Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [243,2,Mod(10,243)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(243, base_ring=CyclotomicField(54))
chi = DirichletCharacter(H, H._module([8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("243.10");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 243 = 3^{5} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 243.g (of order \(27\), degree \(18\), 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: | \(1.94036476912\) |
Analytic rank: | \(0\) |
Dimension: | \(144\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{27})\) |
Twist minimal: | no (minimal twist has level 81) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{27}]$ |
Embedding invariants
Embedding label | 19.5 | ||
Character | \(\chi\) | \(=\) | 243.19 |
Dual form | 243.2.g.a.64.5 |
$q$-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 \(\left(\mathbb{Z}/243\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{26}{27}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.702679 | − | 0.0821314i | 0.496869 | − | 0.0580757i | 0.136032 | − | 0.990704i | \(-0.456565\pi\) |
0.360837 | + | 0.932629i | \(0.382491\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.45908 | + | 0.345808i | −0.729539 | + | 0.172904i | ||||
\(5\) | −3.06981 | − | 1.54172i | −1.37286 | − | 0.689477i | −0.399070 | − | 0.916920i | \(-0.630667\pi\) |
−0.973791 | + | 0.227443i | \(0.926963\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.775884 | − | 2.59163i | −0.293257 | − | 0.979545i | −0.969955 | − | 0.243285i | \(-0.921775\pi\) |
0.676698 | − | 0.736260i | \(-0.263410\pi\) | |||||||
\(8\) | −2.32646 | + | 0.846761i | −0.822527 | + | 0.299375i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.28372 | − | 0.831205i | −0.722174 | − | 0.262850i | ||||
\(11\) | 0.0859074 | − | 1.47497i | 0.0259021 | − | 0.444721i | −0.960278 | − | 0.279045i | \(-0.909982\pi\) |
0.986180 | − | 0.165677i | \(-0.0529808\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.31531 | + | 4.45324i | −0.919502 | + | 1.23511i | 0.0521373 | + | 0.998640i | \(0.483397\pi\) |
−0.971640 | + | 0.236466i | \(0.924011\pi\) | |||||||
\(14\) | −0.758052 | − | 1.75736i | −0.202598 | − | 0.469675i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.11479 | − | 0.559869i | 0.278698 | − | 0.139967i | ||||
\(17\) | 3.86594 | − | 3.24391i | 0.937627 | − | 0.786763i | −0.0395437 | − | 0.999218i | \(-0.512590\pi\) |
0.977171 | + | 0.212455i | \(0.0681460\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.94119 | − | 3.30705i | −0.904171 | − | 0.758690i | 0.0668301 | − | 0.997764i | \(-0.478711\pi\) |
−0.971001 | + | 0.239075i | \(0.923156\pi\) | |||||||
\(20\) | 5.01223 | + | 1.18792i | 1.12077 | + | 0.265627i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.0607763 | − | 1.04349i | −0.0129576 | − | 0.222473i | ||||
\(23\) | 0.497394 | − | 1.66141i | 0.103714 | − | 0.346428i | −0.890343 | − | 0.455290i | \(-0.849536\pi\) |
0.994057 | + | 0.108862i | \(0.0347207\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.06106 | + | 5.45495i | 0.812212 | + | 1.09099i | ||||
\(26\) | −1.96385 | + | 3.40149i | −0.385143 | + | 0.667087i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.02828 | + | 3.51309i | 0.383309 | + | 0.663911i | ||||
\(29\) | −0.851040 | + | 1.97293i | −0.158034 | + | 0.366364i | −0.978775 | − | 0.204936i | \(-0.934301\pi\) |
0.820741 | + | 0.571300i | \(0.193561\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.61206 | + | 2.76862i | 0.469139 | + | 0.497259i | 0.918131 | − | 0.396277i | \(-0.129698\pi\) |
−0.448991 | + | 0.893536i | \(0.648217\pi\) | |||||||
\(32\) | 4.87430 | − | 3.20588i | 0.861662 | − | 0.566724i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.45009 | − | 2.59694i | 0.420186 | − | 0.445371i | ||||
\(35\) | −1.61375 | + | 9.15202i | −0.272773 | + | 1.54697i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.891723 | − | 5.05721i | −0.146598 | − | 0.831401i | −0.966070 | − | 0.258281i | \(-0.916844\pi\) |
0.819472 | − | 0.573120i | \(-0.194267\pi\) | |||||||
\(38\) | −3.04100 | − | 2.00010i | −0.493316 | − | 0.324459i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.44725 | + | 0.987342i | 1.33563 | + | 0.156112i | ||||
\(41\) | −4.48158 | − | 0.523822i | −0.699906 | − | 0.0818072i | −0.241304 | − | 0.970449i | \(-0.577575\pi\) |
−0.458601 | + | 0.888642i | \(0.651649\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.688837 | − | 0.453055i | −0.105047 | − | 0.0690902i | 0.495899 | − | 0.868380i | \(-0.334839\pi\) |
−0.600945 | + | 0.799290i | \(0.705209\pi\) | |||||||
\(44\) | 0.384712 | + | 2.18181i | 0.0579975 | + | 0.328920i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.213054 | − | 1.20829i | 0.0314131 | − | 0.178153i | ||||
\(47\) | −4.60630 | + | 4.88239i | −0.671898 | + | 0.712170i | −0.970201 | − | 0.242301i | \(-0.922098\pi\) |
0.298303 | + | 0.954471i | \(0.403579\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.266150 | + | 0.175050i | −0.0380215 | + | 0.0250071i | ||||
\(50\) | 3.30164 | + | 3.49954i | 0.466923 | + | 0.494909i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.29733 | − | 7.64408i | 0.457258 | − | 1.06004i | ||||
\(53\) | −2.58797 | − | 4.48249i | −0.355485 | − | 0.615717i | 0.631716 | − | 0.775200i | \(-0.282351\pi\) |
−0.987201 | + | 0.159482i | \(0.949017\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.53771 | + | 4.39545i | −0.342185 | + | 0.592682i | ||||
\(56\) | 3.99955 | + | 5.37233i | 0.534463 | + | 0.717908i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.435968 | + | 1.45623i | −0.0572454 | + | 0.191213i | ||||
\(59\) | −0.205501 | − | 3.52832i | −0.0267540 | − | 0.459348i | −0.984906 | − | 0.173089i | \(-0.944625\pi\) |
0.958152 | − | 0.286259i | \(-0.0924118\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.27331 | − | 1.24980i | −0.675178 | − | 0.160020i | −0.121297 | − | 0.992616i | \(-0.538705\pi\) |
−0.553881 | + | 0.832596i | \(0.686854\pi\) | |||||||
\(62\) | 2.06283 | + | 1.73092i | 0.261980 | + | 0.219827i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.25051 | − | 1.04930i | 0.156314 | − | 0.131163i | ||||
\(65\) | 17.0430 | − | 8.55933i | 2.11393 | − | 1.06165i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.59382 | − | 6.01314i | −0.316885 | − | 0.734622i | −0.999991 | − | 0.00430260i | \(-0.998630\pi\) |
0.683106 | − | 0.730320i | \(-0.260629\pi\) | |||||||
\(68\) | −4.51893 | + | 6.06998i | −0.548001 | + | 0.736093i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.382279 | + | 6.56347i | −0.0456910 | + | 0.784485i | ||||
\(71\) | −3.30039 | − | 1.20125i | −0.391685 | − | 0.142562i | 0.138667 | − | 0.990339i | \(-0.455718\pi\) |
−0.530352 | + | 0.847777i | \(0.677940\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.668031 | − | 0.243143i | 0.0781871 | − | 0.0284578i | −0.302630 | − | 0.953108i | \(-0.597865\pi\) |
0.380818 | + | 0.924650i | \(0.375643\pi\) | |||||||
\(74\) | −1.04195 | − | 3.48036i | −0.121124 | − | 0.404584i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.89410 | + | 3.46235i | 0.790808 | + | 0.397159i | ||||
\(77\) | −3.88925 | + | 0.921768i | −0.443221 | + | 0.105045i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.5883 | − | 1.82202i | 1.75383 | − | 0.204993i | 0.822396 | − | 0.568915i | \(-0.192637\pi\) |
0.931429 | + | 0.363922i | \(0.118563\pi\) | |||||||
\(80\) | −4.28536 | −0.479118 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.19214 | −0.352513 | ||||||||
\(83\) | 5.89572 | − | 0.689111i | 0.647140 | − | 0.0756398i | 0.213810 | − | 0.976875i | \(-0.431413\pi\) |
0.433330 | + | 0.901235i | \(0.357339\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.8689 | + | 3.99800i | −1.82969 | + | 0.433644i | ||||
\(86\) | −0.521241 | − | 0.261777i | −0.0562069 | − | 0.0282282i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.04909 | + | 3.50421i | 0.111833 | + | 0.373550i | ||||
\(89\) | 3.78422 | − | 1.37734i | 0.401127 | − | 0.145998i | −0.133576 | − | 0.991039i | \(-0.542646\pi\) |
0.534702 | + | 0.845040i | \(0.320424\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.1135 | + | 5.13688i | 1.47949 | + | 0.538491i | ||||
\(92\) | −0.151207 | + | 2.59613i | −0.0157645 | + | 0.270665i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.83575 | + | 3.80908i | −0.292486 | + | 0.392876i | ||||
\(95\) | 7.00017 | + | 16.2282i | 0.718203 | + | 1.66498i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.7605 | + | 5.40414i | −1.09257 | + | 0.548707i | −0.901460 | − | 0.432862i | \(-0.857504\pi\) |
−0.191106 | + | 0.981569i | \(0.561207\pi\) | |||||||
\(98\) | −0.172641 | + | 0.144863i | −0.0174394 | + | 0.0146334i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.81176 | − | 6.55484i | −0.781176 | − | 0.655484i | ||||
\(101\) | −16.3766 | − | 3.88132i | −1.62953 | − | 0.386206i | −0.688690 | − | 0.725056i | \(-0.741814\pi\) |
−0.940840 | + | 0.338850i | \(0.889962\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.01132 | − | 17.3637i | −0.0996486 | − | 1.71090i | −0.564434 | − | 0.825478i | \(-0.690906\pi\) |
0.464786 | − | 0.885423i | \(-0.346131\pi\) | |||||||
\(104\) | 3.94210 | − | 13.1675i | 0.386555 | − | 1.29118i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.18666 | − | 2.93720i | −0.212388 | − | 0.285286i | ||||
