Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [735,2,Mod(128,735)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(735, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("735.128");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.y (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.86900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 128.9 | ||
Character | \(\chi\) | \(=\) | 735.128 |
Dual form | 735.2.y.g.557.9 |
$q$-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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).
\(n\) | \(346\) | \(442\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.09358 | − | 0.293023i | 0.773275 | − | 0.207198i | 0.149457 | − | 0.988768i | \(-0.452247\pi\) |
0.623818 | + | 0.781570i | \(0.285581\pi\) | |||||||
\(3\) | 0.275979 | − | 1.70992i | 0.159337 | − | 0.987224i | ||||
\(4\) | −0.622004 | + | 0.359114i | −0.311002 | + | 0.179557i | ||||
\(5\) | −0.398678 | + | 2.20024i | −0.178294 | + | 0.983977i | ||||
\(6\) | −0.199242 | − | 1.95080i | −0.0813403 | − | 0.796410i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.17609 | + | 2.17609i | −0.769363 | + | 0.769363i | ||||
\(9\) | −2.84767 | − | 0.943806i | −0.949224 | − | 0.314602i | ||||
\(10\) | 0.208736 | + | 2.52295i | 0.0660082 | + | 0.797827i | ||||
\(11\) | −4.50498 | + | 2.60095i | −1.35830 | + | 0.784217i | −0.989395 | − | 0.145249i | \(-0.953602\pi\) |
−0.368908 | + | 0.929466i | \(0.620268\pi\) | |||||||
\(12\) | 0.442398 | + | 1.16269i | 0.127709 | + | 0.335639i | ||||
\(13\) | 3.24693 | + | 3.24693i | 0.900537 | + | 0.900537i | 0.995482 | − | 0.0949456i | \(-0.0302677\pi\) |
−0.0949456 | + | 0.995482i | \(0.530268\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.65221 | + | 1.28893i | 0.942997 | + | 0.332800i | ||||
\(16\) | −1.02384 | + | 1.77335i | −0.255961 | + | 0.443338i | ||||
\(17\) | 0.309010 | − | 1.15324i | 0.0749460 | − | 0.279702i | −0.918275 | − | 0.395943i | \(-0.870418\pi\) |
0.993221 | + | 0.116241i | \(0.0370844\pi\) | |||||||
\(18\) | −3.39070 | − | 0.197691i | −0.799196 | − | 0.0465961i | ||||
\(19\) | 1.14337 | + | 0.660123i | 0.262306 | + | 0.151443i | 0.625386 | − | 0.780315i | \(-0.284941\pi\) |
−0.363080 | + | 0.931758i | \(0.618275\pi\) | |||||||
\(20\) | −0.542159 | − | 1.51173i | −0.121230 | − | 0.338033i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.16440 | + | 4.16440i | −0.887854 | + | 0.887854i | ||||
\(23\) | 2.06039 | + | 7.68950i | 0.429622 | + | 1.60337i | 0.753618 | + | 0.657312i | \(0.228307\pi\) |
−0.323996 | + | 0.946058i | \(0.605027\pi\) | |||||||
\(24\) | 3.12039 | + | 4.32150i | 0.636946 | + | 0.882121i | ||||
\(25\) | −4.68211 | − | 1.75437i | −0.936422 | − | 0.350875i | ||||
\(26\) | 4.50219 | + | 2.59934i | 0.882953 | + | 0.509773i | ||||
\(27\) | −2.39973 | + | 4.60883i | −0.461829 | + | 0.886969i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.38282 | −0.813870 | −0.406935 | − | 0.913457i | \(-0.633402\pi\) | ||||
−0.406935 | + | 0.913457i | \(0.633402\pi\) | |||||||
\(30\) | 4.37166 | + | 0.339359i | 0.798152 | + | 0.0619582i | ||||
\(31\) | −0.852495 | − | 1.47656i | −0.153113 | − | 0.265199i | 0.779258 | − | 0.626704i | \(-0.215596\pi\) |
−0.932370 | + | 0.361505i | \(0.882263\pi\) | |||||||
\(32\) | 0.992986 | − | 3.70588i | 0.175537 | − | 0.655112i | ||||
\(33\) | 3.20415 | + | 8.42098i | 0.557771 | + | 1.46590i | ||||
\(34\) | − | 1.35170i | − | 0.231815i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.11020 | − | 0.435588i | 0.351700 | − | 0.0725981i | ||||
\(37\) | −0.626531 | − | 2.33824i | −0.103001 | − | 0.384405i | 0.895110 | − | 0.445846i | \(-0.147097\pi\) |
−0.998111 | + | 0.0614409i | \(0.980430\pi\) | |||||||
\(38\) | 1.44379 | + | 0.386863i | 0.234214 | + | 0.0627574i | ||||
\(39\) | 6.44809 | − | 4.65592i | 1.03252 | − | 0.745543i | ||||
\(40\) | −3.92036 | − | 5.65547i | −0.619863 | − | 0.894208i | ||||
\(41\) | 1.82176i | 0.284511i | 0.989830 | + | 0.142255i | \(0.0454354\pi\) | ||||
−0.989830 | + | 0.142255i | \(0.954565\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.281771 | − | 0.281771i | −0.0429697 | − | 0.0429697i | 0.685295 | − | 0.728265i | \(-0.259673\pi\) |
−0.728265 | + | 0.685295i | \(0.759673\pi\) | |||||||
\(44\) | 1.86808 | − | 3.23561i | 0.281624 | − | 0.487786i | ||||
\(45\) | 3.21190 | − | 5.88929i | 0.478802 | − | 0.877923i | ||||
\(46\) | 4.50640 | + | 7.80531i | 0.664432 | + | 1.15083i | ||||
\(47\) | 4.63886 | − | 1.24298i | 0.676647 | − | 0.181307i | 0.0959000 | − | 0.995391i | \(-0.469427\pi\) |
0.580747 | + | 0.814084i | \(0.302760\pi\) | |||||||
\(48\) | 2.74973 | + | 2.24010i | 0.396890 | + | 0.323331i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.63432 | − | 0.546575i | −0.796813 | − | 0.0772973i | ||||
\(51\) | −1.88667 | − | 0.846654i | −0.264187 | − | 0.118555i | ||||
\(52\) | −3.18563 | − | 0.853586i | −0.441767 | − | 0.118371i | ||||
\(53\) | 4.79555 | + | 1.28496i | 0.658719 | + | 0.176503i | 0.572668 | − | 0.819787i | \(-0.305908\pi\) |
0.0860514 | + | 0.996291i | \(0.472575\pi\) | |||||||
\(54\) | −1.27380 | + | 5.74328i | −0.173342 | + | 0.781561i | ||||
\(55\) | −3.92668 | − | 10.9490i | −0.529474 | − | 1.47636i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.44431 | − | 1.77289i | 0.191303 | − | 0.234825i | ||||
\(58\) | −4.79295 | + | 1.28427i | −0.629345 | + | 0.168633i | ||||
\(59\) | −0.908859 | − | 1.57419i | −0.118323 | − | 0.204942i | 0.800780 | − | 0.598959i | \(-0.204419\pi\) |
−0.919103 | + | 0.394017i | \(0.871085\pi\) | |||||||
\(60\) | −2.73457 | + | 0.509844i | −0.353031 | + | 0.0658205i | ||||
\(61\) | −1.23757 | + | 2.14354i | −0.158455 | + | 0.274452i | −0.934312 | − | 0.356457i | \(-0.883985\pi\) |
0.775857 | + | 0.630909i | \(0.217318\pi\) | |||||||
\(62\) | −1.36494 | − | 1.36494i | −0.173347 | − | 0.173347i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 8.43900i | − | 1.05488i | ||||||
\(65\) | −8.43851 | + | 5.84955i | −1.04667 | + | 0.725547i | ||||
\(66\) | 5.97152 | + | 8.27010i | 0.735043 | + | 1.01798i | ||||
\(67\) | −10.8207 | − | 2.89940i | −1.32196 | − | 0.354218i | −0.472249 | − | 0.881465i | \(-0.656558\pi\) |
−0.849712 | + | 0.527247i | \(0.823224\pi\) | |||||||
\(68\) | 0.221940 | + | 0.828292i | 0.0269142 | + | 0.100445i | ||||
\(69\) | 13.7171 | − | 1.40098i | 1.65134 | − | 0.168658i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.06358i | 1.07565i | 0.843057 | + | 0.537825i | \(0.180754\pi\) | ||||
−0.843057 | + | 0.537825i | \(0.819246\pi\) | |||||||
\(72\) | 8.25058 | − | 4.14298i | 0.972341 | − | 0.488255i | ||||
\(73\) | 0.489945 | − | 1.82850i | 0.0573438 | − | 0.214010i | −0.931309 | − | 0.364231i | \(-0.881332\pi\) |
0.988652 | + | 0.150221i | \(0.0479986\pi\) | |||||||
\(74\) | −1.37032 | − | 2.37346i | −0.159296 | − | 0.275909i | ||||
\(75\) | −4.29201 | + | 7.52188i | −0.495598 | + | 0.868552i | ||||
\(76\) | −0.948239 | −0.108771 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.68718 | − | 6.98104i | 0.643947 | − | 0.790447i | ||||
\(79\) | 9.96060 | + | 5.75076i | 1.12066 | + | 0.647011i | 0.941568 | − | 0.336823i | \(-0.109352\pi\) |
0.179087 | + | 0.983833i | \(0.442686\pi\) | |||||||
\(80\) | −3.49361 | − | 2.95970i | −0.390598 | − | 0.330905i | ||||
\(81\) | 7.21846 | + | 5.37530i | 0.802051 | + | 0.597255i | ||||
\(82\) | 0.533817 | + | 1.99223i | 0.0589502 | + | 0.220005i | ||||
\(83\) | −5.46196 | + | 5.46196i | −0.599528 | + | 0.599528i | −0.940187 | − | 0.340659i | \(-0.889350\pi\) |
0.340659 | + | 0.940187i | \(0.389350\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.41421 | + | 1.13967i | 0.261858 | + | 0.123614i | ||||
\(86\) | −0.390704 | − | 0.225573i | −0.0421307 | − | 0.0243241i | ||||
\(87\) | −1.20957 | + | 7.49429i | −0.129679 | + | 0.803472i | ||||
\(88\) | 4.14333 | − | 15.4631i | 0.441681 | − | 1.64838i | ||||
\(89\) | 4.71558 | − | 8.16762i | 0.499850 | − | 0.865766i | −0.500150 | − | 0.865939i | \(-0.666722\pi\) |
1.00000 | 0.000172710i | \(5.49753e-5\pi\) | ||||||||
\(90\) | 1.78676 | − | 7.38154i | 0.188341 | − | 0.778083i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.04298 | − | 4.04298i | −0.421510 | − | 0.421510i | ||||
\(93\) | −2.76008 | + | 1.05020i | −0.286207 | + | 0.108901i | ||||
\(94\) | 4.70873 | − | 2.71858i | 0.485668 | − | 0.280401i | ||||
\(95\) | −1.90827 | + | 2.25251i | −0.195784 | + | 0.231102i | ||||
\(96\) | −6.06272 | − | 2.72067i | −0.618774 | − | 0.277678i | ||||
\(97\) | 3.06315 | − | 3.06315i | 0.311016 | − | 0.311016i | −0.534287 | − | 0.845303i | \(-0.679420\pi\) |
0.845303 | + | 0.534287i | \(0.179420\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.2835 | − | 3.15483i | 1.53605 | − | 0.317072i | ||||
\(100\) | 3.54232 | − | 0.590186i | 0.354232 | − | 0.0590186i | ||||
\(101\) | 3.21850 | − | 1.85820i | 0.320252 | − | 0.184898i | −0.331253 | − | 0.943542i | \(-0.607471\pi\) |
0.651505 | + | 0.758644i | \(0.274138\pi\) | |||||||
\(102\) | −2.31131 | − | 0.373042i | −0.228854 | − | 0.0369367i | ||||
\(103\) | 1.61258 | − | 0.432088i | 0.158892 | − | 0.0425749i | −0.178496 | − | 0.983941i | \(-0.557123\pi\) |
0.337388 | + | 0.941366i | \(0.390457\pi\) | |||||||
\(104\) | −14.1312 | −1.38568 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.62082 | 0.545943 | ||||||||
\(107\) | −1.88524 | + | 0.505148i | −0.182253 | + | 0.0488345i | −0.348791 | − | 0.937200i | \(-0.613408\pi\) |
0.166538 | + | 0.986035i | \(0.446741\pi\) | |||||||
\(108\) | −0.162452 | − | 3.72849i | −0.0156320 | − | 0.358774i | ||||
\(109\) | 5.13991 | − | 2.96753i | 0.492314 | − | 0.284238i | −0.233220 | − | 0.972424i | \(-0.574926\pi\) |
0.725534 | + | 0.688186i | \(0.241593\pi\) | |||||||
\(110\) | −7.50243 | − | 10.8229i | −0.715329 | − | 1.03193i | ||||
\(111\) | −4.17113 | + | 0.426013i | −0.395906 | + | 0.0404353i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.240664 | + | 0.240664i | −0.0226398 | + | 0.0226398i | −0.718336 | − | 0.695696i | \(-0.755096\pi\) |
0.695696 | + | 0.718336i | \(0.255096\pi\) | |||||||
