Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(689,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.689");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.h (of order \(2\), degree \(1\), 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: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 689.8 | ||
Character | \(\chi\) | \(=\) | 690.689 |
Dual form | 690.2.h.b.689.6 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.44698 | + | 0.951967i | −0.835416 | + | 0.549618i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.42959 | − | 1.71938i | 0.639334 | − | 0.768929i | ||||
\(6\) | −1.44698 | + | 0.951967i | −0.590728 | + | 0.388639i | ||||
\(7\) | −4.73682 | −1.79035 | −0.895174 | − | 0.445717i | \(-0.852949\pi\) | ||||
−0.895174 | + | 0.445717i | \(0.852949\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.18752 | − | 2.75496i | 0.395839 | − | 0.918320i | ||||
\(10\) | 1.42959 | − | 1.71938i | 0.452078 | − | 0.543715i | ||||
\(11\) | −0.109553 | −0.0330314 | −0.0165157 | − | 0.999864i | \(-0.505257\pi\) | ||||
−0.0165157 | + | 0.999864i | \(0.505257\pi\) | |||||||
\(12\) | −1.44698 | + | 0.951967i | −0.417708 | + | 0.274809i | ||||
\(13\) | − | 2.46994i | − | 0.685037i | −0.939511 | − | 0.342518i | \(-0.888720\pi\) | ||
0.939511 | − | 0.342518i | \(-0.111280\pi\) | |||||||
\(14\) | −4.73682 | −1.26597 | ||||||||
\(15\) | −0.431808 | + | 3.84884i | −0.111492 | + | 0.993765i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 3.72035i | − | 0.902318i | −0.892443 | − | 0.451159i | \(-0.851011\pi\) | ||
0.892443 | − | 0.451159i | \(-0.148989\pi\) | |||||||
\(18\) | 1.18752 | − | 2.75496i | 0.279900 | − | 0.649350i | ||||
\(19\) | − | 6.76462i | − | 1.55191i | −0.630788 | − | 0.775955i | \(-0.717268\pi\) | ||
0.630788 | − | 0.775955i | \(-0.282732\pi\) | |||||||
\(20\) | 1.42959 | − | 1.71938i | 0.319667 | − | 0.384464i | ||||
\(21\) | 6.85409 | − | 4.50929i | 1.49568 | − | 0.984008i | ||||
\(22\) | −0.109553 | −0.0233567 | ||||||||
\(23\) | 4.67990 | − | 1.04813i | 0.975826 | − | 0.218551i | ||||
\(24\) | −1.44698 | + | 0.951967i | −0.295364 | + | 0.194319i | ||||
\(25\) | −0.912517 | − | 4.91603i | −0.182503 | − | 0.983205i | ||||
\(26\) | − | 2.46994i | − | 0.484394i | ||||||
\(27\) | 0.904315 | + | 5.11686i | 0.174035 | + | 0.984739i | ||||
\(28\) | −4.73682 | −0.895174 | ||||||||
\(29\) | 7.05802i | 1.31064i | 0.755351 | + | 0.655320i | \(0.227466\pi\) | ||||
−0.755351 | + | 0.655320i | \(0.772534\pi\) | |||||||
\(30\) | −0.431808 | + | 3.84884i | −0.0788370 | + | 0.702698i | ||||
\(31\) | −9.34339 | −1.67812 | −0.839061 | − | 0.544038i | \(-0.816895\pi\) | ||||
−0.839061 | + | 0.544038i | \(0.816895\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.158521 | − | 0.104291i | 0.0275949 | − | 0.0181547i | ||||
\(34\) | − | 3.72035i | − | 0.638035i | ||||||
\(35\) | −6.77173 | + | 8.14437i | −1.14463 | + | 1.37665i | ||||
\(36\) | 1.18752 | − | 2.75496i | 0.197920 | − | 0.459160i | ||||
\(37\) | −1.34148 | −0.220538 | −0.110269 | − | 0.993902i | \(-0.535171\pi\) | ||||
−0.110269 | + | 0.993902i | \(0.535171\pi\) | |||||||
\(38\) | − | 6.76462i | − | 1.09737i | ||||||
\(39\) | 2.35130 | + | 3.57395i | 0.376509 | + | 0.572291i | ||||
\(40\) | 1.42959 | − | 1.71938i | 0.226039 | − | 0.271857i | ||||
\(41\) | − | 7.38300i | − | 1.15303i | −0.817086 | − | 0.576516i | \(-0.804412\pi\) | ||
0.817086 | − | 0.576516i | \(-0.195588\pi\) | |||||||
\(42\) | 6.85409 | − | 4.50929i | 1.05761 | − | 0.695799i | ||||
\(43\) | 2.31465 | 0.352980 | 0.176490 | − | 0.984302i | \(-0.443526\pi\) | ||||
0.176490 | + | 0.984302i | \(0.443526\pi\) | |||||||
\(44\) | −0.109553 | −0.0165157 | ||||||||
\(45\) | −3.03915 | − | 5.98027i | −0.453049 | − | 0.891485i | ||||
\(46\) | 4.67990 | − | 1.04813i | 0.690013 | − | 0.154539i | ||||
\(47\) | 5.53476 | 0.807327 | 0.403664 | − | 0.914907i | \(-0.367737\pi\) | ||||
0.403664 | + | 0.914907i | \(0.367737\pi\) | |||||||
\(48\) | −1.44698 | + | 0.951967i | −0.208854 | + | 0.137405i | ||||
\(49\) | 15.4374 | 2.20535 | ||||||||
\(50\) | −0.912517 | − | 4.91603i | −0.129049 | − | 0.695231i | ||||
\(51\) | 3.54165 | + | 5.38329i | 0.495931 | + | 0.753811i | ||||
\(52\) | − | 2.46994i | − | 0.342518i | ||||||
\(53\) | − | 3.77179i | − | 0.518096i | −0.965864 | − | 0.259048i | \(-0.916591\pi\) | ||
0.965864 | − | 0.259048i | \(-0.0834087\pi\) | |||||||
\(54\) | 0.904315 | + | 5.11686i | 0.123062 | + | 0.696316i | ||||
\(55\) | −0.156616 | + | 0.188362i | −0.0211181 | + | 0.0253988i | ||||
\(56\) | −4.73682 | −0.632984 | ||||||||
\(57\) | 6.43970 | + | 9.78829i | 0.852959 | + | 1.29649i | ||||
\(58\) | 7.05802i | 0.926763i | ||||||||
\(59\) | − | 4.18459i | − | 0.544788i | −0.962186 | − | 0.272394i | \(-0.912185\pi\) | ||
0.962186 | − | 0.272394i | \(-0.0878154\pi\) | |||||||
\(60\) | −0.431808 | + | 3.84884i | −0.0557462 | + | 0.496883i | ||||
\(61\) | − | 7.57377i | − | 0.969722i | −0.874591 | − | 0.484861i | \(-0.838870\pi\) | ||
0.874591 | − | 0.484861i | \(-0.161130\pi\) | |||||||
\(62\) | −9.34339 | −1.18661 | ||||||||
\(63\) | −5.62505 | + | 13.0497i | −0.708690 | + | 1.64411i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.24675 | − | 3.53101i | −0.526745 | − | 0.437967i | ||||
\(66\) | 0.158521 | − | 0.104291i | 0.0195126 | − | 0.0128373i | ||||
\(67\) | −5.95975 | −0.728099 | −0.364050 | − | 0.931380i | \(-0.618606\pi\) | ||||
−0.364050 | + | 0.931380i | \(0.618606\pi\) | |||||||
\(68\) | − | 3.72035i | − | 0.451159i | ||||||
\(69\) | −5.77394 | + | 5.97173i | −0.695101 | + | 0.718912i | ||||
\(70\) | −6.77173 | + | 8.14437i | −0.809376 | + | 0.973439i | ||||
\(71\) | − | 9.66771i | − | 1.14735i | −0.819084 | − | 0.573673i | \(-0.805518\pi\) | ||
0.819084 | − | 0.573673i | \(-0.194482\pi\) | |||||||
\(72\) | 1.18752 | − | 2.75496i | 0.139950 | − | 0.324675i | ||||
\(73\) | 9.28694i | 1.08695i | 0.839424 | + | 0.543477i | \(0.182892\pi\) | ||||
−0.839424 | + | 0.543477i | \(0.817108\pi\) | |||||||
\(74\) | −1.34148 | −0.155944 | ||||||||
\(75\) | 6.00029 | + | 6.24472i | 0.692854 | + | 0.721078i | ||||
\(76\) | − | 6.76462i | − | 0.775955i | ||||||
\(77\) | 0.518931 | 0.0591377 | ||||||||
\(78\) | 2.35130 | + | 3.57395i | 0.266232 | + | 0.404671i | ||||
\(79\) | 12.3843i | 1.39334i | 0.717389 | + | 0.696672i | \(0.245337\pi\) | ||||
−0.717389 | + | 0.696672i | \(0.754663\pi\) | |||||||
\(80\) | 1.42959 | − | 1.71938i | 0.159834 | − | 0.192232i | ||||
\(81\) | −6.17961 | − | 6.54312i | −0.686623 | − | 0.727014i | ||||
\(82\) | − | 7.38300i | − | 0.815316i | ||||||
\(83\) | 16.6139i | 1.82362i | 0.410616 | + | 0.911808i | \(0.365314\pi\) | ||||
−0.410616 | + | 0.911808i | \(0.634686\pi\) | |||||||
\(84\) | 6.85409 | − | 4.50929i | 0.747842 | − | 0.492004i | ||||
\(85\) | −6.39669 | − | 5.31860i | −0.693819 | − | 0.576883i | ||||
\(86\) | 2.31465 | 0.249595 | ||||||||
\(87\) | −6.71900 | − | 10.2128i | −0.720352 | − | 1.09493i | ||||
\(88\) | −0.109553 | −0.0116784 | ||||||||
\(89\) | 10.2277 | 1.08413 | 0.542067 | − | 0.840335i | \(-0.317642\pi\) | ||||
0.542067 | + | 0.840335i | \(0.317642\pi\) | |||||||
\(90\) | −3.03915 | − | 5.98027i | −0.320354 | − | 0.630375i | ||||
\(91\) | 11.6996i | 1.22645i | ||||||||
\(92\) | 4.67990 | − | 1.04813i | 0.487913 | − | 0.109275i | ||||
\(93\) | 13.5197 | − | 8.89460i | 1.40193 | − | 0.922327i | ||||
\(94\) | 5.53476 | 0.570867 | ||||||||
\(95\) | −11.6309 | − | 9.67067i | −1.19331 | − | 0.992190i | ||||
\(96\) | −1.44698 | + | 0.951967i | −0.147682 | + | 0.0971597i | ||||
\(97\) | −9.94453 | −1.00971 | −0.504857 | − | 0.863203i | \(-0.668455\pi\) | ||||
−0.504857 | + | 0.863203i | \(0.668455\pi\) | |||||||
\(98\) | 15.4374 | 1.55941 | ||||||||
\(99\) | −0.130096 | + | 0.301813i | −0.0130751 | + | 0.0303334i | ||||
\(100\) | −0.912517 | − | 4.91603i | −0.0912517 | − | 0.491603i | ||||
\(101\) | 8.68562i | 0.864251i | 0.901813 | + | 0.432126i | \(0.142236\pi\) | ||||
−0.901813 | + | 0.432126i | \(0.857764\pi\) | |||||||
\(102\) | 3.54165 | + | 5.38329i | 0.350676 | + | 0.533025i | ||||
\(103\) | 3.27739 | 0.322931 | 0.161465 | − | 0.986878i | \(-0.448378\pi\) | ||||
0.161465 | + | 0.986878i | \(0.448378\pi\) | |||||||
\(104\) | − | 2.46994i | − | 0.242197i | ||||||
\(105\) | 2.04540 | − | 18.2312i | 0.199610 | − | 1.77919i | ||||
\(106\) | − | 3.77179i | − | 0.366349i | ||||||
\(107\) | 1.42323i | 0.137589i | 0.997631 | + | 0.0687945i | \(0.0219153\pi\) | ||||
−0.997631 | + | 0.0687945i | \(0.978085\pi\) | |||||||
\(108\) | 0.904315 | + | 5.11686i | 0.0870177 | + | 0.492370i | ||||
\(109\) | 18.7318i | 1.79418i | 0.441849 | + | 0.897090i | \(0.354323\pi\) | ||||
−0.441849 | + | 0.897090i | \(0.645677\pi\) | |||||||
\(110\) | −0.156616 | + | 0.188362i | −0.0149327 | + | 0.0179597i | ||||
\(111\) | 1.94110 | − | 1.27704i | 0.184241 | − | 0.121212i | ||||
\(112\) | −4.73682 | −0.447587 | ||||||||
\(113\) | − | 3.47135i | − | 0.326557i | −0.986580 | − | 0.163278i | \(-0.947793\pi\) | ||
0.986580 | − | 0.163278i | \(-0.0522069\pi\) | |||||||
\(114\) | 6.43970 | + | 9.78829i | 0.603133 | + | 0.916757i | ||||
