Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,2,Mod(143,350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(350, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("350.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.o (of order \(12\), degree \(4\), 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: | \(2.79476407074\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 257.1 | ||
Root | \(0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.257 |
Dual form | 350.2.o.b.143.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.965926 | + | 0.258819i | −0.683013 | + | 0.183013i | ||||
\(3\) | −0.189469 | + | 0.707107i | −0.109390 | + | 0.408248i | −0.998806 | − | 0.0488497i | \(-0.984444\pi\) |
0.889416 | + | 0.457098i | \(0.151111\pi\) | |||||||
\(4\) | 0.866025 | − | 0.500000i | 0.433013 | − | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 0.732051i | − | 0.298858i | ||||||
\(7\) | −2.19067 | − | 1.48356i | −0.827996 | − | 0.560734i | ||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 2.13397 | + | 1.23205i | 0.711325 | + | 0.410684i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.633975 | + | 1.09808i | 0.191151 | + | 0.331082i | 0.945632 | − | 0.325239i | \(-0.105445\pi\) |
−0.754481 | + | 0.656322i | \(0.772111\pi\) | |||||||
\(12\) | 0.189469 | + | 0.707107i | 0.0546949 | + | 0.204124i | ||||
\(13\) | 4.38134 | + | 4.38134i | 1.21517 | + | 1.21517i | 0.969305 | + | 0.245860i | \(0.0790704\pi\) |
0.245860 | + | 0.969305i | \(0.420930\pi\) | |||||||
\(14\) | 2.50000 | + | 0.866025i | 0.668153 | + | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | −0.448288 | − | 0.120118i | −0.108726 | − | 0.0291330i | 0.204046 | − | 0.978961i | \(-0.434591\pi\) |
−0.312772 | + | 0.949828i | \(0.601257\pi\) | |||||||
\(18\) | −2.38014 | − | 0.637756i | −0.561004 | − | 0.150321i | ||||
\(19\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.46410 | − | 1.26795i | 0.319493 | − | 0.276689i | ||||
\(22\) | −0.896575 | − | 0.896575i | −0.191151 | − | 0.191151i | ||||
\(23\) | 1.34486 | + | 5.01910i | 0.280423 | + | 1.04655i | 0.952119 | + | 0.305727i | \(0.0988995\pi\) |
−0.671696 | + | 0.740827i | \(0.734434\pi\) | |||||||
\(24\) | −0.366025 | − | 0.633975i | −0.0747146 | − | 0.129410i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.36603 | − | 3.09808i | −1.05236 | − | 0.607583i | ||||
\(27\) | −2.82843 | + | 2.82843i | −0.544331 | + | 0.544331i | ||||
\(28\) | −2.63896 | − | 0.189469i | −0.498716 | − | 0.0358062i | ||||
\(29\) | 3.46410i | 0.643268i | 0.946864 | + | 0.321634i | \(0.104232\pi\) | ||||
−0.946864 | + | 0.321634i | \(0.895768\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | + | 0.866025i | −0.269408 | + | 0.155543i | −0.628619 | − | 0.777714i | \(-0.716379\pi\) |
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | −0.258819 | + | 0.965926i | −0.0457532 | + | 0.170753i | ||||
\(33\) | −0.896575 | + | 0.240237i | −0.156074 | + | 0.0418198i | ||||
\(34\) | 0.464102 | 0.0795928 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.46410 | 0.410684 | ||||||||
\(37\) | 6.69213 | − | 1.79315i | 1.10018 | − | 0.294792i | 0.337342 | − | 0.941382i | \(-0.390472\pi\) |
0.762838 | + | 0.646590i | \(0.223806\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.92820 | + | 2.26795i | −0.629016 | + | 0.363163i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.1962i | 1.74855i | 0.485435 | + | 0.874273i | \(0.338661\pi\) | ||||
−0.485435 | + | 0.874273i | \(0.661339\pi\) | |||||||
\(42\) | −1.08604 | + | 1.60368i | −0.167580 | + | 0.247454i | ||||
\(43\) | 7.58871 | − | 7.58871i | 1.15727 | − | 1.15727i | 0.172206 | − | 0.985061i | \(-0.444911\pi\) |
0.985061 | − | 0.172206i | \(-0.0550894\pi\) | |||||||
\(44\) | 1.09808 | + | 0.633975i | 0.165541 | + | 0.0955753i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.59808 | − | 4.50000i | −0.383065 | − | 0.663489i | ||||
\(47\) | 1.01669 | + | 3.79435i | 0.148300 | + | 0.553463i | 0.999586 | + | 0.0287617i | \(0.00915640\pi\) |
−0.851286 | + | 0.524702i | \(0.824177\pi\) | |||||||
\(48\) | 0.517638 | + | 0.517638i | 0.0747146 | + | 0.0747146i | ||||
\(49\) | 2.59808 | + | 6.50000i | 0.371154 | + | 0.928571i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.169873 | − | 0.294229i | 0.0237870 | − | 0.0412002i | ||||
\(52\) | 5.98502 | + | 1.60368i | 0.829973 | + | 0.222391i | ||||
\(53\) | −7.91688 | − | 2.12132i | −1.08747 | − | 0.291386i | −0.329815 | − | 0.944045i | \(-0.606986\pi\) |
−0.757651 | + | 0.652660i | \(0.773653\pi\) | |||||||
\(54\) | 2.00000 | − | 3.46410i | 0.272166 | − | 0.471405i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.59808 | − | 0.500000i | 0.347183 | − | 0.0668153i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.896575 | − | 3.34607i | −0.117726 | − | 0.439360i | ||||
\(59\) | −7.09808 | − | 12.2942i | −0.924091 | − | 1.60057i | −0.793017 | − | 0.609200i | \(-0.791491\pi\) |
−0.131074 | − | 0.991373i | \(-0.541843\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.29423 | − | 3.63397i | −0.805893 | − | 0.465283i | 0.0396344 | − | 0.999214i | \(-0.487381\pi\) |
−0.845528 | + | 0.533931i | \(0.820714\pi\) | |||||||
\(62\) | 1.22474 | − | 1.22474i | 0.155543 | − | 0.155543i | ||||
\(63\) | −2.84701 | − | 5.86491i | −0.358689 | − | 0.738909i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.803848 | − | 0.464102i | 0.0989468 | − | 0.0571270i | ||||
\(67\) | 0.984508 | − | 3.67423i | 0.120277 | − | 0.448879i | −0.879351 | − | 0.476175i | \(-0.842023\pi\) |
0.999627 | + | 0.0272957i | \(0.00868958\pi\) | |||||||
\(68\) | −0.448288 | + | 0.120118i | −0.0543629 | + | 0.0145665i | ||||
\(69\) | −3.80385 | −0.457929 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.3923 | 1.58937 | 0.794687 | − | 0.607019i | \(-0.207635\pi\) | ||||
0.794687 | + | 0.607019i | \(0.207635\pi\) | |||||||
\(72\) | −2.38014 | + | 0.637756i | −0.280502 | + | 0.0751603i | ||||
\(73\) | 2.07055 | − | 7.72741i | 0.242340 | − | 0.904425i | −0.732362 | − | 0.680915i | \(-0.761582\pi\) |
0.974702 | − | 0.223509i | \(-0.0717512\pi\) | |||||||
\(74\) | −6.00000 | + | 3.46410i | −0.697486 | + | 0.402694i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.240237 | − | 3.34607i | 0.0273775 | − | 0.381320i | ||||
\(78\) | 3.20736 | − | 3.20736i | 0.363163 | − | 0.363163i | ||||
\(79\) | −9.86603 | − | 5.69615i | −1.11001 | − | 0.640867i | −0.171181 | − | 0.985240i | \(-0.554758\pi\) |
−0.938833 | + | 0.344372i | \(0.888092\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.23205 | + | 3.86603i | 0.248006 | + | 0.429558i | ||||
\(82\) | −2.89778 | − | 10.8147i | −0.320006 | − | 1.19428i | ||||
\(83\) | 4.24264 | + | 4.24264i | 0.465690 | + | 0.465690i | 0.900515 | − | 0.434825i | \(-0.143190\pi\) |
−0.434825 | + | 0.900515i | \(0.643190\pi\) | |||||||
\(84\) | 0.633975 | − | 1.83013i | 0.0691723 | − | 0.199683i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.36603 | + | 9.29423i | −0.578633 | + | 1.00222i | ||||
\(87\) | −2.44949 | − | 0.656339i | −0.262613 | − | 0.0703669i | ||||
\(88\) | −1.22474 | − | 0.328169i | −0.130558 | − | 0.0349830i | ||||
\(89\) | 5.59808 | − | 9.69615i | 0.593395 | − | 1.02779i | −0.400376 | − | 0.916351i | \(-0.631121\pi\) |
0.993771 | − | 0.111439i | \(-0.0355461\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.09808 | − | 16.0981i | −0.324767 | − | 1.68754i | ||||
\(92\) | 3.67423 | + | 3.67423i | 0.383065 | + | 0.383065i | ||||
\(93\) | −0.328169 | − | 1.22474i | −0.0340296 | − | 0.127000i | ||||
\(94\) | −1.96410 | − | 3.40192i | −0.202582 | − | 0.350882i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.633975 | − | 0.366025i | −0.0647048 | − | 0.0373573i | ||||
\(97\) | 8.05558 | − | 8.05558i | 0.817920 | − | 0.817920i | −0.167887 | − | 0.985806i | \(-0.553694\pi\) |
0.985806 | + | 0.167887i | \(0.0536942\pi\) | |||||||
\(98\) | −4.19187 | − | 5.60609i | −0.423443 | − | 0.566300i | ||||
\(99\) | 3.12436i | 0.314010i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.1962 | + | 8.19615i | −1.41257 | + | 0.815548i | −0.995630 | − | 0.0933864i | \(-0.970231\pi\) |
−0.416940 | + | 0.908934i | \(0.636897\pi\) | |||||||
\(102\) | −0.0879327 | + | 0.328169i | −0.00870664 | + | 0.0324936i | ||||
\(103\) | −12.5570 | + | 3.36465i | −1.23728 | + | 0.331529i | −0.817411 | − | 0.576055i | \(-0.804591\pi\) |
−0.419871 | + | 0.907584i | \(0.637925\pi\) | |||||||
\(104\) | −6.19615 | −0.607583 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.19615 | 0.796081 | ||||||||
\(107\) | −2.12132 | + | 0.568406i | −0.205076 | + | 0.0549499i | −0.359895 | − | 0.932993i | \(-0.617187\pi\) |
0.154819 | + | 0.987943i | \(0.450521\pi\) | |||||||
\(108\) | −1.03528 | + | 3.86370i | −0.0996195 | + | 0.371785i | ||||
\(109\) | 8.83013 | − | 5.09808i | 0.845773 | − | 0.488307i | −0.0134495 | − | 0.999910i | \(-0.504281\pi\) |
0.859222 | + | 0.511602i | \(0.170948\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.07180i | 0.481394i | ||||||||
\(112\) | −2.38014 | + | 1.15539i | −0.224902 | + | 0.109175i | ||||
\(113\) | 4.81105 | − | 4.81105i | 0.452585 | − | 0.452585i | −0.443627 | − | 0.896212i | \(-0.646308\pi\) |
