Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [342,2,Mod(293,342)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(342, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("342.293");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 342 = 2 \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 342.n (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.73088374913\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.152695449.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 3x^{5} - 5x^{4} + 6x^{3} - 16x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 293.1 | ||
Root | \(1.05924 - 0.937022i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 342.293 |
Dual form | 342.2.n.e.335.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/342\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.37899 | + | 1.04804i | −0.796160 | + | 0.605087i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.16085 | − | 0.670219i | 0.519149 | − | 0.299731i | −0.217437 | − | 0.976074i | \(-0.569770\pi\) |
0.736587 | + | 0.676343i | \(0.236436\pi\) | |||||||
\(6\) | −1.37899 | + | 1.04804i | −0.562970 | + | 0.427861i | ||||
\(7\) | 1.55924 | + | 2.70068i | 0.589337 | + | 1.02076i | 0.994319 | + | 0.106438i | \(0.0339445\pi\) |
−0.404982 | + | 0.914325i | \(0.632722\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.803221 | − | 2.89047i | 0.267740 | − | 0.963491i | ||||
\(10\) | 1.16085 | − | 0.670219i | 0.367094 | − | 0.211942i | ||||
\(11\) | −1.36246 | + | 0.786617i | −0.410798 | + | 0.237174i | −0.691132 | − | 0.722728i | \(-0.742888\pi\) |
0.280335 | + | 0.959902i | \(0.409555\pi\) | |||||||
\(12\) | −1.37899 | + | 1.04804i | −0.398080 | + | 0.302543i | ||||
\(13\) | 1.86329i | 0.516782i | 0.966040 | + | 0.258391i | \(0.0831923\pi\) | ||||
−0.966040 | + | 0.258391i | \(0.916808\pi\) | |||||||
\(14\) | 1.55924 | + | 2.70068i | 0.416725 | + | 0.721788i | ||||
\(15\) | −0.898387 | + | 2.14085i | −0.231963 | + | 0.552764i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.18474 | + | 0.684010i | 0.287342 | + | 0.165897i | 0.636742 | − | 0.771077i | \(-0.280281\pi\) |
−0.349401 | + | 0.936973i | \(0.613615\pi\) | |||||||
\(18\) | 0.803221 | − | 2.89047i | 0.189321 | − | 0.681291i | ||||
\(19\) | 4.27933 | + | 0.829035i | 0.981747 | + | 0.190194i | ||||
\(20\) | 1.16085 | − | 0.670219i | 0.259575 | − | 0.149866i | ||||
\(21\) | −4.98060 | − | 2.09007i | −1.08686 | − | 0.456090i | ||||
\(22\) | −1.36246 | + | 0.786617i | −0.290478 | + | 0.167707i | ||||
\(23\) | 2.31685i | 0.483096i | 0.970389 | + | 0.241548i | \(0.0776551\pi\) | ||||
−0.970389 | + | 0.241548i | \(0.922345\pi\) | |||||||
\(24\) | −1.37899 | + | 1.04804i | −0.281485 | + | 0.213930i | ||||
\(25\) | −1.60161 | + | 2.77408i | −0.320323 | + | 0.554815i | ||||
\(26\) | 1.86329i | 0.365420i | ||||||||
\(27\) | 1.92170 | + | 4.82774i | 0.369832 | + | 0.929099i | ||||
\(28\) | 1.55924 | + | 2.70068i | 0.294669 | + | 0.510381i | ||||
\(29\) | 3.31526 | − | 5.74220i | 0.615628 | − | 1.06630i | −0.374646 | − | 0.927168i | \(-0.622236\pi\) |
0.990274 | − | 0.139131i | \(-0.0444311\pi\) | |||||||
\(30\) | −0.898387 | + | 2.14085i | −0.164022 | + | 0.390863i | ||||
\(31\) | −2.34559 | − | 1.35423i | −0.421281 | − | 0.243227i | 0.274344 | − | 0.961632i | \(-0.411539\pi\) |
−0.695625 | + | 0.718405i | \(0.744873\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.05441 | − | 2.51265i | 0.183550 | − | 0.437396i | ||||
\(34\) | 1.18474 | + | 0.684010i | 0.203181 | + | 0.117307i | ||||
\(35\) | 3.62010 | + | 2.09007i | 0.611908 | + | 0.353285i | ||||
\(36\) | 0.803221 | − | 2.89047i | 0.133870 | − | 0.481746i | ||||
\(37\) | − | 4.55619i | − | 0.749034i | −0.927220 | − | 0.374517i | \(-0.877809\pi\) | ||
0.927220 | − | 0.374517i | \(-0.122191\pi\) | |||||||
\(38\) | 4.27933 | + | 0.829035i | 0.694200 | + | 0.134487i | ||||
\(39\) | −1.95280 | − | 2.56945i | −0.312698 | − | 0.411441i | ||||
\(40\) | 1.16085 | − | 0.670219i | 0.183547 | − | 0.105971i | ||||
\(41\) | −5.32171 | − | 9.21747i | −0.831111 | − | 1.43953i | −0.897158 | − | 0.441710i | \(-0.854372\pi\) |
0.0660470 | − | 0.997817i | \(-0.478961\pi\) | |||||||
\(42\) | −4.98060 | − | 2.09007i | −0.768524 | − | 0.322504i | ||||
\(43\) | −8.41611 | −1.28344 | −0.641722 | − | 0.766937i | \(-0.721780\pi\) | ||||
−0.641722 | + | 0.766937i | \(0.721780\pi\) | |||||||
\(44\) | −1.36246 | + | 0.786617i | −0.205399 | + | 0.118587i | ||||
\(45\) | −1.00483 | − | 3.89375i | −0.149791 | − | 0.580446i | ||||
\(46\) | 2.31685i | 0.341600i | ||||||||
\(47\) | 3.82171 | + | 2.20646i | 0.557453 | + | 0.321846i | 0.752123 | − | 0.659023i | \(-0.229030\pi\) |
−0.194669 | + | 0.980869i | \(0.562363\pi\) | |||||||
\(48\) | −1.37899 | + | 1.04804i | −0.199040 | + | 0.151272i | ||||
\(49\) | −1.36246 | + | 2.35985i | −0.194637 | + | 0.337122i | ||||
\(50\) | −1.60161 | + | 2.77408i | −0.226502 | + | 0.392313i | ||||
\(51\) | −2.35061 | + | 0.298414i | −0.329152 | + | 0.0417863i | ||||
\(52\) | 1.86329i | 0.258391i | ||||||||
\(53\) | −4.02331 | − | 6.96859i | −0.552645 | − | 0.957209i | −0.998083 | − | 0.0618959i | \(-0.980285\pi\) |
0.445438 | − | 0.895313i | \(-0.353048\pi\) | |||||||
\(54\) | 1.92170 | + | 4.82774i | 0.261510 | + | 0.656972i | ||||
\(55\) | −1.05441 | + | 1.82629i | −0.142177 | + | 0.246258i | ||||
\(56\) | 1.55924 | + | 2.70068i | 0.208362 | + | 0.360894i | ||||
\(57\) | −6.77002 | + | 3.34169i | −0.896711 | + | 0.442617i | ||||
\(58\) | 3.31526 | − | 5.74220i | 0.435315 | − | 0.753988i | ||||
\(59\) | −5.63697 | − | 9.76351i | −0.733871 | − | 1.27110i | −0.955217 | − | 0.295906i | \(-0.904379\pi\) |
0.221347 | − | 0.975195i | \(-0.428955\pi\) | |||||||
\(60\) | −0.898387 | + | 2.14085i | −0.115981 | + | 0.276382i | ||||
\(61\) | −2.14881 | + | 3.72186i | −0.275127 | + | 0.476535i | −0.970167 | − | 0.242437i | \(-0.922053\pi\) |
0.695040 | + | 0.718971i | \(0.255387\pi\) | |||||||
\(62\) | −2.34559 | − | 1.35423i | −0.297891 | − | 0.171987i | ||||
\(63\) | 9.05867 | − | 2.33770i | 1.14128 | − | 0.294522i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.24881 | + | 2.16300i | 0.154896 | + | 0.268287i | ||||
\(66\) | 1.05441 | − | 2.51265i | 0.129789 | − | 0.309286i | ||||
\(67\) | − | 4.79251i | − | 0.585498i | −0.956189 | − | 0.292749i | \(-0.905430\pi\) | ||
0.956189 | − | 0.292749i | \(-0.0945700\pi\) | |||||||
\(68\) | 1.18474 | + | 0.684010i | 0.143671 | + | 0.0829484i | ||||
\(69\) | −2.42815 | − | 3.19490i | −0.292315 | − | 0.384621i | ||||
\(70\) | 3.62010 | + | 2.09007i | 0.432685 | + | 0.249811i | ||||
\(71\) | 6.82171 | − | 11.8155i | 0.809588 | − | 1.40225i | −0.103562 | − | 0.994623i | \(-0.533024\pi\) |
0.913150 | − | 0.407624i | \(-0.133643\pi\) | |||||||
\(72\) | 0.803221 | − | 2.89047i | 0.0946605 | − | 0.340646i | ||||
\(73\) | 2.70805 | − | 4.69049i | 0.316954 | − | 0.548980i | −0.662897 | − | 0.748711i | \(-0.730673\pi\) |
0.979851 | + | 0.199730i | \(0.0640066\pi\) | |||||||
\(74\) | − | 4.55619i | − | 0.529647i | ||||||
\(75\) | −0.698737 | − | 5.50397i | −0.0806832 | − | 0.635544i | ||||
\(76\) | 4.27933 | + | 0.829035i | 0.490873 | + | 0.0950969i | ||||
\(77\) | −4.24881 | − | 2.45305i | −0.484197 | − | 0.279551i | ||||
\(78\) | −1.95280 | − | 2.56945i | −0.221111 | − | 0.290933i | ||||
\(79\) | 9.76790i | 1.09897i | 0.835502 | + | 0.549487i | \(0.185177\pi\) | ||||
−0.835502 | + | 0.549487i | \(0.814823\pi\) | |||||||
\(80\) | 1.16085 | − | 0.670219i | 0.129787 | − | 0.0749328i | ||||
\(81\) | −7.70967 | − | 4.64338i | −0.856630 | − | 0.515931i | ||||
\(82\) | −5.32171 | − | 9.21747i | −0.587684 | − | 1.01790i | ||||
\(83\) | 3.32873 | − | 1.92184i | 0.365375 | − | 0.210949i | −0.306061 | − | 0.952012i | \(-0.599011\pi\) |
0.671436 | + | 0.741063i | \(0.265678\pi\) | |||||||
\(84\) | −4.98060 | − | 2.09007i | −0.543428 | − | 0.228045i | ||||
\(85\) | 1.83375 | 0.198898 | ||||||||
\(86\) | −8.41611 | −0.907532 | ||||||||
\(87\) | 1.44635 | + | 11.3930i | 0.155065 | + | 1.22145i | ||||
\(88\) | −1.36246 | + | 0.786617i | −0.145239 | + | 0.0838537i | ||||
\(89\) | 3.19119 | + | 5.52730i | 0.338265 | + | 0.585892i | 0.984107 | − | 0.177579i | \(-0.0568266\pi\) |
−0.645841 | + | 0.763472i | \(0.723493\pi\) | |||||||
\(90\) | −1.00483 | − | 3.89375i | −0.105918 | − | 0.410437i | ||||
\(91\) | −5.03214 | + | 2.90531i | −0.527512 | + | 0.304559i | ||||
\(92\) | 2.31685i | 0.241548i | ||||||||
\(93\) | 4.65383 | − | 0.590811i | 0.482580 | − | 0.0612642i | ||||
\(94\) | 3.82171 | + | 2.20646i | 0.394179 | + | 0.227579i | ||||
\(95\) | 5.52331 | − | 1.90570i | 0.566680 | − | 0.195521i | ||||
\(96\) | −1.37899 | + | 1.04804i | −0.140742 | + | 0.106965i | ||||
\(97\) | 6.71422i | 0.681726i | 0.940113 | + | 0.340863i | \(0.110719\pi\) | ||||
−0.940113 | + | 0.340863i | \(0.889281\pi\) | |||||||
\(98\) | −1.36246 | + | 2.35985i | −0.137629 | + | 0.238381i | ||||
\(99\) | 1.17934 | + | 4.56999i | 0.118528 | + | 0.459301i | ||||
\(100\) | −1.60161 | + | 2.77408i | −0.160161 | + | 0.277408i | ||||
\(101\) | 0.458673 | + | 0.264815i | 0.0456397 | + | 0.0263501i | 0.522646 | − | 0.852550i | \(-0.324945\pi\) |
−0.477007 | + | 0.878900i | \(0.658278\pi\) | |||||||
\(102\) | −2.35061 | + | 0.298414i | −0.232745 | + | 0.0295474i | ||||
\(103\) | 17.0390 | + | 9.83749i | 1.67891 | + | 0.969317i | 0.962360 | + | 0.271777i | \(0.0876114\pi\) |
0.716546 | + | 0.697540i | \(0.245722\pi\) | |||||||
\(104\) | 1.86329i | 0.182710i | ||||||||
\(105\) | −7.18255 | + | 0.911835i | −0.700945 | + | 0.0889860i | ||||
\(106\) | −4.02331 | − | 6.96859i | −0.390779 | − | 0.676849i | ||||
\(107\) | −12.9860 | −1.25540 | −0.627700 | − | 0.778455i | \(-0.716004\pi\) | ||||
−0.627700 | + | 0.778455i | \(0.716004\pi\) | |||||||
\(108\) | 1.92170 | + | 4.82774i | 0.184916 | + | 0.464549i | ||||
\(109\) | −10.0233 | − | 5.78696i | −0.960059 | − | 0.554291i | −0.0638681 | − | 0.997958i | \(-0.520344\pi\) |
−0.896191 | + | 0.443668i | \(0.853677\pi\) | |||||||
\(110\) | −1.05441 | + | 1.82629i | −0.100534 | + | 0.174130i | ||||