\(115\) | 4.88822 | − | 9.54491i | 0.455829 | − | 0.890067i | ||||
\(116\) | 7.05802i | 0.655320i | ||||||||
\(117\) | −6.80457 | − | 2.93309i | −0.629083 | − | 0.271164i | ||||
\(118\) | − | 4.18459i | − | 0.385223i | ||||||
\(119\) | 17.6226i | 1.61546i | ||||||||
\(120\) | −0.431808 | + | 3.84884i | −0.0394185 | + | 0.351349i | ||||
\(121\) | −10.9880 | −0.998909 | ||||||||
\(122\) | − | 7.57377i | − | 0.685697i | ||||||
\(123\) | 7.02838 | + | 10.6831i | 0.633727 | + | 0.963261i | ||||
\(124\) | −9.34339 | −0.839061 | ||||||||
\(125\) | −9.75703 | − | 5.45897i | −0.872696 | − | 0.488265i | ||||
\(126\) | −5.62505 | + | 13.0497i | −0.501119 | + | 1.16256i | ||||
\(127\) | 3.36092i | 0.298234i | 0.988820 | + | 0.149117i | \(0.0476431\pi\) | ||||
−0.988820 | + | 0.149117i | \(0.952357\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −3.34925 | + | 2.20347i | −0.294885 | + | 0.194005i | ||||
\(130\) | −4.24675 | − | 3.53101i | −0.372465 | − | 0.309690i | ||||
\(131\) | − | 13.6399i | − | 1.19173i | −0.803086 | − | 0.595863i | \(-0.796810\pi\) | ||
0.803086 | − | 0.595863i | \(-0.203190\pi\) | |||||||
\(132\) | 0.158521 | − | 0.104291i | 0.0137975 | − | 0.00907733i | ||||
\(133\) | 32.0428i | 2.77846i | ||||||||
\(134\) | −5.95975 | −0.514844 | ||||||||
\(135\) | 10.0906 | + | 5.76017i | 0.868461 | + | 0.495757i | ||||
\(136\) | − | 3.72035i | − | 0.319018i | ||||||
\(137\) | 0.102320i | 0.00874176i | 0.999990 | + | 0.00437088i | \(0.00139130\pi\) | ||||
−0.999990 | + | 0.00437088i | \(0.998609\pi\) | |||||||
\(138\) | −5.77394 | + | 5.97173i | −0.491510 | + | 0.508348i | ||||
\(139\) | 1.57186 | 0.133323 | 0.0666617 | − | 0.997776i | \(-0.478765\pi\) | ||||
0.0666617 | + | 0.997776i | \(0.478765\pi\) | |||||||
\(140\) | −6.77173 | + | 8.14437i | −0.572315 | + | 0.688325i | ||||
\(141\) | −8.00870 | + | 5.26891i | −0.674454 | + | 0.443722i | ||||
\(142\) | − | 9.66771i | − | 0.811296i | ||||||
\(143\) | 0.270588i | 0.0226277i | ||||||||
\(144\) | 1.18752 | − | 2.75496i | 0.0989598 | − | 0.229580i | ||||
\(145\) | 12.1354 | + | 10.0901i | 1.00779 | + | 0.837937i | ||||
\(146\) | 9.28694i | 0.768592i | ||||||||
\(147\) | −22.3377 | + | 14.6959i | −1.84238 | + | 1.21210i | ||||
\(148\) | −1.34148 | −0.110269 | ||||||||
\(149\) | −10.9226 | −0.894817 | −0.447408 | − | 0.894330i | \(-0.647653\pi\) | ||||
−0.447408 | + | 0.894330i | \(0.647653\pi\) | |||||||
\(150\) | 6.00029 | + | 6.24472i | 0.489922 | + | 0.509879i | ||||
\(151\) | 6.42872 | 0.523162 | 0.261581 | − | 0.965182i | \(-0.415756\pi\) | ||||
0.261581 | + | 0.965182i | \(0.415756\pi\) | |||||||
\(152\) | − | 6.76462i | − | 0.548683i | ||||||
\(153\) | −10.2494 | − | 4.41798i | −0.828617 | − | 0.357173i | ||||
\(154\) | 0.518931 | 0.0418166 | ||||||||
\(155\) | −13.3573 | + | 16.0648i | −1.07288 | + | 1.29036i | ||||
\(156\) | 2.35130 | + | 3.57395i | 0.188254 | + | 0.286145i | ||||
\(157\) | 24.1285 | 1.92567 | 0.962834 | − | 0.270095i | \(-0.0870552\pi\) | ||||
0.962834 | + | 0.270095i | \(0.0870552\pi\) | |||||||
\(158\) | 12.3843i | 0.985244i | ||||||||
\(159\) | 3.59062 | + | 5.45772i | 0.284755 | + | 0.432825i | ||||
\(160\) | 1.42959 | − | 1.71938i | 0.113019 | − | 0.135929i | ||||
\(161\) | −22.1678 | + | 4.96481i | −1.74707 | + | 0.391281i | ||||
\(162\) | −6.17961 | − | 6.54312i | −0.485516 | − | 0.514076i | ||||
\(163\) | − | 15.4395i | − | 1.20932i | −0.796485 | − | 0.604659i | \(-0.793310\pi\) | ||
0.796485 | − | 0.604659i | \(-0.206690\pi\) | |||||||
\(164\) | − | 7.38300i | − | 0.576516i | ||||||
\(165\) | 0.0473058 | − | 0.421650i | 0.00368275 | − | 0.0328254i | ||||
\(166\) | 16.6139i | 1.28949i | ||||||||
\(167\) | 4.86290 | 0.376302 | 0.188151 | − | 0.982140i | \(-0.439751\pi\) | ||||
0.188151 | + | 0.982140i | \(0.439751\pi\) | |||||||
\(168\) | 6.85409 | − | 4.50929i | 0.528804 | − | 0.347899i | ||||
\(169\) | 6.89942 | 0.530725 | ||||||||
\(170\) | −6.39669 | − | 5.31860i | −0.490604 | − | 0.407918i | ||||
\(171\) | −18.6363 | − | 8.03310i | −1.42515 | − | 0.614307i | ||||
\(172\) | 2.31465 | 0.176490 | ||||||||
\(173\) | 17.0492 | 1.29623 | 0.648114 | − | 0.761543i | \(-0.275558\pi\) | ||||
0.648114 | + | 0.761543i | \(0.275558\pi\) | |||||||
\(174\) | −6.71900 | − | 10.2128i | −0.509366 | − | 0.774232i | ||||
\(175\) | 4.32242 | + | 23.2863i | 0.326745 | + | 1.76028i | ||||
\(176\) | −0.109553 | −0.00825785 | ||||||||
\(177\) | 3.98360 | + | 6.05503i | 0.299425 | + | 0.455124i | ||||
\(178\) | 10.2277 | 0.766598 | ||||||||
\(179\) | − | 8.37101i | − | 0.625679i | −0.949806 | − | 0.312839i | \(-0.898720\pi\) | ||
0.949806 | − | 0.312839i | \(-0.101280\pi\) | |||||||
\(180\) | −3.03915 | − | 5.98027i | −0.226525 | − | 0.445743i | ||||
\(181\) | 3.91727i | 0.291169i | 0.989346 | + | 0.145584i | \(0.0465062\pi\) | ||||
−0.989346 | + | 0.145584i | \(0.953494\pi\) | |||||||
\(182\) | 11.6996i | 0.867234i | ||||||||
\(183\) | 7.20998 | + | 10.9591i | 0.532977 | + | 0.810121i | ||||
\(184\) | 4.67990 | − | 1.04813i | 0.345006 | − | 0.0772693i | ||||
\(185\) | −1.91777 | + | 2.30651i | −0.140997 | + | 0.169578i | ||||
\(186\) | 13.5197 | − | 8.89460i | 0.991314 | − | 0.652183i | ||||
\(187\) | 0.407575i | 0.0298048i | ||||||||
\(188\) | 5.53476 | 0.403664 | ||||||||
\(189\) | −4.28357 | − | 24.2376i | −0.311584 | − | 1.76303i | ||||
\(190\) | −11.6309 | − | 9.67067i | −0.843797 | − | 0.701584i | ||||
\(191\) | 10.0632 | 0.728147 | 0.364073 | − | 0.931370i | \(-0.381386\pi\) | ||||
0.364073 | + | 0.931370i | \(0.381386\pi\) | |||||||
\(192\) | −1.44698 | + | 0.951967i | −0.104427 | + | 0.0687023i | ||||
\(193\) | 1.36921i | 0.0985576i | 0.998785 | + | 0.0492788i | \(0.0156923\pi\) | ||||
−0.998785 | + | 0.0492788i | \(0.984308\pi\) | |||||||
\(194\) | −9.94453 | −0.713976 | ||||||||
\(195\) | 9.50638 | + | 1.06654i | 0.680766 | + | 0.0763764i | ||||
\(196\) | 15.4374 | 1.10267 | ||||||||
\(197\) | 3.46037 | 0.246541 | 0.123271 | − | 0.992373i | \(-0.460662\pi\) | ||||
0.123271 | + | 0.992373i | \(0.460662\pi\) | |||||||
\(198\) | −0.130096 | + | 0.301813i | −0.00924550 | + | 0.0214489i | ||||
\(199\) | − | 2.84735i | − | 0.201843i | −0.994894 | − | 0.100922i | \(-0.967821\pi\) | ||
0.994894 | − | 0.100922i | \(-0.0321791\pi\) | |||||||
\(200\) | −0.912517 | − | 4.91603i | −0.0645247 | − | 0.347616i | ||||
\(201\) | 8.62365 | − | 5.67348i | 0.608265 | − | 0.400177i | ||||
\(202\) | 8.68562i | 0.611118i | ||||||||
\(203\) | − | 33.4325i | − | 2.34650i | ||||||
\(204\) | 3.54165 | + | 5.38329i | 0.247965 | + | 0.376906i | ||||
\(205\) | −12.6942 | − | 10.5547i | −0.886599 | − | 0.737173i | ||||
\(206\) | 3.27739 | 0.228347 | ||||||||
\(207\) | 2.66990 | − | 14.1376i | 0.185571 | − | 0.982631i | ||||
\(208\) | − | 2.46994i | − | 0.171259i | ||||||
\(209\) | 0.741083i | 0.0512618i | ||||||||
\(210\) | 2.04540 | − | 18.2312i | 0.141146 | − | 1.25807i | ||||
\(211\) | −11.9262 | −0.821033 | −0.410517 | − | 0.911853i | \(-0.634652\pi\) | ||||
−0.410517 | + | 0.911853i | \(0.634652\pi\) | |||||||
\(212\) | − | 3.77179i | − | 0.259048i | ||||||
\(213\) | 9.20334 | + | 13.9890i | 0.630603 | + | 0.958511i | ||||
\(214\) | 1.42323i | 0.0972901i | ||||||||
\(215\) | 3.30901 | − | 3.97975i | 0.225672 | − | 0.271417i | ||||
\(216\) | 0.904315 | + | 5.11686i | 0.0615308 | + | 0.348158i | ||||
\(217\) | 44.2579 | 3.00442 | ||||||||
\(218\) | 18.7318i | 1.26868i | ||||||||
\(219\) | −8.84086 | − | 13.4380i | −0.597410 | − | 0.908058i | ||||
\(220\) | −0.156616 | + | 0.188362i | −0.0105590 | + | 0.0126994i | ||||
\(221\) | −9.18903 | −0.618121 | ||||||||
\(222\) | 1.94110 | − | 1.27704i | 0.130278 | − | 0.0857095i | ||||
\(223\) | − | 18.5236i | − | 1.24043i | −0.784432 | − | 0.620215i | \(-0.787045\pi\) | ||
0.784432 | − | 0.620215i | \(-0.212955\pi\) | |||||||
\(224\) | −4.73682 | −0.316492 | ||||||||
\(225\) | −14.6271 | − | 3.32392i | −0.975139 | − | 0.221595i | ||||
\(226\) | − | 3.47135i | − | 0.230910i | ||||||
\(227\) | − | 15.3110i | − | 1.01623i | −0.861290 | − | 0.508115i | \(-0.830343\pi\) | ||
0.861290 | − | 0.508115i | \(-0.169657\pi\) | |||||||
\(228\) | 6.43970 | + | 9.78829i | 0.426479 | + | 0.648245i | ||||
\(229\) | − | 5.31624i | − | 0.351307i | −0.984452 | − | 0.175654i | \(-0.943796\pi\) | ||
0.984452 | − | 0.175654i | \(-0.0562038\pi\) | |||||||
\(230\) | 4.88822 | − | 9.54491i | 0.322320 | − | 0.629373i | ||||
\(231\) | −0.750884 | + | 0.494005i | −0.0494045 | + | 0.0325032i | ||||
\(232\) | 7.05802i | 0.463381i | ||||||||
\(233\) | 8.00870 | 0.524667 | 0.262334 | − | 0.964977i | \(-0.415508\pi\) | ||||
0.262334 | + | 0.964977i | \(0.415508\pi\) | |||||||
\(234\) | −6.80457 | − | 2.93309i | −0.444829 | − | 0.191742i | ||||
\(235\) | 7.91246 | − | 9.51634i | 0.516152 | − | 0.620777i | ||||
\(236\) | − | 4.18459i | − | 0.272394i | ||||||
\(237\) | −11.7895 | − | 17.9199i | −0.765808 | − | 1.16402i | ||||
\(238\) | 17.6226i | 1.14231i | ||||||||
\(239\) | − | 1.30708i | − | 0.0845482i | −0.999106 | − | 0.0422741i | \(-0.986540\pi\) | ||
0.999106 | − | 0.0422741i | \(-0.0134603\pi\) | |||||||
