 | + | 1.09191i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −158.709 | −0.950353 | −0.475176 | − | 0.879891i | \(-0.657616\pi\) | ||||
−0.475176 | + | 0.879891i | \(0.657616\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 87.2028i | − | 0.515993i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 27.2971 | − | 30.4123i | 0.159632 | − | 0.177850i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 76.9955 | − | 76.9955i | 0.445061 | − | 0.445061i | −0.448648 | − | 0.893709i | \(-0.648094\pi\) |
0.893709 | + | 0.448648i | \(0.148094\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 28.8760 | 0.165006 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.46861 | − | 165.681i | −0.0252464 | − | 0.936051i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −101.360 | + | 101.360i | −0.566257 | + | 0.566257i | −0.931078 | − | 0.364821i | \(-0.881130\pi\) |
0.364821 | + | 0.931078i | \(0.381130\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 212.373 | − | 212.373i | 1.17333 | − | 1.17333i | 0.191920 | − | 0.981411i | \(-0.438529\pi\) |
0.981411 | − | 0.191920i | \(-0.0614714\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.70017 | − | 211.343i | −0.0311485 | − | 1.15488i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 127.463 | 0.688991 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 57.2229 | − | 57.2229i | 0.306005 | − | 0.306005i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 124.252 | + | 105.616i | 0.657416 | + | 0.558815i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 36.3314i | − | 0.190217i | −0.995467 | − | 0.0951083i | \(-0.969680\pi\) | ||
0.995467 | − | 0.0951083i | \(-0.0303197\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 47.1090 | 0.244088 | 0.122044 | − | 0.992525i | \(-0.461055\pi\) | ||||
0.122044 | + | 0.992525i | \(0.461055\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 83.9119 | − | 88.5638i | 0.430317 | − | 0.454173i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −32.2783 | − | 32.2783i | −0.163849 | − | 0.163849i | 0.620420 | − | 0.784269i | \(-0.286962\pi\) |
−0.784269 | + | 0.620420i | \(0.786962\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 118.181i | − | 0.593874i | −0.954897 | − | 0.296937i | \(-0.904035\pi\) | ||
0.954897 | − | 0.296937i | \(-0.0959651\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.13784 | − | 190.494i | −0.0255614 | − | 0.947731i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 168.871 | + | 168.871i | 0.831875 | + | 0.831875i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −143.419 | − | 143.419i | −0.699604 | − | 0.699604i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.5136 | + | 305.911i | 0.0797756 | + | 1.47783i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 83.5416i | − | 0.399721i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 63.8884 | + | 63.8884i | 0.302789 | + | 0.302789i | 0.842104 | − | 0.539315i | \(-0.181317\pi\) |
−0.539315 | + | 0.842104i | \(0.681317\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −101.689 | − | 96.3478i | −0.477413 | − | 0.452337i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 228.988 | 1.06506 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 47.7743i | 0.220158i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −200.872 | + | 212.008i | −0.917226 | + | 0.968075i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −28.1292 | + | 28.1292i | −0.127281 | + | 0.127281i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 42.8886 | 0.192326 | 0.0961628 | − | 0.995366i | \(-0.469343\pi\) | ||||
0.0961628 | + | 0.995366i | \(0.469343\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 42.9661 | − | 2.31938i | 0.190961 | − | 0.0103084i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.0035 | + | 23.0035i | −0.101337 | + | 0.101337i | −0.755958 | − | 0.654621i | \(-0.772828\pi\) |
0.654621 | + | 0.755958i | \(0.272828\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −241.282 | + | 241.282i | −1.05363 | + | 1.05363i | −0.0551571 | + | 0.998478i | \(0.517566\pi\) |
−0.998478 | + | 0.0551571i | \(0.982434\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 333.248 | − | 8.98807i | 1.44263 | − | 0.0389094i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −240.310 | −1.03137 | −0.515687 | − | 0.856777i | \(-0.672463\pi\) | ||||
−0.515687 | + | 0.856777i | \(0.672463\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.1818 | + | 16.1818i | −0.0688589 | + | 0.0688589i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −87.4663 | − | 82.8721i | −0.369056 | − | 0.349671i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 218.171i | 0.912851i | 0.889762 | + | 0.456425i | \(0.150870\pi\) | ||||
−0.889762 | + | 0.456425i | \(0.849130\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −88.9611 | −0.369133 | −0.184567 | − | 0.982820i | \(-0.559088\pi\) | ||||
−0.184567 | + | 0.982820i | \(0.559088\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 193.364 | + | 147.172i | 0.795736 | + | 0.605644i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −39.8109 | − | 39.8109i | −0.162493 | − | 0.162493i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 41.0667i | 0.166262i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −150.750 | + | 4.06591i | −0.605423 | + | 0.0163289i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 169.225 | + | 169.225i | 0.674205 | + | 0.674205i | 0.958683 | − | 0.284478i | \(-0.0918201\pi\) |
−0.284478 | + | 0.958683i | \(0.591820\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 442.845 | + | 442.845i | 1.75038 | + | 1.75038i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 59.3125 | − | 1.59973i | 0.232598 | − | 0.00627343i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 393.109i | − | 1.52961i | −0.644262 | − | 0.764804i | \(-0.722836\pi\) | ||
0.644262 | − | 0.764804i | \(-0.277164\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −121.063 | − | 121.063i | −0.467425 | − | 0.467425i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 264.835 | + | 237.707i | 1.01470 | + | 0.910756i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 179.865 | 0.683897 | 0.341948 | − | 0.939719i | \(-0.388913\pi\) | ||||
0.341948 | + | 0.939719i | \(0.388913\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 132.070i | − | 0.498378i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 151.744 | + | 143.774i | 0.568330 | + | 0.538478i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 290.530 | − | 290.530i | 1.08004 | − | 1.08004i | 0.0835324 | − | 0.996505i | \(-0.473380\pi\) |
