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: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 89.3 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.89 |
Dual form | 1386.2.r.b.1277.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||
\(5\) | −1.22474 | + | 2.12132i | −0.547723 | + | 0.948683i | 0.450708 | + | 0.892672i | \(0.351172\pi\) |
−0.998430 | + | 0.0560116i | \(0.982162\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | + | 2.44949i | −0.377964 | + | 0.925820i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.12132 | + | 1.22474i | −0.670820 | + | 0.387298i | ||||
\(11\) | 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 | \(0.889680\pi\) | |||||||
\(14\) | −2.09077 | + | 1.62132i | −0.558782 | + | 0.433316i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.866025 | − | 1.50000i | −0.210042 | − | 0.363803i | 0.741685 | − | 0.670748i | \(-0.234027\pi\) |
−0.951727 | + | 0.306944i | \(0.900693\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.50000 | − | 0.866025i | −0.344124 | − | 0.198680i | 0.317970 | − | 0.948101i | \(-0.396999\pi\) |
−0.662094 | + | 0.749421i | \(0.730332\pi\) | |||||||
\(20\) | −2.44949 | −0.547723 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 1.07616 | + | 0.621320i | 0.224395 | + | 0.129554i | 0.607983 | − | 0.793950i | \(-0.291979\pi\) |
−0.383589 | + | 0.923504i | \(0.625312\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −1.22474 | + | 2.12132i | −0.240192 | + | 0.416025i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.62132 | + | 0.358719i | −0.495383 | + | 0.0677916i | ||||
\(29\) | − | 7.24264i | − | 1.34492i | −0.740131 | − | 0.672462i | \(-0.765237\pi\) | ||
0.740131 | − | 0.672462i | \(-0.234763\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.24264 | + | 4.18154i | −1.30082 | + | 0.751027i | −0.980544 | − | 0.196299i | \(-0.937108\pi\) |
−0.320273 | + | 0.947325i | \(0.603774\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 1.73205i | − | 0.297044i | ||||||
\(35\) | −3.97141 | − | 5.12132i | −0.671290 | − | 0.865661i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.62132 | + | 4.54026i | −0.430942 | + | 0.746414i | −0.996955 | − | 0.0779826i | \(-0.975152\pi\) |
0.566012 | + | 0.824397i | \(0.308485\pi\) | |||||||
\(38\) | −0.866025 | − | 1.50000i | −0.140488 | − | 0.243332i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.12132 | − | 1.22474i | −0.335410 | − | 0.193649i | ||||
\(41\) | −8.36308 | −1.30609 | −0.653047 | − | 0.757317i | \(-0.726510\pi\) | ||||
−0.653047 | + | 0.757317i | \(0.726510\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | 0.152499 | 0.0762493 | − | 0.997089i | \(-0.475706\pi\) | ||||
0.0762493 | + | 0.997089i | \(0.475706\pi\) | |||||||
\(44\) | 0.866025 | + | 0.500000i | 0.130558 | + | 0.0753778i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.621320 | + | 1.07616i | 0.0916087 | + | 0.158671i | ||||
\(47\) | 1.37333 | − | 2.37868i | 0.200321 | − | 0.346966i | −0.748311 | − | 0.663348i | \(-0.769135\pi\) |
0.948632 | + | 0.316382i | \(0.102468\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | − | 4.89898i | −0.714286 | − | 0.699854i | ||||
\(50\) | − | 1.00000i | − | 0.141421i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.12132 | + | 1.22474i | −0.294174 | + | 0.169842i | ||||
\(53\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.44949i | 0.330289i | ||||||||
\(56\) | −2.44949 | − | 1.00000i | −0.327327 | − | 0.133631i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.62132 | − | 6.27231i | 0.475503 | − | 0.823595i | ||||
\(59\) | 2.30090 | + | 3.98528i | 0.299552 | + | 0.518839i | 0.976034 | − | 0.217620i | \(-0.0698294\pi\) |
−0.676481 | + | 0.736460i | \(0.736496\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.00000 | + | 5.19615i | 1.15233 | + | 0.665299i | 0.949454 | − | 0.313905i | \(-0.101637\pi\) |
0.202878 | + | 0.979204i | \(0.434971\pi\) | |||||||
\(62\) | −8.36308 | −1.06211 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −5.19615 | − | 3.00000i | −0.644503 | − | 0.372104i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.24264 | − | 3.88437i | −0.273982 | − | 0.474551i | 0.695896 | − | 0.718143i | \(-0.255008\pi\) |
−0.969878 | + | 0.243592i | \(0.921674\pi\) | |||||||
\(68\) | 0.866025 | − | 1.50000i | 0.105021 | − | 0.181902i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.878680 | − | 6.42090i | −0.105022 | − | 0.767444i | ||||
\(71\) | 1.24264i | 0.147474i | 0.997278 | + | 0.0737372i | \(0.0234926\pi\) | ||||
−0.997278 | + | 0.0737372i | \(0.976507\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.24264 | + | 2.44949i | −0.496564 | + | 0.286691i | −0.727293 | − | 0.686327i | \(-0.759222\pi\) |
0.230730 | + | 0.973018i | \(0.425889\pi\) | |||||||
\(74\) | −4.54026 | + | 2.62132i | −0.527795 | + | 0.304722i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 1.73205i | − | 0.198680i | ||||||
\(77\) | 0.358719 | + | 2.62132i | 0.0408799 | + | 0.298727i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | + | 6.92820i | −0.450035 | + | 0.779484i | −0.998388 | − | 0.0567635i | \(-0.981922\pi\) |
0.548352 | + | 0.836247i | \(0.315255\pi\) | |||||||
\(80\) | −1.22474 | − | 2.12132i | −0.136931 | − | 0.237171i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.24264 | − | 4.18154i | −0.799816 | − | 0.461774i | ||||
\(83\) | 7.94282 | 0.871837 | 0.435919 | − | 0.899986i | \(-0.356424\pi\) | ||||
0.435919 | + | 0.899986i | \(0.356424\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.24264 | 0.460179 | ||||||||
\(86\) | 0.866025 | + | 0.500000i | 0.0933859 | + | 0.0539164i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.500000 | + | 0.866025i | 0.0533002 | + | 0.0923186i | ||||
\(89\) | −2.95680 | + | 5.12132i | −0.313420 | + | 0.542859i | −0.979100 | − | 0.203378i | \(-0.934808\pi\) |
0.665681 | + | 0.746237i | \(0.268141\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.00000 | − | 2.44949i | −0.628971 | − | 0.256776i | ||||
\(92\) | 1.24264i | 0.129554i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.37868 | − | 1.37333i | 0.245342 | − | 0.141648i | ||||
\(95\) | 3.67423 | − | 2.12132i | 0.376969 | − | 0.217643i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.63103i | 0.673279i | 0.941634 | + | 0.336640i | \(0.109290\pi\) | ||||
−0.941634 | + | 0.336640i | \(0.890710\pi\) | |||||||
\(98\) | −1.88064 | − | 6.74264i | −0.189973 | − | 0.681110i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | −6.98975 | − | 12.1066i | −0.695506 | − | 1.20465i | −0.970010 | − | 0.243066i | \(-0.921847\pi\) |
0.274504 | − | 0.961586i | \(-0.411486\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.87868 | + | 5.70346i | 0.973375 | + | 0.561978i | 0.900264 | − | 0.435345i | \(-0.143374\pi\) |
0.0731117 | + | 0.997324i | \(0.476707\pi\) | |||||||
\(104\) | −2.44949 | −0.240192 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.15232 | + | 1.24264i | 0.208072 | + | 0.120131i | 0.600415 | − | 0.799688i | \(-0.295002\pi\) |
−0.392343 | + | 0.919819i | \(0.628335\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.12132 | + | 15.7986i | 0.873664 | + | 1.51323i | 0.858179 | + | 0.513350i | \(0.171596\pi\) |
0.0154849 | + | 0.999880i | \(0.495071\pi\) | |||||||
\(110\) | −1.22474 | + | 2.12132i | −0.116775 | + | 0.202260i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.62132 | − | 2.09077i | −0.153200 | − | 0.197559i | ||||
\(113\) | − | 10.2426i | − | 0.963547i | −0.876296 | − | 0.481773i | \(-0.839993\pi\) | ||
0.876296 | − | 0.481773i | \(-0.160007\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.63604 | + | 1.52192i | −0.245812 | + | 0.141920i | ||||
\(116\) | 6.27231 | − | 3.62132i | 0.582369 | − | 0.336231i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.60181i | 0.423631i | ||||||||
\(119\) | 4.54026 | − | 0.621320i | 0.416205 | − | 0.0569563i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | − | 0.866025i | 0.0454545 | − | 0.0787296i | ||||
\(122\) | 5.19615 | + | 9.00000i | 0.470438 | + | 0.814822i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.24264 | − | 4.18154i | −0.650408 | − | 0.375513i | ||||
\(125\) | −9.79796 | −0.876356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.2426 | 1.88498 | 0.942490 | − | 0.334235i | \(-0.108478\pi\) | ||||
