Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1890,2,Mod(629,1890)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1890, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1890.629");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1890.bf (of order \(6\), degree \(2\), not 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: | \(15.0917259820\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1259.10 | ||
Character | \(\chi\) | \(=\) | 1890.1259 |
Dual form | 1890.2.bf.e.629.10 |
$q$-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 \(\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(1081\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 1.00815 | − | 1.99591i | 0.450857 | − | 0.892596i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.07602 | + | 1.64016i | −0.784663 | + | 0.619923i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.23258 | + | 0.124872i | −0.706003 | + | 0.0394879i | ||||
\(11\) | 1.44107 | − | 0.832005i | 0.434500 | − | 0.250859i | −0.266762 | − | 0.963763i | \(-0.585954\pi\) |
0.701262 | + | 0.712904i | \(0.252620\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.04814 | − | 1.81544i | 0.290703 | − | 0.503512i | −0.683273 | − | 0.730163i | \(-0.739444\pi\) |
0.973976 | + | 0.226651i | \(0.0727776\pi\) | |||||||
\(14\) | 2.45843 | + | 0.977807i | 0.657044 | + | 0.261330i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | − | 7.45463i | − | 1.80801i | −0.427518 | − | 0.904007i | \(-0.640612\pi\) | ||
0.427518 | − | 0.904007i | \(-0.359388\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.66141i | 1.06940i | 0.845042 | + | 0.534700i | \(0.179575\pi\) | ||||
−0.845042 | + | 0.534700i | \(0.820425\pi\) | |||||||
\(20\) | 1.22443 | + | 1.87103i | 0.273791 | + | 0.418376i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.44107 | − | 0.832005i | −0.307238 | − | 0.177384i | ||||
\(23\) | −2.82486 | + | 4.89279i | −0.589023 | + | 1.02022i | 0.405337 | + | 0.914167i | \(0.367154\pi\) |
−0.994361 | + | 0.106051i | \(0.966179\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.96728 | − | 4.02433i | −0.593456 | − | 0.804867i | ||||
\(26\) | −2.09629 | −0.411116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.382411 | − | 2.61797i | −0.0722688 | − | 0.494750i | ||||
\(29\) | 4.10738 | − | 2.37140i | 0.762721 | − | 0.440357i | −0.0675508 | − | 0.997716i | \(-0.521518\pi\) |
0.830272 | + | 0.557359i | \(0.188185\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.73402 | + | 1.00114i | 0.311440 | + | 0.179810i | 0.647571 | − | 0.762005i | \(-0.275785\pi\) |
−0.336131 | + | 0.941815i | \(0.609118\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.45590 | + | 3.72732i | −1.10718 | + | 0.639229i | ||||
\(35\) | 1.18067 | + | 5.79707i | 0.199570 | + | 0.979884i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.86789i | − | 0.800276i | −0.916455 | − | 0.400138i | \(-0.868962\pi\) | ||
0.916455 | − | 0.400138i | \(-0.131038\pi\) | |||||||
\(38\) | 4.03690 | − | 2.33070i | 0.654871 | − | 0.378090i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00815 | − | 1.99591i | 0.159402 | − | 0.315580i | ||||
\(41\) | 4.07169 | − | 7.05238i | 0.635892 | − | 1.10140i | −0.350434 | − | 0.936587i | \(-0.613966\pi\) |
0.986325 | − | 0.164809i | \(-0.0527008\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.25274 | − | 1.30062i | 0.343540 | − | 0.198343i | −0.318296 | − | 0.947991i | \(-0.603111\pi\) |
0.661836 | + | 0.749648i | \(0.269777\pi\) | |||||||
\(44\) | 1.66401i | 0.250859i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.64971 | 0.833005 | ||||||||
\(47\) | −8.90154 | + | 5.13931i | −1.29842 | + | 0.749645i | −0.980132 | − | 0.198348i | \(-0.936442\pi\) |
−0.318292 | + | 0.947993i | \(0.603109\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.61974 | − | 6.81003i | 0.231391 | − | 0.972861i | ||||
\(50\) | −2.00154 | + | 4.58191i | −0.283060 | + | 0.647979i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.04814 | + | 1.81544i | 0.145351 | + | 0.251756i | ||||
\(53\) | −13.8374 | −1.90071 | −0.950354 | − | 0.311170i | \(-0.899279\pi\) | ||||
−0.950354 | + | 0.311170i | \(0.899279\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.207788 | − | 3.71503i | −0.0280181 | − | 0.500935i | ||||
\(56\) | −2.07602 | + | 1.64016i | −0.277420 | + | 0.219176i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.10738 | − | 2.37140i | −0.539325 | − | 0.311380i | ||||
\(59\) | 0.0862901 | − | 0.149459i | 0.0112340 | − | 0.0194579i | −0.860354 | − | 0.509697i | \(-0.829757\pi\) |
0.871588 | + | 0.490240i | \(0.163091\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.17503 | − | 2.98781i | 0.662595 | − | 0.382550i | −0.130670 | − | 0.991426i | \(-0.541713\pi\) |
0.793265 | + | 0.608876i | \(0.208379\pi\) | |||||||
\(62\) | − | 2.00228i | − | 0.254290i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.56676 | − | 3.92222i | −0.318367 | − | 0.486492i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.70611 | − | 2.71707i | −0.574943 | − | 0.331943i | 0.184178 | − | 0.982893i | \(-0.441038\pi\) |
−0.759121 | + | 0.650949i | \(0.774371\pi\) | |||||||
\(68\) | 6.45590 | + | 3.72732i | 0.782893 | + | 0.452003i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.43007 | − | 3.92103i | 0.529495 | − | 0.468652i | ||||
\(71\) | − | 12.0450i | − | 1.42947i | −0.699393 | − | 0.714737i | \(-0.746546\pi\) | ||
0.699393 | − | 0.714737i | \(-0.253454\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.79644 | 0.561381 | 0.280691 | − | 0.959798i | \(-0.409437\pi\) | ||||
0.280691 | + | 0.959798i | \(0.409437\pi\) | |||||||
\(74\) | −4.21571 | + | 2.43394i | −0.490067 | + | 0.282940i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.03690 | − | 2.33070i | −0.463064 | − | 0.267350i | ||||
\(77\) | −1.62708 | + | 4.09086i | −0.185423 | + | 0.466196i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.30891 | − | 10.9273i | −0.709807 | − | 1.22942i | −0.964928 | − | 0.262513i | \(-0.915449\pi\) |
0.255121 | − | 0.966909i | \(-0.417885\pi\) | |||||||
\(80\) | −2.23258 | + | 0.124872i | −0.249610 | + | 0.0139611i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.14339 | −0.899286 | ||||||||
\(83\) | 2.24015 | − | 1.29335i | 0.245888 | − | 0.141964i | −0.371992 | − | 0.928236i | \(-0.621325\pi\) |
0.617880 | + | 0.786272i | \(0.287992\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.8787 | − | 7.51536i | −1.61383 | − | 0.815156i | ||||
\(86\) | −2.25274 | − | 1.30062i | −0.242919 | − | 0.140250i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.44107 | − | 0.832005i | 0.153619 | − | 0.0886920i | ||||
\(89\) | −11.2248 | −1.18982 | −0.594912 | − | 0.803791i | \(-0.702813\pi\) | ||||
−0.594912 | + | 0.803791i | \(0.702813\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.801642 | + | 5.48801i | 0.0840350 | + | 0.575300i | ||||
\(92\) | −2.82486 | − | 4.89279i | −0.294512 | − | 0.510109i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.90154 | + | 5.13931i | 0.918124 | + | 0.530079i | ||||
\(95\) | 9.30373 | + | 4.69938i | 0.954543 | + | 0.482147i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.73188 | + | 8.19586i | 0.480450 | + | 0.832164i | 0.999748 | − | 0.0224290i | \(-0.00713998\pi\) |
−0.519298 | + | 0.854593i | \(0.673807\pi\) | |||||||
\(98\) | −6.70752 | + | 2.00228i | −0.677562 | + | 0.202261i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.96881 | − | 0.557572i | 0.496881 | − | 0.0557572i | ||||
\(101\) | 5.28548 | + | 9.15472i | 0.525925 | + | 0.910928i | 0.999544 | + | 0.0301987i | \(0.00961400\pi\) |
−0.473619 | + | 0.880730i | \(0.657053\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.61856 | − | 13.1957i | 0.750679 | − | 1.30021i | −0.196816 | − | 0.980441i | \(-0.563060\pi\) |
0.947494 | − | 0.319773i | \(-0.103607\pi\) | |||||||
\(104\) | 1.04814 | − | 1.81544i | 0.102779 | − | 0.178018i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.91868 | + | 11.9835i | 0.672002 | + | 1.16394i | ||||
\(107\) | −11.4163 | −1.10366 | −0.551829 | − | 0.833957i | \(-0.686070\pi\) | ||||
−0.551829 | + | 0.833957i | \(0.686070\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.6147 | −1.01670 | −0.508351 | − | 0.861150i | \(-0.669745\pi\) | ||||
−0.508351 | + | 0.861150i | \(0.669745\pi\) | |||||||
\(110\) | −3.11342 | + | 2.03747i | −0.296853 | + | 0.194265i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.45843 | + | 0.977807i | 0.232300 | + | 0.0923941i | ||||
\(113\) | 6.87120 | − | 11.9013i | 0.646388 | − | 1.11958i | −0.337591 | − | 0.941293i | \(-0.609612\pi\) |
0.983979 | − | 0.178284i | \(-0.0570546\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.91769 | + | 10.5708i | 0.645078 | + | 0.985733i | ||||
