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 | 128.4 | ||
Character | \(\chi\) | \(=\) | 735.128 |
Dual form | 735.2.y.g.557.4 |
$q$-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 | −0.623818 | − | 0.781570i | \(-0.714419\pi\) |
−0.149457 | + | 0.988768i | \(0.547753\pi\) | |||||||
\(3\) | 0.615956 | − | 1.61883i | 0.355623 | − | 0.934630i | ||||
\(4\) | −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 | ||||
\(9\) | −2.24120 | − | 1.99425i | −0.747065 | − | 0.664751i | ||||
\(10\) | 0.208736 | + | 2.52295i | 0.0660082 | + | 0.797827i | ||||
\(11\) | 4.50498 | − | 2.60095i | 1.35830 | − | 0.784217i | 0.368908 | − | 0.929466i | \(-0.379732\pi\) |
0.989395 | + | 0.145249i | \(0.0463983\pi\) | |||||||
\(12\) | 0.198216 | + | 1.22812i | 0.0572201 | + | 0.354526i | ||||
\(13\) | 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 | ||||||||
\(15\) | −3.31624 | − | 2.00064i | −0.856249 | − | 0.516563i | ||||
\(16\) | −1.02384 | + | 1.77335i | −0.255961 | + | 0.443338i | ||||
\(17\) | −0.309010 | + | 1.15324i | −0.0749460 | + | 0.279702i | −0.993221 | − | 0.116241i | \(-0.962916\pi\) |
0.918275 | + | 0.395943i | \(0.129582\pi\) | |||||||
\(18\) | 3.03528 | + | 1.52415i | 0.715422 | + | 0.359245i | ||||
\(19\) | 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 | \(-0.771693\pi\) |
0.323996 | − | 0.946058i | \(-0.394973\pi\) | |||||||
\(24\) | −2.18233 | − | 4.86308i | −0.445467 | − | 0.992672i | ||||
\(25\) | −4.68211 | − | 1.75437i | −0.936422 | − | 0.350875i | ||||
\(26\) | −4.50219 | − | 2.59934i | −0.882953 | − | 0.509773i | ||||
\(27\) | −4.60883 | + | 2.39973i | −0.886969 | + | 0.461829i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.38282 | 0.813870 | 0.406935 | − | 0.913457i | \(-0.366598\pi\) | ||||
0.406935 | + | 0.913457i | \(0.366598\pi\) | |||||||
\(30\) | 4.21279 | + | 1.21612i | 0.769147 | + | 0.222032i | ||||
\(31\) | −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 | ||||
\(33\) | −1.43562 | − | 8.89486i | −0.249909 | − | 1.54840i | ||||
\(34\) | − | 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 | ||||
\(39\) | 7.25619 | − | 3.25625i | 1.16192 | − | 0.521417i | ||||
\(40\) | −3.92036 | − | 5.65547i | −0.619863 | − | 0.894208i | ||||
\(41\) | − | 1.82176i | − | 0.284511i | −0.989830 | − | 0.142255i | \(-0.954565\pi\) | ||
0.989830 | − | 0.142255i | \(-0.0454354\pi\) | |||||||
\(42\) | 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 | ||||
\(45\) | −5.28135 | + | 4.13610i | −0.787297 | + | 0.616574i | ||||
\(46\) | 4.50640 | + | 7.80531i | 0.664432 | + | 1.15083i | ||||
\(47\) | −4.63886 | + | 1.24298i | −0.676647 | + | 0.181307i | −0.580747 | − | 0.814084i | \(-0.697240\pi\) |
−0.0959000 | + | 0.995391i | \(0.530573\pi\) | |||||||
\(48\) | 2.24010 | + | 2.74973i | 0.323331 | + | 0.396890i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.63432 | + | 0.546575i | 0.796813 | + | 0.0772973i | ||||
\(51\) | 1.67656 | + | 1.21058i | 0.234766 | + | 0.169515i | ||||
\(52\) | −3.18563 | − | 0.853586i | −0.441767 | − | 0.118371i | ||||
\(53\) | −4.79555 | − | 1.28496i | −0.658719 | − | 0.176503i | −0.0860514 | − | 0.996291i | \(-0.527425\pi\) |
−0.572668 | + | 0.819787i | \(0.694092\pi\) | |||||||
\(54\) | 4.33693 | − | 3.97478i | 0.590181 | − | 0.540899i | ||||
\(55\) | −3.92668 | − | 10.9490i | −0.529474 | − | 1.47636i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.77289 | − | 1.44431i | 0.234825 | − | 0.191303i | ||||
\(58\) | −4.79295 | + | 1.28427i | −0.629345 | + | 0.168633i | ||||
\(59\) | 0.908859 | + | 1.57419i | 0.118323 | + | 0.204942i | 0.919103 | − | 0.394017i | \(-0.128915\pi\) |
−0.800780 | + | 0.598959i | \(0.795581\pi\) | |||||||
\(60\) | 2.78117 | + | 0.0534993i | 0.359048 | + | 0.00690673i | ||||
\(61\) | −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 | ||||
\(66\) | 4.17635 | + | 9.30653i | 0.514074 | + | 1.14556i | ||||
\(67\) | −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 | \(-0.819246\pi\) | ||
0.843057 | − | 0.537825i | \(-0.180754\pi\) | |||||||
\(72\) | −9.21670 | + | 0.537369i | −1.08620 | + | 0.0633295i | ||||
