Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(89,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.bb (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 89.12 | ||
Character | \(\chi\) | \(=\) | 315.89 |
Dual form | 315.2.bb.b.269.12 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.28469 | − | 2.22514i | 0.908411 | − | 1.57341i | 0.0921382 | − | 0.995746i | \(-0.470630\pi\) |
0.816272 | − | 0.577667i | \(-0.196037\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.30084 | − | 3.98517i | −1.15042 | − | 1.99259i | ||||
\(5\) | −1.33613 | − | 1.79297i | −0.597535 | − | 0.801843i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64140 | − | 0.151755i | 0.998354 | − | 0.0573579i | ||||
\(8\) | −6.68468 | −2.36339 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5.70613 | + | 0.669669i | −1.80444 | + | 0.211768i | ||||
\(11\) | −4.88189 | + | 2.81856i | −1.47195 | + | 0.849828i | −0.999503 | − | 0.0315336i | \(-0.989961\pi\) |
−0.472442 | + | 0.881362i | \(0.656628\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.53537 | 0.980535 | 0.490267 | − | 0.871572i | \(-0.336899\pi\) | ||||
0.490267 | + | 0.871572i | \(0.336899\pi\) | |||||||
\(14\) | 3.05569 | − | 6.07244i | 0.816667 | − | 1.62293i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.98605 | + | 6.90403i | −0.996512 | + | 1.72601i | ||||
\(17\) | 4.62703 | − | 2.67142i | 1.12222 | − | 0.647914i | 0.180253 | − | 0.983620i | \(-0.442308\pi\) |
0.941967 | + | 0.335707i | \(0.108975\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.24942 | − | 0.721351i | −0.286636 | − | 0.165489i | 0.349788 | − | 0.936829i | \(-0.386254\pi\) |
−0.636424 | + | 0.771340i | \(0.719587\pi\) | |||||||
\(20\) | −4.07109 | + | 9.45005i | −0.910323 | + | 2.11310i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 14.4839i | 3.08797i | ||||||||
\(23\) | 1.49930 | − | 2.59686i | 0.312626 | − | 0.541484i | −0.666304 | − | 0.745680i | \(-0.732125\pi\) |
0.978930 | + | 0.204196i | \(0.0654581\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.42951 | + | 4.79129i | −0.285903 | + | 0.958259i | ||||
\(26\) | 4.54184 | − | 7.86670i | 0.890728 | − | 1.54279i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.68220 | − | 10.1772i | −1.26282 | − | 1.92332i | ||||
\(29\) | 2.19404i | 0.407423i | 0.979031 | + | 0.203712i | \(0.0653005\pi\) | ||||
−0.979031 | + | 0.203712i | \(0.934699\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.31899 | − | 0.761520i | 0.236898 | − | 0.136773i | −0.376852 | − | 0.926273i | \(-0.622994\pi\) |
0.613750 | + | 0.789500i | \(0.289660\pi\) | |||||||
\(32\) | 3.55696 | + | 6.16083i | 0.628787 | + | 1.08909i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 13.7277i | − | 2.35429i | ||||||
\(35\) | −3.80134 | − | 4.53319i | −0.642544 | − | 0.766249i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.946690 | − | 0.546572i | −0.155635 | − | 0.0898558i | 0.420160 | − | 0.907450i | \(-0.361974\pi\) |
−0.575795 | + | 0.817594i | \(0.695307\pi\) | |||||||
\(38\) | −3.21022 | + | 1.85342i | −0.520766 | + | 0.300665i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.93161 | + | 11.9855i | 1.41221 | + | 1.89507i | ||||
\(41\) | 6.52058 | 1.01834 | 0.509172 | − | 0.860665i | \(-0.329952\pi\) | ||||
0.509172 | + | 0.860665i | \(0.329952\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.486125i | − | 0.0741333i | −0.999313 | − | 0.0370667i | \(-0.988199\pi\) | ||
0.999313 | − | 0.0370667i | \(-0.0118014\pi\) | |||||||
\(44\) | 22.4649 | + | 12.9701i | 3.38671 | + | 1.95532i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.85226 | − | 6.67231i | −0.567985 | − | 0.983779i | ||||
\(47\) | 3.68608 | + | 2.12816i | 0.537671 | + | 0.310424i | 0.744134 | − | 0.668030i | \(-0.232862\pi\) |
−0.206464 | + | 0.978454i | \(0.566196\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.95394 | − | 0.801688i | 0.993420 | − | 0.114527i | ||||
\(50\) | 8.82483 | + | 9.33618i | 1.24802 | + | 1.32034i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.13432 | − | 14.0891i | −1.12803 | − | 1.95380i | ||||
\(53\) | 2.01102 | + | 3.48318i | 0.276235 | + | 0.478452i | 0.970446 | − | 0.241319i | \(-0.0775800\pi\) |
−0.694211 | + | 0.719771i | \(0.744247\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.5764 | + | 4.98714i | 1.56097 | + | 0.672466i | ||||
\(56\) | −17.6569 | + | 1.01443i | −2.35950 | + | 0.135559i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.88206 | + | 2.81866i | 0.641046 | + | 0.370108i | ||||
\(59\) | −5.70978 | − | 9.88963i | −0.743350 | − | 1.28752i | −0.950962 | − | 0.309309i | \(-0.899902\pi\) |
0.207612 | − | 0.978211i | \(-0.433431\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.06957 | + | 3.50427i | 0.777129 | + | 0.448676i | 0.835412 | − | 0.549624i | \(-0.185229\pi\) |
−0.0582826 | + | 0.998300i | \(0.518562\pi\) | |||||||
\(62\) | − | 3.91326i | − | 0.496984i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.33411 | 0.291764 | ||||||||
\(65\) | −4.72371 | − | 6.33883i | −0.585904 | − | 0.786235i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.15623 | − | 1.24490i | 0.263425 | − | 0.152089i | −0.362471 | − | 0.931995i | \(-0.618067\pi\) |
0.625896 | + | 0.779907i | \(0.284733\pi\) | |||||||
\(68\) | −21.2921 | − | 12.2930i | −2.58205 | − | 1.49075i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −14.9705 | + | 2.63479i | −1.78932 | + | 0.314918i | ||||
\(71\) | 8.13849i | 0.965861i | 0.875659 | + | 0.482930i | \(0.160428\pi\) | ||||
−0.875659 | + | 0.482930i | \(0.839572\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.56901 | + | 2.71761i | 0.183639 | + | 0.318072i | 0.943117 | − | 0.332461i | \(-0.107879\pi\) |
−0.759478 | + | 0.650533i | \(0.774546\pi\) | |||||||
\(74\) | −2.43240 | + | 1.40435i | −0.282761 | + | 0.163252i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.63886i | 0.761529i | ||||||||
\(77\) | −12.4673 | + | 8.18578i | −1.42078 | + | 0.932856i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.40252 | + | 11.0895i | −0.720340 | + | 1.24766i | 0.240524 | + | 0.970643i | \(0.422681\pi\) |
−0.960864 | + | 0.277022i | \(0.910653\pi\) | |||||||
\(80\) | 17.7046 | − | 2.07781i | 1.97944 | − | 0.232306i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.37690 | − | 14.5092i | 0.925074 | − | 1.60228i | ||||
\(83\) | − | 6.77241i | − | 0.743368i | −0.928359 | − | 0.371684i | \(-0.878780\pi\) | ||
0.928359 | − | 0.371684i | \(-0.121220\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.9721 | − | 4.72679i | −1.19009 | − | 0.512692i | ||||
\(86\) | −1.08170 | − | 0.624518i | −0.116642 | − | 0.0673435i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 32.6339 | − | 18.8412i | 3.47878 | − | 2.00848i | ||||
\(89\) | −5.16513 | + | 8.94627i | −0.547503 | + | 0.948303i | 0.450942 | + | 0.892553i | \(0.351088\pi\) |
−0.998445 | + | 0.0557494i | \(0.982245\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.33831 | − | 0.536509i | 0.978921 | − | 0.0562414i | ||||
\(92\) | −13.7986 | −1.43860 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.47093 | − | 5.46804i | 0.976852 | − | 0.563985i | ||||
\(95\) | 0.376019 | + | 3.20399i | 0.0385787 | + | 0.328723i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.7321 | −1.49582 | −0.747908 | − | 0.663802i | \(-0.768942\pi\) | ||||
−0.747908 | + | 0.663802i | \(0.768942\pi\) | |||||||
\(98\) | 7.14976 | − | 16.5034i | 0.722235 | − | 1.66710i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 22.3832 | − | 5.32714i | 2.23832 | − | 0.532714i | ||||
\(101\) | 7.46683 | + | 12.9329i | 0.742977 | + | 1.28687i | 0.951134 | + | 0.308779i | \(0.0999202\pi\) |
−0.208157 | + | 0.978095i | \(0.566746\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.95755 | + | 3.39058i | −0.192883 | + | 0.334084i | −0.946205 | − | 0.323569i | \(-0.895117\pi\) |
0.753321 | + | 0.657653i | \(0.228451\pi\) | |||||||
\(104\) | −23.6328 | −2.31739 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.3341 | 1.00374 | ||||||||
\(107\) | −7.41102 | + | 12.8363i | −0.716450 | + | 1.24093i | 0.245948 | + | 0.969283i | \(0.420901\pi\) |
−0.962398 | + | 0.271645i | \(0.912432\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.51932 | − | 9.55974i | −0.528655 | − | 0.915657i | −0.999442 | − | 0.0334099i | \(-0.989363\pi\) |
0.470787 | − | 0.882247i | \(-0.343970\pi\) | |||||||
\(110\) | 25.9692 | − | 19.3523i | 2.47607 | − | 1.84517i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −9.48101 | + | 18.8412i | −0.895871 | + | 1.78032i | ||||
\(113\) | 7.54314 | 0.709599 | 0.354799 | − | 0.934942i | \(-0.384549\pi\) | ||||
0.354799 | + | 0.934942i | \(0.384549\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.65937 | + | 0.781540i | −0.620990 | + | 0.0728790i | ||||
\(116\) | 8.74363 | − | 5.04814i | 0.811826 | − | 0.468708i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −29.3411 | −2.70107 | ||||||||
