Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,2,Mod(11,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.11");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.383281929702\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.163368480538624.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{10} - 2x^{8} + 16x^{6} - 8x^{4} - 32x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 35.5 | ||
Root | \(-1.27715 - 0.607364i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.35 |
Dual form | 48.2.k.a.11.5 |
$q$-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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.607364 | + | 1.27715i | 0.429471 | + | 0.903081i | ||||
\(3\) | 0.0835731 | − | 1.73003i | 0.0482510 | − | 0.998835i | ||||
\(4\) | −1.26222 | + | 1.55139i | −0.631109 | + | 0.775694i | ||||
\(5\) | 0.431733 | + | 0.431733i | 0.193077 | + | 0.193077i | 0.797024 | − | 0.603947i | \(-0.206406\pi\) |
−0.603947 | + | 0.797024i | \(0.706406\pi\) | |||||||
\(6\) | 2.26027 | − | 0.944024i | 0.922751 | − | 0.385396i | ||||
\(7\) | −3.10278 | −1.17274 | −0.586369 | − | 0.810044i | \(-0.699443\pi\) | ||||
−0.586369 | + | 0.810044i | \(0.699443\pi\) | |||||||
\(8\) | −2.74798 | − | 0.669785i | −0.971557 | − | 0.236805i | ||||
\(9\) | −2.98603 | − | 0.289169i | −0.995344 | − | 0.0963895i | ||||
\(10\) | −0.289169 | + | 0.813607i | −0.0914431 | + | 0.257285i | ||||
\(11\) | 2.98603 | − | 2.98603i | 0.900322 | − | 0.900322i | −0.0951415 | − | 0.995464i | \(-0.530330\pi\) |
0.995464 | + | 0.0951415i | \(0.0303304\pi\) | |||||||
\(12\) | 2.57846 | + | 2.31334i | 0.744339 | + | 0.667802i | ||||
\(13\) | 2.10278 | + | 2.10278i | 0.583205 | + | 0.583205i | 0.935783 | − | 0.352578i | \(-0.114695\pi\) |
−0.352578 | + | 0.935783i | \(0.614695\pi\) | |||||||
\(14\) | −1.88451 | − | 3.96271i | −0.503657 | − | 1.05908i | ||||
\(15\) | 0.782994 | − | 0.710831i | 0.202168 | − | 0.183536i | ||||
\(16\) | −0.813607 | − | 3.91638i | −0.203402 | − | 0.979095i | ||||
\(17\) | 2.42945i | 0.589229i | 0.955616 | + | 0.294615i | \(0.0951913\pi\) | ||||
−0.955616 | + | 0.294615i | \(0.904809\pi\) | |||||||
\(18\) | −1.44430 | − | 3.98924i | −0.340424 | − | 0.940272i | ||||
\(19\) | −0.710831 | + | 0.710831i | −0.163076 | + | 0.163076i | −0.783928 | − | 0.620852i | \(-0.786787\pi\) |
0.620852 | + | 0.783928i | \(0.286787\pi\) | |||||||
\(20\) | −1.21473 | + | 0.124844i | −0.271621 | + | 0.0279159i | ||||
\(21\) | −0.259309 | + | 5.36790i | −0.0565858 | + | 1.17137i | ||||
\(22\) | 5.62721 | + | 2.00000i | 1.19973 | + | 0.426401i | ||||
\(23\) | 5.97206i | 1.24526i | 0.782516 | + | 0.622631i | \(0.213936\pi\) | ||||
−0.782516 | + | 0.622631i | \(0.786064\pi\) | |||||||
\(24\) | −1.38841 | + | 4.69812i | −0.283408 | + | 0.959000i | ||||
\(25\) | − | 4.62721i | − | 0.925443i | ||||||
\(26\) | −1.40841 | + | 3.96271i | −0.276212 | + | 0.777151i | ||||
\(27\) | −0.749823 | + | 5.14177i | −0.144304 | + | 0.989533i | ||||
\(28\) | 3.91638 | − | 4.81361i | 0.740127 | − | 0.909686i | ||||
\(29\) | 2.86119 | − | 2.86119i | 0.531309 | − | 0.531309i | −0.389653 | − | 0.920962i | \(-0.627405\pi\) |
0.920962 | + | 0.389653i | \(0.127405\pi\) | |||||||
\(30\) | 1.38340 | + | 0.568267i | 0.252573 | + | 0.103751i | ||||
\(31\) | 0.524438i | 0.0941918i | 0.998890 | + | 0.0470959i | \(0.0149966\pi\) | ||||
−0.998890 | + | 0.0470959i | \(0.985003\pi\) | |||||||
\(32\) | 4.50765 | − | 3.41776i | 0.796847 | − | 0.604181i | ||||
\(33\) | −4.91638 | − | 5.41549i | −0.855832 | − | 0.942715i | ||||
\(34\) | −3.10278 | + | 1.47556i | −0.532122 | + | 0.253057i | ||||
\(35\) | −1.33957 | − | 1.33957i | −0.226429 | − | 0.226429i | ||||
\(36\) | 4.21764 | − | 4.26750i | 0.702940 | − | 0.711250i | ||||
\(37\) | 1.52444 | − | 1.52444i | 0.250616 | − | 0.250616i | −0.570607 | − | 0.821223i | \(-0.693292\pi\) |
0.821223 | + | 0.570607i | \(0.193292\pi\) | |||||||
\(38\) | −1.33957 | − | 0.476105i | −0.217307 | − | 0.0772344i | ||||
\(39\) | 3.81361 | − | 3.46214i | 0.610666 | − | 0.554385i | ||||
\(40\) | −0.897225 | − | 1.47556i | −0.141864 | − | 0.233307i | ||||
\(41\) | 1.81568 | 0.283561 | 0.141780 | − | 0.989898i | \(-0.454717\pi\) | ||||
0.141780 | + | 0.989898i | \(0.454717\pi\) | |||||||
\(42\) | −7.01311 | + | 2.92909i | −1.08215 | + | 0.451969i | ||||
\(43\) | 0.710831 | + | 0.710831i | 0.108401 | + | 0.108401i | 0.759227 | − | 0.650826i | \(-0.225577\pi\) |
−0.650826 | + | 0.759227i | \(0.725577\pi\) | |||||||
\(44\) | 0.863466 | + | 8.40152i | 0.130172 | + | 1.26658i | ||||
\(45\) | −1.16432 | − | 1.41401i | −0.173567 | − | 0.210788i | ||||
\(46\) | −7.62721 | + | 3.62721i | −1.12457 | + | 0.534803i | ||||
\(47\) | −7.53805 | −1.09954 | −0.549769 | − | 0.835317i | \(-0.685284\pi\) | ||||
−0.549769 | + | 0.835317i | \(0.685284\pi\) | |||||||
\(48\) | −6.84347 | + | 1.08026i | −0.987769 | + | 0.155922i | ||||
\(49\) | 2.62721 | 0.375316 | ||||||||
\(50\) | 5.90964 | − | 2.81040i | 0.835749 | − | 0.397451i | ||||
\(51\) | 4.20304 | + | 0.203037i | 0.588543 | + | 0.0284309i | ||||
\(52\) | −5.91638 | + | 0.608056i | −0.820455 | + | 0.0843223i | ||||
\(53\) | −8.83325 | − | 8.83325i | −1.21334 | − | 1.21334i | −0.969921 | − | 0.243419i | \(-0.921731\pi\) |
−0.243419 | − | 0.969921i | \(-0.578269\pi\) | |||||||
\(54\) | −7.02222 | + | 2.16529i | −0.955603 | + | 0.294658i | ||||
\(55\) | 2.57834 | 0.347663 | ||||||||
\(56\) | 8.52636 | + | 2.07819i | 1.13938 | + | 0.277710i | ||||
\(57\) | 1.17036 | + | 1.28917i | 0.155017 | + | 0.170755i | ||||
\(58\) | 5.39194 | + | 1.91638i | 0.707997 | + | 0.251633i | ||||
\(59\) | −0.0804722 | + | 0.0804722i | −0.0104766 | + | 0.0104766i | −0.712326 | − | 0.701849i | \(-0.752358\pi\) |
0.701849 | + | 0.712326i | \(0.252358\pi\) | |||||||
\(60\) | 0.114465 | + | 2.11195i | 0.0147774 | + | 0.272652i | ||||
\(61\) | −5.72999 | − | 5.72999i | −0.733650 | − | 0.733650i | 0.237691 | − | 0.971341i | \(-0.423609\pi\) |
−0.971341 | + | 0.237691i | \(0.923609\pi\) | |||||||
\(62\) | −0.669785 | + | 0.318525i | −0.0850628 | + | 0.0404527i | ||||
\(63\) | 9.26498 | + | 0.897225i | 1.16728 | + | 0.113040i | ||||
\(64\) | 7.10278 | + | 3.68111i | 0.887847 | + | 0.460139i | ||||
\(65\) | 1.81568i | 0.225207i | ||||||||
\(66\) | 3.93035 | − | 9.56812i | 0.483793 | − | 1.17775i | ||||
\(67\) | −0.391944 | + | 0.391944i | −0.0478835 | + | 0.0478835i | −0.730643 | − | 0.682760i | \(-0.760780\pi\) |
0.682760 | + | 0.730643i | \(0.260780\pi\) | |||||||
\(68\) | −3.76903 | − | 3.06650i | −0.457061 | − | 0.371868i | ||||
\(69\) | 10.3319 | + | 0.499104i | 1.24381 | + | 0.0600850i | ||||
\(70\) | 0.897225 | − | 2.52444i | 0.107239 | − | 0.301728i | ||||
\(71\) | − | 5.01985i | − | 0.595747i | −0.954605 | − | 0.297873i | \(-0.903723\pi\) | ||
0.954605 | − | 0.297873i | \(-0.0962774\pi\) | |||||||
\(72\) | 8.01187 | + | 2.79463i | 0.944208 | + | 0.329350i | ||||
\(73\) | 13.4600i | 1.57537i | 0.616078 | + | 0.787686i | \(0.288721\pi\) | ||||
−0.616078 | + | 0.787686i | \(0.711279\pi\) | |||||||
\(74\) | 2.87282 | + | 1.02105i | 0.333959 | + | 0.118694i | ||||
\(75\) | −8.00523 | − | 0.386711i | −0.924365 | − | 0.0446535i | ||||
\(76\) | −0.205550 | − | 2.00000i | −0.0235782 | − | 0.229416i | ||||
\(77\) | −9.26498 | + | 9.26498i | −1.05584 | + | 1.05584i | ||||
\(78\) | 6.73791 | + | 2.76777i | 0.762918 | + | 0.313388i | ||||
\(79\) | 3.47556i | 0.391031i | 0.980701 | + | 0.195516i | \(0.0626380\pi\) | ||||
−0.980701 | + | 0.195516i | \(0.937362\pi\) | |||||||
\(80\) | 1.33957 | − | 2.04209i | 0.149769 | − | 0.228313i | ||||
\(81\) | 8.83276 | + | 1.72693i | 0.981418 | + | 0.191881i | ||||
\(82\) | 1.10278 | + | 2.31889i | 0.121781 | + | 0.256078i | ||||
\(83\) | 4.55202 | + | 4.55202i | 0.499649 | + | 0.499649i | 0.911329 | − | 0.411680i | \(-0.135058\pi\) |
−0.411680 | + | 0.911329i | \(0.635058\pi\) | |||||||
\(84\) | −8.00040 | − | 7.17776i | −0.872915 | − | 0.783158i | ||||
\(85\) | −1.04888 | + | 1.04888i | −0.113767 | + | 0.113767i | ||||
\(86\) | −0.476105 | + | 1.33957i | −0.0513397 | + | 0.144450i | ||||
\(87\) | −4.71083 | − | 5.18907i | −0.505054 | − | 0.556326i | ||||
\(88\) | −10.2056 | + | 6.20555i | −1.08792 | + | 0.661514i | ||||
\(89\) | 12.5579 | 1.33114 | 0.665568 | − | 0.746338i | \(-0.268190\pi\) | ||||
0.665568 | + | 0.746338i | \(0.268190\pi\) | |||||||
\(90\) | 1.09874 | − | 2.34584i | 0.115817 | − | 0.247273i | ||||
\(91\) | −6.52444 | − | 6.52444i | −0.683947 | − | 0.683947i | ||||
\(92\) | −9.26498 | − | 7.53805i | −0.965941 | − | 0.785896i | ||||
\(93\) | 0.907295 | + | 0.0438289i | 0.0940821 | + | 0.00454485i | ||||
\(94\) | −4.57834 | − | 9.62721i | −0.472219 | − | 0.992971i | ||||
\(95\) | −0.613779 | −0.0629724 | ||||||||
\(96\) | −5.53613 | − | 8.08401i | −0.565029 | − | 0.825071i | ||||
\(97\) | −8.67609 | −0.880923 | −0.440462 | − | 0.897771i | \(-0.645185\pi\) | ||||
−0.440462 | + | 0.897771i | \(0.645185\pi\) | |||||||
\(98\) | 1.59567 | + | 3.35534i | 0.161187 | + | 0.338941i | ||||
\(99\) | −9.77985 | + | 8.05292i | −0.982912 | + | 0.809348i | ||||
\(100\) | 7.17860 | + | 5.84056i | 0.717860 | + | 0.584056i | ||||
\(101\) | 0.182046 | + | 0.182046i | 0.0181142 | + | 0.0181142i | 0.716106 | − | 0.697992i | \(-0.245923\pi\) |
−0.697992 | + | 0.716106i | \(0.745923\pi\) | |||||||
\(102\) | 2.29346 | + | 5.49122i | 0.227087 | + | 0.543712i | ||||
\(103\) | 6.35720 | 0.626394 | 0.313197 | − | 0.949688i | \(-0.398600\pi\) | ||||
0.313197 | + | 0.949688i | \(0.398600\pi\) | |||||||
\(104\) | −4.36997 | − | 7.18679i | −0.428511 | − | 0.704723i | ||||
\(105\) | −2.42945 | + | 2.20555i | −0.237090 | + | 0.215240i | ||||
\(106\) | 5.91638 | − | 16.6464i | 0.574650 | − | 1.61684i | ||||
\(107\) | 1.64646 | − | 1.64646i | 0.159169 | − | 0.159169i | −0.623029 | − | 0.782199i | \(-0.714098\pi\) |
0.782199 | + | 0.623029i | \(0.214098\pi\) | |||||||
\(108\) | −7.03043 | − | 7.65330i | −0.676504 | − | 0.736439i | ||||
\(109\) | 6.57331 | + | 6.57331i | 0.629609 | + | 0.629609i | 0.947970 | − | 0.318360i | \(-0.103132\pi\) |
−0.318360 | + | 0.947970i | \(0.603132\pi\) | |||||||
\(110\) | 1.56599 | + | 3.29292i | 0.149311 | + | 0.313968i | ||||
\(111\) | −2.50993 | − | 2.76473i | −0.238232 | − | 0.262417i | ||||
\(112\) | 2.52444 | + | 12.1517i | 0.238537 | + | 1.14822i | ||||