0.996505 | − | 0.0835324i | \(-0.0266202\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −496.550 | −1.83229 | −0.916144 | − | 0.400849i | \(-0.868715\pi\) | ||||
−0.916144 | + | 0.400849i | \(0.868715\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −163.815 | + | 4.41829i | −0.600056 | + | 0.0161842i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 62.1989 | − | 62.1989i | 0.226178 | − | 0.226178i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 93.0101 | − | 93.0101i | 0.335776 | − | 0.335776i | −0.518999 | − | 0.854775i | \(-0.673695\pi\) |
0.854775 | + | 0.518999i | \(0.173695\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.83733 | + | 71.0859i | 0.0137539 | + | 0.254788i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 300.875 | 1.07073 | 0.535365 | − | 0.844621i | \(-0.320174\pi\) | ||||
0.535365 | + | 0.844621i | \(0.320174\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 101.469 | − | 101.469i | 0.358549 | − | 0.358549i | −0.504729 | − | 0.863278i | \(-0.668408\pi\) |
0.863278 | + | 0.504729i | \(0.168408\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 42.1284 | − | 44.4639i | 0.147819 | − | 0.156014i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 272.435i | 0.949250i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 269.653 | 0.933057 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −133.047 | − | 126.058i | −0.457205 | − | 0.433190i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −321.104 | − | 321.104i | −1.09592 | − | 1.09592i | −0.994883 | − | 0.101037i | \(-0.967784\pi\) |
−0.101037 | − | 0.994883i | \(-0.532216\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 248.422i | − | 0.842107i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 495.135 | − | 40.1409i | 1.66712 | − | 0.135155i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −217.690 | − | 217.690i | −0.728061 | − | 0.728061i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −217.490 | − | 217.490i | −0.722558 | − | 0.722558i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.9004 | − | 441.228i | −0.0392753 | − | 1.45620i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 316.888i | − | 1.03898i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 94.2282 | + | 94.2282i | 0.306932 | + | 0.306932i | 0.843718 | − | 0.536786i | \(-0.180362\pi\) |
−0.536786 | + | 0.843718i | \(0.680362\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 118.222 | − | 124.776i | 0.382596 | − | 0.403806i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −245.712 | −0.790070 | −0.395035 | − | 0.918666i | \(-0.629268\pi\) | ||||
−0.395035 | + | 0.918666i | \(0.629268\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 353.841i | 1.13048i | 0.824925 | + | 0.565242i | \(0.191217\pi\) | ||||
−0.824925 | + | 0.565242i | \(0.808783\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 181.899 | + | 163.267i | 0.577458 | + | 0.518307i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 234.024 | − | 234.024i | 0.738245 | − | 0.738245i | −0.233994 | − | 0.972238i | \(-0.575179\pi\) |
0.972238 | + | 0.233994i | \(0.0751795\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 727.494 | 2.28055 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.5747 | + | 392.076i | 0.0329431 | + | 1.22142i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.1224 | + | 14.1224i | −0.0437226 | + | 0.0437226i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −30.5752 | + | 30.5752i | −0.0940777 | + | 0.0940777i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.62193 | + | 319.673i | 0.0263668 | + | 0.977592i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 30.7386 | 0.0934305 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.5392 | + | 32.5392i | −0.0983058 | + | 0.0983058i | −0.754549 | − | 0.656243i | \(-0.772144\pi\) |
0.656243 | + | 0.754549i | \(0.272144\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −189.860 | − | 170.412i | −0.570150 | − | 0.511748i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 285.626i | − | 0.852615i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −185.573 | −0.550660 | −0.275330 | − | 0.961350i | \(-0.588787\pi\) | ||||
−0.275330 | + | 0.961350i | \(0.588787\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 231.621 | − | 244.461i | 0.683247 | − | 0.721124i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 102.906 | + | 102.906i | 0.301776 | + | 0.301776i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 371.574i | 1.08330i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.3802 | + | 459.016i | 0.0358846 | + | 1.33048i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −51.9585 | − | 51.9585i | −0.149736 | − | 0.149736i | 0.628264 | − | 0.778000i | \(-0.283766\pi\) |
−0.778000 | + | 0.628264i | \(0.783766\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −378.719 | − | 378.719i | −1.08515 | − | 1.08515i | −0.996020 | − | 0.0891344i | \(-0.971590\pi\) |
−0.0891344 | − | 0.996020i | \(-0.528410\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −243.394 | + | 19.7322i | −0.693431 | + | 0.0562170i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 326.435i | − | 0.924744i | −0.886686 | − | 0.462372i | \(-0.846998\pi\) | ||
0.886686 | − | 0.462372i | \(-0.153002\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −148.468 | − | 148.468i | −0.418220 | − | 0.418220i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −57.8537 | − | 54.8149i | −0.162055 | − | 0.153543i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −254.927 | −0.710103 | −0.355051 | − | 0.934847i | \(-0.615537\pi\) | ||||
−0.355051 | + | 0.934847i | \(0.615537\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 340.382i | − | 0.942887i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 448.789 | − | 473.668i | 1.23633 | − | 1.30487i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −309.536 | + | 309.536i | −0.848045 | + | 0.848045i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 124.247 | 0.338548 | 0.169274 | − | 0.985569i | \(-0.445858\pi\) | ||||
0.169274 | + | 0.985569i | \(0.445858\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 21.8825 | + | 405.370i | 0.0593021 | + | 1.09856i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −125.439 | + | 125.439i | −0.338110 | + | 0.338110i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 201.674 | − | 201.674i | 0.540680 | − | 0.540680i | −0.383048 | − | 0.923728i | \(-0.625126\pi\) |
