Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(367,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.367");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.j (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 367.2 | ||
Character | \(\chi\) | \(=\) | 690.367 |
Dual form | 690.2.j.b.643.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −1.07661 | + | 1.95982i | −0.481475 | + | 0.876460i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 3.43458 | − | 3.43458i | 1.29815 | − | 1.29815i | 0.368533 | − | 0.929615i | \(-0.379860\pi\) |
0.929615 | − | 0.368533i | \(-0.120140\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 2.14708 | − | 0.624526i | 0.678967 | − | 0.197492i | ||||
\(11\) | 1.77870i | 0.536299i | 0.963377 | + | 0.268149i | \(0.0864121\pi\) | ||||
−0.963377 | + | 0.268149i | \(0.913588\pi\) | |||||||
\(12\) | −0.707107 | − | 0.707107i | −0.204124 | − | 0.204124i | ||||
\(13\) | 1.21834 | − | 1.21834i | 0.337906 | − | 0.337906i | −0.517673 | − | 0.855579i | \(-0.673202\pi\) |
0.855579 | + | 0.517673i | \(0.173202\pi\) | |||||||
\(14\) | −4.85722 | −1.29815 | ||||||||
\(15\) | −0.624526 | − | 2.14708i | −0.161252 | − | 0.554375i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −1.12442 | + | 1.12442i | −0.272711 | + | 0.272711i | −0.830191 | − | 0.557480i | \(-0.811768\pi\) |
0.557480 | + | 0.830191i | \(0.311768\pi\) | |||||||
\(18\) | −0.707107 | + | 0.707107i | −0.166667 | + | 0.166667i | ||||
\(19\) | −2.57499 | −0.590742 | −0.295371 | − | 0.955383i | \(-0.595443\pi\) | ||||
−0.295371 | + | 0.955383i | \(0.595443\pi\) | |||||||
\(20\) | −1.95982 | − | 1.07661i | −0.438230 | − | 0.240737i | ||||
\(21\) | 4.85722i | 1.05993i | ||||||||
\(22\) | 1.25773 | − | 1.25773i | 0.268149 | − | 0.268149i | ||||
\(23\) | 4.76859 | + | 0.510395i | 0.994321 | + | 0.106425i | ||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | −2.68182 | − | 4.21993i | −0.536364 | − | 0.843987i | ||||
\(26\) | −1.72299 | −0.337906 | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 3.43458 | + | 3.43458i | 0.649074 | + | 0.649074i | ||||
\(29\) | − | 3.23574i | − | 0.600862i | −0.953804 | − | 0.300431i | \(-0.902870\pi\) | ||
0.953804 | − | 0.300431i | \(-0.0971305\pi\) | |||||||
\(30\) | −1.07661 | + | 1.95982i | −0.196561 | + | 0.357813i | ||||
\(31\) | 6.41786 | 1.15268 | 0.576341 | − | 0.817209i | \(-0.304480\pi\) | ||||
0.576341 | + | 0.817209i | \(0.304480\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | −1.25773 | − | 1.25773i | −0.218943 | − | 0.218943i | ||||
\(34\) | 1.59016 | 0.272711 | ||||||||
\(35\) | 3.03346 | + | 10.4289i | 0.512749 | + | 1.76280i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.321856 | − | 0.321856i | 0.0529127 | − | 0.0529127i | −0.680155 | − | 0.733068i | \(-0.738088\pi\) |
0.733068 | + | 0.680155i | \(0.238088\pi\) | |||||||
\(38\) | 1.82079 | + | 1.82079i | 0.295371 | + | 0.295371i | ||||
\(39\) | 1.72299i | 0.275899i | ||||||||
\(40\) | 0.624526 | + | 2.14708i | 0.0987462 | + | 0.339484i | ||||
\(41\) | 10.2290 | 1.59750 | 0.798750 | − | 0.601663i | \(-0.205495\pi\) | ||||
0.798750 | + | 0.601663i | \(0.205495\pi\) | |||||||
\(42\) | 3.43458 | − | 3.43458i | 0.529967 | − | 0.529967i | ||||
\(43\) | 6.47101 | + | 6.47101i | 0.986820 | + | 0.986820i | 0.999914 | − | 0.0130943i | \(-0.00416818\pi\) |
−0.0130943 | + | 0.999914i | \(0.504168\pi\) | |||||||
\(44\) | −1.77870 | −0.268149 | ||||||||
\(45\) | 1.95982 | + | 1.07661i | 0.292153 | + | 0.160492i | ||||
\(46\) | −3.01100 | − | 3.73281i | −0.443948 | − | 0.550373i | ||||
\(47\) | 9.10509 | + | 9.10509i | 1.32811 | + | 1.32811i | 0.907014 | + | 0.421100i | \(0.138356\pi\) |
0.421100 | + | 0.907014i | \(0.361644\pi\) | |||||||
\(48\) | 0.707107 | − | 0.707107i | 0.102062 | − | 0.102062i | ||||
\(49\) | − | 16.5926i | − | 2.37038i | ||||||
\(50\) | −1.08761 | + | 4.88028i | −0.153812 | + | 0.690175i | ||||
\(51\) | − | 1.59016i | − | 0.222667i | ||||||
\(52\) | 1.21834 | + | 1.21834i | 0.168953 | + | 0.168953i | ||||
\(53\) | 6.42643 | + | 6.42643i | 0.882738 | + | 0.882738i | 0.993812 | − | 0.111074i | \(-0.0354290\pi\) |
−0.111074 | + | 0.993812i | \(0.535429\pi\) | |||||||
\(54\) | − | 1.00000i | − | 0.136083i | ||||||
\(55\) | −3.48594 | − | 1.91497i | −0.470044 | − | 0.258214i | ||||
\(56\) | − | 4.85722i | − | 0.649074i | ||||||
\(57\) | 1.82079 | − | 1.82079i | 0.241170 | − | 0.241170i | ||||
\(58\) | −2.28801 | + | 2.28801i | −0.300431 | + | 0.300431i | ||||
\(59\) | − | 10.4081i | − | 1.35502i | −0.735514 | − | 0.677510i | \(-0.763059\pi\) | ||
0.735514 | − | 0.677510i | \(-0.236941\pi\) | |||||||
\(60\) | 2.14708 | − | 0.624526i | 0.277187 | − | 0.0806260i | ||||
\(61\) | 14.4727i | 1.85303i | 0.376252 | + | 0.926517i | \(0.377213\pi\) | ||||
−0.376252 | + | 0.926517i | \(0.622787\pi\) | |||||||
\(62\) | −4.53812 | − | 4.53812i | −0.576341 | − | 0.576341i | ||||
\(63\) | −3.43458 | − | 3.43458i | −0.432716 | − | 0.432716i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 1.07605 | + | 3.69940i | 0.133468 | + | 0.458854i | ||||
\(66\) | 1.77870i | 0.218943i | ||||||||
\(67\) | 0.586681 | − | 0.586681i | 0.0716745 | − | 0.0716745i | −0.670361 | − | 0.742035i | \(-0.733861\pi\) |
0.742035 | + | 0.670361i | \(0.233861\pi\) | |||||||
\(68\) | −1.12442 | − | 1.12442i | −0.136355 | − | 0.136355i | ||||
\(69\) | −3.73281 | + | 3.01100i | −0.449377 | + | 0.362482i | ||||
\(70\) | 5.22934 | − | 9.51930i | 0.625026 | − | 1.13777i | ||||
\(71\) | −13.3156 | −1.58027 | −0.790137 | − | 0.612931i | \(-0.789990\pi\) | ||||
−0.790137 | + | 0.612931i | \(0.789990\pi\) | |||||||
\(72\) | −0.707107 | − | 0.707107i | −0.0833333 | − | 0.0833333i | ||||
\(73\) | 3.84689 | − | 3.84689i | 0.450245 | − | 0.450245i | −0.445191 | − | 0.895436i | \(-0.646864\pi\) |
0.895436 | + | 0.445191i | \(0.146864\pi\) | |||||||
\(74\) | −0.455173 | −0.0529127 | ||||||||
\(75\) | 4.88028 | + | 1.08761i | 0.563526 | + | 0.125587i | ||||
\(76\) | − | 2.57499i | − | 0.295371i | ||||||
\(77\) | 6.10909 | + | 6.10909i | 0.696195 | + | 0.696195i | ||||
\(78\) | 1.21834 | − | 1.21834i | 0.137950 | − | 0.137950i | ||||
\(79\) | −6.55768 | −0.737796 | −0.368898 | − | 0.929470i | \(-0.620265\pi\) | ||||
−0.368898 | + | 0.929470i | \(0.620265\pi\) | |||||||
\(80\) | 1.07661 | − | 1.95982i | 0.120369 | − | 0.219115i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −7.23299 | − | 7.23299i | −0.798750 | − | 0.798750i | ||||
\(83\) | −2.56461 | − | 2.56461i | −0.281502 | − | 0.281502i | 0.552206 | − | 0.833708i | \(-0.313786\pi\) |
−0.833708 | + | 0.552206i | \(0.813786\pi\) | |||||||
\(84\) | −4.85722 | −0.529967 | ||||||||
\(85\) | −0.993099 | − | 3.41421i | −0.107717 | − | 0.370323i | ||||
\(86\) | − | 9.15139i | − | 0.986820i | ||||||
\(87\) | 2.28801 | + | 2.28801i | 0.245301 | + | 0.245301i | ||||
\(88\) | 1.25773 | + | 1.25773i | 0.134075 | + | 0.134075i | ||||
\(89\) | −3.44952 | −0.365648 | −0.182824 | − | 0.983146i | \(-0.558524\pi\) | ||||
−0.182824 | + | 0.983146i | \(0.558524\pi\) | |||||||
\(90\) | −0.624526 | − | 2.14708i | −0.0658308 | − | 0.226322i | ||||
\(91\) | − | 8.36895i | − | 0.877304i | ||||||
\(92\) | −0.510395 | + | 4.76859i | −0.0532123 | + | 0.497160i | ||||
\(93\) | −4.53812 | + | 4.53812i | −0.470581 | + | 0.470581i | ||||
\(94\) | − | 12.8765i | − | 1.32811i | ||||||
\(95\) | 2.77226 | − | 5.04652i | 0.284428 | − | 0.517762i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 7.79375 | − | 7.79375i | 0.791335 | − | 0.791335i | −0.190376 | − | 0.981711i | \(-0.560971\pi\) |
0.981711 | + | 0.190376i | \(0.0609707\pi\) | |||||||
\(98\) | −11.7328 | + | 11.7328i | −1.18519 | + | 1.18519i | ||||
\(99\) | 1.77870 | 0.178766 | ||||||||
\(100\) | 4.21993 | − | 2.68182i | 0.421993 | − | 0.268182i | ||||
\(101\) | 0.109089 | 0.0108547 | 0.00542736 | − | 0.999985i | \(-0.498272\pi\) | ||||
0.00542736 | + | 0.999985i | \(0.498272\pi\) | |||||||
\(102\) | −1.12442 | + | 1.12442i | −0.111334 | + | 0.111334i | ||||
\(103\) | −0.451663 | − | 0.451663i | −0.0445037 | − | 0.0445037i | 0.684505 | − | 0.729008i | \(-0.260019\pi\) |
−0.729008 | + | 0.684505i | \(0.760019\pi\) | |||||||
\(104\) | − | 1.72299i | − | 0.168953i | ||||||
\(105\) | −9.51930 | − | 5.22934i | −0.928989 | − | 0.510331i | ||||
\(106\) | − | 9.08835i | − | 0.882738i | ||||||
\(107\) | −5.06879 | + | 5.06879i | −0.490018 | + | 0.490018i | −0.908312 | − | 0.418293i | \(-0.862628\pi\) |
0.418293 | + | 0.908312i | \(0.362628\pi\) | |||||||
\(108\) | −0.707107 | + | 0.707107i | −0.0680414 | + | 0.0680414i | ||||
\(109\) | 7.67531 | 0.735161 | 0.367581 | − | 0.929992i | \(-0.380186\pi\) | ||||
0.367581 | + | 0.929992i | \(0.380186\pi\) | |||||||
\(110\) | 1.11085 | + | 3.81902i | 0.105915 | + | 0.364129i | ||||
\(111\) | 0.455173i | 0.0432031i | ||||||||
\(112\) | −3.43458 | + | 3.43458i | −0.324537 | + | 0.324537i | ||||
\(113\) | −10.3565 | − | 10.3565i | −0.974254 | − | 0.974254i | 0.0254229 | − | 0.999677i | \(-0.491907\pi\) |
−0.999677 | + | 0.0254229i | \(0.991907\pi\) | |||||||
\(114\) | −2.57499 | −0.241170 | ||||||||
\(115\) | −6.13420 | + | 8.79611i | −0.572017 | + | 0.820241i | ||||
\(116\) | 3.23574 | 0.300431 | ||||||||
\(117\) | −1.21834 | − | 1.21834i | −0.112635 | − | 0.112635i | ||||
\(118\) | −7.35964 | + | 7.35964i | −0.677510 | + | 0.677510i | ||||
\(119\) | 7.72378i | 0.708038i | ||||||||