0.942490 | + | 0.334235i | \(0.108478\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.00000 | − | 5.19615i | −0.263117 | − | 0.455733i | ||||
\(131\) | −8.15295 | + | 14.1213i | −0.712326 | + | 1.23379i | 0.251655 | + | 0.967817i | \(0.419025\pi\) |
−0.963982 | + | 0.265969i | \(0.914308\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.62132 | − | 2.80821i | 0.314008 | − | 0.243503i | ||||
\(134\) | − | 4.48528i | − | 0.387469i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.50000 | − | 0.866025i | 0.128624 | − | 0.0742611i | ||||
\(137\) | 8.87039 | − | 5.12132i | 0.757848 | − | 0.437544i | −0.0706744 | − | 0.997499i | \(-0.522515\pi\) |
0.828523 | + | 0.559956i | \(0.189182\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0951i | 0.856258i | 0.903718 | + | 0.428129i | \(0.140827\pi\) | ||||
−0.903718 | + | 0.428129i | \(0.859173\pi\) | |||||||
\(140\) | 2.44949 | − | 6.00000i | 0.207020 | − | 0.507093i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.621320 | + | 1.07616i | −0.0521400 | + | 0.0903092i | ||||
\(143\) | 1.22474 | + | 2.12132i | 0.102418 | + | 0.177394i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.3640 | + | 8.87039i | 1.27591 | + | 0.736646i | ||||
\(146\) | −4.89898 | −0.405442 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.24264 | −0.430942 | ||||||||
\(149\) | 11.4685 | + | 6.62132i | 0.939533 | + | 0.542440i | 0.889814 | − | 0.456324i | \(-0.150834\pi\) |
0.0497192 | + | 0.998763i | \(0.484167\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.62132 | − | 9.73641i | −0.457457 | − | 0.792338i | 0.541369 | − | 0.840785i | \(-0.317906\pi\) |
−0.998826 | + | 0.0484470i | \(0.984573\pi\) | |||||||
\(152\) | 0.866025 | − | 1.50000i | 0.0702439 | − | 0.121666i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.00000 | + | 2.44949i | −0.0805823 | + | 0.197386i | ||||
\(155\) | − | 20.4853i | − | 1.64542i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.621320 | + | 0.358719i | −0.0495868 | + | 0.0286289i | −0.524588 | − | 0.851356i | \(-0.675781\pi\) |
0.475002 | + | 0.879985i | \(0.342447\pi\) | |||||||
\(158\) | −6.92820 | + | 4.00000i | −0.551178 | + | 0.318223i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 2.44949i | − | 0.193649i | ||||||
\(161\) | −2.59808 | + | 2.01472i | −0.204757 | + | 0.158782i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.48528 | + | 16.4290i | −0.742945 | + | 1.28682i | 0.208204 | + | 0.978085i | \(0.433238\pi\) |
−0.951149 | + | 0.308732i | \(0.900095\pi\) | |||||||
\(164\) | −4.18154 | − | 7.24264i | −0.326523 | − | 0.565555i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.87868 | + | 3.97141i | 0.533889 | + | 0.308241i | ||||
\(167\) | 14.2767 | 1.10476 | 0.552381 | − | 0.833592i | \(-0.313719\pi\) | ||||
0.552381 | + | 0.833592i | \(0.313719\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 3.67423 | + | 2.12132i | 0.281801 | + | 0.162698i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.500000 | + | 0.866025i | 0.0381246 | + | 0.0660338i | ||||
\(173\) | −5.91359 | + | 10.2426i | −0.449602 | + | 0.778734i | −0.998360 | − | 0.0572477i | \(-0.981768\pi\) |
0.548758 | + | 0.835981i | \(0.315101\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.62132 | − | 0.358719i | 0.198153 | − | 0.0271166i | ||||
\(176\) | 1.00000i | 0.0753778i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.12132 | + | 2.95680i | −0.383859 | + | 0.221621i | ||||
\(179\) | −7.79423 | + | 4.50000i | −0.582568 | + | 0.336346i | −0.762153 | − | 0.647397i | \(-0.775858\pi\) |
0.179585 | + | 0.983742i | \(0.442524\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.89898i | 0.364138i | 0.983286 | + | 0.182069i | \(0.0582795\pi\) | ||||
−0.983286 | + | 0.182069i | \(0.941721\pi\) | |||||||
\(182\) | −3.97141 | − | 5.12132i | −0.294380 | − | 0.379618i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.621320 | + | 1.07616i | −0.0458043 | + | 0.0793355i | ||||
\(185\) | −6.42090 | − | 11.1213i | −0.472074 | − | 0.817656i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.50000 | − | 0.866025i | −0.109691 | − | 0.0633300i | ||||
\(188\) | 2.74666 | 0.200321 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.24264 | 0.307794 | ||||||||
\(191\) | 14.6969 | + | 8.48528i | 1.06343 | + | 0.613973i | 0.926380 | − | 0.376590i | \(-0.122904\pi\) |
0.137053 | + | 0.990564i | \(0.456237\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.36396 | − | 4.09450i | −0.170162 | − | 0.294729i | 0.768315 | − | 0.640072i | \(-0.221096\pi\) |
−0.938476 | + | 0.345344i | \(0.887762\pi\) | |||||||
\(194\) | −3.31552 | + | 5.74264i | −0.238040 | + | 0.412298i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.74264 | − | 6.77962i | 0.124474 | − | 0.484258i | ||||
\(197\) | − | 21.7279i | − | 1.54805i | −0.633155 | − | 0.774025i | \(-0.718240\pi\) | ||
0.633155 | − | 0.774025i | \(-0.281760\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.36396 | − | 3.67423i | 0.451129 | − | 0.260460i | −0.257178 | − | 0.966364i | \(-0.582793\pi\) |
0.708307 | + | 0.705905i | \(0.249459\pi\) | |||||||
\(200\) | 0.866025 | − | 0.500000i | 0.0612372 | − | 0.0353553i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 13.9795i | − | 0.983594i | ||||||
\(203\) | 17.7408 | + | 7.24264i | 1.24516 | + | 0.508334i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.2426 | − | 17.7408i | 0.715377 | − | 1.23907i | ||||
\(206\) | 5.70346 | + | 9.87868i | 0.397379 | + | 0.688280i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.12132 | − | 1.22474i | −0.147087 | − | 0.0849208i | ||||
\(209\) | −1.73205 | −0.119808 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.51472 | −0.379649 | −0.189824 | − | 0.981818i | \(-0.560792\pi\) | ||||
−0.189824 | + | 0.981818i | \(0.560792\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.24264 | + | 2.15232i | 0.0849452 | + | 0.147129i | ||||
\(215\) | −1.22474 | + | 2.12132i | −0.0835269 | + | 0.144673i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.00000 | − | 21.9223i | −0.203653 | − | 1.48818i | ||||
\(218\) | 18.2426i | 1.23555i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.12132 | + | 1.22474i | −0.143019 | + | 0.0825723i | ||||
\(221\) | 3.67423 | − | 2.12132i | 0.247156 | − | 0.142695i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.47871i | 0.299917i | 0.988692 | + | 0.149958i | \(0.0479140\pi\) | ||||
−0.988692 | + | 0.149958i | \(0.952086\pi\) | |||||||
\(224\) | −0.358719 | − | 2.62132i | −0.0239680 | − | 0.175144i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.12132 | − | 8.87039i | 0.340665 | − | 0.590049i | ||||
\(227\) | −6.63103 | − | 11.4853i | −0.440117 | − | 0.762305i | 0.557581 | − | 0.830123i | \(-0.311730\pi\) |
−0.997698 | + | 0.0678178i | \(0.978396\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.0000 | − | 6.92820i | −0.792982 | − | 0.457829i | 0.0480291 | − | 0.998846i | \(-0.484706\pi\) |
−0.841011 | + | 0.541017i | \(0.818039\pi\) | |||||||
\(230\) | −3.04384 | −0.200705 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.24264 | 0.475503 | ||||||||
\(233\) | −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 | ||||||||
\(235\) | 3.36396 | + | 5.82655i | 0.219441 | + | 0.380082i | ||||
\(236\) | −2.30090 | + | 3.98528i | −0.149776 | + | 0.259420i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.24264 | + | 1.73205i | 0.275010 | + | 0.112272i | ||||
\(239\) | 12.7279i | 0.823301i | 0.911342 | + | 0.411650i | \(0.135048\pi\) | ||||
−0.911342 | + | 0.411650i | \(0.864952\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.9706 | − | 13.2621i | 1.47966 | − | 0.854284i | 0.479929 | − | 0.877307i | \(-0.340662\pi\) |
0.999735 | + | 0.0230229i | \(0.00732905\pi\) | |||||||
\(242\) | 0.866025 | − | 0.500000i | 0.0556702 | − | 0.0321412i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.3923i | 0.665299i | ||||||||
\(245\) | 16.5160 | − | 4.60660i | 1.05517 | − | 0.294305i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.12132 | − | 3.67423i | 0.134976 | − | 0.233786i | ||||
\(248\) | −4.18154 | − | 7.24264i | −0.265528 | − | 0.459908i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.48528 | − | 4.89898i | −0.536656 | − | 0.309839i | ||||