\(113\) | 8.31277i | 0.782000i | 0.920391 | + | 0.391000i | \(0.127871\pi\) | ||||
−0.920391 | + | 0.391000i | \(0.872129\pi\) | |||||||
\(114\) | −0.935629 | + | 2.27771i | −0.0876297 | + | 0.213327i | ||||
\(115\) | −2.57834 | + | 2.57834i | −0.240431 | + | 0.240431i | ||||
\(116\) | 0.827365 | + | 8.05026i | 0.0768189 | + | 0.747447i | ||||
\(117\) | −5.67090 | − | 6.88701i | −0.524274 | − | 0.636704i | ||||
\(118\) | −0.151651 | − | 0.0538991i | −0.0139606 | − | 0.00496182i | ||||
\(119\) | − | 7.53805i | − | 0.691012i | ||||||
\(120\) | −2.62776 | + | 1.42891i | −0.239880 | + | 0.130441i | ||||
\(121\) | − | 6.83276i | − | 0.621160i | ||||||
\(122\) | 3.83786 | − | 10.7982i | 0.347464 | − | 0.977626i | ||||
\(123\) | 0.151742 | − | 3.14118i | 0.0136821 | − | 0.283231i | ||||
\(124\) | −0.813607 | − | 0.661956i | −0.0730640 | − | 0.0594454i | ||||
\(125\) | 4.15639 | − | 4.15639i | 0.371759 | − | 0.371759i | ||||
\(126\) | 4.48132 | + | 12.3777i | 0.399228 | + | 1.10269i | ||||
\(127\) | − | 15.7789i | − | 1.40015i | −0.714070 | − | 0.700074i | \(-0.753150\pi\) | ||
0.714070 | − | 0.700074i | \(-0.246850\pi\) | |||||||
\(128\) | −0.387362 | + | 11.3071i | −0.0342383 | + | 0.999414i | ||||
\(129\) | 1.28917 | − | 1.17036i | 0.113505 | − | 0.103044i | ||||
\(130\) | −2.31889 | + | 1.10278i | −0.203380 | + | 0.0967198i | ||||
\(131\) | 0.0804722 | + | 0.0804722i | 0.00703089 | + | 0.00703089i | 0.710613 | − | 0.703583i | \(-0.248417\pi\) |
−0.703583 | + | 0.710613i | \(0.748417\pi\) | |||||||
\(132\) | 14.6071 | − | 0.791685i | 1.27138 | − | 0.0689073i | ||||
\(133\) | 2.20555 | − | 2.20555i | 0.191245 | − | 0.191245i | ||||
\(134\) | −0.738623 | − | 0.262518i | −0.0638073 | − | 0.0226781i | ||||
\(135\) | −2.54359 | + | 1.89615i | −0.218918 | + | 0.163194i | ||||
\(136\) | 1.62721 | − | 6.67609i | 0.139532 | − | 0.572470i | ||||
\(137\) | −13.2604 | −1.13291 | −0.566457 | − | 0.824091i | \(-0.691686\pi\) | ||||
−0.566457 | + | 0.824091i | \(0.691686\pi\) | |||||||
\(138\) | 5.63777 | + | 13.4985i | 0.479919 | + | 1.14907i | ||||
\(139\) | 8.39194 | + | 8.39194i | 0.711795 | + | 0.711795i | 0.966911 | − | 0.255115i | \(-0.0821134\pi\) |
−0.255115 | + | 0.966911i | \(0.582113\pi\) | |||||||
\(140\) | 3.76903 | − | 0.387362i | 0.318541 | − | 0.0327380i | ||||
\(141\) | −0.629978 | + | 13.0411i | −0.0530537 | + | 1.09826i | ||||
\(142\) | 6.41110 | − | 3.04888i | 0.538008 | − | 0.255856i | ||||
\(143\) | 12.5579 | 1.05014 | ||||||||
\(144\) | 1.29696 | + | 11.9297i | 0.108080 | + | 0.994142i | ||||
\(145\) | 2.47054 | 0.205167 | ||||||||
\(146\) | −17.1904 | + | 8.17510i | −1.42269 | + | 0.676576i | ||||
\(147\) | 0.219564 | − | 4.54517i | 0.0181094 | − | 0.374879i | ||||
\(148\) | 0.440820 | + | 4.28917i | 0.0362351 | + | 0.352567i | ||||
\(149\) | 5.79002 | + | 5.79002i | 0.474337 | + | 0.474337i | 0.903315 | − | 0.428978i | \(-0.141126\pi\) |
−0.428978 | + | 0.903315i | \(0.641126\pi\) | |||||||
\(150\) | −4.36820 | − | 10.4587i | −0.356662 | − | 0.853953i | ||||
\(151\) | 9.94610 | 0.809402 | 0.404701 | − | 0.914449i | \(-0.367376\pi\) | ||||
0.404701 | + | 0.914449i | \(0.367376\pi\) | |||||||
\(152\) | 2.42945 | − | 1.47725i | 0.197055 | − | 0.119820i | ||||
\(153\) | 0.702522 | − | 7.25443i | 0.0567955 | − | 0.586486i | ||||
\(154\) | −17.4600 | − | 6.20555i | −1.40696 | − | 0.500057i | ||||
\(155\) | −0.226417 | + | 0.226417i | −0.0181863 | + | 0.0181863i | ||||
\(156\) | 0.557507 | + | 10.2864i | 0.0446363 | + | 0.823568i | ||||
\(157\) | −9.15165 | − | 9.15165i | −0.730381 | − | 0.730381i | 0.240314 | − | 0.970695i | \(-0.422750\pi\) |
−0.970695 | + | 0.240314i | \(0.922750\pi\) | |||||||
\(158\) | −4.43881 | + | 2.11093i | −0.353133 | + | 0.167937i | ||||
\(159\) | −16.0200 | + | 14.5436i | −1.27047 | + | 1.15338i | ||||
\(160\) | 3.42166 | + | 0.470539i | 0.270506 | + | 0.0371994i | ||||
\(161\) | − | 18.5300i | − | 1.46037i | ||||||
\(162\) | 3.15915 | + | 12.3296i | 0.248206 | + | 0.968707i | ||||
\(163\) | 15.7003 | − | 15.7003i | 1.22974 | − | 1.22974i | 0.265678 | − | 0.964062i | \(-0.414404\pi\) |
0.964062 | − | 0.265678i | \(-0.0855959\pi\) | |||||||
\(164\) | −2.29178 | + | 2.81682i | −0.178958 | + | 0.219956i | ||||
\(165\) | 0.215480 | − | 4.46061i | 0.0167751 | − | 0.347258i | ||||
\(166\) | −3.04888 | + | 8.57834i | −0.236639 | + | 0.665808i | ||||
\(167\) | 19.1437i | 1.48139i | 0.671843 | + | 0.740694i | \(0.265503\pi\) | ||||
−0.671843 | + | 0.740694i | \(0.734497\pi\) | |||||||
\(168\) | 4.30792 | − | 14.5772i | 0.332363 | − | 1.12466i | ||||
\(169\) | − | 4.15667i | − | 0.319744i | ||||||
\(170\) | −1.97662 | − | 0.702522i | −0.151600 | − | 0.0538810i | ||||
\(171\) | 2.32811 | − | 1.91701i | 0.178035 | − | 0.146598i | ||||
\(172\) | −2.00000 | + | 0.205550i | −0.152499 | + | 0.0156730i | ||||
\(173\) | 13.3281 | − | 13.3281i | 1.01331 | − | 1.01331i | 0.0134040 | − | 0.999910i | \(-0.495733\pi\) |
0.999910 | − | 0.0134040i | \(-0.00426674\pi\) | |||||||
\(174\) | 3.76603 | − | 9.16808i | 0.285502 | − | 0.695031i | ||||
\(175\) | 14.3572i | 1.08530i | ||||||||
\(176\) | −14.1239 | − | 9.26498i | −1.06463 | − | 0.698374i | ||||
\(177\) | 0.132494 | + | 0.145945i | 0.00995889 | + | 0.0109699i | ||||
\(178\) | 7.62721 | + | 16.0383i | 0.571684 | + | 1.20212i | ||||
\(179\) | −9.18451 | − | 9.18451i | −0.686483 | − | 0.686483i | 0.274970 | − | 0.961453i | \(-0.411332\pi\) |
−0.961453 | + | 0.274970i | \(0.911332\pi\) | |||||||
\(180\) | 3.66331 | − | 0.0215261i | 0.273047 | − | 0.00160446i | ||||
\(181\) | −16.5139 | + | 16.5139i | −1.22747 | + | 1.22747i | −0.262548 | + | 0.964919i | \(0.584563\pi\) |
−0.964919 | + | 0.262548i | \(0.915437\pi\) | |||||||
\(182\) | 4.36997 | − | 12.2954i | 0.323924 | − | 0.911395i | ||||
\(183\) | −10.3919 | + | 9.43420i | −0.768195 | + | 0.697396i | ||||
\(184\) | 4.00000 | − | 16.4111i | 0.294884 | − | 1.20984i | ||||
\(185\) | 1.31630 | 0.0967764 | ||||||||
\(186\) | 0.495082 | + | 1.18537i | 0.0363012 | + | 0.0869156i | ||||
\(187\) | 7.25443 | + | 7.25443i | 0.530496 | + | 0.530496i | ||||
\(188\) | 9.51467 | − | 11.6944i | 0.693929 | − | 0.852904i | ||||
\(189\) | 2.32653 | − | 15.9537i | 0.169230 | − | 1.16046i | ||||
\(190\) | −0.372787 | − | 0.783887i | −0.0270448 | − | 0.0568692i | ||||
\(191\) | −3.17852 | −0.229989 | −0.114995 | − | 0.993366i | \(-0.536685\pi\) | ||||
−0.114995 | + | 0.993366i | \(0.536685\pi\) | |||||||
\(192\) | 6.96205 | − | 11.9804i | 0.502443 | − | 0.864611i | ||||
\(193\) | −11.4600 | −0.824907 | −0.412454 | − | 0.910979i | \(-0.635328\pi\) | ||||
−0.412454 | + | 0.910979i | \(0.635328\pi\) | |||||||
\(194\) | −5.26954 | − | 11.0807i | −0.378331 | − | 0.795545i | ||||
\(195\) | 3.14118 | + | 0.151742i | 0.224944 | + | 0.0108664i | ||||
\(196\) | −3.31612 | + | 4.07583i | −0.236866 | + | 0.291130i | ||||
\(197\) | 14.8053 | + | 14.8053i | 1.05483 | + | 1.05483i | 0.998407 | + | 0.0564281i | \(0.0179712\pi\) |
0.0564281 | + | 0.998407i | \(0.482029\pi\) | |||||||
\(198\) | −16.2247 | − | 7.59928i | −1.15304 | − | 0.540057i | ||||
\(199\) | −24.4550 | −1.73357 | −0.866783 | − | 0.498686i | \(-0.833816\pi\) | ||||
−0.866783 | + | 0.498686i | \(0.833816\pi\) | |||||||
\(200\) | −3.09924 | + | 12.7155i | −0.219149 | + | 0.899120i | ||||
\(201\) | 0.645320 | + | 0.710831i | 0.0455173 | + | 0.0501382i | ||||
\(202\) | −0.121932 | + | 0.343068i | −0.00857908 | + | 0.0241382i | ||||
\(203\) | −8.87762 | + | 8.87762i | −0.623087 | + | 0.623087i | ||||
\(204\) | −5.62014 | + | 6.26426i | −0.393489 | + | 0.438586i | ||||
\(205\) | 0.783887 | + | 0.783887i | 0.0547491 | + | 0.0547491i | ||||
\(206\) | 3.86113 | + | 8.11909i | 0.269018 | + | 0.565684i | ||||
\(207\) | 1.72693 | − | 17.8328i | 0.120030 | − | 1.23946i | ||||
\(208\) | 6.52444 | − | 9.94610i | 0.452388 | − | 0.689638i | ||||
\(209\) | 4.24513i | 0.293642i | ||||||||
\(210\) | −4.29238 | − | 1.76320i | −0.296202 | − | 0.121673i | ||||
\(211\) | −6.18639 | + | 6.18639i | −0.425889 | + | 0.425889i | −0.887225 | − | 0.461336i | \(-0.847370\pi\) |
0.461336 | + | 0.887225i | \(0.347370\pi\) | |||||||
\(212\) | 24.8533 | − | 2.55430i | 1.70693 | − | 0.175430i | ||||
\(213\) | −8.68451 | − | 0.419525i | −0.595053 | − | 0.0287454i | ||||
\(214\) | 3.10278 | + | 1.10278i | 0.212101 | + | 0.0753842i | ||||
\(215\) | 0.613779i | 0.0418594i | ||||||||
\(216\) | 5.50438 | − | 13.6272i | 0.374526 | − | 0.927217i | ||||
\(217\) | − | 1.62721i | − | 0.110462i | ||||||
\(218\) | −4.40271 | + | 12.3875i | −0.298189 | + | 0.838987i | ||||
\(219\) | 23.2862 | + | 1.12489i | 1.57354 | + | 0.0760132i | ||||
\(220\) | −3.25443 | + | 4.00000i | −0.219413 | + | 0.269680i | ||||
\(221\) | −5.10860 | + | 5.10860i | −0.343641 | + | 0.343641i | ||||
\(222\) | 2.00653 | − | 4.88475i | 0.134670 | − | 0.327843i | ||||
\(223\) | 8.18996i | 0.548441i | 0.961667 | + | 0.274220i | \(0.0884197\pi\) | ||||
−0.961667 | + | 0.274220i | \(0.911580\pi\) | |||||||
\(224\) | −13.9862 | + | 10.6046i | −0.934493 | + | 0.708547i | ||||
\(225\) | −1.33804 | + | 13.8170i | −0.0892030 | + | 0.921133i | ||||
\(226\) | −10.6167 | + | 5.04888i | −0.706209 | + | 0.335846i | ||||
\(227\) | 9.91030 | + | 9.91030i | 0.657770 | + | 0.657770i | 0.954852 | − | 0.297082i | \(-0.0960135\pi\) |
−0.297082 | + | 0.954852i | \(0.596014\pi\) | |||||||
\(228\) | −3.47725 | + | 0.188462i | −0.230286 | + | 0.0124812i | ||||
\(229\) | 7.15165 | − | 7.15165i | 0.472594 | − | 0.472594i | −0.430159 | − | 0.902753i | \(-0.641542\pi\) |
0.902753 | + | 0.430159i | \(0.141542\pi\) | |||||||
\(230\) | −4.85891 | − | 1.72693i | −0.320387 | − | 0.113871i | ||||
\(231\) | 15.2544 | + | 16.8030i | 1.00367 | + | 1.10556i | ||||
\(232\) | −9.77886 | + | 5.94610i | −0.642014 | + | 0.390381i | ||||
\(233\) | −19.6431 | −1.28686 | −0.643432 | − | 0.765503i | \(-0.722490\pi\) | ||||
−0.643432 | + | 0.765503i | \(0.722490\pi\) | |||||||
\(234\) | 5.35144 | − | 11.4255i | 0.349835 | − | 0.746908i | ||||
\(235\) | −3.25443 | − | 3.25443i | −0.212295 | − | 0.212295i | ||||
\(236\) | −0.0232700 | − | 0.226417i | −0.00151475 | − | 0.0147385i | ||||
\(237\) | 6.01284 | + | 0.290464i | 0.390576 | + | 0.0188676i | ||||
\(238\) | 9.62721 | − | 4.57834i | 0.624040 | − | 0.296770i | ||||
