Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(1151,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.bf (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: | \(25.1528766367\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1151.4 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.1151 |
Dual form | 3150.2.bf.a.1601.4 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.62132 | + | 2.09077i | 0.612801 | + | 0.790237i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.59808 | + | 1.50000i | 0.783349 | + | 0.452267i | 0.837616 | − | 0.546259i | \(-0.183949\pi\) |
−0.0542666 | + | 0.998526i | \(0.517282\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.44949i | 0.679366i | 0.940540 | + | 0.339683i | \(0.110320\pi\) | ||||
−0.940540 | + | 0.339683i | \(0.889680\pi\) | |||||||
\(14\) | 2.44949 | + | 1.00000i | 0.654654 | + | 0.267261i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −0.507306 | + | 0.878680i | −0.123040 | + | 0.213111i | −0.920965 | − | 0.389645i | \(-0.872598\pi\) |
0.797925 | + | 0.602756i | \(0.205931\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.878680 | + | 0.507306i | −0.201583 | + | 0.116384i | −0.597394 | − | 0.801948i | \(-0.703797\pi\) |
0.395811 | + | 0.918332i | \(0.370464\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.00000 | 0.639602 | ||||||||
\(23\) | −3.67423 | + | 2.12132i | −0.766131 | + | 0.442326i | −0.831493 | − | 0.555536i | \(-0.812513\pi\) |
0.0653618 | + | 0.997862i | \(0.479180\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.22474 | + | 2.12132i | 0.240192 | + | 0.416025i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.62132 | − | 0.358719i | 0.495383 | − | 0.0677916i | ||||
\(29\) | 1.24264i | 0.230753i | 0.993322 | + | 0.115376i | \(0.0368074\pi\) | ||||
−0.993322 | + | 0.115376i | \(0.963193\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.86396 | + | 2.80821i | 0.873593 | + | 0.504369i | 0.868541 | − | 0.495618i | \(-0.165058\pi\) |
0.00505256 | + | 0.999987i | \(0.498392\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.01461i | 0.174005i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.12132 | + | 7.13834i | 0.677541 | + | 1.17354i | 0.975719 | + | 0.219025i | \(0.0702877\pi\) |
−0.298178 | + | 0.954510i | \(0.596379\pi\) | |||||||
\(38\) | −0.507306 | + | 0.878680i | −0.0822959 | + | 0.142541i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.02922 | −0.316912 | −0.158456 | − | 0.987366i | \(-0.550652\pi\) | ||||
−0.158456 | + | 0.987366i | \(0.550652\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.24264 | −1.25699 | −0.628495 | − | 0.777813i | \(-0.716329\pi\) | ||||
−0.628495 | + | 0.777813i | \(0.716329\pi\) | |||||||
\(44\) | 2.59808 | − | 1.50000i | 0.391675 | − | 0.226134i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.12132 | + | 3.67423i | −0.312772 | + | 0.541736i | ||||
\(47\) | −0.507306 | − | 0.878680i | −0.0739982 | − | 0.128169i | 0.826652 | − | 0.562713i | \(-0.190243\pi\) |
−0.900650 | + | 0.434545i | \(0.856909\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.74264 | + | 6.77962i | −0.248949 | + | 0.968517i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.12132 | + | 1.22474i | 0.294174 | + | 0.169842i | ||||
\(53\) | 1.07616 | + | 0.621320i | 0.147822 | + | 0.0853449i | 0.572087 | − | 0.820193i | \(-0.306134\pi\) |
−0.424265 | + | 0.905538i | \(0.639467\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.09077 | − | 1.62132i | 0.279391 | − | 0.216658i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.621320 | + | 1.07616i | 0.0815834 | + | 0.141307i | ||||
\(59\) | 5.76500 | − | 9.98528i | 0.750540 | − | 1.29997i | −0.197022 | − | 0.980399i | \(-0.563127\pi\) |
0.947561 | − | 0.319574i | \(-0.103540\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.12132 | − | 2.95680i | 0.655718 | − | 0.378579i | −0.134926 | − | 0.990856i | \(-0.543080\pi\) |
0.790643 | + | 0.612277i | \(0.209746\pi\) | |||||||
\(62\) | 5.61642 | 0.713286 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.00000 | + | 8.66025i | −0.610847 | + | 1.05802i | 0.380251 | + | 0.924883i | \(0.375838\pi\) |
−0.991098 | + | 0.133135i | \(0.957496\pi\) | |||||||
\(68\) | 0.507306 | + | 0.878680i | 0.0615199 | + | 0.106556i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.2426i | 1.21558i | 0.794099 | + | 0.607789i | \(0.207943\pi\) | ||||
−0.794099 | + | 0.607789i | \(0.792057\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.24264 | − | 4.18154i | −0.847687 | − | 0.489412i | 0.0121828 | − | 0.999926i | \(-0.496122\pi\) |
−0.859870 | + | 0.510513i | \(0.829455\pi\) | |||||||
\(74\) | 7.13834 | + | 4.12132i | 0.829815 | + | 0.479094i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.01461i | 0.116384i | ||||||||
\(77\) | 1.07616 | + | 7.86396i | 0.122640 | + | 0.896182i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.62132 | + | 9.73641i | 0.632448 | + | 1.09543i | 0.987050 | + | 0.160415i | \(0.0512831\pi\) |
−0.354602 | + | 0.935017i | \(0.615384\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.75736 | + | 1.01461i | −0.194068 | + | 0.112045i | ||||
\(83\) | −3.16693 | −0.347616 | −0.173808 | − | 0.984780i | \(-0.555607\pi\) | ||||
−0.173808 | + | 0.984780i | \(0.555607\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −7.13834 | + | 4.12132i | −0.769747 | + | 0.444413i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.50000 | − | 2.59808i | 0.159901 | − | 0.276956i | ||||
\(89\) | −5.19615 | − | 9.00000i | −0.550791 | − | 0.953998i | −0.998218 | − | 0.0596775i | \(-0.980993\pi\) |
0.447427 | − | 0.894321i | \(-0.352341\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.12132 | + | 3.97141i | −0.536860 | + | 0.416317i | ||||
\(92\) | 4.24264i | 0.442326i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.878680 | − | 0.507306i | −0.0906289 | − | 0.0523246i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.76127i | 0.381900i | 0.981600 | + | 0.190950i | \(0.0611568\pi\) | ||||
−0.981600 | + | 0.190950i | \(0.938843\pi\) | |||||||
\(98\) | 1.88064 | + | 6.74264i | 0.189973 | + | 0.681110i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.2426 | − | 7.64564i | 1.30484 | − | 0.753348i | 0.323607 | − | 0.946192i | \(-0.395105\pi\) |
0.981229 | + | 0.192844i | \(0.0617712\pi\) | |||||||
\(104\) | 2.44949 | 0.240192 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.24264 | 0.120696 | ||||||||
\(107\) | 4.75039 | − | 2.74264i | 0.459238 | − | 0.265141i | −0.252486 | − | 0.967601i | \(-0.581248\pi\) |
0.711724 | + | 0.702459i | \(0.247915\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.757359 | + | 1.31178i | −0.0725419 | + | 0.125646i | −0.900015 | − | 0.435860i | \(-0.856444\pi\) |
0.827473 | + | 0.561506i | \(0.189778\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000 | − | 2.44949i | 0.0944911 | − | 0.231455i | ||||
\(113\) | − | 8.48528i | − | 0.798228i | −0.916901 | − | 0.399114i | \(-0.869318\pi\) | ||
0.916901 | − | 0.399114i | \(-0.130682\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.07616 | + | 0.621320i | 0.0999188 | + | 0.0576881i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 11.5300i | − | 1.06142i | ||||||