\(73\) | 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 | ||||
\(75\) | −5.72400 | + | 6.49891i | −0.660951 | + | 0.750429i | ||||
\(76\) | −0.948239 | −0.108771 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.98104 | + | 5.68718i | −0.790447 | + | 0.643947i | ||||
\(79\) | 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 | ||||
\(81\) | 1.04591 | + | 8.93902i | 0.116212 | + | 0.993224i | ||||
\(82\) | 0.533817 | + | 1.99223i | 0.0589502 | + | 0.220005i | ||||
\(83\) | 5.46196 | − | 5.46196i | 0.599528 | − | 0.599528i | −0.340659 | − | 0.940187i | \(-0.610650\pi\) |
0.940187 | + | 0.340659i | \(0.110650\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.41421 | + | 1.13967i | 0.261858 | + | 0.123614i | ||||
\(86\) | 0.390704 | + | 0.225573i | 0.0421307 | + | 0.0243241i | ||||
\(87\) | 2.69963 | − | 7.09503i | 0.289430 | − | 0.760667i | ||||
\(88\) | 4.14333 | − | 15.4631i | 0.441681 | − | 1.64838i | ||||
\(89\) | −4.71558 | + | 8.16762i | −0.499850 | + | 0.865766i | −1.00000 | 0.000172710i | \(-0.999945\pi\) | |
0.500150 | + | 0.865939i | \(0.333278\pi\) | |||||||
\(90\) | 4.56358 | − | 6.07070i | 0.481044 | − | 0.639908i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.04298 | + | 4.04298i | 0.421510 | + | 0.421510i | ||||
\(93\) | −2.91540 | + | 0.470542i | −0.302313 | + | 0.0487929i | ||||
\(94\) | 4.70873 | − | 2.71858i | 0.485668 | − | 0.280401i | ||||
\(95\) | 1.90827 | − | 2.25251i | 0.195784 | − | 0.231102i | ||||
\(96\) | 5.38753 | + | 3.89013i | 0.549863 | + | 0.397035i | ||||
\(97\) | 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 | −0.651505 | − | 0.758644i | \(-0.725862\pi\) |
0.331253 | + | 0.943542i | \(0.392529\pi\) | |||||||
\(102\) | −2.18818 | − | 0.832591i | −0.216662 | − | 0.0824388i | ||||
\(103\) | 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 | −0.166538 | − | 0.986035i | \(-0.553259\pi\) |
0.348791 | + | 0.937200i | \(0.386592\pi\) | |||||||
\(108\) | 2.00493 | − | 3.14774i | 0.192925 | − | 0.302891i | ||||
\(109\) | 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 | −0.695696 | − | 0.718336i | \(-0.744904\pi\) |
0.718336 | + | 0.695696i | \(0.244904\pi\) | |||||||
\(114\) | −1.51558 | + | 2.09896i | −0.141947 | + | 0.196585i | ||||
\(115\) | −17.7402 | + | 1.46773i | −1.65428 | + | 0.136867i | ||||
\(116\) | −2.72613 | + | 1.57393i | −0.253115 | + | 0.146136i | ||||
\(117\) | −0.801806 | − | 13.7522i | −0.0741270 | − | 1.27139i | ||||
\(118\) | −1.45518 | − | 1.45518i | −0.133960 | − | 0.133960i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −11.5700 | + | 2.86285i | −1.05619 | + | 0.261341i | ||||
\(121\) | 8.02991 | − | 13.9082i | 0.729992 | − | 1.26438i | ||||
\(122\) | 0.725273 | − | 2.70676i | 0.0656631 | − | 0.245058i | ||||
\(123\) | −2.94911 | − | 1.12212i | −0.265912 | − | 0.101178i | ||||
\(124\) | 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 | ||||
\(129\) | −0.629697 | + | 0.282580i | −0.0554418 | + | 0.0248798i | ||||
\(130\) | −7.51410 | + | 8.86960i | −0.659030 | + | 0.777916i | ||||
\(131\) | 11.8458 | + | 6.83920i | 1.03498 | + | 0.597543i | 0.918406 | − | 0.395639i | \(-0.129477\pi\) |
0.116570 | + | 0.993183i | \(0.462810\pi\) | |||||||
\(132\) | 4.08723 | + | 5.01709i | 0.355748 | + | 0.436682i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 12.6829 | 1.09563 | ||||||||
\(135\) | 3.44255 | + | 11.0972i | 0.296288 | + | 0.955099i | ||||
\(136\) | 1.83712 | + | 3.18199i | 0.157532 | + | 0.272853i | ||||
\(137\) | 3.66874 | − | 13.6919i | 0.313441 | − | 1.16978i | −0.611991 | − | 0.790865i | \(-0.709631\pi\) |
0.925432 | − | 0.378914i | \(-0.123702\pi\) | |||||||
\(138\) | 15.4112 | − | 2.48734i | 1.31189 | − | 0.211737i | ||||
\(139\) | 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 | ||||
\(144\) | 5.83115 | − | 1.93262i | 0.485929 | − | 0.161052i | ||||
\(145\) | 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 | −0.991232 | − | 0.132132i | \(-0.957818\pi\) |
0.610046 | + | 0.792366i | \(0.291151\pi\) | |||||||
\(150\) | 4.35530 | − | 8.78431i | 0.355609 | − | 0.717236i | ||||
\(151\) | 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 | ||||
