Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(112,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([5, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.112");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.m (of order \(20\), degree \(8\), not 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: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{20})\) |
Coefficient field: | 16.0.3429742096000000000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 5x^{14} + 16x^{12} + 35x^{10} + 31x^{8} + 315x^{6} + 1296x^{4} + 3645x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 55) |
Sato-Tate group: | $\mathrm{U}(1)[D_{20}]$ |
Embedding invariants
Embedding label | 282.1 | ||
Root | \(0.0369185 - 1.73166i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.282 |
Dual form | 605.2.m.a.118.1 |
$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{7}{10}\right)\) |
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 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(3\) | −0.743682 | − | 1.45956i | −0.429365 | − | 0.842677i | −0.999773 | − | 0.0213149i | \(-0.993215\pi\) |
0.570408 | − | 0.821362i | \(-0.306785\pi\) | |||||||
\(4\) | −1.90211 | + | 0.618034i | −0.951057 | + | 0.309017i | ||||
\(5\) | 2.22328 | + | 0.238794i | 0.994281 | + | 0.106792i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.186107 | − | 0.256155i | 0.0620358 | − | 0.0853849i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 2.31662 | + | 2.31662i | 0.668752 | + | 0.668752i | ||||
\(13\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.30488 | − | 3.42260i | −0.336919 | − | 0.883710i | ||||
\(16\) | 3.23607 | − | 2.35114i | 0.809017 | − | 0.587785i | ||||
\(17\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(20\) | −4.37651 | + | 0.919850i | −0.978618 | + | 0.205685i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.15831 | − | 6.15831i | 1.28410 | − | 1.28410i | 0.345782 | − | 0.938315i | \(-0.387614\pi\) |
0.938315 | − | 0.345782i | \(-0.112386\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.88595 | + | 1.06181i | 0.977191 | + | 0.212362i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.36608 | − | 0.849903i | −1.03270 | − | 0.163564i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.04962 | − | 5.84839i | −1.44575 | − | 1.05040i | −0.986800 | − | 0.161942i | \(-0.948224\pi\) |
−0.458954 | − | 0.888460i | \(-0.651776\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.195685 | + | 0.602256i | −0.0326141 | + | 0.100376i | ||||
\(37\) | 5.44124 | − | 10.6790i | 0.894535 | − | 1.75562i | 0.294497 | − | 0.955652i | \(-0.404848\pi\) |
0.600038 | − | 0.799972i | \(-0.295152\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.474937 | − | 0.525063i | 0.0707995 | − | 0.0782717i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.38125 | + | 1.72283i | −0.493206 | + | 0.251301i | −0.682859 | − | 0.730550i | \(-0.739264\pi\) |
0.189653 | + | 0.981851i | \(0.439264\pi\) | |||||||
\(48\) | −5.83824 | − | 2.97473i | −0.842677 | − | 0.429365i | ||||
\(49\) | −4.11450 | − | 5.66312i | −0.587785 | − | 0.809017i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.4557 | − | 2.13118i | 1.84829 | − | 0.292740i | 0.868940 | − | 0.494918i | \(-0.164802\pi\) |
0.979349 | + | 0.202178i | \(0.0648018\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.15430 | + | 1.02489i | −0.410655 | + | 0.133430i | −0.507057 | − | 0.861913i | \(-0.669267\pi\) |
0.0964021 | + | 0.995342i | \(0.469267\pi\) | |||||||
\(60\) | 4.59731 | + | 5.70370i | 0.593510 | + | 0.736345i | ||||
\(61\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.70228 | + | 6.47214i | −0.587785 | + | 0.809017i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.52506 | + | 1.52506i | 0.186316 | + | 0.186316i | 0.794101 | − | 0.607785i | \(-0.207942\pi\) |
−0.607785 | + | 0.794101i | \(0.707942\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −13.5682 | − | 4.40859i | −1.63342 | − | 0.530732i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.42705 | − | 1.76336i | 0.288038 | − | 0.209272i | −0.434378 | − | 0.900731i | \(-0.643032\pi\) |
