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 | 35.2 | ||
Root | \(1.27715 + 0.607364i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.35 |
Dual form | 48.2.k.a.11.2 |
$q$-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 | ||||
\(3\) | 1.73003 | − | 0.0835731i | 0.998835 | − | 0.0482510i | ||||
\(4\) | −1.26222 | + | 1.55139i | −0.631109 | + | 0.775694i | ||||
\(5\) | −0.431733 | − | 0.431733i | −0.193077 | − | 0.193077i | 0.603947 | − | 0.797024i | \(-0.293594\pi\) |
−0.797024 | + | 0.603947i | \(0.793594\pi\) | |||||||
\(6\) | −1.15749 | − | 2.15875i | −0.472545 | − | 0.881306i | ||||
\(7\) | −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 | −0.995464 | − | 0.0951415i | \(-0.969670\pi\) |
0.0951415 | + | 0.995464i | \(0.469670\pi\) | |||||||
\(12\) | −2.05403 | + | 2.78944i | −0.592946 | + | 0.805242i | ||||
\(13\) | 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 | \(-0.904809\pi\) | ||
0.955616 | − | 0.294615i | \(-0.0951913\pi\) | |||||||
\(18\) | −2.18292 | − | 3.63798i | −0.514519 | − | 0.857479i | ||||
\(19\) | −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 | ||||
\(21\) | −5.36790 | + | 0.259309i | −1.17137 | + | 0.0565858i | ||||
\(22\) | 5.62721 | + | 2.00000i | 1.19973 | + | 0.426401i | ||||
\(23\) | − | 5.97206i | − | 1.24526i | −0.782516 | − | 0.622631i | \(-0.786064\pi\) | ||
0.782516 | − | 0.622631i | \(-0.213936\pi\) | |||||||
\(24\) | 4.81007 | + | 0.929094i | 0.981852 | + | 0.189651i | ||||
\(25\) | − | 4.62721i | − | 0.925443i | ||||||
\(26\) | 1.40841 | − | 3.96271i | 0.276212 | − | 0.777151i | ||||
\(27\) | 5.14177 | − | 0.749823i | 0.989533 | − | 0.144304i | ||||
\(28\) | 3.91638 | − | 4.81361i | 0.740127 | − | 0.909686i | ||||
\(29\) | −2.86119 | + | 2.86119i | −0.531309 | + | 0.531309i | −0.920962 | − | 0.389653i | \(-0.872595\pi\) |
0.389653 | + | 0.920962i | \(0.372595\pi\) | |||||||
\(30\) | −0.432276 | + | 1.43173i | −0.0789224 | + | 0.261398i | ||||
\(31\) | 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 | ||||
\(36\) | −3.32041 | + | 4.99749i | −0.553402 | + | 0.832914i | ||||
\(37\) | 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 | \(-0.545283\pi\) | ||||
−0.141780 | + | 0.989898i | \(0.545283\pi\) | |||||||
\(42\) | 3.59145 | + | 6.69812i | 0.554172 | + | 1.03354i | ||||
\(43\) | 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 | ||||
\(45\) | −1.41401 | − | 1.16432i | −0.210788 | − | 0.173567i | ||||
\(46\) | −7.62721 | + | 3.62721i | −1.12457 | + | 0.534803i | ||||
\(47\) | 7.53805 | 1.09954 | 0.549769 | − | 0.835317i | \(-0.314716\pi\) | ||||
0.549769 | + | 0.835317i | \(0.314716\pi\) | |||||||
\(48\) | −1.73487 | − | 6.70748i | −0.250407 | − | 0.968141i | ||||
\(49\) | 2.62721 | 0.375316 | ||||||||
\(50\) | −5.90964 | + | 2.81040i | −0.835749 | + | 0.397451i | ||||
\(51\) | −0.203037 | − | 4.20304i | −0.0284309 | − | 0.588543i | ||||
\(52\) | −5.91638 | + | 0.608056i | −0.820455 | + | 0.0843223i | ||||
\(53\) | 8.83325 | + | 8.83325i | 1.21334 | + | 1.21334i | 0.969921 | + | 0.243419i | \(0.0782690\pi\) |
0.243419 | + | 0.969921i | \(0.421731\pi\) | |||||||
\(54\) | −4.08056 | − | 6.11139i | −0.555294 | − | 0.831654i | ||||
\(55\) | 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 | −0.701849 | − | 0.712326i | \(-0.747642\pi\) |
0.712326 | + | 0.701849i | \(0.247642\pi\) | |||||||
\(60\) | 2.09108 | − | 0.317502i | 0.269958 | − | 0.0409894i | ||||
\(61\) | −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 | ||||||
\(66\) | 9.90241 | + | 2.98978i | 1.21890 | + | 0.368017i | ||||
\(67\) | −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 | ||||
\(69\) | −0.499104 | − | 10.3319i | −0.0600850 | − | 1.24381i | ||||
\(70\) | 0.897225 | − | 2.52444i | 0.107239 | − | 0.301728i | ||||
\(71\) | 5.01985i | 0.595747i | 0.954605 | + | 0.297873i | \(0.0962774\pi\) | ||||
−0.954605 | + | 0.297873i | \(0.903723\pi\) | |||||||
\(72\) | 8.39923 | + | 1.20537i | 0.989859 | + | 0.142054i | ||||
\(73\) | 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 | ||||
\(75\) | −0.386711 | − | 8.00523i | −0.0446535 | − | 0.924365i | ||||
\(76\) | −0.205550 | − | 2.00000i | −0.0235782 | − | 0.229416i | ||||
\(77\) | 9.26498 | − | 9.26498i | 1.05584 | − | 1.05584i | ||||
\(78\) | 2.10542 | − | 6.97332i | 0.238392 | − | 0.789573i | ||||
\(79\) | 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 | 0.411680 | − | 0.911329i | \(-0.364942\pi\) |
−0.911329 | + | 0.411680i | \(0.864942\pi\) | |||||||
\(84\) | 6.37318 | − | 8.65500i | 0.695371 | − | 0.944338i | ||||
\(85\) | −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 | \(-0.731810\pi\) | ||||
−0.665568 | + | 0.746338i | \(0.731810\pi\) | |||||||
\(90\) | −0.628197 | + | 2.51307i | −0.0662178 | + | 0.264901i | ||||
\(91\) | −6.52444 | − | 6.52444i | −0.683947 | − | 0.683947i | ||||
\(92\) | 9.26498 | + | 7.53805i | 0.965941 | + | 0.785896i | ||||
\(93\) | 0.0438289 | + | 0.907295i | 0.00454485 | + | 0.0940821i | ||||
\(94\) | −4.57834 | − | 9.62721i | −0.472219 | − | 0.992971i | ||||
\(95\) | 0.613779 | 0.0629724 | ||||||||
\(96\) | −7.51275 | + | 6.28956i | −0.766767 | + | 0.641926i | ||||
\(97\) | −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 | ||||
\(99\) | −8.05292 | + | 9.77985i | −0.809348 | + | 0.982912i | ||||
\(100\) | 7.17860 | + | 5.84056i | 0.717860 | + | 0.584056i | ||||
\(101\) | −0.182046 | − | 0.182046i | −0.0181142 | − | 0.0181142i | 0.697992 | − | 0.716106i | \(-0.254077\pi\) |
−0.716106 | + | 0.697992i | \(0.754077\pi\) | |||||||
\(102\) | −5.24459 | + | 2.81208i | −0.519292 | + | 0.278437i | ||||
\(103\) | 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 | −0.782199 | − | 0.623029i | \(-0.785902\pi\) |
0.623029 | + | 0.782199i | \(0.285902\pi\) | |||||||
\(108\) | −5.32677 | + | 8.92331i | −0.512569 | + | 0.858646i | ||||
\(109\) | 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 | \(-0.872129\pi\) | ||
0.920391 | − | 0.391000i | \(-0.127871\pi\) | |||||||
\(114\) | 2.35729 | + | 0.711725i | 0.220781 | + | 0.0666591i | ||||
\(115\) | −2.57834 | + | 2.57834i | −0.240431 | + | 0.240431i | ||||
\(116\) | −0.827365 | − | 8.05026i | −0.0768189 | − | 0.747447i | ||||
\(117\) | 6.88701 | + | 5.67090i | 0.636704 | + | 0.524274i | ||||
\(118\) | −0.151651 | − | 0.0538991i | −0.0139606 | − | 0.00496182i | ||||
\(119\) | 7.53805i | 0.691012i | ||||||||