\(119\) | 11.8164 | − | 7.75844i | 1.08321 | − | 0.711215i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.3886 | − | 17.9935i | 0.944415 | − | 1.63577i | ||||
\(122\) | 15.5950 | − | 9.00378i | 1.41191 | − | 0.815164i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.06957 | − | 3.50427i | −0.545064 | − | 0.314693i | ||||
\(125\) | 10.5007 | − | 3.83871i | 0.939210 | − | 0.343344i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.93715i | − | 0.349366i | −0.984625 | − | 0.174683i | \(-0.944110\pi\) | ||
0.984625 | − | 0.174683i | \(-0.0558900\pi\) | |||||||
\(128\) | −4.11531 | + | 7.12793i | −0.363746 | + | 0.630026i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −20.1733 | + | 2.36753i | −1.76931 | + | 0.207646i | ||||
\(131\) | −1.97399 | + | 3.41906i | −0.172469 | + | 0.298724i | −0.939282 | − | 0.343145i | \(-0.888508\pi\) |
0.766814 | + | 0.641870i | \(0.221841\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.40967 | − | 1.71577i | −0.295656 | − | 0.148776i | ||||
\(134\) | − | 6.39722i | − | 0.552635i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −30.9302 | + | 17.8576i | −2.65225 | + | 1.53127i | ||||
\(137\) | 2.83062 | + | 4.90279i | 0.241837 | + | 0.418873i | 0.961237 | − | 0.275722i | \(-0.0889169\pi\) |
−0.719401 | + | 0.694595i | \(0.755584\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 23.3015i | 1.97640i | 0.153158 | + | 0.988202i | \(0.451056\pi\) | ||||
−0.153158 | + | 0.988202i | \(0.548944\pi\) | |||||||
\(140\) | −9.31927 | + | 25.5791i | −0.787622 | + | 2.16183i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 18.1093 | + | 10.4554i | 1.51970 | + | 0.877398i | ||||
\(143\) | −17.2593 | + | 9.96465i | −1.44329 | + | 0.833286i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.93386 | − | 2.93153i | 0.326689 | − | 0.243450i | ||||
\(146\) | 8.06275 | 0.667278 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.03030i | 0.413488i | ||||||||
\(149\) | −4.04926 | − | 2.33784i | −0.331728 | − | 0.191523i | 0.324880 | − | 0.945755i | \(-0.394676\pi\) |
−0.656608 | + | 0.754232i | \(0.728009\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.930426 | − | 1.61155i | −0.0757170 | − | 0.131146i | 0.825681 | − | 0.564138i | \(-0.190791\pi\) |
−0.901398 | + | 0.432992i | \(0.857458\pi\) | |||||||
\(152\) | 8.35196 | + | 4.82201i | 0.677433 | + | 0.391116i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.19799 | + | 38.2576i | 0.177119 | + | 3.08289i | ||||
\(155\) | −3.12773 | − | 1.34743i | −0.251225 | − | 0.108228i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.28398 | − | 5.68802i | −0.262090 | − | 0.453953i | 0.704707 | − | 0.709498i | \(-0.251078\pi\) |
−0.966797 | + | 0.255545i | \(0.917745\pi\) | |||||||
\(158\) | 16.4505 | + | 28.4930i | 1.30873 | + | 2.26678i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.29365 | − | 14.6092i | 0.497557 | − | 1.15496i | ||||
\(161\) | 3.56616 | − | 7.08687i | 0.281053 | − | 0.558524i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.2598 | − | 9.38762i | −1.27357 | − | 0.735295i | −0.297910 | − | 0.954594i | \(-0.596290\pi\) |
−0.975658 | + | 0.219299i | \(0.929623\pi\) | |||||||
\(164\) | −15.0028 | − | 25.9856i | −1.17152 | − | 2.02914i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.0696 | − | 8.70042i | −1.16963 | − | 0.675284i | ||||
\(167\) | 4.80581i | 0.371884i | 0.982561 | + | 0.185942i | \(0.0595337\pi\) | ||||
−0.982561 | + | 0.185942i | \(0.940466\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.501166 | −0.0385512 | ||||||||
\(170\) | −24.6135 | + | 18.3420i | −1.88777 | + | 1.40677i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.93729 | + | 1.11849i | −0.147717 | + | 0.0852844i | ||||
\(173\) | −2.91312 | − | 1.68189i | −0.221480 | − | 0.127872i | 0.385155 | − | 0.922852i | \(-0.374148\pi\) |
−0.606635 | + | 0.794980i | \(0.707481\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.04881 | + | 12.8726i | −0.230469 | + | 0.973080i | ||||
\(176\) | − | 44.9396i | − | 3.38745i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 13.2712 | + | 22.9863i | 0.994715 | + | 1.72290i | ||||
\(179\) | −9.63782 | + | 5.56440i | −0.720365 | + | 0.415903i | −0.814887 | − | 0.579620i | \(-0.803201\pi\) |
0.0945223 | + | 0.995523i | \(0.469868\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.19549i | − | 0.163190i | −0.996666 | − | 0.0815949i | \(-0.973999\pi\) | ||
0.996666 | − | 0.0815949i | \(-0.0260014\pi\) | |||||||
\(182\) | 10.8030 | − | 21.4683i | 0.800771 | − | 1.59134i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.0223 | + | 17.3592i | −0.738857 | + | 1.27974i | ||||
\(185\) | 0.284911 | + | 2.42768i | 0.0209471 | + | 0.178487i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.0591 | + | 26.0831i | −1.10123 | + | 1.90739i | ||||
\(188\) | − | 19.5862i | − | 1.42847i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.61241 | + | 3.27943i | 0.552262 | + | 0.237915i | ||||
\(191\) | −8.62053 | − | 4.97707i | −0.623760 | − | 0.360128i | 0.154572 | − | 0.987982i | \(-0.450600\pi\) |
−0.778331 | + | 0.627854i | \(0.783934\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.6068 | − | 12.4747i | 1.55529 | − | 0.897948i | 0.557594 | − | 0.830114i | \(-0.311725\pi\) |
0.997697 | − | 0.0678339i | \(-0.0216088\pi\) | |||||||
\(194\) | −18.9261 | + | 32.7810i | −1.35882 | + | 2.35354i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −19.1948 | − | 25.8681i | −1.37105 | − | 1.84772i | ||||
\(197\) | 19.1023 | 1.36098 | 0.680492 | − | 0.732755i | \(-0.261766\pi\) | ||||
0.680492 | + | 0.732755i | \(0.261766\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.59632 | − | 0.921633i | 0.113160 | − | 0.0653329i | −0.442352 | − | 0.896842i | \(-0.645856\pi\) |
0.555512 | + | 0.831509i | \(0.312522\pi\) | |||||||
\(200\) | 9.55586 | − | 32.0283i | 0.675701 | − | 2.26474i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 38.3701 | 2.69971 | ||||||||
\(203\) | 0.332956 | + | 5.79533i | 0.0233689 | + | 0.406753i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.71234 | − | 11.6912i | −0.608496 | − | 0.816551i | ||||
\(206\) | 5.02968 | + | 8.71167i | 0.350435 | + | 0.606971i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −14.0921 | + | 24.4083i | −0.977114 | + | 1.69241i | ||||
\(209\) | 8.13269 | 0.562550 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.77713 | −0.673085 | −0.336543 | − | 0.941668i | \(-0.609258\pi\) | ||||
−0.336543 | + | 0.941668i | \(0.609258\pi\) | |||||||
\(212\) | 9.25406 | − | 16.0285i | 0.635571 | − | 1.10084i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 19.0417 | + | 32.9811i | 1.30166 | + | 2.25454i | ||||
\(215\) | −0.871609 | + | 0.649526i | −0.0594432 | + | 0.0442973i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.36841 | − | 2.21164i | 0.228663 | − | 0.150136i | ||||
\(218\) | −28.3624 | −1.92094 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.76093 | − | 57.6087i | −0.455822 | − | 3.88398i | ||||
\(221\) | 16.3583 | − | 9.44444i | 1.10038 | − | 0.635302i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.84782 | 0.525529 | 0.262765 | − | 0.964860i | \(-0.415366\pi\) | ||||
0.262765 | + | 0.964860i | \(0.415366\pi\) | |||||||
\(224\) | 10.3303 | + | 15.7334i | 0.690220 | + | 1.05123i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.69057 | − | 16.7846i | 0.644607 | − | 1.11649i | ||||
\(227\) | −0.475865 | + | 0.274741i | −0.0315843 | + | 0.0182352i | −0.515709 | − | 0.856764i | \(-0.672471\pi\) |
0.484125 | + | 0.874999i | \(0.339138\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.5833 | − | 10.7291i | −1.22802 | − | 0.708998i | −0.261406 | − | 0.965229i | \(-0.584186\pi\) |
−0.966616 | + | 0.256231i | \(0.917519\pi\) | |||||||
\(230\) | −6.81617 | + | 15.8221i | −0.449445 | + | 1.04328i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 14.6665i | − | 0.962902i | ||||||
\(233\) | 9.38319 | − | 16.2522i | 0.614713 | − | 1.06471i | −0.375722 | − | 0.926733i | \(-0.622605\pi\) |
0.990435 | − | 0.137982i | \(-0.0440615\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.10935 | − | 9.45256i | −0.0723658 | − | 0.616617i | ||||
\(236\) | −26.2746 | + | 45.5089i | −1.71033 | + | 2.96238i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.08325 | − | 36.2604i | −0.135037 | − | 2.35041i | ||||
\(239\) | 7.35866i | 0.475992i | 0.971266 | + | 0.237996i | \(0.0764905\pi\) | ||||
−0.971266 | + | 0.237996i | \(0.923509\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.8467 | − | 13.7679i | 1.53610 | − | 0.886868i | 0.537040 | − | 0.843557i | \(-0.319543\pi\) |
0.999062 | − | 0.0433114i | \(-0.0137908\pi\) | |||||||
\(242\) | −26.6921 | − | 46.2321i | −1.71583 | − | 2.97191i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 32.2511i | − | 2.06466i | ||||||