\(240\) | −0.431808 | + | 3.84884i | −0.0278731 | + | 0.248441i | ||||
\(241\) | 9.16266i | 0.590219i | 0.955463 | + | 0.295109i | \(0.0953561\pi\) | ||||
−0.955463 | + | 0.295109i | \(0.904644\pi\) | |||||||
\(242\) | −10.9880 | −0.706335 | ||||||||
\(243\) | 15.1706 | + | 3.58500i | 0.973196 | + | 0.229978i | ||||
\(244\) | − | 7.57377i | − | 0.484861i | ||||||
\(245\) | 22.0693 | − | 26.5427i | 1.40995 | − | 1.69575i | ||||
\(246\) | 7.02838 | + | 10.6831i | 0.448113 | + | 0.681128i | ||||
\(247\) | −16.7082 | −1.06312 | ||||||||
\(248\) | −9.34339 | −0.593306 | ||||||||
\(249\) | −15.8159 | − | 24.0401i | −1.00229 | − | 1.52348i | ||||
\(250\) | −9.75703 | − | 5.45897i | −0.617089 | − | 0.345255i | ||||
\(251\) | 24.8840 | 1.57067 | 0.785333 | − | 0.619073i | \(-0.212492\pi\) | ||||
0.785333 | + | 0.619073i | \(0.212492\pi\) | |||||||
\(252\) | −5.62505 | + | 13.0497i | −0.354345 | + | 0.822056i | ||||
\(253\) | −0.512695 | + | 0.114826i | −0.0322329 | + | 0.00721903i | ||||
\(254\) | 3.36092i | 0.210883i | ||||||||
\(255\) | 14.3190 | + | 1.60648i | 0.896693 | + | 0.100602i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −18.7650 | −1.17053 | −0.585264 | − | 0.810843i | \(-0.699009\pi\) | ||||
−0.585264 | + | 0.810843i | \(0.699009\pi\) | |||||||
\(258\) | −3.34925 | + | 2.20347i | −0.208515 | + | 0.137182i | ||||
\(259\) | 6.35434 | 0.394839 | ||||||||
\(260\) | −4.24675 | − | 3.53101i | −0.263372 | − | 0.218984i | ||||
\(261\) | 19.4445 | + | 8.38151i | 1.20359 | + | 0.518803i | ||||
\(262\) | − | 13.6399i | − | 0.842677i | ||||||
\(263\) | 9.31348i | 0.574294i | 0.957887 | + | 0.287147i | \(0.0927068\pi\) | ||||
−0.957887 | + | 0.287147i | \(0.907293\pi\) | |||||||
\(264\) | 0.158521 | − | 0.104291i | 0.00975628 | − | 0.00641864i | ||||
\(265\) | −6.48514 | − | 5.39214i | −0.398379 | − | 0.331236i | ||||
\(266\) | 32.0428i | 1.96467i | ||||||||
\(267\) | −14.7993 | + | 9.73643i | −0.905702 | + | 0.595860i | ||||
\(268\) | −5.95975 | −0.364050 | ||||||||
\(269\) | − | 14.0040i | − | 0.853841i | −0.904289 | − | 0.426921i | \(-0.859598\pi\) | ||
0.904289 | − | 0.426921i | \(-0.140402\pi\) | |||||||
\(270\) | 10.0906 | + | 5.76017i | 0.614095 | + | 0.350553i | ||||
\(271\) | 19.5682 | 1.18868 | 0.594340 | − | 0.804214i | \(-0.297413\pi\) | ||||
0.594340 | + | 0.804214i | \(0.297413\pi\) | |||||||
\(272\) | − | 3.72035i | − | 0.225580i | ||||||
\(273\) | −11.1377 | − | 16.9292i | −0.674082 | − | 1.02460i | ||||
\(274\) | 0.102320i | 0.00618136i | ||||||||
\(275\) | 0.0999687 | + | 0.538564i | 0.00602834 | + | 0.0324766i | ||||
\(276\) | −5.77394 | + | 5.97173i | −0.347550 | + | 0.359456i | ||||
\(277\) | 12.1168i | 0.728026i | 0.931394 | + | 0.364013i | \(0.118594\pi\) | ||||
−0.931394 | + | 0.364013i | \(0.881406\pi\) | |||||||
\(278\) | 1.57186 | 0.0942739 | ||||||||
\(279\) | −11.0954 | + | 25.7407i | −0.664266 | + | 1.54105i | ||||
\(280\) | −6.77173 | + | 8.14437i | −0.404688 | + | 0.486719i | ||||
\(281\) | −0.997575 | −0.0595103 | −0.0297552 | − | 0.999557i | \(-0.509473\pi\) | ||||
−0.0297552 | + | 0.999557i | \(0.509473\pi\) | |||||||
\(282\) | −8.00870 | + | 5.26891i | −0.476911 | + | 0.313759i | ||||
\(283\) | 8.27225 | 0.491734 | 0.245867 | − | 0.969304i | \(-0.420927\pi\) | ||||
0.245867 | + | 0.969304i | \(0.420927\pi\) | |||||||
\(284\) | − | 9.66771i | − | 0.573673i | ||||||
\(285\) | 26.0359 | + | 2.92102i | 1.54223 | + | 0.173026i | ||||
\(286\) | 0.270588i | 0.0160002i | ||||||||
\(287\) | 34.9719i | 2.06433i | ||||||||
\(288\) | 1.18752 | − | 2.75496i | 0.0699751 | − | 0.162338i | ||||
\(289\) | 3.15896 | 0.185821 | ||||||||
\(290\) | 12.1354 | + | 10.0901i | 0.712615 | + | 0.592511i | ||||
\(291\) | 14.3896 | − | 9.46687i | 0.843531 | − | 0.554958i | ||||
\(292\) | 9.28694i | 0.543477i | ||||||||
\(293\) | − | 5.35051i | − | 0.312580i | −0.987711 | − | 0.156290i | \(-0.950047\pi\) | ||
0.987711 | − | 0.156290i | \(-0.0499535\pi\) | |||||||
\(294\) | −22.3377 | + | 14.6959i | −1.30276 | + | 0.857083i | ||||
\(295\) | −7.19490 | − | 5.98227i | −0.418903 | − | 0.348301i | ||||
\(296\) | −1.34148 | −0.0779718 | ||||||||
\(297\) | −0.0990701 | − | 0.560565i | −0.00574863 | − | 0.0325273i | ||||
\(298\) | −10.9226 | −0.632731 | ||||||||
\(299\) | −2.58882 | − | 11.5590i | −0.149715 | − | 0.668476i | ||||
\(300\) | 6.00029 | + | 6.24472i | 0.346427 | + | 0.360539i | ||||
\(301\) | −10.9641 | −0.631958 | ||||||||
\(302\) | 6.42872 | 0.369931 | ||||||||
\(303\) | −8.26842 | − | 12.5679i | −0.475008 | − | 0.722009i | ||||
\(304\) | − | 6.76462i | − | 0.387978i | ||||||
\(305\) | −13.0222 | − | 10.8274i | −0.745648 | − | 0.619977i | ||||
\(306\) | −10.2494 | − | 4.41798i | −0.585921 | − | 0.252559i | ||||
\(307\) | − | 23.6777i | − | 1.35136i | −0.737197 | − | 0.675678i | \(-0.763851\pi\) | ||
0.737197 | − | 0.675678i | \(-0.236149\pi\) | |||||||
\(308\) | 0.518931 | 0.0295688 | ||||||||
\(309\) | −4.74232 | + | 3.11997i | −0.269781 | + | 0.177489i | ||||
\(310\) | −13.3573 | + | 16.0648i | −0.758641 | + | 0.912420i | ||||
\(311\) | 12.8720i | 0.729906i | 0.931026 | + | 0.364953i | \(0.118915\pi\) | ||||
−0.931026 | + | 0.364953i | \(0.881085\pi\) | |||||||
\(312\) | 2.35130 | + | 3.57395i | 0.133116 | + | 0.202335i | ||||
\(313\) | −4.59243 | −0.259579 | −0.129790 | − | 0.991542i | \(-0.541430\pi\) | ||||
−0.129790 | + | 0.991542i | \(0.541430\pi\) | |||||||
\(314\) | 24.1285 | 1.36165 | ||||||||
\(315\) | 14.3959 | + | 28.3274i | 0.811116 | + | 1.59607i | ||||
\(316\) | 12.3843i | 0.696672i | ||||||||
\(317\) | 3.67077 | 0.206171 | 0.103085 | − | 0.994673i | \(-0.467129\pi\) | ||||
0.103085 | + | 0.994673i | \(0.467129\pi\) | |||||||
\(318\) | 3.59062 | + | 5.45772i | 0.201352 | + | 0.306054i | ||||
\(319\) | − | 0.773225i | − | 0.0432923i | ||||||
\(320\) | 1.42959 | − | 1.71938i | 0.0799168 | − | 0.0961161i | ||||
\(321\) | −1.35487 | − | 2.05939i | −0.0756215 | − | 0.114944i | ||||
\(322\) | −22.1678 | + | 4.96481i | −1.23536 | + | 0.276678i | ||||
\(323\) | −25.1668 | −1.40032 | ||||||||
\(324\) | −6.17961 | − | 6.54312i | −0.343311 | − | 0.363507i | ||||
\(325\) | −12.1423 | + | 2.25386i | −0.673532 | + | 0.125022i | ||||
\(326\) | − | 15.4395i | − | 0.855116i | ||||||
\(327\) | −17.8320 | − | 27.1046i | −0.986114 | − | 1.49889i | ||||
\(328\) | − | 7.38300i | − | 0.407658i | ||||||
\(329\) | −26.2171 | −1.44540 | ||||||||
\(330\) | 0.0473058 | − | 0.421650i | 0.00260410 | − | 0.0232111i | ||||
\(331\) | −20.9486 | −1.15144 | −0.575721 | − | 0.817646i | \(-0.695278\pi\) | ||||
−0.575721 | + | 0.817646i | \(0.695278\pi\) | |||||||
\(332\) | 16.6139i | 0.911808i | ||||||||
\(333\) | −1.59303 | + | 3.69572i | −0.0872974 | + | 0.202524i | ||||
\(334\) | 4.86290 | 0.266086 | ||||||||
\(335\) | −8.52003 | + | 10.2471i | −0.465499 | + | 0.559856i | ||||
\(336\) | 6.85409 | − | 4.50929i | 0.373921 | − | 0.246002i | ||||
\(337\) | 8.58764 | 0.467799 | 0.233899 | − | 0.972261i | \(-0.424851\pi\) | ||||
0.233899 | + | 0.972261i | \(0.424851\pi\) | |||||||
\(338\) | 6.89942 | 0.375279 | ||||||||
\(339\) | 3.30461 | + | 5.02298i | 0.179482 | + | 0.272811i | ||||
\(340\) | −6.39669 | − | 5.31860i | −0.346909 | − | 0.288442i | ||||
\(341\) | 1.02359 | 0.0554307 | ||||||||
\(342\) | −18.6363 | − | 8.03310i | −1.00773 | − | 0.434381i | ||||
\(343\) | −39.9665 | −2.15799 | ||||||||
\(344\) | 2.31465 | 0.124797 | ||||||||
\(345\) | 2.01327 | + | 18.4647i | 0.108391 | + | 0.994108i | ||||
\(346\) | 17.0492 | 0.916572 | ||||||||
\(347\) | 29.9351 | 1.60700 | 0.803499 | − | 0.595305i | \(-0.202969\pi\) | ||||
0.803499 | + | 0.595305i | \(0.202969\pi\) | |||||||
\(348\) | −6.71900 | − | 10.2128i | −0.360176 | − | 0.547465i | ||||
\(349\) | 22.4642 | 1.20248 | 0.601240 | − | 0.799068i | \(-0.294673\pi\) | ||||
0.601240 | + | 0.799068i | \(0.294673\pi\) | |||||||
\(350\) | 4.32242 | + | 23.2863i | 0.231043 | + | 1.24471i | ||||
\(351\) | 12.6383 | − | 2.23360i | 0.674583 | − | 0.119221i | ||||
\(352\) | −0.109553 | −0.00583918 | ||||||||
\(353\) | −13.4442 | −0.715563 | −0.357782 | − | 0.933805i | \(-0.616467\pi\) | ||||
−0.357782 | + | 0.933805i | \(0.616467\pi\) | |||||||
\(354\) | 3.98360 | + | 6.05503i | 0.211726 | + | 0.321821i | ||||
\(355\) | −16.6224 | − | 13.8209i | −0.882228 | − | 0.733538i | ||||
\(356\) | 10.2277 | 0.542067 | ||||||||
\(357\) | −16.7762 | − | 25.4996i | −0.887889 | − | 1.34958i | ||||
\(358\) | − | 8.37101i | − | 0.442422i | ||||||
\(359\) | 32.7887 | 1.73052 | 0.865260 | − | 0.501323i | \(-0.167153\pi\) | ||||
0.865260 | + | 0.501323i | \(0.167153\pi\) | |||||||
\(360\) | −3.03915 | − | 5.98027i | −0.160177 | − | 0.315188i | ||||
\(361\) | −26.7601 | −1.40843 | ||||||||
\(362\) | 3.91727i | 0.205887i | ||||||||
\(363\) | 15.8994 | − | 10.4602i | 0.834504 | − | 0.549019i | ||||
\(364\) | 11.6996i | 0.613227i | ||||||||
\(365\) | 15.9678 | + | 13.2766i | 0.835790 | + | 0.694927i | ||||
\(366\) | 7.20998 | + | 10.9591i | 0.376872 | + | 0.572842i | ||||
\(367\) | −0.619262 | −0.0323252 | −0.0161626 | − | 0.999869i | \(-0.505145\pi\) | ||||