\(153\) | 2.99241 | − | 1.96840i | 0.241922 | − | 0.159135i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.58867 | + | 1.28702i | −0.288249 | + | 0.103376i | ||||
\(156\) | −3.34401 | + | 4.63120i | −0.267735 | + | 0.370793i | ||||
\(157\) | 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 | ||||
\(159\) | −5.03398 | + | 6.97168i | −0.399221 | + | 0.552890i | ||||
\(160\) | 7.75793 | + | 3.66226i | 0.613319 | + | 0.289527i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −3.76312 | − | 9.46902i | −0.295659 | − | 0.743957i | ||||
\(163\) | −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 | ||||
\(165\) | −20.1432 | − | 0.387479i | −1.56814 | − | 0.0301652i | ||||
\(166\) | −4.37259 | + | 7.57355i | −0.339379 | + | 0.587822i | ||||
\(167\) | −12.4516 | − | 12.4516i | −0.963532 | − | 0.963532i | 0.0358258 | − | 0.999358i | \(-0.488594\pi\) |
−0.999358 | + | 0.0358258i | \(0.988594\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.08513i | 0.621933i | ||||||||
\(170\) | −2.97408 | − | 0.538895i | −0.228101 | − | 0.0413313i | ||||
\(171\) | −1.24606 | − | 3.75963i | −0.0952883 | − | 0.287506i | ||||
\(172\) | 0.276451 | + | 0.0740748i | 0.0210792 | + | 0.00564815i | ||||
\(173\) | 5.04991 | + | 18.8465i | 0.383938 | + | 1.43287i | 0.839835 | + | 0.542842i | \(0.182652\pi\) |
−0.455897 | + | 0.890032i | \(0.650682\pi\) | |||||||
\(174\) | −0.873244 | + | 8.55000i | −0.0662004 | + | 0.648174i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.6519i | 0.802916i | ||||||||
\(177\) | 3.10816 | − | 0.501652i | 0.233623 | − | 0.0377065i | ||||
\(178\) | 2.76354 | − | 10.3137i | 0.207136 | − | 0.773044i | ||||
\(179\) | −3.51580 | − | 6.08955i | −0.262783 | − | 0.455154i | 0.704197 | − | 0.710005i | \(-0.251307\pi\) |
−0.966981 | + | 0.254850i | \(0.917974\pi\) | |||||||
\(180\) | 1.79969 | − | 4.46928i | 0.134141 | − | 0.333121i | ||||
\(181\) | −14.1873 | −1.05454 | −0.527268 | − | 0.849699i | \(-0.676784\pi\) | ||||
−0.527268 | + | 0.849699i | \(0.676784\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.70772 | + | 3.32374i | 0.200161 | + | 0.245698i | ||||
\(184\) | −21.2166 | − | 12.2494i | −1.56411 | − | 0.903039i | ||||
\(185\) | −5.39448 | + | 0.446312i | −0.396610 | + | 0.0328135i | ||||
\(186\) | 3.05033 | − | 1.36885i | 0.223661 | − | 0.100369i | ||||
\(187\) | 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 | 0.902382 | − | 0.430938i | \(-0.141817\pi\) |
0.0779880 | + | 0.996954i | \(0.475150\pi\) | |||||||
\(192\) | −13.6613 | − | 5.19806i | −0.985918 | − | 0.375138i | ||||
\(193\) | 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 | ||||
\(195\) | −4.27165 | − | 17.2635i | −0.305899 | − | 1.23627i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.78986 | + | 2.78986i | 0.198769 | + | 0.198769i | 0.799472 | − | 0.600703i | \(-0.205113\pi\) |
−0.600703 | + | 0.799472i | \(0.705113\pi\) | |||||||
\(198\) | 17.6381 | − | 1.02837i | 1.25349 | − | 0.0730830i | ||||
\(199\) | 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 | ||||
\(201\) | −11.3587 | + | 15.7310i | −0.801182 | + | 1.10958i | ||||
\(202\) | 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 | ||||
\(207\) | −10.7171 | + | 21.3426i | −0.744887 | + | 1.48341i | ||||
\(208\) | −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 | ||||
\(213\) | −14.6724 | − | 5.58277i | −1.00533 | − | 0.382525i | ||||
\(214\) | −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 | ||||
\(219\) | −2.65824 | − | 1.91941i | −0.179627 | − | 0.129702i | ||||
\(220\) | 6.37435 | + | 5.40019i | 0.429759 | + | 0.364081i | ||||
\(221\) | −4.74783 | + | 2.74116i | −0.319374 | + | 0.184391i | ||||
\(222\) | 4.68628 | − | 0.756358i | 0.314522 | − | 0.0507634i | ||||
\(223\) | 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 | ||||||||
\(225\) | 6.99486 | + | 13.2692i | 0.466324 | + | 0.884614i | ||||
\(226\) | −0.192664 | + | 0.333704i | −0.0128158 | + | 0.0221977i | ||||
\(227\) | −1.52755 | + | 5.70090i | −0.101387 | + | 0.378382i | −0.997910 | − | 0.0646150i | \(-0.979418\pi\) |
0.896523 | + | 0.442997i | \(0.146085\pi\) | |||||||