\(245\) | −10.7288 | − | 11.3971i | −0.685436 | − | 0.728133i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.41715 | − | 2.55024i | −0.281057 | − | 0.162268i | ||||
\(248\) | −8.81704 | + | 5.09052i | −0.559883 | + | 0.323248i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.94842 | − | 28.2970i | 0.312966 | − | 1.78966i | ||||
\(251\) | 22.4204 | 1.41516 | 0.707582 | − | 0.706631i | \(-0.249786\pi\) | ||||
0.707582 | + | 0.706631i | \(0.249786\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.9035i | 1.06271i | ||||||||
\(254\) | −8.76072 | − | 5.05801i | −0.549697 | − | 0.317368i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.9079 | + | 22.3571i | 0.806743 | + | 1.39732i | ||||
\(257\) | −14.8328 | − | 8.56373i | −0.925246 | − | 0.534191i | −0.0399409 | − | 0.999202i | \(-0.512717\pi\) |
−0.885305 | + | 0.465011i | \(0.846050\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.58353 | − | 1.30005i | −0.160533 | − | 0.0807810i | ||||
\(260\) | −14.3928 | + | 33.4094i | −0.892604 | + | 2.07196i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.07193 | + | 8.78483i | 0.313345 | + | 0.542729i | ||||
\(263\) | 0.808821 | + | 1.40092i | 0.0498741 | + | 0.0863844i | 0.889885 | − | 0.456186i | \(-0.150785\pi\) |
−0.840011 | + | 0.542570i | \(0.817451\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.55828 | − | 8.25969i | 0.218583 | − | 0.507389i | ||||
\(266\) | −8.19819 | + | 5.38278i | −0.502664 | + | 0.330040i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.92226 | − | 5.72862i | −0.606099 | − | 0.349931i | ||||
\(269\) | −5.84048 | − | 10.1160i | −0.356101 | − | 0.616784i | 0.631205 | − | 0.775616i | \(-0.282561\pi\) |
−0.987306 | + | 0.158832i | \(0.949227\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.05562 | + | 2.91886i | 0.307107 | + | 0.177308i | 0.645631 | − | 0.763649i | \(-0.276594\pi\) |
−0.338524 | + | 0.940958i | \(0.609928\pi\) | |||||||
\(272\) | 42.5936i | 2.58261i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.5459 | 0.878748 | ||||||||
\(275\) | −6.52581 | − | 27.4197i | −0.393521 | − | 1.65347i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.3760 | + | 8.29998i | −0.863770 | + | 0.498698i | −0.865273 | − | 0.501301i | \(-0.832855\pi\) |
0.00150328 | + | 0.999999i | \(0.499521\pi\) | |||||||
\(278\) | 51.8491 | + | 29.9351i | 3.10970 | + | 1.79539i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 25.4108 | + | 30.3030i | 1.51858 | + | 1.81095i | ||||
\(281\) | 20.4255i | 1.21848i | 0.792984 | + | 0.609242i | \(0.208526\pi\) | ||||
−0.792984 | + | 0.609242i | \(0.791474\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.31643 | + | 5.74423i | 0.197141 | + | 0.341459i | 0.947600 | − | 0.319458i | \(-0.103501\pi\) |
−0.750459 | + | 0.660917i | \(0.770168\pi\) | |||||||
\(284\) | 32.4333 | − | 18.7254i | 1.92456 | − | 1.11115i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 51.2058i | 3.02786i | ||||||||
\(287\) | 17.2234 | − | 0.989529i | 1.01667 | − | 0.0584100i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.77293 | − | 9.99901i | 0.339584 | − | 0.588177i | ||||
\(290\) | −1.46928 | − | 12.5195i | −0.0862792 | − | 0.735170i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.22008 | − | 12.5055i | 0.422523 | − | 0.731832i | ||||
\(293\) | − | 16.3716i | − | 0.956437i | −0.878241 | − | 0.478219i | \(-0.841283\pi\) | ||
0.878241 | − | 0.478219i | \(-0.158717\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.1028 | + | 23.4513i | −0.588210 | + | 1.36539i | ||||
\(296\) | 6.32832 | + | 3.65366i | 0.367826 | + | 0.212365i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.4040 | + | 6.00678i | −0.602690 | + | 0.347963i | ||||
\(299\) | 5.30058 | − | 9.18087i | 0.306540 | − | 0.530944i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0737717 | − | 1.28405i | −0.00425213 | − | 0.0740113i | ||||
\(302\) | −4.78122 | −0.275129 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9.96047 | − | 5.75068i | 0.571272 | − | 0.329824i | ||||
\(305\) | −1.82667 | − | 15.5648i | −0.104595 | − | 0.891235i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.5071 | 1.45576 | 0.727882 | − | 0.685702i | \(-0.240505\pi\) | ||||
0.727882 | + | 0.685702i | \(0.240505\pi\) | |||||||
\(308\) | 61.3069 | + | 30.8500i | 3.49329 | + | 1.75784i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.01637 | + | 5.22862i | −0.398503 | + | 0.296966i | ||||
\(311\) | −15.5180 | − | 26.8780i | −0.879946 | − | 1.52411i | −0.851399 | − | 0.524519i | \(-0.824245\pi\) |
−0.0285476 | − | 0.999592i | \(-0.509088\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.52345 | + | 13.0310i | −0.425251 | + | 0.736556i | −0.996444 | − | 0.0842599i | \(-0.973147\pi\) |
0.571193 | + | 0.820816i | \(0.306481\pi\) | |||||||
\(314\) | −16.8755 | −0.952341 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 58.9247 | 3.31477 | ||||||||
\(317\) | −7.79061 | + | 13.4937i | −0.437564 | + | 0.757884i | −0.997501 | − | 0.0706518i | \(-0.977492\pi\) |
0.559937 | + | 0.828535i | \(0.310825\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.18404 | − | 10.7111i | −0.346240 | − | 0.599705i | ||||
\(320\) | −3.11867 | − | 4.18500i | −0.174339 | − | 0.233949i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −11.1879 | − | 17.0396i | −0.623477 | − | 0.949581i | ||||
\(323\) | −7.70812 | −0.428891 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.05386 | + | 16.9390i | −0.280338 | + | 0.939606i | ||||
\(326\) | −41.7776 | + | 24.1203i | −2.31385 | + | 1.33590i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −43.5880 | −2.40675 | ||||||||
\(329\) | 10.0594 | + | 5.06194i | 0.554591 | + | 0.279074i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.83411 | + | 11.8370i | −0.375637 | + | 0.650622i | −0.990422 | − | 0.138073i | \(-0.955909\pi\) |
0.614785 | + | 0.788694i | \(0.289243\pi\) | |||||||
\(332\) | −26.9892 | + | 15.5822i | −1.48123 | + | 0.855186i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.6936 | + | 6.17395i | 0.585128 | + | 0.337824i | ||||
\(335\) | −5.11307 | − | 2.20271i | −0.279357 | − | 0.120347i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 22.8443i | − | 1.24441i | −0.782855 | − | 0.622204i | \(-0.786237\pi\) | ||
0.782855 | − | 0.622204i | \(-0.213763\pi\) | |||||||
\(338\) | −0.643841 | + | 1.11516i | −0.0350203 | + | 0.0606570i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.40797 | + | 54.6012i | 0.347521 | + | 2.96117i | ||||
\(341\) | −4.29278 | + | 7.43531i | −0.232467 | + | 0.402645i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.2464 | − | 3.17287i | 0.985216 | − | 0.171319i | ||||
\(344\) | 3.24959i | 0.175206i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.48488 | + | 4.32140i | −0.402390 | + | 0.232320i | ||||
\(347\) | 9.81241 | + | 16.9956i | 0.526758 | + | 0.912372i | 0.999514 | + | 0.0311781i | \(0.00992591\pi\) |
−0.472756 | + | 0.881193i | \(0.656741\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 6.14050i | − | 0.328693i | −0.986403 | − | 0.164347i | \(-0.947448\pi\) | ||
0.986403 | − | 0.164347i | \(-0.0525516\pi\) | |||||||
\(350\) | 24.7267 | + | 23.3213i | 1.32170 | + | 1.24658i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −34.7293 | − | 20.0510i | −1.85108 | − | 1.06872i | ||||
\(353\) | 20.7882 | − | 12.0021i | 1.10644 | − | 0.638805i | 0.168537 | − | 0.985695i | \(-0.446096\pi\) |
0.937906 | + | 0.346890i | \(0.112762\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.5921 | − | 10.8741i | 0.774468 | − | 0.577136i | ||||
\(356\) | 47.5366 | 2.51943 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 28.5940i | 1.51124i | ||||||||
\(359\) | −14.6798 | − | 8.47541i | −0.774773 | − | 0.447315i | 0.0598018 | − | 0.998210i | \(-0.480953\pi\) |
−0.834575 | + | 0.550895i | \(0.814286\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.45930 | − | 14.6519i | −0.445227 | − | 0.771155i | ||||
\(362\) | −4.88529 | − | 2.82052i | −0.256765 | − | 0.148243i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −23.6240 | − | 35.9803i | −1.23824 | − | 1.88588i | ||||
\(365\) | 2.77620 | − | 6.44427i | 0.145313 | − | 0.337308i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.5018 | − | 30.3140i | −0.913587 | − | 1.58238i | −0.808956 | − | 0.587869i | \(-0.799967\pi\) |
−0.104631 | − | 0.994511i | \(-0.533366\pi\) | |||||||
\(368\) | 11.9526 | + | 20.7024i | 0.623070 | + | 1.07919i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.76796 | + | 2.48484i | 0.299862 | + | 0.129181i | ||||
\(371\) | 5.84048 | + | 8.89529i | 0.303223 | + | 0.461820i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.18881 | − | 2.99576i | −0.268667 | − | 0.155115i | 0.359615 | − | 0.933101i | \(-0.382908\pi\) |
−0.628282 | + | 0.777986i | \(0.716241\pi\) | |||||||