\(114\) | 1.05996 | − | 2.36200i | 0.0992744 | − | 0.221222i | ||||
\(115\) | −17.7402 | + | 1.46773i | −1.65428 | + | 0.136867i | ||||
\(116\) | 2.72613 | − | 1.57393i | 0.253115 | − | 0.146136i | ||||
\(117\) | −6.18172 | − | 12.3107i | −0.571500 | − | 1.13812i | ||||
\(118\) | −1.45518 | − | 1.45518i | −0.133960 | − | 0.133960i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −10.7524 | + | 5.14271i | −0.981551 | + | 0.469463i | ||||
\(121\) | 8.02991 | − | 13.9082i | 0.729992 | − | 1.26438i | ||||
\(122\) | −0.725273 | + | 2.70676i | −0.0656631 | + | 0.245058i | ||||
\(123\) | 3.11506 | + | 0.502767i | 0.280876 | + | 0.0453330i | ||||
\(124\) | 1.06051 | + | 0.612287i | 0.0952367 | + | 0.0549850i | ||||
\(125\) | 5.72670 | − | 9.60234i | 0.512211 | − | 0.858860i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.55939 | + | 4.55939i | −0.404581 | + | 0.404581i | −0.879844 | − | 0.475263i | \(-0.842353\pi\) |
0.475263 | + | 0.879844i | \(0.342353\pi\) | |||||||
\(128\) | −0.486848 | − | 1.81694i | −0.0430317 | − | 0.160597i | ||||
\(129\) | −0.559570 | + | 0.404044i | −0.0492674 | + | 0.0355741i | ||||
\(130\) | −7.51410 | + | 8.86960i | −0.659030 | + | 0.777916i | ||||
\(131\) | −11.8458 | − | 6.83920i | −1.03498 | − | 0.597543i | −0.116570 | − | 0.993183i | \(-0.537190\pi\) |
−0.918406 | + | 0.395639i | \(0.870523\pi\) | |||||||
\(132\) | −5.01709 | − | 4.08723i | −0.436682 | − | 0.355748i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −12.6829 | −1.09563 | ||||||||
\(135\) | −9.18381 | − | 7.11742i | −0.790416 | − | 0.612570i | ||||
\(136\) | 1.83712 | + | 3.18199i | 0.157532 | + | 0.272853i | ||||
\(137\) | −3.66874 | + | 13.6919i | −0.313441 | + | 1.16978i | 0.611991 | + | 0.790865i | \(0.290369\pi\) |
−0.925432 | + | 0.378914i | \(0.876298\pi\) | |||||||
\(138\) | 14.5901 | − | 5.55149i | 1.24200 | − | 0.472574i | ||||
\(139\) | 15.8262i | 1.34236i | 0.741292 | + | 0.671182i | \(0.234213\pi\) | ||||
−0.741292 | + | 0.671182i | \(0.765787\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.845170 | − | 8.27513i | −0.0711761 | − | 0.696892i | ||||
\(142\) | 2.65584 | + | 9.91172i | 0.222873 | + | 0.831773i | ||||
\(143\) | −23.0725 | − | 6.18226i | −1.92942 | − | 0.516986i | ||||
\(144\) | 4.58927 | − | 4.08361i | 0.382439 | − | 0.340301i | ||||
\(145\) | 1.74733 | − | 9.64326i | 0.145108 | − | 0.800829i | ||||
\(146\) | − | 2.14317i | − | 0.177370i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.22940 | + | 1.22940i | 0.101056 | + | 0.101056i | ||||
\(149\) | 4.65297 | − | 8.05918i | 0.381186 | − | 0.660234i | −0.610046 | − | 0.792366i | \(-0.708849\pi\) |
0.991232 | + | 0.132132i | \(0.0421823\pi\) | |||||||
\(150\) | −2.48955 | + | 9.48340i | −0.203271 | + | 0.774317i | ||||
\(151\) | 8.41370 | + | 14.5730i | 0.684697 | + | 1.18593i | 0.973532 | + | 0.228552i | \(0.0733990\pi\) |
−0.288834 | + | 0.957379i | \(0.593268\pi\) | |||||||
\(152\) | −3.92455 | + | 1.05158i | −0.318323 | + | 0.0852945i | ||||
\(153\) | −1.96840 | + | 2.99241i | −0.159135 | + | 0.241922i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.58867 | − | 1.28702i | 0.288249 | − | 0.103376i | ||||
\(156\) | −2.33873 | + | 5.21160i | −0.187248 | + | 0.417262i | ||||
\(157\) | 9.29781 | + | 2.49134i | 0.742046 | + | 0.198831i | 0.609987 | − | 0.792411i | \(-0.291175\pi\) |
0.132059 | + | 0.991242i | \(0.457841\pi\) | |||||||
\(158\) | 12.5778 | + | 3.37021i | 1.00063 | + | 0.268119i | ||||
\(159\) | 3.52066 | − | 7.84540i | 0.279206 | − | 0.622180i | ||||
\(160\) | 7.75793 | + | 3.66226i | 0.613319 | + | 0.289527i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 9.46902 | + | 3.76312i | 0.743957 | + | 0.295659i | ||||
\(163\) | −11.9932 | + | 3.21358i | −0.939383 | + | 0.251707i | −0.695851 | − | 0.718186i | \(-0.744973\pi\) |
−0.243532 | + | 0.969893i | \(0.578306\pi\) | |||||||
\(164\) | −0.654219 | − | 1.13314i | −0.0510859 | − | 0.0884835i | ||||
\(165\) | −19.8056 | + | 3.69264i | −1.54186 | + | 0.287471i | ||||
\(166\) | −4.37259 | + | 7.57355i | −0.339379 | + | 0.587822i | ||||
\(167\) | 12.4516 | + | 12.4516i | 0.963532 | + | 0.963532i | 0.999358 | − | 0.0358258i | \(-0.0114062\pi\) |
−0.0358258 | + | 0.999358i | \(0.511406\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.08513i | 0.621933i | ||||||||
\(170\) | 2.97408 | + | 0.538895i | 0.228101 | + | 0.0413313i | ||||
\(171\) | −2.63291 | − | 2.95893i | −0.201343 | − | 0.226275i | ||||
\(172\) | 0.276451 | + | 0.0740748i | 0.0210792 | + | 0.00564815i | ||||
\(173\) | −5.04991 | − | 18.8465i | −0.383938 | − | 1.43287i | −0.839835 | − | 0.542842i | \(-0.817348\pi\) |
0.455897 | − | 0.890032i | \(-0.349318\pi\) | |||||||
\(174\) | 0.873244 | + | 8.55000i | 0.0662004 | + | 0.648174i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 10.6519i | − | 0.802916i | ||||||
\(177\) | −2.94257 | + | 1.11963i | −0.221177 | + | 0.0841569i | ||||
\(178\) | 2.76354 | − | 10.3137i | 0.207136 | − | 0.773044i | ||||
\(179\) | 3.51580 | + | 6.08955i | 0.262783 | + | 0.455154i | 0.966981 | − | 0.254850i | \(-0.0820262\pi\) |
−0.704197 | + | 0.710005i | \(0.748693\pi\) | |||||||
\(180\) | 0.117110 | + | 4.81660i | 0.00872888 | + | 0.359008i | ||||
\(181\) | −14.1873 | −1.05454 | −0.527268 | − | 0.849699i | \(-0.676784\pi\) | ||||
−0.527268 | + | 0.849699i | \(0.676784\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.32374 | + | 2.70772i | 0.245698 | + | 0.200161i | ||||
\(184\) | −21.2166 | − | 12.2494i | −1.56411 | − | 0.903039i | ||||
\(185\) | 5.39448 | − | 0.446312i | 0.396610 | − | 0.0328135i | ||||
\(186\) | −2.71063 | + | 1.95724i | −0.198753 | + | 0.143512i | ||||
\(187\) | 1.60744 | + | 5.99906i | 0.117548 | + | 0.438694i | ||||
\(188\) | −2.43902 | + | 2.43902i | −0.177884 | + | 0.177884i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.42680 | + | 3.02245i | −0.103511 | + | 0.219272i | ||||
\(191\) | −13.5490 | − | 7.82251i | −0.980370 | − | 0.566017i | −0.0779880 | − | 0.996954i | \(-0.524850\pi\) |
−0.902382 | + | 0.430938i | \(0.858183\pi\) | |||||||
\(192\) | −14.4300 | − | 2.32899i | −1.04140 | − | 0.168080i | ||||
\(193\) | 3.29774 | − | 12.3073i | 0.237376 | − | 0.885901i | −0.739687 | − | 0.672951i | \(-0.765026\pi\) |
0.977063 | − | 0.212950i | \(-0.0683070\pi\) | |||||||
\(194\) | 2.45222 | − | 4.24736i | 0.176059 | − | 0.304943i | ||||
\(195\) | 7.67343 | + | 16.0436i | 0.549506 | + | 1.14890i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.78986 | − | 2.78986i | −0.198769 | − | 0.198769i | 0.600703 | − | 0.799472i | \(-0.294887\pi\) |
−0.799472 | + | 0.600703i | \(0.794887\pi\) | |||||||
\(198\) | 15.7892 | − | 7.92846i | 1.12209 | − | 0.563451i | ||||
\(199\) | 12.4985 | − | 7.21599i | 0.885993 | − | 0.511528i | 0.0133632 | − | 0.999911i | \(-0.495746\pi\) |
0.872630 | + | 0.488383i | \(0.162413\pi\) | |||||||
\(200\) | 14.0064 | − | 6.37102i | 0.990399 | − | 0.450499i | ||||
\(201\) | −7.94405 | + | 17.7024i | −0.560330 | + | 1.24863i | ||||
\(202\) | 2.97518 | − | 2.97518i | 0.209333 | − | 0.209333i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.47757 | − | 0.150909i | 0.103450 | − | 0.0105658i | ||||
\(205\) | −4.00830 | − | 0.726294i | −0.279952 | − | 0.0507266i | ||||
\(206\) | 1.63686 | − | 0.945043i | 0.114046 | − | 0.0658443i | ||||
\(207\) | 1.39006 | − | 23.8418i | 0.0966162 | − | 1.65712i | ||||
\(208\) | −9.08231 | + | 2.43360i | −0.629745 | + | 0.168740i | ||||
\(209\) | −6.86780 | −0.475056 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.9845 | 0.825049 | 0.412524 | − | 0.910947i | \(-0.364647\pi\) | ||||
0.412524 | + | 0.910947i | \(0.364647\pi\) | |||||||
\(212\) | −3.44430 | + | 0.922898i | −0.236556 | + | 0.0633849i | ||||
\(213\) | 15.4980 | + | 2.50136i | 1.06191 | + | 0.171390i | ||||
\(214\) | −1.91363 | + | 1.10484i | −0.130813 | + | 0.0755250i | ||||
\(215\) | 0.732300 | − | 0.507628i | 0.0499424 | − | 0.0346200i | ||||
\(216\) | −4.80718 | − | 15.2512i | −0.327087 | − | 1.03772i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.75133 | − | 4.75133i | 0.321801 | − | 0.321801i | ||||
\(219\) | −2.99138 | − | 1.34240i | −0.202139 | − | 0.0907107i | ||||
\(220\) | 6.37435 | + | 5.40019i | 0.429759 | + | 0.364081i | ||||
\(221\) | 4.74783 | − | 2.74116i | 0.319374 | − | 0.184391i | ||||
\(222\) | −4.43661 | + | 1.68811i | −0.297766 | + | 0.113299i | ||||
\(223\) | 12.1834 | + | 12.1834i | 0.815858 | + | 0.815858i | 0.985505 | − | 0.169647i | \(-0.0542628\pi\) |
−0.169647 | + | 0.985505i | \(0.554263\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.6773 | + | 9.41488i | 0.778489 | + | 0.627659i | ||||
\(226\) | −0.192664 | + | 0.333704i | −0.0128158 | + | 0.0221977i | ||||
\(227\) | 1.52755 | − | 5.70090i | 0.101387 | − | 0.378382i | −0.896523 | − | 0.442997i | \(-0.853915\pi\) |
0.997910 | + | 0.0646150i | \(0.0205819\pi\) | |||||||
\(228\) | −0.261694 | + | 1.62142i | −0.0173311 | + | 0.107381i | ||||
\(229\) | 23.6170 | + | 13.6353i | 1.56065 | + | 0.901043i | 0.997191 | + | 0.0749003i | \(0.0238639\pi\) |
0.563461 | + | 0.826143i | \(0.309469\pi\) | |||||||
\(230\) | −18.9701 | + | 6.80335i | −1.25085 | + | 0.448600i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.53740 | − | 9.53740i | 0.626161 | − | 0.626161i | ||||
\(233\) | −0.720306 | − | 2.68822i | −0.0471888 | − | 0.176111i | 0.938309 | − | 0.345797i | \(-0.112391\pi\) |
−0.985498 | + | 0.169686i | \(0.945725\pi\) | |||||||
\(234\) | −10.3675 | − | 11.6513i | −0.677744 | − | 0.761667i | ||||
\(235\) | 0.885442 | + | 10.7022i | 0.0577599 | + | 0.698132i | ||||
\(236\) | 1.13063 | + | 0.652769i | 0.0735976 | + | 0.0424916i | ||||
\(237\) | 12.5823 | − | 15.4448i | 0.817306 | − | 1.00325i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.42942 | 0.0924613 | 0.0462307 | − | 0.998931i | \(-0.485279\pi\) | ||||
0.0462307 | + | 0.998931i | \(0.485279\pi\) | |||||||
\(240\) | −6.02502 | + | 5.15700i | −0.388914 | + | 0.332883i | ||||
\(241\) | 14.5659 | + | 25.2289i | 0.938274 | + | 1.62514i | 0.768689 | + | 0.639623i | \(0.220909\pi\) |
0.169585 | + | 0.985516i | \(0.445757\pi\) | |||||||