\(251\) | −1.13770 | −0.0718113 | −0.0359056 | − | 0.999355i | \(-0.511432\pi\) | ||||
−0.0359056 | + | 0.999355i | \(0.511432\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.24264 | 0.0781242 | ||||||||
\(254\) | 18.3967 | + | 10.6213i | 1.15431 | + | 0.666441i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −4.39167 | + | 7.60660i | −0.273945 | + | 0.474487i | −0.969868 | − | 0.243629i | \(-0.921662\pi\) |
0.695923 | + | 0.718116i | \(0.254995\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.50000 | − | 10.9612i | −0.528164 | − | 0.681093i | ||||
\(260\) | − | 6.00000i | − | 0.372104i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −14.1213 | + | 8.15295i | −0.872418 | + | 0.503691i | ||||
\(263\) | −8.23999 | + | 4.75736i | −0.508099 | + | 0.293351i | −0.732052 | − | 0.681249i | \(-0.761437\pi\) |
0.223953 | + | 0.974600i | \(0.428104\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.54026 | − | 0.621320i | 0.278381 | − | 0.0380956i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.24264 | − | 3.88437i | 0.136991 | − | 0.237276i | ||||
\(269\) | 10.8996 | + | 18.8787i | 0.664561 | + | 1.15105i | 0.979404 | + | 0.201910i | \(0.0647148\pi\) |
−0.314843 | + | 0.949144i | \(0.601952\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.2426 | + | 5.91359i | 0.622196 | + | 0.359225i | 0.777724 | − | 0.628606i | \(-0.216374\pi\) |
−0.155527 | + | 0.987832i | \(0.549708\pi\) | |||||||
\(272\) | 1.73205 | 0.105021 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.2426 | 0.618781 | ||||||||
\(275\) | −0.866025 | − | 0.500000i | −0.0522233 | − | 0.0301511i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.7279 | − | 18.5813i | −0.644578 | − | 1.11644i | −0.984399 | − | 0.175952i | \(-0.943700\pi\) |
0.339820 | − | 0.940490i | \(-0.389634\pi\) | |||||||
\(278\) | −5.04757 | + | 8.74264i | −0.302733 | + | 0.524349i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.12132 | − | 3.97141i | 0.306057 | − | 0.237337i | ||||
\(281\) | 6.51472i | 0.388636i | 0.980939 | + | 0.194318i | \(0.0622493\pi\) | ||||
−0.980939 | + | 0.194318i | \(0.937751\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.51472 | + | 5.49333i | −0.565591 | + | 0.326544i | −0.755387 | − | 0.655279i | \(-0.772551\pi\) |
0.189795 | + | 0.981824i | \(0.439218\pi\) | |||||||
\(284\) | −1.07616 | + | 0.621320i | −0.0638583 | + | 0.0368686i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.44949i | 0.144841i | ||||||||
\(287\) | 8.36308 | − | 20.4853i | 0.493657 | − | 1.20921i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.00000 | − | 12.1244i | 0.411765 | − | 0.713197i | ||||
\(290\) | 8.87039 | + | 15.3640i | 0.520887 | + | 0.902203i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.24264 | − | 2.44949i | −0.248282 | − | 0.143346i | ||||
\(293\) | 17.4436 | 1.01907 | 0.509533 | − | 0.860451i | \(-0.329818\pi\) | ||||
0.509533 | + | 0.860451i | \(0.329818\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.2721 | −0.656286 | ||||||||
\(296\) | −4.54026 | − | 2.62132i | −0.263897 | − | 0.152361i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.62132 | + | 11.4685i | 0.383563 | + | 0.664350i | ||||
\(299\) | −1.52192 | + | 2.63604i | −0.0880148 | + | 0.152446i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.00000 | + | 2.44949i | −0.0576390 | + | 0.141186i | ||||
\(302\) | − | 11.2426i | − | 0.646941i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.50000 | − | 0.866025i | 0.0860309 | − | 0.0496700i | ||||
\(305\) | −22.0454 | + | 12.7279i | −1.26232 | + | 0.728799i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.1185i | 1.54773i | 0.633349 | + | 0.773866i | \(0.281680\pi\) | ||||
−0.633349 | + | 0.773866i | \(0.718320\pi\) | |||||||
\(308\) | −2.09077 | + | 1.62132i | −0.119133 | + | 0.0923833i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 10.2426 | − | 17.7408i | 0.581743 | − | 1.00761i | ||||
\(311\) | 5.85204 | + | 10.1360i | 0.331839 | + | 0.574762i | 0.982872 | − | 0.184287i | \(-0.0589976\pi\) |
−0.651033 | + | 0.759049i | \(0.725664\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.98528 | − | 5.76500i | −0.564401 | − | 0.325857i | 0.190509 | − | 0.981685i | \(-0.438986\pi\) |
−0.754910 | + | 0.655828i | \(0.772320\pi\) | |||||||
\(314\) | −0.717439 | −0.0404874 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | 14.0665 | + | 8.12132i | 0.790056 | + | 0.456139i | 0.839982 | − | 0.542614i | \(-0.182565\pi\) |
−0.0499265 | + | 0.998753i | \(0.515899\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.62132 | − | 6.27231i | −0.202755 | − | 0.351182i | ||||
\(320\) | 1.22474 | − | 2.12132i | 0.0684653 | − | 0.118585i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.25736 | + | 0.445759i | −0.181526 | + | 0.0248412i | ||||
\(323\) | 3.00000i | 0.166924i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.12132 | − | 1.22474i | 0.117670 | − | 0.0679366i | ||||
\(326\) | −16.4290 | + | 9.48528i | −0.909918 | + | 0.525341i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 8.36308i | − | 0.461774i | ||||||
\(329\) | 4.45322 | + | 5.74264i | 0.245514 | + | 0.316602i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.00000 | − | 12.1244i | 0.384755 | − | 0.666415i | −0.606980 | − | 0.794717i | \(-0.707619\pi\) |
0.991735 | + | 0.128302i | \(0.0409527\pi\) | |||||||
\(332\) | 3.97141 | + | 6.87868i | 0.217959 | + | 0.377517i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.3640 | + | 7.13834i | 0.676526 | + | 0.390592i | ||||
\(335\) | 10.9867 | 0.600265 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.7574 | −0.858358 | −0.429179 | − | 0.903219i | \(-0.641197\pi\) | ||||
−0.429179 | + | 0.903219i | \(0.641197\pi\) | |||||||
\(338\) | 6.06218 | + | 3.50000i | 0.329739 | + | 0.190375i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.12132 | + | 3.67423i | 0.115045 | + | 0.199263i | ||||
\(341\) | −4.18154 | + | 7.24264i | −0.226443 | + | 0.392211i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.0000 | − | 7.34847i | 0.917914 | − | 0.396780i | ||||
\(344\) | 1.00000i | 0.0539164i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.2426 | + | 5.91359i | −0.550648 | + | 0.317917i | ||||
\(347\) | 28.1331 | − | 16.2426i | 1.51026 | − | 0.871951i | 0.510335 | − | 0.859976i | \(-0.329522\pi\) |
0.999928 | − | 0.0119747i | \(-0.00381174\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.6969i | 0.786709i | 0.919387 | + | 0.393355i | \(0.128686\pi\) | ||||
−0.919387 | + | 0.393355i | \(0.871314\pi\) | |||||||
\(350\) | 2.44949 | + | 1.00000i | 0.130931 | + | 0.0534522i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.500000 | + | 0.866025i | −0.0266501 | + | 0.0461593i | ||||
\(353\) | −7.85578 | − | 13.6066i | −0.418121 | − | 0.724206i | 0.577630 | − | 0.816299i | \(-0.303978\pi\) |
−0.995750 | + | 0.0920926i | \(0.970644\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.63604 | − | 1.52192i | −0.139906 | − | 0.0807750i | ||||
\(356\) | −5.91359 | −0.313420 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.00000 | −0.475665 | ||||||||
\(359\) | 30.2854 | + | 17.4853i | 1.59840 | + | 0.922838i | 0.991795 | + | 0.127836i | \(0.0408030\pi\) |
0.606607 | + | 0.795002i | \(0.292530\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.00000 | − | 13.8564i | −0.421053 | − | 0.729285i | ||||
\(362\) | −2.44949 | + | 4.24264i | −0.128742 | + | 0.222988i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.878680 | − | 6.42090i | −0.0460553 | − | 0.336546i | ||||
\(365\) | − | 12.0000i | − | 0.628109i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.75736 | − | 1.01461i | 0.0917334 | − | 0.0529623i | −0.453432 | − | 0.891291i | \(-0.649800\pi\) |
0.545165 | + | 0.838329i | \(0.316467\pi\) | |||||||
\(368\) | −1.07616 | + | 0.621320i | −0.0560986 | + | 0.0323886i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 12.8418i | − | 0.667613i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.0000 | − | 29.4449i | 0.880227 | − | 1.52460i | 0.0291379 | − | 0.999575i | \(-0.490724\pi\) |
0.851089 | − | 0.525022i | \(-0.175943\pi\) | |||||||