\(111\) | 4.77508 | + | 6.28294i | 0.453230 | + | 0.596350i | ||||
\(112\) | 1.55924 | + | 2.70068i | 0.147334 | + | 0.255191i | ||||
\(113\) | −2.79839 | + | 4.84696i | −0.263251 | + | 0.455963i | −0.967104 | − | 0.254382i | \(-0.918128\pi\) |
0.703853 | + | 0.710345i | \(0.251461\pi\) | |||||||
\(114\) | −6.77002 | + | 3.34169i | −0.634070 | + | 0.312978i | ||||
\(115\) | 1.55279 | + | 2.68952i | 0.144799 | + | 0.250799i | ||||
\(116\) | 3.31526 | − | 5.74220i | 0.307814 | − | 0.533150i | ||||
\(117\) | 5.38578 | + | 1.49663i | 0.497915 | + | 0.138363i | ||||
\(118\) | −5.63697 | − | 9.76351i | −0.518925 | − | 0.898804i | ||||
\(119\) | 4.26614i | 0.391077i | ||||||||
\(120\) | −0.898387 | + | 2.14085i | −0.0820111 | + | 0.195432i | ||||
\(121\) | −4.26247 | + | 7.38281i | −0.387497 | + | 0.671164i | ||||
\(122\) | −2.14881 | + | 3.72186i | −0.194544 | + | 0.336961i | ||||
\(123\) | 16.9989 | + | 7.13342i | 1.53274 | + | 0.643199i | ||||
\(124\) | −2.34559 | − | 1.35423i | −0.210641 | − | 0.121613i | ||||
\(125\) | 10.9959i | 0.983505i | ||||||||
\(126\) | 9.05867 | − | 2.33770i | 0.807010 | − | 0.208259i | ||||
\(127\) | −9.65441 | + | 5.57397i | −0.856690 | + | 0.494610i | −0.862902 | − | 0.505370i | \(-0.831356\pi\) |
0.00621242 | + | 0.999981i | \(0.498023\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 11.6057 | − | 8.82043i | 1.02183 | − | 0.776595i | ||||
\(130\) | 1.24881 | + | 2.16300i | 0.109528 | + | 0.189708i | ||||
\(131\) | 11.1976 | − | 6.46496i | 0.978342 | − | 0.564846i | 0.0765727 | − | 0.997064i | \(-0.475602\pi\) |
0.901769 | + | 0.432218i | \(0.142269\pi\) | |||||||
\(132\) | 1.05441 | − | 2.51265i | 0.0917748 | − | 0.218698i | ||||
\(133\) | 4.43355 | + | 12.8498i | 0.384437 | + | 1.11422i | ||||
\(134\) | − | 4.79251i | − | 0.414009i | ||||||
\(135\) | 5.46646 | + | 4.31634i | 0.470478 | + | 0.371491i | ||||
\(136\) | 1.18474 | + | 0.684010i | 0.101591 | + | 0.0586534i | ||||
\(137\) | −3.14341 | − | 1.81485i | −0.268560 | − | 0.155053i | 0.359673 | − | 0.933078i | \(-0.382888\pi\) |
−0.628233 | + | 0.778025i | \(0.716222\pi\) | |||||||
\(138\) | −2.42815 | − | 3.19490i | −0.206698 | − | 0.271968i | ||||
\(139\) | 1.59355 | 0.135163 | 0.0675815 | − | 0.997714i | \(-0.478472\pi\) | ||||
0.0675815 | + | 0.997714i | \(0.478472\pi\) | |||||||
\(140\) | 3.62010 | + | 2.09007i | 0.305954 | + | 0.176643i | ||||
\(141\) | −7.58255 | + | 0.962616i | −0.638566 | + | 0.0810669i | ||||
\(142\) | 6.82171 | − | 11.8155i | 0.572465 | − | 0.991538i | ||||
\(143\) | −1.46569 | − | 2.53865i | −0.122567 | − | 0.212293i | ||||
\(144\) | 0.803221 | − | 2.89047i | 0.0669351 | − | 0.240873i | ||||
\(145\) | − | 8.88780i | − | 0.738092i | ||||||
\(146\) | 2.70805 | − | 4.69049i | 0.224120 | − | 0.388188i | ||||
\(147\) | −0.594402 | − | 4.68212i | −0.0490255 | − | 0.386175i | ||||
\(148\) | − | 4.55619i | − | 0.374517i | ||||||
\(149\) | 5.26170 | − | 3.03785i | 0.431055 | − | 0.248870i | −0.268741 | − | 0.963213i | \(-0.586607\pi\) |
0.699796 | + | 0.714343i | \(0.253274\pi\) | |||||||
\(150\) | −0.698737 | − | 5.50397i | −0.0570517 | − | 0.449398i | ||||
\(151\) | −14.7430 | + | 8.51189i | −1.19977 | + | 0.692688i | −0.960504 | − | 0.278266i | \(-0.910240\pi\) |
−0.239267 | + | 0.970954i | \(0.576907\pi\) | |||||||
\(152\) | 4.27933 | + | 0.829035i | 0.347100 | + | 0.0672436i | ||||
\(153\) | 2.92872 | − | 2.87505i | 0.236773 | − | 0.232434i | ||||
\(154\) | −4.24881 | − | 2.45305i | −0.342379 | − | 0.197672i | ||||
\(155\) | −3.63052 | −0.291610 | ||||||||
\(156\) | −1.95280 | − | 2.56945i | −0.156349 | − | 0.205721i | ||||
\(157\) | −5.71527 | − | 9.89913i | −0.456128 | − | 0.790037i | 0.542624 | − | 0.839975i | \(-0.317431\pi\) |
−0.998752 | + | 0.0499389i | \(0.984097\pi\) | |||||||
\(158\) | 9.76790i | 0.777092i | ||||||||
\(159\) | 12.8515 | + | 5.39300i | 1.01919 | + | 0.427693i | ||||
\(160\) | 1.16085 | − | 0.670219i | 0.0917735 | − | 0.0529855i | ||||
\(161\) | −6.25707 | + | 3.61252i | −0.493126 | + | 0.284706i | ||||
\(162\) | −7.70967 | − | 4.64338i | −0.605729 | − | 0.364818i | ||||
\(163\) | 5.20323 | 0.407548 | 0.203774 | − | 0.979018i | \(-0.434679\pi\) | ||||
0.203774 | + | 0.979018i | \(0.434679\pi\) | |||||||
\(164\) | −5.32171 | − | 9.21747i | −0.415555 | − | 0.719763i | ||||
\(165\) | −0.460009 | − | 3.62351i | −0.0358117 | − | 0.282090i | ||||
\(166\) | 3.32873 | − | 1.92184i | 0.258359 | − | 0.149164i | ||||
\(167\) | 2.44984 | 0.189575 | 0.0947873 | − | 0.995498i | \(-0.469783\pi\) | ||||
0.0947873 | + | 0.995498i | \(0.469783\pi\) | |||||||
\(168\) | −4.98060 | − | 2.09007i | −0.384262 | − | 0.161252i | ||||
\(169\) | 9.52817 | 0.732936 | ||||||||
\(170\) | 1.83375 | 0.140642 | ||||||||
\(171\) | 5.83355 | − | 11.7034i | 0.446103 | − | 0.894982i | ||||
\(172\) | −8.41611 | −0.641722 | ||||||||
\(173\) | 11.5221 | 0.876008 | 0.438004 | − | 0.898973i | \(-0.355686\pi\) | ||||
0.438004 | + | 0.898973i | \(0.355686\pi\) | |||||||
\(174\) | 1.44635 | + | 11.3930i | 0.109648 | + | 0.863698i | ||||
\(175\) | −9.98920 | −0.755112 | ||||||||
\(176\) | −1.36246 | + | 0.786617i | −0.102699 | + | 0.0592935i | ||||
\(177\) | 18.0059 | + | 7.55600i | 1.35340 | + | 0.567944i | ||||
\(178\) | 3.19119 | + | 5.52730i | 0.239190 | + | 0.414288i | ||||
\(179\) | −22.7029 | −1.69690 | −0.848449 | − | 0.529278i | \(-0.822463\pi\) | ||||
−0.848449 | + | 0.529278i | \(0.822463\pi\) | |||||||
\(180\) | −1.00483 | − | 3.89375i | −0.0748955 | − | 0.290223i | ||||
\(181\) | 3.76806 | − | 2.17549i | 0.280078 | − | 0.161703i | −0.353381 | − | 0.935480i | \(-0.614968\pi\) |
0.633459 | + | 0.773777i | \(0.281635\pi\) | |||||||
\(182\) | −5.03214 | + | 2.90531i | −0.373007 | + | 0.215356i | ||||
\(183\) | −0.937465 | − | 7.38444i | −0.0692994 | − | 0.545874i | ||||
\(184\) | 2.31685i | 0.170800i | ||||||||
\(185\) | −3.05365 | − | 5.28907i | −0.224509 | − | 0.388860i | ||||
\(186\) | 4.65383 | − | 0.590811i | 0.341236 | − | 0.0433204i | ||||
\(187\) | −2.15222 | −0.157386 | ||||||||
\(188\) | 3.82171 | + | 2.20646i | 0.278727 | + | 0.160923i | ||||
\(189\) | −10.0418 | + | 12.7175i | −0.730434 | + | 0.925063i | ||||
\(190\) | 5.52331 | − | 1.90570i | 0.400703 | − | 0.138254i | ||||
\(191\) | −14.8549 | + | 8.57646i | −1.07486 | + | 0.620571i | −0.929505 | − | 0.368808i | \(-0.879766\pi\) |
−0.145355 | + | 0.989380i | \(0.546433\pi\) | |||||||
\(192\) | −1.37899 | + | 1.04804i | −0.0995200 | + | 0.0756358i | ||||
\(193\) | 11.6865 | − | 6.74723i | 0.841216 | − | 0.485676i | −0.0164612 | − | 0.999865i | \(-0.505240\pi\) |
0.857677 | + | 0.514188i | \(0.171907\pi\) | |||||||
\(194\) | 6.71422i | 0.482053i | ||||||||
\(195\) | −3.98901 | − | 1.67395i | −0.285659 | − | 0.119874i | ||||
\(196\) | −1.36246 | + | 2.35985i | −0.0973187 | + | 0.168561i | ||||
\(197\) | 9.03983i | 0.644061i | 0.946729 | + | 0.322031i | \(0.104365\pi\) | ||||
−0.946729 | + | 0.322031i | \(0.895635\pi\) | |||||||
\(198\) | 1.17934 | + | 4.56999i | 0.0838120 | + | 0.324775i | ||||
\(199\) | −0.483132 | − | 0.836810i | −0.0342483 | − | 0.0593199i | 0.848393 | − | 0.529367i | \(-0.177570\pi\) |
−0.882642 | + | 0.470047i | \(0.844237\pi\) | |||||||
\(200\) | −1.60161 | + | 2.77408i | −0.113251 | + | 0.196157i | ||||
\(201\) | 5.02274 | + | 6.60881i | 0.354277 | + | 0.466150i | ||||
\(202\) | 0.458673 | + | 0.264815i | 0.0322722 | + | 0.0186323i | ||||
\(203\) | 20.6771 | 1.45125 | ||||||||
\(204\) | −2.35061 | + | 0.298414i | −0.164576 | + | 0.0208931i | ||||
\(205\) | −12.3554 | − | 7.13342i | −0.862942 | − | 0.498220i | ||||
\(206\) | 17.0390 | + | 9.83749i | 1.18717 | + | 0.685411i | ||||
\(207\) | 6.69678 | + | 1.86094i | 0.465458 | + | 0.129344i | ||||
\(208\) | 1.86329i | 0.129196i | ||||||||
\(209\) | −6.48256 | + | 2.23667i | −0.448408 | + | 0.154714i | ||||
\(210\) | −7.18255 | + | 0.911835i | −0.495643 | + | 0.0629226i | ||||
\(211\) | 12.8154 | − | 7.39895i | 0.882245 | − | 0.509364i | 0.0108471 | − | 0.999941i | \(-0.496547\pi\) |
0.871398 | + | 0.490577i | \(0.163214\pi\) | |||||||
\(212\) | −4.02331 | − | 6.96859i | −0.276322 | − | 0.478604i | ||||
\(213\) | 2.97611 | + | 23.4429i | 0.203920 | + | 1.60628i | ||||
\(214\) | −12.9860 | −0.887702 | ||||||||
\(215\) | −9.76987 | + | 5.64064i | −0.666300 | + | 0.384688i | ||||
\(216\) | 1.92170 | + | 4.82774i | 0.130755 | + | 0.328486i | ||||
\(217\) | − | 8.44627i | − | 0.573370i | ||||||
\(218\) | −10.0233 | − | 5.78696i | −0.678865 | − | 0.391943i | ||||
\(219\) | 1.18145 | + | 9.30628i | 0.0798347 | + | 0.628860i | ||||
\(220\) | −1.05441 | + | 1.82629i | −0.0710884 | + | 0.123129i | ||||
\(221\) | −1.27451 | + | 2.20751i | −0.0857325 | + | 0.148493i | ||||
\(222\) | 4.77508 | + | 6.28294i | 0.320482 | + | 0.421683i | ||||
\(223\) | − | 28.0299i | − | 1.87702i | −0.345252 | − | 0.938510i | \(-0.612206\pi\) | ||
0.345252 | − | 0.938510i | \(-0.387794\pi\) | |||||||
\(224\) | 1.55924 | + | 2.70068i | 0.104181 | + | 0.180447i | ||||
\(225\) | 6.73194 | + | 6.85761i | 0.448796 | + | 0.457174i | ||||
\(226\) | −2.79839 | + | 4.84696i | −0.186146 | + | 0.322415i | ||||
\(227\) | 6.29137 | + | 10.8970i | 0.417573 | + | 0.723258i | 0.995695 | − | 0.0926927i | \(-0.0295474\pi\) |
−0.578122 | + | 0.815951i | \(0.696214\pi\) | |||||||
\(228\) | −6.77002 | + | 3.34169i | −0.448355 | + | 0.221309i | ||||
\(229\) | 10.4235 | − | 18.0541i | 0.688805 | − | 1.19305i | −0.283420 | − | 0.958996i | \(-0.591469\pi\) |
0.972225 | − | 0.234049i | \(-0.0751977\pi\) | |||||||
\(230\) | 1.55279 | + | 2.68952i | 0.102388 | + | 0.177342i | ||||
\(231\) | 8.42996 | − | 1.07020i | 0.554651 | − | 0.0704137i | ||||
\(232\) | 3.31526 | − | 5.74220i | 0.217657 | − | 0.376994i | ||||
\(233\) | 18.2017 | + | 10.5088i | 1.19243 | + | 0.688452i | 0.958858 | − | 0.283887i | \(-0.0916241\pi\) |
0.233575 | + | 0.972339i | \(0.424957\pi\) | |||||||
\(234\) | 5.38578 | + | 1.49663i | 0.352079 | + | 0.0978377i | ||||
\(235\) | 5.91525 | 0.385869 | ||||||||
\(236\) | −5.63697 | − | 9.76351i | −0.366935 | − | 0.635551i | ||||