0.722416 | + | 0.691459i | \(0.243032\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.08382 | − | 7.92099i | −0.240619 | − | 0.914637i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(80\) | 7.75613 | − | 4.45449i | 0.867161 | − | 0.498027i | ||||
\(81\) | 2.45665 | + | 7.56078i | 0.272961 | + | 0.840087i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.00000i | 0.953998i | 0.878904 | + | 0.476999i | \(0.158275\pi\) | ||||
−0.878904 | + | 0.476999i | \(0.841725\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.90776 | + | 15.5199i | −0.824441 | + | 1.61806i | ||||
\(93\) | −2.54971 | + | 16.0982i | −0.264393 | + | 1.66931i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.98108 | + | 18.8218i | 0.302683 | + | 1.91107i | 0.401310 | + | 0.915942i | \(0.368555\pi\) |
−0.0986273 | + | 0.995124i | \(0.531445\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.94987 | + | 1.00000i | −0.994987 | + | 0.100000i | ||||
\(101\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.0577 | + | 7.67229i | 1.48368 | + | 0.755973i | 0.993303 | − | 0.115536i | \(-0.0368587\pi\) |
0.490378 | + | 0.871510i | \(0.336859\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(108\) | 10.7322 | − | 1.69981i | 1.03270 | − | 0.163564i | ||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −19.6332 | −1.86351 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.67671 | + | 11.1412i | 0.534020 | + | 1.04807i | 0.987620 | + | 0.156868i | \(0.0501397\pi\) |
−0.453599 | + | 0.891206i | \(0.649860\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.1622 | − | 12.2211i | 1.41388 | − | 1.13962i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 18.9258 | + | 6.14936i | 1.69959 | + | 0.552229i | ||||
\(125\) | 10.6093 | + | 3.52744i | 0.948924 | + | 0.315504i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.7273 | − | 3.17096i | −1.00933 | − | 0.272913i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.3095 | − | 2.89995i | −1.56429 | − | 0.247759i | −0.686617 | − | 0.727019i | \(-0.740905\pi\) |
−0.877673 | + | 0.479260i | \(0.840905\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.02915 | + | 3.65389i | 0.423531 | + | 0.307713i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | − | 1.26650i | − | 0.105542i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.20578 | + | 10.2169i | −0.429365 | + | 0.842677i | ||||
\(148\) | −3.74985 | + | 23.6756i | −0.308236 | + | 1.94612i | ||||
\(149\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.5000 | − | 14.9248i | −1.32531 | − | 1.19879i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.22206 | − | 4.18935i | 0.656192 | − | 0.334346i | −0.0939948 | − | 0.995573i | \(-0.529964\pi\) |
0.750186 | + | 0.661226i | \(0.229964\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.1174 | − | 18.0545i | −1.04028 | − | 1.43182i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.72359 | + | 0.431374i | −0.213328 | + | 0.0337878i | −0.262184 | − | 0.965018i | \(-0.584443\pi\) |
0.0488556 | + | 0.998806i | \(0.484443\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.3637 | − | 4.01722i | 0.951057 | − | 0.309017i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.84169 | + | 3.84169i | 0.288759 | + | 0.288759i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.9722 | − | 6.48936i | −1.49279 | − | 0.485037i | −0.554885 | − | 0.831927i | \(-0.687238\pi\) |
−0.937906 | + | 0.346890i | \(0.887238\pi\) | |||||||
\(180\) | −0.578878 | + | 1.29226i | −0.0431470 | + | 0.0963191i | ||||
\(181\) | −8.04962 | + | 5.84839i | −0.598323 | + | 0.434707i | −0.845283 | − | 0.534318i | \(-0.820568\pi\) |
0.246960 | + | 0.969026i | \(0.420568\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.6475 | − | 22.4432i | 1.07691 | − | 1.65006i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 5.36675 | − | 5.36675i | 0.391411 | − | 0.391411i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.17425 | − | 22.0801i | −0.519111 | − | 1.59766i | −0.775676 | − | 0.631132i | \(-0.782591\pi\) |
0.256565 | − | 0.966527i | \(-0.417409\pi\) | |||||||
\(192\) | 12.9435 | + | 2.05004i | 0.934114 | + | 0.147949i | ||||