−0.0161626 | + | 0.999869i | \(0.505145\pi\) | |||||||
\(368\) | 4.67990 | − | 1.04813i | 0.243956 | − | 0.0546376i | ||||
\(369\) | −20.3399 | − | 8.76744i | −1.05885 | − | 0.456415i | ||||
\(370\) | −1.91777 | + | 2.30651i | −0.0997002 | + | 0.119910i | ||||
\(371\) | 17.8663i | 0.927571i | ||||||||
\(372\) | 13.5197 | − | 8.89460i | 0.700965 | − | 0.461163i | ||||
\(373\) | 33.9726 | 1.75904 | 0.879518 | − | 0.475866i | \(-0.157865\pi\) | ||||
0.879518 | + | 0.475866i | \(0.157865\pi\) | |||||||
\(374\) | 0.407575i | 0.0210752i | ||||||||
\(375\) | 19.3150 | − | 1.38935i | 0.997423 | − | 0.0717456i | ||||
\(376\) | 5.53476 | 0.285433 | ||||||||
\(377\) | 17.4328 | 0.897837 | ||||||||
\(378\) | −4.28357 | − | 24.2376i | −0.220323 | − | 1.24665i | ||||
\(379\) | 6.22071i | 0.319537i | 0.987155 | + | 0.159768i | \(0.0510747\pi\) | ||||
−0.987155 | + | 0.159768i | \(0.948925\pi\) | |||||||
\(380\) | −11.6309 | − | 9.67067i | −0.596654 | − | 0.496095i | ||||
\(381\) | −3.19949 | − | 4.86320i | −0.163915 | − | 0.249149i | ||||
\(382\) | 10.0632 | 0.514877 | ||||||||
\(383\) | − | 0.328653i | − | 0.0167934i | −0.999965 | − | 0.00839669i | \(-0.997327\pi\) | ||
0.999965 | − | 0.00839669i | \(-0.00267278\pi\) | |||||||
\(384\) | −1.44698 | + | 0.951967i | −0.0738410 | + | 0.0485799i | ||||
\(385\) | 0.741861 | − | 0.892238i | 0.0378087 | − | 0.0454727i | ||||
\(386\) | 1.36921i | 0.0696908i | ||||||||
\(387\) | 2.74868 | − | 6.37676i | 0.139723 | − | 0.324149i | ||||
\(388\) | −9.94453 | −0.504857 | ||||||||
\(389\) | 28.8039 | 1.46042 | 0.730208 | − | 0.683225i | \(-0.239423\pi\) | ||||
0.730208 | + | 0.683225i | \(0.239423\pi\) | |||||||
\(390\) | 9.50638 | + | 1.06654i | 0.481374 | + | 0.0540063i | ||||
\(391\) | −3.89942 | − | 17.4109i | −0.197202 | − | 0.880505i | ||||
\(392\) | 15.4374 | 0.779707 | ||||||||
\(393\) | 12.9848 | + | 19.7367i | 0.654994 | + | 0.995586i | ||||
\(394\) | 3.46037 | 0.174331 | ||||||||
\(395\) | 21.2933 | + | 17.7046i | 1.07138 | + | 0.890813i | ||||
\(396\) | −0.130096 | + | 0.301813i | −0.00653756 | + | 0.0151667i | ||||
\(397\) | − | 25.5527i | − | 1.28245i | −0.767352 | − | 0.641226i | \(-0.778426\pi\) | ||
0.767352 | − | 0.641226i | \(-0.221574\pi\) | |||||||
\(398\) | − | 2.84735i | − | 0.142725i | ||||||
\(399\) | −30.5037 | − | 46.3653i | −1.52709 | − | 2.32117i | ||||
\(400\) | −0.912517 | − | 4.91603i | −0.0456258 | − | 0.245801i | ||||
\(401\) | −16.8426 | −0.841080 | −0.420540 | − | 0.907274i | \(-0.638159\pi\) | ||||
−0.420540 | + | 0.907274i | \(0.638159\pi\) | |||||||
\(402\) | 8.62365 | − | 5.67348i | 0.430109 | − | 0.282968i | ||||
\(403\) | 23.0776i | 1.14958i | ||||||||
\(404\) | 8.68562i | 0.432126i | ||||||||
\(405\) | −20.0844 | + | 1.27106i | −0.998003 | + | 0.0631594i | ||||
\(406\) | − | 33.4325i | − | 1.65923i | ||||||
\(407\) | 0.146963 | 0.00728466 | ||||||||
\(408\) | 3.54165 | + | 5.38329i | 0.175338 | + | 0.266512i | ||||
\(409\) | 1.73082 | 0.0855838 | 0.0427919 | − | 0.999084i | \(-0.486375\pi\) | ||||
0.0427919 | + | 0.999084i | \(0.486375\pi\) | |||||||
\(410\) | −12.6942 | − | 10.5547i | −0.626920 | − | 0.521260i | ||||
\(411\) | −0.0974049 | − | 0.148055i | −0.00480463 | − | 0.00730300i | ||||
\(412\) | 3.27739 | 0.161465 | ||||||||
\(413\) | 19.8216i | 0.975359i | ||||||||
\(414\) | 2.66990 | − | 14.1376i | 0.131218 | − | 0.694825i | ||||
\(415\) | 28.5656 | + | 23.7512i | 1.40223 | + | 1.16590i | ||||
\(416\) | − | 2.46994i | − | 0.121099i | ||||||
\(417\) | −2.27445 | + | 1.49636i | −0.111381 | + | 0.0732770i | ||||
\(418\) | 0.741083i | 0.0362475i | ||||||||
\(419\) | −0.0603174 | −0.00294670 | −0.00147335 | − | 0.999999i | \(-0.500469\pi\) | ||||
−0.00147335 | + | 0.999999i | \(0.500469\pi\) | |||||||
\(420\) | 2.04540 | − | 18.2312i | 0.0998051 | − | 0.889593i | ||||
\(421\) | − | 16.7804i | − | 0.817829i | −0.912573 | − | 0.408914i | \(-0.865908\pi\) | ||
0.912573 | − | 0.408914i | \(-0.134092\pi\) | |||||||
\(422\) | −11.9262 | −0.580558 | ||||||||
\(423\) | 6.57262 | − | 15.2480i | 0.319572 | − | 0.741385i | ||||
\(424\) | − | 3.77179i | − | 0.183174i | ||||||
\(425\) | −18.2894 | + | 3.39489i | −0.887164 | + | 0.164676i | ||||
\(426\) | 9.20334 | + | 13.9890i | 0.445903 | + | 0.677770i | ||||
\(427\) | 35.8756i | 1.73614i | ||||||||
\(428\) | 1.42323i | 0.0687945i | ||||||||
\(429\) | −0.257591 | − | 0.391536i | −0.0124366 | − | 0.0189035i | ||||
\(430\) | 3.30901 | − | 3.97975i | 0.159575 | − | 0.191921i | ||||
\(431\) | 4.36493 | 0.210251 | 0.105126 | − | 0.994459i | \(-0.466476\pi\) | ||||
0.105126 | + | 0.994459i | \(0.466476\pi\) | |||||||
\(432\) | 0.904315 | + | 5.11686i | 0.0435089 | + | 0.246185i | ||||
\(433\) | −29.9206 | −1.43789 | −0.718947 | − | 0.695065i | \(-0.755375\pi\) | ||||
−0.718947 | + | 0.695065i | \(0.755375\pi\) | |||||||
\(434\) | 44.2579 | 2.12445 | ||||||||
\(435\) | −27.1651 | − | 3.04771i | −1.30247 | − | 0.146126i | ||||
\(436\) | 18.7318i | 0.897090i | ||||||||
\(437\) | −7.09021 | − | 31.6577i | −0.339171 | − | 1.51439i | ||||
\(438\) | −8.84086 | − | 13.4380i | −0.422433 | − | 0.642094i | ||||
\(439\) | −16.9861 | −0.810702 | −0.405351 | − | 0.914161i | \(-0.632851\pi\) | ||||
−0.405351 | + | 0.914161i | \(0.632851\pi\) | |||||||
\(440\) | −0.156616 | + | 0.188362i | −0.00746637 | + | 0.00897983i | ||||
\(441\) | 18.3322 | − | 42.5295i | 0.872962 | − | 2.02521i | ||||
\(442\) | −9.18903 | −0.437078 | ||||||||
\(443\) | −24.5257 | −1.16525 | −0.582626 | − | 0.812740i | \(-0.697975\pi\) | ||||
−0.582626 | + | 0.812740i | \(0.697975\pi\) | |||||||
\(444\) | 1.94110 | − | 1.27704i | 0.0921203 | − | 0.0606058i | ||||
\(445\) | 14.6215 | − | 17.5853i | 0.693124 | − | 0.833622i | ||||
\(446\) | − | 18.5236i | − | 0.877117i | ||||||
\(447\) | 15.8049 | − | 10.3980i | 0.747544 | − | 0.491808i | ||||
\(448\) | −4.73682 | −0.223793 | ||||||||
\(449\) | 16.0667i | 0.758233i | 0.925349 | + | 0.379117i | \(0.123772\pi\) | ||||
−0.925349 | + | 0.379117i | \(0.876228\pi\) | |||||||
\(450\) | −14.6271 | − | 3.32392i | −0.689527 | − | 0.156691i | ||||
\(451\) | 0.808828i | 0.0380862i | ||||||||
\(452\) | − | 3.47135i | − | 0.163278i | ||||||
\(453\) | −9.30225 | + | 6.11993i | −0.437058 | + | 0.287540i | ||||
\(454\) | − | 15.3110i | − | 0.718582i | ||||||
\(455\) | 20.1161 | + | 16.7257i | 0.943056 | + | 0.784114i | ||||
\(456\) | 6.43970 | + | 9.78829i | 0.301566 | + | 0.458379i | ||||
\(457\) | −13.2071 | −0.617802 | −0.308901 | − | 0.951094i | \(-0.599961\pi\) | ||||
−0.308901 | + | 0.951094i | \(0.599961\pi\) | |||||||
\(458\) | − | 5.31624i | − | 0.248412i | ||||||
\(459\) | 19.0365 | − | 3.36437i | 0.888549 | − | 0.157035i | ||||
\(460\) | 4.88822 | − | 9.54491i | 0.227914 | − | 0.445034i | ||||
\(461\) | − | 25.4941i | − | 1.18738i | −0.804695 | − | 0.593689i | \(-0.797671\pi\) | ||
0.804695 | − | 0.593689i | \(-0.202329\pi\) | |||||||
\(462\) | −0.750884 | + | 0.494005i | −0.0349343 | + | 0.0229832i | ||||
\(463\) | 20.0822i | 0.933298i | 0.884443 | + | 0.466649i | \(0.154539\pi\) | ||||
−0.884443 | + | 0.466649i | \(0.845461\pi\) | |||||||
\(464\) | 7.05802i | 0.327660i | ||||||||
\(465\) | 4.03455 | − | 35.9612i | 0.187098 | − | 1.66766i | ||||
\(466\) | 8.00870 | 0.370996 | ||||||||
\(467\) | − | 14.7644i | − | 0.683215i | −0.939843 | − | 0.341607i | \(-0.889029\pi\) | ||
0.939843 | − | 0.341607i | \(-0.110971\pi\) | |||||||
\(468\) | −6.80457 | − | 2.93309i | −0.314541 | − | 0.135582i | ||||
\(469\) | 28.2302 | 1.30355 | ||||||||
\(470\) | 7.91246 | − | 9.51634i | 0.364975 | − | 0.438956i | ||||
\(471\) | −34.9136 | + | 22.9696i | −1.60873 | + | 1.05838i | ||||
\(472\) | − | 4.18459i | − | 0.192612i | ||||||
\(473\) | −0.253576 | −0.0116594 | ||||||||
\(474\) | −11.7895 | − | 17.9199i | −0.541508 | − | 0.823088i | ||||
\(475\) | −33.2551 | + | 6.17283i | −1.52585 | + | 0.283229i | ||||
\(476\) | 17.6226i | 0.807732i | ||||||||
\(477\) | −10.3911 | − | 4.47907i | −0.475778 | − | 0.205082i | ||||
\(478\) | − | 1.30708i | − | 0.0597846i | ||||||
\(479\) | −0.527998 | −0.0241248 | −0.0120624 | − | 0.999927i | \(-0.503840\pi\) | ||||
−0.0120624 | + | 0.999927i | \(0.503840\pi\) | |||||||
\(480\) | −0.431808 | + | 3.84884i | −0.0197093 | + | 0.175675i | ||||
\(481\) | 3.31336i | 0.151076i | ||||||||
\(482\) | 9.16266i | 0.417348i | ||||||||
\(483\) | 27.3501 | − | 28.2870i | 1.24447 | − | 1.28710i | ||||
\(484\) | −10.9880 | −0.499454 | ||||||||
\(485\) | −14.2167 | + | 17.0984i | −0.645545 | + | 0.776398i | ||||
\(486\) | 15.1706 | + | 3.58500i | 0.688153 | + | 0.162619i | ||||
\(487\) | 15.1423i | 0.686164i | 0.939306 | + | 0.343082i | \(0.111471\pi\) | ||||
−0.939306 | + | 0.343082i | \(0.888529\pi\) | |||||||
\(488\) | − | 7.57377i | − | 0.342849i | ||||||
\(489\) | 14.6979 | + | 22.3407i | 0.664663 | + | 1.01028i | ||||
\(490\) | 22.0693 | − | 26.5427i | 0.996987 | − | 1.19908i | ||||
\(491\) | 23.0745i | 1.04134i | 0.853759 | + | 0.520668i | \(0.174317\pi\) | ||||
−0.853759 | + | 0.520668i | \(0.825683\pi\) | |||||||
\(492\) | 7.02838 | + | 10.6831i | 0.316864 | + | 0.481630i | ||||