\(228\) | −0.584074 | + | 1.53503i | −0.0386813 | + | 0.101660i | ||||
\(229\) | 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 | 0.985498 | − | 0.169686i | \(-0.0542753\pi\) |
−0.938309 | + | 0.345797i | \(0.887609\pi\) | |||||||
\(234\) | 4.90655 | + | 14.8041i | 0.320751 | + | 0.967777i | ||||
\(235\) | 0.885442 | + | 10.7022i | 0.0577599 | + | 0.698132i | ||||
\(236\) | −1.13063 | − | 0.652769i | −0.0735976 | − | 0.0424916i | ||||
\(237\) | 15.4448 | − | 12.5823i | 1.00325 | − | 0.817306i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.42942 | −0.0924613 | −0.0462307 | − | 0.998931i | \(-0.514721\pi\) | ||||
−0.0462307 | + | 0.998931i | \(0.514721\pi\) | |||||||
\(240\) | 6.94315 | − | 3.83251i | 0.448179 | − | 0.247387i | ||||
\(241\) | 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 | ||||
\(243\) | 15.1150 | + | 3.81290i | 0.969625 | + | 0.244597i | ||||
\(244\) | − | 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 | ||||
\(249\) | −5.47764 | − | 12.2063i | −0.347131 | − | 0.773543i | ||||
\(250\) | 3.44887 | − | 12.1789i | 0.218126 | − | 0.770264i | ||||
\(251\) | − | 12.3977i | − | 0.782538i | −0.920276 | − | 0.391269i | \(-0.872036\pi\) | ||
0.920276 | − | 0.391269i | \(-0.127964\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −29.2821 | − | 29.2821i | −1.84095 | − | 1.84095i | ||||
\(254\) | 3.65004 | − | 6.32205i | 0.229024 | − | 0.396681i | ||||
\(255\) | 3.33198 | − | 3.20621i | 0.208656 | − | 0.200780i | ||||
\(256\) | 7.37419 | + | 12.7725i | 0.460887 | + | 0.798280i | ||||
\(257\) | −18.9490 | + | 5.07738i | −1.18201 | + | 0.316718i | −0.795723 | − | 0.605661i | \(-0.792909\pi\) |
−0.386286 | + | 0.922379i | \(0.626242\pi\) | |||||||
\(258\) | 0.605820 | − | 0.493538i | 0.0377167 | − | 0.0307263i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.14813 | + | 6.66884i | −0.195239 | + | 0.413584i | ||||
\(261\) | −9.82276 | − | 8.74046i | −0.608014 | − | 0.541021i | ||||
\(262\) | −14.9584 | − | 4.00808i | −0.924131 | − | 0.247620i | ||||
\(263\) | 16.7901 | + | 4.49890i | 1.03532 | + | 0.277414i | 0.736174 | − | 0.676792i | \(-0.236631\pi\) |
0.299149 | + | 0.954206i | \(0.403297\pi\) | |||||||
\(264\) | −22.4800 | − | 16.2320i | −1.38355 | − | 0.999008i | ||||
\(265\) | −4.73911 | + | 10.0391i | −0.291121 | + | 0.616695i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.3174 | + | 12.6646i | 0.631413 | + | 0.775061i | ||||
\(268\) | 7.77175 | − | 2.08243i | 0.474735 | − | 0.127205i | ||||
\(269\) | −9.57676 | − | 16.5874i | −0.583906 | − | 1.01135i | −0.995011 | − | 0.0997663i | \(-0.968190\pi\) |
0.411105 | − | 0.911588i | \(-0.365143\pi\) | |||||||
\(270\) | −7.01644 | − | 11.1269i | −0.427007 | − | 0.677164i | ||||
\(271\) | 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 | ||||
\(276\) | 9.03519 | − | 4.05458i | 0.543854 | − | 0.244057i | ||||
\(277\) | 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 | \(-0.791005\pi\) | ||
0.792087 | − | 0.610408i | \(-0.208995\pi\) | |||||||
\(282\) | −1.50054 | − | 9.29714i | −0.0893561 | − | 0.553637i | ||||
\(283\) | −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 | ||||
\(285\) | −2.47101 | − | 4.47660i | −0.146370 | − | 0.265171i | ||||
\(286\) | −27.0431 | −1.59909 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 9.61593 | − | 6.32533i | 0.566624 | − | 0.372723i | ||||
\(289\) | 13.4880 | + | 7.78727i | 0.793409 | + | 0.458075i | ||||
\(290\) | 0.914854 | + | 11.0576i | 0.0537221 | + | 0.649327i | ||||
\(291\) | −3.07194 | − | 6.84548i | −0.180080 | − | 0.401289i | ||||
\(292\) | 0.351893 | + | 1.31328i | 0.0205930 | + | 0.0768540i | ||||
\(293\) | −19.7225 | + | 19.7225i | −1.15220 | + | 1.15220i | −0.166088 | + | 0.986111i | \(0.553114\pi\) |
−0.986111 | + | 0.166088i | \(0.946886\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.82594 | − | 1.37211i | 0.222755 | − | 0.0798875i | ||||
\(296\) | −6.45161 | − | 3.72484i | −0.374992 | − | 0.216502i | ||||
\(297\) | −14.5211 | + | 22.7981i | −0.842599 | + | 1.32288i | ||||
\(298\) | 2.72685 | − | 10.1768i | 0.157962 | − | 0.589524i | ||||
\(299\) | 18.2773 | − | 31.6572i | 1.05700 | − | 1.83078i | ||||
