Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(19,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.w (of order \(12\), degree \(4\), 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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 619.2 | ||
Character | \(\chi\) | \(=\) | 784.619 |
Dual form | 784.2.w.e.19.2 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41028 | − | 0.105414i | −0.997218 | − | 0.0745392i | ||||
\(3\) | 0.551303 | + | 2.05749i | 0.318295 | + | 1.18789i | 0.920882 | + | 0.389841i | \(0.127470\pi\) |
−0.602587 | + | 0.798053i | \(0.705863\pi\) | |||||||
\(4\) | 1.97778 | + | 0.297327i | 0.988888 | + | 0.148664i | ||||
\(5\) | 3.47044 | + | 0.929901i | 1.55203 | + | 0.415864i | 0.930129 | − | 0.367233i | \(-0.119695\pi\) |
0.621898 | + | 0.783098i | \(0.286362\pi\) | |||||||
\(6\) | −0.560603 | − | 2.95975i | −0.228865 | − | 1.20831i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.75787 | − | 0.627801i | −0.975056 | − | 0.221961i | ||||
\(9\) | −1.33126 | + | 0.768605i | −0.443754 | + | 0.256202i | ||||
\(10\) | −4.79626 | − | 1.67725i | −1.51671 | − | 0.530394i | ||||
\(11\) | −0.732051 | − | 2.73205i | −0.220722 | − | 0.823744i | −0.984074 | − | 0.177762i | \(-0.943114\pi\) |
0.763352 | − | 0.645983i | \(-0.223552\pi\) | |||||||
\(12\) | 0.478606 | + | 4.23318i | 0.138162 | + | 1.22201i | ||||
\(13\) | 1.17573 | + | 1.17573i | 0.326090 | + | 0.326090i | 0.851098 | − | 0.525008i | \(-0.175938\pi\) |
−0.525008 | + | 0.851098i | \(0.675938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.65306i | 1.97601i | ||||||||
\(16\) | 3.82319 | + | 1.17609i | 0.955798 | + | 0.294023i | ||||
\(17\) | 5.31204 | + | 3.06691i | 1.28836 | + | 0.743834i | 0.978361 | − | 0.206903i | \(-0.0663386\pi\) |
0.309997 | + | 0.950737i | \(0.399672\pi\) | |||||||
\(18\) | 1.95848 | − | 0.943614i | 0.461617 | − | 0.222412i | ||||
\(19\) | −1.33846 | − | 0.358639i | −0.307063 | − | 0.0822774i | 0.101997 | − | 0.994785i | \(-0.467477\pi\) |
−0.409060 | + | 0.912507i | \(0.634143\pi\) | |||||||
\(20\) | 6.58726 | + | 2.87099i | 1.47296 | + | 0.641973i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.744399 | + | 3.93012i | 0.158706 | + | 0.837905i | ||||
\(23\) | −0.103594 | − | 0.179430i | −0.0216009 | − | 0.0374138i | 0.855023 | − | 0.518590i | \(-0.173543\pi\) |
−0.876624 | + | 0.481176i | \(0.840210\pi\) | |||||||
\(24\) | −0.228730 | − | 6.02041i | −0.0466893 | − | 1.22891i | ||||
\(25\) | 6.84910 | + | 3.95433i | 1.36982 | + | 0.790866i | ||||
\(26\) | −1.53417 | − | 1.78205i | −0.300876 | − | 0.349489i | ||||
\(27\) | 2.20324 | + | 2.20324i | 0.424013 | + | 0.424013i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.46733 | + | 3.46733i | −0.643868 | + | 0.643868i | −0.951504 | − | 0.307636i | \(-0.900462\pi\) |
0.307636 | + | 0.951504i | \(0.400462\pi\) | |||||||
\(30\) | 0.806742 | − | 10.7930i | 0.147290 | − | 1.97051i | ||||
\(31\) | 2.87099 | − | 4.97270i | 0.515645 | − | 0.893124i | −0.484190 | − | 0.874963i | \(-0.660886\pi\) |
0.999835 | − | 0.0181610i | \(-0.00578115\pi\) | |||||||
\(32\) | −5.26779 | − | 2.06164i | −0.931223 | − | 0.364450i | ||||
\(33\) | 5.21759 | − | 3.01238i | 0.908266 | − | 0.524388i | ||||
\(34\) | −7.16816 | − | 4.88516i | −1.22933 | − | 0.837798i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.86147 | + | 1.12431i | −0.476911 | + | 0.187385i | ||||
\(37\) | −0.0935566 | + | 0.349158i | −0.0153806 | + | 0.0574012i | −0.973190 | − | 0.230004i | \(-0.926126\pi\) |
0.957809 | + | 0.287405i | \(0.0927927\pi\) | |||||||
\(38\) | 1.84979 | + | 0.646874i | 0.300076 | + | 0.104937i | ||||
\(39\) | −1.77088 | + | 3.06725i | −0.283567 | + | 0.491153i | ||||
\(40\) | −8.98724 | − | 4.74329i | −1.42101 | − | 0.749981i | ||||
\(41\) | −6.75794 | −1.05541 | −0.527707 | − | 0.849427i | \(-0.676948\pi\) | ||||
−0.527707 | + | 0.849427i | \(0.676948\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.207188 | − | 0.207188i | 0.0315959 | − | 0.0315959i | −0.691132 | − | 0.722728i | \(-0.742888\pi\) |
0.722728 | + | 0.691132i | \(0.242888\pi\) | |||||||
\(44\) | −0.635519 | − | 5.62104i | −0.0958080 | − | 0.847404i | ||||
\(45\) | −5.33479 | + | 1.42945i | −0.795264 | + | 0.213090i | ||||
\(46\) | 0.127182 | + | 0.263967i | 0.0187520 | + | 0.0389198i | ||||
\(47\) | −5.46606 | − | 9.46749i | −0.797307 | − | 1.38098i | −0.921364 | − | 0.388700i | \(-0.872924\pi\) |
0.124058 | − | 0.992275i | \(-0.460409\pi\) | |||||||
\(48\) | −0.312065 | + | 8.51457i | −0.0450426 | + | 1.22897i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −9.24230 | − | 6.29870i | −1.30706 | − | 0.890771i | ||||
\(51\) | −3.38159 | + | 12.6203i | −0.473518 | + | 1.76719i | ||||
\(52\) | 1.97576 | + | 2.67492i | 0.273989 | + | 0.370944i | ||||
\(53\) | 9.82209 | − | 2.63182i | 1.34917 | − | 0.361508i | 0.489340 | − | 0.872093i | \(-0.337238\pi\) |
0.859828 | + | 0.510584i | \(0.170571\pi\) | |||||||
\(54\) | −2.87493 | − | 3.33943i | −0.391228 | − | 0.454439i | ||||
\(55\) | − | 10.1621i | − | 1.37026i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.95159i | − | 0.390947i | ||||||
\(58\) | 5.25542 | − | 4.52440i | 0.690070 | − | 0.594083i | ||||
\(59\) | −2.77653 | + | 0.743968i | −0.361473 | + | 0.0968564i | −0.434984 | − | 0.900438i | \(-0.643246\pi\) |
0.0735115 | + | 0.997294i | \(0.476579\pi\) | |||||||
\(60\) | −2.27546 | + | 15.1360i | −0.293761 | + | 1.95405i | ||||
\(61\) | −2.74979 | + | 10.2623i | −0.352074 | + | 1.31396i | 0.532053 | + | 0.846711i | \(0.321421\pi\) |
−0.884127 | + | 0.467247i | \(0.845246\pi\) | |||||||
\(62\) | −4.57310 | + | 6.71026i | −0.580784 | + | 0.852204i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.21173 | + | 3.46279i | 0.901467 | + | 0.432849i | ||||
\(65\) | 2.98700 | + | 5.17363i | 0.370491 | + | 0.641710i | ||||
\(66\) | −7.67581 | + | 3.69829i | −0.944827 | + | 0.455227i | ||||
\(67\) | −1.33671 | + | 0.358169i | −0.163305 | + | 0.0437573i | −0.339545 | − | 0.940590i | \(-0.610273\pi\) |
0.176240 | + | 0.984347i | \(0.443606\pi\) | |||||||
\(68\) | 9.59414 | + | 7.64507i | 1.16346 | + | 0.927101i | ||||
\(69\) | 0.312065 | − | 0.312065i | 0.0375682 | − | 0.0375682i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.09683 | 0.248847 | 0.124424 | − | 0.992229i | \(-0.460292\pi\) | ||||
0.124424 | + | 0.992229i | \(0.460292\pi\) | |||||||
\(72\) | 4.15399 | − | 1.28395i | 0.489552 | − | 0.151315i | ||||
\(73\) | −1.36480 | + | 2.36391i | −0.159738 | + | 0.276675i | −0.934774 | − | 0.355242i | \(-0.884398\pi\) |
0.775036 | + | 0.631917i | \(0.217732\pi\) | |||||||
\(74\) | 0.168747 | − | 0.482548i | 0.0196165 | − | 0.0560950i | ||||
\(75\) | −4.36007 | + | 16.2720i | −0.503458 | + | 1.87893i | ||||
\(76\) | −2.54054 | − | 1.10727i | −0.291420 | − | 0.127012i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.82076 | − | 4.13900i | 0.319389 | − | 0.468650i | ||||
\(79\) | −9.55355 | + | 5.51575i | −1.07486 | + | 0.620570i | −0.929505 | − | 0.368810i | \(-0.879765\pi\) |
−0.145354 | + | 0.989380i | \(0.546432\pi\) | |||||||
\(80\) | 12.1745 | + | 7.63675i | 1.36115 | + | 0.853815i | ||||
\(81\) | −5.62431 | + | 9.74159i | −0.624923 | + | 1.08240i | ||||
\(82\) | 9.53059 | + | 0.712384i | 1.05248 | + | 0.0786697i | ||||
\(83\) | 2.27616 | − | 2.27616i | 0.249841 | − | 0.249841i | −0.571065 | − | 0.820905i | \(-0.693469\pi\) |
0.820905 | + | 0.571065i | \(0.193469\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15.5832 | + | 15.5832i | 1.69023 | + | 1.69023i | ||||
\(86\) | −0.314034 | + | 0.270353i | −0.0338631 | + | 0.0291529i | ||||
\(87\) | −9.04557 | − | 5.22246i | −0.969787 | − | 0.559907i | ||||
\(88\) | 0.303720 | + | 7.99423i | 0.0323767 | + | 0.852188i | ||||
\(89\) | −7.04071 | − | 12.1949i | −0.746314 | − | 1.29265i | −0.949578 | − | 0.313530i | \(-0.898488\pi\) |
0.203264 | − | 0.979124i | \(-0.434845\pi\) | |||||||
\(90\) | 7.67424 | − | 1.45357i | 0.808935 | − | 0.153219i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.151536 | − | 0.385674i | −0.0157988 | − | 0.0402093i | ||||
\(93\) | 11.8141 | + | 3.16558i | 1.22506 | + | 0.328255i | ||||
\(94\) | 6.71066 | + | 13.9280i | 0.692152 | + | 1.43656i | ||||
\(95\) | −4.31154 | − | 2.48927i | −0.442355 | − | 0.255394i | ||||
\(96\) | 1.33766 | − | 11.9750i | 0.136524 | − | 1.22220i | ||||
\(97\) | 2.83866i | 0.288223i | 0.989561 | + | 0.144111i | \(0.0460323\pi\) | ||||
−0.989561 | + | 0.144111i | \(0.953968\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.07442 | + | 3.07442i | 0.308991 | + | 0.308991i | ||||
\(100\) | 12.3703 | + | 9.85720i | 1.23703 | + | 0.985720i | ||||
\(101\) | −1.81478 | − | 6.77286i | −0.180578 | − | 0.673925i | −0.995534 | − | 0.0944028i | \(-0.969906\pi\) |
0.814956 | − | 0.579522i | \(-0.196761\pi\) | |||||||
\(102\) | 6.09935 | − | 17.4416i | 0.603925 | − | 1.72698i | ||||
\(103\) | 11.9500 | − | 6.89933i | 1.17747 | − | 0.679811i | 0.222040 | − | 0.975038i | \(-0.428728\pi\) |
0.955427 | + | 0.295227i | \(0.0953951\pi\) | |||||||
\(104\) | −2.50440 | − | 3.98065i | −0.245577 | − | 0.390335i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.1293 | + | 2.67621i | −1.37236 | + | 0.259937i | ||||
\(107\) | −13.4693 | − | 3.60910i | −1.30213 | − | 0.348905i | −0.459875 | − | 0.887983i | \(-0.652106\pi\) |
−0.842256 | + | 0.539078i | \(0.818773\pi\) | |||||||
\(108\) | 3.70243 | + | 5.01259i | 0.356266 | + | 0.482337i | ||||
\(109\) | 1.70933 | + | 6.37931i | 0.163724 | + | 0.611027i | 0.998199 | + | 0.0599816i | \(0.0191042\pi\) |
−0.834475 | + | 0.551045i | \(0.814229\pi\) | |||||||
\(110\) | −1.07124 | + | 14.3315i | −0.102138 | + | 1.36645i | ||||
\(111\) | −0.769968 | −0.0730821 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.2577 | −1.34125 | −0.670626 | − | 0.741796i | \(-0.733974\pi\) | ||||
−0.670626 | + | 0.741796i | \(0.733974\pi\) | |||||||
\(114\) | −0.311140 | + | 4.16256i | −0.0291409 | + | 0.389860i | ||||
\(115\) | −0.192665 | − | 0.719034i | −0.0179661 | − | 0.0670503i | ||||