\(237\) | −10.2372 | − | 13.4698i | −0.664975 | − | 0.874959i | ||||
\(238\) | 4.26614i | 0.276533i | ||||||||
\(239\) | −4.62407 | − | 2.66971i | −0.299106 | − | 0.172689i | 0.342935 | − | 0.939359i | \(-0.388579\pi\) |
−0.642041 | + | 0.766670i | \(0.721912\pi\) | |||||||
\(240\) | −0.898387 | + | 2.14085i | −0.0579906 | + | 0.138191i | ||||
\(241\) | 20.8012 | + | 12.0096i | 1.33992 | + | 0.773606i | 0.986796 | − | 0.161969i | \(-0.0517845\pi\) |
0.353129 | + | 0.935575i | \(0.385118\pi\) | |||||||
\(242\) | −4.26247 | + | 7.38281i | −0.274002 | + | 0.474585i | ||||
\(243\) | 15.4980 | − | 1.67689i | 0.994197 | − | 0.107572i | ||||
\(244\) | −2.14881 | + | 3.72186i | −0.137564 | + | 0.238267i | ||||
\(245\) | 3.65259i | 0.233355i | ||||||||
\(246\) | 16.9989 | + | 7.13342i | 1.08381 | + | 0.454810i | ||||
\(247\) | −1.54473 | + | 7.97362i | −0.0982887 | + | 0.507349i | ||||
\(248\) | −2.34559 | − | 1.35423i | −0.148945 | − | 0.0859936i | ||||
\(249\) | −2.57611 | + | 6.13884i | −0.163254 | + | 0.389033i | ||||
\(250\) | 10.9959i | 0.695443i | ||||||||
\(251\) | −16.9721 | + | 9.79887i | −1.07127 | + | 0.618499i | −0.928529 | − | 0.371261i | \(-0.878926\pi\) |
−0.142743 | + | 0.989760i | \(0.545592\pi\) | |||||||
\(252\) | 9.05867 | − | 2.33770i | 0.570642 | − | 0.147261i | ||||
\(253\) | −1.82247 | − | 3.15661i | −0.114578 | − | 0.198454i | ||||
\(254\) | −9.65441 | + | 5.57397i | −0.605771 | + | 0.349742i | ||||
\(255\) | −2.52872 | + | 1.92184i | −0.158354 | + | 0.120350i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.582747 | 0.0363507 | 0.0181754 | − | 0.999835i | \(-0.494214\pi\) | ||||
0.0181754 | + | 0.999835i | \(0.494214\pi\) | |||||||
\(258\) | 11.6057 | − | 8.82043i | 0.722541 | − | 0.549136i | ||||
\(259\) | 12.3048 | − | 7.10420i | 0.764585 | − | 0.441434i | ||||
\(260\) | 1.24881 | + | 2.16300i | 0.0774478 | + | 0.134144i | ||||
\(261\) | −13.9348 | − | 14.1949i | −0.862542 | − | 0.878644i | ||||
\(262\) | 11.1976 | − | 6.46496i | 0.691792 | − | 0.399406i | ||||
\(263\) | − | 2.52349i | − | 0.155605i | −0.996969 | − | 0.0778024i | \(-0.975210\pi\) | ||
0.996969 | − | 0.0778024i | \(-0.0247903\pi\) | |||||||
\(264\) | 1.05441 | − | 2.51265i | 0.0648946 | − | 0.154643i | ||||
\(265\) | −9.34096 | − | 5.39300i | −0.573810 | − | 0.331290i | ||||
\(266\) | 4.43355 | + | 12.8498i | 0.271838 | + | 0.787871i | ||||
\(267\) | −10.1934 | − | 4.27759i | −0.623829 | − | 0.261784i | ||||
\(268\) | − | 4.79251i | − | 0.292749i | ||||||
\(269\) | −3.64399 | + | 6.31157i | −0.222178 | + | 0.384823i | −0.955469 | − | 0.295092i | \(-0.904650\pi\) |
0.733291 | + | 0.679915i | \(0.237983\pi\) | |||||||
\(270\) | 5.46646 | + | 4.31634i | 0.332678 | + | 0.262684i | ||||
\(271\) | −14.5699 | + | 25.2359i | −0.885061 | + | 1.53297i | −0.0394174 | + | 0.999223i | \(0.512550\pi\) |
−0.845644 | + | 0.533748i | \(0.820783\pi\) | |||||||
\(272\) | 1.18474 | + | 0.684010i | 0.0718354 | + | 0.0414742i | ||||
\(273\) | 3.89439 | − | 9.28028i | 0.235699 | − | 0.561668i | ||||
\(274\) | −3.14341 | − | 1.81485i | −0.189901 | − | 0.109639i | ||||
\(275\) | − | 5.03943i | − | 0.303889i | ||||||
\(276\) | −2.42815 | − | 3.19490i | −0.146157 | − | 0.192311i | ||||
\(277\) | −7.83232 | − | 13.5660i | −0.470598 | − | 0.815100i | 0.528836 | − | 0.848724i | \(-0.322629\pi\) |
−0.999435 | + | 0.0336235i | \(0.989295\pi\) | |||||||
\(278\) | 1.59355 | 0.0955747 | ||||||||
\(279\) | −5.79839 | + | 5.69213i | −0.347141 | + | 0.340779i | ||||
\(280\) | 3.62010 | + | 2.09007i | 0.216342 | + | 0.124905i | ||||
\(281\) | −12.9021 | + | 22.3470i | −0.769673 | + | 1.33311i | 0.168067 | + | 0.985776i | \(0.446247\pi\) |
−0.937740 | + | 0.347337i | \(0.887086\pi\) | |||||||
\(282\) | −7.58255 | + | 0.962616i | −0.451535 | + | 0.0573230i | ||||
\(283\) | 10.2978 | + | 17.8363i | 0.612142 | + | 1.06026i | 0.990879 | + | 0.134756i | \(0.0430252\pi\) |
−0.378737 | + | 0.925504i | \(0.623641\pi\) | |||||||
\(284\) | 6.82171 | − | 11.8155i | 0.404794 | − | 0.701123i | ||||
\(285\) | −5.61934 | + | 8.41660i | −0.332861 | + | 0.498556i | ||||
\(286\) | −1.46569 | − | 2.53865i | −0.0866682 | − | 0.150114i | ||||
\(287\) | 16.5956 | − | 28.7445i | 0.979610 | − | 1.69673i | ||||
\(288\) | 0.803221 | − | 2.89047i | 0.0473302 | − | 0.170323i | ||||
\(289\) | −7.56426 | − | 13.1017i | −0.444957 | − | 0.770687i | ||||
\(290\) | − | 8.88780i | − | 0.521910i | ||||||
\(291\) | −7.03678 | − | 9.25884i | −0.412503 | − | 0.542763i | ||||
\(292\) | 2.70805 | − | 4.69049i | 0.158477 | − | 0.274490i | ||||
\(293\) | −9.98901 | + | 17.3015i | −0.583564 | + | 1.01076i | 0.411489 | + | 0.911415i | \(0.365009\pi\) |
−0.995053 | + | 0.0993477i | \(0.968324\pi\) | |||||||
\(294\) | −0.594402 | − | 4.68212i | −0.0346663 | − | 0.273067i | ||||
\(295\) | −13.0874 | − | 7.55600i | −0.761977 | − | 0.439928i | ||||
\(296\) | − | 4.55619i | − | 0.264823i | ||||||
\(297\) | −6.41583 | − | 5.06596i | −0.372284 | − | 0.293957i | ||||
\(298\) | 5.26170 | − | 3.03785i | 0.304802 | − | 0.175978i | ||||
\(299\) | −4.31694 | −0.249655 | ||||||||
\(300\) | −0.698737 | − | 5.50397i | −0.0403416 | − | 0.317772i | ||||
\(301\) | −13.1227 | − | 22.7292i | −0.756382 | − | 1.31009i | ||||
\(302\) | −14.7430 | + | 8.51189i | −0.848366 | + | 0.489804i | ||||
\(303\) | −0.910043 | + | 0.115531i | −0.0522806 | + | 0.00663710i | ||||
\(304\) | 4.27933 | + | 0.829035i | 0.245437 | + | 0.0475484i | ||||
\(305\) | 5.76070i | 0.329857i | ||||||||
\(306\) | 2.92872 | − | 2.87505i | 0.167424 | − | 0.164356i | ||||
\(307\) | −28.7886 | − | 16.6211i | −1.64305 | − | 0.948618i | −0.979739 | − | 0.200278i | \(-0.935816\pi\) |
−0.663315 | − | 0.748340i | \(-0.730851\pi\) | |||||||
\(308\) | −4.24881 | − | 2.45305i | −0.242098 | − | 0.139776i | ||||
\(309\) | −33.8067 | + | 4.29181i | −1.92320 | + | 0.244153i | ||||
\(310\) | −3.63052 | −0.206200 | ||||||||
\(311\) | 14.0507 | + | 8.11217i | 0.796742 | + | 0.459999i | 0.842331 | − | 0.538961i | \(-0.181183\pi\) |
−0.0455888 | + | 0.998960i | \(0.514516\pi\) | |||||||
\(312\) | −1.95280 | − | 2.56945i | −0.110555 | − | 0.145466i | ||||
\(313\) | 7.79061 | − | 13.4937i | 0.440351 | − | 0.762711i | −0.557364 | − | 0.830268i | \(-0.688187\pi\) |
0.997715 | + | 0.0675574i | \(0.0215206\pi\) | |||||||
\(314\) | −5.71527 | − | 9.89913i | −0.322531 | − | 0.558640i | ||||
\(315\) | 8.94902 | − | 8.78502i | 0.504220 | − | 0.494980i | ||||
\(316\) | 9.76790i | 0.549487i | ||||||||
\(317\) | 3.61705 | − | 6.26492i | 0.203154 | − | 0.351873i | −0.746389 | − | 0.665510i | \(-0.768214\pi\) |
0.949543 | + | 0.313637i | \(0.101547\pi\) | |||||||
\(318\) | 12.8515 | + | 5.39300i | 0.720675 | + | 0.302425i | ||||
\(319\) | 10.4314i | 0.584044i | ||||||||
\(320\) | 1.16085 | − | 0.670219i | 0.0648937 | − | 0.0374664i | ||||
\(321\) | 17.9075 | − | 13.6098i | 0.999499 | − | 0.759626i | ||||
\(322\) | −6.25707 | + | 3.61252i | −0.348693 | + | 0.201318i | ||||
\(323\) | 4.50283 | + | 3.90930i | 0.250544 | + | 0.217519i | ||||
\(324\) | −7.70967 | − | 4.64338i | −0.428315 | − | 0.257965i | ||||
\(325\) | −5.16889 | − | 2.98426i | −0.286719 | − | 0.165537i | ||||
\(326\) | 5.20323 | 0.288180 | ||||||||
\(327\) | 19.8870 | − | 2.52468i | 1.09975 | − | 0.139615i | ||||
\(328\) | −5.32171 | − | 9.21747i | −0.293842 | − | 0.508949i | ||||
\(329\) | 13.7616i | 0.758703i | ||||||||
\(330\) | −0.460009 | − | 3.62351i | −0.0253227 | − | 0.199467i | ||||
\(331\) | −3.40445 | + | 1.96556i | −0.187126 | + | 0.108037i | −0.590636 | − | 0.806938i | \(-0.701123\pi\) |
0.403511 | + | 0.914975i | \(0.367790\pi\) | |||||||
\(332\) | 3.32873 | − | 1.92184i | 0.182688 | − | 0.105475i | ||||
\(333\) | −13.1696 | − | 3.65963i | −0.721687 | − | 0.200546i | ||||
\(334\) | 2.44984 | 0.134050 | ||||||||
\(335\) | −3.21203 | − | 5.56340i | −0.175492 | − | 0.303961i | ||||
\(336\) | −4.98060 | − | 2.09007i | −0.271714 | − | 0.114022i | ||||
\(337\) | 4.44940 | − | 2.56886i | 0.242374 | − | 0.139935i | −0.373893 | − | 0.927472i | \(-0.621977\pi\) |
0.616267 | + | 0.787537i | \(0.288644\pi\) | |||||||
\(338\) | 9.52817 | 0.518264 | ||||||||
\(339\) | −1.22086 | − | 9.61673i | −0.0663079 | − | 0.522309i | ||||
\(340\) | 1.83375 | 0.0994488 | ||||||||
\(341\) | 4.26104 | 0.230748 | ||||||||
\(342\) | 5.83355 | − | 11.7034i | 0.315442 | − | 0.632848i | ||||
\(343\) | 13.3317 | 0.719847 | ||||||||
\(344\) | −8.41611 | −0.453766 | ||||||||
\(345\) | −4.96001 | − | 2.08142i | −0.267038 | − | 0.112060i | ||||
\(346\) | 11.5221 | 0.619431 | ||||||||
\(347\) | −11.8953 | + | 6.86774i | −0.638571 | + | 0.368679i | −0.784064 | − | 0.620680i | \(-0.786857\pi\) |
0.145493 | + | 0.989359i | \(0.453523\pi\) | |||||||
\(348\) | 1.44635 | + | 11.3930i | 0.0775326 | + | 0.610727i | ||||
\(349\) | −7.49298 | − | 12.9782i | −0.401090 | − | 0.694708i | 0.592768 | − | 0.805374i | \(-0.298035\pi\) |
−0.993858 | + | 0.110665i | \(0.964702\pi\) | |||||||
\(350\) | −9.98920 | −0.533945 | ||||||||
\(351\) | −8.99545 | + | 3.58068i | −0.480142 | + | 0.191122i | ||||
\(352\) | −1.36246 | + | 0.786617i | −0.0726194 | + | 0.0419268i | ||||
\(353\) | 4.84321 | − | 2.79623i | 0.257778 | − | 0.148828i | −0.365542 | − | 0.930795i | \(-0.619117\pi\) |
0.623321 | + | 0.781966i | \(0.285783\pi\) | |||||||
\(354\) | 18.0059 | + | 7.55600i | 0.957001 | + | 0.401597i | ||||
\(355\) | − | 18.2881i | − | 0.970634i | ||||||
\(356\) | 3.19119 | + | 5.52730i | 0.169133 | + | 0.292946i | ||||
\(357\) | −4.47109 | − | 5.88297i | −0.236635 | − | 0.311360i | ||||
\(358\) | −22.7029 | −1.19989 | ||||||||
\(359\) | −25.4808 | − | 14.7113i | −1.34482 | − | 0.776434i | −0.357312 | − | 0.933985i | \(-0.616307\pi\) |
−0.987511 | + | 0.157551i | \(0.949640\pi\) | |||||||
\(360\) | −1.00483 | − | 3.89375i | −0.0529591 | − | 0.205219i | ||||
\(361\) | 17.6254 | + | 7.09544i | 0.927653 | + | 0.373444i | ||||
\(362\) | 3.76806 | − | 2.17549i | 0.198045 | − | 0.114341i | ||||
\(363\) | −1.85959 | − | 14.6480i | −0.0976032 | − | 0.768823i | ||||
\(364\) | −5.03214 | + | 2.90531i | −0.263756 | + | 0.152280i | ||||
