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 | 689.19 | ||
Character | \(\chi\) | \(=\) | 690.689 |
Dual form | 690.2.h.a.689.17 |
$q$-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 | \(-0.494743\pi\) | ||||
0.0165157 | + | 0.999864i | \(0.494743\pi\) | |||||||
\(12\) | 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 | ||||||||
\(15\) | −3.70539 | + | 1.12698i | −0.956727 | + | 0.290985i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.72035i | 0.902318i | 0.892443 | + | 0.451159i | \(0.148989\pi\) | ||||
−0.892443 | + | 0.451159i | \(0.851011\pi\) | |||||||
\(18\) | −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 | \(-0.772534\pi\) | ||
0.755351 | − | 0.655320i | \(-0.227466\pi\) | |||||||
\(30\) | 3.70539 | − | 1.12698i | 0.676508 | − | 0.205758i | ||||
\(31\) | −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 | \(0.195588\pi\) | ||||
−0.817086 | + | 0.576516i | \(0.804412\pi\) | |||||||
\(42\) | 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 | ||||||||
\(45\) | −6.43448 | − | 1.89669i | −0.959196 | − | 0.282741i | ||||
\(46\) | 4.67990 | − | 1.04813i | 0.690013 | − | 0.154539i | ||||
\(47\) | −5.53476 | −0.807327 | −0.403664 | − | 0.914907i | \(-0.632263\pi\) | ||||
−0.403664 | + | 0.914907i | \(0.632263\pi\) | |||||||
\(48\) | 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 | \(0.0834087\pi\) | ||||
−0.965864 | + | 0.259048i | \(0.916591\pi\) | |||||||
\(54\) | 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 | \(0.0878154\pi\) | ||||
−0.962186 | + | 0.272394i | \(0.912185\pi\) | |||||||
\(60\) | −3.70539 | + | 1.12698i | −0.478364 | + | 0.145493i | ||||
\(61\) | − | 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 | ||||||||
\(69\) | −7.76951 | − | 2.93848i | −0.935340 | − | 0.353751i | ||||
\(70\) | −6.77173 | + | 8.14437i | −0.809376 | + | 0.973439i | ||||
\(71\) | 9.66771i | 1.14735i | 0.819084 | + | 0.573673i | \(0.194482\pi\) | ||||
−0.819084 | + | 0.573673i | \(0.805518\pi\) | |||||||
\(72\) | −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 | ||||||||
\(75\) | 3.35950 | − | 7.98209i | 0.387922 | − | 0.921692i | ||||
\(76\) | − | 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 | \(-0.634686\pi\) | ||
0.410616 | − | 0.911808i | \(-0.365314\pi\) | |||||||
\(84\) | −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 | \(-0.682358\pi\) | ||||
−0.542067 | + | 0.840335i | \(0.682358\pi\) | |||||||
\(90\) | 6.43448 | + | 1.89669i | 0.678254 | + | 0.199928i | ||||
\(91\) | 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 | \(-0.857764\pi\) | ||
0.901813 | − | 0.432126i | \(-0.142236\pi\) | |||||||
\(102\) | 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 | ||||||||
\(105\) | 17.5517 | − | 5.33830i | 1.71288 | − | 0.520965i | ||||
\(106\) | − | 3.77179i | − | 0.366349i | ||||||
\(107\) | − | 1.42323i | − | 0.137589i | −0.997631 | − | 0.0687945i | \(-0.978085\pi\) | ||
0.997631 | − | 0.0687945i | \(-0.0219153\pi\) | |||||||
\(108\) | −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 | \(0.0522069\pi\) | ||||
−0.986580 | + | 0.163278i | \(0.947793\pi\) | |||||||
\(114\) | −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 | ||||||
\(120\) | 3.70539 | − | 1.12698i | 0.338254 | − | 0.102879i | ||||
\(121\) | −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 | \(0.203190\pi\) | ||||
−0.803086 | + | 0.595863i | \(0.796810\pi\) | |||||||
\(132\) | 0.158521 | + | 0.104291i | 0.0137975 | + | 0.00907733i | ||||
\(133\) | 32.0428i | 2.77846i | ||||||||