\(107\) | 3.74462 | − | 6.48587i | 0.362006 | − | 0.627013i | −0.626285 | − | 0.779594i | \(-0.715425\pi\) |
0.988291 | + | 0.152581i | \(0.0487586\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.69921 | − | 2.94312i | −0.162755 | − | 0.281899i | 0.773101 | − | 0.634283i | \(-0.218705\pi\) |
−0.935856 | + | 0.352384i | \(0.885371\pi\) | |||||||
\(110\) | −1.42219 | + | 3.29701i | −0.135601 | + | 0.314358i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.31592 | − | 2.45474i | −0.218834 | − | 0.231951i | ||||
\(113\) | −1.71662 | + | 1.12904i | −0.161486 | + | 0.106211i | −0.627680 | − | 0.778472i | \(-0.715995\pi\) |
0.466194 | + | 0.884683i | \(0.345625\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.08833 | + | 4.33338i | −0.381239 | + | 0.404090i | ||||
\(116\) | 0.559478 | − | 3.17296i | 0.0519462 | − | 0.294602i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.434187 | − | 2.46240i | −0.0399701 | − | 0.226682i | ||||
\(119\) | −11.4065 | − | 7.50219i | −1.04563 | − | 0.687725i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.75745 | + | 1.02360i | 0.796132 | + | 0.0930545i | ||||
\(122\) | −3.80809 | − | 0.445102i | −0.344768 | − | 0.0402976i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.76860 | − | 3.13636i | −0.428233 | − | 0.281653i | ||||
\(125\) | −1.07411 | − | 6.09158i | −0.0960713 | − | 0.544847i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.46076 | + | 8.28439i | −0.129622 | + | 0.735121i | 0.848833 | + | 0.528661i | \(0.177306\pi\) |
−0.978455 | + | 0.206460i | \(0.933806\pi\) | |||||||
\(128\) | −7.21464 | + | 7.64707i | −0.637690 | + | 0.675912i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 11.2728 | − | 7.41423i | 0.988689 | − | 0.650271i | ||||
\(131\) | 7.36003 | + | 7.80118i | 0.643049 | + | 0.681592i | 0.964121 | − | 0.265463i | \(-0.0855247\pi\) |
−0.321072 | + | 0.947055i | \(0.604043\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.51276 | + | 12.7800i | −0.478017 | + | 1.10817i | ||||
\(134\) | −2.31649 | − | 4.01228i | −0.200114 | − | 0.346608i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.24712 | + | 10.8203i | −0.535686 | + | 0.927835i | ||||
\(137\) | −6.37060 | − | 8.55720i | −0.544277 | − | 0.731091i | 0.441849 | − | 0.897089i | \(-0.354323\pi\) |
−0.986126 | + | 0.165999i | \(0.946915\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.808205 | + | 2.69959i | −0.0685510 | + | 0.228976i | −0.985399 | − | 0.170260i | \(-0.945539\pi\) |
0.916848 | + | 0.399236i | \(0.130725\pi\) | |||||||
\(140\) | −0.810255 | − | 13.9115i | −0.0684791 | − | 1.17574i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.41778 | − | 0.573024i | −0.202895 | − | 0.0480871i | ||||
\(143\) | 6.28360 | + | 5.27257i | 0.525461 | + | 0.440914i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.65423 | − | 4.74447i | 0.469559 | − | 0.394006i | ||||
\(146\) | 0.449442 | − | 0.225718i | 0.0371961 | − | 0.0186806i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.04992 | + | 7.07050i | 0.250702 | + | 0.581191i | ||||
\(149\) | 0.410135 | − | 0.550907i | 0.0335996 | − | 0.0451321i | −0.785006 | − | 0.619488i | \(-0.787340\pi\) |
0.818606 | + | 0.574356i | \(0.194748\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.0292138 | + | 0.501582i | −0.00237739 | + | 0.0408182i | −0.999288 | − | 0.0377236i | \(-0.987989\pi\) |
0.996911 | + | 0.0785418i | \(0.0250264\pi\) | |||||||
\(152\) | 11.9693 | + | 4.35647i | 0.970838 | + | 0.353356i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.65719 | + | 0.967136i | −0.214122 | + | 0.0779341i | ||||
\(155\) | −3.75010 | − | 12.5262i | −0.301215 | − | 1.00613i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.3361 | − | 5.69318i | −0.904716 | − | 0.454365i | −0.0653065 | − | 0.997865i | \(-0.520802\pi\) |
−0.839409 | + | 0.543500i | \(0.817099\pi\) | |||||||
\(158\) | 10.8040 | − | 2.56059i | 0.859517 | − | 0.203709i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −19.9057 | + | 2.32665i | −1.57369 | + | 0.183938i | ||||
\(161\) | −4.69169 | −0.369757 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.8238 | 1.08276 | 0.541382 | − | 0.840777i | \(-0.317901\pi\) | ||||
0.541382 | + | 0.840777i | \(0.317901\pi\) | |||||||
\(164\) | 6.72012 | − | 0.785469i | 0.524753 | − | 0.0613348i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.08620 | − | 0.968448i | 0.317151 | − | 0.0751662i | ||||
\(167\) | −2.47720 | − | 1.24410i | −0.191692 | − | 0.0962712i | 0.350365 | − | 0.936613i | \(-0.386058\pi\) |
−0.542056 | + | 0.840342i | \(0.682354\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.11159 | − | 17.0739i | −0.393199 | − | 1.31338i | ||||
\(170\) | −11.5250 | + | 4.19477i | −0.883931 | + | 0.321725i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.16174 | + | 0.422837i | 0.0885815 | + | 0.0322410i | ||||
\(173\) | −1.20706 | + | 20.7244i | −0.0917709 | + | 1.57565i | 0.567266 | + | 0.823535i | \(0.308001\pi\) |
−0.659037 | + | 0.752111i | \(0.729036\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.9863 | − | 14.7572i | 0.830487 | − | 1.11554i | ||||
\(176\) | −0.730023 | − | 1.69238i | −0.0550276 | − | 0.127568i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.54597 | − | 1.27863i | 0.190829 | − | 0.0958377i | ||||
\(179\) | 10.8498 | − | 9.10407i | 0.810953 | − | 0.680470i | −0.139882 | − | 0.990168i | \(-0.544672\pi\) |
0.950835 | + | 0.309698i | \(0.100228\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.124097 | − | 0.104130i | −0.00922404 | − | 0.00773989i | 0.638164 | − | 0.769901i | \(-0.279694\pi\) |
−0.647388 | + | 0.762161i | \(0.724139\pi\) | |||||||
\(182\) | 10.3391 | + | 2.45042i | 0.766387 | + | 0.181637i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.249653 | + | 4.28637i | 0.0184047 | + | 0.315996i | ||||
\(185\) | −5.05937 | + | 16.8995i | −0.371972 | + | 1.24247i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.45256 | − | 5.98083i | −0.325604 | − | 0.437362i | ||||
\(188\) | 5.03258 | − | 8.71668i | 0.367038 | − | 0.635729i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.25172 | + | 10.8283i | 0.453548 | + | 0.785568i | ||||
\(191\) | −9.22017 | + | 21.3748i | −0.667148 | + | 1.54662i | 0.161512 | + | 0.986871i | \(0.448363\pi\) |
−0.828660 | + | 0.559753i | \(0.810896\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.36724 | − | 7.80882i | −0.530305 | − | 0.562091i | 0.405732 | − | 0.913992i | \(-0.367017\pi\) |
−0.936037 | + | 0.351901i | \(0.885535\pi\) | |||||||
\(194\) | −7.11735 | + | 4.68115i | −0.510996 | + | 0.336087i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.327800 | − | 0.347448i | 0.0234143 | − | 0.0248177i | ||||
\(197\) | 1.18741 | − | 6.73411i | 0.0845992 | − | 0.479786i | −0.912843 | − | 0.408310i | \(-0.866118\pi\) |
0.997442 | − | 0.0714755i | \(-0.0227708\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.86766 | + | 10.5920i | 0.132395 | + | 0.750848i | 0.976639 | + | 0.214889i | \(0.0689389\pi\) |
−0.844244 | + | 0.535959i | \(0.819950\pi\) | |||||||
\(200\) | −14.0669 | − | 9.25195i | −0.994681 | − | 0.654212i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11.8263 | − | 1.38229i | −0.832092 | − | 0.0972577i | ||||
\(203\) | 5.77342 | + | 0.674816i | 0.405215 | + | 0.0473628i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.9500 | + | 8.51737i | 0.904469 | + | 0.594879i | ||||
\(206\) | −2.13675 | − | 12.1181i | −0.148874 | − | 0.844307i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.20265 | + | 6.82057i | −0.0833888 | + | 0.472922i | ||||
\(209\) | −5.21639 | + | 5.52905i | −0.360825 | + | 0.382453i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.27097 | + | 4.78219i | −0.500554 | + | 0.329220i | −0.774552 | − | 0.632511i | \(-0.782024\pi\) |
0.273997 | + | 0.961730i | \(0.411654\pi\) | |||||||
\(212\) | 5.32612 | + | 5.64536i | 0.365800 | + | 0.387725i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.09857 | − | 4.86504i | 0.143455 | − | 0.332567i | ||||
\(215\) | 1.41612 | + | 2.45278i | 0.0965783 | + | 0.167279i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.14859 | − | 8.91762i | 0.349509 | − | 0.605368i | ||||
\(218\) | −1.43572 | − | 1.92851i | −0.0972393 | − | 0.130615i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.18274 | − | 7.29086i | 0.147160 | − | 0.491550i | ||||
\(221\) | 1.62910 | + | 27.9705i | 0.109585 | + | 1.88150i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.66506 | + | 1.81665i | 0.513290 | + | 0.121652i | 0.479095 | − | 0.877763i | \(-0.340965\pi\) |
0.0341954 | + | 0.999415i | \(0.489113\pi\) | |||||||
\(224\) | −12.0903 | − | 10.1450i | −0.807820 | − | 0.677842i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.11350 | + | 0.934340i | −0.0740691 | + | 0.0621514i | ||||
\(227\) | 17.0823 | − | 8.57908i | 1.13380 | − | 0.569413i | 0.219964 | − | 0.975508i | \(-0.429406\pi\) |
0.913831 | + | 0.406095i | \(0.133110\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.7024 | + | 24.8109i | 0.707234 | + | 1.63955i | 0.767244 | + | 0.641356i | \(0.221628\pi\) |
−0.0600094 | + | 0.998198i | \(0.519113\pi\) | |||||||