\(120\) | −1.67555 | − | 2.47779i | −0.152956 | − | 0.226190i | ||||
\(121\) | − | 6.83276i | − | 0.621160i | ||||||
\(122\) | −3.83786 | + | 10.7982i | −0.347464 | + | 0.977626i | ||||
\(123\) | −3.14118 | + | 0.151742i | −0.283231 | + | 0.0136821i | ||||
\(124\) | −0.813607 | − | 0.661956i | −0.0730640 | − | 0.0594454i | ||||
\(125\) | −4.15639 | + | 4.15639i | −0.371759 | + | 0.371759i | ||||
\(126\) | 6.77310 | + | 11.2878i | 0.603396 | + | 1.00560i | ||||
\(127\) | − | 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 | 0.703583 | − | 0.710613i | \(-0.251583\pi\) |
−0.710613 | + | 0.703583i | \(0.751583\pi\) | |||||||
\(132\) | −2.19597 | − | 14.4627i | −0.191134 | − | 1.25882i | ||||
\(133\) | 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 | \(-0.308314\pi\) | ||||
0.566457 | + | 0.824091i | \(0.308314\pi\) | |||||||
\(138\) | −12.8922 | + | 6.91263i | −1.09746 | + | 0.588442i | ||||
\(139\) | 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 | ||||
\(141\) | 13.0411 | − | 0.629978i | 1.09826 | − | 0.0530537i | ||||
\(142\) | 6.41110 | − | 3.04888i | 0.538008 | − | 0.255856i | ||||
\(143\) | −12.5579 | −1.05014 | ||||||||
\(144\) | −3.56195 | − | 11.4592i | −0.296829 | − | 0.954931i | ||||
\(145\) | 2.47054 | 0.205167 | ||||||||
\(146\) | 17.1904 | − | 8.17510i | 1.42269 | − | 0.676576i | ||||
\(147\) | 4.54517 | − | 0.219564i | 0.374879 | − | 0.0181094i | ||||
\(148\) | 0.440820 | + | 4.28917i | 0.0362351 | + | 0.352567i | ||||
\(149\) | −5.79002 | − | 5.79002i | −0.474337 | − | 0.474337i | 0.428978 | − | 0.903315i | \(-0.358874\pi\) |
−0.903315 | + | 0.428978i | \(0.858874\pi\) | |||||||
\(150\) | −9.98900 | + | 5.35597i | −0.815599 | + | 0.437313i | ||||
\(151\) | 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 | ||||
\(156\) | −10.1847 | + | 1.54641i | −0.815430 | + | 0.123812i | ||||
\(157\) | −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 | ||||||||
\(162\) | −7.57025 | − | 10.2319i | −0.594775 | − | 0.803892i | ||||
\(163\) | 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 | ||||
\(165\) | 4.46061 | − | 0.215480i | 0.347258 | − | 0.0167751i | ||||
\(166\) | −3.04888 | + | 8.57834i | −0.236639 | + | 0.665808i | ||||
\(167\) | − | 19.1437i | − | 1.48139i | −0.671843 | − | 0.740694i | \(-0.734497\pi\) | ||
0.671843 | − | 0.740694i | \(-0.265503\pi\) | |||||||
\(168\) | −14.9246 | − | 2.88277i | −1.15146 | − | 0.222410i | ||||
\(169\) | − | 4.15667i | − | 0.319744i | ||||||
\(170\) | 1.97662 | + | 0.702522i | 0.151600 | + | 0.0538810i | ||||
\(171\) | −1.91701 | + | 2.32811i | −0.146598 | + | 0.178035i | ||||
\(172\) | −2.00000 | + | 0.205550i | −0.152499 | + | 0.0156730i | ||||
\(173\) | −13.3281 | + | 13.3281i | −1.01331 | + | 1.01331i | −0.0134040 | + | 0.999910i | \(0.504267\pi\) |
−0.999910 | + | 0.0134040i | \(0.995733\pi\) | |||||||
\(174\) | 9.48840 | + | 2.86478i | 0.719314 | + | 0.217179i | ||||
\(175\) | 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 | 0.961453 | − | 0.274970i | \(-0.0886680\pi\) |
−0.274970 | + | 0.961453i | \(0.588668\pi\) | |||||||
\(180\) | 3.59111 | − | 0.724048i | 0.267666 | − | 0.0539673i | ||||
\(181\) | −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 | ||||||||
\(186\) | 1.13213 | − | 0.607034i | 0.0830119 | − | 0.0445099i | ||||
\(187\) | 7.25443 | + | 7.25443i | 0.530496 | + | 0.530496i | ||||
\(188\) | −9.51467 | + | 11.6944i | −0.693929 | + | 0.852904i | ||||
\(189\) | −15.9537 | + | 2.32653i | −1.16046 | + | 0.169230i | ||||
\(190\) | −0.372787 | − | 0.783887i | −0.0270448 | − | 0.0568692i | ||||
\(191\) | 3.17852 | 0.229989 | 0.114995 | − | 0.993366i | \(-0.463315\pi\) | ||||
0.114995 | + | 0.993366i | \(0.463315\pi\) | |||||||
\(192\) | 12.5957 | + | 5.77485i | 0.909015 | + | 0.416764i | ||||
\(193\) | −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 | ||||
\(195\) | −0.151742 | − | 3.14118i | −0.0108664 | − | 0.224944i | ||||
\(196\) | −3.31612 | + | 4.07583i | −0.236866 | + | 0.291130i | ||||
\(197\) | −14.8053 | − | 14.8053i | −1.05483 | − | 1.05483i | −0.998407 | − | 0.0564281i | \(-0.982029\pi\) |
−0.0564281 | − | 0.998407i | \(-0.517971\pi\) | |||||||
\(198\) | 17.3814 | + | 4.34485i | 1.23524 | + | 0.308775i | ||||
\(199\) | −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 | ||||
\(204\) | 6.77682 | + | 4.99016i | 0.474472 | + | 0.349381i | ||||
\(205\) | 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 | ||||||
\(210\) | 1.34125 | − | 4.44235i | 0.0925553 | − | 0.306551i | ||||
\(211\) | −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 | ||||
\(213\) | 0.419525 | + | 8.68451i | 0.0287454 | + | 0.595053i | ||||
\(214\) | 3.10278 | + | 1.10278i | 0.212101 | + | 0.0753842i | ||||
\(215\) | − | 0.613779i | − | 0.0418594i | ||||||
\(216\) | 14.6317 | + | 1.38338i | 0.995560 | + | 0.0941272i | ||||
\(217\) | − | 1.62721i | − | 0.110462i | ||||||
\(218\) | 4.40271 | − | 12.3875i | 0.298189 | − | 0.838987i | ||||
\(219\) | 1.12489 | + | 23.2862i | 0.0760132 | + | 1.57354i | ||||
\(220\) | −3.25443 | + | 4.00000i | −0.219413 | + | 0.269680i | ||||
\(221\) | 5.10860 | − | 5.10860i | 0.343641 | − | 0.343641i | ||||
\(222\) | −5.05541 | − | 1.52635i | −0.339297 | − | 0.102442i | ||||
\(223\) | 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 | 0.297082 | − | 0.954852i | \(-0.403986\pi\) |
−0.954852 | + | 0.297082i | \(0.903986\pi\) | |||||||
\(228\) | −0.522755 | − | 3.44289i | −0.0346203 | − | 0.228011i | ||||
\(229\) | 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 | \(-0.277510\pi\) | ||||
0.643432 | + | 0.765503i | \(0.277510\pi\) | |||||||
\(234\) | 3.05966 | − | 12.2400i | 0.200016 | − | 0.800156i | ||||
\(235\) | −3.25443 | − | 3.25443i | −0.212295 | − | 0.212295i | ||||
\(236\) | 0.0232700 | + | 0.226417i | 0.00151475 | + | 0.0147385i | ||||
\(237\) | 0.290464 | + | 6.01284i | 0.0188676 | + | 0.390576i | ||||
\(238\) | 9.62721 | − | 4.57834i | 0.624040 | − | 0.296770i | ||||
\(239\) | −9.44247 | −0.610782 | −0.305391 | − | 0.952227i | \(-0.598787\pi\) | ||||
−0.305391 | + | 0.952227i | \(0.598787\pi\) | |||||||
\(240\) | −2.14684 | + | 3.64484i | −0.138578 | + | 0.235273i | ||||
\(241\) | 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 | ||||
\(243\) | 15.1366 | − | 3.72583i | 0.971017 | − | 0.239012i | ||||
\(244\) | 16.1219 | − | 1.65693i | 1.03210 | − | 0.106074i | ||||
\(245\) | −1.13425 | − | 1.13425i | −0.0724649 | − | 0.0724649i | ||||