\(239\) | 9.44247 | 0.610782 | 0.305391 | − | 0.952227i | \(-0.401213\pi\) | ||||
0.305391 | + | 0.952227i | \(0.401213\pi\) | |||||||
\(240\) | −3.42094 | − | 2.48817i | −0.220820 | − | 0.160610i | ||||
\(241\) | 16.6167 | 1.07037 | 0.535186 | − | 0.844734i | \(-0.320241\pi\) | ||||
0.535186 | + | 0.844734i | \(0.320241\pi\) | |||||||
\(242\) | 8.72646 | − | 4.14997i | 0.560958 | − | 0.266770i | ||||
\(243\) | 3.72583 | − | 15.1366i | 0.239012 | − | 0.971017i | ||||
\(244\) | 16.1219 | − | 1.65693i | 1.03210 | − | 0.106074i | ||||
\(245\) | 1.13425 | + | 1.13425i | 0.0724649 | + | 0.0724649i | ||||
\(246\) | 4.10392 | − | 1.71404i | 0.261656 | − | 0.109283i | ||||
\(247\) | −2.98944 | −0.190213 | ||||||||
\(248\) | 0.351261 | − | 1.44114i | 0.0223051 | − | 0.0915128i | ||||
\(249\) | 8.25557 | − | 7.49472i | 0.523176 | − | 0.474958i | ||||
\(250\) | 7.83276 | + | 2.78389i | 0.495387 | + | 0.176068i | ||||
\(251\) | 2.03382 | − | 2.03382i | 0.128374 | − | 0.128374i | −0.640001 | − | 0.768374i | \(-0.721066\pi\) |
0.768374 | + | 0.640001i | \(0.221066\pi\) | |||||||
\(252\) | −13.0864 | + | 13.2411i | −0.824364 | + | 0.834110i | ||||
\(253\) | 17.8328 | + | 17.8328i | 1.12114 | + | 1.12114i | ||||
\(254\) | 20.1520 | − | 9.58351i | 1.26445 | − | 0.601323i | ||||
\(255\) | 1.72693 | + | 1.90225i | 0.108145 | + | 0.119123i | ||||
\(256\) | −14.6761 | + | 6.37279i | −0.917256 | + | 0.398299i | ||||
\(257\) | − | 15.0761i | − | 0.940421i | −0.882554 | − | 0.470211i | \(-0.844178\pi\) | ||
0.882554 | − | 0.470211i | \(-0.155822\pi\) | |||||||
\(258\) | 2.27771 | + | 0.935629i | 0.141804 | + | 0.0582497i | ||||
\(259\) | −4.72999 | + | 4.72999i | −0.293907 | + | 0.293907i | ||||
\(260\) | −2.81682 | − | 2.29178i | −0.174692 | − | 0.142130i | ||||
\(261\) | −9.37096 | + | 7.71623i | −0.580048 | + | 0.477623i | ||||
\(262\) | −0.0538991 | + | 0.151651i | −0.00332990 | + | 0.00936903i | ||||
\(263\) | − | 29.8138i | − | 1.83840i | −0.393796 | − | 0.919198i | \(-0.628838\pi\) | ||
0.393796 | − | 0.919198i | \(-0.371162\pi\) | |||||||
\(264\) | 9.88290 | + | 18.1746i | 0.608250 | + | 1.11857i | ||||
\(265\) | − | 7.62721i | − | 0.468536i | ||||||
\(266\) | 4.15639 | + | 1.47725i | 0.254844 | + | 0.0905757i | ||||
\(267\) | 1.04950 | − | 21.7256i | 0.0642285 | − | 1.32958i | ||||
\(268\) | −0.113338 | − | 1.10278i | −0.00692321 | − | 0.0673627i | ||||
\(269\) | −16.3713 | + | 16.3713i | −0.998176 | + | 0.998176i | −0.999998 | − | 0.00182258i | \(-0.999420\pi\) |
0.00182258 | + | 0.999998i | \(0.499420\pi\) | |||||||
\(270\) | −3.96655 | − | 2.09690i | −0.241397 | − | 0.127613i | ||||
\(271\) | − | 13.3466i | − | 0.810751i | −0.914150 | − | 0.405375i | \(-0.867141\pi\) | ||
0.914150 | − | 0.405375i | \(-0.132859\pi\) | |||||||
\(272\) | 9.51467 | − | 1.97662i | 0.576912 | − | 0.119850i | ||||
\(273\) | −11.8328 | + | 10.7422i | −0.716151 | + | 0.650149i | ||||
\(274\) | −8.05390 | − | 16.9355i | −0.486554 | − | 1.02311i | ||||
\(275\) | −13.8170 | − | 13.8170i | −0.833197 | − | 0.833197i | ||||
\(276\) | −13.8154 | + | 15.3988i | −0.831588 | + | 0.926896i | ||||
\(277\) | 10.6811 | − | 10.6811i | 0.641766 | − | 0.641766i | −0.309224 | − | 0.950989i | \(-0.600069\pi\) |
0.950989 | + | 0.309224i | \(0.100069\pi\) | |||||||
\(278\) | −5.62080 | + | 15.8147i | −0.337113 | + | 0.948504i | ||||
\(279\) | 0.151651 | − | 1.56599i | 0.00907911 | − | 0.0937533i | ||||
\(280\) | 2.78389 | + | 4.57834i | 0.166369 | + | 0.273608i | ||||
\(281\) | −17.5943 | −1.04959 | −0.524794 | − | 0.851229i | \(-0.675858\pi\) | ||||
−0.524794 | + | 0.851229i | \(0.675858\pi\) | |||||||
\(282\) | −17.0380 | + | 7.11610i | −1.01460 | + | 0.423758i | ||||
\(283\) | −17.1758 | − | 17.1758i | −1.02100 | − | 1.02100i | −0.999775 | − | 0.0212224i | \(-0.993244\pi\) |
−0.0212224 | − | 0.999775i | \(-0.506756\pi\) | |||||||
\(284\) | 7.78774 | + | 6.33615i | 0.462117 | + | 0.375982i | ||||
\(285\) | −0.0512954 | + | 1.06186i | −0.00303848 | + | 0.0628990i | ||||
\(286\) | 7.62721 | + | 16.0383i | 0.451007 | + | 0.948365i | ||||
\(287\) | −5.63363 | −0.332543 | ||||||||
\(288\) | −14.4483 | + | 8.90208i | −0.851373 | + | 0.524560i | ||||
\(289\) | 11.0978 | 0.652809 | ||||||||
\(290\) | 1.50052 | + | 3.15525i | 0.0881133 | + | 0.185282i | ||||
\(291\) | −0.725088 | + | 15.0099i | −0.0425054 | + | 0.879897i | ||||
\(292\) | −20.8816 | − | 16.9894i | −1.22201 | − | 0.994232i | ||||
\(293\) | −3.72465 | − | 3.72465i | −0.217597 | − | 0.217597i | 0.589888 | − | 0.807485i | \(-0.299172\pi\) |
−0.807485 | + | 0.589888i | \(0.799172\pi\) | |||||||
\(294\) | 5.93821 | − | 2.48015i | 0.346323 | − | 0.144645i | ||||
\(295\) | −0.0694851 | −0.00404558 | ||||||||
\(296\) | −5.21017 | + | 3.16808i | −0.302835 | + | 0.184141i | ||||
\(297\) | 13.1145 | + | 17.5925i | 0.760979 | + | 1.02082i | ||||
\(298\) | −3.87807 | + | 10.9114i | −0.224650 | + | 0.632078i | ||||
\(299\) | −12.5579 | + | 12.5579i | −0.726242 | + | 0.726242i | ||||
\(300\) | 10.7043 | − | 11.9311i | 0.618013 | − | 0.688843i | ||||
\(301\) | −2.20555 | − | 2.20555i | −0.127126 | − | 0.127126i | ||||
\(302\) | 6.04090 | + | 12.7027i | 0.347615 | + | 0.730956i | ||||
\(303\) | 0.330160 | − | 0.299731i | 0.0189672 | − | 0.0172191i | ||||
\(304\) | 3.36222 | + | 2.20555i | 0.192837 | + | 0.126497i | ||||
\(305\) | − | 4.94765i | − | 0.283302i | ||||||
\(306\) | 9.69167 | − | 3.50885i | 0.554036 | − | 0.200588i | ||||
\(307\) | −13.4408 | + | 13.4408i | −0.767108 | + | 0.767108i | −0.977596 | − | 0.210488i | \(-0.932495\pi\) |
0.210488 | + | 0.977596i | \(0.432495\pi\) | |||||||
\(308\) | −2.67914 | − | 26.0680i | −0.152658 | − | 1.48536i | ||||
\(309\) | 0.531291 | − | 10.9982i | 0.0302241 | − | 0.625664i | ||||
\(310\) | −0.426686 | − | 0.151651i | −0.0242341 | − | 0.00861320i | ||||
\(311\) | − | 13.8320i | − | 0.784341i | −0.919893 | − | 0.392170i | \(-0.871724\pi\) | ||
0.919893 | − | 0.392170i | \(-0.128276\pi\) | |||||||
\(312\) | −12.7986 | + | 6.95958i | −0.724578 | + | 0.394008i | ||||
\(313\) | 3.94056i | 0.222734i | 0.993779 | + | 0.111367i | \(0.0355229\pi\) | ||||
−0.993779 | + | 0.111367i | \(0.964477\pi\) | |||||||
\(314\) | 6.12964 | − | 17.2464i | 0.345916 | − | 0.973271i | ||||
\(315\) | 3.61264 | + | 4.38736i | 0.203549 | + | 0.247200i | ||||
\(316\) | −5.39194 | − | 4.38692i | −0.303321 | − | 0.246784i | ||||
\(317\) | 8.92199 | − | 8.92199i | 0.501109 | − | 0.501109i | −0.410673 | − | 0.911782i | \(-0.634706\pi\) |
0.911782 | + | 0.410673i | \(0.134706\pi\) | |||||||
\(318\) | −28.3043 | − | 11.6267i | −1.58723 | − | 0.651994i | ||||
\(319\) | − | 17.0872i | − | 0.956699i | ||||||
\(320\) | 1.47725 | + | 4.65576i | 0.0825805 | + | 0.260265i | ||||
\(321\) | −2.71083 | − | 2.98603i | −0.151304 | − | 0.166664i | ||||
\(322\) | 23.6655 | − | 11.2544i | 1.31883 | − | 0.627185i | ||||
\(323\) | −1.72693 | − | 1.72693i | −0.0960891 | − | 0.0960891i | ||||
\(324\) | −13.8280 | + | 11.5233i | −0.768223 | + | 0.640182i | ||||
\(325\) | 9.72999 | − | 9.72999i | 0.539723 | − | 0.539723i | ||||
\(326\) | 29.5874 | + | 10.5158i | 1.63869 | + | 0.582417i | ||||
\(327\) | 11.9214 | − | 10.8227i | 0.659255 | − | 0.598497i | ||||
\(328\) | −4.98944 | − | 1.21611i | −0.275496 | − | 0.0671486i | ||||
\(329\) | 23.3889 | 1.28947 | ||||||||
\(330\) | 5.82774 | − | 2.43401i | 0.320806 | − | 0.133988i | ||||
\(331\) | 9.44082 | + | 9.44082i | 0.518914 | + | 0.518914i | 0.917243 | − | 0.398328i | \(-0.130410\pi\) |
−0.398328 | + | 0.917243i | \(0.630410\pi\) | |||||||
\(332\) | −12.8076 | + | 1.31630i | −0.702908 | + | 0.0722414i | ||||
\(333\) | −4.99284 | + | 4.11120i | −0.273606 | + | 0.225292i | ||||
\(334\) | −24.4494 | + | 11.6272i | −1.33781 | + | 0.636213i | ||||
\(335\) | −0.338430 | −0.0184904 | ||||||||
\(336\) | 21.2337 | − | 3.35181i | 1.15840 | − | 0.182856i | ||||
\(337\) | 5.94056 | 0.323603 | 0.161801 | − | 0.986823i | \(-0.448270\pi\) | ||||
0.161801 | + | 0.986823i | \(0.448270\pi\) | |||||||
\(338\) | 5.30869 | − | 2.52461i | 0.288755 | − | 0.137321i | ||||
\(339\) | 14.3814 | + | 0.694724i | 0.781089 | + | 0.0377322i | ||||
\(340\) | −0.303302 | − | 2.95112i | −0.0164489 | − | 0.160047i | ||||
\(341\) | 1.56599 | + | 1.56599i | 0.0848030 | + | 0.0848030i | ||||
\(342\) | 3.86233 | + | 1.80902i | 0.208851 | + | 0.0978208i | ||||
\(343\) | 13.5678 | 0.732591 | ||||||||
\(344\) | −1.47725 | − | 2.42945i | −0.0796477 | − | 0.130987i | ||||
\(345\) | 4.24513 | + | 4.67609i | 0.228550 | + | 0.251752i | ||||
\(346\) | 25.1169 | + | 8.92694i | 1.35029 | + | 0.479915i | ||||
\(347\) | −4.09918 | + | 4.09918i | −0.220056 | + | 0.220056i | −0.808522 | − | 0.588466i | \(-0.799732\pi\) |
0.588466 | + | 0.808522i | \(0.299732\pi\) | |||||||
\(348\) | 13.9964 | − | 0.758585i | 0.750283 | − | 0.0406644i | ||||
\(349\) | −8.10278 | − | 8.10278i | −0.433732 | − | 0.433732i | 0.456164 | − | 0.889896i | \(-0.349223\pi\) |
−0.889896 | + | 0.456164i | \(0.849223\pi\) | |||||||
\(350\) | −18.3363 | + | 8.72004i | −0.980116 | + | 0.466106i | ||||
\(351\) | −12.3887 | + | 9.23527i | −0.661259 | + | 0.492942i | ||||
\(352\) | 3.25443 | − | 23.6655i | 0.173461 | − | 1.26138i | ||||
\(353\) | 29.2465i | 1.55664i | 0.627870 | + | 0.778318i | \(0.283927\pi\) | ||||
−0.627870 | + | 0.778318i | \(0.716073\pi\) | |||||||
\(354\) | −0.105921 | + | 0.257857i | −0.00562965 | + | 0.0137049i | ||||
\(355\) | 2.16724 | − | 2.16724i | 0.115025 | − | 0.115025i | ||||
\(356\) | −15.8508 | + | 19.4822i | −0.840092 | + | 1.03255i | ||||
\(357\) | −13.0411 | − | 0.629978i | −0.690207 | − | 0.0333420i | ||||
\(358\) | 6.15165 | − | 17.3083i | 0.325125 | − | 0.914773i | ||||
\(359\) | 21.3235i | 1.12541i | 0.826657 | + | 0.562706i | \(0.190240\pi\) | ||||
−0.826657 | + | 0.562706i | \(0.809760\pi\) | |||||||
\(360\) | 2.25246 | + | 4.66552i | 0.118715 | + | 0.245895i | ||||
\(361\) | 17.9894i | 0.946812i | ||||||||
\(362\) | −31.1206 | − | 11.0608i | −1.63566 | − | 0.581340i | ||||
\(363\) | −11.8209 | − | 0.571035i | −0.620437 | − | 0.0299716i | ||||
\(364\) | 18.3572 | − | 1.88666i | 0.962179 | − | 0.0988880i | ||||
\(365\) | −5.81112 | + | 5.81112i | −0.304168 | + | 0.304168i | ||||
\(366\) | −18.3606 | − | 7.54207i | −0.959722 | − | 0.394230i | ||||
\(367\) | 32.8277i | 1.71359i | 0.515654 | + | 0.856797i | \(0.327549\pi\) | ||||