\(230\) | −2.51688 | + | 3.38075i | −0.165958 | + | 0.222920i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.309305 | − | 5.31057i | 0.0203069 | − | 0.348656i | ||||
\(233\) | 17.0044 | + | 6.18909i | 1.11400 | + | 0.405461i | 0.832457 | − | 0.554089i | \(-0.186933\pi\) |
0.281538 | + | 0.959550i | \(0.409156\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.6677 | − | 7.88641i | 1.41345 | − | 0.514453i | ||||
\(236\) | 1.51996 | + | 5.07702i | 0.0989410 | + | 0.330486i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.63130 | − | 4.33480i | −0.559484 | − | 0.280983i | ||||
\(239\) | 10.3119 | − | 2.44398i | 0.667025 | − | 0.158088i | 0.116866 | − | 0.993148i | \(-0.462715\pi\) |
0.550159 | + | 0.835060i | \(0.314567\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.7613 | − | 1.95911i | 1.07969 | − | 0.126198i | 0.442396 | − | 0.896820i | \(-0.354128\pi\) |
0.637292 | + | 0.770622i | \(0.280054\pi\) | |||||||
\(242\) | 6.23775 | 0.400978 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.12635 | 0.520236 | ||||||||
\(245\) | 1.08691 | − | 0.127041i | 0.0694401 | − | 0.00811638i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 27.7934 | − | 6.58715i | 1.76845 | − | 0.419130i | ||||
\(248\) | −8.42120 | − | 4.22928i | −0.534747 | − | 0.268560i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.25506 | − | 4.19221i | −0.0793772 | − | 0.265138i | ||||
\(251\) | 17.5886 | − | 6.40174i | 1.11018 | − | 0.404074i | 0.279123 | − | 0.960255i | \(-0.409956\pi\) |
0.831061 | + | 0.556181i | \(0.187734\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.40781 | − | 0.876370i | −0.151378 | − | 0.0550969i | ||||
\(254\) | −0.346038 | + | 5.94124i | −0.0217124 | + | 0.372787i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.39115 | + | 8.58480i | −0.399447 | + | 0.536550i | ||||
\(257\) | −11.4433 | − | 26.5285i | −0.713812 | − | 1.65480i | −0.755061 | − | 0.655654i | \(-0.772393\pi\) |
0.0412491 | − | 0.999149i | \(-0.486866\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.4146 | + | 6.23483i | −0.771404 | + | 0.387413i | ||||
\(260\) | −21.9072 | + | 18.3823i | −1.35863 | + | 1.14002i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.81246 | + | 4.87724i | 0.359095 | + | 0.301317i | ||||
\(263\) | 23.3642 | + | 5.53742i | 1.44070 | + | 0.341452i | 0.875386 | − | 0.483424i | \(-0.160607\pi\) |
0.565313 | + | 0.824876i | \(0.308755\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.03384 | + | 17.7503i | 0.0635082 | + | 1.09039i | ||||
\(266\) | −2.82406 | + | 9.43301i | −0.173154 | + | 0.578375i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.86397 | + | 7.87668i | 0.358199 | + | 0.481145i | ||||
\(269\) | −12.8618 | + | 22.2774i | −0.784200 | + | 1.35827i | 0.145276 | + | 0.989391i | \(0.453593\pi\) |
−0.929476 | + | 0.368883i | \(0.879740\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.12617 | − | 8.87880i | −0.311393 | − | 0.539348i | 0.667271 | − | 0.744815i | \(-0.267462\pi\) |
−0.978664 | + | 0.205466i | \(0.934129\pi\) | |||||||
\(272\) | 2.49355 | − | 5.78069i | 0.151194 | − | 0.350506i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.17930 | − | 5.48974i | −0.312893 | − | 0.331647i | ||||
\(275\) | 8.39478 | − | 5.52133i | 0.506224 | − | 0.332949i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.07014 | − | 4.31409i | 0.244551 | − | 0.259209i | −0.593459 | − | 0.804865i | \(-0.702238\pi\) |
0.838009 | + | 0.545656i | \(0.183719\pi\) | |||||||
\(278\) | −0.346187 | + | 1.96333i | −0.0207629 | + | 0.117752i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.99526 | − | 22.6582i | −0.238762 | − | 1.35409i | ||||
\(281\) | −17.3504 | − | 11.4115i | −1.03504 | − | 0.680754i | −0.0861213 | − | 0.996285i | \(-0.527447\pi\) |
−0.948916 | + | 0.315530i | \(0.897818\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.6779 | − | 1.36495i | −0.694180 | − | 0.0811380i | −0.238316 | − | 0.971188i | \(-0.576596\pi\) |
−0.455864 | + | 0.890050i | \(0.650670\pi\) | |||||||
\(284\) | 5.23093 | + | 0.611408i | 0.310399 | + | 0.0362804i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.84840 | + | 3.18884i | 0.286692 | + | 0.188560i | ||||
\(287\) | 2.11963 | + | 12.0210i | 0.125118 | + | 0.709580i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.47052 | − | 8.33972i | 0.0865011 | − | 0.490572i | ||||
\(290\) | 3.58344 | − | 3.79823i | 0.210427 | − | 0.223040i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.890628 | + | 0.585775i | −0.0521201 | + | 0.0342799i | ||||
\(293\) | −18.5895 | − | 19.7037i | −1.08601 | − | 1.15110i | −0.987766 | − | 0.155942i | \(-0.950159\pi\) |
−0.0982448 | − | 0.995162i | \(-0.531323\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.80882 | + | 11.1481i | −0.279980 | + | 0.649067i | ||||
\(296\) | 6.35680 | + | 11.0103i | 0.369482 | + | 0.639961i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.242947 | − | 0.420796i | 0.0140735 | − | 0.0243761i | ||||
\(299\) | 5.74964 | + | 7.72311i | 0.332510 | + | 0.446639i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.639695 | + | 2.13673i | −0.0368714 | + | 0.123159i | ||||
\(302\) | 0.0206677 | + | 0.354851i | 0.00118929 | + | 0.0204194i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.24512 | − | 1.48012i | −0.358182 | − | 0.0848907i | ||||
\(305\) | 14.2612 | + | 11.9666i | 0.816596 | + | 0.685205i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.6794 | + | 15.6739i | −1.06609 | + | 0.894557i | −0.994693 | − | 0.102891i | \(-0.967191\pi\) |
−0.0713990 | + | 0.997448i | \(0.522746\pi\) | |||||||
\(308\) | 5.35595 | − | 2.68986i | 0.305184 | − | 0.153269i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.66391 | − | 8.49390i | −0.208096 | − | 0.482421i | ||||
\(311\) | 10.1301 | − | 13.6072i | 0.574428 | − | 0.771591i | −0.416038 | − | 0.909347i | \(-0.636582\pi\) |
0.990466 | + | 0.137756i | \(0.0439891\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.678174 | + | 11.6438i | −0.0383327 | + | 0.658146i | 0.923346 | + | 0.383968i | \(0.125443\pi\) |
−0.961679 | + | 0.274178i | \(0.911594\pi\) | |||||||
\(314\) | −8.43320 | − | 3.06943i | −0.475913 | − | 0.173218i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −22.1145 | + | 8.04903i | −1.24404 | + | 0.452793i | ||||
\(317\) | −7.94087 | − | 26.5244i | −0.446004 | − | 1.48976i | −0.825414 | − | 0.564528i | \(-0.809058\pi\) |
0.379410 | − | 0.925229i | \(-0.376127\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.83691 | + | 1.42475i | 0.158837 | + | 0.0797707i | ||||
\(320\) | −5.45656 | + | 1.29323i | −0.305031 | + | 0.0722937i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.29675 | + | 0.385335i | −0.183721 | + | 0.0214739i | ||||
\(323\) | −25.9641 | −1.44468 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −37.7559 | −2.09432 | ||||||||
\(326\) | 9.71370 | − | 1.13537i | 0.537992 | − | 0.0628822i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10.8698 | − | 2.57618i | 0.600182 | − | 0.142246i | ||||
\(329\) | 16.2273 | + | 8.14967i | 0.894641 | + | 0.449306i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.34775 | + | 17.8627i | 0.293939 | + | 0.981824i | 0.969617 | + | 0.244628i | \(0.0786657\pi\) |
−0.675678 | + | 0.737197i | \(0.736149\pi\) | |||||||
\(332\) | −8.36402 | + | 3.04425i | −0.459035 | + | 0.167075i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.84286 | − | 0.670745i | −0.100837 | − | 0.0367016i | ||||
\(335\) | −1.30804 | + | 22.4581i | −0.0714657 | + | 1.22702i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.0513 | − | 24.2471i | 0.983319 | − | 1.32083i | 0.0364052 | − | 0.999337i | \(-0.488409\pi\) |
0.946913 | − | 0.321489i | \(-0.104183\pi\) | |||||||
\(338\) | −4.99411 | − | 11.5777i | −0.271644 | − | 0.629741i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 23.2305 | − | 11.6668i | 1.25985 | − | 0.632720i | ||||
\(341\) | 4.30804 | − | 3.61487i | 0.233293 | − | 0.195756i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.8464 | − | 11.6185i | −0.747635 | − | 0.627341i | ||||
\(344\) | 1.98618 | + | 0.470733i | 0.107088 | + | 0.0253802i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.853949 | + | 14.6617i | 0.0459086 | + | 0.788219i | ||||
\(347\) | 0.883973 | − | 2.95267i | 0.0474541 | − | 0.158508i | −0.930978 | − | 0.365074i | \(-0.881044\pi\) |
0.978433 | + | 0.206566i | \(0.0662289\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.36161 | − | 7.20189i | −0.287001 | − | 0.385509i | 0.635119 | − | 0.772415i | \(-0.280951\pi\) |
−0.922119 | + | 0.386906i | \(0.873544\pi\) | |||||||
\(350\) | 6.50782 | − | 11.2719i | 0.347858 | − | 0.602507i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.30985 | − | 7.46487i | −0.229716 | − | 0.397879i | ||||
\(353\) | 13.2238 | − | 30.6562i | 0.703832 | − | 1.63167i | −0.0694350 | − | 0.997586i | \(-0.522120\pi\) |
0.773267 | − | 0.634080i | \(-0.218621\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.27961 | + | 8.77587i | 0.439436 | + | 0.465775i | ||||
\(356\) | −5.04518 | + | 3.31827i | −0.267394 | + | 0.175868i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.87620 | − | 7.28835i | 0.363419 | − | 0.385201i | ||||
\(359\) | −0.100805 | + | 0.571693i | −0.00532028 | + | 0.0301728i | −0.987352 | − | 0.158541i | \(-0.949321\pi\) |