\(246\) | 2.10163 | + | 3.91959i | 0.133995 | + | 0.249904i | ||||
\(247\) | −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 | −0.768374 | − | 0.640001i | \(-0.778934\pi\) |
0.640001 | + | 0.768374i | \(0.278934\pi\) | |||||||
\(252\) | 10.3025 | − | 15.5061i | 0.648996 | − | 0.976791i | ||||
\(253\) | 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 | \(0.155822\pi\) | ||||
−0.882554 | + | 0.470211i | \(0.844178\pi\) | |||||||
\(258\) | 0.711725 | − | 2.35729i | 0.0443100 | − | 0.146759i | ||||
\(259\) | −4.72999 | + | 4.72999i | −0.293907 | + | 0.293907i | ||||
\(260\) | 2.81682 | + | 2.29178i | 0.174692 | + | 0.142130i | ||||
\(261\) | −7.71623 | + | 9.37096i | −0.477623 | + | 0.580048i | ||||
\(262\) | −0.0538991 | + | 0.151651i | −0.00332990 | + | 0.00936903i | ||||
\(263\) | 29.8138i | 1.83840i | 0.393796 | + | 0.919198i | \(0.371162\pi\) | ||||
−0.393796 | + | 0.919198i | \(0.628838\pi\) | |||||||
\(264\) | −17.1373 | + | 11.5887i | −1.05473 | + | 0.713236i | ||||
\(265\) | − | 7.62721i | − | 0.468536i | ||||||
\(266\) | −4.15639 | − | 1.47725i | −0.254844 | − | 0.0905757i | ||||
\(267\) | −21.7256 | + | 1.04950i | −1.32958 | + | 0.0642285i | ||||
\(268\) | −0.113338 | − | 1.10278i | −0.00692321 | − | 0.0673627i | ||||
\(269\) | 16.3713 | − | 16.3713i | 0.998176 | − | 0.998176i | −0.00182258 | − | 0.999998i | \(-0.500580\pi\) |
0.999998 | + | 0.00182258i | \(0.000580145\pi\) | |||||||
\(270\) | −0.876776 | + | 4.40020i | −0.0533589 | + | 0.267788i | ||||
\(271\) | − | 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 | ||||
\(276\) | 16.6587 | + | 12.2668i | 1.00274 | + | 0.738373i | ||||
\(277\) | 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 | \(-0.324142\pi\) | ||||
0.524794 | + | 0.851229i | \(0.324142\pi\) | |||||||
\(282\) | −8.72525 | − | 16.2728i | −0.519581 | − | 0.969030i | ||||
\(283\) | −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 | ||||
\(285\) | 1.06186 | − | 0.0512954i | 0.0628990 | − | 0.00303848i | ||||
\(286\) | 7.62721 | + | 16.0383i | 0.451007 | + | 0.948365i | ||||
\(287\) | 5.63363 | 0.332543 | ||||||||
\(288\) | −12.4717 | + | 11.5090i | −0.734900 | + | 0.678176i | ||||
\(289\) | 11.0978 | 0.652809 | ||||||||
\(290\) | −1.50052 | − | 3.15525i | −0.0881133 | − | 0.185282i | ||||
\(291\) | −15.0099 | + | 0.725088i | −0.879897 | + | 0.0425054i | ||||
\(292\) | −20.8816 | − | 16.9894i | −1.22201 | − | 0.994232i | ||||
\(293\) | 3.72465 | + | 3.72465i | 0.217597 | + | 0.217597i | 0.807485 | − | 0.589888i | \(-0.200828\pi\) |
−0.589888 | + | 0.807485i | \(0.700828\pi\) | |||||||
\(294\) | −3.04098 | − | 5.67150i | −0.177354 | − | 0.330769i | ||||
\(295\) | −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 | ||||
\(300\) | 12.9073 | + | 9.50442i | 0.745205 | + | 0.548738i | ||||
\(301\) | −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 | ||||||||
\(306\) | −8.83830 | + | 5.30330i | −0.505252 | + | 0.303169i | ||||
\(307\) | −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 | ||||
\(309\) | 10.9982 | − | 0.531291i | 0.625664 | − | 0.0302241i | ||||
\(310\) | −0.426686 | − | 0.151651i | −0.0242341 | − | 0.00861320i | ||||
\(311\) | 13.8320i | 0.784341i | 0.919893 | + | 0.392170i | \(0.128276\pi\) | ||||
−0.919893 | + | 0.392170i | \(0.871724\pi\) | |||||||
\(312\) | 8.16082 | + | 12.0682i | 0.462016 | + | 0.683226i | ||||
\(313\) | 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 | ||||
\(315\) | 4.38736 | + | 3.61264i | 0.247200 | + | 0.203549i | ||||
\(316\) | −5.39194 | − | 4.38692i | −0.303321 | − | 0.246784i | ||||
\(317\) | −8.92199 | + | 8.92199i | −0.501109 | + | 0.501109i | −0.911782 | − | 0.410673i | \(-0.865294\pi\) |
0.410673 | + | 0.911782i | \(0.365294\pi\) | |||||||
\(318\) | 8.84435 | − | 29.2932i | 0.495966 | − | 1.64268i | ||||
\(319\) | − | 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 | ||||
\(324\) | −8.46974 | + | 15.8828i | −0.470541 | + | 0.882378i | ||||
\(325\) | 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 | ||||||||
\(330\) | −2.98441 | − | 5.56599i | −0.164286 | − | 0.306398i | ||||
\(331\) | 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 | ||||
\(333\) | 4.11120 | − | 4.99284i | 0.225292 | − | 0.273606i | ||||
\(334\) | −24.4494 | + | 11.6272i | −1.33781 | + | 0.636213i | ||||
\(335\) | 0.338430 | 0.0184904 | ||||||||
\(336\) | 5.38291 | + | 20.8118i | 0.293662 | + | 1.13538i | ||||
\(337\) | 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 | ||||
\(339\) | −0.694724 | − | 14.3814i | −0.0377322 | − | 0.781089i | ||||
\(340\) | −0.303302 | − | 2.95112i | −0.0164489 | − | 0.160047i | ||||
\(341\) | −1.56599 | − | 1.56599i | −0.0848030 | − | 0.0848030i | ||||
\(342\) | 4.13767 | + | 1.03430i | 0.223740 | + | 0.0559286i | ||||
\(343\) | 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 | −0.588466 | − | 0.808522i | \(-0.700268\pi\) |
0.808522 | + | 0.588466i | \(0.200268\pi\) | |||||||
\(348\) | −2.10415 | − | 13.8581i | −0.112795 | − | 0.742870i | ||||
\(349\) | −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 | \(-0.716073\pi\) | ||
0.627870 | − | 0.778318i | \(-0.283927\pi\) | |||||||
\(354\) | −0.266866 | − | 0.0805734i | −0.0141838 | − | 0.00428243i | ||||
\(355\) | 2.16724 | − | 2.16724i | 0.115025 | − | 0.115025i | ||||
\(356\) | 15.8508 | − | 19.4822i | 0.840092 | − | 1.03255i | ||||
\(357\) | 0.629978 | + | 13.0411i | 0.0333420 | + | 0.690207i | ||||
\(358\) | 6.15165 | − | 17.3083i | 0.325125 | − | 0.914773i | ||||
\(359\) | − | 21.3235i | − | 1.12541i | −0.826657 | − | 0.562706i | \(-0.809760\pi\) | ||
0.826657 | − | 0.562706i | \(-0.190240\pi\) | |||||||
\(360\) | −3.10583 | − | 4.14662i | −0.163691 | − | 0.218546i | ||||
\(361\) | 17.9894i | 0.946812i | ||||||||
\(362\) | 31.1206 | + | 11.0608i | 1.63566 | + | 0.581340i | ||||
\(363\) | −0.571035 | − | 11.8209i | −0.0299716 | − | 0.620437i | ||||
\(364\) | 18.3572 | − | 1.88666i | 0.962179 | − | 0.0988880i | ||||
\(365\) | 5.81112 | − | 5.81112i | 0.304168 | − | 0.304168i | ||||
\(366\) | −5.73719 | + | 19.0020i | −0.299888 | + | 0.993253i | ||||
\(367\) | 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 | ||||
\(372\) | −1.46289 | − | 1.07721i | −0.0758472 | − | 0.0558507i | ||||
\(373\) | 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 | ||||||||
\(378\) | 12.6611 | + | 18.9623i | 0.651214 | + | 0.975313i | ||||