0.896212 | + | 0.443627i | \(0.146308\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.73205 | + | 3.00000i | 0.160817 | + | 0.278543i | ||||
\(117\) | 3.95164 | + | 14.7477i | 0.365329 | + | 1.36343i | ||||
\(118\) | 10.0382 | + | 10.0382i | 0.924091 | + | 0.924091i | ||||
\(119\) | 0.803848 | + | 0.928203i | 0.0736886 | + | 0.0850883i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.69615 | − | 8.13397i | 0.426923 | − | 0.739452i | ||||
\(122\) | 7.02030 | + | 1.88108i | 0.635588 | + | 0.170305i | ||||
\(123\) | −7.91688 | − | 2.12132i | −0.713841 | − | 0.191273i | ||||
\(124\) | −0.866025 | + | 1.50000i | −0.0777714 | + | 0.134704i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.26795 | + | 4.92820i | 0.380219 | + | 0.439039i | ||||
\(127\) | −4.89898 | − | 4.89898i | −0.434714 | − | 0.434714i | 0.455514 | − | 0.890228i | \(-0.349455\pi\) |
−0.890228 | + | 0.455514i | \(0.849455\pi\) | |||||||
\(128\) | 0.258819 | + | 0.965926i | 0.0228766 | + | 0.0853766i | ||||
\(129\) | 3.92820 | + | 6.80385i | 0.345859 | + | 0.599045i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.90192 | + | 1.09808i | 0.166172 | + | 0.0959394i | 0.580780 | − | 0.814061i | \(-0.302748\pi\) |
−0.414608 | + | 0.910000i | \(0.636081\pi\) | |||||||
\(132\) | −0.656339 | + | 0.656339i | −0.0571270 | + | 0.0571270i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.80385i | 0.328602i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.401924 | − | 0.232051i | 0.0344647 | − | 0.0198982i | ||||
\(137\) | −0.208051 | + | 0.776457i | −0.0177750 | + | 0.0663372i | −0.974244 | − | 0.225498i | \(-0.927599\pi\) |
0.956469 | + | 0.291835i | \(0.0942658\pi\) | |||||||
\(138\) | 3.67423 | − | 0.984508i | 0.312772 | − | 0.0838069i | ||||
\(139\) | −3.46410 | −0.293821 | −0.146911 | − | 0.989150i | \(-0.546933\pi\) | ||||
−0.146911 | + | 0.989150i | \(0.546933\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.87564 | −0.242173 | ||||||||
\(142\) | −12.9360 | + | 3.46618i | −1.08556 | + | 0.290876i | ||||
\(143\) | −2.03339 | + | 7.58871i | −0.170040 | + | 0.634599i | ||||
\(144\) | 2.13397 | − | 1.23205i | 0.177831 | − | 0.102671i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.00000i | 0.662085i | ||||||||
\(147\) | −5.08845 | + | 0.605571i | −0.419688 | + | 0.0499466i | ||||
\(148\) | 4.89898 | − | 4.89898i | 0.402694 | − | 0.402694i | ||||
\(149\) | 7.09808 | + | 4.09808i | 0.581497 | + | 0.335727i | 0.761728 | − | 0.647897i | \(-0.224351\pi\) |
−0.180231 | + | 0.983624i | \(0.557685\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.19615 | − | 15.9282i | −0.748372 | − | 1.29622i | −0.948603 | − | 0.316470i | \(-0.897502\pi\) |
0.200230 | − | 0.979749i | \(-0.435831\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.808643 | − | 0.808643i | −0.0653749 | − | 0.0653749i | ||||
\(154\) | 0.633975 | + | 3.29423i | 0.0510871 | + | 0.265457i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.26795 | + | 3.92820i | −0.181581 | + | 0.314508i | ||||
\(157\) | 1.93185 | + | 0.517638i | 0.154179 | + | 0.0413120i | 0.335083 | − | 0.942189i | \(-0.391236\pi\) |
−0.180904 | + | 0.983501i | \(0.557902\pi\) | |||||||
\(158\) | 11.0041 | + | 2.94855i | 0.875441 | + | 0.234574i | ||||
\(159\) | 3.00000 | − | 5.19615i | 0.237915 | − | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.50000 | − | 12.9904i | 0.354650 | − | 1.02379i | ||||
\(162\) | −3.15660 | − | 3.15660i | −0.248006 | − | 0.248006i | ||||
\(163\) | 3.76217 | + | 14.0406i | 0.294676 | + | 1.09974i | 0.941475 | + | 0.337084i | \(0.109441\pi\) |
−0.646799 | + | 0.762661i | \(0.723893\pi\) | |||||||
\(164\) | 5.59808 | + | 9.69615i | 0.437136 | + | 0.757142i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.19615 | − | 3.00000i | −0.403300 | − | 0.232845i | ||||
\(167\) | −13.3843 | + | 13.3843i | −1.03571 | + | 1.03571i | −0.0363667 | + | 0.999339i | \(0.511578\pi\) |
−0.999339 | + | 0.0363667i | \(0.988422\pi\) | |||||||
\(168\) | −0.138701 | + | 1.93185i | −0.0107010 | + | 0.149046i | ||||
\(169\) | 25.3923i | 1.95325i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.77766 | − | 10.3664i | 0.211795 | − | 0.790428i | ||||
\(173\) | −17.0585 | + | 4.57081i | −1.29693 | + | 0.347512i | −0.840290 | − | 0.542137i | \(-0.817615\pi\) |
−0.456644 | + | 0.889650i | \(0.650949\pi\) | |||||||
\(174\) | 2.53590 | 0.192246 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.26795 | 0.0955753 | ||||||||
\(177\) | 10.0382 | − | 2.68973i | 0.754517 | − | 0.202172i | ||||
\(178\) | −2.89778 | + | 10.8147i | −0.217198 | + | 0.810592i | ||||
\(179\) | 7.09808 | − | 4.09808i | 0.530535 | − | 0.306305i | −0.210699 | − | 0.977551i | \(-0.567574\pi\) |
0.741234 | + | 0.671246i | \(0.234241\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.26795i | 0.540222i | 0.962829 | + | 0.270111i | \(0.0870605\pi\) | ||||
−0.962829 | + | 0.270111i | \(0.912940\pi\) | |||||||
\(182\) | 7.15900 | + | 14.7477i | 0.530660 | + | 1.09317i | ||||
\(183\) | 3.76217 | − | 3.76217i | 0.278107 | − | 0.278107i | ||||
\(184\) | −4.50000 | − | 2.59808i | −0.331744 | − | 0.191533i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.633975 | + | 1.09808i | 0.0464853 | + | 0.0805149i | ||||
\(187\) | −0.152304 | − | 0.568406i | −0.0111376 | − | 0.0415660i | ||||
\(188\) | 2.77766 | + | 2.77766i | 0.202582 | + | 0.202582i | ||||
\(189\) | 10.3923 | − | 2.00000i | 0.755929 | − | 0.145479i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.76795 | − | 4.79423i | 0.200282 | − | 0.346898i | −0.748337 | − | 0.663318i | \(-0.769148\pi\) |
0.948619 | + | 0.316420i | \(0.102481\pi\) | |||||||
\(192\) | 0.707107 | + | 0.189469i | 0.0510310 | + | 0.0136737i | ||||
\(193\) | 11.7112 | + | 3.13801i | 0.842993 | + | 0.225879i | 0.654374 | − | 0.756171i | \(-0.272932\pi\) |
0.188619 | + | 0.982050i | \(0.439599\pi\) | |||||||
\(194\) | −5.69615 | + | 9.86603i | −0.408960 | + | 0.708339i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.50000 | + | 4.33013i | 0.392857 | + | 0.309295i | ||||
\(197\) | −5.79555 | − | 5.79555i | −0.412916 | − | 0.412916i | 0.469837 | − | 0.882753i | \(-0.344313\pi\) |
−0.882753 | + | 0.469837i | \(0.844313\pi\) | |||||||
\(198\) | −0.808643 | − | 3.01790i | −0.0574677 | − | 0.214473i | ||||
\(199\) | 9.86603 | + | 17.0885i | 0.699384 | + | 1.21137i | 0.968680 | + | 0.248311i | \(0.0798756\pi\) |
−0.269296 | + | 0.963057i | \(0.586791\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.41154 | + | 1.39230i | 0.170097 | + | 0.0982056i | ||||
\(202\) | 11.5911 | − | 11.5911i | 0.815548 | − | 0.815548i | ||||
\(203\) | 5.13922 | − | 7.58871i | 0.360702 | − | 0.532623i | ||||
\(204\) | − | 0.339746i | − | 0.0237870i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 11.2583 | − | 6.50000i | 0.784405 | − | 0.452876i | ||||
\(207\) | −3.31388 | + | 12.3676i | −0.230331 | + | 0.859605i | ||||
\(208\) | 5.98502 | − | 1.60368i | 0.414987 | − | 0.111195i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.1962 | −0.701932 | −0.350966 | − | 0.936388i | \(-0.614147\pi\) | ||||
−0.350966 | + | 0.936388i | \(0.614147\pi\) | |||||||
\(212\) | −7.91688 | + | 2.12132i | −0.543733 | + | 0.145693i | ||||
\(213\) | −2.53742 | + | 9.46979i | −0.173861 | + | 0.648859i | ||||
\(214\) | 1.90192 | − | 1.09808i | 0.130013 | − | 0.0750629i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 4.00000i | − | 0.272166i | ||||||
\(217\) | 4.57081 | + | 0.328169i | 0.310287 | + | 0.0222776i | ||||
\(218\) | −7.20977 | + | 7.20977i | −0.488307 | + | 0.488307i | ||||
\(219\) | 5.07180 | + | 2.92820i | 0.342720 | + | 0.197870i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.43782 | − | 2.49038i | −0.0967184 | − | 0.167521i | ||||
\(222\) | −1.31268 | − | 4.89898i | −0.0881012 | − | 0.328798i | ||||
\(223\) | 6.64136 | + | 6.64136i | 0.444739 | + | 0.444739i | 0.893601 | − | 0.448862i | \(-0.148171\pi\) |
−0.448862 | + | 0.893601i | \(0.648171\pi\) | |||||||
\(224\) | 2.00000 | − | 1.73205i | 0.133631 | − | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.40192 | + | 5.89230i | −0.226293 | + | 0.391950i | ||||
\(227\) | −26.5283 | − | 7.10823i | −1.76074 | − | 0.471790i | −0.773879 | − | 0.633334i | \(-0.781686\pi\) |
−0.986866 | + | 0.161544i | \(0.948353\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.09808 | − | 12.2942i | 0.469054 | − | 0.812425i | −0.530320 | − | 0.847797i | \(-0.677928\pi\) |
0.999374 | + | 0.0353720i | \(0.0112616\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.32051 | + | 0.803848i | 0.152678 | + | 0.0528893i | ||||
\(232\) | −2.44949 | − | 2.44949i | −0.160817 | − | 0.160817i | ||||
\(233\) | −1.55291 | − | 5.79555i | −0.101735 | − | 0.379679i | 0.896219 | − | 0.443611i | \(-0.146303\pi\) |
−0.997954 | + | 0.0639315i | \(0.979636\pi\) | |||||||
\(234\) | −7.63397 | − | 13.2224i | −0.499049 | − | 0.864377i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −12.2942 | − | 7.09808i | −0.800286 | − | 0.462045i | ||||
\(237\) | 5.89709 | − | 5.89709i | 0.383057 | − | 0.383057i | ||||
\(238\) | −1.01669 | − | 0.688524i | −0.0659025 | − | 0.0446304i | ||||
\(239\) | − | 22.8564i | − | 1.47846i | −0.673454 | − | 0.739229i | \(-0.735190\pi\) | ||