\(116\) | 4.74279i | 0.440357i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.172580 | −0.0158873 | ||||||||
\(119\) | 12.2268 | + | 15.4760i | 1.12083 | + | 1.41868i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.11554 | + | 7.12832i | −0.374140 | + | 0.648029i | ||||
\(122\) | −5.17503 | − | 2.98781i | −0.468526 | − | 0.270503i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.73402 | + | 1.00114i | −0.155720 | + | 0.0899050i | ||||
\(125\) | −11.0236 | + | 1.86529i | −0.985985 | + | 0.166837i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 14.1949i | − | 1.25960i | −0.776759 | − | 0.629798i | \(-0.783138\pi\) | ||
0.776759 | − | 0.629798i | \(-0.216862\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.11336 | + | 4.18399i | −0.185354 | + | 0.366960i | ||||
\(131\) | 1.14681 | − | 1.98633i | 0.100197 | − | 0.173547i | −0.811569 | − | 0.584257i | \(-0.801386\pi\) |
0.911766 | + | 0.410710i | \(0.134719\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.64546 | − | 9.67719i | −0.662946 | − | 0.839119i | ||||
\(134\) | 5.43415i | 0.469439i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 7.45463i | − | 0.639229i | ||||||
\(137\) | 5.41797 | + | 9.38419i | 0.462888 | + | 0.801746i | 0.999103 | − | 0.0423355i | \(-0.0134798\pi\) |
−0.536215 | + | 0.844081i | \(0.680147\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.63600 | − | 4.40865i | −0.647677 | − | 0.373936i | 0.139889 | − | 0.990167i | \(-0.455326\pi\) |
−0.787566 | + | 0.616231i | \(0.788659\pi\) | |||||||
\(140\) | −5.61075 | − | 1.87604i | −0.474195 | − | 0.158554i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.4312 | + | 6.02248i | −0.875371 | + | 0.505396i | ||||
\(143\) | − | 3.48824i | − | 0.291701i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.592241 | − | 10.5887i | −0.0491830 | − | 0.879340i | ||||
\(146\) | −2.39822 | − | 4.15384i | −0.198478 | − | 0.343774i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.21571 | + | 2.43394i | 0.346529 | + | 0.200069i | ||||
\(149\) | −12.4184 | − | 7.16974i | −1.01735 | − | 0.587368i | −0.104016 | − | 0.994576i | \(-0.533169\pi\) |
−0.913336 | + | 0.407207i | \(0.866503\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.45207 | + | 5.97917i | 0.280926 | + | 0.486578i | 0.971613 | − | 0.236576i | \(-0.0760252\pi\) |
−0.690687 | + | 0.723154i | \(0.742692\pi\) | |||||||
\(152\) | 4.66141i | 0.378090i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.35632 | − | 0.636335i | 0.351043 | − | 0.0512773i | ||||
\(155\) | 3.74633 | − | 2.45165i | 0.300913 | − | 0.196922i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.48808 | + | 12.9697i | −0.597614 | + | 1.03510i | 0.395559 | + | 0.918441i | \(0.370551\pi\) |
−0.993172 | + | 0.116657i | \(0.962782\pi\) | |||||||
\(158\) | −6.30891 | + | 10.9273i | −0.501910 | + | 0.869333i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.22443 | + | 1.87103i | 0.0967998 | + | 0.147918i | ||||
\(161\) | −2.16051 | − | 14.7908i | −0.170272 | − | 1.16568i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 8.03539i | − | 0.629380i | −0.949194 | − | 0.314690i | \(-0.898099\pi\) | ||
0.949194 | − | 0.314690i | \(-0.101901\pi\) | |||||||
\(164\) | 4.07169 | + | 7.05238i | 0.317946 | + | 0.550698i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.24015 | − | 1.29335i | −0.173869 | − | 0.100384i | ||||
\(167\) | −4.12075 | − | 2.37911i | −0.318873 | − | 0.184101i | 0.332017 | − | 0.943273i | \(-0.392271\pi\) |
−0.650890 | + | 0.759172i | \(0.725604\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.30279 | + | 7.45265i | 0.330984 | + | 0.573281i | ||||
\(170\) | 0.930873 | + | 16.6430i | 0.0713947 | + | 1.27646i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.60124i | 0.198343i | ||||||||
\(173\) | 14.9456 | − | 8.62882i | 1.13629 | − | 0.656037i | 0.190781 | − | 0.981633i | \(-0.438898\pi\) |
0.945509 | + | 0.325595i | \(0.105565\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.7607 | + | 3.48779i | 0.964618 | + | 0.263652i | ||||
\(176\) | −1.44107 | − | 0.832005i | −0.108625 | − | 0.0627147i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.61239 | + | 9.72094i | 0.420666 | + | 0.728616i | ||||
\(179\) | − | 0.602635i | − | 0.0450430i | −0.999746 | − | 0.0225215i | \(-0.992831\pi\) | ||
0.999746 | − | 0.0225215i | \(-0.00716943\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 12.7778i | − | 0.949769i | −0.880048 | − | 0.474885i | \(-0.842490\pi\) | ||
0.880048 | − | 0.474885i | \(-0.157510\pi\) | |||||||
\(182\) | 4.35194 | − | 3.43825i | 0.322587 | − | 0.254860i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.82486 | + | 4.89279i | −0.208251 | + | 0.360702i | ||||
\(185\) | −9.71584 | − | 4.90754i | −0.714323 | − | 0.360810i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.20229 | − | 10.7427i | −0.453556 | − | 0.785582i | ||||
\(188\) | − | 10.2786i | − | 0.749645i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.582079 | − | 10.4070i | −0.0422284 | − | 0.755000i | ||||
\(191\) | −16.3178 | + | 9.42111i | −1.18072 | + | 0.681687i | −0.956180 | − | 0.292778i | \(-0.905420\pi\) |
−0.224537 | + | 0.974466i | \(0.572087\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.89207 | − | 3.40179i | −0.424120 | − | 0.244866i | 0.272718 | − | 0.962094i | \(-0.412077\pi\) |
−0.696839 | + | 0.717228i | \(0.745411\pi\) | |||||||
\(194\) | 4.73188 | − | 8.19586i | 0.339730 | − | 0.588429i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.08779 | + | 4.80775i | 0.363413 | + | 0.343410i | ||||
\(197\) | −8.58750 | −0.611834 | −0.305917 | − | 0.952058i | \(-0.598963\pi\) | ||||
−0.305917 | + | 0.952058i | \(0.598963\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.10064i | 0.361575i | 0.983522 | + | 0.180788i | \(0.0578646\pi\) | ||||
−0.983522 | + | 0.180788i | \(0.942135\pi\) | |||||||
\(200\) | −2.96728 | − | 4.02433i | −0.209818 | − | 0.284563i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.28548 | − | 9.15472i | 0.371885 | − | 0.644124i | ||||
\(203\) | −4.63754 | + | 11.6598i | −0.325491 | + | 0.818360i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.97102 | − | 15.2365i | −0.696406 | − | 1.06417i | ||||
\(206\) | −15.2371 | −1.06162 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.09629 | −0.145351 | ||||||||
\(209\) | 3.87831 | + | 6.71743i | 0.268268 | + | 0.464655i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.01715 | − | 8.68995i | 0.345395 | − | 0.598241i | −0.640031 | − | 0.768349i | \(-0.721078\pi\) |
0.985425 | + | 0.170108i | \(0.0544118\pi\) | |||||||
\(212\) | 6.91868 | − | 11.9835i | 0.475177 | − | 0.823031i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.70816 | + | 9.88683i | 0.390202 | + | 0.675850i | ||||
\(215\) | −0.324822 | − | 5.80748i | −0.0221527 | − | 0.396067i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.24190 | + | 0.765693i | −0.355844 | + | 0.0519786i | ||||
\(218\) | 5.30734 | + | 9.19258i | 0.359458 | + | 0.622600i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.32121 | + | 1.67757i | 0.223916 | + | 0.113101i | ||||
\(221\) | −13.5334 | − | 7.81352i | −0.910356 | − | 0.525594i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.87226 | − | 15.3672i | −0.594131 | − | 1.02906i | −0.993669 | − | 0.112348i | \(-0.964163\pi\) |
0.399538 | − | 0.916717i | \(-0.369171\pi\) | |||||||
\(224\) | −0.382411 | − | 2.61797i | −0.0255509 | − | 0.174920i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.7424 | −0.914131 | ||||||||
\(227\) | 0.411273 | − | 0.237449i | 0.0272972 | − | 0.0157600i | −0.486289 | − | 0.873798i | \(-0.661650\pi\) |
0.513586 | + | 0.858038i | \(0.328317\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.51279 | + | 5.49221i | 0.628623 | + | 0.362936i | 0.780219 | − | 0.625507i | \(-0.215108\pi\) |
−0.151596 | + | 0.988443i | \(0.548441\pi\) | |||||||
\(230\) | 5.69574 | − | 11.2763i | 0.375566 | − | 0.743537i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.10738 | − | 2.37140i | 0.269663 | − | 0.155690i | ||||
\(233\) | 21.4794 | 1.40716 | 0.703582 | − | 0.710614i | \(-0.251583\pi\) | ||||
0.703582 | + | 0.710614i | \(0.251583\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.28351 | + | 22.9478i | 0.0837269 | + | 1.49695i | ||||
\(236\) | 0.0862901 | + | 0.149459i | 0.00561701 | + | 0.00972894i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.28919 | − | 18.3267i | 0.472488 | − | 1.18794i | ||||
\(239\) | 14.6228 | + | 8.44250i | 0.945873 | + | 0.546100i | 0.891797 | − | 0.452437i | \(-0.149445\pi\) |
0.0540768 | + | 0.998537i | \(0.482778\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.00911 | + | 4.62406i | −0.515912 | + | 0.297862i | −0.735261 | − | 0.677784i | \(-0.762940\pi\) |