\(116\) | −7.88854 | + | 5.82668i | −0.732433 | + | 0.540993i | ||||
\(117\) | −2.46889 | − | 0.661536i | −0.228249 | − | 0.0611590i | ||||
\(118\) | 3.99410 | − | 0.756517i | 0.367687 | − | 0.0696430i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 4.80460 | − | 21.1062i | 0.438598 | − | 1.92672i | ||||
\(121\) | 2.59808 | − | 1.50000i | 0.236189 | − | 0.136364i | ||||
\(122\) | 4.95976 | − | 14.1829i | 0.449036 | − | 1.28406i | ||||
\(123\) | −3.72568 | − | 13.9044i | −0.335933 | − | 1.25372i | ||||
\(124\) | 7.15670 | − | 8.98127i | 0.642691 | − | 0.806542i | ||||
\(125\) | 7.38956 | + | 7.38956i | 0.660942 | + | 0.660942i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.16426i | 0.546990i | 0.961873 | + | 0.273495i | \(0.0881797\pi\) | ||||
−0.961873 | + | 0.273495i | \(0.911820\pi\) | |||||||
\(128\) | −9.80553 | − | 5.64372i | −0.866695 | − | 0.498839i | ||||
\(129\) | 0.540512 | + | 0.312065i | 0.0475894 | + | 0.0274758i | ||||
\(130\) | −3.66712 | − | 7.61113i | −0.321628 | − | 0.667541i | ||||
\(131\) | 1.67122 | + | 0.447802i | 0.146015 | + | 0.0391246i | 0.331086 | − | 0.943600i | \(-0.392585\pi\) |
−0.185071 | + | 0.982725i | \(0.559252\pi\) | |||||||
\(132\) | 11.2149 | − | 4.40647i | 0.976131 | − | 0.383534i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.92288 | − | 0.364211i | 0.166112 | − | 0.0314630i | ||||
\(135\) | 5.59741 | + | 9.69499i | 0.481748 | + | 0.834412i | ||||
\(136\) | −12.7245 | − | 11.7930i | −1.09112 | − | 1.01124i | ||||
\(137\) | −6.72332 | − | 3.88171i | −0.574412 | − | 0.331637i | 0.184498 | − | 0.982833i | \(-0.440934\pi\) |
−0.758910 | + | 0.651196i | \(0.774268\pi\) | |||||||
\(138\) | −0.472994 | + | 0.407202i | −0.0402640 | + | 0.0346634i | ||||
\(139\) | 6.45272 | + | 6.45272i | 0.547313 | + | 0.547313i | 0.925663 | − | 0.378350i | \(-0.123508\pi\) |
−0.378350 | + | 0.925663i | \(0.623508\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.4658 | − | 16.4658i | 1.38667 | − | 1.38667i | ||||
\(142\) | −2.95711 | − | 0.221036i | −0.248155 | − | 0.0185489i | ||||
\(143\) | 2.35147 | − | 4.07286i | 0.196640 | − | 0.340590i | ||||
\(144\) | −5.99363 | + | 1.37284i | −0.499469 | + | 0.114403i | ||||
\(145\) | −15.2574 | + | 8.80889i | −1.26706 | + | 0.731539i | ||||
\(146\) | 2.17394 | − | 3.18990i | 0.179917 | − | 0.263998i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.288848 | + | 0.662739i | −0.0237432 | + | 0.0544768i | ||||
\(149\) | 2.13714 | − | 7.97593i | 0.175082 | − | 0.653413i | −0.821456 | − | 0.570272i | \(-0.806838\pi\) |
0.996538 | − | 0.0831417i | \(-0.0264954\pi\) | |||||||
\(150\) | 7.86422 | − | 22.4885i | 0.642111 | − | 1.83618i | ||||
\(151\) | −0.778116 | + | 1.34774i | −0.0633222 | + | 0.109677i | −0.895949 | − | 0.444158i | \(-0.853503\pi\) |
0.832626 | + | 0.553835i | \(0.186836\pi\) | |||||||
\(152\) | 3.46615 | + | 1.82937i | 0.281142 | + | 0.148381i | ||||
\(153\) | −9.42896 | −0.762286 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.5877 | − | 14.5877i | 1.17171 | − | 1.17171i | ||||
\(156\) | −4.41438 | + | 5.53980i | −0.353433 | + | 0.443539i | ||||
\(157\) | 3.89673 | − | 1.04412i | 0.310993 | − | 0.0833302i | −0.0999470 | − | 0.994993i | \(-0.531867\pi\) |
0.410940 | + | 0.911663i | \(0.365201\pi\) | |||||||
\(158\) | 14.0546 | − | 6.77166i | 1.11813 | − | 0.538725i | ||||
\(159\) | 10.8299 | + | 18.7579i | 0.858867 | + | 1.48760i | ||||
\(160\) | −16.3644 | − | 12.0533i | −1.29372 | − | 0.952899i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 8.95875 | − | 13.1455i | 0.703866 | − | 1.03281i | ||||
\(163\) | 0.298045 | − | 1.11232i | 0.0233447 | − | 0.0871237i | −0.953271 | − | 0.302118i | \(-0.902306\pi\) |
0.976615 | + | 0.214994i | \(0.0689732\pi\) | |||||||
\(164\) | −13.3657 | − | 2.00932i | −1.04369 | − | 0.156902i | ||||
\(165\) | 20.9085 | − | 5.60243i | 1.62773 | − | 0.436148i | ||||
\(166\) | −3.44996 | + | 2.97008i | −0.267769 | + | 0.230523i | ||||
\(167\) | 6.52564i | 0.504969i | 0.967601 | + | 0.252485i | \(0.0812477\pi\) | ||||
−0.967601 | + | 0.252485i | \(0.918752\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 10.2353i | − | 0.787331i | ||||||
\(170\) | −20.3339 | − | 23.6193i | −1.55954 | − | 1.81152i | ||||
\(171\) | 2.05749 | − | 0.551303i | 0.157340 | − | 0.0421592i | ||||
\(172\) | 0.471375 | − | 0.348169i | 0.0359420 | − | 0.0265476i | ||||
\(173\) | 1.38954 | − | 5.18582i | 0.105644 | − | 0.394271i | −0.892773 | − | 0.450507i | \(-0.851243\pi\) |
0.998417 | + | 0.0562362i | \(0.0179100\pi\) | |||||||
\(174\) | 12.2063 | + | 8.31866i | 0.925354 | + | 0.630636i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.414376 | − | 11.3061i | 0.0312348 | − | 0.852231i | ||||
\(177\) | −3.06142 | − | 5.30253i | −0.230110 | − | 0.398563i | ||||
\(178\) | 8.64386 | + | 17.9404i | 0.647885 | + | 1.34469i | ||||
\(179\) | −22.0932 | + | 5.91986i | −1.65132 | + | 0.442471i | −0.959983 | − | 0.280058i | \(-0.909646\pi\) |
−0.691341 | + | 0.722529i | \(0.742980\pi\) | |||||||
\(180\) | −10.9760 | + | 1.24096i | −0.818106 | + | 0.0924956i | ||||
\(181\) | 3.70233 | − | 3.70233i | 0.275192 | − | 0.275192i | −0.555994 | − | 0.831186i | \(-0.687662\pi\) |
0.831186 | + | 0.555994i | \(0.187662\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −22.6307 | −1.67291 | ||||||||
\(184\) | 0.173053 | + | 0.559882i | 0.0127576 | + | 0.0412751i | ||||
\(185\) | −0.649365 | + | 1.12473i | −0.0477422 | + | 0.0826920i | ||||
\(186\) | −16.3275 | − | 5.70972i | −1.19719 | − | 0.418657i | ||||
\(187\) | 4.49026 | − | 16.7579i | 0.328361 | − | 1.22546i | ||||
\(188\) | −7.99569 | − | 20.3498i | −0.583146 | − | 1.48416i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.81807 | + | 3.96506i | 0.422087 | + | 0.287656i | ||||
\(191\) | −1.38573 | + | 0.800051i | −0.100268 | + | 0.0578896i | −0.549295 | − | 0.835628i | \(-0.685104\pi\) |
0.449028 | + | 0.893518i | \(0.351770\pi\) | |||||||
\(192\) | −3.14881 | + | 16.7471i | −0.227246 | + | 1.20862i | ||||
\(193\) | 8.25169 | − | 14.2923i | 0.593969 | − | 1.02879i | −0.399722 | − | 0.916636i | \(-0.630893\pi\) |
0.993691 | − | 0.112149i | \(-0.0357733\pi\) | |||||||
\(194\) | 0.299236 | − | 4.00331i | 0.0214839 | − | 0.287421i | ||||
\(195\) | −8.99796 | + | 8.99796i | −0.644357 | + | 0.644357i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.2127 | − | 12.2127i | −0.870117 | − | 0.870117i | 0.122368 | − | 0.992485i | \(-0.460951\pi\) |
−0.992485 | + | 0.122368i | \(0.960951\pi\) | |||||||
\(198\) | −4.01170 | − | 4.65988i | −0.285099 | − | 0.331163i | ||||
\(199\) | 14.0301 | + | 8.10030i | 0.994569 | + | 0.574215i | 0.906637 | − | 0.421912i | \(-0.138641\pi\) |
0.0879323 | + | 0.996126i | \(0.471974\pi\) | |||||||
\(200\) | −16.4064 | − | 15.2054i | −1.16011 | − | 1.07518i | ||||
\(201\) | −1.47386 | − | 2.55280i | −0.103958 | − | 0.180061i | ||||
\(202\) | 1.84539 | + | 9.74293i | 0.129841 | + | 0.685510i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −10.4404 | + | 23.9546i | −0.730973 | + | 1.67716i | ||||
\(205\) | −23.4530 | − | 6.28422i | −1.63803 | − | 0.438909i | ||||
\(206\) | −17.5801 | + | 8.47028i | −1.22486 | + | 0.590152i | ||||
\(207\) | 0.275822 | + | 0.159246i | 0.0191710 | + | 0.0110684i | ||||
\(208\) | 3.11228 | + | 5.87783i | 0.215798 | + | 0.407554i | ||||
\(209\) | 3.91928i | 0.271102i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.22959 | − | 1.22959i | −0.0846487 | − | 0.0846487i | 0.663515 | − | 0.748163i | \(-0.269064\pi\) |
−0.748163 | + | 0.663515i | \(0.769064\pi\) | |||||||
\(212\) | 20.2084 | − | 2.28478i | 1.38792 | − | 0.156919i | ||||
\(213\) | 1.15599 | + | 4.31420i | 0.0792070 | + | 0.295604i | ||||
\(214\) | 18.6151 | + | 6.50970i | 1.27250 | + | 0.444994i | ||||
\(215\) | 0.911699 | − | 0.526369i | 0.0621773 | − | 0.0358981i | ||||
\(216\) | −4.69306 | − | 7.45944i | −0.319322 | − | 0.507551i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.73816 | − | 9.17679i | −0.117723 | − | 0.621531i | ||||
\(219\) | −5.61615 | − | 1.50484i | −0.379504 | − | 0.101688i | ||||
\(220\) | 3.02149 | − | 20.0985i | 0.203709 | − | 1.35504i | ||||
\(221\) | 2.63968 | + | 9.85141i | 0.177564 | + | 0.662678i | ||||
\(222\) | 1.08587 | + | 0.0811656i | 0.0728788 | + | 0.00544748i | ||||
\(223\) | −3.08465 | −0.206564 | −0.103282 | − | 0.994652i | \(-0.532934\pi\) | ||||
−0.103282 | + | 0.994652i | \(0.532934\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.1573 | −0.810485 | ||||||||
\(226\) | 20.1073 | + | 1.50297i | 1.33752 | + | 0.0999759i | ||||
\(227\) | 2.25836 | + | 8.42831i | 0.149893 | + | 0.559407i | 0.999489 | + | 0.0319729i | \(0.0101790\pi\) |
−0.849596 | + | 0.527434i | \(0.823154\pi\) | |||||||
\(228\) | 0.877588 | − | 5.83758i | 0.0581197 | − | 0.386603i | ||||
\(229\) | 16.2919 | + | 4.36541i | 1.07660 | + | 0.288474i | 0.753203 | − | 0.657789i | \(-0.228508\pi\) |
0.323398 | + | 0.946263i | \(0.395175\pi\) | |||||||
\(230\) | 0.195914 | + | 1.03435i | 0.0129182 | + | 0.0682029i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 11.7393 | − | 7.38567i | 0.770720 | − | 0.484893i | ||||
\(233\) | 12.9805 | − | 7.49428i | 0.850380 | − | 0.490967i | −0.0103994 | − | 0.999946i | \(-0.503310\pi\) |
0.860779 | + | 0.508979i | \(0.169977\pi\) | |||||||
\(234\) | 3.41208 | + | 1.19321i | 0.223055 | + | 0.0780024i | ||||
\(235\) | −10.1658 | − | 37.9392i | −0.663143 | − | 2.47488i | ||||
\(236\) | −5.71255 | + | 0.645864i | −0.371855 | + | 0.0420422i | ||||
\(237\) | −16.6155 | − | 16.6155i | −1.07929 | − | 1.07929i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.9930i | 1.22856i | 0.789090 | + | 0.614278i | \(0.210553\pi\) | ||||
−0.789090 | + | 0.614278i | \(0.789447\pi\) | |||||||
\(240\) | −9.00071 | + | 29.2591i | −0.580994 | + | 1.88867i | ||||
\(241\) | −21.0900 | − | 12.1763i | −1.35853 | − | 0.784346i | −0.369101 | − | 0.929389i | \(-0.620334\pi\) |
−0.989425 | + | 0.145044i | \(0.953668\pi\) | |||||||
\(242\) | −3.82213 | + | 1.84154i | −0.245696 | + | 0.118379i | ||||
