Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1638,2,Mod(127,1638)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1638, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1638.127");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1638.bj (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: | \(13.0794958511\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.195105024.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 5x^{6} + 4x^{5} - 20x^{4} + 12x^{3} + 45x^{2} - 108x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 546) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1135.2 | ||
Root | \(1.72124 + 0.193255i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1638.1135 |
Dual form | 1638.2.bj.f.127.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).
\(n\) | \(379\) | \(703\) | \(911\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
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 | ||||
\(5\) | 3.05596i | 1.36667i | 0.730106 | + | 0.683334i | \(0.239471\pi\) | ||||
−0.730106 | + | 0.683334i | \(0.760529\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.866025 | − | 0.500000i | 0.327327 | − | 0.188982i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.52798 | − | 2.64654i | 0.483190 | − | 0.836910i | ||||
\(11\) | 2.98127 | + | 1.72124i | 0.898886 | + | 0.518972i | 0.876839 | − | 0.480785i | \(-0.159648\pi\) |
0.0220475 | + | 0.999757i | \(0.492982\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.25253 | + | 1.55596i | 0.902091 | + | 0.431546i | ||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.41449 | + | 2.44997i | 0.343064 | + | 0.594205i | 0.985000 | − | 0.172554i | \(-0.0552018\pi\) |
−0.641936 | + | 0.766758i | \(0.721868\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.49425 | − | 0.862708i | 0.342805 | − | 0.197919i | −0.318707 | − | 0.947853i | \(-0.603248\pi\) |
0.661512 | + | 0.749935i | \(0.269915\pi\) | |||||||
\(20\) | −2.64654 | + | 1.52798i | −0.591785 | + | 0.341667i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.72124 | − | 2.98127i | −0.366969 | − | 0.635608i | ||||
\(23\) | −1.53130 | + | 2.65229i | −0.319298 | + | 0.553040i | −0.980342 | − | 0.197307i | \(-0.936780\pi\) |
0.661044 | + | 0.750347i | \(0.270114\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.33891 | −0.867781 | ||||||||
\(26\) | −2.03880 | − | 2.97377i | −0.399841 | − | 0.583204i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.866025 | + | 0.500000i | 0.163663 | + | 0.0944911i | ||||
\(29\) | 1.92531 | − | 3.33473i | 0.357520 | − | 0.619243i | −0.630026 | − | 0.776574i | \(-0.716956\pi\) |
0.987546 | + | 0.157331i | \(0.0502890\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.978370i | − | 0.175720i | −0.996133 | − | 0.0878602i | \(-0.971997\pi\) | ||
0.996133 | − | 0.0878602i | \(-0.0280029\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 2.82898i | − | 0.485166i | ||||||
\(35\) | 1.52798 | + | 2.64654i | 0.258276 | + | 0.447347i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.58394 | + | 2.64654i | 0.753596 | + | 0.435089i | 0.826992 | − | 0.562214i | \(-0.190050\pi\) |
−0.0733959 | + | 0.997303i | \(0.523384\pi\) | |||||||
\(38\) | −1.72542 | −0.279899 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.05596 | 0.483190 | ||||||||
\(41\) | −8.62781 | − | 4.98127i | −1.34744 | − | 0.777943i | −0.359551 | − | 0.933125i | \(-0.617070\pi\) |
−0.987886 | + | 0.155182i | \(0.950404\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.51082 | − | 2.61681i | −0.230397 | − | 0.399060i | 0.727528 | − | 0.686078i | \(-0.240669\pi\) |
−0.957925 | + | 0.287019i | \(0.907336\pi\) | |||||||
\(44\) | 3.44247i | 0.518972i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.65229 | − | 1.53130i | 0.391058 | − | 0.225778i | ||||
\(47\) | − | 8.04447i | − | 1.17341i | −0.809802 | − | 0.586703i | \(-0.800425\pi\) | ||
0.809802 | − | 0.586703i | \(-0.199575\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.500000 | − | 0.866025i | 0.0714286 | − | 0.123718i | ||||
\(50\) | 3.75760 | + | 2.16945i | 0.531405 | + | 0.306807i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.278764 | + | 3.59476i | 0.0386576 | + | 0.498503i | ||||
\(53\) | 8.33405 | 1.14477 | 0.572385 | − | 0.819985i | \(-0.306018\pi\) | ||||
0.572385 | + | 0.819985i | \(0.306018\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.26003 | + | 9.11064i | −0.709263 | + | 1.22848i | ||||
\(56\) | −0.500000 | − | 0.866025i | −0.0668153 | − | 0.115728i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.33473 | + | 1.92531i | −0.437871 | + | 0.252805i | ||||
\(59\) | −8.64080 | + | 4.98877i | −1.12494 | + | 0.649482i | −0.942656 | − | 0.333765i | \(-0.891681\pi\) |
−0.182279 | + | 0.983247i | \(0.558348\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.77260 | + | 9.99843i | 0.739106 | + | 1.28017i | 0.952899 | + | 0.303289i | \(0.0980849\pi\) |
−0.213793 | + | 0.976879i | \(0.568582\pi\) | |||||||
\(62\) | −0.489185 | + | 0.847293i | −0.0621266 | + | 0.107606i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −4.75496 | + | 9.93962i | −0.589781 | + | 1.23286i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.11410 | + | 2.37527i | 0.502617 | + | 0.290186i | 0.729794 | − | 0.683668i | \(-0.239616\pi\) |
−0.227177 | + | 0.973854i | \(0.572950\pi\) | |||||||
\(68\) | −1.41449 | + | 2.44997i | −0.171532 | + | 0.297102i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 3.05596i | − | 0.365257i | ||||||
\(71\) | 3.17784 | − | 1.83473i | 0.377140 | − | 0.217742i | −0.299433 | − | 0.954117i | \(-0.596798\pi\) |
0.676573 | + | 0.736375i | \(0.263464\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.1119i | 1.18351i | 0.806117 | + | 0.591756i | \(0.201565\pi\) | ||||
−0.806117 | + | 0.591756i | \(0.798435\pi\) | |||||||
\(74\) | −2.64654 | − | 4.58394i | −0.307654 | − | 0.532873i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.49425 | + | 0.862708i | 0.171403 | + | 0.0989594i | ||||
\(77\) | 3.44247 | 0.392306 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.49843 | −0.506113 | −0.253057 | − | 0.967451i | \(-0.581436\pi\) | ||||
−0.253057 | + | 0.967451i | \(0.581436\pi\) | |||||||
\(80\) | −2.64654 | − | 1.52798i | −0.295892 | − | 0.170833i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.98127 | + | 8.62781i | 0.550089 | + | 0.952782i | ||||
\(83\) | − | 7.15869i | − | 0.785768i | −0.919588 | − | 0.392884i | \(-0.871477\pi\) | ||
0.919588 | − | 0.392884i | \(-0.128523\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.48701 | + | 4.32263i | −0.812081 | + | 0.468855i | ||||
\(86\) | 3.02163i | 0.325831i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.72124 | − | 2.98127i | 0.183484 | − | 0.317804i | ||||
\(89\) | 6.84426 | + | 3.95154i | 0.725490 | + | 0.418862i | 0.816770 | − | 0.576963i | \(-0.195762\pi\) |
−0.0912800 | + | 0.995825i | \(0.529096\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.59476 | − | 0.278764i | 0.376833 | − | 0.0292224i | ||||
\(92\) | −3.06260 | −0.319298 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.02224 | + | 6.96672i | −0.414862 | + | 0.718562i | ||||
\(95\) | 2.63640 | + | 4.56638i | 0.270489 | + | 0.468501i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.88016 | + | 4.54961i | −0.800109 | + | 0.461943i | −0.843509 | − | 0.537115i | \(-0.819514\pi\) |
0.0434004 | + | 0.999058i | \(0.486181\pi\) | |||||||
\(98\) | −0.866025 | + | 0.500000i | −0.0874818 | + | 0.0505076i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.16945 | − | 3.75760i | −0.216945 | − | 0.375760i | ||||
\(101\) | −9.42664 | + | 16.3274i | −0.937985 | + | 1.62464i | −0.168764 | + | 0.985657i | \(0.553977\pi\) |
−0.769222 | + | 0.638982i | \(0.779356\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.7079 | −1.35068 | −0.675338 | − | 0.737509i | \(-0.736002\pi\) | ||||
−0.675338 | + | 0.737509i | \(0.736002\pi\) | |||||||
\(104\) | 1.55596 | − | 3.25253i | 0.152575 | − | 0.318937i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.21750 | − | 4.16702i | −0.701025 | − | 0.404737i | ||||
\(107\) | −1.65736 | + | 2.87063i | −0.160223 | + | 0.277514i | −0.934948 | − | 0.354784i | \(-0.884555\pi\) |
0.774726 | + | 0.632297i | \(0.217888\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.67525i | 0.830938i | 0.909607 | + | 0.415469i | \(0.136383\pi\) | ||||
−0.909607 | + | 0.415469i | \(0.863617\pi\) | |||||||