\(365\) | − | 7.25996i | − | 0.380004i | ||||||
\(366\) | −0.937465 | − | 7.38444i | −0.0490021 | − | 0.385991i | ||||
\(367\) | 1.08275 | − | 1.87537i | 0.0565189 | − | 0.0978936i | −0.836382 | − | 0.548148i | \(-0.815333\pi\) |
0.892901 | + | 0.450254i | \(0.148667\pi\) | |||||||
\(368\) | 2.31685i | 0.120774i | ||||||||
\(369\) | −30.9173 | + | 7.97859i | −1.60949 | + | 0.415349i | ||||
\(370\) | −3.05365 | − | 5.28907i | −0.158752 | − | 0.274966i | ||||
\(371\) | 12.5466 | − | 21.7314i | 0.651389 | − | 1.12824i | ||||
\(372\) | 4.65383 | − | 0.590811i | 0.241290 | − | 0.0306321i | ||||
\(373\) | 27.1481 | + | 15.6739i | 1.40567 | + | 0.811566i | 0.994967 | − | 0.100202i | \(-0.0319490\pi\) |
0.410706 | + | 0.911768i | \(0.365282\pi\) | |||||||
\(374\) | −2.15222 | −0.111288 | ||||||||
\(375\) | −11.5242 | − | 15.1632i | −0.595106 | − | 0.783027i | ||||
\(376\) | 3.82171 | + | 2.20646i | 0.197089 | + | 0.113790i | ||||
\(377\) | 10.6994 | + | 6.17727i | 0.551045 | + | 0.318146i | ||||
\(378\) | −10.0418 | + | 12.7175i | −0.516494 | + | 0.654118i | ||||
\(379\) | 10.4146i | 0.534964i | 0.963563 | + | 0.267482i | \(0.0861916\pi\) | ||||
−0.963563 | + | 0.267482i | \(0.913808\pi\) | |||||||
\(380\) | 5.52331 | − | 1.90570i | 0.283340 | − | 0.0977605i | ||||
\(381\) | 7.47157 | − | 17.8047i | 0.382780 | − | 0.912160i | ||||
\(382\) | −14.8549 | + | 8.57646i | −0.760041 | + | 0.438810i | ||||
\(383\) | −3.19119 | − | 5.52730i | −0.163062 | − | 0.282432i | 0.772903 | − | 0.634524i | \(-0.218804\pi\) |
−0.935965 | + | 0.352092i | \(0.885470\pi\) | |||||||
\(384\) | −1.37899 | + | 1.04804i | −0.0703712 | + | 0.0534826i | ||||
\(385\) | −6.57633 | −0.335161 | ||||||||
\(386\) | 11.6865 | − | 6.74723i | 0.594830 | − | 0.343425i | ||||
\(387\) | −6.75999 | + | 24.3265i | −0.343630 | + | 1.23659i | ||||
\(388\) | 6.71422i | 0.340863i | ||||||||
\(389\) | −5.45620 | − | 3.15014i | −0.276640 | − | 0.159718i | 0.355261 | − | 0.934767i | \(-0.384392\pi\) |
−0.631901 | + | 0.775049i | \(0.717725\pi\) | |||||||
\(390\) | −3.98901 | − | 1.67395i | −0.201991 | − | 0.0847638i | ||||
\(391\) | −1.58475 | + | 2.74486i | −0.0801440 | + | 0.138813i | ||||
\(392\) | −1.36246 | + | 2.35985i | −0.0688147 | + | 0.119191i | ||||
\(393\) | −8.66587 | + | 20.6507i | −0.437136 | + | 1.04169i | ||||
\(394\) | 9.03983i | 0.455420i | ||||||||
\(395\) | 6.54663 | + | 11.3391i | 0.329397 | + | 0.570532i | ||||
\(396\) | 1.17934 | + | 4.56999i | 0.0592640 | + | 0.229650i | ||||
\(397\) | 13.0601 | − | 22.6207i | 0.655467 | − | 1.13530i | −0.326309 | − | 0.945263i | \(-0.605805\pi\) |
0.981776 | − | 0.190040i | \(-0.0608617\pi\) | |||||||
\(398\) | −0.483132 | − | 0.836810i | −0.0242172 | − | 0.0419455i | ||||
\(399\) | −19.5809 | − | 13.0732i | −0.980272 | − | 0.654478i | ||||
\(400\) | −1.60161 | + | 2.77408i | −0.0800806 | + | 0.138704i | ||||
\(401\) | −11.1900 | − | 19.3817i | −0.558804 | − | 0.967877i | −0.997597 | − | 0.0692887i | \(-0.977927\pi\) |
0.438793 | − | 0.898588i | \(-0.355406\pi\) | |||||||
\(402\) | 5.02274 | + | 6.60881i | 0.250512 | + | 0.329618i | ||||
\(403\) | 2.52331 | − | 4.37051i | 0.125695 | − | 0.217711i | ||||
\(404\) | 0.458673 | + | 0.264815i | 0.0228199 | + | 0.0131751i | ||||
\(405\) | −12.0619 | − | 0.223110i | −0.599360 | − | 0.0110864i | ||||
\(406\) | 20.6771 | 1.02619 | ||||||||
\(407\) | 3.58398 | + | 6.20764i | 0.177651 | + | 0.307701i | ||||
\(408\) | −2.35061 | + | 0.298414i | −0.116373 | + | 0.0147737i | ||||
\(409\) | 28.9740i | 1.43267i | 0.697755 | + | 0.716337i | \(0.254182\pi\) | ||||
−0.697755 | + | 0.716337i | \(0.745818\pi\) | |||||||
\(410\) | −12.3554 | − | 7.13342i | −0.610192 | − | 0.352294i | ||||
\(411\) | 6.23677 | − | 0.791767i | 0.307637 | − | 0.0390550i | ||||
\(412\) | 17.0390 | + | 9.83749i | 0.839453 | + | 0.484659i | ||||
\(413\) | 17.5788 | − | 30.4473i | 0.864995 | − | 1.49822i | ||||
\(414\) | 6.69678 | + | 1.86094i | 0.329129 | + | 0.0914601i | ||||
\(415\) | 2.57611 | − | 4.46195i | 0.126456 | − | 0.219029i | ||||
\(416\) | 1.86329i | 0.0913551i | ||||||||
\(417\) | −2.19749 | + | 1.67010i | −0.107611 | + | 0.0817853i | ||||
\(418\) | −6.48256 | + | 2.23667i | −0.317072 | + | 0.109399i | ||||
\(419\) | 17.0286 | + | 9.83148i | 0.831902 | + | 0.480299i | 0.854504 | − | 0.519445i | \(-0.173861\pi\) |
−0.0226012 | + | 0.999745i | \(0.507195\pi\) | |||||||
\(420\) | −7.18255 | + | 0.911835i | −0.350473 | + | 0.0444930i | ||||
\(421\) | − | 18.6819i | − | 0.910498i | −0.890364 | − | 0.455249i | \(-0.849550\pi\) | ||
0.890364 | − | 0.455249i | \(-0.150450\pi\) | |||||||
\(422\) | 12.8154 | − | 7.39895i | 0.623842 | − | 0.360175i | ||||
\(423\) | 9.44740 | − | 9.27426i | 0.459348 | − | 0.450930i | ||||
\(424\) | −4.02331 | − | 6.96859i | −0.195389 | − | 0.338424i | ||||
\(425\) | −3.79499 | + | 2.19104i | −0.184084 | + | 0.106281i | ||||
\(426\) | 2.97611 | + | 23.4429i | 0.144193 | + | 1.13581i | ||||
\(427\) | −13.4021 | −0.648572 | ||||||||
\(428\) | −12.9860 | −0.627700 | ||||||||
\(429\) | 4.68179 | + | 1.96467i | 0.226039 | + | 0.0948551i | ||||
\(430\) | −9.76987 | + | 5.64064i | −0.471145 | + | 0.272016i | ||||
\(431\) | −20.5053 | − | 35.5162i | −0.987706 | − | 1.71076i | −0.629234 | − | 0.777216i | \(-0.716631\pi\) |
−0.358471 | − | 0.933541i | \(-0.616702\pi\) | |||||||
\(432\) | 1.92170 | + | 4.82774i | 0.0924579 | + | 0.232275i | ||||
\(433\) | −29.7693 | + | 17.1873i | −1.43062 | + | 0.825969i | −0.997168 | − | 0.0752083i | \(-0.976038\pi\) |
−0.433452 | + | 0.901177i | \(0.642705\pi\) | |||||||
\(434\) | − | 8.44627i | − | 0.405434i | ||||||
\(435\) | 9.31478 | + | 12.2562i | 0.446609 | + | 0.587639i | ||||
\(436\) | −10.0233 | − | 5.78696i | −0.480030 | − | 0.277145i | ||||
\(437\) | −1.92075 | + | 9.91455i | −0.0918817 | + | 0.474277i | ||||
\(438\) | 1.18145 | + | 9.30628i | 0.0564517 | + | 0.444671i | ||||
\(439\) | 33.2179i | 1.58541i | 0.609608 | + | 0.792703i | \(0.291327\pi\) | ||||
−0.609608 | + | 0.792703i | \(0.708673\pi\) | |||||||
\(440\) | −1.05441 | + | 1.82629i | −0.0502671 | + | 0.0870652i | ||||
\(441\) | 5.72673 | + | 5.83364i | 0.272702 | + | 0.277792i | ||||
\(442\) | −1.27451 | + | 2.20751i | −0.0606220 | + | 0.105000i | ||||
\(443\) | −20.3759 | − | 11.7640i | −0.968090 | − | 0.558927i | −0.0694363 | − | 0.997586i | \(-0.522120\pi\) |
−0.898653 | + | 0.438660i | \(0.855453\pi\) | |||||||
\(444\) | 4.77508 | + | 6.28294i | 0.226615 | + | 0.298175i | ||||
\(445\) | 7.40900 | + | 4.27759i | 0.351220 | + | 0.202777i | ||||
\(446\) | − | 28.0299i | − | 1.32725i | ||||||
\(447\) | −4.07204 | + | 9.70363i | −0.192601 | + | 0.458966i | ||||
\(448\) | 1.55924 | + | 2.70068i | 0.0736672 | + | 0.127595i | ||||
\(449\) | 26.0258 | 1.22823 | 0.614116 | − | 0.789215i | \(-0.289513\pi\) | ||||
0.614116 | + | 0.789215i | \(0.289513\pi\) | |||||||
\(450\) | 6.73194 | + | 6.85761i | 0.317347 | + | 0.323271i | ||||
\(451\) | 14.5012 | + | 8.37229i | 0.682837 | + | 0.394236i | ||||
\(452\) | −2.79839 | + | 4.84696i | −0.131625 | + | 0.227982i | ||||
\(453\) | 11.4097 | − | 27.1891i | 0.536073 | − | 1.27746i | ||||
\(454\) | 6.29137 | + | 10.8970i | 0.295269 | + | 0.511421i | ||||
\(455\) | −3.89439 | + | 6.74528i | −0.182572 | + | 0.316223i | ||||
\(456\) | −6.77002 | + | 3.34169i | −0.317035 | + | 0.156489i | ||||
\(457\) | 17.8876 | + | 30.9822i | 0.836746 | + | 1.44929i | 0.892601 | + | 0.450848i | \(0.148878\pi\) |
−0.0558550 | + | 0.998439i | \(0.517788\pi\) | |||||||
\(458\) | 10.4235 | − | 18.0541i | 0.487059 | − | 0.843610i | ||||
\(459\) | −1.02550 | + | 7.03408i | −0.0478665 | + | 0.328323i | ||||
\(460\) | 1.55279 | + | 2.68952i | 0.0723994 | + | 0.125399i | ||||
\(461\) | 31.5166i | 1.46788i | 0.679217 | + | 0.733938i | \(0.262320\pi\) | ||||
−0.679217 | + | 0.733938i | \(0.737680\pi\) | |||||||
\(462\) | 8.42996 | − | 1.07020i | 0.392197 | − | 0.0497900i | ||||
\(463\) | −9.60721 | + | 16.6402i | −0.446485 | + | 0.773334i | −0.998154 | − | 0.0607285i | \(-0.980658\pi\) |
0.551670 | + | 0.834063i | \(0.313991\pi\) | |||||||
\(464\) | 3.31526 | − | 5.74220i | 0.153907 | − | 0.266575i | ||||
\(465\) | 5.00645 | − | 3.80493i | 0.232168 | − | 0.176450i | ||||
\(466\) | 18.2017 | + | 10.5088i | 0.843178 | + | 0.486809i | ||||
\(467\) | 10.9865i | 0.508396i | 0.967152 | + | 0.254198i | \(0.0818115\pi\) | ||||
−0.967152 | + | 0.254198i | \(0.918189\pi\) | |||||||
\(468\) | 5.38578 | + | 1.49663i | 0.248958 | + | 0.0691817i | ||||
\(469\) | 12.9430 | − | 7.47267i | 0.597654 | − | 0.345056i | ||||
\(470\) | 5.91525 | 0.272850 | ||||||||
\(471\) | 18.2560 | + | 7.66096i | 0.841191 | + | 0.352998i | ||||
\(472\) | −5.63697 | − | 9.76351i | −0.259462 | − | 0.449402i | ||||
\(473\) | 11.4666 | − | 6.62026i | 0.527236 | − | 0.304400i | ||||
\(474\) | −10.2372 | − | 13.4698i | −0.470208 | − | 0.618689i | ||||
\(475\) | −9.15364 | + | 10.5434i | −0.419998 | + | 0.483764i | ||||
\(476\) | 4.26614i | 0.195538i | ||||||||
\(477\) | −23.3741 | + | 6.03197i | −1.07023 | + | 0.276185i | ||||
\(478\) | −4.62407 | − | 2.66971i | −0.211500 | − | 0.122110i | ||||
\(479\) | −7.41668 | − | 4.28202i | −0.338877 | − | 0.195651i | 0.320898 | − | 0.947114i | \(-0.396015\pi\) |
−0.659775 | + | 0.751463i | \(0.729349\pi\) | |||||||
\(480\) | −0.898387 | + | 2.14085i | −0.0410056 | + | 0.0977158i | ||||
\(481\) | 8.48949 | 0.387087 | ||||||||
\(482\) | 20.8012 | + | 12.0096i | 0.947470 | + | 0.547022i | ||||
\(483\) | 4.84236 | − | 11.5393i | 0.220335 | − | 0.525056i | ||||
\(484\) | −4.26247 | + | 7.38281i | −0.193748 | + | 0.335582i | ||||
\(485\) | 4.50000 | + | 7.79423i | 0.204334 | + | 0.353918i | ||||
\(486\) | 15.4980 | − | 1.67689i | 0.703004 | − | 0.0760651i | ||||
\(487\) | 39.5989i | 1.79440i | 0.441628 | + | 0.897198i | \(0.354401\pi\) | ||||
−0.441628 | + | 0.897198i | \(0.645599\pi\) | |||||||
\(488\) | −2.14881 | + | 3.72186i | −0.0972722 | + | 0.168480i | ||||
\(489\) | −7.17519 | + | 5.45319i | −0.324473 | + | 0.246602i | ||||
\(490\) | 3.65259i | 0.165007i | ||||||||