\(374\) | −0.866025 | − | 1.50000i | −0.0447811 | − | 0.0775632i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.37868 | + | 1.37333i | 0.122671 | + | 0.0708242i | ||||
\(377\) | 17.7408 | 0.913696 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.27208 | −0.373542 | −0.186771 | − | 0.982404i | \(-0.559802\pi\) | ||||
−0.186771 | + | 0.982404i | \(0.559802\pi\) | |||||||
\(380\) | 3.67423 | + | 2.12132i | 0.188484 | + | 0.108821i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.48528 | + | 14.6969i | 0.434145 | + | 0.751961i | ||||
\(383\) | −17.5051 | + | 30.3198i | −0.894471 | + | 1.54927i | −0.0600136 | + | 0.998198i | \(0.519114\pi\) |
−0.834458 | + | 0.551072i | \(0.814219\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.00000 | − | 2.44949i | −0.305788 | − | 0.124838i | ||||
\(386\) | − | 4.72792i | − | 0.240645i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.74264 | + | 3.31552i | −0.291538 | + | 0.168320i | ||||
\(389\) | −9.76191 | + | 5.63604i | −0.494948 | + | 0.285759i | −0.726625 | − | 0.687034i | \(-0.758912\pi\) |
0.231677 | + | 0.972793i | \(0.425579\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.15232i | − | 0.108847i | ||||||
\(392\) | 4.89898 | − | 5.00000i | 0.247436 | − | 0.252538i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.8640 | − | 18.8169i | 0.547318 | − | 0.947983i | ||||
\(395\) | −9.79796 | − | 16.9706i | −0.492989 | − | 0.853882i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.34924 | − | 0.778985i | −0.0677165 | − | 0.0390962i | 0.465759 | − | 0.884911i | \(-0.345781\pi\) |
−0.533476 | + | 0.845815i | \(0.679115\pi\) | |||||||
\(398\) | 7.34847 | 0.368345 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 17.1104 | + | 9.87868i | 0.854451 | + | 0.493318i | 0.862150 | − | 0.506653i | \(-0.169117\pi\) |
−0.00769892 | + | 0.999970i | \(0.502451\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.2426 | − | 17.7408i | −0.510222 | − | 0.883731i | ||||
\(404\) | 6.98975 | − | 12.1066i | 0.347753 | − | 0.602326i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11.7426 | + | 15.1427i | 0.582777 | + | 0.751519i | ||||
\(407\) | 5.24264i | 0.259868i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.3640 | + | 7.13834i | −0.611359 | + | 0.352968i | −0.773497 | − | 0.633800i | \(-0.781494\pi\) |
0.162138 | + | 0.986768i | \(0.448161\pi\) | |||||||
\(410\) | 17.7408 | − | 10.2426i | 0.876154 | − | 0.505848i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.4069i | 0.561978i | ||||||||
\(413\) | −12.0628 | + | 1.65076i | −0.593572 | + | 0.0812285i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.72792 | + | 16.8493i | −0.477525 | + | 0.827097i | ||||
\(416\) | −1.22474 | − | 2.12132i | −0.0600481 | − | 0.104006i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.50000 | − | 0.866025i | −0.0733674 | − | 0.0423587i | ||||
\(419\) | 14.9941 | 0.732510 | 0.366255 | − | 0.930514i | \(-0.380640\pi\) | ||||
0.366255 | + | 0.930514i | \(0.380640\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.6985 | −1.49615 | −0.748076 | − | 0.663613i | \(-0.769022\pi\) | ||||
−0.748076 | + | 0.663613i | \(0.769022\pi\) | |||||||
\(422\) | −4.77589 | − | 2.75736i | −0.232487 | − | 0.134226i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.866025 | + | 1.50000i | −0.0420084 | + | 0.0727607i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.7279 | + | 16.8493i | −1.05149 | + | 0.815393i | ||||
\(428\) | 2.48528i | 0.120131i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.12132 | + | 1.22474i | −0.102299 | + | 0.0590624i | ||||
\(431\) | −14.6969 | + | 8.48528i | −0.707927 | + | 0.408722i | −0.810293 | − | 0.586025i | \(-0.800692\pi\) |
0.102366 | + | 0.994747i | \(0.467359\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.8639i | 0.858483i | 0.903190 | + | 0.429241i | \(0.141219\pi\) | ||||
−0.903190 | + | 0.429241i | \(0.858781\pi\) | |||||||
\(434\) | 8.36308 | − | 20.4853i | 0.401441 | − | 0.983325i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.12132 | + | 15.7986i | −0.436832 | + | 0.756615i | ||||
\(437\) | −1.07616 | − | 1.86396i | −0.0514796 | − | 0.0891653i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.3787 | + | 10.0336i | 0.829439 | + | 0.478877i | 0.853661 | − | 0.520830i | \(-0.174377\pi\) |
−0.0242215 | + | 0.999707i | \(0.507711\pi\) | |||||||
\(440\) | −2.44949 | −0.116775 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.24264 | 0.201802 | ||||||||
\(443\) | −2.59808 | − | 1.50000i | −0.123438 | − | 0.0712672i | 0.437009 | − | 0.899457i | \(-0.356038\pi\) |
−0.560448 | + | 0.828190i | \(0.689371\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.24264 | − | 12.5446i | −0.343334 | − | 0.594672i | ||||
\(446\) | −2.23936 | + | 3.87868i | −0.106037 | + | 0.183661i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000 | − | 2.44949i | 0.0472456 | − | 0.115728i | ||||
\(449\) | 37.4558i | 1.76765i | 0.467817 | + | 0.883825i | \(0.345041\pi\) | ||||
−0.467817 | + | 0.883825i | \(0.654959\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.24264 | + | 4.18154i | −0.341043 | + | 0.196901i | ||||
\(452\) | 8.87039 | − | 5.12132i | 0.417228 | − | 0.240887i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 13.2621i | − | 0.622419i | ||||||
\(455\) | 12.5446 | − | 9.72792i | 0.588101 | − | 0.456052i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.8492 | − | 22.2555i | 0.601062 | − | 1.04107i | −0.391598 | − | 0.920136i | \(-0.628078\pi\) |
0.992661 | − | 0.120934i | \(-0.0385889\pi\) | |||||||
\(458\) | −6.92820 | − | 12.0000i | −0.323734 | − | 0.560723i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.63604 | − | 1.52192i | −0.122906 | − | 0.0709598i | ||||
\(461\) | −4.77589 | −0.222435 | −0.111218 | − | 0.993796i | \(-0.535475\pi\) | ||||
−0.111218 | + | 0.993796i | \(0.535475\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.4558 | 0.997138 | 0.498569 | − | 0.866850i | \(-0.333859\pi\) | ||||
0.498569 | + | 0.866850i | \(0.333859\pi\) | |||||||
\(464\) | 6.27231 | + | 3.62132i | 0.291185 | + | 0.168116i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.257359 | − | 0.445759i | −0.0119219 | − | 0.0206494i | ||||
\(467\) | 2.59808 | − | 4.50000i | 0.120225 | − | 0.208235i | −0.799632 | − | 0.600491i | \(-0.794972\pi\) |
0.919856 | + | 0.392256i | \(0.128305\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.7574 | − | 1.60896i | 0.542904 | − | 0.0742948i | ||||
\(470\) | 6.72792i | 0.310336i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.98528 | + | 2.30090i | −0.183437 | + | 0.105908i | ||||
\(473\) | 0.866025 | − | 0.500000i | 0.0398199 | − | 0.0229900i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.73205i | 0.0794719i | ||||||||
\(476\) | 2.80821 | + | 3.62132i | 0.128714 | + | 0.165983i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.36396 | + | 11.0227i | −0.291081 | + | 0.504167i | ||||
\(479\) | −18.0379 | − | 31.2426i | −0.824175 | − | 1.42751i | −0.902548 | − | 0.430589i | \(-0.858306\pi\) |
0.0783735 | − | 0.996924i | \(-0.475027\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.1213 | − | 6.42090i | −0.507089 | − | 0.292768i | ||||
\(482\) | 26.5241 | 1.20814 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −14.0665 | − | 8.12132i | −0.638729 | − | 0.368770i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.6066 | + | 35.6917i | 0.933774 | + | 1.61734i | 0.776805 | + | 0.629741i | \(0.216839\pi\) |
0.156969 | + | 0.987604i | \(0.449828\pi\) | |||||||
\(488\) | −5.19615 | + | 9.00000i | −0.235219 | + | 0.407411i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 16.6066 | + | 4.26858i | 0.750210 | + | 0.192835i | ||||
\(491\) | 42.7279i | 1.92828i | 0.265387 | + | 0.964142i | \(0.414500\pi\) | ||||
−0.265387 | + | 0.964142i | \(0.585500\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.8640 | + | 6.27231i | −0.489288 | + | 0.282491i | ||||
\(494\) | 3.67423 | − | 2.12132i | 0.165312 | − | 0.0954427i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 8.36308i | − | 0.375513i | ||||||
\(497\) | −3.04384 | − | 1.24264i | −0.136535 | − | 0.0557401i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.6066 | + | 32.2276i | −0.832946 | + | 1.44270i | 0.0627461 | + | 0.998030i | \(0.480014\pi\) |