\(110\) | 9.11064 | − | 5.26003i | 0.868666 | − | 0.501524i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | −5.60557 | − | 9.70914i | −0.527328 | − | 0.913359i | −0.999493 | − | 0.0318486i | \(-0.989861\pi\) |
0.472165 | − | 0.881510i | \(-0.343473\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.10529 | − | 4.67959i | −0.755822 | − | 0.436374i | ||||
\(116\) | 3.85061 | 0.357520 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.97753 | 0.918506 | ||||||||
\(119\) | 2.44997 | + | 1.41449i | 0.224588 | + | 0.129666i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.425305 | + | 0.736650i | 0.0386641 | + | 0.0669682i | ||||
\(122\) | − | 11.5452i | − | 1.04525i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.847293 | − | 0.489185i | 0.0760892 | − | 0.0439301i | ||||
\(125\) | 2.02028i | 0.180699i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.55753 | − | 4.42977i | 0.226944 | − | 0.393078i | −0.729957 | − | 0.683493i | \(-0.760460\pi\) |
0.956901 | + | 0.290415i | \(0.0937932\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 9.08773 | − | 6.23048i | 0.797047 | − | 0.546450i | ||||
\(131\) | 18.7757 | 1.64044 | 0.820219 | − | 0.572049i | \(-0.193851\pi\) | ||||
0.820219 | + | 0.572049i | \(0.193851\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.862708 | − | 1.49425i | 0.0748063 | − | 0.129568i | ||||
\(134\) | −2.37527 | − | 4.11410i | −0.205192 | − | 0.355404i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.44997 | − | 1.41449i | 0.210083 | − | 0.121292i | ||||
\(137\) | −2.30457 | + | 1.33055i | −0.196893 | + | 0.113676i | −0.595205 | − | 0.803574i | \(-0.702929\pi\) |
0.398312 | + | 0.917250i | \(0.369596\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.35322 | + | 14.4682i | 0.708511 | + | 1.22718i | 0.965409 | + | 0.260739i | \(0.0839662\pi\) |
−0.256898 | + | 0.966439i | \(0.582700\pi\) | |||||||
\(140\) | −1.52798 | + | 2.64654i | −0.129138 | + | 0.223674i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.66945 | −0.307934 | ||||||||
\(143\) | 7.01850 | + | 10.2371i | 0.586916 | + | 0.856071i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.1908 | + | 5.88366i | 0.846300 | + | 0.488611i | ||||
\(146\) | 5.05596 | − | 8.75718i | 0.418434 | − | 0.724750i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.29308i | 0.435089i | ||||||||
\(149\) | −2.16642 | + | 1.25078i | −0.177480 | + | 0.102468i | −0.586108 | − | 0.810233i | \(-0.699341\pi\) |
0.408628 | + | 0.912701i | \(0.366007\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 12.6465i | − | 1.02916i | −0.857444 | − | 0.514578i | \(-0.827949\pi\) | ||
0.857444 | − | 0.514578i | \(-0.172051\pi\) | |||||||
\(152\) | −0.862708 | − | 1.49425i | −0.0699749 | − | 0.121200i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.98127 | − | 1.72124i | −0.240237 | − | 0.138701i | ||||
\(155\) | 2.98986 | 0.240151 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.8131 | 1.42164 | 0.710822 | − | 0.703372i | \(-0.248323\pi\) | ||||
0.710822 | + | 0.703372i | \(0.248323\pi\) | |||||||
\(158\) | 3.89576 | + | 2.24922i | 0.309930 | + | 0.178938i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.52798 | + | 2.64654i | 0.120798 | + | 0.209227i | ||||
\(161\) | 3.06260i | 0.241366i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.68884 | + | 4.43915i | −0.602236 | + | 0.347701i | −0.769921 | − | 0.638139i | \(-0.779704\pi\) |
0.167684 | + | 0.985841i | \(0.446371\pi\) | |||||||
\(164\) | − | 9.96254i | − | 0.777943i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.57934 | + | 6.19961i | −0.277811 | + | 0.481183i | ||||
\(167\) | 8.46097 | + | 4.88494i | 0.654730 | + | 0.378008i | 0.790266 | − | 0.612764i | \(-0.209942\pi\) |
−0.135536 | + | 0.990772i | \(0.543276\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.15796 | + | 10.1216i | 0.627535 | + | 0.778588i | ||||
\(170\) | 8.64526 | 0.663061 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.51082 | − | 2.61681i | 0.115199 | − | 0.199530i | ||||
\(173\) | −4.33762 | − | 7.51299i | −0.329783 | − | 0.571202i | 0.652685 | − | 0.757629i | \(-0.273642\pi\) |
−0.982469 | + | 0.186427i | \(0.940309\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.75760 | + | 2.16945i | −0.284048 | + | 0.163995i | ||||
\(176\) | −2.98127 | + | 1.72124i | −0.224722 | + | 0.129743i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.95154 | − | 6.84426i | −0.296180 | − | 0.512999i | ||||
\(179\) | 11.7139 | − | 20.2891i | 0.875540 | − | 1.51648i | 0.0193531 | − | 0.999813i | \(-0.493839\pi\) |
0.856187 | − | 0.516667i | \(-0.172827\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.66632 | 0.569833 | 0.284917 | − | 0.958552i | \(-0.408034\pi\) | ||||
0.284917 | + | 0.958552i | \(0.408034\pi\) | |||||||
\(182\) | −3.25253 | − | 1.55596i | −0.241094 | − | 0.115336i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.65229 | + | 1.53130i | 0.195529 | + | 0.112889i | ||||
\(185\) | −8.08773 | + | 14.0084i | −0.594622 | + | 1.02992i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.73869i | 0.712163i | ||||||||
\(188\) | 6.96672 | − | 4.02224i | 0.508100 | − | 0.293352i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 5.27281i | − | 0.382530i | ||||||
\(191\) | 12.7472 | + | 22.0789i | 0.922357 | + | 1.59757i | 0.795757 | + | 0.605616i | \(0.207073\pi\) |
0.126600 | + | 0.991954i | \(0.459593\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.38361 | − | 4.26293i | −0.531484 | − | 0.306852i | 0.210137 | − | 0.977672i | \(-0.432609\pi\) |
−0.741621 | + | 0.670820i | \(0.765942\pi\) | |||||||
\(194\) | 9.09922 | 0.653286 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −20.5094 | − | 11.8411i | −1.46124 | − | 0.843645i | −0.462168 | − | 0.886792i | \(-0.652928\pi\) |
−0.999069 | + | 0.0431470i | \(0.986262\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.4233 | − | 21.5178i | −0.880666 | − | 1.52536i | −0.850602 | − | 0.525810i | \(-0.823762\pi\) |
−0.0300637 | − | 0.999548i | \(-0.509571\pi\) | |||||||
\(200\) | 4.33891i | 0.306807i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 16.3274 | − | 9.42664i | 1.14879 | − | 0.663256i | ||||
\(203\) | − | 3.85061i | − | 0.270260i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.2226 | − | 26.3663i | 1.06319 | − | 1.84150i | ||||
\(206\) | 11.8714 | + | 6.85393i | 0.827116 | + | 0.477536i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.97377 | + | 2.03880i | −0.206194 | + | 0.141365i | ||||
\(209\) | 5.93970 | 0.410857 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.386509 | + | 0.669453i | −0.0266084 | + | 0.0460871i | −0.879023 | − | 0.476779i | \(-0.841804\pi\) |
0.852415 | + | 0.522867i | \(0.175137\pi\) | |||||||
\(212\) | 4.16702 | + | 7.21750i | 0.286192 | + | 0.495700i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.87063 | − | 1.65736i | 0.196232 | − | 0.113295i | ||||
\(215\) | 7.99687 | − | 4.61699i | 0.545382 | − | 0.314876i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.489185 | − | 0.847293i | −0.0332080 | − | 0.0575180i | ||||
\(218\) | 4.33762 | − | 7.51299i | 0.293781 | − | 0.508844i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −10.5201 | −0.709263 | ||||||||
\(221\) | 0.788619 | + | 10.1695i | 0.0530482 | + | 0.684075i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.6502 | − | 10.7677i | −1.24891 | − | 0.721060i | −0.278019 | − | 0.960575i | \(-0.589678\pi\) |
−0.970892 | + | 0.239516i | \(0.923011\pi\) | |||||||
\(224\) | 0.500000 | − | 0.866025i | 0.0334077 | − | 0.0578638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.2111i | 0.745754i | ||||||||
\(227\) | −15.1939 | + | 8.77218i | −1.00845 | + | 0.582230i | −0.910738 | − | 0.412985i | \(-0.864486\pi\) |
−0.0977139 | + | 0.995215i | \(0.531153\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.3222i | 0.682109i | 0.940043 | + | 0.341055i | \(0.110784\pi\) | ||||
−0.940043 | + | 0.341055i | \(0.889216\pi\) | |||||||
\(230\) | 4.67959 | + | 8.10529i | 0.308563 | + | 0.534447i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.33473 | − | 1.92531i | −0.218936 | − | 0.126402i | ||||
\(233\) | 17.8290 | 1.16802 | 0.584008 | − | 0.811748i | \(-0.301484\pi\) | ||||
0.584008 | + | 0.811748i | \(0.301484\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 24.5836 | 1.60366 | ||||||||
\(236\) | −8.64080 | − | 4.98877i | −0.562468 | − | 0.324741i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.41449 | − | 2.44997i | −0.0916878 | − | 0.158808i | ||||