\(193\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.3262 | + | 8.22899i | 0.809017 | + | 0.587785i | ||||
\(197\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.8997i | 1.41066i | 0.708881 | + | 0.705328i | \(0.249200\pi\) | ||||
−0.708881 | + | 0.705328i | \(0.750800\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.09176 | − | 3.36008i | 0.0770066 | − | 0.237002i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.431374 | − | 2.72359i | −0.0299826 | − | 0.189303i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(212\) | −24.2772 | + | 12.3699i | −1.66737 | + | 0.849565i | ||||
\(213\) | −4.37868 | − | 2.23105i | −0.300022 | − | 0.152869i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.90334 | + | 19.4364i | 0.663177 | + | 1.30156i | 0.940177 | + | 0.340687i | \(0.110660\pi\) |
−0.277000 | + | 0.960870i | \(0.589340\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.18130 | − | 1.05395i | 0.0787534 | − | 0.0702633i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.5452 | + | 24.1489i | −1.15942 | + | 1.59580i | −0.446055 | + | 0.895005i | \(0.647172\pi\) |
−0.713362 | + | 0.700796i | \(0.752828\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.92887 | + | 3.02292i | −0.517222 | + | 0.197194i | ||||
\(236\) | 5.36641 | − | 3.89893i | 0.349324 | − | 0.253798i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(240\) | −12.2697 | − | 8.00779i | −0.792005 | − | 0.516901i | ||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.31662 | + | 2.31662i | −0.148612 | + | 0.148612i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.79536 | − | 13.5732i | −0.498027 | − | 0.867161i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.8435 | − | 15.8702i | −1.37875 | − | 1.00172i | −0.996996 | − | 0.0774530i | \(-0.975321\pi\) |
−0.381751 | − | 0.924265i | \(-0.624679\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.94427 | − | 15.2169i | 0.309017 | − | 0.951057i | ||||
\(257\) | 2.73926 | − | 5.37610i | 0.170870 | − | 0.335352i | −0.789652 | − | 0.613555i | \(-0.789739\pi\) |
0.960522 | + | 0.278203i | \(0.0897388\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 30.4248 | − | 1.52506i | 1.86898 | − | 0.0936839i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.1360 | − | 6.69314i | 0.803912 | − | 0.409614i | ||||
\(268\) | −3.84338 | − | 1.95830i | −0.234772 | − | 0.119622i | ||||
\(269\) | 7.79785 | + | 10.7328i | 0.475443 | + | 0.654392i | 0.977621 | − | 0.210373i | \(-0.0674677\pi\) |
−0.502178 | + | 0.864764i | \(0.667468\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 28.5330 | 1.71748 | ||||||||
\(277\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.99619 | + | 0.973520i | −0.179377 | + | 0.0582831i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(284\) | −3.52671 | + | 4.85410i | −0.209272 | + | 0.288038i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.1680 | + | 5.25329i | 0.951057 | + | 0.309017i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 25.2546 | − | 18.3485i | 1.48045 | − | 1.07561i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.25763 | + | 1.52540i | −0.422555 | + | 0.0888121i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 8.85910 | + | 13.7787i | 0.511481 | + | 0.795516i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 27.6834i | − | 1.57485i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.70820 | − | 11.4127i | 0.210273 | − | 0.647154i | −0.789183 | − | 0.614159i | \(-0.789495\pi\) |
0.999456 | − | 0.0329949i | \(-0.0105045\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.20014 | − | 7.57739i | 0.0678360 | − | 0.428299i | −0.930275 | − | 0.366863i | \(-0.880432\pi\) |
0.998111 | − | 0.0614365i | \(-0.0195682\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.418529 | + | 2.64249i | 0.0235069 | + | 0.148417i | 0.996650 | − | 0.0817838i | \(-0.0260617\pi\) |
−0.973143 | + | 0.230201i | \(0.926062\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −12.0000 | + | 13.2665i | −0.670820 | + | 0.741620i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −9.34564 | − | 12.8632i | −0.519202 | − | 0.714620i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.94987 | 0.546895 | 0.273447 | − | 0.961887i | \(-0.411836\pi\) | ||||