0.673454 | − | 0.739229i | \(-0.264810\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.00000 | + | 1.73205i | −0.193247 | + | 0.111571i | −0.593502 | − | 0.804833i | \(-0.702255\pi\) |
0.400255 | + | 0.916404i | \(0.368922\pi\) | |||||||
\(242\) | −2.43091 | + | 9.07227i | −0.156265 | + | 0.583188i | ||||
\(243\) | −14.7477 | + | 3.95164i | −0.946066 | + | 0.253498i | ||||
\(244\) | −7.26795 | −0.465283 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 8.19615 | 0.522568 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.448288 | − | 1.67303i | 0.0284663 | − | 0.106238i | ||||
\(249\) | −3.80385 | + | 2.19615i | −0.241059 | + | 0.139176i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.39230i | 0.277240i | 0.990346 | + | 0.138620i | \(0.0442666\pi\) | ||||
−0.990346 | + | 0.138620i | \(0.955733\pi\) | |||||||
\(252\) | −5.39804 | − | 3.65565i | −0.340044 | − | 0.230284i | ||||
\(253\) | −4.65874 | + | 4.65874i | −0.292893 | + | 0.292893i | ||||
\(254\) | 6.00000 | + | 3.46410i | 0.376473 | + | 0.217357i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 1.13681 | + | 4.24264i | 0.0709124 | + | 0.264649i | 0.992275 | − | 0.124055i | \(-0.0395898\pi\) |
−0.921363 | + | 0.388703i | \(0.872923\pi\) | |||||||
\(258\) | −5.55532 | − | 5.55532i | −0.345859 | − | 0.345859i | ||||
\(259\) | −17.3205 | − | 6.00000i | −1.07624 | − | 0.372822i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.26795 | + | 7.39230i | −0.264179 | + | 0.457572i | ||||
\(262\) | −2.12132 | − | 0.568406i | −0.131056 | − | 0.0351162i | ||||
\(263\) | 3.46618 | + | 0.928761i | 0.213734 | + | 0.0572699i | 0.364097 | − | 0.931361i | \(-0.381378\pi\) |
−0.150363 | + | 0.988631i | \(0.548044\pi\) | |||||||
\(264\) | 0.464102 | − | 0.803848i | 0.0285635 | − | 0.0494734i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.79555 | + | 5.79555i | 0.354682 | + | 0.354682i | ||||
\(268\) | −0.984508 | − | 3.67423i | −0.0601384 | − | 0.224440i | ||||
\(269\) | −6.29423 | − | 10.9019i | −0.383766 | − | 0.664702i | 0.607831 | − | 0.794066i | \(-0.292040\pi\) |
−0.991597 | + | 0.129364i | \(0.958706\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.0885 | + | 11.5981i | 1.22029 | + | 0.704533i | 0.964979 | − | 0.262327i | \(-0.0844899\pi\) |
0.255308 | + | 0.966860i | \(0.417823\pi\) | |||||||
\(272\) | −0.328169 | + | 0.328169i | −0.0198982 | + | 0.0198982i | ||||
\(273\) | 11.9700 | + | 0.859411i | 0.724460 | + | 0.0520139i | ||||
\(274\) | − | 0.803848i | − | 0.0485622i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.29423 | + | 1.90192i | −0.198289 | + | 0.114482i | ||||
\(277\) | −1.70522 | + | 6.36396i | −0.102457 | + | 0.382373i | −0.998044 | − | 0.0625119i | \(-0.980089\pi\) |
0.895588 | + | 0.444885i | \(0.146756\pi\) | |||||||
\(278\) | 3.34607 | − | 0.896575i | 0.200684 | − | 0.0537730i | ||||
\(279\) | −4.26795 | −0.255515 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.4641 | 1.45941 | 0.729703 | − | 0.683764i | \(-0.239658\pi\) | ||||
0.729703 | + | 0.683764i | \(0.239658\pi\) | |||||||
\(282\) | 2.77766 | − | 0.744272i | 0.165407 | − | 0.0443207i | ||||
\(283\) | 0.619174 | − | 2.31079i | 0.0368061 | − | 0.137362i | −0.945078 | − | 0.326845i | \(-0.894014\pi\) |
0.981884 | + | 0.189483i | \(0.0606812\pi\) | |||||||
\(284\) | 11.5981 | − | 6.69615i | 0.688219 | − | 0.397344i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 7.85641i | − | 0.464559i | ||||||
\(287\) | 16.6102 | − | 24.5271i | 0.980470 | − | 1.44779i | ||||
\(288\) | −1.74238 | + | 1.74238i | −0.102671 | + | 0.102671i | ||||
\(289\) | −14.5359 | − | 8.39230i | −0.855053 | − | 0.493665i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.16987 | + | 7.22243i | 0.244442 | + | 0.423386i | ||||
\(292\) | −2.07055 | − | 7.72741i | −0.121170 | − | 0.452212i | ||||
\(293\) | −22.5259 | − | 22.5259i | −1.31598 | − | 1.31598i | −0.916932 | − | 0.399044i | \(-0.869342\pi\) |
−0.399044 | − | 0.916932i | \(-0.630658\pi\) | |||||||
\(294\) | 4.75833 | − | 1.90192i | 0.277511 | − | 0.110922i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.46410 | + | 6.00000i | −0.201347 | + | 0.348743i | ||||
\(297\) | −4.89898 | − | 1.31268i | −0.284268 | − | 0.0761693i | ||||
\(298\) | −7.91688 | − | 2.12132i | −0.458612 | − | 0.122885i | ||||
\(299\) | −16.0981 | + | 27.8827i | −0.930976 | + | 1.61250i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −27.8827 | + | 5.36603i | −1.60713 | + | 0.309293i | ||||
\(302\) | 13.0053 | + | 13.0053i | 0.748372 | + | 0.748372i | ||||
\(303\) | −3.10583 | − | 11.5911i | −0.178425 | − | 0.665892i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.990381 | + | 0.571797i | 0.0566163 | + | 0.0326874i | ||||
\(307\) | 8.76268 | − | 8.76268i | 0.500113 | − | 0.500113i | −0.411360 | − | 0.911473i | \(-0.634946\pi\) |
0.911473 | + | 0.411360i | \(0.134946\pi\) | |||||||
\(308\) | −1.46498 | − | 3.01790i | −0.0834751 | − | 0.171961i | ||||
\(309\) | − | 9.51666i | − | 0.541384i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.696152 | + | 0.401924i | −0.0394752 | + | 0.0227910i | −0.519608 | − | 0.854405i | \(-0.673922\pi\) |
0.480133 | + | 0.877196i | \(0.340589\pi\) | |||||||
\(312\) | 1.17398 | − | 4.38134i | 0.0664634 | − | 0.248045i | ||||
\(313\) | 18.3526 | − | 4.91756i | 1.03735 | − | 0.277957i | 0.300335 | − | 0.953834i | \(-0.402902\pi\) |
0.737015 | + | 0.675877i | \(0.236235\pi\) | |||||||
\(314\) | −2.00000 | −0.112867 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.3923 | −0.640867 | ||||||||
\(317\) | 15.8338 | − | 4.24264i | 0.889312 | − | 0.238290i | 0.214892 | − | 0.976638i | \(-0.431060\pi\) |
0.674420 | + | 0.738347i | \(0.264394\pi\) | |||||||
\(318\) | −1.55291 | + | 5.79555i | −0.0870831 | + | 0.324999i | ||||
\(319\) | −3.80385 | + | 2.19615i | −0.212975 | + | 0.122961i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 1.60770i | − | 0.0897328i | ||||||
\(322\) | −0.984508 | + | 13.7124i | −0.0548645 | + | 0.764164i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 3.86603 | + | 2.23205i | 0.214779 | + | 0.124003i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7.26795 | − | 12.5885i | −0.402534 | − | 0.697210i | ||||
\(327\) | 1.93185 | + | 7.20977i | 0.106832 | + | 0.398701i | ||||
\(328\) | −7.91688 | − | 7.91688i | −0.437136 | − | 0.437136i | ||||
\(329\) | 3.40192 | − | 9.82051i | 0.187554 | − | 0.541422i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.00000 | − | 12.1244i | 0.384755 | − | 0.666415i | −0.606980 | − | 0.794717i | \(-0.707619\pi\) |
0.991735 | + | 0.128302i | \(0.0409527\pi\) | |||||||
\(332\) | 5.79555 | + | 1.55291i | 0.318072 | + | 0.0852272i | ||||
\(333\) | 16.4901 | + | 4.41851i | 0.903651 | + | 0.242133i | ||||
\(334\) | 9.46410 | − | 16.3923i | 0.517853 | − | 0.896947i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.366025 | − | 1.90192i | −0.0199683 | − | 0.103758i | ||||
\(337\) | −6.12372 | − | 6.12372i | −0.333581 | − | 0.333581i | 0.520364 | − | 0.853945i | \(-0.325796\pi\) |
−0.853945 | + | 0.520364i | \(0.825796\pi\) | |||||||
\(338\) | −6.57201 | − | 24.5271i | −0.357470 | − | 1.33410i | ||||
\(339\) | 2.49038 | + | 4.31347i | 0.135259 | + | 0.234275i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.90192 | − | 1.09808i | −0.102995 | − | 0.0594642i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.95164 | − | 18.0938i | 0.213368 | − | 0.976972i | ||||
\(344\) | 10.7321i | 0.578633i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.2942 | − | 8.83013i | 0.822223 | − | 0.474711i | ||||
\(347\) | 1.55291 | − | 5.79555i | 0.0833648 | − | 0.311122i | −0.911635 | − | 0.411001i | \(-0.865179\pi\) |
0.995000 | + | 0.0998797i | \(0.0318458\pi\) | |||||||
\(348\) | −2.44949 | + | 0.656339i | −0.131306 | + | 0.0351835i | ||||
\(349\) | −16.9808 | −0.908959 | −0.454480 | − | 0.890757i | \(-0.650175\pi\) | ||||
−0.454480 | + | 0.890757i | \(0.650175\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −24.7846 | −1.32290 | ||||||||
\(352\) | −1.22474 | + | 0.328169i | −0.0652791 | + | 0.0174915i | ||||
\(353\) | 6.09154 | − | 22.7339i | 0.324220 | − | 1.21001i | −0.590874 | − | 0.806764i | \(-0.701217\pi\) |
0.915094 | − | 0.403241i | \(-0.132116\pi\) | |||||||
\(354\) | −9.00000 | + | 5.19615i | −0.478345 | + | 0.276172i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 11.1962i | − | 0.593395i | ||||||
\(357\) | −0.808643 | + | 0.392541i | −0.0427979 | + | 0.0207755i | ||||
\(358\) | −5.79555 | + | 5.79555i | −0.306305 | + | 0.306305i | ||||
\(359\) | −9.00000 | − | 5.19615i | −0.475002 | − | 0.274242i | 0.243329 | − | 0.969944i | \(-0.421760\pi\) |
−0.718331 | + | 0.695701i | \(0.755094\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.50000 | + | 16.4545i | 0.500000 | + | 0.866025i | ||||
\(362\) | −1.88108 | − | 7.02030i | −0.0988676 | − | 0.368979i | ||||
\(363\) | 4.86181 | + | 4.86181i | 0.255179 | + | 0.255179i | ||||
\(364\) | −10.7321 | − | 12.3923i | −0.562512 | − | 0.649533i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.66025 | + | 4.60770i | −0.139054 | + | 0.240848i | ||||
\(367\) | 17.7656 | + | 4.76028i | 0.927357 | + | 0.248485i | 0.690727 | − | 0.723115i | \(-0.257291\pi\) |