\(300\) | 1.22650 | − | 6.09792i | 0.0708122 | − | 0.352064i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −13.4712 | − | 13.4712i | −0.775182 | − | 0.775182i | ||||
\(303\) | 1.02565 | + | 6.35476i | 0.0589220 | + | 0.365071i | ||||
\(304\) | −2.34126 | + | 1.35173i | −0.134281 | + | 0.0775269i | ||||
\(305\) | 4.22290 | + | 3.57753i | 0.241803 | + | 0.204849i | ||||
\(306\) | −2.69564 | + | 3.02943i | −0.154100 | + | 0.173181i | ||||
\(307\) | 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 | 0.215560 | − | 0.976491i | \(-0.430842\pi\) |
0.953446 | + | 0.301565i | \(0.0975089\pi\) | |||||||
\(312\) | 8.70421 | − | 22.8760i | 0.492779 | − | 1.29510i | ||||
\(313\) | −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 | 0.219342 | − | 0.975648i | \(-0.429609\pi\) |
0.677780 | + | 0.735265i | \(0.262942\pi\) | |||||||
\(318\) | 3.46218 | − | 9.09913i | 0.194150 | − | 0.510254i | ||||
\(319\) | 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 | ||||
\(324\) | −3.86069 | − | 5.18451i | −0.214483 | − | 0.288028i | ||||
\(325\) | −9.50617 | − | 20.8988i | −0.527307 | − | 1.15926i | ||||
\(326\) | 12.1739 | − | 7.02859i | 0.674248 | − | 0.389277i | ||||
\(327\) | −1.63795 | − | 10.1485i | −0.0905789 | − | 0.561213i | ||||
\(328\) | −3.96430 | − | 3.96430i | −0.218892 | − | 0.218892i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 22.1416 | − | 5.47867i | 1.21886 | − | 0.301591i | ||||
\(331\) | 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 | ||||
\(333\) | −3.25887 | + | 6.48992i | −0.178585 | + | 0.355646i | ||||
\(334\) | 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 | ||||
\(339\) | −0.241354 | − | 0.537831i | −0.0131086 | − | 0.0292110i | ||||
\(340\) | −1.91092 | + | 0.158100i | −0.103634 | + | 0.00857418i | ||||
\(341\) | −7.68095 | − | 4.43460i | −0.415947 | − | 0.240147i | ||||
\(342\) | 2.46431 | + | 3.74632i | 0.133255 | + | 0.202578i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.22632 | −0.0661186 | ||||||||
\(345\) | −8.55117 | + | 29.6223i | −0.460380 | + | 1.59481i | ||||
\(346\) | −11.0449 | − | 19.1304i | −0.593779 | − | 1.02845i | ||||
\(347\) | 7.39306 | − | 27.5913i | 0.396880 | − | 1.48118i | −0.421674 | − | 0.906748i | \(-0.638557\pi\) |
0.818554 | − | 0.574430i | \(-0.194776\pi\) | |||||||
\(348\) | 0.868746 | + | 5.38261i | 0.0465697 | + | 0.288538i | ||||
\(349\) | − | 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 | −0.781164 | − | 0.624326i | \(-0.785374\pi\) |
−0.988671 | + | 0.150101i | \(0.952040\pi\) | |||||||
\(354\) | −3.25201 | + | 1.45936i | −0.172842 | + | 0.0775639i | ||||
\(355\) | −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 | −0.615194 | − | 0.788376i | \(-0.710922\pi\) |
0.990351 | + | 0.138585i | \(0.0442555\pi\) | |||||||
\(360\) | −2.49215 | + | 20.4932i | −0.131348 | + | 1.08009i | ||||
\(361\) | −8.62847 | − | 14.9450i | −0.454130 | − | 0.786577i | ||||
\(362\) | 15.5149 | − | 4.15721i | 0.815447 | − | 0.218498i | ||||
\(363\) | −17.5689 | − | 21.5659i | −0.922129 | − | 1.13192i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.82781 | − | 1.80698i | −0.200357 | − | 0.0945816i | ||||
\(366\) | −3.93503 | − | 2.84133i | −0.205687 | − | 0.148519i | ||||
\(367\) | 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 | ||||
\(369\) | −3.63304 | + | 4.08291i | −0.189129 | + | 0.212548i | ||||
\(370\) | 5.76850 | − | 2.06878i | 0.299890 | − | 0.107551i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.64441 | − | 1.33964i | 0.0852589 | − | 0.0694572i | ||||
\(373\) | −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 | ||||
\(375\) | 12.0171 | + | 15.1851i | 0.620562 | + | 0.784158i | ||||
\(376\) | −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 | ||||
\(381\) | 4.57248 | + | 10.1892i | 0.234255 | + | 0.522011i | ||||
\(382\) | −17.1090 | − | 4.58435i | −0.875373 | − | 0.234556i | ||||
\(383\) | −6.59450 | − | 24.6110i | −0.336963 | − | 1.25756i | −0.901725 | − | 0.432310i | \(-0.857698\pi\) |
0.564761 | − | 0.825254i | \(-0.308968\pi\) | |||||||