0.273447 | + | 0.961887i | \(0.411836\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.72283 | − | 3.38125i | −0.0944107 | − | 0.185291i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.02647 | + | 3.75482i | 0.165354 | + | 0.205148i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.0395 | − | 16.5710i | 0.653898 | − | 0.900013i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −29.1133 | − | 13.0415i | −1.56741 | − | 0.702133i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.7414 | − | 22.7414i | 1.21040 | − | 1.21040i | 0.239511 | − | 0.970894i | \(-0.423013\pi\) |
0.970894 | − | 0.239511i | \(-0.0769871\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.81709 | − | 3.34087i | 0.308739 | − | 0.177315i | ||||
\(356\) | −5.56231 | − | 17.1190i | −0.294802 | − | 0.907306i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.3713 | + | 11.1679i | 0.809017 | + | 0.587785i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.0718 | − | 29.5801i | 0.786744 | − | 1.54407i | −0.0514358 | − | 0.998676i | \(-0.516380\pi\) |
0.838179 | − | 0.545395i | \(-0.183620\pi\) | |||||||
\(368\) | 5.44966 | − | 34.4078i | 0.284083 | − | 1.79363i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −5.09942 | − | 32.1965i | −0.264393 | − | 1.66931i | ||||
\(373\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.74144 | − | 18.1082i | −0.141567 | − | 0.935103i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.5452 | + | 24.1489i | 0.901235 | + | 1.24044i | 0.970073 | + | 0.242815i | \(0.0780709\pi\) |
−0.0688378 | + | 0.997628i | \(0.521929\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.5540 | + | 4.68089i | −1.51014 | + | 0.239182i | −0.855914 | − | 0.517119i | \(-0.827005\pi\) |
−0.654224 | + | 0.756301i | \(0.727005\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −17.3029 | − | 33.9588i | −0.878421 | − | 1.72400i | ||||
\(389\) | −34.6973 | + | 11.2738i | −1.75922 | + | 0.571606i | −0.997119 | − | 0.0758507i | \(-0.975833\pi\) |
−0.762102 | + | 0.647456i | \(0.775833\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.8997 | + | 18.8997i | 0.948551 | + | 0.948551i | 0.998740 | − | 0.0501886i | \(-0.0159822\pi\) |
−0.0501886 | + | 0.998740i | \(0.515982\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18.3078 | − | 8.05147i | 0.915388 | − | 0.402574i | ||||
\(401\) | −21.4656 | + | 15.5957i | −1.07194 | + | 0.778812i | −0.976261 | − | 0.216600i | \(-0.930503\pi\) |
−0.0956827 | + | 0.995412i | \(0.530503\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.65635 | + | 17.3964i | 0.181685 | + | 0.864433i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.38384 | + | 28.8805i | 0.462871 | + | 1.42457i | ||||
\(412\) | −33.3832 | − | 5.28738i | −1.64467 | − | 0.260491i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.0000i | 1.17248i | 0.810139 | + | 0.586238i | \(0.199392\pi\) | ||||
−0.810139 | + | 0.586238i | \(0.800608\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.2987 | + | 37.8516i | −0.599403 | + | 1.84477i | −0.0679432 | + | 0.997689i | \(0.521644\pi\) |
−0.531460 | + | 0.847084i | \(0.678356\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.187964 | + | 1.18676i | −0.00913910 | + | 0.0577020i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(432\) | −19.3632 | + | 9.86606i | −0.931614 | + | 0.474681i | ||||
\(433\) | −0.535294 | − | 0.272746i | −0.0257246 | − | 0.0131073i | 0.441081 | − | 0.897467i | \(-0.354595\pi\) |
−0.466805 | + | 0.884360i | \(0.654595\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.21637 | −0.105542 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.97031 | − | 9.75478i | −0.236146 | − | 0.463464i | 0.742271 | − | 0.670099i | \(-0.233748\pi\) |
−0.978418 | + | 0.206636i | \(0.933748\pi\) | |||||||
\(444\) | 37.3447 | − | 12.1340i | 1.77230 | − | 0.575855i | ||||
\(445\) | −2.14915 | + | 20.0095i | −0.101879 | + | 0.948543i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.9236 | − | 31.5517i | 1.08183 | − | 1.48902i | 0.224346 | − | 0.974510i | \(-0.427976\pi\) |