\(491\) | 10.8270 | − | 6.25098i | 0.488616 | − | 0.282103i | −0.235384 | − | 0.971902i | \(-0.575635\pi\) |
0.724000 | + | 0.689800i | \(0.242301\pi\) | |||||||
\(492\) | 16.9989 | + | 7.13342i | 0.766368 | + | 0.321599i | ||||
\(493\) | 7.85544 | − | 4.53534i | 0.353791 | − | 0.204262i | ||||
\(494\) | −1.54473 | + | 7.97362i | −0.0695006 | + | 0.358750i | ||||
\(495\) | 4.43193 | + | 4.51467i | 0.199200 | + | 0.202919i | ||||
\(496\) | −2.34559 | − | 1.35423i | −0.105320 | − | 0.0608067i | ||||
\(497\) | 42.5467 | 1.90848 | ||||||||
\(498\) | −2.57611 | + | 6.13884i | −0.115438 | + | 0.275088i | ||||
\(499\) | −7.58113 | − | 13.1309i | −0.339378 | − | 0.587820i | 0.644938 | − | 0.764235i | \(-0.276883\pi\) |
−0.984316 | + | 0.176415i | \(0.943550\pi\) | |||||||
\(500\) | 10.9959i | 0.491752i | ||||||||
\(501\) | −3.37831 | + | 2.56754i | −0.150932 | + | 0.114709i | ||||
\(502\) | −16.9721 | + | 9.79887i | −0.757504 | + | 0.437345i | ||||
\(503\) | 5.06362 | − | 2.92348i | 0.225776 | − | 0.130352i | −0.382846 | − | 0.923812i | \(-0.625056\pi\) |
0.608622 | + | 0.793460i | \(0.291723\pi\) | |||||||
\(504\) | 9.05867 | − | 2.33770i | 0.403505 | − | 0.104129i | ||||
\(505\) | 0.709937 | 0.0315918 | ||||||||
\(506\) | −1.82247 | − | 3.15661i | −0.0810187 | − | 0.140329i | ||||
\(507\) | −13.1392 | + | 9.98591i | −0.583534 | + | 0.443490i | ||||
\(508\) | −9.65441 | + | 5.57397i | −0.428345 | + | 0.247305i | ||||
\(509\) | −12.7109 | −0.563400 | −0.281700 | − | 0.959503i | \(-0.590898\pi\) | ||||
−0.281700 | + | 0.959503i | \(0.590898\pi\) | |||||||
\(510\) | −2.52872 | + | 1.92184i | −0.111973 | + | 0.0851005i | ||||
\(511\) | 16.8900 | 0.747171 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.22124 | + | 22.2527i | 0.186372 | + | 0.982479i | ||||
\(514\) | 0.582747 | 0.0257039 | ||||||||
\(515\) | 26.3731 | 1.16214 | ||||||||
\(516\) | 11.6057 | − | 8.82043i | 0.510913 | − | 0.388298i | ||||
\(517\) | −6.94257 | −0.305334 | ||||||||
\(518\) | 12.3048 | − | 7.10420i | 0.540644 | − | 0.312141i | ||||
\(519\) | −15.8888 | + | 12.0756i | −0.697442 | + | 0.530060i | ||||
\(520\) | 1.24881 | + | 2.16300i | 0.0547639 | + | 0.0948539i | ||||
\(521\) | −41.6061 | −1.82279 | −0.911397 | − | 0.411527i | \(-0.864995\pi\) | ||||
−0.911397 | + | 0.411527i | \(0.864995\pi\) | |||||||
\(522\) | −13.9348 | − | 14.1949i | −0.609909 | − | 0.621295i | ||||
\(523\) | 18.7605 | − | 10.8314i | 0.820338 | − | 0.473622i | −0.0301950 | − | 0.999544i | \(-0.509613\pi\) |
0.850533 | + | 0.525922i | \(0.176280\pi\) | |||||||
\(524\) | 11.1976 | − | 6.46496i | 0.489171 | − | 0.282423i | ||||
\(525\) | 13.7750 | − | 10.4691i | 0.601190 | − | 0.456908i | ||||
\(526\) | − | 2.52349i | − | 0.110029i | ||||||
\(527\) | −1.85261 | − | 3.20882i | −0.0807011 | − | 0.139778i | ||||
\(528\) | 1.05441 | − | 2.51265i | 0.0458874 | − | 0.109349i | ||||
\(529\) | 17.6322 | 0.766619 | ||||||||
\(530\) | −9.34096 | − | 5.39300i | −0.405745 | − | 0.234257i | ||||
\(531\) | −32.7489 | + | 8.45125i | −1.42118 | + | 0.366753i | ||||
\(532\) | 4.43355 | + | 12.8498i | 0.192219 | + | 0.557109i | ||||
\(533\) | 17.1748 | − | 9.91586i | 0.743922 | − | 0.429503i | ||||
\(534\) | −10.1934 | − | 4.27759i | −0.441113 | − | 0.185109i | ||||
\(535\) | −15.0748 | + | 8.70344i | −0.651740 | + | 0.376282i | ||||
\(536\) | − | 4.79251i | − | 0.207005i | ||||||
\(537\) | 31.3071 | − | 23.7936i | 1.35100 | − | 1.02677i | ||||
\(538\) | −3.64399 | + | 6.31157i | −0.157103 | + | 0.272111i | ||||
\(539\) | − | 4.28694i | − | 0.184652i | ||||||
\(540\) | 5.46646 | + | 4.31634i | 0.235239 | + | 0.185746i | ||||
\(541\) | 14.3410 | + | 24.8393i | 0.616566 | + | 1.06792i | 0.990108 | + | 0.140310i | \(0.0448099\pi\) |
−0.373542 | + | 0.927613i | \(0.621857\pi\) | |||||||
\(542\) | −14.5699 | + | 25.2359i | −0.625833 | + | 1.08397i | ||||
\(543\) | −2.91611 | + | 6.94906i | −0.125142 | + | 0.298213i | ||||
\(544\) | 1.18474 | + | 0.684010i | 0.0507953 | + | 0.0293267i | ||||
\(545\) | −15.5141 | −0.664552 | ||||||||
\(546\) | 3.89439 | − | 9.28028i | 0.166664 | − | 0.397159i | ||||
\(547\) | −20.7857 | − | 12.0006i | −0.888733 | − | 0.513110i | −0.0152052 | − | 0.999884i | \(-0.504840\pi\) |
−0.873528 | + | 0.486774i | \(0.838173\pi\) | |||||||
\(548\) | −3.14341 | − | 1.81485i | −0.134280 | − | 0.0775266i | ||||
\(549\) | 9.03195 | + | 9.20056i | 0.385474 | + | 0.392670i | ||||
\(550\) | − | 5.03943i | − | 0.214882i | ||||||
\(551\) | 18.9476 | − | 21.8243i | 0.807194 | − | 0.929747i | ||||
\(552\) | −2.42815 | − | 3.19490i | −0.103349 | − | 0.135984i | ||||
\(553\) | −26.3800 | + | 15.2305i | −1.12179 | + | 0.647667i | ||||
\(554\) | −7.83232 | − | 13.5660i | −0.332763 | − | 0.576363i | ||||
\(555\) | 9.75411 | + | 4.09323i | 0.414039 | + | 0.173748i | ||||
\(556\) | 1.59355 | 0.0675815 | ||||||||
\(557\) | −1.35487 | + | 0.782235i | −0.0574077 | + | 0.0331443i | −0.528429 | − | 0.848977i | \(-0.677219\pi\) |
0.471021 | + | 0.882122i | \(0.343885\pi\) | |||||||
\(558\) | −5.79839 | + | 5.69213i | −0.245466 | + | 0.240967i | ||||
\(559\) | − | 15.6816i | − | 0.663261i | ||||||
\(560\) | 3.62010 | + | 2.09007i | 0.152977 | + | 0.0883214i | ||||
\(561\) | 2.96788 | − | 2.25561i | 0.125304 | − | 0.0952320i | ||||
\(562\) | −12.9021 | + | 22.3470i | −0.544241 | + | 0.942653i | ||||
\(563\) | −2.73715 | + | 4.74089i | −0.115357 | + | 0.199805i | −0.917923 | − | 0.396760i | \(-0.870135\pi\) |
0.802565 | + | 0.596564i | \(0.203468\pi\) | |||||||
\(564\) | −7.58255 | + | 0.962616i | −0.319283 | + | 0.0405335i | ||||
\(565\) | 7.50214i | 0.315618i | ||||||||
\(566\) | 10.2978 | + | 17.8363i | 0.432850 | + | 0.749718i | ||||
\(567\) | 0.519058 | − | 28.0615i | 0.0217984 | − | 1.17847i | ||||
\(568\) | 6.82171 | − | 11.8155i | 0.286232 | − | 0.495769i | ||||
\(569\) | 16.9645 | + | 29.3835i | 0.711191 | + | 1.23182i | 0.964410 | + | 0.264410i | \(0.0851772\pi\) |
−0.253220 | + | 0.967409i | \(0.581490\pi\) | |||||||
\(570\) | −5.61934 | + | 8.41660i | −0.235368 | + | 0.352533i | ||||
\(571\) | 10.3019 | − | 17.8434i | 0.431120 | − | 0.746723i | −0.565850 | − | 0.824508i | \(-0.691452\pi\) |
0.996970 | + | 0.0777859i | \(0.0247851\pi\) | |||||||
\(572\) | −1.46569 | − | 2.53865i | −0.0612837 | − | 0.106146i | ||||
\(573\) | 11.4962 | − | 27.3954i | 0.480261 | − | 1.14446i | ||||
\(574\) | 16.5956 | − | 28.7445i | 0.692689 | − | 1.19977i | ||||
\(575\) | −6.42710 | − | 3.71069i | −0.268029 | − | 0.154746i | ||||
\(576\) | 0.803221 | − | 2.89047i | 0.0334675 | − | 0.120436i | ||||
\(577\) | 30.9865 | 1.28999 | 0.644993 | − | 0.764188i | \(-0.276860\pi\) | ||||
0.644993 | + | 0.764188i | \(0.276860\pi\) | |||||||
\(578\) | −7.56426 | − | 13.1017i | −0.314632 | − | 0.544958i | ||||
\(579\) | −9.04425 | + | 21.5523i | −0.375866 | + | 0.895685i | ||||
\(580\) | − | 8.88780i | − | 0.369046i | ||||||
\(581\) | 10.3806 | + | 5.99322i | 0.430658 | + | 0.248641i | ||||
\(582\) | −7.03678 | − | 9.25884i | −0.291684 | − | 0.383791i | ||||
\(583\) | 10.9632 | + | 6.32962i | 0.454050 | + | 0.262146i | ||||
\(584\) | 2.70805 | − | 4.69049i | 0.112060 | − | 0.194094i | ||||
\(585\) | 7.25517 | − | 1.87228i | 0.299964 | − | 0.0774093i | ||||
\(586\) | −9.98901 | + | 17.3015i | −0.412642 | + | 0.714717i | ||||
\(587\) | 3.68629i | 0.152150i | 0.997102 | + | 0.0760748i | \(0.0242388\pi\) | ||||
−0.997102 | + | 0.0760748i | \(0.975761\pi\) | |||||||
\(588\) | −0.594402 | − | 4.68212i | −0.0245127 | − | 0.193088i | ||||
\(589\) | −8.91487 | − | 7.73978i | −0.367331 | − | 0.318912i | ||||
\(590\) | −13.0874 | − | 7.55600i | −0.538799 | − | 0.311076i | ||||
\(591\) | −9.47411 | − | 12.4658i | −0.389713 | − | 0.512776i | ||||
\(592\) | − | 4.55619i | − | 0.187258i | ||||||
\(593\) | 13.9558 | − | 8.05741i | 0.573098 | − | 0.330878i | −0.185288 | − | 0.982684i | \(-0.559322\pi\) |
0.758386 | + | 0.651806i | \(0.225988\pi\) | |||||||
\(594\) | −6.41583 | − | 5.06596i | −0.263245 | − | 0.207859i | ||||
\(595\) | 2.85925 | + | 4.95237i | 0.117218 | + | 0.203027i | ||||
\(596\) | 5.26170 | − | 3.03785i | 0.215528 | − | 0.124435i | ||||
\(597\) | 1.54324 | + | 0.647609i | 0.0631608 | + | 0.0265049i | ||||
\(598\) | −4.31694 | −0.176533 | ||||||||
\(599\) | 41.3371 | 1.68899 | 0.844494 | − | 0.535566i | \(-0.179902\pi\) | ||||
0.844494 | + | 0.535566i | \(0.179902\pi\) | |||||||
\(600\) | −0.698737 | − | 5.50397i | −0.0285258 | − | 0.224699i | ||||
\(601\) | 32.2081 | − | 18.5954i | 1.31380 | − | 0.758521i | 0.331075 | − | 0.943604i | \(-0.392589\pi\) |
0.982723 | + | 0.185083i | \(0.0592554\pi\) | |||||||
\(602\) | −13.1227 | − | 22.7292i | −0.534843 | − | 0.926375i | ||||
\(603\) | −13.8526 | − | 3.84944i | −0.564122 | − | 0.156761i | ||||
\(604\) | −14.7430 | + | 8.51189i | −0.599885 | + | 0.346344i | ||||
\(605\) | 11.4271i | 0.464579i | ||||||||
\(606\) | −0.910043 | + | 0.115531i | −0.0369680 | + | 0.00469314i | ||||
\(607\) | −27.8067 | − | 16.0542i | −1.12864 | − | 0.651621i | −0.185048 | − | 0.982729i | \(-0.559244\pi\) |
−0.943593 | + | 0.331108i | \(0.892577\pi\) | |||||||
\(608\) | 4.27933 | + | 0.829035i | 0.173550 | + | 0.0336218i | ||||
\(609\) | −28.5136 | + | 21.6705i | −1.15543 | + | 0.878133i | ||||
\(610\) | 5.76070i | 0.233244i | ||||||||
\(611\) | −4.11127 | + | 7.12093i | −0.166324 | + | 0.288082i | ||||
\(612\) | 2.92872 | − | 2.87505i | 0.118387 | − | 0.116217i | ||||
\(613\) | −4.60047 | + | 7.96825i | −0.185811 | + | 0.321834i | −0.943850 | − | 0.330376i | \(-0.892825\pi\) |
0.758038 | + | 0.652210i | \(0.226158\pi\) | |||||||
\(614\) | −28.7886 | − | 16.6211i | −1.16181 | − | 0.670774i | ||||
\(615\) | 24.5141 | − | 3.11210i | 0.988505 | − | 0.125492i | ||||
\(616\) | −4.24881 | − | 2.45305i | −0.171189 | − | 0.0988362i | ||||
\(617\) | 39.8393i | 1.60387i | 0.597413 | + | 0.801934i | \(0.296196\pi\) | ||||
−0.597413 | + | 0.801934i | \(0.703804\pi\) | |||||||
\(618\) | −33.8067 | + | 4.29181i | −1.35991 | + | 0.172642i | ||||
\(619\) | −17.8989 | − | 31.0017i | −0.719416 | − | 1.24606i | −0.961231 | − | 0.275743i | \(-0.911076\pi\) |