0.236630 | + | 0.971600i | \(0.423957\pi\) | |||||||
\(368\) | 5.01910 | + | 1.34486i | 0.261639 | + | 0.0701058i | ||||
\(369\) | −13.7942 | + | 23.8923i | −0.718099 | + | 1.24378i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.1962 | + | 16.3923i | 0.737028 | + | 0.851046i | ||||
\(372\) | −0.896575 | − | 0.896575i | −0.0464853 | − | 0.0464853i | ||||
\(373\) | 4.39494 | + | 16.4022i | 0.227562 | + | 0.849271i | 0.981362 | + | 0.192168i | \(0.0615519\pi\) |
−0.753800 | + | 0.657103i | \(0.771781\pi\) | |||||||
\(374\) | 0.294229 | + | 0.509619i | 0.0152142 | + | 0.0263518i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.40192 | − | 1.96410i | −0.175441 | − | 0.101291i | ||||
\(377\) | −15.1774 | + | 15.1774i | −0.781676 | + | 0.781676i | ||||
\(378\) | −9.52056 | + | 4.62158i | −0.489685 | + | 0.237708i | ||||
\(379\) | − | 8.58846i | − | 0.441159i | −0.975369 | − | 0.220580i | \(-0.929205\pi\) | ||
0.975369 | − | 0.220580i | \(-0.0707949\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.39230 | − | 2.53590i | 0.225025 | − | 0.129918i | ||||
\(382\) | −1.43280 | + | 5.34727i | −0.0733082 | + | 0.273590i | ||||
\(383\) | 22.9742 | − | 6.15591i | 1.17393 | − | 0.314552i | 0.381411 | − | 0.924406i | \(-0.375438\pi\) |
0.792514 | + | 0.609853i | \(0.208772\pi\) | |||||||
\(384\) | −0.732051 | −0.0373573 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.1244 | −0.617113 | ||||||||
\(387\) | 25.5438 | − | 6.84443i | 1.29846 | − | 0.347922i | ||||
\(388\) | 2.94855 | − | 11.0041i | 0.149690 | − | 0.558650i | ||||
\(389\) | −3.50962 | + | 2.02628i | −0.177945 | + | 0.102736i | −0.586327 | − | 0.810075i | \(-0.699426\pi\) |
0.408382 | + | 0.912811i | \(0.366093\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.41154i | − | 0.121957i | ||||||
\(392\) | −6.43331 | − | 2.75908i | −0.324931 | − | 0.139354i | ||||
\(393\) | −1.13681 | + | 1.13681i | −0.0573446 | + | 0.0573446i | ||||
\(394\) | 7.09808 | + | 4.09808i | 0.357596 | + | 0.206458i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.56218 | + | 2.70577i | 0.0785024 | + | 0.135970i | ||||
\(397\) | 0.517638 | + | 1.93185i | 0.0259795 | + | 0.0969569i | 0.977698 | − | 0.210014i | \(-0.0673511\pi\) |
−0.951719 | + | 0.306971i | \(0.900684\pi\) | |||||||
\(398\) | −13.9527 | − | 13.9527i | −0.699384 | − | 0.699384i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.53590 | − | 9.58846i | 0.276450 | − | 0.478825i | −0.694050 | − | 0.719927i | \(-0.744175\pi\) |
0.970500 | + | 0.241102i | \(0.0775088\pi\) | |||||||
\(402\) | −2.68973 | − | 0.720710i | −0.134151 | − | 0.0359457i | ||||
\(403\) | −10.3664 | − | 2.77766i | −0.516385 | − | 0.138365i | ||||
\(404\) | −8.19615 | + | 14.1962i | −0.407774 | + | 0.706285i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.00000 | + | 8.66025i | −0.148888 | + | 0.429801i | ||||
\(407\) | 6.21166 | + | 6.21166i | 0.307900 | + | 0.307900i | ||||
\(408\) | 0.0879327 | + | 0.328169i | 0.00435332 | + | 0.0162468i | ||||
\(409\) | 6.40192 | + | 11.0885i | 0.316555 | + | 0.548289i | 0.979767 | − | 0.200143i | \(-0.0641406\pi\) |
−0.663212 | + | 0.748432i | \(0.730807\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.509619 | − | 0.294229i | −0.0251376 | − | 0.0145132i | ||||
\(412\) | −9.19239 | + | 9.19239i | −0.452876 | + | 0.452876i | ||||
\(413\) | −2.68973 | + | 37.4631i | −0.132353 | + | 1.84344i | ||||
\(414\) | − | 12.8038i | − | 0.629275i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.36603 | + | 3.09808i | −0.263091 | + | 0.151896i | ||||
\(417\) | 0.656339 | − | 2.44949i | 0.0321410 | − | 0.119952i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.9808 | 1.41580 | 0.707901 | − | 0.706311i | \(-0.249642\pi\) | ||||
0.707901 | + | 0.706311i | \(0.249642\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.6077 | −0.760673 | −0.380336 | − | 0.924848i | \(-0.624192\pi\) | ||||
−0.380336 | + | 0.924848i | \(0.624192\pi\) | |||||||
\(422\) | 9.84873 | − | 2.63896i | 0.479429 | − | 0.128462i | ||||
\(423\) | −2.50524 | + | 9.34967i | −0.121809 | + | 0.454597i | ||||
\(424\) | 7.09808 | − | 4.09808i | 0.344713 | − | 0.199020i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 9.80385i | − | 0.474998i | ||||||
\(427\) | 8.39735 | + | 17.2987i | 0.406376 | + | 0.837144i | ||||
\(428\) | −1.55291 | + | 1.55291i | −0.0750629 | + | 0.0750629i | ||||
\(429\) | −4.98076 | − | 2.87564i | −0.240473 | − | 0.138837i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.76795 | + | 15.1865i | 0.422337 | + | 0.731510i | 0.996168 | − | 0.0874646i | \(-0.0278765\pi\) |
−0.573830 | + | 0.818974i | \(0.694543\pi\) | |||||||
\(432\) | 1.03528 | + | 3.86370i | 0.0498097 | + | 0.185893i | ||||
\(433\) | −22.7525 | − | 22.7525i | −1.09342 | − | 1.09342i | −0.995161 | − | 0.0982548i | \(-0.968674\pi\) |
−0.0982548 | − | 0.995161i | \(-0.531326\pi\) | |||||||
\(434\) | −4.50000 | + | 0.866025i | −0.216007 | + | 0.0415705i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.09808 | − | 8.83013i | 0.244154 | − | 0.422886i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −5.65685 | − | 1.51575i | −0.270295 | − | 0.0724253i | ||||
\(439\) | 2.93782 | − | 5.08846i | 0.140215 | − | 0.242859i | −0.787363 | − | 0.616490i | \(-0.788554\pi\) |
0.927577 | + | 0.373631i | \(0.121887\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.46410 | + | 17.0718i | −0.117338 | + | 0.812943i | ||||
\(442\) | 2.03339 | + | 2.03339i | 0.0967184 | + | 0.0967184i | ||||
\(443\) | 3.10583 | + | 11.5911i | 0.147562 | + | 0.550710i | 0.999628 | + | 0.0272752i | \(0.00868305\pi\) |
−0.852066 | + | 0.523435i | \(0.824650\pi\) | |||||||
\(444\) | 2.53590 | + | 4.39230i | 0.120348 | + | 0.208450i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.13397 | − | 4.69615i | −0.385155 | − | 0.222369i | ||||
\(447\) | −4.24264 | + | 4.24264i | −0.200670 | + | 0.200670i | ||||
\(448\) | −1.48356 | + | 2.19067i | −0.0700918 | + | 0.103499i | ||||
\(449\) | 8.32051i | 0.392669i | 0.980537 | + | 0.196335i | \(0.0629039\pi\) | ||||
−0.980537 | + | 0.196335i | \(0.937096\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.2942 | + | 7.09808i | −0.578913 | + | 0.334235i | ||||
\(452\) | 1.76097 | − | 6.57201i | 0.0828288 | − | 0.309121i | ||||
\(453\) | 13.0053 | − | 3.48477i | 0.611043 | − | 0.163729i | ||||
\(454\) | 27.4641 | 1.28895 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.4273 | + | 8.42091i | −1.47011 | + | 0.393914i | −0.902967 | − | 0.429709i | \(-0.858616\pi\) |
−0.567138 | + | 0.823623i | \(0.691949\pi\) | |||||||
\(458\) | −3.67423 | + | 13.7124i | −0.171686 | + | 0.640740i | ||||
\(459\) | 1.60770 | − | 0.928203i | 0.0750408 | − | 0.0433248i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 24.0000i | − | 1.11779i | −0.829238 | − | 0.558896i | \(-0.811225\pi\) | ||
0.829238 | − | 0.558896i | \(-0.188775\pi\) | |||||||
\(462\) | −2.44949 | − | 0.175865i | −0.113961 | − | 0.00818200i | ||||
\(463\) | −6.60420 | + | 6.60420i | −0.306923 | + | 0.306923i | −0.843715 | − | 0.536792i | \(-0.819636\pi\) |
0.536792 | + | 0.843715i | \(0.319636\pi\) | |||||||
\(464\) | 3.00000 | + | 1.73205i | 0.139272 | + | 0.0804084i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.00000 | + | 5.19615i | 0.138972 | + | 0.240707i | ||||
\(467\) | −5.97142 | − | 22.2856i | −0.276324 | − | 1.03126i | −0.954949 | − | 0.296771i | \(-0.904090\pi\) |
0.678624 | − | 0.734486i | \(-0.262576\pi\) | |||||||
\(468\) | 10.7961 | + | 10.7961i | 0.499049 | + | 0.499049i | ||||
\(469\) | −7.60770 | + | 6.58846i | −0.351291 | + | 0.304227i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.732051 | + | 1.26795i | −0.0337311 | + | 0.0584240i | ||||
\(472\) | 13.7124 | + | 3.67423i | 0.631166 | + | 0.169120i | ||||
\(473\) | 13.1440 | + | 3.52193i | 0.604363 | + | 0.161939i | ||||
\(474\) | −4.16987 | + | 7.22243i | −0.191529 | + | 0.331737i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.16025 | + | 0.401924i | 0.0531802 | + | 0.0184221i | ||||
\(477\) | −14.2808 | − | 14.2808i | −0.653875 | − | 0.653875i | ||||
\(478\) | 5.91567 | + | 22.0776i | 0.270577 | + | 1.00981i | ||||
\(479\) | 6.40192 | + | 11.0885i | 0.292511 | + | 0.506645i | 0.974403 | − | 0.224809i | \(-0.0721757\pi\) |
−0.681892 | + | 0.731453i | \(0.738842\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 37.1769 | + | 21.4641i | 1.69512 | + | 0.978679i | ||||
\(482\) | 2.44949 | − | 2.44949i | 0.111571 | − | 0.111571i | ||||
\(483\) | 8.33298 | + | 5.64325i | 0.379164 | + | 0.256777i | ||||
\(484\) | − | 9.39230i | − | 0.426923i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 13.2224 | − | 7.63397i | 0.599782 | − | 0.346284i | ||||
\(487\) | −2.41730 | + | 9.02150i | −0.109539 | + | 0.408803i | −0.998820 | − | 0.0485561i | \(-0.984538\pi\) |
0.889282 | + | 0.457359i | \(0.151205\pi\) | |||||||
\(488\) | 7.02030 | − | 1.88108i | 0.317794 | − | 0.0851527i | ||||
\(489\) | −10.6410 | −0.481203 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.0526 | −0.724442 | −0.362221 | − | 0.932092i | \(-0.617981\pi\) | ||||
−0.362221 | + | 0.932092i | \(0.617981\pi\) | |||||||