0.857487 | − | 0.514505i | \(-0.172024\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −17.6834 | − | 17.6834i | −0.831756 | − | 0.831756i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −21.2872 | + | 32.6167i | −0.992522 | + | 1.52076i | ||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.4248 | + | 30.4248i | −1.41396 | + | 1.41396i | −0.693615 | + | 0.720346i | \(0.743983\pi\) |
−0.720346 | + | 0.693615i | \(0.756017\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.51288 | + | 35.1820i | −0.441149 | + | 1.63153i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.0171 | + | 4.43748i | 1.29648 | + | 0.205342i | 0.766267 | − | 0.642523i | \(-0.222112\pi\) |
0.530212 | + | 0.847865i | \(0.322112\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.2292 | − | 8.88503i | −0.563492 | − | 0.409401i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.95830 | − | 3.84338i | 0.0896645 | − | 0.175976i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.13325 | + | 42.5581i | 0.0968659 | + | 1.93246i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.8228 | − | 10.6097i | 0.943571 | − | 0.480773i | 0.0866600 | − | 0.996238i | \(-0.472381\pi\) |
0.856911 | + | 0.515465i | \(0.172381\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.65510 | + | 3.65443i | 0.120068 | + | 0.165259i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −39.7995 | −1.78705 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.9258 | + | 6.14936i | −0.847235 | + | 0.275283i | −0.700287 | − | 0.713861i | \(-0.746945\pi\) |
−0.146947 | + | 0.989144i | \(0.546945\pi\) | |||||||
\(500\) | −22.3602 | − | 0.152689i | −0.999977 | − | 0.00682845i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.0581 | − | 15.0581i | −0.668752 | − | 0.668752i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.15430 | + | 1.02489i | 0.139812 | + | 0.0454276i | 0.378087 | − | 0.925770i | \(-0.376582\pi\) |
−0.238275 | + | 0.971198i | \(0.576582\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 31.6454 | + | 20.6534i | 1.39446 | + | 0.910095i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.3236 | + | 41.0059i | 0.583718 | + | 1.79650i | 0.604358 | + | 0.796713i | \(0.293430\pi\) |
−0.0206400 | + | 0.999787i | \(0.506570\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 52.8496i | − | 2.29781i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.324507 | + | 0.998729i | −0.0140824 | + | 0.0433411i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.38136 | + | 33.9766i | 0.232223 | + | 1.46620i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 24.2665 | − | 1.21637i | 1.04426 | − | 0.0523444i | ||||
\(541\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.5224 | + | 7.39955i | 0.623217 | + | 0.317545i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(548\) | 36.6191 | − | 5.79989i | 1.56429 | − | 0.247759i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −43.6502 | − | 4.68830i | −1.85285 | − | 0.199007i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(564\) | −11.8242 | − | 3.84193i | −0.497891 | − | 0.161774i | ||||
\(565\) | 9.96048 | + | 26.1255i | 0.419041 | + | 1.09911i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −26.8918 | + | 26.8918i | −1.12342 | + | 1.12342i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 36.6282 | − | 23.5503i | 1.52750 | − | 0.982114i | ||||
\(576\) | 0.782740 | + | 2.40902i | 0.0326141 | + | 0.100376i | ||||
\(577\) | 39.7739 | + | 6.29956i | 1.65581 | + | 0.262254i | 0.913212 | − | 0.407486i | \(-0.133594\pi\) |
0.742596 | + | 0.669740i | \(0.233594\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.5384 | + | 34.4210i | −0.723885 | + | 1.42070i | 0.175916 | + | 0.984405i | \(0.443711\pi\) |
−0.899801 | + | 0.436300i | \(0.856289\pi\) | |||||||
\(588\) | 3.58758 | − | 22.6511i | 0.147949 | − | 0.934114i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.49970 | − | 47.3512i | −0.308236 | − | 1.94612i | ||||
\(593\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 29.0449 | − | 14.7991i | 1.18873 | − | 0.605686i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.1603 | + | 29.1246i | 0.864585 | + | 1.19000i | 0.980457 | + | 0.196735i | \(0.0630339\pi\) |