\(134\) | 5.95975 | 0.514844 | ||||||||
\(135\) | −7.50500 | − | 8.86989i | −0.645928 | − | 0.763399i | ||||
\(136\) | − | 3.72035i | − | 0.319018i | ||||||
\(137\) | − | 0.102320i | − | 0.00874176i | −0.999990 | − | 0.00437088i | \(-0.998609\pi\) | ||
0.999990 | − | 0.00437088i | \(-0.00139130\pi\) | |||||||
\(138\) | 7.76951 | + | 2.93848i | 0.661385 | + | 0.250140i | ||||
\(139\) | 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 | \(-0.352347\pi\) | ||||
0.447408 | + | 0.894330i | \(0.352347\pi\) | |||||||
\(150\) | −3.35950 | + | 7.98209i | −0.274302 | + | 0.651735i | ||||
\(151\) | 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 | ||||||||
\(165\) | −0.405935 | + | 0.123464i | −0.0316020 | + | 0.00961165i | ||||
\(166\) | 16.6139i | 1.28949i | ||||||||
\(167\) | −4.86290 | −0.376302 | −0.188151 | − | 0.982140i | \(-0.560249\pi\) | ||||
−0.188151 | + | 0.982140i | \(0.560249\pi\) | |||||||
\(168\) | 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 | \(-0.724442\pi\) | ||||
−0.648114 | + | 0.761543i | \(0.724442\pi\) | |||||||
\(174\) | −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 | \(0.101280\pi\) | ||||
−0.949806 | + | 0.312839i | \(0.898720\pi\) | |||||||
\(180\) | −6.43448 | − | 1.89669i | −0.479598 | − | 0.141371i | ||||
\(181\) | 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 | \(-0.618614\pi\) | ||||
−0.364073 | + | 0.931370i | \(0.618614\pi\) | |||||||
\(192\) | 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 | ||||||||
\(195\) | 2.78357 | + | 9.15207i | 0.199336 | + | 0.655393i | ||||
\(196\) | 15.4374 | 1.10267 | ||||||||
\(197\) | −3.46037 | −0.246541 | −0.123271 | − | 0.992373i | \(-0.539338\pi\) | ||||
−0.123271 | + | 0.992373i | \(0.539338\pi\) | |||||||
\(198\) | −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 | ||||||||
\(207\) | −8.44502 | − | 11.6482i | −0.586969 | − | 0.809609i | ||||
\(208\) | − | 2.46994i | − | 0.171259i | ||||||
\(209\) | − | 0.741083i | − | 0.0512618i | ||||||
\(210\) | −17.5517 | + | 5.33830i | −1.21119 | + | 0.368378i | ||||
\(211\) | −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 | ||||||||
\(225\) | 12.4598 | − | 8.35181i | 0.830655 | − | 0.556787i | ||||
\(226\) | − | 3.47135i | − | 0.230910i | ||||||
\(227\) | 15.3110i | 1.01623i | 0.861290 | + | 0.508115i | \(0.169657\pi\) | ||||
−0.861290 | + | 0.508115i | \(0.830343\pi\) | |||||||
\(228\) | 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 | \(-0.584492\pi\) | ||||
−0.262334 | + | 0.964977i | \(0.584492\pi\) | |||||||
\(234\) | −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 | \(0.0134603\pi\) | ||||
−0.999106 | + | 0.0422741i | \(0.986540\pi\) | |||||||
\(240\) | −3.70539 | + | 1.12698i | −0.239182 | + | 0.0727464i | ||||
\(241\) | 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 | \(-0.787508\pi\) | ||||
−0.785333 | + | 0.619073i | \(0.787508\pi\) | |||||||
\(252\) | −5.62505 | − | 13.0497i | −0.354345 | − | 0.822056i | ||||
\(253\) | −0.512695 | + | 0.114826i | −0.0322329 | + | 0.00721903i | ||||
\(254\) | − | 3.36092i | − | 0.210883i | ||||||
\(255\) | −4.19277 | − | 13.7854i | −0.262562 | − | 0.863273i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.7650 | 1.17053 | 0.585264 | − | 0.810843i | \(-0.300991\pi\) | ||||
0.585264 | + | 0.810843i | \(0.300991\pi\) | |||||||
\(258\) | −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 | \(-0.907293\pi\) | ||
0.957887 | − | 0.287147i | \(-0.0927068\pi\) | |||||||