\(119\) | −2.65962 | + | 0.363961i | −0.243807 | + | 0.0333643i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | − | 1.73205i | −0.0909091 | − | 0.157459i | ||||
\(122\) | 2.95680 | − | 5.12132i | 0.267696 | − | 0.463663i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.86396 | − | 2.80821i | 0.436797 | − | 0.252185i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.24264 | 0.465209 | 0.232605 | − | 0.972571i | \(-0.425275\pi\) | ||||
0.232605 | + | 0.972571i | \(0.425275\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.59808 | + | 4.50000i | 0.226995 | + | 0.393167i | 0.956916 | − | 0.290365i | \(-0.0937766\pi\) |
−0.729921 | + | 0.683531i | \(0.760443\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.48528 | − | 1.01461i | −0.215501 | − | 0.0879780i | ||||
\(134\) | 10.0000i | 0.863868i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.878680 | + | 0.507306i | 0.0753462 | + | 0.0435011i | ||||
\(137\) | 12.5446 | + | 7.24264i | 1.07176 | + | 0.618781i | 0.928662 | − | 0.370928i | \(-0.120960\pi\) |
0.143098 | + | 0.989709i | \(0.454294\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.1903i | 1.71252i | 0.516549 | + | 0.856258i | \(0.327217\pi\) | ||||
−0.516549 | + | 0.856258i | \(0.672783\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.12132 | + | 8.87039i | 0.429772 | + | 0.744386i | ||||
\(143\) | −3.67423 | + | 6.36396i | −0.307255 | + | 0.532181i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.36308 | −0.692134 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.24264 | 0.677541 | ||||||||
\(149\) | 17.7408 | − | 10.2426i | 1.45338 | − | 0.839110i | 0.454709 | − | 0.890640i | \(-0.349743\pi\) |
0.998671 | + | 0.0515300i | \(0.0164098\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.62132 | − | 2.80821i | 0.131941 | − | 0.228529i | −0.792484 | − | 0.609893i | \(-0.791212\pi\) |
0.924425 | + | 0.381364i | \(0.124546\pi\) | |||||||
\(152\) | 0.507306 | + | 0.878680i | 0.0411479 | + | 0.0712703i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.86396 | + | 6.27231i | 0.391949 | + | 0.505437i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.7279 | + | 7.34847i | 1.01580 | + | 0.586472i | 0.912884 | − | 0.408219i | \(-0.133850\pi\) |
0.102915 | + | 0.994690i | \(0.467183\pi\) | |||||||
\(158\) | 9.73641 | + | 5.62132i | 0.774587 | + | 0.447208i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.3923 | − | 4.24264i | −0.819028 | − | 0.334367i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.12132 | + | 5.40629i | 0.244481 | + | 0.423453i | 0.961985 | − | 0.273101i | \(-0.0880492\pi\) |
−0.717505 | + | 0.696554i | \(0.754716\pi\) | |||||||
\(164\) | −1.01461 | + | 1.75736i | −0.0792279 | + | 0.137227i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.74264 | + | 1.58346i | −0.212870 | + | 0.122901i | ||||
\(167\) | 23.0600 | 1.78444 | 0.892219 | − | 0.451603i | \(-0.149148\pi\) | ||||
0.892219 | + | 0.451603i | \(0.149148\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.12132 | + | 7.13834i | −0.314248 | + | 0.544293i | ||||
\(173\) | −10.3923 | − | 18.0000i | −0.790112 | − | 1.36851i | −0.925897 | − | 0.377776i | \(-0.876689\pi\) |
0.135785 | − | 0.990738i | \(-0.456644\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 3.00000i | − | 0.226134i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.00000 | − | 5.19615i | −0.674579 | − | 0.389468i | ||||
\(179\) | −8.23999 | − | 4.75736i | −0.615886 | − | 0.355582i | 0.159380 | − | 0.987217i | \(-0.449051\pi\) |
−0.775265 | + | 0.631636i | \(0.782384\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.02922i | − | 0.150831i | −0.997152 | − | 0.0754155i | \(-0.975972\pi\) | ||
0.997152 | − | 0.0754155i | \(-0.0240283\pi\) | |||||||
\(182\) | −2.44949 | + | 6.00000i | −0.181568 | + | 0.444750i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.12132 | + | 3.67423i | 0.156386 | + | 0.270868i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.63604 | + | 1.52192i | −0.192766 | + | 0.111294i | ||||
\(188\) | −1.01461 | −0.0739982 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.34847 | − | 4.24264i | 0.531717 | − | 0.306987i | −0.209999 | − | 0.977702i | \(-0.567346\pi\) |
0.741715 | + | 0.670715i | \(0.234013\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.74264 | + | 6.48244i | −0.269401 | + | 0.466617i | −0.968707 | − | 0.248206i | \(-0.920159\pi\) |
0.699306 | + | 0.714822i | \(0.253492\pi\) | |||||||
\(194\) | 1.88064 | + | 3.25736i | 0.135022 | + | 0.233865i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.00000 | + | 4.89898i | 0.357143 | + | 0.349927i | ||||
\(197\) | − | 9.51472i | − | 0.677896i | −0.940805 | − | 0.338948i | \(-0.889929\pi\) | ||
0.940805 | − | 0.338948i | \(-0.110071\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.9706 | − | 8.06591i | −0.990347 | − | 0.571777i | −0.0849690 | − | 0.996384i | \(-0.527079\pi\) |
−0.905378 | + | 0.424607i | \(0.860412\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.59808 | + | 2.01472i | −0.182349 | + | 0.141406i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.64564 | − | 13.2426i | 0.532697 | − | 0.922658i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.12132 | − | 1.22474i | 0.147087 | − | 0.0849208i | ||||
\(209\) | −3.04384 | −0.210547 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.24264 | 0.567447 | 0.283723 | − | 0.958906i | \(-0.408430\pi\) | ||||
0.283723 | + | 0.958906i | \(0.408430\pi\) | |||||||
\(212\) | 1.07616 | − | 0.621320i | 0.0739109 | − | 0.0426725i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.74264 | − | 4.75039i | 0.187483 | − | 0.324730i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.01472 | + | 14.7224i | 0.136768 | + | 0.999424i | ||||
\(218\) | 1.51472i | 0.102590i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.15232 | − | 1.24264i | −0.144780 | − | 0.0835891i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 12.5446i | − | 0.840050i | −0.907513 | − | 0.420025i | \(-0.862021\pi\) | ||
0.907513 | − | 0.420025i | \(-0.137979\pi\) | |||||||
\(224\) | −0.358719 | − | 2.62132i | −0.0239680 | − | 0.175144i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.24264 | − | 7.34847i | −0.282216 | − | 0.488813i | ||||
\(227\) | 7.79423 | − | 13.5000i | 0.517321 | − | 0.896026i | −0.482476 | − | 0.875909i | \(-0.660263\pi\) |
0.999798 | − | 0.0201176i | \(-0.00640405\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.0000 | + | 6.92820i | −0.792982 | + | 0.457829i | −0.841011 | − | 0.541017i | \(-0.818039\pi\) |
0.0480291 | + | 0.998846i | \(0.484706\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.24264 | 0.0815834 | ||||||||
\(233\) | −5.82655 | + | 3.36396i | −0.381710 | + | 0.220380i | −0.678562 | − | 0.734543i | \(-0.737397\pi\) |
0.296852 | + | 0.954924i | \(0.404063\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.76500 | − | 9.98528i | −0.375270 | − | 0.649986i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.12132 | + | 1.64501i | −0.137505 | + | 0.106630i | ||||
\(239\) | 12.7279i | 0.823301i | 0.911342 | + | 0.411650i | \(0.135048\pi\) | ||||
−0.911342 | + | 0.411650i | \(0.864952\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.7426 | + | 8.51167i | 0.949657 | + | 0.548285i | 0.892974 | − | 0.450108i | \(-0.148614\pi\) |
