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 | 89.4 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.89 |
Dual form | 1386.2.r.c.1277.4 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | −0.434275 | − | 0.900780i | \(-0.642995\pi\) |
0.997236 | − | 0.0742968i | \(-0.0236712\pi\) | |||||||
\(6\) | 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 | \(0.110320\pi\) | ||||
−0.940540 | + | 0.339683i | \(0.889680\pi\) | |||||||
\(14\) | 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 | 0.985028 | + | 0.172396i | \(0.0551510\pi\) |
−0.343214 | + | 0.939257i | \(0.611516\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.52761 | − | 2.61401i | −1.03870 | − | 0.599696i | −0.119238 | − | 0.992866i | \(-0.538045\pi\) |
−0.919466 | + | 0.393170i | \(0.871379\pi\) | |||||||
\(20\) | 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 | \(-0.160864\pi\) |
0.0182299 | + | 0.999834i | \(0.494197\pi\) | |||||||
\(24\) | 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 | 0.350645 | − | 0.936509i | \(-0.385962\pi\) |
0.986363 | + | 0.164587i | \(0.0526291\pi\) | |||||||
\(32\) | −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 | 0.282129 | − | 0.959376i | \(-0.408959\pi\) |
0.689780 | − | 0.724019i | \(-0.257707\pi\) | |||||||
\(38\) | −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 | \(-0.548025\pi\) | ||||
−0.150302 | + | 0.988640i | \(0.548025\pi\) | |||||||
\(42\) | 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 | \(-0.803679\pi\) |
0.908783 | + | 0.417269i | \(0.137013\pi\) | |||||||
\(48\) | 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 | \(-0.656199\pi\) |
0.528203 | + | 0.849118i | \(0.322866\pi\) | |||||||
\(54\) | 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 | \(-0.0378220\pi\) |
−0.599135 | + | 0.800648i | \(0.704489\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.7536 | + | 6.20857i | 1.37685 | + | 0.794925i | 0.991779 | − | 0.127961i | \(-0.0408432\pi\) |
0.385072 | + | 0.922886i | \(0.374177\pi\) | |||||||
\(62\) | 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 | −0.949182 | − | 0.314728i | \(-0.898087\pi\) |
0.202028 | − | 0.979380i | \(-0.435247\pi\) | |||||||
\(68\) | −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 | −0.907566 | − | 0.419910i | \(-0.862062\pi\) |
−0.0901305 | + | 0.995930i | \(0.528728\pi\) | |||||||
\(74\) | 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 | −0.596536 | − | 0.802587i | \(-0.703457\pi\) |
0.993328 | + | 0.115322i | \(0.0367899\pi\) | |||||||
\(80\) | 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 | \(-0.328311\pi\) | ||||
0.513602 | + | 0.858029i | \(0.328311\pi\) | |||||||
\(84\) | 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 | 0.0500147 | + | 0.998748i | \(0.484073\pi\) |
−0.889949 | + | 0.456060i | \(0.849260\pi\) | |||||||
\(90\) | 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 | \(0.243826\pi\) | ||||
−0.720689 | + | 0.693259i | \(0.756174\pi\) | |||||||
\(98\) | 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 | \(-0.188513\pi\) |
−0.898276 | + | 0.439432i | \(0.855180\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.08978 | − | 5.24799i | −0.895643 | − | 0.517100i | −0.0198589 | − | 0.999803i | \(-0.506322\pi\) |
−0.875784 | + | 0.482703i | \(0.839655\pi\) | |||||||
\(104\) | −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 | \(-0.377991\pi\) |
−0.616188 | + | 0.787599i | \(0.711324\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.76941 | − | 11.7250i | −0.648392 | − | 1.12305i | −0.983507 | − | 0.180870i | \(-0.942109\pi\) |
0.335115 | − | 0.942177i | \(-0.391225\pi\) | |||||||