\(379\) | −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 | ||||
\(381\) | −1.31869 | − | 27.2980i | −0.0675585 | − | 1.39852i | ||||
\(382\) | −1.93051 | − | 4.05944i | −0.0987737 | − | 0.207699i | ||||
\(383\) | −32.9757 | −1.68498 | −0.842491 | − | 0.538711i | \(-0.818912\pi\) | ||||
−0.842491 | + | 0.538711i | \(0.818912\pi\) | |||||||
\(384\) | −0.274819 | − | 19.5940i | −0.0140243 | − | 0.999902i | ||||
\(385\) | −8.00000 | −0.407718 | ||||||||
\(386\) | 6.96037 | + | 14.6361i | 0.354274 | + | 0.744958i | ||||
\(387\) | 2.32811 | + | 1.91701i | 0.118345 | + | 0.0974473i | ||||
\(388\) | 10.9511 | − | 13.4600i | 0.555959 | − | 0.683327i | ||||
\(389\) | 3.97434 | + | 3.97434i | 0.201507 | + | 0.201507i | 0.800645 | − | 0.599138i | \(-0.204490\pi\) |
−0.599138 | + | 0.800645i | \(0.704490\pi\) | |||||||
\(390\) | −3.91959 | + | 2.10163i | −0.198476 | + | 0.106420i | ||||
\(391\) | −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 | ||||
\(396\) | −5.00779 | − | 24.8375i | −0.251651 | − | 1.24813i | ||||
\(397\) | −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 | \(0.266769\pi\) | ||||
−0.668891 | + | 0.743361i | \(0.733231\pi\) | |||||||
\(402\) | 1.29978 | + | 0.392436i | 0.0648272 | + | 0.0195729i | ||||
\(403\) | −1.10278 | + | 1.10278i | −0.0549331 | + | 0.0549331i | ||||
\(404\) | 0.512205 | − | 0.0526419i | 0.0254832 | − | 0.00261903i | ||||
\(405\) | −4.55897 | − | 3.06782i | −0.226537 | − | 0.152441i | ||||
\(406\) | −16.7300 | − | 5.94610i | −0.830295 | − | 0.295100i | ||||
\(407\) | 9.10404i | 0.451270i | ||||||||
\(408\) | 2.25719 | − | 11.6858i | 0.111748 | − | 0.578536i | ||||
\(409\) | 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 | ||||
\(411\) | 22.9410 | − | 1.10821i | 1.13159 | − | 0.0546642i | ||||
\(412\) | −8.02418 | + | 9.86248i | −0.395323 | + | 0.485890i | ||||
\(413\) | −0.249687 | + | 0.249687i | −0.0122863 | + | 0.0122863i | ||||
\(414\) | −21.7262 | + | 13.0365i | −1.06779 | + | 0.640710i | ||||
\(415\) | 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 | 0.962570 | − | 0.271032i | \(-0.0873650\pi\) |
−0.271032 | + | 0.962570i | \(0.587365\pi\) | |||||||
\(420\) | −6.48817 | + | 0.985138i | −0.316590 | + | 0.0480698i | ||||
\(421\) | −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 | ||||||||
\(426\) | 10.8366 | − | 5.81045i | 0.525036 | − | 0.281517i | ||||
\(427\) | 17.7789 | + | 17.7789i | 0.860380 | + | 0.860380i | ||||
\(428\) | −0.476105 | − | 4.63249i | −0.0230134 | − | 0.223920i | ||||
\(429\) | −21.7256 | + | 1.04950i | −1.04892 | + | 0.0506705i | ||||
\(430\) | −0.783887 | + | 0.372787i | −0.0378024 | + | 0.0179774i | ||||
\(431\) | 20.7097 | 0.997553 | 0.498776 | − | 0.866731i | \(-0.333783\pi\) | ||||
0.498776 | + | 0.866731i | \(0.333783\pi\) | |||||||
\(432\) | −7.11997 | − | 19.5271i | −0.342560 | − | 0.939496i | ||||
\(433\) | −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 | ||||
\(435\) | 4.27411 | − | 0.206471i | 0.204928 | − | 0.00989951i | ||||
\(436\) | −18.4947 | + | 1.90080i | −0.885736 | + | 0.0910316i | ||||
\(437\) | 4.24513 | + | 4.24513i | 0.203072 | + | 0.203072i | ||||
\(438\) | 29.0567 | − | 15.5798i | 1.38838 | − | 0.744434i | ||||
\(439\) | 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 | −0.604249 | − | 0.796796i | \(-0.706527\pi\) |
0.796796 | + | 0.604249i | \(0.206527\pi\) | |||||||
\(444\) | 1.12109 | + | 7.38356i | 0.0532047 | + | 0.350408i | ||||
\(445\) | 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 | \(-0.959452\pi\) | ||
0.991897 | − | 0.127042i | \(-0.0405483\pi\) | |||||||
\(450\) | −16.8337 | + | 10.1008i | −0.793548 | + | 0.476157i | ||||
\(451\) | 5.42166 | − | 5.42166i | 0.255296 | − | 0.255296i | ||||
\(452\) | 12.8963 | + | 10.4925i | 0.606592 | + | 0.493528i | ||||
\(453\) | 17.2071 | − | 0.831227i | 0.808459 | − | 0.0390544i | ||||
\(454\) | −6.63778 | + | 18.6761i | −0.311526 | + | 0.876512i | ||||
\(455\) | 5.63363i | 0.264109i | ||||||||
\(456\) | −4.07958 | + | 2.75872i | −0.191044 | + | 0.129189i | ||||
\(457\) | − | 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 | ||||
\(459\) | −1.82166 | − | 12.4917i | −0.0850279 | − | 0.583062i | ||||
\(460\) | −0.745574 | − | 7.25443i | −0.0347626 | − | 0.338239i | ||||
\(461\) | −22.7962 | + | 22.7962i | −1.06172 | + | 1.06172i | −0.0637594 | + | 0.997965i | \(0.520309\pi\) |
−0.997965 | + | 0.0637594i | \(0.979691\pi\) | |||||||
\(462\) | −30.7250 | − | 9.27662i | −1.42945 | − | 0.431588i | ||||
\(463\) | 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 | 0.445100 | − | 0.895481i | \(-0.353168\pi\) |
−0.895481 | + | 0.445100i | \(0.853168\pi\) | |||||||
\(468\) | −17.4907 | + | 3.52651i | −0.808506 | + | 0.163013i | ||||
\(469\) | 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 | ||||||||
\(474\) | 7.50287 | − | 4.02294i | 0.344618 | − | 0.184780i | ||||
\(475\) | 3.28917 | + | 3.28917i | 0.150917 | + | 0.150917i | ||||
\(476\) | −11.6944 | − | 9.51467i | −0.536014 | − | 0.436104i | ||||
\(477\) | 28.9307 | + | 23.8221i | 1.32464 | + | 1.09074i | ||||
\(478\) | 5.73501 | + | 12.0594i | 0.262313 | + | 0.551586i | ||||
\(479\) | 28.2478 | 1.29067 | 0.645337 | − | 0.763898i | \(-0.276717\pi\) | ||||
0.645337 | + | 0.763898i | \(0.276717\pi\) | |||||||
\(480\) | 5.95892 | + | 0.528089i | 0.271986 | + | 0.0241038i | ||||
\(481\) | 6.41110 | 0.292321 | ||||||||
\(482\) | −10.0923 | − | 21.2219i | −0.459694 | − | 0.966633i | ||||
\(483\) | 1.54861 | + | 32.0575i | 0.0704641 | + | 1.45866i | ||||
\(484\) | 10.6003 | + | 8.62444i | 0.481830 | + | 0.392020i | ||||
\(485\) | 3.74576 | + | 3.74576i | 0.170086 | + | 0.170086i | ||||
\(486\) | −13.9519 | − | 17.0688i | −0.632871 | − | 0.774257i | ||||
\(487\) | 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 | \(0.638722\pi\) |
−0.906529 | + | 0.422143i | \(0.861278\pi\) | |||||||
\(492\) | 3.72945 | − | 5.06472i | 0.168136 | − | 0.228335i | ||||
\(493\) | 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 | ||||||
\(498\) | −4.55774 | + | 15.0956i | −0.204237 | + | 0.676451i | ||||
\(499\) | 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 | ||||
\(501\) | −1.59990 | − | 33.1193i | −0.0714784 | − | 1.47966i | ||||
\(502\) | 3.83276 | + | 1.36222i | 0.171065 | + | 0.0607990i | ||||
\(503\) | − | 27.6805i | − | 1.23421i | −0.786879 | − | 0.617107i | \(-0.788304\pi\) | ||
0.786879 | − | 0.617107i | \(-0.211696\pi\) | |||||||