−0.895692 | + | 0.444675i | \(0.853319\pi\) | |||||||
\(500\) | −4.89898 | − | 8.48528i | −0.219089 | − | 0.379473i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.985281 | − | 0.568852i | −0.0439753 | − | 0.0253891i | ||||
\(503\) | 0.594346 | 0.0265006 | 0.0132503 | − | 0.999912i | \(-0.495782\pi\) | ||||
0.0132503 | + | 0.999912i | \(0.495782\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 34.2426 | 1.52378 | ||||||||
\(506\) | 1.07616 | + | 0.621320i | 0.0478411 | + | 0.0276211i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.6213 | + | 18.3967i | 0.471245 | + | 0.816220i | ||||
\(509\) | 0.594346 | − | 1.02944i | 0.0263439 | − | 0.0456290i | −0.852553 | − | 0.522641i | \(-0.824947\pi\) |
0.878897 | + | 0.477012i | \(0.158280\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.75736 | − | 12.8418i | −0.0777410 | − | 0.568088i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.60660 | + | 4.39167i | −0.335513 | + | 0.193708i | ||||
\(515\) | −24.1977 | + | 13.9706i | −1.06628 | + | 0.615617i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.74666i | − | 0.120798i | ||||||
\(518\) | −1.88064 | − | 13.7426i | −0.0826305 | − | 0.603817i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.00000 | − | 5.19615i | 0.131559 | − | 0.227866i | ||||
\(521\) | −16.4290 | − | 28.4558i | −0.719767 | − | 1.24667i | −0.961092 | − | 0.276229i | \(-0.910915\pi\) |
0.241325 | − | 0.970444i | \(-0.422418\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.72792 | + | 3.88437i | 0.294191 | + | 0.169852i | 0.639831 | − | 0.768516i | \(-0.279005\pi\) |
−0.345639 | + | 0.938368i | \(0.612338\pi\) | |||||||
\(524\) | −16.3059 | −0.712326 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.51472 | −0.414861 | ||||||||
\(527\) | 12.5446 | + | 7.24264i | 0.546452 | + | 0.315494i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.7279 | − | 18.5813i | −0.466431 | − | 0.807883i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.24264 | + | 1.73205i | 0.183942 | + | 0.0750939i | ||||
\(533\) | − | 20.4853i | − | 0.887316i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.27208 | + | 3.04384i | −0.227932 | + | 0.131596i | ||||
\(536\) | 3.88437 | − | 2.24264i | 0.167779 | − | 0.0968673i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 21.7992i | 0.939831i | ||||||||
\(539\) | −6.77962 | − | 1.74264i | −0.292019 | − | 0.0750608i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.2426 | − | 31.5972i | 0.784312 | − | 1.35847i | −0.145097 | − | 0.989417i | \(-0.546349\pi\) |
0.929409 | − | 0.369051i | \(-0.120317\pi\) | |||||||
\(542\) | 5.91359 | + | 10.2426i | 0.254010 | + | 0.439959i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.50000 | + | 0.866025i | 0.0643120 | + | 0.0371305i | ||||
\(545\) | −44.6852 | −1.91410 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.4853 | −1.17519 | −0.587593 | − | 0.809157i | \(-0.699924\pi\) | ||||
−0.587593 | + | 0.809157i | \(0.699924\pi\) | |||||||
\(548\) | 8.87039 | + | 5.12132i | 0.378924 | + | 0.218772i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.500000 | − | 0.866025i | −0.0213201 | − | 0.0369274i | ||||
\(551\) | −6.27231 | + | 10.8640i | −0.267209 | + | 0.462820i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.9706 | − | 16.7262i | −0.551564 | − | 0.711269i | ||||
\(554\) | − | 21.4558i | − | 0.911571i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.74264 | + | 5.04757i | −0.370771 | + | 0.214064i | ||||
\(557\) | −17.9254 | + | 10.3492i | −0.759524 | + | 0.438511i | −0.829125 | − | 0.559063i | \(-0.811161\pi\) |
0.0696007 | + | 0.997575i | \(0.477827\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.44949i | 0.103602i | ||||||||
\(560\) | 6.42090 | − | 0.878680i | 0.271332 | − | 0.0371310i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.25736 | + | 5.64191i | −0.137403 | + | 0.237990i | ||||
\(563\) | −14.7840 | − | 25.6066i | −0.623070 | − | 1.07919i | −0.988911 | − | 0.148512i | \(-0.952552\pi\) |
0.365840 | − | 0.930678i | \(-0.380782\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.7279 | + | 12.5446i | 0.914101 | + | 0.527756i | ||||
\(566\) | −10.9867 | −0.461803 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.24264 | −0.0521400 | ||||||||
\(569\) | 19.4473 | + | 11.2279i | 0.815275 | + | 0.470699i | 0.848784 | − | 0.528739i | \(-0.177335\pi\) |
−0.0335097 | + | 0.999438i | \(0.510668\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.25736 | + | 9.10601i | 0.220014 | + | 0.381075i | 0.954812 | − | 0.297211i | \(-0.0960565\pi\) |
−0.734798 | + | 0.678286i | \(0.762723\pi\) | |||||||
\(572\) | −1.22474 | + | 2.12132i | −0.0512092 | + | 0.0886969i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 17.4853 | − | 13.5592i | 0.729822 | − | 0.565951i | ||||
\(575\) | − | 1.24264i | − | 0.0518217i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.00000 | − | 1.73205i | 0.124892 | − | 0.0721062i | −0.436253 | − | 0.899824i | \(-0.643695\pi\) |
0.561144 | + | 0.827718i | \(0.310361\pi\) | |||||||
\(578\) | 12.1244 | − | 7.00000i | 0.504307 | − | 0.291162i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 17.7408i | 0.736646i | ||||||||
\(581\) | −7.94282 | + | 19.4558i | −0.329523 | + | 0.807164i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −2.44949 | − | 4.24264i | −0.101361 | − | 0.175562i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.1066 | + | 8.72180i | 0.624048 | + | 0.360294i | ||||
\(587\) | −34.0467 | −1.40526 | −0.702628 | − | 0.711557i | \(-0.747990\pi\) | ||||
−0.702628 | + | 0.711557i | \(0.747990\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.4853 | 0.596856 | ||||||||
\(590\) | −9.76191 | − | 5.63604i | −0.401891 | − | 0.232032i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.62132 | − | 4.54026i | −0.107736 | − | 0.186604i | ||||
\(593\) | 12.6932 | − | 21.9853i | 0.521248 | − | 0.902827i | −0.478447 | − | 0.878116i | \(-0.658800\pi\) |
0.999695 | − | 0.0247109i | \(-0.00786652\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.24264 | + | 10.3923i | −0.173931 | + | 0.426043i | ||||
\(596\) | 13.2426i | 0.542440i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.63604 | + | 1.52192i | −0.107796 | + | 0.0622358i | ||||
\(599\) | −15.5885 | + | 9.00000i | −0.636927 | + | 0.367730i | −0.783430 | − | 0.621480i | \(-0.786532\pi\) |
0.146503 | + | 0.989210i | \(0.453198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 17.1464i | − | 0.699417i | −0.936858 | − | 0.349709i | \(-0.886281\pi\) | ||
0.936858 | − | 0.349709i | \(-0.113719\pi\) | |||||||
\(602\) | −2.09077 | + | 1.62132i | −0.0852134 | + | 0.0660801i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.62132 | − | 9.73641i | 0.228728 | − | 0.396169i | ||||
\(605\) | 1.22474 | + | 2.12132i | 0.0497930 | + | 0.0862439i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.5147 | + | 7.22538i | 0.507957 | + | 0.293269i | 0.731993 | − | 0.681312i | \(-0.238590\pi\) |
−0.224037 | + | 0.974581i | \(0.571924\pi\) | |||||||
\(608\) | 1.73205 | 0.0702439 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −25.4558 | −1.03068 | ||||||||
\(611\) | 5.82655 | + | 3.36396i | 0.235717 | + | 0.136091i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.63604 | − | 6.29780i | −0.146858 | − | 0.254366i | 0.783206 | − | 0.621762i | \(-0.213583\pi\) |
−0.930065 | + | 0.367396i | \(0.880249\pi\) | |||||||
\(614\) | −13.5592 | + | 23.4853i | −0.547206 | + | 0.947789i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.62132 | + | 0.358719i | −0.105616 | + | 0.0144532i | ||||
\(617\) | − | 33.2132i | − | 1.33711i | −0.743661 | − | 0.668557i | \(-0.766912\pi\) | ||
0.743661 | − | 0.668557i | \(-0.233088\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.2132 | − | 7.05130i | 0.490890 | − | 0.283416i | −0.234054 | − | 0.972224i | \(-0.575199\pi\) |
0.724944 | + | 0.688808i | \(0.241866\pi\) | |||||||
\(620\) | 17.7408 | − | 10.2426i | 0.712487 | − | 0.411354i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11.7041i | 0.469291i | ||||||||
\(623\) | −9.58783 | − | 12.3640i | −0.384128 | − | 0.495352i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | − | 25.1147i | 0.580000 | − | 1.00459i | ||||