\(492\) | −7.91688 | + | 2.12132i | −0.356920 | + | 0.0956365i | ||||
\(493\) | 0.416102 | − | 1.55291i | 0.0187403 | − | 0.0699397i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.73205i | 0.0777714i | ||||||||
\(497\) | −29.3381 | − | 19.8683i | −1.31599 | − | 0.891217i | ||||
\(498\) | 3.10583 | − | 3.10583i | 0.139176 | − | 0.139176i | ||||
\(499\) | 15.2487 | + | 8.80385i | 0.682626 | + | 0.394114i | 0.800844 | − | 0.598873i | \(-0.204385\pi\) |
−0.118218 | + | 0.992988i | \(0.537718\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.92820 | − | 12.0000i | −0.309529 | − | 0.536120i | ||||
\(502\) | −1.13681 | − | 4.24264i | −0.0507384 | − | 0.189358i | ||||
\(503\) | 7.82894 | + | 7.82894i | 0.349075 | + | 0.349075i | 0.859765 | − | 0.510690i | \(-0.170610\pi\) |
−0.510690 | + | 0.859765i | \(0.670610\pi\) | |||||||
\(504\) | 6.16025 | + | 2.13397i | 0.274400 | + | 0.0950548i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.29423 | − | 5.70577i | 0.146446 | − | 0.253652i | ||||
\(507\) | −17.9551 | − | 4.81105i | −0.797413 | − | 0.213666i | ||||
\(508\) | −6.69213 | − | 1.79315i | −0.296915 | − | 0.0795582i | ||||
\(509\) | 17.4904 | − | 30.2942i | 0.775248 | − | 1.34277i | −0.159408 | − | 0.987213i | \(-0.550958\pi\) |
0.934655 | − | 0.355555i | \(-0.115708\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.0000 | + | 13.8564i | −0.707798 | + | 0.612971i | ||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.19615 | − | 3.80385i | −0.0968681 | − | 0.167781i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6.80385 | + | 3.92820i | 0.299523 | + | 0.172930i | ||||
\(517\) | −3.52193 | + | 3.52193i | −0.154894 | + | 0.154894i | ||||
\(518\) | 18.2832 | + | 1.31268i | 0.803319 | + | 0.0576757i | ||||
\(519\) | − | 12.9282i | − | 0.567485i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.0885 | − | 16.7942i | 1.27439 | − | 0.735769i | 0.298578 | − | 0.954385i | \(-0.403488\pi\) |
0.975811 | + | 0.218617i | \(0.0701545\pi\) | |||||||
\(522\) | 2.20925 | − | 8.24504i | 0.0966964 | − | 0.360876i | ||||
\(523\) | −9.65926 | + | 2.58819i | −0.422370 | + | 0.113174i | −0.463742 | − | 0.885970i | \(-0.653494\pi\) |
0.0413724 | + | 0.999144i | \(0.486827\pi\) | |||||||
\(524\) | 2.19615 | 0.0959394 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.58846 | −0.156464 | ||||||||
\(527\) | 0.776457 | − | 0.208051i | 0.0338230 | − | 0.00906285i | ||||
\(528\) | −0.240237 | + | 0.896575i | −0.0104550 | + | 0.0390184i | ||||
\(529\) | −3.46410 | + | 2.00000i | −0.150613 | + | 0.0869565i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 34.9808i | − | 1.51804i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −49.0542 | + | 49.0542i | −2.12477 | + | 2.12477i | ||||
\(534\) | −7.09808 | − | 4.09808i | −0.307164 | − | 0.177341i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.90192 | + | 3.29423i | 0.0821506 | + | 0.142289i | ||||
\(537\) | 1.55291 | + | 5.79555i | 0.0670132 | + | 0.250097i | ||||
\(538\) | 8.90138 | + | 8.90138i | 0.383766 | + | 0.383766i | ||||
\(539\) | −5.49038 | + | 6.97372i | −0.236487 | + | 0.300379i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.09808 | − | 15.7583i | 0.391157 | − | 0.677504i | −0.601446 | − | 0.798914i | \(-0.705408\pi\) |
0.992602 | + | 0.121410i | \(0.0387417\pi\) | |||||||
\(542\) | −22.4058 | − | 6.00361i | −0.962410 | − | 0.257877i | ||||
\(543\) | −5.13922 | − | 1.37705i | −0.220545 | − | 0.0590948i | ||||
\(544\) | 0.232051 | − | 0.401924i | 0.00994910 | − | 0.0172323i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −11.7846 | + | 2.26795i | −0.504335 | + | 0.0970593i | ||||
\(547\) | 20.0764 | + | 20.0764i | 0.858405 | + | 0.858405i | 0.991150 | − | 0.132746i | \(-0.0423793\pi\) |
−0.132746 | + | 0.991150i | \(0.542379\pi\) | |||||||
\(548\) | 0.208051 | + | 0.776457i | 0.00888750 | + | 0.0331686i | ||||
\(549\) | −8.95448 | − | 15.5096i | −0.382168 | − | 0.661934i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 2.68973 | − | 2.68973i | 0.114482 | − | 0.114482i | ||||
\(553\) | 13.1626 | + | 27.1153i | 0.559731 | + | 1.15306i | ||||
\(554\) | − | 6.58846i | − | 0.279917i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.00000 | + | 1.73205i | −0.127228 | + | 0.0734553i | ||||
\(557\) | −0.568406 | + | 2.12132i | −0.0240841 | + | 0.0898832i | −0.976922 | − | 0.213597i | \(-0.931482\pi\) |
0.952838 | + | 0.303480i | \(0.0981487\pi\) | |||||||
\(558\) | 4.12252 | − | 1.10463i | 0.174520 | − | 0.0467626i | ||||
\(559\) | 66.4974 | 2.81254 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.430781 | 0.0181876 | ||||||||
\(562\) | −23.6305 | + | 6.33178i | −0.996793 | + | 0.267090i | ||||
\(563\) | 7.91688 | − | 29.5462i | 0.333657 | − | 1.24522i | −0.571662 | − | 0.820489i | \(-0.693701\pi\) |
0.905318 | − | 0.424734i | \(-0.139632\pi\) | |||||||
\(564\) | −2.49038 | + | 1.43782i | −0.104864 | + | 0.0605432i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.39230i | 0.100556i | ||||||||
\(567\) | 0.845807 | − | 11.7806i | 0.0355206 | − | 0.494738i | ||||
\(568\) | −9.46979 | + | 9.46979i | −0.397344 | + | 0.397344i | ||||
\(569\) | 20.5981 | + | 11.8923i | 0.863516 | + | 0.498551i | 0.865188 | − | 0.501447i | \(-0.167199\pi\) |
−0.00167195 | + | 0.999999i | \(0.500532\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.58846 | + | 14.8756i | 0.359416 | + | 0.622526i | 0.987863 | − | 0.155326i | \(-0.0496427\pi\) |
−0.628448 | + | 0.777852i | \(0.716309\pi\) | |||||||
\(572\) | 2.03339 | + | 7.58871i | 0.0850202 | + | 0.317300i | ||||
\(573\) | 2.86559 | + | 2.86559i | 0.119712 | + | 0.119712i | ||||
\(574\) | −9.69615 | + | 27.9904i | −0.404710 | + | 1.16830i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.23205 | − | 2.13397i | 0.0513355 | − | 0.0889156i | ||||
\(577\) | 8.10634 | + | 2.17209i | 0.337472 | + | 0.0904252i | 0.423575 | − | 0.905861i | \(-0.360775\pi\) |
−0.0861036 | + | 0.996286i | \(0.527442\pi\) | |||||||
\(578\) | 16.2127 | + | 4.34418i | 0.674359 | + | 0.180694i | ||||
\(579\) | −4.43782 | + | 7.68653i | −0.184430 | + | 0.319441i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.00000 | − | 15.5885i | −0.124461 | − | 0.646718i | ||||
\(582\) | −5.89709 | − | 5.89709i | −0.244442 | − | 0.244442i | ||||
\(583\) | −2.68973 | − | 10.0382i | −0.111397 | − | 0.415740i | ||||
\(584\) | 4.00000 | + | 6.92820i | 0.165521 | + | 0.286691i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 27.5885 | + | 15.9282i | 1.13967 | + | 0.657988i | ||||
\(587\) | −2.68973 | + | 2.68973i | −0.111017 | + | 0.111017i | −0.760433 | − | 0.649416i | \(-0.775013\pi\) |
0.649416 | + | 0.760433i | \(0.275013\pi\) | |||||||
\(588\) | −4.10394 | + | 3.06866i | −0.169244 | + | 0.126550i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.19615 | − | 3.00000i | 0.213741 | − | 0.123404i | ||||
\(592\) | 1.79315 | − | 6.69213i | 0.0736980 | − | 0.275045i | ||||
\(593\) | 32.7721 | − | 8.78127i | 1.34579 | − | 0.360603i | 0.487211 | − | 0.873284i | \(-0.338014\pi\) |
0.858579 | + | 0.512681i | \(0.171348\pi\) | |||||||
\(594\) | 5.07180 | 0.208098 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.19615 | 0.335727 | ||||||||
\(597\) | −13.9527 | + | 3.73861i | −0.571045 | + | 0.153011i | ||||
\(598\) | 8.33298 | − | 31.0991i | 0.340761 | − | 1.27174i | ||||
\(599\) | −24.1865 | + | 13.9641i | −0.988235 | + | 0.570558i | −0.904746 | − | 0.425951i | \(-0.859940\pi\) |
−0.0834887 | + | 0.996509i | \(0.526606\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 2.78461i | − | 0.113587i | −0.998386 | − | 0.0567933i | \(-0.981912\pi\) | ||
0.998386 | − | 0.0567933i | \(-0.0180876\pi\) | |||||||
\(602\) | 25.5438 | − | 12.3998i | 1.04109 | − | 0.505376i | ||||
\(603\) | 6.62776 | − | 6.62776i | 0.269903 | − | 0.269903i | ||||
\(604\) | −15.9282 | − | 9.19615i | −0.648109 | − | 0.374186i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 6.00000 | + | 10.3923i | 0.243733 | + | 0.422159i | ||||
\(607\) | −6.77508 | − | 25.2850i | −0.274992 | − | 1.02628i | −0.955847 | − | 0.293866i | \(-0.905058\pi\) |
0.680854 | − | 0.732419i | \(-0.261609\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.39230 | + | 5.07180i | 0.177985 | + | 0.205520i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.1699 | + | 21.0788i | −0.492340 | + | 0.852759i | ||||
\(612\) | −1.10463 | − | 0.295984i | −0.0446519 | − | 0.0119644i | ||||
\(613\) | −17.3867 | − | 4.65874i | −0.702241 | − | 0.188165i | −0.110007 | − | 0.993931i | \(-0.535087\pi\) |
−0.592234 | + | 0.805766i | \(0.701754\pi\) | |||||||
\(614\) | −6.19615 | + | 10.7321i | −0.250056 | + | 0.433110i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.19615 | + | 2.53590i | 0.0884855 | + | 0.102174i | ||||
\(617\) | 5.94786 | + | 5.94786i | 0.239452 | + | 0.239452i | 0.816623 | − | 0.577171i | \(-0.195844\pi\) |
−0.577171 | + | 0.816623i | \(0.695844\pi\) | |||||||
\(618\) | 2.46309 | + | 9.19239i | 0.0990801 | + | 0.369772i | ||||
\(619\) | 12.4641 | + | 21.5885i | 0.500975 | + | 0.867713i | 0.999999 | + | 0.00112567i | \(0.000358312\pi\) |
−0.499025 | + | 0.866588i | \(0.666308\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.0000 | − | 10.3923i | −0.722315 | − | 0.417029i | ||||