0.219348 | + | 0.975647i | \(0.429607\pi\) | |||||||
\(242\) | 8.23107 | 0.529113 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.97562i | 0.382550i | ||||||||
\(245\) | −11.9592 | − | 10.0984i | −0.764048 | − | 0.645160i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.46249 | + | 4.88582i | 0.538456 | + | 0.310877i | ||||
\(248\) | 1.73402 | + | 1.00114i | 0.110111 | + | 0.0635724i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.12721 | + | 8.61411i | 0.450764 | + | 0.544804i | ||||
\(251\) | −9.36996 | −0.591426 | −0.295713 | − | 0.955277i | \(-0.595557\pi\) | ||||
−0.295713 | + | 0.955277i | \(0.595557\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.40117i | 0.591047i | ||||||||
\(254\) | −12.2932 | + | 7.09746i | −0.771342 | + | 0.445334i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 5.62239 | + | 3.24609i | 0.350715 | + | 0.202485i | 0.665000 | − | 0.746843i | \(-0.268431\pi\) |
−0.314285 | + | 0.949329i | \(0.601765\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.98412 | + | 10.1058i | 0.496109 | + | 0.627946i | ||||
\(260\) | 4.68012 | − | 0.261767i | 0.290249 | − | 0.0162341i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.29362 | −0.141700 | ||||||||
\(263\) | −4.41420 | − | 7.64563i | −0.272192 | − | 0.471450i | 0.697231 | − | 0.716846i | \(-0.254415\pi\) |
−0.969423 | + | 0.245397i | \(0.921082\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.9501 | + | 27.6181i | −0.856948 | + | 1.69657i | ||||
\(266\) | −4.55796 | + | 11.4598i | −0.279466 | + | 0.702643i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.70611 | − | 2.71707i | 0.287471 | − | 0.165972i | ||||
\(269\) | 11.6257 | 0.708833 | 0.354416 | − | 0.935088i | \(-0.384680\pi\) | ||||
0.354416 | + | 0.935088i | \(0.384680\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.8123i | 1.02128i | 0.859796 | + | 0.510638i | \(0.170591\pi\) | ||||
−0.859796 | + | 0.510638i | \(0.829409\pi\) | |||||||
\(272\) | −6.45590 | + | 3.72732i | −0.391446 | + | 0.226002i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.41797 | − | 9.38419i | 0.327311 | − | 0.566920i | ||||
\(275\) | −7.62433 | − | 3.33057i | −0.459765 | − | 0.200841i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.93149 | − | 1.11514i | 0.116052 | − | 0.0670026i | −0.440850 | − | 0.897581i | \(-0.645323\pi\) |
0.556902 | + | 0.830578i | \(0.311990\pi\) | |||||||
\(278\) | 8.81729i | 0.528826i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.18067 | + | 5.79707i | 0.0705587 | + | 0.346441i | ||||
\(281\) | 2.79869 | − | 1.61582i | 0.166956 | − | 0.0963919i | −0.414194 | − | 0.910189i | \(-0.635936\pi\) |
0.581150 | + | 0.813797i | \(0.302603\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.23291 | − | 5.59957i | 0.192177 | − | 0.332860i | −0.753795 | − | 0.657110i | \(-0.771779\pi\) |
0.945971 | + | 0.324250i | \(0.105112\pi\) | |||||||
\(284\) | 10.4312 | + | 6.02248i | 0.618981 | + | 0.357369i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.02090 | + | 1.74412i | −0.178630 | + | 0.103132i | ||||
\(287\) | 3.11412 | + | 21.3191i | 0.183821 | + | 1.25843i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −38.5715 | −2.26891 | ||||||||
\(290\) | −8.87393 | + | 5.80722i | −0.521095 | + | 0.341012i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.39822 | + | 4.15384i | −0.140345 | + | 0.243085i | ||||
\(293\) | 16.0415 | + | 9.26155i | 0.937153 | + | 0.541066i | 0.889067 | − | 0.457777i | \(-0.151354\pi\) |
0.0480865 | + | 0.998843i | \(0.484688\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.211313 | − | 0.322903i | −0.0123031 | − | 0.0188002i | ||||
\(296\) | − | 4.86789i | − | 0.282940i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.3395i | 0.830664i | ||||||||
\(299\) | 5.92171 | + | 10.2567i | 0.342461 | + | 0.593160i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.54351 | + | 6.39498i | −0.146606 | + | 0.368600i | ||||
\(302\) | 3.45207 | − | 5.97917i | 0.198645 | − | 0.344062i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.03690 | − | 2.33070i | 0.231532 | − | 0.133675i | ||||
\(305\) | −0.746186 | − | 13.3410i | −0.0427265 | − | 0.763905i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.44142 | −0.196412 | −0.0982062 | − | 0.995166i | \(-0.531310\pi\) | ||||
−0.0982062 | + | 0.995166i | \(0.531310\pi\) | |||||||
\(308\) | −2.72924 | − | 3.45452i | −0.155513 | − | 0.196840i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.99636 | − | 2.01859i | −0.226978 | − | 0.114648i | ||||
\(311\) | 16.6186 | − | 28.7842i | 0.942352 | − | 1.63220i | 0.181385 | − | 0.983412i | \(-0.441942\pi\) |
0.760967 | − | 0.648790i | \(-0.224725\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.967111 | + | 1.67509i | 0.0546644 | + | 0.0946815i | 0.892063 | − | 0.451912i | \(-0.149258\pi\) |
−0.837398 | + | 0.546593i | \(0.815924\pi\) | |||||||
\(314\) | 14.9762 | 0.845153 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.6178 | 0.709807 | ||||||||
\(317\) | 5.12038 | + | 8.86877i | 0.287589 | + | 0.498120i | 0.973234 | − | 0.229817i | \(-0.0738128\pi\) |
−0.685644 | + | 0.727937i | \(0.740479\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.94603 | − | 6.83472i | 0.220935 | − | 0.382671i | ||||
\(320\) | 1.00815 | − | 1.99591i | 0.0563571 | − | 0.111575i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −11.7289 | + | 9.26644i | −0.653628 | + | 0.516399i | ||||
\(323\) | 34.7491 | 1.93349 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.4161 | + | 1.16883i | −0.577779 | + | 0.0648351i | ||||
\(326\) | −6.95885 | + | 4.01770i | −0.385415 | + | 0.222520i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.07169 | − | 7.05238i | 0.224822 | − | 0.389402i | ||||
\(329\) | 10.0505 | − | 25.2693i | 0.554102 | − | 1.39314i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.81788 | − | 4.88070i | −0.154884 | − | 0.268268i | 0.778133 | − | 0.628100i | \(-0.216167\pi\) |
−0.933017 | + | 0.359832i | \(0.882834\pi\) | |||||||
\(332\) | 2.58670i | 0.141964i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.75823i | 0.260359i | ||||||||
\(335\) | −10.1675 | + | 6.65374i | −0.555508 | + | 0.363533i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.8563 | + | 6.84524i | 0.645854 | + | 0.372884i | 0.786866 | − | 0.617124i | \(-0.211702\pi\) |
−0.141012 | + | 0.990008i | \(0.545036\pi\) | |||||||
\(338\) | 4.30279 | − | 7.45265i | 0.234041 | − | 0.405371i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 13.9479 | − | 9.12768i | 0.756429 | − | 0.495018i | ||||
\(341\) | 3.33181 | 0.180428 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.80693 | + | 16.7944i | 0.421535 | + | 0.906812i | ||||
\(344\) | 2.25274 | − | 1.30062i | 0.121460 | − | 0.0701248i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.9456 | − | 8.62882i | −0.803478 | − | 0.463888i | ||||
\(347\) | 4.89520 | − | 8.47874i | 0.262788 | − | 0.455163i | −0.704193 | − | 0.710008i | \(-0.748691\pi\) |
0.966982 | + | 0.254845i | \(0.0820246\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.0539 | + | 8.11400i | −0.752286 | + | 0.434332i | −0.826519 | − | 0.562909i | \(-0.809682\pi\) |
0.0742335 | + | 0.997241i | \(0.476349\pi\) | |||||||
\(350\) | −3.35984 | − | 12.7950i | −0.179591 | − | 0.683920i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.66401i | 0.0886920i | ||||||||
\(353\) | 20.9960 | − | 12.1220i | 1.11750 | − | 0.645191i | 0.176741 | − | 0.984257i | \(-0.443444\pi\) |
0.940762 | + | 0.339066i | \(0.110111\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −24.0406 | − | 12.1431i | −1.27594 | − | 0.644489i | ||||
\(356\) | 5.61239 | − | 9.72094i | 0.297456 | − | 0.515209i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.521897 | + | 0.301317i | −0.0275831 | + | 0.0159251i | ||||
\(359\) | 31.3617i | 1.65521i | 0.561313 | + | 0.827604i | \(0.310296\pi\) | ||||
−0.561313 | + | 0.827604i | \(0.689704\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.72872 | −0.143617 | ||||||||
\(362\) | −11.0659 | + | 6.38892i | −0.581612 | + | 0.335794i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.15358 | − | 2.04976i | −0.270121 | − | 0.107437i | ||||
\(365\) | 4.83552 | − | 9.57325i | 0.253103 | − | 0.501087i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.616195 | + | 1.06728i | 0.0321651 | + | 0.0557116i | 0.881660 | − | 0.471885i | \(-0.156426\pi\) |
−0.849495 | + | 0.527597i | \(0.823093\pi\) | |||||||
\(368\) | 5.64971 | 0.294512 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.607862 | + | 10.8679i | 0.0316012 | + | 0.564997i | ||||
\(371\) | 28.7267 | − | 22.6955i | 1.49142 | − | 1.17829i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.9159 | + | 13.8079i | 1.23832 | + | 0.714944i | 0.968751 | − | 0.248037i | \(-0.0797855\pi\) |