−0.115872 | + | 0.993264i | \(0.536966\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.674478 | − | 0.106827i | 0.0274669 | − | 0.00435032i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34.2665 | − | 34.2665i | −1.37952 | − | 1.37952i | −0.845428 | − | 0.534089i | \(-0.820655\pi\) |
−0.534089 | − | 0.845428i | \(-0.679345\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.951057 | − | 0.309017i | −0.0382262 | − | 0.0124204i | 0.289841 | − | 0.957075i | \(-0.406397\pi\) |
−0.328068 | + | 0.944654i | \(0.606397\pi\) | |||||||
\(620\) | 40.6089 | + | 18.1911i | 1.63089 | + | 0.730573i | ||||
\(621\) | −38.2800 | + | 27.8120i | −1.53612 | + | 1.11606i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.7451 | + | 10.3759i | 0.909804 | + | 0.415037i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13.0501 | + | 13.0501i | −0.520757 | + | 0.520757i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.16312 | + | 6.65740i | 0.0861124 | + | 0.265027i | 0.984836 | − | 0.173489i | \(-0.0555042\pi\) |
−0.898723 | + | 0.438516i | \(0.855504\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 36.1091 | + | 26.2348i | 1.43182 | + | 1.04028i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 0.949874i | − | 0.0375764i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.17425 | + | 22.0801i | −0.283366 | + | 0.872111i | 0.703518 | + | 0.710678i | \(0.251612\pi\) |
−0.986884 | + | 0.161433i | \(0.948388\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.83709 | − | 49.4815i | 0.309065 | − | 1.95136i | 0.000979141 | − | 1.00000i | \(-0.499688\pi\) |
0.308086 | − | 0.951359i | \(-0.400312\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.75596 | + | 48.9692i | 0.304918 | + | 1.92518i | 0.373709 | + | 0.927546i | \(0.378086\pi\) |
−0.0687910 | + | 0.997631i | \(0.521914\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.91397 | − | 2.50379i | 0.192446 | − | 0.0980561i | ||||
\(653\) | −30.0423 | − | 15.3073i | −1.17565 | − | 0.599021i | −0.246647 | − | 0.969105i | \(-0.579329\pi\) |
−0.928998 | + | 0.370084i | \(0.879329\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.0000 | −0.505641 | −0.252821 | − | 0.967513i | \(-0.581358\pi\) | ||||
−0.252821 | + | 0.967513i | \(0.581358\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.0036 | − | 28.9090i | 0.812047 | − | 1.11769i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.3160 | − | 9.85035i | −0.974412 | − | 0.379140i | ||||
\(676\) | −21.0344 | + | 15.2824i | −0.809017 | + | 0.587785i | ||||
\(677\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.2164 | + | 11.2164i | −0.429183 | + | 0.429183i | −0.888350 | − | 0.459167i | \(-0.848148\pi\) |
0.459167 | + | 0.888350i | \(0.348148\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −40.0148 | − | 10.8196i | −1.52889 | − | 0.413396i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 48.2947 | + | 7.64913i | 1.84256 | + | 0.291832i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.7533 | − | 9.99235i | −0.523200 | − | 0.380127i | 0.294608 | − | 0.955618i | \(-0.404811\pi\) |
−0.817808 | + | 0.575491i | \(0.804811\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.3087 | + | 9.32456i | 0.388248 | + | 0.351183i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −9.68162 | − | 4.93303i | −0.363857 | − | 0.185395i | ||||
\(709\) | −11.1679 | − | 15.3713i | −0.419420 | − | 0.577282i | 0.546064 | − | 0.837743i | \(-0.316125\pi\) |
−0.965484 | + | 0.260461i | \(0.916125\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −85.5883 | + | 13.5558i | −3.20531 | + | 0.507671i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 42.0000 | 1.56961 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 48.5039 | − | 15.7599i | 1.80889 | − | 0.587744i | 0.808890 | − | 0.587961i | \(-0.200069\pi\) |
1.00000 | 0.000216702i | \(6.89785e-5\pi\) | ||||||||
\(720\) | 0.302432 | − | 2.81578i | 0.0112710 | − | 0.104938i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.6968 | − | 16.0992i | 0.434707 | − | 0.598323i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.5251 | + | 21.5251i | 0.798320 | + | 0.798320i | 0.982831 | − | 0.184510i | \(-0.0590699\pi\) |