0.0566826 | + | 0.998392i | \(0.481948\pi\) | |||||||
\(242\) | −1.73205 | − | 1.00000i | −0.111340 | − | 0.0642824i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 5.91359i | − | 0.378579i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.24264 | − | 2.15232i | −0.0790673 | − | 0.136949i | ||||
\(248\) | 2.80821 | − | 4.86396i | 0.178321 | − | 0.308862i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.6177 | 1.11202 | 0.556009 | − | 0.831176i | \(-0.312332\pi\) | ||||
0.556009 | + | 0.831176i | \(0.312332\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.7279 | −0.800198 | ||||||||
\(254\) | 4.54026 | − | 2.62132i | 0.284881 | − | 0.164476i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −12.5446 | − | 21.7279i | −0.782512 | − | 1.35535i | −0.930474 | − | 0.366358i | \(-0.880605\pi\) |
0.147962 | − | 0.988993i | \(-0.452729\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.24264 | + | 20.1903i | −0.512173 | + | 1.25456i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.50000 | + | 2.59808i | 0.278011 | + | 0.160510i | ||||
\(263\) | −23.5673 | − | 13.6066i | −1.45322 | − | 0.839019i | −0.454561 | − | 0.890716i | \(-0.650204\pi\) |
−0.998663 | + | 0.0516967i | \(0.983537\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.65962 | + | 0.363961i | −0.163072 | + | 0.0223159i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.00000 | + | 8.66025i | 0.305424 | + | 0.529009i | ||||
\(269\) | −5.25770 | + | 9.10660i | −0.320568 | + | 0.555239i | −0.980605 | − | 0.195993i | \(-0.937207\pi\) |
0.660038 | + | 0.751232i | \(0.270540\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.62132 | + | 5.55487i | −0.584454 | + | 0.337434i | −0.762901 | − | 0.646515i | \(-0.776226\pi\) |
0.178448 | + | 0.983949i | \(0.442892\pi\) | |||||||
\(272\) | 1.01461 | 0.0615199 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.4853 | 0.875088 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.4853 | + | 18.1610i | −0.630000 | + | 1.09119i | 0.357552 | + | 0.933893i | \(0.383612\pi\) |
−0.987551 | + | 0.157298i | \(0.949722\pi\) | |||||||
\(278\) | 10.0951 | + | 17.4853i | 0.605466 | + | 1.04870i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.00000i | − | 0.357930i | −0.983855 | − | 0.178965i | \(-0.942725\pi\) | ||
0.983855 | − | 0.178965i | \(-0.0572749\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.63604 | + | 3.25397i | 0.335028 | + | 0.193428i | 0.658071 | − | 0.752956i | \(-0.271373\pi\) |
−0.323043 | + | 0.946384i | \(0.604706\pi\) | |||||||
\(284\) | 8.87039 | + | 5.12132i | 0.526361 | + | 0.303894i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.34847i | 0.434524i | ||||||||
\(287\) | −3.29002 | − | 4.24264i | −0.194204 | − | 0.250435i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.98528 | + | 13.8309i | 0.469722 | + | 0.813583i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.24264 | + | 4.18154i | −0.423843 | + | 0.244706i | ||||
\(293\) | 4.18154 | 0.244288 | 0.122144 | − | 0.992512i | \(-0.461023\pi\) | ||||
0.122144 | + | 0.992512i | \(0.461023\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.13834 | − | 4.12132i | 0.414907 | − | 0.239547i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.2426 | − | 17.7408i | 0.593340 | − | 1.02770i | ||||
\(299\) | −5.19615 | − | 9.00000i | −0.300501 | − | 0.520483i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.3640 | − | 17.2335i | −0.770286 | − | 0.993321i | ||||
\(302\) | − | 3.24264i | − | 0.186593i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.878680 | + | 0.507306i | 0.0503957 | + | 0.0290960i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 24.6690i | − | 1.40793i | −0.710233 | − | 0.703966i | \(-0.751411\pi\) | ||
0.710233 | − | 0.703966i | \(-0.248589\pi\) | |||||||
\(308\) | 7.34847 | + | 3.00000i | 0.418718 | + | 0.170941i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.37769 | − | 16.2426i | 0.531760 | − | 0.921036i | −0.467552 | − | 0.883965i | \(-0.654864\pi\) |
0.999313 | − | 0.0370703i | \(-0.0118026\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.985281 | − | 0.568852i | 0.0556914 | − | 0.0321534i | −0.471896 | − | 0.881654i | \(-0.656430\pi\) |
0.527587 | + | 0.849501i | \(0.323097\pi\) | |||||||
\(314\) | 14.6969 | 0.829396 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.2426 | 0.632448 | ||||||||
\(317\) | −6.27231 | + | 3.62132i | −0.352288 | + | 0.203394i | −0.665693 | − | 0.746226i | \(-0.731864\pi\) |
0.313404 | + | 0.949620i | \(0.398530\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.86396 | + | 3.22848i | −0.104362 | + | 0.180760i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −11.1213 | + | 1.52192i | −0.619767 | + | 0.0848132i | ||||
\(323\) | − | 1.02944i | − | 0.0572794i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.40629 | + | 3.12132i | 0.299426 | + | 0.172874i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.02922i | 0.112045i | ||||||||
\(329\) | 1.01461 | − | 2.48528i | 0.0559374 | − | 0.137018i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.72792 | − | 15.1172i | −0.479730 | − | 0.830917i | 0.520000 | − | 0.854166i | \(-0.325932\pi\) |
−0.999730 | + | 0.0232497i | \(0.992599\pi\) | |||||||
\(332\) | −1.58346 | + | 2.74264i | −0.0869039 | + | 0.150522i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 19.9706 | − | 11.5300i | 1.09274 | − | 0.630894i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.00000 | 0.272367 | 0.136184 | − | 0.990684i | \(-0.456516\pi\) | ||||
0.136184 | + | 0.990684i | \(0.456516\pi\) | |||||||
\(338\) | 6.06218 | − | 3.50000i | 0.329739 | − | 0.190375i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.42463 | + | 14.5919i | 0.456219 | + | 0.790195i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.0000 | + | 7.34847i | −0.917914 | + | 0.396780i | ||||
\(344\) | 8.24264i | 0.444413i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.0000 | − | 10.3923i | −0.967686 | − | 0.558694i | ||||
\(347\) | −12.5446 | − | 7.24264i | −0.673431 | − | 0.388805i | 0.123945 | − | 0.992289i | \(-0.460445\pi\) |
−0.797375 | + | 0.603484i | \(0.793779\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 36.9164i | − | 1.97609i | −0.154163 | − | 0.988045i | \(-0.549268\pi\) | ||
0.154163 | − | 0.988045i | \(-0.450732\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.50000 | − | 2.59808i | −0.0799503 | − | 0.138478i | ||||
\(353\) | −9.37769 | + | 16.2426i | −0.499124 | + | 0.864509i | −0.999999 | − | 0.00101095i | \(-0.999678\pi\) |
0.500875 | + | 0.865519i | \(0.333012\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −10.3923 | −0.550791 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.51472 | −0.502869 | ||||||||
\(359\) | 15.5885 | − | 9.00000i | 0.822727 | − | 0.475002i | −0.0286287 | − | 0.999590i | \(-0.509114\pi\) |
0.851356 | + | 0.524588i | \(0.175781\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.98528 | + | 15.5630i | −0.472910 | + | 0.819103i | ||||
\(362\) | −1.01461 | − | 1.75736i | −0.0533268 | − | 0.0923648i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.878680 | + | 6.42090i | 0.0460553 | + | 0.336546i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.3492 | − | 9.43924i | −0.853424 | − | 0.492724i | 0.00838099 | − | 0.999965i | \(-0.497332\pi\) |