0.269569 | + | 0.962981i | \(0.413119\pi\) | |||||||
\(374\) | −6.20229 | + | 10.7427i | −0.320713 | + | 0.555491i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.90154 | + | 5.13931i | −0.459062 | + | 0.265040i | ||||
\(377\) | − | 9.94225i | − | 0.512052i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.2265 | 1.19307 | 0.596533 | − | 0.802589i | \(-0.296545\pi\) | ||||
0.596533 | + | 0.802589i | \(0.296545\pi\) | |||||||
\(380\) | −8.72165 | + | 5.70757i | −0.447411 | + | 0.292792i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.3178 | + | 9.42111i | 0.834893 | + | 0.482026i | ||||
\(383\) | 20.6052 | + | 11.8964i | 1.05288 | + | 0.607880i | 0.923454 | − | 0.383709i | \(-0.125354\pi\) |
0.129425 | + | 0.991589i | \(0.458687\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.52462 | + | 7.37168i | 0.332526 | + | 0.375696i | ||||
\(386\) | 6.80357i | 0.346293i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.46377 | −0.480450 | ||||||||
\(389\) | 8.18328 | − | 4.72462i | 0.414909 | − | 0.239548i | −0.277988 | − | 0.960585i | \(-0.589668\pi\) |
0.692897 | + | 0.721037i | \(0.256334\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.4740 | + | 21.0583i | 1.84457 | + | 1.06496i | ||||
\(392\) | 1.61974 | − | 6.81003i | 0.0818091 | − | 0.343958i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.29375 | + | 7.43699i | 0.216316 | + | 0.374670i | ||||
\(395\) | −28.1703 | + | 1.57561i | −1.41740 | + | 0.0792775i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.7234 | 1.09026 | 0.545132 | − | 0.838350i | \(-0.316479\pi\) | ||||
0.545132 | + | 0.838350i | \(0.316479\pi\) | |||||||
\(398\) | 4.41729 | − | 2.55032i | 0.221419 | − | 0.127836i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00154 | + | 4.58191i | −0.100077 | + | 0.229095i | ||||
\(401\) | 10.6544 | + | 6.15134i | 0.532057 | + | 0.307183i | 0.741854 | − | 0.670562i | \(-0.233947\pi\) |
−0.209797 | + | 0.977745i | \(0.567280\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.63501 | − | 2.09867i | 0.181073 | − | 0.104542i | ||||
\(404\) | −10.5710 | −0.525925 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.4165 | − | 1.81369i | 0.616220 | − | 0.0900122i | ||||
\(407\) | −4.05010 | − | 7.01498i | −0.200756 | − | 0.347720i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.50285 | + | 1.44502i | 0.123758 | + | 0.0714517i | 0.560601 | − | 0.828086i | \(-0.310570\pi\) |
−0.436843 | + | 0.899538i | \(0.643903\pi\) | |||||||
\(410\) | −8.20973 | + | 16.2534i | −0.405450 | + | 0.802700i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.61856 | + | 13.1957i | 0.375339 | + | 0.650107i | ||||
\(413\) | 0.0659965 | + | 0.451810i | 0.00324748 | + | 0.0222321i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.323006 | − | 5.77502i | −0.0158558 | − | 0.283484i | ||||
\(416\) | 1.04814 | + | 1.81544i | 0.0513894 | + | 0.0890091i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.87831 | − | 6.71743i | 0.189694 | − | 0.328560i | ||||
\(419\) | −12.7397 | + | 22.0658i | −0.622374 | + | 1.07798i | 0.366668 | + | 0.930352i | \(0.380499\pi\) |
−0.989042 | + | 0.147632i | \(0.952835\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.96965 | − | 5.14359i | −0.144732 | − | 0.250683i | 0.784541 | − | 0.620077i | \(-0.212899\pi\) |
−0.929273 | + | 0.369394i | \(0.879565\pi\) | |||||||
\(422\) | −10.0343 | −0.488462 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −13.8374 | −0.672002 | ||||||||
\(425\) | −29.9999 | + | 22.1200i | −1.45521 | + | 1.07298i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.84300 | + | 14.6907i | −0.282763 | + | 0.710930i | ||||
\(428\) | 5.70816 | − | 9.88683i | 0.275914 | − | 0.477898i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.86701 | + | 3.18504i | −0.234708 | + | 0.153596i | ||||
\(431\) | 29.4344i | 1.41781i | 0.705306 | + | 0.708903i | \(0.250810\pi\) | ||||
−0.705306 | + | 0.708903i | \(0.749190\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.2559 | 0.685093 | 0.342546 | − | 0.939501i | \(-0.388711\pi\) | ||||
0.342546 | + | 0.939501i | \(0.388711\pi\) | |||||||
\(434\) | 3.28406 | + | 4.15678i | 0.157640 | + | 0.199532i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.30734 | − | 9.19258i | 0.254176 | − | 0.440245i | ||||
\(437\) | −22.8073 | − | 13.1678i | −1.09102 | − | 0.629902i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.41191 | − | 5.43397i | 0.449206 | − | 0.259349i | −0.258289 | − | 0.966068i | \(-0.583159\pi\) |
0.707495 | + | 0.706719i | \(0.249825\pi\) | |||||||
\(440\) | −0.207788 | − | 3.71503i | −0.00990590 | − | 0.177107i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.6270i | 0.743303i | ||||||||
\(443\) | 5.24859 | + | 9.09083i | 0.249368 | + | 0.431918i | 0.963351 | − | 0.268245i | \(-0.0864438\pi\) |
−0.713983 | + | 0.700164i | \(0.753110\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.3162 | + | 22.4036i | −0.536441 | + | 1.06203i | ||||
\(446\) | −8.87226 | + | 15.3672i | −0.420114 | + | 0.727659i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.07602 | + | 1.64016i | −0.0980828 | + | 0.0774904i | ||||
\(449\) | − | 37.0684i | − | 1.74937i | −0.484695 | − | 0.874683i | \(-0.661070\pi\) | ||
0.484695 | − | 0.874683i | \(-0.338930\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 13.5507i | − | 0.638076i | ||||||
\(452\) | 6.87120 | + | 11.9013i | 0.323194 | + | 0.559789i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.411273 | − | 0.237449i | −0.0193020 | − | 0.0111440i | ||||
\(455\) | 11.7617 | + | 3.93272i | 0.551398 | + | 0.184369i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.5211 | − | 10.1158i | 0.819601 | − | 0.473197i | −0.0306780 | − | 0.999529i | \(-0.509767\pi\) |
0.850279 | + | 0.526333i | \(0.176433\pi\) | |||||||
\(458\) | − | 10.9844i | − | 0.513269i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12.6134 | + | 0.705490i | −0.588104 | + | 0.0328936i | ||||
\(461\) | 6.80701 | + | 11.7901i | 0.317034 | + | 0.549119i | 0.979868 | − | 0.199648i | \(-0.0639798\pi\) |
−0.662834 | + | 0.748766i | \(0.730646\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.8188 | − | 11.4424i | −0.921057 | − | 0.531773i | −0.0370852 | − | 0.999312i | \(-0.511807\pi\) |
−0.883972 | + | 0.467539i | \(0.845141\pi\) | |||||||
\(464\) | −4.10738 | − | 2.37140i | −0.190680 | − | 0.110089i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.7397 | − | 18.6017i | −0.497507 | − | 0.861708i | ||||
\(467\) | − | 3.34545i | − | 0.154809i | −0.997000 | − | 0.0774044i | \(-0.975337\pi\) | ||
0.997000 | − | 0.0774044i | \(-0.0246633\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.2264 | − | 2.07808i | 0.656916 | − | 0.0959567i | ||||
\(470\) | 19.2316 | − | 12.5855i | 0.887089 | − | 0.580524i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.0862901 | − | 0.149459i | 0.00397182 | − | 0.00687940i | ||||
\(473\) | 2.16425 | − | 3.74858i | 0.0995121 | − | 0.172360i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.7591 | − | 13.8317i | 0.860725 | − | 0.634642i | ||||
\(476\) | −19.5160 | + | 2.85073i | −0.894514 | + | 0.130663i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 16.8850i | − | 0.772302i | ||||||
\(479\) | −8.15257 | − | 14.1207i | −0.372500 | − | 0.645189i | 0.617449 | − | 0.786611i | \(-0.288166\pi\) |
−0.989949 | + | 0.141421i | \(0.954833\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.83734 | − | 5.10224i | −0.402948 | − | 0.232642i | ||||
\(482\) | 8.00911 | + | 4.62406i | 0.364805 | + | 0.210620i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.11554 | − | 7.12832i | −0.187070 | − | 0.324014i | ||||
\(485\) | 21.1286 | − | 1.18176i | 0.959401 | − | 0.0536609i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.20248i | 0.235747i | 0.993029 | + | 0.117873i | \(0.0376077\pi\) | ||||
−0.993029 | + | 0.117873i | \(0.962392\pi\) | |||||||
\(488\) | 5.17503 | − | 2.98781i | 0.234263 | − | 0.135252i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.76581 | + | 15.4062i | −0.124947 | + | 0.695980i | ||||
\(491\) | 20.6633 | + | 11.9299i | 0.932521 | + | 0.538391i | 0.887608 | − | 0.460600i | \(-0.152366\pi\) |
0.0449127 | + | 0.998991i | \(0.485699\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.6779 | − | 30.6190i | −0.796172 | − | 1.37901i | ||||
\(494\) | − | 9.77165i | − | 0.439647i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 2.00228i | − | 0.0899050i | ||||||
\(497\) | 19.7557 | + | 25.0056i | 0.886164 | + | 1.12166i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.1660 | − | 28.0003i | 0.723688 | − | 1.25346i | −0.235824 | − | 0.971796i | \(-0.575779\pi\) |
0.959512 | − | 0.281668i | \(-0.0908877\pi\) | |||||||