\(120\) | −1.95982 | − | 1.07661i | −0.178907 | − | 0.0982807i | ||||
\(121\) | 7.83622 | 0.712384 | ||||||||
\(122\) | 10.2337 | − | 10.2337i | 0.926517 | − | 0.926517i | ||||
\(123\) | −7.23299 | + | 7.23299i | −0.652177 | + | 0.652177i | ||||
\(124\) | 6.41786i | 0.576341i | ||||||||
\(125\) | 11.1576 | − | 0.712667i | 0.997966 | − | 0.0637429i | ||||
\(126\) | 4.85722i | 0.432716i | ||||||||
\(127\) | 8.30451 | + | 8.30451i | 0.736906 | + | 0.736906i | 0.971978 | − | 0.235072i | \(-0.0755326\pi\) |
−0.235072 | + | 0.971978i | \(0.575533\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | −9.15139 | −0.805735 | ||||||||
\(130\) | 1.85499 | − | 3.37676i | 0.162693 | − | 0.296161i | ||||
\(131\) | −12.6605 | −1.10615 | −0.553077 | − | 0.833130i | \(-0.686546\pi\) | ||||
−0.553077 | + | 0.833130i | \(0.686546\pi\) | |||||||
\(132\) | 1.25773 | − | 1.25773i | 0.109472 | − | 0.109472i | ||||
\(133\) | −8.84399 | + | 8.84399i | −0.766871 | + | 0.766871i | ||||
\(134\) | −0.829692 | −0.0716745 | ||||||||
\(135\) | −2.14708 | + | 0.624526i | −0.184792 | + | 0.0537506i | ||||
\(136\) | 1.59016i | 0.136355i | ||||||||
\(137\) | −1.04108 | + | 1.04108i | −0.0889456 | + | 0.0889456i | −0.750180 | − | 0.661234i | \(-0.770033\pi\) |
0.661234 | + | 0.750180i | \(0.270033\pi\) | |||||||
\(138\) | 4.76859 | + | 0.510395i | 0.405930 | + | 0.0434477i | ||||
\(139\) | 8.89535i | 0.754494i | 0.926113 | + | 0.377247i | \(0.123129\pi\) | ||||
−0.926113 | + | 0.377247i | \(0.876871\pi\) | |||||||
\(140\) | −10.4289 | + | 3.03346i | −0.881400 | + | 0.256374i | ||||
\(141\) | −12.8765 | −1.08440 | ||||||||
\(142\) | 9.41557 | + | 9.41557i | 0.790137 | + | 0.790137i | ||||
\(143\) | 2.16706 | + | 2.16706i | 0.181219 | + | 0.181219i | ||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | 6.34148 | + | 3.48363i | 0.526631 | + | 0.289300i | ||||
\(146\) | −5.44033 | −0.450245 | ||||||||
\(147\) | 11.7328 | + | 11.7328i | 0.967702 | + | 0.967702i | ||||
\(148\) | 0.321856 | + | 0.321856i | 0.0264564 | + | 0.0264564i | ||||
\(149\) | −11.3358 | −0.928666 | −0.464333 | − | 0.885661i | \(-0.653706\pi\) | ||||
−0.464333 | + | 0.885661i | \(0.653706\pi\) | |||||||
\(150\) | −2.68182 | − | 4.21993i | −0.218970 | − | 0.344556i | ||||
\(151\) | −8.75190 | −0.712219 | −0.356110 | − | 0.934444i | \(-0.615897\pi\) | ||||
−0.356110 | + | 0.934444i | \(0.615897\pi\) | |||||||
\(152\) | −1.82079 | + | 1.82079i | −0.147686 | + | 0.147686i | ||||
\(153\) | 1.12442 | + | 1.12442i | 0.0909036 | + | 0.0909036i | ||||
\(154\) | − | 8.63956i | − | 0.696195i | ||||||
\(155\) | −6.90954 | + | 12.5779i | −0.554988 | + | 1.01028i | ||||
\(156\) | −1.72299 | −0.137950 | ||||||||
\(157\) | 14.2015 | − | 14.2015i | 1.13340 | − | 1.13340i | 0.143791 | − | 0.989608i | \(-0.454071\pi\) |
0.989608 | − | 0.143791i | \(-0.0459294\pi\) | |||||||
\(158\) | 4.63698 | + | 4.63698i | 0.368898 | + | 0.368898i | ||||
\(159\) | −9.08835 | −0.720753 | ||||||||
\(160\) | −2.14708 | + | 0.624526i | −0.169742 | + | 0.0493731i | ||||
\(161\) | 18.1311 | − | 14.6251i | 1.42893 | − | 1.15262i | ||||
\(162\) | 0.707107 | + | 0.707107i | 0.0555556 | + | 0.0555556i | ||||
\(163\) | −3.88265 | + | 3.88265i | −0.304113 | + | 0.304113i | −0.842621 | − | 0.538508i | \(-0.818988\pi\) |
0.538508 | + | 0.842621i | \(0.318988\pi\) | |||||||
\(164\) | 10.2290i | 0.798750i | ||||||||
\(165\) | 3.81902 | − | 1.11085i | 0.297310 | − | 0.0864792i | ||||
\(166\) | 3.62690i | 0.281502i | ||||||||
\(167\) | −6.37019 | − | 6.37019i | −0.492940 | − | 0.492940i | 0.416291 | − | 0.909231i | \(-0.363330\pi\) |
−0.909231 | + | 0.416291i | \(0.863330\pi\) | |||||||
\(168\) | 3.43458 | + | 3.43458i | 0.264983 | + | 0.264983i | ||||
\(169\) | 10.0313i | 0.771639i | ||||||||
\(170\) | −1.71199 | + | 3.11644i | −0.131303 | + | 0.239020i | ||||
\(171\) | 2.57499i | 0.196914i | ||||||||
\(172\) | −6.47101 | + | 6.47101i | −0.493410 | + | 0.493410i | ||||
\(173\) | 6.60779 | − | 6.60779i | 0.502381 | − | 0.502381i | −0.409796 | − | 0.912177i | \(-0.634400\pi\) |
0.912177 | + | 0.409796i | \(0.134400\pi\) | |||||||
\(174\) | − | 3.23574i | − | 0.245301i | ||||||
\(175\) | −23.7046 | − | 5.28277i | −1.79190 | − | 0.399340i | ||||
\(176\) | − | 1.77870i | − | 0.134075i | ||||||
\(177\) | 7.35964 | + | 7.35964i | 0.553184 | + | 0.553184i | ||||
\(178\) | 2.43918 | + | 2.43918i | 0.182824 | + | 0.182824i | ||||
\(179\) | − | 0.676121i | − | 0.0505357i | −0.999681 | − | 0.0252678i | \(-0.991956\pi\) | ||
0.999681 | − | 0.0252678i | \(-0.00804386\pi\) | |||||||
\(180\) | −1.07661 | + | 1.95982i | −0.0802458 | + | 0.146077i | ||||
\(181\) | − | 17.9595i | − | 1.33492i | −0.744647 | − | 0.667458i | \(-0.767382\pi\) | ||
0.744647 | − | 0.667458i | \(-0.232618\pi\) | |||||||
\(182\) | −5.91774 | + | 5.91774i | −0.438652 | + | 0.438652i | ||||
\(183\) | −10.2337 | − | 10.2337i | −0.756498 | − | 0.756498i | ||||
\(184\) | 3.73281 | − | 3.01100i | 0.275186 | − | 0.221974i | ||||
\(185\) | 0.284267 | + | 0.977294i | 0.0208997 | + | 0.0718521i | ||||
\(186\) | 6.41786 | 0.470581 | ||||||||
\(187\) | −2.00000 | − | 2.00000i | −0.146254 | − | 0.146254i | ||||
\(188\) | −9.10509 | + | 9.10509i | −0.664057 | + | 0.664057i | ||||
\(189\) | 4.85722 | 0.353311 | ||||||||
\(190\) | −5.52871 | + | 1.60815i | −0.401095 | + | 0.116667i | ||||
\(191\) | − | 12.7383i | − | 0.921709i | −0.887476 | − | 0.460855i | \(-0.847543\pi\) | ||
0.887476 | − | 0.460855i | \(-0.152457\pi\) | |||||||
\(192\) | 0.707107 | + | 0.707107i | 0.0510310 | + | 0.0510310i | ||||
\(193\) | −1.84399 | + | 1.84399i | −0.132733 | + | 0.132733i | −0.770352 | − | 0.637619i | \(-0.779919\pi\) |
0.637619 | + | 0.770352i | \(0.279919\pi\) | |||||||
\(194\) | −11.0220 | −0.791335 | ||||||||
\(195\) | −3.37676 | − | 1.85499i | −0.241814 | − | 0.132838i | ||||
\(196\) | 16.5926 | 1.18519 | ||||||||
\(197\) | −12.1629 | − | 12.1629i | −0.866568 | − | 0.866568i | 0.125523 | − | 0.992091i | \(-0.459939\pi\) |
−0.992091 | + | 0.125523i | \(0.959939\pi\) | |||||||
\(198\) | −1.25773 | − | 1.25773i | −0.0893831 | − | 0.0893831i | ||||
\(199\) | −5.37229 | −0.380832 | −0.190416 | − | 0.981704i | \(-0.560984\pi\) | ||||
−0.190416 | + | 0.981704i | \(0.560984\pi\) | |||||||
\(200\) | −4.88028 | − | 1.08761i | −0.345088 | − | 0.0769058i | ||||
\(201\) | 0.829692i | 0.0585219i | ||||||||
\(202\) | −0.0771372 | − | 0.0771372i | −0.00542736 | − | 0.00542736i | ||||
\(203\) | −11.1134 | − | 11.1134i | −0.780007 | − | 0.780007i | ||||
\(204\) | 1.59016 | 0.111334 | ||||||||
\(205\) | −11.0126 | + | 20.0470i | −0.769156 | + | 1.40014i | ||||
\(206\) | 0.638749i | 0.0445037i | ||||||||
\(207\) | 0.510395 | − | 4.76859i | 0.0354749 | − | 0.331440i | ||||
\(208\) | −1.21834 | + | 1.21834i | −0.0844765 | + | 0.0844765i | ||||
\(209\) | − | 4.58013i | − | 0.316814i | ||||||
\(210\) | 3.03346 | + | 10.4289i | 0.209329 | + | 0.719660i | ||||
\(211\) | 8.05312 | 0.554400 | 0.277200 | − | 0.960812i | \(-0.410594\pi\) | ||||
0.277200 | + | 0.960812i | \(0.410594\pi\) | |||||||
\(212\) | −6.42643 | + | 6.42643i | −0.441369 | + | 0.441369i | ||||
\(213\) | 9.41557 | − | 9.41557i | 0.645144 | − | 0.645144i | ||||
\(214\) | 7.16835 | 0.490018 | ||||||||
\(215\) | −19.6488 | + | 5.71528i | −1.34004 | + | 0.389779i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 22.0426 | − | 22.0426i | 1.49635 | − | 1.49635i | ||||
\(218\) | −5.42726 | − | 5.42726i | −0.367581 | − | 0.367581i | ||||
\(219\) | 5.44033i | 0.367623i | ||||||||
\(220\) | 1.91497 | − | 3.48594i | 0.129107 | − | 0.235022i | ||||
\(221\) | 2.73983i | 0.184301i | ||||||||
\(222\) | 0.321856 | − | 0.321856i | 0.0216015 | − | 0.0216015i | ||||
\(223\) | 7.99544 | − | 7.99544i | 0.535414 | − | 0.535414i | −0.386764 | − | 0.922179i | \(-0.626407\pi\) |
0.922179 | + | 0.386764i | \(0.126407\pi\) | |||||||
\(224\) | 4.85722 | 0.324537 | ||||||||
\(225\) | −4.21993 | + | 2.68182i | −0.281329 | + | 0.178788i | ||||
\(226\) | 14.6462i | 0.974254i | ||||||||
\(227\) | −13.1571 | + | 13.1571i | −0.873268 | + | 0.873268i | −0.992827 | − | 0.119559i | \(-0.961852\pi\) |
0.119559 | + | 0.992827i | \(0.461852\pi\) | |||||||
\(228\) | 1.82079 | + | 1.82079i | 0.120585 | + | 0.120585i | ||||
\(229\) | −6.27877 | −0.414913 | −0.207456 | − | 0.978244i | \(-0.566518\pi\) | ||||
−0.207456 | + | 0.978244i | \(0.566518\pi\) | |||||||
\(230\) | 10.5573 | − | 1.88225i | 0.696129 | − | 0.124112i | ||||
\(231\) | −8.63956 | −0.568441 | ||||||||
\(232\) | −2.28801 | − | 2.28801i | −0.150215 | − | 0.150215i | ||||
\(233\) | 11.9743 | − | 11.9743i | 0.784465 | − | 0.784465i | −0.196116 | − | 0.980581i | \(-0.562833\pi\) |
0.980581 | + | 0.196116i | \(0.0628329\pi\) | |||||||
\(234\) | 1.72299i | 0.112635i | ||||||||
\(235\) | −27.6470 | + | 8.04174i | −1.80349 | + | 0.524585i | ||||
\(236\) | 10.4081 | 0.677510 | ||||||||
\(237\) | 4.63698 | − | 4.63698i | 0.301204 | − | 0.301204i | ||||
\(238\) | 5.46154 | − | 5.46154i | 0.354019 | − | 0.354019i | ||||
\(239\) | − | 4.39325i | − | 0.284176i | −0.989854 | − | 0.142088i | \(-0.954618\pi\) | ||
0.989854 | − | 0.142088i | \(-0.0453816\pi\) | |||||||
\(240\) | 0.624526 | + | 2.14708i | 0.0403130 | + | 0.138594i | ||||
\(241\) | − | 7.44107i | − | 0.479321i | −0.970857 | − | 0.239661i | \(-0.922964\pi\) | ||
0.970857 | − | 0.239661i | \(-0.0770362\pi\) | |||||||