−0.861804 | + | 0.507241i | \(0.830666\pi\) | |||||||
\(368\) | 3.67423 | + | 2.12132i | 0.191533 | + | 0.110581i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.445759 | + | 3.25736i | 0.0231427 | + | 0.169114i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.7279 | + | 18.5813i | 0.555471 | + | 0.962104i | 0.997867 | + | 0.0652837i | \(0.0207952\pi\) |
−0.442396 | + | 0.896820i | \(0.645871\pi\) | |||||||
\(374\) | −1.52192 | + | 2.63604i | −0.0786965 | + | 0.136306i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.878680 | + | 0.507306i | −0.0453144 | + | 0.0261623i | ||||
\(377\) | −3.04384 | −0.156766 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.48528 | −0.230393 | −0.115197 | − | 0.993343i | \(-0.536750\pi\) | ||||
−0.115197 | + | 0.993343i | \(0.536750\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.24264 | − | 7.34847i | 0.217072 | − | 0.375980i | ||||
\(383\) | −6.21076 | − | 10.7574i | −0.317355 | − | 0.549675i | 0.662580 | − | 0.748991i | \(-0.269461\pi\) |
−0.979935 | + | 0.199316i | \(0.936128\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.48528i | 0.380991i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.25736 | + | 1.88064i | 0.165367 | + | 0.0954749i | ||||
\(389\) | −16.8493 | − | 9.72792i | −0.854291 | − | 0.493225i | 0.00780525 | − | 0.999970i | \(-0.497515\pi\) |
−0.862096 | + | 0.506744i | \(0.830849\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 4.30463i | − | 0.217695i | ||||||
\(392\) | 6.77962 | + | 1.74264i | 0.342422 | + | 0.0880166i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.75736 | − | 8.23999i | −0.239672 | − | 0.415125i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.0000 | + | 6.92820i | −0.602263 | + | 0.347717i | −0.769931 | − | 0.638127i | \(-0.779710\pi\) |
0.167668 | + | 0.985843i | \(0.446376\pi\) | |||||||
\(398\) | −16.1318 | −0.808615 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.87868 | + | 11.9142i | −0.342651 | + | 0.593490i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.24264 | + | 3.04384i | −0.0616712 | + | 0.151063i | ||||
\(407\) | 24.7279i | 1.22572i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.98528 | − | 2.30090i | −0.197059 | − | 0.113772i | 0.398224 | − | 0.917288i | \(-0.369627\pi\) |
−0.595283 | + | 0.803516i | \(0.702960\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 15.2913i | − | 0.753348i | ||||||
\(413\) | 30.2238 | − | 4.13604i | 1.48722 | − | 0.203521i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.22474 | − | 2.12132i | 0.0600481 | − | 0.104006i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.63604 | + | 1.52192i | −0.128933 | + | 0.0744394i | ||||
\(419\) | −4.05845 | −0.198268 | −0.0991341 | − | 0.995074i | \(-0.531607\pi\) | ||||
−0.0991341 | + | 0.995074i | \(0.531607\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.75736 | −0.280597 | −0.140298 | − | 0.990109i | \(-0.544806\pi\) | ||||
−0.140298 | + | 0.990109i | \(0.544806\pi\) | |||||||
\(422\) | 7.13834 | − | 4.12132i | 0.347489 | − | 0.200623i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.621320 | − | 1.07616i | 0.0301740 | − | 0.0522629i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.4853 | + | 5.91359i | 0.700992 | + | 0.286179i | ||||
\(428\) | − | 5.48528i | − | 0.265141i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.7408 | + | 10.2426i | 0.854543 | + | 0.493371i | 0.862181 | − | 0.506600i | \(-0.169098\pi\) |
−0.00763808 | + | 0.999971i | \(0.502431\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3.46410i | − | 0.166474i | −0.996530 | − | 0.0832370i | \(-0.973474\pi\) | ||
0.996530 | − | 0.0832370i | \(-0.0265259\pi\) | |||||||
\(434\) | 9.10601 | + | 11.7426i | 0.437103 | + | 0.563665i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.757359 | + | 1.31178i | 0.0362709 | + | 0.0628231i | ||||
\(437\) | 2.15232 | − | 3.72792i | 0.102959 | − | 0.178331i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.5919 | − | 13.6208i | 1.12598 | − | 0.650084i | 0.183059 | − | 0.983102i | \(-0.441400\pi\) |
0.942921 | + | 0.333018i | \(0.108067\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.48528 | −0.118213 | ||||||||
\(443\) | 29.8396 | − | 17.2279i | 1.41772 | − | 0.818523i | 0.421625 | − | 0.906770i | \(-0.361460\pi\) |
0.996099 | + | 0.0882469i | \(0.0281264\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6.27231 | − | 10.8640i | −0.297003 | − | 0.514423i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.62132 | − | 2.09077i | −0.0766002 | − | 0.0987796i | ||||
\(449\) | 10.2426i | 0.483380i | 0.970354 | + | 0.241690i | \(0.0777017\pi\) | ||||
−0.970354 | + | 0.241690i | \(0.922298\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.27208 | − | 3.04384i | −0.248252 | − | 0.143329i | ||||
\(452\) | −7.34847 | − | 4.24264i | −0.345643 | − | 0.199557i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 15.5885i | − | 0.731603i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.5000 | − | 19.9186i | −0.537947 | − | 0.931752i | −0.999014 | − | 0.0443868i | \(-0.985867\pi\) |
0.461067 | − | 0.887365i | \(-0.347467\pi\) | |||||||
\(458\) | −6.92820 | + | 12.0000i | −0.323734 | + | 0.560723i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.8138 | −1.06255 | −0.531273 | − | 0.847201i | \(-0.678286\pi\) | ||||
−0.531273 | + | 0.847201i | \(0.678286\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.4558 | −0.997138 | −0.498569 | − | 0.866850i | \(-0.666141\pi\) | ||||
−0.498569 | + | 0.866850i | \(0.666141\pi\) | |||||||
\(464\) | 1.07616 | − | 0.621320i | 0.0499594 | − | 0.0288441i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.36396 | + | 5.82655i | −0.155832 | + | 0.269910i | ||||
\(467\) | −9.50079 | − | 16.4558i | −0.439644 | − | 0.761486i | 0.558018 | − | 0.829829i | \(-0.311562\pi\) |
−0.997662 | + | 0.0683432i | \(0.978229\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26.2132 | + | 3.58719i | −1.21041 | + | 0.165641i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.98528 | − | 5.76500i | −0.459610 | − | 0.265356i | ||||
\(473\) | −21.4150 | − | 12.3640i | −0.984663 | − | 0.568496i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.01461 | + | 2.48528i | −0.0465047 | + | 0.113913i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.36396 | + | 11.0227i | 0.291081 | + | 0.504167i | ||||
\(479\) | −18.2481 | + | 31.6066i | −0.833776 | + | 1.44414i | 0.0612470 | + | 0.998123i | \(0.480492\pi\) |
−0.895023 | + | 0.446020i | \(0.852841\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.4853 | + | 10.0951i | −0.797260 | + | 0.460298i | ||||
\(482\) | 17.0233 | 0.775392 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.00000 | −0.0909091 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.1066 | − | 24.4334i | 0.639231 | − | 1.10718i | −0.346371 | − | 0.938098i | \(-0.612586\pi\) |
0.985602 | − | 0.169083i | \(-0.0540806\pi\) | |||||||
\(488\) | −2.95680 | − | 5.12132i | −0.133848 | − | 0.231831i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 19.9706i | − | 0.901259i | −0.892711 | − | 0.450629i | \(-0.851200\pi\) | ||