0.923728 | + | 0.383048i | \(0.125126\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 401.589 | − | 10.8313i | 1.07091 | − | 0.0288835i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −357.616 | −0.948583 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −227.541 | + | 227.541i | −0.600372 | + | 0.600372i | −0.940411 | − | 0.340040i | \(-0.889560\pi\) |
0.340040 | + | 0.940411i | \(0.389560\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 203.910 | + | 193.199i | 0.535196 | + | 0.507084i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 128.933i | 0.336641i | 0.985732 | + | 0.168320i | \(0.0538343\pi\) | ||||
−0.985732 | + | 0.168320i | \(0.946166\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 499.671 | 1.29785 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −341.084 | − | 306.145i | −0.881353 | − | 0.791073i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 107.474 | + | 107.474i | 0.276283 | + | 0.276283i | 0.831623 | − | 0.555340i | \(-0.187412\pi\) |
−0.555340 | + | 0.831623i | \(0.687412\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 149.723i | − | 0.382922i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −345.738 | + | 9.32494i | −0.879739 | + | 0.0237276i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −127.702 | − | 127.702i | −0.323297 | − | 0.323297i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 259.306 | + | 259.306i | 0.653163 | + | 0.653163i | 0.953753 | − | 0.300591i | \(-0.0971837\pi\) |
−0.300591 | + | 0.953753i | \(0.597184\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −82.2444 | + | 2.21822i | −0.206126 | + | 0.00555946i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 335.810i | 0.837431i | 0.908117 | + | 0.418716i | \(0.137520\pi\) | ||||
−0.908117 | + | 0.418716i | \(0.862480\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −50.5856 | − | 50.5856i | −0.125523 | − | 0.125523i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 283.771 | + | 228.322i | 0.700669 | + | 0.563759i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −521.539 | −1.28142 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 66.3618i | − | 0.162254i | −0.996704 | − | 0.0811269i | \(-0.974148\pi\) | ||
0.996704 | − | 0.0811269i | \(-0.0258519\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −53.4658 | − | 50.6575i | −0.130087 | − | 0.123254i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −235.948 | + | 235.948i | −0.571303 | + | 0.571303i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −226.035 | −0.544662 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.0167 | + | 0.351074i | −0.0312150 | + | 0.000841904i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −371.566 | + | 371.566i | −0.886792 | + | 0.886792i | −0.994214 | − | 0.107422i | \(-0.965740\pi\) |
0.107422 | + | 0.994214i | \(0.465740\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −487.629 | + | 487.629i | −1.15826 | + | 1.15826i | −0.173416 | + | 0.984849i | \(0.555481\pi\) |
−0.984849 | + | 0.173416i | \(0.944519\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 45.7376 | − | 2.46899i | 0.108127 | − | 0.00583685i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −21.0290 | −0.0494800 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −300.976 | + | 300.976i | −0.704862 | + | 0.704862i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −343.341 | + | 362.375i | −0.800328 | + | 0.844696i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 505.901i | 1.17378i | 0.809665 | + | 0.586892i | \(0.199649\pi\) | ||||
−0.809665 | + | 0.586892i | \(0.800351\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −758.226 | −1.75110 | −0.875550 | − | 0.483128i | \(-0.839500\pi\) | ||||
−0.875550 | + | 0.483128i | \(0.839500\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 387.199 | + | 366.861i | 0.890113 | + | 0.843359i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −109.293 | − | 109.293i | −0.250097 | − | 0.250097i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 145.760i | − | 0.332026i | −0.986124 | − | 0.166013i | \(-0.946911\pi\) | ||
0.986124 | − | 0.166013i | \(-0.0530895\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.07425 | + | 112.525i | 0.0137738 | + | 0.255158i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −607.046 | − | 607.046i | −1.37031 | − | 1.37031i | −0.859983 | − | 0.510323i | \(-0.829526\pi\) |
−0.510323 | − | 0.859983i | \(-0.670474\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 221.549 | + | 221.549i | 0.497864 | + | 0.497864i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.670702 | − | 24.8674i | −0.00150045 | − | 0.0556318i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 190.654i | 0.424620i | 0.977202 | + | 0.212310i | \(0.0680986\pi\) | ||||
−0.977202 | + | 0.212310i | \(0.931901\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 586.824 | + | 586.824i | 1.30116 | + | 1.30116i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 370.497 | − | 391.037i | 0.817875 | − | 0.863216i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −245.624 | −0.539834 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 128.091i | − | 0.280287i | −0.990131 | − | 0.140143i | \(-0.955244\pi\) | ||
0.990131 | − | 0.140143i | \(-0.0447563\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −90.4863 | − | 76.9150i | −0.197138 | − | 0.167571i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −74.2060 | + | 74.2060i | −0.160968 | + | 0.160968i | −0.782995 | − | 0.622028i | \(-0.786309\pi\) |
0.622028 | + | 0.782995i | \(0.286309\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −620.192 | −1.33951 | −0.669753 | − | 0.742584i | \(-0.733600\pi\) | ||||
−0.669753 | + | 0.742584i | \(0.733600\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.87684 | + | 106.664i | 0.00618675 | + | 0.229384i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −331.708 | + | 331.708i | −0.710296 | + | 0.710296i | −0.966597 | − | 0.256301i | \(-0.917496\pi\) |
0.256301 | + | 0.966597i | \(0.417496\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −271.284 | + | 271.284i | −0.578431 | + | 0.578431i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.70082 | − | 63.0607i | −0.00361108 | − | 0.133887i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −936.946 | −1.98086 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.3505 | + | 15.3505i | −0.0323168 | + | 0.0323168i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −176.571 | + | 196.722i | −0.370170 | + | 0.412415i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 867.941i | − | 1.81198i | −0.423294 | − | 0.905992i | \(-0.639126\pi\) | ||