\(374\) | 38.6924 | + | 67.0173i | 2.00074 | + | 3.46538i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −24.6403 | − | 14.2261i | −1.27073 | − | 0.733655i | ||||
\(377\) | 7.75675i | 0.399493i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.12842 | −0.160696 | −0.0803481 | − | 0.996767i | \(-0.525603\pi\) | ||||
−0.0803481 | + | 0.996767i | \(0.525603\pi\) | |||||||
\(380\) | 11.9033 | − | 8.87037i | 0.610626 | − | 0.455040i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −22.1494 | + | 12.7879i | −1.13326 | + | 0.654288i | ||||
\(383\) | −14.6929 | − | 8.48295i | −0.750772 | − | 0.433459i | 0.0752006 | − | 0.997168i | \(-0.476040\pi\) |
−0.825973 | + | 0.563710i | \(0.809374\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 31.3348 | + | 11.4162i | 1.59697 | + | 0.581825i | ||||
\(386\) | − | 64.1043i | − | 3.26282i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 33.8961 | + | 58.7099i | 1.72082 | + | 2.98054i | ||||
\(389\) | 0.389255 | − | 0.224737i | 0.0197360 | − | 0.0113946i | −0.490100 | − | 0.871666i | \(-0.663040\pi\) |
0.509836 | + | 0.860272i | \(0.329706\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 16.0210i | − | 0.810218i | ||||||
\(392\) | −46.4849 | + | 5.35903i | −2.34784 | + | 0.270672i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 24.5405 | − | 42.5054i | 1.23633 | − | 2.14139i | ||||
\(395\) | 28.4378 | − | 3.33744i | 1.43086 | − | 0.167925i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.3663 | + | 19.6870i | −0.570459 | + | 0.988064i | 0.426060 | + | 0.904695i | \(0.359901\pi\) |
−0.996519 | + | 0.0833689i | \(0.973432\pi\) | |||||||
\(398\) | − | 4.73604i | − | 0.237396i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −27.3811 | − | 28.9677i | −1.36906 | − | 1.44839i | ||||
\(401\) | −8.41308 | − | 4.85729i | −0.420129 | − | 0.242562i | 0.275004 | − | 0.961443i | \(-0.411321\pi\) |
−0.695132 | + | 0.718882i | \(0.744654\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.66312 | − | 2.69225i | 0.232287 | − | 0.134111i | ||||
\(404\) | 34.3599 | − | 59.5132i | 1.70947 | − | 2.96089i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13.3232 | + | 6.70431i | 0.661219 | + | 0.332729i | ||||
\(407\) | 6.16218 | 0.305448 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.51628 | − | 2.03013i | 0.173869 | − | 0.100383i | −0.410540 | − | 0.911843i | \(-0.634660\pi\) |
0.584409 | + | 0.811459i | \(0.301326\pi\) | |||||||
\(410\) | −37.2073 | + | 4.36663i | −1.83754 | + | 0.215652i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 18.0161 | 0.887587 | ||||||||
\(413\) | −16.5826 | − | 25.2559i | −0.815976 | − | 1.24276i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.1428 | + | 9.04882i | −0.596064 | + | 0.444189i | ||||
\(416\) | 12.5752 | + | 21.7808i | 0.616548 | + | 1.06789i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10.4480 | − | 18.0964i | 0.511026 | − | 0.885124i | ||||
\(419\) | 20.9314 | 1.02257 | 0.511283 | − | 0.859412i | \(-0.329170\pi\) | ||||
0.511283 | + | 0.859412i | \(0.329170\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.7795 | −0.963992 | −0.481996 | − | 0.876173i | \(-0.660088\pi\) | ||||
−0.481996 | + | 0.876173i | \(0.660088\pi\) | |||||||
\(422\) | −12.5605 | + | 21.7555i | −0.611438 | + | 1.05904i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −13.4430 | − | 23.2840i | −0.652851 | − | 1.13077i | ||||
\(425\) | 6.18513 | + | 25.9883i | 0.300023 | + | 1.26062i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.5639 | + | 8.33508i | 0.801585 | + | 0.403363i | ||||
\(428\) | 68.2062 | 3.29687 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.325542 | + | 2.77389i | 0.0156991 | + | 0.133769i | ||||
\(431\) | −9.23148 | + | 5.32980i | −0.444665 | + | 0.256727i | −0.705574 | − | 0.708636i | \(-0.749311\pi\) |
0.260910 | + | 0.965363i | \(0.415978\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.2351 | −1.02050 | −0.510248 | − | 0.860028i | \(-0.670446\pi\) | ||||
−0.510248 | + | 0.860028i | \(0.670446\pi\) | |||||||
\(434\) | −0.593855 | − | 10.3365i | −0.0285060 | − | 0.496166i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −25.3981 | + | 43.9908i | −1.21635 | + | 2.10678i | ||||
\(437\) | −3.74650 | + | 2.16304i | −0.179220 | + | 0.103472i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.5707 | + | 10.7218i | 0.886333 | + | 0.511725i | 0.872741 | − | 0.488183i | \(-0.162340\pi\) |
0.0135918 | + | 0.999908i | \(0.495673\pi\) | |||||||
\(440\) | −77.3849 | − | 33.3375i | −3.68918 | − | 1.58930i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 48.5326i | − | 2.30846i | ||||||
\(443\) | 0.0854851 | − | 0.148064i | 0.00406152 | − | 0.00703475i | −0.863988 | − | 0.503513i | \(-0.832041\pi\) |
0.868049 | + | 0.496478i | \(0.165374\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.9417 | − | 2.69243i | 1.08754 | − | 0.127633i | ||||
\(446\) | 10.0820 | − | 17.4625i | 0.477396 | − | 0.826874i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.16531 | − | 0.354212i | 0.291283 | − | 0.0167350i | ||||
\(449\) | 9.38752i | 0.443025i | 0.975158 | + | 0.221512i | \(0.0710993\pi\) | ||||
−0.975158 | + | 0.221512i | \(0.928901\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −31.8328 | + | 18.3786i | −1.49895 | + | 0.865417i | ||||
\(452\) | −17.3556 | − | 30.0607i | −0.816337 | − | 1.41394i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.41182i | 0.0662602i | ||||||||
\(455\) | −13.4391 | − | 16.0265i | −0.630036 | − | 0.751334i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.6293 | + | 8.44623i | 0.684330 | + | 0.395098i | 0.801484 | − | 0.598016i | \(-0.204044\pi\) |
−0.117155 | + | 0.993114i | \(0.537377\pi\) | |||||||
\(458\) | −47.7475 | + | 27.5670i | −2.23110 | + | 1.28812i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 18.4367 | + | 24.7405i | 0.859616 | + | 1.15353i | ||||
\(461\) | −31.0360 | −1.44549 | −0.722746 | − | 0.691113i | \(-0.757120\pi\) | ||||
−0.722746 | + | 0.691113i | \(0.757120\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 11.9434i | − | 0.555055i | −0.960718 | − | 0.277528i | \(-0.910485\pi\) | ||
0.960718 | − | 0.277528i | \(-0.0895150\pi\) | |||||||
\(464\) | −15.1477 | − | 8.74555i | −0.703216 | − | 0.406002i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.1089 | − | 41.7579i | −1.11682 | − | 1.93440i | ||||
\(467\) | −29.9304 | − | 17.2803i | −1.38501 | − | 0.799638i | −0.392265 | − | 0.919852i | \(-0.628308\pi\) |
−0.992748 | + | 0.120215i | \(0.961642\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.50653 | − | 3.61549i | 0.254268 | − | 0.166948i | ||||
\(470\) | −22.4584 | − | 9.67512i | −1.03593 | − | 0.446280i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 38.1681 | + | 66.1090i | 1.75683 | + | 3.04292i | ||||
\(473\) | 1.37017 | + | 2.37321i | 0.0630006 | + | 0.109120i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.24227 | − | 4.95514i | 0.240532 | − | 0.227357i | ||||
\(476\) | −58.1064 | − | 29.2395i | −2.66330 | − | 1.34019i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 16.3741 | + | 9.45357i | 0.748932 | + | 0.432396i | ||||
\(479\) | 1.48615 | + | 2.57409i | 0.0679040 | + | 0.117613i | 0.897978 | − | 0.440039i | \(-0.145036\pi\) |
−0.830074 | + | 0.557653i | \(0.811702\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.34690 | − | 1.93233i | −0.152605 | − | 0.0881068i | ||||
\(482\) | − | 70.7498i | − | 3.22256i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −95.6097 | −4.34589 | ||||||||
\(485\) | 19.6840 | + | 26.4142i | 0.893803 | + | 1.19941i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.6695 | + | 11.3562i | −0.891310 | + | 0.514598i | −0.874371 | − | 0.485258i | \(-0.838726\pi\) |
−0.0169394 | + | 0.999857i | \(0.505392\pi\) | |||||||
\(488\) | −40.5732 | − | 23.4249i | −1.83666 | − | 1.06040i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −39.1432 | + | 9.23138i | −1.76831 | + | 0.417031i | ||||
\(491\) | − | 13.0036i | − | 0.586846i | −0.955983 | − | 0.293423i | \(-0.905206\pi\) | ||
0.955983 | − | 0.293423i | \(-0.0947944\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.86120 | + | 10.1519i | 0.263975 | + | 0.457219i | ||||
\(494\) | −11.3493 | + | 6.55253i | −0.510630 | + | 0.294812i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.1418i | 0.545184i | ||||||||
\(497\) | 1.23505 | + | 21.4970i | 0.0553997 | + | 0.964271i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.8039 | − | 18.7129i | 0.483648 | − | 0.837702i | −0.516176 | − | 0.856483i | \(-0.672645\pi\) |
0.999824 | + | 0.0187802i | \(0.00597826\pi\) | |||||||
\(500\) | −39.4583 | − | 33.0148i | −1.76463 | − | 1.47647i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 28.8032 | − | 49.8886i | 1.28555 | − | 2.22664i | ||||
\(503\) | 32.4125i | 1.44520i | 0.691265 | + | 0.722601i | \(0.257054\pi\) | ||||