\(493\) | 26.2583 | 1.18262 | ||||||||
\(494\) | −16.7082 | −0.751736 | ||||||||
\(495\) | 0.332947 | + | 0.655154i | 0.0149648 | + | 0.0294470i | ||||
\(496\) | −9.34339 | −0.419530 | ||||||||
\(497\) | 45.7942i | 2.05415i | ||||||||
\(498\) | −15.8159 | − | 24.0401i | −0.708728 | − | 1.07726i | ||||
\(499\) | 2.99246 | 0.133961 | 0.0669805 | − | 0.997754i | \(-0.478663\pi\) | ||||
0.0669805 | + | 0.997754i | \(0.478663\pi\) | |||||||
\(500\) | −9.75703 | − | 5.45897i | −0.436348 | − | 0.244132i | ||||
\(501\) | −7.03652 | + | 4.62932i | −0.314369 | + | 0.206823i | ||||
\(502\) | 24.8840 | 1.11063 | ||||||||
\(503\) | 35.8449i | 1.59825i | 0.601167 | + | 0.799123i | \(0.294703\pi\) | ||||
−0.601167 | + | 0.799123i | \(0.705297\pi\) | |||||||
\(504\) | −5.62505 | + | 13.0497i | −0.250560 | + | 0.581281i | ||||
\(505\) | 14.9339 | + | 12.4169i | 0.664548 | + | 0.552545i | ||||
\(506\) | −0.512695 | + | 0.114826i | −0.0227921 | + | 0.00510462i | ||||
\(507\) | −9.98334 | + | 6.56802i | −0.443376 | + | 0.291696i | ||||
\(508\) | 3.36092i | 0.149117i | ||||||||
\(509\) | 15.8139i | 0.700937i | 0.936575 | + | 0.350468i | \(0.113978\pi\) | ||||
−0.936575 | + | 0.350468i | \(0.886022\pi\) | |||||||
\(510\) | 14.3190 | + | 1.60648i | 0.634058 | + | 0.0711361i | ||||
\(511\) | − | 43.9905i | − | 1.94603i | ||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 34.6136 | − | 6.11735i | 1.52823 | − | 0.270087i | ||||
\(514\) | −18.7650 | −0.827688 | ||||||||
\(515\) | 4.68534 | − | 5.63507i | 0.206461 | − | 0.248311i | ||||
\(516\) | −3.34925 | + | 2.20347i | −0.147443 | + | 0.0970023i | ||||
\(517\) | −0.606348 | −0.0266671 | ||||||||
\(518\) | 6.35434 | 0.279193 | ||||||||
\(519\) | −24.6699 | + | 16.2303i | −1.08289 | + | 0.712431i | ||||
\(520\) | −4.24675 | − | 3.53101i | −0.186232 | − | 0.154845i | ||||
\(521\) | −21.4453 | −0.939538 | −0.469769 | − | 0.882789i | \(-0.655663\pi\) | ||||
−0.469769 | + | 0.882789i | \(0.655663\pi\) | |||||||
\(522\) | 19.4445 | + | 8.38151i | 0.851065 | + | 0.366849i | ||||
\(523\) | 21.4978 | 0.940033 | 0.470017 | − | 0.882658i | \(-0.344248\pi\) | ||||
0.470017 | + | 0.882658i | \(0.344248\pi\) | |||||||
\(524\) | − | 13.6399i | − | 0.595863i | ||||||
\(525\) | −28.4223 | − | 29.5801i | −1.24045 | − | 1.29098i | ||||
\(526\) | 9.31348i | 0.406087i | ||||||||
\(527\) | 34.7607i | 1.51420i | ||||||||
\(528\) | 0.158521 | − | 0.104291i | 0.00689873 | − | 0.00453866i | ||||
\(529\) | 20.8028 | − | 9.81029i | 0.904471 | − | 0.426534i | ||||
\(530\) | −6.48514 | − | 5.39214i | −0.281696 | − | 0.234219i | ||||
\(531\) | −11.5284 | − | 4.96928i | −0.500289 | − | 0.215648i | ||||
\(532\) | 32.0428i | 1.38923i | ||||||||
\(533\) | −18.2355 | −0.789869 | ||||||||
\(534\) | −14.7993 | + | 9.73643i | −0.640428 | + | 0.421336i | ||||
\(535\) | 2.44707 | + | 2.03464i | 0.105796 | + | 0.0879654i | ||||
\(536\) | −5.95975 | −0.257422 | ||||||||
\(537\) | 7.96893 | + | 12.1127i | 0.343885 | + | 0.522702i | ||||
\(538\) | − | 14.0040i | − | 0.603757i | ||||||
\(539\) | −1.69121 | −0.0728456 | ||||||||
\(540\) | 10.0906 | + | 5.76017i | 0.434231 | + | 0.247878i | ||||
\(541\) | −28.9815 | −1.24601 | −0.623005 | − | 0.782218i | \(-0.714088\pi\) | ||||
−0.623005 | + | 0.782218i | \(0.714088\pi\) | |||||||
\(542\) | 19.5682 | 0.840524 | ||||||||
\(543\) | −3.72911 | − | 5.66822i | −0.160032 | − | 0.243247i | ||||
\(544\) | − | 3.72035i | − | 0.159509i | ||||||
\(545\) | 32.2070 | + | 26.7789i | 1.37960 | + | 1.14708i | ||||
\(546\) | −11.1377 | − | 16.9292i | −0.476648 | − | 0.724501i | ||||
\(547\) | − | 31.1585i | − | 1.33224i | −0.745844 | − | 0.666121i | \(-0.767954\pi\) | ||
0.745844 | − | 0.666121i | \(-0.232046\pi\) | |||||||
\(548\) | 0.102320i | 0.00437088i | ||||||||
\(549\) | −20.8654 | − | 8.99399i | −0.890515 | − | 0.383854i | ||||
\(550\) | 0.0999687 | + | 0.538564i | 0.00426268 | + | 0.0229644i | ||||
\(551\) | 47.7448 | 2.03400 | ||||||||
\(552\) | −5.77394 | + | 5.97173i | −0.245755 | + | 0.254174i | ||||
\(553\) | − | 58.6622i | − | 2.49457i | ||||||
\(554\) | 12.1168i | 0.514792i | ||||||||
\(555\) | 0.579261 | − | 5.16313i | 0.0245883 | − | 0.219163i | ||||
\(556\) | 1.57186 | 0.0666617 | ||||||||
\(557\) | − | 33.0466i | − | 1.40023i | −0.714030 | − | 0.700115i | \(-0.753132\pi\) | ||
0.714030 | − | 0.700115i | \(-0.246868\pi\) | |||||||
\(558\) | −11.0954 | + | 25.7407i | −0.469707 | + | 1.08969i | ||||
\(559\) | − | 5.71703i | − | 0.241805i | ||||||
\(560\) | −6.77173 | + | 8.14437i | −0.286158 | + | 0.344163i | ||||
\(561\) | −0.387998 | − | 0.589754i | −0.0163813 | − | 0.0248994i | ||||
\(562\) | −0.997575 | −0.0420801 | ||||||||
\(563\) | − | 22.9282i | − | 0.966310i | −0.875535 | − | 0.483155i | \(-0.839491\pi\) | ||
0.875535 | − | 0.483155i | \(-0.160509\pi\) | |||||||
\(564\) | −8.00870 | + | 5.26891i | −0.337227 | + | 0.221861i | ||||
\(565\) | −5.96855 | − | 4.96262i | −0.251099 | − | 0.208779i | ||||
\(566\) | 8.27225 | 0.347709 | ||||||||
\(567\) | 29.2717 | + | 30.9936i | 1.22929 | + | 1.30161i | ||||
\(568\) | − | 9.66771i | − | 0.405648i | ||||||
\(569\) | −7.12332 | −0.298625 | −0.149312 | − | 0.988790i | \(-0.547706\pi\) | ||||
−0.149312 | + | 0.988790i | \(0.547706\pi\) | |||||||
\(570\) | 26.0359 | + | 2.92102i | 1.09052 | + | 0.122348i | ||||
\(571\) | − | 15.0075i | − | 0.628044i | −0.949416 | − | 0.314022i | \(-0.898323\pi\) | ||
0.949416 | − | 0.314022i | \(-0.101677\pi\) | |||||||
\(572\) | 0.270588i | 0.0113139i | ||||||||
\(573\) | −14.5613 | + | 9.57982i | −0.608305 | + | 0.400203i | ||||
\(574\) | 34.9719i | 1.45970i | ||||||||
\(575\) | −9.42312 | − | 22.0501i | −0.392971 | − | 0.919551i | ||||
\(576\) | 1.18752 | − | 2.75496i | 0.0494799 | − | 0.114790i | ||||
\(577\) | 32.3173i | 1.34539i | 0.739922 | + | 0.672693i | \(0.234862\pi\) | ||||
−0.739922 | + | 0.672693i | \(0.765138\pi\) | |||||||
\(578\) | 3.15896 | 0.131396 | ||||||||
\(579\) | −1.30344 | − | 1.98122i | −0.0541691 | − | 0.0823366i | ||||
\(580\) | 12.1354 | + | 10.0901i | 0.503895 | + | 0.418969i | ||||
\(581\) | − | 78.6972i | − | 3.26491i | ||||||
\(582\) | 14.3896 | − | 9.46687i | 0.596467 | − | 0.392414i | ||||
\(583\) | 0.413210i | 0.0171134i | ||||||||
\(584\) | 9.28694i | 0.384296i | ||||||||
\(585\) | −14.7709 | + | 7.50650i | −0.610700 | + | 0.310355i | ||||
\(586\) | − | 5.35051i | − | 0.221028i | ||||||
\(587\) | −9.64803 | −0.398217 | −0.199108 | − | 0.979977i | \(-0.563805\pi\) | ||||
−0.199108 | + | 0.979977i | \(0.563805\pi\) | |||||||
\(588\) | −22.3377 | + | 14.6959i | −0.921190 | + | 0.606049i | ||||
\(589\) | 63.2045i | 2.60429i | ||||||||
\(590\) | −7.19490 | − | 5.98227i | −0.296209 | − | 0.246286i | ||||
\(591\) | −5.00710 | + | 3.29416i | −0.205964 | + | 0.135504i | ||||
\(592\) | −1.34148 | −0.0551344 | ||||||||
\(593\) | 12.6479 | 0.519385 | 0.259693 | − | 0.965691i | \(-0.416379\pi\) | ||||
0.259693 | + | 0.965691i | \(0.416379\pi\) | |||||||
\(594\) | −0.0990701 | − | 0.560565i | −0.00406490 | − | 0.0230003i | ||||
\(595\) | 30.3000 | + | 25.1932i | 1.24218 | + | 1.03282i | ||||
\(596\) | −10.9226 | −0.447408 | ||||||||
\(597\) | 2.71058 | + | 4.12007i | 0.110937 | + | 0.168623i | ||||
\(598\) | −2.58882 | − | 11.5590i | −0.105865 | − | 0.472684i | ||||
\(599\) | − | 24.2565i | − | 0.991094i | −0.868581 | − | 0.495547i | \(-0.834968\pi\) | ||
0.868581 | − | 0.495547i | \(-0.165032\pi\) | |||||||
\(600\) | 6.00029 | + | 6.24472i | 0.244961 | + | 0.254940i | ||||
\(601\) | 3.91095 | 0.159531 | 0.0797655 | − | 0.996814i | \(-0.474583\pi\) | ||||
0.0797655 | + | 0.996814i | \(0.474583\pi\) | |||||||
\(602\) | −10.9641 | −0.446862 | ||||||||
\(603\) | −7.07730 | + | 16.4189i | −0.288210 | + | 0.668628i | ||||
\(604\) | 6.42872 | 0.261581 | ||||||||
\(605\) | −15.7084 | + | 18.8925i | −0.638637 | + | 0.768090i | ||||
\(606\) | −8.26842 | − | 12.5679i | −0.335882 | − | 0.510537i | ||||
\(607\) | − | 31.9532i | − | 1.29694i | −0.761241 | − | 0.648469i | \(-0.775410\pi\) | ||
0.761241 | − | 0.648469i | \(-0.224590\pi\) | |||||||
\(608\) | − | 6.76462i | − | 0.274342i | ||||||
\(609\) | 31.8267 | + | 48.3763i | 1.28968 | + | 1.96031i | ||||
\(610\) | −13.0222 | − | 10.8274i | −0.527252 | − | 0.438390i | ||||
\(611\) | − | 13.6705i | − | 0.553049i | ||||||
\(612\) | −10.2494 | − | 4.41798i | −0.414308 | − | 0.178586i | ||||
\(613\) | 6.81990 | 0.275453 | 0.137727 | − | 0.990470i | \(-0.456020\pi\) | ||||
0.137727 | + | 0.990470i | \(0.456020\pi\) | |||||||
\(614\) | − | 23.6777i | − | 0.955553i | ||||||
\(615\) | 28.4160 | + | 3.18804i | 1.14584 | + | 0.128554i | ||||
\(616\) | 0.518931 | 0.0209083 | ||||||||
\(617\) | 7.46733i | 0.300623i | 0.988639 | + | 0.150312i | \(0.0480277\pi\) | ||||
−0.988639 | + | 0.150312i | \(0.951972\pi\) | |||||||
\(618\) | −4.74232 | + | 3.11997i | −0.190764 | + | 0.125503i | ||||
\(619\) | − | 41.5273i | − | 1.66912i | −0.550915 | − | 0.834561i | \(-0.685721\pi\) | ||
0.550915 | − | 0.834561i | \(-0.314279\pi\) | |||||||
\(620\) | −13.3573 | + | 16.0648i | −0.536440 | + | 0.645178i | ||||
