Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(89,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.r (of order \(6\), degree \(2\), 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: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1277.1 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.1277 |
Dual form | 1386.2.r.a.89.1 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −1.25882 | − | 2.18034i | −0.562961 | − | 0.975077i | −0.997236 | − | 0.0742968i | \(-0.976329\pi\) |
0.434275 | − | 0.900780i | \(-0.357005\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.48356 | + | 2.19067i | 0.560734 | + | 0.827996i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.18034 | + | 1.25882i | 0.689484 | + | 0.398074i | ||||
\(11\) | −0.866025 | − | 0.500000i | −0.261116 | − | 0.150756i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.44949i | − | 0.679366i | −0.940540 | − | 0.339683i | \(-0.889680\pi\) | ||
0.940540 | − | 0.339683i | \(-0.110320\pi\) | |||||||
\(14\) | −2.38014 | − | 1.15539i | −0.636119 | − | 0.308792i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.64626 | + | 4.58346i | −0.641813 | + | 1.11165i | 0.343214 | + | 0.939257i | \(0.388484\pi\) |
−0.985028 | + | 0.172396i | \(0.944849\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.52761 | + | 2.61401i | −1.03870 | + | 0.599696i | −0.919466 | − | 0.393170i | \(-0.871379\pi\) |
−0.119238 | + | 0.992866i | \(0.538045\pi\) | |||||||
\(20\) | −2.51764 | −0.562961 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −4.28376 | + | 2.47323i | −0.893226 | + | 0.515704i | −0.874996 | − | 0.484129i | \(-0.839136\pi\) |
−0.0182299 | + | 0.999834i | \(0.505803\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.669251 | + | 1.15918i | −0.133850 | + | 0.231835i | ||||
\(26\) | 1.22474 | + | 2.12132i | 0.240192 | + | 0.416025i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.63896 | − | 0.189469i | 0.498716 | − | 0.0358062i | ||||
\(29\) | − | 8.05986i | − | 1.49668i | −0.663317 | − | 0.748339i | \(-0.730852\pi\) | ||
0.663317 | − | 0.748339i | \(-0.269148\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.44414 | + | 4.29788i | 1.33701 | + | 0.771922i | 0.986363 | − | 0.164587i | \(-0.0526291\pi\) |
0.350645 | + | 0.936509i | \(0.385962\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 5.29253i | − | 0.907661i | ||||||
\(35\) | 2.90887 | − | 5.99233i | 0.491688 | − | 1.01289i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.91189 | + | 10.2397i | 0.971909 | + | 1.68340i | 0.689780 | + | 0.724019i | \(0.257707\pi\) |
0.282129 | + | 0.959376i | \(0.408959\pi\) | |||||||
\(38\) | 2.61401 | − | 4.52761i | 0.424049 | − | 0.734475i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.18034 | − | 1.25882i | 0.344742 | − | 0.199037i | ||||
\(41\) | 1.92480 | 0.300604 | 0.150302 | − | 0.988640i | \(-0.451975\pi\) | ||||
0.150302 | + | 0.988640i | \(0.451975\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.9841 | −1.82756 | −0.913782 | − | 0.406204i | \(-0.866852\pi\) | ||||
−0.913782 | + | 0.406204i | \(0.866852\pi\) | |||||||
\(44\) | −0.866025 | + | 0.500000i | −0.130558 | + | 0.0753778i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.47323 | − | 4.28376i | 0.364658 | − | 0.631606i | ||||
\(47\) | −0.637756 | − | 1.10463i | −0.0930263 | − | 0.161126i | 0.815757 | − | 0.578395i | \(-0.196321\pi\) |
−0.908783 | + | 0.417269i | \(0.862987\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.59808 | + | 6.50000i | −0.371154 | + | 0.928571i | ||||
\(50\) | − | 1.33850i | − | 0.189293i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.12132 | − | 1.22474i | −0.294174 | − | 0.169842i | ||||
\(53\) | −0.414578 | − | 0.239357i | −0.0569467 | − | 0.0328782i | 0.471256 | − | 0.881996i | \(-0.343801\pi\) |
−0.528203 | + | 0.849118i | \(0.677134\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.51764i | 0.339478i | ||||||||
\(56\) | −2.19067 | + | 1.48356i | −0.292741 | + | 0.198250i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.02993 | + | 6.98004i | 0.529155 | + | 0.916524i | ||||
\(59\) | −3.02494 | + | 5.23936i | −0.393814 | + | 0.682106i | −0.992949 | − | 0.118542i | \(-0.962178\pi\) |
0.599135 | + | 0.800648i | \(0.295511\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.7536 | − | 6.20857i | 1.37685 | − | 0.794925i | 0.385072 | − | 0.922886i | \(-0.374177\pi\) |
0.991779 | + | 0.127961i | \(0.0408432\pi\) | |||||||
\(62\) | −8.59575 | −1.09166 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −5.34072 | + | 3.08346i | −0.662434 | + | 0.382457i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.11571 | + | 10.5927i | −0.747153 | + | 1.29411i | 0.202028 | + | 0.979380i | \(0.435247\pi\) |
−0.949182 | + | 0.314728i | \(0.898087\pi\) | |||||||
\(68\) | 2.64626 | + | 4.58346i | 0.320907 | + | 0.555827i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.477014 | + | 6.64394i | 0.0570140 | + | 0.794103i | ||||
\(71\) | 14.7055i | 1.74522i | 0.488416 | + | 0.872611i | \(0.337575\pi\) | ||||
−0.488416 | + | 0.872611i | \(0.662425\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.52432 | − | 4.92152i | −0.997696 | − | 0.576020i | −0.0901305 | − | 0.995930i | \(-0.528728\pi\) |
−0.907566 | + | 0.419910i | \(0.862062\pi\) | |||||||
\(74\) | −10.2397 | − | 5.91189i | −1.19034 | − | 0.687243i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.22803i | 0.599696i | ||||||||
\(77\) | −0.189469 | − | 2.63896i | −0.0215920 | − | 0.300737i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.52677 | + | 6.10854i | 0.396792 | + | 0.687265i | 0.993328 | − | 0.115322i | \(-0.0367899\pi\) |
−0.596536 | + | 0.802587i | \(0.703457\pi\) | |||||||
\(80\) | −1.25882 | + | 2.18034i | −0.140740 | + | 0.243769i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.66693 | + | 0.962402i | −0.184081 | + | 0.106279i | ||||
\(83\) | −9.35827 | −1.02720 | −0.513602 | − | 0.858029i | \(-0.671689\pi\) | ||||
−0.513602 | + | 0.858029i | \(0.671689\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.3247 | 1.44526 | ||||||||
\(86\) | 10.3786 | − | 5.99207i | 1.11915 | − | 0.646142i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.500000 | − | 0.866025i | 0.0533002 | − | 0.0923186i | ||||
\(89\) | 7.92392 | + | 13.7246i | 0.839934 | + | 1.45481i | 0.889949 | + | 0.456060i | \(0.150740\pi\) |
−0.0500147 | + | 0.998748i | \(0.515927\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.36603 | − | 3.63397i | 0.562512 | − | 0.380944i | ||||
\(92\) | 4.94646i | 0.515704i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.10463 | + | 0.637756i | 0.113934 | + | 0.0657796i | ||||
\(95\) | 11.3989 | + | 6.58114i | 1.16950 | + | 0.675211i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.6556i | − | 1.38652i | −0.720689 | − | 0.693259i | \(-0.756174\pi\) | ||
0.720689 | − | 0.693259i | \(-0.243826\pi\) | |||||||
\(98\) | −1.00000 | − | 6.92820i | −0.101015 | − | 0.699854i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.669251 | + | 1.15918i | 0.0669251 | + | 0.115918i | ||||
\(101\) | 0.689211 | − | 1.19375i | 0.0685791 | − | 0.118782i | −0.829697 | − | 0.558214i | \(-0.811487\pi\) |
0.898276 | + | 0.439432i | \(0.144820\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.08978 | + | 5.24799i | −0.895643 | + | 0.517100i | −0.875784 | − | 0.482703i | \(-0.839655\pi\) |
−0.0198589 | + | 0.999803i | \(0.506322\pi\) | |||||||
\(104\) | 2.44949 | 0.240192 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.478713 | 0.0464968 | ||||||||
\(107\) | 2.50535 | − | 1.44646i | 0.242201 | − | 0.139835i | −0.373987 | − | 0.927434i | \(-0.622009\pi\) |
0.616188 | + | 0.787599i | \(0.288676\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.76941 | + | 11.7250i | −0.648392 | + | 1.12305i | 0.335115 | + | 0.942177i | \(0.391225\pi\) |
−0.983507 | + | 0.180870i | \(0.942109\pi\) | |||||||
\(110\) | −1.25882 | − | 2.18034i | −0.120024 | − | 0.207887i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.15539 | − | 2.38014i | 0.109175 | − | 0.224902i | ||||
\(113\) | 14.5699i | 1.37062i | 0.728250 | + | 0.685312i | \(0.240334\pi\) | ||||
−0.728250 | + | 0.685312i | \(0.759666\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.7850 | + | 6.22670i | 1.00570 | + | 0.580643i | ||||
\(116\) | −6.98004 | − | 4.02993i | −0.648080 | − | 0.374169i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 6.04989i | − | 0.556937i | ||||||