\(242\) | 4.70590 | − | 17.5626i | 0.302506 | − | 1.12897i | ||||
\(243\) | 11.1835 | − | 10.8595i | 0.717421 | − | 0.696640i | ||||
\(244\) | − | 1.77772i | − | 0.113807i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.55388 | − | 0.362971i | 0.226587 | − | 0.0231422i | ||||
\(247\) | 1.56906 | + | 5.85581i | 0.0998369 | + | 0.372596i | ||||
\(248\) | 5.06824 | + | 1.35803i | 0.321833 | + | 0.0862350i | ||||
\(249\) | 7.83215 | + | 10.8469i | 0.496342 | + | 0.687396i | ||||
\(250\) | 3.44887 | − | 12.1789i | 0.218126 | − | 0.770264i | ||||
\(251\) | 12.3977i | 0.782538i | 0.920276 | + | 0.391269i | \(0.127964\pi\) | ||||
−0.920276 | + | 0.391269i | \(0.872036\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −29.2821 | − | 29.2821i | −1.84095 | − | 1.84095i | ||||
\(254\) | −3.65004 | + | 6.32205i | −0.229024 | + | 0.396681i | ||||
\(255\) | 2.61502 | − | 3.81359i | 0.163759 | − | 0.238817i | ||||
\(256\) | 7.37419 | + | 12.7725i | 0.460887 | + | 0.798280i | ||||
\(257\) | 18.9490 | − | 5.07738i | 1.18201 | − | 0.316718i | 0.386286 | − | 0.922379i | \(-0.373758\pi\) |
0.795723 | + | 0.605661i | \(0.207091\pi\) | |||||||
\(258\) | −0.493538 | + | 0.605820i | −0.0307263 | + | 0.0377167i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.14813 | − | 6.66884i | 0.195239 | − | 0.413584i | ||||
\(261\) | 12.4808 | + | 4.13653i | 0.772544 | + | 0.256045i | ||||
\(262\) | −14.9584 | − | 4.00808i | −0.924131 | − | 0.247620i | ||||
\(263\) | −16.7901 | − | 4.49890i | −1.03532 | − | 0.277414i | −0.299149 | − | 0.954206i | \(-0.596703\pi\) |
−0.736174 | + | 0.676792i | \(0.763369\pi\) | |||||||
\(264\) | −25.2973 | − | 11.3523i | −1.55694 | − | 0.698685i | ||||
\(265\) | −4.73911 | + | 10.0391i | −0.291121 | + | 0.616695i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.6646 | − | 10.3174i | −0.775061 | − | 0.631413i | ||||
\(268\) | 7.77175 | − | 2.08243i | 0.474735 | − | 0.127205i | ||||
\(269\) | 9.57676 | + | 16.5874i | 0.583906 | + | 1.01135i | 0.995011 | + | 0.0997663i | \(0.0318095\pi\) |
−0.411105 | + | 0.911588i | \(0.634857\pi\) | |||||||
\(270\) | −12.1288 | − | 5.09238i | −0.738133 | − | 0.309912i | ||||
\(271\) | 9.23146 | − | 15.9894i | 0.560771 | − | 0.971284i | −0.436658 | − | 0.899627i | \(-0.643838\pi\) |
0.997429 | − | 0.0716565i | \(-0.0228285\pi\) | |||||||
\(272\) | 1.72872 | + | 1.72872i | 0.104819 | + | 0.104819i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.0482i | 0.969505i | ||||||||
\(275\) | 25.6559 | − | 4.27453i | 1.54711 | − | 0.257764i | ||||
\(276\) | −8.02897 | + | 5.79741i | −0.483287 | + | 0.348963i | ||||
\(277\) | 10.4648 | + | 2.80403i | 0.628768 | + | 0.168478i | 0.559111 | − | 0.829093i | \(-0.311143\pi\) |
0.0696576 | + | 0.997571i | \(0.477809\pi\) | |||||||
\(278\) | 4.63745 | + | 17.3072i | 0.278136 | + | 1.03802i | ||||
\(279\) | 1.03404 | + | 5.00936i | 0.0619061 | + | 0.299903i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.4646i | 1.22082i | 0.792087 | + | 0.610408i | \(0.208995\pi\) | ||||
−0.792087 | + | 0.610408i | \(0.791005\pi\) | |||||||
\(282\) | −3.34906 | − | 8.80183i | −0.199434 | − | 0.524141i | ||||
\(283\) | −3.01798 | + | 11.2633i | −0.179400 | + | 0.669531i | 0.816360 | + | 0.577544i | \(0.195989\pi\) |
−0.995760 | + | 0.0919876i | \(0.970678\pi\) | |||||||
\(284\) | −3.25486 | − | 5.63759i | −0.193141 | − | 0.334529i | ||||
\(285\) | 3.32497 | + | 3.88463i | 0.196954 | + | 0.230106i | ||||
\(286\) | −27.0431 | −1.59909 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −6.32533 | + | 9.61593i | −0.372723 | + | 0.566624i | ||||
\(289\) | 13.4880 | + | 7.78727i | 0.793409 | + | 0.458075i | ||||
\(290\) | −0.914854 | − | 11.0576i | −0.0537221 | − | 0.649327i | ||||
\(291\) | −4.39239 | − | 6.08312i | −0.257486 | − | 0.356599i | ||||
\(292\) | 0.351893 | + | 1.31328i | 0.0205930 | + | 0.0768540i | ||||
\(293\) | 19.7225 | − | 19.7225i | 1.15220 | − | 1.15220i | 0.166088 | − | 0.986111i | \(-0.446886\pi\) |
0.986111 | − | 0.166088i | \(-0.0531135\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.82594 | − | 1.37211i | 0.222755 | − | 0.0798875i | ||||
\(296\) | 6.45161 | + | 3.72484i | 0.374992 | + | 0.216502i | ||||
\(297\) | −1.17659 | − | 27.0043i | −0.0682726 | − | 1.56695i | ||||
\(298\) | 2.72685 | − | 10.1768i | 0.157962 | − | 0.589524i | ||||
\(299\) | −18.2773 | + | 31.6572i | −1.05700 | + | 1.83078i | ||||
\(300\) | −0.0315680 | − | 6.21996i | −0.00182258 | − | 0.359110i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 13.4712 | + | 13.4712i | 0.775182 | + | 0.775182i | ||||
\(303\) | −2.28914 | − | 6.01621i | −0.131508 | − | 0.345622i | ||||
\(304\) | −2.34126 | + | 1.35173i | −0.134281 | + | 0.0775269i | ||||
\(305\) | −4.22290 | − | 3.57753i | −0.241803 | − | 0.204849i | ||||
\(306\) | −1.27575 | + | 3.84921i | −0.0729296 | + | 0.220045i | ||||
\(307\) | 13.2997 | − | 13.2997i | 0.759057 | − | 0.759057i | −0.217094 | − | 0.976151i | \(-0.569658\pi\) |
0.976151 | + | 0.217094i | \(0.0696578\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.293801 | − | 2.87663i | −0.0167137 | − | 0.163646i | ||||
\(310\) | 3.54736 | − | 2.45902i | 0.201476 | − | 0.139663i | ||||
\(311\) | −20.6156 | + | 11.9024i | −1.16901 | + | 0.674926i | −0.953446 | − | 0.301565i | \(-0.902491\pi\) |
−0.215560 | + | 0.976491i | \(0.569158\pi\) | |||||||
\(312\) | −3.89992 | + | 24.1633i | −0.220789 | + | 1.36798i | ||||
\(313\) | −25.8660 | + | 6.93078i | −1.46203 | + | 0.391751i | −0.900192 | − | 0.435494i | \(-0.856574\pi\) |
−0.561842 | + | 0.827244i | \(0.689907\pi\) | |||||||
\(314\) | 10.8979 | 0.615003 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.26072 | −0.464702 | ||||||||
\(317\) | −15.9728 | + | 4.27990i | −0.897122 | + | 0.240383i | −0.677780 | − | 0.735265i | \(-0.737058\pi\) |
−0.219342 | + | 0.975648i | \(0.570391\pi\) | |||||||
\(318\) | 1.55123 | − | 9.61117i | 0.0869886 | − | 0.538968i | ||||
\(319\) | 19.7445 | − | 11.3995i | 1.10548 | − | 0.638250i | ||||
\(320\) | 18.5678 | + | 3.36444i | 1.03797 | + | 0.188078i | ||||
\(321\) | 0.343478 | + | 3.36302i | 0.0191711 | + | 0.187706i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.11459 | − | 1.11459i | 0.0620177 | − | 0.0620177i | ||||
\(324\) | −6.42026 | − | 0.751204i | −0.356681 | − | 0.0417336i | ||||
\(325\) | −9.50617 | − | 20.8988i | −0.527307 | − | 1.15926i | ||||
\(326\) | −12.1739 | + | 7.02859i | −0.674248 | + | 0.389277i | ||||
\(327\) | −3.65574 | − | 9.60782i | −0.202163 | − | 0.531314i | ||||
\(328\) | −3.96430 | − | 3.96430i | −0.218892 | − | 0.218892i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −20.5769 | + | 9.84167i | −1.13272 | + | 0.541766i | ||||
\(331\) | 5.79489 | − | 10.0370i | 0.318516 | − | 0.551685i | −0.661663 | − | 0.749802i | \(-0.730149\pi\) |
0.980179 | + | 0.198116i | \(0.0634823\pi\) | |||||||
\(332\) | 1.43590 | − | 5.35884i | 0.0788050 | − | 0.294104i | ||||
\(333\) | −0.422695 | + | 7.24987i | −0.0231635 | + | 0.397291i | ||||
\(334\) | 17.2653 | + | 9.96815i | 0.944718 | + | 0.545433i | ||||
\(335\) | 10.6934 | − | 22.6523i | 0.584241 | − | 1.23762i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.46127 | + | 5.46127i | −0.297494 | + | 0.297494i | −0.840032 | − | 0.542537i | \(-0.817464\pi\) |
0.542537 | + | 0.840032i | \(0.317464\pi\) | |||||||
\(338\) | 2.36913 | + | 8.84171i | 0.128864 | + | 0.480926i | ||||
\(339\) | 0.345098 | + | 0.477935i | 0.0187432 | + | 0.0259579i | ||||
\(340\) | −1.91092 | + | 0.158100i | −0.103634 | + | 0.00857418i | ||||
\(341\) | 7.68095 | + | 4.43460i | 0.415947 | + | 0.240147i | ||||
\(342\) | −3.74632 | − | 2.46431i | −0.202578 | − | 0.133255i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.22632 | 0.0661186 | ||||||||
\(345\) | −2.38621 | + | 30.7394i | −0.128469 | + | 1.65495i | ||||
\(346\) | −11.0449 | − | 19.1304i | −0.593779 | − | 1.02845i | ||||
\(347\) | −7.39306 | + | 27.5913i | −0.396880 | + | 1.48118i | 0.421674 | + | 0.906748i | \(0.361443\pi\) |
−0.818554 | + | 0.574430i | \(0.805224\pi\) | |||||||
\(348\) | −1.93895 | − | 5.09585i | −0.103939 | − | 0.273166i | ||||
\(349\) | − | 11.9748i | − | 0.640997i | −0.947249 | − | 0.320498i | \(-0.896150\pi\) | ||
0.947249 | − | 0.320498i | \(-0.103850\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −22.7563 | + | 7.17278i | −1.21464 | + | 0.382855i | ||||
\(352\) | 5.16542 | + | 19.2776i | 0.275318 | + | 1.02750i | ||||
\(353\) | 33.2522 | + | 8.90989i | 1.76983 | + | 0.474226i | 0.988671 | − | 0.150101i | \(-0.0479597\pi\) |
0.781164 | + | 0.624326i | \(0.214626\pi\) | |||||||
\(354\) | −2.88984 | + | 2.08665i | −0.153593 | + | 0.110904i | ||||
\(355\) | −19.9421 | − | 3.61345i | −1.05841 | − | 0.191782i | ||||
\(356\) | 6.77373i | 0.359007i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.62917 | + | 5.62917i | 0.297511 | + | 0.297511i | ||||
\(359\) | −7.10821 | + | 12.3118i | −0.375157 | + | 0.649791i | −0.990351 | − | 0.138585i | \(-0.955745\pi\) |
0.615194 | + | 0.788376i | \(0.289078\pi\) | |||||||
\(360\) | 5.82622 | + | 19.8050i | 0.307069 | + | 1.04381i | ||||
\(361\) | −8.62847 | − | 14.9450i | −0.454130 | − | 0.786577i | ||||
\(362\) | −15.5149 | + | 4.15721i | −0.815447 | + | 0.218498i | ||||
\(363\) | −21.5659 | − | 17.5689i | −1.13192 | − | 0.922129i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.82781 | + | 1.80698i | 0.200357 | + | 0.0945816i | ||||
\(366\) | 4.42818 | + | 1.98717i | 0.231465 | + | 0.103871i | ||||
\(367\) | 22.8159 | + | 6.11351i | 1.19098 | + | 0.319122i | 0.799274 | − | 0.600967i | \(-0.205218\pi\) |
0.391708 | + | 0.920090i | \(0.371885\pi\) | |||||||
\(368\) | −15.7457 | − | 4.21905i | −0.820801 | − | 0.219933i | ||||
\(369\) | 1.71938 | − | 5.18777i | 0.0895076 | − | 0.270064i | ||||
\(370\) | 5.76850 | − | 2.06878i | 0.299890 | − | 0.107551i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.33964 | − | 1.64441i | 0.0694572 | − | 0.0852589i | ||||
\(373\) | −6.25471 | + | 1.67595i | −0.323857 | + | 0.0867772i | −0.417085 | − | 0.908868i | \(-0.636948\pi\) |