−0.184510 | + | 0.982831i | \(0.559070\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.7864 | + | 9.02836i | 1.02913 | + | 0.334384i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −14.0136 | + | 21.4720i | −0.516901 | + | 0.792005i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(740\) | −13.9906 | + | 51.7421i | −0.514303 | + | 1.90208i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.10739 | + | 21.8743i | −0.259352 | + | 0.798205i | 0.733588 | + | 0.679594i | \(0.237844\pi\) |
−0.992941 | + | 0.118611i | \(0.962156\pi\) | |||||||
\(752\) | −6.89133 | + | 13.5250i | −0.251301 | + | 0.493206i | ||||
\(753\) | −6.91890 | + | 43.6842i | −0.252139 | + | 1.59194i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.60586 | − | 54.3353i | −0.312785 | − | 1.97485i | −0.179232 | − | 0.983807i | \(-0.557361\pi\) |
−0.133554 | − | 0.991042i | \(-0.542639\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 27.2925 | + | 37.5649i | 0.987407 | + | 1.35905i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −25.8869 | + | 4.10009i | −0.934114 | + | 0.147949i | ||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.88388 | −0.355959 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.0763 | − | 25.6636i | −0.470320 | − | 0.923056i | −0.997318 | − | 0.0731890i | \(-0.976682\pi\) |
0.526998 | − | 0.849867i | \(-0.323318\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −33.1202 | − | 37.1221i | −1.18971 | − | 1.33347i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −26.6296 | − | 8.65248i | −0.951057 | − | 0.309017i | ||||
\(785\) | 19.2803 | − | 7.35072i | 0.688145 | − | 0.262358i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −24.8523 | − | 43.2726i | −0.881421 | − | 1.53472i | ||||
\(796\) | −12.2987 | − | 37.8516i | −0.435917 | − | 1.34161i | ||||
\(797\) | −41.4729 | − | 6.56866i | −1.46905 | − | 0.232674i | −0.629940 | − | 0.776644i | \(-0.716921\pi\) |
−0.839105 | + | 0.543970i | \(0.816921\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.30539 | + | 1.67497i | 0.0814571 | + | 0.0591820i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 7.06600i | 0.249198i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.86606 | − | 19.3632i | 0.347302 | − | 0.681618i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.15831 | + | 0.308689i | −0.215716 | + | 0.0108129i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.3746 | + | 2.11834i | −0.466211 | + | 0.0738405i | −0.385121 | − | 0.922866i | \(-0.625840\pi\) |
−0.0810902 | + | 0.996707i | \(0.525840\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(828\) | 2.50379 | + | 4.91397i | 0.0870128 | + | 0.170772i | ||||
\(829\) | −27.5806 | + | 8.96149i | −0.957915 | + | 0.311246i | −0.745928 | − | 0.666027i | \(-0.767994\pi\) |
−0.211987 | + | 0.977272i | \(0.567994\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 38.2243 | + | 38.2243i | 1.32123 | + | 1.32123i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34.6973 | + | 11.2738i | 1.19788 | + | 0.389216i | 0.838982 | − | 0.544160i | \(-0.183151\pi\) |
0.358901 | + | 0.933376i | \(0.383151\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.4615 | − | 17.0458i | 0.809017 | − | 0.587785i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 28.4473 | − | 5.97903i | 0.978618 | − | 0.205685i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 38.5330 | − | 38.5330i | 1.32323 | − | 1.32323i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32.2560 | − | 99.2738i | −1.10572 | − | 3.40306i | ||||
\(852\) | 9.70760 | + | 1.53753i | 0.332577 | + | 0.0526750i | ||||
\(853\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 31.0000i | − | 1.05771i | −0.848713 | − | 0.528853i | \(-0.822622\pi\) | ||
0.848713 | − | 0.528853i | \(-0.177378\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.11837 | − | 57.5711i | 0.310393 | − | 1.95974i | 0.0311832 | − | 0.999514i | \(-0.490072\pi\) |