\(264\) | −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 | \(0.140402\pi\) | ||||
−0.904289 | + | 0.426921i | \(0.859598\pi\) | |||||||
\(270\) | 7.50500 | + | 8.86989i | 0.456740 | + | 0.539804i | ||||
\(271\) | 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 | ||||
\(276\) | −7.76951 | − | 2.93848i | −0.467670 | − | 0.176876i | ||||
\(277\) | 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 | \(-0.490527\pi\) | ||||
0.0297552 | + | 0.999557i | \(0.490527\pi\) | |||||||
\(282\) | 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 | ||||||||
\(285\) | 7.62360 | + | 25.0656i | 0.451583 | + | 1.48476i | ||||
\(286\) | 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 | \(0.0499535\pi\) | ||||
−0.987711 | + | 0.156290i | \(0.950047\pi\) | |||||||
\(294\) | −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 | ||||
\(300\) | 3.35950 | − | 7.98209i | 0.193961 | − | 0.460846i | ||||
\(301\) | −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 | \(-0.881085\pi\) | ||
0.931026 | − | 0.364953i | \(-0.118915\pi\) | |||||||
\(312\) | −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 | ||||||||
\(315\) | 30.4790 | + | 8.98425i | 1.71729 | + | 0.506205i | ||||
\(316\) | 12.3843i | 0.696672i | ||||||||
\(317\) | −3.67077 | −0.206171 | −0.103085 | − | 0.994673i | \(-0.532871\pi\) | ||||
−0.103085 | + | 0.994673i | \(0.532871\pi\) | |||||||
\(318\) | 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 | ||||||||
\(330\) | 0.405935 | − | 0.123464i | 0.0223460 | − | 0.00679646i | ||||
\(331\) | −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 | ||||||||
\(345\) | 16.1596 | − | 9.15789i | 0.870004 | − | 0.493044i | ||||
\(346\) | 17.0492 | 0.916572 | ||||||||
\(347\) | −29.9351 | −1.60700 | −0.803499 | − | 0.595305i | \(-0.797031\pi\) | ||||
−0.803499 | + | 0.595305i | \(0.797031\pi\) | |||||||
\(348\) | 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 | \(-0.383533\pi\) | ||||
0.357782 | + | 0.933805i | \(0.383533\pi\) | |||||||
\(354\) | 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 | \(-0.832847\pi\) | ||||
−0.865260 | + | 0.501323i | \(0.832847\pi\) | |||||||
\(360\) | 6.43448 | + | 1.89669i | 0.339127 | + | 0.0999641i | ||||
\(361\) | −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 | ||||||
\(375\) | 8.92150 | + | 17.1874i | 0.460704 | + | 0.887554i | ||||
\(376\) | 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 | \(0.00267278\pi\) | ||||
−0.999965 | + | 0.00839669i | \(0.997327\pi\) | |||||||
\(384\) | −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 | \(-0.760577\pi\) | ||||
−0.730208 | + | 0.683225i | \(0.760577\pi\) | |||||||
\(390\) | −2.78357 | − | 9.15207i | −0.140952 | − | 0.463433i | ||||
\(391\) | −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 | \(-0.361841\pi\) | ||||
0.420540 | + | 0.907274i | \(0.361841\pi\) | |||||||
\(402\) | 8.62365 | + | 5.67348i | 0.430109 | + | 0.282968i | ||||
\(403\) | 23.0776i | 1.14958i | ||||||||
\(404\) | − | 8.68562i | − | 0.432126i | ||||||
\(405\) | −2.41577 | − | 19.9791i | −0.120040 | − | 0.992769i | ||||
\(406\) | − | 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 | ||||||
\(414\) | 8.44502 | + | 11.6482i | 0.415050 | + | 0.572480i | ||||
\(415\) | 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 | \(-0.499531\pi\) | ||||
0.00147335 | + | 0.999999i | \(0.499531\pi\) | |||||||
\(420\) | 17.5517 | − | 5.33830i | 0.856438 | − | 0.260483i | ||||
\(421\) | − | 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 | \(-0.533524\pi\) | ||||