\(239\) | − | 5.71271i | − | 0.369525i | −0.982783 | − | 0.184762i | \(-0.940848\pi\) | ||
0.982783 | − | 0.184762i | \(-0.0591515\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.868738 | − | 0.501566i | 0.0559603 | − | 0.0323087i | −0.471759 | − | 0.881728i | \(-0.656381\pi\) |
0.527719 | + | 0.849419i | \(0.323047\pi\) | |||||||
\(242\) | − | 0.850611i | − | 0.0546793i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.77260 | + | 9.99843i | −0.369553 | + | 0.640084i | ||||
\(245\) | 2.64654 | + | 1.52798i | 0.169081 | + | 0.0976191i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.20245 | − | 0.480984i | 0.394653 | − | 0.0306043i | ||||
\(248\) | −0.978370 | −0.0621266 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.01014 | − | 1.74961i | 0.0638867 | − | 0.110655i | ||||
\(251\) | 0.336293 | + | 0.582476i | 0.0212266 | + | 0.0367656i | 0.876444 | − | 0.481505i | \(-0.159910\pi\) |
−0.855217 | + | 0.518270i | \(0.826576\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.13042 | + | 5.27145i | −0.574025 | + | 0.331413i | ||||
\(254\) | −4.42977 | + | 2.55753i | −0.277948 | + | 0.160474i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −12.1717 | + | 21.0820i | −0.759248 | + | 1.31506i | 0.183986 | + | 0.982929i | \(0.441100\pi\) |
−0.943234 | + | 0.332128i | \(0.892234\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.29308 | 0.328896 | ||||||||
\(260\) | −10.9854 | + | 0.851893i | −0.681289 | + | 0.0528322i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −16.2602 | − | 9.38784i | −1.00456 | − | 0.579983i | ||||
\(263\) | −8.54648 | + | 14.8029i | −0.526999 | + | 0.912788i | 0.472506 | + | 0.881327i | \(0.343349\pi\) |
−0.999505 | + | 0.0314610i | \(0.989984\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.4685i | 1.56452i | ||||||||
\(266\) | −1.49425 | + | 0.862708i | −0.0916186 | + | 0.0528960i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.75055i | 0.290186i | ||||||||
\(269\) | −13.3297 | − | 23.0877i | −0.812727 | − | 1.40768i | −0.910949 | − | 0.412519i | \(-0.864649\pi\) |
0.0982223 | − | 0.995165i | \(-0.468684\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.1739 | + | 12.2247i | 1.28622 | + | 0.742600i | 0.977978 | − | 0.208708i | \(-0.0669257\pi\) |
0.308243 | + | 0.951308i | \(0.400259\pi\) | |||||||
\(272\) | −2.82898 | −0.171532 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.66109 | 0.160763 | ||||||||
\(275\) | −12.9354 | − | 7.46828i | −0.780037 | − | 0.450354i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.2406 | − | 24.6655i | −0.855636 | − | 1.48201i | −0.876054 | − | 0.482214i | \(-0.839833\pi\) |
0.0204175 | − | 0.999792i | \(-0.493500\pi\) | |||||||
\(278\) | − | 16.7064i | − | 1.00199i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.64654 | − | 1.52798i | 0.158161 | − | 0.0913143i | ||||
\(281\) | − | 9.76032i | − | 0.582252i | −0.956685 | − | 0.291126i | \(-0.905970\pi\) | ||
0.956685 | − | 0.291126i | \(-0.0940298\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.83562 | − | 10.1076i | 0.346891 | − | 0.600833i | −0.638804 | − | 0.769369i | \(-0.720571\pi\) |
0.985696 | + | 0.168536i | \(0.0539039\pi\) | |||||||
\(284\) | 3.17784 | + | 1.83473i | 0.188570 | + | 0.108871i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.959638 | − | 12.3749i | −0.0567446 | − | 0.731741i | ||||
\(287\) | −9.96254 | −0.588070 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.49843 | − | 7.79152i | 0.264614 | − | 0.458324i | ||||
\(290\) | −5.88366 | − | 10.1908i | −0.345500 | − | 0.598424i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.75718 | + | 5.05596i | −0.512475 | + | 0.295878i | ||||
\(293\) | −18.8968 | + | 10.9101i | −1.10396 | + | 0.637373i | −0.937259 | − | 0.348634i | \(-0.886646\pi\) |
−0.166704 | + | 0.986007i | \(0.553312\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.2455 | − | 26.4059i | −0.887626 | − | 1.53741i | ||||
\(296\) | 2.64654 | − | 4.58394i | 0.153827 | − | 0.266436i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.50157 | 0.144912 | ||||||||
\(299\) | −9.10746 | + | 6.24401i | −0.526698 | + | 0.361101i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.61681 | − | 1.51082i | −0.150830 | − | 0.0870819i | ||||
\(302\) | −6.32323 | + | 10.9522i | −0.363861 | + | 0.630226i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.72542i | 0.0989594i | ||||||||
\(305\) | −30.5548 | + | 17.6408i | −1.74957 | + | 1.01011i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4.87046i | − | 0.277972i | −0.990294 | − | 0.138986i | \(-0.955616\pi\) | ||
0.990294 | − | 0.138986i | \(-0.0443843\pi\) | |||||||
\(308\) | 1.72124 | + | 2.98127i | 0.0980765 | + | 0.169874i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.58930 | − | 1.49493i | −0.147062 | − | 0.0849064i | ||||
\(311\) | 3.90344 | 0.221344 | 0.110672 | − | 0.993857i | \(-0.464700\pi\) | ||||
0.110672 | + | 0.993857i | \(0.464700\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.0528 | 1.47259 | 0.736297 | − | 0.676659i | \(-0.236573\pi\) | ||||
0.736297 | + | 0.676659i | \(0.236573\pi\) | |||||||
\(314\) | −15.4266 | − | 8.90657i | −0.870576 | − | 0.502627i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.24922 | − | 3.89576i | −0.126528 | − | 0.219154i | ||||
\(317\) | − | 11.1107i | − | 0.624040i | −0.950076 | − | 0.312020i | \(-0.898994\pi\) | ||
0.950076 | − | 0.312020i | \(-0.101006\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.4797 | − | 6.62781i | 0.642740 | − | 0.371086i | ||||
\(320\) | − | 3.05596i | − | 0.170833i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.53130 | − | 2.65229i | 0.0853359 | − | 0.147806i | ||||
\(323\) | 4.22722 | + | 2.44058i | 0.235209 | + | 0.135798i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.1124 | − | 6.75118i | −0.782818 | − | 0.374488i | ||||
\(326\) | 8.87831 | 0.491724 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.98127 | + | 8.62781i | −0.275045 | + | 0.476391i | ||||
\(329\) | −4.02224 | − | 6.96672i | −0.221753 | − | 0.384087i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.6854 | − | 7.32391i | 0.697252 | − | 0.402559i | −0.109071 | − | 0.994034i | \(-0.534788\pi\) |
0.806323 | + | 0.591475i | \(0.201454\pi\) | |||||||
\(332\) | 6.19961 | − | 3.57934i | 0.340248 | − | 0.196442i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.88494 | − | 8.46097i | −0.267292 | − | 0.462964i | ||||
\(335\) | −7.25875 | + | 12.5725i | −0.396588 | + | 0.686910i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.5456 | −1.50050 | −0.750251 | − | 0.661153i | \(-0.770068\pi\) | ||||
−0.750251 | + | 0.661153i | \(0.770068\pi\) | |||||||
\(338\) | −2.00418 | − | 12.8446i | −0.109013 | − | 0.698653i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.48701 | − | 4.32263i | −0.406040 | − | 0.234427i | ||||
\(341\) | 1.68401 | − | 2.91678i | 0.0911940 | − | 0.157953i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | −2.61681 | + | 1.51082i | −0.141089 | + | 0.0814577i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.67525i | 0.466384i | ||||||||
\(347\) | 2.62073 | + | 4.53924i | 0.140688 | + | 0.243679i | 0.927756 | − | 0.373187i | \(-0.121735\pi\) |
−0.787068 | + | 0.616867i | \(0.788402\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.52901 | − | 2.61482i | −0.242432 | − | 0.139968i | 0.373862 | − | 0.927484i | \(-0.378033\pi\) |
−0.616294 | + | 0.787516i | \(0.711367\pi\) | |||||||
\(350\) | 4.33891 | 0.231924 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.44247 | 0.183484 | ||||||||
\(353\) | −3.26227 | − | 1.88348i | −0.173633 | − | 0.100247i | 0.410665 | − | 0.911786i | \(-0.365297\pi\) |
−0.584298 | + | 0.811539i | \(0.698630\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.60686 | + | 9.71136i | 0.297581 | + | 0.515425i | ||||
\(356\) | 7.90307i | 0.418862i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.2891 | + | 11.7139i | −1.07231 | + | 0.619100i | ||||
\(359\) | − | 20.6003i | − | 1.08724i | −0.839330 | − | 0.543622i | \(-0.817053\pi\) | ||
0.839330 | − | 0.543622i | \(-0.182947\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.01147 | + | 13.8763i | −0.421656 | + | 0.730330i | ||||
\(362\) | −6.63923 | − | 3.83316i | −0.348950 | − | 0.201466i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.03880 | + | 2.97377i | 0.106862 | + | 0.155868i | ||||