\(621\) | 9.59524 | + | 22.9985i | 0.385044 | + | 0.922898i | ||||
\(622\) | 12.8720i | 0.516122i | ||||||||
\(623\) | −48.4467 | −1.94098 | ||||||||
\(624\) | 2.35130 | + | 3.57395i | 0.0941272 | + | 0.143073i | ||||
\(625\) | −23.3346 | + | 8.97191i | −0.933385 | + | 0.358877i | ||||
\(626\) | −4.59243 | −0.183550 | ||||||||
\(627\) | −0.705486 | − | 1.07233i | −0.0281744 | − | 0.0428249i | ||||
\(628\) | 24.1285 | 0.962834 | ||||||||
\(629\) | 4.99077i | 0.198995i | ||||||||
\(630\) | 14.3959 | + | 28.3274i | 0.573545 | + | 1.12859i | ||||
\(631\) | 36.9311i | 1.47020i | 0.677956 | + | 0.735102i | \(0.262866\pi\) | ||||
−0.677956 | + | 0.735102i | \(0.737134\pi\) | |||||||
\(632\) | 12.3843i | 0.492622i | ||||||||
\(633\) | 17.2570 | − | 11.3533i | 0.685904 | − | 0.451255i | ||||
\(634\) | 3.67077 | 0.145785 | ||||||||
\(635\) | 5.77870 | + | 4.80476i | 0.229321 | + | 0.190671i | ||||
\(636\) | 3.59062 | + | 5.45772i | 0.142377 | + | 0.216413i | ||||
\(637\) | − | 38.1294i | − | 1.51074i | ||||||
\(638\) | − | 0.773225i | − | 0.0306123i | ||||||
\(639\) | −26.6342 | − | 11.4806i | −1.05363 | − | 0.454164i | ||||
\(640\) | 1.42959 | − | 1.71938i | 0.0565097 | − | 0.0679644i | ||||
\(641\) | 23.5864 | 0.931606 | 0.465803 | − | 0.884888i | \(-0.345765\pi\) | ||||
0.465803 | + | 0.884888i | \(0.345765\pi\) | |||||||
\(642\) | −1.35487 | − | 2.05939i | −0.0534725 | − | 0.0812777i | ||||
\(643\) | −25.9305 | −1.02260 | −0.511299 | − | 0.859403i | \(-0.670836\pi\) | ||||
−0.511299 | + | 0.859403i | \(0.670836\pi\) | |||||||
\(644\) | −22.1678 | + | 4.96481i | −0.873534 | + | 0.195641i | ||||
\(645\) | −0.999484 | + | 8.90870i | −0.0393546 | + | 0.350780i | ||||
\(646\) | −25.1668 | −0.990174 | ||||||||
\(647\) | 5.05526 | 0.198743 | 0.0993713 | − | 0.995050i | \(-0.468317\pi\) | ||||
0.0993713 | + | 0.995050i | \(0.468317\pi\) | |||||||
\(648\) | −6.17961 | − | 6.54312i | −0.242758 | − | 0.257038i | ||||
\(649\) | 0.458433i | 0.0179951i | ||||||||
\(650\) | −12.1423 | + | 2.25386i | −0.476259 | + | 0.0884036i | ||||
\(651\) | −64.0404 | + | 42.1321i | −2.50994 | + | 1.65129i | ||||
\(652\) | − | 15.4395i | − | 0.604659i | ||||||
\(653\) | −9.19815 | −0.359952 | −0.179976 | − | 0.983671i | \(-0.557602\pi\) | ||||
−0.179976 | + | 0.983671i | \(0.557602\pi\) | |||||||
\(654\) | −17.8320 | − | 27.1046i | −0.697288 | − | 1.05987i | ||||
\(655\) | −23.4522 | − | 19.4996i | −0.916352 | − | 0.761911i | ||||
\(656\) | − | 7.38300i | − | 0.288258i | ||||||
\(657\) | 25.5851 | + | 11.0284i | 0.998171 | + | 0.430259i | ||||
\(658\) | −26.2171 | −1.02205 | ||||||||
\(659\) | −40.3687 | −1.57254 | −0.786270 | − | 0.617883i | \(-0.787991\pi\) | ||||
−0.786270 | + | 0.617883i | \(0.787991\pi\) | |||||||
\(660\) | 0.0473058 | − | 0.421650i | 0.00184137 | − | 0.0164127i | ||||
\(661\) | 16.6400i | 0.647220i | 0.946191 | + | 0.323610i | \(0.104897\pi\) | ||||
−0.946191 | + | 0.323610i | \(0.895103\pi\) | |||||||
\(662\) | −20.9486 | −0.814192 | ||||||||
\(663\) | 13.2964 | − | 8.74766i | 0.516388 | − | 0.339731i | ||||
\(664\) | 16.6139i | 0.644746i | ||||||||
\(665\) | 55.0936 | + | 45.8082i | 2.13644 | + | 1.77636i | ||||
\(666\) | −1.59303 | + | 3.69572i | −0.0617286 | + | 0.143206i | ||||
\(667\) | 7.39773 | + | 33.0308i | 0.286441 | + | 1.27896i | ||||
\(668\) | 4.86290 | 0.188151 | ||||||||
\(669\) | 17.6338 | + | 26.8033i | 0.681764 | + | 1.03628i | ||||
\(670\) | −8.52003 | + | 10.2471i | −0.329157 | + | 0.395878i | ||||
\(671\) | 0.829727i | 0.0320313i | ||||||||
\(672\) | 6.85409 | − | 4.50929i | 0.264402 | − | 0.173950i | ||||
\(673\) | 32.2214i | 1.24204i | 0.783793 | + | 0.621022i | \(0.213282\pi\) | ||||
−0.783793 | + | 0.621022i | \(0.786718\pi\) | |||||||
\(674\) | 8.58764 | 0.330784 | ||||||||
\(675\) | 24.3294 | − | 9.11485i | 0.936439 | − | 0.350831i | ||||
\(676\) | 6.89942 | 0.265362 | ||||||||
\(677\) | 23.6610i | 0.909366i | 0.890653 | + | 0.454683i | \(0.150247\pi\) | ||||
−0.890653 | + | 0.454683i | \(0.849753\pi\) | |||||||
\(678\) | 3.30461 | + | 5.02298i | 0.126913 | + | 0.192906i | ||||
\(679\) | 47.1054 | 1.80774 | ||||||||
\(680\) | −6.39669 | − | 5.31860i | −0.245302 | − | 0.203959i | ||||
\(681\) | 14.5756 | + | 22.1548i | 0.558538 | + | 0.848974i | ||||
\(682\) | 1.02359 | 0.0391954 | ||||||||
\(683\) | 2.38670 | 0.0913245 | 0.0456622 | − | 0.998957i | \(-0.485460\pi\) | ||||
0.0456622 | + | 0.998957i | \(0.485460\pi\) | |||||||
\(684\) | −18.6363 | − | 8.03310i | −0.712575 | − | 0.307153i | ||||
\(685\) | 0.175926 | + | 0.146276i | 0.00672179 | + | 0.00558890i | ||||
\(686\) | −39.9665 | −1.52593 | ||||||||
\(687\) | 5.06089 | + | 7.69251i | 0.193085 | + | 0.293487i | ||||
\(688\) | 2.31465 | 0.0882451 | ||||||||
\(689\) | −9.31608 | −0.354915 | ||||||||
\(690\) | 2.01327 | + | 18.4647i | 0.0766439 | + | 0.702941i | ||||
\(691\) | 12.4301 | 0.472862 | 0.236431 | − | 0.971648i | \(-0.424022\pi\) | ||||
0.236431 | + | 0.971648i | \(0.424022\pi\) | |||||||
\(692\) | 17.0492 | 0.648114 | ||||||||
\(693\) | 0.616239 | − | 1.42963i | 0.0234090 | − | 0.0543073i | ||||
\(694\) | 29.9351 | 1.13632 | ||||||||
\(695\) | 2.24712 | − | 2.70262i | 0.0852383 | − | 0.102516i | ||||
\(696\) | −6.71900 | − | 10.2128i | −0.254683 | − | 0.387116i | ||||
\(697\) | −27.4674 | −1.04040 | ||||||||
\(698\) | 22.4642 | 0.850282 | ||||||||
\(699\) | −11.5884 | + | 7.62402i | −0.438315 | + | 0.288367i | ||||
\(700\) | 4.32242 | + | 23.2863i | 0.163372 | + | 0.880140i | ||||
\(701\) | 40.2008 | 1.51836 | 0.759181 | − | 0.650879i | \(-0.225600\pi\) | ||||
0.759181 | + | 0.650879i | \(0.225600\pi\) | |||||||
\(702\) | 12.6383 | − | 2.23360i | 0.477002 | − | 0.0843017i | ||||
\(703\) | 9.07459i | 0.342255i | ||||||||
\(704\) | −0.109553 | −0.00412892 | ||||||||
\(705\) | −2.38995 | + | 21.3024i | −0.0900109 | + | 0.802294i | ||||
\(706\) | −13.4442 | −0.505980 | ||||||||
\(707\) | − | 41.1422i | − | 1.54731i | ||||||
\(708\) | 3.98360 | + | 6.05503i | 0.149713 | + | 0.227562i | ||||
\(709\) | 4.06296i | 0.152588i | 0.997085 | + | 0.0762938i | \(0.0243087\pi\) | ||||
−0.997085 | + | 0.0762938i | \(0.975691\pi\) | |||||||
\(710\) | −16.6224 | − | 13.8209i | −0.623829 | − | 0.518690i | ||||
\(711\) | 34.1183 | + | 14.7066i | 1.27954 | + | 0.551540i | ||||
\(712\) | 10.2277 | 0.383299 | ||||||||
\(713\) | −43.7261 | + | 9.79310i | −1.63755 | + | 0.366754i | ||||
\(714\) | −16.7762 | − | 25.4996i | −0.627832 | − | 0.954300i | ||||
\(715\) | 0.465243 | + | 0.386831i | 0.0173991 | + | 0.0144667i | ||||
\(716\) | − | 8.37101i | − | 0.312839i | ||||||
\(717\) | 1.24430 | + | 1.89133i | 0.0464693 | + | 0.0706329i | ||||
\(718\) | 32.7887 | 1.22366 | ||||||||
\(719\) | 27.4547i | 1.02389i | 0.859019 | + | 0.511944i | \(0.171075\pi\) | ||||
−0.859019 | + | 0.511944i | \(0.828925\pi\) | |||||||
\(720\) | −3.03915 | − | 5.98027i | −0.113262 | − | 0.222871i | ||||
\(721\) | −15.5244 | −0.578158 | ||||||||
\(722\) | −26.7601 | −0.995908 | ||||||||
\(723\) | −8.72255 | − | 13.2582i | −0.324395 | − | 0.493078i | ||||
\(724\) | 3.91727i | 0.145584i | ||||||||
\(725\) | 34.6974 | − | 6.44056i | 1.28863 | − | 0.239196i | ||||
\(726\) | 15.8994 | − | 10.4602i | 0.590084 | − | 0.388215i | ||||
\(727\) | −39.9198 | −1.48054 | −0.740272 | − | 0.672308i | \(-0.765303\pi\) | ||||
−0.740272 | + | 0.672308i | \(0.765303\pi\) | |||||||
\(728\) | 11.6996i | 0.433617i | ||||||||
\(729\) | −25.3644 | + | 9.25449i | −0.939423 | + | 0.342759i | ||||
\(730\) | 15.9678 | + | 13.2766i | 0.590993 | + | 0.491388i | ||||
\(731\) | − | 8.61131i | − | 0.318501i | ||||||
\(732\) | 7.20998 | + | 10.9591i | 0.266489 | + | 0.405061i | ||||
\(733\) | 30.5739 | 1.12927 | 0.564636 | − | 0.825340i | \(-0.309016\pi\) | ||||
0.564636 | + | 0.825340i | \(0.309016\pi\) | |||||||
\(734\) | −0.619262 | −0.0228574 | ||||||||
\(735\) | −6.66600 | + | 59.4161i | −0.245879 | + | 2.19160i | ||||
\(736\) | 4.67990 | − | 1.04813i | 0.172503 | − | 0.0386346i | ||||
\(737\) | 0.652906 | 0.0240501 | ||||||||
\(738\) | −20.3399 | − | 8.76744i | −0.748721 | − | 0.322734i | ||||
\(739\) | 14.6803 | 0.540022 | 0.270011 | − | 0.962857i | \(-0.412973\pi\) | ||||
0.270011 | + | 0.962857i | \(0.412973\pi\) | |||||||
\(740\) | −1.91777 | + | 2.30651i | −0.0704987 | + | 0.0847889i | ||||
\(741\) | 24.1764 | − | 15.9056i | 0.888144 | − | 0.584308i | ||||
\(742\) | 17.8663i | 0.655892i | ||||||||
\(743\) | 11.9149i | 0.437115i | 0.975824 | + | 0.218557i | \(0.0701351\pi\) | ||||
−0.975824 | + | 0.218557i | \(0.929865\pi\) | |||||||
\(744\) | 13.5197 | − | 8.89460i | 0.495657 | − | 0.326092i | ||||
\(745\) | −15.6149 | + | 18.7801i | −0.572087 | + | 0.688050i | ||||
\(746\) | 33.9726 | 1.24383 | ||||||||
\(747\) | 45.7707 | + | 19.7293i | 1.67466 | + | 0.721859i | ||||
\(748\) | 0.407575i | 0.0149024i | ||||||||
\(749\) | − | 6.74159i | − | 0.246332i | ||||||
\(750\) | 19.3150 | − | 1.38935i | 0.705285 | − | 0.0507318i | ||||
\(751\) | 47.3378i | 1.72738i | 0.504024 | + | 0.863690i | \(0.331852\pi\) | ||||
−0.504024 | + | 0.863690i | \(0.668148\pi\) | |||||||