0.423294 | − | 0.905992i | \(-0.360874\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 256.374 | 0.533002 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 424.210 | − | 447.727i | 0.878281 | − | 0.926970i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −194.251 | − | 194.251i | −0.400517 | − | 0.400517i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 815.778i | − | 1.67511i | −0.546354 | − | 0.837554i | \(-0.683985\pi\) | ||
0.546354 | − | 0.837554i | \(-0.316015\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.56317 | − | 280.417i | −0.0154666 | − | 0.573450i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 337.746 | + | 337.746i | 0.687874 | + | 0.687874i | 0.961762 | − | 0.273888i | \(-0.0883098\pi\) |
−0.273888 | + | 0.961762i | \(0.588310\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −122.980 | − | 122.980i | −0.249453 | − | 0.249453i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 743.486 | − | 40.1345i | 1.50199 | − | 0.0810799i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 282.026i | 0.567457i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −515.289 | − | 515.289i | −1.03264 | − | 1.03264i | −0.999449 | − | 0.0331940i | \(-0.989432\pi\) |
−0.0331940 | − | 0.999449i | \(-0.510568\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 345.627 | + | 327.473i | 0.689875 | + | 0.653639i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −196.781 | −0.391215 | −0.195607 | − | 0.980682i | \(-0.562668\pi\) | ||||
−0.195607 | + | 0.980682i | \(0.562668\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 661.576i | − | 1.31005i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −179.930 | + | 189.905i | −0.354892 | + | 0.374567i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 29.3054 | − | 29.3054i | 0.0575744 | − | 0.0575744i | −0.677733 | − | 0.735308i | \(-0.737038\pi\) |
0.735308 | + | 0.677733i | \(0.237038\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 587.988 | 1.15066 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −122.197 | + | 9.90664i | −0.238202 | + | 0.0193112i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 182.175 | − | 182.175i | 0.353739 | − | 0.353739i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 66.2109 | − | 66.2109i | 0.128068 | − | 0.128068i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −326.546 | + | 8.80731i | −0.629182 | + | 0.0169698i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 770.641 | 1.47916 | 0.739578 | − | 0.673071i | \(-0.235025\pi\) | ||||
0.739578 | + | 0.673071i | \(0.235025\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 258.725 | − | 258.725i | 0.494694 | − | 0.494694i | −0.415087 | − | 0.909782i | \(-0.636249\pi\) |
0.909782 | + | 0.415087i | \(0.136249\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −62.8846 | − | 59.5815i | −0.119780 | − | 0.113489i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 34.7917i | − | 0.0660183i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 629.695 | 1.19035 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −332.127 | + | 370.031i | −0.625475 | + | 0.696857i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −288.466 | − | 288.466i | −0.541212 | − | 0.541212i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 587.878i | 1.09884i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 429.878 | − | 11.5943i | 0.800517 | − | 0.0215909i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 162.894 | + | 162.894i | 0.302214 | + | 0.302214i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 122.667 | + | 122.667i | 0.226742 | + | 0.226742i | 0.811330 | − | 0.584588i | \(-0.198744\pi\) |
−0.584588 | + | 0.811330i | \(0.698744\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −900.694 | + | 24.2927i | −1.65874 | + | 0.0447380i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 479.316i | 0.879479i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 334.075 | + | 334.075i | 0.610740 | + | 0.610740i | 0.943139 | − | 0.332399i | \(-0.107858\pi\) |
−0.332399 | + | 0.943139i | \(0.607858\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −423.663 | + | 472.013i | −0.771699 | + | 0.859768i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −179.543 | −0.325849 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 242.581i | 0.438663i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −277.582 | − | 263.002i | −0.500148 | − | 0.473878i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 159.480 | − | 159.480i | 0.286320 | − | 0.286320i | −0.549303 | − | 0.835623i | \(-0.685107\pi\) |
0.835623 | + | 0.549303i | \(0.185107\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 460.576 | 0.823929 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −242.688 | + | 6.54557i | −0.432599 | + | 0.0116677i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 341.226 | − | 341.226i | 0.606086 | − | 0.606086i | −0.335835 | − | 0.941921i | \(-0.609018\pi\) |
0.941921 | + | 0.335835i | \(0.109018\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 356.918 | − | 356.918i | 0.631713 | − | 0.631713i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −52.6646 | − | 486.380i | −0.0928828 | − | 0.857813i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 882.975 | 1.55180 | 0.775901 | − | 0.630855i | \(-0.217296\pi\) | ||||
0.775901 | + | 0.630855i | \(0.217296\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 370.112 | − | 370.112i | 0.648181 | − | 0.648181i | −0.304372 | − | 0.952553i | \(-0.598447\pi\) |
0.952553 | + | 0.304372i | \(0.0984466\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −74.9645 | + | 79.1204i | −0.130828 | + | 0.138081i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 162.742i | − | 0.283030i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −698.607 | −1.21076 | −0.605378 | − | 0.795938i | \(-0.706978\pi\) | ||||
−0.605378 | + | 0.795938i | \(0.706978\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −102.591 | − | 97.2025i | −0.177187 | − | 0.167880i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 214.685 | + | 214.685i | 0.369509 | + | 0.369509i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 540.389i | 0.926911i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −365.477 | + | 19.7290i | −0.624747 | + | 0.0337248i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −196.072 | − | 196.072i | −0.334024 | − | 0.334024i | 0.520088 | − | 0.854112i | \(-0.325899\pi\) |
−0.854112 | + | 0.520088i | \(0.825899\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −25.3968 | − | 25.3968i | −0.0431185 | − | 0.0431185i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.69222 | + | 136.895i | 0.00624742 | + | 0.231633i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 774.011i | − | 1.30525i | −0.757683 | − | 0.652623i | \(-0.773669\pi\) | ||