−0.691265 | + | 0.722601i | \(0.742946\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.2118 | − | 30.6679i | 0.587915 | − | 1.36470i | ||||
\(506\) | 37.6126 | + | 21.7157i | 1.67209 | + | 0.965379i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15.6902 | + | 9.05875i | −0.696141 | + | 0.401917i | ||||
\(509\) | 18.2802 | − | 31.6622i | 0.810255 | − | 1.40340i | −0.102430 | − | 0.994740i | \(-0.532662\pi\) |
0.912685 | − | 0.408663i | \(-0.134005\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.55679 | + | 6.94017i | 0.201580 | + | 0.307015i | ||||
\(512\) | 49.8691 | 2.20392 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −38.1110 | + | 22.0034i | −1.68101 | + | 0.970529i | ||||
\(515\) | 8.69477 | − | 1.02041i | 0.383137 | − | 0.0449648i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −23.9934 | −1.05523 | ||||||||
\(518\) | −6.21181 | + | 4.07856i | −0.272931 | + | 0.179202i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 31.5765 | + | 42.3731i | 1.38472 | + | 1.85818i | ||||
\(521\) | 9.43608 | + | 16.3438i | 0.413402 | + | 0.716033i | 0.995259 | − | 0.0972577i | \(-0.0310071\pi\) |
−0.581857 | + | 0.813291i | \(0.697674\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.1124 | − | 24.4434i | 0.617092 | − | 1.06884i | −0.372921 | − | 0.927863i | \(-0.621644\pi\) |
0.990014 | − | 0.140972i | \(-0.0450229\pi\) | |||||||
\(524\) | 18.1674 | 0.793645 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.15633 | 0.181225 | ||||||||
\(527\) | 4.06867 | − | 7.04715i | 0.177234 | − | 0.306979i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00420 | + | 12.1316i | 0.304530 | + | 0.527462i | ||||
\(530\) | −13.8077 | − | 18.5288i | −0.599769 | − | 0.804839i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.00748 | + | 17.5358i | 0.0436797 | + | 0.760275i | ||||
\(533\) | 23.0527 | 0.998521 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.9172 | − | 3.86314i | 1.42313 | − | 0.167018i | ||||
\(536\) | −14.4137 | + | 8.32175i | −0.622577 | + | 0.359445i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −30.0128 | −1.29394 | ||||||||
\(539\) | −31.6888 | + | 23.5139i | −1.36493 | + | 1.01281i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.2269 | + | 24.6417i | −0.611661 | + | 1.05943i | 0.379299 | + | 0.925274i | \(0.376165\pi\) |
−0.990960 | + | 0.134154i | \(0.957168\pi\) | |||||||
\(542\) | 12.9898 | − | 7.49965i | 0.557959 | − | 0.322138i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 32.9163 | + | 19.0042i | 1.41127 | + | 0.814799i | ||||
\(545\) | −9.76584 | + | 22.6690i | −0.418323 | + | 0.971035i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.9338i | 0.937820i | 0.883246 | + | 0.468910i | \(0.155353\pi\) | ||||
−0.883246 | + | 0.468910i | \(0.844647\pi\) | |||||||
\(548\) | 13.0256 | − | 22.5610i | 0.556427 | − | 0.963760i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −69.3965 | − | 20.7049i | −2.95907 | − | 0.882860i | ||||
\(551\) | 1.58268 | − | 2.74127i | 0.0674242 | − | 0.116782i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.2287 | + | 30.2633i | −0.647590 | + | 1.28693i | ||||
\(554\) | 42.6515i | 1.81209i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 92.8603 | − | 53.6129i | 3.93815 | − | 2.27369i | ||||
\(557\) | 12.2168 | + | 21.1601i | 0.517643 | + | 0.896583i | 0.999790 | + | 0.0204933i | \(0.00652367\pi\) |
−0.482147 | + | 0.876090i | \(0.660143\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.71863i | − | 0.0726903i | ||||||
\(560\) | 46.4496 | − | 8.17507i | 1.96285 | − | 0.345460i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 45.4497 | + | 26.2404i | 1.91718 | + | 1.10688i | ||||
\(563\) | −18.4585 | + | 10.6570i | −0.777932 | + | 0.449139i | −0.835697 | − | 0.549191i | \(-0.814936\pi\) |
0.0577647 | + | 0.998330i | \(0.481603\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.0786 | − | 13.5247i | −0.424010 | − | 0.568987i | ||||
\(566\) | 17.0423 | 0.716341 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 54.4032i | − | 2.28271i | ||||||
\(569\) | 24.1707 | + | 13.9549i | 1.01329 | + | 0.585022i | 0.912152 | − | 0.409851i | \(-0.134419\pi\) |
0.101135 | + | 0.994873i | \(0.467753\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.1936 | + | 40.1725i | 0.970622 | + | 1.68117i | 0.693685 | + | 0.720279i | \(0.255986\pi\) |
0.276937 | + | 0.960888i | \(0.410681\pi\) | |||||||
\(572\) | 79.4217 | + | 45.8541i | 3.32079 | + | 1.91726i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 19.9249 | − | 39.5958i | 0.831648 | − | 1.65270i | ||||
\(575\) | 10.2991 | + | 10.8958i | 0.429501 | + | 0.454388i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.2167 | − | 28.0881i | −0.675108 | − | 1.16932i | −0.976437 | − | 0.215801i | \(-0.930764\pi\) |
0.301329 | − | 0.953520i | \(-0.402570\pi\) | |||||||
\(578\) | −14.8328 | − | 25.6912i | −0.616964 | − | 1.06861i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −20.7338 | − | 8.93214i | −0.860925 | − | 0.370887i | ||||
\(581\) | −1.02774 | − | 17.8886i | −0.0426380 | − | 0.742145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.6351 | − | 11.3363i | −0.813204 | − | 0.469504i | ||||
\(584\) | −10.4883 | − | 18.1663i | −0.434011 | − | 0.751728i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −36.4291 | − | 21.0323i | −1.50487 | − | 0.868838i | ||||
\(587\) | − | 0.790380i | − | 0.0326225i | −0.999867 | − | 0.0163112i | \(-0.994808\pi\) | ||
0.999867 | − | 0.0163112i | \(-0.00519226\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.19729 | −0.0905379 | ||||||||
\(590\) | 39.2035 | + | 52.6079i | 1.61398 | + | 2.16583i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.54710 | − | 4.35732i | 0.310184 | − | 0.179085i | ||||
\(593\) | 17.5672 | + | 10.1424i | 0.721397 | + | 0.416499i | 0.815267 | − | 0.579086i | \(-0.196590\pi\) |
−0.0938695 | + | 0.995585i | \(0.529924\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −29.6989 | − | 10.8202i | −1.21754 | − | 0.443587i | ||||
\(596\) | 21.5160i | 0.881328i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −13.6192 | − | 23.5891i | −0.556929 | − | 0.964630i | ||||
\(599\) | −8.77781 | + | 5.06787i | −0.358652 | + | 0.207068i | −0.668489 | − | 0.743722i | \(-0.733059\pi\) |
0.309837 | + | 0.950790i | \(0.399725\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.6657i | 1.45483i | 0.686196 | + | 0.727417i | \(0.259279\pi\) | ||||
−0.686196 | + | 0.727417i | \(0.740721\pi\) | |||||||
\(602\) | −2.95196 | − | 1.48545i | −0.120313 | − | 0.0605423i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.28152 | + | 7.41581i | −0.174213 | + | 0.301745i | ||||
\(605\) | −46.1424 | + | 5.41525i | −1.87596 | + | 0.220161i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.1333 | + | 22.7475i | −0.533063 | + | 0.923292i | 0.466192 | + | 0.884684i | \(0.345626\pi\) |
−0.999254 | + | 0.0386080i | \(0.987708\pi\) | |||||||
\(608\) | − | 10.2633i | − | 0.416230i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −36.9805 | − | 15.9312i | −1.49730 | − | 0.645036i | ||||
\(611\) | 13.0317 | + | 7.52384i | 0.527205 | + | 0.304382i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.4144 | − | 12.9410i | 0.905310 | − | 0.522681i | 0.0263906 | − | 0.999652i | \(-0.491599\pi\) |
0.878919 | + | 0.476971i | \(0.158265\pi\) | |||||||
\(614\) | 32.7686 | − | 56.7568i | 1.32243 | − | 2.29052i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 83.3398 | − | 54.7194i | 3.35786 | − | 2.20471i | ||||
\(617\) | −16.1754 | −0.651198 | −0.325599 | − | 0.945508i | \(-0.605566\pi\) | ||||
−0.325599 | + | 0.945508i | \(0.605566\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.29108 | − | 3.05481i | 0.212667 | − | 0.122783i | −0.389883 | − | 0.920864i | \(-0.627485\pi\) |
0.602550 | + | 0.798081i | \(0.294151\pi\) | |||||||
\(620\) | 1.82667 | + | 15.5648i | 0.0733609 | + | 0.625095i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −79.7432 | −3.19741 | ||||||||
\(623\) | −12.2855 | + | 24.4145i | −0.492209 | + | 0.978145i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.9130 | − | 13.6984i | −0.836519 | − | 0.547938i | ||||
\(626\) | 19.3306 | + | 33.4815i | 0.772605 | + | 1.33819i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15.1118 | + | 26.1744i | −0.603027 | + | 1.04447i | ||||
\(629\) | −5.84048 | −0.232875 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.89949 | 0.0756174 | 0.0378087 | − | 0.999285i | \(-0.487962\pi\) | ||||
0.0378087 | + | 0.999285i | \(0.487962\pi\) | |||||||
\(632\) | 42.7988 | − | 74.1297i | 1.70245 | − | 2.94872i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 20.0170 | + | 34.6704i | 0.794976 | + | 1.37694i | ||||
\(635\) | −7.05921 | + | 5.26055i | −0.280136 | + | 0.208758i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.5847 | − | 2.83426i | 0.974083 | − | 0.112298i | ||||