\(752\) | 5.53476 | 0.201832 | ||||||||
\(753\) | −36.0068 | + | 23.6888i | −1.31216 | + | 0.863267i | ||||
\(754\) | 17.4328 | 0.634867 | ||||||||
\(755\) | 9.19047 | − | 11.0534i | 0.334475 | − | 0.402274i | ||||
\(756\) | −4.28357 | − | 24.2376i | −0.155792 | − | 0.881513i | ||||
\(757\) | −48.7061 | −1.77025 | −0.885126 | − | 0.465352i | \(-0.845928\pi\) | ||||
−0.885126 | + | 0.465352i | \(0.845928\pi\) | |||||||
\(758\) | 6.22071i | 0.225947i | ||||||||
\(759\) | 0.632551 | − | 0.654220i | 0.0229601 | − | 0.0237467i | ||||
\(760\) | −11.6309 | − | 9.67067i | −0.421898 | − | 0.350792i | ||||
\(761\) | 44.5378i | 1.61450i | 0.590213 | + | 0.807248i | \(0.299044\pi\) | ||||
−0.590213 | + | 0.807248i | \(0.700956\pi\) | |||||||
\(762\) | −3.19949 | − | 4.86320i | −0.115905 | − | 0.176175i | ||||
\(763\) | − | 88.7290i | − | 3.21220i | ||||||
\(764\) | 10.0632 | 0.364073 | ||||||||
\(765\) | −22.2487 | + | 11.3067i | −0.804404 | + | 0.408795i | ||||
\(766\) | − | 0.328653i | − | 0.0118747i | ||||||
\(767\) | −10.3357 | −0.373200 | ||||||||
\(768\) | −1.44698 | + | 0.951967i | −0.0522135 | + | 0.0343512i | ||||
\(769\) | − | 2.64729i | − | 0.0954636i | −0.998860 | − | 0.0477318i | \(-0.984801\pi\) | ||
0.998860 | − | 0.0477318i | \(-0.0151993\pi\) | |||||||
\(770\) | 0.741861 | − | 0.892238i | 0.0267348 | − | 0.0321540i | ||||
\(771\) | 27.1526 | − | 17.8636i | 0.977877 | − | 0.643343i | ||||
\(772\) | 1.36921i | 0.0492788i | ||||||||
\(773\) | 42.9774i | 1.54579i | 0.634533 | + | 0.772896i | \(0.281192\pi\) | ||||
−0.634533 | + | 0.772896i | \(0.718808\pi\) | |||||||
\(774\) | 2.74868 | − | 6.37676i | 0.0987994 | − | 0.229208i | ||||
\(775\) | 8.52600 | + | 45.9323i | 0.306263 | + | 1.64994i | ||||
\(776\) | −9.94453 | −0.356988 | ||||||||
\(777\) | −9.19461 | + | 6.04912i | −0.329855 | + | 0.217011i | ||||
\(778\) | 28.8039 | 1.03267 | ||||||||
\(779\) | −49.9432 | −1.78940 | ||||||||
\(780\) | 9.50638 | + | 1.06654i | 0.340383 | + | 0.0381882i | ||||
\(781\) | 1.05912i | 0.0378984i | ||||||||
\(782\) | −3.89942 | − | 17.4109i | −0.139443 | − | 0.622611i | ||||
\(783\) | −36.1148 | + | 6.38267i | −1.29064 | + | 0.228098i | ||||
\(784\) | 15.4374 | 0.551336 | ||||||||
\(785\) | 34.4940 | − | 41.4861i | 1.23115 | − | 1.48070i | ||||
\(786\) | 12.9848 | + | 19.7367i | 0.463151 | + | 0.703986i | ||||
\(787\) | −23.4951 | −0.837510 | −0.418755 | − | 0.908099i | \(-0.637533\pi\) | ||||
−0.418755 | + | 0.908099i | \(0.637533\pi\) | |||||||
\(788\) | 3.46037 | 0.123271 | ||||||||
\(789\) | −8.86613 | − | 13.4764i | −0.315643 | − | 0.479774i | ||||
\(790\) | 21.2933 | + | 17.7046i | 0.757582 | + | 0.629900i | ||||
\(791\) | 16.4431i | 0.584650i | ||||||||
\(792\) | −0.130096 | + | 0.301813i | −0.00462275 | + | 0.0107245i | ||||
\(793\) | −18.7067 | −0.664295 | ||||||||
\(794\) | − | 25.5527i | − | 0.906831i | ||||||
\(795\) | 14.5170 | + | 1.62869i | 0.514865 | + | 0.0577637i | ||||
\(796\) | − | 2.84735i | − | 0.100922i | ||||||
\(797\) | − | 22.3667i | − | 0.792268i | −0.918193 | − | 0.396134i | \(-0.870352\pi\) | ||
0.918193 | − | 0.396134i | \(-0.129648\pi\) | |||||||
\(798\) | −30.5037 | − | 46.3653i | −1.07982 | − | 1.64131i | ||||
\(799\) | − | 20.5913i | − | 0.728466i | ||||||
\(800\) | −0.912517 | − | 4.91603i | −0.0322623 | − | 0.173808i | ||||
\(801\) | 12.1456 | − | 28.1769i | 0.429142 | − | 0.995581i | ||||
\(802\) | −16.8426 | −0.594733 | ||||||||
\(803\) | − | 1.01741i | − | 0.0359036i | ||||||
\(804\) | 8.62365 | − | 5.67348i | 0.304133 | − | 0.200088i | ||||
\(805\) | −23.1546 | + | 45.2125i | −0.816092 | + | 1.59353i | ||||
\(806\) | 23.0776i | 0.812872i | ||||||||
\(807\) | 13.3314 | + | 20.2636i | 0.469287 | + | 0.713312i | ||||
\(808\) | 8.68562i | 0.305559i | ||||||||
\(809\) | 49.1755i | 1.72892i | 0.502702 | + | 0.864460i | \(0.332339\pi\) | ||||
−0.502702 | + | 0.864460i | \(0.667661\pi\) | |||||||
\(810\) | −20.0844 | + | 1.27106i | −0.705695 | + | 0.0446604i | ||||
\(811\) | −42.2987 | −1.48531 | −0.742654 | − | 0.669675i | \(-0.766433\pi\) | ||||
−0.742654 | + | 0.669675i | \(0.766433\pi\) | |||||||
\(812\) | − | 33.4325i | − | 1.17325i | ||||||
\(813\) | −28.3148 | + | 18.6282i | −0.993043 | + | 0.653321i | ||||
\(814\) | 0.146963 | 0.00515104 | ||||||||
\(815\) | −26.5464 | − | 22.0723i | −0.929879 | − | 0.773158i | ||||
\(816\) | 3.54165 | + | 5.38329i | 0.123983 | + | 0.188453i | ||||
\(817\) | − | 15.6577i | − | 0.547794i | ||||||
\(818\) | 1.73082 | 0.0605169 | ||||||||
\(819\) | 32.2320 | + | 13.8935i | 1.12628 | + | 0.485478i | ||||
\(820\) | −12.6942 | − | 10.5547i | −0.443300 | − | 0.368586i | ||||
\(821\) | 0.358202i | 0.0125013i | 0.999980 | + | 0.00625067i | \(0.00198966\pi\) | ||||
−0.999980 | + | 0.00625067i | \(0.998010\pi\) | |||||||
\(822\) | −0.0974049 | − | 0.148055i | −0.00339739 | − | 0.00516400i | ||||
\(823\) | 3.19924i | 0.111519i | 0.998444 | + | 0.0557593i | \(0.0177579\pi\) | ||||
−0.998444 | + | 0.0557593i | \(0.982242\pi\) | |||||||
\(824\) | 3.27739 | 0.114173 | ||||||||
\(825\) | −0.657348 | − | 0.684126i | −0.0228859 | − | 0.0238182i | ||||
\(826\) | 19.8216i | 0.689683i | ||||||||
\(827\) | 40.6080i | 1.41208i | 0.708173 | + | 0.706039i | \(0.249520\pi\) | ||||
−0.708173 | + | 0.706039i | \(0.750480\pi\) | |||||||
\(828\) | 2.66990 | − | 14.1376i | 0.0927853 | − | 0.491315i | ||||
\(829\) | −16.9961 | −0.590298 | −0.295149 | − | 0.955451i | \(-0.595369\pi\) | ||||
−0.295149 | + | 0.955451i | \(0.595369\pi\) | |||||||
\(830\) | 28.5656 | + | 23.7512i | 0.991527 | + | 0.824416i | ||||
\(831\) | −11.5348 | − | 17.5327i | −0.400136 | − | 0.608204i | ||||
\(832\) | − | 2.46994i | − | 0.0856296i | ||||||
\(833\) | − | 57.4327i | − | 1.98992i | ||||||
\(834\) | −2.27445 | + | 1.49636i | −0.0787579 | + | 0.0518147i | ||||
\(835\) | 6.95197 | − | 8.36115i | 0.240583 | − | 0.289350i | ||||
\(836\) | 0.741083i | 0.0256309i | ||||||||
\(837\) | −8.44936 | − | 47.8088i | −0.292053 | − | 1.65251i | ||||
\(838\) | −0.0603174 | −0.00208363 | ||||||||
\(839\) | 19.0943 | 0.659209 | 0.329605 | − | 0.944119i | \(-0.393085\pi\) | ||||
0.329605 | + | 0.944119i | \(0.393085\pi\) | |||||||
\(840\) | 2.04540 | − | 18.2312i | 0.0705729 | − | 0.629037i | ||||
\(841\) | −20.8156 | −0.717779 | ||||||||
\(842\) | − | 16.7804i | − | 0.578292i | ||||||
\(843\) | 1.44347 | − | 0.949658i | 0.0497159 | − | 0.0327080i | ||||
\(844\) | −11.9262 | −0.410517 | ||||||||
\(845\) | 9.86338 | − | 11.8627i | 0.339310 | − | 0.408090i | ||||
\(846\) | 6.57262 | − | 15.2480i | 0.225971 | − | 0.524238i | ||||
\(847\) | 52.0481 | 1.78839 | ||||||||
\(848\) | − | 3.77179i | − | 0.129524i | ||||||
\(849\) | −11.9698 | + | 7.87491i | −0.410803 | + | 0.270266i | ||||
\(850\) | −18.2894 | + | 3.39489i | −0.627320 | + | 0.116444i | ||||
\(851\) | −6.27798 | + | 1.40605i | −0.215206 | + | 0.0481986i | ||||
\(852\) | 9.20334 | + | 13.9890i | 0.315301 | + | 0.479256i | ||||
\(853\) | − | 3.50621i | − | 0.120050i | −0.998197 | − | 0.0600251i | \(-0.980882\pi\) | ||
0.998197 | − | 0.0600251i | \(-0.0191181\pi\) | |||||||
\(854\) | 35.8756i | 1.22764i | ||||||||
\(855\) | −40.4542 | + | 20.5587i | −1.38351 | + | 0.703092i | ||||
\(856\) | 1.42323i | 0.0486451i | ||||||||
\(857\) | 26.4700 | 0.904198 | 0.452099 | − | 0.891968i | \(-0.350675\pi\) | ||||
0.452099 | + | 0.891968i | \(0.350675\pi\) | |||||||
\(858\) | −0.257591 | − | 0.391536i | −0.00879401 | − | 0.0133668i | ||||
\(859\) | 14.5773 | 0.497372 | 0.248686 | − | 0.968584i | \(-0.420001\pi\) | ||||
0.248686 | + | 0.968584i | \(0.420001\pi\) | |||||||
\(860\) | 3.30901 | − | 3.97975i | 0.112836 | − | 0.135708i | ||||
\(861\) | −33.2921 | − | 50.6038i | −1.13459 | − | 1.72457i | ||||
\(862\) | 4.36493 | 0.148670 | ||||||||
\(863\) | −11.1724 | −0.380312 | −0.190156 | − | 0.981754i | \(-0.560899\pi\) | ||||
−0.190156 | + | 0.981754i | \(0.560899\pi\) | |||||||
\(864\) | 0.904315 | + | 5.11686i | 0.0307654 | + | 0.174079i | ||||
\(865\) | 24.3735 | − | 29.3140i | 0.828723 | − | 0.996707i | ||||
\(866\) | −29.9206 | −1.01674 | ||||||||
\(867\) | −4.57097 | + | 3.00723i | −0.155238 | + | 0.102131i | ||||
\(868\) | 44.2579 | 1.50221 | ||||||||
\(869\) | − | 1.35674i | − | 0.0460241i | ||||||
\(870\) | −27.1651 | − | 3.04771i | −0.920985 | − | 0.103327i | ||||
\(871\) | 14.7202i | 0.498775i | ||||||||
\(872\) | 18.7318i | 0.634338i | ||||||||
\(873\) | −11.8093 | + | 27.3968i | −0.399684 | + | 0.927241i | ||||
\(874\) | −7.09021 | − | 31.6577i | −0.239830 | − | 1.07084i | ||||
\(875\) | 46.2173 | + | 25.8581i | 1.56243 | + | 0.874164i | ||||
\(876\) | −8.84086 | − | 13.4380i | −0.298705 | − | 0.454029i | ||||
\(877\) | − | 16.8838i | − | 0.570124i | −0.958509 | − | 0.285062i | \(-0.907986\pi\) | ||
0.958509 | − | 0.285062i | \(-0.0920143\pi\) | |||||||
\(878\) | −16.9861 | −0.573253 | ||||||||
\(879\) | 5.09351 | + | 7.74210i | 0.171800 | + | 0.261135i | ||||
\(880\) | −0.156616 | + | 0.188362i | −0.00527952 | + | 0.00634970i | ||||
\(881\) | 20.1111 | 0.677559 | 0.338780 | − | 0.940866i | \(-0.389986\pi\) | ||||