\(243\) | −14.1149 | − | 3.78208i | −0.905472 | − | 0.242620i | ||||
\(244\) | −8.48973 | + | 19.4790i | −0.543500 | + | 1.24702i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.78852 | + | 20.0019i | 0.241547 | + | 1.27527i | ||||
\(247\) | −1.15201 | − | 1.99533i | −0.0733005 | − | 0.126960i | ||||
\(248\) | −11.0397 | + | 11.9117i | −0.701022 | + | 0.756392i | ||||
\(249\) | 5.93803 | + | 3.42832i | 0.376307 | + | 0.217261i | ||||
\(250\) | −9.64238 | − | 11.2003i | −0.609837 | − | 0.708370i | ||||
\(251\) | −13.3452 | − | 13.3452i | −0.842342 | − | 0.842342i | 0.146821 | − | 0.989163i | \(-0.453096\pi\) |
−0.989163 | + | 0.146821i | \(0.953096\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.414376 | + | 0.414376i | −0.0260516 | + | 0.0260516i | ||||
\(254\) | 0.649802 | − | 8.69333i | 0.0407722 | − | 0.545468i | ||||
\(255\) | −23.4712 | + | 40.6533i | −1.46982 | + | 2.54581i | ||||
\(256\) | 13.2336 | + | 8.99287i | 0.827100 | + | 0.562054i | ||||
\(257\) | 4.67708 | − | 2.70031i | 0.291748 | − | 0.168441i | −0.346982 | − | 0.937872i | \(-0.612793\pi\) |
0.638730 | + | 0.769431i | \(0.279460\pi\) | |||||||
\(258\) | −0.729376 | − | 0.497076i | −0.0454090 | − | 0.0309466i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.36935 | + | 11.1204i | 0.270975 | + | 0.689657i | ||||
\(261\) | 1.95092 | − | 7.28095i | 0.120759 | − | 0.450679i | ||||
\(262\) | −2.30968 | − | 0.807696i | −0.142693 | − | 0.0498997i | ||||
\(263\) | 0.181180 | − | 0.313813i | 0.0111721 | − | 0.0193506i | −0.860385 | − | 0.509644i | \(-0.829777\pi\) |
0.871557 | + | 0.490294i | \(0.163110\pi\) | |||||||
\(264\) | −16.2806 | + | 5.03215i | −1.00200 | + | 0.309707i | ||||
\(265\) | 36.5343 | 2.24428 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 21.2093 | − | 21.2093i | 1.29799 | − | 1.29799i | ||||
\(268\) | −2.75020 | + | 0.310939i | −0.167995 | + | 0.0189936i | ||||
\(269\) | 25.8214 | − | 6.91882i | 1.57436 | − | 0.421848i | 0.637185 | − | 0.770711i | \(-0.280099\pi\) |
0.937174 | + | 0.348863i | \(0.113432\pi\) | |||||||
\(270\) | −6.87192 | − | 14.2627i | −0.418211 | − | 0.868000i | ||||
\(271\) | −4.83748 | − | 8.37876i | −0.293856 | − | 0.508973i | 0.680862 | − | 0.732411i | \(-0.261605\pi\) |
−0.974718 | + | 0.223438i | \(0.928272\pi\) | |||||||
\(272\) | 16.7020 | + | 17.9728i | 1.01271 | + | 1.08976i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.07257 | + | 6.18303i | 0.548094 | + | 0.373531i | ||||
\(275\) | 5.78954 | − | 21.6069i | 0.349122 | − | 1.30294i | ||||
\(276\) | 0.709979 | − | 0.524408i | 0.0427357 | − | 0.0315657i | ||||
\(277\) | 4.03815 | − | 1.08202i | 0.242629 | − | 0.0650122i | −0.135455 | − | 0.990783i | \(-0.543250\pi\) |
0.378084 | + | 0.925771i | \(0.376583\pi\) | |||||||
\(278\) | −8.41993 | − | 9.78035i | −0.504994 | − | 0.586587i | ||||
\(279\) | 8.82664i | 0.528437i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 19.8602i | − | 1.18476i | −0.805658 | − | 0.592382i | \(-0.798188\pi\) | ||
0.805658 | − | 0.592382i | \(-0.201812\pi\) | |||||||
\(282\) | −24.9572 | + | 21.4857i | −1.48618 | + | 1.27945i | ||||
\(283\) | 26.6591 | − | 7.14328i | 1.58472 | − | 0.424624i | 0.644335 | − | 0.764743i | \(-0.277134\pi\) |
0.940382 | + | 0.340119i | \(0.110467\pi\) | |||||||
\(284\) | 4.14705 | + | 0.623444i | 0.246082 | + | 0.0369946i | ||||
\(285\) | 2.74468 | − | 10.2433i | 0.162581 | − | 0.606761i | ||||
\(286\) | −3.74556 | + | 5.49599i | −0.221480 | + | 0.324985i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 8.59741 | − | 1.30427i | 0.506607 | − | 0.0768547i | ||||
\(289\) | 10.3118 | + | 17.8606i | 0.606578 | + | 1.05062i | ||||
\(290\) | 22.4458 | − | 10.8146i | 1.31807 | − | 0.635058i | ||||
\(291\) | −5.84053 | + | 1.56497i | −0.342378 | + | 0.0917399i | ||||
\(292\) | −3.40213 | + | 4.26949i | −0.199095 | + | 0.249853i | ||||
\(293\) | 18.3063 | − | 18.3063i | 1.06947 | − | 1.06947i | 0.0720669 | − | 0.997400i | \(-0.477041\pi\) |
0.997400 | − | 0.0720669i | \(-0.0229595\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.3276 | −0.601295 | ||||||||
\(296\) | 0.477219 | − | 0.904198i | 0.0277378 | − | 0.0525555i | ||||
\(297\) | 4.40647 | − | 7.63224i | 0.255690 | − | 0.442867i | ||||
\(298\) | −3.85475 | + | 11.0230i | −0.223299 | + | 0.638545i | ||||
\(299\) | 0.0891631 | − | 0.332761i | 0.00515644 | − | 0.0192441i | ||||
\(300\) | −13.4614 | + | 30.8860i | −0.777192 | + | 1.78320i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.23943 | − | 1.81866i | 0.0713213 | − | 0.104652i | ||||
\(303\) | 12.9346 | − | 7.46780i | 0.743074 | − | 0.429014i | ||||
\(304\) | −4.69539 | − | 2.94530i | −0.269299 | − | 0.168924i | ||||
\(305\) | −19.0859 | + | 33.0578i | −1.09286 | + | 1.89288i | ||||
\(306\) | 13.2975 | + | 0.993948i | 0.760166 | + | 0.0568202i | ||||
\(307\) | −10.7614 | + | 10.7614i | −0.614188 | + | 0.614188i | −0.944034 | − | 0.329847i | \(-0.893003\pi\) |
0.329847 | + | 0.944034i | \(0.393003\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.7834 | + | 20.7834i | 1.18233 | + | 1.18233i | ||||
\(310\) | −22.1105 | + | 19.0350i | −1.25579 | + | 1.08112i | ||||
\(311\) | 1.63450 | + | 0.943681i | 0.0926842 | + | 0.0535113i | 0.545626 | − | 0.838029i | \(-0.316292\pi\) |
−0.452942 | + | 0.891540i | \(0.649625\pi\) | |||||||
\(312\) | 6.80948 | − | 7.34733i | 0.385511 | − | 0.415961i | ||||
\(313\) | 10.9206 | + | 18.9150i | 0.617267 | + | 1.06914i | 0.989982 | + | 0.141192i | \(0.0450936\pi\) |
−0.372715 | + | 0.927946i | \(0.621573\pi\) | |||||||
\(314\) | −5.60554 | + | 1.06174i | −0.316339 | + | 0.0599173i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.5348 | + | 8.06838i | −1.15517 | + | 0.453882i | ||||
\(317\) | 19.4859 | + | 5.22124i | 1.09444 | + | 0.293254i | 0.760498 | − | 0.649340i | \(-0.224955\pi\) |
0.333941 | + | 0.942594i | \(0.391621\pi\) | |||||||
\(318\) | −13.2958 | − | 27.5956i | −0.745593 | − | 1.54748i | ||||
\(319\) | 12.0112 | + | 6.93467i | 0.672498 | + | 0.388267i | ||||
\(320\) | 21.8078 | + | 18.7236i | 1.21909 | + | 1.04668i | ||||
\(321\) | − | 29.7028i | − | 1.65785i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.01003 | − | 6.01003i | −0.334407 | − | 0.334407i | ||||
\(324\) | −14.0201 | + | 17.5944i | −0.778892 | + | 0.977467i | ||||
\(325\) | 3.40348 | + | 12.7020i | 0.188791 | + | 0.704578i | ||||
\(326\) | −0.537582 | + | 1.53726i | −0.0297739 | + | 0.0851412i | ||||
\(327\) | −12.1830 | + | 7.03387i | −0.673722 | + | 0.388974i | ||||
\(328\) | 18.6376 | + | 4.24264i | 1.02909 | + | 0.234261i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −30.0775 | + | 5.69693i | −1.65571 | + | 0.313606i | ||||
\(331\) | 7.17595 | + | 1.92279i | 0.394426 | + | 0.105686i | 0.450580 | − | 0.892736i | \(-0.351217\pi\) |
−0.0561542 | + | 0.998422i | \(0.517884\pi\) | |||||||
\(332\) | 5.17849 | − | 3.82496i | 0.284207 | − | 0.209922i | ||||
\(333\) | −0.143816 | − | 0.536729i | −0.00788107 | − | 0.0294126i | ||||
\(334\) | 0.687896 | − | 9.20298i | 0.0376400 | − | 0.503565i | ||||
\(335\) | −4.97202 | −0.271650 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.0799 | −0.658034 | −0.329017 | − | 0.944324i | \(-0.606717\pi\) | ||||
−0.329017 | + | 0.944324i | \(0.606717\pi\) | |||||||
\(338\) | −1.07895 | + | 14.4346i | −0.0586870 | + | 0.785140i | ||||
\(339\) | −7.86032 | − | 29.3351i | −0.426914 | − | 1.59326i | ||||
\(340\) | 26.1867 | + | 35.4533i | 1.42017 | + | 1.92273i | ||||
\(341\) | −15.6874 | − | 4.20342i | −0.849520 | − | 0.227628i | ||||
\(342\) | −2.95975 | + | 0.560603i | −0.160045 | + | 0.0303139i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.701472 | + | 0.441326i | −0.0378208 | + | 0.0237947i | ||||
\(345\) | 1.37319 | − | 0.792812i | 0.0739301 | − | 0.0426836i | ||||
\(346\) | −2.50629 | + | 7.16698i | −0.134739 | + | 0.385299i | ||||
\(347\) | 7.08259 | + | 26.4326i | 0.380213 | + | 1.41897i | 0.845576 | + | 0.533855i | \(0.179257\pi\) |
−0.465363 | + | 0.885120i | \(0.654076\pi\) | |||||||
\(348\) | −16.3373 | − | 13.0183i | −0.875772 | − | 0.697857i | ||||
\(349\) | 2.96915 | + | 2.96915i | 0.158935 | + | 0.158935i | 0.782095 | − | 0.623160i | \(-0.214151\pi\) |
−0.623160 | + | 0.782095i | \(0.714151\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.18084i | 0.276533i | ||||||||
\(352\) | −1.77621 | + | 15.9011i | −0.0946725 | + | 0.847532i | ||||
\(353\) | −14.1327 | − | 8.15953i | −0.752209 | − | 0.434288i | 0.0742828 | − | 0.997237i | \(-0.476333\pi\) |
−0.826491 | + | 0.562949i | \(0.809667\pi\) | |||||||
\(354\) | 3.75849 | + | 7.80077i | 0.199762 | + | 0.414606i | ||||
\(355\) | 7.27691 | + | 1.94984i | 0.386218 | + | 0.103487i | ||||
\(356\) | −10.2991 | − | 26.2121i | −0.545850 | − | 1.38924i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 31.7816 | − | 6.01971i | 1.67971 | − | 0.318152i | ||||
\(359\) | −8.26786 | − | 14.3203i | −0.436361 | − | 0.755799i | 0.561045 | − | 0.827785i | \(-0.310400\pi\) |
−0.997406 | + | 0.0719864i | \(0.977066\pi\) | |||||||
\(360\) | 15.6101 | − | 0.593066i | 0.822725 | − | 0.0312573i | ||||
\(361\) | −14.7916 | − | 8.53995i | −0.778507 | − | 0.449471i | ||||
\(362\) | −5.61160 | + | 4.83105i | −0.294939 | + | 0.253914i | ||||
\(363\) | 4.51857 | + | 4.51857i | 0.237163 | + | 0.237163i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.93467 | + | 6.93467i | −0.362977 | + | 0.362977i | ||||
\(366\) | 31.9155 | + | 2.38560i | 1.66825 | + | 0.124697i | ||||
\(367\) | 11.8390 | − | 20.5058i | 0.617992 | − | 1.07039i | −0.371860 | − | 0.928289i | \(-0.621280\pi\) |
0.989852 | − | 0.142104i | \(-0.0453868\pi\) | |||||||
\(368\) | −0.185033 | − | 0.807833i | −0.00964554 | − | 0.0421112i | ||||
\(369\) | 8.99660 | − | 5.19419i | 0.468344 | − | 0.270399i | ||||
\(370\) | 1.03435 | − | 1.51773i | 0.0537732 | − | 0.0789033i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 22.4244 | + | 9.77345i | 1.16265 | + | 0.506730i | ||||
\(373\) | 8.04803 | − | 30.0357i | 0.416711 | − | 1.55519i | −0.364672 | − | 0.931136i | \(-0.618819\pi\) |