0.241816 | − | 0.970322i | \(-0.422257\pi\) | |||||||
\(620\) | −3.63052 | −0.145805 | ||||||||
\(621\) | −11.1851 | + | 4.45228i | −0.448844 | + | 0.178664i | ||||
\(622\) | 14.0507 | + | 8.11217i | 0.563381 | + | 0.325268i | ||||
\(623\) | −9.95165 | + | 17.2368i | −0.398705 | + | 0.690577i | ||||
\(624\) | −1.95280 | − | 2.56945i | −0.0781745 | − | 0.102860i | ||||
\(625\) | −0.638393 | − | 1.10573i | −0.0255357 | − | 0.0442292i | ||||
\(626\) | 7.79061 | − | 13.4937i | 0.311375 | − | 0.539318i | ||||
\(627\) | 6.59526 | − | 9.87833i | 0.263389 | − | 0.394503i | ||||
\(628\) | −5.71527 | − | 9.89913i | −0.228064 | − | 0.395018i | ||||
\(629\) | 3.11648 | − | 5.39791i | 0.124262 | − | 0.215229i | ||||
\(630\) | 8.94902 | − | 8.78502i | 0.356537 | − | 0.350003i | ||||
\(631\) | −3.63535 | − | 6.29661i | −0.144721 | − | 0.250664i | 0.784548 | − | 0.620068i | \(-0.212895\pi\) |
−0.929269 | + | 0.369404i | \(0.879562\pi\) | |||||||
\(632\) | 9.76790i | 0.388546i | ||||||||
\(633\) | −9.91783 | + | 23.6341i | −0.394198 | + | 0.939370i | ||||
\(634\) | 3.61705 | − | 6.26492i | 0.143652 | − | 0.248812i | ||||
\(635\) | −7.47157 | + | 12.9411i | −0.296500 | + | 0.513553i | ||||
\(636\) | 12.8515 | + | 5.39300i | 0.509594 | + | 0.213847i | ||||
\(637\) | −4.39708 | − | 2.53865i | −0.174219 | − | 0.100585i | ||||
\(638\) | 10.4314i | 0.412982i | ||||||||
\(639\) | −28.6732 | − | 29.2085i | −1.13429 | − | 1.15547i | ||||
\(640\) | 1.16085 | − | 0.670219i | 0.0458868 | − | 0.0264927i | ||||
\(641\) | −6.12610 | −0.241966 | −0.120983 | − | 0.992655i | \(-0.538605\pi\) | ||||
−0.120983 | + | 0.992655i | \(0.538605\pi\) | |||||||
\(642\) | 17.9075 | − | 13.6098i | 0.706753 | − | 0.537137i | ||||
\(643\) | 6.48958 | + | 11.2403i | 0.255924 | + | 0.443273i | 0.965146 | − | 0.261712i | \(-0.0842870\pi\) |
−0.709222 | + | 0.704985i | \(0.750954\pi\) | |||||||
\(644\) | −6.25707 | + | 3.61252i | −0.246563 | + | 0.142353i | ||||
\(645\) | 7.56092 | − | 18.0176i | 0.297711 | − | 0.709442i | ||||
\(646\) | 4.50283 | + | 3.90930i | 0.177161 | + | 0.153809i | ||||
\(647\) | − | 8.95357i | − | 0.352001i | −0.984390 | − | 0.176001i | \(-0.943684\pi\) | ||
0.984390 | − | 0.176001i | \(-0.0563161\pi\) | |||||||
\(648\) | −7.70967 | − | 4.64338i | −0.302865 | − | 0.182409i | ||||
\(649\) | 15.3603 | + | 8.86827i | 0.602944 | + | 0.348110i | ||||
\(650\) | −5.16889 | − | 2.98426i | −0.202741 | − | 0.117052i | ||||
\(651\) | 8.85204 | + | 11.6473i | 0.346939 | + | 0.456494i | ||||
\(652\) | 5.20323 | 0.203774 | ||||||||
\(653\) | −41.1032 | − | 23.7309i | −1.60849 | − | 0.928664i | −0.989708 | − | 0.143103i | \(-0.954292\pi\) |
−0.618785 | − | 0.785561i | \(-0.712375\pi\) | |||||||
\(654\) | 19.8870 | − | 2.52468i | 0.777644 | − | 0.0987230i | ||||
\(655\) | 8.66587 | − | 15.0097i | 0.338604 | − | 0.586479i | ||||
\(656\) | −5.32171 | − | 9.21747i | −0.207778 | − | 0.359882i | ||||
\(657\) | −11.3826 | − | 11.5951i | −0.444076 | − | 0.452366i | ||||
\(658\) | 13.7616i | 0.536484i | ||||||||
\(659\) | 1.58977 | − | 2.75355i | 0.0619285 | − | 0.107263i | −0.833399 | − | 0.552672i | \(-0.813608\pi\) |
0.895327 | + | 0.445409i | \(0.146942\pi\) | |||||||
\(660\) | −0.460009 | − | 3.62351i | −0.0179058 | − | 0.141045i | ||||
\(661\) | 21.3823i | 0.831677i | 0.909438 | + | 0.415838i | \(0.136512\pi\) | ||||
−0.909438 | + | 0.415838i | \(0.863488\pi\) | |||||||
\(662\) | −3.40445 | + | 1.96556i | −0.132318 | + | 0.0763937i | ||||
\(663\) | −0.556030 | − | 4.37986i | −0.0215944 | − | 0.170100i | ||||
\(664\) | 3.32873 | − | 1.92184i | 0.129180 | − | 0.0745819i | ||||
\(665\) | 13.7589 | + | 11.9453i | 0.533546 | + | 0.463218i | ||||
\(666\) | −13.1696 | − | 3.65963i | −0.510310 | − | 0.141808i | ||||
\(667\) | 13.3038 | + | 7.68094i | 0.515125 | + | 0.297407i | ||||
\(668\) | 2.44984 | 0.0947873 | ||||||||
\(669\) | 29.3765 | + | 38.6529i | 1.13576 | + | 1.49441i | ||||
\(670\) | −3.21203 | − | 5.56340i | −0.124092 | − | 0.214933i | ||||
\(671\) | − | 6.76118i | − | 0.261012i | ||||||
\(672\) | −4.98060 | − | 2.09007i | −0.192131 | − | 0.0806260i | ||||
\(673\) | 18.9878 | − | 10.9626i | 0.731925 | − | 0.422577i | −0.0872011 | − | 0.996191i | \(-0.527792\pi\) |
0.819126 | + | 0.573614i | \(0.194459\pi\) | |||||||
\(674\) | 4.44940 | − | 2.56886i | 0.171384 | − | 0.0989488i | ||||
\(675\) | −16.4703 | − | 2.40122i | −0.633943 | − | 0.0924232i | ||||
\(676\) | 9.52817 | 0.366468 | ||||||||
\(677\) | 12.7482 | + | 22.0806i | 0.489955 | + | 0.848626i | 0.999933 | − | 0.0115609i | \(-0.00368003\pi\) |
−0.509979 | + | 0.860187i | \(0.670347\pi\) | |||||||
\(678\) | −1.22086 | − | 9.61673i | −0.0468868 | − | 0.369328i | ||||
\(679\) | −18.1330 | + | 10.4691i | −0.695880 | + | 0.401767i | ||||
\(680\) | 1.83375 | 0.0703209 | ||||||||
\(681\) | −20.0962 | − | 8.43320i | −0.770089 | − | 0.323161i | ||||
\(682\) | 4.26104 | 0.163164 | ||||||||
\(683\) | 7.99277 | 0.305835 | 0.152917 | − | 0.988239i | \(-0.451133\pi\) | ||||
0.152917 | + | 0.988239i | \(0.451133\pi\) | |||||||
\(684\) | 5.83355 | − | 11.7034i | 0.223052 | − | 0.447491i | ||||
\(685\) | −4.86539 | −0.185897 | ||||||||
\(686\) | 13.3317 | 0.509008 | ||||||||
\(687\) | 4.54748 | + | 35.8206i | 0.173497 | + | 1.36664i | ||||
\(688\) | −8.41611 | −0.320861 | ||||||||
\(689\) | 12.9845 | − | 7.49658i | 0.494669 | − | 0.285597i | ||||
\(690\) | −4.96001 | − | 2.08142i | −0.188824 | − | 0.0792384i | ||||
\(691\) | 14.5886 | + | 25.2682i | 0.554977 | + | 0.961249i | 0.997905 | + | 0.0646917i | \(0.0206064\pi\) |
−0.442928 | + | 0.896557i | \(0.646060\pi\) | |||||||
\(692\) | 11.5221 | 0.438004 | ||||||||
\(693\) | −10.5032 | + | 10.3107i | −0.398984 | + | 0.391672i | ||||
\(694\) | −11.8953 | + | 6.86774i | −0.451538 | + | 0.260696i | ||||
\(695\) | 1.84988 | − | 1.06803i | 0.0701698 | − | 0.0405125i | ||||
\(696\) | 1.44635 | + | 11.3930i | 0.0548238 | + | 0.431849i | ||||
\(697\) | − | 14.5604i | − | 0.551515i | ||||||
\(698\) | −7.49298 | − | 12.9782i | −0.283614 | − | 0.491233i | ||||
\(699\) | −36.1136 | + | 4.58467i | −1.36594 | + | 0.173408i | ||||
\(700\) | −9.98920 | −0.377556 | ||||||||
\(701\) | −37.3427 | − | 21.5598i | −1.41042 | − | 0.814304i | −0.414988 | − | 0.909827i | \(-0.636214\pi\) |
−0.995427 | + | 0.0955229i | \(0.969548\pi\) | |||||||
\(702\) | −8.99545 | + | 3.58068i | −0.339512 | + | 0.135144i | ||||
\(703\) | 3.77725 | − | 19.4975i | 0.142461 | − | 0.735361i | ||||
\(704\) | −1.36246 | + | 0.786617i | −0.0513497 | + | 0.0296468i | ||||
\(705\) | −8.15707 | + | 6.19943i | −0.307213 | + | 0.233484i | ||||
\(706\) | 4.84321 | − | 2.79623i | 0.182277 | − | 0.105237i | ||||
\(707\) | 1.65164i | 0.0621164i | ||||||||
\(708\) | 18.0059 | + | 7.55600i | 0.676702 | + | 0.283972i | ||||
\(709\) | 1.08275 | − | 1.87537i | 0.0406634 | − | 0.0704311i | −0.844977 | − | 0.534802i | \(-0.820386\pi\) |
0.885641 | + | 0.464371i | \(0.153720\pi\) | |||||||
\(710\) | − | 18.2881i | − | 0.686342i | ||||||
\(711\) | 28.2338 | + | 7.84578i | 1.05885 | + | 0.294240i | ||||
\(712\) | 3.19119 | + | 5.52730i | 0.119595 | + | 0.207144i | ||||
\(713\) | 3.13754 | − | 5.43438i | 0.117502 | − | 0.203519i | ||||
\(714\) | −4.47109 | − | 5.88297i | −0.167326 | − | 0.220164i | ||||
\(715\) | −3.40291 | − | 1.96467i | −0.127262 | − | 0.0734745i | ||||
\(716\) | −22.7029 | −0.848449 | ||||||||
\(717\) | 9.17451 | − | 1.16472i | 0.342628 | − | 0.0434972i | ||||
\(718\) | −25.4808 | − | 14.7113i | −0.950933 | − | 0.549022i | ||||
\(719\) | 20.9879 | + | 12.1173i | 0.782715 | + | 0.451901i | 0.837392 | − | 0.546603i | \(-0.184079\pi\) |
−0.0546765 | + | 0.998504i | \(0.517413\pi\) | |||||||
\(720\) | −1.00483 | − | 3.89375i | −0.0374478 | − | 0.145111i | ||||
\(721\) | 61.3561i | 2.28502i | ||||||||
\(722\) | 17.6254 | + | 7.09544i | 0.655950 | + | 0.264065i | ||||
\(723\) | −41.2712 | + | 5.23944i | −1.53489 | + | 0.194857i | ||||
\(724\) | 3.76806 | − | 2.17549i | 0.140039 | − | 0.0808514i | ||||
\(725\) | 10.6195 | + | 18.3936i | 0.394399 | + | 0.683120i | ||||
\(726\) | −1.85959 | − | 14.6480i | −0.0690159 | − | 0.543640i | ||||
\(727\) | −40.2844 | −1.49406 | −0.747032 | − | 0.664788i | \(-0.768522\pi\) | ||||
−0.747032 | + | 0.664788i | \(0.768522\pi\) | |||||||
\(728\) | −5.03214 | + | 2.90531i | −0.186504 | + | 0.107678i | ||||
\(729\) | −19.6141 | + | 18.5549i | −0.726449 | + | 0.687220i | ||||
\(730\) | − | 7.25996i | − | 0.268703i | ||||||
\(731\) | −9.97090 | − | 5.75670i | −0.368787 | − | 0.212919i | ||||
\(732\) | −0.937465 | − | 7.38444i | −0.0346497 | − | 0.272937i | ||||
\(733\) | 7.49638 | − | 12.9841i | 0.276885 | − | 0.479579i | −0.693724 | − | 0.720241i | \(-0.744031\pi\) |
0.970609 | + | 0.240662i | \(0.0773645\pi\) | |||||||
\(734\) | 1.08275 | − | 1.87537i | 0.0399649 | − | 0.0692213i | ||||
\(735\) | −3.82806 | − | 5.03688i | −0.141200 | − | 0.185788i | ||||
\(736\) | 2.31685i | 0.0854000i | ||||||||
\(737\) | 3.76987 | + | 6.52960i | 0.138865 | + | 0.240521i | ||||
\(738\) | −30.9173 | + | 7.97859i | −1.13808 | + | 0.293696i | ||||
\(739\) | 2.78010 | − | 4.81527i | 0.102268 | − | 0.177133i | −0.810351 | − | 0.585945i | \(-0.800724\pi\) |
0.912619 | + | 0.408812i | \(0.134057\pi\) | |||||||
\(740\) | −3.05365 | − | 5.28907i | −0.112254 | − | 0.194430i | ||||
\(741\) | −6.22651 | − | 12.6145i | −0.228737 | − | 0.463404i | ||||
\(742\) | 12.5466 | − | 21.7314i | 0.460601 | − | 0.797785i | ||||
\(743\) | −18.7635 | − | 32.4994i | −0.688367 | − | 1.19229i | −0.972366 | − | 0.233461i | \(-0.924995\pi\) |
0.284000 | − | 0.958824i | \(-0.408339\pi\) | |||||||
\(744\) | 4.65383 | − | 0.590811i | 0.170618 | − | 0.0216602i | ||||
\(745\) | 4.07204 | − | 7.05299i | 0.149188 | − | 0.258401i | ||||
\(746\) | 27.1481 | + | 15.6739i | 0.993961 | + | 0.573864i | ||||
\(747\) | −2.88133 | − | 11.1653i | −0.105422 | − | 0.408515i | ||||
\(748\) | −2.15222 | −0.0786928 | ||||||||
\(749\) | −20.2482 | − | 35.0710i | −0.739854 | − | 1.28147i | ||||
\(750\) | −11.5242 | − | 15.1632i | −0.420803 | − | 0.553683i | ||||