\(626\) | −5.76500 | − | 9.98528i | −0.230416 | − | 0.399092i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.621320 | − | 0.358719i | −0.0247934 | − | 0.0143145i | ||||
\(629\) | 9.08052 | 0.362064 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.6985 | −0.863803 | −0.431902 | − | 0.901921i | \(-0.642157\pi\) | ||||
−0.431902 | + | 0.901921i | \(0.642157\pi\) | |||||||
\(632\) | −6.92820 | − | 4.00000i | −0.275589 | − | 0.159111i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.12132 | + | 14.0665i | 0.322539 | + | 0.558654i | ||||
\(635\) | −26.0168 | + | 45.0624i | −1.03245 | + | 1.78825i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.0000 | − | 12.2474i | 0.475457 | − | 0.485262i | ||||
\(638\) | − | 7.24264i | − | 0.286739i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.12132 | − | 1.22474i | 0.0838525 | − | 0.0484123i | ||||
\(641\) | −21.4150 | + | 12.3640i | −0.845842 | + | 0.488347i | −0.859246 | − | 0.511563i | \(-0.829067\pi\) |
0.0134037 | + | 0.999910i | \(0.495733\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 30.1623i | − | 1.18949i | −0.803916 | − | 0.594743i | \(-0.797254\pi\) | ||
0.803916 | − | 0.594743i | \(-0.202746\pi\) | |||||||
\(644\) | −3.04384 | − | 1.24264i | −0.119944 | − | 0.0489669i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.50000 | + | 2.59808i | −0.0590167 | + | 0.102220i | ||||
\(647\) | −14.8710 | − | 25.7574i | −0.584640 | − | 1.01263i | −0.994920 | − | 0.100667i | \(-0.967902\pi\) |
0.410280 | − | 0.911960i | \(-0.365431\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.98528 | + | 2.30090i | 0.156436 | + | 0.0903184i | ||||
\(650\) | 2.44949 | 0.0960769 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −18.9706 | −0.742945 | ||||||||
\(653\) | −39.1558 | − | 22.6066i | −1.53228 | − | 0.884665i | −0.999256 | − | 0.0385672i | \(-0.987721\pi\) |
−0.533028 | − | 0.846097i | \(-0.678946\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.9706 | − | 34.5900i | −0.780314 | − | 1.35154i | ||||
\(656\) | 4.18154 | − | 7.24264i | 0.163262 | − | 0.282778i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.985281 | + | 7.19988i | 0.0384103 | + | 0.280681i | ||||
\(659\) | 7.75736i | 0.302184i | 0.988520 | + | 0.151092i | \(0.0482789\pi\) | ||||
−0.988520 | + | 0.151092i | \(0.951721\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.3787 | − | 6.56948i | 0.442579 | − | 0.255523i | −0.262112 | − | 0.965038i | \(-0.584419\pi\) |
0.704691 | + | 0.709514i | \(0.251086\pi\) | |||||||
\(662\) | 12.1244 | − | 7.00000i | 0.471226 | − | 0.272063i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.94282i | 0.308241i | ||||||||
\(665\) | 1.52192 | + | 11.1213i | 0.0590174 | + | 0.431266i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.50000 | − | 7.79423i | 0.174241 | − | 0.301794i | ||||
\(668\) | 7.13834 | + | 12.3640i | 0.276191 | + | 0.478376i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.51472 | + | 5.49333i | 0.367586 | + | 0.212226i | ||||
\(671\) | 10.3923 | 0.401190 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.7574 | 1.14706 | 0.573531 | − | 0.819184i | \(-0.305573\pi\) | ||||
0.573531 | + | 0.819184i | \(0.305573\pi\) | |||||||
\(674\) | −13.6463 | − | 7.87868i | −0.525635 | − | 0.303475i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.50000 | + | 6.06218i | 0.134615 | + | 0.233161i | ||||
\(677\) | 12.9033 | − | 22.3492i | 0.495916 | − | 0.858951i | −0.504073 | − | 0.863661i | \(-0.668166\pi\) |
0.999989 | + | 0.00470976i | \(0.00149917\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.2426 | − | 6.63103i | −0.623335 | − | 0.254476i | ||||
\(680\) | 4.24264i | 0.162698i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.24264 | + | 4.18154i | −0.277335 | + | 0.160119i | ||||
\(683\) | −20.3389 | + | 11.7426i | −0.778244 | + | 0.449320i | −0.835808 | − | 0.549022i | \(-0.815000\pi\) |
0.0575633 | + | 0.998342i | \(0.481667\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25.0892i | 0.958611i | ||||||||
\(686\) | 18.3967 | + | 2.13604i | 0.702388 | + | 0.0815543i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.500000 | + | 0.866025i | −0.0190623 | + | 0.0330169i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.4853 | − | 20.4874i | −1.34992 | − | 0.779379i | −0.361685 | − | 0.932300i | \(-0.617799\pi\) |
−0.988238 | + | 0.152921i | \(0.951132\pi\) | |||||||
\(692\) | −11.8272 | −0.449602 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 32.4853 | 1.23312 | ||||||||
\(695\) | −21.4150 | − | 12.3640i | −0.812318 | − | 0.468992i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.24264 | + | 12.5446i | 0.274335 | + | 0.475161i | ||||
\(698\) | −7.34847 | + | 12.7279i | −0.278144 | + | 0.481759i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.62132 | + | 2.09077i | 0.0612801 | + | 0.0790237i | ||||
\(701\) | − | 49.2426i | − | 1.85987i | −0.367725 | − | 0.929934i | \(-0.619863\pi\) | ||
0.367725 | − | 0.929934i | \(-0.380137\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.86396 | − | 4.54026i | 0.296595 | − | 0.171239i | ||||
\(704\) | −0.866025 | + | 0.500000i | −0.0326396 | + | 0.0188445i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 15.7116i | − | 0.591312i | ||||||
\(707\) | 36.6447 | − | 5.01472i | 1.37817 | − | 0.188598i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.62132 | + | 9.73641i | −0.211113 | + | 0.365659i | −0.952063 | − | 0.305901i | \(-0.901042\pi\) |
0.740950 | + | 0.671560i | \(0.234376\pi\) | |||||||
\(710\) | −1.52192 | − | 2.63604i | −0.0571166 | − | 0.0989288i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.12132 | − | 2.95680i | −0.191930 | − | 0.110811i | ||||
\(713\) | −10.3923 | −0.389195 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.00000 | −0.224387 | ||||||||
\(716\) | −7.79423 | − | 4.50000i | −0.291284 | − | 0.168173i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 17.4853 | + | 30.2854i | 0.652545 | + | 1.13024i | ||||
\(719\) | 15.6500 | − | 27.1066i | 0.583647 | − | 1.01091i | −0.411396 | − | 0.911457i | \(-0.634959\pi\) |
0.995043 | − | 0.0994490i | \(-0.0317080\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.8492 | + | 18.4943i | −0.888192 | + | 0.688762i | ||||
\(722\) | − | 16.0000i | − | 0.595458i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.24264 | + | 2.44949i | −0.157676 | + | 0.0910346i | ||||
\(725\) | −6.27231 | + | 3.62132i | −0.232948 | + | 0.134492i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.1051i | 1.41324i | 0.707593 | + | 0.706620i | \(0.249781\pi\) | ||||
−0.707593 | + | 0.706620i | \(0.750219\pi\) | |||||||
\(728\) | 2.44949 | − | 6.00000i | 0.0907841 | − | 0.222375i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.00000 | − | 10.3923i | 0.222070 | − | 0.384636i | ||||
\(731\) | −0.866025 | − | 1.50000i | −0.0320311 | − | 0.0554795i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.4558 | + | 26.8213i | 1.71589 | + | 0.990667i | 0.926095 | + | 0.377291i | \(0.123144\pi\) |
0.789791 | + | 0.613376i | \(0.210189\pi\) | |||||||
\(734\) | 2.02922 | 0.0749000 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.24264 | −0.0458043 | ||||||||
\(737\) | −3.88437 | − | 2.24264i | −0.143083 | − | 0.0826087i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.7279 | + | 41.0980i | 0.872846 | + | 1.51181i | 0.859040 | + | 0.511908i | \(0.171061\pi\) |
0.0138057 | + | 0.999905i | \(0.495605\pi\) | |||||||
\(740\) | 6.42090 | − | 11.1213i | 0.236037 | − | 0.408828i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 23.6985i | − | 0.869413i | −0.900572 | − | 0.434707i | \(-0.856852\pi\) | ||
0.900572 | − | 0.434707i | \(-0.143148\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28.0919 | + | 16.2189i | −1.02921 | + | 0.594213i | ||||
\(746\) | 29.4449 | − | 17.0000i | 1.07805 | − | 0.622414i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 1.73205i | − | 0.0633300i | ||||||
\(749\) | −5.19615 | + | 4.02944i | −0.189863 | + | 0.147232i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.1213 | − | 26.1909i | 0.551785 | − | 0.955719i | −0.446361 | − | 0.894853i | \(-0.647280\pi\) |
0.998146 | − | 0.0608664i | \(-0.0193864\pi\) | |||||||