\(638\) | −31.7782 | −1.25811 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 18.2788 | − | 2.14519i | 0.722532 | − | 0.0847960i | ||||
\(641\) | 9.82533 | − | 5.67266i | 0.388077 | − | 0.224057i | −0.293249 | − | 0.956036i | \(-0.594737\pi\) |
0.681327 | + | 0.731979i | \(0.261403\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.2255 | 0.718742 | 0.359371 | − | 0.933195i | \(-0.382991\pi\) | ||||
0.359371 | + | 0.933195i | \(0.382991\pi\) | |||||||
\(644\) | −36.4476 | + | 2.09400i | −1.43623 | + | 0.0825152i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.90252 | + | 17.1517i | −0.389609 | + | 0.674823i | ||||
\(647\) | 21.2533 | − | 12.2706i | 0.835552 | − | 0.482406i | −0.0201980 | − | 0.999796i | \(-0.506430\pi\) |
0.855750 | + | 0.517390i | \(0.173096\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 55.7490 | + | 32.1867i | 2.18834 | + | 1.26344i | ||||
\(650\) | 31.1990 | + | 33.0069i | 1.22373 | + | 1.29464i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 86.3976i | 3.38359i | ||||||||
\(653\) | −4.37656 | + | 7.58043i | −0.171268 | + | 0.296645i | −0.938863 | − | 0.344290i | \(-0.888120\pi\) |
0.767595 | + | 0.640935i | \(0.221453\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.76779 | − | 1.02898i | 0.342586 | − | 0.0402057i | ||||
\(656\) | −25.9913 | + | 45.0183i | −1.01479 | + | 1.75767i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 24.1867 | − | 15.8805i | 0.942894 | − | 0.619087i | ||||
\(659\) | − | 2.51324i | − | 0.0979020i | −0.998801 | − | 0.0489510i | \(-0.984412\pi\) | ||
0.998801 | − | 0.0489510i | \(-0.0155878\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.5393 | + | 19.9413i | −1.34342 | + | 0.775626i | −0.987308 | − | 0.158815i | \(-0.949233\pi\) |
−0.356116 | + | 0.934442i | \(0.615899\pi\) | |||||||
\(662\) | 17.5594 | + | 30.4137i | 0.682465 | + | 1.18206i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 45.2714i | 1.75687i | ||||||||
\(665\) | 1.47944 | + | 8.40595i | 0.0573700 | + | 0.325969i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.69763 | + | 3.28953i | 0.220613 | + | 0.127371i | ||||
\(668\) | 19.1520 | − | 11.0574i | 0.741011 | − | 0.427823i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −11.4700 | + | 8.54751i | −0.443127 | + | 0.330219i | ||||
\(671\) | −39.5080 | −1.52519 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 36.0634i | − | 1.39014i | −0.718941 | − | 0.695071i | \(-0.755373\pi\) | ||
0.718941 | − | 0.695071i | \(-0.244627\pi\) | |||||||
\(674\) | −50.8318 | − | 29.3478i | −1.95797 | − | 1.13043i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.15310 | + | 1.99723i | 0.0443501 | + | 0.0768166i | ||||
\(677\) | −6.84487 | − | 3.95189i | −0.263070 | − | 0.151883i | 0.362664 | − | 0.931920i | \(-0.381867\pi\) |
−0.625734 | + | 0.780036i | \(0.715200\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −38.9132 | + | 2.23566i | −1.49335 | + | 0.0857968i | ||||
\(680\) | 73.3450 | + | 31.5971i | 2.81265 | + | 1.21169i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 11.0298 | + | 19.1041i | 0.422351 | + | 0.731534i | ||||
\(683\) | 12.6430 | + | 21.8984i | 0.483772 | + | 0.837918i | 0.999826 | − | 0.0186377i | \(-0.00593291\pi\) |
−0.516054 | + | 0.856556i | \(0.672600\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.00849 | − | 11.6260i | 0.191365 | − | 0.444206i | ||||
\(686\) | 16.3809 | − | 44.6771i | 0.625425 | − | 1.70578i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.35622 | + | 1.93772i | 0.127955 | + | 0.0738747i | ||||
\(689\) | 7.10969 | + | 12.3143i | 0.270858 | + | 0.469139i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.1380 | − | 7.58522i | −0.499792 | − | 0.288555i | 0.228835 | − | 0.973465i | \(-0.426508\pi\) |
−0.728628 | + | 0.684910i | \(0.759842\pi\) | |||||||
\(692\) | 15.4790i | 0.588424i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 50.4235 | 1.91405 | ||||||||
\(695\) | 41.7789 | − | 31.1338i | 1.58476 | − | 1.18097i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30.1709 | − | 17.4192i | 1.14280 | − | 0.659799i | ||||
\(698\) | −13.6635 | − | 7.88861i | −0.517170 | − | 0.298588i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 58.3145 | − | 17.4678i | 2.20408 | − | 0.660222i | ||||
\(701\) | − | 34.6815i | − | 1.30990i | −0.755671 | − | 0.654951i | \(-0.772689\pi\) | ||
0.755671 | − | 0.654951i | \(-0.227311\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.788541 | + | 1.36579i | 0.0297404 | + | 0.0515118i | ||||
\(704\) | −11.3949 | + | 6.57883i | −0.429460 | + | 0.247949i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 61.6755i | − | 2.32119i | ||||||
\(707\) | 21.6855 | + | 33.0278i | 0.815566 | + | 1.24214i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.2311 | + | 29.8451i | −0.647126 | + | 1.12086i | 0.336680 | + | 0.941619i | \(0.390696\pi\) |
−0.983806 | + | 0.179237i | \(0.942637\pi\) | |||||||
\(710\) | −5.45009 | − | 46.4393i | −0.204538 | − | 1.74284i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 34.5273 | − | 59.8030i | 1.29396 | − | 2.24121i | ||||
\(713\) | − | 4.56699i | − | 0.171035i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 40.9270 | + | 17.6314i | 1.53058 | + | 0.659376i | ||||
\(716\) | 44.3502 | + | 25.6056i | 1.65744 | + | 0.956925i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −37.7180 | + | 21.7765i | −1.40762 | + | 0.812692i | ||||
\(719\) | −13.4825 | + | 23.3523i | −0.502812 | + | 0.870895i | 0.497183 | + | 0.867646i | \(0.334368\pi\) |
−0.999995 | + | 0.00324951i | \(0.998966\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.65613 | + | 9.25293i | −0.173403 | + | 0.344597i | ||||
\(722\) | −43.4702 | −1.61779 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.74942 | + | 5.05148i | −0.325170 | + | 0.187737i | ||||
\(725\) | −10.5123 | − | 3.13642i | −0.390417 | − | 0.116484i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.4196 | −0.386442 | −0.193221 | − | 0.981155i | \(-0.561894\pi\) | ||||
−0.193221 | + | 0.981155i | \(0.561894\pi\) | |||||||
\(728\) | −62.4236 | + | 3.58639i | −2.31357 | + | 0.132921i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10.7729 | − | 14.4563i | −0.398722 | − | 0.535052i | ||||
\(731\) | −1.29864 | − | 2.24931i | −0.0480320 | − | 0.0831938i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.3541 | + | 19.6659i | −0.419374 | + | 0.726377i | −0.995877 | − | 0.0907181i | \(-0.971084\pi\) |
0.576503 | + | 0.817095i | \(0.304417\pi\) | |||||||
\(734\) | −89.9374 | −3.31965 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 21.3318 | 0.786300 | ||||||||
\(737\) | −7.01764 | + | 12.1549i | −0.258498 | + | 0.447732i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.8897 | − | 25.7898i | −0.547728 | − | 0.948692i | −0.998430 | − | 0.0560176i | \(-0.982160\pi\) |
0.450702 | − | 0.892674i | \(-0.351174\pi\) | |||||||
\(740\) | 9.01919 | − | 6.72113i | 0.331552 | − | 0.247074i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 27.2965 | − | 1.56825i | 1.00209 | − | 0.0575723i | ||||
\(743\) | −34.8044 | −1.27685 | −0.638424 | − | 0.769684i | \(-0.720414\pi\) | ||||
−0.638424 | + | 0.769684i | \(0.720414\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.21865 | + | 10.3839i | 0.0446477 | + | 0.380435i | ||||
\(746\) | −13.3320 | + | 7.69723i | −0.488119 | + | 0.281816i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 138.594 | 5.06751 | ||||||||
\(749\) | −17.6275 | + | 35.0303i | −0.644093 | + | 1.27998i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.74522 | + | 6.48691i | −0.136665 | + | 0.236711i | −0.926232 | − | 0.376953i | \(-0.876972\pi\) |
0.789567 | + | 0.613664i | \(0.210305\pi\) | |||||||
\(752\) | −29.3858 | + | 16.9659i | −1.07159 | + | 0.618683i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 17.2599 | + | 9.96499i | 0.628568 | + | 0.362904i | ||||
\(755\) | −1.64629 | + | 3.82146i | −0.0599146 | + | 0.139077i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 2.66139i | − | 0.0967300i | −0.998830 | − | 0.0483650i | \(-0.984599\pi\) | ||
0.998830 | − | 0.0483650i | \(-0.0154011\pi\) | |||||||
\(758\) | −4.01904 | + | 6.96118i | −0.145978 | + | 0.252842i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.51357 | − | 21.4177i | −0.0911767 | − | 0.776901i | ||||
\(761\) | 2.78479 | − | 4.82340i | 0.100949 | − | 0.174848i | −0.811127 | − | 0.584870i | \(-0.801146\pi\) |
0.912076 | + | 0.410022i | \(0.134479\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.0294 | − | 24.4135i | −0.580304 | − | 0.883827i | ||||
\(764\) | 45.8057i | 1.65719i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −37.7516 | + | 21.7959i | −1.36402 | + | 0.787517i | ||||
\(767\) | −20.1862 | − | 34.9635i | −0.728881 | − | 1.26246i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.5002i | 0.414709i | 0.978266 | + | 0.207355i | \(0.0664854\pi\) | ||||