\(242\) | −5.54104 | − | 5.54104i | −0.356192 | − | 0.356192i | ||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | −14.4727 | −0.926517 | ||||||||
\(245\) | 32.5186 | + | 17.8638i | 2.07754 | + | 1.14128i | ||||
\(246\) | 10.2290 | 0.652177 | ||||||||
\(247\) | −3.13720 | + | 3.13720i | −0.199615 | + | 0.199615i | ||||
\(248\) | 4.53812 | − | 4.53812i | 0.288171 | − | 0.288171i | ||||
\(249\) | 3.62690 | 0.229845 | ||||||||
\(250\) | −8.39355 | − | 7.38569i | −0.530855 | − | 0.467112i | ||||
\(251\) | 12.7768i | 0.806466i | 0.915097 | + | 0.403233i | \(0.132114\pi\) | ||||
−0.915097 | + | 0.403233i | \(0.867886\pi\) | |||||||
\(252\) | 3.43458 | − | 3.43458i | 0.216358 | − | 0.216358i | ||||
\(253\) | −0.907840 | + | 8.48191i | −0.0570754 | + | 0.533253i | ||||
\(254\) | − | 11.7443i | − | 0.736906i | ||||||
\(255\) | 3.11644 | + | 1.71199i | 0.195159 | + | 0.107209i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.2990 | − | 12.2990i | −0.767192 | − | 0.767192i | 0.210420 | − | 0.977611i | \(-0.432517\pi\) |
−0.977611 | + | 0.210420i | \(0.932517\pi\) | |||||||
\(258\) | 6.47101 | + | 6.47101i | 0.402868 | + | 0.402868i | ||||
\(259\) | − | 2.21088i | − | 0.137377i | ||||||
\(260\) | −3.69940 | + | 1.07605i | −0.229427 | + | 0.0667339i | ||||
\(261\) | −3.23574 | −0.200287 | ||||||||
\(262\) | 8.95233 | + | 8.95233i | 0.553077 | + | 0.553077i | ||||
\(263\) | 0.838721 | + | 0.838721i | 0.0517177 | + | 0.0517177i | 0.732493 | − | 0.680775i | \(-0.238357\pi\) |
−0.680775 | + | 0.732493i | \(0.738357\pi\) | |||||||
\(264\) | −1.77870 | −0.109472 | ||||||||
\(265\) | −19.5134 | + | 5.67591i | −1.19870 | + | 0.348668i | ||||
\(266\) | 12.5073 | 0.766871 | ||||||||
\(267\) | 2.43918 | − | 2.43918i | 0.149275 | − | 0.149275i | ||||
\(268\) | 0.586681 | + | 0.586681i | 0.0358372 | + | 0.0358372i | ||||
\(269\) | 25.8476i | 1.57595i | 0.615704 | + | 0.787977i | \(0.288872\pi\) | ||||
−0.615704 | + | 0.787977i | \(0.711128\pi\) | |||||||
\(270\) | 1.95982 | + | 1.07661i | 0.119271 | + | 0.0655204i | ||||
\(271\) | −32.0433 | −1.94649 | −0.973246 | − | 0.229764i | \(-0.926205\pi\) | ||||
−0.973246 | + | 0.229764i | \(0.926205\pi\) | |||||||
\(272\) | 1.12442 | − | 1.12442i | 0.0681777 | − | 0.0681777i | ||||
\(273\) | 5.91774 | + | 5.91774i | 0.358158 | + | 0.358158i | ||||
\(274\) | 1.47231 | 0.0889456 | ||||||||
\(275\) | 7.50601 | − | 4.77016i | 0.452629 | − | 0.287651i | ||||
\(276\) | −3.01100 | − | 3.73281i | −0.181241 | − | 0.224689i | ||||
\(277\) | −18.2414 | − | 18.2414i | −1.09602 | − | 1.09602i | −0.994871 | − | 0.101147i | \(-0.967749\pi\) |
−0.101147 | − | 0.994871i | \(-0.532251\pi\) | |||||||
\(278\) | 6.28997 | − | 6.28997i | 0.377247 | − | 0.377247i | ||||
\(279\) | − | 6.41786i | − | 0.384227i | ||||||
\(280\) | 9.51930 | + | 5.22934i | 0.568887 | + | 0.312513i | ||||
\(281\) | − | 3.19489i | − | 0.190591i | −0.995449 | − | 0.0952954i | \(-0.969620\pi\) | ||
0.995449 | − | 0.0952954i | \(-0.0303796\pi\) | |||||||
\(282\) | 9.10509 | + | 9.10509i | 0.542200 | + | 0.542200i | ||||
\(283\) | 22.6171 | + | 22.6171i | 1.34444 | + | 1.34444i | 0.891579 | + | 0.452865i | \(0.149598\pi\) |
0.452865 | + | 0.891579i | \(0.350402\pi\) | |||||||
\(284\) | − | 13.3156i | − | 0.790137i | ||||||
\(285\) | 1.60815 | + | 5.52871i | 0.0952583 | + | 0.327493i | ||||
\(286\) | − | 3.06468i | − | 0.181219i | ||||||
\(287\) | 35.1323 | − | 35.1323i | 2.07379 | − | 2.07379i | ||||
\(288\) | 0.707107 | − | 0.707107i | 0.0416667 | − | 0.0416667i | ||||
\(289\) | 14.4714i | 0.851258i | ||||||||
\(290\) | −2.02080 | − | 6.94740i | −0.118666 | − | 0.407965i | ||||
\(291\) | 11.0220i | 0.646123i | ||||||||
\(292\) | 3.84689 | + | 3.84689i | 0.225122 | + | 0.225122i | ||||
\(293\) | −2.26468 | − | 2.26468i | −0.132304 | − | 0.132304i | 0.637854 | − | 0.770158i | \(-0.279823\pi\) |
−0.770158 | + | 0.637854i | \(0.779823\pi\) | |||||||
\(294\) | − | 16.5926i | − | 0.967702i | ||||||
\(295\) | 20.3981 | + | 11.2055i | 1.18762 | + | 0.652408i | ||||
\(296\) | − | 0.455173i | − | 0.0264564i | ||||||
\(297\) | −1.25773 | + | 1.25773i | −0.0729810 | + | 0.0729810i | ||||
\(298\) | 8.01563 | + | 8.01563i | 0.464333 | + | 0.464333i | ||||
\(299\) | 6.43159 | − | 5.18792i | 0.371948 | − | 0.300025i | ||||
\(300\) | −1.08761 | + | 4.88028i | −0.0627933 | + | 0.281763i | ||||
\(301\) | 44.4504 | 2.56208 | ||||||||
\(302\) | 6.18852 | + | 6.18852i | 0.356110 | + | 0.356110i | ||||
\(303\) | −0.0771372 | + | 0.0771372i | −0.00443142 | + | 0.00443142i | ||||
\(304\) | 2.57499 | 0.147686 | ||||||||
\(305\) | −28.3639 | − | 15.5814i | −1.62411 | − | 0.892190i | ||||
\(306\) | − | 1.59016i | − | 0.0909036i | ||||||
\(307\) | 6.36515 | + | 6.36515i | 0.363278 | + | 0.363278i | 0.865018 | − | 0.501740i | \(-0.167307\pi\) |
−0.501740 | + | 0.865018i | \(0.667307\pi\) | |||||||
\(308\) | −6.10909 | + | 6.10909i | −0.348098 | + | 0.348098i | ||||
\(309\) | 0.638749 | 0.0363371 | ||||||||
\(310\) | 13.7797 | − | 4.00812i | 0.782634 | − | 0.227646i | ||||
\(311\) | 11.5795 | 0.656615 | 0.328307 | − | 0.944571i | \(-0.393522\pi\) | ||||
0.328307 | + | 0.944571i | \(0.393522\pi\) | |||||||
\(312\) | 1.21834 | + | 1.21834i | 0.0689748 | + | 0.0689748i | ||||
\(313\) | 0.636677 | + | 0.636677i | 0.0359871 | + | 0.0359871i | 0.724871 | − | 0.688884i | \(-0.241899\pi\) |
−0.688884 | + | 0.724871i | \(0.741899\pi\) | |||||||
\(314\) | −20.0839 | −1.13340 | ||||||||
\(315\) | 10.4289 | − | 3.03346i | 0.587600 | − | 0.170916i | ||||
\(316\) | − | 6.55768i | − | 0.368898i | ||||||
\(317\) | 16.8675 | + | 16.8675i | 0.947373 | + | 0.947373i | 0.998683 | − | 0.0513100i | \(-0.0163396\pi\) |
−0.0513100 | + | 0.998683i | \(0.516340\pi\) | |||||||
\(318\) | 6.42643 | + | 6.42643i | 0.360376 | + | 0.360376i | ||||
\(319\) | 5.75542 | 0.322241 | ||||||||
\(320\) | 1.95982 | + | 1.07661i | 0.109557 | + | 0.0601844i | ||||
\(321\) | − | 7.16835i | − | 0.400098i | ||||||
\(322\) | −23.1621 | − | 2.47910i | −1.29078 | − | 0.138155i | ||||
\(323\) | 2.89535 | − | 2.89535i | 0.161102 | − | 0.161102i | ||||
\(324\) | − | 1.00000i | − | 0.0555556i | ||||||
\(325\) | −8.40866 | − | 1.87394i | −0.466429 | − | 0.103948i | ||||
\(326\) | 5.49090 | 0.304113 | ||||||||
\(327\) | −5.42726 | + | 5.42726i | −0.300128 | + | 0.300128i | ||||
\(328\) | 7.23299 | − | 7.23299i | 0.399375 | − | 0.399375i | ||||
\(329\) | 62.5443 | 3.44818 | ||||||||
\(330\) | −3.48594 | − | 1.91497i | −0.191895 | − | 0.105416i | ||||
\(331\) | −9.50258 | −0.522309 | −0.261155 | − | 0.965297i | \(-0.584103\pi\) | ||||
−0.261155 | + | 0.965297i | \(0.584103\pi\) | |||||||
\(332\) | 2.56461 | − | 2.56461i | 0.140751 | − | 0.140751i | ||||
\(333\) | −0.321856 | − | 0.321856i | −0.0176376 | − | 0.0176376i | ||||
\(334\) | 9.00881i | 0.492940i | ||||||||
\(335\) | 0.518164 | + | 1.78142i | 0.0283103 | + | 0.0973292i | ||||
\(336\) | − | 4.85722i | − | 0.264983i | ||||||
\(337\) | −12.5879 | + | 12.5879i | −0.685708 | + | 0.685708i | −0.961280 | − | 0.275572i | \(-0.911133\pi\) |
0.275572 | + | 0.961280i | \(0.411133\pi\) | |||||||
\(338\) | 7.09321 | − | 7.09321i | 0.385820 | − | 0.385820i | ||||
\(339\) | 14.6462 | 0.795475 | ||||||||
\(340\) | 3.41421 | − | 0.993099i | 0.185162 | − | 0.0538583i | ||||
\(341\) | 11.4155i | 0.618182i | ||||||||
\(342\) | 1.82079 | − | 1.82079i | 0.0984571 | − | 0.0984571i | ||||
\(343\) | −32.9466 | − | 32.9466i | −1.77895 | − | 1.77895i | ||||
\(344\) | 9.15139 | 0.493410 | ||||||||
\(345\) | −1.88225 | − | 10.5573i | −0.101337 | − | 0.568387i | ||||
\(346\) | −9.34483 | −0.502381 | ||||||||
\(347\) | −17.5983 | − | 17.5983i | −0.944725 | − | 0.944725i | 0.0538250 | − | 0.998550i | \(-0.482859\pi\) |
−0.998550 | + | 0.0538250i | \(0.982859\pi\) | |||||||
\(348\) | −2.28801 | + | 2.28801i | −0.122650 | + | 0.122650i | ||||
\(349\) | − | 21.7045i | − | 1.16181i | −0.813970 | − | 0.580907i | \(-0.802698\pi\) | ||
0.813970 | − | 0.580907i | \(-0.197302\pi\) | |||||||
\(350\) | 13.0262 | + | 20.4972i | 0.696280 | + | 1.09562i | ||||
\(351\) | 1.72299 | 0.0919664 | ||||||||
\(352\) | −1.25773 | + | 1.25773i | −0.0670374 | + | 0.0670374i | ||||
\(353\) | 13.2550 | − | 13.2550i | 0.705492 | − | 0.705492i | −0.260092 | − | 0.965584i | \(-0.583753\pi\) |
0.965584 | + | 0.260092i | \(0.0837528\pi\) | |||||||
\(354\) | − | 10.4081i | − | 0.553184i | ||||||
\(355\) | 14.3357 | − | 26.0963i | 0.760862 | − | 1.38505i | ||||
\(356\) | − | 3.44952i | − | 0.182824i | ||||||
\(357\) | −5.46154 | − | 5.46154i | −0.289055 | − | 0.289055i | ||||
\(358\) | −0.478090 | + | 0.478090i | −0.0252678 | + | 0.0252678i | ||||
\(359\) | −9.12191 | −0.481436 | −0.240718 | − | 0.970595i | \(-0.577383\pi\) | ||||
−0.240718 | + | 0.970595i | \(0.577383\pi\) | |||||||
\(360\) | 2.14708 | − | 0.624526i | 0.113161 | − | 0.0329154i | ||||
\(361\) | −12.3694 | −0.651023 | ||||||||
\(362\) | −12.6993 | + | 12.6993i | −0.667458 | + | 0.667458i | ||||
\(363\) | −5.54104 | + | 5.54104i | −0.290829 | + | 0.290829i | ||||
\(364\) | 8.36895 | 0.438652 | ||||||||
\(365\) | 3.39762 | + | 11.6808i | 0.177840 | + | 0.611403i | ||||
\(366\) | 14.4727i | 0.756498i | ||||||||
\(367\) | −14.3884 | + | 14.3884i | −0.751067 | + | 0.751067i | −0.974678 | − | 0.223611i | \(-0.928215\pi\) |
0.223611 | + | 0.974678i | \(0.428215\pi\) | |||||||
\(368\) | −4.76859 | − | 0.510395i | −0.248580 | − | 0.0266062i | ||||