\(504\) | −26.0609 | − | 3.73999i | −1.16085 | − | 0.166593i | ||||
\(505\) | 0.157190i | 0.00699488i | ||||||||
\(506\) | 11.9441 | − | 33.6061i | 0.530981 | − | 1.49397i | ||||
\(507\) | −0.347386 | − | 7.19119i | −0.0154280 | − | 0.319372i | ||||
\(508\) | 24.4791 | + | 19.9164i | 1.08609 | + | 0.883647i | ||||
\(509\) | 17.3235 | − | 17.3235i | 0.767851 | − | 0.767851i | −0.209877 | − | 0.977728i | \(-0.567306\pi\) |
0.977728 | + | 0.209877i | \(0.0673063\pi\) | |||||||
\(510\) | 3.47833 | + | 1.05019i | 0.154023 | + | 0.0465034i | ||||
\(511\) | − | 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 | ||||
\(516\) | −3.44289 | + | 0.522755i | −0.151565 | + | 0.0230130i | ||||
\(517\) | −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 | \(-0.571215\pi\) | ||||
−0.221868 | + | 0.975077i | \(0.571215\pi\) | |||||||
\(522\) | 16.6547 | + | 4.16319i | 0.728955 | + | 0.182218i | ||||
\(523\) | 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 | ||||
\(525\) | 1.19988 | + | 24.8384i | 0.0523669 | + | 1.08404i | ||||
\(526\) | 38.0766 | − | 18.1078i | 1.66022 | − | 0.789538i | ||||
\(527\) | 1.27410 | 0.0555006 | ||||||||
\(528\) | 25.2091 | + | 14.8484i | 1.09709 | + | 0.646192i | ||||
\(529\) | −12.6655 | −0.550675 | ||||||||
\(530\) | −9.74109 | + | 4.63249i | −0.423126 | + | 0.201223i | ||||
\(531\) | 0.217023 | − | 0.263563i | 0.00941798 | − | 0.0114376i | ||||
\(532\) | 0.637776 | + | 6.20555i | 0.0276511 | + | 0.269045i | ||||
\(533\) | −3.81796 | − | 3.81796i | −0.165374 | − | 0.165374i | ||||
\(534\) | 14.5357 | + | 27.1094i | 0.629021 | + | 1.17314i | ||||
\(535\) | 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 | ||||
\(540\) | 6.15223 | − | 1.55275i | 0.264750 | − | 0.0668196i | ||||
\(541\) | 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 | ||||||
\(546\) | −6.53264 | + | 21.6366i | −0.279571 | + | 0.925963i | ||||
\(547\) | 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 | ||||
\(549\) | −18.7669 | − | 15.4530i | −0.800950 | − | 0.659518i | ||||
\(550\) | 9.25443 | − | 26.0383i | 0.394610 | − | 1.11028i | ||||
\(551\) | − | 4.06764i | − | 0.173287i | ||||||
\(552\) | 5.54861 | − | 28.7260i | 0.236164 | − | 1.22266i | ||||
\(553\) | − | 10.7839i | − | 0.458578i | ||||||
\(554\) | −20.1287 | − | 7.15405i | −0.855186 | − | 0.303947i | ||||
\(555\) | −2.27724 | + | 0.110007i | −0.0966636 | + | 0.00466955i | ||||
\(556\) | −23.6116 | + | 2.42669i | −1.00136 | + | 0.102914i | ||||
\(557\) | 6.90317 | − | 6.90317i | 0.292497 | − | 0.292497i | −0.545569 | − | 0.838066i | \(-0.683686\pi\) |
0.838066 | + | 0.545569i | \(0.183686\pi\) | |||||||
\(558\) | 1.90789 | − | 1.14480i | 0.0807675 | − | 0.0484635i | ||||
\(559\) | 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 | 0.978940 | − | 0.204146i | \(-0.0654418\pi\) |
−0.204146 | + | 0.978940i | \(0.565442\pi\) | |||||||
\(564\) | −15.4834 | + | 21.0269i | −0.651967 | + | 0.885394i | ||||
\(565\) | −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 | \(-0.133757\pi\) | ||||
0.913003 | + | 0.407953i | \(0.133757\pi\) | |||||||
\(570\) | −0.710446 | − | 1.32500i | −0.0297573 | − | 0.0554980i | ||||
\(571\) | 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 | ||||
\(573\) | 5.49894 | − | 0.265638i | 0.229721 | − | 0.0110972i | ||||
\(574\) | −3.42166 | − | 7.19499i | −0.142817 | − | 0.300313i | ||||
\(575\) | −27.6340 | −1.15242 | ||||||||
\(576\) | 22.2736 | + | 8.93802i | 0.928065 | + | 0.372417i | ||||
\(577\) | 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 | ||||
\(579\) | −19.8261 | + | 0.957746i | −0.823946 | + | 0.0398026i | ||||
\(580\) | −3.11836 | + | 3.83276i | −0.129483 | + | 0.159147i | ||||
\(581\) | 14.1239 | + | 14.1239i | 0.585958 | + | 0.585958i | ||||
\(582\) | 10.0425 | + | 18.7295i | 0.416276 | + | 0.776363i | ||||
\(583\) | −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 | −0.986310 | − | 0.164904i | \(-0.947268\pi\) |
0.164904 | + | 0.986310i | \(0.447268\pi\) | |||||||
\(588\) | −5.39637 | + | 7.32845i | −0.222542 | + | 0.302220i | ||||
\(589\) | −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 | \(-0.862181\pi\) | ||
0.907723 | − | 0.419570i | \(-0.137819\pi\) | |||||||
\(594\) | 30.4335 | + | 6.06412i | 1.24870 | + | 0.248814i | ||||
\(595\) | 3.25443 | − | 3.25443i | 0.133418 | − | 0.133418i | ||||
\(596\) | 16.2908 | − | 1.67429i | 0.667298 | − | 0.0685816i | ||||
\(597\) | −42.3079 | + | 2.04378i | −1.73155 | + | 0.0836462i | ||||
\(598\) | −23.6655 | − | 8.41110i | −0.967755 | − | 0.343955i | ||||
\(599\) | − | 32.6704i | − | 1.33488i | −0.744665 | − | 0.667438i | \(-0.767391\pi\) | ||
0.744665 | − | 0.667438i | \(-0.232609\pi\) | |||||||
\(600\) | 4.29912 | − | 22.2572i | 0.175511 | − | 0.908647i | ||||
\(601\) | 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 | ||||
\(603\) | −1.05702 | + | 1.28369i | −0.0430451 | + | 0.0522760i | ||||
\(604\) | −12.5542 | + | 15.4303i | −0.510821 | + | 0.627848i | ||||
\(605\) | −2.94993 | + | 2.94993i | −0.119932 | + | 0.119932i | ||||
\(606\) | −0.182275 | + | 0.603709i | −0.00740440 | + | 0.0245240i | ||||
\(607\) | 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 | ||||
\(612\) | 12.1412 | + | 8.06679i | 0.490777 | + | 0.326081i | ||||
\(613\) | −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 | \(-0.524023\pi\) | ||||
−0.0753992 | + | 0.997153i | \(0.524023\pi\) | |||||||
\(618\) | −7.35843 | − | 13.7236i | −0.295999 | − | 0.552045i | ||||
\(619\) | −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 | ||||
\(621\) | −4.47799 | − | 30.7070i | −0.179696 | − | 1.23223i | ||||
\(622\) | 17.6655 | − | 8.40105i | 0.708323 | − | 0.336852i | ||||
\(623\) | 38.9643 | 1.56107 | ||||||||
\(624\) | 10.4563 | − | 17.7524i | 0.418586 | − | 0.710663i | ||||
\(625\) | −19.5472 | −0.781887 | ||||||||
\(626\) | 5.03268 | − | 2.39335i | 0.201147 | − | 0.0956576i | ||||
\(627\) | −0.354779 | − | 7.34422i | −0.0141685 | − | 0.293300i | ||||
\(628\) | 25.7491 | − | 2.64637i | 1.02750 | − | 0.105602i | ||||
\(629\) | −3.70355 | − | 3.70355i | −0.147670 | − | 0.147670i | ||||
\(630\) | 1.94915 | − | 7.79750i | 0.0776561 | − | 0.310660i | ||||
\(631\) | −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 | ||||
\(636\) | −42.7835 | + | 6.49609i | −1.69648 | + | 0.257587i | ||||
\(637\) | 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 | \(-0.815583\pi\) | ||