−0.105126 | + | 0.994459i | \(0.533524\pi\) | |||||||
\(432\) | −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 | ||||||||
\(435\) | 7.95425 | + | 26.1527i | 0.381377 | + | 1.25393i | ||||
\(436\) | 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 | \(-0.302025\pi\) | ||||
0.582626 | + | 0.812740i | \(0.302025\pi\) | |||||||
\(444\) | −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 | \(-0.876228\pi\) | ||
0.925349 | − | 0.379117i | \(-0.123772\pi\) | |||||||
\(450\) | −12.4598 | + | 8.35181i | −0.587362 | + | 0.393708i | ||||
\(451\) | 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 | \(0.202329\pi\) | ||||
−0.804695 | + | 0.593689i | \(0.797671\pi\) | |||||||
\(462\) | 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 | ||||||
\(465\) | 34.6209 | − | 10.5298i | 1.60551 | − | 0.488309i | ||||
\(466\) | 8.00870 | 0.370996 | ||||||||
\(467\) | 14.7644i | 0.683215i | 0.939843 | + | 0.341607i | \(0.110971\pi\) | ||||
−0.939843 | + | 0.341607i | \(0.889029\pi\) | |||||||
\(468\) | 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 | \(-0.496160\pi\) | ||||
0.0120624 | + | 0.999927i | \(0.496160\pi\) | |||||||
\(480\) | 3.70539 | − | 1.12698i | 0.169127 | − | 0.0514394i | ||||
\(481\) | 3.31336i | 0.151076i | ||||||||
\(482\) | − | 9.16266i | − | 0.417348i | ||||||
\(483\) | 36.8028 | + | 13.9190i | 1.67458 | + | 0.633338i | ||||
\(484\) | −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 | \(-0.825683\pi\) | ||
0.853759 | − | 0.520668i | \(-0.174317\pi\) | |||||||
\(492\) | −7.02838 | + | 10.6831i | −0.316864 | + | 0.481630i | ||||
\(493\) | 26.2583 | 1.18262 | ||||||||
\(494\) | 16.7082 | 0.751736 | ||||||||
\(495\) | −0.704915 | − | 0.207787i | −0.0316836 | − | 0.00933934i | ||||
\(496\) | −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 | \(-0.705297\pi\) | ||
0.601167 | − | 0.799123i | \(-0.294703\pi\) | |||||||
\(504\) | 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 | \(-0.886022\pi\) | ||
0.936575 | − | 0.350468i | \(-0.113978\pi\) | |||||||
\(510\) | 4.19277 | + | 13.7854i | 0.185659 | + | 0.610426i | ||||
\(511\) | − | 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 | \(-0.344337\pi\) | ||||
0.469769 | + | 0.882789i | \(0.344337\pi\) | |||||||
\(522\) | −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 | ||||||||
\(525\) | −15.9133 | + | 37.8097i | −0.694515 | + | 1.65015i | ||||
\(526\) | 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 | ||||||||
\(540\) | −7.50500 | − | 8.86989i | −0.322964 | − | 0.381699i | ||||
\(541\) | −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 | ||||||||
\(552\) | 7.76951 | + | 2.93848i | 0.330692 | + | 0.125070i | ||||
\(553\) | − | 58.6622i | − | 2.49457i | ||||||
\(554\) | − | 12.1168i | − | 0.514792i | ||||||
\(555\) | 4.97070 | − | 1.51182i | 0.210994 | − | 0.0641733i | ||||
\(556\) | 1.57186 | 0.0666617 | ||||||||
\(557\) | 33.0466i | 1.40023i | 0.714030 | + | 0.700115i | \(0.246868\pi\) | ||||
−0.714030 | + | 0.700115i | \(0.753132\pi\) | |||||||
\(558\) | 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 | \(0.160509\pi\) | ||||
−0.875535 | + | 0.483155i | \(0.839491\pi\) | |||||||
\(564\) | −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 | \(-0.452294\pi\) | ||||
0.149312 | + | 0.988790i | \(0.452294\pi\) | |||||||
\(570\) | −7.62360 | − | 25.0656i | −0.319318 | − | 1.04988i | ||||
\(571\) | − | 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 | ||||||
\(585\) | −4.68469 | + | 15.8928i | −0.193688 | + | 0.657085i | ||||