0.279210 | − | 0.960230i | \(-0.409928\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.35634 | − | 27.5049i | −0.147949 | − | 0.934114i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.37610 | + | 2.73926i | 0.181954 | + | 0.0927099i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 57.0000 | 1.92038 | 0.960189 | − | 0.279350i | \(-0.0901189\pi\) | ||||
0.960189 | + | 0.279350i | \(0.0901189\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.5889 | + | 22.7445i | 0.389997 | + | 0.765413i | 0.999628 | − | 0.0272727i | \(-0.00868225\pi\) |
−0.609631 | + | 0.792686i | \(0.708682\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.62378 | + | 9.45852i | 0.256271 | + | 0.317945i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −30.8496 | − | 30.8496i | −1.03292 | − | 1.03292i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −42.8542 | − | 19.1969i | −1.43246 | − | 0.641682i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −1.59559 | + | 2.73482i | −0.0531863 | + | 0.0911605i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19.2931 | + | 11.0804i | −0.641325 | + | 0.368325i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.1068 | + | 5.71876i | 1.19891 | + | 0.189888i | 0.723781 | − | 0.690030i | \(-0.242403\pi\) |
0.475126 | + | 0.879918i | \(0.342403\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.36641 | + | 3.89893i | 0.177797 | + | 0.129177i | 0.673124 | − | 0.739529i | \(-0.264952\pi\) |
−0.495327 | + | 0.868706i | \(0.664952\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.4481 | − | 56.7774i | 0.609542 | − | 1.87598i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 37.9248 | − | 46.3997i | 1.24696 | − | 1.52561i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.76765 | − | 2.42924i | 0.156590 | − | 0.0797866i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.1914 | − | 42.9313i | −1.02336 | − | 1.40853i | −0.909823 | − | 0.414996i | \(-0.863783\pi\) |
−0.113534 | − | 0.993534i | \(-0.536217\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19.4152 | + | 3.07507i | −0.635625 | + | 0.100673i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.9522 | + | 3.88349i | −0.390044 | + | 0.126733i | ||||
\(940\) | 13.2133 | − | 10.6502i | 0.430972 | − | 0.347373i | ||||
\(941\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −7.79785 | + | 10.7328i | −0.253798 | + | 0.349324i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.8918 | − | 16.8918i | −0.548910 | − | 0.548910i | 0.377215 | − | 0.926126i | \(-0.376882\pi\) |
−0.926126 | + | 0.377215i | \(0.876882\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.54562 | − | 2.57604i | 0.114974 | − | 0.0835338i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.6778 | − | 50.8034i | −0.345525 | − | 1.64396i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 28.2874 | + | 7.64864i | 0.912973 | + | 0.246859i | ||||
\(961\) | 21.0132 | + | 64.6718i | 0.677844 | + | 2.08619i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.3236 | − | 41.0059i | 0.427575 | − | 1.31594i | −0.472932 | − | 0.881099i | \(-0.656804\pi\) |
0.900507 | − | 0.434842i | \(-0.143196\pi\) | |||||||
\(972\) | 2.97473 | − | 5.83824i | 0.0954145 | − | 0.187261i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.25018 | − | 20.5209i | −0.103983 | − | 0.656520i | −0.983535 | − | 0.180718i | \(-0.942158\pi\) |
0.879552 | − | 0.475802i | \(-0.157842\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 23.2164 | + | 21.0000i | 0.741620 | + | 0.670820i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.14632 | − | 4.66028i | −0.291722 | − | 0.148640i | 0.302005 | − | 0.953306i | \(-0.402344\pi\) |
−0.593727 | + | 0.804666i | \(0.702344\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 59.6992 | 1.89641 | 0.948205 | − | 0.317660i | \(-0.102897\pi\) | ||||
0.948205 | + | 0.317660i | \(0.102897\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.39955 | − | 14.5224i | −0.234817 | − | 0.460855i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.75194 | + | 44.2427i | −0.150647 | + | 1.40259i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −38.2743 | + | 52.6800i | −1.21095 | + | 1.66672i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))