0.0932279 | + | 0.995645i | \(0.470281\pi\) | |||||||
\(374\) | 3.51572 | + | 6.08941i | 0.181794 | + | 0.314876i | ||||
\(375\) | −14.8388 | − | 12.4423i | −0.766273 | − | 0.642515i | ||||
\(376\) | −7.38973 | + | 12.7994i | −0.381096 | + | 0.660078i | ||||
\(377\) | −14.2307 | − | 14.2307i | −0.732920 | − | 0.732920i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 12.6506i | − | 0.649816i | −0.945746 | − | 0.324908i | \(-0.894667\pi\) | ||
0.945746 | − | 0.324908i | \(-0.105333\pi\) | |||||||
\(380\) | 0.378042 | − | 2.08635i | 0.0193931 | − | 0.107028i | ||||
\(381\) | 6.53791 | + | 9.05450i | 0.334947 | + | 0.463876i | ||||
\(382\) | −17.1090 | − | 4.58435i | −0.875373 | − | 0.234556i | ||||
\(383\) | 6.59450 | + | 24.6110i | 0.336963 | + | 1.25756i | 0.901725 | + | 0.432310i | \(0.142302\pi\) |
−0.564761 | + | 0.825254i | \(0.691032\pi\) | |||||||
\(384\) | −3.24119 | + | 0.331035i | −0.165401 | + | 0.0168930i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 14.4253i | − | 0.734229i | ||||||
\(387\) | 0.536454 | + | 1.06833i | 0.0272695 | + | 0.0543062i | ||||
\(388\) | −0.805272 | + | 3.00532i | −0.0408815 | + | 0.152572i | ||||
\(389\) | −8.86076 | − | 15.3473i | −0.449259 | − | 0.778139i | 0.549079 | − | 0.835770i | \(-0.314978\pi\) |
−0.998338 | + | 0.0576315i | \(0.981645\pi\) | |||||||
\(390\) | 13.0926 | + | 15.2964i | 0.662970 | + | 0.774561i | ||||
\(391\) | 9.50453 | 0.480665 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.9637 | + | 18.3680i | −0.754819 | + | 0.926543i | ||||
\(394\) | −3.86842 | − | 2.23343i | −0.194888 | − | 0.112519i | ||||
\(395\) | −16.6241 | + | 19.6230i | −0.836450 | + | 0.987341i | ||||
\(396\) | −8.37346 | + | 7.45085i | −0.420782 | + | 0.374419i | ||||
\(397\) | −1.62162 | − | 6.05197i | −0.0813868 | − | 0.303740i | 0.913219 | − | 0.407470i | \(-0.133589\pi\) |
−0.994605 | + | 0.103730i | \(0.966922\pi\) | |||||||
\(398\) | 11.5536 | − | 11.5536i | 0.579128 | − | 0.579128i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.90488 | − | 6.50682i | 0.395244 | − | 0.325341i | ||||
\(401\) | 29.8588 | + | 17.2390i | 1.49108 | + | 0.860874i | 0.999948 | − | 0.0102128i | \(-0.00325089\pi\) |
0.491129 | + | 0.871087i | \(0.336584\pi\) | |||||||
\(402\) | −3.50021 | + | 21.6867i | −0.174574 | + | 1.08164i | ||||
\(403\) | 2.02631 | − | 7.56230i | 0.100938 | − | 0.376705i | ||||
\(404\) | −1.33461 | + | 2.31162i | −0.0663995 | + | 0.115007i | ||||
\(405\) | −14.7048 | + | 13.7393i | −0.730686 | + | 0.682713i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.90417 | + | 8.90417i | 0.441364 | + | 0.441364i | ||||
\(408\) | 5.94796 | − | 2.26317i | 0.294468 | − | 0.112044i | ||||
\(409\) | −16.9449 | + | 9.78314i | −0.837871 | + | 0.483745i | −0.856540 | − | 0.516081i | \(-0.827390\pi\) |
0.0186690 | + | 0.999826i | \(0.494057\pi\) | |||||||
\(410\) | −4.59621 | + | 0.380267i | −0.226990 | + | 0.0187800i | ||||
\(411\) | 22.3996 | + | 10.0519i | 1.10489 | + | 0.495825i | ||||
\(412\) | −0.847860 | + | 0.847860i | −0.0417711 | + | 0.0417711i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −5.46604 | − | 26.4801i | −0.268641 | − | 1.30143i | ||||
\(415\) | −9.84007 | − | 14.1952i | −0.483030 | − | 0.696815i | ||||
\(416\) | 15.2569 | − | 8.80857i | 0.748030 | − | 0.431876i | ||||
\(417\) | 27.0617 | + | 4.36771i | 1.32522 | + | 0.213888i | ||||
\(418\) | −7.51046 | + | 2.01242i | −0.367349 | + | 0.0984308i | ||||
\(419\) | −17.0209 | −0.831524 | −0.415762 | − | 0.909474i | \(-0.636485\pi\) | ||||
−0.415762 | + | 0.909474i | \(0.636485\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.7474 | 1.05990 | 0.529951 | − | 0.848028i | \(-0.322210\pi\) | ||||
0.529951 | + | 0.848028i | \(0.322210\pi\) | |||||||
\(422\) | 13.1060 | − | 3.51174i | 0.637990 | − | 0.170949i | ||||
\(423\) | −14.3831 | − | 0.838588i | −0.699329 | − | 0.0407735i | ||||
\(424\) | −13.2317 | + | 7.63934i | −0.642589 | + | 0.370999i | ||||
\(425\) | −3.47004 | + | 4.85749i | −0.168322 | + | 0.235623i | ||||
\(426\) | 17.6812 | − | 1.80585i | 0.856658 | − | 0.0874936i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.991221 | − | 0.991221i | 0.0479125 | − | 0.0479125i | ||||
\(429\) | −16.9387 | + | 37.7460i | −0.817808 | + | 1.82239i | ||||
\(430\) | 0.652079 | − | 0.769711i | 0.0314460 | − | 0.0371188i | ||||
\(431\) | −9.34548 | + | 5.39562i | −0.450156 | + | 0.259898i | −0.707896 | − | 0.706317i | \(-0.750356\pi\) |
0.257740 | + | 0.966214i | \(0.417022\pi\) | |||||||
\(432\) | −5.71612 | − | 8.97429i | −0.275017 | − | 0.431776i | ||||
\(433\) | −0.466927 | − | 0.466927i | −0.0224391 | − | 0.0224391i | 0.695798 | − | 0.718237i | \(-0.255051\pi\) |
−0.718237 | + | 0.695798i | \(0.755051\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −16.0070 | − | 5.64914i | −0.767477 | − | 0.270856i | ||||
\(436\) | −2.13136 | + | 3.69163i | −0.102074 | + | 0.176797i | ||||
\(437\) | −2.72023 | + | 10.1520i | −0.130126 | + | 0.485638i | ||||
\(438\) | −3.66465 | − | 0.591470i | −0.175104 | − | 0.0282615i | ||||
\(439\) | −8.17235 | − | 4.71831i | −0.390045 | − | 0.225193i | 0.292135 | − | 0.956377i | \(-0.405634\pi\) |
−0.682180 | + | 0.731185i | \(0.738968\pi\) | |||||||
\(440\) | 32.3708 | + | 15.2811i | 1.54322 | + | 0.728500i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.38889 | − | 4.38889i | 0.208758 | − | 0.208758i | ||||
\(443\) | −6.18422 | − | 23.0798i | −0.293821 | − | 1.09656i | −0.942149 | − | 0.335194i | \(-0.891198\pi\) |
0.648328 | − | 0.761361i | \(-0.275469\pi\) | |||||||
\(444\) | 2.44147 | − | 1.76289i | 0.115867 | − | 0.0836632i | ||||
\(445\) | 16.0907 | + | 13.6317i | 0.762774 | + | 0.646202i | ||||
\(446\) | 16.8934 | + | 9.75342i | 0.799927 | + | 0.461838i | ||||
\(447\) | −12.4965 | − | 10.1804i | −0.591062 | − | 0.481516i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.5643 | 0.545753 | 0.272876 | − | 0.962049i | \(-0.412025\pi\) | ||||
0.272876 | + | 0.962049i | \(0.412025\pi\) | |||||||
\(450\) | 15.5288 | + | 6.87417i | 0.732036 | + | 0.324051i | ||||
\(451\) | −4.73831 | − | 8.20699i | −0.223118 | − | 0.386452i | ||||
\(452\) | 0.0632681 | − | 0.236120i | 0.00297588 | − | 0.0111061i | ||||
\(453\) | 27.2406 | − | 10.3649i | 1.27988 | − | 0.486988i | ||||
\(454\) | − | 6.68197i | − | 0.313601i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.715027 | + | 7.00090i | 0.0334842 | + | 0.327847i | ||||
\(457\) | −6.53036 | − | 24.3716i | −0.305477 | − | 1.14006i | −0.932534 | − | 0.361083i | \(-0.882407\pi\) |
0.627056 | − | 0.778974i | \(-0.284260\pi\) | |||||||
\(458\) | 29.8224 | + | 7.99088i | 1.39351 | + | 0.373389i | ||||
\(459\) | 4.57355 | + | 4.19165i | 0.213475 | + | 0.195649i | ||||
\(460\) | 10.5074 | − | 7.28369i | 0.489909 | − | 0.339604i | ||||
\(461\) | − | 13.0571i | − | 0.608129i | −0.952651 | − | 0.304064i | \(-0.901656\pi\) | ||
0.952651 | − | 0.304064i | \(-0.0983438\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.3925 | + | 17.3925i | 0.808298 | + | 0.808298i | 0.984376 | − | 0.176079i | \(-0.0563413\pi\) |
−0.176079 | + | 0.984376i | \(0.556341\pi\) | |||||||
\(464\) | 4.48733 | − | 7.77228i | 0.208319 | − | 0.360819i | ||||
\(465\) | −1.21031 | − | 6.49154i | −0.0561267 | − | 0.301038i | ||||
\(466\) | −1.57542 | − | 2.72871i | −0.0729799 | − | 0.126405i | ||||
\(467\) | −12.8489 | + | 3.44285i | −0.594576 | + | 0.159316i | −0.543544 | − | 0.839381i | \(-0.682918\pi\) |
−0.0510324 | + | 0.998697i | \(0.516251\pi\) | |||||||
\(468\) | 8.26600 | + | 5.43734i | 0.382096 | + | 0.251341i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.10427 | + | 11.4442i | 0.189316 | + | 0.527880i | ||||
\(471\) | 6.82600 | − | 15.2110i | 0.314526 | − | 0.700885i | ||||
\(472\) | 5.40333 | + | 1.44782i | 0.248708 | + | 0.0666412i | ||||
\(473\) | 2.00225 | + | 0.536501i | 0.0920634 | + | 0.0246683i | ||||
\(474\) | 9.23400 | − | 20.5769i | 0.424131 | − | 0.945129i | ||||
\(475\) | −4.19527 | − | 5.09667i | −0.192492 | − | 0.233851i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.4434 | − | 8.18522i | −0.569744 | − | 0.374776i | ||||
\(478\) | 1.56318 | − | 0.418852i | 0.0714980 | − | 0.0191578i | ||||
\(479\) | −19.4344 | − | 33.6614i | −0.887982 | − | 1.53803i | −0.842257 | − | 0.539075i | \(-0.818774\pi\) |
−0.0457243 | − | 0.998954i | \(-0.514560\pi\) | |||||||
\(480\) | 8.40321 | − | 12.2548i | 0.383552 | − | 0.559351i | ||||
\(481\) | 5.55782 | − | 9.62642i | 0.253415 | − | 0.438927i | ||||
\(482\) | 23.3216 | + | 23.3216i | 1.06227 | + | 1.06227i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.5346i | 0.524301i | ||||||||
\(485\) | 5.51846 | + | 7.96088i | 0.250580 | + | 0.361485i | ||||
\(486\) | 9.04790 | − | 15.1528i | 0.410421 | − | 0.687343i | ||||
\(487\) | −32.7230 | − | 8.76810i | −1.48282 | − | 0.397321i | −0.575515 | − | 0.817791i | \(-0.695198\pi\) |
−0.907306 | + | 0.420471i | \(0.861865\pi\) | |||||||
\(488\) | −1.97146 | − | 7.35758i | −0.0892437 | − | 0.333062i | ||||
\(489\) | 2.18509 | + | 21.3944i | 0.0988131 | + | 0.967488i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 25.6453i | − | 1.15736i | −0.815556 | − | 0.578678i | \(-0.803569\pi\) | ||
0.815556 | − | 0.578678i | \(-0.196431\pi\) | |||||||
\(492\) | −2.11813 | + | 0.805941i | −0.0954929 | + | 0.0363346i | ||||
\(493\) | −1.35434 | + | 5.05445i | −0.0609963 | + | 0.227641i | ||||
\(494\) | 3.43177 | + | 5.94401i | 0.154403 | + | 0.267433i | ||||
\(495\) | 0.848193 | + | 34.8851i | 0.0381234 | + | 1.56797i | ||||
\(496\) | 3.49129 | 0.156764 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 11.7434 | + | 9.56694i | 0.526236 | + | 0.428705i | ||||
\(499\) | 25.2063 | + | 14.5529i | 1.12839 | + | 0.651476i | 0.943529 | − | 0.331289i | \(-0.107484\pi\) |
0.184860 | + | 0.982765i | \(0.440817\pi\) | |||||||
\(500\) | −0.113691 | + | 8.02924i | −0.00508440 | + | 0.359078i | ||||
\(501\) | 24.7276 | − | 17.8549i | 1.10475 | − | 0.797697i | ||||
\(502\) | 3.63282 | + | 13.5579i | 0.162141 | + | 0.605117i | ||||
\(503\) | −10.1763 | + | 10.1763i | −0.453738 | + | 0.453738i | −0.896593 | − | 0.442855i | \(-0.853965\pi\) |