\(365\) | −30.9017 | −1.61747 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.9579 | − | 24.1759i | 0.728598 | − | 1.26197i | −0.228877 | − | 0.973455i | \(-0.573505\pi\) |
0.957476 | − | 0.288514i | \(-0.0931612\pi\) | |||||||
\(368\) | −1.53130 | − | 2.65229i | −0.0798245 | − | 0.138260i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 14.0084 | − | 8.08773i | 0.728260 | − | 0.420461i | ||||
\(371\) | 7.21750 | − | 4.16702i | 0.374714 | − | 0.216341i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.7091 | − | 27.2090i | −0.813388 | − | 1.40883i | −0.910479 | − | 0.413554i | \(-0.864287\pi\) |
0.0970910 | − | 0.995276i | \(-0.469046\pi\) | |||||||
\(374\) | 4.86934 | − | 8.43395i | 0.251788 | − | 0.436109i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.04447 | −0.414862 | ||||||||
\(377\) | 11.4508 | − | 7.85061i | 0.589748 | − | 0.404327i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.5747 | − | 15.9203i | −1.41642 | − | 0.817770i | −0.420437 | − | 0.907322i | \(-0.638123\pi\) |
−0.995982 | + | 0.0895514i | \(0.971457\pi\) | |||||||
\(380\) | −2.63640 | + | 4.56638i | −0.135245 | + | 0.234251i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 25.4945i | − | 1.30441i | ||||||
\(383\) | 4.08962 | − | 2.36114i | 0.208970 | − | 0.120649i | −0.391863 | − | 0.920024i | \(-0.628169\pi\) |
0.600832 | + | 0.799375i | \(0.294836\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.5201i | 0.536152i | ||||||||
\(386\) | 4.26293 | + | 7.38361i | 0.216977 | + | 0.375816i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.88016 | − | 4.54961i | −0.400054 | − | 0.230972i | ||||
\(389\) | 30.5902 | 1.55099 | 0.775493 | − | 0.631356i | \(-0.217501\pi\) | ||||
0.775493 | + | 0.631356i | \(0.217501\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.66403 | −0.438159 | ||||||||
\(392\) | −0.866025 | − | 0.500000i | −0.0437409 | − | 0.0252538i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.8411 | + | 20.5094i | 0.596547 | + | 1.03325i | ||||
\(395\) | − | 13.7470i | − | 0.691689i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.1133 | − | 5.83891i | 0.507571 | − | 0.293046i | −0.224264 | − | 0.974529i | \(-0.571998\pi\) |
0.731835 | + | 0.681482i | \(0.238664\pi\) | |||||||
\(398\) | 24.8466i | 1.24545i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.16945 | − | 3.75760i | 0.108473 | − | 0.187880i | ||||
\(401\) | −8.01677 | − | 4.62849i | −0.400339 | − | 0.231136i | 0.286292 | − | 0.958143i | \(-0.407577\pi\) |
−0.686630 | + | 0.727007i | \(0.740911\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.52231 | − | 3.18218i | 0.0758315 | − | 0.158516i | ||||
\(404\) | −18.8533 | −0.937985 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.92531 | + | 3.33473i | −0.0955513 | + | 0.165500i | ||||
\(407\) | 9.11064 | + | 15.7801i | 0.451598 | + | 0.782190i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.1693 | + | 12.7994i | −1.09620 | + | 0.632891i | −0.935220 | − | 0.354066i | \(-0.884799\pi\) |
−0.160980 | + | 0.986958i | \(0.551465\pi\) | |||||||
\(410\) | −26.3663 | + | 15.2226i | −1.30214 | + | 0.751789i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.85393 | − | 11.8714i | −0.337669 | − | 0.584860i | ||||
\(413\) | −4.98877 | + | 8.64080i | −0.245481 | + | 0.425186i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 21.8767 | 1.07388 | ||||||||
\(416\) | 3.59476 | − | 0.278764i | 0.176248 | − | 0.0136675i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.14393 | − | 2.96985i | −0.251598 | − | 0.145260i | ||||
\(419\) | 14.1018 | − | 24.4251i | 0.688920 | − | 1.19324i | −0.283268 | − | 0.959041i | \(-0.591419\pi\) |
0.972188 | − | 0.234203i | \(-0.0752481\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.07012i | 0.247102i | 0.992338 | + | 0.123551i | \(0.0394283\pi\) | ||||
−0.992338 | + | 0.123551i | \(0.960572\pi\) | |||||||
\(422\) | 0.669453 | − | 0.386509i | 0.0325885 | − | 0.0188150i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 8.33405i | − | 0.404737i | ||||||
\(425\) | −6.13734 | − | 10.6302i | −0.297705 | − | 0.515640i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.99843 | + | 5.77260i | 0.483858 | + | 0.279356i | ||||
\(428\) | −3.31471 | −0.160223 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.23399 | −0.445302 | ||||||||
\(431\) | 13.9808 | + | 8.07185i | 0.673434 | + | 0.388807i | 0.797376 | − | 0.603482i | \(-0.206221\pi\) |
−0.123943 | + | 0.992289i | \(0.539554\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.3014 | − | 19.5747i | −0.543113 | − | 0.940699i | −0.998723 | − | 0.0505195i | \(-0.983912\pi\) |
0.455610 | − | 0.890179i | \(-0.349421\pi\) | |||||||
\(434\) | 0.978370i | 0.0469633i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.51299 | + | 4.33762i | −0.359807 | + | 0.207735i | ||||
\(437\) | 5.28425i | 0.252780i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.1486 | − | 24.5060i | 0.675273 | − | 1.16961i | −0.301115 | − | 0.953588i | \(-0.597359\pi\) |
0.976389 | − | 0.216020i | \(-0.0693077\pi\) | |||||||
\(440\) | 9.11064 | + | 5.26003i | 0.434333 | + | 0.250762i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.40179 | − | 9.20136i | 0.209372 | − | 0.437664i | ||||
\(443\) | 1.38096 | 0.0656112 | 0.0328056 | − | 0.999462i | \(-0.489556\pi\) | ||||
0.0328056 | + | 0.999462i | \(0.489556\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.0757 | + | 20.9158i | −0.572445 | + | 0.991504i | ||||
\(446\) | 10.7677 | + | 18.6502i | 0.509866 | + | 0.883114i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.866025 | + | 0.500000i | −0.0409159 | + | 0.0236228i | ||||
\(449\) | 32.0480 | − | 18.5029i | 1.51244 | − | 0.873208i | 0.512547 | − | 0.858659i | \(-0.328702\pi\) |
0.999894 | − | 0.0145487i | \(-0.00463115\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.1479 | − | 29.7010i | −0.807462 | − | 1.39856i | ||||
\(452\) | 5.60557 | − | 9.70914i | 0.263664 | − | 0.456679i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 17.5444 | 0.823398 | ||||||||
\(455\) | 0.851893 | + | 10.9854i | 0.0399374 | + | 0.515006i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.0530 | + | 6.95878i | 0.563813 | + | 0.325518i | 0.754675 | − | 0.656099i | \(-0.227795\pi\) |
−0.190861 | + | 0.981617i | \(0.561128\pi\) | |||||||
\(458\) | 5.16109 | − | 8.93928i | 0.241162 | − | 0.417705i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 9.35918i | − | 0.436374i | ||||||
\(461\) | −4.19845 | + | 2.42397i | −0.195541 | + | 0.112896i | −0.594574 | − | 0.804041i | \(-0.702679\pi\) |
0.399033 | + | 0.916937i | \(0.369346\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.4377i | 1.13571i | 0.823127 | + | 0.567857i | \(0.192227\pi\) | ||||
−0.823127 | + | 0.567857i | \(0.807773\pi\) | |||||||
\(464\) | 1.92531 | + | 3.33473i | 0.0893801 | + | 0.154811i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.4404 | − | 8.91449i | −0.715260 | − | 0.412956i | ||||
\(467\) | 36.0027 | 1.66600 | 0.833002 | − | 0.553270i | \(-0.186620\pi\) | ||||
0.833002 | + | 0.553270i | \(0.186620\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.75055 | 0.219360 | ||||||||
\(470\) | −21.2900 | − | 12.2918i | −0.982035 | − | 0.566978i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.98877 | + | 8.64080i | 0.229627 | + | 0.397725i | ||||
\(473\) | − | 10.4019i | − | 0.478279i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.48343 | + | 3.74321i | −0.297480 | + | 0.171750i | ||||
\(476\) | 2.82898i | 0.129666i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.85636 | + | 4.94735i | −0.130647 | + | 0.226287i | ||||
\(479\) | 8.22108 | + | 4.74644i | 0.375631 | + | 0.216870i | 0.675915 | − | 0.736979i | \(-0.263748\pi\) |
−0.300285 | + | 0.953850i | \(0.597082\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.7915 | + | 15.7404i | 0.492051 | + | 0.717701i | ||||
\(482\) | −1.00313 | −0.0456914 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.425305 | + | 0.736650i | −0.0193321 | + | 0.0334841i | ||||
\(485\) | −13.9034 | − | 24.0815i | −0.631323 | − | 1.09348i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −35.4383 | + | 20.4603i | −1.60586 | + | 0.927144i | −0.615578 | + | 0.788076i | \(0.711078\pi\) |
−0.990283 | + | 0.139069i | \(0.955589\pi\) | |||||||
\(488\) | 9.99843 | − | 5.77260i | 0.452608 | − | 0.261313i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.52798 | − | 2.64654i | −0.0690272 | − | 0.119559i | ||||