\(110\) | 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 | \(-0.812255\pi\) |
0.897213 | + | 0.441599i | \(0.145588\pi\) | |||||||
\(132\) | 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 | \(-0.868912\pi\) |
−0.111540 | + | 0.993760i | \(0.535578\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.5911i | 1.15278i | 0.817174 | + | 0.576391i | \(0.195540\pi\) | ||||
−0.817174 | + | 0.576391i | \(0.804460\pi\) | |||||||
\(140\) | 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 | \(-0.245488\pi\) |
−0.245101 | + | 0.969498i | \(0.578821\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00877 | − | 6.94339i | −0.326229 | − | 0.565045i | 0.655532 | − | 0.755168i | \(-0.272445\pi\) |
−0.981760 | + | 0.190123i | \(0.939111\pi\) | |||||||
\(152\) | 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 | −0.523279 | + | 0.852161i | \(0.675291\pi\) |
−0.999633 | + | 0.0270921i | \(0.991375\pi\) | |||||||
\(158\) | 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 | −0.598837 | − | 0.800871i | \(-0.704370\pi\) |
0.992993 | + | 0.118172i | \(0.0377035\pi\) | |||||||
\(164\) | −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 | \(-0.558993\pi\) | ||||
−0.184274 | + | 0.982875i | \(0.558993\pi\) | |||||||
\(168\) | 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 | 0.437266 | + | 0.899332i | \(0.355947\pi\) |
−0.997478 | + | 0.0709824i | \(0.977387\pi\) | |||||||
\(174\) | 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 | \(-0.638679\pi\) |
0.574117 | + | 0.818773i | \(0.305346\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.9236i | 0.886271i | 0.896455 | + | 0.443136i | \(0.146134\pi\) | ||||
−0.896455 | + | 0.443136i | \(0.853866\pi\) | |||||||
\(182\) | 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 | 0.998835 | + | 0.0482604i | \(0.0153677\pi\) |
0.541212 | + | 0.840886i | \(0.317966\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.05657 | + | 12.2223i | 0.507943 | + | 0.879783i | 0.999958 | + | 0.00919638i | \(0.00292734\pi\) |
−0.492015 | + | 0.870587i | \(0.663739\pi\) | |||||||
\(194\) | −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 | −0.424377 | − | 0.905486i | \(-0.639507\pi\) |
0.571985 | + | 0.820264i | \(0.306173\pi\) | |||||||
\(200\) | 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 | \(-0.919313\pi\) | ||
0.968044 | − | 0.250781i | \(-0.0806875\pi\) | |||||||
\(224\) | −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 | \(-0.271728\pi\) |
−0.981330 | + | 0.192334i | \(0.938394\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.195181 | + | 0.112688i | 0.0128980 | + | 0.00744664i | 0.506435 | − | 0.862278i | \(-0.330963\pi\) |
−0.493537 | + | 0.869725i | \(0.664296\pi\) | |||||||
\(230\) | 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 | \(-0.338700\pi\) |
−0.514530 | + | 0.857472i | \(0.672034\pi\) | |||||||
\(234\) | 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 | −0.883759 | − | 0.467943i | \(-0.844995\pi\) |
−0.0366285 | + | 0.999329i | \(0.511662\pi\) | |||||||
\(242\) | 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 | \(-0.700151\pi\) | ||||
−0.588169 | + | 0.808738i | \(0.700151\pi\) | |||||||
\(252\) | 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 | \(-0.821905\pi\) |
0.883415 | + | 0.468591i | \(0.155238\pi\) | |||||||
\(258\) | 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 | \(-0.737385\pi\) |
0.296887 | + | 0.954913i | \(0.404052\pi\) | |||||||
\(264\) | 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 | \(-0.300398\pi\) |
−0.994652 | + | 0.103286i | \(0.967064\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.92100 | + | 3.41849i | 0.359675 | + | 0.207659i | 0.668938 | − | 0.743318i | \(-0.266749\pi\) |