0.757683 | − | 0.652623i | \(-0.226331\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −84.4675 | − | 84.4675i | −0.141962 | − | 0.141962i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −243.849 | + | 257.368i | −0.408458 | + | 0.431102i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 783.533 | 1.30807 | 0.654034 | − | 0.756465i | \(-0.273075\pi\) | ||||
0.654034 | + | 0.756465i | \(0.273075\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 797.210i | 1.32647i | 0.748410 | + | 0.663236i | \(0.230818\pi\) | ||||
−0.748410 | + | 0.663236i | \(0.769182\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −381.868 | + | 425.448i | −0.633280 | + | 0.705552i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 691.565 | − | 691.565i | 1.14308 | − | 1.14308i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −433.576 | −0.714293 | −0.357146 | − | 0.934048i | \(-0.616250\pi\) | ||||
−0.357146 | + | 0.934048i | \(0.616250\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −19.3167 | − | 716.197i | −0.0317186 | − | 1.17602i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −32.5475 | + | 32.5475i | −0.0532692 | + | 0.0532692i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 493.642 | − | 493.642i | 0.805289 | − | 0.805289i | −0.178628 | − | 0.983917i | \(-0.557166\pi\) |
0.983917 | + | 0.178628i | \(0.0571658\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.4053 | + | 608.253i | 0.0266752 | + | 0.989029i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −685.069 | −1.11032 | −0.555161 | − | 0.831743i | \(-0.687343\pi\) | ||||
−0.555161 | + | 0.831743i | \(0.687343\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −379.995 | + | 379.995i | −0.613885 | + | 0.613885i | −0.943956 | − | 0.330071i | \(-0.892927\pi\) |
0.330071 | + | 0.943956i | \(0.392927\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 595.241 | − | 700.269i | 0.958520 | − | 1.12765i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 420.850i | − | 0.675521i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 482.618 | 0.772189 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −172.376 | + | 181.932i | −0.274922 | + | 0.290163i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 88.1642 | + | 88.1642i | 0.140166 | + | 0.140166i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 489.285i | − | 0.775412i | −0.921783 | − | 0.387706i | \(-0.873268\pi\) | ||
0.921783 | − | 0.387706i | \(-0.126732\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.30802 | − | 270.957i | −0.0115451 | − | 0.428052i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 297.712 | + | 297.712i | 0.468838 | + | 0.468838i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −80.0739 | − | 80.0739i | −0.125705 | − | 0.125705i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 22.6529 | + | 419.641i | 0.0354505 | + | 0.656716i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 492.158i | − | 0.767797i | −0.923375 | − | 0.383898i | \(-0.874581\pi\) | ||
0.923375 | − | 0.383898i | \(-0.125419\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −169.985 | − | 169.985i | −0.264362 | − | 0.264362i | 0.562462 | − | 0.826823i | \(-0.309854\pi\) |
−0.826823 | + | 0.562462i | \(0.809854\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −498.677 | − | 472.483i | −0.773142 | − | 0.732532i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1003.50 | 1.55101 | 0.775503 | − | 0.631343i | \(-0.217496\pi\) | ||||
0.775503 | + | 0.631343i | \(0.217496\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1016.46i | 1.56620i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 98.5754 | − | 104.040i | 0.151422 | − | 0.159816i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −407.090 | + | 407.090i | −0.623415 | + | 0.623415i | −0.946403 | − | 0.322988i | \(-0.895313\pi\) |
0.322988 | + | 0.946403i | \(0.395313\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −518.398 | −0.791448 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 874.897 | − | 47.2283i | 1.33165 | − | 0.0718848i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 635.355 | − | 635.355i | 0.964119 | − | 0.964119i | −0.0352587 | − | 0.999378i | \(-0.511226\pi\) |
0.999378 | + | 0.0352587i | \(0.0112255\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 196.325 | − | 196.325i | 0.297013 | − | 0.297013i | −0.542830 | − | 0.839843i | \(-0.682647\pi\) |
0.839843 | + | 0.542830i | \(0.182647\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 119.299 | − | 3.21762i | 0.179937 | − | 0.00485312i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −123.317 | −0.185439 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 951.737 | − | 951.737i | 1.42689 | − | 1.42689i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −93.4003 | − | 88.4944i | −0.139612 | − | 0.132279i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1296.60i | 1.93234i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −489.653 | −0.727568 | −0.363784 | − | 0.931483i | \(-0.618515\pi\) | ||||
−0.363784 | + | 0.931483i | \(0.618515\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −98.3549 | − | 83.6034i | −0.145711 | − | 0.123857i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 832.940 | + | 832.940i | 1.23034 | + | 1.23034i | 0.963833 | + | 0.266507i | \(0.0858695\pi\) |
0.266507 | + | 0.963833i | \(0.414131\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 368.994i | 0.543438i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 97.5600 | − | 2.63131i | 0.143260 | − | 0.00386388i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 773.804 | + | 773.804i | 1.13295 | + | 1.13295i | 0.989684 | + | 0.143264i | \(0.0457599\pi\) |
0.143264 | + | 0.989684i | \(0.454240\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −78.0611 | − | 78.0611i | −0.113958 | − | 0.113958i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1023.30 | − | 27.5996i | 1.48952 | − | 0.0401741i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 265.640i | − | 0.385545i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −840.306 | − | 840.306i | −1.21607 | − | 1.21607i | −0.968996 | − | 0.247077i | \(-0.920530\pi\) |
−0.247077 | − | 0.968996i | \(-0.579470\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −744.274 | − | 668.035i | −1.07399 | − | 0.963975i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.5171 | −0.0280822 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 198.401i | − | 0.284650i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 523.334 | + | 495.845i | 0.748689 | + | 0.709364i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −529.432 | + | 529.432i | −0.755253 | + | 0.755253i | −0.975454 | − | 0.220201i | \(-0.929329\pi\) |