\(119\) | −13.9668 | + | 1.00277i | −1.28033 | + | 0.0919236i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | + | 0.866025i | 0.0454545 | + | 0.0787296i | ||||
\(122\) | −6.20857 | + | 10.7536i | −0.562097 | + | 0.973581i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.44414 | − | 4.29788i | 0.668504 | − | 0.385961i | ||||
\(125\) | −9.21833 | −0.824512 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.59675 | −0.585367 | −0.292683 | − | 0.956209i | \(-0.594548\pi\) | ||||
−0.292683 | + | 0.956209i | \(0.594548\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.08346 | − | 5.34072i | 0.270438 | − | 0.468412i | ||||
\(131\) | −0.757359 | − | 1.31178i | −0.0661708 | − | 0.114611i | 0.831042 | − | 0.556210i | \(-0.187745\pi\) |
−0.897213 | + | 0.441599i | \(0.854412\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.4434 | − | 6.04044i | −1.07898 | − | 0.523772i | ||||
\(134\) | − | 12.2314i | − | 1.05663i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.58346 | − | 2.64626i | −0.393029 | − | 0.226915i | ||||
\(137\) | 12.0316 | + | 6.94646i | 1.02793 | + | 0.593476i | 0.916391 | − | 0.400284i | \(-0.131088\pi\) |
0.111540 | + | 0.993760i | \(0.464422\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 13.5911i | − | 1.15278i | −0.817174 | − | 0.576391i | \(-0.804460\pi\) | ||
0.817174 | − | 0.576391i | \(-0.195540\pi\) | |||||||
\(140\) | −3.73508 | − | 5.51532i | −0.315672 | − | 0.466129i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.35275 | − | 12.7353i | −0.617029 | − | 1.06873i | ||||
\(143\) | −1.22474 | + | 2.12132i | −0.102418 | + | 0.177394i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.5732 | + | 10.1459i | −1.45938 | + | 0.842571i | ||||
\(146\) | 9.84304 | 0.814616 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.8238 | 0.971909 | ||||||||
\(149\) | −5.76098 | + | 3.32611i | −0.471958 | + | 0.272485i | −0.717059 | − | 0.697012i | \(-0.754512\pi\) |
0.245101 | + | 0.969498i | \(0.421179\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00877 | + | 6.94339i | −0.326229 | + | 0.565045i | −0.981760 | − | 0.190123i | \(-0.939111\pi\) |
0.655532 | + | 0.755168i | \(0.272445\pi\) | |||||||
\(152\) | −2.61401 | − | 4.52761i | −0.212025 | − | 0.367237i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.48356 | + | 2.19067i | 0.119549 | + | 0.176529i | ||||
\(155\) | − | 21.6410i | − | 1.73825i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.0820 | − | 11.0170i | −1.52291 | − | 0.879254i | −0.999633 | − | 0.0270921i | \(-0.991375\pi\) |
−0.523279 | − | 0.852161i | \(-0.675291\pi\) | |||||||
\(158\) | −6.10854 | − | 3.52677i | −0.485969 | − | 0.280575i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 2.51764i | − | 0.199037i | ||||||
\(161\) | −11.7733 | − | 5.71512i | −0.927864 | − | 0.450414i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.03225 | + | 8.71611i | 0.394156 | + | 0.682699i | 0.992993 | − | 0.118172i | \(-0.0377035\pi\) |
−0.598837 | + | 0.800871i | \(0.704370\pi\) | |||||||
\(164\) | 0.962402 | − | 1.66693i | 0.0751509 | − | 0.130165i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.10450 | − | 4.67914i | 0.629031 | − | 0.363171i | ||||
\(167\) | 4.76268 | 0.368547 | 0.184274 | − | 0.982875i | \(-0.441007\pi\) | ||||
0.184274 | + | 0.982875i | \(0.441007\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | −11.5395 | + | 6.66234i | −0.885040 | + | 0.510978i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.99207 | + | 10.3786i | −0.456891 | + | 0.791359i | ||||
\(173\) | 7.36843 | + | 12.7625i | 0.560211 | + | 0.970314i | 0.997478 | + | 0.0709824i | \(0.0226134\pi\) |
−0.437266 | + | 0.899332i | \(0.644053\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.53225 | + | 0.253604i | −0.267013 | + | 0.0191707i | ||||
\(176\) | 1.00000i | 0.0753778i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.7246 | − | 7.92392i | −1.02871 | − | 0.593923i | ||||
\(179\) | −2.03491 | − | 1.17486i | −0.152096 | − | 0.0878129i | 0.422020 | − | 0.906586i | \(-0.361321\pi\) |
−0.574117 | + | 0.818773i | \(0.694654\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 11.9236i | − | 0.886271i | −0.896455 | − | 0.443136i | \(-0.853866\pi\) | ||
0.896455 | − | 0.443136i | \(-0.146134\pi\) | |||||||
\(182\) | −2.83013 | + | 5.83013i | −0.209783 | + | 0.432158i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.47323 | − | 4.28376i | −0.182329 | − | 0.315803i | ||||
\(185\) | 14.8840 | − | 25.7798i | 1.09429 | − | 1.89537i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.58346 | − | 2.64626i | 0.335176 | − | 0.193514i | ||||
\(188\) | −1.27551 | −0.0930263 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −13.1623 | −0.954892 | ||||||||
\(191\) | −21.2839 | + | 12.2882i | −1.54005 | + | 0.889146i | −0.541212 | + | 0.840886i | \(0.682034\pi\) |
−0.998835 | + | 0.0482604i | \(0.984632\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.05657 | − | 12.2223i | 0.507943 | − | 0.879783i | −0.492015 | − | 0.870587i | \(-0.663739\pi\) |
0.999958 | − | 0.00919638i | \(-0.00292734\pi\) | |||||||
\(194\) | 6.82780 | + | 11.8261i | 0.490208 | + | 0.849065i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.33013 | + | 5.50000i | 0.309295 | + | 0.392857i | ||||
\(197\) | − | 0.579219i | − | 0.0412676i | −0.999787 | − | 0.0206338i | \(-0.993432\pi\) | ||
0.999787 | − | 0.0206338i | \(-0.00656841\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.08228 | + | 1.20220i | 0.147609 | + | 0.0852220i | 0.571985 | − | 0.820264i | \(-0.306173\pi\) |
−0.424377 | + | 0.905486i | \(0.639507\pi\) | |||||||
\(200\) | −1.15918 | − | 0.669251i | −0.0819661 | − | 0.0473232i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.37842i | 0.0969854i | ||||||||
\(203\) | 17.6565 | − | 11.9573i | 1.23924 | − | 0.839239i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.42298 | − | 4.19672i | −0.169228 | − | 0.293112i | ||||
\(206\) | 5.24799 | − | 9.08978i | 0.365645 | − | 0.633315i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.12132 | + | 1.22474i | −0.147087 | + | 0.0849208i | ||||
\(209\) | 5.22803 | 0.361630 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.99343 | −0.412605 | −0.206302 | − | 0.978488i | \(-0.566143\pi\) | ||||
−0.206302 | + | 0.978488i | \(0.566143\pi\) | |||||||
\(212\) | −0.414578 | + | 0.239357i | −0.0284733 | + | 0.0164391i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.44646 | + | 2.50535i | −0.0988782 | + | 0.171262i | ||||
\(215\) | 15.0859 | + | 26.1295i | 1.02885 | + | 1.78202i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.62863 | + | 22.6838i | 0.110558 | + | 1.53988i | ||||
\(218\) | − | 13.5388i | − | 0.916964i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.18034 | + | 1.25882i | 0.146998 | + | 0.0848696i | ||||
\(221\) | 11.2271 | + | 6.48200i | 0.755220 | + | 0.436026i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.48993i | 0.501563i | 0.968044 | + | 0.250781i | \(0.0806875\pi\) | ||||
−0.968044 | + | 0.250781i | \(0.919313\pi\) | |||||||
\(224\) | 0.189469 | + | 2.63896i | 0.0126594 | + | 0.176323i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.28497 | − | 12.6179i | −0.484589 | − | 0.839332i | ||||
\(227\) | 4.88304 | − | 8.45768i | 0.324099 | − | 0.561356i | −0.657231 | − | 0.753689i | \(-0.728272\pi\) |
0.981330 | + | 0.192334i | \(0.0616056\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.195181 | − | 0.112688i | 0.0128980 | − | 0.00744664i | −0.493537 | − | 0.869725i | \(-0.664296\pi\) |
0.506435 | + | 0.862278i | \(0.330963\pi\) | |||||||
\(230\) | −12.4534 | −0.821153 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.05986 | 0.529155 | ||||||||
\(233\) | 0.445759 | − | 0.257359i | 0.0292027 | − | 0.0168602i | −0.485328 | − | 0.874332i | \(-0.661300\pi\) |
0.514530 | + | 0.857472i | \(0.327966\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.60564 | + | 2.78105i | −0.104740 | + | 0.181416i | ||||
\(236\) | 3.02494 | + | 5.23936i | 0.196907 | + | 0.341053i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 11.5942 | − | 7.85180i | 0.751540 | − | 0.508957i | ||||
\(239\) | − | 15.4899i | − | 1.00196i | −0.865459 | − | 0.500980i | \(-0.832973\pi\) | ||
0.865459 | − | 0.500980i | \(-0.167027\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.2882 | − | 8.24932i | −0.920387 | − | 0.531386i | −0.0366285 | − | 0.999329i | \(-0.511662\pi\) |