0.781383 | − | 0.624051i | \(-0.214514\pi\) | |||||||
\(374\) | −8.09905 | + | 23.1600i | −0.418792 | + | 1.19757i | ||||
\(375\) | −11.1301 | + | 19.2779i | −0.574754 | + | 0.995504i | ||||
\(376\) | 9.13100 | + | 29.5417i | 0.470895 | + | 1.52350i | ||||
\(377\) | −8.15332 | −0.419918 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.0100 | + | 20.0100i | −1.02785 | + | 1.02785i | −0.0282452 | + | 0.999601i | \(0.508992\pi\) |
−0.999601 | + | 0.0282452i | \(0.991008\pi\) | |||||||
\(380\) | −7.78713 | − | 6.20515i | −0.399471 | − | 0.318318i | ||||
\(381\) | −12.6829 | + | 3.39838i | −0.649766 | + | 0.174104i | ||||
\(382\) | 2.03860 | − | 0.982219i | 0.104304 | − | 0.0502547i | ||||
\(383\) | 2.58822 | + | 4.48293i | 0.132252 | + | 0.229067i | 0.924544 | − | 0.381075i | \(-0.124446\pi\) |
−0.792292 | + | 0.610142i | \(0.791113\pi\) | |||||||
\(384\) | 6.20609 | − | 23.2862i | 0.316703 | − | 1.18832i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.1438 | + | 19.2863i | −0.669002 | + | 0.981649i | ||||
\(387\) | −0.116576 | + | 0.435068i | −0.00592590 | + | 0.0221158i | ||||
\(388\) | −0.844013 | + | 5.61424i | −0.0428483 | + | 0.285020i | ||||
\(389\) | 5.68099 | − | 1.52222i | 0.288038 | − | 0.0771795i | −0.111907 | − | 0.993719i | \(-0.535696\pi\) |
0.399945 | + | 0.916539i | \(0.369029\pi\) | |||||||
\(390\) | 13.6382 | − | 11.7411i | 0.690595 | − | 0.594535i | ||||
\(391\) | − | 1.27085i | − | 0.0642698i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.68540i | 0.185904i | ||||||||
\(394\) | 15.9359 | + | 18.5107i | 0.802839 | + | 0.932554i | ||||
\(395\) | −38.2841 | + | 10.2582i | −1.92628 | + | 0.516146i | ||||
\(396\) | 5.16641 | + | 6.99462i | 0.259622 | + | 0.351493i | ||||
\(397\) | 5.43037 | − | 20.2664i | 0.272542 | − | 1.01714i | −0.684928 | − | 0.728611i | \(-0.740166\pi\) |
0.957470 | − | 0.288531i | \(-0.0931669\pi\) | |||||||
\(398\) | −18.9325 | − | 12.9027i | −0.949001 | − | 0.646752i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 21.5348 | + | 23.1734i | 1.07674 | + | 1.15867i | ||||
\(401\) | −11.0544 | − | 19.1468i | −0.552032 | − | 0.956147i | −0.998128 | − | 0.0611622i | \(-0.980519\pi\) |
0.446096 | − | 0.894985i | \(-0.352814\pi\) | |||||||
\(402\) | 1.80945 | + | 3.75553i | 0.0902473 | + | 0.187309i | ||||
\(403\) | 9.22210 | − | 2.47105i | 0.459386 | − | 0.123092i | ||||
\(404\) | −1.57548 | − | 13.9348i | −0.0783829 | − | 0.693282i | ||||
\(405\) | −28.5775 | + | 28.5775i | −1.42003 | + | 1.42003i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.02241 | 0.0506787 | ||||||||
\(408\) | 17.2490 | − | 32.6822i | 0.853954 | − | 1.61801i | ||||
\(409\) | 0.729129 | − | 1.26289i | 0.0360531 | − | 0.0624458i | −0.847436 | − | 0.530898i | \(-0.821855\pi\) |
0.883489 | + | 0.468452i | \(0.155188\pi\) | |||||||
\(410\) | 32.4129 | + | 11.3348i | 1.60076 | + | 0.559785i | ||||
\(411\) | 4.28000 | − | 15.9732i | 0.211117 | − | 0.787899i | ||||
\(412\) | 25.6858 | − | 10.0923i | 1.26545 | − | 0.497210i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.372199 | − | 0.253657i | −0.0182926 | − | 0.0124666i | ||||
\(415\) | 10.0159 | − | 5.78266i | 0.491659 | − | 0.283860i | ||||
\(416\) | −3.76958 | − | 8.61746i | −0.184819 | − | 0.422506i | ||||
\(417\) | −9.71902 | + | 16.8338i | −0.475942 | + | 0.824357i | ||||
\(418\) | 0.413148 | − | 5.52728i | 0.0202077 | − | 0.270348i | ||||
\(419\) | 24.2050 | − | 24.2050i | 1.18249 | − | 1.18249i | 0.203398 | − | 0.979096i | \(-0.434802\pi\) |
0.979096 | − | 0.203398i | \(-0.0651984\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.1878 | + | 19.1878i | 0.935158 | + | 0.935158i | 0.998022 | − | 0.0628646i | \(-0.0200236\pi\) |
−0.0628646 | + | 0.998022i | \(0.520024\pi\) | |||||||
\(422\) | 1.60445 | + | 1.86369i | 0.0781036 | + | 0.0907229i | ||||
\(423\) | 14.5535 | + | 8.40248i | 0.707617 | + | 0.408543i | ||||
\(424\) | −28.7403 | + | 1.09192i | −1.39575 | + | 0.0530281i | ||||
\(425\) | 24.2551 | + | 42.0111i | 1.17655 | + | 2.03784i | ||||
\(426\) | −1.17549 | − | 6.20609i | −0.0569525 | − | 0.300686i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −25.5663 | − | 11.1428i | −1.23579 | − | 0.538607i | ||||
\(429\) | 9.67625 | + | 2.59274i | 0.467174 | + | 0.125179i | ||||
\(430\) | −1.34124 | + | 0.646222i | −0.0646802 | + | 0.0311636i | ||||
\(431\) | 17.6927 | + | 10.2149i | 0.852228 | + | 0.492034i | 0.861402 | − | 0.507924i | \(-0.169587\pi\) |
−0.00917369 | + | 0.999958i | \(0.502920\pi\) | |||||||
\(432\) | 5.83219 | + | 11.0146i | 0.280601 | + | 0.529941i | ||||
\(433\) | 22.7267i | 1.09218i | 0.837727 | + | 0.546089i | \(0.183884\pi\) | ||||
−0.837727 | + | 0.546089i | \(0.816116\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −26.5357 | − | 26.5357i | −1.27229 | − | 1.27229i | ||||
\(436\) | 1.48393 | + | 13.1251i | 0.0710673 | + | 0.628577i | ||||
\(437\) | 0.0743057 | + | 0.277313i | 0.00355453 | + | 0.0132657i | ||||
\(438\) | 7.76170 | + | 2.71427i | 0.370868 | + | 0.129693i | ||||
\(439\) | −30.8968 | + | 17.8383i | −1.47462 | + | 0.851375i | −0.999591 | − | 0.0285924i | \(-0.990898\pi\) |
−0.475034 | + | 0.879968i | \(0.657564\pi\) | |||||||
\(440\) | −6.37980 | + | 28.0259i | −0.304145 | + | 1.33608i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.68420 | − | 14.1715i | −0.127674 | − | 0.674070i | ||||
\(443\) | 6.99171 | + | 1.87342i | 0.332186 | + | 0.0890091i | 0.421057 | − | 0.907034i | \(-0.361659\pi\) |
−0.0888708 | + | 0.996043i | \(0.528326\pi\) | |||||||
\(444\) | −1.52282 | − | 0.228932i | −0.0722700 | − | 0.0108647i | ||||
\(445\) | −13.0943 | − | 48.8687i | −0.620731 | − | 2.31660i | ||||
\(446\) | 4.35022 | + | 0.325167i | 0.205989 | + | 0.0153971i | ||||
\(447\) | 17.5886 | 0.831913 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −35.6346 | −1.68170 | −0.840851 | − | 0.541266i | \(-0.817945\pi\) | ||||
−0.840851 | + | 0.541266i | \(0.817945\pi\) | |||||||
\(450\) | 17.1452 | + | 1.28155i | 0.808230 | + | 0.0604129i | ||||
\(451\) | 4.94716 | + | 18.4630i | 0.232953 | + | 0.869391i | ||||
\(452\) | −28.1985 | − | 4.23921i | −1.32635 | − | 0.199395i | ||||
\(453\) | −3.20194 | − | 0.857956i | −0.150440 | − | 0.0403103i | ||||
\(454\) | −2.29645 | − | 12.1243i | −0.107778 | − | 0.569023i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.85301 | + | 8.14010i | −0.0867751 | + | 0.381195i | ||||
\(457\) | −4.14209 | + | 2.39144i | −0.193759 | + | 0.111867i | −0.593741 | − | 0.804656i | \(-0.702350\pi\) |
0.399982 | + | 0.916523i | \(0.369016\pi\) | |||||||
\(458\) | −22.5160 | − | 7.87385i | −1.05210 | − | 0.367921i | ||||
\(459\) | 4.94656 | + | 18.4608i | 0.230886 | + | 0.861677i | ||||
\(460\) | −0.167259 | − | 1.47937i | −0.00779848 | − | 0.0689761i | ||||
\(461\) | 6.54100 | + | 6.54100i | 0.304645 | + | 0.304645i | 0.842828 | − | 0.538183i | \(-0.180889\pi\) |
−0.538183 | + | 0.842828i | \(0.680889\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.771348i | 0.0358476i | 0.999839 | + | 0.0179238i | \(0.00570563\pi\) | ||||
−0.999839 | + | 0.0179238i | \(0.994294\pi\) | |||||||
\(464\) | −17.3342 | + | 9.17838i | −0.804720 | + | 0.426095i | ||||
\(465\) | 38.0564 | + | 21.9719i | 1.76482 | + | 1.01892i | ||||
\(466\) | −19.0961 | + | 9.20070i | −0.884610 | + | 0.426214i | ||||
\(467\) | 3.42988 | + | 0.919035i | 0.158716 | + | 0.0425278i | 0.337302 | − | 0.941396i | \(-0.390486\pi\) |
−0.178586 | + | 0.983924i | \(0.557152\pi\) | |||||||
\(468\) | −4.68621 | − | 2.04244i | −0.216620 | − | 0.0944117i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 10.3373 | + | 54.5765i | 0.476822 | + | 2.51743i | ||||
\(471\) | 4.29656 | + | 7.44186i | 0.197975 | + | 0.342903i | ||||
\(472\) | 8.12437 | − | 0.308665i | 0.373955 | − | 0.0142074i | ||||
\(473\) | −0.717721 | − | 0.414376i | −0.0330008 | − | 0.0190530i | ||||
\(474\) | 21.6810 | + | 25.1840i | 0.995841 | + | 1.15674i | ||||
\(475\) | −7.74906 | − | 7.74906i | −0.355551 | − | 0.355551i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.0530 | + | 11.0530i | −0.506080 | + | 0.506080i | ||||
\(478\) | 2.00214 | − | 26.7855i | 0.0915756 | − | 1.22514i | ||||
\(479\) | 4.96517 | − | 8.59993i | 0.226865 | − | 0.392941i | −0.730013 | − | 0.683434i | \(-0.760486\pi\) |
0.956877 | + | 0.290493i | \(0.0938192\pi\) | |||||||
\(480\) | 15.7779 | − | 40.3147i | 0.720157 | − | 1.84011i | ||||
\(481\) | −0.520514 | + | 0.300519i | −0.0237334 | + | 0.0137025i | ||||
\(482\) | 28.4592 | + | 19.3952i | 1.29628 | + | 0.883427i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.58440 | − | 2.19418i | 0.253836 | − | 0.0997356i | ||||
\(485\) | −2.63968 | + | 9.85141i | −0.119862 | + | 0.447329i | ||||
\(486\) | 19.5073 | + | 6.82170i | 0.884868 | + | 0.309439i | ||||
\(487\) | −3.70370 | + | 6.41499i | −0.167830 | + | 0.290691i | −0.937657 | − | 0.347563i | \(-0.887009\pi\) |
0.769826 | + | 0.638253i | \(0.220343\pi\) | |||||||
\(488\) | 14.0263 | − | 26.5759i | 0.634939 | − | 1.20304i | ||||
\(489\) | 2.45290 | 0.110924 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.4988 | − | 21.4988i | 0.970229 | − | 0.970229i | −0.0293409 | − | 0.999569i | \(-0.509341\pi\) |
0.999569 | + | 0.0293409i | \(0.00934085\pi\) | |||||||
\(492\) | −3.23439 | − | 28.6076i | −0.145818 | − | 1.28973i | ||||
\(493\) | −29.0526 | + | 7.78462i | −1.30846 | + | 0.350602i | ||||
\(494\) | 1.41431 | + | 2.93542i | 0.0636330 | + | 0.132071i | ||||
\(495\) | 7.81068 | + | 13.5285i | 0.351064 | + | 0.608061i | ||||
\(496\) | 16.8247 | − | 15.6351i | 0.755452 | − | 0.702035i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −8.01288 | − | 5.46085i | −0.359066 | − | 0.244706i | ||||
\(499\) | −8.53593 | + | 31.8565i | −0.382121 | + | 1.42609i | 0.460535 | + | 0.887641i | \(0.347658\pi\) |
−0.842656 | + | 0.538452i | \(0.819009\pi\) | |||||||
\(500\) | 12.4178 | + | 16.8120i | 0.555340 | + | 0.751856i | ||||
\(501\) | −13.4265 | + | 3.59761i | −0.599850 | + | 0.160729i | ||||
\(502\) | 17.4137 | + | 20.2272i | 0.777211 | + | 0.902786i | ||||