0.220201 | + | 0.975454i | \(0.429329\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 128.714 | 0.183092 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 68.6288 | − | 1.85100i | 0.0973458 | − | 0.00262553i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −628.357 | + | 628.357i | −0.888765 | + | 0.888765i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 56.2182 | − | 56.2182i | 0.0792923 | − | 0.0792923i | −0.666348 | − | 0.745641i | \(-0.732144\pi\) |
0.745641 | + | 0.666348i | \(0.232144\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 19.4845 | + | 360.948i | 0.0274044 | + | 0.507663i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 269.251 | 0.377631 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −529.074 | + | 529.074i | −0.739964 | + | 0.739964i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 450.165 | − | 475.121i | 0.627845 | − | 0.662651i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 966.944i | 1.34485i | 0.740167 | + | 0.672423i | \(0.234746\pi\) | ||||
−0.740167 | + | 0.672423i | \(0.765254\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −346.056 | −0.479967 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 193.734 | + | 183.558i | 0.267959 | + | 0.253884i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −133.674 | − | 133.674i | −0.184378 | − | 0.184378i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1338.18i | 1.84069i | 0.391110 | + | 0.920344i | \(0.372091\pi\) | ||||
−0.391110 | + | 0.920344i | \(0.627909\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −117.429 | − | 719.480i | −0.161083 | − | 0.986941i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 158.387 | + | 158.387i | 0.216672 | + | 0.216672i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −757.046 | − | 757.046i | −1.03280 | − | 1.03280i | −0.999443 | − | 0.0333615i | \(-0.989379\pi\) |
−0.0333615 | − | 0.999443i | \(-0.510621\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.55386 | + | 168.842i | 0.00619573 | + | 0.229717i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1168.69i | 1.58574i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 495.335 | + | 495.335i | 0.670278 | + | 0.670278i | 0.957780 | − | 0.287502i | \(-0.0928249\pi\) |
−0.287502 | + | 0.957780i | \(0.592825\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 84.7353 | − | 89.4328i | 0.114353 | − | 0.120692i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1421.01 | 1.91253 | 0.956266 | − | 0.292500i | \(-0.0944872\pi\) | ||||
0.956266 | + | 0.292500i | \(0.0944872\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 37.2861i | − | 0.0500485i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 336.685 | + | 302.197i | 0.450716 | + | 0.404547i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 558.359 | − | 558.359i | 0.745473 | − | 0.745473i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 143.509 | 0.191090 | 0.0955452 | − | 0.995425i | \(-0.469541\pi\) | ||||
0.0955452 | + | 0.995425i | \(0.469541\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −19.3572 | − | 717.702i | −0.0257068 | − | 0.953123i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 570.921 | − | 570.921i | 0.756187 | − | 0.756187i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −651.883 | + | 651.883i | −0.861140 | + | 0.861140i | −0.991471 | − | 0.130331i | \(-0.958396\pi\) |
0.130331 | + | 0.991471i | \(0.458396\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −50.6558 | − | 1878.15i | −0.0667402 | − | 2.47450i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 434.623 | 0.571122 | 0.285561 | − | 0.958361i | \(-0.407820\pi\) | ||||
0.285561 | + | 0.958361i | \(0.407820\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 455.249 | − | 455.249i | 0.596656 | − | 0.596656i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −132.468 | − | 118.899i | −0.173161 | − | 0.155423i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 499.665i | − | 0.651453i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.1894 | 0.0223529 | 0.0111764 | − | 0.999938i | \(-0.496442\pi\) | ||||
0.0111764 | + | 0.999938i | \(0.496442\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −811.125 | + | 856.091i | −1.05204 | + | 1.11036i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −553.125 | − | 553.125i | −0.715557 | − | 0.715557i | 0.252135 | − | 0.967692i | \(-0.418867\pi\) |
−0.967692 | + | 0.252135i | \(0.918867\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 37.8171i | − | 0.0487963i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13.8481 | + | 513.440i | 0.0178225 | + | 0.660798i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −144.826 | − | 144.826i | −0.185913 | − | 0.185913i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 607.484 | + | 607.484i | 0.777828 | + | 0.777828i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −86.2686 | − | 1064.12i | −0.110177 | − | 1.35902i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 94.5530i | − | 0.120450i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 274.851 | + | 274.851i | 0.349239 | + | 0.349239i | 0.859826 | − | 0.510587i | \(-0.170572\pi\) |
−0.510587 | + | 0.859826i | \(0.670572\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −391.699 | − | 371.125i | −0.496450 | − | 0.470374i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −677.993 | −0.857134 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 637.374i | − | 0.803750i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −272.508 | + | 287.615i | −0.342777 | + | 0.361780i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −165.770 | + | 165.770i | −0.207993 | + | 0.207993i | −0.803414 | − | 0.595421i | \(-0.796985\pi\) |
0.595421 | + | 0.803414i | \(0.296985\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.3854 | −0.0280168 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33.8035 | − | 626.204i | −0.0422016 | − | 0.781778i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1266.52 | − | 1266.52i | 1.57724 | − | 1.57724i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 653.690 | − | 653.690i | 0.812037 | − | 0.812037i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1232.17 | + | 33.2329i | −1.52685 | + | 0.0411808i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 184.708 | 0.228316 | 0.114158 | − | 0.993463i | \(-0.463583\pi\) | ||||