0.892711 | − | 0.450629i | \(-0.148800\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.09188 | − | 0.630399i | −0.0491759 | − | 0.0283917i | ||||
\(494\) | −2.15232 | − | 1.24264i | −0.0968373 | − | 0.0559090i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 5.61642i | − | 0.252185i | ||||||
\(497\) | −21.4150 | + | 16.6066i | −0.960594 | + | 0.744908i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.9706 | + | 31.1259i | 0.804473 | + | 1.39339i | 0.916646 | + | 0.399699i | \(0.130885\pi\) |
−0.112173 | + | 0.993689i | \(0.535781\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15.2574 | − | 8.80884i | 0.680969 | − | 0.393158i | ||||
\(503\) | 3.29002 | 0.146695 | 0.0733474 | − | 0.997306i | \(-0.476632\pi\) | ||||
0.0733474 | + | 0.997306i | \(0.476632\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −11.0227 | + | 6.36396i | −0.490019 | + | 0.282913i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.62132 | − | 4.54026i | 0.116302 | − | 0.201441i | ||||
\(509\) | −20.8462 | − | 36.1066i | −0.923990 | − | 1.60040i | −0.793178 | − | 0.608990i | \(-0.791575\pi\) |
−0.130812 | − | 0.991407i | \(-0.541758\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.00000 | − | 21.9223i | −0.132712 | − | 0.969786i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −21.7279 | − | 12.5446i | −0.958378 | − | 0.553320i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 3.04384i | − | 0.133868i | ||||||
\(518\) | 2.95680 | + | 21.6066i | 0.129914 | + | 0.949340i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.0081 | + | 17.3345i | −0.438462 | + | 0.759439i | −0.997571 | − | 0.0696551i | \(-0.977810\pi\) |
0.559109 | + | 0.829094i | \(0.311143\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.8492 | − | 13.7694i | 1.04285 | − | 0.602092i | 0.122214 | − | 0.992504i | \(-0.461001\pi\) |
0.920641 | + | 0.390411i | \(0.127667\pi\) | |||||||
\(524\) | 5.19615 | 0.226995 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −27.2132 | −1.18655 | ||||||||
\(527\) | −4.93503 | + | 2.84924i | −0.214973 | + | 0.124115i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.50000 | + | 4.33013i | −0.108696 | + | 0.188266i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.12132 | + | 1.64501i | −0.0919709 | + | 0.0713203i | ||||
\(533\) | − | 4.97056i | − | 0.215299i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.66025 | + | 5.00000i | 0.374066 | + | 0.215967i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.5154i | 0.453351i | ||||||||
\(539\) | −14.6969 | + | 15.0000i | −0.633042 | + | 0.646096i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.36396 | + | 9.29065i | 0.230615 | + | 0.399436i | 0.957989 | − | 0.286804i | \(-0.0925930\pi\) |
−0.727374 | + | 0.686241i | \(0.759260\pi\) | |||||||
\(542\) | −5.55487 | + | 9.62132i | −0.238602 | + | 0.413271i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.878680 | − | 0.507306i | 0.0376731 | − | 0.0217506i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.6985 | −0.842246 | −0.421123 | − | 0.907003i | \(-0.638364\pi\) | ||||
−0.421123 | + | 0.907003i | \(0.638364\pi\) | |||||||
\(548\) | 12.5446 | − | 7.24264i | 0.535880 | − | 0.309390i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.630399 | − | 1.09188i | −0.0268559 | − | 0.0465158i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.2426 | + | 27.5387i | −0.478086 | + | 1.17107i | ||||
\(554\) | 20.9706i | 0.890954i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.4853 | + | 10.0951i | 0.741541 | + | 0.428129i | ||||
\(557\) | −13.6208 | − | 7.86396i | −0.577131 | − | 0.333207i | 0.182861 | − | 0.983139i | \(-0.441464\pi\) |
−0.759992 | + | 0.649932i | \(0.774797\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 20.1903i | − | 0.853957i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.00000 | − | 5.19615i | −0.126547 | − | 0.219186i | ||||
\(563\) | −12.0989 | + | 20.9558i | −0.509906 | + | 0.883184i | 0.490028 | + | 0.871707i | \(0.336987\pi\) |
−0.999934 | + | 0.0114768i | \(0.996347\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.50794 | 0.273549 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.2426 | 0.429772 | ||||||||
\(569\) | 1.52192 | − | 0.878680i | 0.0638021 | − | 0.0368362i | −0.467760 | − | 0.883856i | \(-0.654939\pi\) |
0.531562 | + | 0.847020i | \(0.321605\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.36396 | − | 14.4868i | 0.350021 | − | 0.606254i | −0.636232 | − | 0.771498i | \(-0.719508\pi\) |
0.986253 | + | 0.165244i | \(0.0528412\pi\) | |||||||
\(572\) | 3.67423 | + | 6.36396i | 0.153627 | + | 0.266091i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.97056 | − | 2.02922i | −0.207467 | − | 0.0846982i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.7426 | − | 10.2437i | −0.738636 | − | 0.426452i | 0.0829373 | − | 0.996555i | \(-0.473570\pi\) |
−0.821573 | + | 0.570103i | \(0.806903\pi\) | |||||||
\(578\) | 13.8309 | + | 7.98528i | 0.575290 | + | 0.332144i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.13461 | − | 6.62132i | −0.213019 | − | 0.274699i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.86396 | + | 3.22848i | 0.0771974 | + | 0.133710i | ||||
\(584\) | −4.18154 | + | 7.24264i | −0.173033 | + | 0.299703i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.62132 | − | 2.09077i | 0.149595 | − | 0.0863689i | ||||
\(587\) | 5.19615 | 0.214468 | 0.107234 | − | 0.994234i | \(-0.465801\pi\) | ||||
0.107234 | + | 0.994234i | \(0.465801\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.69848 | −0.234802 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.12132 | − | 7.13834i | 0.169385 | − | 0.293384i | ||||
\(593\) | 15.2042 | + | 26.3345i | 0.624363 | + | 1.08143i | 0.988664 | + | 0.150148i | \(0.0479749\pi\) |
−0.364300 | + | 0.931282i | \(0.618692\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 20.4853i | − | 0.839110i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.00000 | − | 5.19615i | −0.368037 | − | 0.212486i | ||||
\(599\) | −37.6339 | − | 21.7279i | −1.53768 | − | 0.887779i | −0.998974 | − | 0.0452836i | \(-0.985581\pi\) |
−0.538704 | − | 0.842495i | \(-0.681086\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.03668i | 0.246241i | 0.992392 | + | 0.123121i | \(0.0392902\pi\) | ||||
−0.992392 | + | 0.123121i | \(0.960710\pi\) | |||||||
\(602\) | −20.1903 | − | 8.24264i | −0.822894 | − | 0.335945i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.62132 | − | 2.80821i | −0.0659706 | − | 0.114264i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.6213 | − | 12.4831i | 0.877582 | − | 0.506672i | 0.00772182 | − | 0.999970i | \(-0.497542\pi\) |
0.869860 | + | 0.493298i | \(0.164209\pi\) | |||||||
\(608\) | 1.01461 | 0.0411479 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.15232 | − | 1.24264i | 0.0870734 | − | 0.0502719i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.60660 | − | 4.51477i | 0.105280 | − | 0.182350i | −0.808573 | − | 0.588396i | \(-0.799760\pi\) |
0.913852 | + | 0.406046i | \(0.133093\pi\) | |||||||
\(614\) | −12.3345 | − | 21.3640i | −0.497779 | − | 0.862179i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.86396 | − | 1.07616i | 0.316848 | − | 0.0433597i | ||||
\(617\) | 41.6985i | 1.67872i | 0.543578 | + | 0.839359i | \(0.317069\pi\) | ||||