−0.883759 | + | 0.467943i | \(0.844995\pi\) | |||||||
\(242\) | −0.866025 | − | 0.500000i | −0.0556702 | − | 0.0321412i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 12.4171i | − | 0.794925i | ||||||
\(245\) | 17.4427 | − | 2.51764i | 1.11437 | − | 0.160846i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.40300 | + | 11.0903i | 0.407413 | + | 0.705660i | ||||
\(248\) | −4.29788 | + | 7.44414i | −0.272915 | + | 0.472703i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.98331 | − | 4.60916i | 0.504909 | − | 0.291509i | ||||
\(251\) | 18.6367 | 1.17634 | 0.588169 | − | 0.808738i | \(-0.299849\pi\) | ||||
0.588169 | + | 0.808738i | \(0.299849\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.94646 | 0.310981 | ||||||||
\(254\) | 5.71295 | − | 3.29837i | 0.358463 | − | 0.206958i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −0.575454 | − | 0.996716i | −0.0358959 | − | 0.0621734i | 0.847519 | − | 0.530764i | \(-0.178095\pi\) |
−0.883415 | + | 0.468591i | \(0.844762\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.6611 | + | 28.1423i | −0.848862 | + | 1.74867i | ||||
\(260\) | 6.16693i | 0.382457i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.31178 | + | 0.757359i | 0.0810423 | + | 0.0467898i | ||||
\(263\) | 6.18929 | + | 3.57339i | 0.381648 | + | 0.220345i | 0.678535 | − | 0.734568i | \(-0.262615\pi\) |
−0.296887 | + | 0.954913i | \(0.595948\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.20523i | 0.0740365i | ||||||||
\(266\) | 13.7966 | − | 0.990548i | 0.845921 | − | 0.0607344i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.11571 | + | 10.5927i | 0.373577 | + | 0.647054i | ||||
\(269\) | 6.68968 | − | 11.5869i | 0.407877 | − | 0.706464i | −0.586774 | − | 0.809750i | \(-0.699602\pi\) |
0.994652 | + | 0.103286i | \(0.0329358\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.92100 | − | 3.41849i | 0.359675 | − | 0.207659i | −0.309263 | − | 0.950977i | \(-0.600082\pi\) |
0.668938 | + | 0.743318i | \(0.266749\pi\) | |||||||
\(272\) | 5.29253 | 0.320907 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.8929 | −0.839302 | ||||||||
\(275\) | 1.15918 | − | 0.669251i | 0.0699010 | − | 0.0403573i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.87404 | − | 4.97798i | 0.172684 | − | 0.299098i | −0.766673 | − | 0.642037i | \(-0.778089\pi\) |
0.939357 | + | 0.342940i | \(0.111423\pi\) | |||||||
\(278\) | 6.79555 | + | 11.7702i | 0.407570 | + | 0.705932i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.99233 | + | 2.90887i | 0.358110 | + | 0.173838i | ||||
\(281\) | 6.45821i | 0.385265i | 0.981271 | + | 0.192632i | \(0.0617025\pi\) | ||||
−0.981271 | + | 0.192632i | \(0.938298\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.87843 | + | 3.39391i | 0.349436 | + | 0.201747i | 0.664437 | − | 0.747344i | \(-0.268671\pi\) |
−0.315001 | + | 0.949091i | \(0.602005\pi\) | |||||||
\(284\) | 12.7353 | + | 7.35275i | 0.755703 | + | 0.436305i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 2.44949i | − | 0.144841i | ||||||
\(287\) | 2.85557 | + | 4.21661i | 0.168559 | + | 0.248899i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.50543 | − | 9.53568i | −0.323849 | − | 0.560923i | ||||
\(290\) | 10.1459 | − | 17.5732i | 0.595788 | − | 1.03193i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.52432 | + | 4.92152i | −0.498848 | + | 0.288010i | ||||
\(293\) | −3.15159 | −0.184118 | −0.0920589 | − | 0.995754i | \(-0.529345\pi\) | ||||
−0.0920589 | + | 0.995754i | \(0.529345\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.2314 | 0.886808 | ||||||||
\(296\) | −10.2397 | + | 5.91189i | −0.595170 | + | 0.343622i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.32611 | − | 5.76098i | 0.192676 | − | 0.333725i | ||||
\(299\) | 6.05816 | + | 10.4930i | 0.350352 | + | 0.606828i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.7792 | − | 26.2533i | −1.02478 | − | 1.51322i | ||||
\(302\) | − | 8.01753i | − | 0.461357i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.52761 | + | 2.61401i | 0.259676 | + | 0.149924i | ||||
\(305\) | −27.0736 | − | 15.6309i | −1.55023 | − | 0.895024i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 15.0711i | − | 0.860151i | −0.902793 | − | 0.430076i | \(-0.858487\pi\) | ||
0.902793 | − | 0.430076i | \(-0.141513\pi\) | |||||||
\(308\) | −2.38014 | − | 1.15539i | −0.135621 | − | 0.0658347i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 10.8205 | + | 18.7417i | 0.614563 | + | 1.06445i | ||||
\(311\) | 15.9573 | − | 27.6388i | 0.904854 | − | 1.56725i | 0.0837402 | − | 0.996488i | \(-0.473313\pi\) |
0.821113 | − | 0.570765i | \(-0.193353\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.8126 | − | 7.97469i | 0.780733 | − | 0.450756i | −0.0559572 | − | 0.998433i | \(-0.517821\pi\) |
0.836690 | + | 0.547677i | \(0.184488\pi\) | |||||||
\(314\) | 22.0340 | 1.24345 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.05354 | 0.396792 | ||||||||
\(317\) | −21.9318 | + | 12.6623i | −1.23181 | + | 0.711188i | −0.967408 | − | 0.253224i | \(-0.918509\pi\) |
−0.264405 | + | 0.964412i | \(0.585176\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.02993 | + | 6.98004i | −0.225633 | + | 0.390807i | ||||
\(320\) | 1.25882 | + | 2.18034i | 0.0703701 | + | 0.121885i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 13.0535 | − | 0.937200i | 0.727444 | − | 0.0522281i | ||||
\(323\) | − | 27.6695i | − | 1.53957i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.83939 | + | 1.63932i | 0.157501 | + | 0.0909333i | ||||
\(326\) | −8.71611 | − | 5.03225i | −0.482741 | − | 0.278711i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.92480i | 0.106279i | ||||||||
\(329\) | 1.47372 | − | 3.03590i | 0.0812488 | − | 0.167374i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.03882 | − | 12.1916i | −0.386888 | − | 0.670110i | 0.605141 | − | 0.796118i | \(-0.293117\pi\) |
−0.992029 | + | 0.126008i | \(0.959783\pi\) | |||||||
\(332\) | −4.67914 | + | 8.10450i | −0.256801 | + | 0.444792i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.12460 | + | 2.38134i | −0.225688 | + | 0.130301i | ||||
\(335\) | 30.7943 | 1.68247 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.15142 | −0.444036 | −0.222018 | − | 0.975043i | \(-0.571264\pi\) | ||||
−0.222018 | + | 0.975043i | \(0.571264\pi\) | |||||||
\(338\) | −6.06218 | + | 3.50000i | −0.329739 | + | 0.190375i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.66234 | − | 11.5395i | 0.361316 | − | 0.625817i | ||||
\(341\) | −4.29788 | − | 7.44414i | −0.232743 | − | 0.403123i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.0938 | + | 3.95164i | −0.976972 | + | 0.213368i | ||||
\(344\) | − | 11.9841i | − | 0.646142i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.7625 | − | 7.36843i | −0.686116 | − | 0.396129i | ||||
\(347\) | 19.5502 | + | 11.2873i | 1.04951 | + | 0.605933i | 0.922511 | − | 0.385970i | \(-0.126133\pi\) |
0.126996 | + | 0.991903i | \(0.459466\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 22.9498i | − | 1.22848i | −0.789121 | − | 0.614238i | \(-0.789464\pi\) | ||
0.789121 | − | 0.614238i | \(-0.210536\pi\) | |||||||
\(350\) | 2.93222 | − | 1.98575i | 0.156734 | − | 0.106143i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.500000 | − | 0.866025i | −0.0266501 | − | 0.0461593i | ||||
\(353\) | −12.5990 | + | 21.8222i | −0.670579 | + | 1.16148i | 0.307161 | + | 0.951658i | \(0.400621\pi\) |
−0.977740 | + | 0.209820i | \(0.932712\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 32.0630 | − | 18.5116i | 1.70173 | − | 0.982492i | ||||
\(356\) | 15.8478 | 0.839934 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.34971 | 0.124186 | ||||||||
\(359\) | 17.0558 | − | 9.84714i | 0.900168 | − | 0.519712i | 0.0229134 | − | 0.999737i | \(-0.492706\pi\) |
0.877255 | + | 0.480025i | \(0.159372\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.16614 | − | 7.21597i | 0.219271 | − | 0.379788i | ||||
\(362\) | 5.96178 | + | 10.3261i | 0.313344 | + | 0.542728i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.464102 | − | 6.46410i | −0.0243255 | − | 0.338811i | ||||
\(365\) | 24.7812i | 1.29711i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.81282 | + | 1.62398i | 0.146828 | + | 0.0847712i | 0.571614 | − | 0.820523i | \(-0.306317\pi\) |
−0.424786 | + | 0.905294i | \(0.639651\pi\) | |||||||