\(503\) | 38.8858i | 1.73383i | 0.498456 | + | 0.866915i | \(0.333901\pi\) | ||||
−0.498456 | + | 0.866915i | \(0.666099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 25.1924i | − | 1.12105i | ||||||
\(506\) | 0.628068 | − | 0.540705i | 0.0279210 | − | 0.0240373i | ||||
\(507\) | 21.0591 | − | 5.64276i | 0.935265 | − | 0.250604i | ||||
\(508\) | −1.83280 | + | 12.1915i | −0.0813175 | + | 0.540911i | ||||
\(509\) | −3.00516 | + | 11.2154i | −0.133201 | + | 0.497114i | −0.999999 | − | 0.00154626i | \(-0.999508\pi\) |
0.866798 | + | 0.498660i | \(0.166174\pi\) | |||||||
\(510\) | 37.3864 | − | 54.8584i | 1.65550 | − | 2.42917i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −17.7151 | − | 14.0775i | −0.782904 | − | 0.622142i | ||||
\(513\) | −2.15878 | − | 3.73911i | −0.0953123 | − | 0.165086i | ||||
\(514\) | −6.88064 | + | 3.31516i | −0.303492 | + | 0.146226i | ||||
\(515\) | 47.8874 | − | 12.8314i | 2.11017 | − | 0.565418i | ||||
\(516\) | 0.976226 | + | 0.777903i | 0.0429759 | + | 0.0342453i | ||||
\(517\) | −21.8642 | + | 21.8642i | −0.961588 | + | 0.961588i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.4358 | 0.501978 | ||||||||
\(520\) | −4.98975 | − | 16.1435i | −0.218815 | − | 0.707937i | ||||
\(521\) | −5.97165 | + | 10.3432i | −0.261623 | + | 0.453144i | −0.966673 | − | 0.256013i | \(-0.917591\pi\) |
0.705051 | + | 0.709157i | \(0.250924\pi\) | |||||||
\(522\) | −3.51886 | + | 10.0625i | −0.154016 | + | 0.440424i | ||||
\(523\) | 4.87035 | − | 18.1764i | 0.212965 | − | 0.794798i | −0.773908 | − | 0.633299i | \(-0.781700\pi\) |
0.986873 | − | 0.161499i | \(-0.0516328\pi\) | |||||||
\(524\) | 3.17215 | + | 1.38255i | 0.138576 | + | 0.0603970i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.288595 | + | 0.423465i | −0.0125833 | + | 0.0184640i | ||||
\(527\) | 30.5016 | − | 17.6101i | 1.32867 | − | 0.767109i | ||||
\(528\) | 23.4907 | − | 5.38053i | 1.02230 | − | 0.234157i | ||||
\(529\) | 11.4785 | − | 19.8814i | 0.499067 | − | 0.864409i | ||||
\(530\) | −51.5236 | − | 3.85124i | −2.23804 | − | 0.167287i | ||||
\(531\) | 3.12447 | − | 3.12447i | 0.135590 | − | 0.135590i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.94554 | − | 7.94554i | −0.344160 | − | 0.344160i | ||||
\(534\) | −32.1468 | + | 27.6753i | −1.39113 | + | 1.19763i | ||||
\(535\) | −43.3884 | − | 25.0503i | −1.87585 | − | 1.08302i | ||||
\(536\) | 3.91132 | − | 0.148601i | 0.168943 | − | 0.00641857i | ||||
\(537\) | −24.3601 | − | 42.1930i | −1.05122 | − | 1.82076i | ||||
\(538\) | −37.1447 | + | 7.03553i | −1.60142 | + | 0.303323i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 8.18783 | + | 20.8388i | 0.352348 | + | 0.896758i | ||||
\(541\) | −16.5663 | − | 4.43893i | −0.712241 | − | 0.190844i | −0.115534 | − | 0.993304i | \(-0.536858\pi\) |
−0.596707 | + | 0.802459i | \(0.703525\pi\) | |||||||
\(542\) | 5.93895 | + | 12.3263i | 0.255100 | + | 0.529461i | ||||
\(543\) | 9.65863 | + | 5.57641i | 0.414492 | + | 0.239307i | ||||
\(544\) | −21.6599 | − | 27.1073i | −0.928659 | − | 1.16222i | ||||
\(545\) | 23.7285i | 1.01642i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.7858 | + | 16.7858i | 0.717710 | + | 0.717710i | 0.968136 | − | 0.250426i | \(-0.0805706\pi\) |
−0.250426 | + | 0.968136i | \(0.580571\pi\) | |||||||
\(548\) | −12.1431 | − | 9.67618i | −0.518727 | − | 0.413346i | ||||
\(549\) | −4.22700 | − | 15.7754i | −0.180404 | − | 0.673277i | ||||
\(550\) | −10.4425 | + | 29.8614i | −0.445272 | + | 1.27329i | ||||
\(551\) | 5.88440 | − | 3.39736i | 0.250684 | − | 0.144732i | ||||
\(552\) | −1.05655 | + | 0.664720i | −0.0449697 | + | 0.0282924i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −5.80898 | + | 1.10027i | −0.246800 | + | 0.0467460i | ||||
\(555\) | −2.67213 | − | 0.715994i | −0.113425 | − | 0.0303922i | ||||
\(556\) | 10.8435 | + | 14.6806i | 0.459865 | + | 0.622597i | ||||
\(557\) | 3.74143 | + | 13.9632i | 0.158529 | + | 0.591639i | 0.998777 | + | 0.0494370i | \(0.0157427\pi\) |
−0.840248 | + | 0.542202i | \(0.817591\pi\) | |||||||
\(558\) | 0.930455 | − | 12.4480i | 0.0393893 | − | 0.526967i | ||||
\(559\) | 0.487196 | 0.0206062 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 36.9547 | 1.56023 | ||||||||
\(562\) | −2.09356 | + | 28.0085i | −0.0883113 | + | 1.18147i | ||||
\(563\) | −7.85123 | − | 29.3012i | −0.330890 | − | 1.23490i | −0.908257 | − | 0.418413i | \(-0.862586\pi\) |
0.577367 | − | 0.816485i | \(-0.304080\pi\) | |||||||
\(564\) | 37.4615 | − | 27.6700i | 1.57741 | − | 1.16512i | ||||
\(565\) | −49.4805 | − | 13.2583i | −2.08166 | − | 0.557779i | ||||
\(566\) | −38.3498 | + | 7.26377i | −1.61196 | + | 0.305319i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.78278 | − | 1.31639i | −0.242640 | − | 0.0552344i | ||||
\(569\) | −34.5771 | + | 19.9631i | −1.44955 | + | 0.836896i | −0.998454 | − | 0.0555808i | \(-0.982299\pi\) |
−0.451093 | + | 0.892477i | \(0.648966\pi\) | |||||||
\(570\) | −4.95056 | + | 14.1566i | −0.207356 | + | 0.592954i | ||||
\(571\) | −7.55536 | − | 28.1970i | −0.316182 | − | 1.18001i | −0.922884 | − | 0.385078i | \(-0.874175\pi\) |
0.606702 | − | 0.794929i | \(-0.292492\pi\) | |||||||
\(572\) | 5.86165 | − | 7.35605i | 0.245088 | − | 0.307572i | ||||
\(573\) | −2.41005 | − | 2.41005i | −0.100681 | − | 0.100681i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1.63858i | − | 0.0683336i | ||||||
\(576\) | −12.2622 | + | 0.933091i | −0.510926 | + | 0.0388788i | ||||
\(577\) | 0.793111 | + | 0.457903i | 0.0330177 | + | 0.0190628i | 0.516418 | − | 0.856337i | \(-0.327265\pi\) |
−0.483400 | + | 0.875399i | \(0.660598\pi\) | |||||||
\(578\) | −12.6598 | − | 26.2755i | −0.526578 | − | 1.09292i | ||||
\(579\) | 33.9556 | + | 9.09837i | 1.41115 | + | 0.378115i | ||||
\(580\) | −32.7949 | + | 12.8856i | −1.36174 | + | 0.535043i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 8.40175 | − | 1.59136i | 0.348264 | − | 0.0659641i | ||||
\(583\) | −14.3805 | − | 24.9078i | −0.595581 | − | 1.03158i | ||||
\(584\) | 5.24802 | − | 5.66254i | 0.217165 | − | 0.234317i | ||||
\(585\) | −7.95296 | − | 4.59164i | −0.328814 | − | 0.189841i | ||||
\(586\) | −27.7468 | + | 23.8873i | −1.14621 | + | 0.986774i | ||||
\(587\) | −19.0031 | − | 19.0031i | −0.784343 | − | 0.784343i | 0.196218 | − | 0.980560i | \(-0.437134\pi\) |
−0.980560 | + | 0.196218i | \(0.937134\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.62611 | + | 5.62611i | −0.231820 | + | 0.231820i | ||||
\(590\) | 14.5648 | + | 1.08868i | 0.599622 | + | 0.0448201i | ||||
\(591\) | 18.3946 | − | 31.8604i | 0.756653 | − | 1.31056i | ||||
\(592\) | −0.768327 | + | 1.22487i | −0.0315780 | + | 0.0503417i | ||||
\(593\) | −31.5452 | + | 18.2126i | −1.29541 | + | 0.747903i | −0.979607 | − | 0.200924i | \(-0.935606\pi\) |
−0.315798 | + | 0.948826i | \(0.602272\pi\) | |||||||
\(594\) | −7.01891 | + | 10.2991i | −0.287989 | + | 0.422576i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.59825 | − | 15.1392i | 0.270275 | − | 0.620124i | ||||
\(597\) | −8.93144 | + | 33.3326i | −0.365540 | + | 1.36421i | ||||
\(598\) | −0.160823 | + | 0.459887i | −0.00657653 | + | 0.0188062i | ||||
\(599\) | 2.13462 | − | 3.69727i | 0.0872181 | − | 0.151066i | −0.819116 | − | 0.573628i | \(-0.805536\pi\) |
0.906334 | + | 0.422562i | \(0.138869\pi\) | |||||||
\(600\) | 22.2401 | − | 42.1389i | 0.907948 | − | 1.72031i | ||||
\(601\) | −26.3491 | −1.07480 | −0.537400 | − | 0.843327i | \(-0.680594\pi\) | ||||
−0.537400 | + | 0.843327i | \(0.680594\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.50422 | − | 1.50422i | 0.0612564 | − | 0.0612564i | ||||
\(604\) | −1.93966 | + | 2.43417i | −0.0789236 | + | 0.0990448i | ||||
\(605\) | 10.4113 | − | 2.78970i | 0.423280 | − | 0.113418i | ||||
\(606\) | −19.0286 | + | 9.16820i | −0.772986 | + | 0.372433i | ||||
\(607\) | −15.4145 | − | 26.6988i | −0.625657 | − | 1.08367i | −0.988413 | − | 0.151786i | \(-0.951498\pi\) |
0.362756 | − | 0.931884i | \(-0.381836\pi\) | |||||||
\(608\) | 6.31134 | + | 4.64865i | 0.255959 | + | 0.188528i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 30.4013 | − | 44.6088i | 1.23091 | − | 1.80616i | ||||
\(611\) | 4.70462 | − | 17.5579i | 0.190329 | − | 0.710316i | ||||
\(612\) | −18.6484 | − | 2.80349i | −0.753816 | − | 0.113324i | ||||
\(613\) | −2.96469 | + | 0.794387i | −0.119743 | + | 0.0320850i | −0.318193 | − | 0.948026i | \(-0.603076\pi\) |
0.198450 | + | 0.980111i | \(0.436409\pi\) | |||||||
\(614\) | 16.3110 | − | 14.0422i | 0.658260 | − | 0.566698i | ||||
\(615\) | − | 51.7189i | − | 2.08551i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 36.8410i | 1.48316i | 0.670863 | + | 0.741581i | \(0.265924\pi\) | ||||
−0.670863 | + | 0.741581i | \(0.734076\pi\) | |||||||
\(618\) | −27.1195 | − | 31.5012i | −1.09091 | − | 1.26717i | ||||
\(619\) | −42.4639 | + | 11.3782i | −1.70677 | + | 0.457327i | −0.974629 | − | 0.223827i | \(-0.928145\pi\) |
−0.732140 | + | 0.681155i | \(0.761478\pi\) | |||||||
\(620\) | 33.1886 | − | 24.5139i | 1.33289 | − | 0.984503i | ||||
\(621\) | 0.167085 | − | 0.623570i | 0.00670489 | − | 0.0250230i | ||||
\(622\) | −2.20563 | − | 1.50315i | −0.0884377 | − | 0.0602710i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −10.3778 | + | 9.64397i | −0.415444 | + | 0.386068i | ||||
\(625\) | −0.998199 | − | 1.72893i | −0.0399279 | − | 0.0691572i | ||||
\(626\) | −13.4071 | − | 27.8266i | −0.535857 | − | 1.11217i | ||||
\(627\) | −8.06389 | + | 2.16071i | −0.322041 | + | 0.0862905i | ||||
\(628\) | 8.01730 | − | 0.906441i | 0.319925 | − | 0.0361709i | ||||
\(629\) | −1.56781 | + | 1.56781i | −0.0625127 | + | 0.0625127i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.6001 | −1.17836 | −0.589181 | − | 0.808001i | \(-0.700549\pi\) | ||||
−0.589181 | + | 0.808001i | \(0.700549\pi\) | |||||||
\(632\) | 29.8103 | − | 9.21401i | 1.18579 | − | 0.366513i | ||||
\(633\) | 1.85200 | − | 3.20776i | 0.0736104 | − | 0.127497i | ||||