−0.543578 | + | 0.839359i | \(0.682931\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −41.3345 | − | 23.8645i | −1.66137 | − | 0.959195i | −0.972060 | − | 0.234733i | \(-0.924578\pi\) |
−0.689315 | − | 0.724462i | \(-0.742088\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 18.7554i | − | 0.752022i | ||||||
\(623\) | 10.3923 | − | 25.4558i | 0.416359 | − | 1.01987i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0.568852 | − | 0.985281i | 0.0227359 | − | 0.0393798i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.7279 | − | 7.34847i | 0.507899 | − | 0.293236i | ||||
\(629\) | −8.36308 | −0.333458 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.2426 | 1.32337 | 0.661684 | − | 0.749783i | \(-0.269842\pi\) | ||||
0.661684 | + | 0.749783i | \(0.269842\pi\) | |||||||
\(632\) | 9.73641 | − | 5.62132i | 0.387294 | − | 0.223604i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.62132 | + | 6.27231i | −0.143821 | + | 0.249105i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.6066 | − | 4.26858i | −0.657978 | − | 0.169127i | ||||
\(638\) | 3.72792i | 0.147590i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.1119 | − | 20.8492i | −1.42634 | − | 0.823496i | −0.429507 | − | 0.903064i | \(-0.641313\pi\) |
−0.996829 | + | 0.0795681i | \(0.974646\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.62357i | 0.103463i | 0.998661 | + | 0.0517317i | \(0.0164741\pi\) | ||||
−0.998661 | + | 0.0517317i | \(0.983526\pi\) | |||||||
\(644\) | −8.87039 | + | 6.87868i | −0.349542 | + | 0.271058i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.514719 | − | 0.891519i | −0.0202513 | − | 0.0350763i | ||||
\(647\) | 5.82655 | − | 10.0919i | 0.229065 | − | 0.396753i | −0.728466 | − | 0.685082i | \(-0.759766\pi\) |
0.957531 | + | 0.288329i | \(0.0930997\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 29.9558 | − | 17.2950i | 1.17587 | − | 0.678889i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.24264 | 0.244481 | ||||||||
\(653\) | 9.31615 | − | 5.37868i | 0.364569 | − | 0.210484i | −0.306514 | − | 0.951866i | \(-0.599163\pi\) |
0.671083 | + | 0.741382i | \(0.265829\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.01461 | + | 1.75736i | 0.0396139 | + | 0.0686134i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.363961 | − | 2.65962i | −0.0141887 | − | 0.103683i | ||||
\(659\) | − | 6.00000i | − | 0.233727i | −0.993148 | − | 0.116863i | \(-0.962716\pi\) | ||
0.993148 | − | 0.116863i | \(-0.0372840\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.1213 | + | 20.2773i | 1.36606 | + | 0.788696i | 0.990422 | − | 0.138071i | \(-0.0440901\pi\) |
0.375639 | + | 0.926766i | \(0.377423\pi\) | |||||||
\(662\) | −15.1172 | − | 8.72792i | −0.587547 | − | 0.339220i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.16693i | 0.122901i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.63604 | − | 4.56575i | −0.102068 | − | 0.176787i | ||||
\(668\) | 11.5300 | − | 19.9706i | 0.446109 | − | 0.772684i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.7408 | 0.684875 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.9706 | 0.615620 | 0.307810 | − | 0.951448i | \(-0.400404\pi\) | ||||
0.307810 | + | 0.951448i | \(0.400404\pi\) | |||||||
\(674\) | 4.33013 | − | 2.50000i | 0.166790 | − | 0.0962964i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.50000 | − | 6.06218i | 0.134615 | − | 0.233161i | ||||
\(677\) | −6.27231 | − | 10.8640i | −0.241064 | − | 0.417536i | 0.719953 | − | 0.694023i | \(-0.244163\pi\) |
−0.961018 | + | 0.276487i | \(0.910830\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.86396 | + | 6.09823i | −0.301791 | + | 0.234029i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 14.5919 | + | 8.42463i | 0.558752 | + | 0.322596i | ||||
\(683\) | 22.4912 | + | 12.9853i | 0.860601 | + | 0.496868i | 0.864213 | − | 0.503125i | \(-0.167817\pi\) |
−0.00361277 | + | 0.999993i | \(0.501150\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −11.0482 | + | 14.8640i | −0.421822 | + | 0.567509i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.12132 | + | 7.13834i | 0.157124 | + | 0.272147i | ||||
\(689\) | −1.52192 | + | 2.63604i | −0.0579805 | + | 0.100425i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.727922 | + | 0.420266i | −0.0276915 | + | 0.0159877i | −0.513782 | − | 0.857921i | \(-0.671756\pi\) |
0.486090 | + | 0.873909i | \(0.338423\pi\) | |||||||
\(692\) | −20.7846 | −0.790112 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.4853 | −0.549854 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.02944 | − | 1.78304i | 0.0389927 | − | 0.0675374i | ||||
\(698\) | −18.4582 | − | 31.9706i | −0.698654 | − | 1.21010i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.6985i | 1.46162i | 0.682580 | + | 0.730811i | \(0.260858\pi\) | ||||
−0.682580 | + | 0.730811i | \(0.739142\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.24264 | − | 4.18154i | −0.273161 | − | 0.157710i | ||||
\(704\) | −2.59808 | − | 1.50000i | −0.0979187 | − | 0.0565334i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.7554i | 0.705868i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.48528 | + | 6.03668i | 0.130892 | + | 0.226712i | 0.924021 | − | 0.382342i | \(-0.124882\pi\) |
−0.793128 | + | 0.609055i | \(0.791549\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.00000 | + | 5.19615i | −0.337289 | + | 0.194734i | ||||
\(713\) | −23.8284 | −0.892382 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.23999 | + | 4.75736i | −0.307943 | + | 0.177791i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.00000 | − | 15.5885i | 0.335877 | − | 0.581756i | ||||
\(719\) | −11.5300 | − | 19.9706i | −0.429997 | − | 0.744776i | 0.566876 | − | 0.823803i | \(-0.308152\pi\) |
−0.996872 | + | 0.0790270i | \(0.974819\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 37.4558 | + | 15.2913i | 1.39493 | + | 0.569477i | ||||
\(722\) | 17.9706i | 0.668795i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.75736 | − | 1.01461i | −0.0653117 | − | 0.0377078i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 26.4010i | − | 0.979160i | −0.871958 | − | 0.489580i | \(-0.837150\pi\) | ||
0.871958 | − | 0.489580i | \(-0.162850\pi\) | |||||||
\(728\) | 3.97141 | + | 5.12132i | 0.147190 | + | 0.189809i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.18154 | − | 7.24264i | 0.154660 | − | 0.267879i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.0919 | − | 19.6830i | 1.25921 | − | 0.727007i | 0.286291 | − | 0.958143i | \(-0.407578\pi\) |
0.972921 | + | 0.231136i | \(0.0742443\pi\) | |||||||
\(734\) | −18.8785 | −0.696817 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.24264 | 0.156386 | ||||||||
\(737\) | −25.9808 | + | 15.0000i | −0.957014 | + | 0.552532i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.7279 | − | 30.7057i | 0.652132 | − | 1.12953i | −0.330472 | − | 0.943816i | \(-0.607208\pi\) |
0.982605 | − | 0.185710i | \(-0.0594586\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.01472 | + | 2.59808i | 0.0739626 | + | 0.0953784i | ||||
\(743\) | 21.5147i | 0.789298i | 0.918832 | + | 0.394649i | \(0.129134\pi\) | ||||