\(368\) | 4.28376 | + | 2.47323i | 0.223307 | + | 0.128926i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 29.7680i | 1.54756i | ||||||||
\(371\) | −0.0907012 | − | 1.26330i | −0.00470897 | − | 0.0655875i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.41177 | − | 5.90935i | −0.176655 | − | 0.305975i | 0.764078 | − | 0.645124i | \(-0.223194\pi\) |
−0.940733 | + | 0.339149i | \(0.889861\pi\) | |||||||
\(374\) | −2.64626 | + | 4.58346i | −0.136835 | + | 0.237005i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.10463 | − | 0.637756i | 0.0569668 | − | 0.0328898i | ||||
\(377\) | −19.7425 | −1.01679 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.8929 | 0.970464 | 0.485232 | − | 0.874385i | \(-0.338735\pi\) | ||||
0.485232 | + | 0.874385i | \(0.338735\pi\) | |||||||
\(380\) | 11.3989 | − | 6.58114i | 0.584750 | − | 0.337605i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 12.2882 | − | 21.2839i | 0.628722 | − | 1.08898i | ||||
\(383\) | −13.2165 | − | 22.8916i | −0.675329 | − | 1.16970i | −0.976373 | − | 0.216094i | \(-0.930668\pi\) |
0.301043 | − | 0.953610i | \(-0.402665\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.51532 | + | 3.73508i | −0.281087 | + | 0.190357i | ||||
\(386\) | 14.1131i | 0.718340i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11.8261 | − | 6.82780i | −0.600380 | − | 0.346629i | ||||
\(389\) | −10.1046 | − | 5.83391i | −0.512325 | − | 0.295791i | 0.221464 | − | 0.975169i | \(-0.428917\pi\) |
−0.733789 | + | 0.679378i | \(0.762250\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 26.1793i | − | 1.32394i | ||||||
\(392\) | −6.50000 | − | 2.59808i | −0.328300 | − | 0.131223i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.289609 | + | 0.501618i | 0.0145903 | + | 0.0252711i | ||||
\(395\) | 8.87913 | − | 15.3791i | 0.446757 | − | 0.773806i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.68678 | + | 5.01532i | −0.435977 | + | 0.251711i | −0.701890 | − | 0.712286i | \(-0.747660\pi\) |
0.265913 | + | 0.963997i | \(0.414327\pi\) | |||||||
\(398\) | −2.40441 | −0.120522 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.33850 | 0.0669251 | ||||||||
\(401\) | −4.52281 | + | 2.61125i | −0.225858 | + | 0.130399i | −0.608660 | − | 0.793431i | \(-0.708293\pi\) |
0.382802 | + | 0.923831i | \(0.374959\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.5276 | − | 18.2343i | 0.524417 | − | 0.908318i | ||||
\(404\) | −0.689211 | − | 1.19375i | −0.0342895 | − | 0.0593912i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.31231 | + | 19.1836i | −0.462162 | + | 0.952065i | ||||
\(407\) | − | 11.8238i | − | 0.586083i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.6456 | − | 9.61037i | −0.823074 | − | 0.475202i | 0.0284013 | − | 0.999597i | \(-0.490958\pi\) |
−0.851475 | + | 0.524395i | \(0.824292\pi\) | |||||||
\(410\) | 4.19672 | + | 2.42298i | 0.207261 | + | 0.119662i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.4960i | 0.517100i | ||||||||
\(413\) | −15.9654 | + | 1.14626i | −0.785606 | + | 0.0564040i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.7804 | + | 20.4042i | 0.578276 | + | 1.00160i | ||||
\(416\) | 1.22474 | − | 2.12132i | 0.0600481 | − | 0.104006i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.52761 | + | 2.61401i | −0.221452 | + | 0.127856i | ||||
\(419\) | 17.4755 | 0.853733 | 0.426866 | − | 0.904315i | \(-0.359617\pi\) | ||||
0.426866 | + | 0.904315i | \(0.359617\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.8519 | 1.35742 | 0.678710 | − | 0.734406i | \(-0.262539\pi\) | ||||
0.678710 | + | 0.734406i | \(0.262539\pi\) | |||||||
\(422\) | 5.19046 | − | 2.99672i | 0.252668 | − | 0.145878i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.239357 | − | 0.414578i | 0.0116242 | − | 0.0201337i | ||||
\(425\) | −3.54203 | − | 6.13497i | −0.171814 | − | 0.297590i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 29.5545 | + | 14.3467i | 1.43024 | + | 0.694285i | ||||
\(428\) | − | 2.89293i | − | 0.139835i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −26.1295 | − | 15.0859i | −1.26008 | − | 0.727505i | ||||
\(431\) | 30.1846 | + | 17.4271i | 1.45394 | + | 0.839434i | 0.998702 | − | 0.0509348i | \(-0.0162201\pi\) |
0.455240 | + | 0.890369i | \(0.349553\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.2068i | 1.30748i | 0.756721 | + | 0.653738i | \(0.226800\pi\) | ||||
−0.756721 | + | 0.653738i | \(0.773200\pi\) | |||||||
\(434\) | −12.7524 | − | 18.8305i | −0.612132 | − | 0.903891i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.76941 | + | 11.7250i | 0.324196 | + | 0.561524i | ||||
\(437\) | 12.9301 | − | 22.3956i | 0.618532 | − | 1.07133i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.0987 | + | 11.6040i | −0.959260 | + | 0.553829i | −0.895945 | − | 0.444165i | \(-0.853501\pi\) |
−0.0633147 | + | 0.997994i | \(0.520167\pi\) | |||||||
\(440\) | −2.51764 | −0.120024 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.9640 | −0.616634 | ||||||||
\(443\) | −15.7172 | + | 9.07435i | −0.746749 | + | 0.431135i | −0.824518 | − | 0.565836i | \(-0.808554\pi\) |
0.0777693 | + | 0.996971i | \(0.475220\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.9496 | − | 34.5537i | 0.945700 | − | 1.63800i | ||||
\(446\) | −3.74496 | − | 6.48647i | −0.177329 | − | 0.307143i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.48356 | − | 2.19067i | −0.0700918 | − | 0.103499i | ||||
\(449\) | − | 31.9656i | − | 1.50855i | −0.656560 | − | 0.754274i | \(-0.727989\pi\) | ||
0.656560 | − | 0.754274i | \(-0.272011\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.66693 | − | 0.962402i | −0.0784926 | − | 0.0453177i | ||||
\(452\) | 12.6179 | + | 7.28497i | 0.593497 | + | 0.342656i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.76608i | 0.458345i | ||||||||
\(455\) | −14.6781 | − | 7.12524i | −0.688122 | − | 0.334036i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.9607 | − | 22.4486i | −0.606276 | − | 1.05010i | −0.991848 | − | 0.127424i | \(-0.959329\pi\) |
0.385572 | − | 0.922678i | \(-0.374004\pi\) | |||||||
\(458\) | −0.112688 | + | 0.195181i | −0.00526557 | + | 0.00912023i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 10.7850 | − | 6.22670i | 0.502852 | − | 0.290322i | ||||
\(461\) | −21.8282 | −1.01664 | −0.508321 | − | 0.861168i | \(-0.669734\pi\) | ||||
−0.508321 | + | 0.861168i | \(0.669734\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.92621 | 0.228940 | 0.114470 | − | 0.993427i | \(-0.463483\pi\) | ||||
0.114470 | + | 0.993427i | \(0.463483\pi\) | |||||||
\(464\) | −6.98004 | + | 4.02993i | −0.324040 | + | 0.187085i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.257359 | + | 0.445759i | −0.0119219 | + | 0.0206494i | ||||
\(467\) | −1.87404 | − | 3.24592i | −0.0867200 | − | 0.150203i | 0.819403 | − | 0.573218i | \(-0.194305\pi\) |
−0.906123 | + | 0.423015i | \(0.860972\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −32.2782 | + | 2.31747i | −1.49047 | + | 0.107011i | ||||
\(470\) | − | 3.21128i | − | 0.148125i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.23936 | − | 3.02494i | −0.241161 | − | 0.139234i | ||||
\(473\) | 10.3786 | + | 5.99207i | 0.477207 | + | 0.275516i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 6.99772i | − | 0.321078i | ||||||
\(476\) | −6.11496 | + | 12.5970i | −0.280279 | + | 0.577381i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.74496 | + | 13.4147i | 0.354246 | + | 0.613573i | ||||
\(479\) | 1.93134 | − | 3.34517i | 0.0882450 | − | 0.152845i | −0.818524 | − | 0.574472i | \(-0.805207\pi\) |
0.906769 | + | 0.421627i | \(0.138541\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.0820 | − | 14.4811i | 1.14364 | − | 0.660282i | ||||
\(482\) | 16.4986 | 0.751493 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −29.7739 | + | 17.1899i | −1.35196 | + | 0.780555i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.80946 | + | 10.0623i | −0.263252 | + | 0.455966i | −0.967104 | − | 0.254381i | \(-0.918128\pi\) |
0.703852 | + | 0.710346i | \(0.251462\pi\) | |||||||
\(488\) | 6.20857 | + | 10.7536i | 0.281049 | + | 0.486790i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −13.8470 | + | 10.9017i | −0.625544 | + | 0.492488i | ||||
\(491\) | − | 25.7345i | − | 1.16138i | −0.814124 | − | 0.580691i | \(-0.802783\pi\) | ||
0.814124 | − | 0.580691i | \(-0.197217\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 36.9421 | + | 21.3285i | 1.66379 | + | 0.960588i | ||||