0.836811 | − | 0.547491i | \(-0.184417\pi\) | |||||||
\(642\) | 5.46007 | + | 1.64853i | 0.215492 | + | 0.0650623i | ||||
\(643\) | 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 | ||||
\(645\) | −0.0512954 | − | 1.06186i | −0.00201976 | − | 0.0418106i | ||||
\(646\) | 1.15667 | − | 3.25443i | 0.0455087 | − | 0.128044i | ||||
\(647\) | 5.29520i | 0.208176i | 0.994568 | + | 0.104088i | \(0.0331923\pi\) | ||||
−0.994568 | + | 0.104088i | \(0.966808\pi\) | |||||||
\(648\) | 25.4289 | + | 1.17048i | 0.998942 | + | 0.0459809i | ||||
\(649\) | 0.480585i | 0.0188646i | ||||||||
\(650\) | −18.3363 | − | 6.51700i | −0.719208 | − | 0.255618i | ||||
\(651\) | −0.135991 | − | 2.81513i | −0.00532992 | − | 0.110334i | ||||
\(652\) | 4.54002 | + | 44.1744i | 0.177801 | + | 1.73000i | ||||
\(653\) | −29.7039 | + | 29.7039i | −1.16240 | + | 1.16240i | −0.178457 | + | 0.983948i | \(0.557110\pi\) |
−0.983948 | + | 0.178457i | \(0.942890\pi\) | |||||||
\(654\) | 6.58157 | − | 21.7987i | 0.257360 | − | 0.852398i | ||||
\(655\) | 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 | 0.686707 | − | 0.726934i | \(-0.259056\pi\) |
−0.726934 | + | 0.686707i | \(0.759056\pi\) | |||||||
\(660\) | −5.29597 | + | 7.19212i | −0.206145 | + | 0.279953i | ||||
\(661\) | 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 | ||||||||
\(666\) | −8.87359 | − | 2.21815i | −0.343845 | − | 0.0859514i | ||||
\(667\) | 17.0872 | + | 17.0872i | 0.661619 | + | 0.661619i | ||||
\(668\) | 29.6994 | + | 24.1636i | 1.14910 | + | 0.934918i | ||||
\(669\) | 0.684461 | + | 14.1689i | 0.0264628 | + | 0.547802i | ||||
\(670\) | −0.205550 | − | 0.432226i | −0.00794109 | − | 0.0166983i | ||||
\(671\) | 34.2198 | 1.32104 | ||||||||
\(672\) | 23.3104 | − | 19.5151i | 0.899217 | − | 0.752811i | ||||
\(673\) | −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 | ||||
\(675\) | −3.46959 | − | 23.7920i | −0.133545 | − | 0.915756i | ||||
\(676\) | 6.44861 | + | 5.24663i | 0.248024 | + | 0.201794i | ||||
\(677\) | 8.13073 | + | 8.13073i | 0.312489 | + | 0.312489i | 0.845873 | − | 0.533384i | \(-0.179080\pi\) |
−0.533384 | + | 0.845873i | \(0.679080\pi\) | |||||||
\(678\) | −17.9452 | + | 9.62199i | −0.689182 | + | 0.369530i | ||||
\(679\) | 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 | −0.370497 | − | 0.928834i | \(-0.620813\pi\) |
0.928834 | + | 0.370497i | \(0.120813\pi\) | |||||||
\(684\) | −1.19212 | − | 5.91262i | −0.0455817 | − | 0.226075i | ||||
\(685\) | −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 | ||||||||
\(690\) | 8.55040 | + | 2.58158i | 0.325508 | + | 0.0982790i | ||||
\(691\) | −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 | ||||
\(693\) | 24.9864 | − | 30.3447i | 0.949154 | − | 1.15270i | ||||
\(694\) | −7.72496 | − | 2.74557i | −0.293236 | − | 0.104221i | ||||
\(695\) | − | 7.24616i | − | 0.274863i | ||||||
\(696\) | −16.4208 | + | 11.1042i | −0.622430 | + | 0.420904i | ||||
\(697\) | 4.41110i | 0.167082i | ||||||||
\(698\) | −5.42712 | + | 15.2698i | −0.205420 | + | 0.577970i | ||||
\(699\) | 33.9833 | − | 1.64164i | 1.28536 | − | 0.0620924i | ||||
\(700\) | −22.2736 | − | 18.1219i | −0.841862 | − | 0.684945i | ||||
\(701\) | 14.7166 | − | 14.7166i | 0.555837 | − | 0.555837i | −0.372282 | − | 0.928120i | \(-0.621425\pi\) |
0.928120 | + | 0.372282i | \(0.121425\pi\) | |||||||
\(702\) | 4.27038 | − | 21.4314i | 0.161175 | − | 0.808875i | ||||
\(703\) | 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 | ||||
\(708\) | 0.0591803 | + | 0.389765i | 0.00222413 | + | 0.0146483i | ||||
\(709\) | −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 | ||||||||
\(714\) | 16.2728 | − | 8.72525i | 0.608993 | − | 0.326534i | ||||
\(715\) | 5.42166 | + | 5.42166i | 0.202759 | + | 0.202759i | ||||
\(716\) | −25.8416 | + | 2.65587i | −0.965746 | + | 0.0992546i | ||||
\(717\) | −16.3358 | + | 0.789136i | −0.610071 | + | 0.0294708i | ||||
\(718\) | −27.2333 | + | 12.9511i | −1.01634 | + | 0.483332i | ||||
\(719\) | −27.3421 | −1.01969 | −0.509844 | − | 0.860267i | \(-0.670297\pi\) | ||||
−0.509844 | + | 0.860267i | \(0.670297\pi\) | |||||||
\(720\) | −3.40949 | + | 6.48511i | −0.127064 | + | 0.241686i | ||||
\(721\) | −19.7250 | −0.734596 | ||||||||
\(722\) | 22.9752 | − | 10.9261i | 0.855048 | − | 0.406628i | ||||
\(723\) | 28.7474 | − | 1.38871i | 1.06913 | − | 0.0516465i | ||||
\(724\) | −4.77529 | − | 46.4635i | −0.177472 | − | 1.72680i | ||||
\(725\) | 13.2393 | + | 13.2393i | 0.491696 | + | 0.491696i | ||||
\(726\) | −14.7502 | + | 7.90889i | −0.547433 | + | 0.293526i | ||||
\(727\) | 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 | ||||
\(732\) | 27.7530 | − | 4.21391i | 1.02578 | − | 0.155751i | ||||
\(733\) | −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 | ||||||
\(738\) | 3.96347 | + | 6.60538i | 0.145897 | + | 0.243148i | ||||
\(739\) | −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 | ||||
\(741\) | −5.17183 | + | 0.249837i | −0.189992 | + | 0.00917798i | ||||
\(742\) | −18.3572 | + | 51.6499i | −0.673914 | + | 1.89613i | ||||
\(743\) | 1.29064i | 0.0473490i | 0.999720 | + | 0.0236745i | \(0.00753652\pi\) | ||||
−0.999720 | + | 0.0236745i | \(0.992463\pi\) | |||||||
\(744\) | −0.487252 | + | 2.52258i | −0.0178635 | + | 0.0924824i | ||||
\(745\) | 4.99948i | 0.183167i | ||||||||
\(746\) | −2.55766 | − | 0.909033i | −0.0936427 | − | 0.0332821i | ||||
\(747\) | −14.9088 | − | 12.2762i | −0.545483 | − | 0.449162i | ||||
\(748\) | −20.4111 | + | 2.09775i | −0.746304 | + | 0.0767014i | ||||
\(749\) | 5.10860 | − | 5.10860i | 0.186664 | − | 0.186664i | ||||
\(750\) | 13.7836 | + | 4.16161i | 0.503306 | + | 0.151960i | ||||
\(751\) | 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 | ||||
\(756\) | 16.5278 | − | 27.6870i | 0.601109 | − | 1.00697i | ||||
\(757\) | 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 | \(-0.677240\pi\) | ||||
−0.528485 | + | 0.848943i | \(0.677240\pi\) | |||||||
\(762\) | −34.0626 | + | 18.2639i | −1.23396 | + | 0.661633i | ||||
\(763\) | −20.3955 | − | 20.3955i | −0.738367 | − | 0.738367i | ||||
\(764\) | −4.01198 | + | 4.93111i | −0.145148 | + | 0.178401i | ||||
\(765\) | −2.82867 | + | 3.43528i | −0.102271 | + | 0.124203i | ||||
\(766\) | 20.0283 | + | 42.1149i | 0.723651 | + | 1.52167i | ||||
\(767\) | 0.338430 | 0.0122200 | ||||||||
\(768\) | −24.8575 | + | 12.2517i | −0.896969 | + | 0.442094i | ||||