\(752\) | 1.37333 | + | 2.37868i | 0.0500802 | + | 0.0867415i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 15.3640 | + | 8.87039i | 0.559522 | + | 0.323040i | ||||
\(755\) | 27.5387 | 1.00224 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −51.6690 | −1.87794 | −0.938972 | − | 0.343994i | \(-0.888220\pi\) | ||||
−0.938972 | + | 0.343994i | \(0.888220\pi\) | |||||||
\(758\) | −6.29780 | − | 3.63604i | −0.228747 | − | 0.132067i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.12132 | + | 3.67423i | 0.0769484 | + | 0.133278i | ||||
\(761\) | 13.1390 | − | 22.7574i | 0.476287 | − | 0.824954i | −0.523344 | − | 0.852122i | \(-0.675316\pi\) |
0.999631 | + | 0.0271681i | \(0.00864893\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −47.8198 | + | 6.54399i | −1.73119 | + | 0.236908i | ||||
\(764\) | 16.9706i | 0.613973i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −30.3198 | + | 17.5051i | −1.09550 | + | 0.632487i | ||||
\(767\) | −9.76191 | + | 5.63604i | −0.352482 | + | 0.203506i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 33.0321i | − | 1.19117i | −0.803294 | − | 0.595583i | \(-0.796921\pi\) | ||
0.803294 | − | 0.595583i | \(-0.203079\pi\) | |||||||
\(770\) | −3.97141 | − | 5.12132i | −0.143120 | − | 0.184560i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.36396 | − | 4.09450i | 0.0850808 | − | 0.147364i | ||||
\(773\) | 8.45012 | + | 14.6360i | 0.303930 | + | 0.526422i | 0.977022 | − | 0.213136i | \(-0.0683679\pi\) |
−0.673093 | + | 0.739558i | \(0.735035\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.24264 | + | 4.18154i | 0.260163 | + | 0.150205i | ||||
\(776\) | −6.63103 | −0.238040 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.2721 | −0.404124 | ||||||||
\(779\) | 12.5446 | + | 7.24264i | 0.449458 | + | 0.259495i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.621320 | + | 1.07616i | 0.0222326 | + | 0.0385080i | ||||
\(782\) | 1.07616 | − | 1.86396i | 0.0384833 | − | 0.0666551i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.74264 | − | 1.88064i | 0.240809 | − | 0.0671656i | ||||
\(785\) | − | 1.75736i | − | 0.0627228i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.4706 | + | 15.8601i | −0.979220 | + | 0.565353i | −0.902034 | − | 0.431664i | \(-0.857927\pi\) |
−0.0771853 | + | 0.997017i | \(0.524593\pi\) | |||||||
\(788\) | 18.8169 | − | 10.8640i | 0.670325 | − | 0.387013i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 19.5959i | − | 0.697191i | ||||||
\(791\) | 25.0892 | + | 10.2426i | 0.892071 | + | 0.364186i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.7279 | + | 22.0454i | −0.451982 | + | 0.782855i | ||||
\(794\) | −0.778985 | − | 1.34924i | −0.0276452 | − | 0.0478828i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.36396 | + | 3.67423i | 0.225565 | + | 0.130230i | ||||
\(797\) | −27.9590 | −0.990359 | −0.495179 | − | 0.868791i | \(-0.664898\pi\) | ||||
−0.495179 | + | 0.868791i | \(0.664898\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.75736 | −0.168303 | ||||||||
\(800\) | 0.866025 | + | 0.500000i | 0.0306186 | + | 0.0176777i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.87868 | + | 17.1104i | 0.348828 | + | 0.604188i | ||||
\(803\) | −2.44949 | + | 4.24264i | −0.0864406 | + | 0.149720i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.09188 | − | 7.97887i | −0.0384838 | − | 0.281218i | ||||
\(806\) | − | 20.4853i | − | 0.721563i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.1066 | − | 6.98975i | 0.425909 | − | 0.245899i | ||||
\(809\) | 19.0016 | − | 10.9706i | 0.668060 | − | 0.385704i | −0.127281 | − | 0.991867i | \(-0.540625\pi\) |
0.795341 | + | 0.606162i | \(0.207292\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.8713i | 0.768006i | 0.923332 | + | 0.384003i | \(0.125455\pi\) | ||||
−0.923332 | + | 0.384003i | \(0.874545\pi\) | |||||||
\(812\) | 2.59808 | + | 18.9853i | 0.0911746 | + | 0.666253i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.62132 | + | 4.54026i | −0.0918772 | + | 0.159136i | ||||
\(815\) | −23.2341 | − | 40.2426i | −0.813855 | − | 1.40964i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.50000 | − | 0.866025i | −0.0524784 | − | 0.0302984i | ||||
\(818\) | −14.2767 | −0.499172 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 20.4853 | 0.715377 | ||||||||
\(821\) | 22.9369 | + | 13.2426i | 0.800504 | + | 0.462171i | 0.843647 | − | 0.536898i | \(-0.180404\pi\) |
−0.0431432 | + | 0.999069i | \(0.513737\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.393398 | + | 0.681386i | 0.0137130 | + | 0.0237516i | 0.872800 | − | 0.488077i | \(-0.162302\pi\) |
−0.859087 | + | 0.511829i | \(0.828968\pi\) | |||||||
\(824\) | −5.70346 | + | 9.87868i | −0.198689 | + | 0.344140i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.2721 | − | 4.60181i | −0.392206 | − | 0.160117i | ||||
\(827\) | 2.48528i | 0.0864217i | 0.999066 | + | 0.0432109i | \(0.0137587\pi\) | ||||
−0.999066 | + | 0.0432109i | \(0.986241\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.3198 | − | 22.7013i | 1.36563 | − | 0.788449i | 0.375266 | − | 0.926917i | \(-0.377551\pi\) |
0.990367 | + | 0.138468i | \(0.0442179\pi\) | |||||||
\(830\) | −16.8493 | + | 9.72792i | −0.584846 | + | 0.337661i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 2.44949i | − | 0.0849208i | ||||||
\(833\) | −3.01834 | + | 11.7426i | −0.104579 | + | 0.406858i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.4853 | + | 30.2854i | −0.605103 | + | 1.04807i | ||||
\(836\) | −0.866025 | − | 1.50000i | −0.0299521 | − | 0.0518786i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12.9853 | + | 7.49706i | 0.448569 | + | 0.258981i | ||||
\(839\) | −24.2487 | −0.837158 | −0.418579 | − | 0.908180i | \(-0.637472\pi\) | ||||
−0.418579 | + | 0.908180i | \(0.637472\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.4558 | −0.808822 | ||||||||
\(842\) | −26.5857 | − | 15.3492i | −0.916203 | − | 0.528970i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.75736 | − | 4.77589i | −0.0949122 | − | 0.164393i | ||||
\(845\) | −8.57321 | + | 14.8492i | −0.294928 | + | 0.510829i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.62132 | + | 2.09077i | 0.0557092 | + | 0.0718397i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.50000 | + | 0.866025i | −0.0514496 | + | 0.0297044i | ||||
\(851\) | −5.64191 | + | 3.25736i | −0.193402 | + | 0.111661i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.2474i | 0.419345i | 0.977772 | + | 0.209672i | \(0.0672397\pi\) | ||||
−0.977772 | + | 0.209672i | \(0.932760\pi\) | |||||||
\(854\) | −27.2416 | + | 3.72792i | −0.932187 | + | 0.127567i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.24264 | + | 2.15232i | −0.0424726 | + | 0.0735647i | ||||
\(857\) | −17.8894 | − | 30.9853i | −0.611089 | − | 1.05844i | −0.991057 | − | 0.133438i | \(-0.957398\pi\) |
0.379968 | − | 0.925000i | \(-0.375935\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.0919 | − | 5.82655i | −0.344331 | − | 0.198799i | 0.317855 | − | 0.948139i | \(-0.397038\pi\) |
−0.662185 | + | 0.749340i | \(0.730371\pi\) | |||||||
\(860\) | −2.44949 | −0.0835269 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.9706 | −0.578020 | ||||||||
\(863\) | 22.0454 | + | 12.7279i | 0.750434 | + | 0.433264i | 0.825851 | − | 0.563889i | \(-0.190695\pi\) |
−0.0754164 | + | 0.997152i | \(0.524029\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.4853 | − | 25.0892i | −0.492514 | − | 0.853060i | ||||
\(866\) | −8.93193 | + | 15.4706i | −0.303519 | + | 0.525711i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 17.4853 | − | 13.5592i | 0.593489 | − | 0.460230i | ||||
\(869\) | 8.00000i | 0.271381i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.51472 | − | 5.49333i | 0.322394 | − | 0.186134i | ||||
\(872\) | −15.7986 | + | 9.12132i | −0.535008 | + | 0.308887i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 2.15232i | − | 0.0728032i | ||||||
\(875\) | 9.79796 | − | 24.0000i | 0.331231 | − | 0.811348i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.8787 | + | 24.0386i | −0.468650 | + | 0.811725i | −0.999358 | − | 0.0358295i | \(-0.988593\pi\) |
0.530708 | + | 0.847555i | \(0.321926\pi\) | |||||||