−0.515654 | + | 0.856797i | \(0.672451\pi\) | |||||||
\(368\) | 23.3889 | − | 4.85891i | 1.21923 | − | 0.253288i | ||||
\(369\) | −5.42166 | − | 0.525036i | −0.282240 | − | 0.0273323i | ||||
\(370\) | 0.799473 | + | 1.68111i | 0.0415626 | + | 0.0873969i | ||||
\(371\) | 27.4076 | + | 27.4076i | 1.42293 | + | 1.42293i | ||||
\(372\) | −1.21320 | + | 1.35224i | −0.0629015 | + | 0.0701106i | ||||
\(373\) | 1.35720 | − | 1.35720i | 0.0702732 | − | 0.0702732i | −0.671097 | − | 0.741370i | \(-0.734176\pi\) |
0.741370 | + | 0.671097i | \(0.234176\pi\) | |||||||
\(374\) | −4.85891 | + | 13.6711i | −0.251248 | + | 0.706914i | ||||
\(375\) | −6.84333 | − | 7.53805i | −0.353388 | − | 0.389263i | ||||
\(376\) | 20.7144 | + | 5.04888i | 1.06826 | + | 0.260376i | ||||
\(377\) | 12.0329 | 0.619724 | ||||||||
\(378\) | 21.7884 | − | 6.71840i | 1.12067 | − | 0.345557i | ||||
\(379\) | −17.3869 | − | 17.3869i | −0.893106 | − | 0.893106i | 0.101708 | − | 0.994814i | \(-0.467569\pi\) |
−0.994814 | + | 0.101708i | \(0.967569\pi\) | |||||||
\(380\) | 0.774723 | − | 0.952209i | 0.0397425 | − | 0.0488473i | ||||
\(381\) | −27.2980 | − | 1.31869i | −1.39852 | − | 0.0675585i | ||||
\(382\) | −1.93051 | − | 4.05944i | −0.0987737 | − | 0.207699i | ||||
\(383\) | 32.9757 | 1.68498 | 0.842491 | − | 0.538711i | \(-0.181088\pi\) | ||||
0.842491 | + | 0.538711i | \(0.181088\pi\) | |||||||
\(384\) | 19.5292 | + | 1.61512i | 0.996598 | + | 0.0824211i | ||||
\(385\) | −8.00000 | −0.407718 | ||||||||
\(386\) | −6.96037 | − | 14.6361i | −0.354274 | − | 0.744958i | ||||
\(387\) | −1.91701 | − | 2.32811i | −0.0974473 | − | 0.118345i | ||||
\(388\) | 10.9511 | − | 13.4600i | 0.555959 | − | 0.683327i | ||||
\(389\) | −3.97434 | − | 3.97434i | −0.201507 | − | 0.201507i | 0.599138 | − | 0.800645i | \(-0.295510\pi\) |
−0.800645 | + | 0.599138i | \(0.795510\pi\) | |||||||
\(390\) | 1.71404 | + | 4.10392i | 0.0867938 | + | 0.207810i | ||||
\(391\) | −14.5089 | −0.733744 | ||||||||
\(392\) | −7.21953 | − | 1.75967i | −0.364641 | − | 0.0888767i | ||||
\(393\) | 0.145945 | − | 0.132494i | 0.00736195 | − | 0.00668346i | ||||
\(394\) | −9.91638 | + | 27.9008i | −0.499580 | + | 1.40562i | ||||
\(395\) | −1.50052 | + | 1.50052i | −0.0754991 | + | 0.0754991i | ||||
\(396\) | −0.148883 | − | 25.3369i | −0.00748164 | − | 1.27323i | ||||
\(397\) | −15.9355 | − | 15.9355i | −0.799782 | − | 0.799782i | 0.183279 | − | 0.983061i | \(-0.441329\pi\) |
−0.983061 | + | 0.183279i | \(0.941329\pi\) | |||||||
\(398\) | −14.8530 | − | 31.2326i | −0.744516 | − | 1.56555i | ||||
\(399\) | −3.63135 | − | 4.00000i | −0.181795 | − | 0.200250i | ||||
\(400\) | −18.1219 | + | 3.76473i | −0.906097 | + | 0.188237i | ||||
\(401\) | − | 29.7716i | − | 1.48672i | −0.668891 | − | 0.743361i | \(-0.733231\pi\) | ||
0.668891 | − | 0.743361i | \(-0.266769\pi\) | |||||||
\(402\) | −0.515894 | + | 1.25590i | −0.0257305 | + | 0.0626387i | ||||
\(403\) | −1.10278 | + | 1.10278i | −0.0549331 | + | 0.0549331i | ||||
\(404\) | −0.512205 | + | 0.0526419i | −0.0254832 | + | 0.00261903i | ||||
\(405\) | 3.06782 | + | 4.55897i | 0.152441 | + | 0.226537i | ||||
\(406\) | −16.7300 | − | 5.94610i | −0.830295 | − | 0.295100i | ||||
\(407\) | − | 9.10404i | − | 0.451270i | ||||||
\(408\) | −11.4139 | − | 3.37307i | −0.565071 | − | 0.166992i | ||||
\(409\) | 15.6655i | 0.774610i | 0.921952 | + | 0.387305i | \(0.126594\pi\) | ||||
−0.921952 | + | 0.387305i | \(0.873406\pi\) | |||||||
\(410\) | −0.525036 | + | 1.47725i | −0.0259297 | + | 0.0729559i | ||||
\(411\) | −1.10821 | + | 22.9410i | −0.0546642 | + | 1.13159i | ||||
\(412\) | −8.02418 | + | 9.86248i | −0.395323 | + | 0.485890i | ||||
\(413\) | 0.249687 | − | 0.249687i | 0.0122863 | − | 0.0122863i | ||||
\(414\) | 23.8240 | − | 8.62542i | 1.17088 | − | 0.423916i | ||||
\(415\) | 3.93051i | 0.192941i | ||||||||
\(416\) | 16.6654 | + | 2.29178i | 0.817086 | + | 0.112364i | ||||
\(417\) | 15.2197 | − | 13.8170i | 0.745311 | − | 0.676621i | ||||
\(418\) | −5.42166 | + | 2.57834i | −0.265182 | + | 0.126111i | ||||
\(419\) | −14.1554 | − | 14.1554i | −0.691538 | − | 0.691538i | 0.271032 | − | 0.962570i | \(-0.412635\pi\) |
−0.962570 | + | 0.271032i | \(0.912635\pi\) | |||||||
\(420\) | −0.355160 | − | 6.55291i | −0.0173300 | − | 0.319749i | ||||
\(421\) | −7.35720 | + | 7.35720i | −0.358568 | + | 0.358568i | −0.863285 | − | 0.504717i | \(-0.831597\pi\) |
0.504717 | + | 0.863285i | \(0.331597\pi\) | |||||||
\(422\) | −11.6583 | − | 4.14356i | −0.567519 | − | 0.201705i | ||||
\(423\) | 22.5089 | + | 2.17977i | 1.09442 | + | 0.105984i | ||||
\(424\) | 18.3572 | + | 30.1900i | 0.891504 | + | 1.46615i | ||||
\(425\) | 11.2416 | 0.545298 | ||||||||
\(426\) | −4.73886 | − | 11.3462i | −0.229599 | − | 0.549726i | ||||
\(427\) | 17.7789 | + | 17.7789i | 0.860380 | + | 0.860380i | ||||
\(428\) | 0.476105 | + | 4.63249i | 0.0230134 | + | 0.223920i | ||||
\(429\) | 1.04950 | − | 21.7256i | 0.0506705 | − | 1.04892i | ||||
\(430\) | −0.783887 | + | 0.372787i | −0.0378024 | + | 0.0179774i | ||||
\(431\) | −20.7097 | −0.997553 | −0.498776 | − | 0.866731i | \(-0.666217\pi\) | ||||
−0.498776 | + | 0.866731i | \(0.666217\pi\) | |||||||
\(432\) | 20.7472 | − | 1.24678i | 0.998199 | − | 0.0599858i | ||||
\(433\) | −23.4005 | −1.12456 | −0.562279 | − | 0.826948i | \(-0.690075\pi\) | ||||
−0.562279 | + | 0.826948i | \(0.690075\pi\) | |||||||
\(434\) | 2.07819 | − | 0.988310i | 0.0997565 | − | 0.0474404i | ||||
\(435\) | 0.206471 | − | 4.27411i | 0.00989951 | − | 0.204928i | ||||
\(436\) | −18.4947 | + | 1.90080i | −0.885736 | + | 0.0910316i | ||||
\(437\) | −4.24513 | − | 4.24513i | −0.203072 | − | 0.203072i | ||||
\(438\) | 12.7065 | + | 30.4232i | 0.607142 | + | 1.45368i | ||||
\(439\) | 20.2594 | 0.966931 | 0.483465 | − | 0.875363i | \(-0.339378\pi\) | ||||
0.483465 | + | 0.875363i | \(0.339378\pi\) | |||||||
\(440\) | −7.08522 | − | 1.72693i | −0.337774 | − | 0.0823283i | ||||
\(441\) | −7.84494 | − | 0.759707i | −0.373569 | − | 0.0361765i | ||||
\(442\) | −9.62721 | − | 3.42166i | −0.457920 | − | 0.162752i | ||||
\(443\) | −4.05264 | + | 4.05264i | −0.192547 | + | 0.192547i | −0.796796 | − | 0.604249i | \(-0.793473\pi\) |
0.604249 | + | 0.796796i | \(0.293473\pi\) | |||||||
\(444\) | 7.45725 | − | 0.404173i | 0.353905 | − | 0.0191812i | ||||
\(445\) | 5.42166 | + | 5.42166i | 0.257011 | + | 0.257011i | ||||
\(446\) | −10.4598 | + | 4.97429i | −0.495286 | + | 0.235539i | ||||
\(447\) | 10.5008 | − | 9.53303i | 0.496671 | − | 0.450897i | ||||
\(448\) | −22.0383 | − | 11.4217i | −1.04121 | − | 0.539623i | ||||
\(449\) | 5.38394i | 0.254084i | 0.991897 | + | 0.127042i | \(0.0405483\pi\) | ||||
−0.991897 | + | 0.127042i | \(0.959452\pi\) | |||||||
\(450\) | −18.4590 | + | 6.68306i | −0.870168 | + | 0.315043i | ||||
\(451\) | 5.42166 | − | 5.42166i | 0.255296 | − | 0.255296i | ||||
\(452\) | −12.8963 | − | 10.4925i | −0.606592 | − | 0.493528i | ||||
\(453\) | 0.831227 | − | 17.2071i | 0.0390544 | − | 0.808459i | ||||
\(454\) | −6.63778 | + | 18.6761i | −0.311526 | + | 0.876512i | ||||
\(455\) | − | 5.63363i | − | 0.264109i | ||||||
\(456\) | −2.35265 | − | 4.32650i | −0.110173 | − | 0.202607i | ||||
\(457\) | − | 28.0766i | − | 1.31337i | −0.754165 | − | 0.656685i | \(-0.771958\pi\) | ||
0.754165 | − | 0.656685i | \(-0.228042\pi\) | |||||||
\(458\) | 13.4774 | + | 4.79007i | 0.629756 | + | 0.223825i | ||||
\(459\) | −12.4917 | − | 1.82166i | −0.583062 | − | 0.0850279i | ||||
\(460\) | −0.745574 | − | 7.25443i | −0.0347626 | − | 0.338239i | ||||
\(461\) | 22.7962 | − | 22.7962i | 1.06172 | − | 1.06172i | 0.0637594 | − | 0.997965i | \(-0.479691\pi\) |
0.997965 | − | 0.0637594i | \(-0.0203090\pi\) | |||||||
\(462\) | −12.1950 | + | 29.6877i | −0.567362 | + | 1.38120i | ||||
\(463\) | 0.740035i | 0.0343923i | 0.999852 | + | 0.0171962i | \(0.00547398\pi\) | ||||
−0.999852 | + | 0.0171962i | \(0.994526\pi\) | |||||||
\(464\) | −13.5334 | − | 8.87762i | −0.628272 | − | 0.412133i | ||||
\(465\) | 0.372787 | + | 0.410632i | 0.0172876 | + | 0.0190426i | ||||
\(466\) | −11.9305 | − | 25.0872i | −0.552670 | − | 1.16214i | ||||
\(467\) | 9.73282 | + | 9.73282i | 0.450381 | + | 0.450381i | 0.895481 | − | 0.445100i | \(-0.146832\pi\) |
−0.445100 | + | 0.895481i | \(0.646832\pi\) | |||||||
\(468\) | 17.8423 | − | 0.104844i | 0.824762 | − | 0.00484641i | ||||
\(469\) | 1.21611 | − | 1.21611i | 0.0561549 | − | 0.0561549i | ||||
\(470\) | 2.17977 | − | 6.13301i | 0.100545 | − | 0.282895i | ||||
\(471\) | −16.5975 | + | 15.0678i | −0.764772 | + | 0.694289i | ||||
\(472\) | 0.275035 | − | 0.167237i | 0.0126595 | − | 0.00769770i | ||||
\(473\) | 4.24513 | 0.195191 | ||||||||
\(474\) | 3.28101 | + | 7.85571i | 0.150702 | + | 0.360825i | ||||
\(475\) | 3.28917 | + | 3.28917i | 0.150917 | + | 0.150917i | ||||
\(476\) | 11.6944 | + | 9.51467i | 0.536014 | + | 0.436104i | ||||
\(477\) | 23.8221 | + | 28.9307i | 1.09074 | + | 1.32464i | ||||
\(478\) | 5.73501 | + | 12.0594i | 0.262313 | + | 0.551586i | ||||
\(479\) | −28.2478 | −1.29067 | −0.645337 | − | 0.763898i | \(-0.723283\pi\) | ||||
−0.645337 | + | 0.763898i | \(0.723283\pi\) | |||||||
\(480\) | 1.10001 | − | 5.88027i | 0.0502082 | − | 0.268396i | ||||
\(481\) | 6.41110 | 0.292321 | ||||||||
\(482\) | 10.0923 | + | 21.2219i | 0.459694 | + | 0.966633i | ||||
\(483\) | −32.0575 | − | 1.54861i | −1.45866 | − | 0.0704641i | ||||
\(484\) | 10.6003 | + | 8.62444i | 0.481830 | + | 0.392020i | ||||
\(485\) | −3.74576 | − | 3.74576i | −0.170086 | − | 0.170086i | ||||
\(486\) | 21.5947 | − | 4.43501i | 0.979555 | − | 0.201176i | ||||
\(487\) | 19.7094 | 0.893117 | 0.446559 | − | 0.894754i | \(-0.352649\pi\) | ||||
0.446559 | + | 0.894754i | \(0.352649\pi\) | |||||||
\(488\) | 11.9080 | + | 19.5837i | 0.539051 | + | 0.886515i | ||||
\(489\) | −25.8499 | − | 28.4741i | −1.16897 | − | 1.28764i | ||||
\(490\) | −0.759707 | + | 2.13752i | −0.0343201 | + | 0.0965632i | ||||
\(491\) | 29.4414 | − | 29.4414i | 1.32867 | − | 1.32867i | 0.422143 | − | 0.906529i | \(-0.361278\pi\) |
0.906529 | − | 0.422143i | \(-0.138722\pi\) | |||||||
\(492\) | 4.68165 | + | 4.20027i | 0.211065 | + | 0.189363i | ||||
\(493\) | 6.95112 | + | 6.95112i | 0.313063 | + | 0.313063i | ||||
\(494\) | −1.81568 | − | 3.81796i | −0.0816911 | − | 0.171778i | ||||