0.982032 | + | 0.188714i | \(0.0604320\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.29708 | + | 7.35609i | 0.0682672 | + | 0.387162i | ||||
\(362\) | −0.0957525 | − | 0.0629774i | −0.00503264 | − | 0.00331002i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −22.3690 | − | 2.61456i | −1.17245 | − | 0.137040i | ||||
\(365\) | −2.42559 | − | 0.283510i | −0.126961 | − | 0.0148396i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.2493 | − | 13.9759i | −1.10920 | − | 0.729534i | −0.143620 | − | 0.989633i | \(-0.545874\pi\) |
−0.965582 | + | 0.260099i | \(0.916245\pi\) | |||||||
\(368\) | −0.375682 | − | 2.13060i | −0.0195838 | − | 0.111065i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.16714 | + | 12.2904i | −0.112664 | + | 0.638950i | ||||
\(371\) | −9.60900 | + | 10.1850i | −0.498875 | + | 0.528776i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.67641 | + | 6.36427i | −0.501025 | + | 0.329530i | −0.774738 | − | 0.632282i | \(-0.782118\pi\) |
0.273713 | + | 0.961811i | \(0.411748\pi\) | |||||||
\(374\) | −3.61994 | − | 3.83691i | −0.187182 | − | 0.198402i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.58214 | − | 15.2591i | 0.339448 | − | 0.786928i | ||||
\(377\) | −5.96447 | − | 10.3308i | −0.307186 | − | 0.532062i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.18651 | − | 15.9115i | 0.471880 | − | 0.817319i | −0.527603 | − | 0.849491i | \(-0.676909\pi\) |
0.999482 | + | 0.0321718i | \(0.0102424\pi\) | |||||||
\(380\) | −15.8256 | − | 21.2575i | −0.811838 | − | 1.09049i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.72328 | + | 15.7769i | −0.241664 | + | 0.807215i | ||||
\(383\) | −1.55227 | − | 26.6514i | −0.0793171 | − | 1.36182i | −0.769713 | − | 0.638390i | \(-0.779601\pi\) |
0.690396 | − | 0.723432i | \(-0.257436\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.3604 | + | 3.16646i | 0.680907 | + | 0.161378i | ||||
\(386\) | −5.81815 | − | 4.88201i | −0.296136 | − | 0.248488i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.8316 | − | 11.6061i | 0.702196 | − | 0.589212i | ||||
\(389\) | 2.83188 | − | 1.42222i | 0.143582 | − | 0.0721095i | −0.375558 | − | 0.926799i | \(-0.622549\pi\) |
0.519140 | + | 0.854689i | \(0.326252\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.46657 | − | 8.03640i | −0.175312 | − | 0.406418i | ||||
\(392\) | 0.470962 | − | 0.632612i | 0.0237872 | − | 0.0319517i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.281283 | − | 4.82945i | 0.0141708 | − | 0.243304i | ||||
\(395\) | −50.6623 | − | 18.4396i | −2.54910 | − | 0.927795i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.81860 | − | 1.38986i | 0.191650 | − | 0.0697550i | −0.244412 | − | 0.969671i | \(-0.578595\pi\) |
0.436062 | + | 0.899916i | \(0.356373\pi\) | |||||||
\(398\) | 2.18230 | + | 7.28940i | 0.109389 | + | 0.365384i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.58129 | + | 3.80747i | 0.379064 | + | 0.190373i | ||||
\(401\) | −20.7711 | + | 4.92283i | −1.03726 | + | 0.245835i | −0.713757 | − | 0.700393i | \(-0.753008\pi\) |
−0.323501 | + | 0.946228i | \(0.604860\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.9891 | + | 2.45328i | −1.04554 | + | 0.122206i | ||||
\(404\) | 25.2369 | 1.25558 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.11229 | 0.204089 | ||||||||
\(407\) | −7.53586 | + | 0.880816i | −0.373539 | + | 0.0436604i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.5944 | + | 5.11798i | −1.06778 | + | 0.253068i | −0.726691 | − | 0.686965i | \(-0.758943\pi\) |
−0.341085 | + | 0.940032i | \(0.610795\pi\) | |||||||
\(410\) | 9.79926 | + | 4.92137i | 0.483951 | + | 0.243049i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.48012 | + | 24.9853i | 0.368519 | + | 1.23094i | ||||
\(413\) | −8.98466 | + | 3.27015i | −0.442106 | + | 0.160913i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19.1612 | − | 6.97410i | −0.940585 | − | 0.342345i | ||||
\(416\) | −1.88329 | + | 32.3349i | −0.0923360 | + | 1.58535i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.21134 | + | 4.31358i | −0.157072 | + | 0.210984i | ||||
\(419\) | 10.1002 | + | 23.4148i | 0.493425 | + | 1.14389i | 0.965045 | + | 0.262086i | \(0.0844103\pi\) |
−0.471620 | + | 0.881802i | \(0.656330\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.6167 | − | 8.34520i | 0.809847 | − | 0.406720i | 0.00484167 | − | 0.999988i | \(-0.498459\pi\) |
0.805005 | + | 0.593268i | \(0.202163\pi\) | |||||||
\(422\) | −4.71639 | + | 3.95752i | −0.229590 | + | 0.192649i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.81639 | + | 8.23693i | 0.476726 | + | 0.400021i | ||||
\(425\) | 33.3951 | + | 7.91479i | 1.61990 | + | 0.383924i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.852460 | + | 14.6362i | 0.0412534 | + | 0.708294i | ||||
\(428\) | −3.22083 | + | 10.7583i | −0.155684 | + | 0.520022i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.19653 | + | 1.60721i | 0.0577016 | + | 0.0775067i | ||||
\(431\) | −3.46440 | + | 6.00052i | −0.166874 | + | 0.289035i | −0.937319 | − | 0.348472i | \(-0.886701\pi\) |
0.770445 | + | 0.637507i | \(0.220034\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.4509 | − | 21.5656i | −0.598352 | − | 1.03638i | −0.993064 | − | 0.117571i | \(-0.962489\pi\) |
0.394713 | − | 0.918805i | \(-0.370844\pi\) | |||||||
\(434\) | 2.88539 | − | 6.68909i | 0.138503 | − | 0.321087i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.49703 | + | 3.70663i | 0.167477 | + | 0.177516i | ||||
\(437\) | −7.45469 | + | 4.90303i | −0.356606 | + | 0.234544i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.58416 | − | 5.91886i | 0.266517 | − | 0.282492i | −0.580269 | − | 0.814425i | \(-0.697053\pi\) |
0.846786 | + | 0.531933i | \(0.178534\pi\) | |||||||
\(440\) | 2.18199 | − | 12.3747i | 0.104022 | − | 0.589938i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.44199 | + | 19.5205i | 0.163719 | + | 0.928495i | ||||
\(443\) | 21.0995 | + | 13.8773i | 1.00247 | + | 0.659332i | 0.940870 | − | 0.338769i | \(-0.110011\pi\) |
0.0615961 | + | 0.998101i | \(0.480381\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.7403 | − | 1.60601i | −0.651354 | − | 0.0761324i | ||||
\(446\) | 5.53528 | + | 0.646982i | 0.262103 | + | 0.0306355i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.68966 | − | 2.42673i | −0.174320 | − | 0.114652i | ||||
\(449\) | 6.85970 | + | 38.9033i | 0.323729 | + | 1.83596i | 0.518458 | + | 0.855103i | \(0.326506\pi\) |
−0.194728 | + | 0.980857i | \(0.562383\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.15762 | + | 6.56522i | −0.0545104 | + | 0.309144i | ||||
\(452\) | 2.11425 | − | 2.24097i | 0.0994459 | − | 0.105407i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.2988 | − | 7.43134i | 0.530279 | − | 0.348770i | ||||
\(455\) | −35.4060 | − | 37.5282i | −1.65986 | − | 1.75935i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.26023 | − | 19.1494i | 0.386397 | − | 0.895770i | −0.608375 | − | 0.793650i | \(-0.708178\pi\) |
0.994772 | − | 0.102120i | \(-0.0325625\pi\) | |||||||
\(458\) | 9.55811 | + | 16.5551i | 0.446621 | + | 0.773570i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.46668 | − | 7.73651i | 0.208260 | − | 0.360717i | ||||
\(461\) | −10.1557 | − | 13.6414i | −0.472996 | − | 0.635344i | 0.500039 | − | 0.866003i | \(-0.333319\pi\) |
−0.973035 | + | 0.230659i | \(0.925912\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.70861 | + | 9.04739i | −0.125880 | + | 0.420468i | −0.997577 | − | 0.0695778i | \(-0.977835\pi\) |
0.871697 | + | 0.490046i | \(0.163020\pi\) | |||||||
\(464\) | 0.155852 | + | 2.67588i | 0.00723525 | + | 0.124224i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.4570 | + | 2.95235i | 0.577057 | + | 0.136765i | ||||
\(467\) | −23.3985 | − | 19.6337i | −1.08275 | − | 0.908538i | −0.0866068 | − | 0.996243i | \(-0.527602\pi\) |
−0.996147 | + | 0.0877046i | \(0.972047\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.5714 | + | 11.3877i | −0.626667 | + | 0.525836i | ||||
\(470\) | 14.5777 | − | 7.32122i | 0.672421 | − | 0.337703i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.46573 | + | 8.03446i | 0.159523 | + | 0.369816i | ||||
\(473\) | −0.727420 | + | 0.977095i | −0.0334468 | + | 0.0449269i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.03439 | − | 34.9291i | 0.0933442 | − | 1.60266i | ||||
\(476\) | 19.2373 | + | 7.00181i | 0.881741 | + | 0.320928i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.04526 | − | 2.56427i | 0.322243 | − | 0.117287i | ||||
\(479\) | −3.56899 | − | 11.9212i | −0.163071 | − | 0.544696i | 0.836925 | − | 0.547317i | \(-0.184351\pi\) |
−0.999997 | + | 0.00262129i | \(0.999166\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.4773 | + | 12.7952i | 1.16167 | + | 0.583410i | ||||
\(482\) | 11.6169 | − | 2.75326i | 0.529135 | − | 0.125407i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.1318 | + | 1.53488i | −0.596899 | + | 0.0697674i | ||||
\(485\) | 41.3645 | 1.87826 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.2205 | 0.599077 | 0.299538 | − | 0.954084i | \(-0.403167\pi\) | ||||
0.299538 | + | 0.954084i | \(0.403167\pi\) | |||||||
\(488\) | 13.3264 | − | 1.55763i | 0.603258 | − | 0.0705107i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.753314 | − | 0.178539i | 0.0340313 | − | 0.00806556i | ||||