−0.309263 | + | 0.950977i | \(0.600082\pi\) | |||||||
\(272\) | −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 | 0.939357 | − | 0.342940i | \(-0.111423\pi\) |
−0.766673 | + | 0.642037i | \(0.778089\pi\) | |||||||
\(278\) | −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 | −0.315001 | − | 0.949091i | \(-0.602005\pi\) |
0.664437 | + | 0.747344i | \(0.268671\pi\) | |||||||
\(284\) | −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 | \(-0.470655\pi\) | ||||
0.0920589 | + | 0.995754i | \(0.470655\pi\) | |||||||
\(294\) | 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 | \(0.141513\pi\) | ||||
−0.902793 | + | 0.430076i | \(0.858487\pi\) | |||||||
\(308\) | 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 | −0.821113 | − | 0.570765i | \(-0.806647\pi\) |
−0.0837402 | − | 0.996488i | \(-0.526687\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.8126 | + | 7.97469i | 0.780733 | + | 0.450756i | 0.836690 | − | 0.547677i | \(-0.184488\pi\) |
−0.0559572 | + | 0.998433i | \(0.517821\pi\) | |||||||
\(314\) | −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 | \(-0.0814910\pi\) |
0.264405 | + | 0.964412i | \(0.414824\pi\) | |||||||
\(318\) | 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 | −0.992029 | − | 0.126008i | \(-0.959783\pi\) |
0.605141 | + | 0.796118i | \(0.293117\pi\) | |||||||
\(332\) | 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 | \(-0.873867\pi\) |
−0.126996 | + | 0.991903i | \(0.540534\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.9498i | 1.22848i | 0.789121 | + | 0.614238i | \(0.210536\pi\) | ||||
−0.789121 | + | 0.614238i | \(0.789464\pi\) | |||||||
\(350\) | −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 | 0.977740 | + | 0.209820i | \(0.0672877\pi\) |
−0.307161 | + | 0.951658i | \(0.599379\pi\) | |||||||
\(354\) | 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 | \(-0.507294\pi\) |
−0.877255 | + | 0.480025i | \(0.840628\pi\) | |||||||
\(360\) | 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 | −0.424786 | − | 0.905294i | \(-0.639651\pi\) |
0.571614 | + | 0.820523i | \(0.306317\pi\) | |||||||
\(368\) | −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 | −0.940733 | − | 0.339149i | \(-0.889861\pi\) |
0.764078 | + | 0.645124i | \(0.223194\pi\) | |||||||
\(374\) | 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 | −0.301043 | − | 0.953610i | \(-0.597335\pi\) |
0.976373 | − | 0.216094i | \(-0.0693318\pi\) | |||||||
\(384\) | 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 | \(-0.571083\pi\) |
0.733789 | + | 0.679378i | \(0.237750\pi\) | |||||||
\(390\) | 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 | 0.265913 | − | 0.963997i | \(-0.414327\pi\) |
−0.701890 | + | 0.712286i | \(0.747660\pi\) | |||||||
\(398\) | 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 | \(-0.291707\pi\) |
−0.382802 | + | 0.923831i | \(0.625041\pi\) | |||||||
\(402\) | 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 | −0.851475 | − | 0.524395i | \(-0.824292\pi\) |
0.0284013 | + | 0.999597i | \(0.490958\pi\) | |||||||
\(410\) | −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 | \(-0.640383\pi\) | ||||
−0.426866 | + | 0.904315i | \(0.640383\pi\) | |||||||
\(420\) | 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 | \(-0.983780\pi\) |
−0.455240 | + | 0.890369i | \(0.650447\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 27.2068i | − | 1.30748i | −0.756721 | − | 0.653738i | \(-0.773200\pi\) | ||
0.756721 | − | 0.653738i | \(-0.226800\pi\) | |||||||
\(434\) | 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 | −0.0633147 | − | 0.997994i | \(-0.520167\pi\) |