\(369\) | − | 10.2290i | − | 0.532500i | ||||||
\(370\) | 0.490044 | − | 0.892058i | 0.0254762 | − | 0.0463759i | ||||
\(371\) | 44.1441 | 2.29185 | ||||||||
\(372\) | −4.53812 | − | 4.53812i | −0.235290 | − | 0.235290i | ||||
\(373\) | −2.31754 | − | 2.31754i | −0.119998 | − | 0.119998i | 0.644558 | − | 0.764556i | \(-0.277041\pi\) |
−0.764556 | + | 0.644558i | \(0.777041\pi\) | |||||||
\(374\) | 2.82843i | 0.146254i | ||||||||
\(375\) | −7.38569 | + | 8.39355i | −0.381395 | + | 0.433441i | ||||
\(376\) | 12.8765 | 0.664057 | ||||||||
\(377\) | −3.94222 | − | 3.94222i | −0.203035 | − | 0.203035i | ||||
\(378\) | −3.43458 | − | 3.43458i | −0.176656 | − | 0.176656i | ||||
\(379\) | −29.3993 | −1.51014 | −0.755070 | − | 0.655644i | \(-0.772397\pi\) | ||||
−0.755070 | + | 0.655644i | \(0.772397\pi\) | |||||||
\(380\) | 5.04652 | + | 2.77226i | 0.258881 | + | 0.142214i | ||||
\(381\) | −11.7443 | −0.601681 | ||||||||
\(382\) | −9.00732 | + | 9.00732i | −0.460855 | + | 0.460855i | ||||
\(383\) | 8.99894 | + | 8.99894i | 0.459824 | + | 0.459824i | 0.898598 | − | 0.438773i | \(-0.144587\pi\) |
−0.438773 | + | 0.898598i | \(0.644587\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | −18.5498 | + | 5.39563i | −0.945388 | + | 0.274987i | ||||
\(386\) | 2.60779 | 0.132733 | ||||||||
\(387\) | 6.47101 | − | 6.47101i | 0.328940 | − | 0.328940i | ||||
\(388\) | 7.79375 | + | 7.79375i | 0.395668 | + | 0.395668i | ||||
\(389\) | −28.2251 | −1.43107 | −0.715534 | − | 0.698578i | \(-0.753817\pi\) | ||||
−0.715534 | + | 0.698578i | \(0.753817\pi\) | |||||||
\(390\) | 1.07605 | + | 3.69940i | 0.0544880 | + | 0.187326i | ||||
\(391\) | −5.93578 | + | 4.78799i | −0.300185 | + | 0.242139i | ||||
\(392\) | −11.7328 | − | 11.7328i | −0.592594 | − | 0.592594i | ||||
\(393\) | 8.95233 | − | 8.95233i | 0.451585 | − | 0.451585i | ||||
\(394\) | 17.2009i | 0.866568i | ||||||||
\(395\) | 7.06007 | − | 12.8519i | 0.355230 | − | 0.646649i | ||||
\(396\) | 1.77870i | 0.0893831i | ||||||||
\(397\) | 8.54761 | + | 8.54761i | 0.428992 | + | 0.428992i | 0.888285 | − | 0.459293i | \(-0.151897\pi\) |
−0.459293 | + | 0.888285i | \(0.651897\pi\) | |||||||
\(398\) | 3.79878 | + | 3.79878i | 0.190416 | + | 0.190416i | ||||
\(399\) | − | 12.5073i | − | 0.626147i | ||||||
\(400\) | 2.68182 | + | 4.21993i | 0.134091 | + | 0.210997i | ||||
\(401\) | 38.2744i | 1.91133i | 0.294451 | + | 0.955667i | \(0.404863\pi\) | ||||
−0.294451 | + | 0.955667i | \(0.595137\pi\) | |||||||
\(402\) | 0.586681 | − | 0.586681i | 0.0292610 | − | 0.0292610i | ||||
\(403\) | 7.81912 | − | 7.81912i | 0.389498 | − | 0.389498i | ||||
\(404\) | 0.109089i | 0.00542736i | ||||||||
\(405\) | 1.07661 | − | 1.95982i | 0.0534972 | − | 0.0973844i | ||||
\(406\) | 15.7167i | 0.780007i | ||||||||
\(407\) | 0.572485 | + | 0.572485i | 0.0283770 | + | 0.0283770i | ||||
\(408\) | −1.12442 | − | 1.12442i | −0.0556669 | − | 0.0556669i | ||||
\(409\) | − | 32.8990i | − | 1.62675i | −0.581738 | − | 0.813376i | \(-0.697627\pi\) | ||
0.581738 | − | 0.813376i | \(-0.302373\pi\) | |||||||
\(410\) | 21.9625 | − | 6.38827i | 1.08465 | − | 0.315494i | ||||
\(411\) | − | 1.47231i | − | 0.0726238i | ||||||
\(412\) | 0.451663 | − | 0.451663i | 0.0222519 | − | 0.0222519i | ||||
\(413\) | −35.7474 | − | 35.7474i | −1.75902 | − | 1.75902i | ||||
\(414\) | −3.73281 | + | 3.01100i | −0.183458 | + | 0.147983i | ||||
\(415\) | 7.78726 | − | 2.26509i | 0.382261 | − | 0.111189i | ||||
\(416\) | 1.72299 | 0.0844765 | ||||||||
\(417\) | −6.28997 | − | 6.28997i | −0.308021 | − | 0.308021i | ||||
\(418\) | −3.23864 | + | 3.23864i | −0.158407 | + | 0.158407i | ||||
\(419\) | 22.0511 | 1.07727 | 0.538634 | − | 0.842540i | \(-0.318941\pi\) | ||||
0.538634 | + | 0.842540i | \(0.318941\pi\) | |||||||
\(420\) | 5.22934 | − | 9.51930i | 0.255166 | − | 0.464495i | ||||
\(421\) | − | 36.8446i | − | 1.79570i | −0.440305 | − | 0.897848i | \(-0.645130\pi\) | ||
0.440305 | − | 0.897848i | \(-0.354870\pi\) | |||||||
\(422\) | −5.69442 | − | 5.69442i | −0.277200 | − | 0.277200i | ||||
\(423\) | 9.10509 | − | 9.10509i | 0.442705 | − | 0.442705i | ||||
\(424\) | 9.08835 | 0.441369 | ||||||||
\(425\) | 7.76044 | + | 1.72948i | 0.376437 | + | 0.0838921i | ||||
\(426\) | −13.3156 | −0.645144 | ||||||||
\(427\) | 49.7075 | + | 49.7075i | 2.40551 | + | 2.40551i | ||||
\(428\) | −5.06879 | − | 5.06879i | −0.245009 | − | 0.245009i | ||||
\(429\) | −3.06468 | −0.147964 | ||||||||
\(430\) | 17.9351 | + | 9.85249i | 0.864908 | + | 0.475129i | ||||
\(431\) | − | 32.4060i | − | 1.56094i | −0.625192 | − | 0.780471i | \(-0.714979\pi\) | ||
0.625192 | − | 0.780471i | \(-0.285021\pi\) | |||||||
\(432\) | −0.707107 | − | 0.707107i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | −1.69960 | − | 1.69960i | −0.0816773 | − | 0.0816773i | 0.665088 | − | 0.746765i | \(-0.268394\pi\) |
−0.746765 | + | 0.665088i | \(0.768394\pi\) | |||||||
\(434\) | −31.1730 | −1.49635 | ||||||||
\(435\) | −6.94740 | + | 2.02080i | −0.333102 | + | 0.0968901i | ||||
\(436\) | 7.67531i | 0.367581i | ||||||||
\(437\) | −12.2791 | − | 1.31426i | −0.587387 | − | 0.0628695i | ||||
\(438\) | 3.84689 | − | 3.84689i | 0.183812 | − | 0.183812i | ||||
\(439\) | 33.8924i | 1.61760i | 0.588085 | + | 0.808799i | \(0.299882\pi\) | ||||
−0.588085 | + | 0.808799i | \(0.700118\pi\) | |||||||
\(440\) | −3.81902 | + | 1.11085i | −0.182065 | + | 0.0529575i | ||||
\(441\) | −16.5926 | −0.790125 | ||||||||
\(442\) | 1.93736 | − | 1.93736i | 0.0921506 | − | 0.0921506i | ||||
\(443\) | 2.44684 | − | 2.44684i | 0.116253 | − | 0.116253i | −0.646587 | − | 0.762840i | \(-0.723804\pi\) |
0.762840 | + | 0.646587i | \(0.223804\pi\) | |||||||
\(444\) | −0.455173 | −0.0216015 | ||||||||
\(445\) | 3.71379 | − | 6.76045i | 0.176050 | − | 0.320476i | ||||
\(446\) | −11.3073 | −0.535414 | ||||||||
\(447\) | 8.01563 | − | 8.01563i | 0.379126 | − | 0.379126i | ||||
\(448\) | −3.43458 | − | 3.43458i | −0.162268 | − | 0.162268i | ||||
\(449\) | − | 4.49307i | − | 0.212041i | −0.994364 | − | 0.106021i | \(-0.966189\pi\) | ||
0.994364 | − | 0.106021i | \(-0.0338110\pi\) | |||||||
\(450\) | 4.88028 | + | 1.08761i | 0.230058 | + | 0.0512705i | ||||
\(451\) | 18.1943i | 0.856738i | ||||||||
\(452\) | 10.3565 | − | 10.3565i | 0.487127 | − | 0.487127i | ||||
\(453\) | 6.18852 | − | 6.18852i | 0.290762 | − | 0.290762i | ||||
\(454\) | 18.6070 | 0.873268 | ||||||||
\(455\) | 16.4017 | + | 9.01010i | 0.768922 | + | 0.422400i | ||||
\(456\) | − | 2.57499i | − | 0.120585i | ||||||
\(457\) | −1.48242 | + | 1.48242i | −0.0693445 | + | 0.0693445i | −0.740928 | − | 0.671584i | \(-0.765614\pi\) |
0.671584 | + | 0.740928i | \(0.265614\pi\) | |||||||
\(458\) | 4.43976 | + | 4.43976i | 0.207456 | + | 0.207456i | ||||
\(459\) | −1.59016 | −0.0742225 | ||||||||
\(460\) | −8.79611 | − | 6.13420i | −0.410121 | − | 0.286009i | ||||
\(461\) | −0.0650793 | −0.00303104 | −0.00151552 | − | 0.999999i | \(-0.500482\pi\) | ||||
−0.00151552 | + | 0.999999i | \(0.500482\pi\) | |||||||
\(462\) | 6.10909 | + | 6.10909i | 0.284221 | + | 0.284221i | ||||
\(463\) | −8.88726 | + | 8.88726i | −0.413026 | + | 0.413026i | −0.882791 | − | 0.469765i | \(-0.844338\pi\) |
0.469765 | + | 0.882791i | \(0.344338\pi\) | |||||||
\(464\) | 3.23574i | 0.150215i | ||||||||
\(465\) | −4.00812 | − | 13.7797i | −0.185872 | − | 0.639018i | ||||
\(466\) | −16.9343 | −0.784465 | ||||||||
\(467\) | −4.47713 | + | 4.47713i | −0.207177 | + | 0.207177i | −0.803066 | − | 0.595889i | \(-0.796800\pi\) |
0.595889 | + | 0.803066i | \(0.296800\pi\) | |||||||
\(468\) | 1.21834 | − | 1.21834i | 0.0563177 | − | 0.0563177i | ||||
\(469\) | − | 4.03000i | − | 0.186088i | ||||||
\(470\) | 25.2358 | + | 13.8630i | 1.16404 | + | 0.639454i | ||||
\(471\) | 20.0839i | 0.925417i | ||||||||
\(472\) | −7.35964 | − | 7.35964i | −0.338755 | − | 0.338755i | ||||
\(473\) | −11.5100 | + | 11.5100i | −0.529230 | + | 0.529230i | ||||
\(474\) | −6.55768 | −0.301204 | ||||||||
\(475\) | 6.90565 | + | 10.8663i | 0.316853 | + | 0.498579i | ||||
\(476\) | −7.72378 | −0.354019 | ||||||||
\(477\) | 6.42643 | − | 6.42643i | 0.294246 | − | 0.294246i | ||||
\(478\) | −3.10650 | + | 3.10650i | −0.142088 | + | 0.142088i | ||||
\(479\) | 33.4775 | 1.52962 | 0.764812 | − | 0.644253i | \(-0.222832\pi\) | ||||
0.764812 | + | 0.644253i | \(0.222832\pi\) | |||||||
\(480\) | 1.07661 | − | 1.95982i | 0.0491403 | − | 0.0894533i | ||||
\(481\) | − | 0.784258i | − | 0.0357591i | ||||||
\(482\) | −5.26163 | + | 5.26163i | −0.239661 | + | 0.239661i | ||||
\(483\) | −2.47910 | + | 23.1621i | −0.112803 | + | 1.05391i | ||||
\(484\) | 7.83622i | 0.356192i | ||||||||
\(485\) | 6.88354 | + | 23.6652i | 0.312566 | + | 1.07458i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −0.188074 | − | 0.188074i | −0.00852246 | − | 0.00852246i | 0.702833 | − | 0.711355i | \(-0.251918\pi\) |
−0.711355 | + | 0.702833i | \(0.751918\pi\) | |||||||
\(488\) | 10.2337 | + | 10.2337i | 0.463259 | + | 0.463259i | ||||
\(489\) | − | 5.49090i | − | 0.248307i | ||||||
\(490\) | −10.3625 | − | 35.6258i | −0.468131 | − | 1.60941i | ||||
\(491\) | −15.9414 | −0.719427 | −0.359713 | − | 0.933063i | \(-0.617126\pi\) | ||||
−0.359713 | + | 0.933063i | \(0.617126\pi\) | |||||||
\(492\) | −7.23299 | − | 7.23299i | −0.326088 | − | 0.326088i | ||||