\(384\) | 3.24119 | + | 0.331035i | 0.165401 | + | 0.0168930i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.4253i | 0.734229i | ||||||||
\(387\) | 0.0695813 | + | 1.19343i | 0.00353702 | + | 0.0606653i | ||||
\(388\) | −0.805272 | + | 3.00532i | −0.0408815 | + | 0.152572i | ||||
\(389\) | 8.86076 | + | 15.3473i | 0.449259 | + | 0.778139i | 0.998338 | − | 0.0576315i | \(-0.0183549\pi\) |
−0.549079 | + | 0.835770i | \(0.685022\pi\) | |||||||
\(390\) | 9.72999 | + | 17.6273i | 0.492697 | + | 0.892594i | ||||
\(391\) | 9.50453 | 0.480665 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.3680 | − | 14.9637i | 0.926543 | − | 0.754819i | ||||
\(394\) | −3.86842 | − | 2.23343i | −0.194888 | − | 0.112519i | ||||
\(395\) | 16.6241 | − | 19.6230i | 0.836450 | − | 0.987341i | ||||
\(396\) | 10.6394 | − | 3.52621i | 0.534648 | − | 0.177199i | ||||
\(397\) | −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 | −0.491129 | − | 0.871087i | \(-0.663416\pi\) |
−0.999948 | + | 0.0102128i | \(0.996749\pi\) | |||||||
\(402\) | 7.81210 | − | 20.5314i | 0.389632 | − | 1.02401i | ||||
\(403\) | 2.02631 | − | 7.56230i | 0.100938 | − | 0.376705i | ||||
\(404\) | 1.33461 | − | 2.31162i | 0.0663995 | − | 0.115007i | ||||
\(405\) | 20.0850 | + | 1.26253i | 0.998030 | + | 0.0627356i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.90417 | − | 8.90417i | −0.441364 | − | 0.441364i | ||||
\(408\) | 6.28267 | − | 1.01401i | 0.311039 | − | 0.0502012i | ||||
\(409\) | −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 | ||||
\(411\) | −19.9050 | − | 14.3727i | −0.981843 | − | 0.708951i | ||||
\(412\) | −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 | ||||
\(417\) | 25.6199 | + | 9.74828i | 1.25461 | + | 0.477375i | ||||
\(418\) | −7.51046 | + | 2.01242i | −0.367349 | + | 0.0984308i | ||||
\(419\) | 17.0209 | 0.831524 | 0.415762 | − | 0.909474i | \(-0.363515\pi\) | ||||
0.415762 | + | 0.909474i | \(0.363515\pi\) | |||||||
\(420\) | 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 | ||||
\(423\) | 12.8754 | + | 6.46530i | 0.626024 | + | 0.314354i | ||||
\(424\) | −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 | ||||
\(429\) | 24.2196 | − | 33.5423i | 1.16934 | − | 1.61944i | ||||
\(430\) | 0.652079 | − | 0.769711i | 0.0314460 | − | 0.0371188i | ||||
\(431\) | 9.34548 | − | 5.39562i | 0.450156 | − | 0.259898i | −0.257740 | − | 0.966214i | \(-0.582978\pi\) |
0.707896 | + | 0.706317i | \(0.249644\pi\) | |||||||
\(432\) | 0.463155 | − | 10.6300i | 0.0222836 | − | 0.511437i | ||||
\(433\) | −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 | ||||||||
\(435\) | −14.5345 | − | 8.76846i | −0.696875 | − | 0.420415i | ||||
\(436\) | −2.13136 | + | 3.69163i | −0.102074 | + | 0.176797i | ||||
\(437\) | 2.72023 | − | 10.1520i | 0.130126 | − | 0.485638i | ||||
\(438\) | 3.46942 | + | 1.32010i | 0.165775 | + | 0.0630768i | ||||
\(439\) | −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 | \(0.108802\pi\) |
−0.648328 | + | 0.761361i | \(0.724531\pi\) | |||||||
\(444\) | 2.74745 | − | 1.23293i | 0.130388 | − | 0.0585123i | ||||
\(445\) | 16.0907 | + | 13.6317i | 0.762774 | + | 0.646202i | ||||
\(446\) | −16.8934 | − | 9.75342i | −0.799927 | − | 0.461838i | ||||
\(447\) | 10.1804 | + | 12.4965i | 0.481516 | + | 0.591062i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.5643 | −0.545753 | −0.272876 | − | 0.962049i | \(-0.587975\pi\) | ||||
−0.272876 | + | 0.962049i | \(0.587975\pi\) | |||||||
\(450\) | −11.5376 | − | 12.4612i | −0.543888 | − | 0.587428i | ||||
\(451\) | −4.73831 | − | 8.20699i | −0.223118 | − | 0.386452i | ||||
\(452\) | −0.0632681 | + | 0.236120i | −0.00297588 | + | 0.0111061i | ||||
\(453\) | 28.7736 | − | 4.64401i | 1.35190 | − | 0.218195i | ||||
\(454\) | − | 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 | ||||
\(459\) | −1.34330 | − | 6.05663i | −0.0626997 | − | 0.282699i | ||||
\(460\) | 10.5074 | − | 7.28369i | 0.489909 | − | 0.339604i | ||||
\(461\) | 13.0571i | 0.608129i | 0.952651 | + | 0.304064i | \(0.0983438\pi\) | ||||
−0.952651 | + | 0.304064i | \(0.901656\pi\) | |||||||
\(462\) | 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 | ||||