\(751\) | − | 22.9911i | − | 0.838958i | −0.907765 | − | 0.419479i | \(-0.862213\pi\) | ||
0.907765 | − | 0.419479i | \(-0.137787\pi\) | |||||||
\(752\) | 3.82171 | + | 2.20646i | 0.139363 | + | 0.0804614i | ||||
\(753\) | 13.1348 | − | 31.3000i | 0.478658 | − | 1.14064i | ||||
\(754\) | 10.6994 | + | 6.17727i | 0.389647 | + | 0.224963i | ||||
\(755\) | −11.4097 | + | 19.7621i | −0.415240 | + | 0.719217i | ||||
\(756\) | −10.0418 | + | 12.7175i | −0.365217 | + | 0.462531i | ||||
\(757\) | −4.27174 | + | 7.39888i | −0.155259 | + | 0.268917i | −0.933153 | − | 0.359479i | \(-0.882955\pi\) |
0.777894 | + | 0.628395i | \(0.216288\pi\) | |||||||
\(758\) | 10.4146i | 0.378277i | ||||||||
\(759\) | 5.82142 | + | 2.44291i | 0.211304 | + | 0.0886720i | ||||
\(760\) | 5.52331 | − | 1.90570i | 0.200352 | − | 0.0691271i | ||||
\(761\) | 21.3234 | + | 12.3111i | 0.772972 | + | 0.446276i | 0.833934 | − | 0.551864i | \(-0.186083\pi\) |
−0.0609616 | + | 0.998140i | \(0.519417\pi\) | |||||||
\(762\) | 7.47157 | − | 17.8047i | 0.270666 | − | 0.644995i | ||||
\(763\) | − | 36.0931i | − | 1.30666i | ||||||
\(764\) | −14.8549 | + | 8.57646i | −0.537430 | + | 0.310286i | ||||
\(765\) | 1.47290 | − | 5.30039i | 0.0532529 | − | 0.191636i | ||||
\(766\) | −3.19119 | − | 5.52730i | −0.115302 | − | 0.199709i | ||||
\(767\) | 18.1922 | − | 10.5033i | 0.656883 | − | 0.379251i | ||||
\(768\) | −1.37899 | + | 1.04804i | −0.0497600 | + | 0.0378179i | ||||
\(769\) | 1.61139 | 0.0581081 | 0.0290540 | − | 0.999578i | \(-0.490751\pi\) | ||||
0.0290540 | + | 0.999578i | \(0.490751\pi\) | |||||||
\(770\) | −6.57633 | −0.236994 | ||||||||
\(771\) | −0.803601 | + | 0.610742i | −0.0289410 | + | 0.0219953i | ||||
\(772\) | 11.6865 | − | 6.74723i | 0.420608 | − | 0.242838i | ||||
\(773\) | −7.30144 | − | 12.6465i | −0.262614 | − | 0.454862i | 0.704321 | − | 0.709881i | \(-0.251251\pi\) |
−0.966936 | + | 0.255020i | \(0.917918\pi\) | |||||||
\(774\) | −6.75999 | + | 24.3265i | −0.242983 | + | 0.874399i | ||||
\(775\) | 7.51347 | − | 4.33790i | 0.269892 | − | 0.155822i | ||||
\(776\) | 6.71422i | 0.241027i | ||||||||
\(777\) | −9.52274 | + | 22.6926i | −0.341626 | + | 0.814092i | ||||
\(778\) | −5.45620 | − | 3.15014i | −0.195614 | − | 0.112938i | ||||
\(779\) | −15.1318 | − | 43.8565i | −0.542151 | − | 1.57132i | ||||
\(780\) | −3.98901 | − | 1.67395i | −0.142829 | − | 0.0599371i | ||||
\(781\) | 21.4643i | 0.768053i | ||||||||
\(782\) | −1.58475 | + | 2.74486i | −0.0566704 | + | 0.0981560i | ||||
\(783\) | 34.0928 | + | 4.97042i | 1.21838 | + | 0.177628i | ||||
\(784\) | −1.36246 | + | 2.35985i | −0.0486593 | + | 0.0842804i | ||||
\(785\) | −13.2692 | − | 7.66096i | −0.473597 | − | 0.273431i | ||||
\(786\) | −8.66587 | + | 20.6507i | −0.309101 | + | 0.736585i | ||||
\(787\) | −17.1570 | − | 9.90558i | −0.611580 | − | 0.353096i | 0.162004 | − | 0.986790i | \(-0.448204\pi\) |
−0.773584 | + | 0.633694i | \(0.781538\pi\) | |||||||
\(788\) | 9.03983i | 0.322031i | ||||||||
\(789\) | 2.64472 | + | 3.47986i | 0.0941544 | + | 0.123886i | ||||
\(790\) | 6.54663 | + | 11.3391i | 0.232919 | + | 0.403427i | ||||
\(791\) | −17.4535 | −0.620574 | ||||||||
\(792\) | 1.17934 | + | 4.56999i | 0.0419060 | + | 0.162387i | ||||
\(793\) | −6.93488 | − | 4.00385i | −0.246265 | − | 0.142181i | ||||
\(794\) | 13.0601 | − | 22.6207i | 0.463485 | − | 0.802780i | ||||
\(795\) | 18.5332 | − | 2.35281i | 0.657304 | − | 0.0834456i | ||||
\(796\) | −0.483132 | − | 0.836810i | −0.0171242 | − | 0.0296599i | ||||
\(797\) | 1.12757 | − | 1.95300i | 0.0399404 | − | 0.0691789i | −0.845364 | − | 0.534190i | \(-0.820617\pi\) |
0.885305 | + | 0.465012i | \(0.153950\pi\) | |||||||
\(798\) | −19.5809 | − | 13.0732i | −0.693157 | − | 0.462786i | ||||
\(799\) | 3.01849 | + | 5.22817i | 0.106786 | + | 0.184959i | ||||
\(800\) | −1.60161 | + | 2.77408i | −0.0566256 | + | 0.0980784i | ||||
\(801\) | 18.5397 | − | 4.78440i | 0.655069 | − | 0.169048i | ||||
\(802\) | −11.1900 | − | 19.3817i | −0.395134 | − | 0.684392i | ||||
\(803\) | 8.52081i | 0.300693i | ||||||||
\(804\) | 5.02274 | + | 6.60881i | 0.177138 | + | 0.233075i | ||||
\(805\) | −4.84236 | + | 8.38721i | −0.170671 | + | 0.295610i | ||||
\(806\) | 2.52331 | − | 4.37051i | 0.0888800 | − | 0.153945i | ||||
\(807\) | −1.58977 | − | 12.5226i | −0.0559624 | − | 0.440817i | ||||
\(808\) | 0.458673 | + | 0.264815i | 0.0161361 | + | 0.00931617i | ||||
\(809\) | 29.5377i | 1.03849i | 0.854626 | + | 0.519244i | \(0.173787\pi\) | ||||
−0.854626 | + | 0.519244i | \(0.826213\pi\) | |||||||
\(810\) | −12.0619 | − | 0.223110i | −0.423811 | − | 0.00783930i | ||||
\(811\) | −3.70272 | + | 2.13777i | −0.130020 | + | 0.0750671i | −0.563599 | − | 0.826048i | \(-0.690584\pi\) |
0.433579 | + | 0.901115i | \(0.357250\pi\) | |||||||
\(812\) | 20.6771 | 0.725626 | ||||||||
\(813\) | −6.35645 | − | 50.0699i | −0.222930 | − | 1.75603i | ||||
\(814\) | 3.58398 | + | 6.20764i | 0.125618 | + | 0.217578i | ||||
\(815\) | 6.04018 | − | 3.48730i | 0.211578 | − | 0.122155i | ||||
\(816\) | −2.35061 | + | 0.298414i | −0.0822879 | + | 0.0104466i | ||||
\(817\) | −36.0153 | − | 6.97725i | −1.26002 | − | 0.244103i | ||||
\(818\) | 28.9740i | 1.01305i | ||||||||
\(819\) | 4.35580 | + | 16.8789i | 0.152204 | + | 0.589796i | ||||
\(820\) | −12.3554 | − | 7.13342i | −0.431471 | − | 0.249110i | ||||
\(821\) | −38.2537 | − | 22.0858i | −1.33506 | − | 0.770799i | −0.348992 | − | 0.937126i | \(-0.613476\pi\) |
−0.986071 | + | 0.166327i | \(0.946809\pi\) | |||||||
\(822\) | 6.23677 | − | 0.791767i | 0.217532 | − | 0.0276160i | ||||
\(823\) | 36.4851 | 1.27179 | 0.635895 | − | 0.771775i | \(-0.280631\pi\) | ||||
0.635895 | + | 0.771775i | \(0.280631\pi\) | |||||||
\(824\) | 17.0390 | + | 9.83749i | 0.593583 | + | 0.342705i | ||||
\(825\) | 5.28152 | + | 6.94931i | 0.183879 | + | 0.241944i | ||||
\(826\) | 17.5788 | − | 30.4473i | 0.611644 | − | 1.05940i | ||||
\(827\) | 13.4855 | + | 23.3576i | 0.468937 | + | 0.812223i | 0.999370 | − | 0.0355041i | \(-0.0113037\pi\) |
−0.530432 | + | 0.847727i | \(0.677970\pi\) | |||||||
\(828\) | 6.69678 | + | 1.86094i | 0.232729 | + | 0.0646721i | ||||
\(829\) | − | 17.9429i | − | 0.623184i | −0.950216 | − | 0.311592i | \(-0.899138\pi\) | ||
0.950216 | − | 0.311592i | \(-0.100862\pi\) | |||||||
\(830\) | 2.57611 | − | 4.46195i | 0.0894180 | − | 0.154877i | ||||
\(831\) | 25.0184 | + | 10.4987i | 0.867878 | + | 0.364197i | ||||
\(832\) | 1.86329i | 0.0645978i | ||||||||
\(833\) | −3.22832 | + | 1.86387i | −0.111855 | + | 0.0645794i | ||||
\(834\) | −2.19749 | + | 1.67010i | −0.0760927 | + | 0.0578310i | ||||
\(835\) | 2.84391 | − | 1.64193i | 0.0984176 | − | 0.0568214i | ||||
\(836\) | −6.48256 | + | 2.23667i | −0.224204 | + | 0.0773569i | ||||
\(837\) | 2.03033 | − | 13.9263i | 0.0701786 | − | 0.481365i | ||||
\(838\) | 17.0286 | + | 9.83148i | 0.588244 | + | 0.339623i | ||||
\(839\) | −12.4953 | −0.431387 | −0.215693 | − | 0.976461i | \(-0.569201\pi\) | ||||
−0.215693 | + | 0.976461i | \(0.569201\pi\) | |||||||
\(840\) | −7.18255 | + | 0.911835i | −0.247822 | + | 0.0314613i | ||||
\(841\) | −7.48190 | − | 12.9590i | −0.257996 | − | 0.446863i | ||||
\(842\) | − | 18.6819i | − | 0.643819i | ||||||
\(843\) | −5.62880 | − | 44.3382i | −0.193866 | − | 1.52709i | ||||
\(844\) | 12.8154 | − | 7.39895i | 0.441123 | − | 0.254682i | ||||
\(845\) | 11.0608 | − | 6.38596i | 0.380503 | − | 0.219684i | ||||
\(846\) | 9.44740 | − | 9.27426i | 0.324808 | − | 0.318856i | ||||
\(847\) | −26.5848 | −0.913466 | ||||||||
\(848\) | −4.02331 | − | 6.96859i | −0.138161 | − | 0.239302i | ||||
\(849\) | −32.8938 | − | 13.8036i | −1.12891 | − | 0.473738i | ||||
\(850\) | −3.79499 | + | 2.19104i | −0.130167 | + | 0.0751520i | ||||
\(851\) | 10.5560 | 0.361855 | ||||||||
\(852\) | 2.97611 | + | 23.4429i | 0.101960 | + | 0.803142i | ||||
\(853\) | −5.90674 | −0.202243 | −0.101121 | − | 0.994874i | \(-0.532243\pi\) | ||||
−0.101121 | + | 0.994874i | \(0.532243\pi\) | |||||||
\(854\) | −13.4021 | −0.458609 | ||||||||
\(855\) | −1.07194 | − | 17.4957i | −0.0366596 | − | 0.598340i | ||||
\(856\) | −12.9860 | −0.443851 | ||||||||
\(857\) | 46.9567 | 1.60401 | 0.802006 | − | 0.597316i | \(-0.203766\pi\) | ||||
0.802006 | + | 0.597316i | \(0.203766\pi\) | |||||||
\(858\) | 4.68179 | + | 1.96467i | 0.159834 | + | 0.0670727i | ||||
\(859\) | 40.5249 | 1.38269 | 0.691346 | − | 0.722523i | \(-0.257018\pi\) | ||||
0.691346 | + | 0.722523i | \(0.257018\pi\) | |||||||
\(860\) | −9.76987 | + | 5.64064i | −0.333150 | + | 0.192344i | ||||
\(861\) | 7.24020 | + | 57.0312i | 0.246745 | + | 1.94362i | ||||
\(862\) | −20.5053 | − | 35.5162i | −0.698413 | − | 1.20969i | ||||
\(863\) | −3.89951 | −0.132741 | −0.0663704 | − | 0.997795i | \(-0.521142\pi\) | ||||
−0.0663704 | + | 0.997795i | \(0.521142\pi\) | |||||||
\(864\) | 1.92170 | + | 4.82774i | 0.0653776 | + | 0.164243i | ||||
\(865\) | 13.3754 | − | 7.72232i | 0.454779 | − | 0.262567i | ||||
\(866\) | −29.7693 | + | 17.1873i | −1.01160 | + | 0.584048i | ||||
\(867\) | 24.1621 | + | 10.1394i | 0.820589 | + | 0.344353i | ||||
\(868\) | − | 8.44627i | − | 0.286685i | ||||||
\(869\) | −7.68360 | − | 13.3084i | −0.260648 | − | 0.451456i | ||||
\(870\) | 9.31478 | + | 12.2562i | 0.315801 | + | 0.415523i | ||||
\(871\) | 8.92981 | 0.302575 | ||||||||
\(872\) | −10.0233 | − | 5.78696i | −0.339432 | − | 0.195971i | ||||
\(873\) | 19.4073 | + | 5.39300i | 0.656837 | + | 0.182526i | ||||
\(874\) | −1.92075 | + | 9.91455i | −0.0649702 | + | 0.335365i | ||||
\(875\) | −29.6965 | + | 17.1453i | −1.00392 | + | 0.579616i | ||||
\(876\) | 1.18145 | + | 9.30628i | 0.0399174 | + | 0.314430i | ||||
\(877\) | 0.162660 | − | 0.0939119i | 0.00549264 | − | 0.00317118i | −0.497251 | − | 0.867607i | \(-0.665657\pi\) |
0.502744 | + | 0.864435i | \(0.332324\pi\) | |||||||
\(878\) | 33.2179i | 1.12105i | ||||||||
\(879\) | −4.35791 | − | 34.3274i | −0.146989 | − | 1.15784i | ||||
\(880\) | −1.05441 | + | 1.82629i | −0.0355442 | + | 0.0615644i | ||||