\(494\) | −11.0903 | − | 6.40300i | −0.498977 | − | 0.288085i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 8.59575i | − | 0.385961i | ||||||
\(497\) | −32.2149 | + | 21.8165i | −1.44504 | + | 0.978606i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.3984 | − | 19.7425i | −0.510261 | − | 0.883797i | −0.999929 | − | 0.0118887i | \(-0.996216\pi\) |
0.489669 | − | 0.871909i | \(-0.337118\pi\) | |||||||
\(500\) | −4.60916 | + | 7.98331i | −0.206128 | + | 0.357024i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −16.1399 | + | 9.31835i | −0.720357 | + | 0.415898i | ||||
\(503\) | −20.4955 | −0.913848 | −0.456924 | − | 0.889506i | \(-0.651049\pi\) | ||||
−0.456924 | + | 0.889506i | \(0.651049\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.47037 | −0.154429 | ||||||||
\(506\) | −4.28376 | + | 2.47323i | −0.190436 | + | 0.109949i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.29837 | + | 5.71295i | −0.146342 | + | 0.253471i | ||||
\(509\) | 5.99259 | + | 10.3795i | 0.265617 | + | 0.460062i | 0.967725 | − | 0.252008i | \(-0.0810911\pi\) |
−0.702108 | + | 0.712070i | \(0.747758\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.86495 | − | 25.9754i | −0.0825004 | − | 1.14908i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.996716 | + | 0.575454i | 0.0439633 | + | 0.0253822i | ||||
\(515\) | 22.8848 | + | 13.2125i | 1.00842 | + | 0.582214i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.27551i | 0.0560970i | ||||||||
\(518\) | −2.24024 | − | 31.2025i | −0.0984303 | − | 1.37096i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.08346 | − | 5.34072i | −0.135219 | − | 0.234206i | ||||
\(521\) | 2.33369 | − | 4.04208i | 0.102241 | − | 0.177087i | −0.810367 | − | 0.585923i | \(-0.800732\pi\) |
0.912608 | + | 0.408837i | \(0.134065\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.5494 | + | 10.1322i | −0.767383 | + | 0.443049i | −0.831940 | − | 0.554865i | \(-0.812770\pi\) |
0.0645573 | + | 0.997914i | \(0.479436\pi\) | |||||||
\(524\) | −1.51472 | −0.0661708 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.14678 | −0.311614 | ||||||||
\(527\) | −39.3983 | + | 22.7466i | −1.71622 | + | 0.990859i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.733751 | − | 1.27089i | 0.0319022 | − | 0.0552562i | ||||
\(530\) | −0.602614 | − | 1.04376i | −0.0261759 | − | 0.0453379i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −11.4529 | + | 7.75611i | −0.496546 | + | 0.336270i | ||||
\(533\) | − | 4.71479i | − | 0.204220i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.30756 | − | 3.64167i | −0.272700 | − | 0.157443i | ||||
\(536\) | −10.5927 | − | 6.11571i | −0.457536 | − | 0.264159i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13.3794i | 0.576826i | ||||||||
\(539\) | 5.50000 | − | 4.33013i | 0.236902 | − | 0.186512i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.53334 | + | 11.3161i | 0.280890 | + | 0.486516i | 0.971604 | − | 0.236612i | \(-0.0760370\pi\) |
−0.690714 | + | 0.723128i | \(0.742704\pi\) | |||||||
\(542\) | −3.41849 | + | 5.92100i | −0.146837 | + | 0.254329i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.58346 | + | 2.64626i | −0.196514 | + | 0.113458i | ||||
\(545\) | 34.0858 | 1.46008 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.2492 | 1.03682 | 0.518411 | − | 0.855132i | \(-0.326524\pi\) | ||||
0.518411 | + | 0.855132i | \(0.326524\pi\) | |||||||
\(548\) | 12.0316 | − | 6.94646i | 0.513966 | − | 0.296738i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.669251 | + | 1.15918i | −0.0285369 | + | 0.0494274i | ||||
\(551\) | 21.0686 | + | 36.4918i | 0.897552 | + | 1.55461i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.14962 | + | 16.7884i | −0.346557 | + | 0.713915i | ||||
\(554\) | 5.74807i | 0.244212i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.7702 | − | 6.79555i | −0.499170 | − | 0.288196i | ||||
\(557\) | 20.6838 | + | 11.9418i | 0.876402 | + | 0.505991i | 0.869471 | − | 0.493985i | \(-0.164460\pi\) |
0.00693183 | + | 0.999976i | \(0.497794\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29.3550i | 1.24159i | ||||||||
\(560\) | −6.64394 | + | 0.477014i | −0.280758 | + | 0.0201575i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.22911 | − | 5.59298i | −0.136212 | − | 0.235925i | ||||
\(563\) | −1.15091 | + | 1.99343i | −0.0485050 | + | 0.0840131i | −0.889259 | − | 0.457405i | \(-0.848779\pi\) |
0.840754 | + | 0.541418i | \(0.182112\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 31.7674 | − | 18.3409i | 1.33646 | − | 0.771608i | ||||
\(566\) | −6.78783 | −0.285314 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.7055 | −0.617029 | ||||||||
\(569\) | 21.7718 | − | 12.5699i | 0.912720 | − | 0.526959i | 0.0314144 | − | 0.999506i | \(-0.489999\pi\) |
0.881305 | + | 0.472548i | \(0.156666\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.9626 | + | 31.1122i | −0.751713 | + | 1.30200i | 0.195279 | + | 0.980748i | \(0.437439\pi\) |
−0.946992 | + | 0.321257i | \(0.895895\pi\) | |||||||
\(572\) | 1.22474 | + | 2.12132i | 0.0512092 | + | 0.0886969i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.58130 | − | 2.22391i | −0.191220 | − | 0.0928241i | ||||
\(575\) | − | 6.62085i | − | 0.276108i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.60396 | − | 1.50340i | −0.108404 | − | 0.0625874i | 0.444818 | − | 0.895621i | \(-0.353269\pi\) |
−0.553222 | + | 0.833034i | \(0.686602\pi\) | |||||||
\(578\) | 9.53568 | + | 5.50543i | 0.396632 | + | 0.228996i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 20.2918i | 0.842571i | ||||||||
\(581\) | −13.8836 | − | 20.5009i | −0.575989 | − | 0.850520i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.239357 | + | 0.414578i | 0.00991314 | + | 0.0171701i | ||||
\(584\) | 4.92152 | − | 8.52432i | 0.203654 | − | 0.352739i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.72936 | − | 1.57579i | 0.112749 | − | 0.0650954i | ||||
\(587\) | 30.2752 | 1.24959 | 0.624796 | − | 0.780788i | \(-0.285182\pi\) | ||||
0.624796 | + | 0.780788i | \(0.285182\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −44.9389 | −1.85167 | ||||||||
\(590\) | −13.1908 | + | 7.61571i | −0.543057 | + | 0.313534i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.91189 | − | 10.2397i | 0.242977 | − | 0.420849i | ||||
\(593\) | 2.54071 | + | 4.40063i | 0.104334 | + | 0.180712i | 0.913466 | − | 0.406915i | \(-0.133395\pi\) |
−0.809132 | + | 0.587627i | \(0.800062\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19.7680 | + | 29.1900i | 0.810409 | + | 1.19667i | ||||
\(596\) | 6.65221i | 0.272485i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10.4930 | − | 6.05816i | −0.429092 | − | 0.247736i | ||||
\(599\) | −34.0097 | − | 19.6355i | −1.38960 | − | 0.802285i | −0.396329 | − | 0.918108i | \(-0.629716\pi\) |
−0.993270 | + | 0.115823i | \(0.963049\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.04133i | 0.328013i | 0.986459 | + | 0.164006i | \(0.0524417\pi\) | ||||
−0.986459 | + | 0.164006i | \(0.947558\pi\) | |||||||
\(602\) | 28.5239 | + | 13.8464i | 1.16255 | + | 0.564338i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.00877 | + | 6.94339i | 0.163114 | + | 0.282522i | ||||
\(605\) | 1.25882 | − | 2.18034i | 0.0511783 | − | 0.0886434i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.6848 | − | 17.1385i | 1.20487 | − | 0.695632i | 0.243236 | − | 0.969967i | \(-0.421791\pi\) |
0.961634 | + | 0.274335i | \(0.0884578\pi\) | |||||||
\(608\) | −5.22803 | −0.212025 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 31.2618 | 1.26576 | ||||||||
\(611\) | −2.70577 | + | 1.56218i | −0.109464 | + | 0.0631990i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.8924 | + | 32.7226i | −0.763057 | + | 1.32165i | 0.178211 | + | 0.983992i | \(0.442969\pi\) |
−0.941268 | + | 0.337661i | \(0.890364\pi\) | |||||||
\(614\) | 7.53553 | + | 13.0519i | 0.304109 | + | 0.526733i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.63896 | − | 0.189469i | 0.106327 | − | 0.00763391i | ||||
\(617\) | − | 0.0377832i | − | 0.00152109i | −1.00000 | 0.000760547i | \(-0.999758\pi\) | |||
1.00000 | 0.000760547i | \(-0.000242090\pi\) | ||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.61028 | + | 3.23910i | 0.225496 | + | 0.130190i | 0.608493 | − | 0.793559i | \(-0.291774\pi\) |
−0.382996 | + | 0.923750i | \(0.625108\pi\) | |||||||