\(465\) | −0.127001 | + | 6.60218i | −0.00588953 | + | 0.306169i | ||||
\(466\) | −1.57542 | − | 2.72871i | −0.0729799 | − | 0.126405i | ||||
\(467\) | 12.8489 | − | 3.44285i | 0.594576 | − | 0.159316i | 0.0510324 | − | 0.998697i | \(-0.483749\pi\) |
0.543544 | + | 0.839381i | \(0.317082\pi\) | |||||||
\(468\) | 5.43734 | + | 8.26600i | 0.251341 | + | 0.382096i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.10427 | − | 11.4442i | −0.189316 | − | 0.527880i | ||||
\(471\) | 9.76010 | − | 13.5170i | 0.449721 | − | 0.622830i | ||||
\(472\) | 5.40333 | + | 1.44782i | 0.248708 | + | 0.0666412i | ||||
\(473\) | −2.00225 | − | 0.536501i | −0.0920634 | − | 0.0246683i | ||||
\(474\) | −13.2031 | + | 18.2853i | −0.606440 | + | 0.839873i | ||||
\(475\) | −4.19527 | − | 5.09667i | −0.192492 | − | 0.233851i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.18522 | + | 12.4434i | 0.374776 | + | 0.569744i | ||||
\(478\) | 1.56318 | − | 0.418852i | 0.0714980 | − | 0.0191578i | ||||
\(479\) | 19.4344 | + | 33.6614i | 0.887982 | + | 1.53803i | 0.842257 | + | 0.539075i | \(0.181226\pi\) |
0.0457243 | + | 0.998954i | \(0.485440\pi\) | |||||||
\(480\) | 10.7071 | − | 10.3030i | 0.488710 | − | 0.470263i | ||||
\(481\) | 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 | ||||
\(486\) | −17.6466 | + | 0.259334i | −0.800467 | + | 0.0117636i | ||||
\(487\) | −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 | \(0.196431\pi\) | ||||
−0.815556 | + | 0.578678i | \(0.803569\pi\) | |||||||
\(492\) | 2.23733 | − | 0.361102i | 0.100867 | − | 0.0162797i | ||||
\(493\) | −1.35434 | + | 5.05445i | −0.0609963 | + | 0.227641i | ||||
\(494\) | −3.43177 | − | 5.94401i | −0.154403 | − | 0.267433i | ||||
\(495\) | −13.0346 | + | 32.3696i | −0.585861 | + | 1.45491i | ||||
\(496\) | 3.49129 | 0.156764 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 9.56694 | + | 11.7434i | 0.428705 | + | 0.526236i | ||||
\(499\) | 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 | ||||
\(501\) | −27.8266 | + | 12.4873i | −1.24320 | + | 0.557892i | ||||
\(502\) | 3.63282 | + | 13.5579i | 0.162141 | + | 0.605117i | ||||
\(503\) | 10.1763 | − | 10.1763i | 0.453738 | − | 0.453738i | −0.442855 | − | 0.896593i | \(-0.646035\pi\) |
0.896593 | + | 0.442855i | \(0.146035\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.80534 | + | 7.82229i | 0.124836 | + | 0.348087i | ||||
\(506\) | 40.6025 | + | 23.4418i | 1.80500 | + | 1.04212i | ||||
\(507\) | 13.0884 | + | 4.98009i | 0.581277 | + | 0.221174i | ||||
\(508\) | 1.19862 | − | 4.47331i | 0.0531801 | − | 0.198471i | ||||
\(509\) | 15.6485 | − | 27.1040i | 0.693607 | − | 1.20136i | −0.277042 | − | 0.960858i | \(-0.589354\pi\) |
0.970648 | − | 0.240504i | \(-0.0773127\pi\) | |||||||
\(510\) | −2.70428 | + | 4.48257i | −0.119747 | + | 0.198492i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −14.4671 | − | 14.4671i | −0.639360 | − | 0.639360i | ||||
\(513\) | −6.85370 | − | 0.298619i | −0.302598 | − | 0.0131844i | ||||
\(514\) | 19.2344 | − | 11.1050i | 0.848394 | − | 0.489821i | ||||
\(515\) | −0.307800 | − | 3.72032i | −0.0135633 | − | 0.163937i | ||||
\(516\) | 0.290196 | − | 0.401899i | 0.0127752 | − | 0.0176926i | ||||
\(517\) | −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 | −0.886245 | − | 0.463217i | \(-0.846695\pi\) |
−0.0419642 | + | 0.999119i | \(0.513362\pi\) | |||||||
\(522\) | 13.3031 | + | 6.68006i | 0.582260 | + | 0.292378i | ||||
\(523\) | 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 | ||||
\(528\) | 17.2436 | + | 6.56110i | 0.750429 | + | 0.285535i | ||||
\(529\) | −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 | ||||
\(534\) | −14.9938 | − | 10.8265i | −0.648847 | − | 0.468508i | ||||
\(535\) | −0.359845 | − | 4.34937i | −0.0155574 | − | 0.188040i | ||||
\(536\) | −29.8562 | + | 17.2375i | −1.28959 | + | 0.744545i | ||||
\(537\) | −12.0235 | + | 1.94058i | −0.518852 | + | 0.0837420i | ||||
\(538\) | 15.3334 | + | 15.3334i | 0.661071 | + | 0.661071i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −6.12646 | − | 5.66627i | −0.263641 | − | 0.243837i | ||||