\(769\) | 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 | ||||
\(771\) | 1.25996 | + | 26.0822i | 0.0453762 | + | 0.939326i | ||||
\(772\) | 14.4650 | − | 17.7789i | 0.520607 | − | 0.639875i | ||||
\(773\) | 26.6607 | + | 26.6607i | 0.958918 | + | 0.958918i | 0.999189 | − | 0.0402703i | \(-0.0128219\pi\) |
−0.0402703 | + | 0.999189i | \(0.512822\pi\) | |||||||
\(774\) | 1.03430 | − | 4.13767i | 0.0371772 | − | 0.148726i | ||||
\(775\) | 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 | ||||
\(780\) | 5.06472 | + | 3.72945i | 0.181346 | + | 0.133536i | ||||
\(781\) | −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 | ||||||||
\(786\) | −0.0805734 | + | 0.266866i | −0.00287396 | + | 0.00951879i | ||||
\(787\) | −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 | ||||
\(789\) | 2.49163 | + | 51.5788i | 0.0887044 | + | 1.83625i | ||||
\(790\) | −2.82774 | − | 1.00502i | −0.100606 | − | 0.0357571i | ||||
\(791\) | 25.7927i | 0.917082i | ||||||||
\(792\) | −28.6796 | + | 21.4811i | −1.01909 | + | 0.763297i | ||||
\(793\) | − | 24.0978i | − | 0.855736i | ||||||
\(794\) | −10.6734 | + | 30.0307i | −0.378784 | + | 1.06575i | ||||
\(795\) | −0.637430 | − | 13.1953i | −0.0226073 | − | 0.467990i | ||||
\(796\) | 30.8675 | − | 37.9391i | 1.09407 | − | 1.34472i | ||||
\(797\) | 11.2627 | − | 11.2627i | 0.398945 | − | 0.398945i | −0.478916 | − | 0.877861i | \(-0.658970\pi\) |
0.877861 | + | 0.478916i | \(0.158970\pi\) | |||||||
\(798\) | −7.31415 | − | 2.20832i | −0.258918 | − | 0.0781737i | ||||
\(799\) | − | 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 | ||||
\(804\) | −0.288240 | − | 1.89837i | −0.0101655 | − | 0.0669502i | ||||
\(805\) | 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 | \(-0.825969\pi\) | ||||
−0.854227 | + | 0.519900i | \(0.825969\pi\) | |||||||
\(810\) | −1.14911 | + | 7.68577i | −0.0403757 | + | 0.270050i | ||||
\(811\) | 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 | ||||
\(813\) | −1.11542 | − | 23.0901i | −0.0391195 | − | 0.809806i | ||||
\(814\) | 11.6272 | − | 5.52946i | 0.407534 | − | 0.193808i | ||||
\(815\) | −13.5567 | −0.474869 | ||||||||
\(816\) | −16.2955 | + | 4.21479i | −0.570457 | + | 0.147547i | ||||
\(817\) | −1.01056 | −0.0353551 | ||||||||
\(818\) | 20.0072 | − | 9.51467i | 0.699536 | − | 0.332673i | ||||
\(819\) | −21.3688 | − | 17.5955i | −0.746688 | − | 0.614837i | ||||
\(820\) | −2.20555 | + | 0.226676i | −0.0770212 | + | 0.00791585i | ||||
\(821\) | −33.7881 | − | 33.7881i | −1.17921 | − | 1.17921i | −0.979945 | − | 0.199268i | \(-0.936143\pi\) |
−0.199268 | − | 0.979945i | \(-0.563857\pi\) | |||||||
\(822\) | −15.3489 | − | 28.6260i | −0.535353 | − | 0.998445i | ||||
\(823\) | −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 | −0.415609 | − | 0.909543i | \(-0.636432\pi\) |
0.909543 | + | 0.415609i | \(0.136432\pi\) | |||||||
\(828\) | 29.8453 | + | 19.8297i | 1.03720 | + | 0.689130i | ||||
\(829\) | 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 | ||||||
\(834\) | 8.40249 | − | 27.8297i | 0.290954 | − | 0.963665i | ||||
\(835\) | −8.26499 | + | 8.26499i | −0.286022 | + | 0.286022i | ||||
\(836\) | 6.58584 | + | 5.35828i | 0.227776 | + | 0.185320i | ||||
\(837\) | 0.393236 | + | 2.69654i | 0.0135922 | + | 0.0932060i | ||||
\(838\) | 9.48110 | − | 26.6761i | 0.327519 | − | 0.921510i | ||||
\(839\) | 3.11543i | 0.107557i | 0.998553 | + | 0.0537784i | \(0.0171265\pi\) | ||||
−0.998553 | + | 0.0537784i | \(0.982874\pi\) | |||||||
\(840\) | 5.19884 | + | 7.68802i | 0.179377 | + | 0.265262i | ||||
\(841\) | 12.6272i | 0.435421i | ||||||||
\(842\) | 13.8647 | + | 4.92775i | 0.477810 | + | 0.169821i | ||||
\(843\) | 30.4387 | − | 1.47041i | 1.04837 | − | 0.0506436i | ||||
\(844\) | −1.78891 | − | 17.4061i | −0.0615768 | − | 0.599142i | ||||
\(845\) | −1.79457 | + | 1.79457i | −0.0617352 | + | 0.0617352i | ||||
\(846\) | −16.4549 | − | 27.4232i | −0.565733 | − | 0.942831i | ||||
\(847\) | 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 | ||||
\(852\) | −14.0026 | − | 10.3109i | −0.479720 | − | 0.353246i | ||||
\(853\) | 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 | \(-0.577315\pi\) | ||||
−0.240511 | + | 0.970646i | \(0.577315\pi\) | |||||||
\(858\) | 14.5357 | + | 27.1094i | 0.496241 | + | 0.925499i | ||||
\(859\) | −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 | ||||
\(861\) | 9.74637 | − | 0.470820i | 0.332155 | − | 0.0160455i | ||||
\(862\) | −12.5783 | − | 26.4494i | −0.428420 | − | 0.900871i | ||||
\(863\) | 14.4458 | 0.491740 | 0.245870 | − | 0.969303i | \(-0.420926\pi\) | ||||
0.245870 | + | 0.969303i | \(0.420926\pi\) | |||||||
\(864\) | −20.6146 | + | 20.9533i | −0.701321 | + | 0.712845i | ||||
\(865\) | 11.5083 | 0.391295 | ||||||||
\(866\) | 14.2126 | + | 29.8860i | 0.482965 | + | 1.01557i | ||||
\(867\) | 19.1995 | − | 0.927474i | 0.652049 | − | 0.0314987i | ||||
\(868\) | 2.52444 | + | 2.05390i | 0.0856850 | + | 0.0697139i | ||||
\(869\) | −10.3781 | − | 10.3781i | −0.352054 | − | 0.352054i | ||||
\(870\) | −2.85964 | − | 5.33328i | −0.0969507 | − | 0.180815i | ||||
\(871\) | −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 | ||||
\(876\) | −37.5458 | − | 27.6472i | −1.26855 | − | 0.934111i | ||||
\(877\) | 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 | \(-0.944941\pi\) | ||
0.985077 | − | 0.172113i | \(-0.0550594\pi\) | |||||||
\(882\) | −5.73499 | − | 9.55774i | −0.193107 | − | 0.321826i | ||||
\(883\) | 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 | ||||
\(885\) | −0.120211 | + | 0.00580708i | −0.00404087 | + | 0.000195203i | ||||
\(886\) | −7.63726 | − | 2.71440i | −0.256579 | − | 0.0911921i | ||||
\(887\) | 34.2664i | 1.15055i | 0.817959 | + | 0.575276i | \(0.195105\pi\) | ||||
−0.817959 | + | 0.575276i | \(0.804895\pi\) | |||||||
\(888\) | 8.74900 | − | 5.91631i | 0.293597 | − | 0.198538i | ||||
\(889\) | 48.9583i | 1.64201i | ||||||||
\(890\) | 3.63135 | − | 10.2172i | 0.121723 | − | 0.342481i | ||||
\(891\) | −21.2182 | + | 31.5316i | −0.710837 | + | 1.05635i | ||||
\(892\) | −12.7058 | − | 10.3375i | −0.425422 | − | 0.346126i | ||||
\(893\) | −5.35828 | + | 5.35828i | −0.179308 | + | 0.179308i | ||||
\(894\) | −5.79729 | + | 19.2011i | −0.193890 | + | 0.642181i | ||||
\(895\) | − | 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 | ||||
\(900\) | 23.1244 | + | 15.3643i | 0.770814 | + | 0.512142i | ||||