\(491\) | 2.55753 | − | 4.42977i | 0.115420 | − | 0.199913i | −0.802528 | − | 0.596615i | \(-0.796512\pi\) |
0.917947 | + | 0.396702i | \(0.129845\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.8933 | 0.490610 | ||||||||
\(494\) | −5.61197 | − | 2.68468i | −0.252495 | − | 0.120790i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.847293 | + | 0.489185i | 0.0380446 | + | 0.0219651i | ||||
\(497\) | 1.83473 | − | 3.17784i | 0.0822987 | − | 0.142546i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.5827i | 0.876640i | 0.898819 | + | 0.438320i | \(0.144426\pi\) | ||||
−0.898819 | + | 0.438320i | \(0.855574\pi\) | |||||||
\(500\) | −1.74961 | + | 1.01014i | −0.0782450 | + | 0.0451747i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 0.672585i | − | 0.0300189i | ||||||
\(503\) | −14.5429 | − | 25.1890i | −0.648436 | − | 1.12312i | −0.983496 | − | 0.180928i | \(-0.942090\pi\) |
0.335060 | − | 0.942197i | \(-0.391243\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −49.8960 | − | 28.8075i | −2.22034 | − | 1.28191i | ||||
\(506\) | 10.5429 | 0.468689 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.11506 | 0.226944 | ||||||||
\(509\) | 4.52051 | + | 2.60992i | 0.200368 | + | 0.115682i | 0.596827 | − | 0.802370i | \(-0.296428\pi\) |
−0.396459 | + | 0.918052i | \(0.629761\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.05596 | + | 8.75718i | 0.223663 | + | 0.387395i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 21.0820 | − | 12.1717i | 0.929885 | − | 0.536870i | ||||
\(515\) | − | 41.8907i | − | 1.84592i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.8464 | − | 23.9827i | 0.608965 | − | 1.05476i | ||||
\(518\) | −4.58394 | − | 2.64654i | −0.201407 | − | 0.116282i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.93962 | + | 4.75496i | 0.435881 | + | 0.208519i | ||||
\(521\) | 14.5259 | 0.636389 | 0.318195 | − | 0.948025i | \(-0.396923\pi\) | ||||
0.318195 | + | 0.948025i | \(0.396923\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.9367 | + | 24.1391i | −0.609410 | + | 1.05553i | 0.381927 | + | 0.924192i | \(0.375260\pi\) |
−0.991338 | + | 0.131337i | \(0.958073\pi\) | |||||||
\(524\) | 9.38784 | + | 16.2602i | 0.410110 | + | 0.710331i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.8029 | − | 8.54648i | 0.645439 | − | 0.372644i | ||||
\(527\) | 2.39698 | − | 1.38389i | 0.104414 | − | 0.0602834i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.81025 | + | 11.7957i | 0.296098 | + | 0.512856i | ||||
\(530\) | 12.7343 | − | 22.0564i | 0.553141 | − | 0.958069i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.72542 | 0.0748063 | ||||||||
\(533\) | −20.3116 | − | 29.6263i | −0.879792 | − | 1.28326i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.77252 | − | 5.06482i | −0.379269 | − | 0.218971i | ||||
\(536\) | 2.37527 | − | 4.11410i | 0.102596 | − | 0.177702i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 26.6594i | 1.14937i | ||||||||
\(539\) | 2.98127 | − | 1.72124i | 0.128412 | − | 0.0741389i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 1.42341i | − | 0.0611970i | −0.999532 | − | 0.0305985i | \(-0.990259\pi\) | ||
0.999532 | − | 0.0305985i | \(-0.00974133\pi\) | |||||||
\(542\) | −12.2247 | − | 21.1739i | −0.525097 | − | 0.909496i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.44997 | + | 1.41449i | 0.105042 | + | 0.0606458i | ||||
\(545\) | −26.5112 | −1.13562 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.33008 | −0.398925 | −0.199463 | − | 0.979905i | \(-0.563920\pi\) | ||||
−0.199463 | + | 0.979905i | \(0.563920\pi\) | |||||||
\(548\) | −2.30457 | − | 1.33055i | −0.0984465 | − | 0.0568381i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.46828 | + | 12.9354i | 0.318449 | + | 0.551569i | ||||
\(551\) | − | 6.64390i | − | 0.283040i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.89576 | + | 2.24922i | −0.165664 | + | 0.0956464i | ||||
\(554\) | 28.4812i | 1.21005i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.35322 | + | 14.4682i | −0.354256 | + | 0.613589i | ||||
\(557\) | −9.34071 | − | 5.39286i | −0.395779 | − | 0.228503i | 0.288882 | − | 0.957365i | \(-0.406716\pi\) |
−0.684661 | + | 0.728862i | \(0.740050\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.842322 | − | 10.8620i | −0.0356264 | − | 0.459415i | ||||
\(560\) | −3.05596 | −0.129138 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.88016 | + | 8.45268i | −0.205857 | + | 0.356555i | ||||
\(563\) | −12.7541 | − | 22.0908i | −0.537522 | − | 0.931016i | −0.999037 | − | 0.0438831i | \(-0.986027\pi\) |
0.461514 | − | 0.887133i | \(-0.347306\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 29.6708 | − | 17.1304i | 1.24826 | − | 0.720682i | ||||
\(566\) | −10.1076 | + | 5.83562i | −0.424853 | + | 0.245289i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.83473 | − | 3.17784i | −0.0769834 | − | 0.133339i | ||||
\(569\) | 4.10835 | − | 7.11587i | 0.172231 | − | 0.298313i | −0.766969 | − | 0.641685i | \(-0.778236\pi\) |
0.939200 | + | 0.343372i | \(0.111569\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.70500 | 0.113201 | 0.0566003 | − | 0.998397i | \(-0.481974\pi\) | ||||
0.0566003 | + | 0.998397i | \(0.481974\pi\) | |||||||
\(572\) | −5.35636 | + | 11.1968i | −0.223961 | + | 0.468160i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.62781 | + | 4.98127i | 0.360118 | + | 0.207914i | ||||
\(575\) | 6.64416 | − | 11.5080i | 0.277081 | − | 0.479918i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.4253i | 0.891946i | 0.895046 | + | 0.445973i | \(0.147142\pi\) | ||||
−0.895046 | + | 0.445973i | \(0.852858\pi\) | |||||||
\(578\) | −7.79152 | + | 4.49843i | −0.324084 | + | 0.187110i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 11.7673i | 0.488611i | ||||||||
\(581\) | −3.57934 | − | 6.19961i | −0.148496 | − | 0.257203i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.8460 | + | 14.3449i | 1.02902 | + | 0.594104i | ||||
\(584\) | 10.1119 | 0.418434 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.8202 | 0.901382 | ||||||||
\(587\) | 4.96515 | + | 2.86663i | 0.204934 | + | 0.118319i | 0.598955 | − | 0.800783i | \(-0.295583\pi\) |
−0.394021 | + | 0.919101i | \(0.628916\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.844048 | − | 1.46193i | −0.0347784 | − | 0.0602379i | ||||
\(590\) | 30.4910i | 1.25529i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.58394 | + | 2.64654i | −0.188399 | + | 0.108772i | ||||
\(593\) | 17.3442i | 0.712240i | 0.934440 | + | 0.356120i | \(0.115901\pi\) | ||||
−0.934440 | + | 0.356120i | \(0.884099\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.32263 | + | 7.48701i | −0.177211 | + | 0.306938i | ||||
\(596\) | −2.16642 | − | 1.25078i | −0.0887400 | − | 0.0512341i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 11.0093 | − | 0.853743i | 0.450204 | − | 0.0349121i | ||||
\(599\) | 31.5835 | 1.29047 | 0.645234 | − | 0.763985i | \(-0.276760\pi\) | ||||
0.645234 | + | 0.763985i | \(0.276760\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.4478 | + | 21.5603i | −0.507757 | + | 0.879462i | 0.492202 | + | 0.870481i | \(0.336192\pi\) |
−0.999960 | + | 0.00898069i | \(0.997141\pi\) | |||||||
\(602\) | 1.51082 | + | 2.61681i | 0.0615762 | + | 0.106653i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.9522 | − | 6.32323i | 0.445637 | − | 0.257289i | ||||
\(605\) | −2.25118 | + | 1.29972i | −0.0915233 | + | 0.0528410i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.62951 | − | 13.2147i | −0.309672 | − | 0.536368i | 0.668618 | − | 0.743606i | \(-0.266886\pi\) |
−0.978291 | + | 0.207238i | \(0.933553\pi\) | |||||||
\(608\) | 0.862708 | − | 1.49425i | 0.0349874 | − | 0.0606000i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 35.2817 | 1.42851 | ||||||||
\(611\) | 12.5169 | − | 26.1649i | 0.506379 | − | 1.05852i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −39.6220 | − | 22.8757i | −1.60032 | − | 0.923943i | −0.991423 | − | 0.130690i | \(-0.958281\pi\) |
−0.608892 | − | 0.793253i | \(-0.708386\pi\) | |||||||
\(614\) | −2.43523 | + | 4.21794i | −0.0982779 | + | 0.170222i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 3.44247i | − | 0.138701i | ||||||
\(617\) | −36.6167 | + | 21.1406i | −1.47413 | + | 0.851090i | −0.999575 | − | 0.0291358i | \(-0.990724\pi\) |
−0.474555 | + | 0.880226i | \(0.657391\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.0261i | 0.885303i | 0.896694 | + | 0.442651i | \(0.145962\pi\) | ||||