−0.895945 | + | 0.444165i | \(0.853501\pi\) | |||||||
\(440\) | 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 | \(-0.191446\pi\) |
−0.0777693 | + | 0.996971i | \(0.524780\pi\) | |||||||
\(444\) | 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 | 0.385572 | + | 0.922678i | \(0.374004\pi\) |
−0.991848 | + | 0.127424i | \(0.959329\pi\) | |||||||
\(458\) | 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 | \(-0.330266\pi\) | ||||
0.508321 | + | 0.861168i | \(0.330266\pi\) | |||||||
\(462\) | 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 | \(-0.805695\pi\) |
0.906123 | + | 0.423015i | \(0.139028\pi\) | |||||||
\(468\) | 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 | \(-0.194793\pi\) |
−0.906769 | + | 0.421627i | \(0.861459\pi\) | |||||||
\(480\) | 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 | 0.703852 | − | 0.710346i | \(-0.251462\pi\) |
−0.967104 | + | 0.254381i | \(0.918128\pi\) | |||||||
\(488\) | −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 | 0.489669 | + | 0.871909i | \(0.337118\pi\) |
−0.999929 | + | 0.0118887i | \(0.996216\pi\) | |||||||
\(500\) | 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 | \(-0.348951\pi\) | ||||
0.456924 | + | 0.889506i | \(0.348951\pi\) | |||||||
\(504\) | 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 | \(-0.918909\pi\) |
0.702108 | + | 0.712070i | \(0.252242\pi\) | |||||||
\(510\) | 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 | \(-0.199268\pi\) |
−0.912608 | + | 0.408837i | \(0.865935\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.5494 | − | 10.1322i | −0.767383 | − | 0.443049i | 0.0645573 | − | 0.997914i | \(-0.479436\pi\) |
−0.831940 | + | 0.554865i | \(0.812770\pi\) | |||||||
\(524\) | 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 | −0.690714 | − | 0.723128i | \(-0.742704\pi\) |
0.971604 | + | 0.236612i | \(0.0760370\pi\) | |||||||
\(542\) | 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 | \(-0.835540\pi\) |
−0.00693183 | + | 0.999976i | \(0.502206\pi\) | |||||||
\(558\) | 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 | \(-0.151221\pi\) |
−0.840754 | + | 0.541418i | \(0.817888\pi\) | |||||||
\(564\) | 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 | \(-0.510001\pi\) |
−0.881305 | + | 0.472548i | \(0.843334\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.9626 | − | 31.1122i | −0.751713 | − | 1.30200i | −0.946992 | − | 0.321257i | \(-0.895895\pi\) |
0.195279 | − | 0.980748i | \(-0.437439\pi\) | |||||||
\(572\) | −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 | −0.553222 | − | 0.833034i | \(-0.686602\pi\) |
0.444818 | + | 0.895621i | \(0.353269\pi\) | |||||||
\(578\) | −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 | \(-0.714818\pi\) | ||||
−0.624796 | + | 0.780788i | \(0.714818\pi\) | |||||||
\(588\) | 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 | \(-0.866605\pi\) |
0.809132 | + | 0.587627i | \(0.199938\pi\) | |||||||
\(594\) | 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 | \(-0.370284\pi\) |
0.993270 | + | 0.115823i | \(0.0369505\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 8.04133i | − | 0.328013i | −0.986459 | − | 0.164006i | \(-0.947558\pi\) | ||
0.986459 | − | 0.164006i | \(-0.0524417\pi\) | |||||||
\(602\) | −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 | 0.961634 | − | 0.274335i | \(-0.0884578\pi\) |
0.243236 | + | 0.969967i | \(0.421791\pi\) | |||||||
\(608\) | 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 | −0.941268 | − | 0.337661i | \(-0.890364\pi\) |
0.178211 | − | 0.983992i | \(-0.442969\pi\) | |||||||