\(622\) | 0.568406 | − | 0.568406i | 0.0227910 | − | 0.0227910i | ||||
\(623\) | −26.6484 | + | 12.9360i | −1.06765 | + | 0.518269i | ||||
\(624\) | 4.53590i | 0.181581i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −16.4545 | + | 9.50000i | −0.657653 | + | 0.379696i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.93185 | − | 0.517638i | 0.0770893 | − | 0.0206560i | ||||
\(629\) | −3.21539 | −0.128206 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.3923 | −0.692377 | −0.346188 | − | 0.938165i | \(-0.612524\pi\) | ||||
−0.346188 | + | 0.938165i | \(0.612524\pi\) | |||||||
\(632\) | 11.0041 | − | 2.94855i | 0.437720 | − | 0.117287i | ||||
\(633\) | 1.93185 | − | 7.20977i | 0.0767842 | − | 0.286563i | ||||
\(634\) | −14.1962 | + | 8.19615i | −0.563801 | + | 0.325511i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 6.00000i | − | 0.237915i | ||||||
\(637\) | −17.0957 | + | 39.8618i | −0.677355 | + | 1.57938i | ||||
\(638\) | 3.10583 | − | 3.10583i | 0.122961 | − | 0.122961i | ||||
\(639\) | 28.5788 | + | 16.5000i | 1.13056 | + | 0.652730i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.5000 | − | 23.3827i | −0.533218 | − | 0.923561i | −0.999247 | − | 0.0387913i | \(-0.987649\pi\) |
0.466029 | − | 0.884769i | \(-0.345684\pi\) | |||||||
\(642\) | 0.416102 | + | 1.55291i | 0.0164222 | + | 0.0612886i | ||||
\(643\) | −14.8356 | − | 14.8356i | −0.585060 | − | 0.585060i | 0.351229 | − | 0.936290i | \(-0.385764\pi\) |
−0.936290 | + | 0.351229i | \(0.885764\pi\) | |||||||
\(644\) | −2.59808 | − | 13.5000i | −0.102379 | − | 0.531975i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.7351 | + | 6.62776i | 0.972438 | + | 0.260564i | 0.709857 | − | 0.704346i | \(-0.248760\pi\) |
0.262581 | + | 0.964910i | \(0.415426\pi\) | |||||||
\(648\) | −4.31199 | − | 1.15539i | −0.169391 | − | 0.0453882i | ||||
\(649\) | 9.00000 | − | 15.5885i | 0.353281 | − | 0.611900i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.09808 | + | 3.16987i | −0.0430370 | + | 0.124237i | ||||
\(652\) | 10.2784 | + | 10.2784i | 0.402534 | + | 0.402534i | ||||
\(653\) | −5.22715 | − | 19.5080i | −0.204554 | − | 0.763406i | −0.989585 | − | 0.143950i | \(-0.954020\pi\) |
0.785031 | − | 0.619457i | \(-0.212647\pi\) | |||||||
\(654\) | −3.73205 | − | 6.46410i | −0.145935 | − | 0.252766i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.69615 | + | 5.59808i | 0.378571 | + | 0.218568i | ||||
\(657\) | 13.9391 | − | 13.9391i | 0.543815 | − | 0.543815i | ||||
\(658\) | −0.744272 | + | 10.3664i | −0.0290147 | + | 0.404123i | ||||
\(659\) | − | 29.3205i | − | 1.14216i | −0.820893 | − | 0.571082i | \(-0.806524\pi\) | ||
0.820893 | − | 0.571082i | \(-0.193476\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.29423 | + | 3.63397i | −0.244817 | + | 0.141345i | −0.617389 | − | 0.786658i | \(-0.711809\pi\) |
0.372572 | + | 0.928003i | \(0.378476\pi\) | |||||||
\(662\) | −3.62347 | + | 13.5230i | −0.140830 | + | 0.525585i | ||||
\(663\) | 2.03339 | − | 0.544845i | 0.0789702 | − | 0.0211600i | ||||
\(664\) | −6.00000 | −0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −17.0718 | −0.661519 | ||||||||
\(667\) | −17.3867 | + | 4.65874i | −0.673214 | + | 0.180387i | ||||
\(668\) | −4.89898 | + | 18.2832i | −0.189547 | + | 0.707400i | ||||
\(669\) | −5.95448 | + | 3.43782i | −0.230214 | + | 0.132914i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 9.21539i | − | 0.355756i | ||||||
\(672\) | 0.845807 | + | 1.74238i | 0.0326277 | + | 0.0672139i | ||||
\(673\) | −6.12372 | + | 6.12372i | −0.236052 | + | 0.236052i | −0.815213 | − | 0.579161i | \(-0.803380\pi\) |
0.579161 | + | 0.815213i | \(0.303380\pi\) | |||||||
\(674\) | 7.50000 | + | 4.33013i | 0.288889 | + | 0.166790i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.6962 | + | 21.9904i | 0.488314 | + | 0.845784i | ||||
\(677\) | 1.72878 | + | 6.45189i | 0.0664424 | + | 0.247966i | 0.991157 | − | 0.132695i | \(-0.0423630\pi\) |
−0.924715 | + | 0.380661i | \(0.875696\pi\) | |||||||
\(678\) | −3.52193 | − | 3.52193i | −0.135259 | − | 0.135259i | ||||
\(679\) | −29.5981 | + | 5.69615i | −1.13587 | + | 0.218598i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.0526 | − | 17.4115i | 0.385215 | − | 0.667212i | ||||
\(682\) | 2.12132 | + | 0.568406i | 0.0812296 | + | 0.0217654i | ||||
\(683\) | −14.2808 | − | 3.82654i | −0.546441 | − | 0.146418i | −0.0249712 | − | 0.999688i | \(-0.507949\pi\) |
−0.521470 | + | 0.853270i | \(0.674616\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.866025 | + | 18.5000i | 0.0330650 | + | 0.706333i | ||||
\(687\) | 7.34847 | + | 7.34847i | 0.280362 | + | 0.280362i | ||||
\(688\) | −2.77766 | − | 10.3664i | −0.105897 | − | 0.395214i | ||||
\(689\) | −25.3923 | − | 43.9808i | −0.967370 | − | 1.67553i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.5885 | + | 12.4641i | 0.821264 | + | 0.474157i | 0.850852 | − | 0.525405i | \(-0.176086\pi\) |
−0.0295884 | + | 0.999562i | \(0.509420\pi\) | |||||||
\(692\) | −12.4877 | + | 12.4877i | −0.474711 | + | 0.474711i | ||||
\(693\) | 4.63518 | − | 6.84443i | 0.176076 | − | 0.259999i | ||||
\(694\) | 6.00000i | 0.227757i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.19615 | − | 1.26795i | 0.0832449 | − | 0.0480615i | ||||
\(697\) | 1.34486 | − | 5.01910i | 0.0509403 | − | 0.190112i | ||||
\(698\) | 16.4022 | − | 4.39494i | 0.620831 | − | 0.166351i | ||||
\(699\) | 4.39230 | 0.166132 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.8564 | −1.42982 | −0.714908 | − | 0.699218i | \(-0.753532\pi\) | ||||
−0.714908 | + | 0.699218i | \(0.753532\pi\) | |||||||
\(702\) | 23.9401 | − | 6.41473i | 0.903561 | − | 0.242108i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.09808 | − | 0.633975i | 0.0413853 | − | 0.0238938i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23.5359i | 0.885785i | ||||||||
\(707\) | 43.2586 | + | 3.10583i | 1.62691 | + | 0.116807i | ||||
\(708\) | 7.34847 | − | 7.34847i | 0.276172 | − | 0.276172i | ||||
\(709\) | −45.5429 | − | 26.2942i | −1.71040 | − | 0.987500i | −0.934008 | − | 0.357251i | \(-0.883714\pi\) |
−0.776393 | − | 0.630250i | \(-0.782953\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.0359 | − | 24.3109i | −0.526387 | − | 0.911730i | ||||
\(712\) | 2.89778 | + | 10.8147i | 0.108599 | + | 0.405296i | ||||
\(713\) | −6.36396 | − | 6.36396i | −0.238332 | − | 0.238332i | ||||
\(714\) | 0.679492 | − | 0.588457i | 0.0254293 | − | 0.0220225i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.09808 | − | 7.09808i | 0.153152 | − | 0.265268i | ||||
\(717\) | 16.1619 | + | 4.33057i | 0.603578 | + | 0.161728i | ||||
\(718\) | 10.0382 | + | 2.68973i | 0.374622 | + | 0.100380i | ||||
\(719\) | −19.7942 | + | 34.2846i | −0.738200 | + | 1.27860i | 0.215105 | + | 0.976591i | \(0.430991\pi\) |
−0.953305 | + | 0.302009i | \(0.902343\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 32.5000 | + | 11.2583i | 1.21036 | + | 0.419282i | ||||
\(722\) | −13.4350 | − | 13.4350i | −0.500000 | − | 0.500000i | ||||
\(723\) | −0.656339 | − | 2.44949i | −0.0244095 | − | 0.0910975i | ||||
\(724\) | 3.63397 | + | 6.29423i | 0.135056 | + | 0.233923i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.95448 | − | 3.43782i | −0.220992 | − | 0.127590i | ||||
\(727\) | −13.4350 | + | 13.4350i | −0.498278 | + | 0.498278i | −0.910902 | − | 0.412624i | \(-0.864612\pi\) |
0.412624 | + | 0.910902i | \(0.364612\pi\) | |||||||
\(728\) | 13.5737 | + | 9.19239i | 0.503076 | + | 0.340693i | ||||
\(729\) | 2.21539i | 0.0820515i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.31347 | + | 2.49038i | −0.159539 | + | 0.0921101i | ||||
\(732\) | 1.37705 | − | 5.13922i | 0.0508972 | − | 0.189951i | ||||
\(733\) | −13.5230 | + | 3.62347i | −0.499482 | + | 0.133836i | −0.499760 | − | 0.866164i | \(-0.666578\pi\) |
0.000277595 | 1.00000i | \(0.499912\pi\) | ||||||||
\(734\) | −18.3923 | −0.678872 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.19615 | −0.191533 | ||||||||
\(737\) | 4.65874 | − | 1.24831i | 0.171607 | − | 0.0459820i | ||||
\(738\) | 7.14042 | − | 26.6484i | 0.262842 | − | 0.980941i | ||||
\(739\) | 17.3205 | − | 10.0000i | 0.637145 | − | 0.367856i | −0.146369 | − | 0.989230i | \(-0.546759\pi\) |
0.783514 | + | 0.621374i | \(0.213425\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −17.9551 | − | 12.1595i | −0.659151 | − | 0.446390i | ||||
\(743\) | 24.8874 | − | 24.8874i | 0.913032 | − | 0.913032i | −0.0834781 | − | 0.996510i | \(-0.526603\pi\) |
0.996510 | + | 0.0834781i | \(0.0266029\pi\) | |||||||
\(744\) | 1.09808 | + | 0.633975i | 0.0402574 | + | 0.0232426i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −8.49038 | − | 14.7058i | −0.310855 | − | 0.538417i | ||||
\(747\) | 3.82654 | + | 14.2808i | 0.140006 | + | 0.522508i | ||||
\(748\) | −0.416102 | − | 0.416102i | −0.0152142 | − | 0.0152142i | ||||
\(749\) | 5.49038 | + | 1.90192i | 0.200614 | + | 0.0694948i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.00000 | + | 12.1244i | −0.255434 | + | 0.442424i | −0.965013 | − | 0.262201i | \(-0.915552\pi\) |
0.709580 | + | 0.704625i | \(0.248885\pi\) | |||||||