−0.918832 | + | 0.394649i | \(0.870866\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 18.5813 | + | 10.7279i | 0.680310 | + | 0.392777i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.04384i | 0.111294i | ||||||||
\(749\) | 13.4361 | + | 5.48528i | 0.490946 | + | 0.200428i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.3787 | − | 23.1726i | −0.488195 | − | 0.845578i | 0.511713 | − | 0.859157i | \(-0.329011\pi\) |
−0.999908 | + | 0.0135781i | \(0.995678\pi\) | |||||||
\(752\) | −0.507306 | + | 0.878680i | −0.0184995 | + | 0.0320422i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.63604 | + | 1.52192i | −0.0959989 | + | 0.0554250i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.2426 | 1.53533 | 0.767667 | − | 0.640848i | \(-0.221417\pi\) | ||||
0.767667 | + | 0.640848i | \(0.221417\pi\) | |||||||
\(758\) | −3.88437 | + | 2.24264i | −0.141087 | + | 0.0814564i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.53653 | + | 4.39340i | 0.0919491 | + | 0.159261i | 0.908331 | − | 0.418252i | \(-0.137357\pi\) |
−0.816382 | + | 0.577512i | \(0.804024\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.97056 | + | 0.543359i | −0.143744 | + | 0.0196709i | ||||
\(764\) | − | 8.48528i | − | 0.306987i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.7574 | − | 6.21076i | −0.388679 | − | 0.224404i | ||||
\(767\) | 24.4588 | + | 14.1213i | 0.883158 | + | 0.509891i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 49.0408i | − | 1.76846i | −0.467056 | − | 0.884228i | \(-0.654685\pi\) | ||
0.467056 | − | 0.884228i | \(-0.345315\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.74264 | + | 6.48244i | 0.134701 | + | 0.233308i | ||||
\(773\) | −11.5300 | + | 19.9706i | −0.414706 | + | 0.718291i | −0.995398 | − | 0.0958322i | \(-0.969449\pi\) |
0.580692 | + | 0.814123i | \(0.302782\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.76127 | 0.135022 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −19.4558 | −0.697526 | ||||||||
\(779\) | 1.78304 | − | 1.02944i | 0.0638840 | − | 0.0368834i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.3640 | + | 26.6112i | −0.549766 | + | 0.952222i | ||||
\(782\) | −2.15232 | − | 3.72792i | −0.0769667 | − | 0.133310i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.74264 | − | 1.88064i | 0.240809 | − | 0.0671656i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.1213 | − | 18.5453i | −1.14500 | − | 0.661067i | −0.197337 | − | 0.980336i | \(-0.563229\pi\) |
−0.947664 | + | 0.319269i | \(0.896563\pi\) | |||||||
\(788\) | −8.23999 | − | 4.75736i | −0.293537 | − | 0.169474i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.7408 | − | 13.7574i | 0.630789 | − | 0.489155i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.24264 | + | 12.5446i | 0.257194 | + | 0.445473i | ||||
\(794\) | −6.92820 | + | 12.0000i | −0.245873 | + | 0.425864i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.9706 | + | 8.06591i | −0.495173 | + | 0.285889i | ||||
\(797\) | −37.6339 | −1.33306 | −0.666530 | − | 0.745478i | \(-0.732221\pi\) | ||||
−0.666530 | + | 0.745478i | \(0.732221\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.02944 | 0.0364189 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.5446 | − | 21.7279i | −0.442690 | − | 0.766762i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 13.7574i | 0.484582i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35.4815 | + | 20.4853i | 1.24746 | + | 0.720224i | 0.970603 | − | 0.240686i | \(-0.0773723\pi\) |
0.276862 | + | 0.960910i | \(0.410706\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 31.1769i | − | 1.09477i | −0.836881 | − | 0.547385i | \(-0.815623\pi\) | ||
0.836881 | − | 0.547385i | \(-0.184377\pi\) | |||||||
\(812\) | 0.445759 | + | 3.25736i | 0.0156431 | + | 0.114311i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12.3640 | + | 21.4150i | 0.433357 | + | 0.750596i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.24264 | − | 4.18154i | 0.253388 | − | 0.146294i | ||||
\(818\) | −4.60181 | −0.160898 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.6454 | + | 24.6213i | −1.48833 | + | 0.859290i | −0.999911 | − | 0.0133172i | \(-0.995761\pi\) |
−0.488423 | + | 0.872607i | \(0.662428\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.9706 | + | 32.8580i | −0.661272 | + | 1.14536i | 0.319009 | + | 0.947752i | \(0.396650\pi\) |
−0.980282 | + | 0.197606i | \(0.936683\pi\) | |||||||
\(824\) | −7.64564 | − | 13.2426i | −0.266349 | − | 0.461329i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 24.1066 | − | 18.6938i | 0.838776 | − | 0.650442i | ||||
\(827\) | 4.02944i | 0.140117i | 0.997543 | + | 0.0700586i | \(0.0223186\pi\) | ||||
−0.997543 | + | 0.0700586i | \(0.977681\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.3345 | − | 20.4004i | −1.22722 | − | 0.708535i | −0.260772 | − | 0.965401i | \(-0.583977\pi\) |
−0.966447 | + | 0.256865i | \(0.917310\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 2.44949i | − | 0.0849208i | ||||||
\(833\) | −5.07306 | − | 4.97056i | −0.175771 | − | 0.172220i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.52192 | + | 2.63604i | −0.0526366 | + | 0.0911693i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.51472 | + | 2.02922i | −0.121414 | + | 0.0700984i | ||||
\(839\) | 24.0746 | 0.831149 | 0.415574 | − | 0.909559i | \(-0.363581\pi\) | ||||
0.415574 | + | 0.909559i | \(0.363581\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.4558 | 0.946753 | ||||||||
\(842\) | −4.98602 | + | 2.87868i | −0.171830 | + | 0.0992059i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.12132 | − | 7.13834i | 0.141862 | − | 0.245712i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.00000 | − | 4.89898i | 0.0687208 | − | 0.168331i | ||||
\(848\) | − | 1.24264i | − | 0.0426725i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.2854 | − | 17.4853i | −1.03817 | − | 0.599388i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 2.27541i | − | 0.0779085i | −0.999241 | − | 0.0389543i | \(-0.987597\pi\) | ||
0.999241 | − | 0.0389543i | \(-0.0124027\pi\) | |||||||
\(854\) | 15.5014 | − | 2.12132i | 0.530448 | − | 0.0725901i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.74264 | − | 4.75039i | −0.0937415 | − | 0.162365i | ||||
\(857\) | −10.0081 | + | 17.3345i | −0.341870 | + | 0.592136i | −0.984780 | − | 0.173806i | \(-0.944394\pi\) |
0.642910 | + | 0.765942i | \(0.277727\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.87868 | − | 2.23936i | 0.132339 | − | 0.0764059i | −0.432369 | − | 0.901697i | \(-0.642322\pi\) |
0.564708 | + | 0.825291i | \(0.308989\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.4853 | 0.697731 | ||||||||
\(863\) | 43.7215 | − | 25.2426i | 1.48830 | − | 0.859269i | 0.488388 | − | 0.872627i | \(-0.337585\pi\) |
0.999911 | + | 0.0133573i | \(0.00425189\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.73205 | − | 3.00000i | −0.0588575 | − | 0.101944i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 13.7574 | + | 5.61642i | 0.466955 | + | 0.190634i | ||||
\(869\) | 33.7279i | 1.14414i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.2132 | − | 12.2474i | −0.718782 | − | 0.414989i | ||||