0.338780 | + | 0.940866i | \(0.389986\pi\) | |||||||
\(882\) | 18.3322 | − | 42.5295i | 0.617277 | − | 1.43204i | ||||
\(883\) | − | 1.20645i | − | 0.0406003i | −0.999794 | − | 0.0203002i | \(-0.993538\pi\) | ||
0.999794 | − | 0.0203002i | \(-0.00646219\pi\) | |||||||
\(884\) | −9.18903 | −0.309061 | ||||||||
\(885\) | 16.1058 | + | 1.80694i | 0.541391 | + | 0.0607397i | ||||
\(886\) | −24.5257 | −0.823958 | ||||||||
\(887\) | −19.2753 | −0.647200 | −0.323600 | − | 0.946194i | \(-0.604893\pi\) | ||||
−0.323600 | + | 0.946194i | \(0.604893\pi\) | |||||||
\(888\) | 1.94110 | − | 1.27704i | 0.0651389 | − | 0.0428548i | ||||
\(889\) | − | 15.9201i | − | 0.533942i | ||||||
\(890\) | 14.6215 | − | 17.5853i | 0.490112 | − | 0.589459i | ||||
\(891\) | 0.676993 | + | 0.716817i | 0.0226801 | + | 0.0240143i | ||||
\(892\) | − | 18.5236i | − | 0.620215i | ||||||
\(893\) | − | 37.4405i | − | 1.25290i | ||||||
\(894\) | 15.8049 | − | 10.3980i | 0.528593 | − | 0.347761i | ||||
\(895\) | −14.3929 | − | 11.9672i | −0.481103 | − | 0.400018i | ||||
\(896\) | −4.73682 | −0.158246 | ||||||||
\(897\) | 14.7498 | + | 14.2613i | 0.492481 | + | 0.476170i | ||||
\(898\) | 16.0667i | 0.536152i | ||||||||
\(899\) | − | 65.9458i | − | 2.19941i | ||||||
\(900\) | −14.6271 | − | 3.32392i | −0.487569 | − | 0.110797i | ||||
\(901\) | −14.0324 | −0.467487 | ||||||||
\(902\) | 0.808828i | 0.0269310i | ||||||||
\(903\) | 15.8648 | − | 10.4374i | 0.527947 | − | 0.347336i | ||||
\(904\) | − | 3.47135i | − | 0.115455i | ||||||
\(905\) | 6.73527 | + | 5.60011i | 0.223888 | + | 0.186154i | ||||
\(906\) | −9.30225 | + | 6.11993i | −0.309047 | + | 0.203321i | ||||
\(907\) | 16.5189 | 0.548502 | 0.274251 | − | 0.961658i | \(-0.411570\pi\) | ||||
0.274251 | + | 0.961658i | \(0.411570\pi\) | |||||||
\(908\) | − | 15.3110i | − | 0.508115i | ||||||
\(909\) | 23.9285 | + | 10.3143i | 0.793659 | + | 0.342104i | ||||
\(910\) | 20.1161 | + | 16.7257i | 0.666841 | + | 0.554452i | ||||
\(911\) | 1.38119 | 0.0457608 | 0.0228804 | − | 0.999738i | \(-0.492716\pi\) | ||||
0.0228804 | + | 0.999738i | \(0.492716\pi\) | |||||||
\(912\) | 6.43970 | + | 9.78829i | 0.213240 | + | 0.324123i | ||||
\(913\) | − | 1.82010i | − | 0.0602366i | ||||||
\(914\) | −13.2071 | −0.436852 | ||||||||
\(915\) | 29.1502 | + | 3.27042i | 0.963676 | + | 0.108117i | ||||
\(916\) | − | 5.31624i | − | 0.175654i | ||||||
\(917\) | 64.6098i | 2.13360i | ||||||||
\(918\) | 19.0365 | − | 3.36437i | 0.628299 | − | 0.111041i | ||||
\(919\) | 8.35624i | 0.275647i | 0.990457 | + | 0.137823i | \(0.0440107\pi\) | ||||
−0.990457 | + | 0.137823i | \(0.955989\pi\) | |||||||
\(920\) | 4.88822 | − | 9.54491i | 0.161160 | − | 0.314686i | ||||
\(921\) | 22.5404 | + | 34.2612i | 0.742730 | + | 1.12894i | ||||
\(922\) | − | 25.4941i | − | 0.839603i | ||||||
\(923\) | −23.8786 | −0.785974 | ||||||||
\(924\) | −0.750884 | + | 0.494005i | −0.0247023 | + | 0.0162516i | ||||
\(925\) | 1.22412 | + | 6.59474i | 0.0402489 | + | 0.216834i | ||||
\(926\) | 20.0822i | 0.659941i | ||||||||
\(927\) | 3.89196 | − | 9.02907i | 0.127829 | − | 0.296554i | ||||
\(928\) | 7.05802i | 0.231691i | ||||||||
\(929\) | − | 3.75617i | − | 0.123236i | −0.998100 | − | 0.0616180i | \(-0.980374\pi\) | ||
0.998100 | − | 0.0616180i | \(-0.0196261\pi\) | |||||||
\(930\) | 4.03455 | − | 35.9612i | 0.132298 | − | 1.17921i | ||||
\(931\) | − | 104.428i | − | 3.42250i | ||||||
\(932\) | 8.00870 | 0.262334 | ||||||||
\(933\) | −12.2538 | − | 18.6256i | −0.401170 | − | 0.609775i | ||||
\(934\) | − | 14.7644i | − | 0.483106i | ||||||
\(935\) | 0.700775 | + | 0.582667i | 0.0229178 | + | 0.0190552i | ||||
\(936\) | −6.80457 | − | 2.93309i | −0.222414 | − | 0.0958711i | ||||
\(937\) | −8.00163 | −0.261402 | −0.130701 | − | 0.991422i | \(-0.541723\pi\) | ||||
−0.130701 | + | 0.991422i | \(0.541723\pi\) | |||||||
\(938\) | 28.2302 | 0.921750 | ||||||||
\(939\) | 6.64517 | − | 4.37184i | 0.216857 | − | 0.142670i | ||||
\(940\) | 7.91246 | − | 9.51634i | 0.258076 | − | 0.310389i | ||||
\(941\) | −43.2565 | −1.41012 | −0.705060 | − | 0.709148i | \(-0.749080\pi\) | ||||
−0.705060 | + | 0.709148i | \(0.749080\pi\) | |||||||
\(942\) | −34.9136 | + | 22.9696i | −1.13755 | + | 0.748389i | ||||
\(943\) | −7.73836 | − | 34.5517i | −0.251996 | − | 1.12516i | ||||
\(944\) | − | 4.18459i | − | 0.136197i | ||||||
\(945\) | −47.7974 | − | 27.2849i | −1.55485 | − | 0.887577i | ||||
\(946\) | −0.253576 | −0.00824446 | ||||||||
\(947\) | 43.5718 | 1.41589 | 0.707947 | − | 0.706266i | \(-0.249622\pi\) | ||||
0.707947 | + | 0.706266i | \(0.249622\pi\) | |||||||
\(948\) | −11.7895 | − | 17.9199i | −0.382904 | − | 0.582011i | ||||
\(949\) | 22.9381 | 0.744603 | ||||||||
\(950\) | −33.2551 | + | 6.17283i | −1.07894 | + | 0.200273i | ||||
\(951\) | −5.31153 | + | 3.49445i | −0.172238 | + | 0.113315i | ||||
\(952\) | 17.6226i | 0.571153i | ||||||||
\(953\) | − | 29.1349i | − | 0.943773i | −0.881659 | − | 0.471887i | \(-0.843573\pi\) | ||
0.881659 | − | 0.471887i | \(-0.156427\pi\) | |||||||
\(954\) | −10.3911 | − | 4.47907i | −0.336426 | − | 0.145015i | ||||
\(955\) | 14.3863 | − | 17.3024i | 0.465529 | − | 0.559893i | ||||
\(956\) | − | 1.30708i | − | 0.0422741i | ||||||
\(957\) | 0.736084 | + | 1.11884i | 0.0237942 | + | 0.0361670i | ||||
\(958\) | −0.527998 | −0.0170588 | ||||||||
\(959\) | − | 0.484669i | − | 0.0156508i | ||||||
\(960\) | −0.431808 | + | 3.84884i | −0.0139365 | + | 0.124221i | ||||
\(961\) | 56.2989 | 1.81609 | ||||||||
\(962\) | 3.31336i | 0.106827i | ||||||||
\(963\) | 3.92095 | + | 1.69011i | 0.126351 | + | 0.0544631i | ||||
\(964\) | 9.16266i | 0.295109i | ||||||||
\(965\) | 2.35418 | + | 1.95741i | 0.0757838 | + | 0.0630113i | ||||
\(966\) | 27.3501 | − | 28.2870i | 0.879975 | − | 0.910119i | ||||
\(967\) | 13.1496i | 0.422863i | 0.977393 | + | 0.211432i | \(0.0678126\pi\) | ||||
−0.977393 | + | 0.211432i | \(0.932187\pi\) | |||||||
\(968\) | −10.9880 | −0.353168 | ||||||||
\(969\) | 36.4159 | − | 23.9580i | 1.16985 | − | 0.769640i | ||||
\(970\) | −14.2167 | + | 17.0984i | −0.456469 | + | 0.548997i | ||||
\(971\) | −54.4195 | −1.74641 | −0.873203 | − | 0.487358i | \(-0.837961\pi\) | ||||
−0.873203 | + | 0.487358i | \(0.837961\pi\) | |||||||
\(972\) | 15.1706 | + | 3.58500i | 0.486598 | + | 0.114989i | ||||
\(973\) | −7.44561 | −0.238695 | ||||||||
\(974\) | 15.1423i | 0.485191i | ||||||||
\(975\) | 15.4240 | − | 14.8203i | 0.493965 | − | 0.474630i | ||||
\(976\) | − | 7.57377i | − | 0.242431i | ||||||
\(977\) | − | 59.8495i | − | 1.91476i | −0.288837 | − | 0.957378i | \(-0.593269\pi\) | ||
0.288837 | − | 0.957378i | \(-0.406731\pi\) | |||||||
\(978\) | 14.6979 | + | 22.3407i | 0.469988 | + | 0.714378i | ||||
\(979\) | −1.12047 | −0.0358104 | ||||||||
\(980\) | 22.0693 | − | 26.5427i | 0.704977 | − | 0.847877i | ||||
\(981\) | 51.6053 | + | 22.2443i | 1.64763 | + | 0.710206i | ||||
\(982\) | 23.0745i | 0.736336i | ||||||||
\(983\) | − | 50.9264i | − | 1.62430i | −0.583448 | − | 0.812150i | \(-0.698297\pi\) | ||
0.583448 | − | 0.812150i | \(-0.301703\pi\) | |||||||
\(984\) | 7.02838 | + | 10.6831i | 0.224056 | + | 0.340564i | ||||
\(985\) | 4.94693 | − | 5.94968i | 0.157622 | − | 0.189573i | ||||
\(986\) | 26.2583 | 0.836235 | ||||||||
\(987\) | 37.9357 | − | 24.9578i | 1.20751 | − | 0.794417i | ||||
\(988\) | −16.7082 | −0.531558 | ||||||||
\(989\) | 10.8323 | − | 2.42605i | 0.344447 | − | 0.0771441i | ||||
\(990\) | 0.332947 | + | 0.655154i | 0.0105817 | + | 0.0208222i | ||||
\(991\) | 31.4399 | 0.998722 | 0.499361 | − | 0.866394i | \(-0.333568\pi\) | ||||
0.499361 | + | 0.866394i | \(0.333568\pi\) | |||||||
\(992\) | −9.34339 | −0.296653 | ||||||||
\(993\) | 30.3123 | − | 19.9424i | 0.961932 | − | 0.632854i | ||||
\(994\) | 45.7942i | 1.45250i | ||||||||
\(995\) | −4.89567 | − | 4.07056i | −0.155203 | − | 0.129045i | ||||
\(996\) | −15.8159 | − | 24.0401i | −0.501147 | − | 0.761739i | ||||
\(997\) | 55.3486i | 1.75291i | 0.481487 | + | 0.876453i | \(0.340097\pi\) | ||||
−0.481487 | + | 0.876453i | \(0.659903\pi\) | |||||||
\(998\) | 2.99246 | 0.0947248 | ||||||||
\(999\) | −1.21312 | − | 6.86415i | −0.0383814 | − | 0.217172i |
(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.h.b.689.8 | yes | 24 | |
3.2 | odd | 2 | 690.2.h.a.689.19 | yes | 24 | ||
5.4 | even | 2 | 690.2.h.a.689.18 | yes | 24 | ||
15.14 | odd | 2 | inner | 690.2.h.b.689.5 | yes | 24 | |
23.22 | odd | 2 | inner | 690.2.h.b.689.7 | yes | 24 | |
69.68 | even | 2 | 690.2.h.a.689.20 | yes | 24 | ||
115.114 | odd | 2 | 690.2.h.a.689.17 | ✓ | 24 | ||
345.344 | even | 2 | inner | 690.2.h.b.689.6 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.h.a.689.17 | ✓ | 24 | 115.114 | odd | 2 | ||
690.2.h.a.689.18 | yes | 24 | 5.4 | even | 2 | ||
690.2.h.a.689.19 | yes | 24 | 3.2 | odd | 2 | ||
690.2.h.a.689.20 | yes | 24 | 69.68 | even | 2 | ||
690.2.h.b.689.5 | yes | 24 | 15.14 | odd | 2 | inner | |
690.2.h.b.689.6 | yes | 24 | 345.344 | even | 2 | inner | |
690.2.h.b.689.7 | yes | 24 | 23.22 | odd | 2 | inner | |
690.2.h.b.689.8 | yes | 24 | 1.1 | even | 1 | trivial |