−0.978266 | + | 0.207355i | \(0.933515\pi\) | |||||||
\(770\) | 65.6581 | − | 55.0581i | 2.36615 | − | 1.98416i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −99.4275 | − | 57.4045i | −3.57847 | − | 2.06603i | ||||
\(773\) | 21.9748 | − | 12.6872i | 0.790378 | − | 0.456325i | −0.0497174 | − | 0.998763i | \(-0.515832\pi\) |
0.840096 | + | 0.542438i | \(0.182499\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.76315 | + | 7.40828i | 0.0633341 | + | 0.266113i | ||||
\(776\) | 98.4793 | 3.53520 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 1.15486i | − | 0.0414039i | ||||||
\(779\) | −8.14692 | − | 4.70363i | −0.291894 | − | 0.168525i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.9388 | − | 39.7312i | −0.820816 | − | 1.42169i | ||||
\(782\) | −35.6491 | − | 20.5820i | −1.27481 | − | 0.736011i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −22.1838 | + | 51.2058i | −0.792280 | + | 1.82878i | ||||
\(785\) | −5.81065 | + | 13.4880i | −0.207391 | + | 0.481408i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.9967 | − | 20.7789i | −0.427636 | − | 0.740688i | 0.569026 | − | 0.822319i | \(-0.307320\pi\) |
−0.996663 | + | 0.0816315i | \(0.973987\pi\) | |||||||
\(788\) | −43.9514 | − | 76.1260i | −1.56570 | − | 2.71188i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 29.1073 | − | 67.5656i | 1.03559 | − | 2.40388i | ||||
\(791\) | 19.9244 | − | 1.14471i | 0.708431 | − | 0.0407011i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.4582 | + | 12.3889i | 0.762002 | + | 0.439942i | ||||
\(794\) | 29.2043 | + | 50.5833i | 1.03642 | + | 1.79514i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.34573 | − | 4.24106i | −0.260363 | − | 0.150320i | ||||
\(797\) | − | 28.1188i | − | 0.996020i | −0.867171 | − | 0.498010i | \(-0.834064\pi\) | ||
0.867171 | − | 0.498010i | \(-0.165936\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.7408 | 0.804513 | ||||||||
\(800\) | −34.6031 | + | 8.23542i | −1.22340 | + | 0.291166i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −21.6163 | + | 12.4802i | −0.763299 | + | 0.440691i | ||||
\(803\) | −15.3195 | − | 8.84470i | −0.540612 | − | 0.312123i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.4714 | + | 3.07495i | −0.615787 | + | 0.108378i | ||||
\(806\) | − | 13.8348i | − | 0.487310i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −49.9134 | − | 86.4525i | −1.75595 | − | 3.04139i | ||||
\(809\) | −24.2977 | + | 14.0283i | −0.854263 | + | 0.493209i | −0.862087 | − | 0.506761i | \(-0.830843\pi\) |
0.00782425 | + | 0.999969i | \(0.497509\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 43.4980i | − | 1.52742i | −0.645559 | − | 0.763710i | \(-0.723376\pi\) | ||
0.645559 | − | 0.763710i | \(-0.276624\pi\) | |||||||
\(812\) | 22.3293 | − | 14.6610i | 0.783605 | − | 0.514501i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.91647 | − | 13.7117i | 0.277472 | − | 0.480596i | ||||
\(815\) | 4.89348 | + | 41.6965i | 0.171411 | + | 1.46057i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.350667 | + | 0.607373i | −0.0122683 | + | 0.0212493i | ||||
\(818\) | − | 10.4323i | − | 0.364757i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −26.5459 | + | 61.6198i | −0.927022 | + | 2.15186i | ||||
\(821\) | −31.5875 | − | 18.2371i | −1.10241 | − | 0.636477i | −0.165558 | − | 0.986200i | \(-0.552942\pi\) |
−0.936853 | + | 0.349723i | \(0.886276\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.9277 | + | 23.0523i | −1.39179 | + | 0.803551i | −0.993514 | − | 0.113713i | \(-0.963725\pi\) |
−0.398278 | + | 0.917265i | \(0.630392\pi\) | |||||||
\(824\) | 13.0856 | − | 22.6650i | 0.455859 | − | 0.789571i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −77.5015 | + | 4.45265i | −2.69662 | + | 0.154928i | ||||
\(827\) | −20.1533 | −0.700800 | −0.350400 | − | 0.936600i | \(-0.613954\pi\) | ||||
−0.350400 | + | 0.936600i | \(0.613954\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.13818 | − | 3.54388i | 0.213188 | − | 0.123084i | −0.389604 | − | 0.920982i | \(-0.627388\pi\) |
0.602792 | + | 0.797898i | \(0.294055\pi\) | |||||||
\(830\) | 4.53527 | + | 38.6443i | 0.157422 | + | 1.34136i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.25194 | 0.286085 | ||||||||
\(833\) | 30.0344 | − | 22.2863i | 1.04063 | − | 0.772175i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.61669 | − | 6.42118i | 0.298193 | − | 0.222214i | ||||
\(836\) | −18.7120 | − | 32.4102i | −0.647169 | − | 1.12093i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 26.8903 | − | 46.5754i | 0.928911 | − | 1.60892i | ||||
\(839\) | 33.0805 | 1.14206 | 0.571032 | − | 0.820928i | \(-0.306543\pi\) | ||||
0.571032 | + | 0.820928i | \(0.306543\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.1862 | 0.834006 | ||||||||
\(842\) | −25.4104 | + | 44.0121i | −0.875701 | + | 1.51676i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 22.4956 | + | 38.9635i | 0.774331 | + | 1.34118i | ||||
\(845\) | 0.669622 | + | 0.898577i | 0.0230357 | + | 0.0309120i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.7097 | − | 49.1045i | 0.849036 | − | 1.68725i | ||||
\(848\) | −32.0640 | −1.10108 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 65.7736 | + | 19.6240i | 2.25602 | + | 0.673098i | ||||
\(851\) | −2.83875 | + | 1.63895i | −0.0973109 | + | 0.0561825i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.1187 | 1.30516 | 0.652580 | − | 0.757719i | \(-0.273686\pi\) | ||||
0.652580 | + | 0.757719i | \(0.273686\pi\) | |||||||
\(854\) | 39.8262 | − | 26.1492i | 1.36282 | − | 0.894806i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 49.5403 | − | 85.8063i | 1.69325 | − | 2.93280i | ||||
\(857\) | 6.09347 | − | 3.51807i | 0.208149 | − | 0.120175i | −0.392302 | − | 0.919837i | \(-0.628321\pi\) |
0.600451 | + | 0.799662i | \(0.294988\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.2343 | + | 12.8370i | 0.758624 | + | 0.437992i | 0.828802 | − | 0.559543i | \(-0.189023\pi\) |
−0.0701772 | + | 0.997535i | \(0.522356\pi\) | |||||||
\(860\) | 4.59390 | + | 1.97906i | 0.156651 | + | 0.0674853i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.3885i | 0.932855i | ||||||||
\(863\) | 25.4929 | − | 44.1550i | 0.867788 | − | 1.50305i | 0.00353683 | − | 0.999994i | \(-0.498874\pi\) |
0.864252 | − | 0.503060i | \(-0.167792\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.876718 | + | 7.47036i | 0.0298093 | + | 0.254000i | ||||
\(866\) | −27.2805 | + | 47.2512i | −0.927029 | + | 1.60566i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −16.5639 | − | 8.33508i | −0.562217 | − | 0.282911i | ||||
\(869\) | − | 72.1835i | − | 2.44866i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.62306 | − | 4.40117i | 0.258297 | − | 0.149128i | ||||
\(872\) | 36.8949 | + | 63.9038i | 1.24942 | + | 2.16406i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 11.1153i | 0.375982i | ||||||||
\(875\) | 27.1539 | − | 11.7331i | 0.917970 | − | 0.396650i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.3881 | + | 19.2766i | 1.12743 | + | 0.650925i | 0.943289 | − | 0.331974i | \(-0.107715\pi\) |
0.184146 | + | 0.982899i | \(0.441048\pi\) | |||||||
\(878\) | 47.7152 | − | 27.5484i | 1.61031 | − | 0.929712i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −80.5756 | + | 60.0452i | −2.71620 | + | 2.02412i | ||||
\(881\) | −34.4764 | −1.16154 | −0.580770 | − | 0.814068i | \(-0.697248\pi\) | ||||
−0.580770 | + | 0.814068i | \(0.697248\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.5869i | 0.861068i | 0.902574 | + | 0.430534i | \(0.141675\pi\) | ||||
−0.902574 | + | 0.430534i | \(0.858325\pi\) | |||||||
\(884\) | −75.2754 | − | 43.4603i | −2.53179 | − | 1.46173i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.219643 | − | 0.380433i | −0.00737905 | − | 0.0127809i | ||||
\(887\) | 20.6076 | + | 11.8978i | 0.691936 | + | 0.399489i | 0.804337 | − | 0.594174i | \(-0.202521\pi\) |
−0.112401 | + | 0.993663i | \(0.535854\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.597481 | − | 10.3996i | −0.0200389 | − | 0.348791i | ||||
\(890\) | 23.4819 | − | 54.5075i | 0.787114 | − | 1.82710i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −18.0566 | − | 31.2749i | −0.604579 | − | 1.04716i | ||||
\(893\) | −3.07031 | − | 5.31792i | −0.102744 | − | 0.177958i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.8542 | + | 9.84561i | 0.763932 | + | 0.329102i | ||||
\(896\) | −9.78847 | + | 19.4522i | −0.327010 | + | 0.649852i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 20.8886 | + | 12.0600i | 0.697061 | + | 0.402448i | ||||
\(899\) | 1.67081 | + | 2.89392i | 0.0557245 | + | 0.0965177i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.6101 | + | 10.7445i | 0.619991 | + | 0.357952i | ||||
\(902\) | 94.4432i | 3.14461i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −50.4235 | −1.67706 | ||||||||