\(500\) | 3.89643 | − | 10.4794i | 0.174254 | − | 0.468653i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.68498 | + | 8.11462i | 0.209101 | + | 0.362173i | ||||
\(503\) | − | 10.0768i | − | 0.449301i | −0.974439 | − | 0.224651i | \(-0.927876\pi\) | ||
0.974439 | − | 0.224651i | \(-0.0721241\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.6005 | − | 1.32001i | 1.05021 | − | 0.0587399i | ||||
\(506\) | 8.14166 | − | 4.70059i | 0.361941 | − | 0.208967i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.2932 | + | 7.09746i | 0.545421 | + | 0.314899i | ||||
\(509\) | 10.5573 | − | 18.2858i | 0.467944 | − | 0.810503i | −0.531385 | − | 0.847131i | \(-0.678328\pi\) |
0.999329 | + | 0.0366275i | \(0.0116615\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.95752 | + | 7.86694i | −0.440495 | + | 0.348013i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 6.49218i | − | 0.286358i | ||||||
\(515\) | −18.6568 | − | 28.5092i | −0.822117 | − | 1.25626i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.55186 | + | 14.8122i | −0.376110 | + | 0.651442i | ||||
\(518\) | 4.75985 | − | 11.9674i | 0.209136 | − | 0.525816i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.56676 | − | 3.92222i | −0.112560 | − | 0.172001i | ||||
\(521\) | 21.9402 | 0.961216 | 0.480608 | − | 0.876936i | \(-0.340416\pi\) | ||||
0.480608 | + | 0.876936i | \(0.340416\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.10550 | 0.310702 | 0.155351 | − | 0.987859i | \(-0.450349\pi\) | ||||
0.155351 | + | 0.987859i | \(0.450349\pi\) | |||||||
\(524\) | 1.14681 | + | 1.98633i | 0.0500986 | + | 0.0867733i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.41420 | + | 7.64563i | −0.192468 | + | 0.333365i | ||||
\(527\) | 7.46313 | − | 12.9265i | 0.325099 | − | 0.563088i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.45963 | − | 7.72430i | −0.193897 | − | 0.335839i | ||||
\(530\) | 30.8930 | − | 1.72790i | 1.34191 | − | 0.0750551i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 12.2034 | − | 1.78257i | 0.529085 | − | 0.0772843i | ||||
\(533\) | −8.53543 | − | 14.7838i | −0.369711 | − | 0.640358i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.5093 | + | 22.7859i | −0.497592 | + | 0.985121i | ||||
\(536\) | −4.70611 | − | 2.71707i | −0.203273 | − | 0.117360i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.81286 | − | 10.0682i | −0.250610 | − | 0.434070i | ||||
\(539\) | −3.33181 | − | 11.1614i | −0.143511 | − | 0.480755i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.7965 | −1.58200 | −0.791002 | − | 0.611813i | \(-0.790441\pi\) | ||||
−0.791002 | + | 0.611813i | \(0.790441\pi\) | |||||||
\(542\) | 14.5599 | − | 8.40617i | 0.625402 | − | 0.361076i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.45590 | + | 3.72732i | 0.276794 | + | 0.159807i | ||||
\(545\) | −10.7012 | + | 21.1859i | −0.458387 | + | 0.907504i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.6902 | − | 8.48140i | 0.628108 | − | 0.362638i | −0.151911 | − | 0.988394i | \(-0.548543\pi\) |
0.780019 | + | 0.625756i | \(0.215209\pi\) | |||||||
\(548\) | −10.8359 | −0.462888 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.927806 | + | 8.26815i | 0.0395618 | + | 0.352555i | ||||
\(551\) | 11.0540 | + | 19.1462i | 0.470918 | + | 0.815654i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 31.0200 | + | 12.3378i | 1.31911 | + | 0.524656i | ||||
\(554\) | −1.93149 | − | 1.11514i | −0.0820610 | − | 0.0473780i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.63600 | − | 4.40865i | 0.323839 | − | 0.186968i | ||||
\(557\) | 2.63451 | 0.111628 | 0.0558139 | − | 0.998441i | \(-0.482225\pi\) | ||||
0.0558139 | + | 0.998441i | \(0.482225\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5.45295i | − | 0.230635i | ||||||
\(560\) | 4.43007 | − | 3.92103i | 0.187205 | − | 0.165694i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.79869 | − | 1.61582i | −0.118055 | − | 0.0681594i | ||||
\(563\) | 20.7641 | + | 11.9882i | 0.875104 | + | 0.505242i | 0.869041 | − | 0.494740i | \(-0.164737\pi\) |
0.00606320 | + | 0.999982i | \(0.498070\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.8266 | − | 25.7125i | −0.707902 | − | 1.08173i | ||||
\(566\) | −6.46583 | −0.271779 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 12.0450i | − | 0.505396i | ||||||
\(569\) | −36.5400 | + | 21.0964i | −1.53184 | + | 0.884407i | −0.532560 | + | 0.846392i | \(0.678770\pi\) |
−0.999277 | + | 0.0380144i | \(0.987897\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.7469 | − | 22.0783i | 0.533441 | − | 0.923947i | −0.465796 | − | 0.884892i | \(-0.654232\pi\) |
0.999237 | − | 0.0390547i | \(-0.0124347\pi\) | |||||||
\(572\) | 3.02090 | + | 1.74412i | 0.126310 | + | 0.0729253i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 16.9058 | − | 13.3565i | 0.705637 | − | 0.557488i | ||||
\(575\) | 28.0724 | − | 3.15012i | 1.17070 | − | 0.131369i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.7696 | 1.36422 | 0.682108 | − | 0.731251i | \(-0.261063\pi\) | ||||
0.682108 | + | 0.731251i | \(0.261063\pi\) | |||||||
\(578\) | 19.2858 | + | 33.4039i | 0.802182 | + | 1.38942i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.46617 | + | 4.78143i | 0.393061 | + | 0.198538i | ||||
\(581\) | −2.52930 | + | 6.35923i | −0.104933 | + | 0.263825i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.9407 | + | 11.5128i | −0.825858 | + | 0.476810i | ||||
\(584\) | 4.79644 | 0.198478 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 18.5231i | − | 0.765182i | ||||||
\(587\) | −19.1726 | + | 11.0693i | −0.791337 | + | 0.456879i | −0.840433 | − | 0.541915i | \(-0.817699\pi\) |
0.0490959 | + | 0.998794i | \(0.484366\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.66672 | + | 8.08300i | −0.192289 | + | 0.333054i | ||||
\(590\) | −0.173986 | + | 0.344454i | −0.00716290 | + | 0.0141809i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.21571 | + | 2.43394i | −0.173265 | + | 0.100034i | ||||
\(593\) | − | 26.0392i | − | 1.06930i | −0.845073 | − | 0.534650i | \(-0.820443\pi\) | ||
0.845073 | − | 0.534650i | \(-0.179557\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 43.2150 | − | 8.80148i | 1.77164 | − | 0.360825i | ||||
\(596\) | 12.4184 | − | 7.16974i | 0.508676 | − | 0.293684i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.92171 | − | 10.2567i | 0.242157 | − | 0.419428i | ||||
\(599\) | −18.1227 | − | 10.4631i | −0.740472 | − | 0.427512i | 0.0817689 | − | 0.996651i | \(-0.473943\pi\) |
−0.822241 | + | 0.569140i | \(0.807276\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.4768 | − | 14.7091i | 1.03922 | − | 0.599995i | 0.119609 | − | 0.992821i | \(-0.461836\pi\) |
0.919613 | + | 0.392826i | \(0.128503\pi\) | |||||||
\(602\) | 6.80997 | − | 0.994743i | 0.277554 | − | 0.0405427i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.90415 | −0.280926 | ||||||||
\(605\) | 10.0784 | + | 15.4006i | 0.409745 | + | 0.626124i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.62507 | + | 11.4750i | −0.268903 | + | 0.465754i | −0.968579 | − | 0.248707i | \(-0.919994\pi\) |
0.699676 | + | 0.714461i | \(0.253328\pi\) | |||||||
\(608\) | −4.03690 | − | 2.33070i | −0.163718 | − | 0.0945225i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11.1806 | + | 7.31673i | −0.452688 | + | 0.296246i | ||||
\(611\) | 21.5469i | 0.871695i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.3252i | 0.699759i | 0.936795 | + | 0.349880i | \(0.113778\pi\) | ||||
−0.936795 | + | 0.349880i | \(0.886222\pi\) | |||||||
\(614\) | 1.72071 | + | 2.98036i | 0.0694423 | + | 0.120278i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.62708 | + | 4.09086i | −0.0655569 | + | 0.164825i | ||||
\(617\) | 9.93911 | − | 17.2150i | 0.400133 | − | 0.693052i | −0.593608 | − | 0.804754i | \(-0.702297\pi\) |
0.993742 | + | 0.111703i | \(0.0356304\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.8618 | + | 17.8181i | −1.24044 | + | 0.716168i | −0.969184 | − | 0.246339i | \(-0.920772\pi\) |
−0.271256 | + | 0.962507i | \(0.587439\pi\) | |||||||
\(620\) | 0.250028 | + | 4.47025i | 0.0100414 | + | 0.179529i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −33.2371 | −1.33269 | ||||||||
\(623\) | 23.3029 | − | 18.4105i | 0.933611 | − | 0.737599i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.39051 | + | 23.8826i | −0.295620 | + | 0.955305i | ||||
\(626\) | 0.967111 | − | 1.67509i | 0.0386535 | − | 0.0669499i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.48808 | − | 12.9697i | −0.298807 | − | 0.517549i | ||||
\(629\) | −36.2883 | −1.44691 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.1609 | 1.12107 | 0.560533 | − | 0.828132i | \(-0.310596\pi\) | ||||