0.114158 | + | 0.993463i | \(0.463583\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −585.531 | + | 585.531i | −0.721986 | + | 0.721986i | −0.969010 | − | 0.247023i | \(-0.920548\pi\) |
0.247023 | + | 0.969010i | \(0.420548\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1081.36 | + | 1024.56i | 1.33008 | + | 1.26022i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 420.457i | − | 0.515898i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 231.235 | 0.283029 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 365.864 | + | 328.387i | 0.446720 | + | 0.400961i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 659.299 | + | 659.299i | 0.803044 | + | 0.803044i | 0.983570 | − | 0.180526i | \(-0.0577801\pi\) |
−0.180526 | + | 0.983570i | \(0.557780\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1397.61i | − | 1.69819i | −0.528237 | − | 0.849097i | \(-0.677147\pi\) | ||
0.528237 | − | 0.849097i | \(-0.322853\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −263.792 | + | 7.11476i | −0.319748 | + | 0.00862395i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 78.1971 | + | 78.1971i | 0.0945551 | + | 0.0945551i | 0.752802 | − | 0.658247i | \(-0.228702\pi\) |
−0.658247 | + | 0.752802i | \(0.728702\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.4254 | + | 30.4254i | 0.0367014 | + | 0.0367014i | 0.725219 | − | 0.688518i | \(-0.241738\pi\) |
−0.688518 | + | 0.725219i | \(0.741738\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −394.465 | + | 10.6392i | −0.474687 | + | 0.0128028i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 55.0731i | − | 0.0661141i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 504.622 | + | 504.622i | 0.604338 | + | 0.604338i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 138.319 | − | 162.725i | 0.165255 | − | 0.194414i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −694.526 | −0.827802 | −0.413901 | − | 0.910322i | \(-0.635834\pi\) | ||||
−0.413901 | + | 0.910322i | \(0.635834\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 722.489i | − | 0.859084i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −655.228 | − | 620.812i | −0.777258 | − | 0.736432i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −277.265 | + | 277.265i | −0.328125 | + | 0.328125i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1313.68 | −1.55098 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −430.341 | + | 11.6068i | −0.506880 | + | 0.0136711i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −682.298 | + | 682.298i | −0.801761 | + | 0.801761i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −727.489 | + | 727.489i | −0.852860 | + | 0.852860i | −0.990484 | − | 0.137625i | \(-0.956053\pi\) |
0.137625 | + | 0.990484i | \(0.456053\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −183.490 | + | 9.90506i | −0.214608 | + | 0.0115849i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1275.44 | 1.48826 | 0.744128 | − | 0.668037i | \(-0.232865\pi\) | ||||
0.744128 | + | 0.668037i | \(0.232865\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.20191 | − | 2.20191i | 0.00256334 | − | 0.00256334i | −0.705824 | − | 0.708387i | \(-0.749423\pi\) |
0.708387 | + | 0.705824i | \(0.249423\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 562.130 | − | 593.293i | 0.652880 | − | 0.689074i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1311.55i | − | 1.51976i | −0.650063 | − | 0.759880i | \(-0.725258\pi\) | ||
0.650063 | − | 0.759880i | \(-0.274742\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −489.622 | −0.566037 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −587.236 | − | 556.391i | −0.677319 | − | 0.641743i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 522.518 | + | 522.518i | 0.601287 | + | 0.601287i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 574.496i | − | 0.659582i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 29.6383 | + | 549.046i | 0.0339500 | + | 0.628918i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −571.908 | − | 571.908i | −0.653609 | − | 0.653609i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 449.158 | + | 449.158i | 0.512152 | + | 0.512152i | 0.915185 | − | 0.403033i | \(-0.132044\pi\) |
−0.403033 | + | 0.915185i | \(0.632044\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 36.7303 | + | 1361.84i | 0.0417864 | + | 1.54930i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 982.786i | 1.11553i | 0.829998 | + | 0.557767i | \(0.188342\pi\) | ||||
−0.829998 | + | 0.557767i | \(0.811658\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 233.961 | + | 233.961i | 0.264962 | + | 0.264962i | 0.827066 | − | 0.562104i | \(-0.190008\pi\) |
−0.562104 | + | 0.827066i | \(0.690008\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −512.582 | + | 540.999i | −0.579189 | + | 0.611298i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1421.57 | 1.60267 | 0.801334 | − | 0.598217i | \(-0.204124\pi\) | ||||
0.801334 | + | 0.598217i | \(0.204124\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 565.527i | − | 0.636138i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1161.10 | − | 934.222i | −1.30314 | − | 1.04851i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.3406 | + | 16.3406i | −0.0182986 | + | 0.0182986i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 644.558 | 0.720176 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 24.9010 | + | 923.246i | 0.0277603 | + | 1.02926i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 221.159 | − | 221.159i | 0.246006 | − | 0.246006i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 91.3508 | − | 91.3508i | 0.101388 | − | 0.101388i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24.8781 | + | 922.396i | 0.0275505 | + | 1.02148i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1350.50 | −1.49226 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −358.736 | + | 358.736i | −0.395519 | + | 0.395519i | −0.876649 | − | 0.481130i | \(-0.840226\pi\) |
0.481130 | + | 0.876649i | \(0.340226\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −884.494 | + | 985.436i | −0.973041 | + | 1.08409i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 353.455i | − | 0.387986i | −0.981003 | − | 0.193993i | \(-0.937856\pi\) | ||
0.981003 | − | 0.193993i | \(-0.0621439\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 924.862 | 1.01299 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −653.852 | + | 690.100i | −0.714592 | + | 0.754207i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 492.368 | + | 492.368i | 0.536934 | + | 0.536934i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1519.58i | 1.65351i | 0.562560 | + | 0.826757i | \(0.309817\pi\) | ||||