\(491\) | 16.2050 | + | 8.13845i | 0.731321 | + | 0.367283i | 0.775168 | − | 0.631755i | \(-0.217665\pi\) |
−0.0438474 | + | 0.999038i | \(0.513962\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.10994 | + | 10.3879i | 0.140065 | + | 0.467848i | ||||
\(494\) | 18.9888 | − | 6.91136i | 0.854347 | − | 0.310957i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.46196 | + | 1.62402i | 0.200348 | + | 0.0729207i | ||||
\(497\) | −0.552464 | + | 9.48544i | −0.0247814 | + | 0.425480i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.68067 | + | 7.63047i | −0.254302 | + | 0.341587i | −0.910880 | − | 0.412671i | \(-0.864596\pi\) |
0.656578 | + | 0.754258i | \(0.272003\pi\) | |||||||
\(500\) | 3.67372 | + | 8.51665i | 0.164294 | + | 0.380876i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11.8334 | − | 5.94295i | 0.528150 | − | 0.265247i | ||||
\(503\) | −13.1149 | + | 11.0047i | −0.584766 | + | 0.490677i | −0.886508 | − | 0.462713i | \(-0.846876\pi\) |
0.301743 | + | 0.953389i | \(0.402432\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 44.2891 | + | 37.1630i | 1.97084 | + | 1.65373i | ||||
\(506\) | −1.76389 | − | 0.418051i | −0.0784146 | − | 0.0185846i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.733442 | − | 12.5927i | −0.0325412 | − | 0.558711i | ||||
\(509\) | 8.28987 | − | 27.6901i | 0.367442 | − | 1.22734i | −0.551909 | − | 0.833904i | \(-0.686100\pi\) |
0.919351 | − | 0.393438i | \(-0.128714\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.14845 | − | 1.54264i | −0.0508046 | − | 0.0682424i | ||||
\(512\) | 6.72742 | − | 11.6522i | 0.297313 | − | 0.514961i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.2198 | − | 17.7012i | −0.450775 | − | 0.780765i | ||||
\(515\) | −23.6654 | + | 54.8626i | −1.04282 | + | 2.41754i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.80568 | + | 7.21360i | 0.299314 | + | 0.317254i | ||||
\(518\) | −8.21138 | + | 5.40071i | −0.360787 | + | 0.237294i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −32.4021 | + | 34.3443i | −1.42093 | + | 1.50610i | ||||
\(521\) | −0.716780 | + | 4.06506i | −0.0314027 | + | 0.178093i | −0.996475 | − | 0.0838901i | \(-0.973266\pi\) |
0.965072 | + | 0.261984i | \(0.0843766\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.273945 | + | 1.55362i | 0.0119788 | + | 0.0679351i | 0.990211 | − | 0.139577i | \(-0.0445744\pi\) |
−0.978232 | + | 0.207512i | \(0.933463\pi\) | |||||||
\(524\) | −13.4366 | − | 8.83737i | −0.586979 | − | 0.386062i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.8723 | + | 1.97209i | 0.735669 | + | 0.0859874i | ||||
\(527\) | 19.0792 | + | 2.23004i | 0.831102 | + | 0.0971419i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.7033 | + | 10.9860i | 0.726232 | + | 0.477650i | ||||
\(530\) | 2.18431 | + | 12.3879i | 0.0948806 | + | 0.538094i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.62411 | − | 20.5534i | 0.157125 | − | 0.891102i | ||||
\(533\) | 17.1906 | − | 18.2209i | 0.744606 | − | 0.789236i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −21.4947 | + | 14.1373i | −0.929295 | + | 0.611207i | ||||
\(536\) | 11.1261 | + | 11.7930i | 0.480574 | + | 0.509379i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.20807 | + | 16.7102i | −0.310762 | + | 0.720428i | ||||
\(539\) | 0.235330 | + | 0.407603i | 0.0101364 | + | 0.0175567i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.71173 | + | 9.89300i | −0.245566 | + | 0.425333i | −0.962291 | − | 0.272023i | \(-0.912307\pi\) |
0.716724 | + | 0.697357i | \(0.245641\pi\) | |||||||
\(542\) | −4.33128 | − | 5.81792i | −0.186045 | − | 0.249901i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.44416 | − | 28.2055i | 0.362041 | − | 1.20930i | ||||
\(545\) | 0.678798 | + | 11.6545i | 0.0290765 | + | 0.499224i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.89641 | − | 1.87148i | −0.337626 | − | 0.0800188i | 0.0583057 | − | 0.998299i | \(-0.481430\pi\) |
−0.395932 | + | 0.918280i | \(0.629578\pi\) | |||||||
\(548\) | 12.2543 | + | 10.2826i | 0.523479 | + | 0.439251i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.44536 | − | 4.56920i | 0.232191 | − | 0.194831i | ||||
\(551\) | 9.87869 | − | 4.96127i | 0.420847 | − | 0.211357i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.8167 | − | 38.9856i | −0.715121 | − | 1.65784i | ||||
\(554\) | 2.50568 | − | 3.36571i | 0.106456 | − | 0.142995i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.245694 | − | 4.21840i | 0.0104197 | − | 0.178900i | ||||
\(557\) | −11.2047 | − | 4.07820i | −0.474760 | − | 0.172799i | 0.0935472 | − | 0.995615i | \(-0.470179\pi\) |
−0.568308 | + | 0.822816i | \(0.692402\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.30127 | − | 1.56553i | 0.181924 | − | 0.0662151i | ||||
\(560\) | 3.32494 | + | 11.1061i | 0.140504 | + | 0.469317i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.1290 | − | 6.59363i | −0.553813 | − | 0.278135i | ||||
\(563\) | −19.7078 | + | 4.67084i | −0.830586 | + | 0.196852i | −0.623850 | − | 0.781544i | \(-0.714432\pi\) |
−0.206736 | + | 0.978397i | \(0.566284\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.01035 | − | 0.819393i | 0.294928 | − | 0.0344721i | ||||
\(566\) | −8.31793 | −0.349629 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.69539 | 0.364851 | ||||||||
\(569\) | −14.5280 | + | 1.69808i | −0.609045 | + | 0.0711871i | −0.415024 | − | 0.909810i | \(-0.636227\pi\) |
−0.194020 | + | 0.980997i | \(0.562153\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.4579 | − | 5.32262i | 0.939834 | − | 0.222745i | 0.267977 | − | 0.963425i | \(-0.413645\pi\) |
0.671857 | + | 0.740681i | \(0.265497\pi\) | |||||||
\(572\) | −10.9916 | − | 5.52017i | −0.459580 | − | 0.230810i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.47673 | + | 8.27285i | 0.103377 | + | 0.345302i | ||||
\(575\) | 11.0829 | − | 4.03383i | 0.462187 | − | 0.168222i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.1182 | − | 10.2342i | −1.17057 | − | 0.426054i | −0.317711 | − | 0.948188i | \(-0.602914\pi\) |
−0.852864 | + | 0.522133i | \(0.825136\pi\) | |||||||
\(578\) | 0.348349 | − | 5.98093i | 0.0144894 | − | 0.248774i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.60929 | + | 8.87782i | −0.274436 | + | 0.368631i | ||||
\(581\) | −6.36032 | − | 14.7449i | −0.263871 | − | 0.611721i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.83388 | + | 3.43210i | −0.283030 | + | 0.142143i | ||||
\(584\) | −1.34826 | + | 1.13132i | −0.0557914 | + | 0.0468146i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.6808 | − | 12.3186i | −0.606457 | − | 0.508877i | ||||
\(587\) | −0.309986 | − | 0.0734680i | −0.0127945 | − | 0.00303235i | 0.224214 | − | 0.974540i | \(-0.428019\pi\) |
−0.237008 | + | 0.971508i | \(0.576167\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.13865 | − | 19.5499i | −0.0469173 | − | 0.805538i | ||||
\(590\) | −2.46345 | + | 8.22849i | −0.101419 | + | 0.338761i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.82546 | − | 5.13849i | −0.157226 | − | 0.211191i | ||||
\(593\) | −15.7701 | + | 27.3146i | −0.647601 | + | 1.12168i | 0.336093 | + | 0.941829i | \(0.390894\pi\) |
−0.983694 | + | 0.179849i | \(0.942439\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23.4496 | + | 40.6160i | 0.961341 | + | 1.66509i | ||||
\(596\) | −0.407911 | + | 0.945644i | −0.0167087 | + | 0.0387351i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.67446 | + | 4.95464i | 0.191153 | + | 0.202610i | ||||
\(599\) | −17.9196 | + | 11.7859i | −0.732173 | + | 0.481558i | −0.860036 | − | 0.510234i | \(-0.829559\pi\) |
0.127862 | + | 0.991792i | \(0.459188\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.281882 | + | 0.298777i | −0.0114982 | + | 0.0121874i | −0.733097 | − | 0.680124i | \(-0.761926\pi\) |
0.721599 | + | 0.692311i | \(0.243407\pi\) | |||||||
\(602\) | −0.274008 | + | 1.55397i | −0.0111677 | + | 0.0633353i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.130826 | − | 0.741950i | −0.00532323 | − | 0.0301895i | ||||
\(605\) | −25.3056 | − | 16.6438i | −1.02882 | − | 0.676666i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.2675 | + | 4.47283i | 1.55323 | + | 0.181546i | 0.848987 | − | 0.528414i | \(-0.177213\pi\) |
0.704242 | + | 0.709960i | \(0.251287\pi\) | |||||||
\(608\) | −29.8125 | − | 3.48459i | −1.20906 | − | 0.141319i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11.0039 | + | 7.23738i | 0.445535 | + | 0.293033i | ||||
\(611\) | −6.47113 | − | 36.6996i | −0.261794 | − | 1.48471i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.63138 | − | 43.2797i | 0.308228 | − | 1.74805i | −0.299677 | − | 0.954041i | \(-0.596879\pi\) |
0.607905 | − | 0.794010i | \(-0.292010\pi\) | |||||||
\(614\) | −11.8383 | + | 12.5479i | −0.477756 | + | 0.506392i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.26764 | − | 5.43771i | 0.333113 | − | 0.219092i | ||||
\(617\) | 23.5508 | + | 24.9623i | 0.948118 | + | 1.00495i | 0.999980 | + | 0.00629197i | \(0.00200281\pi\) |
−0.0518624 | + | 0.998654i | \(0.516516\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.19382 | + | 5.08585i | −0.0881772 | + | 0.204418i | −0.956598 | − | 0.291409i | \(-0.905876\pi\) |
0.868421 | + | 0.495827i | \(0.165135\pi\) | |||||||