0.442855 | + | 0.896593i | \(0.353965\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.80534 | + | 7.82229i | 0.124836 | + | 0.348087i | ||||
\(506\) | −40.6025 | − | 23.4418i | −1.80500 | − | 1.04212i | ||||
\(507\) | 13.8250 | + | 2.23133i | 0.613988 | + | 0.0990967i | ||||
\(508\) | 1.19862 | − | 4.47331i | 0.0531801 | − | 0.198471i | ||||
\(509\) | −15.6485 | + | 27.1040i | −0.693607 | + | 1.20136i | 0.277042 | + | 0.960858i | \(0.410646\pi\) |
−0.970648 | + | 0.240504i | \(0.922687\pi\) | |||||||
\(510\) | 1.74225 | − | 4.93672i | 0.0771481 | − | 0.218601i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 14.4671 | + | 14.4671i | 0.639360 | + | 0.639360i | ||||
\(513\) | −5.78617 | + | 3.68546i | −0.255466 | + | 0.162717i | ||||
\(514\) | 19.2344 | − | 11.1050i | 0.848394 | − | 0.489821i | ||||
\(515\) | 0.307800 | + | 3.72032i | 0.0135633 | + | 0.163937i | ||||
\(516\) | 0.202957 | − | 0.452267i | 0.00893468 | − | 0.0199099i | ||||
\(517\) | −17.6651 | + | 17.6651i | −0.776908 | + | 0.776908i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −33.6198 | + | 3.43371i | −1.47574 | + | 0.150723i | ||||
\(520\) | 5.63380 | − | 31.0921i | 0.247058 | − | 1.36348i | ||||
\(521\) | 21.1868 | − | 12.2322i | 0.928209 | − | 0.535902i | 0.0419642 | − | 0.999119i | \(-0.486638\pi\) |
0.886245 | + | 0.463217i | \(0.153305\pi\) | |||||||
\(522\) | 14.8608 | + | 0.866443i | 0.650441 | + | 0.0379232i | ||||
\(523\) | 2.49696 | − | 0.669057i | 0.109184 | − | 0.0292558i | −0.203813 | − | 0.979010i | \(-0.565334\pi\) |
0.312997 | + | 0.949754i | \(0.398667\pi\) | |||||||
\(524\) | 9.82422 | 0.429173 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.6796 | −0.858069 | ||||||||
\(527\) | −1.96627 | + | 0.526859i | −0.0856519 | + | 0.0229504i | ||||
\(528\) | −18.2139 | − | 2.93970i | −0.792659 | − | 0.127934i | ||||
\(529\) | −34.9645 | + | 20.1868i | −1.52020 | + | 0.877686i | ||||
\(530\) | −2.24090 | + | 12.3672i | −0.0973383 | + | 0.537195i | ||||
\(531\) | 1.10240 | + | 5.34056i | 0.0478402 | + | 0.231761i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.91512 | + | 5.91512i | −0.256212 | + | 0.256212i | ||||
\(534\) | −16.8729 | − | 7.57181i | −0.730163 | − | 0.327664i | ||||
\(535\) | −0.359845 | − | 4.34937i | −0.0155574 | − | 0.188040i | ||||
\(536\) | 29.8562 | − | 17.2375i | 1.28959 | − | 0.744545i | ||||
\(537\) | 11.3829 | − | 4.33116i | 0.491210 | − | 0.186903i | ||||
\(538\) | 15.3334 | + | 15.3334i | 0.661071 | + | 0.661071i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 8.26834 | + | 1.12903i | 0.355813 | + | 0.0485858i | ||||
\(541\) | −20.9419 | + | 36.2725i | −0.900364 | + | 1.55948i | −0.0733424 | + | 0.997307i | \(0.523367\pi\) |
−0.827022 | + | 0.562170i | \(0.809967\pi\) | |||||||
\(542\) | 5.41005 | − | 20.1906i | 0.232382 | − | 0.867261i | ||||
\(543\) | −3.91541 | + | 24.2592i | −0.168026 | + | 1.04106i | ||||
\(544\) | −3.96693 | − | 2.29031i | −0.170081 | − | 0.0981961i | ||||
\(545\) | 4.48011 | + | 12.4921i | 0.191907 | + | 0.535104i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.6813 | + | 21.6813i | −0.927024 | + | 0.927024i | −0.997513 | − | 0.0704885i | \(-0.977544\pi\) |
0.0704885 | + | 0.997513i | \(0.477544\pi\) | |||||||
\(548\) | −2.63499 | − | 9.83392i | −0.112561 | − | 0.420084i | ||||
\(549\) | 5.54728 | − | 4.93606i | 0.236752 | − | 0.210666i | ||||
\(550\) | 26.8041 | − | 12.1923i | 1.14293 | − | 0.519881i | ||||
\(551\) | −5.01118 | − | 2.89320i | −0.213483 | − | 0.123255i | ||||
\(552\) | −26.8009 | + | 32.8982i | −1.14072 | + | 1.40024i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 12.2657 | 0.521119 | ||||||||
\(555\) | 0.725605 | − | 9.34732i | 0.0308002 | − | 0.396772i | ||||
\(556\) | −5.68343 | − | 9.84400i | −0.241031 | − | 0.417478i | ||||
\(557\) | 4.80240 | − | 17.9228i | 0.203484 | − | 0.759413i | −0.786422 | − | 0.617689i | \(-0.788069\pi\) |
0.989906 | − | 0.141724i | \(-0.0452644\pi\) | |||||||
\(558\) | 2.59865 | + | 5.17512i | 0.110010 | + | 0.219080i | ||||
\(559\) | − | 1.82978i | − | 0.0773916i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.7015 | − | 1.09299i | 0.451819 | − | 0.0461460i | ||||
\(562\) | 5.99660 | + | 22.3796i | 0.252951 | + | 0.944027i | ||||
\(563\) | −21.7425 | − | 5.82588i | −0.916336 | − | 0.245531i | −0.230317 | − | 0.973116i | \(-0.573976\pi\) |
−0.686018 | + | 0.727584i | \(0.740643\pi\) | |||||||
\(564\) | 3.49742 | + | 4.84365i | 0.147268 | + | 0.203955i | ||||
\(565\) | −0.433571 | − | 0.625466i | −0.0182405 | − | 0.0263135i | ||||
\(566\) | 13.2016i | 0.554903i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −19.7231 | − | 19.7231i | −0.827565 | − | 0.827565i | ||||
\(569\) | 13.9152 | − | 24.1018i | 0.583354 | − | 1.01040i | −0.411724 | − | 0.911309i | \(-0.635073\pi\) |
0.995078 | − | 0.0990907i | \(-0.0315934\pi\) | |||||||
\(570\) | 4.77439 | + | 3.27385i | 0.199977 | + | 0.137126i | ||||
\(571\) | 2.05777 | + | 3.56417i | 0.0861151 | + | 0.149156i | 0.905866 | − | 0.423565i | \(-0.139221\pi\) |
−0.819751 | + | 0.572720i | \(0.805888\pi\) | |||||||
\(572\) | 16.5713 | − | 4.44027i | 0.692882 | − | 0.185657i | ||||
\(573\) | −17.1151 | + | 21.0089i | −0.714994 | + | 0.877658i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.84325 | − | 39.6178i | 0.160275 | − | 1.65218i | ||||
\(576\) | −7.96478 | + | 24.0315i | −0.331866 | + | 1.00131i | ||||
\(577\) | −20.9197 | − | 5.60542i | −0.870899 | − | 0.233357i | −0.204423 | − | 0.978883i | \(-0.565532\pi\) |
−0.666477 | + | 0.745526i | \(0.732198\pi\) | |||||||
\(578\) | 17.0320 | + | 4.56370i | 0.708436 | + | 0.189825i | ||||
\(579\) | −20.1345 | − | 9.03544i | −0.836760 | − | 0.375500i | ||||
\(580\) | 2.37619 | + | 6.62564i | 0.0986657 | + | 0.275115i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −6.58590 | − | 5.36528i | −0.272994 | − | 0.222398i | ||||
\(583\) | −24.9460 | + | 6.68426i | −1.03316 | + | 0.276834i | ||||
\(584\) | 2.91281 | + | 5.04514i | 0.120533 | + | 0.208769i | ||||
\(585\) | 29.5509 | − | 8.69328i | 1.22178 | − | 0.359423i | ||||
\(586\) | 15.7889 | − | 27.3472i | 0.652233 | − | 1.12970i | ||||
\(587\) | −23.2211 | − | 23.2211i | −0.958439 | − | 0.958439i | 0.0407314 | − | 0.999170i | \(-0.487031\pi\) |
−0.999170 | + | 0.0407314i | \(0.987031\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 2.25101i | − | 0.0927512i | ||||||
\(590\) | 3.78189 | − | 2.62160i | 0.155698 | − | 0.107929i | ||||
\(591\) | −5.54039 | + | 4.00050i | −0.227901 | + | 0.164559i | ||||
\(592\) | 4.78800 | + | 1.28294i | 0.196786 | + | 0.0527285i | ||||
\(593\) | −8.89227 | − | 33.1864i | −0.365162 | − | 1.36280i | −0.867201 | − | 0.497958i | \(-0.834083\pi\) |
0.502040 | − | 0.864845i | \(-0.332583\pi\) | |||||||
\(594\) | −9.19956 | − | 29.1865i | −0.377463 | − | 1.19754i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.68380i | 0.273779i | ||||||||
\(597\) | −8.88948 | − | 23.3629i | −0.363822 | − | 0.956179i | ||||
\(598\) | −10.7113 | + | 39.9753i | −0.438019 | + | 1.63471i | ||||
\(599\) | −11.3932 | − | 19.7336i | −0.465515 | − | 0.806295i | 0.533710 | − | 0.845668i | \(-0.320797\pi\) |
−0.999225 | + | 0.0393726i | \(0.987464\pi\) | |||||||
\(600\) | −7.02848 | − | 25.7080i | −0.286937 | − | 1.04953i | ||||
\(601\) | 41.7276 | 1.70210 | 0.851052 | − | 0.525082i | \(-0.175965\pi\) | ||||
0.851052 | + | 0.525082i | \(0.175965\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 28.0774 | + | 18.4692i | 1.14340 | + | 0.752124i | ||||
\(604\) | −10.4667 | − | 6.04296i | −0.425885 | − | 0.245885i | ||||
\(605\) | 27.4001 | + | 23.2126i | 1.11397 | + | 0.943728i | ||||
\(606\) | −4.26624 | − | 5.90841i | −0.173304 | − | 0.240013i | ||||
\(607\) | 6.41144 | + | 23.9278i | 0.260232 | + | 0.971200i | 0.965104 | + | 0.261866i | \(0.0843378\pi\) |
−0.704872 | + | 0.709335i | \(0.748996\pi\) | |||||||
\(608\) | 3.58168 | − | 3.58168i | 0.145256 | − | 0.145256i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.66636 | − | 2.67490i | −0.229424 | − | 0.108303i | ||||
\(611\) | 19.0979 | + | 11.0262i | 0.772620 | + | 0.446072i | ||||
\(612\) | 0.149734 | − | 2.56817i | 0.00605264 | − | 0.103812i | ||||
\(613\) | −9.51154 | + | 35.4975i | −0.384167 | + | 1.43373i | 0.455308 | + | 0.890334i | \(0.349529\pi\) |
−0.839475 | + | 0.543398i | \(0.817137\pi\) | |||||||
\(614\) | 10.6472 | − | 18.4414i | 0.429684 | − | 0.744235i | ||||
\(615\) | −2.34811 | + | 6.65345i | −0.0946851 | + | 0.268293i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.12737 | − | 8.12737i | −0.327196 | − | 0.327196i | 0.524323 | − | 0.851519i | \(-0.324318\pi\) |
−0.851519 | + | 0.524323i | \(0.824318\pi\) | |||||||
\(618\) | −1.16421 | − | 3.05972i | −0.0468314 | − | 0.123080i | ||||
\(619\) | −6.24057 | + | 3.60299i | −0.250830 | + | 0.144817i | −0.620144 | − | 0.784488i | \(-0.712926\pi\) |
0.369314 | + | 0.929304i | \(0.379593\pi\) | |||||||
\(620\) | −1.76998 | + | 2.08927i | −0.0710841 | + | 0.0839073i | ||||
\(621\) | −40.3840 | − | 8.95673i | −1.62055 | − | 0.359421i | ||||
\(622\) | −19.0571 | + | 19.0571i | −0.764120 | + | 0.764120i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.65474 | + | 16.2017i | 0.0662424 | + | 0.648586i | ||||
\(625\) | 18.8444 | + | 16.4283i | 0.753774 | + | 0.657134i | ||||
\(626\) | −26.2556 | + | 15.1587i | −1.04938 | + | 0.605862i | ||||
\(627\) | −1.89537 | + | 11.7434i | −0.0756938 | + | 0.468987i | ||||
\(628\) | −6.67796 | + | 1.78935i | −0.266479 | + | 0.0714030i | ||||
\(629\) | −2.89017 | −0.115238 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.8770 | −1.18938 | −0.594692 | − | 0.803954i | \(-0.702726\pi\) | ||||
−0.594692 | + | 0.803954i | \(0.702726\pi\) | |||||||
\(632\) | −34.1893 | + | 9.16099i | −1.35998 | + | 0.364405i | ||||
\(633\) | 3.30748 | − | 20.4926i | 0.131460 | − | 0.814508i | ||||
\(634\) | −16.2134 | + | 9.36080i | −0.643915 | + | 0.371765i | ||||
\(635\) | −8.21403 | − | 11.8495i | −0.325964 | − | 0.470232i | ||||