\(495\) | −7.69899 | − | 0.745574i | −0.346044 | − | 0.0335111i | ||||
\(496\) | 2.05390 | − | 0.426686i | 0.0922228 | − | 0.0191588i | ||||
\(497\) | 15.5755i | 0.698656i | ||||||||
\(498\) | 14.5860 | + | 5.99158i | 0.653615 | + | 0.268489i | ||||
\(499\) | 4.43026 | − | 4.43026i | 0.198326 | − | 0.198326i | −0.600956 | − | 0.799282i | \(-0.705213\pi\) |
0.799282 | + | 0.600956i | \(0.205213\pi\) | |||||||
\(500\) | 1.20190 | + | 11.6944i | 0.0537504 | + | 0.522991i | ||||
\(501\) | 33.1193 | + | 1.59990i | 1.47966 | + | 0.0714784i | ||||
\(502\) | 3.83276 | + | 1.36222i | 0.171065 | + | 0.0607990i | ||||
\(503\) | 27.6805i | 1.23421i | 0.786879 | + | 0.617107i | \(0.211696\pi\) | ||||
−0.786879 | + | 0.617107i | \(0.788304\pi\) | |||||||
\(504\) | −24.8590 | − | 8.67111i | −1.10731 | − | 0.386242i | ||||
\(505\) | 0.157190i | 0.00699488i | ||||||||
\(506\) | −11.9441 | + | 33.6061i | −0.530981 | + | 1.49397i | ||||
\(507\) | −7.19119 | − | 0.347386i | −0.319372 | − | 0.0154280i | ||||
\(508\) | 24.4791 | + | 19.9164i | 1.08609 | + | 0.883647i | ||||
\(509\) | −17.3235 | + | 17.3235i | −0.767851 | + | 0.767851i | −0.977728 | − | 0.209877i | \(-0.932694\pi\) |
0.209877 | + | 0.977728i | \(0.432694\pi\) | |||||||
\(510\) | −1.38058 | + | 3.36091i | −0.0611330 | + | 0.148823i | ||||
\(511\) | − | 41.7633i | − | 1.84750i | ||||||
\(512\) | −17.0527 | − | 14.8730i | −0.753631 | − | 0.657298i | ||||
\(513\) | −3.12193 | − | 4.18793i | −0.137837 | − | 0.184902i | ||||
\(514\) | 19.2544 | − | 9.15667i | 0.849276 | − | 0.403884i | ||||
\(515\) | 2.74461 | + | 2.74461i | 0.120942 | + | 0.120942i | ||||
\(516\) | 0.188462 | + | 3.47725i | 0.00829659 | + | 0.153077i | ||||
\(517\) | −22.5089 | + | 22.5089i | −0.989938 | + | 0.989938i | ||||
\(518\) | −8.91372 | − | 3.16808i | −0.391646 | − | 0.139197i | ||||
\(519\) | −21.9441 | − | 24.1719i | −0.963240 | − | 1.06103i | ||||
\(520\) | 1.21611 | − | 4.98944i | 0.0533301 | − | 0.218801i | ||||
\(521\) | 10.1284 | 0.443735 | 0.221868 | − | 0.975077i | \(-0.428785\pi\) | ||||
0.221868 | + | 0.975077i | \(0.428785\pi\) | |||||||
\(522\) | −15.5464 | − | 7.28156i | −0.680445 | − | 0.318705i | ||||
\(523\) | 1.45641 | + | 1.45641i | 0.0636842 | + | 0.0636842i | 0.738232 | − | 0.674547i | \(-0.235661\pi\) |
−0.674547 | + | 0.738232i | \(0.735661\pi\) | |||||||
\(524\) | −0.226417 | + | 0.0232700i | −0.00989108 | + | 0.00101656i | ||||
\(525\) | 24.8384 | + | 1.19988i | 1.08404 | + | 0.0523669i | ||||
\(526\) | 38.0766 | − | 18.1078i | 1.66022 | − | 0.789538i | ||||
\(527\) | −1.27410 | −0.0555006 | ||||||||
\(528\) | −17.2091 | + | 23.6605i | −0.748930 | + | 1.02969i | ||||
\(529\) | −12.6655 | −0.550675 | ||||||||
\(530\) | 9.74109 | − | 4.63249i | 0.423126 | − | 0.201223i | ||||
\(531\) | 0.263563 | − | 0.217023i | 0.0114376 | − | 0.00941798i | ||||
\(532\) | 0.637776 | + | 6.20555i | 0.0276511 | + | 0.269045i | ||||
\(533\) | 3.81796 | + | 3.81796i | 0.165374 | + | 0.165374i | ||||
\(534\) | 28.3842 | − | 11.8550i | 1.22831 | − | 0.513014i | ||||
\(535\) | 1.42166 | 0.0614638 | ||||||||
\(536\) | 1.33957 | − | 0.814535i | 0.0578606 | − | 0.0351825i | ||||
\(537\) | −16.6571 | + | 15.1219i | −0.718806 | + | 0.652560i | ||||
\(538\) | −30.8519 | − | 10.9653i | −1.33012 | − | 0.472746i | ||||
\(539\) | 7.84494 | − | 7.84494i | 0.337905 | − | 0.337905i | ||||
\(540\) | 0.268914 | − | 6.33945i | 0.0115722 | − | 0.272807i | ||||
\(541\) | 5.18996 | + | 5.18996i | 0.223134 | + | 0.223134i | 0.809817 | − | 0.586683i | \(-0.199566\pi\) |
−0.586683 | + | 0.809817i | \(0.699566\pi\) | |||||||
\(542\) | 17.0456 | − | 8.10626i | 0.732173 | − | 0.348194i | ||||
\(543\) | 27.1894 | + | 29.9497i | 1.16681 | + | 1.28526i | ||||
\(544\) | 8.30330 | + | 10.9511i | 0.356001 | + | 0.469526i | ||||
\(545\) | 5.67583i | 0.243126i | ||||||||
\(546\) | −20.9062 | − | 8.58776i | −0.894703 | − | 0.367522i | ||||
\(547\) | 12.6413 | − | 12.6413i | 0.540505 | − | 0.540505i | −0.383172 | − | 0.923677i | \(-0.625168\pi\) |
0.923677 | + | 0.383172i | \(0.125168\pi\) | |||||||
\(548\) | 16.7376 | − | 20.5721i | 0.714993 | − | 0.878795i | ||||
\(549\) | 15.4530 | + | 18.7669i | 0.659518 | + | 0.800950i | ||||
\(550\) | 9.25443 | − | 26.0383i | 0.394610 | − | 1.11028i | ||||
\(551\) | 4.06764i | 0.173287i | ||||||||
\(552\) | −28.0575 | − | 8.29166i | −1.19420 | − | 0.352916i | ||||
\(553\) | − | 10.7839i | − | 0.458578i | ||||||
\(554\) | 20.1287 | + | 7.15405i | 0.855186 | + | 0.303947i | ||||
\(555\) | 0.110007 | − | 2.27724i | 0.00466955 | − | 0.0966636i | ||||
\(556\) | −23.6116 | + | 2.42669i | −1.00136 | + | 0.102914i | ||||
\(557\) | −6.90317 | + | 6.90317i | −0.292497 | + | 0.292497i | −0.838066 | − | 0.545569i | \(-0.816314\pi\) |
0.545569 | + | 0.838066i | \(0.316314\pi\) | |||||||
\(558\) | 2.09211 | − | 0.757443i | 0.0885660 | − | 0.0320651i | ||||
\(559\) | 2.98944i | 0.126440i | ||||||||
\(560\) | −4.15639 | + | 6.33615i | −0.175639 | + | 0.267751i | ||||
\(561\) | 13.1567 | − | 11.9441i | 0.555475 | − | 0.504281i | ||||
\(562\) | −10.6861 | − | 22.4705i | −0.450767 | − | 0.947862i | ||||
\(563\) | −18.3840 | − | 18.3840i | −0.774794 | − | 0.774794i | 0.204146 | − | 0.978940i | \(-0.434558\pi\) |
−0.978940 | + | 0.204146i | \(0.934558\pi\) | |||||||
\(564\) | −19.4366 | − | 17.4380i | −0.818428 | − | 0.734274i | ||||
\(565\) | −3.58890 | + | 3.58890i | −0.150986 | + | 0.150986i | ||||
\(566\) | 11.5041 | − | 32.3681i | 0.483554 | − | 1.36053i | ||||
\(567\) | −27.4061 | − | 5.35828i | −1.15095 | − | 0.225027i | ||||
\(568\) | −3.36222 | + | 13.7944i | −0.141076 | + | 0.578802i | ||||
\(569\) | −43.5570 | −1.82601 | −0.913003 | − | 0.407953i | \(-0.866243\pi\) | ||||
−0.913003 | + | 0.407953i | \(0.866243\pi\) | |||||||
\(570\) | −1.38731 | + | 0.579422i | −0.0581079 | + | 0.0242693i | ||||
\(571\) | 7.00859 | + | 7.00859i | 0.293301 | + | 0.293301i | 0.838383 | − | 0.545082i | \(-0.183502\pi\) |
−0.545082 | + | 0.838383i | \(0.683502\pi\) | |||||||
\(572\) | −15.8508 | + | 19.4822i | −0.662756 | + | 0.814591i | ||||
\(573\) | −0.265638 | + | 5.49894i | −0.0110972 | + | 0.229721i | ||||
\(574\) | −3.42166 | − | 7.19499i | −0.142817 | − | 0.300313i | ||||
\(575\) | 27.6340 | 1.15242 | ||||||||
\(576\) | −20.1446 | − | 13.0458i | −0.839360 | − | 0.543576i | ||||
\(577\) | 28.4494 | 1.18436 | 0.592182 | − | 0.805804i | \(-0.298267\pi\) | ||||
0.592182 | + | 0.805804i | \(0.298267\pi\) | |||||||
\(578\) | 6.74037 | + | 14.1735i | 0.280362 | + | 0.589539i | ||||
\(579\) | −0.957746 | + | 19.8261i | −0.0398026 | + | 0.823946i | ||||
\(580\) | −3.11836 | + | 3.83276i | −0.129483 | + | 0.159147i | ||||
\(581\) | −14.1239 | − | 14.1239i | −0.585958 | − | 0.585958i | ||||
\(582\) | −19.6103 | + | 8.19044i | −0.812873 | + | 0.339504i | ||||
\(583\) | −52.7527 | −2.18479 | ||||||||
\(584\) | 9.01530 | − | 36.9877i | 0.373056 | − | 1.53056i | ||||
\(585\) | 0.525036 | − | 5.42166i | 0.0217076 | − | 0.224158i | ||||
\(586\) | 2.49472 | − | 7.01916i | 0.103056 | − | 0.289959i | ||||
\(587\) | 19.9011 | − | 19.9011i | 0.821405 | − | 0.821405i | −0.164904 | − | 0.986310i | \(-0.552732\pi\) |
0.986310 | + | 0.164904i | \(0.0527315\pi\) | |||||||
\(588\) | 6.77418 | + | 6.07762i | 0.279362 | + | 0.250637i | ||||
\(589\) | −0.372787 | − | 0.372787i | −0.0153604 | − | 0.0153604i | ||||
\(590\) | −0.0422027 | − | 0.0887428i | −0.00173746 | − | 0.00365348i | ||||
\(591\) | 26.8510 | − | 24.3764i | 1.10450 | − | 1.00271i | ||||
\(592\) | −7.21057 | − | 4.72999i | −0.296353 | − | 0.194401i | ||||
\(593\) | 20.4344i | 0.839140i | 0.907723 | + | 0.419570i | \(0.137819\pi\) | ||||
−0.907723 | + | 0.419570i | \(0.862181\pi\) | |||||||
\(594\) | −14.5029 | + | 27.4342i | −0.595063 | + | 1.12564i | ||||
\(595\) | 3.25443 | − | 3.25443i | 0.133418 | − | 0.133418i | ||||
\(596\) | −16.2908 | + | 1.67429i | −0.667298 | + | 0.0685816i | ||||
\(597\) | −2.04378 | + | 42.3079i | −0.0836462 | + | 1.73155i | ||||
\(598\) | −23.6655 | − | 8.41110i | −0.967755 | − | 0.343955i | ||||
\(599\) | 32.6704i | 1.33488i | 0.744665 | + | 0.667438i | \(0.232609\pi\) | ||||
−0.744665 | + | 0.667438i | \(0.767391\pi\) | |||||||
\(600\) | 21.7392 | + | 6.42446i | 0.887499 | + | 0.262278i | ||||
\(601\) | 6.73553i | 0.274748i | 0.990519 | + | 0.137374i | \(0.0438662\pi\) | ||||
−0.990519 | + | 0.137374i | \(0.956134\pi\) | |||||||
\(602\) | 1.47725 | − | 4.15639i | 0.0602080 | − | 0.169402i | ||||
\(603\) | 1.28369 | − | 1.05702i | 0.0522760 | − | 0.0430451i | ||||
\(604\) | −12.5542 | + | 15.4303i | −0.510821 | + | 0.627848i | ||||
\(605\) | 2.94993 | − | 2.94993i | 0.119932 | − | 0.119932i | ||||
\(606\) | 0.583328 | + | 0.239617i | 0.0236961 | + | 0.00973378i | ||||
\(607\) | 21.2388i | 0.862058i | 0.902338 | + | 0.431029i | \(0.141849\pi\) | ||||
−0.902338 | + | 0.431029i | \(0.858151\pi\) | |||||||
\(608\) | −0.774723 | + | 5.63363i | −0.0314192 | + | 0.228474i | ||||
\(609\) | 14.6167 | + | 16.1005i | 0.592297 | + | 0.652426i | ||||
\(610\) | 6.31889 | − | 3.00502i | 0.255844 | − | 0.121670i | ||||
\(611\) | −15.8508 | − | 15.8508i | −0.641256 | − | 0.641256i | ||||
\(612\) | 10.3677 | + | 10.2466i | 0.419089 | + | 0.414193i | ||||
\(613\) | −9.62219 | + | 9.62219i | −0.388637 | + | 0.388637i | −0.874201 | − | 0.485564i | \(-0.838614\pi\) |
0.485564 | + | 0.874201i | \(0.338614\pi\) | |||||||
\(614\) | −25.3294 | − | 9.00246i | −1.02221 | − | 0.363310i | ||||
\(615\) | 1.42166 | − | 1.29064i | 0.0573270 | − | 0.0520436i | ||||
\(616\) | 31.6655 | − | 19.2544i | 1.27584 | − | 0.775783i | ||||
\(617\) | 3.74576 | 0.150798 | 0.0753992 | − | 0.997153i | \(-0.475977\pi\) | ||||
0.0753992 | + | 0.997153i | \(0.475977\pi\) | |||||||
\(618\) | 14.3690 | − | 6.00135i | 0.578005 | − | 0.241410i | ||||
\(619\) | −13.0680 | − | 13.0680i | −0.525249 | − | 0.525249i | 0.393903 | − | 0.919152i | \(-0.371124\pi\) |
−0.919152 | + | 0.393903i | \(0.871124\pi\) | |||||||
\(620\) | −0.0654727 | − | 0.637049i | −0.00262945 | − | 0.0255845i | ||||
\(621\) | −30.7070 | − | 4.47799i | −1.23223 | − | 0.179696i | ||||
\(622\) | 17.6655 | − | 8.40105i | 0.708323 | − | 0.336852i | ||||
\(623\) | −38.9643 | −1.56107 | ||||||||
\(624\) | −16.6618 | − | 12.1187i | −0.667007 | − | 0.485137i | ||||
\(625\) | −19.5472 | −0.781887 | ||||||||