\(752\) | 3.79435 | + | 1.01669i | 0.138366 | + | 0.0370750i | ||||
\(753\) | −3.10583 | − | 0.832204i | −0.113183 | − | 0.0303272i | ||||
\(754\) | 10.7321 | − | 18.5885i | 0.390838 | − | 0.676952i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 8.00000 | − | 6.92820i | 0.290957 | − | 0.251976i | ||||
\(757\) | −2.20925 | − | 2.20925i | −0.0802967 | − | 0.0802967i | 0.665818 | − | 0.746114i | \(-0.268083\pi\) |
−0.746114 | + | 0.665818i | \(0.768083\pi\) | |||||||
\(758\) | 2.22286 | + | 8.29581i | 0.0807378 | + | 0.301317i | ||||
\(759\) | −2.41154 | − | 4.17691i | −0.0875335 | − | 0.151612i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34.2846 | − | 19.7942i | −1.24282 | − | 0.717540i | −0.273150 | − | 0.961972i | \(-0.588065\pi\) |
−0.969667 | + | 0.244431i | \(0.921399\pi\) | |||||||
\(762\) | −3.58630 | + | 3.58630i | −0.129918 | + | 0.129918i | ||||
\(763\) | −26.9072 | − | 1.93185i | −0.974107 | − | 0.0699377i | ||||
\(764\) | − | 5.53590i | − | 0.200282i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −20.5981 | + | 11.8923i | −0.744239 | + | 0.429686i | ||||
\(767\) | 22.7661 | − | 84.9643i | 0.822037 | − | 3.06788i | ||||
\(768\) | 0.707107 | − | 0.189469i | 0.0255155 | − | 0.00683686i | ||||
\(769\) | −9.71281 | −0.350253 | −0.175126 | − | 0.984546i | \(-0.556033\pi\) | ||||
−0.175126 | + | 0.984546i | \(0.556033\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.21539 | −0.115799 | ||||||||
\(772\) | 11.7112 | − | 3.13801i | 0.421496 | − | 0.112940i | ||||
\(773\) | 4.72311 | − | 17.6269i | 0.169879 | − | 0.633996i | −0.827489 | − | 0.561482i | \(-0.810231\pi\) |
0.997367 | − | 0.0725134i | \(-0.0231020\pi\) | |||||||
\(774\) | −22.9019 | + | 13.2224i | −0.823193 | + | 0.475270i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11.3923i | 0.408960i | ||||||||
\(777\) | 7.52433 | − | 11.1106i | 0.269934 | − | 0.398592i | ||||
\(778\) | 2.86559 | − | 2.86559i | 0.102736 | − | 0.102736i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.49038 | + | 14.7058i | 0.303810 | + | 0.526214i | ||||
\(782\) | 0.624153 | + | 2.32937i | 0.0223197 | + | 0.0832982i | ||||
\(783\) | −9.79796 | − | 9.79796i | −0.350150 | − | 0.350150i | ||||
\(784\) | 6.92820 | + | 1.00000i | 0.247436 | + | 0.0357143i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.803848 | − | 1.39230i | 0.0286723 | − | 0.0496619i | ||||
\(787\) | 23.9401 | + | 6.41473i | 0.853372 | + | 0.228660i | 0.658884 | − | 0.752244i | \(-0.271029\pi\) |
0.194488 | + | 0.980905i | \(0.437695\pi\) | |||||||
\(788\) | −7.91688 | − | 2.12132i | −0.282027 | − | 0.0755689i | ||||
\(789\) | −1.31347 | + | 2.27499i | −0.0467606 | + | 0.0809918i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.6769 | + | 3.40192i | −0.628519 | + | 0.120958i | ||||
\(792\) | −2.20925 | − | 2.20925i | −0.0785024 | − | 0.0785024i | ||||
\(793\) | −11.6555 | − | 43.4988i | −0.413898 | − | 1.54469i | ||||
\(794\) | −1.00000 | − | 1.73205i | −0.0354887 | − | 0.0614682i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.0885 | + | 9.86603i | 0.605684 | + | 0.349692i | ||||
\(797\) | −10.6945 | + | 10.6945i | −0.378820 | + | 0.378820i | −0.870676 | − | 0.491856i | \(-0.836318\pi\) |
0.491856 | + | 0.870676i | \(0.336318\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.82309i | − | 0.0644961i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 23.8923 | − | 13.7942i | 0.844193 | − | 0.487395i | ||||
\(802\) | −2.86559 | + | 10.6945i | −0.101188 | + | 0.377637i | ||||
\(803\) | 9.79796 | − | 2.62536i | 0.345762 | − | 0.0926468i | ||||
\(804\) | 2.78461 | 0.0982056 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10.7321 | 0.378020 | ||||||||
\(807\) | 8.90138 | − | 2.38512i | 0.313344 | − | 0.0839601i | ||||
\(808\) | 4.24264 | − | 15.8338i | 0.149256 | − | 0.557029i | ||||
\(809\) | −16.3923 | + | 9.46410i | −0.576323 | + | 0.332740i | −0.759671 | − | 0.650308i | \(-0.774640\pi\) |
0.183348 | + | 0.983048i | \(0.441307\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 23.9090i | − | 0.839557i | −0.907627 | − | 0.419779i | \(-0.862108\pi\) | ||
0.907627 | − | 0.419779i | \(-0.137892\pi\) | |||||||
\(812\) | 0.656339 | − | 9.14162i | 0.0230330 | − | 0.320808i | ||||
\(813\) | −12.0072 | + | 12.0072i | −0.421111 | + | 0.421111i | ||||
\(814\) | −7.60770 | − | 4.39230i | −0.266650 | − | 0.153950i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.169873 | − | 0.294229i | −0.00594674 | − | 0.0103001i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −9.05369 | − | 9.05369i | −0.316555 | − | 0.316555i | ||||
\(819\) | 13.2224 | − | 38.1699i | 0.462029 | − | 1.33376i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.0526 | + | 27.8038i | −0.560238 | + | 0.970361i | 0.437237 | + | 0.899346i | \(0.355957\pi\) |
−0.997475 | + | 0.0710147i | \(0.977376\pi\) | |||||||
\(822\) | 0.568406 | + | 0.152304i | 0.0198254 | + | 0.00531221i | ||||
\(823\) | 3.34607 | + | 0.896575i | 0.116637 | + | 0.0312527i | 0.316665 | − | 0.948537i | \(-0.397437\pi\) |
−0.200029 | + | 0.979790i | \(0.564104\pi\) | |||||||
\(824\) | 6.50000 | − | 11.2583i | 0.226438 | − | 0.392203i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.09808 | − | 36.8827i | −0.246974 | − | 1.28331i | ||||
\(827\) | 7.34847 | + | 7.34847i | 0.255531 | + | 0.255531i | 0.823234 | − | 0.567702i | \(-0.192168\pi\) |
−0.567702 | + | 0.823234i | \(0.692168\pi\) | |||||||
\(828\) | 3.31388 | + | 12.3676i | 0.115165 | + | 0.429803i | ||||
\(829\) | −0.169873 | − | 0.294229i | −0.00589993 | − | 0.0102190i | 0.863060 | − | 0.505101i | \(-0.168545\pi\) |
−0.868960 | + | 0.494882i | \(0.835211\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.17691 | − | 2.41154i | −0.144896 | − | 0.0836555i | ||||
\(832\) | 4.38134 | − | 4.38134i | 0.151896 | − | 0.151896i | ||||
\(833\) | −0.383917 | − | 3.22595i | −0.0133019 | − | 0.111772i | ||||
\(834\) | 2.53590i | 0.0878110i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.79315 | − | 6.69213i | 0.0619804 | − | 0.231314i | ||||
\(838\) | −27.9933 | + | 7.50077i | −0.967011 | + | 0.259110i | ||||
\(839\) | 4.01924 | 0.138760 | 0.0693798 | − | 0.997590i | \(-0.477898\pi\) | ||||
0.0693798 | + | 0.997590i | \(0.477898\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.0000 | 0.586207 | ||||||||
\(842\) | 15.0759 | − | 4.03957i | 0.519549 | − | 0.139213i | ||||
\(843\) | −4.63518 | + | 17.2987i | −0.159644 | + | 0.595800i | ||||
\(844\) | −8.83013 | + | 5.09808i | −0.303946 | + | 0.175483i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 9.67949i | − | 0.332788i | ||||||
\(847\) | −22.3550 | + | 10.8518i | −0.768127 | + | 0.372873i | ||||
\(848\) | −5.79555 | + | 5.79555i | −0.199020 | + | 0.199020i | ||||
\(849\) | 1.51666 | + | 0.875644i | 0.0520517 | + | 0.0300520i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.0000 | + | 31.1769i | 0.617032 | + | 1.06873i | ||||
\(852\) | 2.53742 | + | 9.46979i | 0.0869307 | + | 0.324430i | ||||
\(853\) | −1.83032 | − | 1.83032i | −0.0626688 | − | 0.0626688i | 0.675078 | − | 0.737747i | \(-0.264110\pi\) |
−0.737747 | + | 0.675078i | \(0.764110\pi\) | |||||||
\(854\) | −12.5885 | − | 14.5359i | −0.430768 | − | 0.497408i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.09808 | − | 1.90192i | 0.0375315 | − | 0.0650064i | ||||
\(857\) | −34.3572 | − | 9.20599i | −1.17362 | − | 0.314471i | −0.381227 | − | 0.924481i | \(-0.624498\pi\) |
−0.792393 | + | 0.610011i | \(0.791165\pi\) | |||||||
\(858\) | 5.55532 | + | 1.48854i | 0.189655 | + | 0.0508180i | ||||
\(859\) | 0.509619 | − | 0.882686i | 0.0173880 | − | 0.0301169i | −0.857200 | − | 0.514983i | \(-0.827798\pi\) |
0.874588 | + | 0.484866i | \(0.161132\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.1962 | + | 16.3923i | 0.483804 | + | 0.558648i | ||||
\(862\) | −12.3998 | − | 12.3998i | −0.422337 | − | 0.422337i | ||||
\(863\) | 6.00361 | + | 22.4058i | 0.204365 | + | 0.762701i | 0.989642 | + | 0.143556i | \(0.0458539\pi\) |
−0.785277 | + | 0.619145i | \(0.787479\pi\) | |||||||
\(864\) | −2.00000 | − | 3.46410i | −0.0680414 | − | 0.117851i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 27.8660 | + | 16.0885i | 0.946926 | + | 0.546708i | ||||
\(867\) | 8.68835 | − | 8.68835i | 0.295072 | − | 0.295072i | ||||
\(868\) | 4.12252 | − | 2.00120i | 0.139928 | − | 0.0679252i | ||||
\(869\) | − | 14.4449i | − | 0.490008i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.4115 | − | 11.7846i | 0.691619 | − | 0.399306i | ||||
\(872\) | −2.63896 | + | 9.84873i | −0.0893664 | + | 0.333520i | ||||
\(873\) | 27.1153 | − | 7.26552i | 0.917713 | − | 0.245900i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.85641 | 0.197870 | ||||||||
\(877\) | −40.4810 | + | 10.8468i | −1.36694 | + | 0.366272i | −0.866362 | − | 0.499417i | \(-0.833548\pi\) |
−0.500583 | + | 0.865689i | \(0.666881\pi\) | |||||||
\(878\) | −1.52073 | + | 5.67544i | −0.0513221 | + | 0.191537i | ||||
\(879\) | 20.1962 | − | 11.6603i | 0.681199 | − | 0.393291i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.58846i | − | 0.120898i | −0.998171 | − | 0.0604491i | \(-0.980747\pi\) | ||
0.998171 | − | 0.0604491i | \(-0.0192533\pi\) | |||||||