\(905\) | −3.93646 | + | 2.93346i | −0.130852 | + | 0.0975116i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.5806 | − | 19.3878i | 1.11503 | − | 0.643760i | 0.174899 | − | 0.984586i | \(-0.444040\pi\) |
0.940126 | + | 0.340826i | \(0.110707\pi\) | |||||||
\(908\) | 2.18978 | + | 1.26427i | 0.0726704 | + | 0.0419563i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −52.9263 | + | 9.31496i | −1.75449 | + | 0.308788i | ||||
\(911\) | − | 31.4438i | − | 1.04178i | −0.853624 | − | 0.520889i | \(-0.825600\pi\) | ||
0.853624 | − | 0.520889i | \(-0.174400\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.0884 | + | 33.0622i | 0.631735 | + | 1.09420i | ||||
\(914\) | 37.5881 | − | 21.7015i | 1.24330 | − | 0.717822i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 98.7437i | 3.26258i | ||||||||
\(917\) | −4.69524 | + | 9.33064i | −0.155050 | + | 0.308125i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.9872 | + | 24.2266i | −0.461396 | + | 0.799161i | −0.999031 | − | 0.0440170i | \(-0.985984\pi\) |
0.537635 | + | 0.843178i | \(0.319318\pi\) | |||||||
\(920\) | 44.5158 | − | 5.22435i | 1.46764 | − | 0.172242i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −39.8716 | + | 69.0596i | −1.31310 | + | 2.27436i | ||||
\(923\) | 28.7726i | 0.947060i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.97209 | − | 3.75454i | 0.130602 | − | 0.123448i | ||||
\(926\) | −26.5757 | − | 15.3435i | −0.873332 | − | 0.504218i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −13.5171 | + | 7.80411i | −0.443721 | + | 0.256183i | ||||
\(929\) | −11.2452 | + | 19.4772i | −0.368943 | + | 0.639027i | −0.989400 | − | 0.145212i | \(-0.953613\pi\) |
0.620458 | + | 0.784240i | \(0.286947\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.26667 | − | 4.01459i | −0.303703 | − | 0.131573i | ||||
\(932\) | −86.3568 | −2.82871 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −76.9023 | + | 44.3996i | −2.51632 | + | 1.45280i | ||||
\(935\) | 66.8873 | − | 7.84986i | 2.18745 | − | 0.256718i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.0994 | −1.04864 | −0.524321 | − | 0.851521i | \(-0.675681\pi\) | ||||
−0.524321 | + | 0.851521i | \(0.675681\pi\) | |||||||
\(938\) | −0.970808 | − | 16.8976i | −0.0316980 | − | 0.551725i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −35.1176 | + | 26.1698i | −1.14541 | + | 0.853563i | ||||
\(941\) | −5.10912 | − | 8.84925i | −0.166552 | − | 0.288477i | 0.770653 | − | 0.637255i | \(-0.219930\pi\) |
−0.937206 | + | 0.348778i | \(0.886597\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.77631 | − | 16.9331i | 0.318360 | − | 0.551416i | ||||
\(944\) | 91.0378 | 2.96303 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.04097 | 0.228922 | ||||||||
\(947\) | 5.14953 | − | 8.91925i | 0.167337 | − | 0.289837i | −0.770146 | − | 0.637868i | \(-0.779816\pi\) |
0.937483 | + | 0.348031i | \(0.113150\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.54703 | + | 9.60774i | 0.180064 | + | 0.311880i | ||||
\(950\) | −4.29123 | − | 18.0306i | −0.139226 | − | 0.584990i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −78.9890 | + | 51.8627i | −2.56005 | + | 1.68088i | ||||
\(953\) | −0.930159 | −0.0301308 | −0.0150654 | − | 0.999887i | \(-0.504796\pi\) | ||||
−0.0150654 | + | 0.999887i | \(0.504796\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.59440 | + | 22.1064i | 0.0839527 | + | 0.715346i | ||||
\(956\) | 29.3255 | − | 16.9311i | 0.948455 | − | 0.547591i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.63696 | 0.246739 | ||||||||
\(959\) | 8.22082 | + | 12.5206i | 0.265464 | + | 0.404312i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.3402 | + | 24.8379i | −0.462586 | + | 0.801223i | ||||
\(962\) | −8.59943 | + | 4.96488i | −0.277257 | + | 0.160074i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −109.735 | − | 63.3555i | −3.53432 | − | 2.04054i | ||||
\(965\) | −51.2363 | − | 22.0726i | −1.64935 | − | 0.710543i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 4.22117i | − | 0.135744i | −0.997694 | − | 0.0678719i | \(-0.978379\pi\) | ||
0.997694 | − | 0.0678719i | \(-0.0216209\pi\) | |||||||
\(968\) | −69.4443 | + | 120.281i | −2.23202 | + | 3.86598i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 84.0632 | − | 9.86561i | 2.69911 | − | 0.316766i | ||||
\(971\) | 2.28935 | − | 3.96527i | 0.0734688 | − | 0.127252i | −0.826951 | − | 0.562275i | \(-0.809926\pi\) |
0.900419 | + | 0.435023i | \(0.143260\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.53610 | + | 61.5483i | 0.113362 | + | 1.97315i | ||||
\(974\) | 58.3566i | 1.86987i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −48.3872 | + | 27.9364i | −1.54884 | + | 0.894221i | ||||
\(977\) | −22.7556 | − | 39.4138i | −0.728015 | − | 1.26096i | −0.957721 | − | 0.287698i | \(-0.907110\pi\) |
0.229707 | − | 0.973260i | \(-0.426223\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 58.2329i | − | 1.86113i | ||||||
\(980\) | −20.7341 | + | 68.9788i | −0.662327 | + | 2.20345i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −28.9350 | − | 16.7056i | −0.923351 | − | 0.533097i | ||||
\(983\) | −9.10765 | + | 5.25831i | −0.290489 | + | 0.167714i | −0.638162 | − | 0.769902i | \(-0.720305\pi\) |
0.347673 | + | 0.937616i | \(0.386972\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.5232 | − | 34.2500i | −0.813236 | − | 1.09130i | ||||
\(986\) | 30.1192 | 0.959192 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 23.4708i | 0.746706i | ||||||||
\(989\) | −1.26240 | − | 0.728847i | −0.0401420 | − | 0.0231760i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.9539 | + | 24.1689i | 0.443262 | + | 0.767752i | 0.997929 | − | 0.0643204i | \(-0.0204880\pi\) |
−0.554668 | + | 0.832072i | \(0.687155\pi\) | |||||||
\(992\) | 9.38319 | + | 5.41739i | 0.297916 | + | 0.172002i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 49.4205 | + | 24.8687i | 1.56752 | + | 0.788787i | ||||
\(995\) | −3.78535 | − | 1.63073i | −0.120004 | − | 0.0516977i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.4567 | + | 33.7000i | 0.616201 | + | 1.06729i | 0.990173 | + | 0.139851i | \(0.0446623\pi\) |
−0.373972 | + | 0.927440i | \(0.622004\pi\) | |||||||
\(998\) | −27.7592 | − | 48.0803i | −0.878701 | − | 1.52196i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 315.2.bb.b.89.12 | yes | 24 | |
3.2 | odd | 2 | inner | 315.2.bb.b.89.1 | ✓ | 24 | |
5.2 | odd | 4 | 1575.2.bk.i.26.12 | 24 | |||
5.3 | odd | 4 | 1575.2.bk.i.26.2 | 24 | |||
5.4 | even | 2 | inner | 315.2.bb.b.89.2 | yes | 24 | |
7.2 | even | 3 | 2205.2.g.b.2204.4 | 24 | |||
7.3 | odd | 6 | inner | 315.2.bb.b.269.11 | yes | 24 | |
7.5 | odd | 6 | 2205.2.g.b.2204.3 | 24 | |||
15.2 | even | 4 | 1575.2.bk.i.26.1 | 24 | |||
15.8 | even | 4 | 1575.2.bk.i.26.11 | 24 | |||
15.14 | odd | 2 | inner | 315.2.bb.b.89.11 | yes | 24 | |
21.2 | odd | 6 | 2205.2.g.b.2204.22 | 24 | |||
21.5 | even | 6 | 2205.2.g.b.2204.21 | 24 | |||
21.17 | even | 6 | inner | 315.2.bb.b.269.2 | yes | 24 | |
35.3 | even | 12 | 1575.2.bk.i.1151.11 | 24 | |||
35.9 | even | 6 | 2205.2.g.b.2204.24 | 24 | |||
35.17 | even | 12 | 1575.2.bk.i.1151.1 | 24 | |||
35.19 | odd | 6 | 2205.2.g.b.2204.23 | 24 | |||
35.24 | odd | 6 | inner | 315.2.bb.b.269.1 | yes | 24 | |
105.17 | odd | 12 | 1575.2.bk.i.1151.12 | 24 | |||
105.38 | odd | 12 | 1575.2.bk.i.1151.2 | 24 | |||
105.44 | odd | 6 | 2205.2.g.b.2204.2 | 24 | |||
105.59 | even | 6 | inner | 315.2.bb.b.269.12 | yes | 24 | |
105.89 | even | 6 | 2205.2.g.b.2204.1 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.bb.b.89.1 | ✓ | 24 | 3.2 | odd | 2 | inner | |
315.2.bb.b.89.2 | yes | 24 | 5.4 | even | 2 | inner | |
315.2.bb.b.89.11 | yes | 24 | 15.14 | odd | 2 | inner | |
315.2.bb.b.89.12 | yes | 24 | 1.1 | even | 1 | trivial | |
315.2.bb.b.269.1 | yes | 24 | 35.24 | odd | 6 | inner | |
315.2.bb.b.269.2 | yes | 24 | 21.17 | even | 6 | inner | |
315.2.bb.b.269.11 | yes | 24 | 7.3 | odd | 6 | inner | |
315.2.bb.b.269.12 | yes | 24 | 105.59 | even | 6 | inner | |
1575.2.bk.i.26.1 | 24 | 15.2 | even | 4 | |||
1575.2.bk.i.26.2 | 24 | 5.3 | odd | 4 | |||
1575.2.bk.i.26.11 | 24 | 15.8 | even | 4 | |||
1575.2.bk.i.26.12 | 24 | 5.2 | odd | 4 | |||
1575.2.bk.i.1151.1 | 24 | 35.17 | even | 12 | |||
1575.2.bk.i.1151.2 | 24 | 105.38 | odd | 12 | |||
1575.2.bk.i.1151.11 | 24 | 35.3 | even | 12 | |||
1575.2.bk.i.1151.12 | 24 | 105.17 | odd | 12 | |||
2205.2.g.b.2204.1 | 24 | 105.89 | even | 6 | |||
2205.2.g.b.2204.2 | 24 | 105.44 | odd | 6 | |||
2205.2.g.b.2204.3 | 24 | 7.5 | odd | 6 | |||
2205.2.g.b.2204.4 | 24 | 7.2 | even | 3 | |||
2205.2.g.b.2204.21 | 24 | 21.5 | even | 6 | |||
2205.2.g.b.2204.22 | 24 | 21.2 | odd | 6 | |||
2205.2.g.b.2204.23 | 24 | 35.19 | odd | 6 | |||
2205.2.g.b.2204.24 | 24 | 35.9 | even | 6 |