0.560533 | + | 0.828132i | \(0.310596\pi\) | |||||||
\(632\) | −6.30891 | − | 10.9273i | −0.250955 | − | 0.434666i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.12038 | − | 8.86877i | 0.203356 | − | 0.352224i | ||||
\(635\) | −28.3317 | − | 14.3106i | −1.12431 | − | 0.567898i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.6655 | − | 10.0784i | −0.422581 | − | 0.399321i | ||||
\(638\) | −7.89205 | −0.312449 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.23258 | + | 0.124872i | −0.0882504 | + | 0.00493599i | ||||
\(641\) | −25.4170 | + | 14.6745i | −1.00391 | + | 0.579608i | −0.909403 | − | 0.415916i | \(-0.863461\pi\) |
−0.0945076 | + | 0.995524i | \(0.530128\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.7337 | − | 28.9836i | 0.659912 | − | 1.14300i | −0.320726 | − | 0.947172i | \(-0.603927\pi\) |
0.980638 | − | 0.195830i | \(-0.0627400\pi\) | |||||||
\(644\) | 13.8894 | + | 5.52433i | 0.547321 | + | 0.217689i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −17.3745 | − | 30.0936i | −0.683592 | − | 1.18402i | ||||
\(647\) | 19.6226i | 0.771445i | 0.922615 | + | 0.385723i | \(0.126048\pi\) | ||||
−0.922615 | + | 0.385723i | \(0.873952\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 0.287175i | − | 0.0112726i | ||||||
\(650\) | 6.22027 | + | 8.43615i | 0.243979 | + | 0.330893i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.95885 | + | 4.01770i | 0.272530 | + | 0.157345i | ||||
\(653\) | −9.70880 | + | 16.8161i | −0.379935 | + | 0.658066i | −0.991052 | − | 0.133474i | \(-0.957387\pi\) |
0.611118 | + | 0.791540i | \(0.290720\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.80838 | − | 4.29144i | −0.109732 | − | 0.167680i | ||||
\(656\) | −8.14339 | −0.317946 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −26.9091 | + | 3.93065i | −1.04903 | + | 0.153233i | ||||
\(659\) | 10.8291 | − | 6.25219i | 0.421842 | − | 0.243551i | −0.274023 | − | 0.961723i | \(-0.588354\pi\) |
0.695865 | + | 0.718172i | \(0.255021\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.75358 | − | 2.16713i | −0.145997 | − | 0.0842916i | 0.425222 | − | 0.905089i | \(-0.360196\pi\) |
−0.571219 | + | 0.820798i | \(0.693529\pi\) | |||||||
\(662\) | −2.81788 | + | 4.88070i | −0.109520 | + | 0.189694i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.24015 | − | 1.29335i | 0.0869347 | − | 0.0501918i | ||||
\(665\) | −27.0225 | + | 5.50360i | −1.04789 | + | 0.213420i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.7954i | 1.03752i | ||||||||
\(668\) | 4.12075 | − | 2.37911i | 0.159436 | − | 0.0920507i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.8460 | + | 5.47842i | 0.419019 | + | 0.211650i | ||||
\(671\) | 4.97174 | − | 8.61131i | 0.191932 | − | 0.332436i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.47592 | − | 0.852124i | 0.0568926 | − | 0.0328470i | −0.471284 | − | 0.881982i | \(-0.656209\pi\) |
0.528177 | + | 0.849135i | \(0.322876\pi\) | |||||||
\(674\) | − | 13.6905i | − | 0.527338i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.60558 | −0.330984 | ||||||||
\(677\) | −5.08519 | + | 2.93594i | −0.195440 | + | 0.112837i | −0.594527 | − | 0.804076i | \(-0.702661\pi\) |
0.399087 | + | 0.916913i | \(0.369327\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −23.2660 | − | 9.25374i | −0.892869 | − | 0.355126i | ||||
\(680\) | −14.8787 | − | 7.51536i | −0.570574 | − | 0.288201i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.66591 | − | 2.88543i | −0.0637908 | − | 0.110489i | ||||
\(683\) | 10.9483 | 0.418926 | 0.209463 | − | 0.977817i | \(-0.432828\pi\) | ||||
0.209463 | + | 0.977817i | \(0.432828\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.1921 | − | 1.35310i | 0.924332 | − | 0.0516994i | ||||
\(686\) | 10.6409 | − | 15.1582i | 0.406272 | − | 0.578743i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.25274 | − | 1.30062i | −0.0858850 | − | 0.0495857i | ||||
\(689\) | −14.5035 | + | 25.1209i | −0.552541 | + | 0.957029i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.4759 | − | 19.9047i | 1.31153 | − | 0.757210i | 0.329177 | − | 0.944268i | \(-0.393229\pi\) |
0.982349 | + | 0.187058i | \(0.0598953\pi\) | |||||||
\(692\) | 17.2576i | 0.656037i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.79041 | −0.371639 | ||||||||
\(695\) | −16.4975 | + | 10.7962i | −0.625784 | + | 0.409522i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −52.5729 | − | 30.3530i | −1.99134 | − | 1.14970i | ||||
\(698\) | 14.0539 | + | 8.11400i | 0.531946 | + | 0.307119i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −9.40086 | + | 9.30719i | −0.355319 | + | 0.351779i | ||||
\(701\) | − | 7.84396i | − | 0.296262i | −0.988968 | − | 0.148131i | \(-0.952674\pi\) | ||
0.988968 | − | 0.148131i | \(-0.0473258\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.6912 | 0.855815 | ||||||||
\(704\) | 1.44107 | − | 0.832005i | 0.0543125 | − | 0.0313574i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20.9960 | − | 12.1220i | −0.790194 | − | 0.456219i | ||||
\(707\) | −25.9880 | − | 10.3364i | −0.977379 | − | 0.388739i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.3461 | + | 17.9200i | 0.388557 | + | 0.673001i | 0.992256 | − | 0.124212i | \(-0.0396402\pi\) |
−0.603698 | + | 0.797213i | \(0.706307\pi\) | |||||||
\(710\) | 1.50408 | + | 26.8913i | 0.0564470 | + | 1.00921i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.2248 | −0.420666 | ||||||||
\(713\) | −9.79674 | + | 5.65615i | −0.366891 | + | 0.211825i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.96220 | − | 3.51666i | −0.260371 | − | 0.131516i | ||||
\(716\) | 0.521897 | + | 0.301317i | 0.0195042 | + | 0.0112608i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 27.1600 | − | 15.6809i | 1.01360 | − | 0.585204i | ||||
\(719\) | −21.2881 | −0.793910 | −0.396955 | − | 0.917838i | \(-0.629933\pi\) | ||||
−0.396955 | + | 0.917838i | \(0.629933\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.82684 | + | 39.8903i | 0.217003 | + | 1.48559i | ||||
\(722\) | 1.36436 | + | 2.36314i | 0.0507763 | + | 0.0879471i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.0659 | + | 6.38892i | 0.411262 | + | 0.237442i | ||||
\(725\) | −21.7310 | − | 9.49287i | −0.807070 | − | 0.352556i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.79802 | + | 8.31041i | 0.177949 | + | 0.308216i | 0.941178 | − | 0.337912i | \(-0.109721\pi\) |
−0.763229 | + | 0.646128i | \(0.776387\pi\) | |||||||
\(728\) | 0.801642 | + | 5.48801i | 0.0297108 | + | 0.203399i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10.7084 | + | 0.598941i | −0.396337 | + | 0.0221678i | ||||
\(731\) | −9.69565 | − | 16.7934i | −0.358607 | − | 0.621125i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.1972 | + | 38.4466i | −0.819871 | + | 1.42006i | 0.0859066 | + | 0.996303i | \(0.472621\pi\) |
−0.905777 | + | 0.423754i | \(0.860712\pi\) | |||||||
\(734\) | 0.616195 | − | 1.06728i | 0.0227442 | − | 0.0393941i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.82486 | − | 4.89279i | −0.104126 | − | 0.180351i | ||||
\(737\) | −9.04247 | −0.333084 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.8223 | −0.655603 | −0.327801 | − | 0.944747i | \(-0.606308\pi\) | ||||
−0.327801 | + | 0.944747i | \(0.606308\pi\) | |||||||
\(740\) | 9.10798 | − | 5.96039i | 0.334816 | − | 0.219108i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −34.0182 | − | 13.5303i | −1.24885 | − | 0.496712i | ||||
\(743\) | −25.2903 | + | 43.8041i | −0.927811 | + | 1.60702i | −0.140835 | + | 0.990033i | \(0.544979\pi\) |
−0.786976 | + | 0.616983i | \(0.788355\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26.8297 | + | 17.5577i | −0.982963 | + | 0.643265i | ||||
\(746\) | − | 27.6157i | − | 1.01108i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 12.4046 | 0.453556 | ||||||||
\(749\) | 23.7005 | − | 18.7246i | 0.865999 | − | 0.684183i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.2173 | + | 38.4816i | −0.810722 | + | 1.40421i | 0.101637 | + | 0.994822i | \(0.467592\pi\) |
−0.912359 | + | 0.409390i | \(0.865741\pi\) | |||||||
\(752\) | 8.90154 | + | 5.13931i | 0.324606 | + | 0.187411i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.61024 | + | 4.97113i | −0.313567 | + | 0.181038i | ||||
\(755\) | 15.4140 | − | 0.862134i | 0.560975 | − | 0.0313763i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.2968i | 0.955774i | 0.878421 | + | 0.477887i | \(0.158597\pi\) | ||||
−0.878421 | + | 0.477887i | \(0.841403\pi\) | |||||||
\(758\) | −11.6133 | − | 20.1148i | −0.421812 | − | 0.730601i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9.30373 | + | 4.69938i | 0.337482 | + | 0.170465i | ||||
\(761\) | −11.6947 | + | 20.2558i | −0.423932 | + | 0.734272i | −0.996320 | − | 0.0857107i | \(-0.972684\pi\) |