\(634\) | −26.9302 | − | 9.41750i | −1.06954 | − | 0.374017i | ||||
\(635\) | −5.73215 | + | 21.3927i | −0.227474 | + | 0.848943i | ||||
\(636\) | 15.8419 | + | 40.3190i | 0.628171 | + | 1.59875i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −16.2081 | − | 11.0460i | −0.641686 | − | 0.437314i | ||||
\(639\) | −2.79143 | + | 1.61163i | −0.110427 | + | 0.0637552i | ||||
\(640\) | −28.7814 | − | 28.7044i | −1.13768 | − | 1.13464i | ||||
\(641\) | −6.92621 | + | 11.9965i | −0.273569 | + | 0.473835i | −0.969773 | − | 0.244009i | \(-0.921537\pi\) |
0.696204 | + | 0.717844i | \(0.254871\pi\) | |||||||
\(642\) | −3.13110 | + | 41.8892i | −0.123575 | + | 1.65324i | ||||
\(643\) | 27.3875 | − | 27.3875i | 1.08006 | − | 1.08006i | 0.0835527 | − | 0.996503i | \(-0.473373\pi\) |
0.996503 | − | 0.0835527i | \(-0.0266267\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.58562 | + | 1.58562i | 0.0624339 | + | 0.0624339i | ||||
\(646\) | 7.84228 | + | 9.10937i | 0.308550 | + | 0.358403i | ||||
\(647\) | 19.7138 | + | 11.3818i | 0.775029 | + | 0.447463i | 0.834666 | − | 0.550757i | \(-0.185661\pi\) |
−0.0596369 | + | 0.998220i | \(0.518994\pi\) | |||||||
\(648\) | 21.6269 | − | 23.3351i | 0.849585 | − | 0.916690i | ||||
\(649\) | 4.06512 | + | 7.04099i | 0.159570 | + | 0.276383i | ||||
\(650\) | −3.46089 | − | 18.2721i | −0.135747 | − | 0.716690i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.920190 | − | 2.11130i | 0.0360374 | − | 0.0826850i | ||||
\(653\) | 2.70273 | + | 0.724195i | 0.105766 | + | 0.0283399i | 0.311314 | − | 0.950307i | \(-0.399231\pi\) |
−0.205548 | + | 0.978647i | \(0.565898\pi\) | |||||||
\(654\) | 17.9229 | − | 8.63545i | 0.700842 | − | 0.337673i | ||||
\(655\) | 5.38345 | + | 3.10814i | 0.210349 | + | 0.121445i | ||||
\(656\) | −25.8369 | − | 7.94797i | −1.00876 | − | 0.310316i | ||||
\(657\) | − | 4.19598i | − | 0.163701i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.71933 | + | 2.71933i | 0.105930 | + | 0.105930i | 0.758085 | − | 0.652155i | \(-0.226135\pi\) |
−0.652155 | + | 0.758085i | \(0.726135\pi\) | |||||||
\(660\) | 43.0182 | − | 4.86366i | 1.67448 | − | 0.189318i | ||||
\(661\) | 7.21586 | + | 26.9300i | 0.280665 | + | 1.04745i | 0.951949 | + | 0.306255i | \(0.0990760\pi\) |
−0.671285 | + | 0.741199i | \(0.734257\pi\) | |||||||
\(662\) | −9.91740 | − | 3.46812i | −0.385451 | − | 0.134792i | ||||
\(663\) | −18.8139 | + | 10.8622i | −0.730673 | + | 0.421854i | ||||
\(664\) | −7.70632 | + | 4.84838i | −0.299063 | + | 0.188154i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.146242 | + | 0.772098i | 0.00566676 | + | 0.0299182i | ||||
\(667\) | 0.981340 | + | 0.262949i | 0.0379976 | + | 0.0101814i | ||||
\(668\) | −1.94025 | + | 12.9063i | −0.0750706 | + | 0.499358i | ||||
\(669\) | −1.70058 | − | 6.34665i | −0.0657482 | − | 0.245376i | ||||
\(670\) | 7.01193 | + | 0.524122i | 0.270895 | + | 0.0202486i | ||||
\(671\) | 30.0502 | 1.16008 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.95707 | 0.152534 | 0.0762670 | − | 0.997087i | \(-0.475700\pi\) | ||||
0.0762670 | + | 0.997087i | \(0.475700\pi\) | |||||||
\(674\) | 17.0360 | + | 1.27340i | 0.656204 | + | 0.0490494i | ||||
\(675\) | 6.37787 | + | 23.8025i | 0.245484 | + | 0.916160i | ||||
\(676\) | 3.04323 | − | 20.2431i | 0.117047 | − | 0.778582i | ||||
\(677\) | 11.0349 | + | 2.95679i | 0.424105 | + | 0.113639i | 0.464558 | − | 0.885543i | \(-0.346213\pi\) |
−0.0404526 | + | 0.999181i | \(0.512880\pi\) | |||||||
\(678\) | 7.99291 | + | 42.1993i | 0.306966 | + | 1.62065i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −33.1933 | − | 52.7596i | −1.27291 | − | 2.02324i | ||||
\(681\) | −16.0961 | + | 9.29311i | −0.616806 | + | 0.356113i | ||||
\(682\) | 21.6805 | + | 7.58168i | 0.830189 | + | 0.290318i | ||||
\(683\) | −6.28333 | − | 23.4497i | −0.240425 | − | 0.897277i | −0.975628 | − | 0.219431i | \(-0.929580\pi\) |
0.735203 | − | 0.677847i | \(-0.237087\pi\) | |||||||
\(684\) | 4.23318 | − | 0.478606i | 0.161860 | − | 0.0182999i | ||||
\(685\) | −19.7233 | − | 19.7233i | −0.753587 | − | 0.753587i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 35.9272i | 1.37071i | ||||||||
\(688\) | 1.03579 | − | 0.548448i | 0.0394892 | − | 0.0209094i | ||||
\(689\) | 14.6425 | + | 8.45384i | 0.557834 | + | 0.322066i | ||||
\(690\) | −2.02016 | + | 0.973332i | −0.0769060 | + | 0.0370541i | ||||
\(691\) | 16.1198 | + | 4.31928i | 0.613225 | + | 0.164313i | 0.552046 | − | 0.833814i | \(-0.313847\pi\) |
0.0611789 | + | 0.998127i | \(0.480514\pi\) | |||||||
\(692\) | 4.29008 | − | 9.84324i | 0.163084 | − | 0.374184i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.20205 | − | 38.0239i | −0.273386 | − | 1.44337i | ||||
\(695\) | 16.3934 | + | 28.3942i | 0.621836 | + | 1.07705i | ||||
\(696\) | 21.6679 | + | 20.0817i | 0.821318 | + | 0.761195i | ||||
\(697\) | −35.8985 | − | 20.7260i | −1.35975 | − | 0.785052i | ||||
\(698\) | −3.87434 | − | 4.50032i | −0.146646 | − | 0.170340i | ||||
\(699\) | 22.5756 | + | 22.5756i | 0.853888 | + | 0.853888i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.7735 | − | 22.7735i | 0.860141 | − | 0.860141i | −0.131213 | − | 0.991354i | \(-0.541887\pi\) |
0.991354 | + | 0.131213i | \(0.0418871\pi\) | |||||||
\(702\) | 0.546135 | − | 7.30643i | 0.0206125 | − | 0.275764i | ||||
\(703\) | 0.250443 | − | 0.433780i | 0.00944564 | − | 0.0163603i | ||||
\(704\) | 4.18116 | − | 22.2378i | 0.157583 | − | 0.838117i | ||||
\(705\) | 72.4553 | − | 41.8321i | 2.72882 | − | 1.57549i | ||||
\(706\) | 19.0709 | + | 12.9970i | 0.717744 | + | 0.489149i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.47821 | − | 11.3975i | −0.168301 | − | 0.428343i | ||||
\(709\) | −6.83770 | + | 25.5187i | −0.256795 | + | 0.958373i | 0.710288 | + | 0.703912i | \(0.248565\pi\) |
−0.967083 | + | 0.254462i | \(0.918102\pi\) | |||||||
\(710\) | −10.0569 | − | 3.51691i | −0.377430 | − | 0.131987i | ||||
\(711\) | 8.47886 | − | 14.6858i | 0.317982 | − | 0.550761i | ||||
\(712\) | 11.7614 | + | 38.0521i | 0.440779 | + | 1.42606i | ||||
\(713\) | −1.18967 | −0.0445536 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.9480 | − | 11.9480i | 0.446829 | − | 0.446829i | ||||
\(716\) | −45.4555 | + | 5.13923i | −1.69875 | + | 0.192062i | ||||
\(717\) | −39.0780 | + | 10.4709i | −1.45939 | + | 0.391043i | ||||
\(718\) | 10.1504 | + | 21.0672i | 0.378810 | + | 0.786222i | ||||
\(719\) | −6.50750 | − | 11.2713i | −0.242689 | − | 0.420349i | 0.718790 | − | 0.695227i | \(-0.244696\pi\) |
−0.961479 | + | 0.274877i | \(0.911363\pi\) | |||||||
\(720\) | −22.0771 | − | 0.809141i | −0.822766 | − | 0.0301549i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 19.9601 | + | 13.6030i | 0.742838 | + | 0.506250i | ||||
\(723\) | 13.4257 | − | 50.1054i | 0.499307 | − | 1.86344i | ||||
\(724\) | 8.42319 | − | 6.22158i | 0.313045 | − | 0.231223i | ||||
\(725\) | −37.4591 | + | 10.0371i | −1.39120 | + | 0.372770i | ||||
\(726\) | −5.89612 | − | 6.84876i | −0.218826 | − | 0.254181i | ||||
\(727\) | − | 19.1133i | − | 0.708874i | −0.935080 | − | 0.354437i | \(-0.884673\pi\) | ||
0.935080 | − | 0.354437i | \(-0.115327\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.61946i | 0.0970171i | ||||||||
\(730\) | 10.5108 | − | 9.04881i | 0.389023 | − | 0.334911i | ||||
\(731\) | 1.73602 | − | 0.465165i | 0.0642090 | − | 0.0172047i | ||||
\(732\) | −44.7584 | − | 6.72871i | −1.65432 | − | 0.248700i | ||||
\(733\) | −12.2643 | + | 45.7708i | −0.452991 | + | 1.69058i | 0.240939 | + | 0.970540i | \(0.422545\pi\) |
−0.693929 | + | 0.720043i | \(0.744122\pi\) | |||||||
\(734\) | −18.8579 | + | 27.6709i | −0.696059 | + | 1.02135i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.175792 | + | 1.15878i | 0.00647977 | + | 0.0427130i | ||||
\(737\) | 1.95707 | + | 3.38975i | 0.0720897 | + | 0.124863i | ||||
\(738\) | −13.2353 | + | 6.37689i | −0.487197 | + | 0.234737i | ||||
\(739\) | −10.9480 | + | 2.93350i | −0.402728 | + | 0.107911i | −0.454497 | − | 0.890748i | \(-0.650181\pi\) |
0.0517686 | + | 0.998659i | \(0.483514\pi\) | |||||||
\(740\) | −1.61871 | + | 2.03139i | −0.0595050 | + | 0.0746755i | ||||
\(741\) | 3.47028 | − | 3.47028i | 0.127484 | − | 0.127484i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.9072 | 1.42737 | 0.713683 | − | 0.700469i | \(-0.247026\pi\) | ||||
0.713683 | + | 0.700469i | \(0.247026\pi\) | |||||||
\(744\) | −30.5944 | − | 16.1472i | −1.12165 | − | 0.591983i | ||||
\(745\) | 14.8336 | − | 25.6926i | 0.543463 | − | 0.941305i | ||||
\(746\) | −14.5162 | + | 41.5103i | −0.531474 | + | 1.51980i | ||||
\(747\) | −1.28070 | + | 4.77963i | −0.0468583 | + | 0.174878i | ||||
\(748\) | 13.8633 | − | 31.8083i | 0.506893 | − | 1.16303i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 17.7287 | − | 26.0139i | 0.647360 | − | 0.949893i | ||||
\(751\) | −15.2975 | + | 8.83202i | −0.558214 | + | 0.322285i | −0.752428 | − | 0.658674i | \(-0.771118\pi\) |
0.194215 | + | 0.980959i | \(0.437784\pi\) | |||||||
\(752\) | −9.76314 | − | 42.6246i | −0.356025 | − | 1.55436i | ||||
\(753\) | 20.1004 | − | 34.8149i | 0.732499 | − | 1.26873i | ||||
\(754\) | 11.4985 | + | 0.859478i | 0.418749 | + | 0.0313003i | ||||
\(755\) | −3.95367 | + | 3.95367i | −0.143889 | + | 0.143889i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.2828 | − | 21.2828i | −0.773535 | − | 0.773535i | 0.205187 | − | 0.978723i | \(-0.434220\pi\) |
−0.978723 | + | 0.205187i | \(0.934220\pi\) | |||||||
\(758\) | 30.3291 | − | 26.1104i | 1.10160 | − | 0.948372i | ||||
\(759\) | −1.08102 | − | 0.624129i | −0.0392387 | − | 0.0226545i | ||||
\(760\) | 10.3279 | + | 9.57187i | 0.374633 | + | 0.347208i | ||||
\(761\) | 7.59613 | + | 13.1569i | 0.275359 | + | 0.476937i | 0.970226 | − | 0.242202i | \(-0.0778698\pi\) |
−0.694866 | + | 0.719139i | \(0.744536\pi\) | |||||||
\(762\) | 18.2447 | − | 3.45570i | 0.660936 | − | 0.125187i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.97854 | + | 1.17031i | −0.107760 | + | 0.0423402i | ||||
\(765\) | −32.7226 | − | 8.76800i | −1.18309 | − | 0.317008i | ||||