−0.896694 | + | 0.442651i | \(0.854038\pi\) | |||||||
\(620\) | 1.49493 | + | 2.58930i | 0.0600379 | + | 0.103989i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.38048 | − | 1.95172i | −0.135545 | − | 0.0782569i | ||||
\(623\) | 7.90307 | 0.316630 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.8684 | −1.11474 | ||||||||
\(626\) | −22.5624 | − | 13.0264i | −0.901775 | − | 0.520640i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.90657 | + | 15.4266i | 0.355411 | + | 0.615590i | ||||
\(629\) | 14.9740i | 0.597054i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.0721 | − | 10.4339i | 0.719440 | − | 0.415369i | −0.0951064 | − | 0.995467i | \(-0.530319\pi\) |
0.814547 | + | 0.580098i | \(0.196986\pi\) | |||||||
\(632\) | 4.49843i | 0.178938i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.55536 | + | 9.62216i | −0.220631 | + | 0.382145i | ||||
\(635\) | 13.5372 | + | 7.81571i | 0.537208 | + | 0.310157i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.97377 | − | 2.03880i | 0.117825 | − | 0.0807800i | ||||
\(638\) | −13.2556 | −0.524795 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.52798 | + | 2.64654i | −0.0603988 | + | 0.104614i | ||||
\(641\) | 10.4526 | + | 18.1045i | 0.412853 | + | 0.715083i | 0.995200 | − | 0.0978574i | \(-0.0311989\pi\) |
−0.582347 | + | 0.812940i | \(0.697866\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.8703 | − | 19.5550i | 1.33571 | − | 0.771174i | 0.349544 | − | 0.936920i | \(-0.386337\pi\) |
0.986168 | + | 0.165746i | \(0.0530032\pi\) | |||||||
\(644\) | −2.65229 | + | 1.53130i | −0.104515 | + | 0.0603416i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.44058 | − | 4.22722i | −0.0960235 | − | 0.166318i | ||||
\(647\) | 3.96755 | − | 6.87201i | 0.155981 | − | 0.270166i | −0.777435 | − | 0.628963i | \(-0.783480\pi\) |
0.933416 | + | 0.358797i | \(0.116813\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −34.3474 | −1.34825 | ||||||||
\(650\) | 8.84615 | + | 12.9029i | 0.346974 | + | 0.506094i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.68884 | − | 4.43915i | −0.301118 | − | 0.173851i | ||||
\(653\) | 21.3998 | − | 37.0655i | 0.837439 | − | 1.45049i | −0.0545901 | − | 0.998509i | \(-0.517385\pi\) |
0.892029 | − | 0.451978i | \(-0.149281\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 57.3778i | 2.24194i | ||||||||
\(656\) | 8.62781 | − | 4.98127i | 0.336859 | − | 0.194486i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.04447i | 0.313606i | ||||||||
\(659\) | 0.364274 | + | 0.630941i | 0.0141901 | + | 0.0245780i | 0.873033 | − | 0.487661i | \(-0.162150\pi\) |
−0.858843 | + | 0.512239i | \(0.828816\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.04352 | − | 1.17983i | −0.0794836 | − | 0.0458899i | 0.459731 | − | 0.888058i | \(-0.347946\pi\) |
−0.539215 | + | 0.842168i | \(0.681279\pi\) | |||||||
\(662\) | −14.6478 | −0.569304 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.15869 | −0.277811 | ||||||||
\(665\) | 4.56638 | + | 2.63640i | 0.177077 | + | 0.102235i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.89644 | + | 10.2129i | 0.228311 | + | 0.395446i | ||||
\(668\) | 9.76989i | 0.378008i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12.5725 | − | 7.25875i | 0.485719 | − | 0.280430i | ||||
\(671\) | 39.7440i | 1.53430i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.6279 | − | 27.0682i | 0.602410 | − | 1.04340i | −0.390045 | − | 0.920796i | \(-0.627541\pi\) |
0.992455 | − | 0.122609i | \(-0.0391260\pi\) | |||||||
\(674\) | 23.8552 | + | 13.7728i | 0.918867 | + | 0.530508i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.68662 | + | 12.1258i | −0.180255 | + | 0.466378i | ||||
\(677\) | 41.7294 | 1.60379 | 0.801895 | − | 0.597464i | \(-0.203825\pi\) | ||||
0.801895 | + | 0.597464i | \(0.203825\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.54961 | + | 7.88016i | −0.174598 | + | 0.302413i | ||||
\(680\) | 4.32263 | + | 7.48701i | 0.165765 | + | 0.287114i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.91678 | + | 1.68401i | −0.111689 | + | 0.0644839i | ||||
\(683\) | 7.98473 | − | 4.60999i | 0.305527 | − | 0.176396i | −0.339396 | − | 0.940644i | \(-0.610223\pi\) |
0.644923 | + | 0.764247i | \(0.276889\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.06610 | − | 7.04269i | −0.155358 | − | 0.269087i | ||||
\(686\) | −0.500000 | + | 0.866025i | −0.0190901 | + | 0.0330650i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.02163 | 0.115199 | ||||||||
\(689\) | 27.1068 | + | 12.9675i | 1.03269 | + | 0.494021i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.97487 | − | 4.60429i | −0.303378 | − | 0.175156i | 0.340581 | − | 0.940215i | \(-0.389376\pi\) |
−0.643960 | + | 0.765060i | \(0.722709\pi\) | |||||||
\(692\) | 4.33762 | − | 7.51299i | 0.164892 | − | 0.285601i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 5.24146i | − | 0.198963i | ||||||
\(695\) | −44.2143 | + | 25.5271i | −1.67714 | + | 0.968300i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 28.1838i | − | 1.06754i | ||||||
\(698\) | 2.61482 | + | 4.52901i | 0.0989725 | + | 0.171425i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.75760 | − | 2.16945i | −0.142024 | − | 0.0819976i | ||||
\(701\) | −20.8683 | −0.788184 | −0.394092 | − | 0.919071i | \(-0.628941\pi\) | ||||
−0.394092 | + | 0.919071i | \(0.628941\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.13277 | 0.344449 | ||||||||
\(704\) | −2.98127 | − | 1.72124i | −0.112361 | − | 0.0648715i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.88348 | + | 3.26227i | 0.0708855 | + | 0.122777i | ||||
\(707\) | 18.8533i | 0.709050i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.8731 | + | 7.43226i | −0.483458 | + | 0.279124i | −0.721856 | − | 0.692043i | \(-0.756711\pi\) |
0.238399 | + | 0.971167i | \(0.423378\pi\) | |||||||
\(710\) | − | 11.2137i | − | 0.420843i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.95154 | − | 6.84426i | 0.148090 | − | 0.256499i | ||||
\(713\) | 2.59492 | + | 1.49818i | 0.0971804 | + | 0.0561072i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31.2843 | + | 21.4483i | −1.16996 | + | 0.802120i | ||||
\(716\) | 23.4278 | 0.875540 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.3002 | + | 17.8404i | −0.384399 | + | 0.665798i | ||||
\(719\) | 12.8265 | + | 22.2162i | 0.478349 | + | 0.828524i | 0.999692 | − | 0.0248229i | \(-0.00790218\pi\) |
−0.521343 | + | 0.853347i | \(0.674569\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.8714 | + | 6.85393i | −0.442112 | + | 0.255254i | ||||
\(722\) | 13.8763 | − | 8.01147i | 0.516421 | − | 0.298156i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.83316 | + | 6.63923i | 0.142458 | + | 0.246745i | ||||
\(725\) | −8.35372 | + | 14.4691i | −0.310249 | + | 0.537368i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.6568 | 1.54497 | 0.772483 | − | 0.635036i | \(-0.219015\pi\) | ||||
0.772483 | + | 0.635036i | \(0.219015\pi\) | |||||||
\(728\) | −0.278764 | − | 3.59476i | −0.0103317 | − | 0.133231i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 26.7616 | + | 15.4508i | 0.990492 | + | 0.571861i | ||||
\(731\) | 4.27407 | − | 7.40290i | 0.158082 | − | 0.273806i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 26.4965i | − | 0.978671i | −0.872096 | − | 0.489336i | \(-0.837239\pi\) | ||
0.872096 | − | 0.489336i | \(-0.162761\pi\) | |||||||
\(734\) | −24.1759 | + | 13.9579i | −0.892347 | + | 0.515197i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.06260i | 0.112889i | ||||||||
\(737\) | 8.17682 | + | 14.1627i | 0.301197 | + | 0.521688i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.1009 | + | 10.4506i | 0.665853 | + | 0.384431i | 0.794504 | − | 0.607259i | \(-0.207731\pi\) |
−0.128650 | + | 0.991690i | \(0.541064\pi\) | |||||||
\(740\) | −16.1755 | −0.594622 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.33405 | −0.305953 | ||||||||
\(743\) | −4.88999 | − | 2.82323i | −0.179396 | − | 0.103574i | 0.407613 | − | 0.913155i | \(-0.366361\pi\) |
−0.587009 | + | 0.809580i | \(0.699695\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.82235 | − | 6.62050i | −0.140040 | − | 0.242556i | ||||
\(746\) | 31.4183i | 1.15030i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.43395 | + | 4.86934i | −0.308376 | + | 0.178041i | ||||