\(493\) | 3.63831 | + | 3.63831i | 0.163861 | + | 0.163861i | ||||
\(494\) | 4.43667 | 0.199615 | ||||||||
\(495\) | −1.91497 | + | 3.48594i | −0.0860715 | + | 0.156681i | ||||
\(496\) | −6.41786 | −0.288171 | ||||||||
\(497\) | −45.7335 | + | 45.7335i | −2.05143 | + | 2.05143i | ||||
\(498\) | −2.56461 | − | 2.56461i | −0.114923 | − | 0.114923i | ||||
\(499\) | 23.4075i | 1.04786i | 0.851761 | + | 0.523931i | \(0.175535\pi\) | ||||
−0.851761 | + | 0.523931i | \(0.824465\pi\) | |||||||
\(500\) | 0.712667 | + | 11.1576i | 0.0318714 | + | 0.498983i | ||||
\(501\) | 9.00881 | 0.402484 | ||||||||
\(502\) | 9.03458 | − | 9.03458i | 0.403233 | − | 0.403233i | ||||
\(503\) | −11.3295 | − | 11.3295i | −0.505158 | − | 0.505158i | 0.407878 | − | 0.913036i | \(-0.366269\pi\) |
−0.913036 | + | 0.407878i | \(0.866269\pi\) | |||||||
\(504\) | −4.85722 | −0.216358 | ||||||||
\(505\) | −0.117446 | + | 0.213794i | −0.00522627 | + | 0.00951372i | ||||
\(506\) | 6.63956 | − | 5.35568i | 0.295164 | − | 0.238089i | ||||
\(507\) | −7.09321 | − | 7.09321i | −0.315020 | − | 0.315020i | ||||
\(508\) | −8.30451 | + | 8.30451i | −0.368453 | + | 0.368453i | ||||
\(509\) | 21.9841i | 0.974429i | 0.873282 | + | 0.487214i | \(0.161987\pi\) | ||||
−0.873282 | + | 0.487214i | \(0.838013\pi\) | |||||||
\(510\) | −0.993099 | − | 3.41421i | −0.0439751 | − | 0.151184i | ||||
\(511\) | − | 26.4249i | − | 1.16897i | ||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −1.82079 | − | 1.82079i | −0.0803898 | − | 0.0803898i | ||||
\(514\) | 17.3934i | 0.767192i | ||||||||
\(515\) | 1.37145 | − | 0.398915i | 0.0604332 | − | 0.0175783i | ||||
\(516\) | − | 9.15139i | − | 0.402868i | ||||||
\(517\) | −16.1952 | + | 16.1952i | −0.712266 | + | 0.712266i | ||||
\(518\) | −1.56333 | + | 1.56333i | −0.0686886 | + | 0.0686886i | ||||
\(519\) | 9.34483i | 0.410192i | ||||||||
\(520\) | 3.37676 | + | 1.85499i | 0.148081 | + | 0.0813466i | ||||
\(521\) | − | 6.76810i | − | 0.296516i | −0.988949 | − | 0.148258i | \(-0.952633\pi\) | ||
0.988949 | − | 0.148258i | \(-0.0473665\pi\) | |||||||
\(522\) | 2.28801 | + | 2.28801i | 0.100144 | + | 0.100144i | ||||
\(523\) | 12.2965 | + | 12.2965i | 0.537690 | + | 0.537690i | 0.922850 | − | 0.385160i | \(-0.125854\pi\) |
−0.385160 | + | 0.922850i | \(0.625854\pi\) | |||||||
\(524\) | − | 12.6605i | − | 0.553077i | ||||||
\(525\) | 20.4972 | − | 13.0262i | 0.894570 | − | 0.568510i | ||||
\(526\) | − | 1.18613i | − | 0.0517177i | ||||||
\(527\) | −7.21634 | + | 7.21634i | −0.314349 | + | 0.314349i | ||||
\(528\) | 1.25773 | + | 1.25773i | 0.0547358 | + | 0.0547358i | ||||
\(529\) | 22.4790 | + | 4.86773i | 0.977348 | + | 0.211640i | ||||
\(530\) | 17.8116 | + | 9.78461i | 0.773685 | + | 0.425016i | ||||
\(531\) | −10.4081 | −0.451673 | ||||||||
\(532\) | −8.84399 | − | 8.84399i | −0.383435 | − | 0.383435i | ||||
\(533\) | 12.4624 | − | 12.4624i | 0.539805 | − | 0.539805i | ||||
\(534\) | −3.44952 | −0.149275 | ||||||||
\(535\) | −4.47682 | − | 15.3911i | −0.193550 | − | 0.665413i | ||||
\(536\) | − | 0.829692i | − | 0.0358372i | ||||||
\(537\) | 0.478090 | + | 0.478090i | 0.0206311 | + | 0.0206311i | ||||
\(538\) | 18.2770 | − | 18.2770i | 0.787977 | − | 0.787977i | ||||
\(539\) | 29.5133 | 1.27123 | ||||||||
\(540\) | −0.624526 | − | 2.14708i | −0.0268753 | − | 0.0923958i | ||||
\(541\) | −11.2899 | −0.485390 | −0.242695 | − | 0.970103i | \(-0.578031\pi\) | ||||
−0.242695 | + | 0.970103i | \(0.578031\pi\) | |||||||
\(542\) | 22.6580 | + | 22.6580i | 0.973246 | + | 0.973246i | ||||
\(543\) | 12.6993 | + | 12.6993i | 0.544977 | + | 0.544977i | ||||
\(544\) | −1.59016 | −0.0681777 | ||||||||
\(545\) | −8.26332 | + | 15.0423i | −0.353962 | + | 0.644339i | ||||
\(546\) | − | 8.36895i | − | 0.358158i | ||||||
\(547\) | 3.14045 | + | 3.14045i | 0.134276 | + | 0.134276i | 0.771050 | − | 0.636774i | \(-0.219732\pi\) |
−0.636774 | + | 0.771050i | \(0.719732\pi\) | |||||||
\(548\) | −1.04108 | − | 1.04108i | −0.0444728 | − | 0.0444728i | ||||
\(549\) | 14.4727 | 0.617678 | ||||||||
\(550\) | −8.68056 | − | 1.93454i | −0.370140 | − | 0.0824889i | ||||
\(551\) | 8.33198i | 0.354954i | ||||||||
\(552\) | −0.510395 | + | 4.76859i | −0.0217238 | + | 0.202965i | ||||
\(553\) | −22.5228 | + | 22.5228i | −0.957769 | + | 0.957769i | ||||
\(554\) | 25.7972i | 1.09602i | ||||||||
\(555\) | −0.892058 | − | 0.490044i | −0.0378658 | − | 0.0208012i | ||||
\(556\) | −8.89535 | −0.377247 | ||||||||
\(557\) | −11.8068 | + | 11.8068i | −0.500272 | + | 0.500272i | −0.911522 | − | 0.411251i | \(-0.865092\pi\) |
0.411251 | + | 0.911522i | \(0.365092\pi\) | |||||||
\(558\) | −4.53812 | + | 4.53812i | −0.192114 | + | 0.192114i | ||||
\(559\) | 15.7677 | 0.666905 | ||||||||
\(560\) | −3.03346 | − | 10.4289i | −0.128187 | − | 0.440700i | ||||
\(561\) | 2.82843 | 0.119416 | ||||||||
\(562\) | −2.25912 | + | 2.25912i | −0.0952954 | + | 0.0952954i | ||||
\(563\) | −28.7684 | − | 28.7684i | −1.21244 | − | 1.21244i | −0.970221 | − | 0.242221i | \(-0.922124\pi\) |
−0.242221 | − | 0.970221i | \(-0.577876\pi\) | |||||||
\(564\) | − | 12.8765i | − | 0.542200i | ||||||
\(565\) | 31.4467 | − | 9.14696i | 1.32297 | − | 0.384816i | ||||
\(566\) | − | 31.9853i | − | 1.34444i | ||||||
\(567\) | −3.43458 | + | 3.43458i | −0.144239 | + | 0.144239i | ||||
\(568\) | −9.41557 | + | 9.41557i | −0.395068 | + | 0.395068i | ||||
\(569\) | −21.2280 | −0.889925 | −0.444963 | − | 0.895549i | \(-0.646783\pi\) | ||||
−0.444963 | + | 0.895549i | \(0.646783\pi\) | |||||||
\(570\) | 2.77226 | − | 5.04652i | 0.116117 | − | 0.211375i | ||||
\(571\) | 22.5582i | 0.944030i | 0.881591 | + | 0.472015i | \(0.156473\pi\) | ||||
−0.881591 | + | 0.472015i | \(0.843527\pi\) | |||||||
\(572\) | −2.16706 | + | 2.16706i | −0.0906093 | + | 0.0906093i | ||||
\(573\) | 9.00732 | + | 9.00732i | 0.376286 | + | 0.376286i | ||||
\(574\) | −49.6845 | −2.07379 | ||||||||
\(575\) | −10.6347 | − | 21.4919i | −0.443497 | − | 0.896276i | ||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 17.1528 | + | 17.1528i | 0.714078 | + | 0.714078i | 0.967386 | − | 0.253307i | \(-0.0815184\pi\) |
−0.253307 | + | 0.967386i | \(0.581518\pi\) | |||||||
\(578\) | 10.2328 | − | 10.2328i | 0.425629 | − | 0.425629i | ||||
\(579\) | − | 2.60779i | − | 0.108376i | ||||||
\(580\) | −3.48363 | + | 6.34148i | −0.144650 | + | 0.263316i | ||||
\(581\) | −17.6167 | −0.730863 | ||||||||
\(582\) | 7.79375 | − | 7.79375i | 0.323061 | − | 0.323061i | ||||
\(583\) | −11.4307 | + | 11.4307i | −0.473412 | + | 0.473412i | ||||
\(584\) | − | 5.44033i | − | 0.225122i | ||||||
\(585\) | 3.69940 | − | 1.07605i | 0.152951 | − | 0.0444893i | ||||
\(586\) | 3.20275i | 0.132304i | ||||||||
\(587\) | −18.6292 | − | 18.6292i | −0.768907 | − | 0.768907i | 0.209007 | − | 0.977914i | \(-0.432977\pi\) |
−0.977914 | + | 0.209007i | \(0.932977\pi\) | |||||||
\(588\) | −11.7328 | + | 11.7328i | −0.483851 | + | 0.483851i | ||||
\(589\) | −16.5259 | −0.680938 | ||||||||
\(590\) | −6.50013 | − | 22.3471i | −0.267606 | − | 0.920014i | ||||
\(591\) | 17.2009 | 0.707550 | ||||||||
\(592\) | −0.321856 | + | 0.321856i | −0.0132282 | + | 0.0132282i | ||||
\(593\) | 4.49108 | − | 4.49108i | 0.184427 | − | 0.184427i | −0.608855 | − | 0.793282i | \(-0.708371\pi\) |
0.793282 | + | 0.608855i | \(0.208371\pi\) | |||||||
\(594\) | 1.77870 | 0.0729810 | ||||||||
\(595\) | −15.1373 | − | 8.31550i | −0.620567 | − | 0.340902i | ||||
\(596\) | − | 11.3358i | − | 0.464333i | ||||||
\(597\) | 3.79878 | − | 3.79878i | 0.155474 | − | 0.155474i | ||||
\(598\) | −8.21624 | − | 0.879404i | −0.335987 | − | 0.0359615i | ||||
\(599\) | 22.1900i | 0.906660i | 0.891343 | + | 0.453330i | \(0.149764\pi\) | ||||
−0.891343 | + | 0.453330i | \(0.850236\pi\) | |||||||
\(600\) | 4.21993 | − | 2.68182i | 0.172278 | − | 0.109485i | ||||
\(601\) | −15.6107 | −0.636776 | −0.318388 | − | 0.947961i | \(-0.603141\pi\) | ||||
−0.318388 | + | 0.947961i | \(0.603141\pi\) | |||||||
\(602\) | −31.4312 | − | 31.4312i | −1.28104 | − | 1.28104i | ||||
\(603\) | −0.586681 | − | 0.586681i | −0.0238915 | − | 0.0238915i | ||||
\(604\) | − | 8.75190i | − | 0.356110i | ||||||
\(605\) | −8.43656 | + | 15.3576i | −0.342995 | + | 0.624376i | ||||
\(606\) | 0.109089 | 0.00443142 | ||||||||
\(607\) | 1.06267 | + | 1.06267i | 0.0431325 | + | 0.0431325i | 0.728344 | − | 0.685212i | \(-0.240290\pi\) |
−0.685212 | + | 0.728344i | \(0.740290\pi\) | |||||||
\(608\) | −1.82079 | − | 1.82079i | −0.0738428 | − | 0.0738428i | ||||
\(609\) | 15.7167 | 0.636873 | ||||||||
\(610\) | 9.03856 | + | 31.0740i | 0.365960 | + | 1.25815i | ||||
\(611\) | 22.1861 | 0.897555 | ||||||||
\(612\) | −1.12442 | + | 1.12442i | −0.0454518 | + | 0.0454518i | ||||
\(613\) | −14.1331 | − | 14.1331i | −0.570829 | − | 0.570829i | 0.361531 | − | 0.932360i | \(-0.382254\pi\) |
−0.932360 | + | 0.361531i | \(0.882254\pi\) | |||||||
\(614\) | − | 9.00168i | − | 0.363278i | ||||||
\(615\) | −6.38827 | − | 21.9625i | −0.257600 | − | 0.885614i | ||||
\(616\) | 8.63956 | 0.348098 | ||||||||
\(617\) | −19.3155 | + | 19.3155i | −0.777614 | + | 0.777614i | −0.979425 | − | 0.201811i | \(-0.935317\pi\) |
0.201811 | + | 0.979425i | \(0.435317\pi\) | |||||||
\(618\) | −0.451663 | − | 0.451663i | −0.0181686 | − | 0.0181686i | ||||
\(619\) | −42.0979 | −1.69206 | −0.846028 | − | 0.533138i | \(-0.821012\pi\) | ||||
−0.846028 | + | 0.533138i | \(0.821012\pi\) | |||||||