\(620\) | −18.7417 | − | 10.8205i | −0.752683 | − | 0.434562i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 31.9145i | 1.27966i | ||||||||
\(623\) | −18.3105 | + | 37.7201i | −0.733595 | + | 1.51122i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.9505 | + | 25.8950i | 0.598018 | + | 1.03580i | ||||
\(626\) | −7.97469 | + | 13.8126i | −0.318733 | + | 0.552061i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −19.0820 | + | 11.0170i | −0.761456 | + | 0.439627i | ||||
\(629\) | −62.5777 | −2.49514 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.8145 | −0.709184 | −0.354592 | − | 0.935021i | \(-0.615380\pi\) | ||||
−0.354592 | + | 0.935021i | \(0.615380\pi\) | |||||||
\(632\) | −6.10854 | + | 3.52677i | −0.242985 | + | 0.140287i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12.6623 | − | 21.9318i | 0.502886 | − | 0.871023i | ||||
\(635\) | 8.30411 | + | 14.3831i | 0.329539 | + | 0.570778i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.9217 | + | 6.36396i | 0.630840 | + | 0.252149i | ||||
\(638\) | − | 8.05986i | − | 0.319093i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.18034 | − | 1.25882i | −0.0861854 | − | 0.0497592i | ||||
\(641\) | −16.1473 | − | 9.32265i | −0.637780 | − | 0.368222i | 0.145979 | − | 0.989288i | \(-0.453367\pi\) |
−0.783759 | + | 0.621065i | \(0.786700\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 7.04112i | − | 0.277674i | −0.990315 | − | 0.138837i | \(-0.955664\pi\) | ||
0.990315 | − | 0.138837i | \(-0.0443365\pi\) | |||||||
\(644\) | −10.8361 | + | 7.33839i | −0.427001 | + | 0.289173i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.8347 | + | 23.9625i | 0.544321 | + | 0.942791i | ||||
\(647\) | −25.0127 | + | 43.3232i | −0.983350 | + | 1.70321i | −0.334299 | + | 0.942467i | \(0.608500\pi\) |
−0.649051 | + | 0.760745i | \(0.724834\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.23936 | − | 3.02494i | 0.205663 | − | 0.118739i | ||||
\(650\) | −3.27865 | −0.128599 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.0645 | 0.394156 | ||||||||
\(653\) | −2.68285 | + | 1.54894i | −0.104988 | + | 0.0606149i | −0.551575 | − | 0.834126i | \(-0.685973\pi\) |
0.446587 | + | 0.894740i | \(0.352639\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.90676 | + | 3.30260i | −0.0745031 | + | 0.129043i | ||||
\(656\) | −0.962402 | − | 1.66693i | −0.0375755 | − | 0.0650826i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.241670 | + | 3.36603i | 0.00942127 | + | 0.131221i | ||||
\(659\) | 41.9739i | 1.63507i | 0.575878 | + | 0.817536i | \(0.304660\pi\) | ||||
−0.575878 | + | 0.817536i | \(0.695340\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.8408 | − | 13.1872i | −0.888405 | − | 0.512921i | −0.0149846 | − | 0.999888i | \(-0.504770\pi\) |
−0.873420 | + | 0.486967i | \(0.838103\pi\) | |||||||
\(662\) | 12.1916 | + | 7.03882i | 0.473840 | + | 0.273571i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 9.35827i | − | 0.363171i | ||||||
\(665\) | 2.49384 | + | 34.7347i | 0.0967070 | + | 1.34695i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.9339 | + | 34.5265i | 0.771843 | + | 1.33687i | ||||
\(668\) | 2.38134 | − | 4.12460i | 0.0921369 | − | 0.159586i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −26.6687 | + | 15.3972i | −1.03030 | + | 0.594844i | ||||
\(671\) | −12.4171 | −0.479358 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.60164 | −0.254475 | −0.127237 | − | 0.991872i | \(-0.540611\pi\) | ||||
−0.127237 | + | 0.991872i | \(0.540611\pi\) | |||||||
\(674\) | 7.05934 | − | 4.07571i | 0.271916 | − | 0.156991i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.50000 | − | 6.06218i | 0.134615 | − | 0.233161i | ||||
\(677\) | −4.52228 | − | 7.83282i | −0.173805 | − | 0.301040i | 0.765942 | − | 0.642910i | \(-0.222273\pi\) |
−0.939747 | + | 0.341870i | \(0.888940\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29.9149 | − | 20.2590i | 1.14803 | − | 0.777468i | ||||
\(680\) | 13.3247i | 0.510978i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7.44414 | + | 4.29788i | 0.285051 | + | 0.164574i | ||||
\(683\) | −27.2954 | − | 15.7590i | −1.04443 | − | 0.603003i | −0.123346 | − | 0.992364i | \(-0.539363\pi\) |
−0.921085 | + | 0.389361i | \(0.872696\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 34.9774i | − | 1.33642i | ||||||
\(686\) | 13.6938 | − | 12.4691i | 0.522834 | − | 0.476073i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.99207 | + | 10.3786i | 0.228446 | + | 0.395679i | ||||
\(689\) | −0.586302 | + | 1.01550i | −0.0223363 | + | 0.0386876i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.3742 | − | 15.2272i | 1.00332 | − | 0.579268i | 0.0940927 | − | 0.995563i | \(-0.470005\pi\) |
0.909230 | + | 0.416295i | \(0.136672\pi\) | |||||||
\(692\) | 14.7369 | 0.560211 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −22.5746 | −0.856919 | ||||||||
\(695\) | −29.6332 | + | 17.1087i | −1.12405 | + | 0.648972i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.09354 | + | 8.82227i | −0.192932 | + | 0.334167i | ||||
\(698\) | 11.4749 | + | 19.8751i | 0.434332 | + | 0.752284i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.54650 | + | 3.18582i | −0.0584521 | + | 0.120413i | ||||
\(701\) | − | 26.3465i | − | 0.995093i | −0.867437 | − | 0.497547i | \(-0.834234\pi\) | ||
0.867437 | − | 0.497547i | \(-0.165766\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −53.5334 | − | 30.9075i | −2.01905 | − | 1.16570i | ||||
\(704\) | 0.866025 | + | 0.500000i | 0.0326396 | + | 0.0188445i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 25.1981i | − | 0.948342i | ||||||
\(707\) | 3.63760 | − | 0.261168i | 0.136806 | − | 0.00982223i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.35292 | − | 9.27154i | −0.201033 | − | 0.348200i | 0.747828 | − | 0.663892i | \(-0.231097\pi\) |
−0.948862 | + | 0.315692i | \(0.897763\pi\) | |||||||
\(710\) | −18.5116 | + | 32.0630i | −0.694726 | + | 1.20330i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −13.7246 | + | 7.92392i | −0.514353 | + | 0.296962i | ||||
\(713\) | −42.5186 | −1.59233 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.16693 | 0.230630 | ||||||||
\(716\) | −2.03491 | + | 1.17486i | −0.0760482 | + | 0.0439065i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.84714 | + | 17.0558i | −0.367492 | + | 0.636515i | ||||
\(719\) | −15.3059 | − | 26.5107i | −0.570815 | − | 0.988681i | −0.996482 | − | 0.0838012i | \(-0.973294\pi\) |
0.425667 | − | 0.904880i | \(-0.360039\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.9819 | − | 12.1270i | −0.930374 | − | 0.451633i | ||||
\(722\) | 8.33229i | 0.310096i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.3261 | − | 5.96178i | −0.383767 | − | 0.221568i | ||||
\(725\) | 9.34279 | + | 5.39406i | 0.346983 | + | 0.200331i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 7.03188i | − | 0.260798i | −0.991462 | − | 0.130399i | \(-0.958374\pi\) | ||
0.991462 | − | 0.130399i | \(-0.0416258\pi\) | |||||||
\(728\) | 3.63397 | + | 5.36603i | 0.134684 | + | 0.198878i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −12.3906 | − | 21.4612i | −0.458597 | − | 0.794313i | ||||
\(731\) | 31.7132 | − | 54.9289i | 1.17296 | − | 2.03162i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.5539 | − | 11.2895i | 0.722240 | − | 0.416985i | −0.0933367 | − | 0.995635i | \(-0.529753\pi\) |
0.815577 | + | 0.578649i | \(0.196420\pi\) | |||||||
\(734\) | −3.24796 | −0.119885 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.94646 | −0.182329 | ||||||||
\(737\) | 10.5927 | − | 6.11571i | 0.390188 | − | 0.225275i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.24921 | + | 16.0201i | −0.340238 | + | 0.589309i | −0.984477 | − | 0.175515i | \(-0.943841\pi\) |
0.644239 | + | 0.764824i | \(0.277174\pi\) | |||||||
\(740\) | −14.8840 | − | 25.7798i | −0.547147 | − | 0.947686i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.710202 | + | 1.04870i | 0.0260723 | + | 0.0384991i | ||||
\(743\) | − | 22.8029i | − | 0.836558i | −0.908319 | − | 0.418279i | \(-0.862633\pi\) | ||
0.908319 | − | 0.418279i | \(-0.137367\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.5041 | + | 8.37393i | 0.531388 | + | 0.306797i | ||||
\(746\) | 5.90935 | + | 3.41177i | 0.216357 | + | 0.124914i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 5.29253i | − | 0.193514i | ||||||