\(636\) | 0.627529 | + | 6.14419i | 0.0248831 | + | 0.243633i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 18.2518 | − | 18.2518i | 0.722597 | − | 0.722597i | ||||
\(639\) | 8.55426 | − | 25.8101i | 0.338401 | − | 1.02103i | ||||
\(640\) | 4.19180 | − | 0.346809i | 0.165696 | − | 0.0137088i | ||||
\(641\) | −16.7716 | + | 9.68307i | −0.662437 | + | 0.382458i | −0.793205 | − | 0.608955i | \(-0.791589\pi\) |
0.130768 | + | 0.991413i | \(0.458256\pi\) | |||||||
\(642\) | 1.36106 | + | 3.57707i | 0.0537168 | + | 0.141176i | ||||
\(643\) | −11.6091 | − | 11.6091i | −0.457819 | − | 0.457819i | 0.440120 | − | 0.897939i | \(-0.354936\pi\) |
−0.897939 | + | 0.440120i | \(0.854936\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.665906 | − | 1.39227i | −0.0262200 | − | 0.0548206i | ||||
\(646\) | 0.892292 | − | 1.54550i | 0.0351068 | − | 0.0608067i | ||||
\(647\) | −3.89878 | + | 14.5504i | −0.153277 | + | 0.572037i | 0.845970 | + | 0.533231i | \(0.179022\pi\) |
−0.999247 | + | 0.0388063i | \(0.987644\pi\) | |||||||
\(648\) | −27.4051 | + | 4.01089i | −1.07657 | + | 0.157563i | ||||
\(649\) | 8.18879 | + | 4.72780i | 0.321438 | + | 0.185582i | ||||
\(650\) | −16.5196 | − | 20.0689i | −0.647950 | − | 0.787168i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.30580 | − | 6.30580i | 0.246954 | − | 0.246954i | ||||
\(653\) | 1.34444 | + | 5.01751i | 0.0526119 | + | 0.196350i | 0.987230 | − | 0.159304i | \(-0.0509249\pi\) |
−0.934618 | + | 0.355654i | \(0.884258\pi\) | |||||||
\(654\) | −6.81314 | − | 9.43567i | −0.266415 | − | 0.368964i | ||||
\(655\) | 19.7705 | − | 23.3370i | 0.772499 | − | 0.911854i | ||||
\(656\) | −3.23062 | − | 1.86520i | −0.126134 | − | 0.0728237i | ||||
\(657\) | −3.12095 | + | 4.74456i | −0.121760 | + | 0.185103i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 45.6844 | 1.77961 | 0.889807 | − | 0.456338i | \(-0.150839\pi\) | ||||
0.889807 | + | 0.456338i | \(0.150839\pi\) | |||||||
\(660\) | 10.9931 | − | 9.40931i | 0.427906 | − | 0.366257i | ||||
\(661\) | −10.9259 | − | 18.9242i | −0.424968 | − | 0.736065i | 0.571450 | − | 0.820637i | \(-0.306381\pi\) |
−0.996417 | + | 0.0845715i | \(0.973048\pi\) | |||||||
\(662\) | 3.39607 | − | 12.6743i | 0.131992 | − | 0.492601i | ||||
\(663\) | −3.37687 | − | 8.87493i | −0.131147 | − | 0.344674i | ||||
\(664\) | − | 23.7714i | − | 0.922510i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.66213 | + | 8.05215i | 0.0644062 | + | 0.312014i | ||||
\(667\) | −9.03034 | − | 33.7017i | −0.349656 | − | 1.30493i | ||||
\(668\) | −12.2165 | − | 3.27340i | −0.472670 | − | 0.126651i | ||||
\(669\) | 24.1949 | − | 17.4702i | 0.935431 | − | 0.675439i | ||||
\(670\) | 5.05638 | − | 27.9054i | 0.195345 | − | 1.07808i | ||||
\(671\) | − | 12.8755i | − | 0.497051i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.1963 | + | 12.1963i | 0.470132 | + | 0.470132i | 0.901957 | − | 0.431825i | \(-0.142130\pi\) |
−0.431825 | + | 0.901957i | \(0.642130\pi\) | |||||||
\(674\) | −4.37204 | + | 7.57259i | −0.168405 | + | 0.291685i | ||||
\(675\) | 19.3214 | − | 17.3690i | 0.743682 | − | 0.668534i | ||||
\(676\) | −2.90349 | − | 5.02899i | −0.111673 | − | 0.193423i | ||||
\(677\) | −41.0980 | + | 11.0122i | −1.57952 | + | 0.423232i | −0.938779 | − | 0.344521i | \(-0.888041\pi\) |
−0.640746 | + | 0.767753i | \(0.721375\pi\) | |||||||
\(678\) | 0.517437 | + | 0.421536i | 0.0198721 | + | 0.0161890i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −7.73356 | + | 2.77352i | −0.296568 | + | 0.106360i | ||||
\(681\) | −9.32652 | − | 4.18532i | −0.357393 | − | 0.160382i | ||||
\(682\) | 9.69914 | + | 2.59888i | 0.371399 | + | 0.0995162i | ||||
\(683\) | −2.02836 | − | 0.543497i | −0.0776129 | − | 0.0207963i | 0.219804 | − | 0.975544i | \(-0.429458\pi\) |
−0.297417 | + | 0.954748i | \(0.596125\pi\) | |||||||
\(684\) | 2.70027 | + | 0.894954i | 0.103248 | + | 0.0342194i | ||||
\(685\) | −28.6628 | − | 13.5308i | −1.09515 | − | 0.516984i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29.8330 | − | 36.6201i | 1.13820 | − | 1.39714i | ||||
\(688\) | 0.788169 | − | 0.211189i | 0.0300487 | − | 0.00805152i | ||||
\(689\) | 11.3986 | + | 19.7430i | 0.434253 | + | 0.752149i | ||||
\(690\) | 6.39784 | + | 34.3151i | 0.243562 | + | 1.30635i | ||||
\(691\) | 21.1417 | − | 36.6184i | 0.804267 | − | 1.39303i | −0.112519 | − | 0.993650i | \(-0.535892\pi\) |
0.916785 | − | 0.399381i | \(-0.130775\pi\) | |||||||
\(692\) | 9.90912 | + | 9.90912i | 0.376688 | + | 0.376688i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 32.3395i | 1.22759i | ||||||||
\(695\) | −34.8215 | − | 6.30957i | −1.32086 | − | 0.239336i | ||||
\(696\) | −13.6761 | − | 18.9403i | −0.518391 | − | 0.717932i | ||||
\(697\) | 2.10093 | + | 0.562942i | 0.0795783 | + | 0.0213229i | ||||
\(698\) | −3.50889 | − | 13.0954i | −0.132814 | − | 0.495667i | ||||
\(699\) | −4.79544 | + | 0.489776i | −0.181380 | + | 0.0185250i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.8399i | 1.61804i | 0.587781 | + | 0.809020i | \(0.300002\pi\) | ||||
−0.587781 | + | 0.809020i | \(0.699998\pi\) | |||||||
\(702\) | −22.7840 | + | 14.5121i | −0.859926 | + | 0.547724i | ||||
\(703\) | 0.827175 | − | 3.08706i | 0.0311975 | − | 0.116431i | ||||
\(704\) | 21.9495 | + | 38.0176i | 0.827251 | + | 1.43284i | ||||
\(705\) | 18.5442 | + | 1.43953i | 0.698416 | + | 0.0542160i | ||||
\(706\) | 38.9746 | 1.46683 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.42821 | − | 1.75314i | 0.0536756 | − | 0.0658869i | ||||
\(709\) | 18.8669 | + | 10.8928i | 0.708560 | + | 0.409087i | 0.810528 | − | 0.585700i | \(-0.199180\pi\) |
−0.101968 | + | 0.994788i | \(0.532514\pi\) | |||||||
\(710\) | −22.8670 | + | 1.89190i | −0.858182 | + | 0.0710016i | ||||
\(711\) | −22.9369 | − | 25.7771i | −0.860202 | − | 0.966718i | ||||
\(712\) | 7.51195 | + | 28.0350i | 0.281522 | + | 1.05065i | ||||
\(713\) | 9.59756 | − | 9.59756i | 0.359432 | − | 0.359432i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.8009 | − | 48.3003i | 0.852706 | − | 1.80633i | ||||
\(716\) | −4.37369 | − | 2.52515i | −0.163452 | − | 0.0943693i | ||||
\(717\) | 0.394489 | − | 2.44419i | 0.0147325 | − | 0.0912800i | ||||
\(718\) | −4.16574 | + | 15.5467i | −0.155464 | + | 0.580199i | ||||
\(719\) | 22.9808 | − | 39.8040i | 0.857041 | − | 1.48444i | −0.0176984 | − | 0.999843i | \(-0.505634\pi\) |
0.874739 | − | 0.484594i | \(-0.161033\pi\) | |||||||
\(720\) | 7.15528 | + | 11.7255i | 0.266662 | + | 0.436985i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −13.8151 | − | 13.8151i | −0.514145 | − | 0.514145i | ||||
\(723\) | 47.1594 | − | 17.9440i | 1.75388 | − | 0.667343i | ||||
\(724\) | 8.82459 | − | 5.09488i | 0.327963 | − | 0.189350i | ||||
\(725\) | 20.5209 | + | 7.68911i | 0.762126 | + | 0.285566i | ||||
\(726\) | −28.7320 | − | 12.8936i | −1.06635 | − | 0.478528i | ||||
\(727\) | 4.37251 | − | 4.37251i | 0.162168 | − | 0.162168i | −0.621359 | − | 0.783526i | \(-0.713419\pi\) |
0.783526 | + | 0.621359i | \(0.213419\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.4826 | − | 22.1199i | −0.573428 | − | 0.819256i | ||||
\(730\) | 4.71549 | + | 0.854434i | 0.174528 | + | 0.0316240i | ||||
\(731\) | −0.412020 | + | 0.237880i | −0.0152391 | + | 0.00879831i | ||||
\(732\) | −3.03976 | − | 0.490613i | −0.112353 | − | 0.0181336i | ||||
\(733\) | −43.7493 | + | 11.7226i | −1.61592 | + | 0.432984i | −0.949798 | − | 0.312863i | \(-0.898712\pi\) |
−0.666118 | + | 0.745846i | \(0.732045\pi\) | |||||||
\(734\) | 26.7423 | 0.987078 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 30.5423 | 1.12580 | ||||||||
\(737\) | 56.2884 | − | 15.0824i | 2.07341 | − | 0.555568i | ||||
\(738\) | 0.360144 | − | 6.17704i | 0.0132571 | − | 0.227380i | ||||
\(739\) | −17.1560 | + | 9.90500i | −0.631092 | + | 0.364361i | −0.781175 | − | 0.624312i | \(-0.785379\pi\) |
0.150083 | + | 0.988673i | \(0.452046\pi\) | |||||||
\(740\) | −3.19511 | + | 2.21484i | −0.117455 | + | 0.0814193i | ||||
\(741\) | 10.4460 | − | 1.06689i | 0.383744 | − | 0.0391932i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.6828 | − | 14.6828i | 0.538660 | − | 0.538660i | −0.384475 | − | 0.923135i | \(-0.625618\pi\) |
0.923135 | + | 0.384475i | \(0.125618\pi\) | |||||||
\(744\) | 3.72085 | − | 8.29151i | 0.136413 | − | 0.303981i | ||||
\(745\) | 15.8771 | + | 13.4507i | 0.581692 | + | 0.492795i | ||||
\(746\) | −6.34892 | + | 3.66555i | −0.232450 | + | 0.134205i | ||||
\(747\) | 20.7089 | − | 10.3988i | 0.757699 | − | 0.380474i | ||||
\(748\) | −3.15418 | − | 3.15418i | −0.115328 | − | 0.115328i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −19.8732 | − | 9.25844i | −0.725668 | − | 0.338070i | ||||
\(751\) | 13.3416 | − | 23.1083i | 0.486841 | − | 0.843234i | −0.513044 | − | 0.858362i | \(-0.671482\pi\) |
0.999886 | + | 0.0151284i | \(0.00481571\pi\) | |||||||
\(752\) | −2.54524 | + | 9.49895i | −0.0928152 | + | 0.346391i | ||||
\(753\) | 21.1992 | + | 3.42151i | 0.772541 | + | 0.124687i | ||||
\(754\) | −19.7323 | − | 11.3925i | −0.718608 | − | 0.414889i | ||||
\(755\) | −35.4184 | + | 12.7023i | −1.28901 | + | 0.462282i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.11078 | + | 4.11078i | −0.149409 | + | 0.149409i | −0.777854 | − | 0.628445i | \(-0.783692\pi\) |
0.628445 | + | 0.777854i | \(0.283692\pi\) | |||||||
\(758\) | −3.70691 | − | 13.8344i | −0.134641 | − | 0.502487i | ||||
\(759\) | −58.1513 | + | 41.9888i | −2.11076 | + | 1.52410i | ||||
\(760\) | −0.749099 | − | 9.05420i | −0.0271727 | − | 0.328430i | ||||
\(761\) | −19.3001 | − | 11.1429i | −0.699629 | − | 0.403931i | 0.107580 | − | 0.994196i | \(-0.465690\pi\) |
−0.807209 | + | 0.590265i | \(0.799023\pi\) | |||||||
\(762\) | 9.80288 | + | 7.98603i | 0.355121 | + | 0.289303i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 11.2367 | 0.406530 | ||||||||
\(765\) | −5.79926 | − | 5.52395i | −0.209673 | − | 0.199719i | ||||
\(766\) | 14.4232 | + | 24.9817i | 0.521131 | + | 0.902625i | ||||
\(767\) | 2.16028 | − | 8.06229i | 0.0780033 | − | 0.291112i | ||||
\(768\) | 23.8751 | − | 9.08436i | 0.861517 | − | 0.327804i | ||||