\(766\) | −3.17755 | − | 6.59502i | −0.114810 | − | 0.238288i | ||||
\(767\) | −4.13916 | − | 2.38975i | −0.149457 | − | 0.0862888i | ||||
\(768\) | −11.2070 | + | 32.1858i | −0.404399 | + | 1.16141i | ||||
\(769\) | − | 40.3950i | − | 1.45668i | −0.685216 | − | 0.728340i | \(-0.740292\pi\) | ||
0.685216 | − | 0.728340i | \(-0.259708\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.13436 | + | 8.13436i | 0.292952 | + | 0.292952i | ||||
\(772\) | 20.5695 | − | 25.8136i | 0.740312 | − | 0.929051i | ||||
\(773\) | −4.97644 | − | 18.5723i | −0.178990 | − | 0.668001i | −0.995837 | − | 0.0911466i | \(-0.970947\pi\) |
0.816847 | − | 0.576854i | \(-0.195720\pi\) | |||||||
\(774\) | 0.210267 | − | 0.601279i | 0.00755790 | − | 0.0216125i | ||||
\(775\) | 39.3274 | − | 22.7057i | 1.41268 | − | 0.815613i | ||||
\(776\) | 1.78212 | − | 7.82868i | 0.0639742 | − | 0.281033i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.17225 | + | 1.54789i | −0.292989 | + | 0.0554947i | ||||
\(779\) | 9.04523 | + | 2.42366i | 0.324079 | + | 0.0868367i | ||||
\(780\) | −20.4713 | + | 15.1206i | −0.732990 | + | 0.541405i | ||||
\(781\) | −1.53498 | − | 5.72864i | −0.0549260 | − | 0.204987i | ||||
\(782\) | −0.133966 | + | 1.79226i | −0.00479062 | + | 0.0640910i | ||||
\(783\) | −15.2787 | −0.546017 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.4943 | 0.517323 | ||||||||
\(786\) | 0.388494 | − | 5.19744i | 0.0138571 | − | 0.185387i | ||||
\(787\) | 10.6201 | + | 39.6347i | 0.378566 | + | 1.41283i | 0.848064 | + | 0.529893i | \(0.177768\pi\) |
−0.469499 | + | 0.882933i | \(0.655565\pi\) | |||||||
\(788\) | −20.5228 | − | 27.7851i | −0.731093 | − | 0.989803i | ||||
\(789\) | 0.745554 | + | 0.199771i | 0.0265424 | + | 0.00711202i | ||||
\(790\) | 55.0727 | − | 10.4312i | 1.95940 | − | 0.371127i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6.54874 | − | 10.4090i | −0.232699 | − | 0.369867i | ||||
\(793\) | −15.2988 | + | 8.83277i | −0.543276 | + | 0.313661i | ||||
\(794\) | −9.79471 | + | 28.0089i | −0.347601 | + | 0.993997i | ||||
\(795\) | 20.1415 | + | 75.1690i | 0.714345 | + | 2.66597i | ||||
\(796\) | 25.3400 | + | 20.1921i | 0.898153 | + | 0.715690i | ||||
\(797\) | 21.9291 | + | 21.9291i | 0.776770 | + | 0.776770i | 0.979280 | − | 0.202510i | \(-0.0649099\pi\) |
−0.202510 | + | 0.979280i | \(0.564910\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 67.0556i | − | 2.37226i | ||||||
\(800\) | −27.9272 | − | 34.9510i | −0.987377 | − | 1.23570i | ||||
\(801\) | 18.7461 | + | 10.8231i | 0.662360 | + | 0.382414i | ||||
\(802\) | 13.5715 | + | 28.1677i | 0.479226 | + | 0.994635i | ||||
\(803\) | 7.45742 | + | 1.99821i | 0.263167 | + | 0.0705153i | ||||
\(804\) | −2.15595 | − | 5.48709i | −0.0760344 | − | 0.193515i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.2662 | + | 2.51274i | −0.467283 | + | 0.0885073i | ||||
\(807\) | 28.4708 | + | 49.3130i | 1.00222 | + | 1.73590i | ||||
\(808\) | 0.752935 | + | 19.8180i | 0.0264882 | + | 0.697196i | ||||
\(809\) | 2.56402 | + | 1.48034i | 0.0901462 | + | 0.0520459i | 0.544395 | − | 0.838829i | \(-0.316759\pi\) |
−0.454249 | + | 0.890875i | \(0.650092\pi\) | |||||||
\(810\) | 43.3148 | − | 37.2898i | 1.52193 | − | 1.31023i | ||||
\(811\) | 10.4787 | + | 10.4787i | 0.367956 | + | 0.367956i | 0.866731 | − | 0.498775i | \(-0.166217\pi\) |
−0.498775 | + | 0.866731i | \(0.666217\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.5723 | − | 14.5723i | 0.511073 | − | 0.511073i | ||||
\(814\) | −1.44188 | − | 0.107776i | −0.0505378 | − | 0.00377755i | ||||
\(815\) | 2.06870 | − | 3.58309i | 0.0724633 | − | 0.125510i | ||||
\(816\) | −27.7711 | + | 44.2727i | −0.972183 | + | 1.54985i | ||||
\(817\) | −0.351619 | + | 0.203007i | −0.0123016 | + | 0.00710232i | ||||
\(818\) | −1.16140 | + | 1.70416i | −0.0406075 | + | 0.0595847i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −44.5164 | − | 19.4020i | −1.55458 | − | 0.677547i | ||||
\(821\) | −3.92432 | + | 14.6458i | −0.136960 | + | 0.511140i | 0.863023 | + | 0.505165i | \(0.168569\pi\) |
−0.999982 | + | 0.00597486i | \(0.998098\pi\) | |||||||
\(822\) | −7.71980 | + | 22.0755i | −0.269259 | + | 0.769970i | ||||
\(823\) | −4.94250 | + | 8.56066i | −0.172285 | + | 0.298406i | −0.939218 | − | 0.343321i | \(-0.888448\pi\) |
0.766934 | + | 0.641726i | \(0.221782\pi\) | |||||||
\(824\) | −37.2880 | + | 11.5253i | −1.29899 | + | 0.401502i | ||||
\(825\) | 47.6477 | 1.65888 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.5166 | + | 16.5166i | −0.574338 | + | 0.574338i | −0.933338 | − | 0.359000i | \(-0.883118\pi\) |
0.359000 | + | 0.933338i | \(0.383118\pi\) | |||||||
\(828\) | 0.498166 | + | 0.396962i | 0.0173125 | + | 0.0137954i | ||||
\(829\) | 32.6031 | − | 8.73597i | 1.13235 | − | 0.303413i | 0.356480 | − | 0.934303i | \(-0.383977\pi\) |
0.775872 | + | 0.630890i | \(0.217310\pi\) | |||||||
\(830\) | −14.7347 | + | 7.09935i | −0.511450 | + | 0.246422i | ||||
\(831\) | 4.45249 | + | 7.71194i | 0.154455 | + | 0.267524i | ||||
\(832\) | 4.40776 | + | 12.5504i | 0.152812 | + | 0.435107i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 15.4811 | − | 22.7159i | 0.536065 | − | 0.786587i | ||||
\(835\) | −6.06820 | + | 22.6468i | −0.209999 | + | 0.783726i | ||||
\(836\) | −1.16531 | + | 7.75145i | −0.0403030 | + | 0.268090i | ||||
\(837\) | 17.2815 | − | 4.63057i | 0.597337 | − | 0.160056i | ||||
\(838\) | −36.6874 | + | 31.5843i | −1.26735 | + | 1.09106i | ||||
\(839\) | 30.3282i | 1.04705i | 0.852012 | + | 0.523523i | \(0.175383\pi\) | ||||
−0.852012 | + | 0.523523i | \(0.824617\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.95519i | 0.170869i | ||||||||
\(842\) | −25.0375 | − | 29.0829i | −0.862850 | − | 1.00226i | ||||
\(843\) | 40.8623 | − | 10.9490i | 1.40737 | − | 0.377104i | ||||
\(844\) | −2.06627 | − | 2.79745i | −0.0711239 | − | 0.0962922i | ||||
\(845\) | 9.51782 | − | 35.5210i | 0.327423 | − | 1.22196i | ||||
\(846\) | −19.6388 | − | 13.3840i | −0.675196 | − | 0.460151i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 40.6470 | + | 1.48974i | 1.39582 | + | 0.0511578i | ||||
\(849\) | 29.3945 | + | 50.9127i | 1.00882 | + | 1.74732i | ||||
\(850\) | −29.7779 | − | 61.8042i | −1.02137 | − | 2.11987i | ||||
\(851\) | 0.0723414 | − | 0.0193838i | 0.00247983 | − | 0.000664469i | ||||
\(852\) | 1.00355 | + | 8.87623i | 0.0343812 | + | 0.304095i | ||||
\(853\) | 10.6402 | − | 10.6402i | 0.364313 | − | 0.364313i | −0.501085 | − | 0.865398i | \(-0.667066\pi\) |
0.865398 | + | 0.501085i | \(0.167066\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.65306 | 0.261729 | ||||||||
\(856\) | 34.8810 | + | 18.4095i | 1.19221 | + | 0.629224i | ||||
\(857\) | −18.3762 | + | 31.8285i | −0.627719 | + | 1.08724i | 0.360289 | + | 0.932841i | \(0.382678\pi\) |
−0.988008 | + | 0.154401i | \(0.950655\pi\) | |||||||
\(858\) | −13.3729 | − | 4.67651i | −0.456544 | − | 0.159653i | ||||
\(859\) | −7.13827 | + | 26.6404i | −0.243555 | + | 0.908958i | 0.730550 | + | 0.682859i | \(0.239264\pi\) |
−0.974104 | + | 0.226099i | \(0.927403\pi\) | |||||||
\(860\) | 1.95964 | − | 0.769968i | 0.0668231 | − | 0.0262557i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −23.8749 | − | 16.2709i | −0.813182 | − | 0.554190i | ||||
\(863\) | −32.5024 | + | 18.7653i | −1.10639 | + | 0.638777i | −0.937893 | − | 0.346924i | \(-0.887226\pi\) |
−0.168501 | + | 0.985701i | \(0.553893\pi\) | |||||||
\(864\) | −7.06392 | − | 16.1485i | −0.240319 | − | 0.549382i | ||||
\(865\) | 9.64460 | − | 16.7049i | 0.327926 | − | 0.567985i | ||||
\(866\) | 2.39572 | − | 32.0510i | 0.0814100 | − | 1.08914i | ||||
\(867\) | −31.0631 | + | 31.0631i | −1.05496 | + | 1.05496i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 22.0630 | + | 22.0630i | 0.748436 | + | 0.748436i | ||||
\(870\) | 34.6255 | + | 40.2200i | 1.17392 | + | 1.36359i | ||||
\(871\) | −1.99272 | − | 1.15050i | −0.0675208 | − | 0.0389832i | ||||
\(872\) | −0.709184 | − | 18.6664i | −0.0240160 | − | 0.632126i | ||||
\(873\) | −2.18181 | − | 3.77901i | −0.0738432 | − | 0.127900i | ||||
\(874\) | −0.0755591 | − | 0.398921i | −0.00255582 | − | 0.0134937i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.6600 | − | 4.64607i | −0.360170 | − | 0.156976i | ||||
\(877\) | −33.0809 | − | 8.86399i | −1.11706 | − | 0.299316i | −0.347368 | − | 0.937729i | \(-0.612924\pi\) |
−0.769694 | + | 0.638413i | \(0.779591\pi\) | |||||||
\(878\) | 45.4536 | − | 21.9000i | 1.53398 | − | 0.739089i | ||||
\(879\) | 47.7575 | + | 27.5728i | 1.61082 | + | 0.930007i | ||||
\(880\) | 11.9516 | − | 38.8519i | 0.402890 | − | 1.30970i | ||||
\(881\) | − | 11.3518i | − | 0.382453i | −0.981546 | − | 0.191226i | \(-0.938754\pi\) | ||
0.981546 | − | 0.191226i | \(-0.0612464\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.21956 | − | 3.21956i | −0.108347 | − | 0.108347i | 0.650855 | − | 0.759202i | \(-0.274411\pi\) |
−0.759202 | + | 0.650855i | \(0.774411\pi\) | |||||||
\(884\) | 2.29160 | + | 20.2687i | 0.0770747 | + | 0.681711i | ||||
\(885\) | −5.69363 | − | 21.2489i | −0.191389 | − | 0.714275i | ||||
\(886\) | −9.66278 | − | 3.37908i | −0.324628 | − | 0.113522i | ||||
\(887\) | 23.4899 | − | 13.5619i | 0.788714 | − | 0.455364i | −0.0507957 | − | 0.998709i | \(-0.516176\pi\) |
0.839510 | + | 0.543345i | \(0.182842\pi\) | |||||||
\(888\) | 2.12347 | + | 0.483386i | 0.0712591 | + | 0.0162214i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 13.3152 | + | 70.2989i | 0.446327 | + | 2.35642i | ||||
\(891\) | 30.7318 | + | 8.23456i | 1.02955 | + | 0.275868i | ||||
\(892\) | −6.10075 | − | 0.917152i | −0.204268 | − | 0.0307085i | ||||
\(893\) | 3.92068 | + | 14.6322i | 0.131201 | + | 0.489647i | ||||
\(894\) | −24.8049 | − | 1.85409i | −0.829599 | − | 0.0620102i | ||||
\(895\) | −82.1780 | −2.74691 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.733810 | 0.0245012 | ||||||||
\(898\) | 50.2548 | + | 3.75640i | 1.67702 | + | 0.125353i | ||||
\(899\) | 7.28734 | + | 27.1967i | 0.243046 | + | 0.907061i | ||||