\(620\) | 9.80334 | + | 16.9799i | 0.393711 | + | 0.681928i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.00067 | − | 10.3935i | 0.240605 | − | 0.416740i | ||||
\(623\) | −6.50569 | − | 8.73866i | −0.260645 | − | 0.350107i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.65804 | − | 12.2187i | 0.146322 | − | 0.488749i | ||||
\(626\) | 0.479783 | + | 8.23755i | 0.0191760 | + | 0.329239i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 18.5089 | + | 4.38670i | 0.738587 | + | 0.175048i | ||||
\(629\) | −19.8525 | − | 16.6582i | −0.791569 | − | 0.664206i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.4299 | + | 16.3036i | −0.773492 | + | 0.649037i | −0.941601 | − | 0.336732i | \(-0.890678\pi\) |
0.168109 | + | 0.985768i | \(0.446234\pi\) | |||||||
\(632\) | −34.7228 | + | 17.4384i | −1.38120 | + | 0.693664i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.75837 | − | 17.9859i | −0.308124 | − | 0.714312i | ||||
\(635\) | 17.2565 | − | 23.1794i | 0.684802 | − | 0.919848i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.102833 | − | 1.76558i | 0.00407440 | − | 0.0699547i | ||||
\(638\) | 2.11046 | + | 0.768143i | 0.0835537 | + | 0.0304111i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 33.9372 | − | 12.3521i | 1.34149 | − | 0.488261i | ||||
\(641\) | 6.05781 | + | 20.2345i | 0.239269 | + | 0.799215i | 0.990300 | + | 0.138947i | \(0.0443719\pi\) |
−0.751031 | + | 0.660267i | \(0.770443\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.2822 | − | 7.17277i | −0.563233 | − | 0.282866i | 0.144314 | − | 0.989532i | \(-0.453902\pi\) |
−0.707548 | + | 0.706665i | \(0.750199\pi\) | |||||||
\(644\) | 6.84553 | − | 1.62242i | 0.269752 | − | 0.0639324i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.2445 | + | 2.13247i | −0.717819 | + | 0.0839010i | ||||
\(647\) | 34.6617 | 1.36269 | 0.681346 | − | 0.731961i | \(-0.261395\pi\) | ||||
0.681346 | + | 0.731961i | \(0.261395\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.22183 | −0.204975 | ||||||||
\(650\) | −26.5303 | + | 3.10094i | −1.04060 | + | 0.121629i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.1700 | + | 4.78038i | −0.789918 | + | 0.187214i | ||||
\(653\) | 19.2963 | + | 9.69097i | 0.755123 | + | 0.379237i | 0.784336 | − | 0.620336i | \(-0.213004\pi\) |
−0.0292132 | + | 0.999573i | \(0.509300\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.5667 | − | 35.2952i | −0.412875 | − | 1.37910i | ||||
\(656\) | −5.28930 | + | 1.92515i | −0.206512 | + | 0.0751644i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.0719 | + | 4.39383i | 0.470613 | + | 0.171289i | ||||
\(659\) | 0.469329 | − | 8.05806i | 0.0182824 | − | 0.313897i | −0.976752 | − | 0.214370i | \(-0.931230\pi\) |
0.995035 | − | 0.0995270i | \(-0.0317330\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.5095 | + | 27.5490i | −0.797727 | + | 1.07153i | 0.198092 | + | 0.980184i | \(0.436526\pi\) |
−0.995819 | + | 0.0913501i | \(0.970882\pi\) | |||||||
\(662\) | 5.22484 | + | 12.1125i | 0.203069 | + | 0.470768i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13.1326 | + | 6.59546i | −0.509645 | + | 0.255953i | ||||
\(665\) | 36.6263 | − | 30.7331i | 1.42031 | − | 1.19178i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.85455 | + | 2.39525i | 0.110529 | + | 0.0927445i | ||||
\(668\) | 4.04465 | + | 0.958599i | 0.156492 | + | 0.0370893i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.925388 | + | 15.8883i | 0.0357509 | + | 0.613819i | ||||
\(671\) | −2.29643 | + | 7.67062i | −0.0886529 | + | 0.296121i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.11229 | + | 1.49406i | 0.0428755 | + | 0.0575918i | 0.823044 | − | 0.567978i | \(-0.192274\pi\) |
−0.780168 | + | 0.625570i | \(0.784867\pi\) | |||||||
\(674\) | 10.6928 | − | 18.5205i | 0.411873 | − | 0.713385i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.3625 | + | 23.1445i | 0.513942 | + | 0.890173i | ||||
\(677\) | 5.68035 | − | 13.1685i | 0.218314 | − | 0.506108i | −0.773501 | − | 0.633795i | \(-0.781496\pi\) |
0.991814 | + | 0.127687i | \(0.0407554\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22.3545 | + | 23.6944i | 0.857886 | + | 0.909306i | ||||
\(680\) | 35.8594 | − | 23.5851i | 1.37514 | − | 0.904446i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.73027 | − | 2.89392i | 0.104548 | − | 0.110814i | ||||
\(683\) | 4.45517 | − | 25.2665i | 0.170472 | − | 0.966797i | −0.772768 | − | 0.634688i | \(-0.781129\pi\) |
0.943241 | − | 0.332109i | \(-0.107760\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.36375 | + | 36.0906i | 0.243147 | + | 1.37895i | ||||
\(686\) | −10.6838 | − | 7.02686i | −0.407910 | − | 0.268287i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.02156 | − | 0.119403i | −0.0389466 | − | 0.00455221i | ||||
\(689\) | 28.5415 | + | 3.33602i | 1.08735 | + | 0.127092i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.0368 | − | 24.3595i | −1.40895 | − | 0.926678i | −0.999900 | − | 0.0141644i | \(-0.995491\pi\) |
−0.409046 | − | 0.912514i | \(-0.634138\pi\) | |||||||
\(692\) | −5.40546 | − | 30.6559i | −0.205485 | − | 1.16536i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.378642 | − | 2.14738i | 0.0143730 | − | 0.0815136i | ||||
\(695\) | 6.64304 | − | 7.04121i | 0.251985 | − | 0.267088i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.0247 | + | 12.5128i | −0.720613 | + | 0.473955i | ||||
\(698\) | −4.35899 | − | 4.62026i | −0.164990 | − | 0.174880i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −10.9267 | + | 25.3310i | −0.412992 | + | 0.957422i | ||||
\(701\) | −5.89393 | − | 10.2086i | −0.222611 | − | 0.385573i | 0.732989 | − | 0.680240i | \(-0.238125\pi\) |
−0.955600 | + | 0.294667i | \(0.904791\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.2100 | + | 22.8804i | −0.498225 | + | 0.862951i | ||||
\(704\) | −1.44027 | − | 1.93461i | −0.0542821 | − | 0.0729135i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.77425 | − | 22.6276i | 0.254952 | − | 0.851600i | ||||
\(707\) | 2.64737 | + | 45.4535i | 0.0995645 | + | 1.70946i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.1090 | − | 7.84699i | −1.24344 | − | 0.294700i | −0.444315 | − | 0.895870i | \(-0.646553\pi\) |
−0.799121 | + | 0.601171i | \(0.794701\pi\) | |||||||
\(710\) | 6.53868 | + | 5.48661i | 0.245392 | + | 0.205909i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.63755 | + | 6.40867i | −0.286229 | + | 0.240175i | ||||
\(713\) | 5.89904 | − | 2.96261i | 0.220921 | − | 0.110950i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.1607 | − | 25.8733i | −0.417385 | − | 0.967607i | ||||
\(716\) | −12.6825 | + | 17.0355i | −0.473965 | + | 0.636646i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.0238795 | + | 0.409996i | −0.000891177 | + | 0.0153009i | ||||
\(719\) | −22.1565 | − | 8.06429i | −0.826297 | − | 0.300747i | −0.105959 | − | 0.994371i | \(-0.533791\pi\) |
−0.720338 | + | 0.693623i | \(0.756013\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −44.2158 | + | 16.0932i | −1.64668 | + | 0.599343i | ||||
\(722\) | 1.51559 | + | 5.06244i | 0.0564046 | + | 0.188404i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.217075 | + | 0.109019i | 0.00806755 | + | 0.00405167i | ||||
\(725\) | −14.2184 | + | 3.36981i | −0.528057 | + | 0.125152i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.85231 | + | 1.03469i | −0.328314 | + | 0.0383744i | −0.278653 | − | 0.960392i | \(-0.589888\pi\) |
−0.0496606 | + | 0.998766i | \(0.515814\pi\) | |||||||
\(728\) | −37.1841 | −1.37813 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.72769 | −0.0639448 | ||||||||
\(731\) | −4.13266 | + | 0.483039i | −0.152852 | + | 0.0178659i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.3268 | − | 5.52856i | 0.861597 | − | 0.204202i | 0.224016 | − | 0.974586i | \(-0.428083\pi\) |
0.637581 | + | 0.770383i | \(0.279935\pi\) | |||||||
\(734\) | −16.0793 | − | 8.07531i | −0.593497 | − | 0.298065i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.90183 | − | 9.69279i | −0.106963 | − | 0.357281i | ||||
\(737\) | −9.09205 | + | 3.30924i | −0.334910 | + | 0.121897i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.2622 | + | 9.55867i | 0.966071 | + | 0.351621i | 0.776410 | − | 0.630228i | \(-0.217039\pi\) |
0.189662 | + | 0.981850i | \(0.439261\pi\) | |||||||
\(740\) | 1.53804 | − | 26.4072i | 0.0565396 | − | 0.970748i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.91554 | + | 7.94595i | −0.217166 | + | 0.291705i | ||||
\(743\) | −15.5338 | − | 36.0115i | −0.569882 | − | 1.32113i | −0.922728 | − | 0.385453i | \(-0.874045\pi\) |
0.352846 | − | 0.935681i | \(-0.385214\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.10838 | + | 1.05887i | −0.0772451 | + | 0.0387940i | ||||
\(746\) | −6.27670 | + | 5.26678i | −0.229806 | + | 0.192830i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.56485 | + | 7.18676i | 0.313162 | + | 0.262774i | ||||
\(749\) | −19.7144 | − | 4.67240i | −0.720348 | − | 0.170726i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.57245 | − | 26.9978i | −0.0573794 | − | 0.985165i | −0.897011 | − | 0.442009i | \(-0.854266\pi\) |
0.839631 | − | 0.543157i | \(-0.182771\pi\) | |||||||