\(749\) | 3.31471i | 0.121117i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.70439 | − | 13.3444i | 0.281137 | − | 0.486944i | −0.690528 | − | 0.723306i | \(-0.742622\pi\) |
0.971665 | + | 0.236362i | \(0.0759551\pi\) | |||||||
\(752\) | 6.96672 | + | 4.02224i | 0.254050 | + | 0.146676i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −13.8420 | + | 1.07341i | −0.504097 | + | 0.0390914i | ||||
\(755\) | 38.6471 | 1.40651 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.7686 | − | 30.7761i | 0.645811 | − | 1.11858i | −0.338303 | − | 0.941037i | \(-0.609853\pi\) |
0.984114 | − | 0.177540i | \(-0.0568139\pi\) | |||||||
\(758\) | 15.9203 | + | 27.5747i | 0.578251 | + | 1.00156i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.56638 | − | 2.63640i | 0.165640 | − | 0.0956324i | ||||
\(761\) | −36.2213 | + | 20.9124i | −1.31302 | + | 0.758073i | −0.982595 | − | 0.185759i | \(-0.940526\pi\) |
−0.330425 | + | 0.943832i | \(0.607192\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.33762 | + | 7.51299i | 0.157033 | + | 0.271988i | ||||
\(764\) | −12.7472 | + | 22.0789i | −0.461179 | + | 0.798785i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.72228 | −0.170623 | ||||||||
\(767\) | −35.8668 | + | 2.78138i | −1.29508 | + | 0.100430i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.4609 | + | 8.92635i | 0.557534 | + | 0.321893i | 0.752155 | − | 0.658986i | \(-0.229014\pi\) |
−0.194621 | + | 0.980879i | \(0.562348\pi\) | |||||||
\(770\) | 5.26003 | − | 9.11064i | 0.189558 | − | 0.328325i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 8.52586i | − | 0.306852i | ||||||
\(773\) | −10.4892 | + | 6.05596i | −0.377272 | + | 0.217818i | −0.676630 | − | 0.736323i | \(-0.736561\pi\) |
0.299359 | + | 0.954141i | \(0.403227\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.24506i | 0.152487i | ||||||||
\(776\) | 4.54961 | + | 7.88016i | 0.163322 | + | 0.282881i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −26.4919 | − | 15.2951i | −0.949781 | − | 0.548357i | ||||
\(779\) | −17.1895 | −0.615878 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.6320 | 0.452008 | ||||||||
\(782\) | 7.50327 | + | 4.33201i | 0.268316 | + | 0.154913i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.500000 | + | 0.866025i | 0.0178571 | + | 0.0309295i | ||||
\(785\) | 54.4363i | 1.94292i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.7604 | − | 16.0275i | 0.989551 | − | 0.571317i | 0.0844108 | − | 0.996431i | \(-0.473099\pi\) |
0.905140 | + | 0.425114i | \(0.139766\pi\) | |||||||
\(788\) | − | 23.6823i | − | 0.843645i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.87352 | + | 11.9053i | −0.244549 | + | 0.423571i | ||||
\(791\) | −9.70914 | − | 5.60557i | −0.345217 | − | 0.199311i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.21839 | + | 41.5022i | 0.114288 | + | 1.47379i | ||||
\(794\) | −11.6778 | −0.414430 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.4233 | − | 21.5178i | 0.440333 | − | 0.762679i | ||||
\(797\) | −4.56545 | − | 7.90758i | −0.161716 | − | 0.280101i | 0.773768 | − | 0.633469i | \(-0.218370\pi\) |
−0.935484 | + | 0.353368i | \(0.885036\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.7087 | − | 11.3788i | 0.697244 | − | 0.402554i | ||||
\(800\) | −3.75760 | + | 2.16945i | −0.132851 | + | 0.0767018i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.62849 | + | 8.01677i | 0.163438 | + | 0.283082i | ||||
\(803\) | −17.4050 | + | 30.1464i | −0.614209 | + | 1.06384i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.35918 | −0.329868 | ||||||||
\(806\) | −2.90945 | + | 1.99470i | −0.102481 | + | 0.0702602i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 16.3274 | + | 9.42664i | 0.574396 | + | 0.331628i | ||||
\(809\) | 10.7311 | − | 18.5869i | 0.377287 | − | 0.653480i | −0.613380 | − | 0.789788i | \(-0.710190\pi\) |
0.990666 | + | 0.136308i | \(0.0435238\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.2671i | 1.55443i | 0.629236 | + | 0.777214i | \(0.283368\pi\) | ||||
−0.629236 | + | 0.777214i | \(0.716632\pi\) | |||||||
\(812\) | 3.33473 | − | 1.92531i | 0.117026 | − | 0.0675650i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 18.2213i | − | 0.638656i | ||||||
\(815\) | −13.5659 | − | 23.4968i | −0.475192 | − | 0.823057i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.51508 | − | 2.60678i | −0.157963 | − | 0.0911998i | ||||
\(818\) | 25.5989 | 0.895043 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 30.4451 | 1.06319 | ||||||||
\(821\) | 8.07131 | + | 4.65997i | 0.281691 | + | 0.162634i | 0.634188 | − | 0.773178i | \(-0.281334\pi\) |
−0.352498 | + | 0.935813i | \(0.614668\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.8426 | + | 25.7082i | 0.517381 | + | 0.896131i | 0.999796 | + | 0.0201878i | \(0.00642642\pi\) |
−0.482415 | + | 0.875943i | \(0.660240\pi\) | |||||||
\(824\) | 13.7079i | 0.477536i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.64080 | − | 4.98877i | 0.300652 | − | 0.173581i | ||||
\(827\) | − | 22.6364i | − | 0.787146i | −0.919293 | − | 0.393573i | \(-0.871239\pi\) | ||
0.919293 | − | 0.393573i | \(-0.128761\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.82167 | + | 8.35138i | −0.167463 | + | 0.290055i | −0.937527 | − | 0.347912i | \(-0.886891\pi\) |
0.770064 | + | 0.637967i | \(0.220224\pi\) | |||||||
\(830\) | −18.9458 | − | 10.9383i | −0.657617 | − | 0.379675i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.25253 | − | 1.55596i | −0.112761 | − | 0.0539433i | ||||
\(833\) | 2.82898 | 0.0980184 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.9282 | + | 25.8564i | −0.516612 | + | 0.894798i | ||||
\(836\) | 2.96985 | + | 5.14393i | 0.102714 | + | 0.177906i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −24.4251 | + | 14.1018i | −0.843751 | + | 0.487140i | ||||
\(839\) | 28.9983 | − | 16.7422i | 1.00113 | − | 0.578005i | 0.0925499 | − | 0.995708i | \(-0.470498\pi\) |
0.908583 | + | 0.417704i | \(0.137165\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.08640 | + | 12.2740i | 0.244359 | + | 0.423241i | ||||
\(842\) | 2.53506 | − | 4.39085i | 0.0873639 | − | 0.151319i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.773018 | −0.0266084 | ||||||||
\(845\) | −30.9314 | + | 24.9304i | −1.06407 | + | 0.857633i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.736650 | + | 0.425305i | 0.0253116 | + | 0.0146137i | ||||
\(848\) | −4.16702 | + | 7.21750i | −0.143096 | + | 0.247850i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 12.2747i | 0.421018i | ||||||||
\(851\) | −14.0388 | + | 8.10529i | −0.481243 | + | 0.277846i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 23.7246i | − | 0.812316i | −0.913803 | − | 0.406158i | \(-0.866868\pi\) | ||
0.913803 | − | 0.406158i | \(-0.133132\pi\) | |||||||
\(854\) | −5.77260 | − | 9.99843i | −0.197534 | − | 0.342139i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.87063 | + | 1.65736i | 0.0981159 | + | 0.0566473i | ||||
\(857\) | 24.4823 | 0.836299 | 0.418149 | − | 0.908378i | \(-0.362679\pi\) | ||||
0.418149 | + | 0.908378i | \(0.362679\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.7787 | −0.913676 | −0.456838 | − | 0.889550i | \(-0.651018\pi\) | ||||
−0.456838 | + | 0.889550i | \(0.651018\pi\) | |||||||
\(860\) | 7.99687 | + | 4.61699i | 0.272691 | + | 0.157438i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.07185 | − | 13.9808i | −0.274928 | − | 0.476190i | ||||
\(863\) | − | 54.8533i | − | 1.86723i | −0.358282 | − | 0.933614i | \(-0.616637\pi\) | ||
0.358282 | − | 0.933614i | \(-0.383363\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.9594 | − | 13.2556i | 0.780643 | − | 0.450705i | ||||
\(866\) | 22.6029i | 0.768077i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.489185 | − | 0.847293i | 0.0166040 | − | 0.0287590i | ||||
\(869\) | −13.4110 | − | 7.74287i | −0.454938 | − | 0.262659i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.68540 | + | 14.1270i | 0.328177 | + | 0.478677i | ||||
\(872\) | 8.67525 | 0.293781 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.64213 | − | 4.57630i | 0.0893713 | − | 0.154796i | ||||
\(875\) | 1.01014 | + | 1.74961i | 0.0341489 | + | 0.0591476i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.67626 | − | 2.69984i | 0.157906 | − | 0.0911671i | −0.418965 | − | 0.908002i | \(-0.637607\pi\) |
0.576871 | + | 0.816835i | \(0.304274\pi\) | |||||||