\(620\) | −12.5779 | − | 6.90954i | −0.505140 | − | 0.277494i | ||||
\(621\) | 3.01100 | + | 3.73281i | 0.120827 | + | 0.149792i | ||||
\(622\) | −8.18796 | − | 8.18796i | −0.328307 | − | 0.328307i | ||||
\(623\) | −11.8476 | + | 11.8476i | −0.474666 | + | 0.474666i | ||||
\(624\) | − | 1.72299i | − | 0.0689748i | ||||||
\(625\) | −10.6157 | + | 22.6342i | −0.424628 | + | 0.905368i | ||||
\(626\) | − | 0.900397i | − | 0.0359871i | ||||||
\(627\) | 3.23864 | + | 3.23864i | 0.129339 | + | 0.129339i | ||||
\(628\) | 14.2015 | + | 14.2015i | 0.566700 | + | 0.566700i | ||||
\(629\) | 0.723799i | 0.0288598i | ||||||||
\(630\) | −9.51930 | − | 5.22934i | −0.379258 | − | 0.208342i | ||||
\(631\) | 16.9667i | 0.675434i | 0.941248 | + | 0.337717i | \(0.109655\pi\) | ||||
−0.941248 | + | 0.337717i | \(0.890345\pi\) | |||||||
\(632\) | −4.63698 | + | 4.63698i | −0.184449 | + | 0.184449i | ||||
\(633\) | −5.69442 | + | 5.69442i | −0.226333 | + | 0.226333i | ||||
\(634\) | − | 23.8542i | − | 0.947373i | ||||||
\(635\) | −25.2161 | + | 7.33465i | −1.00067 | + | 0.291067i | ||||
\(636\) | − | 9.08835i | − | 0.360376i | ||||||
\(637\) | −20.2154 | − | 20.2154i | −0.800964 | − | 0.800964i | ||||
\(638\) | −4.06969 | − | 4.06969i | −0.161121 | − | 0.161121i | ||||
\(639\) | 13.3156i | 0.526758i | ||||||||
\(640\) | −0.624526 | − | 2.14708i | −0.0246866 | − | 0.0848709i | ||||
\(641\) | 5.44396i | 0.215023i | 0.994204 | + | 0.107512i | \(0.0342883\pi\) | ||||
−0.994204 | + | 0.107512i | \(0.965712\pi\) | |||||||
\(642\) | −5.06879 | + | 5.06879i | −0.200049 | + | 0.200049i | ||||
\(643\) | 4.81939 | + | 4.81939i | 0.190058 | + | 0.190058i | 0.795721 | − | 0.605663i | \(-0.207092\pi\) |
−0.605663 | + | 0.795721i | \(0.707092\pi\) | |||||||
\(644\) | 14.6251 | + | 18.1311i | 0.576310 | + | 0.714465i | ||||
\(645\) | 9.85249 | − | 17.9351i | 0.387941 | − | 0.706194i | ||||
\(646\) | −4.09465 | −0.161102 | ||||||||
\(647\) | −8.57433 | − | 8.57433i | −0.337092 | − | 0.337092i | 0.518180 | − | 0.855272i | \(-0.326610\pi\) |
−0.855272 | + | 0.518180i | \(0.826610\pi\) | |||||||
\(648\) | −0.707107 | + | 0.707107i | −0.0277778 | + | 0.0277778i | ||||
\(649\) | 18.5129 | 0.726696 | ||||||||
\(650\) | 4.62075 | + | 7.27090i | 0.181241 | + | 0.285188i | ||||
\(651\) | 31.1730i | 1.22177i | ||||||||
\(652\) | −3.88265 | − | 3.88265i | −0.152056 | − | 0.152056i | ||||
\(653\) | 11.9157 | − | 11.9157i | 0.466297 | − | 0.466297i | −0.434416 | − | 0.900713i | \(-0.643045\pi\) |
0.900713 | + | 0.434416i | \(0.143045\pi\) | |||||||
\(654\) | 7.67531 | 0.300128 | ||||||||
\(655\) | 13.6304 | − | 24.8124i | 0.532585 | − | 0.969499i | ||||
\(656\) | −10.2290 | −0.399375 | ||||||||
\(657\) | −3.84689 | − | 3.84689i | −0.150082 | − | 0.150082i | ||||
\(658\) | −44.2255 | − | 44.2255i | −1.72409 | − | 1.72409i | ||||
\(659\) | 0.738479 | 0.0287670 | 0.0143835 | − | 0.999897i | \(-0.495421\pi\) | ||||
0.0143835 | + | 0.999897i | \(0.495421\pi\) | |||||||
\(660\) | 1.11085 | + | 3.81902i | 0.0432396 | + | 0.148655i | ||||
\(661\) | 8.03867i | 0.312668i | 0.987704 | + | 0.156334i | \(0.0499676\pi\) | ||||
−0.987704 | + | 0.156334i | \(0.950032\pi\) | |||||||
\(662\) | 6.71934 | + | 6.71934i | 0.261155 | + | 0.261155i | ||||
\(663\) | −1.93736 | − | 1.93736i | −0.0752407 | − | 0.0752407i | ||||
\(664\) | −3.62690 | −0.140751 | ||||||||
\(665\) | −7.81113 | − | 26.8542i | −0.302902 | − | 1.04136i | ||||
\(666\) | 0.455173i | 0.0176376i | ||||||||
\(667\) | 1.65150 | − | 15.4299i | 0.0639465 | − | 0.597449i | ||||
\(668\) | 6.37019 | − | 6.37019i | 0.246470 | − | 0.246470i | ||||
\(669\) | 11.3073i | 0.437164i | ||||||||
\(670\) | 0.893255 | − | 1.62605i | 0.0345095 | − | 0.0628198i | ||||
\(671\) | −25.7426 | −0.993780 | ||||||||
\(672\) | −3.43458 | + | 3.43458i | −0.132492 | + | 0.132492i | ||||
\(673\) | −32.1774 | + | 32.1774i | −1.24035 | + | 1.24035i | −0.280488 | + | 0.959857i | \(0.590496\pi\) |
−0.959857 | + | 0.280488i | \(0.909504\pi\) | |||||||
\(674\) | 17.8020 | 0.685708 | ||||||||
\(675\) | 1.08761 | − | 4.88028i | 0.0418622 | − | 0.187842i | ||||
\(676\) | −10.0313 | −0.385820 | ||||||||
\(677\) | 12.9663 | − | 12.9663i | 0.498335 | − | 0.498335i | −0.412585 | − | 0.910919i | \(-0.635374\pi\) |
0.910919 | + | 0.412585i | \(0.135374\pi\) | |||||||
\(678\) | −10.3565 | − | 10.3565i | −0.397737 | − | 0.397737i | ||||
\(679\) | − | 53.5365i | − | 2.05454i | ||||||
\(680\) | −3.11644 | − | 1.71199i | −0.119510 | − | 0.0656517i | ||||
\(681\) | − | 18.6070i | − | 0.713020i | ||||||
\(682\) | 8.07196 | − | 8.07196i | 0.309091 | − | 0.309091i | ||||
\(683\) | 27.7204 | − | 27.7204i | 1.06069 | − | 1.06069i | 0.0626558 | − | 0.998035i | \(-0.480043\pi\) |
0.998035 | − | 0.0626558i | \(-0.0199570\pi\) | |||||||
\(684\) | −2.57499 | −0.0984571 | ||||||||
\(685\) | −0.919497 | − | 3.16118i | −0.0351322 | − | 0.120782i | ||||
\(686\) | 46.5936i | 1.77895i | ||||||||
\(687\) | 4.43976 | − | 4.43976i | 0.169387 | − | 0.169387i | ||||
\(688\) | −6.47101 | − | 6.47101i | −0.246705 | − | 0.246705i | ||||
\(689\) | 15.6591 | 0.596565 | ||||||||
\(690\) | −6.13420 | + | 8.79611i | −0.233525 | + | 0.334862i | ||||
\(691\) | 23.1360 | 0.880137 | 0.440068 | − | 0.897964i | \(-0.354954\pi\) | ||||
0.440068 | + | 0.897964i | \(0.354954\pi\) | |||||||
\(692\) | 6.60779 | + | 6.60779i | 0.251191 | + | 0.251191i | ||||
\(693\) | 6.10909 | − | 6.10909i | 0.232065 | − | 0.232065i | ||||
\(694\) | 24.8877i | 0.944725i | ||||||||
\(695\) | −17.4333 | − | 9.57683i | −0.661284 | − | 0.363270i | ||||
\(696\) | 3.23574 | 0.122650 | ||||||||
\(697\) | −11.5016 | + | 11.5016i | −0.435656 | + | 0.435656i | ||||
\(698\) | −15.3474 | + | 15.3474i | −0.580907 | + | 0.580907i | ||||
\(699\) | 16.9343i | 0.640513i | ||||||||
\(700\) | 5.28277 | − | 23.7046i | 0.199670 | − | 0.895950i | ||||
\(701\) | − | 27.0938i | − | 1.02332i | −0.859189 | − | 0.511659i | \(-0.829031\pi\) | ||
0.859189 | − | 0.511659i | \(-0.170969\pi\) | |||||||
\(702\) | −1.21834 | − | 1.21834i | −0.0459832 | − | 0.0459832i | ||||
\(703\) | −0.828774 | + | 0.828774i | −0.0312578 | + | 0.0312578i | ||||
\(704\) | 1.77870 | 0.0670374 | ||||||||
\(705\) | 13.8630 | − | 25.2358i | 0.522112 | − | 0.950434i | ||||
\(706\) | −18.7454 | −0.705492 | ||||||||
\(707\) | 0.374673 | − | 0.374673i | 0.0140910 | − | 0.0140910i | ||||
\(708\) | −7.35964 | + | 7.35964i | −0.276592 | + | 0.276592i | ||||
\(709\) | 7.87786 | 0.295859 | 0.147930 | − | 0.988998i | \(-0.452739\pi\) | ||||
0.147930 | + | 0.988998i | \(0.452739\pi\) | |||||||
\(710\) | −28.5897 | + | 8.31595i | −1.07295 | + | 0.312092i | ||||
\(711\) | 6.55768i | 0.245932i | ||||||||
\(712\) | −2.43918 | + | 2.43918i | −0.0914121 | + | 0.0914121i | ||||
\(713\) | 30.6042 | + | 3.27564i | 1.14614 | + | 0.122674i | ||||
\(714\) | 7.72378i | 0.289055i | ||||||||
\(715\) | −6.58013 | + | 1.91398i | −0.246083 | + | 0.0715786i | ||||
\(716\) | 0.676121 | 0.0252678 | ||||||||
\(717\) | 3.10650 | + | 3.10650i | 0.116014 | + | 0.116014i | ||||
\(718\) | 6.45016 | + | 6.45016i | 0.240718 | + | 0.240718i | ||||
\(719\) | 18.0186i | 0.671980i | 0.941865 | + | 0.335990i | \(0.109071\pi\) | ||||
−0.941865 | + | 0.335990i | \(0.890929\pi\) | |||||||
\(720\) | −1.95982 | − | 1.07661i | −0.0730383 | − | 0.0401229i | ||||
\(721\) | −3.10255 | −0.115545 | ||||||||
\(722\) | 8.74652 | + | 8.74652i | 0.325512 | + | 0.325512i | ||||
\(723\) | 5.26163 | + | 5.26163i | 0.195682 | + | 0.195682i | ||||
\(724\) | 17.9595 | 0.667458 | ||||||||
\(725\) | −13.6546 | + | 8.67767i | −0.507119 | + | 0.322280i | ||||
\(726\) | 7.83622 | 0.290829 | ||||||||
\(727\) | 19.6163 | − | 19.6163i | 0.727530 | − | 0.727530i | −0.242598 | − | 0.970127i | \(-0.577999\pi\) |
0.970127 | + | 0.242598i | \(0.0779994\pi\) | |||||||
\(728\) | −5.91774 | − | 5.91774i | −0.219326 | − | 0.219326i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 5.85711 | − | 10.6621i | 0.216781 | − | 0.394621i | ||||
\(731\) | −14.5522 | −0.538233 | ||||||||
\(732\) | 10.2337 | − | 10.2337i | 0.378249 | − | 0.378249i | ||||
\(733\) | −16.5747 | − | 16.5747i | −0.612200 | − | 0.612200i | 0.331319 | − | 0.943519i | \(-0.392506\pi\) |
−0.943519 | + | 0.331319i | \(0.892506\pi\) | |||||||
\(734\) | 20.3482 | 0.751067 | ||||||||
\(735\) | −35.6258 | + | 10.3625i | −1.31408 | + | 0.382228i | ||||
\(736\) | 3.01100 | + | 3.73281i | 0.110987 | + | 0.137593i | ||||
\(737\) | 1.04353 | + | 1.04353i | 0.0384389 | + | 0.0384389i | ||||
\(738\) | −7.23299 | + | 7.23299i | −0.266250 | + | 0.266250i | ||||
\(739\) | 45.4934i | 1.67350i | 0.547585 | + | 0.836750i | \(0.315547\pi\) | ||||
−0.547585 | + | 0.836750i | \(0.684453\pi\) | |||||||
\(740\) | −0.977294 | + | 0.284267i | −0.0359260 | + | 0.0104499i | ||||
\(741\) | − | 4.43667i | − | 0.162985i | ||||||
\(742\) | −31.2146 | − | 31.2146i | −1.14592 | − | 1.14592i | ||||
\(743\) | 4.79938 | + | 4.79938i | 0.176072 | + | 0.176072i | 0.789641 | − | 0.613569i | \(-0.210267\pi\) |
−0.613569 | + | 0.789641i | \(0.710267\pi\) | |||||||
\(744\) | 6.41786i | 0.235290i | ||||||||
\(745\) | 12.2043 | − | 22.2162i | 0.447129 | − | 0.813938i | ||||
\(746\) | 3.27750i | 0.119998i | ||||||||
\(747\) | −2.56461 | + | 2.56461i | −0.0938340 | + | 0.0938340i | ||||
\(748\) | 2.00000 | − | 2.00000i | 0.0731272 | − | 0.0731272i | ||||