\(586\) | − | 5.35051i | − | 0.221028i | ||||||
\(587\) | 9.64803 | 0.398217 | 0.199108 | − | 0.979977i | \(-0.436195\pi\) | ||||
0.199108 | + | 0.979977i | \(0.436195\pi\) | |||||||
\(588\) | 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 | \(-0.583621\pi\) | ||||
−0.259693 | + | 0.965691i | \(0.583621\pi\) | |||||||
\(594\) | 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 | \(0.165032\pi\) | ||||
−0.868581 | + | 0.495547i | \(0.834968\pi\) | |||||||
\(600\) | −3.35950 | + | 7.98209i | −0.137151 | + | 0.325867i | ||||
\(601\) | 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 | ||||||||
\(615\) | −8.32051 | − | 27.3569i | −0.335515 | − | 1.10314i | ||||
\(616\) | 0.518931 | 0.0209083 | ||||||||
\(617\) | − | 7.46733i | − | 0.300623i | −0.988639 | − | 0.150312i | \(-0.951972\pi\) | ||
0.988639 | − | 0.150312i | \(-0.0480277\pi\) | |||||||
\(618\) | −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 | ||||
\(621\) | −1.13104 | − | 24.8942i | −0.0453871 | − | 0.998969i | ||||
\(622\) | 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 | ||||||
\(630\) | −30.4790 | − | 8.98425i | −1.21431 | − | 0.357941i | ||||
\(631\) | 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 | \(-0.654235\pi\) | ||||
−0.465803 | + | 0.884888i | \(0.654235\pi\) | |||||||
\(642\) | −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 | ||||
\(645\) | −8.57667 | + | 2.60857i | −0.337706 | + | 0.102712i | ||||
\(646\) | −25.1668 | −0.990174 | ||||||||
\(647\) | −5.05526 | −0.198743 | −0.0993713 | − | 0.995050i | \(-0.531683\pi\) | ||||
−0.0993713 | + | 0.995050i | \(0.531683\pi\) | |||||||
\(648\) | 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 | \(-0.442398\pi\) | ||||
0.179976 | + | 0.983671i | \(0.442398\pi\) | |||||||
\(654\) | 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 | \(-0.212009\pi\) | ||||
0.786270 | + | 0.617883i | \(0.212009\pi\) | |||||||
\(660\) | −0.405935 | + | 0.123464i | −0.0158010 | + | 0.00480582i | ||||
\(661\) | 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 | ||||||||
\(675\) | 25.9798 | − | 0.223583i | 0.999963 | − | 0.00860573i | ||||
\(676\) | 6.89942 | 0.265362 | ||||||||
\(677\) | − | 23.6610i | − | 0.909366i | −0.890653 | − | 0.454683i | \(-0.849753\pi\) | ||
0.890653 | − | 0.454683i | \(-0.150247\pi\) | |||||||
\(678\) | 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 | \(-0.514540\pi\) | ||||
−0.0456622 | + | 0.998957i | \(0.514540\pi\) | |||||||
\(684\) | 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 | ||||||||
\(690\) | −16.1596 | + | 9.15789i | −0.615186 | + | 0.348635i | ||||
\(691\) | 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 | \(-0.774400\pi\) | ||||
−0.759181 | + | 0.650879i | \(0.774400\pi\) | |||||||
\(702\) | −12.6383 | − | 2.23360i | −0.477002 | − | 0.0843017i | ||||
\(703\) | 9.07459i | 0.342255i | ||||||||
\(704\) | 0.109553 | 0.00412892 | ||||||||
\(705\) | 20.5084 | − | 6.23757i | 0.772392 | − | 0.234920i | ||||
\(706\) | −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 | \(-0.828925\pi\) | ||
0.859019 | − | 0.511944i | \(-0.171075\pi\) | |||||||
\(720\) | −6.43448 | − | 1.89669i | −0.239799 | − | 0.0706853i | ||||
\(721\) | −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 | ||||||||
\(735\) | −57.2017 | + | 17.3977i | −2.10991 | + | 0.641723i | ||||
\(736\) | 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 | \(-0.929865\pi\) | ||
0.975824 | − | 0.218557i | \(-0.0701351\pi\) | |||||||
\(744\) | 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 | ||||||||