−0.562560 | + | 0.826757i | \(0.690183\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.7785 | − | 399.631i | −0.0117030 | − | 0.433910i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −298.622 | − | 298.622i | −0.323534 | − | 0.323534i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 95.8309 | + | 95.8309i | 0.103601 | + | 0.103601i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −514.915 | + | 27.7959i | −0.555464 | + | 0.0299848i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 95.2916i | − | 0.102574i | −0.998684 | − | 0.0512872i | \(-0.983668\pi\) | ||
0.998684 | − | 0.0512872i | \(-0.0163324\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −40.2015 | − | 40.2015i | −0.0431810 | − | 0.0431810i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 535.097 | + | 506.991i | 0.573523 | + | 0.543398i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −363.886 | −0.389182 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 701.772i | 0.748956i | 0.927236 | + | 0.374478i | \(0.122178\pi\) | ||||
−0.927236 | + | 0.374478i | \(0.877822\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 730.101 | − | 770.576i | 0.777530 | − | 0.820634i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −88.8345 | + | 88.8345i | −0.0944044 | + | 0.0944044i | −0.752732 | − | 0.658327i | \(-0.771264\pi\) |
0.658327 | + | 0.752732i | \(0.271264\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1535.41 | 1.62822 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −59.2526 | − | 730.875i | −0.0627012 | − | 0.773413i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −345.769 | + | 345.769i | −0.365120 | + | 0.365120i | −0.865694 | − | 0.500574i | \(-0.833122\pi\) |
0.500574 | + | 0.865694i | \(0.333122\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −622.588 | + | 622.588i | −0.656046 | + | 0.656046i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −992.517 | + | 26.7693i | −1.04366 | + | 0.0281486i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1627.75 | −1.70803 | −0.854013 | − | 0.520251i | \(-0.825838\pi\) | ||||
−0.854013 | + | 0.520251i | \(0.825838\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −115.517 | + | 115.517i | −0.120961 | + | 0.120961i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1584.30 | − | 1501.08i | −1.65548 | − | 1.56853i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 148.283i | 0.154623i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −898.433 | −0.934894 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 785.963 | − | 875.660i | 0.816161 | − | 0.909304i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −149.785 | − | 149.785i | −0.155218 | − | 0.155218i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1444.31i | − | 1.49360i | −0.665049 | − | 0.746799i | \(-0.731590\pi\) | ||
0.665049 | − | 0.746799i | \(-0.268410\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 59.8945 | − | 1.61542i | 0.0618106 | − | 0.00166710i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 165.972 | + | 165.972i | 0.170929 | + | 0.170929i | 0.787388 | − | 0.616458i | \(-0.211433\pi\) |
−0.616458 | + | 0.787388i | \(0.711433\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.5371 | + | 18.5371i | 0.0190515 | + | 0.0190515i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 129.673 | − | 3.49742i | 0.132998 | − | 0.00358710i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1708.09i | 1.74830i | 0.485658 | + | 0.874149i | \(0.338580\pi\) | ||||
−0.485658 | + | 0.874149i | \(0.661420\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −906.510 | − | 906.510i | −0.925955 | − | 0.925955i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 640.822 | − | 713.955i | 0.653233 | − | 0.727783i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −285.345 | −0.290279 | −0.145140 | − | 0.989411i | \(-0.546363\pi\) | ||||
−0.145140 | + | 0.989411i | \(0.546363\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 205.261i | 0.208386i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −66.9408 | − | 63.4247i | −0.0678225 | − | 0.0642601i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1225.75 | + | 1225.75i | −1.23938 | + | 1.23938i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 437.191 | 0.441162 | 0.220581 | − | 0.975369i | \(-0.429205\pi\) | ||||
0.220581 | + | 0.975369i | \(0.429205\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 138.002 | − | 3.72207i | 0.138975 | − | 0.00374831i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −375.762 | + | 375.762i | −0.377650 | + | 0.377650i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1029.10 | − | 1029.10i | 1.03220 | − | 1.03220i | 0.0327341 | − | 0.999464i | \(-0.489579\pi\) |
0.999464 | − | 0.0327341i | \(-0.0104215\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 61.8458 | + | 762.862i | 0.0619077 | + | 0.763626i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 384.3.i.c.161.3 | 20 | ||
3.2 | odd | 2 | inner | 384.3.i.c.161.4 | 20 | ||
4.3 | odd | 2 | 384.3.i.d.161.8 | 20 | |||
8.3 | odd | 2 | 48.3.i.b.29.8 | yes | 20 | ||
8.5 | even | 2 | 192.3.i.b.17.8 | 20 | |||
12.11 | even | 2 | 384.3.i.d.161.7 | 20 | |||
16.3 | odd | 4 | 48.3.i.b.5.3 | ✓ | 20 | ||
16.5 | even | 4 | inner | 384.3.i.c.353.4 | 20 | ||
16.11 | odd | 4 | 384.3.i.d.353.7 | 20 | |||
16.13 | even | 4 | 192.3.i.b.113.7 | 20 | |||
24.5 | odd | 2 | 192.3.i.b.17.7 | 20 | |||
24.11 | even | 2 | 48.3.i.b.29.3 | yes | 20 | ||
48.5 | odd | 4 | inner | 384.3.i.c.353.3 | 20 | ||
48.11 | even | 4 | 384.3.i.d.353.8 | 20 | |||
48.29 | odd | 4 | 192.3.i.b.113.8 | 20 | |||
48.35 | even | 4 | 48.3.i.b.5.8 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.i.b.5.3 | ✓ | 20 | 16.3 | odd | 4 | ||
48.3.i.b.5.8 | yes | 20 | 48.35 | even | 4 | ||
48.3.i.b.29.3 | yes | 20 | 24.11 | even | 2 | ||
48.3.i.b.29.8 | yes | 20 | 8.3 | odd | 2 | ||
192.3.i.b.17.7 | 20 | 24.5 | odd | 2 | |||
192.3.i.b.17.8 | 20 | 8.5 | even | 2 | |||
192.3.i.b.113.7 | 20 | 16.13 | even | 4 | |||
192.3.i.b.113.8 | 20 | 48.29 | odd | 4 | |||
384.3.i.c.161.3 | 20 | 1.1 | even | 1 | trivial | ||
384.3.i.c.161.4 | 20 | 3.2 | odd | 2 | inner | ||
384.3.i.c.353.3 | 20 | 48.5 | odd | 4 | inner | ||
384.3.i.c.353.4 | 20 | 16.5 | even | 4 | inner | ||
384.3.i.d.161.7 | 20 | 12.11 | even | 2 | |||
384.3.i.d.161.8 | 20 | 4.3 | odd | 2 | |||
384.3.i.d.353.7 | 20 | 16.11 | odd | 4 | |||
384.3.i.d.353.8 | 20 | 48.11 | even | 4 |