\(752\) | −2.40156 | + | 8.02177i | −0.0875759 | + | 0.292524i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.03959 | − | 6.76935i | −0.183531 | − | 0.246525i | ||||
\(755\) | 0.862979 | − | 1.49472i | 0.0314070 | − | 0.0543986i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.2471 | − | 17.7485i | −0.372437 | − | 0.645080i | 0.617503 | − | 0.786569i | \(-0.288144\pi\) |
−0.989940 | + | 0.141489i | \(0.954811\pi\) | |||||||
\(758\) | 5.14834 | − | 11.9352i | 0.186996 | − | 0.433506i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −30.0270 | − | 31.8268i | −1.08919 | − | 1.15448i | ||||
\(761\) | 12.5960 | − | 8.28454i | 0.456606 | − | 0.300314i | −0.300292 | − | 0.953847i | \(-0.597084\pi\) |
0.756898 | + | 0.653533i | \(0.226714\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.30909 | + | 6.68724i | −0.228404 | + | 0.242094i | ||||
\(764\) | 6.06139 | − | 34.3758i | 0.219293 | − | 1.24367i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.27966 | − | 18.5999i | −0.118499 | − | 0.672041i | ||||
\(767\) | 16.3937 | + | 10.7823i | 0.591943 | + | 0.389327i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.4640 | − | 1.57372i | −0.485526 | − | 0.0567498i | −0.130191 | − | 0.991489i | \(-0.541559\pi\) |
−0.355335 | + | 0.934739i | \(0.615633\pi\) | |||||||
\(770\) | 9.64811 | + | 1.12770i | 0.347694 | + | 0.0406396i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13.4497 | + | 8.84602i | 0.484066 | + | 0.318375i | ||||
\(773\) | −0.729570 | − | 4.13760i | −0.0262408 | − | 0.148819i | 0.968872 | − | 0.247561i | \(-0.0796292\pi\) |
−0.995113 | + | 0.0987422i | \(0.968518\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.49496 | + | 25.4922i | −0.161464 | + | 0.915705i | ||||
\(776\) | 20.4579 | − | 21.6841i | 0.734395 | − | 0.778414i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.87309 | − | 1.23195i | 0.0671536 | − | 0.0441676i | ||||
\(779\) | 15.9305 | + | 16.8853i | 0.570768 | + | 0.604979i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.05533 | + | 4.76480i | −0.0735456 | + | 0.170498i | ||||
\(782\) | −3.09593 | − | 5.36230i | −0.110710 | − | 0.191755i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.198697 | + | 0.344153i | −0.00709632 | + | 0.0122912i | ||||
\(785\) | 26.0223 | + | 34.9540i | 0.928775 | + | 1.24756i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.79703 | − | 9.34272i | 0.0997032 | − | 0.333032i | −0.893555 | − | 0.448953i | \(-0.851797\pi\) |
0.993258 | + | 0.115921i | \(0.0369821\pi\) | |||||||
\(788\) | 0.596191 | + | 10.2362i | 0.0212384 | + | 0.364650i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −37.1138 | − | 8.79614i | −1.32045 | − | 0.312952i | ||||
\(791\) | 4.25795 | + | 3.57284i | 0.151395 | + | 0.127036i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23.0483 | − | 19.3398i | 0.818470 | − | 0.686778i | ||||
\(794\) | 2.56910 | − | 1.29025i | 0.0911740 | − | 0.0457893i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.38786 | − | 14.8087i | −0.226412 | − | 0.524881i | ||||
\(797\) | −6.07994 | + | 8.16677i | −0.215362 | + | 0.289282i | −0.896656 | − | 0.442729i | \(-0.854010\pi\) |
0.681293 | + | 0.732011i | \(0.261418\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.96964 | + | 33.8174i | −0.0696808 | + | 1.19637i | ||||
\(800\) | 37.2827 | + | 13.5698i | 1.31814 | + | 0.479765i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −14.1911 | + | 5.16513i | −0.501105 | + | 0.182387i | ||||
\(803\) | −0.301241 | − | 1.00622i | −0.0106306 | − | 0.0355086i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.4026 | + | 7.23325i | 0.507625 | + | 0.254939i | ||||
\(806\) | −14.5471 | + | 3.44773i | −0.512400 | + | 0.121441i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 41.3859 | − | 4.83732i | 1.45595 | − | 0.170176i | ||||
\(809\) | −20.1073 | −0.706936 | −0.353468 | − | 0.935447i | \(-0.614998\pi\) | ||||
−0.353468 | + | 0.935447i | \(0.614998\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.159394 | −0.00559707 | −0.00279854 | − | 0.999996i | \(-0.500891\pi\) | ||||
−0.00279854 | + | 0.999996i | \(0.500891\pi\) | |||||||
\(812\) | −8.65723 | + | 1.01188i | −0.303809 | + | 0.0355102i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5.22295 | + | 1.23786i | −0.183064 | + | 0.0433870i | ||||
\(815\) | −42.4365 | − | 21.3124i | −1.48648 | − | 0.746541i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.21656 | + | 4.06359i | 0.0425620 | + | 0.142167i | ||||
\(818\) | −14.7536 | + | 5.36988i | −0.515848 | + | 0.187753i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −21.8405 | − | 7.94928i | −0.762702 | − | 0.277601i | ||||
\(821\) | −0.275861 | + | 4.73635i | −0.00962762 | + | 0.165300i | 0.990067 | + | 0.140595i | \(0.0449016\pi\) |
−0.999695 | + | 0.0247047i | \(0.992135\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.8519 | − | 21.2928i | 0.552564 | − | 0.742222i | −0.434829 | − | 0.900513i | \(-0.643191\pi\) |
0.987392 | + | 0.158291i | \(0.0505985\pi\) | |||||||
\(824\) | 17.0557 | + | 39.5397i | 0.594165 | + | 1.37743i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.04475 | + | 3.03579i | −0.210324 | + | 0.105629i | ||||
\(827\) | −5.34609 | + | 4.48590i | −0.185902 | + | 0.155990i | −0.730989 | − | 0.682389i | \(-0.760941\pi\) |
0.545087 | + | 0.838379i | \(0.316496\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.3490 | + | 23.7877i | 0.984603 | + | 0.826180i | 0.984777 | − | 0.173820i | \(-0.0556111\pi\) |
−0.000174449 | 1.00000i | \(0.500056\pi\) | ||||||||
\(830\) | −14.0370 | − | 3.32682i | −0.487230 | − | 0.115476i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.526962 | + | 9.04759i | 0.0182691 | + | 0.313669i | ||||
\(833\) | −0.461075 | + | 1.54010i | −0.0159753 | + | 0.0533612i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.68650 | + | 7.63829i | 0.196789 | + | 0.264334i | ||||
\(836\) | 5.69913 | − | 9.87118i | 0.197109 | − | 0.341402i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 9.02026 | + | 15.6236i | 0.311600 | + | 0.539707i | ||||
\(839\) | 3.05189 | − | 7.07508i | 0.105363 | − | 0.244259i | −0.857376 | − | 0.514690i | \(-0.827907\pi\) |
0.962739 | + | 0.270431i | \(0.0871662\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.7328 | + | 17.7357i | 0.576994 | + | 0.611578i | ||||
\(842\) | 10.9908 | − | 7.22875i | 0.378767 | − | 0.249119i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.95519 | − | 9.49195i | 0.308250 | − | 0.326726i | ||||
\(845\) | −10.6315 | + | 60.2943i | −0.365735 | + | 2.07419i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.14197 | − | 23.4903i | −0.142320 | − | 0.807136i | ||||
\(848\) | −5.39465 | − | 3.54812i | −0.185253 | − | 0.121843i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 24.1161 | + | 2.81877i | 0.827176 | + | 0.0966830i | ||||
\(851\) | −8.84564 | − | 1.03391i | −0.303225 | − | 0.0354419i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.4706 | + | 18.7254i | 0.974815 | + | 0.641146i | 0.933718 | − | 0.358009i | \(-0.116544\pi\) |
0.0410969 | + | 0.999155i | \(0.486915\pi\) | |||||||
\(854\) | 1.80110 | + | 10.2145i | 0.0616322 | + | 0.349534i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.21971 | + | 18.2599i | −0.110048 | + | 0.624110i | ||||
\(857\) | −27.1852 | + | 28.8146i | −0.928629 | + | 0.984290i | −0.999913 | − | 0.0131665i | \(-0.995809\pi\) |
0.0712840 | + | 0.997456i | \(0.477290\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.6548 | − | 30.0277i | 1.55772 | − | 1.02453i | 0.580003 | − | 0.814614i | \(-0.303051\pi\) |
0.977719 | − | 0.209916i | \(-0.0673191\pi\) | |||||||
\(860\) | −2.91441 | − | 3.08910i | −0.0993807 | − | 0.105337i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.94153 | + | 4.50098i | −0.0661289 | + | 0.153304i | ||||
\(863\) | 0.634182 | + | 1.09844i | 0.0215878 | + | 0.0373912i | 0.876617 | − | 0.481188i | \(-0.159795\pi\) |
−0.855030 | + | 0.518579i | \(0.826461\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35.6566 | − | 61.7590i | 1.21236 | − | 2.09987i | ||||
\(866\) | −10.5202 | − | 14.1311i | −0.357491 | − | 0.480194i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.42841 | + | 14.7919i | −0.150310 | + | 0.502071i | ||||
\(869\) | −1.34827 | − | 23.1489i | −0.0457370 | − | 0.785273i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.3773 | + | 8.38457i | 1.19871 | + | 0.284100i | ||||
\(872\) | 6.44525 | + | 5.40821i | 0.218264 | + | 0.183145i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.83556 | + | 4.05752i | −0.163565 | + | 0.137248i | ||||
\(875\) | −14.9538 | + | 7.51006i | −0.505529 | + | 0.253886i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.3720 | + | 40.2727i | 0.586609 | + | 1.35991i | 0.910378 | + | 0.413777i | \(0.135791\pi\) |
−0.323769 | + | 0.946136i | \(0.604950\pi\) | |||||||
\(878\) | 3.43775 | − | 4.61769i | 0.116018 | − | 0.155840i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.368144 | + | 6.32079i | −0.0124101 | + | 0.213074i | ||||
\(881\) | 25.7921 | + | 9.38756i | 0.868959 | + | 0.316275i | 0.737745 | − | 0.675079i | \(-0.235891\pi\) |
0.131213 | + | 0.991354i | \(0.458113\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.1938 | + | 6.98597i | −0.645923 | + | 0.235097i | −0.644147 | − | 0.764902i | \(-0.722787\pi\) |
−0.00177579 | + | 0.999998i | \(0.500565\pi\) | |||||||