\(878\) | −24.5060 | + | 14.1486i | −0.827038 | + | 0.477490i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.26003 | − | 9.11064i | −0.177316 | − | 0.307120i | ||||
\(881\) | 8.18333 | − | 14.1739i | 0.275703 | − | 0.477532i | −0.694609 | − | 0.719387i | \(-0.744423\pi\) |
0.970312 | + | 0.241855i | \(0.0777559\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.8294 | 0.364440 | 0.182220 | − | 0.983258i | \(-0.441672\pi\) | ||||
0.182220 | + | 0.983258i | \(0.441672\pi\) | |||||||
\(884\) | −8.41274 | + | 5.76772i | −0.282951 | + | 0.193989i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.19594 | − | 0.690478i | −0.0401785 | − | 0.0231971i | ||||
\(887\) | −16.5776 | + | 28.7133i | −0.556623 | + | 0.964099i | 0.441153 | + | 0.897432i | \(0.354570\pi\) |
−0.997775 | + | 0.0666668i | \(0.978764\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 5.11506i | − | 0.171553i | ||||||
\(890\) | 20.9158 | − | 12.0757i | 0.701099 | − | 0.404780i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 21.5354i | − | 0.721060i | ||||||
\(893\) | −6.94003 | − | 12.0205i | −0.232239 | − | 0.402250i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 62.0028 | + | 35.7973i | 2.07252 | + | 1.19657i | ||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −37.0059 | −1.23490 | ||||||||
\(899\) | −3.26260 | − | 1.88366i | −0.108814 | − | 0.0628236i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.7884 | + | 20.4182i | 0.392730 | + | 0.680228i | ||||
\(902\) | 34.2957i | 1.14192i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.70914 | + | 5.60557i | −0.322921 | + | 0.186439i | ||||
\(905\) | 23.4280i | 0.778773i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.5349 | − | 26.9073i | 0.515829 | − | 0.893442i | −0.484002 | − | 0.875067i | \(-0.660817\pi\) |
0.999831 | − | 0.0183754i | \(-0.00584940\pi\) | |||||||
\(908\) | −15.1939 | − | 8.77218i | −0.504226 | − | 0.291115i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.75496 | − | 9.93962i | 0.157625 | − | 0.329495i | ||||
\(911\) | 7.26309 | 0.240637 | 0.120318 | − | 0.992735i | \(-0.461608\pi\) | ||||
0.120318 | + | 0.992735i | \(0.461608\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.3218 | − | 21.3420i | 0.407792 | − | 0.706316i | ||||
\(914\) | −6.95878 | − | 12.0530i | −0.230176 | − | 0.398676i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.93928 | + | 5.16109i | −0.295362 | + | 0.170527i | ||||
\(917\) | 16.2602 | − | 9.38784i | 0.536960 | − | 0.310014i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.0863 | − | 29.5943i | −0.563625 | − | 0.976226i | −0.997176 | − | 0.0750977i | \(-0.976073\pi\) |
0.433552 | − | 0.901129i | \(-0.357260\pi\) | |||||||
\(920\) | −4.67959 | + | 8.10529i | −0.154282 | + | 0.267224i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.84795 | 0.159659 | ||||||||
\(923\) | 13.1908 | − | 1.02291i | 0.434180 | − | 0.0336696i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.8893 | − | 11.4831i | −0.653956 | − | 0.377562i | ||||
\(926\) | 12.2188 | − | 21.1636i | 0.401536 | − | 0.695480i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 3.85061i | − | 0.126402i | ||||||
\(929\) | 11.8252 | − | 6.82728i | 0.387972 | − | 0.223996i | −0.293309 | − | 0.956018i | \(-0.594756\pi\) |
0.681281 | + | 0.732022i | \(0.261423\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1.72542i | − | 0.0565482i | ||||||
\(932\) | 8.91449 | + | 15.4404i | 0.292004 | + | 0.505765i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −31.1792 | − | 18.0013i | −1.02022 | − | 0.589022i | ||||
\(935\) | −29.7611 | −0.973291 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.5716 | 1.42342 | 0.711712 | − | 0.702472i | \(-0.247920\pi\) | ||||
0.711712 | + | 0.702472i | \(0.247920\pi\) | |||||||
\(938\) | −4.11410 | − | 2.37527i | −0.134330 | − | 0.0775555i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12.2918 | + | 21.2900i | 0.400914 | + | 0.694404i | ||||
\(941\) | 55.8282i | 1.81995i | 0.414666 | + | 0.909973i | \(0.363898\pi\) | ||||
−0.414666 | + | 0.909973i | \(0.636102\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.4235 | − | 15.2556i | 0.860468 | − | 0.496791i | ||||
\(944\) | − | 9.97753i | − | 0.324741i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.20094 | + | 9.00829i | −0.169097 | + | 0.292885i | ||||
\(947\) | −45.4573 | − | 26.2448i | −1.47716 | − | 0.852842i | −0.477497 | − | 0.878633i | \(-0.658456\pi\) |
−0.999667 | + | 0.0257916i | \(0.991789\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.7338 | + | 32.8894i | −0.510740 | + | 1.06763i | ||||
\(950\) | 7.48642 | 0.242891 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.41449 | − | 2.44997i | 0.0458439 | − | 0.0794040i | ||||
\(953\) | 3.50985 | + | 6.07925i | 0.113695 | + | 0.196926i | 0.917257 | − | 0.398295i | \(-0.130398\pi\) |
−0.803562 | + | 0.595221i | \(0.797065\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −67.4721 | + | 38.9551i | −2.18335 | + | 1.26056i | ||||
\(956\) | 4.94735 | − | 2.85636i | 0.160009 | − | 0.0923812i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.74644 | − | 8.22108i | −0.153351 | − | 0.265611i | ||||
\(959\) | −1.33055 | + | 2.30457i | −0.0429656 | + | 0.0744186i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.0428 | 0.969122 | ||||||||
\(962\) | −1.47552 | − | 19.0274i | −0.0475727 | − | 0.613467i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.868738 | + | 0.501566i | 0.0279802 | + | 0.0161543i | ||||
\(965\) | 13.0274 | − | 22.5640i | 0.419365 | − | 0.726362i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 36.8770i | − | 1.18588i | −0.805245 | − | 0.592942i | \(-0.797966\pi\) | ||
0.805245 | − | 0.592942i | \(-0.202034\pi\) | |||||||
\(968\) | 0.736650 | − | 0.425305i | 0.0236768 | − | 0.0136698i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 27.8069i | 0.892825i | ||||||||
\(971\) | 13.8202 | + | 23.9372i | 0.443511 | + | 0.768183i | 0.997947 | − | 0.0640432i | \(-0.0203996\pi\) |
−0.554437 | + | 0.832226i | \(0.687066\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.4682 | + | 8.35322i | 0.463830 | + | 0.267792i | ||||
\(974\) | 40.9206 | 1.31118 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.5452 | −0.369553 | ||||||||
\(977\) | 48.1904 | + | 27.8227i | 1.54175 | + | 0.890128i | 0.998729 | + | 0.0504061i | \(0.0160516\pi\) |
0.543017 | + | 0.839721i | \(0.317282\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.6030 | + | 23.5612i | 0.434755 | + | 0.753018i | ||||
\(980\) | 3.05596i | 0.0976191i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.42977 | + | 2.55753i | −0.141360 | + | 0.0816140i | ||||
\(983\) | 25.0022i | 0.797446i | 0.917071 | + | 0.398723i | \(0.130547\pi\) | ||||
−0.917071 | + | 0.398723i | \(0.869453\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.1860 | − | 62.6761i | 1.15298 | − | 1.99703i | ||||
\(986\) | −9.43388 | − | 5.44665i | −0.300436 | − | 0.173457i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.51777 | + | 5.13099i | 0.111915 | + | 0.163239i | ||||
\(989\) | 9.25404 | 0.294261 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.6076 | − | 23.5690i | 0.432258 | − | 0.748694i | −0.564809 | − | 0.825222i | \(-0.691050\pi\) |
0.997067 | + | 0.0765281i | \(0.0243835\pi\) | |||||||
\(992\) | −0.489185 | − | 0.847293i | −0.0155316 | − | 0.0269016i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.17784 | + | 1.83473i | −0.100795 | + | 0.0581940i | ||||
\(995\) | 65.7577 | − | 37.9652i | 2.08466 | − | 1.20358i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.42706 | + | 14.5961i | 0.266888 | + | 0.462263i | 0.968056 | − | 0.250732i | \(-0.0806714\pi\) |
−0.701169 | + | 0.712995i | \(0.747338\pi\) | |||||||
\(998\) | 9.79133 | − | 16.9591i | 0.309939 | − | 0.536830i | ||||
\(999\) | 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 | 1638.2.bj.f.1135.2 | 8 | ||
3.2 | odd | 2 | 546.2.s.e.43.3 | ✓ | 8 | ||
13.10 | even | 6 | inner | 1638.2.bj.f.127.1 | 8 | ||
39.20 | even | 12 | 7098.2.a.co.1.3 | 4 | |||
39.23 | odd | 6 | 546.2.s.e.127.4 | yes | 8 | ||
39.32 | even | 12 | 7098.2.a.cn.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.s.e.43.3 | ✓ | 8 | 3.2 | odd | 2 | ||
546.2.s.e.127.4 | yes | 8 | 39.23 | odd | 6 | ||
1638.2.bj.f.127.1 | 8 | 13.10 | even | 6 | inner | ||
1638.2.bj.f.1135.2 | 8 | 1.1 | even | 1 | trivial | ||
7098.2.a.cn.1.2 | 4 | 39.32 | even | 12 | |||
7098.2.a.co.1.3 | 4 | 39.20 | even | 12 |