\(881\) | 43.6041i | 1.46906i | 0.678577 | + | 0.734529i | \(0.262597\pi\) | ||||
−0.678577 | + | 0.734529i | \(0.737403\pi\) | |||||||
\(882\) | 5.72673 | + | 5.83364i | 0.192829 | + | 0.196429i | ||||
\(883\) | 12.7475 | + | 22.0793i | 0.428987 | + | 0.743027i | 0.996783 | − | 0.0801421i | \(-0.0255374\pi\) |
−0.567797 | + | 0.823169i | \(0.692204\pi\) | |||||||
\(884\) | −1.27451 | + | 2.20751i | −0.0428663 | + | 0.0742465i | ||||
\(885\) | 25.9664 | − | 3.29647i | 0.872850 | − | 0.110809i | ||||
\(886\) | −20.3759 | − | 11.7640i | −0.684543 | − | 0.395221i | ||||
\(887\) | −20.6950 | −0.694870 | −0.347435 | − | 0.937704i | \(-0.612947\pi\) | ||||
−0.347435 | + | 0.937704i | \(0.612947\pi\) | |||||||
\(888\) | 4.77508 | + | 6.28294i | 0.160241 | + | 0.210842i | ||||
\(889\) | −30.1071 | − | 17.3823i | −1.00976 | − | 0.582985i | ||||
\(890\) | 7.40900 | + | 4.27759i | 0.248350 | + | 0.143385i | ||||
\(891\) | 14.1567 | + | 0.261858i | 0.474267 | + | 0.00877258i | ||||
\(892\) | − | 28.0299i | − | 0.938510i | ||||||
\(893\) | 14.5251 | + | 12.6105i | 0.486065 | + | 0.421995i | ||||
\(894\) | −4.07204 | + | 9.70363i | −0.136190 | + | 0.324538i | ||||
\(895\) | −26.3548 | + | 15.2159i | −0.880943 | + | 0.508613i | ||||
\(896\) | 1.55924 | + | 2.70068i | 0.0520906 | + | 0.0902235i | ||||
\(897\) | 5.95302 | − | 4.52433i | 0.198765 | − | 0.151063i | ||||
\(898\) | 26.0258 | 0.868492 | ||||||||
\(899\) | −15.5525 | + | 8.97924i | −0.518705 | + | 0.299474i | ||||
\(900\) | 6.73194 | + | 6.85761i | 0.224398 | + | 0.228587i | ||||
\(901\) | − | 11.0079i | − | 0.366728i | ||||||
\(902\) | 14.5012 | + | 8.37229i | 0.482838 | + | 0.278767i | ||||
\(903\) | 41.9173 | + | 17.5902i | 1.39492 | + | 0.585366i | ||||
\(904\) | −2.79839 | + | 4.84696i | −0.0930731 | + | 0.161207i | ||||
\(905\) | 2.91611 | − | 5.05085i | 0.0969347 | − | 0.167896i | ||||
\(906\) | 11.4097 | − | 27.1891i | 0.379061 | − | 0.903297i | ||||
\(907\) | 26.4564i | 0.878471i | 0.898372 | + | 0.439235i | \(0.144751\pi\) | ||||
−0.898372 | + | 0.439235i | \(0.855249\pi\) | |||||||
\(908\) | 6.29137 | + | 10.8970i | 0.208787 | + | 0.361629i | ||||
\(909\) | 1.13386 | − | 1.11308i | 0.0376077 | − | 0.0369185i | ||||
\(910\) | −3.89439 | + | 6.74528i | −0.129098 | + | 0.223604i | ||||
\(911\) | −16.1131 | − | 27.9087i | −0.533850 | − | 0.924656i | −0.999218 | − | 0.0395383i | \(-0.987411\pi\) |
0.465368 | − | 0.885117i | \(-0.345922\pi\) | |||||||
\(912\) | −6.77002 | + | 3.34169i | −0.224178 | + | 0.110654i | ||||
\(913\) | −3.02351 | + | 5.23687i | −0.100063 | + | 0.173315i | ||||
\(914\) | 17.8876 | + | 30.9822i | 0.591669 | + | 1.02480i | ||||
\(915\) | −6.03745 | − | 7.94395i | −0.199592 | − | 0.262619i | ||||
\(916\) | 10.4235 | − | 18.0541i | 0.344403 | − | 0.596523i | ||||
\(917\) | 34.9196 | + | 20.1608i | 1.15315 | + | 0.665770i | ||||
\(918\) | −1.02550 | + | 7.03408i | −0.0338467 | + | 0.232159i | ||||
\(919\) | −15.4379 | −0.509249 | −0.254625 | − | 0.967040i | \(-0.581952\pi\) | ||||
−0.254625 | + | 0.967040i | \(0.581952\pi\) | |||||||
\(920\) | 1.55279 | + | 2.68952i | 0.0511941 | + | 0.0886708i | ||||
\(921\) | 57.1188 | − | 7.25132i | 1.88213 | − | 0.238939i | ||||
\(922\) | 31.5166i | 1.03794i | ||||||||
\(923\) | 22.0157 | + | 12.7108i | 0.724656 | + | 0.418381i | ||||
\(924\) | 8.42996 | − | 1.07020i | 0.277325 | − | 0.0352068i | ||||
\(925\) | 12.6392 | + | 7.29726i | 0.415575 | + | 0.239932i | ||||
\(926\) | −9.60721 | + | 16.6402i | −0.315712 | + | 0.546830i | ||||
\(927\) | 42.1211 | − | 41.3492i | 1.38344 | − | 1.35809i | ||||
\(928\) | 3.31526 | − | 5.74220i | 0.108829 | − | 0.188497i | ||||
\(929\) | − | 25.4656i | − | 0.835500i | −0.908562 | − | 0.417750i | \(-0.862819\pi\) | ||
0.908562 | − | 0.417750i | \(-0.137181\pi\) | |||||||
\(930\) | 5.00645 | − | 3.80493i | 0.164168 | − | 0.124769i | ||||
\(931\) | −7.78683 | + | 8.96907i | −0.255203 | + | 0.293949i | ||||
\(932\) | 18.2017 | + | 10.5088i | 0.596217 | + | 0.344226i | ||||
\(933\) | −27.8776 | + | 3.53911i | −0.912673 | + | 0.115865i | ||||
\(934\) | 10.9865i | 0.359490i | ||||||||
\(935\) | −2.49841 | + | 1.44246i | −0.0817067 | + | 0.0471734i | ||||
\(936\) | 5.38578 | + | 1.49663i | 0.176040 | + | 0.0489189i | ||||
\(937\) | −25.6097 | − | 44.3573i | −0.836632 | − | 1.44909i | −0.892695 | − | 0.450661i | \(-0.851188\pi\) |
0.0560633 | − | 0.998427i | \(-0.482145\pi\) | |||||||
\(938\) | 12.9430 | − | 7.47267i | 0.422605 | − | 0.243991i | ||||
\(939\) | 3.39882 | + | 26.7726i | 0.110916 | + | 0.873690i | ||||
\(940\) | 5.91525 | 0.192934 | ||||||||
\(941\) | −29.7494 | −0.969802 | −0.484901 | − | 0.874569i | \(-0.661144\pi\) | ||||
−0.484901 | + | 0.874569i | \(0.661144\pi\) | |||||||
\(942\) | 18.2560 | + | 7.66096i | 0.594812 | + | 0.249608i | ||||
\(943\) | 21.3554 | − | 12.3296i | 0.695429 | − | 0.401506i | ||||
\(944\) | −5.63697 | − | 9.76351i | −0.183468 | − | 0.317775i | ||||
\(945\) | −3.13354 | + | 21.4934i | −0.101934 | + | 0.699180i | ||||
\(946\) | 11.4666 | − | 6.62026i | 0.372812 | − | 0.215243i | ||||
\(947\) | 56.8300i | 1.84673i | 0.383929 | + | 0.923363i | \(0.374571\pi\) | ||||
−0.383929 | + | 0.923363i | \(0.625429\pi\) | |||||||
\(948\) | −10.2372 | − | 13.4698i | −0.332487 | − | 0.437479i | ||||
\(949\) | 8.73972 | + | 5.04588i | 0.283703 | + | 0.163796i | ||||
\(950\) | −9.15364 | + | 10.5434i | −0.296983 | + | 0.342073i | ||||
\(951\) | 1.57802 | + | 12.4301i | 0.0511707 | + | 0.403073i | ||||
\(952\) | 4.26614i | 0.138267i | ||||||||
\(953\) | −21.6382 | + | 37.4785i | −0.700930 | + | 1.21405i | 0.267210 | + | 0.963638i | \(0.413898\pi\) |
−0.968140 | + | 0.250408i | \(0.919435\pi\) | |||||||
\(954\) | −23.3741 | + | 6.03197i | −0.756765 | + | 0.195292i | ||||
\(955\) | −11.4962 | + | 19.9120i | −0.372009 | + | 0.644338i | ||||
\(956\) | −4.62407 | − | 2.66971i | −0.149553 | − | 0.0863446i | ||||
\(957\) | −10.9325 | − | 14.3847i | −0.353397 | − | 0.464992i | ||||
\(958\) | −7.41668 | − | 4.28202i | −0.239622 | − | 0.138346i | ||||
\(959\) | − | 11.3192i | − | 0.365515i | ||||||
\(960\) | −0.898387 | + | 2.14085i | −0.0289953 | + | 0.0690955i | ||||
\(961\) | −11.8321 | − | 20.4938i | −0.381682 | − | 0.661092i | ||||
\(962\) | 8.48949 | 0.273712 | ||||||||
\(963\) | −10.4306 | + | 37.5356i | −0.336121 | + | 1.20957i | ||||
\(964\) | 20.8012 | + | 12.0096i | 0.669962 | + | 0.386803i | ||||
\(965\) | 9.04425 | − | 15.6651i | 0.291145 | − | 0.504277i | ||||
\(966\) | 4.84236 | − | 11.5393i | 0.155800 | − | 0.371270i | ||||
\(967\) | −6.21231 | − | 10.7600i | −0.199774 | − | 0.346020i | 0.748681 | − | 0.662931i | \(-0.230688\pi\) |
−0.948455 | + | 0.316911i | \(0.897354\pi\) | |||||||
\(968\) | −4.26247 | + | 7.38281i | −0.137001 | + | 0.237292i | ||||
\(969\) | −10.3065 | − | 0.671729i | −0.331091 | − | 0.0215790i | ||||
\(970\) | 4.50000 | + | 7.79423i | 0.144486 | + | 0.250258i | ||||
\(971\) | −3.91725 | + | 6.78488i | −0.125711 | + | 0.217737i | −0.922011 | − | 0.387165i | \(-0.873454\pi\) |
0.796300 | + | 0.604902i | \(0.206788\pi\) | |||||||
\(972\) | 15.4980 | − | 1.67689i | 0.497099 | − | 0.0537862i | ||||
\(973\) | 2.48472 | + | 4.30367i | 0.0796566 | + | 0.137969i | ||||
\(974\) | 39.5989i | 1.26883i | ||||||||
\(975\) | 10.2555 | − | 1.30195i | 0.328438 | − | 0.0416957i | ||||
\(976\) | −2.14881 | + | 3.72186i | −0.0687819 | + | 0.119134i | ||||
\(977\) | 3.82294 | − | 6.62153i | 0.122307 | − | 0.211841i | −0.798370 | − | 0.602167i | \(-0.794304\pi\) |
0.920677 | + | 0.390325i | \(0.127638\pi\) | |||||||
\(978\) | −7.17519 | + | 5.45319i | −0.229437 | + | 0.174374i | ||||
\(979\) | −8.69574 | − | 5.02049i | −0.277917 | − | 0.160455i | ||||
\(980\) | 3.65259i | 0.116678i | ||||||||
\(981\) | −24.7780 | + | 24.3239i | −0.791101 | + | 0.776603i | ||||
\(982\) | 10.8270 | − | 6.25098i | 0.345504 | − | 0.199477i | ||||
\(983\) | −60.1166 | −1.91742 | −0.958710 | − | 0.284384i | \(-0.908211\pi\) | ||||
−0.958710 | + | 0.284384i | \(0.908211\pi\) | |||||||
\(984\) | 16.9989 | + | 7.13342i | 0.541904 | + | 0.227405i | ||||
\(985\) | 6.05867 | + | 10.4939i | 0.193045 | + | 0.334364i | ||||
\(986\) | 7.85544 | − | 4.53534i | 0.250168 | − | 0.144435i | ||||
\(987\) | −14.4227 | − | 18.9771i | −0.459081 | − | 0.604049i | ||||
\(988\) | −1.54473 | + | 7.97362i | −0.0491444 | + | 0.253675i | ||||
\(989\) | − | 19.4988i | − | 0.620026i | ||||||
\(990\) | 4.43193 | + | 4.51467i | 0.140856 | + | 0.143486i | ||||
\(991\) | −42.4523 | − | 24.5099i | −1.34854 | − | 0.778581i | −0.360499 | − | 0.932760i | \(-0.617394\pi\) |
−0.988043 | + | 0.154178i | \(0.950727\pi\) | |||||||
\(992\) | −2.34559 | − | 1.35423i | −0.0744727 | − | 0.0429968i | ||||
\(993\) | 2.63471 | − | 6.27849i | 0.0836101 | − | 0.199242i | ||||
\(994\) | 42.5467 | 1.34950 | ||||||||
\(995\) | −1.12169 | − | 0.647609i | −0.0355600 | − | 0.0205306i | ||||
\(996\) | −2.57611 | + | 6.13884i | −0.0816271 | + | 0.194517i | ||||
\(997\) | −14.1173 | + | 24.4519i | −0.447101 | + | 0.774401i | −0.998196 | − | 0.0600414i | \(-0.980877\pi\) |
0.551095 | + | 0.834442i | \(0.314210\pi\) | |||||||
\(998\) | −7.58113 | − | 13.1309i | −0.239976 | − | 0.415651i | ||||
\(999\) | 21.9961 | − | 8.75565i | 0.695926 | − | 0.277016i |
(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 | 342.2.n.e.293.1 | yes | 8 | |
3.2 | odd | 2 | 1026.2.n.e.179.1 | 8 | |||
9.2 | odd | 6 | 342.2.j.e.65.2 | ✓ | 8 | ||
9.7 | even | 3 | 1026.2.j.e.521.4 | 8 | |||
19.12 | odd | 6 | 342.2.j.e.221.2 | yes | 8 | ||
57.50 | even | 6 | 1026.2.j.e.449.1 | 8 | |||
171.88 | odd | 6 | 1026.2.n.e.791.1 | 8 | |||
171.164 | even | 6 | inner | 342.2.n.e.335.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
342.2.j.e.65.2 | ✓ | 8 | 9.2 | odd | 6 | ||
342.2.j.e.221.2 | yes | 8 | 19.12 | odd | 6 | ||
342.2.n.e.293.1 | yes | 8 | 1.1 | even | 1 | trivial | |
342.2.n.e.335.1 | yes | 8 | 171.164 | even | 6 | inner | |
1026.2.j.e.449.1 | 8 | 57.50 | even | 6 | |||
1026.2.j.e.521.4 | 8 | 9.7 | even | 3 | |||
1026.2.n.e.179.1 | 8 | 3.2 | odd | 2 | |||
1026.2.n.e.791.1 | 8 | 171.88 | odd | 6 |