\(749\) | 34.8183i | 1.27223i | ||||||||
\(750\) | 11.1576 | − | 0.712667i | 0.407418 | − | 0.0260229i | ||||
\(751\) | 48.8764i | 1.78352i | 0.452505 | + | 0.891762i | \(0.350531\pi\) | ||||
−0.452505 | + | 0.891762i | \(0.649469\pi\) | |||||||
\(752\) | −9.10509 | − | 9.10509i | −0.332029 | − | 0.332029i | ||||
\(753\) | −9.03458 | − | 9.03458i | −0.329238 | − | 0.329238i | ||||
\(754\) | 5.57514i | 0.203035i | ||||||||
\(755\) | 9.42238 | − | 17.1522i | 0.342916 | − | 0.624231i | ||||
\(756\) | 4.85722i | 0.176656i | ||||||||
\(757\) | 7.64728 | − | 7.64728i | 0.277945 | − | 0.277945i | −0.554343 | − | 0.832288i | \(-0.687030\pi\) |
0.832288 | + | 0.554343i | \(0.187030\pi\) | |||||||
\(758\) | 20.7884 | + | 20.7884i | 0.755070 | + | 0.755070i | ||||
\(759\) | −5.35568 | − | 6.63956i | −0.194399 | − | 0.241001i | ||||
\(760\) | −1.60815 | − | 5.52871i | −0.0583336 | − | 0.200547i | ||||
\(761\) | 31.0826 | 1.12674 | 0.563372 | − | 0.826203i | \(-0.309504\pi\) | ||||
0.563372 | + | 0.826203i | \(0.309504\pi\) | |||||||
\(762\) | 8.30451 | + | 8.30451i | 0.300841 | + | 0.300841i | ||||
\(763\) | 26.3614 | − | 26.3614i | 0.954348 | − | 0.954348i | ||||
\(764\) | 12.7383 | 0.460855 | ||||||||
\(765\) | −3.41421 | + | 0.993099i | −0.123441 | + | 0.0359056i | ||||
\(766\) | − | 12.7264i | − | 0.459824i | ||||||
\(767\) | −12.6806 | − | 12.6806i | −0.457869 | − | 0.457869i | ||||
\(768\) | −0.707107 | + | 0.707107i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | 13.6176 | 0.491062 | 0.245531 | − | 0.969389i | \(-0.421038\pi\) | ||||
0.245531 | + | 0.969389i | \(0.421038\pi\) | |||||||
\(770\) | 16.9320 | + | 9.30144i | 0.610187 | + | 0.335201i | ||||
\(771\) | 17.3934 | 0.626409 | ||||||||
\(772\) | −1.84399 | − | 1.84399i | −0.0663665 | − | 0.0663665i | ||||
\(773\) | 6.20764 | + | 6.20764i | 0.223273 | + | 0.223273i | 0.809875 | − | 0.586602i | \(-0.199535\pi\) |
−0.586602 | + | 0.809875i | \(0.699535\pi\) | |||||||
\(774\) | −9.15139 | −0.328940 | ||||||||
\(775\) | −17.2116 | − | 27.0830i | −0.618257 | − | 0.972849i | ||||
\(776\) | − | 11.0220i | − | 0.395668i | ||||||
\(777\) | 1.56333 | + | 1.56333i | 0.0560840 | + | 0.0560840i | ||||
\(778\) | 19.9581 | + | 19.9581i | 0.715534 | + | 0.715534i | ||||
\(779\) | −26.3395 | −0.943711 | ||||||||
\(780\) | 1.85499 | − | 3.37676i | 0.0664192 | − | 0.120907i | ||||
\(781\) | − | 23.6845i | − | 0.847499i | ||||||
\(782\) | 7.58285 | + | 0.811611i | 0.271162 | + | 0.0290231i | ||||
\(783\) | 2.28801 | − | 2.28801i | 0.0817669 | − | 0.0817669i | ||||
\(784\) | 16.5926i | 0.592594i | ||||||||
\(785\) | 12.5429 | + | 43.1218i | 0.447676 | + | 1.53908i | ||||
\(786\) | −12.6605 | −0.451585 | ||||||||
\(787\) | 6.14851 | − | 6.14851i | 0.219171 | − | 0.219171i | −0.588978 | − | 0.808149i | \(-0.700470\pi\) |
0.808149 | + | 0.588978i | \(0.200470\pi\) | |||||||
\(788\) | 12.1629 | − | 12.1629i | 0.433284 | − | 0.433284i | ||||
\(789\) | −1.18613 | −0.0422274 | ||||||||
\(790\) | −14.0799 | + | 4.09544i | −0.500940 | + | 0.145709i | ||||
\(791\) | −71.1401 | −2.52945 | ||||||||
\(792\) | 1.25773 | − | 1.25773i | 0.0446916 | − | 0.0446916i | ||||
\(793\) | 17.6326 | + | 17.6326i | 0.626152 | + | 0.626152i | ||||
\(794\) | − | 12.0881i | − | 0.428992i | ||||||
\(795\) | 9.78461 | − | 17.8116i | 0.347024 | − | 0.631711i | ||||
\(796\) | − | 5.37229i | − | 0.190416i | ||||||
\(797\) | 16.7828 | − | 16.7828i | 0.594476 | − | 0.594476i | −0.344361 | − | 0.938837i | \(-0.611904\pi\) |
0.938837 | + | 0.344361i | \(0.111904\pi\) | |||||||
\(798\) | −8.84399 | + | 8.84399i | −0.313074 | + | 0.313074i | ||||
\(799\) | −20.4758 | −0.724382 | ||||||||
\(800\) | 1.08761 | − | 4.88028i | 0.0384529 | − | 0.172544i | ||||
\(801\) | 3.44952i | 0.121883i | ||||||||
\(802\) | 27.0641 | − | 27.0641i | 0.955667 | − | 0.955667i | ||||
\(803\) | 6.84247 | + | 6.84247i | 0.241466 | + | 0.241466i | ||||
\(804\) | −0.829692 | −0.0292610 | ||||||||
\(805\) | 9.14252 | + | 51.2793i | 0.322232 | + | 1.80736i | ||||
\(806\) | −11.0579 | −0.389498 | ||||||||
\(807\) | −18.2770 | − | 18.2770i | −0.643381 | − | 0.643381i | ||||
\(808\) | 0.0771372 | − | 0.0771372i | 0.00271368 | − | 0.00271368i | ||||
\(809\) | 17.9358i | 0.630588i | 0.948994 | + | 0.315294i | \(0.102103\pi\) | ||||
−0.948994 | + | 0.315294i | \(0.897897\pi\) | |||||||
\(810\) | −2.14708 | + | 0.624526i | −0.0754408 | + | 0.0219436i | ||||
\(811\) | 43.1441 | 1.51500 | 0.757498 | − | 0.652838i | \(-0.226422\pi\) | ||||
0.757498 | + | 0.652838i | \(0.226422\pi\) | |||||||
\(812\) | 11.1134 | − | 11.1134i | 0.390004 | − | 0.390004i | ||||
\(813\) | 22.6580 | − | 22.6580i | 0.794652 | − | 0.794652i | ||||
\(814\) | − | 0.809617i | − | 0.0283770i | ||||||
\(815\) | −3.42921 | − | 11.7894i | −0.120120 | − | 0.412965i | ||||
\(816\) | 1.59016i | 0.0556669i | ||||||||
\(817\) | −16.6628 | − | 16.6628i | −0.582956 | − | 0.582956i | ||||
\(818\) | −23.2631 | + | 23.2631i | −0.813376 | + | 0.813376i | ||||
\(819\) | −8.36895 | −0.292435 | ||||||||
\(820\) | −20.0470 | − | 11.0126i | −0.700072 | − | 0.384578i | ||||
\(821\) | 5.77627 | 0.201593 | 0.100797 | − | 0.994907i | \(-0.467861\pi\) | ||||
0.100797 | + | 0.994907i | \(0.467861\pi\) | |||||||
\(822\) | −1.04108 | + | 1.04108i | −0.0363119 | + | 0.0363119i | ||||
\(823\) | −27.2467 | + | 27.2467i | −0.949762 | + | 0.949762i | −0.998797 | − | 0.0490353i | \(-0.984385\pi\) |
0.0490353 | + | 0.998797i | \(0.484385\pi\) | |||||||
\(824\) | −0.638749 | −0.0222519 | ||||||||
\(825\) | −1.93454 | + | 8.68056i | −0.0673519 | + | 0.302218i | ||||
\(826\) | 50.5545i | 1.75902i | ||||||||
\(827\) | −12.7737 | + | 12.7737i | −0.444186 | + | 0.444186i | −0.893416 | − | 0.449230i | \(-0.851698\pi\) |
0.449230 | + | 0.893416i | \(0.351698\pi\) | |||||||
\(828\) | 4.76859 | + | 0.510395i | 0.165720 | + | 0.0177374i | ||||
\(829\) | 3.68926i | 0.128133i | 0.997946 | + | 0.0640667i | \(0.0204070\pi\) | ||||
−0.997946 | + | 0.0640667i | \(0.979593\pi\) | |||||||
\(830\) | −7.10809 | − | 3.90476i | −0.246725 | − | 0.135536i | ||||
\(831\) | 25.7972 | 0.894896 | ||||||||
\(832\) | −1.21834 | − | 1.21834i | −0.0422382 | − | 0.0422382i | ||||
\(833\) | 18.6570 | + | 18.6570i | 0.646427 | + | 0.646427i | ||||
\(834\) | 8.89535i | 0.308021i | ||||||||
\(835\) | 19.3427 | − | 5.62624i | 0.669381 | − | 0.194704i | ||||
\(836\) | 4.58013 | 0.158407 | ||||||||
\(837\) | 4.53812 | + | 4.53812i | 0.156860 | + | 0.156860i | ||||
\(838\) | −15.5925 | − | 15.5925i | −0.538634 | − | 0.538634i | ||||
\(839\) | 36.6605 | 1.26566 | 0.632831 | − | 0.774290i | \(-0.281893\pi\) | ||||
0.632831 | + | 0.774290i | \(0.281893\pi\) | |||||||
\(840\) | −10.4289 | + | 3.03346i | −0.359830 | + | 0.104664i | ||||
\(841\) | 18.5300 | 0.638965 | ||||||||
\(842\) | −26.0531 | + | 26.0531i | −0.897848 | + | 0.897848i | ||||
\(843\) | 2.25912 | + | 2.25912i | 0.0778084 | + | 0.0778084i | ||||
\(844\) | 8.05312i | 0.277200i | ||||||||
\(845\) | −19.6596 | − | 10.7998i | −0.676311 | − | 0.371525i | ||||
\(846\) | −12.8765 | −0.442705 | ||||||||
\(847\) | 26.9141 | − | 26.9141i | 0.924779 | − | 0.924779i | ||||
\(848\) | −6.42643 | − | 6.42643i | −0.220685 | − | 0.220685i | ||||
\(849\) | −31.9853 | −1.09773 | ||||||||
\(850\) | −4.26453 | − | 6.71039i | −0.146272 | − | 0.230164i | ||||
\(851\) | 1.69907 | − | 1.37053i | 0.0582435 | − | 0.0469810i | ||||
\(852\) | 9.41557 | + | 9.41557i | 0.322572 | + | 0.322572i | ||||
\(853\) | 25.4890 | − | 25.4890i | 0.872727 | − | 0.872727i | −0.120042 | − | 0.992769i | \(-0.538303\pi\) |
0.992769 | + | 0.120042i | \(0.0383029\pi\) | |||||||
\(854\) | − | 70.2970i | − | 2.40551i | ||||||
\(855\) | −5.04652 | − | 2.77226i | −0.172587 | − | 0.0948092i | ||||
\(856\) | 7.16835i | 0.245009i | ||||||||
\(857\) | 29.0469 | + | 29.0469i | 0.992223 | + | 0.992223i | 0.999970 | − | 0.00774669i | \(-0.00246587\pi\) |
−0.00774669 | + | 0.999970i | \(0.502466\pi\) | |||||||
\(858\) | 2.16706 | + | 2.16706i | 0.0739822 | + | 0.0739822i | ||||
\(859\) | − | 50.9359i | − | 1.73791i | −0.494892 | − | 0.868954i | \(-0.664792\pi\) | ||
0.494892 | − | 0.868954i | \(-0.335208\pi\) | |||||||
\(860\) | −5.71528 | − | 19.6488i | −0.194890 | − | 0.670019i | ||||
\(861\) | 49.6845i | 1.69324i | ||||||||
\(862\) | −22.9145 | + | 22.9145i | −0.780471 | + | 0.780471i | ||||
\(863\) | 4.14395 | − | 4.14395i | 0.141062 | − | 0.141062i | −0.633050 | − | 0.774111i | \(-0.718197\pi\) |
0.774111 | + | 0.633050i | \(0.218197\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | 5.83609 | + | 20.0641i | 0.198433 | + | 0.682201i | ||||
\(866\) | 2.40359i | 0.0816773i | ||||||||
\(867\) | −10.2328 | − | 10.2328i | −0.347524 | − | 0.347524i | ||||
\(868\) | 22.0426 | + | 22.0426i | 0.748176 | + | 0.748176i | ||||
\(869\) | − | 11.6642i | − | 0.395679i | ||||||
\(870\) | 6.34148 | + | 3.48363i | 0.214996 | + | 0.118106i | ||||
\(871\) | − | 1.42955i | − | 0.0484385i | ||||||
\(872\) | 5.42726 | − | 5.42726i | 0.183790 | − | 0.183790i | ||||
\(873\) | −7.79375 | − | 7.79375i | −0.263778 | − | 0.263778i | ||||
\(874\) | 7.75329 | + | 9.61193i | 0.262259 | + | 0.325128i | ||||
\(875\) | 35.8739 | − | 40.7694i | 1.21276 | − | 1.37826i | ||||
\(876\) | −5.44033 | −0.183812 | ||||||||
\(877\) | −16.3814 | − | 16.3814i | −0.553162 | − | 0.553162i | 0.374190 | − | 0.927352i | \(-0.377921\pi\) |