0.572388 | + | 0.819983i | \(0.306017\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.0363 | − | 17.4098i | 0.797768 | − | 0.630277i | ||||
\(764\) | − | 18.8422i | − | 0.681687i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 23.7929i | − | 0.859672i | ||||||
\(767\) | −0.180889 | − | 0.313309i | −0.00653152 | − | 0.0113129i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.6845 | + | 12.5196i | 0.781963 | + | 0.451467i | 0.837126 | − | 0.547011i | \(-0.184234\pi\) |
−0.0551625 | + | 0.998477i | \(0.517568\pi\) | |||||||
\(770\) | 3.12175 | − | 9.33633i | 0.112500 | − | 0.336458i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.89207 | − | 3.40179i | 0.212060 | − | 0.122433i | ||||
\(773\) | 55.5416i | 1.99769i | 0.0480317 | + | 0.998846i | \(0.484705\pi\) | ||||
−0.0480317 | + | 0.998846i | \(0.515295\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.11642 | − | 9.94895i | −0.0401028 | − | 0.357377i | ||||
\(776\) | 4.73188 | + | 8.19586i | 0.169865 | + | 0.294214i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.18328 | − | 4.72462i | −0.293385 | − | 0.169386i | ||||
\(779\) | 32.8740 | + | 18.9798i | 1.17783 | + | 0.680023i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.0215 | − | 17.3577i | −0.358596 | − | 0.621107i | ||||
\(782\) | − | 42.1165i | − | 1.50608i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.70752 | + | 2.00228i | −0.239554 | + | 0.0715100i | ||||
\(785\) | 18.3373 | + | 28.0209i | 0.654485 | + | 1.00011i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.49527 | − | 12.9822i | 0.267177 | − | 0.462765i | −0.700954 | − | 0.713206i | \(-0.747242\pi\) |
0.968132 | + | 0.250441i | \(0.0805757\pi\) | |||||||
\(788\) | 4.29375 | − | 7.43699i | 0.152959 | − | 0.264932i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 15.4496 | + | 23.6084i | 0.549674 | + | 0.839947i | ||||
\(791\) | 5.25524 | + | 35.9772i | 0.186855 | + | 1.27920i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 12.5266i | − | 0.444833i | ||||||
\(794\) | −10.8617 | − | 18.8130i | −0.385467 | − | 0.667648i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.41729 | − | 2.55032i | −0.156567 | − | 0.0903938i | ||||
\(797\) | 43.9990 | + | 25.4028i | 1.55852 | + | 0.899814i | 0.997399 | + | 0.0720822i | \(0.0229644\pi\) |
0.561124 | + | 0.827732i | \(0.310369\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.3116 | + | 66.3577i | 1.35537 | + | 2.34757i | ||||
\(800\) | 4.96881 | − | 0.557572i | 0.175674 | − | 0.0197132i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 12.3027i | − | 0.434423i | ||||||
\(803\) | 6.91203 | − | 3.99066i | 0.243920 | − | 0.140827i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −31.6991 | − | 10.5991i | −1.11725 | − | 0.373569i | ||||
\(806\) | −3.63501 | − | 2.09867i | −0.128038 | − | 0.0739227i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.28548 | + | 9.15472i | 0.185942 | + | 0.322062i | ||||
\(809\) | 38.3573i | 1.34857i | 0.738471 | + | 0.674285i | \(0.235548\pi\) | ||||
−0.738471 | + | 0.674285i | \(0.764452\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 0.237330i | − | 0.00833379i | −0.999991 | − | 0.00416689i | \(-0.998674\pi\) | ||
0.999991 | − | 0.00416689i | \(-0.00132637\pi\) | |||||||
\(812\) | −7.77895 | − | 9.84614i | −0.272988 | − | 0.345532i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.05010 | + | 7.01498i | −0.141956 | + | 0.245875i | ||||
\(815\) | −16.0379 | − | 8.10086i | −0.561782 | − | 0.283761i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.06273 | + | 10.5009i | 0.212108 | + | 0.367382i | ||||
\(818\) | − | 2.89004i | − | 0.101048i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 18.1807 | − | 1.01688i | 0.634899 | − | 0.0355110i | ||||
\(821\) | −34.0959 | + | 19.6853i | −1.18995 | + | 0.687020i | −0.958296 | − | 0.285777i | \(-0.907748\pi\) |
−0.231658 | + | 0.972797i | \(0.574415\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.0228 | − | 6.94134i | −0.419087 | − | 0.241960i | 0.275600 | − | 0.961273i | \(-0.411124\pi\) |
−0.694687 | + | 0.719312i | \(0.744457\pi\) | |||||||
\(824\) | 7.61856 | − | 13.1957i | 0.265405 | − | 0.459695i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.358280 | − | 0.283060i | 0.0124662 | − | 0.00984890i | ||||
\(827\) | −53.7207 | −1.86805 | −0.934027 | − | 0.357204i | \(-0.883730\pi\) | ||||
−0.934027 | + | 0.357204i | \(0.883730\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 40.2685i | − | 1.39858i | −0.714836 | − | 0.699292i | \(-0.753499\pi\) | ||
0.714836 | − | 0.699292i | \(-0.246501\pi\) | |||||||
\(830\) | −4.83981 | + | 3.16724i | −0.167992 | + | 0.109936i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.04814 | − | 1.81544i | 0.0363378 | − | 0.0629390i | ||||
\(833\) | −50.7662 | − | 12.0745i | −1.75895 | − | 0.418358i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.90281 | + | 5.82612i | −0.308094 | + | 0.201621i | ||||
\(836\) | −7.75663 | −0.268268 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 25.4794 | 0.880170 | ||||||||
\(839\) | −12.6898 | − | 21.9794i | −0.438100 | − | 0.758812i | 0.559443 | − | 0.828869i | \(-0.311015\pi\) |
−0.997543 | + | 0.0700572i | \(0.977682\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.25296 | + | 5.63429i | −0.112171 | + | 0.194286i | ||||
\(842\) | −2.96965 | + | 5.14359i | −0.102341 | + | 0.177260i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.01715 | + | 8.68995i | 0.172697 | + | 0.299120i | ||||
\(845\) | 19.2126 | − | 1.07460i | 0.660935 | − | 0.0369672i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.14765 | − | 21.5487i | −0.108155 | − | 0.740422i | ||||
\(848\) | 6.91868 | + | 11.9835i | 0.237589 | + | 0.411516i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 34.1564 | + | 14.9207i | 1.17156 | + | 0.511776i | ||||
\(851\) | 23.8176 | + | 13.7511i | 0.816456 | + | 0.471381i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.2962 | − | 29.9580i | −0.592212 | − | 1.02574i | −0.993934 | − | 0.109979i | \(-0.964921\pi\) |
0.401722 | − | 0.915762i | \(-0.368412\pi\) | |||||||
\(854\) | 15.6440 | − | 2.28514i | 0.535326 | − | 0.0781959i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.4163 | −0.390202 | ||||||||
\(857\) | −16.9137 | + | 9.76512i | −0.577761 | + | 0.333570i | −0.760243 | − | 0.649639i | \(-0.774920\pi\) |
0.182482 | + | 0.983209i | \(0.441587\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.4126 | − | 25.0643i | −1.48122 | − | 0.855182i | −0.481446 | − | 0.876476i | \(-0.659888\pi\) |
−0.999773 | + | 0.0212940i | \(0.993221\pi\) | |||||||
\(860\) | 5.19183 | + | 2.62243i | 0.177040 | + | 0.0894243i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 25.4910 | − | 14.7172i | 0.868225 | − | 0.501270i | ||||
\(863\) | −17.7867 | −0.605465 | −0.302733 | − | 0.953076i | \(-0.597899\pi\) | ||||
−0.302733 | + | 0.953076i | \(0.597899\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.15499 | − | 38.5290i | −0.0732720 | − | 1.31003i | ||||
\(866\) | −7.12793 | − | 12.3459i | −0.242217 | − | 0.419532i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.95784 | − | 4.92247i | 0.0664535 | − | 0.167079i | ||||
\(869\) | −18.1832 | − | 10.4981i | −0.616823 | − | 0.356123i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.86535 | + | 5.69576i | −0.334275 | + | 0.192994i | ||||
\(872\) | −10.6147 | −0.359458 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 26.3356i | 0.890815i | ||||||||
\(875\) | 19.8260 | − | 21.9529i | 0.670240 | − | 0.742145i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.1879 | − | 10.5008i | −0.614163 | − | 0.354587i | 0.160430 | − | 0.987047i | \(-0.448712\pi\) |
−0.774593 | + | 0.632460i | \(0.782045\pi\) | |||||||
\(878\) | −9.41191 | − | 5.43397i | −0.317637 | − | 0.183388i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.11342 | + | 2.03747i | −0.104953 | + | 0.0686829i | ||||
\(881\) | 57.9674 | 1.95297 | 0.976486 | − | 0.215580i | \(-0.0691642\pi\) | ||||
0.976486 | + | 0.215580i | \(0.0691642\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 42.6213i | − | 1.43432i | −0.696908 | − | 0.717161i | \(-0.745441\pi\) | ||
0.696908 | − | 0.717161i | \(-0.254559\pi\) | |||||||
\(884\) | 13.5334 | − | 7.81352i | 0.455178 | − | 0.262797i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.24859 | − | 9.09083i | 0.176330 | − | 0.305412i | ||||
\(887\) | −3.27263 | − | 1.88945i | −0.109884 | − | 0.0634416i | 0.444051 | − | 0.896002i | \(-0.353541\pi\) |
−0.553935 | + | 0.832560i | \(0.686874\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.2820 | + | 29.4690i | 0.780852 | + | 0.988358i | ||||