\(901\) | 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 | ||||||||
\(906\) | −11.5126 | − | 21.4712i | −0.382479 | − | 0.713331i | ||||
\(907\) | −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 | ||||
\(909\) | −0.596236 | − | 0.490953i | −0.0197759 | − | 0.0162839i | ||||
\(910\) | 7.19499 | − | 3.42166i | 0.238512 | − | 0.113427i | ||||
\(911\) | −24.1636 | −0.800576 | −0.400288 | − | 0.916389i | \(-0.631090\pi\) | ||||
−0.400288 | + | 0.916389i | \(0.631090\pi\) | |||||||
\(912\) | 6.00108 | + | 3.53468i | 0.198716 | + | 0.117045i | ||||
\(913\) | 27.1849 | 0.899690 | ||||||||
\(914\) | −35.8580 | + | 17.0527i | −1.18608 | + | 0.564054i | ||||
\(915\) | 0.413491 | + | 8.55960i | 0.0136696 | + | 0.282972i | ||||
\(916\) | 2.06803 | + | 20.1219i | 0.0683297 | + | 0.664847i | ||||
\(917\) | 0.249687 | + | 0.249687i | 0.00824540 | + | 0.00824540i | ||||
\(918\) | −14.8473 | + | 9.91353i | −0.490035 | + | 0.327195i | ||||
\(919\) | −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 | ||||
\(924\) | 6.81359 | + | 44.8746i | 0.224151 | + | 1.47627i | ||||
\(925\) | −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 | \(0.161551\pi\) | ||||
−0.873949 | + | 0.486018i | \(0.838449\pi\) | |||||||
\(930\) | −0.750855 | − | 0.226702i | −0.0246215 | − | 0.00743384i | ||||
\(931\) | −1.86751 | + | 1.86751i | −0.0612050 | + | 0.0612050i | ||||
\(932\) | −24.7939 | + | 30.4741i | −0.812152 | + | 0.998212i | ||||
\(933\) | 1.15598 | + | 23.9298i | 0.0378452 | + | 0.783427i | ||||
\(934\) | −6.51890 | + | 18.3416i | −0.213305 | + | 0.600156i | ||||
\(935\) | − | 6.26395i | − | 0.204853i | ||||||
\(936\) | 15.1271 | + | 20.1963i | 0.494444 | + | 0.660137i | ||||
\(937\) | − | 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 | ||||
\(939\) | 0.329325 | + | 6.81730i | 0.0107471 | + | 0.222474i | ||||
\(940\) | 9.15667 | − | 0.941078i | 0.298658 | − | 0.0306946i | ||||
\(941\) | 15.6688 | − | 15.6688i | 0.510788 | − | 0.510788i | −0.403980 | − | 0.914768i | \(-0.632374\pi\) |
0.914768 | + | 0.403980i | \(0.132374\pi\) | |||||||
\(942\) | −9.16315 | + | 30.3491i | −0.298552 | + | 0.988828i | ||||
\(943\) | 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 | 0.963444 | − | 0.267908i | \(-0.0863325\pi\) |
−0.267908 | + | 0.963444i | \(0.586332\pi\) | |||||||
\(948\) | −9.69487 | − | 7.13890i | −0.314875 | − | 0.231861i | ||||
\(949\) | −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 | \(-0.334109\pi\) | ||||
0.497888 | + | 0.867241i | \(0.334109\pi\) | |||||||
\(954\) | 12.8529 | − | 51.4174i | 0.416128 | − | 1.66470i | ||||
\(955\) | −1.37227 | − | 1.37227i | −0.0444056 | − | 0.0444056i | ||||
\(956\) | 11.9185 | − | 14.6489i | 0.385471 | − | 0.473780i | ||||
\(957\) | −1.42803 | − | 29.5614i | −0.0461616 | − | 0.955585i | ||||
\(958\) | −17.1567 | − | 36.0766i | −0.554307 | − | 1.16558i | ||||
\(959\) | −41.1441 | −1.32861 | ||||||||
\(960\) | −2.94478 | − | 7.93116i | −0.0950424 | − | 0.255977i | ||||
\(961\) | 30.7250 | 0.991128 | ||||||||
\(962\) | −3.89387 | − | 8.18793i | −0.125543 | − | 0.263989i | ||||
\(963\) | −4.44028 | + | 5.39249i | −0.143086 | + | 0.173770i | ||||
\(964\) | −20.9739 | + | 25.7789i | −0.675522 | + | 0.830281i | ||||
\(965\) | 4.94765 | + | 4.94765i | 0.159271 | + | 0.159271i | ||||
\(966\) | 40.0016 | − | 21.4483i | 1.28703 | − | 0.690089i | ||||
\(967\) | −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 | −0.449747 | − | 0.893156i | \(-0.648486\pi\) |
0.893156 | + | 0.449747i | \(0.148486\pi\) | |||||||
\(972\) | −13.3256 | + | 28.1856i | −0.427417 | + | 0.904054i | ||||
\(973\) | −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 | \(-0.917085\pi\) | ||
0.966265 | − | 0.257550i | \(-0.0829154\pi\) | |||||||
\(978\) | −52.0659 | − | 15.7200i | −1.66489 | − | 0.502670i | ||||
\(979\) | 37.4983 | − | 37.4983i | 1.19845 | − | 1.19845i | ||||
\(980\) | 3.19135 | − | 0.327991i | 0.101944 | − | 0.0104773i | ||||
\(981\) | 21.5289 | + | 17.7273i | 0.687365 | + | 0.565990i | ||||
\(982\) | 55.4827 | + | 19.7194i | 1.77052 | + | 0.629272i | ||||
\(983\) | 37.0765i | 1.18256i | 0.806468 | + | 0.591278i | \(0.201376\pi\) | ||||
−0.806468 | + | 0.591278i | \(0.798624\pi\) | |||||||
\(984\) | −8.73353 | − | 1.68693i | −0.278415 | − | 0.0537775i | ||||
\(985\) | 12.7839i | 0.407329i | ||||||||
\(986\) | 4.65576 | − | 13.0995i | 0.148270 | − | 0.417172i | ||||
\(987\) | −40.4635 | + | 1.95468i | −1.28797 | + | 0.0622182i | ||||
\(988\) | 3.77332 | − | 4.63778i | 0.120045 | − | 0.147547i | ||||
\(989\) | 4.24513 | − | 4.24513i | 0.134987 | − | 0.134987i | ||||
\(990\) | −5.62830 | − | 9.37993i | −0.178879 | − | 0.298114i | ||||
\(991\) | 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 | ||||
\(996\) | 22.0476 | − | 3.34761i | 0.698603 | − | 0.106073i | ||||
\(997\) | 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.35.2 | yes | 12 | |
3.2 | odd | 2 | inner | 48.2.k.a.35.5 | yes | 12 | |
4.3 | odd | 2 | 192.2.k.a.47.1 | 12 | |||
8.3 | odd | 2 | 384.2.k.a.95.6 | 12 | |||
8.5 | even | 2 | 384.2.k.b.95.1 | 12 | |||
12.11 | even | 2 | 192.2.k.a.47.3 | 12 | |||
16.3 | odd | 4 | 384.2.k.b.287.3 | 12 | |||
16.5 | even | 4 | 192.2.k.a.143.3 | 12 | |||
16.11 | odd | 4 | inner | 48.2.k.a.11.5 | yes | 12 | |
16.13 | even | 4 | 384.2.k.a.287.4 | 12 | |||
24.5 | odd | 2 | 384.2.k.b.95.3 | 12 | |||
24.11 | even | 2 | 384.2.k.a.95.4 | 12 | |||
48.5 | odd | 4 | 192.2.k.a.143.1 | 12 | |||
48.11 | even | 4 | inner | 48.2.k.a.11.2 | ✓ | 12 | |
48.29 | odd | 4 | 384.2.k.a.287.6 | 12 | |||
48.35 | even | 4 | 384.2.k.b.287.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.2.k.a.11.2 | ✓ | 12 | 48.11 | even | 4 | inner | |
48.2.k.a.11.5 | yes | 12 | 16.11 | odd | 4 | inner | |
48.2.k.a.35.2 | yes | 12 | 1.1 | even | 1 | trivial | |
48.2.k.a.35.5 | yes | 12 | 3.2 | odd | 2 | inner | |
192.2.k.a.47.1 | 12 | 4.3 | odd | 2 | |||
192.2.k.a.47.3 | 12 | 12.11 | even | 2 | |||
192.2.k.a.143.1 | 12 | 48.5 | odd | 4 | |||
192.2.k.a.143.3 | 12 | 16.5 | even | 4 | |||
384.2.k.a.95.4 | 12 | 24.11 | even | 2 | |||
384.2.k.a.95.6 | 12 | 8.3 | odd | 2 | |||
384.2.k.a.287.4 | 12 | 16.13 | even | 4 | |||
384.2.k.a.287.6 | 12 | 48.29 | odd | 4 | |||
384.2.k.b.95.1 | 12 | 8.5 | even | 2 | |||
384.2.k.b.95.3 | 12 | 24.5 | odd | 2 | |||
384.2.k.b.287.1 | 12 | 48.35 | even | 4 | |||
384.2.k.b.287.3 | 12 | 16.3 | odd | 4 |