\(626\) | −5.03268 | + | 2.39335i | −0.201147 | + | 0.0956576i | ||||
\(627\) | 7.34422 | + | 0.354779i | 0.293300 | + | 0.0141685i | ||||
\(628\) | 25.7491 | − | 2.64637i | 1.02750 | − | 0.105602i | ||||
\(629\) | 3.70355 | + | 3.70355i | 0.147670 | + | 0.147670i | ||||
\(630\) | −3.40913 | + | 7.27860i | −0.135823 | + | 0.289986i | ||||
\(631\) | −7.51388 | −0.299123 | −0.149561 | − | 0.988752i | \(-0.547786\pi\) | ||||
−0.149561 | + | 0.988752i | \(0.547786\pi\) | |||||||
\(632\) | 2.32788 | − | 9.55077i | 0.0925981 | − | 0.379909i | ||||
\(633\) | 10.1857 | + | 11.2197i | 0.404843 | + | 0.445942i | ||||
\(634\) | 16.8136 | + | 5.97582i | 0.667754 | + | 0.237330i | ||||
\(635\) | 6.81226 | − | 6.81226i | 0.270336 | − | 0.270336i | ||||
\(636\) | −2.34195 | − | 43.2105i | −0.0928645 | − | 1.71341i | ||||
\(637\) | 5.52444 | + | 5.52444i | 0.218886 | + | 0.218886i | ||||
\(638\) | 21.8229 | − | 10.3781i | 0.863976 | − | 0.410874i | ||||
\(639\) | −1.45158 | + | 14.9894i | −0.0574238 | + | 0.592973i | ||||
\(640\) | −5.04888 | + | 4.71440i | −0.199574 | + | 0.186353i | ||||
\(641\) | 27.7227i | 1.09498i | 0.836811 | + | 0.547491i | \(0.184417\pi\) | ||||
−0.836811 | + | 0.547491i | \(0.815583\pi\) | |||||||
\(642\) | 2.16715 | − | 5.27574i | 0.0855304 | − | 0.208217i | ||||
\(643\) | 19.7003 | − | 19.7003i | 0.776903 | − | 0.776903i | −0.202400 | − | 0.979303i | \(-0.564874\pi\) |
0.979303 | + | 0.202400i | \(0.0648742\pi\) | |||||||
\(644\) | 28.7472 | + | 23.3889i | 1.13280 | + | 0.921651i | ||||
\(645\) | 1.06186 | + | 0.0512954i | 0.0418106 | + | 0.00201976i | ||||
\(646\) | 1.15667 | − | 3.25443i | 0.0455087 | − | 0.128044i | ||||
\(647\) | − | 5.29520i | − | 0.208176i | −0.994568 | − | 0.104088i | \(-0.966808\pi\) | ||
0.994568 | − | 0.104088i | \(-0.0331923\pi\) | |||||||
\(648\) | −23.1156 | − | 10.6616i | −0.908065 | − | 0.418828i | ||||
\(649\) | 0.480585i | 0.0188646i | ||||||||
\(650\) | 18.3363 | + | 6.51700i | 0.719208 | + | 0.255618i | ||||
\(651\) | −2.81513 | − | 0.135991i | −0.110334 | − | 0.00532992i | ||||
\(652\) | 4.54002 | + | 44.1744i | 0.177801 | + | 1.73000i | ||||
\(653\) | 29.7039 | − | 29.7039i | 1.16240 | − | 1.16240i | 0.178457 | − | 0.983948i | \(-0.442890\pi\) |
0.983948 | − | 0.178457i | \(-0.0571104\pi\) | |||||||
\(654\) | 21.0628 | + | 8.65210i | 0.823622 | + | 0.338324i | ||||
\(655\) | 0.0694851i | 0.00271501i | ||||||||
\(656\) | −1.47725 | − | 7.11088i | −0.0576767 | − | 0.277633i | ||||
\(657\) | 3.89220 | − | 40.1919i | 0.151849 | − | 1.56804i | ||||
\(658\) | 14.2056 | + | 29.8711i | 0.553790 | + | 1.16450i | ||||
\(659\) | 1.03268 | + | 1.03268i | 0.0402276 | + | 0.0402276i | 0.726934 | − | 0.686707i | \(-0.240944\pi\) |
−0.686707 | + | 0.726934i | \(0.740944\pi\) | |||||||
\(660\) | 6.64815 | + | 5.96456i | 0.258779 | + | 0.232170i | ||||
\(661\) | 29.8277 | − | 29.8277i | 1.16016 | − | 1.16016i | 0.175725 | − | 0.984439i | \(-0.443773\pi\) |
0.984439 | − | 0.175725i | \(-0.0562271\pi\) | |||||||
\(662\) | −6.32332 | + | 17.7913i | −0.245763 | + | 0.691480i | ||||
\(663\) | 8.41110 | + | 9.26498i | 0.326660 | + | 0.359822i | ||||
\(664\) | −9.45998 | − | 15.5577i | −0.367118 | − | 0.603757i | ||||
\(665\) | 1.90442 | 0.0738502 | ||||||||
\(666\) | −8.28308 | − | 3.87961i | −0.320963 | − | 0.150332i | ||||
\(667\) | 17.0872 | + | 17.0872i | 0.661619 | + | 0.661619i | ||||
\(668\) | −29.6994 | − | 24.1636i | −1.14910 | − | 0.934918i | ||||
\(669\) | 14.1689 | + | 0.684461i | 0.547802 | + | 0.0264628i | ||||
\(670\) | −0.205550 | − | 0.432226i | −0.00794109 | − | 0.0166983i | ||||
\(671\) | −34.2198 | −1.32104 | ||||||||
\(672\) | 17.1774 | + | 25.0829i | 0.662631 | + | 0.967593i | ||||
\(673\) | −0.891685 | −0.0343719 | −0.0171860 | − | 0.999852i | \(-0.505471\pi\) | ||||
−0.0171860 | + | 0.999852i | \(0.505471\pi\) | |||||||
\(674\) | 3.60808 | + | 7.58698i | 0.138978 | + | 0.292240i | ||||
\(675\) | 23.7920 | + | 3.46959i | 0.915756 | + | 0.133545i | ||||
\(676\) | 6.44861 | + | 5.24663i | 0.248024 | + | 0.201794i | ||||
\(677\) | −8.13073 | − | 8.13073i | −0.312489 | − | 0.312489i | 0.533384 | − | 0.845873i | \(-0.320920\pi\) |
−0.845873 | + | 0.533384i | \(0.820920\pi\) | |||||||
\(678\) | 7.84746 | + | 18.7891i | 0.301380 | + | 0.721591i | ||||
\(679\) | 26.9200 | 1.03309 | ||||||||
\(680\) | 3.58481 | − | 2.17977i | 0.137471 | − | 0.0835902i | ||||
\(681\) | 17.9734 | − | 16.3169i | 0.688742 | − | 0.625266i | ||||
\(682\) | −1.04888 | + | 2.95112i | −0.0401635 | + | 0.113004i | ||||
\(683\) | −14.5917 | + | 14.5917i | −0.558337 | + | 0.558337i | −0.928834 | − | 0.370497i | \(-0.879187\pi\) |
0.370497 | + | 0.928834i | \(0.379187\pi\) | |||||||
\(684\) | 0.0354419 | + | 6.03150i | 0.00135515 | + | 0.230620i | ||||
\(685\) | −5.72496 | − | 5.72496i | −0.218740 | − | 0.218740i | ||||
\(686\) | 8.24057 | + | 17.3281i | 0.314626 | + | 0.661589i | ||||
\(687\) | −11.7749 | − | 12.9703i | −0.449241 | − | 0.494847i | ||||
\(688\) | 2.20555 | − | 3.36222i | 0.0840858 | − | 0.128184i | ||||
\(689\) | − | 37.1487i | − | 1.41525i | ||||||
\(690\) | −3.39373 | + | 8.26175i | −0.129197 | + | 0.314519i | ||||
\(691\) | −11.2197 | + | 11.2197i | −0.426817 | + | 0.426817i | −0.887543 | − | 0.460726i | \(-0.847589\pi\) |
0.460726 | + | 0.887543i | \(0.347589\pi\) | |||||||
\(692\) | 3.85406 | + | 37.4999i | 0.146509 | + | 1.42553i | ||||
\(693\) | 30.3447 | − | 24.9864i | 1.15270 | − | 0.949154i | ||||
\(694\) | −7.72496 | − | 2.74557i | −0.293236 | − | 0.104221i | ||||
\(695\) | 7.24616i | 0.274863i | ||||||||
\(696\) | 9.46970 | + | 17.4147i | 0.358948 | + | 0.660102i | ||||
\(697\) | 4.41110i | 0.167082i | ||||||||
\(698\) | 5.42712 | − | 15.2698i | 0.205420 | − | 0.577970i | ||||
\(699\) | −1.64164 | + | 33.9833i | −0.0620924 | + | 1.28536i | ||||
\(700\) | −22.2736 | − | 18.1219i | −0.841862 | − | 0.684945i | ||||
\(701\) | −14.7166 | + | 14.7166i | −0.555837 | + | 0.555837i | −0.928120 | − | 0.372282i | \(-0.878575\pi\) |
0.372282 | + | 0.928120i | \(0.378575\pi\) | |||||||
\(702\) | −19.3193 | − | 10.2130i | −0.729158 | − | 0.385466i | ||||
\(703\) | 2.16724i | 0.0817389i | ||||||||
\(704\) | 32.2010 | − | 10.2172i | 1.21362 | − | 0.385075i | ||||
\(705\) | −5.90225 | + | 5.35828i | −0.222292 | + | 0.201805i | ||||
\(706\) | −37.3522 | + | 17.7633i | −1.40577 | + | 0.668530i | ||||
\(707\) | −0.564847 | − | 0.564847i | −0.0212433 | − | 0.0212433i | ||||
\(708\) | −0.393654 | + | 0.0213356i | −0.0147944 | + | 0.000801839i | ||||
\(709\) | −23.2978 | + | 23.2978i | −0.874966 | + | 0.874966i | −0.993009 | − | 0.118043i | \(-0.962338\pi\) |
0.118043 | + | 0.993009i | \(0.462338\pi\) | |||||||
\(710\) | 4.08419 | + | 1.45158i | 0.153277 | + | 0.0544770i | ||||
\(711\) | 1.00502 | − | 10.3781i | 0.0376913 | − | 0.389211i | ||||
\(712\) | −34.5089 | − | 8.41110i | −1.29327 | − | 0.315219i | ||||
\(713\) | −3.13198 | −0.117293 | ||||||||
\(714\) | −7.11610 | − | 17.0380i | −0.266313 | − | 0.637632i | ||||
\(715\) | 5.42166 | + | 5.42166i | 0.202759 | + | 0.202759i | ||||
\(716\) | 25.8416 | − | 2.65587i | 0.965746 | − | 0.0992546i | ||||
\(717\) | 0.789136 | − | 16.3358i | 0.0294708 | − | 0.610071i | ||||
\(718\) | −27.2333 | + | 12.9511i | −1.01634 | + | 0.483332i | ||||
\(719\) | 27.3421 | 1.01969 | 0.509844 | − | 0.860267i | \(-0.329703\pi\) | ||||
0.509844 | + | 0.860267i | \(0.329703\pi\) | |||||||
\(720\) | −4.59051 | + | 5.71039i | −0.171078 | + | 0.212814i | ||||
\(721\) | −19.7250 | −0.734596 | ||||||||
\(722\) | −22.9752 | + | 10.9261i | −0.855048 | + | 0.406628i | ||||
\(723\) | 1.38871 | − | 28.7474i | 0.0516465 | − | 1.06913i | ||||
\(724\) | −4.77529 | − | 46.4635i | −0.177472 | − | 1.72680i | ||||
\(725\) | −13.2393 | − | 13.2393i | −0.491696 | − | 0.491696i | ||||
\(726\) | −6.45029 | − | 15.4439i | −0.239393 | − | 0.573176i | ||||
\(727\) | 24.1517 | 0.895735 | 0.447868 | − | 0.894100i | \(-0.352184\pi\) | ||||
0.447868 | + | 0.894100i | \(0.352184\pi\) | |||||||
\(728\) | 13.5590 | + | 22.2990i | 0.502532 | + | 0.826456i | ||||
\(729\) | −25.8755 | − | 7.71083i | −0.958353 | − | 0.285586i | ||||
\(730\) | −10.9511 | − | 3.89220i | −0.405319 | − | 0.144057i | ||||
\(731\) | −1.72693 | + | 1.72693i | −0.0638729 | + | 0.0638729i | ||||
\(732\) | −1.51919 | − | 28.0300i | −0.0561508 | − | 1.03602i | ||||
\(733\) | −6.00502 | − | 6.00502i | −0.221801 | − | 0.221801i | 0.587456 | − | 0.809256i | \(-0.300130\pi\) |
−0.809256 | + | 0.587456i | \(0.800130\pi\) | |||||||
\(734\) | −41.9259 | + | 19.9384i | −1.54751 | + | 0.735939i | ||||
\(735\) | 2.05709 | − | 1.86751i | 0.0758770 | − | 0.0688840i | ||||
\(736\) | 20.4111 | + | 26.9200i | 0.752363 | + | 0.992283i | ||||
\(737\) | 2.34071i | 0.0862212i | ||||||||
\(738\) | −2.62237 | − | 7.24316i | −0.0965308 | − | 0.266624i | ||||
\(739\) | −10.9008 | + | 10.9008i | −0.400992 | + | 0.400992i | −0.878583 | − | 0.477590i | \(-0.841510\pi\) |
0.477590 | + | 0.878583i | \(0.341510\pi\) | |||||||
\(740\) | −1.66146 | + | 2.04209i | −0.0610765 | + | 0.0750688i | ||||
\(741\) | −0.249837 | + | 5.17183i | −0.00917798 | + | 0.189992i | ||||
\(742\) | −18.3572 | + | 51.6499i | −0.673914 | + | 1.89613i | ||||
\(743\) | − | 1.29064i | − | 0.0473490i | −0.999720 | − | 0.0236745i | \(-0.992463\pi\) | ||
0.999720 | − | 0.0236745i | \(-0.00753652\pi\) | |||||||
\(744\) | −2.46387 | − | 0.728134i | −0.0903299 | − | 0.0266947i | ||||
\(745\) | 4.99948i | 0.183167i | ||||||||
\(746\) | 2.55766 | + | 0.909033i | 0.0936427 | + | 0.0332821i | ||||
\(747\) | −12.2762 | − | 14.9088i | −0.449162 | − | 0.545483i | ||||
\(748\) | −20.4111 | + | 2.09775i | −0.746304 | + | 0.0767014i | ||||
\(749\) | −5.10860 | + | 5.10860i | −0.186664 | + | 0.186664i | ||||
\(750\) | 5.47083 | − | 13.3183i | 0.199766 | − | 0.486315i | ||||
\(751\) | 1.46552i | 0.0534774i | 0.999642 | + | 0.0267387i | \(0.00851221\pi\) | ||||
−0.999642 | + | 0.0267387i | \(0.991488\pi\) | |||||||
\(752\) | 6.13301 | + | 29.5219i | 0.223648 | + | 1.07655i | ||||
\(753\) | −3.34861 | − | 3.68855i | −0.122030 | − | 0.134418i | ||||
\(754\) | 7.30833 | + | 15.3678i | 0.266154 | + | 0.559661i | ||||
\(755\) | 4.29406 | + | 4.29406i | 0.156277 | + | 0.156277i | ||||
\(756\) | 21.8138 | + | 23.7465i | 0.793362 | + | 0.863651i | ||||