\(884\) | −12.0494 | − | 40.2478i | −0.405265 | − | 1.35368i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.9659 | + | 8.01838i | 0.536385 | + | 0.269383i | ||||
\(887\) | 36.8182 | − | 8.72608i | 1.23623 | − | 0.292993i | 0.440009 | − | 0.897993i | \(-0.354975\pi\) |
0.796225 | + | 0.605000i | \(0.206827\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.6035 | − | 2.64197i | 0.758097 | − | 0.0886088i | ||||
\(890\) | −9.78695 | −0.328059 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.8121 | −0.395499 | ||||||||
\(893\) | 34.3006 | − | 4.00917i | 1.14783 | − | 0.134162i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −47.3428 | + | 11.2204i | −1.58249 | + | 0.375058i | ||||
\(896\) | 25.4161 | + | 12.7645i | 0.849093 | + | 0.426431i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.01535 | + | 26.7731i | 0.267476 | + | 0.893431i | ||||
\(899\) | −7.68526 | + | 2.79721i | −0.256318 | + | 0.0932921i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.5457 | − | 8.93390i | −0.817735 | − | 0.297631i | ||||
\(902\) | −0.274228 | + | 4.70832i | −0.00913081 | + | 0.156770i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.03761 | − | 4.08022i | 0.101030 | − | 0.135706i | ||||
\(905\) | 0.220415 | + | 0.510980i | 0.00732685 | + | 0.0169856i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.38063 | + | 3.70669i | −0.245070 | + | 0.123079i | −0.567095 | − | 0.823652i | \(-0.691933\pi\) |
0.322025 | + | 0.946731i | \(0.395636\pi\) | |||||||
\(908\) | −21.9578 | + | 18.4247i | −0.728694 | + | 0.611447i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −27.9613 | − | 23.4623i | −0.926909 | − | 0.777769i | ||||
\(911\) | −32.7705 | − | 7.76674i | −1.08573 | − | 0.257324i | −0.351478 | − | 0.936196i | \(-0.614321\pi\) |
−0.734256 | + | 0.678872i | \(0.762469\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.509935 | − | 8.75524i | −0.0168764 | − | 0.289756i | ||||
\(914\) | 4.23153 | − | 14.1343i | 0.139967 | − | 0.467521i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −24.1954 | − | 32.5001i | −0.799440 | − | 1.07383i | ||||
\(917\) | 14.5073 | − | 25.1273i | 0.479072 | − | 0.829777i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.1853 | − | 22.8376i | −0.434943 | − | 0.753343i | 0.562348 | − | 0.826901i | \(-0.309898\pi\) |
−0.997291 | + | 0.0735573i | \(0.976565\pi\) | |||||||
\(920\) | 5.84199 | − | 13.5433i | 0.192605 | − | 0.446508i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −8.25656 | − | 8.75144i | −0.271915 | − | 0.288213i | ||||
\(923\) | 16.2913 | − | 10.7149i | 0.536234 | − | 0.352687i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23.9655 | − | 25.4019i | 0.787980 | − | 0.835210i | ||||
\(926\) | −1.16021 | + | 6.57988i | −0.0381269 | + | 0.216228i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.17675 | + | 12.3450i | 0.0714554 | + | 0.405244i | ||||
\(929\) | 43.9934 | + | 28.9349i | 1.44338 | + | 0.949324i | 0.998557 | + | 0.0537033i | \(0.0171025\pi\) |
0.444819 | + | 0.895620i | \(0.353268\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.62785 | + | 0.190268i | 0.0533506 | + | 0.00623579i | ||||
\(932\) | −26.9510 | − | 3.15012i | −0.882808 | − | 0.103185i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −18.0542 | − | 11.8744i | −0.590751 | − | 0.388543i | ||||
\(935\) | 4.44778 | + | 25.2246i | 0.145458 | + | 0.824933i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.27631 | − | 7.23831i | 0.0416952 | − | 0.236465i | −0.956837 | − | 0.290625i | \(-0.906137\pi\) |
0.998532 | + | 0.0541595i | \(0.0172479\pi\) | |||||||
\(938\) | −8.60102 | + | 9.11655i | −0.280833 | + | 0.297666i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −28.8877 | + | 18.9998i | −0.942214 | + | 0.619704i | ||||
\(941\) | 17.9105 | + | 18.9841i | 0.583867 | + | 0.618862i | 0.950207 | − | 0.311618i | \(-0.100871\pi\) |
−0.366341 | + | 0.930481i | \(0.619390\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.09939 | + | 7.18520i | −0.100930 | + | 0.233982i | ||||
\(944\) | −2.20449 | − | 3.81828i | −0.0717499 | − | 0.124274i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.430893 | + | 0.746328i | −0.0140095 | + | 0.0242652i | ||||
\(947\) | −5.65952 | − | 7.60205i | −0.183910 | − | 0.247033i | 0.700601 | − | 0.713553i | \(-0.252915\pi\) |
−0.884511 | + | 0.466520i | \(0.845508\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.13196 | + | 3.78100i | −0.0367449 | + | 0.122736i | ||||
\(950\) | −1.43925 | − | 24.7110i | −0.0466956 | − | 0.801732i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 32.8894 | + | 7.79492i | 1.06595 | + | 0.252635i | ||||
\(953\) | 39.9630 | + | 33.5329i | 1.29453 | + | 1.08624i | 0.991063 | + | 0.133395i | \(0.0425878\pi\) |
0.303464 | + | 0.952843i | \(0.401857\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 61.2580 | − | 51.4016i | 1.98226 | − | 1.66332i | ||||
\(956\) | −14.2008 | + | 7.13190i | −0.459286 | + | 0.230662i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.48696 | − | 8.08369i | −0.112659 | − | 0.261172i | ||||
\(959\) | −17.2343 | + | 23.1496i | −0.556523 | + | 0.747541i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.960082 | − | 16.4840i | 0.0309704 | − | 0.531741i | ||||
\(962\) | 18.9533 | + | 6.89842i | 0.611078 | + | 0.222414i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −23.7785 | + | 8.65468i | −0.765855 | + | 0.278748i | ||||
\(965\) | 10.5770 | + | 35.3298i | 0.340487 | + | 1.13731i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.03800 | + | 2.02796i | 0.129853 | + | 0.0652148i | 0.512540 | − | 0.858664i | \(-0.328705\pi\) |
−0.382686 | + | 0.923878i | \(0.625001\pi\) | |||||||
\(968\) | −21.2406 | + | 5.03411i | −0.682698 | + | 0.161802i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 29.0659 | − | 3.39732i | 0.933251 | − | 0.109081i | ||||
\(971\) | −12.4268 | −0.398796 | −0.199398 | − | 0.979919i | \(-0.563899\pi\) | ||||
−0.199398 | + | 0.979919i | \(0.563899\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.62342 | 0.244396 | ||||||||
\(974\) | 9.28975 | − | 1.08582i | 0.297663 | − | 0.0347918i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.57836 | + | 1.55910i | −0.210568 | + | 0.0499056i | ||||
\(977\) | −16.8202 | − | 8.44744i | −0.538127 | − | 0.270258i | 0.158909 | − | 0.987293i | \(-0.449202\pi\) |
−0.697037 | + | 0.717035i | \(0.745499\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.70645 | − | 5.69995i | −0.0545385 | − | 0.182171i | ||||
\(980\) | −1.54195 | + | 0.561225i | −0.0492559 | + | 0.0179277i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.0553 | + | 4.38778i | 0.384701 | + | 0.140020i | ||||
\(983\) | 0.665467 | − | 11.4256i | 0.0212251 | − | 0.364421i | −0.970926 | − | 0.239379i | \(-0.923056\pi\) |
0.992151 | − | 0.125042i | \(-0.0399067\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.0272 | + | 18.8418i | −0.446944 | + | 0.600350i | ||||
\(986\) | 3.03846 | + | 7.04395i | 0.0967644 | + | 0.224325i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −38.2748 | + | 19.2223i | −1.21768 | + | 0.611543i | ||||
\(989\) | −1.09533 | + | 0.919094i | −0.0348296 | + | 0.0292255i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.6012 | − | 18.9647i | −0.717951 | − | 0.602432i | 0.208867 | − | 0.977944i | \(-0.433022\pi\) |
−0.926818 | + | 0.375512i | \(0.877467\pi\) | |||||||
\(992\) | 21.6078 | + | 5.12114i | 0.686048 | + | 0.162596i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.390848 | + | 6.71060i | 0.0123969 | + | 0.212847i | ||||
\(995\) | 10.5965 | − | 35.3949i | 0.335933 | − | 1.12209i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.5603 | + | 35.6767i | 0.841173 | + | 1.12989i | 0.990006 | + | 0.141029i | \(0.0450410\pi\) |
−0.148833 | + | 0.988862i | \(0.547552\pi\) | |||||||
\(998\) | −3.36499 | + | 5.82833i | −0.106517 | + | 0.184493i | ||||
\(999\) | 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 | 243.2.g.a.19.5 | 144 | ||
3.2 | odd | 2 | 81.2.g.a.61.4 | yes | 144 | ||
9.2 | odd | 6 | 729.2.g.c.541.5 | 144 | |||
9.4 | even | 3 | 729.2.g.a.55.4 | 144 | |||
9.5 | odd | 6 | 729.2.g.d.55.5 | 144 | |||
9.7 | even | 3 | 729.2.g.b.541.4 | 144 | |||
81.2 | odd | 54 | 6561.2.a.c.1.47 | 72 | |||
81.4 | even | 27 | inner | 243.2.g.a.64.5 | 144 | ||
81.23 | odd | 54 | 729.2.g.d.676.5 | 144 | |||
81.31 | even | 27 | 729.2.g.b.190.4 | 144 | |||
81.50 | odd | 54 | 729.2.g.c.190.5 | 144 | |||
81.58 | even | 27 | 729.2.g.a.676.4 | 144 | |||
81.77 | odd | 54 | 81.2.g.a.4.4 | ✓ | 144 | ||
81.79 | even | 27 | 6561.2.a.d.1.26 | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
81.2.g.a.4.4 | ✓ | 144 | 81.77 | odd | 54 | ||
81.2.g.a.61.4 | yes | 144 | 3.2 | odd | 2 | ||
243.2.g.a.19.5 | 144 | 1.1 | even | 1 | trivial | ||
243.2.g.a.64.5 | 144 | 81.4 | even | 27 | inner | ||
729.2.g.a.55.4 | 144 | 9.4 | even | 3 | |||
729.2.g.a.676.4 | 144 | 81.58 | even | 27 | |||
729.2.g.b.190.4 | 144 | 81.31 | even | 27 | |||
729.2.g.b.541.4 | 144 | 9.7 | even | 3 | |||
729.2.g.c.190.5 | 144 | 81.50 | odd | 54 | |||
729.2.g.c.541.5 | 144 | 9.2 | odd | 6 | |||
729.2.g.d.55.5 | 144 | 9.5 | odd | 6 | |||
729.2.g.d.676.5 | 144 | 81.23 | odd | 54 | |||
6561.2.a.c.1.47 | 72 | 81.2 | odd | 54 | |||
6561.2.a.d.1.26 | 72 | 81.79 | even | 27 |