\(750\) | −8.92150 | − | 17.1874i | −0.325767 | − | 0.627595i | ||||
\(751\) | 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 | ||||||
\(759\) | −0.851171 | − | 0.321918i | −0.0308956 | − | 0.0116849i | ||||
\(760\) | −11.6309 | − | 9.67067i | −0.421898 | − | 0.350792i | ||||
\(761\) | − | 44.5378i | − | 1.61450i | −0.590213 | − | 0.807248i | \(-0.700956\pi\) | ||
0.590213 | − | 0.807248i | \(-0.299044\pi\) | |||||||
\(762\) | 3.19949 | − | 4.86320i | 0.115905 | − | 0.176175i | ||||
\(763\) | − | 88.7290i | − | 3.21220i | ||||||
\(764\) | −10.0632 | −0.364073 | ||||||||
\(765\) | 7.05635 | − | 23.9386i | 0.255123 | − | 0.865500i | ||||
\(766\) | − | 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 | \(-0.718808\pi\) | ||
0.634533 | − | 0.772896i | \(-0.281192\pi\) | |||||||
\(774\) | −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 | ||||||||
\(780\) | 2.78357 | + | 9.15207i | 0.0996679 | + | 0.327697i | ||||
\(781\) | 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 | ||||||||
\(795\) | −4.25074 | − | 13.9760i | −0.150758 | − | 0.495676i | ||||
\(796\) | − | 2.84735i | − | 0.100922i | ||||||
\(797\) | 22.3667i | 0.792268i | 0.918193 | + | 0.396134i | \(0.129648\pi\) | ||||
−0.918193 | + | 0.396134i | \(0.870352\pi\) | |||||||
\(798\) | 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 | \(-0.667661\pi\) | ||
0.502702 | − | 0.864460i | \(-0.332339\pi\) | |||||||
\(810\) | 2.41577 | + | 19.9791i | 0.0848813 | + | 0.701994i | ||||
\(811\) | −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 | \(-0.998010\pi\) | ||
0.999980 | − | 0.00625067i | \(-0.00198966\pi\) | |||||||
\(822\) | −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 | ||||||||
\(825\) | 0.368042 | − | 0.874459i | 0.0128136 | − | 0.0304448i | ||||
\(826\) | 19.8216i | 0.689683i | ||||||||
\(827\) | − | 40.6080i | − | 1.41208i | −0.708173 | − | 0.706039i | \(-0.750480\pi\) | ||
0.708173 | − | 0.706039i | \(-0.249520\pi\) | |||||||
\(828\) | −8.44502 | − | 11.6482i | −0.293485 | − | 0.404805i | ||||
\(829\) | −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 | \(-0.606915\pi\) | ||||
−0.329605 | + | 0.944119i | \(0.606915\pi\) | |||||||
\(840\) | −17.5517 | + | 5.33830i | −0.605593 | + | 0.184189i | ||||
\(841\) | −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 | ||||||
\(855\) | −12.8304 | + | 43.5268i | −0.438789 | + | 1.48859i | ||||
\(856\) | 1.42323i | 0.0486451i | ||||||||
\(857\) | −26.4700 | −0.904198 | −0.452099 | − | 0.891968i | \(-0.649325\pi\) | ||||
−0.452099 | + | 0.891968i | \(0.649325\pi\) | |||||||
\(858\) | −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 | \(-0.439101\pi\) | ||||
0.190156 | + | 0.981754i | \(0.439101\pi\) | |||||||
\(864\) | 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 | ||||||||
\(870\) | −7.95425 | − | 26.1527i | −0.269674 | − | 0.886659i | ||||
\(871\) | 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 | \(-0.610014\pi\) | ||||
−0.338780 | + | 0.940866i | \(0.610014\pi\) | |||||||
\(882\) | −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 | ||||||||
\(885\) | −4.71596 | − | 15.5055i | −0.158525 | − | 0.521213i | ||||
\(886\) | −24.5257 | −0.823958 | ||||||||
\(887\) | 19.2753 | 0.647200 | 0.323600 | − | 0.946194i | \(-0.395107\pi\) | ||||
0.323600 | + | 0.946194i | \(0.395107\pi\) | |||||||
\(888\) | 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 | ||||||||
\(897\) | −7.25785 | + | 19.1902i | −0.242333 | + | 0.640742i | ||||