\(749\) | 6.88557 | + | 3.34247i | 0.251593 | + | 0.122131i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.6992 | + | 27.1918i | 0.572871 | + | 0.992242i | 0.996269 | + | 0.0862983i | \(0.0275038\pi\) |
−0.423398 | + | 0.905944i | \(0.639163\pi\) | |||||||
\(752\) | −0.637756 | + | 1.10463i | −0.0232566 | + | 0.0402816i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 17.0975 | − | 9.87127i | 0.622656 | − | 0.359490i | ||||
\(755\) | 20.1852 | 0.734616 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.6251 | −0.567905 | −0.283953 | − | 0.958838i | \(-0.591646\pi\) | ||||
−0.283953 | + | 0.958838i | \(0.591646\pi\) | |||||||
\(758\) | −16.3618 | + | 9.44646i | −0.594286 | + | 0.343111i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.58114 | + | 11.3989i | −0.238723 | + | 0.413481i | ||||
\(761\) | −20.4241 | − | 35.3755i | −0.740372 | − | 1.28236i | −0.952326 | − | 0.305082i | \(-0.901316\pi\) |
0.211954 | − | 0.977280i | \(-0.432017\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −35.7284 | + | 2.56518i | −1.29345 | + | 0.0928658i | ||||
\(764\) | 24.5765i | 0.889146i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 22.8916 | + | 13.2165i | 0.827106 | + | 0.477530i | ||||
\(767\) | 12.8338 | + | 7.40957i | 0.463400 | + | 0.267544i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.71477i | − | 0.0618361i | −0.999522 | − | 0.0309181i | \(-0.990157\pi\) | ||
0.999522 | − | 0.0309181i | \(-0.00984309\pi\) | |||||||
\(770\) | 2.90887 | − | 5.99233i | 0.104828 | − | 0.215949i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.05657 | − | 12.2223i | −0.253972 | − | 0.439892i | ||||
\(773\) | 8.25433 | − | 14.2969i | 0.296887 | − | 0.514224i | −0.678535 | − | 0.734568i | \(-0.737385\pi\) |
0.975422 | + | 0.220344i | \(0.0707180\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.96399 | + | 5.75272i | −0.357917 | + | 0.206644i | ||||
\(776\) | 13.6556 | 0.490208 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.6678 | 0.418312 | ||||||||
\(779\) | −8.71475 | + | 5.03146i | −0.312238 | + | 0.180271i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.35275 | − | 12.7353i | 0.263102 | − | 0.455706i | ||||
\(782\) | 13.0897 | + | 22.6719i | 0.468085 | + | 0.810747i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.92820 | − | 1.00000i | 0.247436 | − | 0.0357143i | ||||
\(785\) | 55.4737i | 1.97994i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.9077 | + | 21.8860i | 1.35126 | + | 0.780153i | 0.988427 | − | 0.151699i | \(-0.0484744\pi\) |
0.362838 | + | 0.931852i | \(0.381808\pi\) | |||||||
\(788\) | −0.501618 | − | 0.289609i | −0.0178694 | − | 0.0103169i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 17.7583i | 0.631810i | ||||||||
\(791\) | −31.9179 | + | 21.6154i | −1.13487 | + | 0.768556i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.2078 | − | 26.3407i | −0.540046 | − | 0.935386i | ||||
\(794\) | 5.01532 | − | 8.68678i | 0.177987 | − | 0.308282i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.08228 | − | 1.20220i | 0.0738045 | − | 0.0426110i | ||||
\(797\) | −27.8981 | −0.988203 | −0.494102 | − | 0.869404i | \(-0.664503\pi\) | ||||
−0.494102 | + | 0.869404i | \(0.664503\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.75069 | 0.238822 | ||||||||
\(800\) | −1.15918 | + | 0.669251i | −0.0409831 | + | 0.0236616i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.61125 | − | 4.52281i | 0.0922063 | − | 0.159706i | ||||
\(803\) | 4.92152 | + | 8.52432i | 0.173677 | + | 0.300817i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.35953 | + | 32.8640i | 0.0831625 | + | 1.15830i | ||||
\(806\) | 21.0552i | 0.741638i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.19375 | + | 0.689211i | 0.0419959 | + | 0.0242464i | ||||
\(809\) | 9.97340 | + | 5.75815i | 0.350646 | + | 0.202446i | 0.664970 | − | 0.746870i | \(-0.268444\pi\) |
−0.314324 | + | 0.949316i | \(0.601778\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.86619i | 0.276219i | 0.990417 | + | 0.138110i | \(0.0441026\pi\) | ||||
−0.990417 | + | 0.138110i | \(0.955897\pi\) | |||||||
\(812\) | −1.52709 | − | 21.2696i | −0.0535904 | − | 0.746417i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.91189 | + | 10.2397i | 0.207212 | + | 0.358901i | ||||
\(815\) | 12.6694 | − | 21.9440i | 0.443789 | − | 0.768665i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 54.2595 | − | 31.3267i | 1.89830 | − | 1.09598i | ||||
\(818\) | 19.2207 | 0.672037 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.84596 | −0.169228 | ||||||||
\(821\) | −7.40031 | + | 4.27257i | −0.258272 | + | 0.149114i | −0.623546 | − | 0.781786i | \(-0.714309\pi\) |
0.365274 | + | 0.930900i | \(0.380975\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.71503 | − | 8.16668i | 0.164356 | − | 0.284673i | −0.772071 | − | 0.635537i | \(-0.780779\pi\) |
0.936426 | + | 0.350864i | \(0.114112\pi\) | |||||||
\(824\) | −5.24799 | − | 9.08978i | −0.182822 | − | 0.316658i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.2533 | − | 8.97540i | 0.461142 | − | 0.312294i | ||||
\(827\) | 10.9084i | 0.379323i | 0.981850 | + | 0.189662i | \(0.0607391\pi\) | ||||
−0.981850 | + | 0.189662i | \(0.939261\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.54168 | − | 5.50889i | −0.331396 | − | 0.191332i | 0.325065 | − | 0.945692i | \(-0.394614\pi\) |
−0.656461 | + | 0.754360i | \(0.727947\pi\) | |||||||
\(830\) | −20.4042 | − | 11.7804i | −0.708240 | − | 0.408903i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.44949i | 0.0849208i | ||||||||
\(833\) | −22.9173 | − | 29.1089i | −0.794038 | − | 1.00856i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.99536 | − | 10.3843i | −0.207478 | − | 0.359362i | ||||
\(836\) | 2.61401 | − | 4.52761i | 0.0904076 | − | 0.156591i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −15.1342 | + | 8.73774i | −0.522803 | + | 0.301840i | ||||
\(839\) | 19.2163 | 0.663422 | 0.331711 | − | 0.943381i | \(-0.392374\pi\) | ||||
0.331711 | + | 0.943381i | \(0.392374\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −35.9613 | −1.24004 | ||||||||
\(842\) | −24.1205 | + | 13.9260i | −0.831246 | + | 0.479920i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.99672 | + | 5.19046i | −0.103151 | + | 0.178663i | ||||
\(845\) | −8.81173 | − | 15.2624i | −0.303133 | − | 0.525041i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.15539 | + | 2.38014i | −0.0396998 | + | 0.0817826i | ||||
\(848\) | 0.478713i | 0.0164391i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.13497 | + | 3.54203i | 0.210428 | + | 0.121491i | ||||
\(851\) | −50.6503 | − | 29.2430i | −1.73627 | − | 1.00244i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 50.2570i | − | 1.72077i | −0.509649 | − | 0.860383i | \(-0.670225\pi\) | ||
0.509649 | − | 0.860383i | \(-0.329775\pi\) | |||||||
\(854\) | −32.7683 | + | 2.35266i | −1.12131 | + | 0.0805063i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.44646 | + | 2.50535i | 0.0494391 | + | 0.0856310i | ||||
\(857\) | −6.92321 | + | 11.9914i | −0.236492 | + | 0.409617i | −0.959705 | − | 0.281008i | \(-0.909331\pi\) |
0.723213 | + | 0.690625i | \(0.242664\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.3460 | + | 6.55059i | −0.387119 | + | 0.223503i | −0.680911 | − | 0.732366i | \(-0.738416\pi\) |
0.293792 | + | 0.955869i | \(0.405083\pi\) | |||||||
\(860\) | 30.1717 | 1.02885 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −34.8542 | −1.18714 | ||||||||
\(863\) | 29.1086 | − | 16.8058i | 0.990867 | − | 0.572077i | 0.0853335 | − | 0.996352i | \(-0.472804\pi\) |
0.905533 | + | 0.424275i | \(0.139471\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.5510 | − | 32.1313i | 0.630754 | − | 1.09250i | ||||
\(866\) | −13.6034 | − | 23.5618i | −0.462262 | − | 0.800662i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 20.4591 | + | 9.93149i | 0.694427 | + | 0.337097i | ||||
\(869\) | − | 7.05354i | − | 0.239275i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.9468 | + | 14.9804i | 0.879173 | + | 0.507591i | ||||
\(872\) | −11.7250 | − | 6.76941i | −0.397057 | − | 0.229241i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 25.8603i | 0.874736i | ||||||||
\(875\) | −13.6760 | − | 20.1943i | −0.462332 | − | 0.682693i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.0399 | + | 24.3178i | 0.474093 | + | 0.821153i | 0.999560 | − | 0.0296608i | \(-0.00944271\pi\) |