\(614\) | −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 | −0.382996 | − | 0.923750i | \(-0.625108\pi\) |
0.608493 | + | 0.793559i | \(0.291774\pi\) | |||||||
\(620\) | 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 | \(-0.546633\pi\) |
0.783759 | + | 0.621065i | \(0.213300\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.04112i | 0.277674i | 0.990315 | + | 0.138837i | \(0.0443365\pi\) | ||||
−0.990315 | + | 0.138837i | \(0.955664\pi\) | |||||||
\(644\) | 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 | 0.649051 | + | 0.760745i | \(0.275166\pi\) |
0.334299 | + | 0.942467i | \(0.391500\pi\) | |||||||
\(648\) | 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 | \(-0.314027\pi\) |
−0.446587 | + | 0.894740i | \(0.647361\pi\) | |||||||
\(654\) | 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 | −0.873420 | − | 0.486967i | \(-0.838103\pi\) |
−0.0149846 | + | 0.999888i | \(0.504770\pi\) | |||||||
\(662\) | −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 | \(-0.777727\pi\) |
0.939747 | + | 0.341870i | \(0.111060\pi\) | |||||||
\(678\) | 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 | \(-0.460637\pi\) |
0.921085 | + | 0.389361i | \(0.127304\pi\) | |||||||
\(684\) | 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 | 0.909230 | − | 0.416295i | \(-0.136672\pi\) |
0.0940927 | + | 0.995563i | \(0.470005\pi\) | |||||||
\(692\) | −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 | −0.948862 | − | 0.315692i | \(-0.897763\pi\) |
0.747828 | + | 0.663892i | \(0.231097\pi\) | |||||||
\(710\) | 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 | −0.425667 | − | 0.904880i | \(-0.639961\pi\) |
0.996482 | − | 0.0838012i | \(-0.0267061\pi\) | |||||||
\(720\) | 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 | \(0.0416258\pi\) | ||||
−0.991462 | + | 0.130399i | \(0.958374\pi\) | |||||||
\(728\) | −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 | 0.815577 | − | 0.578649i | \(-0.196420\pi\) |
−0.0933367 | + | 0.995635i | \(0.529753\pi\) | |||||||
\(734\) | 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 | 0.644239 | − | 0.764824i | \(-0.277174\pi\) |
−0.984477 | + | 0.175515i | \(0.943841\pi\) | |||||||
\(740\) | 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 | −0.423398 | − | 0.905944i | \(-0.639163\pi\) |
0.996269 | − | 0.0862983i | \(-0.0275038\pi\) | |||||||
\(752\) | 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 | −0.211954 | − | 0.977280i | \(-0.567983\pi\) |
0.952326 | − | 0.305082i | \(-0.0986840\pi\) | |||||||
\(762\) | 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 | \(0.00984309\pi\) | ||||
−0.999522 | + | 0.0309181i | \(0.990157\pi\) | |||||||
\(770\) | −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 | \(-0.262615\pi\) |
−0.975422 | + | 0.220344i | \(0.929282\pi\) | |||||||
\(774\) | 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 | 0.362838 | − | 0.931852i | \(-0.381808\pi\) |
0.988427 | + | 0.151699i | \(0.0484744\pi\) | |||||||
\(788\) | 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 | \(-0.335497\pi\) | ||||
0.494102 | + | 0.869404i | \(0.335497\pi\) | |||||||
\(798\) | 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 | \(-0.731556\pi\) |
0.314324 | + | 0.949316i | \(0.398222\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 7.86619i | − | 0.276219i | −0.990417 | − | 0.138110i | \(-0.955897\pi\) | ||
0.990417 | − | 0.138110i | \(-0.0441026\pi\) | |||||||
\(812\) | 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 | \(-0.285691\pi\) |
−0.365274 | + | 0.930900i | \(0.619025\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.71503 | + | 8.16668i | 0.164356 | + | 0.284673i | 0.936426 | − | 0.350864i | \(-0.114112\pi\) |