−0.927352 | + | 0.374190i | \(0.877921\pi\) | |||||||
\(878\) | 23.9656 | − | 23.9656i | 0.808799 | − | 0.808799i | ||||
\(879\) | 3.20275 | 0.108026 | ||||||||
\(880\) | 3.48594 | + | 1.91497i | 0.117511 | + | 0.0645536i | ||||
\(881\) | − | 47.5503i | − | 1.60201i | −0.598657 | − | 0.801005i | \(-0.704299\pi\) | ||
0.598657 | − | 0.801005i | \(-0.295701\pi\) | |||||||
\(882\) | 11.7328 | + | 11.7328i | 0.395063 | + | 0.395063i | ||||
\(883\) | 15.3437 | − | 15.3437i | 0.516357 | − | 0.516357i | −0.400110 | − | 0.916467i | \(-0.631028\pi\) |
0.916467 | + | 0.400110i | \(0.131028\pi\) | |||||||
\(884\) | −2.73983 | −0.0921506 | ||||||||
\(885\) | −22.3471 | + | 6.50013i | −0.751188 | + | 0.218500i | ||||
\(886\) | −3.46036 | −0.116253 | ||||||||
\(887\) | −19.8747 | − | 19.8747i | −0.667327 | − | 0.667327i | 0.289770 | − | 0.957096i | \(-0.406421\pi\) |
−0.957096 | + | 0.289770i | \(0.906421\pi\) | |||||||
\(888\) | 0.321856 | + | 0.321856i | 0.0108008 | + | 0.0108008i | ||||
\(889\) | 57.0449 | 1.91323 | ||||||||
\(890\) | −7.40641 | + | 2.15431i | −0.248263 | + | 0.0722128i | ||||
\(891\) | − | 1.77870i | − | 0.0595888i | ||||||
\(892\) | 7.99544 | + | 7.99544i | 0.267707 | + | 0.267707i | ||||
\(893\) | −23.4455 | − | 23.4455i | −0.784573 | − | 0.784573i | ||||
\(894\) | −11.3358 | −0.379126 | ||||||||
\(895\) | 1.32508 | + | 0.727919i | 0.0442925 | + | 0.0243317i | ||||
\(896\) | 4.85722i | 0.162268i | ||||||||
\(897\) | −0.879404 | + | 8.21624i | −0.0293625 | + | 0.274332i | ||||
\(898\) | −3.17708 | + | 3.17708i | −0.106021 | + | 0.106021i | ||||
\(899\) | − | 20.7665i | − | 0.692603i | ||||||
\(900\) | −2.68182 | − | 4.21993i | −0.0893940 | − | 0.140664i | ||||
\(901\) | −14.4520 | −0.481465 | ||||||||
\(902\) | 12.8653 | − | 12.8653i | 0.428369 | − | 0.428369i | ||||
\(903\) | −31.4312 | + | 31.4312i | −1.04596 | + | 1.04596i | ||||
\(904\) | −14.6462 | −0.487127 | ||||||||
\(905\) | 35.1974 | + | 19.3353i | 1.17000 | + | 0.642729i | ||||
\(906\) | −8.75190 | −0.290762 | ||||||||
\(907\) | 28.1205 | − | 28.1205i | 0.933726 | − | 0.933726i | −0.0642101 | − | 0.997936i | \(-0.520453\pi\) |
0.997936 | + | 0.0642101i | \(0.0204528\pi\) | |||||||
\(908\) | −13.1571 | − | 13.1571i | −0.436634 | − | 0.436634i | ||||
\(909\) | − | 0.109089i | − | 0.00361824i | ||||||
\(910\) | −5.22662 | − | 17.9688i | −0.173261 | − | 0.595661i | ||||
\(911\) | 51.4776i | 1.70553i | 0.522296 | + | 0.852764i | \(0.325075\pi\) | ||||
−0.522296 | + | 0.852764i | \(0.674925\pi\) | |||||||
\(912\) | −1.82079 | + | 1.82079i | −0.0602924 | + | 0.0602924i | ||||
\(913\) | 4.56167 | − | 4.56167i | 0.150969 | − | 0.150969i | ||||
\(914\) | 2.09645 | 0.0693445 | ||||||||
\(915\) | 31.0740 | − | 9.03856i | 1.02728 | − | 0.298805i | ||||
\(916\) | − | 6.27877i | − | 0.207456i | ||||||
\(917\) | −43.4835 | + | 43.4835i | −1.43595 | + | 1.43595i | ||||
\(918\) | 1.12442 | + | 1.12442i | 0.0371112 | + | 0.0371112i | ||||
\(919\) | −52.5111 | −1.73218 | −0.866090 | − | 0.499888i | \(-0.833375\pi\) | ||||
−0.866090 | + | 0.499888i | \(0.833375\pi\) | |||||||
\(920\) | 1.88225 | + | 10.5573i | 0.0620560 | + | 0.348065i | ||||
\(921\) | −9.00168 | −0.296616 | ||||||||
\(922\) | 0.0460180 | + | 0.0460180i | 0.00151552 | + | 0.00151552i | ||||
\(923\) | −16.2229 | + | 16.2229i | −0.533984 | + | 0.533984i | ||||
\(924\) | − | 8.63956i | − | 0.284221i | ||||||
\(925\) | −2.22137 | − | 0.495051i | −0.0730381 | − | 0.0162772i | ||||
\(926\) | 12.5685 | 0.413026 | ||||||||
\(927\) | −0.451663 | + | 0.451663i | −0.0148346 | + | 0.0148346i | ||||
\(928\) | 2.28801 | − | 2.28801i | 0.0751077 | − | 0.0751077i | ||||
\(929\) | 10.7225i | 0.351793i | 0.984409 | + | 0.175897i | \(0.0562825\pi\) | ||||
−0.984409 | + | 0.175897i | \(0.943718\pi\) | |||||||
\(930\) | −6.90954 | + | 12.5779i | −0.226573 | + | 0.412445i | ||||
\(931\) | 42.7258i | 1.40028i | ||||||||
\(932\) | 11.9743 | + | 11.9743i | 0.392232 | + | 0.392232i | ||||
\(933\) | −8.18796 | + | 8.18796i | −0.268062 | + | 0.268062i | ||||
\(934\) | 6.33162 | 0.207177 | ||||||||
\(935\) | 6.07287 | − | 1.76643i | 0.198604 | − | 0.0577683i | ||||
\(936\) | −1.72299 | −0.0563177 | ||||||||
\(937\) | −6.98650 | + | 6.98650i | −0.228239 | + | 0.228239i | −0.811957 | − | 0.583718i | \(-0.801597\pi\) |
0.583718 | + | 0.811957i | \(0.301597\pi\) | |||||||
\(938\) | −2.84964 | + | 2.84964i | −0.0930440 | + | 0.0930440i | ||||
\(939\) | −0.900397 | −0.0293834 | ||||||||
\(940\) | −8.04174 | − | 27.6470i | −0.262293 | − | 0.901746i | ||||
\(941\) | − | 29.7146i | − | 0.968667i | −0.874883 | − | 0.484333i | \(-0.839062\pi\) | ||
0.874883 | − | 0.484333i | \(-0.160938\pi\) | |||||||
\(942\) | 14.2015 | − | 14.2015i | 0.462708 | − | 0.462708i | ||||
\(943\) | 48.7779 | + | 5.22082i | 1.58843 | + | 0.170013i | ||||
\(944\) | 10.4081i | 0.338755i | ||||||||
\(945\) | −5.22934 | + | 9.51930i | −0.170110 | + | 0.309663i | ||||
\(946\) | 16.2776 | 0.529230 | ||||||||
\(947\) | 18.3257 | + | 18.3257i | 0.595506 | + | 0.595506i | 0.939113 | − | 0.343608i | \(-0.111649\pi\) |
−0.343608 | + | 0.939113i | \(0.611649\pi\) | |||||||
\(948\) | 4.63698 | + | 4.63698i | 0.150602 | + | 0.150602i | ||||
\(949\) | − | 9.37362i | − | 0.304281i | ||||||
\(950\) | 2.80059 | − | 12.5666i | 0.0908630 | − | 0.407716i | ||||
\(951\) | −23.8542 | −0.773527 | ||||||||
\(952\) | 5.46154 | + | 5.46154i | 0.177009 | + | 0.177009i | ||||
\(953\) | 13.5507 | + | 13.5507i | 0.438952 | + | 0.438952i | 0.891659 | − | 0.452707i | \(-0.149542\pi\) |
−0.452707 | + | 0.891659i | \(0.649542\pi\) | |||||||
\(954\) | −9.08835 | −0.294246 | ||||||||
\(955\) | 24.9648 | + | 13.7142i | 0.807841 | + | 0.443780i | ||||
\(956\) | 4.39325 | 0.142088 | ||||||||
\(957\) | −4.06969 | + | 4.06969i | −0.131555 | + | 0.131555i | ||||
\(958\) | −23.6721 | − | 23.6721i | −0.764812 | − | 0.764812i | ||||
\(959\) | 7.15135i | 0.230929i | ||||||||
\(960\) | −2.14708 | + | 0.624526i | −0.0692968 | + | 0.0201565i | ||||
\(961\) | 10.1890 | 0.328677 | ||||||||
\(962\) | −0.554554 | + | 0.554554i | −0.0178795 | + | 0.0178795i | ||||
\(963\) | 5.06879 | + | 5.06879i | 0.163339 | + | 0.163339i | ||||
\(964\) | 7.44107 | 0.239661 | ||||||||
\(965\) | −1.62863 | − | 5.59914i | −0.0524276 | − | 0.180243i | ||||
\(966\) | 18.1311 | − | 14.6251i | 0.583358 | − | 0.470555i | ||||
\(967\) | 40.6269 | + | 40.6269i | 1.30647 | + | 1.30647i | 0.923943 | + | 0.382529i | \(0.124947\pi\) |
0.382529 | + | 0.923943i | \(0.375053\pi\) | |||||||
\(968\) | 5.54104 | − | 5.54104i | 0.178096 | − | 0.178096i | ||||
\(969\) | 4.09465i | 0.131539i | ||||||||
\(970\) | 11.8664 | − | 21.6012i | 0.381008 | − | 0.693574i | ||||
\(971\) | − | 35.7932i | − | 1.14866i | −0.818624 | − | 0.574330i | \(-0.805263\pi\) | ||
0.818624 | − | 0.574330i | \(-0.194737\pi\) | |||||||
\(972\) | 0.707107 | + | 0.707107i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | 30.5518 | + | 30.5518i | 0.979445 | + | 0.979445i | ||||
\(974\) | 0.265977i | 0.00852246i | ||||||||
\(975\) | 7.27090 | − | 4.62075i | 0.232855 | − | 0.147982i | ||||
\(976\) | − | 14.4727i | − | 0.463259i | ||||||
\(977\) | 7.74791 | − | 7.74791i | 0.247878 | − | 0.247878i | −0.572221 | − | 0.820099i | \(-0.693918\pi\) |
0.820099 | + | 0.572221i | \(0.193918\pi\) | |||||||
\(978\) | −3.88265 | + | 3.88265i | −0.124154 | + | 0.124154i | ||||
\(979\) | − | 6.13567i | − | 0.196097i | ||||||
\(980\) | −17.8638 | + | 32.5186i | −0.570638 | + | 1.03877i | ||||
\(981\) | − | 7.67531i | − | 0.245054i | ||||||
\(982\) | 11.2723 | + | 11.2723i | 0.359713 | + | 0.359713i | ||||
\(983\) | 25.9694 | + | 25.9694i | 0.828296 | + | 0.828296i | 0.987281 | − | 0.158985i | \(-0.0508223\pi\) |
−0.158985 | + | 0.987281i | \(0.550822\pi\) | |||||||
\(984\) | 10.2290i | 0.326088i | ||||||||
\(985\) | 36.9317 | − | 10.7424i | 1.17674 | − | 0.342281i | ||||
\(986\) | − | 5.14535i | − | 0.163861i | ||||||
\(987\) | −44.2255 | + | 44.2255i | −1.40771 | + | 1.40771i | ||||
\(988\) | −3.13720 | − | 3.13720i | −0.0998077 | − | 0.0998077i | ||||
\(989\) | 27.5549 | + | 34.1604i | 0.876194 | + | 1.08624i | ||||
\(990\) | 3.81902 | − | 1.11085i | 0.121376 | − | 0.0353050i | ||||
\(991\) | −52.9168 | −1.68096 | −0.840478 | − | 0.541846i | \(-0.817726\pi\) | ||||
−0.840478 | + | 0.541846i | \(0.817726\pi\) | |||||||
\(992\) | 4.53812 | + | 4.53812i | 0.144085 | + | 0.144085i | ||||
\(993\) | 6.71934 | − | 6.71934i | 0.213232 | − | 0.213232i | ||||
\(994\) | 64.6770 | 2.05143 | ||||||||
\(995\) | 5.78386 | − | 10.5287i | 0.183361 | − | 0.333784i | ||||
\(996\) | 3.62690i | 0.114923i | ||||||||
\(997\) | 20.1714 | + | 20.1714i | 0.638835 | + | 0.638835i | 0.950268 | − | 0.311433i | \(-0.100809\pi\) |
−0.311433 | + | 0.950268i | \(0.600809\pi\) | |||||||
\(998\) | 16.5516 | − | 16.5516i | 0.523931 | − | 0.523931i | ||||
\(999\) | 0.455173 | 0.0144010 |
(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 | 690.2.j.b.367.2 | ✓ | 24 | |
5.3 | odd | 4 | inner | 690.2.j.b.643.5 | yes | 24 | |
23.22 | odd | 2 | inner | 690.2.j.b.367.5 | yes | 24 | |
115.68 | even | 4 | inner | 690.2.j.b.643.2 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.j.b.367.2 | ✓ | 24 | 1.1 | even | 1 | trivial | |
690.2.j.b.367.5 | yes | 24 | 23.22 | odd | 2 | inner | |
690.2.j.b.643.2 | yes | 24 | 115.68 | even | 4 | inner | |
690.2.j.b.643.5 | yes | 24 | 5.3 | odd | 4 | inner |