\(757\) | 4.71943 | − | 4.71943i | 0.171530 | − | 0.171530i | −0.616121 | − | 0.787651i | \(-0.711297\pi\) |
0.787651 | + | 0.616121i | \(0.211297\pi\) | |||||||
\(758\) | 11.6455 | − | 32.7659i | 0.422984 | − | 1.19011i | ||||
\(759\) | 32.3416 | − | 29.3609i | 1.17393 | − | 1.06573i | ||||
\(760\) | 1.68665 | + | 0.411100i | 0.0611813 | + | 0.0149122i | ||||
\(761\) | 29.1578 | 1.05697 | 0.528485 | − | 0.848943i | \(-0.322760\pi\) | ||||
0.528485 | + | 0.848943i | \(0.322760\pi\) | |||||||
\(762\) | −14.8956 | − | 35.6645i | −0.539612 | − | 1.29199i | ||||
\(763\) | −20.3955 | − | 20.3955i | −0.738367 | − | 0.738367i | ||||
\(764\) | 4.01198 | − | 4.93111i | 0.145148 | − | 0.178401i | ||||
\(765\) | 3.43528 | − | 2.82867i | 0.124203 | − | 0.102271i | ||||
\(766\) | 20.0283 | + | 42.1149i | 0.723651 | + | 1.52167i | ||||
\(767\) | −0.338430 | −0.0122200 | ||||||||
\(768\) | 9.79861 | + | 25.9227i | 0.353577 | + | 0.935405i | ||||
\(769\) | 20.8122 | 0.750505 | 0.375253 | − | 0.926923i | \(-0.377556\pi\) | ||||
0.375253 | + | 0.926923i | \(0.377556\pi\) | |||||||
\(770\) | −4.85891 | − | 10.2172i | −0.175103 | − | 0.368202i | ||||
\(771\) | −26.0822 | − | 1.25996i | −0.939326 | − | 0.0453762i | ||||
\(772\) | 14.4650 | − | 17.7789i | 0.520607 | − | 0.639875i | ||||
\(773\) | −26.6607 | − | 26.6607i | −0.958918 | − | 0.958918i | 0.0402703 | − | 0.999189i | \(-0.487178\pi\) |
−0.999189 | + | 0.0402703i | \(0.987178\pi\) | |||||||
\(774\) | 1.80902 | − | 3.86233i | 0.0650240 | − | 0.138828i | ||||
\(775\) | 2.42669 | 0.0871691 | ||||||||
\(776\) | 23.8417 | + | 5.81112i | 0.855867 | + | 0.208607i | ||||
\(777\) | 7.78774 | + | 8.57834i | 0.279384 | + | 0.307746i | ||||
\(778\) | 2.66196 | − | 7.48970i | 0.0954357 | − | 0.268519i | ||||
\(779\) | −1.29064 | + | 1.29064i | −0.0462419 | + | 0.0462419i | ||||
\(780\) | −4.20027 | + | 4.68165i | −0.150394 | + | 0.167630i | ||||
\(781\) | −14.9894 | − | 14.9894i | −0.536364 | − | 0.536364i | ||||
\(782\) | −8.81215 | − | 18.5300i | −0.315122 | − | 0.662630i | ||||
\(783\) | 12.5662 | + | 16.8569i | 0.449078 | + | 0.602418i | ||||
\(784\) | −2.13752 | − | 10.2892i | −0.0763399 | − | 0.367470i | ||||
\(785\) | − | 7.90214i | − | 0.282040i | ||||||
\(786\) | 0.257857 | + | 0.105921i | 0.00919744 | + | 0.00377809i | ||||
\(787\) | −32.7875 | + | 32.7875i | −1.16875 | + | 1.16875i | −0.186243 | + | 0.982504i | \(0.559631\pi\) |
−0.982504 | + | 0.186243i | \(0.940369\pi\) | |||||||
\(788\) | −41.6563 | + | 4.28123i | −1.48395 | + | 0.152513i | ||||
\(789\) | −51.5788 | − | 2.49163i | −1.83625 | − | 0.0887044i | ||||
\(790\) | −2.82774 | − | 1.00502i | −0.100606 | − | 0.0357571i | ||||
\(791\) | − | 25.7927i | − | 0.917082i | ||||||
\(792\) | 32.2685 | − | 15.5788i | 1.14661 | − | 0.553570i | ||||
\(793\) | − | 24.0978i | − | 0.855736i | ||||||
\(794\) | 10.6734 | − | 30.0307i | 0.378784 | − | 1.06575i | ||||
\(795\) | −13.1953 | − | 0.637430i | −0.467990 | − | 0.0226073i | ||||
\(796\) | 30.8675 | − | 37.9391i | 1.09407 | − | 1.34472i | ||||
\(797\) | −11.2627 | + | 11.2627i | −0.398945 | + | 0.398945i | −0.877861 | − | 0.478916i | \(-0.841030\pi\) |
0.478916 | + | 0.877861i | \(0.341030\pi\) | |||||||
\(798\) | 2.90305 | − | 7.06723i | 0.102767 | − | 0.250177i | ||||
\(799\) | − | 18.3133i | − | 0.647880i | ||||||
\(800\) | −15.8147 | − | 20.8578i | −0.559135 | − | 0.737436i | ||||
\(801\) | −37.4983 | − | 3.63135i | −1.32494 | − | 0.128307i | ||||
\(802\) | 38.0227 | − | 18.0822i | 1.34263 | − | 0.638503i | ||||
\(803\) | 40.1919 | + | 40.1919i | 1.41834 | + | 1.41834i | ||||
\(804\) | −1.91731 | + | 0.103916i | −0.0676183 | + | 0.00366483i | ||||
\(805\) | 8.00000 | − | 8.00000i | 0.281963 | − | 0.281963i | ||||
\(806\) | −2.07819 | − | 0.738623i | −0.0732012 | − | 0.0260169i | ||||
\(807\) | 26.9547 | + | 29.6911i | 0.948850 | + | 1.04518i | ||||
\(808\) | −0.378326 | − | 0.622190i | −0.0133095 | − | 0.0218886i | ||||
\(809\) | 48.5934 | 1.70845 | 0.854227 | − | 0.519900i | \(-0.174031\pi\) | ||||
0.854227 | + | 0.519900i | \(0.174031\pi\) | |||||||
\(810\) | −3.95920 | + | 6.68702i | −0.139112 | + | 0.234958i | ||||
\(811\) | 19.2197 | + | 19.2197i | 0.674894 | + | 0.674894i | 0.958840 | − | 0.283946i | \(-0.0916436\pi\) |
−0.283946 | + | 0.958840i | \(0.591644\pi\) | |||||||
\(812\) | −2.56713 | − | 24.9781i | −0.0900886 | − | 0.876561i | ||||
\(813\) | −23.0901 | − | 1.11542i | −0.809806 | − | 0.0391195i | ||||
\(814\) | 11.6272 | − | 5.52946i | 0.407534 | − | 0.193808i | ||||
\(815\) | 13.5567 | 0.474869 | ||||||||
\(816\) | −2.62445 | − | 16.6259i | −0.0918740 | − | 0.582023i | ||||
\(817\) | −1.01056 | −0.0353551 | ||||||||
\(818\) | −20.0072 | + | 9.51467i | −0.699536 | + | 0.332673i | ||||
\(819\) | 17.5955 | + | 21.3688i | 0.614837 | + | 0.746688i | ||||
\(820\) | −2.20555 | + | 0.226676i | −0.0770212 | + | 0.00791585i | ||||
\(821\) | 33.7881 | + | 33.7881i | 1.17921 | + | 1.17921i | 0.979945 | + | 0.199268i | \(0.0638565\pi\) |
0.199268 | + | 0.979945i | \(0.436143\pi\) | |||||||
\(822\) | −29.9721 | + | 12.5182i | −1.04540 | + | 0.436621i | ||||
\(823\) | −4.37833 | −0.152619 | −0.0763094 | − | 0.997084i | \(-0.524314\pi\) | ||||
−0.0763094 | + | 0.997084i | \(0.524314\pi\) | |||||||
\(824\) | −17.4695 | − | 4.25796i | −0.608577 | − | 0.148333i | ||||
\(825\) | −25.0586 | + | 22.7491i | −0.872429 | + | 0.792024i | ||||
\(826\) | 0.470539 | + | 0.167237i | 0.0163721 | + | 0.00581892i | ||||
\(827\) | −14.2044 | + | 14.2044i | −0.493934 | + | 0.493934i | −0.909543 | − | 0.415609i | \(-0.863568\pi\) |
0.415609 | + | 0.909543i | \(0.363568\pi\) | |||||||
\(828\) | 25.4858 | + | 25.1880i | 0.885691 | + | 0.875343i | ||||
\(829\) | 14.8483 | + | 14.8483i | 0.515704 | + | 0.515704i | 0.916269 | − | 0.400564i | \(-0.131186\pi\) |
−0.400564 | + | 0.916269i | \(0.631186\pi\) | |||||||
\(830\) | −5.01985 | + | 2.38725i | −0.174242 | + | 0.0828627i | ||||
\(831\) | −17.5860 | − | 19.3713i | −0.610053 | − | 0.671984i | ||||
\(832\) | 7.19499 | + | 22.6761i | 0.249441 | + | 0.786152i | ||||
\(833\) | 6.38269i | 0.221147i | ||||||||
\(834\) | 26.8903 | + | 11.0459i | 0.931133 | + | 0.382487i | ||||
\(835\) | −8.26499 | + | 8.26499i | −0.286022 | + | 0.286022i | ||||
\(836\) | −6.58584 | − | 5.35828i | −0.227776 | − | 0.185320i | ||||
\(837\) | −2.69654 | − | 0.393236i | −0.0932060 | − | 0.0135922i | ||||
\(838\) | 9.48110 | − | 26.6761i | 0.327519 | − | 0.921510i | ||||
\(839\) | − | 3.11543i | − | 0.107557i | −0.998553 | − | 0.0537784i | \(-0.982874\pi\) | ||
0.998553 | − | 0.0537784i | \(-0.0171265\pi\) | |||||||
\(840\) | 8.15333 | − | 4.43359i | 0.281317 | − | 0.152973i | ||||
\(841\) | 12.6272i | 0.435421i | ||||||||
\(842\) | −13.8647 | − | 4.92775i | −0.477810 | − | 0.169821i | ||||
\(843\) | −1.47041 | + | 30.4387i | −0.0506436 | + | 1.04837i | ||||
\(844\) | −1.78891 | − | 17.4061i | −0.0615768 | − | 0.599142i | ||||
\(845\) | 1.79457 | − | 1.79457i | 0.0617352 | − | 0.0617352i | ||||
\(846\) | 10.8872 | + | 30.0711i | 0.374309 | + | 1.03386i | ||||
\(847\) | 21.2005i | 0.728459i | ||||||||
\(848\) | −27.4076 | + | 41.7812i | −0.941180 | + | 1.43477i | ||||
\(849\) | −31.1502 | + | 28.2793i | −1.06907 | + | 0.970544i | ||||
\(850\) | 6.82774 | + | 14.3572i | 0.234190 | + | 0.492448i | ||||
\(851\) | 9.10404 | + | 9.10404i | 0.312082 | + | 0.312082i | ||||
\(852\) | 11.6126 | − | 12.9435i | 0.397841 | − | 0.443437i | ||||
\(853\) | 35.4550 | − | 35.4550i | 1.21395 | − | 1.21395i | 0.244240 | − | 0.969715i | \(-0.421462\pi\) |
0.969715 | − | 0.244240i | \(-0.0785383\pi\) | |||||||
\(854\) | −11.9080 | + | 33.5045i | −0.407484 | + | 1.14650i | ||||
\(855\) | 1.83276 | + | 0.177486i | 0.0626792 | + | 0.00606988i | ||||
\(856\) | −5.62721 | + | 3.42166i | −0.192334 | + | 0.116950i | ||||
\(857\) | 14.0817 | 0.481021 | 0.240511 | − | 0.970646i | \(-0.422685\pi\) | ||||
0.240511 | + | 0.970646i | \(0.422685\pi\) | |||||||
\(858\) | 28.3842 | − | 11.8550i | 0.969022 | − | 0.404722i | ||||
\(859\) | −30.9547 | − | 30.9547i | −1.05616 | − | 1.05616i | −0.998326 | − | 0.0578344i | \(-0.981580\pi\) |
−0.0578344 | − | 0.998326i | \(-0.518420\pi\) | |||||||
\(860\) | −0.952209 | − | 0.774723i | −0.0324701 | − | 0.0264179i | ||||
\(861\) | −0.470820 | + | 9.74637i | −0.0160455 | + | 0.332155i | ||||
\(862\) | −12.5783 | − | 26.4494i | −0.428420 | − | 0.900871i | ||||
\(863\) | −14.4458 | −0.491740 | −0.245870 | − | 0.969303i | \(-0.579074\pi\) | ||||
−0.245870 | + | 0.969303i | \(0.579074\pi\) | |||||||
\(864\) | 14.1934 | + | 25.7400i | 0.482870 | + | 0.875692i | ||||
\(865\) | 11.5083 | 0.391295 | ||||||||
\(866\) | −14.2126 | − | 29.8860i | −0.482965 | − | 1.01557i | ||||
\(867\) | 0.927474 | − | 19.1995i | 0.0314987 | − | 0.652049i | ||||
\(868\) | 2.52444 | + | 2.05390i | 0.0856850 | + | 0.0697139i | ||||
\(869\) | 10.3781 | + | 10.3781i | 0.352054 | + | 0.352054i | ||||
\(870\) | 5.58408 | − | 2.33225i | 0.189318 | − | 0.0790706i | ||||
\(871\) | −1.64834 | −0.0558518 | ||||||||
\(872\) | −13.6606 | − | 22.4660i | −0.462607 | − | 0.760796i | ||||
\(873\) | 25.9071 | + | 2.50885i | 0.876822 | + | 0.0849118i | ||||
\(874\) | 2.84333 | − | 8.00000i | 0.0961769 | − | 0.270604i | ||||
\(875\) | −12.8963 | + | 12.8963i | −0.435976 | + | 0.435976i | ||||
\(876\) | −31.1374 | + | 34.7061i | −1.05204 | + | 1.17261i | ||||
\(877\) | 11.3672 | + | 11.3672i | 0.383845 | + | 0.383845i | 0.872485 | − | 0.488641i | \(-0.162507\pi\) |
−0.488641 | + | 0.872485i | \(0.662507\pi\) | |||||||
\(878\) | 12.3049 | + | 25.8743i | 0.415269 | + | 0.873217i | ||||
\(879\) | −6.75506 | + | 6.13249i | −0.227842 | + | 0.206844i | ||||
\(880\) | −2.09775 | − | 10.0978i | −0.0707152 | − | 0.340395i | ||||
\(881\) | 10.2172i | 0.344226i | 0.985077 | + | 0.172113i | \(0.0550594\pi\) | ||||
−0.985077 | + | 0.172113i | \(0.944941\pi\) | |||||||
\(882\) | −3.79447 | − | 10.4806i | −0.127766 | − | 0.352899i | ||||
\(883\) | 0.230246 | − | 0.230246i | 0.00774840 | − | 0.00774840i | −0.703222 | − | 0.710970i | \(-0.748256\pi\) |
0.710970 | + | 0.703222i | \(0.248256\pi\) | |||||||
\(884\) | −1.47725 | − | 14.3736i | −0.0496851 | − | 0.483436i | ||||
\(885\) | −0.00580708 | + | 0.120211i | −0.000195203 | + | 0.00404087i | ||||
\(886\) | −7.63726 | − | 2.71440i | −0.256579 | − | 0.0911921i | ||||