\(769\) | − | 37.7021i | − | 1.35957i | −0.733410 | − | 0.679786i | \(-0.762073\pi\) | ||
0.733410 | − | 0.679786i | \(-0.237927\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.45239 | − | 33.8026i | −0.124335 | − | 1.21737i | ||||
\(772\) | 2.36853 | + | 8.83948i | 0.0852453 | + | 0.318140i | ||||
\(773\) | −28.0806 | − | 7.52416i | −1.00999 | − | 0.270625i | −0.284363 | − | 0.958717i | \(-0.591782\pi\) |
−0.725624 | + | 0.688091i | \(0.758449\pi\) | |||||||
\(774\) | 0.899698 | + | 1.01111i | 0.0323390 | + | 0.0363434i | ||||
\(775\) | 1.40103 | + | 8.40904i | 0.0503266 | + | 0.302062i | ||||
\(776\) | 13.3314i | 0.478568i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14.1870 | − | 14.1870i | −0.508630 | − | 0.508630i | ||||
\(779\) | −1.20258 | + | 2.08294i | −0.0430871 | + | 0.0746290i | ||||
\(780\) | −10.5344 | − | 7.22352i | −0.377191 | − | 0.258644i | ||||
\(781\) | −23.5739 | − | 40.8313i | −0.843542 | − | 1.46106i | ||||
\(782\) | 10.3939 | − | 2.78505i | 0.371686 | − | 0.0995930i | ||||
\(783\) | 10.5176 | − | 20.1997i | 0.375868 | − | 0.721877i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.18838 | + | 19.4642i | −0.327947 | + | 0.694706i | ||||
\(786\) | −10.9817 | + | 24.4715i | −0.391704 | + | 0.872870i | ||||
\(787\) | 12.9105 | + | 3.45935i | 0.460209 | + | 0.123313i | 0.481472 | − | 0.876461i | \(-0.340102\pi\) |
−0.0212633 | + | 0.999774i | \(0.506769\pi\) | |||||||
\(788\) | 2.73718 | + | 0.733426i | 0.0975081 | + | 0.0261272i | ||||
\(789\) | −12.3265 | + | 27.4682i | −0.438835 | + | 0.977894i | ||||
\(790\) | −12.4297 | + | 26.3305i | −0.442230 | + | 0.936797i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −26.3930 | + | 40.1234i | −0.937836 | + | 1.42572i | ||||
\(793\) | −10.9782 | + | 2.94161i | −0.389848 | + | 0.104459i | ||||
\(794\) | −3.54673 | − | 6.14312i | −0.125869 | − | 0.218011i | ||||
\(795\) | 15.8581 | + | 10.8741i | 0.562431 | + | 0.385664i | ||||
\(796\) | −5.18273 | + | 8.97676i | −0.183697 | + | 0.318173i | ||||
\(797\) | 5.16008 | + | 5.16008i | 0.182779 | + | 0.182779i | 0.792566 | − | 0.609786i | \(-0.208745\pi\) |
−0.609786 | + | 0.792566i | \(0.708745\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 5.73382i | − | 0.202848i | ||||||
\(800\) | −11.1508 | + | 15.6093i | −0.394239 | + | 0.551871i | ||||
\(801\) | −21.1371 | + | 18.8081i | −0.746842 | + | 0.664552i | ||||
\(802\) | 37.7043 | + | 10.1028i | 1.33138 | + | 0.356743i | ||||
\(803\) | 2.54865 | + | 9.51169i | 0.0899399 | + | 0.335660i | ||||
\(804\) | −1.41596 | − | 13.8638i | −0.0499371 | − | 0.488939i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 8.86371i | − | 0.312211i | ||||||
\(807\) | 31.0062 | − | 11.7977i | 1.09147 | − | 0.415300i | ||||
\(808\) | −2.96012 | + | 11.0473i | −0.104137 | + | 0.388644i | ||||
\(809\) | 6.43076 | + | 11.1384i | 0.226093 | + | 0.391605i | 0.956647 | − | 0.291250i | \(-0.0940712\pi\) |
−0.730554 | + | 0.682855i | \(0.760738\pi\) | |||||||
\(810\) | −12.0549 | + | 19.3338i | −0.423565 | + | 0.679322i | ||||
\(811\) | −0.485057 | −0.0170327 | −0.00851633 | − | 0.999964i | \(-0.502711\pi\) | ||||
−0.00851633 | + | 0.999964i | \(0.502711\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.7929 | − | 20.1978i | −0.869524 | − | 0.708368i | ||||
\(814\) | 12.3465 | + | 7.12827i | 0.432745 | + | 0.249846i | ||||
\(815\) | −2.28921 | − | 27.6692i | −0.0801875 | − | 0.969209i | ||||
\(816\) | 3.43308 | − | 2.47889i | 0.120182 | − | 0.0867786i | ||||
\(817\) | −0.136164 | − | 0.508172i | −0.00476378 | − | 0.0177787i | ||||
\(818\) | −15.6638 | + | 15.6638i | −0.547673 | + | 0.547673i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.75401 | − | 0.987682i | 0.0961740 | − | 0.0344913i | ||||
\(821\) | −24.3941 | − | 14.0839i | −0.851360 | − | 0.491533i | 0.00974941 | − | 0.999952i | \(-0.496897\pi\) |
−0.861110 | + | 0.508419i | \(0.830230\pi\) | |||||||
\(822\) | 27.4411 | + | 4.42896i | 0.957119 | + | 0.154478i | ||||
\(823\) | 2.78920 | − | 10.4094i | 0.0972255 | − | 0.362850i | −0.900122 | − | 0.435638i | \(-0.856523\pi\) |
0.997347 | + | 0.0727875i | \(0.0231895\pi\) | |||||||
\(824\) | −2.56884 | + | 4.44937i | −0.0894899 | + | 0.155001i | ||||
\(825\) | −0.228637 | − | 45.0492i | −0.00796012 | − | 1.56841i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.0314 | − | 24.0314i | −0.835652 | − | 0.835652i | 0.152631 | − | 0.988283i | \(-0.451225\pi\) |
−0.988283 | + | 0.152631i | \(0.951225\pi\) | |||||||
\(828\) | 7.69730 | + | 15.3289i | 0.267500 | + | 0.532715i | ||||
\(829\) | −16.2018 | + | 9.35410i | −0.562711 | + | 0.324881i | −0.754233 | − | 0.656607i | \(-0.771991\pi\) |
0.191522 | + | 0.981488i | \(0.438658\pi\) | |||||||
\(830\) | −14.9204 | − | 12.6402i | −0.517894 | − | 0.438746i | ||||
\(831\) | 7.68274 | − | 17.1201i | 0.266511 | − | 0.593891i | ||||
\(832\) | 27.4009 | − | 27.4009i | 0.949954 | − | 0.949954i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 30.8738 | − | 3.15326i | 1.06907 | − | 0.109188i | ||||
\(835\) | −32.3606 | + | 22.4323i | −1.11989 | + | 0.776302i | ||||
\(836\) | 4.27180 | − | 2.46633i | 0.147743 | − | 0.0852997i | ||||
\(837\) | 8.85099 | − | 0.385642i | 0.305935 | − | 0.0133297i | ||||
\(838\) | −18.6136 | + | 4.98750i | −0.642996 | + | 0.172290i | ||||
\(839\) | −1.64172 | −0.0566785 | −0.0283392 | − | 0.999598i | \(-0.509022\pi\) | ||||
−0.0283392 | + | 0.999598i | \(0.509022\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.79087 | −0.337616 | ||||||||
\(842\) | 23.7824 | − | 6.37248i | 0.819596 | − | 0.219610i | ||||
\(843\) | 34.9929 | + | 5.64781i | 1.20522 | + | 0.194521i | ||||
\(844\) | −7.45443 | + | 4.30382i | −0.256592 | + | 0.148143i | ||||
\(845\) | −17.7892 | − | 3.22336i | −0.611968 | − | 0.110887i | ||||
\(846\) | −15.9747 | + | 3.29751i | −0.549222 | + | 0.113371i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.18859 | + | 7.18859i | −0.246857 | + | 0.246857i | ||||
\(849\) | 18.4264 | + | 8.26894i | 0.632393 | + | 0.283789i | ||||
\(850\) | −2.37139 | + | 6.32883i | −0.0813382 | + | 0.217077i | ||||
\(851\) | 16.6890 | − | 9.63541i | 0.572092 | − | 0.330298i | ||||
\(852\) | −10.5381 | + | 4.00971i | −0.361030 | + | 0.137370i | ||||
\(853\) | −3.77850 | − | 3.77850i | −0.129373 | − | 0.129373i | 0.639455 | − | 0.768828i | \(-0.279160\pi\) |
−0.768828 | + | 0.639455i | \(0.779160\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.56004 | − | 4.61337i | 0.258548 | − | 0.157774i | ||||
\(856\) | 3.00320 | − | 5.20169i | 0.102647 | − | 0.177790i | ||||
\(857\) | −3.07062 | + | 11.4597i | −0.104890 | + | 0.391456i | −0.998333 | − | 0.0577219i | \(-0.981616\pi\) |
0.893442 | + | 0.449178i | \(0.148283\pi\) | |||||||
\(858\) | −7.46332 | + | 46.2416i | −0.254794 | + | 1.57866i | ||||
\(859\) | 10.7728 | + | 6.21966i | 0.367562 | + | 0.212212i | 0.672393 | − | 0.740194i | \(-0.265267\pi\) |
−0.304831 | + | 0.952407i | \(0.598600\pi\) | |||||||
\(860\) | −0.273197 | + | 0.578727i | −0.00931595 | + | 0.0197344i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.63896 | + | 8.63896i | −0.294244 | + | 0.294244i | ||||
\(863\) | 3.08580 | + | 11.5164i | 0.105042 | + | 0.392022i | 0.998350 | − | 0.0574232i | \(-0.0182884\pi\) |
−0.893308 | + | 0.449445i | \(0.851622\pi\) | |||||||
\(864\) | 14.6968 | + | 13.4696i | 0.499997 | + | 0.458246i | ||||
\(865\) | 43.4802 | − | 3.59733i | 1.47837 | − | 0.122313i | ||||
\(866\) | −0.647440 | − | 0.373800i | −0.0220009 | − | 0.0127022i | ||||
\(867\) | 17.0380 | − | 20.9142i | 0.578642 | − | 0.710285i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −59.8298 | −2.02959 | ||||||||
\(870\) | −19.1602 | − | 1.48735i | −0.649592 | − | 0.0504259i | ||||
\(871\) | −25.7200 | − | 44.5483i | −0.871488 | − | 1.50946i | ||||
\(872\) | −4.72729 | + | 17.6425i | −0.160086 | + | 0.597450i | ||||
\(873\) | −11.6139 | + | 5.83183i | −0.393070 | + | 0.197378i | ||||
\(874\) | 11.8991i | 0.402493i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.34273 | − | 0.239271i | 0.0791534 | − | 0.00808423i | ||||
\(877\) | −0.937500 | − | 3.49880i | −0.0316571 | − | 0.118146i | 0.948289 | − | 0.317408i | \(-0.102812\pi\) |
−0.979946 | + | 0.199262i | \(0.936146\pi\) | |||||||
\(878\) | −10.3197 | − | 2.76514i | −0.348272 | − | 0.0933191i | ||||
\(879\) | −28.2809 | − | 39.1669i | −0.953891 | − | 1.32107i | ||||
\(880\) | 23.4367 | + | 4.24667i | 0.790051 | + | 0.143155i | ||||
\(881\) | − | 16.9744i | − | 0.571882i | −0.958247 | − | 0.285941i | \(-0.907694\pi\) | ||
0.958247 | − | 0.285941i | \(-0.0923061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.2023 | + | 21.2023i | 0.713513 | + | 0.713513i | 0.967268 | − | 0.253756i | \(-0.0816660\pi\) |
−0.253756 | + | 0.967268i | \(0.581666\pi\) | |||||||
\(884\) | −1.96878 | + | 3.41003i | −0.0662173 | + | 0.114692i | ||||
\(885\) | −1.29033 | − | 6.92073i | −0.0433739 | − | 0.232638i | ||||
\(886\) | −13.5258 | − | 23.4274i | −0.454409 | − | 0.787060i | ||||
\(887\) | 17.1474 | − | 4.59462i | 0.575752 | − | 0.154272i | 0.0408187 | − | 0.999167i | \(-0.487003\pi\) |
0.534933 | + | 0.844894i | \(0.320337\pi\) | |||||||
\(888\) | 8.14969 | − | 10.0038i | 0.273486 | − | 0.335705i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 21.5908 | + | 10.1923i | 0.723726 | + | 0.341647i | ||||
\(891\) | −46.4999 | − | 5.44074i | −1.55781 | − | 0.182272i | ||||
\(892\) | −11.9533 | − | 3.20288i | −0.400227 | − | 0.107240i | ||||
\(893\) | 6.12444 | + | 1.64104i | 0.204947 | + | 0.0549153i | ||||
\(894\) | −16.6489 | − | 7.47128i | −0.556823 | − | 0.249877i | ||||
\(895\) | −14.8001 | + | 5.30784i | −0.494714 | + | 0.177422i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 49.0873 | + | 39.9895i | 1.63898 | + | 1.33521i | ||||
\(898\) | 12.6464 | − | 3.38860i | 0.422017 | − | 0.113079i | ||||
\(899\) | 3.73633 | + | 6.47152i | 0.124614 | + | 0.215837i | ||||
\(900\) | −10.6444 | − | 1.66260i | −0.354812 | − | 0.0554200i | ||||
\(901\) | 2.96375 | − | 5.13336i | 0.0987368 | − | 0.171017i | ||||