\(890\) | 25.0602 | − | 1.40166i | 0.840020 | − | 0.0469837i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 17.7445 | 0.594131 | ||||||||
\(893\) | −23.9564 | − | 41.4937i | −0.801671 | − | 1.38853i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.20280 | − | 0.607544i | −0.0402052 | − | 0.0203080i | ||||
\(896\) | 2.45843 | + | 0.977807i | 0.0821305 | + | 0.0326662i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −32.1022 | + | 18.5342i | −1.07126 | + | 0.618494i | ||||
\(899\) | 9.49639 | 0.316722 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 103.152i | 3.43651i | ||||||||
\(902\) | −11.7352 | + | 6.77533i | −0.390740 | + | 0.225594i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.87120 | − | 11.9013i | 0.228533 | − | 0.395830i | ||||
\(905\) | −25.5034 | − | 12.8819i | −0.847760 | − | 0.428210i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43.9682 | + | 25.3850i | −1.45994 | + | 0.842896i | −0.999008 | − | 0.0445394i | \(-0.985818\pi\) |
−0.460932 | + | 0.887436i | \(0.652485\pi\) | |||||||
\(908\) | 0.474897i | 0.0157600i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.47503 | − | 12.1523i | −0.0820464 | − | 0.402845i | ||||
\(911\) | 6.59422 | − | 3.80717i | 0.218476 | − | 0.126137i | −0.386768 | − | 0.922177i | \(-0.626409\pi\) |
0.605244 | + | 0.796040i | \(0.293075\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.15215 | − | 3.72763i | 0.0712257 | − | 0.123367i | ||||
\(914\) | −17.5211 | − | 10.1158i | −0.579545 | − | 0.334601i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.51279 | + | 5.49221i | −0.314312 | + | 0.181468i | ||||
\(917\) | 0.877104 | + | 6.00462i | 0.0289645 | + | 0.198290i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.4157 | −0.343581 | −0.171791 | − | 0.985133i | \(-0.554955\pi\) | ||||
−0.171791 | + | 0.985133i | \(0.554955\pi\) | |||||||
\(920\) | 6.91769 | + | 10.5708i | 0.228069 | + | 0.348509i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.80701 | − | 11.7901i | 0.224177 | − | 0.388286i | ||||
\(923\) | −21.8669 | − | 12.6249i | −0.719757 | − | 0.415552i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.5900 | + | 14.4444i | −0.644115 | + | 0.474928i | ||||
\(926\) | 22.8848i | 0.752040i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.74279i | 0.155690i | ||||||||
\(929\) | −21.5567 | − | 37.3374i | −0.707253 | − | 1.22500i | −0.965872 | − | 0.259019i | \(-0.916601\pi\) |
0.258619 | − | 0.965980i | \(-0.416733\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 31.7443 | + | 7.55026i | 1.04038 | + | 0.247450i | ||||
\(932\) | −10.7397 | + | 18.6017i | −0.351791 | + | 0.609320i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.89724 | + | 1.67272i | −0.0948006 | + | 0.0547332i | ||||
\(935\) | −27.6942 | + | 1.54898i | −0.905697 | + | 0.0506571i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.2891 | 0.532140 | 0.266070 | − | 0.963954i | \(-0.414275\pi\) | ||||
0.266070 | + | 0.963954i | \(0.414275\pi\) | |||||||
\(938\) | −8.91288 | − | 11.2814i | −0.291016 | − | 0.368351i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −20.5151 | − | 10.3624i | −0.669130 | − | 0.337983i | ||||
\(941\) | 14.8611 | − | 25.7402i | 0.484458 | − | 0.839106i | −0.515383 | − | 0.856960i | \(-0.672350\pi\) |
0.999841 | + | 0.0178543i | \(0.00568350\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.0039 | + | 39.8439i | 0.749110 | + | 1.29750i | ||||
\(944\) | −0.172580 | −0.00561701 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.32849 | −0.140731 | ||||||||
\(947\) | 12.6233 | + | 21.8642i | 0.410202 | + | 0.710490i | 0.994912 | − | 0.100752i | \(-0.0321249\pi\) |
−0.584710 | + | 0.811243i | \(0.698792\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.02736 | − | 8.70764i | 0.163195 | − | 0.282662i | ||||
\(950\) | −21.3581 | − | 9.32997i | −0.692949 | − | 0.302704i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 12.2268 | + | 15.4760i | 0.396273 | + | 0.501579i | ||||
\(953\) | −46.4580 | −1.50492 | −0.752461 | − | 0.658636i | \(-0.771134\pi\) | ||||
−0.752461 | + | 0.658636i | \(0.771134\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.35286 | + | 42.0667i | 0.0761368 | + | 1.36125i | ||||
\(956\) | −14.6228 | + | 8.44250i | −0.472937 | + | 0.273050i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.15257 | + | 14.1207i | −0.263397 | + | 0.456218i | ||||
\(959\) | −26.6394 | − | 10.5955i | −0.860232 | − | 0.342145i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.4954 | − | 23.3748i | −0.435337 | − | 0.754025i | ||||
\(962\) | 10.2045i | 0.329006i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 9.24813i | − | 0.297862i | ||||||
\(965\) | −12.7297 | + | 8.33051i | −0.409784 | + | 0.268169i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.7680 | + | 22.3827i | 1.24670 | + | 0.719780i | 0.970449 | − | 0.241307i | \(-0.0775761\pi\) |
0.276246 | + | 0.961087i | \(0.410909\pi\) | |||||||
\(968\) | −4.11554 | + | 7.12832i | −0.132278 | + | 0.229113i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11.5877 | − | 17.7070i | −0.372060 | − | 0.568539i | ||||
\(971\) | 5.45198 | 0.174962 | 0.0874812 | − | 0.996166i | \(-0.472118\pi\) | ||||
0.0874812 | + | 0.996166i | \(0.472118\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 23.0834 | − | 3.37183i | 0.740020 | − | 0.108096i | ||||
\(974\) | 4.50548 | − | 2.60124i | 0.144365 | − | 0.0833491i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.17503 | − | 2.98781i | −0.165649 | − | 0.0956374i | ||||
\(977\) | 9.53359 | − | 16.5127i | 0.305007 | − | 0.528287i | −0.672256 | − | 0.740319i | \(-0.734675\pi\) |
0.977263 | + | 0.212032i | \(0.0680080\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.1757 | + | 9.33907i | −0.516979 | + | 0.298478i | ||||
\(980\) | 14.7250 | − | 5.30783i | 0.470374 | − | 0.169552i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 23.8599i | − | 0.761400i | ||||||
\(983\) | 26.7964 | − | 15.4709i | 0.854674 | − | 0.493446i | −0.00755133 | − | 0.999971i | \(-0.502404\pi\) |
0.862225 | + | 0.506525i | \(0.169070\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.65746 | + | 17.1398i | −0.275850 | + | 0.546121i | ||||
\(986\) | −17.6779 | + | 30.6190i | −0.562979 | + | 0.975107i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.46249 | + | 4.88582i | −0.269228 | + | 0.155439i | ||||
\(989\) | 14.6963i | 0.467314i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.5926 | 0.685912 | 0.342956 | − | 0.939351i | \(-0.388572\pi\) | ||||
0.342956 | + | 0.939351i | \(0.388572\pi\) | |||||||
\(992\) | −1.73402 | + | 1.00114i | −0.0550553 | + | 0.0317862i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 11.7777 | − | 29.6117i | 0.373565 | − | 0.939228i | ||||
\(995\) | 10.1804 | + | 5.14220i | 0.322741 | + | 0.163019i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.8955 | − | 46.5843i | −0.851788 | − | 1.47534i | −0.879593 | − | 0.475726i | \(-0.842185\pi\) |
0.0278059 | − | 0.999613i | \(-0.491148\pi\) | |||||||
\(998\) | −32.3319 | −1.02345 | ||||||||
\(999\) | 0 | 0 |
(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 | 1890.2.bf.e.1259.10 | 32 | ||
3.2 | odd | 2 | 630.2.bf.f.419.16 | yes | 32 | ||
5.4 | even | 2 | 1890.2.bf.f.1259.13 | 32 | |||
7.6 | odd | 2 | inner | 1890.2.bf.e.1259.7 | 32 | ||
9.2 | odd | 6 | 1890.2.bf.f.629.4 | 32 | |||
9.7 | even | 3 | 630.2.bf.e.209.16 | yes | 32 | ||
15.14 | odd | 2 | 630.2.bf.e.419.1 | yes | 32 | ||
21.20 | even | 2 | 630.2.bf.f.419.1 | yes | 32 | ||
35.34 | odd | 2 | 1890.2.bf.f.1259.4 | 32 | |||
45.29 | odd | 6 | inner | 1890.2.bf.e.629.7 | 32 | ||
45.34 | even | 6 | 630.2.bf.f.209.1 | yes | 32 | ||
63.20 | even | 6 | 1890.2.bf.f.629.13 | 32 | |||
63.34 | odd | 6 | 630.2.bf.e.209.1 | ✓ | 32 | ||
105.104 | even | 2 | 630.2.bf.e.419.16 | yes | 32 | ||
315.34 | odd | 6 | 630.2.bf.f.209.16 | yes | 32 | ||
315.209 | even | 6 | inner | 1890.2.bf.e.629.10 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.bf.e.209.1 | ✓ | 32 | 63.34 | odd | 6 | ||
630.2.bf.e.209.16 | yes | 32 | 9.7 | even | 3 | ||
630.2.bf.e.419.1 | yes | 32 | 15.14 | odd | 2 | ||
630.2.bf.e.419.16 | yes | 32 | 105.104 | even | 2 | ||
630.2.bf.f.209.1 | yes | 32 | 45.34 | even | 6 | ||
630.2.bf.f.209.16 | yes | 32 | 315.34 | odd | 6 | ||
630.2.bf.f.419.1 | yes | 32 | 21.20 | even | 2 | ||
630.2.bf.f.419.16 | yes | 32 | 3.2 | odd | 2 | ||
1890.2.bf.e.629.7 | 32 | 45.29 | odd | 6 | inner | ||
1890.2.bf.e.629.10 | 32 | 315.209 | even | 6 | inner | ||
1890.2.bf.e.1259.7 | 32 | 7.6 | odd | 2 | inner | ||
1890.2.bf.e.1259.10 | 32 | 1.1 | even | 1 | trivial | ||
1890.2.bf.f.629.4 | 32 | 9.2 | odd | 6 | |||
1890.2.bf.f.629.13 | 32 | 63.20 | even | 6 | |||
1890.2.bf.f.1259.4 | 32 | 35.34 | odd | 2 | |||
1890.2.bf.f.1259.13 | 32 | 5.4 | even | 2 |