\(872\) | 1.31178 | + | 0.757359i | 0.0444226 | + | 0.0256474i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 4.30463i | − | 0.145606i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.24264 | − | 10.8126i | −0.210799 | − | 0.365115i | 0.741166 | − | 0.671322i | \(-0.234273\pi\) |
−0.951965 | + | 0.306207i | \(0.900940\pi\) | |||||||
\(878\) | 13.6208 | − | 23.5919i | 0.459679 | − | 0.796187i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.7862 | 1.34043 | 0.670215 | − | 0.742167i | \(-0.266202\pi\) | ||||
0.670215 | + | 0.742167i | \(0.266202\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.45584 | 0.318214 | 0.159107 | − | 0.987261i | \(-0.449138\pi\) | ||||
0.159107 | + | 0.987261i | \(0.449138\pi\) | |||||||
\(884\) | −2.15232 | + | 1.24264i | −0.0723902 | + | 0.0417945i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17.2279 | − | 29.8396i | 0.578783 | − | 1.00248i | ||||
\(887\) | 22.4296 | + | 38.8492i | 0.753113 | + | 1.30443i | 0.946307 | + | 0.323269i | \(0.104782\pi\) |
−0.193194 | + | 0.981161i | \(0.561885\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.50000 | + | 10.9612i | 0.285081 | + | 0.367625i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10.8640 | − | 6.27231i | −0.363752 | − | 0.210012i | ||||
\(893\) | 0.891519 | + | 0.514719i | 0.0298335 | + | 0.0172244i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.44949 | − | 1.00000i | −0.0818317 | − | 0.0334077i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.12132 | + | 8.87039i | 0.170901 | + | 0.296009i | ||||
\(899\) | −3.48960 | + | 6.04416i | −0.116385 | + | 0.201584i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.09188 | + | 0.630399i | −0.0363759 | + | 0.0210016i | ||||
\(902\) | −6.08767 | −0.202697 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.48528 | −0.282216 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.8492 | − | 23.9876i | 0.459857 | − | 0.796495i | −0.539096 | − | 0.842244i | \(-0.681234\pi\) |
0.998953 | + | 0.0457492i | \(0.0145675\pi\) | |||||||
\(908\) | −7.79423 | − | 13.5000i | −0.258661 | − | 0.448013i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 18.7279i | − | 0.620484i | −0.950658 | − | 0.310242i | \(-0.899590\pi\) | ||
0.950658 | − | 0.310242i | \(-0.100410\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.22792 | − | 4.75039i | −0.272304 | − | 0.157215i | ||||
\(914\) | −19.9186 | − | 11.5000i | −0.658848 | − | 0.380386i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.8564i | 0.457829i | ||||||||
\(917\) | −5.19615 | + | 12.7279i | −0.171592 | + | 0.420313i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.75736 | − | 16.9002i | −0.321866 | − | 0.557488i | 0.659007 | − | 0.752136i | \(-0.270977\pi\) |
−0.980873 | + | 0.194649i | \(0.937643\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −19.7574 | + | 11.4069i | −0.650674 | + | 0.375667i | ||||
\(923\) | −25.0892 | −0.825823 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −18.5813 | + | 10.7279i | −0.610620 | + | 0.352541i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.621320 | − | 1.07616i | 0.0203958 | − | 0.0353266i | ||||
\(929\) | −1.64501 | − | 2.84924i | −0.0539711 | − | 0.0934806i | 0.837778 | − | 0.546012i | \(-0.183855\pi\) |
−0.891749 | + | 0.452531i | \(0.850521\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.90812 | − | 6.84116i | −0.0625360 | − | 0.224210i | ||||
\(932\) | 6.72792i | 0.220380i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −16.4558 | − | 9.50079i | −0.538452 | − | 0.310875i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.00746i | 0.130918i | 0.997855 | + | 0.0654590i | \(0.0208512\pi\) | ||||
−0.997855 | + | 0.0654590i | \(0.979149\pi\) | |||||||
\(938\) | −20.9077 | + | 16.2132i | −0.682661 | + | 0.529380i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.0423 | + | 45.1066i | −0.848955 | + | 1.47043i | 0.0331867 | + | 0.999449i | \(0.489434\pi\) |
−0.882142 | + | 0.470984i | \(0.843899\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.45584 | − | 4.30463i | 0.242796 | − | 0.140178i | ||||
\(944\) | −11.5300 | −0.375270 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.7279 | −0.803974 | ||||||||
\(947\) | 19.8931 | − | 11.4853i | 0.646439 | − | 0.373221i | −0.140652 | − | 0.990059i | \(-0.544920\pi\) |
0.787090 | + | 0.616838i | \(0.211586\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.2426 | − | 17.7408i | 0.332490 | − | 0.575890i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.363961 | + | 2.65962i | 0.0117960 | + | 0.0861989i | ||||
\(953\) | 41.6985i | 1.35075i | 0.737476 | + | 0.675373i | \(0.236017\pi\) | ||||
−0.737476 | + | 0.675373i | \(0.763983\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11.0227 | + | 6.36396i | 0.356500 | + | 0.205825i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 36.4962i | 1.17914i | ||||||||
\(959\) | 5.19615 | + | 37.9706i | 0.167793 | + | 1.22613i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.272078 | + | 0.471253i | 0.00877671 | + | 0.0152017i | ||||
\(962\) | −10.0951 | + | 17.4853i | −0.325480 | + | 0.563748i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 14.7426 | − | 8.51167i | 0.474828 | − | 0.274142i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.2721 | −0.716222 | −0.358111 | − | 0.933679i | \(-0.616579\pi\) | ||||
−0.358111 | + | 0.933679i | \(0.616579\pi\) | |||||||
\(968\) | −1.73205 | + | 1.00000i | −0.0556702 | + | 0.0321412i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.6581 | + | 44.4411i | 0.823407 | + | 1.42618i | 0.903130 | + | 0.429367i | \(0.141263\pi\) |
−0.0797229 | + | 0.996817i | \(0.525404\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −42.2132 | + | 32.7349i | −1.35329 | + | 1.04943i | ||||
\(974\) | − | 28.2132i | − | 0.904009i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.12132 | − | 2.95680i | −0.163929 | − | 0.0946447i | ||||
\(977\) | −27.5027 | − | 15.8787i | −0.879889 | − | 0.508004i | −0.00926698 | − | 0.999957i | \(-0.502950\pi\) |
−0.870622 | + | 0.491953i | \(0.836283\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 31.1769i | − | 0.996419i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.98528 | − | 17.2950i | −0.318643 | − | 0.551906i | ||||
\(983\) | −4.05845 | + | 7.02944i | −0.129444 | + | 0.224204i | −0.923461 | − | 0.383691i | \(-0.874653\pi\) |
0.794017 | + | 0.607895i | \(0.207986\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.26080 | −0.0401520 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.48528 | −0.0790673 | ||||||||
\(989\) | 30.2854 | − | 17.4853i | 0.963020 | − | 0.556000i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.89340 | + | 8.47561i | −0.155444 | + | 0.269237i | −0.933221 | − | 0.359304i | \(-0.883014\pi\) |
0.777777 | + | 0.628541i | \(0.216347\pi\) | |||||||
\(992\) | −2.80821 | − | 4.86396i | −0.0891607 | − | 0.154431i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −10.2426 | + | 25.0892i | −0.324877 | + | 0.795782i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.27208 | + | 4.77589i | 0.261979 | + | 0.151254i | 0.625237 | − | 0.780435i | \(-0.285002\pi\) |
−0.363258 | + | 0.931689i | \(0.618336\pi\) | |||||||
\(998\) | 31.1259 | + | 17.9706i | 0.985274 | + | 0.568848i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))