−0.525467 | + | 0.850814i | \(0.676109\pi\) | |||||||
\(878\) | 11.6040 | − | 20.0987i | 0.391616 | − | 0.678299i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.18034 | − | 1.25882i | 0.0734992 | − | 0.0424348i | ||||
\(881\) | −20.4395 | −0.688623 | −0.344312 | − | 0.938855i | \(-0.611888\pi\) | ||||
−0.344312 | + | 0.938855i | \(0.611888\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.7609 | −0.967880 | −0.483940 | − | 0.875101i | \(-0.660795\pi\) | ||||
−0.483940 | + | 0.875101i | \(0.660795\pi\) | |||||||
\(884\) | 11.2271 | − | 6.48200i | 0.377610 | − | 0.218013i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.07435 | − | 15.7172i | 0.304859 | − | 0.528031i | ||||
\(887\) | 24.6498 | + | 42.6947i | 0.827659 | + | 1.43355i | 0.899870 | + | 0.436158i | \(0.143661\pi\) |
−0.0722117 | + | 0.997389i | \(0.523006\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.78670 | − | 14.4513i | −0.328235 | − | 0.484681i | ||||
\(890\) | 39.8991i | 1.33742i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.48647 | + | 3.74496i | 0.217183 | + | 0.125391i | ||||
\(893\) | 5.77502 | + | 3.33421i | 0.193254 | + | 0.111575i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.91573i | 0.197741i | ||||||||
\(896\) | 2.38014 | + | 1.15539i | 0.0795149 | + | 0.0385990i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.9828 | + | 27.6830i | 0.533352 | + | 0.923793i | ||||
\(899\) | 34.6403 | − | 59.9987i | 1.15532 | − | 2.00107i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.19417 | − | 1.26680i | 0.0730983 | − | 0.0422033i | ||||
\(902\) | 1.92480 | 0.0640889 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.5699 | −0.484589 | ||||||||
\(905\) | −25.9974 | + | 15.0096i | −0.864183 | + | 0.498936i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.2780 | + | 31.6584i | −0.606911 | + | 1.05120i | 0.384835 | + | 0.922985i | \(0.374258\pi\) |
−0.991746 | + | 0.128215i | \(0.959075\pi\) | |||||||
\(908\) | −4.88304 | − | 8.45768i | −0.162049 | − | 0.280678i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 16.2743 | − | 1.16844i | 0.539487 | − | 0.0387334i | ||||
\(911\) | − | 33.3749i | − | 1.10576i | −0.833261 | − | 0.552880i | \(-0.813529\pi\) | ||
0.833261 | − | 0.552880i | \(-0.186471\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.10450 | + | 4.67914i | 0.268220 | + | 0.154857i | ||||
\(914\) | 22.4486 | + | 12.9607i | 0.742534 | + | 0.428702i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 0.225376i | − | 0.00744664i | ||||||
\(917\) | 1.75010 | − | 3.60524i | 0.0577933 | − | 0.119056i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.34095 | + | 7.51874i | 0.143195 | + | 0.248020i | 0.928698 | − | 0.370837i | \(-0.120929\pi\) |
−0.785503 | + | 0.618857i | \(0.787596\pi\) | |||||||
\(920\) | −6.22670 | + | 10.7850i | −0.205288 | + | 0.355570i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 18.9038 | − | 10.9141i | 0.622563 | − | 0.359437i | ||||
\(923\) | 36.0210 | 1.18564 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.8262 | −0.520361 | ||||||||
\(926\) | −4.26622 | + | 2.46311i | −0.140197 | + | 0.0809427i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.02993 | − | 6.98004i | 0.132289 | − | 0.229131i | ||||
\(929\) | 18.8642 | + | 32.6738i | 0.618915 | + | 1.07199i | 0.989684 | + | 0.143267i | \(0.0457608\pi\) |
−0.370769 | + | 0.928725i | \(0.620906\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.22803 | − | 36.2208i | −0.171342 | − | 1.18709i | ||||
\(932\) | − | 0.514719i | − | 0.0168602i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.24592 | + | 1.87404i | 0.106210 | + | 0.0613203i | ||||
\(935\) | −11.5395 | − | 6.66234i | −0.377382 | − | 0.217882i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.55832i | − | 0.0835768i | −0.999126 | − | 0.0417884i | \(-0.986694\pi\) | ||
0.999126 | − | 0.0417884i | \(-0.0133055\pi\) | |||||||
\(938\) | 26.7950 | − | 18.1461i | 0.874889 | − | 0.592491i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.60564 | + | 2.78105i | 0.0523702 | + | 0.0907078i | ||||
\(941\) | −24.3638 | + | 42.1993i | −0.794236 | + | 1.37566i | 0.129087 | + | 0.991633i | \(0.458795\pi\) |
−0.923323 | + | 0.384024i | \(0.874538\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.24540 | + | 4.76049i | −0.268507 | + | 0.155023i | ||||
\(944\) | 6.04989 | 0.196907 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.9841 | −0.389638 | ||||||||
\(947\) | −30.4320 | + | 17.5699i | −0.988908 | + | 0.570946i | −0.904948 | − | 0.425523i | \(-0.860090\pi\) |
−0.0839599 | + | 0.996469i | \(0.526757\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.0552 | + | 20.8802i | −0.391329 | + | 0.677801i | ||||
\(950\) | 3.49886 | + | 6.06021i | 0.113518 | + | 0.196619i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.00277 | − | 13.9668i | −0.0324999 | − | 0.452665i | ||||
\(953\) | − | 1.34315i | − | 0.0435088i | −0.999763 | − | 0.0217544i | \(-0.993075\pi\) | ||
0.999763 | − | 0.0217544i | \(-0.00692518\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 53.5851 | + | 30.9374i | 1.73397 | + | 1.00111i | ||||
\(956\) | −13.4147 | − | 7.74496i | −0.433861 | − | 0.250490i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.86267i | 0.124797i | ||||||||
\(959\) | 2.63227 | + | 36.6629i | 0.0850006 | + | 1.18391i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.4435 | + | 37.1412i | 0.691726 | + | 1.19810i | ||||
\(962\) | −14.4811 | + | 25.0820i | −0.466890 | + | 0.808677i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.2882 | + | 8.24932i | −0.460194 | + | 0.265693i | ||||
\(965\) | −35.5318 | −1.14381 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.3045 | −1.10316 | −0.551580 | − | 0.834122i | \(-0.685975\pi\) | ||||
−0.551580 | + | 0.834122i | \(0.685975\pi\) | |||||||
\(968\) | −0.866025 | + | 0.500000i | −0.0278351 | + | 0.0160706i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 17.1899 | − | 29.7739i | 0.551936 | − | 0.955981i | ||||
\(971\) | −2.71114 | − | 4.69583i | −0.0870046 | − | 0.150696i | 0.819239 | − | 0.573452i | \(-0.194396\pi\) |
−0.906244 | + | 0.422756i | \(0.861063\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.7736 | − | 20.1633i | 0.954499 | − | 0.646405i | ||||
\(974\) | − | 11.6189i | − | 0.372294i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.7536 | − | 6.20857i | −0.344213 | − | 0.198731i | ||||
\(977\) | 3.04148 | + | 1.75600i | 0.0973056 | + | 0.0561794i | 0.547863 | − | 0.836568i | \(-0.315441\pi\) |
−0.450558 | + | 0.892747i | \(0.648775\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 15.8478i | − | 0.506499i | ||||||
\(980\) | 6.54102 | − | 16.3646i | 0.208945 | − | 0.522749i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.8672 | + | 22.2867i | 0.410610 | + | 0.711198i | ||||
\(983\) | −0.0659506 | + | 0.114230i | −0.00210350 | + | 0.00364336i | −0.867075 | − | 0.498177i | \(-0.834003\pi\) |
0.864972 | + | 0.501821i | \(0.167336\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.26289 | + | 0.729131i | −0.0402391 | + | 0.0232321i | ||||
\(986\) | −42.6570 | −1.35848 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.8060 | 0.407413 | ||||||||
\(989\) | 51.3372 | − | 29.6396i | 1.63243 | − | 0.942483i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.6398 | + | 23.6249i | −0.433283 | + | 0.750468i | −0.997154 | − | 0.0753949i | \(-0.975978\pi\) |
0.563871 | + | 0.825863i | \(0.309312\pi\) | |||||||
\(992\) | 4.29788 | + | 7.44414i | 0.136458 | + | 0.236352i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 16.9907 | − | 35.0011i | 0.538911 | − | 1.11017i | ||||
\(995\) | − | 6.05343i | − | 0.191907i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.6642 | + | 22.9001i | 1.25618 | + | 0.725254i | 0.972329 | − | 0.233615i | \(-0.0750555\pi\) |
0.283848 | + | 0.958869i | \(0.408389\pi\) | |||||||
\(998\) | 19.7425 | + | 11.3984i | 0.624939 | + | 0.360809i | ||||
\(999\) | 0 | 0 |
(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 | 1386.2.r.a.1277.1 | yes | 8 | |
3.2 | odd | 2 | 1386.2.r.c.1277.4 | yes | 8 | ||
7.5 | odd | 6 | 1386.2.r.c.89.4 | yes | 8 | ||
21.5 | even | 6 | inner | 1386.2.r.a.89.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.r.a.89.1 | ✓ | 8 | 21.5 | even | 6 | inner | |
1386.2.r.a.1277.1 | yes | 8 | 1.1 | even | 1 | trivial | |
1386.2.r.c.89.4 | yes | 8 | 7.5 | odd | 6 | ||
1386.2.r.c.1277.4 | yes | 8 | 3.2 | odd | 2 |