\(902\) | −7.58653 | − | 7.58653i | −0.252604 | − | 0.252604i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 1.04741i | − | 0.0348364i | ||||||
\(905\) | 5.65617 | − | 31.2155i | 0.188018 | − | 1.03764i | ||||
\(906\) | 26.7525 | − | 19.3170i | 0.888794 | − | 0.641764i | ||||
\(907\) | 11.7609 | + | 3.15133i | 0.390515 | + | 0.104638i | 0.448733 | − | 0.893666i | \(-0.351875\pi\) |
−0.0582185 | + | 0.998304i | \(0.518542\pi\) | |||||||
\(908\) | 1.09713 | + | 4.09455i | 0.0364096 | + | 0.135882i | ||||
\(909\) | −10.9190 | + | 2.25391i | −0.362160 | + | 0.0747574i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 23.0151i | − | 0.762525i | −0.924467 | − | 0.381263i | \(-0.875489\pi\) | ||
0.924467 | − | 0.381263i | \(-0.124511\pi\) | |||||||
\(912\) | 1.66521 | + | 4.37642i | 0.0551407 | + | 0.144918i | ||||
\(913\) | 10.3997 | − | 38.8124i | 0.344181 | − | 1.28450i | ||||
\(914\) | −14.2829 | − | 24.7387i | −0.472436 | − | 0.818283i | ||||
\(915\) | −7.28274 | + | 6.23351i | −0.240760 | + | 0.206073i | ||||
\(916\) | −19.5865 | −0.647155 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.22977 | + | 3.24373i | 0.205613 | + | 0.107059i | ||||
\(919\) | 19.1372 | + | 11.0488i | 0.631277 | + | 0.364468i | 0.781246 | − | 0.624223i | \(-0.214584\pi\) |
−0.149970 | + | 0.988691i | \(0.547918\pi\) | |||||||
\(920\) | 35.4102 | − | 41.7981i | 1.16744 | − | 1.37804i | ||||
\(921\) | −19.0711 | − | 26.4120i | −0.628414 | − | 0.870305i | ||||
\(922\) | −3.82602 | − | 14.2789i | −0.126003 | − | 0.470251i | ||||
\(923\) | −29.4288 | + | 29.4288i | −0.968662 | + | 0.968662i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.16867 | + | 12.0471i | −0.0384255 | + | 0.396106i | ||||
\(926\) | 24.1164 | + | 13.9236i | 0.792514 | + | 0.457558i | ||||
\(927\) | −4.99989 | − | 0.291513i | −0.164218 | − | 0.00957453i | ||||
\(928\) | −4.35208 | + | 16.2422i | −0.142864 | + | 0.533176i | ||||
\(929\) | 25.8842 | − | 44.8327i | 0.849232 | − | 1.47091i | −0.0326620 | − | 0.999466i | \(-0.510398\pi\) |
0.881894 | − | 0.471447i | \(-0.156268\pi\) | |||||||
\(930\) | −3.22573 | − | 6.74434i | −0.105776 | − | 0.221156i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.41341 | + | 1.41341i | 0.0462979 | + | 0.0462979i | ||||
\(933\) | 14.6628 | + | 38.5360i | 0.480038 | + | 1.26161i | ||||
\(934\) | −13.0424 | + | 7.53004i | −0.426761 | + | 0.246391i | ||||
\(935\) | −13.8402 | + | 1.14507i | −0.452623 | + | 0.0374478i | ||||
\(936\) | 40.2410 | + | 13.3371i | 1.31532 | + | 0.435937i | ||||
\(937\) | −32.8470 | + | 32.8470i | −1.07307 | + | 1.07307i | −0.0759541 | + | 0.997111i | \(0.524200\pi\) |
−0.997111 | + | 0.0759541i | \(0.975800\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.71262 | + | 46.1417i | 0.153790 | + | 1.50578i | ||||
\(940\) | −4.39405 | − | 6.33881i | −0.143318 | − | 0.206749i | ||||
\(941\) | 13.0709 | − | 7.54651i | 0.426100 | − | 0.246009i | −0.271584 | − | 0.962415i | \(-0.587547\pi\) |
0.697684 | + | 0.716406i | \(0.254214\pi\) | |||||||
\(942\) | 3.00759 | − | 18.6345i | 0.0979925 | − | 0.607146i | ||||
\(943\) | −14.0084 | + | 3.75354i | −0.456176 | + | 0.122232i | ||||
\(944\) | 3.72212 | 0.121145 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.34682 | 0.0763016 | ||||||||
\(947\) | −38.1493 | + | 10.2221i | −1.23968 | + | 0.332173i | −0.818343 | − | 0.574730i | \(-0.805107\pi\) |
−0.421341 | + | 0.906902i | \(0.638441\pi\) | |||||||
\(948\) | −2.27979 | + | 14.1252i | −0.0740440 | + | 0.458765i | ||||
\(949\) | 7.52784 | − | 4.34620i | 0.244364 | − | 0.141084i | ||||
\(950\) | −6.08129 | − | 4.34428i | −0.197303 | − | 0.140947i | ||||
\(951\) | 2.91014 | + | 28.4934i | 0.0943678 | + | 0.923963i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.2553 | + | 11.2553i | −0.364595 | + | 0.364595i | −0.865501 | − | 0.500906i | \(-0.833000\pi\) |
0.500906 | + | 0.865501i | \(0.333000\pi\) | |||||||
\(954\) | −16.0063 | − | 5.30496i | −0.518222 | − | 0.171755i | ||||
\(955\) | 22.6131 | − | 26.6923i | 0.731742 | − | 0.863744i | ||||
\(956\) | −0.889104 | + | 0.513324i | −0.0287557 | + | 0.0166021i | ||||
\(957\) | −14.0432 | − | 36.9077i | −0.453953 | − | 1.19306i | ||||
\(958\) | −31.1166 | − | 31.1166i | −1.00533 | − | 1.00533i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 10.8773 | − | 30.8210i | 0.351062 | − | 0.994745i | ||||
\(961\) | 14.0465 | − | 24.3293i | 0.453113 | − | 0.784815i | ||||
\(962\) | 3.25714 | − | 12.1558i | 0.105014 | − | 0.391919i | ||||
\(963\) | 5.84530 | + | 0.340803i | 0.188362 | + | 0.0109822i | ||||
\(964\) | −18.1201 | − | 10.4617i | −0.583611 | − | 0.336948i | ||||
\(965\) | 25.7643 | + | 12.1625i | 0.829384 | + | 0.391524i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.6914 | − | 21.6914i | 0.697548 | − | 0.697548i | −0.266333 | − | 0.963881i | \(-0.585812\pi\) |
0.963881 | + | 0.266333i | \(0.0858122\pi\) | |||||||
\(968\) | 12.7917 | + | 47.7393i | 0.411141 | + | 1.53440i | ||||
\(969\) | −1.59827 | − | 2.21347i | −0.0513437 | − | 0.0711071i | ||||
\(970\) | 8.36758 | + | 7.08879i | 0.268667 | + | 0.227607i | ||||
\(971\) | 49.8746 | + | 28.7951i | 1.60055 | + | 0.924079i | 0.991377 | + | 0.131043i | \(0.0418327\pi\) |
0.609175 | + | 0.793036i | \(0.291501\pi\) | |||||||
\(972\) | −3.05636 | + | 10.7708i | −0.0980328 | + | 0.345475i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −38.3544 | −1.22895 | ||||||||
\(975\) | −38.3589 | + | 10.4872i | −1.22847 | + | 0.335858i | ||||
\(976\) | −2.53416 | − | 4.38930i | −0.0811165 | − | 0.140498i | ||||
\(977\) | 2.74417 | − | 10.2414i | 0.0877939 | − | 0.327651i | −0.908035 | − | 0.418895i | \(-0.862418\pi\) |
0.995829 | + | 0.0912438i | \(0.0290842\pi\) | |||||||
\(978\) | 8.65861 | + | 22.7561i | 0.276872 | + | 0.727660i | ||||
\(979\) | 49.0600i | 1.56796i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.4375 | + | 3.59947i | −0.556738 | + | 0.114922i | ||||
\(982\) | −7.51465 | − | 28.0451i | −0.239802 | − | 0.894954i | ||||
\(983\) | 2.62602 | + | 0.703639i | 0.0837569 | + | 0.0224426i | 0.300454 | − | 0.953796i | \(-0.402862\pi\) |
−0.216697 | + | 0.976239i | \(0.569528\pi\) | |||||||
\(984\) | −7.87272 | + | 5.68459i | −0.250973 | + | 0.181218i | ||||
\(985\) | 7.25062 | − | 5.02611i | 0.231024 | − | 0.160145i | ||||
\(986\) | 5.92428i | 0.188668i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.07887 | − | 3.07887i | −0.0979519 | − | 0.0979519i | ||||
\(989\) | 1.58612 | − | 2.74724i | 0.0504356 | − | 0.0873571i | ||||
\(990\) | 11.1497 | + | 37.9010i | 0.354361 | + | 1.20457i | ||||
\(991\) | 15.8721 | + | 27.4913i | 0.504194 | + | 0.873289i | 0.999988 | + | 0.00484916i | \(0.00154354\pi\) |
−0.495795 | + | 0.868440i | \(0.665123\pi\) | |||||||
\(992\) | −6.31848 | + | 1.69303i | −0.200612 | + | 0.0537538i | ||||
\(993\) | −15.5633 | − | 12.6788i | −0.493886 | − | 0.402350i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.8941 | + | 30.3765i | 0.345365 | + | 0.962999i | ||||
\(996\) | −8.76692 | − | 3.93420i | −0.277790 | − | 0.124660i | ||||
\(997\) | 17.3880 | + | 4.65909i | 0.550683 | + | 0.147555i | 0.523422 | − | 0.852073i | \(-0.324655\pi\) |
0.0272604 | + | 0.999628i | \(0.491322\pi\) | |||||||
\(998\) | 31.8293 | + | 8.52865i | 1.00754 | + | 0.269970i | ||||
\(999\) | 12.2801 | + | 2.72359i | 0.388524 | + | 0.0861705i |
(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 | 735.2.y.g.128.9 | 48 | ||
3.2 | odd | 2 | inner | 735.2.y.g.128.4 | 48 | ||
5.2 | odd | 4 | inner | 735.2.y.g.422.9 | 48 | ||
7.2 | even | 3 | 735.2.j.h.638.4 | 24 | |||
7.3 | odd | 6 | 735.2.y.j.263.4 | 48 | |||
7.4 | even | 3 | inner | 735.2.y.g.263.4 | 48 | ||
7.5 | odd | 6 | 105.2.j.a.8.4 | ✓ | 24 | ||
7.6 | odd | 2 | 735.2.y.j.128.9 | 48 | |||
15.2 | even | 4 | inner | 735.2.y.g.422.4 | 48 | ||
21.2 | odd | 6 | 735.2.j.h.638.9 | 24 | |||
21.5 | even | 6 | 105.2.j.a.8.9 | yes | 24 | ||
21.11 | odd | 6 | inner | 735.2.y.g.263.9 | 48 | ||
21.17 | even | 6 | 735.2.y.j.263.9 | 48 | |||
21.20 | even | 2 | 735.2.y.j.128.4 | 48 | |||
35.2 | odd | 12 | 735.2.j.h.197.9 | 24 | |||
35.12 | even | 12 | 105.2.j.a.92.9 | yes | 24 | ||
35.17 | even | 12 | 735.2.y.j.557.4 | 48 | |||
35.19 | odd | 6 | 525.2.j.b.218.9 | 24 | |||
35.27 | even | 4 | 735.2.y.j.422.9 | 48 | |||
35.32 | odd | 12 | inner | 735.2.y.g.557.4 | 48 | ||
35.33 | even | 12 | 525.2.j.b.407.4 | 24 | |||
105.2 | even | 12 | 735.2.j.h.197.4 | 24 | |||
105.17 | odd | 12 | 735.2.y.j.557.9 | 48 | |||
105.32 | even | 12 | inner | 735.2.y.g.557.9 | 48 | ||
105.47 | odd | 12 | 105.2.j.a.92.4 | yes | 24 | ||
105.62 | odd | 4 | 735.2.y.j.422.4 | 48 | |||
105.68 | odd | 12 | 525.2.j.b.407.9 | 24 | |||
105.89 | even | 6 | 525.2.j.b.218.4 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.j.a.8.4 | ✓ | 24 | 7.5 | odd | 6 | ||
105.2.j.a.8.9 | yes | 24 | 21.5 | even | 6 | ||
105.2.j.a.92.4 | yes | 24 | 105.47 | odd | 12 | ||
105.2.j.a.92.9 | yes | 24 | 35.12 | even | 12 | ||
525.2.j.b.218.4 | 24 | 105.89 | even | 6 | |||
525.2.j.b.218.9 | 24 | 35.19 | odd | 6 | |||
525.2.j.b.407.4 | 24 | 35.33 | even | 12 | |||
525.2.j.b.407.9 | 24 | 105.68 | odd | 12 | |||
735.2.j.h.197.4 | 24 | 105.2 | even | 12 | |||
735.2.j.h.197.9 | 24 | 35.2 | odd | 12 | |||
735.2.j.h.638.4 | 24 | 7.2 | even | 3 | |||
735.2.j.h.638.9 | 24 | 21.2 | odd | 6 | |||
735.2.y.g.128.4 | 48 | 3.2 | odd | 2 | inner | ||
735.2.y.g.128.9 | 48 | 1.1 | even | 1 | trivial | ||
735.2.y.g.263.4 | 48 | 7.4 | even | 3 | inner | ||
735.2.y.g.263.9 | 48 | 21.11 | odd | 6 | inner | ||
735.2.y.g.422.4 | 48 | 15.2 | even | 4 | inner | ||
735.2.y.g.422.9 | 48 | 5.2 | odd | 4 | inner | ||
735.2.y.g.557.4 | 48 | 35.32 | odd | 12 | inner | ||
735.2.y.g.557.9 | 48 | 105.32 | even | 12 | inner | ||
735.2.y.j.128.4 | 48 | 21.20 | even | 2 | |||
735.2.y.j.128.9 | 48 | 7.6 | odd | 2 | |||
735.2.y.j.263.4 | 48 | 7.3 | odd | 6 | |||
735.2.y.j.263.9 | 48 | 21.17 | even | 6 | |||
735.2.y.j.422.4 | 48 | 105.62 | odd | 4 | |||
735.2.y.j.422.9 | 48 | 35.27 | even | 4 | |||
735.2.y.j.557.4 | 48 | 35.17 | even | 12 | |||
735.2.y.j.557.9 | 48 | 105.17 | odd | 12 |