\(887\) | − | 34.2664i | − | 1.15055i | −0.817959 | − | 0.575276i | \(-0.804895\pi\) | ||
0.817959 | − | 0.575276i | \(-0.195105\pi\) | |||||||
\(888\) | 5.04545 | + | 9.27853i | 0.169314 | + | 0.311367i | ||||
\(889\) | 48.9583i | 1.64201i | ||||||||
\(890\) | −3.63135 | + | 10.2172i | −0.121723 | + | 0.342481i | ||||
\(891\) | 31.5316 | − | 21.2182i | 1.05635 | − | 0.710837i | ||||
\(892\) | −12.7058 | − | 10.3375i | −0.425422 | − | 0.346126i | ||||
\(893\) | 5.35828 | − | 5.35828i | 0.179308 | − | 0.179308i | ||||
\(894\) | 18.5529 | + | 7.62108i | 0.620502 | + | 0.254887i | ||||
\(895\) | − | 7.93051i | − | 0.265088i | ||||||
\(896\) | 1.20190 | − | 35.0833i | 0.0401525 | − | 1.17205i | ||||
\(897\) | 20.6761 | + | 22.7751i | 0.690355 | + | 0.760438i | ||||
\(898\) | −6.87610 | + | 3.27001i | −0.229458 | + | 0.109122i | ||||
\(899\) | 1.50052 | + | 1.50052i | 0.0500450 | + | 0.0500450i | ||||
\(900\) | −19.7466 | − | 19.5159i | −0.658221 | − | 0.650530i | ||||
\(901\) | 21.4600 | − | 21.4600i | 0.714935 | − | 0.714935i | ||||
\(902\) | 10.2172 | + | 3.63135i | 0.340195 | + | 0.120911i | ||||
\(903\) | −4.00000 | + | 3.63135i | −0.133112 | + | 0.120844i | ||||
\(904\) | 5.56777 | − | 22.8433i | 0.185181 | − | 0.759758i | ||||
\(905\) | −14.2592 | −0.473991 | ||||||||
\(906\) | 22.4809 | − | 9.38936i | 0.746877 | − | 0.311941i | ||||
\(907\) | −26.5436 | − | 26.5436i | −0.881366 | − | 0.881366i | 0.112308 | − | 0.993673i | \(-0.464176\pi\) |
−0.993673 | + | 0.112308i | \(0.964176\pi\) | |||||||
\(908\) | −27.8837 | + | 2.86575i | −0.925353 | + | 0.0951032i | ||||
\(909\) | −0.490953 | − | 0.596236i | −0.0162839 | − | 0.0197759i | ||||
\(910\) | 7.19499 | − | 3.42166i | 0.238512 | − | 0.113427i | ||||
\(911\) | 24.1636 | 0.800576 | 0.400288 | − | 0.916389i | \(-0.368910\pi\) | ||||
0.400288 | + | 0.916389i | \(0.368910\pi\) | |||||||
\(912\) | 4.09667 | − | 5.63244i | 0.135654 | − | 0.186509i | ||||
\(913\) | 27.1849 | 0.899690 | ||||||||
\(914\) | 35.8580 | − | 17.0527i | 1.18608 | − | 0.564054i | ||||
\(915\) | −8.55960 | − | 0.413491i | −0.282972 | − | 0.0136696i | ||||
\(916\) | 2.06803 | + | 20.1219i | 0.0683297 | + | 0.664847i | ||||
\(917\) | −0.249687 | − | 0.249687i | −0.00824540 | − | 0.00824540i | ||||
\(918\) | −5.26046 | − | 17.0602i | −0.173621 | − | 0.563069i | ||||
\(919\) | −25.8272 | −0.851961 | −0.425981 | − | 0.904732i | \(-0.640071\pi\) | ||||
−0.425981 | + | 0.904732i | \(0.640071\pi\) | |||||||
\(920\) | 8.81215 | − | 5.35828i | 0.290528 | − | 0.176657i | ||||
\(921\) | 22.1298 | + | 24.3764i | 0.729201 | + | 0.803228i | ||||
\(922\) | 42.9597 | + | 15.2686i | 1.41480 | + | 0.502843i | ||||
\(923\) | 10.5556 | − | 10.5556i | 0.347443 | − | 0.347443i | ||||
\(924\) | −45.3224 | + | 2.45642i | −1.49100 | + | 0.0808103i | ||||
\(925\) | −7.05390 | − | 7.05390i | −0.231931 | − | 0.231931i | ||||
\(926\) | −0.945134 | + | 0.449470i | −0.0310590 | + | 0.0147705i | ||||
\(927\) | −18.9828 | − | 1.83830i | −0.623477 | − | 0.0603778i | ||||
\(928\) | 3.11836 | − | 22.6761i | 0.102365 | − | 0.744379i | ||||
\(929\) | − | 29.6272i | − | 0.972036i | −0.873949 | − | 0.486018i | \(-0.838449\pi\) | ||
0.873949 | − | 0.486018i | \(-0.161551\pi\) | |||||||
\(930\) | −0.298021 | + | 0.725507i | −0.00977248 | + | 0.0237903i | ||||
\(931\) | −1.86751 | + | 1.86751i | −0.0612050 | + | 0.0612050i | ||||
\(932\) | 24.7939 | − | 30.4741i | 0.812152 | − | 0.998212i | ||||
\(933\) | −23.9298 | − | 1.15598i | −0.783427 | − | 0.0378452i | ||||
\(934\) | −6.51890 | + | 18.3416i | −0.213305 | + | 0.600156i | ||||
\(935\) | 6.26395i | 0.204853i | ||||||||
\(936\) | 10.9707 | + | 22.7236i | 0.358588 | + | 0.742745i | ||||
\(937\) | − | 33.4005i | − | 1.09115i | −0.838063 | − | 0.545574i | \(-0.816312\pi\) | ||
0.838063 | − | 0.545574i | \(-0.183688\pi\) | |||||||
\(938\) | 2.29178 | + | 0.814535i | 0.0748293 | + | 0.0265955i | ||||
\(939\) | 6.81730 | + | 0.329325i | 0.222474 | + | 0.0107471i | ||||
\(940\) | 9.15667 | − | 0.941078i | 0.298658 | − | 0.0306946i | ||||
\(941\) | −15.6688 | + | 15.6688i | −0.510788 | + | 0.510788i | −0.914768 | − | 0.403980i | \(-0.867626\pi\) |
0.403980 | + | 0.914768i | \(0.367626\pi\) | |||||||
\(942\) | −29.3246 | − | 12.0458i | −0.955446 | − | 0.392474i | ||||
\(943\) | 10.8433i | 0.353107i | ||||||||
\(944\) | 0.380633 | + | 0.249687i | 0.0123885 | + | 0.00812663i | ||||
\(945\) | 7.89220 | − | 5.88332i | 0.256733 | − | 0.191384i | ||||
\(946\) | 2.57834 | + | 5.42166i | 0.0838290 | + | 0.176273i | ||||
\(947\) | −21.4040 | − | 21.4040i | −0.695536 | − | 0.695536i | 0.267908 | − | 0.963444i | \(-0.413668\pi\) |
−0.963444 | + | 0.267908i | \(0.913668\pi\) | |||||||
\(948\) | −8.04014 | + | 8.96161i | −0.261132 | + | 0.291060i | ||||
\(949\) | −28.3033 | + | 28.3033i | −0.918764 | + | 0.918764i | ||||
\(950\) | −2.20304 | + | 6.19848i | −0.0714760 | + | 0.201105i | ||||
\(951\) | −14.6897 | − | 16.1810i | −0.476346 | − | 0.524704i | ||||
\(952\) | −5.04888 | + | 20.7144i | −0.163635 | + | 0.671358i | ||||
\(953\) | −30.7403 | −0.995777 | −0.497888 | − | 0.867241i | \(-0.665891\pi\) | ||||
−0.497888 | + | 0.867241i | \(0.665891\pi\) | |||||||
\(954\) | −22.4801 | + | 47.9957i | −0.727820 | + | 1.55392i | ||||
\(955\) | −1.37227 | − | 1.37227i | −0.0444056 | − | 0.0444056i | ||||
\(956\) | −11.9185 | + | 14.6489i | −0.385471 | + | 0.473780i | ||||
\(957\) | −29.5614 | − | 1.42803i | −0.955585 | − | 0.0461616i | ||||
\(958\) | −17.1567 | − | 36.0766i | −0.554307 | − | 1.16558i | ||||
\(959\) | 41.1441 | 1.32861 | ||||||||
\(960\) | 8.17808 | − | 2.16659i | 0.263946 | − | 0.0699263i | ||||
\(961\) | 30.7250 | 0.991128 | ||||||||
\(962\) | 3.89387 | + | 8.18793i | 0.125543 | + | 0.263989i | ||||
\(963\) | −5.39249 | + | 4.44028i | −0.173770 | + | 0.143086i | ||||
\(964\) | −20.9739 | + | 25.7789i | −0.675522 | + | 0.830281i | ||||
\(965\) | −4.94765 | − | 4.94765i | −0.159271 | − | 0.159271i | ||||
\(966\) | −17.4927 | − | 41.8827i | −0.562819 | − | 1.34755i | ||||
\(967\) | −15.8172 | −0.508646 | −0.254323 | − | 0.967119i | \(-0.581853\pi\) | ||||
−0.254323 | + | 0.967119i | \(0.581853\pi\) | |||||||
\(968\) | −4.57648 | + | 18.7763i | −0.147094 | + | 0.603493i | ||||
\(969\) | −3.13198 | + | 2.84333i | −0.100614 | + | 0.0913408i | ||||
\(970\) | 2.50885 | − | 7.05892i | 0.0805544 | − | 0.226648i | ||||
\(971\) | −13.8170 | + | 13.8170i | −0.443409 | + | 0.443409i | −0.893156 | − | 0.449747i | \(-0.851514\pi\) |
0.449747 | + | 0.893156i | \(0.351514\pi\) | |||||||
\(972\) | 18.7800 | + | 24.8860i | 0.602369 | + | 0.798218i | ||||
\(973\) | −26.0383 | − | 26.0383i | −0.834750 | − | 0.834750i | ||||
\(974\) | 11.9708 | + | 25.1718i | 0.383568 | + | 0.806557i | ||||
\(975\) | −16.0200 | − | 17.6464i | −0.513052 | − | 0.565136i | ||||
\(976\) | −17.7789 | + | 27.1028i | −0.569088 | + | 0.867539i | ||||
\(977\) | 16.1005i | 0.515101i | 0.966265 | + | 0.257550i | \(0.0829154\pi\) | ||||
−0.966265 | + | 0.257550i | \(0.917085\pi\) | |||||||
\(978\) | 20.6654 | − | 50.3083i | 0.660807 | − | 1.60868i | ||||
\(979\) | 37.4983 | − | 37.4983i | 1.19845 | − | 1.19845i | ||||
\(980\) | −3.19135 | + | 0.327991i | −0.101944 | + | 0.0104773i | ||||
\(981\) | −17.7273 | − | 21.5289i | −0.565990 | − | 0.687365i | ||||
\(982\) | 55.4827 | + | 19.7194i | 1.77052 | + | 0.629272i | ||||
\(983\) | − | 37.0765i | − | 1.18256i | −0.806468 | − | 0.591278i | \(-0.798624\pi\) | ||
0.806468 | − | 0.591278i | \(-0.201376\pi\) | |||||||
\(984\) | −2.52090 | + | 8.53026i | −0.0803633 | + | 0.271935i | ||||
\(985\) | 12.7839i | 0.407329i | ||||||||
\(986\) | −4.65576 | + | 13.0995i | −0.148270 | + | 0.417172i | ||||
\(987\) | 1.95468 | − | 40.4635i | 0.0622182 | − | 1.28797i | ||||
\(988\) | 3.77332 | − | 4.63778i | 0.120045 | − | 0.147547i | ||||
\(989\) | −4.24513 | + | 4.24513i | −0.134987 | + | 0.134987i | ||||
\(990\) | −3.72388 | − | 10.2856i | −0.118353 | − | 0.326898i | ||||
\(991\) | 40.7089i | 1.29316i | 0.762846 | + | 0.646580i | \(0.223801\pi\) | ||||
−0.762846 | + | 0.646580i | \(0.776199\pi\) | |||||||
\(992\) | 1.79241 | + | 2.36398i | 0.0569089 | + | 0.0750565i | ||||
\(993\) | 17.1219 | − | 15.5439i | 0.543348 | − | 0.493272i | ||||
\(994\) | −19.8922 | + | 9.45998i | −0.630942 | + | 0.300052i | ||||
\(995\) | −10.5580 | − | 10.5580i | −0.334712 | − | 0.334712i | ||||
\(996\) | 1.20687 | + | 22.2676i | 0.0382413 | + | 0.705575i | ||||
\(997\) | 9.52444 | − | 9.52444i | 0.301642 | − | 0.301642i | −0.540014 | − | 0.841656i | \(-0.681581\pi\) |
0.841656 | + | 0.540014i | \(0.181581\pi\) | |||||||
\(998\) | 8.34887 | + | 2.96732i | 0.264279 | + | 0.0939289i | ||||
\(999\) | 6.69525 | + | 8.98136i | 0.211828 | + | 0.284158i |
(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 | 48.2.k.a.35.5 | yes | 12 | |
3.2 | odd | 2 | inner | 48.2.k.a.35.2 | yes | 12 | |
4.3 | odd | 2 | 192.2.k.a.47.3 | 12 | |||
8.3 | odd | 2 | 384.2.k.a.95.4 | 12 | |||
8.5 | even | 2 | 384.2.k.b.95.3 | 12 | |||
12.11 | even | 2 | 192.2.k.a.47.1 | 12 | |||
16.3 | odd | 4 | 384.2.k.b.287.1 | 12 | |||
16.5 | even | 4 | 192.2.k.a.143.1 | 12 | |||
16.11 | odd | 4 | inner | 48.2.k.a.11.2 | ✓ | 12 | |
16.13 | even | 4 | 384.2.k.a.287.6 | 12 | |||
24.5 | odd | 2 | 384.2.k.b.95.1 | 12 | |||
24.11 | even | 2 | 384.2.k.a.95.6 | 12 | |||
48.5 | odd | 4 | 192.2.k.a.143.3 | 12 | |||
48.11 | even | 4 | inner | 48.2.k.a.11.5 | yes | 12 | |
48.29 | odd | 4 | 384.2.k.a.287.4 | 12 | |||
48.35 | even | 4 | 384.2.k.b.287.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.2.k.a.11.2 | ✓ | 12 | 16.11 | odd | 4 | inner | |
48.2.k.a.11.5 | yes | 12 | 48.11 | even | 4 | inner | |
48.2.k.a.35.2 | yes | 12 | 3.2 | odd | 2 | inner | |
48.2.k.a.35.5 | yes | 12 | 1.1 | even | 1 | trivial | |
192.2.k.a.47.1 | 12 | 12.11 | even | 2 | |||
192.2.k.a.47.3 | 12 | 4.3 | odd | 2 | |||
192.2.k.a.143.1 | 12 | 16.5 | even | 4 | |||
192.2.k.a.143.3 | 12 | 48.5 | odd | 4 | |||
384.2.k.a.95.4 | 12 | 8.3 | odd | 2 | |||
384.2.k.a.95.6 | 12 | 24.11 | even | 2 | |||
384.2.k.a.287.4 | 12 | 48.29 | odd | 4 | |||
384.2.k.a.287.6 | 12 | 16.13 | even | 4 | |||
384.2.k.b.95.1 | 12 | 24.5 | odd | 2 | |||
384.2.k.b.95.3 | 12 | 8.5 | even | 2 | |||
384.2.k.b.287.1 | 12 | 16.3 | odd | 4 | |||
384.2.k.b.287.3 | 12 | 48.35 | even | 4 |