−0.772071 | + | 0.635537i | \(0.780779\pi\) | |||||||
\(824\) | 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 | −0.656461 | − | 0.754360i | \(-0.727947\pi\) |
0.325065 | + | 0.945692i | \(0.394614\pi\) | |||||||
\(830\) | 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 | \(-0.607626\pi\) | ||||
−0.331711 | + | 0.943381i | \(0.607626\pi\) | |||||||
\(840\) | 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 | \(0.329775\pi\) | ||||
−0.509649 | + | 0.860383i | \(0.670225\pi\) | |||||||
\(854\) | 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 | \(-0.0906688\pi\) |
−0.723213 | + | 0.690625i | \(0.757336\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.3460 | − | 6.55059i | −0.387119 | − | 0.223503i | 0.293792 | − | 0.955869i | \(-0.405083\pi\) |
−0.680911 | + | 0.732366i | \(0.738416\pi\) | |||||||
\(860\) | −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 | \(-0.527196\pi\) |
−0.905533 | + | 0.424275i | \(0.860529\pi\) | |||||||
\(864\) | 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 | −0.525467 | − | 0.850814i | \(-0.676109\pi\) |
0.999560 | + | 0.0296608i | \(0.00944271\pi\) | |||||||
\(878\) | −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 | \(-0.388112\pi\) | ||||
0.344312 | + | 0.938855i | \(0.388112\pi\) | |||||||
\(882\) | 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 | 0.0722117 | + | 0.997389i | \(0.476994\pi\) |
−0.899870 | + | 0.436158i | \(0.856339\pi\) | |||||||
\(888\) | 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 | −0.991746 | − | 0.128215i | \(-0.959075\pi\) |
0.384835 | − | 0.922985i | \(-0.374258\pi\) | |||||||
\(908\) | 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 | −0.785503 | − | 0.618857i | \(-0.787596\pi\) |
0.928698 | + | 0.370837i | \(0.120929\pi\) | |||||||
\(920\) | 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 | 0.370769 | + | 0.928725i | \(0.379094\pi\) |
−0.989684 | + | 0.143267i | \(0.954239\pi\) | |||||||
\(930\) | 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 | \(0.0133055\pi\) | ||||
−0.999126 | + | 0.0417884i | \(0.986694\pi\) | |||||||
\(938\) | −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 | 0.923323 | + | 0.384024i | \(0.125462\pi\) |
−0.129087 | + | 0.991633i | \(0.541205\pi\) | |||||||
\(942\) | 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 | \(-0.139910\pi\) |
0.0839599 | + | 0.996469i | \(0.473243\pi\) | |||||||
\(948\) | 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 | \(-0.805604\pi\) |
0.906244 | + | 0.422756i | \(0.138937\pi\) | |||||||
\(972\) | 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 | \(-0.684559\pi\) |
0.450558 | + | 0.892747i | \(0.351225\pi\) | |||||||
\(978\) | 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 | \(-0.165997\pi\) |
−0.864972 | + | 0.501821i | \(0.832664\pi\) | |||||||
\(984\) | 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 | 0.563871 | − | 0.825863i | \(-0.309312\pi\) |
−0.997154 | + | 0.0753949i | \(0.975978\pi\) | |||||||
\(992\) | −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 | 0.283848 | − | 0.958869i | \(-0.408389\pi\) |
0.972329 | + | 0.233615i | \(0.0750555\pi\) | |||||||
\(998\) | −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.c.89.4 | yes | 8 | |
3.2 | odd | 2 | 1386.2.r.a.89.1 | ✓ | 8 | ||
7.3 | odd | 6 | 1386.2.r.a.1277.1 | yes | 8 | ||
21.17 | even | 6 | inner | 1386.2.r.c.1277.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.r.a.89.1 | ✓ | 8 | 3.2 | odd | 2 | ||
1386.2.r.a.1277.1 | yes | 8 | 7.3 | odd | 6 | ||
1386.2.r.c.89.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1386.2.r.c.1277.4 | yes | 8 | 21.17 | even | 6 | inner |