\(900\) | −24.0444 | − | 3.61469i | −0.801479 | − | 0.120490i | ||||
\(901\) | 60.2469 | + | 16.1431i | 2.00711 | + | 0.537805i | ||||
\(902\) | −5.03060 | − | 26.5595i | −0.167501 | − | 0.884336i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 39.3209 | + | 8.95100i | 1.30780 | + | 0.297706i | ||||
\(905\) | 16.2915 | − | 9.40592i | 0.541549 | − | 0.312663i | ||||
\(906\) | 4.42518 | + | 1.54749i | 0.147017 | + | 0.0514119i | ||||
\(907\) | 13.6318 | + | 50.8747i | 0.452638 | + | 1.68927i | 0.694941 | + | 0.719067i | \(0.255431\pi\) |
−0.242303 | + | 0.970201i | \(0.577903\pi\) | |||||||
\(908\) | 1.96056 | + | 17.3408i | 0.0650635 | + | 0.575474i | ||||
\(909\) | 7.62161 | + | 7.62161i | 0.252793 | + | 0.252793i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 18.3761i | − | 0.608827i | −0.952540 | − | 0.304414i | \(-0.901540\pi\) | ||
0.952540 | − | 0.304414i | \(-0.0984605\pi\) | |||||||
\(912\) | 3.47134 | − | 11.2845i | 0.114948 | − | 0.373667i | ||||
\(913\) | −7.88484 | − | 4.55231i | −0.260950 | − | 0.150660i | ||||
\(914\) | 6.09360 | − | 2.93596i | 0.201558 | − | 0.0971130i | ||||
\(915\) | −78.5383 | − | 21.0443i | −2.59640 | − | 0.695702i | ||||
\(916\) | 30.9238 | + | 13.4778i | 1.02175 | + | 0.445320i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −5.02999 | − | 26.5563i | −0.166015 | − | 0.876490i | ||||
\(919\) | −22.0221 | − | 38.1433i | −0.726441 | − | 1.25823i | −0.958378 | − | 0.285502i | \(-0.907840\pi\) |
0.231937 | − | 0.972731i | \(-0.425494\pi\) | |||||||
\(920\) | 0.0799345 | + | 2.10396i | 0.00263536 | + | 0.0693655i | ||||
\(921\) | −28.0744 | − | 16.2088i | −0.925083 | − | 0.534097i | ||||
\(922\) | −8.53512 | − | 9.91415i | −0.281089 | − | 0.326505i | ||||
\(923\) | 2.46531 | + | 2.46531i | 0.0811467 | + | 0.0811467i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.02146 | + | 2.02146i | −0.0664653 | + | 0.0664653i | ||||
\(926\) | 0.0813112 | − | 1.08782i | 0.00267205 | − | 0.0357479i | ||||
\(927\) | −10.6057 | + | 18.3696i | −0.348338 | + | 0.603338i | ||||
\(928\) | 25.4136 | − | 11.1168i | 0.834242 | − | 0.364927i | ||||
\(929\) | −18.4252 | + | 10.6378i | −0.604512 | + | 0.349015i | −0.770814 | − | 0.637060i | \(-0.780150\pi\) |
0.166303 | + | 0.986075i | \(0.446817\pi\) | |||||||
\(930\) | −51.3540 | − | 34.9982i | −1.68396 | − | 1.14764i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 27.9007 | − | 10.9626i | 0.913919 | − | 0.359091i | ||||
\(933\) | −1.04051 | + | 3.88323i | −0.0340647 | + | 0.127131i | ||||
\(934\) | −4.74021 | − | 1.65765i | −0.155105 | − | 0.0542401i | ||||
\(935\) | 31.1664 | − | 53.9817i | 1.01925 | − | 1.76539i | ||||
\(936\) | 6.39356 | + | 3.37440i | 0.208980 | + | 0.110296i | ||||
\(937\) | −1.53994 | −0.0503075 | −0.0251537 | − | 0.999684i | \(-0.508008\pi\) | ||||
−0.0251537 | + | 0.999684i | \(0.508008\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32.8969 | + | 32.8969i | −1.07355 | + | 1.07355i | ||||
\(940\) | −8.82527 | − | 78.0579i | −0.287849 | − | 2.54597i | ||||
\(941\) | 20.9217 | − | 5.60595i | 0.682028 | − | 0.182749i | 0.0988611 | − | 0.995101i | \(-0.468480\pi\) |
0.583167 | + | 0.812352i | \(0.301813\pi\) | |||||||
\(942\) | −5.27487 | − | 10.9480i | −0.171864 | − | 0.356706i | ||||
\(943\) | 0.700083 | + | 1.21258i | 0.0227978 | + | 0.0394870i | ||||
\(944\) | −11.4902 | − | 0.421122i | −0.373973 | − | 0.0137064i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.968506 | + | 0.660045i | 0.0314888 | + | 0.0214599i | ||||
\(947\) | −11.8581 | + | 44.2550i | −0.385336 | + | 1.43809i | 0.452300 | + | 0.891866i | \(0.350604\pi\) |
−0.837636 | + | 0.546228i | \(0.816063\pi\) | |||||||
\(948\) | −27.9215 | − | 37.8020i | −0.906849 | − | 1.22775i | ||||
\(949\) | −4.38397 | + | 1.17468i | −0.142310 | + | 0.0381318i | ||||
\(950\) | 10.1115 | + | 11.7452i | 0.328060 | + | 0.381065i | ||||
\(951\) | 42.9706i | 1.39342i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41.8875i | 1.35687i | 0.734661 | + | 0.678435i | \(0.237341\pi\) | ||||
−0.734661 | + | 0.678435i | \(0.762659\pi\) | |||||||
\(954\) | 16.7529 | − | 14.4226i | 0.542395 | − | 0.466949i | ||||
\(955\) | −5.55305 | + | 1.48794i | −0.179693 | + | 0.0481485i | ||||
\(956\) | −5.64714 | + | 37.5639i | −0.182642 | + | 1.21490i | ||||
\(957\) | −7.64621 | + | 28.5361i | −0.247167 | + | 0.922440i | ||||
\(958\) | −7.90884 | + | 11.6049i | −0.255523 | + | 0.374937i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −26.5009 | + | 55.1918i | −0.855314 | + | 1.78131i | ||||
\(961\) | −0.985195 | − | 1.70641i | −0.0317805 | − | 0.0550454i | ||||
\(962\) | 0.765750 | − | 0.368946i | 0.0246888 | − | 0.0118953i | ||||
\(963\) | 20.7052 | − | 5.54795i | 0.667216 | − | 0.178780i | ||||
\(964\) | −38.0909 | − | 30.3527i | −1.22683 | − | 0.977593i | ||||
\(965\) | 41.9274 | − | 41.9274i | 1.34969 | − | 1.34969i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.99067 | −0.0640156 | −0.0320078 | − | 0.999488i | \(-0.510190\pi\) | ||||
−0.0320078 | + | 0.999488i | \(0.510190\pi\) | |||||||
\(968\) | −8.10687 | + | 2.50574i | −0.260565 | + | 0.0805374i | ||||
\(969\) | 9.05224 | − | 15.6789i | 0.290800 | − | 0.503680i | ||||
\(970\) | 4.76116 | − | 13.6150i | 0.152872 | − | 0.437151i | ||||
\(971\) | −1.48269 | + | 5.53347i | −0.0475818 | + | 0.177578i | −0.985627 | − | 0.168934i | \(-0.945967\pi\) |
0.938045 | + | 0.346512i | \(0.112634\pi\) | |||||||
\(972\) | −26.7916 | − | 11.6768i | −0.859341 | − | 0.374535i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 5.89948 | − | 8.65650i | 0.189031 | − | 0.277372i | ||||
\(975\) | −24.2578 | + | 14.0053i | −0.776873 | + | 0.448528i | ||||
\(976\) | −22.5824 | + | 36.0009i | −0.722846 | + | 1.15236i | ||||
\(977\) | −12.5203 | + | 21.6858i | −0.400560 | + | 0.693790i | −0.993794 | − | 0.111241i | \(-0.964518\pi\) |
0.593234 | + | 0.805030i | \(0.297851\pi\) | |||||||
\(978\) | −3.45928 | − | 0.258571i | −0.110616 | − | 0.00826820i | ||||
\(979\) | −28.1629 | + | 28.1629i | −0.900089 | + | 0.900089i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.17874 | − | 7.17874i | −0.229199 | − | 0.229199i | ||||
\(982\) | −32.5856 | + | 28.0531i | −1.03985 | + | 0.895209i | ||||
\(983\) | 27.2577 | + | 15.7373i | 0.869387 | + | 0.501941i | 0.867144 | − | 0.498057i | \(-0.165953\pi\) |
0.00224251 | + | 0.999997i | \(0.499286\pi\) | |||||||
\(984\) | 1.54574 | + | 40.6856i | 0.0492765 | + | 1.29701i | ||||
\(985\) | −31.0268 | − | 53.7399i | −0.988595 | − | 1.71230i | ||||
\(986\) | 41.7929 | − | 7.91593i | 1.33096 | − | 0.252095i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.68514 | − | 4.28885i | −0.0536116 | − | 0.136446i | ||||
\(989\) | −0.0586393 | − | 0.0157124i | −0.00186462 | − | 0.000499624i | ||||
\(990\) | −9.58914 | − | 19.9023i | −0.304763 | − | 0.632537i | ||||
\(991\) | −45.8894 | − | 26.4943i | −1.45773 | − | 0.841619i | −0.458827 | − | 0.888526i | \(-0.651730\pi\) |
−0.998899 | + | 0.0469070i | \(0.985064\pi\) | |||||||
\(992\) | −25.3757 | + | 20.2762i | −0.805680 | + | 0.643771i | ||||
\(993\) | 15.8245i | 0.502175i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 41.1582 | + | 41.1582i | 1.30480 | + | 1.30480i | ||||
\(996\) | 10.7248 | + | 8.54599i | 0.339827 | + | 0.270790i | ||||
\(997\) | −2.62262 | − | 9.78775i | −0.0830592 | − | 0.309981i | 0.911880 | − | 0.410456i | \(-0.134630\pi\) |
−0.994940 | + | 0.100475i | \(0.967964\pi\) | |||||||
\(998\) | 15.3962 | − | 44.0268i | 0.487358 | − | 1.39364i | ||||
\(999\) | −0.975405 | + | 0.563150i | −0.0308604 | + | 0.0178173i |
(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 | 784.2.w.e.619.2 | 32 | ||
7.2 | even | 3 | inner | 784.2.w.e.411.3 | 32 | ||
7.3 | odd | 6 | 112.2.j.d.27.7 | ✓ | 16 | ||
7.4 | even | 3 | 112.2.j.d.27.8 | yes | 16 | ||
7.5 | odd | 6 | inner | 784.2.w.e.411.4 | 32 | ||
7.6 | odd | 2 | inner | 784.2.w.e.619.1 | 32 | ||
16.3 | odd | 4 | inner | 784.2.w.e.227.4 | 32 | ||
28.3 | even | 6 | 448.2.j.d.335.7 | 16 | |||
28.11 | odd | 6 | 448.2.j.d.335.2 | 16 | |||
56.3 | even | 6 | 896.2.j.g.671.2 | 16 | |||
56.11 | odd | 6 | 896.2.j.g.671.7 | 16 | |||
56.45 | odd | 6 | 896.2.j.h.671.7 | 16 | |||
56.53 | even | 6 | 896.2.j.h.671.2 | 16 | |||
112.3 | even | 12 | 112.2.j.d.83.8 | yes | 16 | ||
112.11 | odd | 12 | 896.2.j.h.223.7 | 16 | |||
112.19 | even | 12 | inner | 784.2.w.e.19.2 | 32 | ||
112.45 | odd | 12 | 448.2.j.d.111.2 | 16 | |||
112.51 | odd | 12 | inner | 784.2.w.e.19.1 | 32 | ||
112.53 | even | 12 | 896.2.j.g.223.2 | 16 | |||
112.59 | even | 12 | 896.2.j.h.223.2 | 16 | |||
112.67 | odd | 12 | 112.2.j.d.83.7 | yes | 16 | ||
112.83 | even | 4 | inner | 784.2.w.e.227.3 | 32 | ||
112.101 | odd | 12 | 896.2.j.g.223.7 | 16 | |||
112.109 | even | 12 | 448.2.j.d.111.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.j.d.27.7 | ✓ | 16 | 7.3 | odd | 6 | ||
112.2.j.d.27.8 | yes | 16 | 7.4 | even | 3 | ||
112.2.j.d.83.7 | yes | 16 | 112.67 | odd | 12 | ||
112.2.j.d.83.8 | yes | 16 | 112.3 | even | 12 | ||
448.2.j.d.111.2 | 16 | 112.45 | odd | 12 | |||
448.2.j.d.111.7 | 16 | 112.109 | even | 12 | |||
448.2.j.d.335.2 | 16 | 28.11 | odd | 6 | |||
448.2.j.d.335.7 | 16 | 28.3 | even | 6 | |||
784.2.w.e.19.1 | 32 | 112.51 | odd | 12 | inner | ||
784.2.w.e.19.2 | 32 | 112.19 | even | 12 | inner | ||
784.2.w.e.227.3 | 32 | 112.83 | even | 4 | inner | ||
784.2.w.e.227.4 | 32 | 16.3 | odd | 4 | inner | ||
784.2.w.e.411.3 | 32 | 7.2 | even | 3 | inner | ||
784.2.w.e.411.4 | 32 | 7.5 | odd | 6 | inner | ||
784.2.w.e.619.1 | 32 | 7.6 | odd | 2 | inner | ||
784.2.w.e.619.2 | 32 | 1.1 | even | 1 | trivial | ||
896.2.j.g.223.2 | 16 | 112.53 | even | 12 | |||
896.2.j.g.223.7 | 16 | 112.101 | odd | 12 | |||
896.2.j.g.671.2 | 16 | 56.3 | even | 6 | |||
896.2.j.g.671.7 | 16 | 56.11 | odd | 6 | |||
896.2.j.h.223.2 | 16 | 112.59 | even | 12 | |||
896.2.j.h.223.7 | 16 | 112.11 | odd | 12 | |||
896.2.j.h.671.2 | 16 | 56.53 | even | 6 | |||
896.2.j.h.671.7 | 16 | 56.45 | odd | 6 |