\(898\) | 16.0667i | 0.536152i | ||||||||
\(899\) | 65.9458i | 2.19941i | ||||||||
\(900\) | 12.4598 | − | 8.35181i | 0.415327 | − | 0.278394i | ||||
\(901\) | −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 | \(-0.507284\pi\) | ||||
−0.0228804 | + | 0.999738i | \(0.507284\pi\) | |||||||
\(912\) | 6.43970 | − | 9.78829i | 0.213240 | − | 0.324123i | ||||
\(913\) | − | 1.82010i | − | 0.0602366i | ||||||
\(914\) | 13.2071 | 0.436852 | ||||||||
\(915\) | 8.53550 | + | 28.0638i | 0.282175 | + | 0.927760i | ||||
\(916\) | − | 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 | \(0.0196261\pi\) | ||||
−0.998100 | + | 0.0616180i | \(0.980374\pi\) | |||||||
\(930\) | −34.6209 | + | 10.5298i | −1.13526 | + | 0.345287i | ||||
\(931\) | − | 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 | \(-0.250920\pi\) | ||||
0.705060 | + | 0.709148i | \(0.250920\pi\) | |||||||
\(942\) | −34.9136 | − | 22.9696i | −1.13755 | − | 0.748389i | ||||
\(943\) | −7.73836 | − | 34.5517i | −0.251996 | − | 1.12516i | ||||
\(944\) | 4.18459i | 0.136197i | ||||||||
\(945\) | 35.5498 | + | 42.0150i | 1.15644 | + | 1.36675i | ||||
\(946\) | −0.253576 | −0.00824446 | ||||||||
\(947\) | −43.5718 | −1.41589 | −0.707947 | − | 0.706266i | \(-0.750378\pi\) | ||||
−0.707947 | + | 0.706266i | \(0.750378\pi\) | |||||||
\(948\) | −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 | \(0.156427\pi\) | ||||
−0.881659 | + | 0.471887i | \(0.843573\pi\) | |||||||
\(954\) | 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 | ||||||||
\(960\) | −3.70539 | + | 1.12698i | −0.119591 | + | 0.0363732i | ||||
\(961\) | 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 | ||||
\(966\) | −36.8028 | − | 13.9190i | −1.18411 | − | 0.447837i | ||||
\(967\) | 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 | \(-0.162039\pi\) | ||||
0.873203 | + | 0.487358i | \(0.162039\pi\) | |||||||
\(972\) | −15.1706 | + | 3.58500i | −0.486598 | + | 0.114989i | ||||
\(973\) | −7.44561 | −0.238695 | ||||||||
\(974\) | − | 15.1423i | − | 0.485191i | ||||||
\(975\) | −19.7152 | − | 8.29775i | −0.631393 | − | 0.265741i | ||||
\(976\) | − | 7.57377i | − | 0.242431i | ||||||
\(977\) | 59.8495i | 1.91476i | 0.288837 | + | 0.957378i | \(0.406731\pi\) | ||||
−0.288837 | + | 0.957378i | \(0.593269\pi\) | |||||||
\(978\) | −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 | \(0.301703\pi\) | ||||
−0.583448 | + | 0.812150i | \(0.698297\pi\) | |||||||
\(984\) | 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 | ||||
\(990\) | 0.704915 | + | 0.207787i | 0.0224037 | + | 0.00660391i | ||||
\(991\) | 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.a.689.19 | yes | 24 | |
3.2 | odd | 2 | 690.2.h.b.689.8 | yes | 24 | ||
5.4 | even | 2 | 690.2.h.b.689.5 | yes | 24 | ||
15.14 | odd | 2 | inner | 690.2.h.a.689.18 | yes | 24 | |
23.22 | odd | 2 | inner | 690.2.h.a.689.20 | yes | 24 | |
69.68 | even | 2 | 690.2.h.b.689.7 | yes | 24 | ||
115.114 | odd | 2 | 690.2.h.b.689.6 | yes | 24 | ||
345.344 | even | 2 | inner | 690.2.h.a.689.17 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.h.a.689.17 | ✓ | 24 | 345.344 | even | 2 | inner | |
690.2.h.a.689.18 | yes | 24 | 15.14 | odd | 2 | inner | |
690.2.h.a.689.19 | yes | 24 | 1.1 | even | 1 | trivial | |
690.2.h.a.689.20 | yes | 24 | 23.22 | odd | 2 | inner | |
690.2.h.b.689.5 | yes | 24 | 5.4 | even | 2 | ||
690.2.h.b.689.6 | yes | 24 | 115.114 | odd | 2 | ||
690.2.h.b.689.7 | yes | 24 | 69.68 | even | 2 | ||
690.2.h.b.689.8 | yes | 24 | 3.2 | odd | 2 |