\(878\) | 10.0336 | + | 17.3787i | 0.338617 | + | 0.586502i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.12132 | − | 1.22474i | −0.0715097 | − | 0.0412861i | ||||
\(881\) | −14.6969 | −0.495152 | −0.247576 | − | 0.968868i | \(-0.579634\pi\) | ||||
−0.247576 | + | 0.968868i | \(0.579634\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.27208 | −0.244725 | −0.122362 | − | 0.992485i | \(-0.539047\pi\) | ||||
−0.122362 | + | 0.992485i | \(0.539047\pi\) | |||||||
\(884\) | 3.67423 | + | 2.12132i | 0.123578 | + | 0.0713477i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.50000 | − | 2.59808i | −0.0503935 | − | 0.0872841i | ||||
\(887\) | 6.92820 | − | 12.0000i | 0.232626 | − | 0.402921i | −0.725954 | − | 0.687743i | \(-0.758601\pi\) |
0.958580 | + | 0.284823i | \(0.0919348\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.2426 | + | 52.0336i | −0.712455 | + | 1.74515i | ||||
\(890\) | − | 14.4853i | − | 0.485548i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.87868 | + | 2.23936i | −0.129868 | + | 0.0749792i | ||||
\(893\) | −4.11999 | + | 2.37868i | −0.137870 | + | 0.0795995i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 22.0454i | − | 0.736897i | ||||||
\(896\) | 2.09077 | − | 1.62132i | 0.0698477 | − | 0.0541645i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.7279 | + | 32.4377i | −0.624959 | + | 1.08246i | ||||
\(899\) | 30.2854 | + | 52.4558i | 1.01007 | + | 1.74950i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −8.36308 | −0.278460 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.2426 | 0.340665 | ||||||||
\(905\) | −10.3923 | − | 6.00000i | −0.345452 | − | 0.199447i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.7574 | − | 27.2925i | −0.523215 | − | 0.906234i | −0.999635 | − | 0.0270166i | \(-0.991399\pi\) |
0.476420 | − | 0.879218i | \(-0.341934\pi\) | |||||||
\(908\) | 6.63103 | − | 11.4853i | 0.220058 | − | 0.381152i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 15.7279 | − | 2.15232i | 0.521376 | − | 0.0713486i | ||||
\(911\) | − | 15.7279i | − | 0.521089i | −0.965462 | − | 0.260545i | \(-0.916098\pi\) | ||
0.965462 | − | 0.260545i | \(-0.0839021\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.87868 | − | 3.97141i | 0.227651 | − | 0.131434i | ||||
\(914\) | 22.2555 | − | 12.8492i | 0.736148 | − | 0.425015i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 13.8564i | − | 0.457829i | ||||||
\(917\) | −26.4371 | − | 34.0919i | −0.873029 | − | 1.12581i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.62132 | + | 14.9326i | −0.284391 | + | 0.492580i | −0.972461 | − | 0.233064i | \(-0.925125\pi\) |
0.688070 | + | 0.725644i | \(0.258458\pi\) | |||||||
\(920\) | −1.52192 | − | 2.63604i | −0.0501761 | − | 0.0869076i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.13604 | − | 2.38794i | −0.136213 | − | 0.0786427i | ||||
\(923\) | −3.04384 | −0.100189 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.24264 | 0.172377 | ||||||||
\(926\) | 18.5813 | + | 10.7279i | 0.610620 | + | 0.352541i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.62132 | + | 6.27231i | 0.118876 | + | 0.205899i | ||||
\(929\) | 7.55860 | − | 13.0919i | 0.247990 | − | 0.429531i | −0.714978 | − | 0.699147i | \(-0.753563\pi\) |
0.962968 | + | 0.269616i | \(0.0868968\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.25736 | + | 11.6786i | 0.106756 | + | 0.382751i | ||||
\(932\) | − | 0.514719i | − | 0.0168602i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.50000 | − | 2.59808i | 0.147244 | − | 0.0850117i | ||||
\(935\) | 3.67423 | − | 2.12132i | 0.120160 | − | 0.0693746i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.59466i | 0.248107i | 0.992276 | + | 0.124053i | \(0.0395894\pi\) | ||||
−0.992276 | + | 0.124053i | \(0.960411\pi\) | |||||||
\(938\) | 10.9867 | + | 4.48528i | 0.358727 | + | 0.146450i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.36396 | + | 5.82655i | −0.109720 | + | 0.190041i | ||||
\(941\) | −9.43924 | − | 16.3492i | −0.307710 | − | 0.532970i | 0.670151 | − | 0.742225i | \(-0.266229\pi\) |
−0.977861 | + | 0.209255i | \(0.932896\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.00000 | − | 5.19615i | −0.293080 | − | 0.169210i | ||||
\(944\) | −4.60181 | −0.149776 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.00000 | 0.0325128 | ||||||||
\(947\) | 18.1865 | + | 10.5000i | 0.590983 | + | 0.341204i | 0.765486 | − | 0.643452i | \(-0.222499\pi\) |
−0.174503 | + | 0.984657i | \(0.555832\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.00000 | − | 10.3923i | −0.194768 | − | 0.337348i | ||||
\(950\) | −0.866025 | + | 1.50000i | −0.0280976 | + | 0.0486664i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.621320 | + | 4.54026i | 0.0201371 | + | 0.147151i | ||||
\(953\) | 48.0000i | 1.55487i | 0.628962 | + | 0.777436i | \(0.283480\pi\) | ||||
−0.628962 | + | 0.777436i | \(0.716520\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −36.0000 | + | 20.7846i | −1.16493 | + | 0.672574i | ||||
\(956\) | −11.0227 | + | 6.36396i | −0.356500 | + | 0.205825i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 36.0759i | − | 1.16556i | ||||||
\(959\) | 3.67423 | + | 26.8492i | 0.118647 | + | 0.867007i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.4706 | − | 33.7240i | 0.628083 | − | 1.08787i | ||||
\(962\) | −6.42090 | − | 11.1213i | −0.207018 | − | 0.358566i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 22.9706 | + | 13.2621i | 0.739832 | + | 0.427142i | ||||
\(965\) | 11.5810 | 0.372805 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.2426 | 1.06901 | 0.534506 | − | 0.845165i | \(-0.320498\pi\) | ||||
0.534506 | + | 0.845165i | \(0.320498\pi\) | |||||||
\(968\) | 0.866025 | + | 0.500000i | 0.0278351 | + | 0.0160706i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.12132 | − | 14.0665i | −0.260760 | − | 0.451649i | ||||
\(971\) | −0.840532 | + | 1.45584i | −0.0269740 | + | 0.0467203i | −0.879197 | − | 0.476458i | \(-0.841920\pi\) |
0.852223 | + | 0.523178i | \(0.175254\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.7279 | − | 10.0951i | −0.792741 | − | 0.323635i | ||||
\(974\) | 41.2132i | 1.32056i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.00000 | + | 5.19615i | −0.288083 | + | 0.166325i | ||||
\(977\) | 9.13151 | − | 5.27208i | 0.292143 | − | 0.168669i | −0.346765 | − | 0.937952i | \(-0.612720\pi\) |
0.638908 | + | 0.769283i | \(0.279387\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.91359i | 0.188999i | ||||||||
\(980\) | 12.2474 | + | 12.0000i | 0.391230 | + | 0.383326i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −21.3640 | + | 37.0035i | −0.681751 | + | 1.18083i | ||||
\(983\) | 27.3031 | + | 47.2904i | 0.870834 | + | 1.50833i | 0.861135 | + | 0.508376i | \(0.169754\pi\) |
0.00969837 | + | 0.999953i | \(0.496913\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 46.0919 | + | 26.6112i | 1.46861 | + | 0.847902i | ||||
\(986\) | −12.5446 | −0.399502 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.24264 | 0.134976 | ||||||||
\(989\) | 1.07616 | + | 0.621320i | 0.0342198 | + | 0.0197568i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.24264 | + | 3.88437i | 0.0712398 | + | 0.123391i | 0.899445 | − | 0.437034i | \(-0.143971\pi\) |
−0.828205 | + | 0.560425i | \(0.810638\pi\) | |||||||
\(992\) | 4.18154 | − | 7.24264i | 0.132764 | − | 0.229954i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.01472 | − | 2.59808i | −0.0639030 | − | 0.0824060i | ||||
\(995\) | 18.0000i | 0.570638i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.5772 | − | 15.9217i | 0.873378 | − | 0.504245i | 0.00490839 | − | 0.999988i | \(-0.498438\pi\) |
0.868469 | + | 0.495743i | \(0.165104\pi\) | |||||||
\(998\) | −32.2276 | + | 18.6066i | −1.02015 | + | 0.588982i | ||||
\(999\) | 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.b.89.3 | yes | 8 | |
3.2 | odd | 2 | inner | 1386.2.r.b.89.2 | ✓ | 8 | |
7.3 | odd | 6 | inner | 1386.2.r.b.1277.2 | yes | 8 | |
21.17 | even | 6 | inner | 1386.2.r.b.1277.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.r.b.89.2 | ✓ | 8 | 3.2 | odd | 2 | inner | |
1386.2.r.b.89.3 | yes | 8 | 1.1 | even | 1 | trivial | |
1386.2.r.b.1277.2 | yes | 8 | 7.3 | odd | 6 | inner | |
1386.2.r.b.1277.3 | yes | 8 | 21.17 | even | 6 | inner |