\(882\) | −2.03837 | − | 17.1278i | −0.0686354 | − | 0.576725i | ||||
\(883\) | 27.4249 | − | 27.4249i | 0.922920 | − | 0.922920i | −0.0743148 | − | 0.997235i | \(-0.523677\pi\) |
0.997235 | + | 0.0743148i | \(0.0236770\pi\) | |||||||
\(884\) | −2.49038 | − | 1.43782i | −0.0837606 | − | 0.0483592i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.00000 | − | 10.3923i | −0.201574 | − | 0.349136i | ||||
\(887\) | 2.68973 | + | 10.0382i | 0.0903122 | + | 0.337050i | 0.996267 | − | 0.0863246i | \(-0.0275122\pi\) |
−0.905955 | + | 0.423374i | \(0.860846\pi\) | |||||||
\(888\) | −3.58630 | − | 3.58630i | −0.120348 | − | 0.120348i | ||||
\(889\) | 3.46410 | + | 18.0000i | 0.116182 | + | 0.603701i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.83013 | + | 4.90192i | −0.0948128 | + | 0.164221i | ||||
\(892\) | 9.07227 | + | 2.43091i | 0.303762 | + | 0.0813928i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 3.00000 | − | 5.19615i | 0.100335 | − | 0.173785i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.866025 | − | 2.50000i | 0.0289319 | − | 0.0835191i | ||||
\(897\) | −16.6660 | − | 16.6660i | −0.556460 | − | 0.556460i | ||||
\(898\) | −2.15351 | − | 8.03699i | −0.0718634 | − | 0.268198i | ||||
\(899\) | −3.00000 | − | 5.19615i | −0.100056 | − | 0.173301i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.29423 | + | 1.90192i | 0.109747 | + | 0.0633623i | ||||
\(902\) | 10.0382 | − | 10.0382i | 0.334235 | − | 0.334235i | ||||
\(903\) | 1.48854 | − | 20.7327i | 0.0495356 | − | 0.689942i | ||||
\(904\) | 6.80385i | 0.226293i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −11.6603 | + | 6.73205i | −0.387386 | + | 0.223657i | ||||
\(907\) | −12.8159 | + | 47.8294i | −0.425543 | + | 1.58815i | 0.337190 | + | 0.941437i | \(0.390524\pi\) |
−0.762733 | + | 0.646713i | \(0.776143\pi\) | |||||||
\(908\) | −26.5283 | + | 7.10823i | −0.880372 | + | 0.235895i | ||||
\(909\) | −40.3923 | −1.33973 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 52.1769 | 1.72870 | 0.864349 | − | 0.502892i | \(-0.167731\pi\) | ||||
0.864349 | + | 0.502892i | \(0.167731\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.96902 | + | 7.34847i | −0.0651649 | + | 0.243199i | ||||
\(914\) | 28.1769 | − | 16.2679i | 0.932009 | − | 0.538096i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 14.1962i | − | 0.469054i | ||||||
\(917\) | −2.53742 | − | 5.22715i | −0.0837931 | − | 0.172616i | ||||
\(918\) | −1.31268 | + | 1.31268i | −0.0433248 | + | 0.0433248i | ||||
\(919\) | −6.06218 | − | 3.50000i | −0.199973 | − | 0.115454i | 0.396670 | − | 0.917961i | \(-0.370166\pi\) |
−0.596643 | + | 0.802507i | \(0.703499\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.53590 | + | 7.85641i | 0.149463 | + | 0.258877i | ||||
\(922\) | 6.21166 | + | 23.1822i | 0.204570 | + | 0.763466i | ||||
\(923\) | 58.6763 | + | 58.6763i | 1.93135 | + | 1.93135i | ||||
\(924\) | 2.41154 | − | 0.464102i | 0.0793339 | − | 0.0152678i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 4.66987 | − | 8.08846i | 0.153462 | − | 0.265803i | ||||
\(927\) | −30.9418 | − | 8.29083i | −1.01626 | − | 0.272307i | ||||
\(928\) | −3.34607 | − | 0.896575i | −0.109840 | − | 0.0294315i | ||||
\(929\) | −1.60770 | + | 2.78461i | −0.0527468 | + | 0.0913601i | −0.891193 | − | 0.453624i | \(-0.850131\pi\) |
0.838446 | + | 0.544984i | \(0.183464\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −4.24264 | − | 4.24264i | −0.138972 | − | 0.138972i | ||||
\(933\) | −0.152304 | − | 0.568406i | −0.00498621 | − | 0.0186088i | ||||
\(934\) | 11.5359 | + | 19.9808i | 0.377466 | + | 0.653791i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −13.2224 | − | 7.63397i | −0.432189 | − | 0.249524i | ||||
\(937\) | 38.7386 | − | 38.7386i | 1.26553 | − | 1.26553i | 0.317163 | − | 0.948371i | \(-0.397270\pi\) |
0.948371 | − | 0.317163i | \(-0.102730\pi\) | |||||||
\(938\) | 5.64325 | − | 8.33298i | 0.184259 | − | 0.272081i | ||||
\(939\) | 13.9090i | 0.453902i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.7058 | + | 8.49038i | −0.479394 | + | 0.276779i | −0.720164 | − | 0.693804i | \(-0.755933\pi\) |
0.240770 | + | 0.970582i | \(0.422600\pi\) | |||||||
\(942\) | 0.378937 | − | 1.41421i | 0.0123464 | − | 0.0460776i | ||||
\(943\) | −56.1946 | + | 15.0573i | −1.82995 | + | 0.490333i | ||||
\(944\) | −14.1962 | −0.462045 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13.6077 | −0.442424 | ||||||||
\(947\) | −20.0764 | + | 5.37945i | −0.652395 | + | 0.174809i | −0.569812 | − | 0.821775i | \(-0.692984\pi\) |
−0.0825835 | + | 0.996584i | \(0.526317\pi\) | |||||||
\(948\) | 2.15849 | − | 8.05558i | 0.0701043 | − | 0.261633i | ||||
\(949\) | 42.9282 | − | 24.7846i | 1.39351 | − | 0.804542i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.0000i | 0.389127i | ||||||||
\(952\) | −1.22474 | − | 0.0879327i | −0.0396942 | − | 0.00284992i | ||||
\(953\) | −6.21166 | + | 6.21166i | −0.201215 | + | 0.201215i | −0.800521 | − | 0.599305i | \(-0.795444\pi\) |
0.599305 | + | 0.800521i | \(0.295444\pi\) | |||||||
\(954\) | 17.4904 | + | 10.0981i | 0.566272 | + | 0.326937i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −11.4282 | − | 19.7942i | −0.369615 | − | 0.640191i | ||||
\(957\) | −0.832204 | − | 3.10583i | −0.0269013 | − | 0.100397i | ||||
\(958\) | −9.05369 | − | 9.05369i | −0.292511 | − | 0.292511i | ||||
\(959\) | 1.60770 | − | 1.39230i | 0.0519152 | − | 0.0449599i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.0000 | + | 24.2487i | −0.451613 | + | 0.782216i | ||||
\(962\) | −41.4655 | − | 11.1106i | −1.33690 | − | 0.358221i | ||||
\(963\) | −5.22715 | − | 1.40061i | −0.168443 | − | 0.0451340i | ||||
\(964\) | −1.73205 | + | 3.00000i | −0.0557856 | + | 0.0966235i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −9.50962 | − | 3.29423i | −0.305967 | − | 0.105990i | ||||
\(967\) | 15.9217 | + | 15.9217i | 0.512007 | + | 0.512007i | 0.915141 | − | 0.403134i | \(-0.132079\pi\) |
−0.403134 | + | 0.915141i | \(0.632079\pi\) | |||||||
\(968\) | 2.43091 | + | 9.07227i | 0.0781323 | + | 0.291594i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37.3923 | − | 21.5885i | −1.19998 | − | 0.692807i | −0.239426 | − | 0.970915i | \(-0.576959\pi\) |
−0.960550 | + | 0.278108i | \(0.910293\pi\) | |||||||
\(972\) | −10.7961 | + | 10.7961i | −0.346284 | + | 0.346284i | ||||
\(973\) | 7.58871 | + | 5.13922i | 0.243283 | + | 0.164756i | ||||
\(974\) | − | 9.33975i | − | 0.299265i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.29423 | + | 3.63397i | −0.201473 | + | 0.116321i | ||||
\(977\) | −10.2462 | + | 38.2395i | −0.327806 | + | 1.22339i | 0.583654 | + | 0.812003i | \(0.301622\pi\) |
−0.911460 | + | 0.411388i | \(0.865044\pi\) | |||||||
\(978\) | 10.2784 | − | 2.75410i | 0.328668 | − | 0.0880663i | ||||
\(979\) | 14.1962 | 0.453711 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 25.1244 | 0.802159 | ||||||||
\(982\) | 15.5056 | − | 4.15471i | 0.494803 | − | 0.132582i | ||||
\(983\) | −14.1050 | + | 52.6405i | −0.449879 | + | 1.67897i | 0.252845 | + | 0.967507i | \(0.418634\pi\) |
−0.702723 | + | 0.711463i | \(0.748033\pi\) | |||||||
\(984\) | 7.09808 | − | 4.09808i | 0.226278 | − | 0.130642i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.60770i | 0.0511994i | ||||||||
\(987\) | 6.29959 | + | 4.26620i | 0.200518 | + | 0.135795i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 48.2942 | + | 27.8827i | 1.53567 | + | 0.886618i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.50000 | − | 16.4545i | −0.301777 | − | 0.522694i | 0.674761 | − | 0.738036i | \(-0.264247\pi\) |
−0.976539 | + | 0.215342i | \(0.930913\pi\) | |||||||
\(992\) | −0.448288 | − | 1.67303i | −0.0142331 | − | 0.0531188i | ||||
\(993\) | 7.24693 | + | 7.24693i | 0.229974 | + | 0.229974i | ||||
\(994\) | 33.4808 | + | 11.5981i | 1.06195 | + | 0.367869i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.19615 | + | 3.80385i | −0.0695878 | + | 0.120530i | ||||
\(997\) | 20.4553 | + | 5.48099i | 0.647827 | + | 0.173585i | 0.567746 | − | 0.823204i | \(-0.307816\pi\) |
0.0800807 | + | 0.996788i | \(0.474482\pi\) | |||||||
\(998\) | −17.0077 | − | 4.55721i | −0.538370 | − | 0.144256i | ||||
\(999\) | −13.8564 | + | 24.0000i | −0.438397 | + | 0.759326i |
(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 | 350.2.o.b.257.1 | yes | 8 | |
5.2 | odd | 4 | 350.2.o.a.243.1 | yes | 8 | ||
5.3 | odd | 4 | 350.2.o.a.243.2 | yes | 8 | ||
5.4 | even | 2 | inner | 350.2.o.b.257.2 | yes | 8 | |
7.3 | odd | 6 | 350.2.o.a.157.2 | yes | 8 | ||
35.3 | even | 12 | inner | 350.2.o.b.143.1 | yes | 8 | |
35.17 | even | 12 | inner | 350.2.o.b.143.2 | yes | 8 | |
35.24 | odd | 6 | 350.2.o.a.157.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
350.2.o.a.157.1 | ✓ | 8 | 35.24 | odd | 6 | ||
350.2.o.a.157.2 | yes | 8 | 7.3 | odd | 6 | ||
350.2.o.a.243.1 | yes | 8 | 5.2 | odd | 4 | ||
350.2.o.a.243.2 | yes | 8 | 5.3 | odd | 4 | ||
350.2.o.b.143.1 | yes | 8 | 35.3 | even | 12 | inner | |
350.2.o.b.143.2 | yes | 8 | 35.17 | even | 12 | inner | |
350.2.o.b.257.1 | yes | 8 | 1.1 | even | 1 | trivial | |
350.2.o.b.257.2 | yes | 8 | 5.4 | even | 2 | inner |