\(541\) | −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 | ||||
\(543\) | −8.73878 | + | 22.9668i | −0.375017 | + | 0.985601i | ||||
\(544\) | −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 | ||||
\(549\) | 7.04839 | − | 2.33605i | 0.300818 | − | 0.0997003i | ||||
\(550\) | 26.8041 | − | 12.1923i | 1.14293 | − | 0.519881i | ||||
\(551\) | 5.01118 | + | 2.89320i | 0.213483 | + | 0.123255i | ||||
\(552\) | −32.8982 | + | 26.8009i | −1.40024 | + | 1.14072i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −12.2657 | −0.521119 | ||||||||
\(555\) | −2.60026 | + | 9.00764i | −0.110375 | + | 0.382353i | ||||
\(556\) | −5.68343 | − | 9.84400i | −0.241031 | − | 0.417478i | ||||
\(557\) | −4.80240 | + | 17.9228i | −0.203484 | + | 0.759413i | 0.786422 | + | 0.617689i | \(0.211931\pi\) |
−0.989906 | + | 0.141724i | \(0.954736\pi\) | |||||||
\(558\) | −0.337061 | − | 5.78111i | −0.0142689 | − | 0.244734i | ||||
\(559\) | − | 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 | 0.686018 | − | 0.727584i | \(-0.259357\pi\) |
0.230317 | + | 0.973116i | \(0.426024\pi\) | |||||||
\(564\) | −2.44602 | − | 5.45068i | −0.102996 | − | 0.229515i | ||||
\(565\) | −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 | \(0.364927\pi\) |
−0.995078 | + | 0.0990907i | \(0.968407\pi\) | |||||||
\(570\) | 4.01398 | + | 4.17144i | 0.168127 | + | 0.174722i | ||||
\(571\) | 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 | ||||
\(573\) | 21.0089 | − | 17.1151i | 0.877658 | − | 0.714994i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.84325 | + | 39.6178i | −0.160275 | + | 1.65218i | ||||
\(576\) | −16.8295 | + | 18.9135i | −0.701229 | + | 0.788061i | ||||
\(577\) | −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 | ||||
\(579\) | −17.8922 | − | 12.9192i | −0.743573 | − | 0.536906i | ||||
\(580\) | 2.37619 | + | 6.62564i | 0.0986657 | + | 0.275115i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 5.36528 | + | 6.58590i | 0.222398 | + | 0.272994i | ||||
\(583\) | −24.9460 | + | 6.68426i | −1.03316 | + | 0.276834i | ||||
\(584\) | −2.91281 | − | 5.04514i | −0.120533 | − | 0.208769i | ||||
\(585\) | −30.5778 | − | 3.71853i | −1.26424 | − | 0.153742i | ||||
\(586\) | 15.7889 | − | 27.3472i | 0.652233 | − | 1.12970i | ||||
\(587\) | 23.2211 | + | 23.2211i | 0.958439 | + | 0.958439i | 0.999170 | − | 0.0407314i | \(-0.0129688\pi\) |
−0.0407314 | + | 0.999170i | \(0.512969\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 2.25101i | − | 0.0927512i | ||||||
\(590\) | −3.78189 | + | 2.62160i | −0.155698 | + | 0.107929i | ||||
\(591\) | 6.23473 | − | 2.79787i | 0.256463 | − | 0.115089i | ||||
\(592\) | 4.78800 | + | 1.28294i | 0.196786 | + | 0.0527285i | ||||
\(593\) | 8.89227 | + | 33.1864i | 0.365162 | + | 1.36280i | 0.867201 | + | 0.497958i | \(0.165917\pi\) |
−0.502040 | + | 0.864845i | \(0.667417\pi\) | |||||||
\(594\) | 9.19956 | − | 29.1865i | 0.377463 | − | 1.19754i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 6.68380i | − | 0.273779i | ||||||
\(597\) | −3.98293 | − | 24.6776i | −0.163010 | − | 1.00999i | ||||
\(598\) | −10.7113 | + | 39.9753i | −0.438019 | + | 1.63471i | ||||
\(599\) | 11.3932 | + | 19.7336i | 0.465515 | + | 0.806295i | 0.999225 | − | 0.0393726i | \(-0.0125359\pi\) |
−0.533710 | + | 0.845668i | \(0.679203\pi\) | |||||||
\(600\) | 1.68626 | + | 26.5981i | 0.0688414 | + | 1.08586i | ||||
\(601\) | 41.7276 | 1.70210 | 0.851052 | − | 0.525082i | \(-0.175965\pi\) | ||||
0.851052 | + | 0.525082i | \(0.175965\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.4692 | + | 28.0774i | 0.752124 | + | 1.14340i | ||||
\(604\) | −10.4667 | − | 6.04296i | −0.425885 | − | 0.245885i | ||||
\(605\) | −27.4001 | − | 23.2126i | −1.11397 | − | 0.943728i | ||||
\(606\) | −2.98371 | − | 6.64887i | −0.121205 | − | 0.270092i | ||||
\(607\) | 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 | ||||
\(612\) | −1.15441 | + | 2.29897i | −0.0466643 | + | 0.0929303i | ||||
\(613\) | −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 | ||||
\(615\) | −3.64468 | + | 6.04138i | −0.146968 | + | 0.243612i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.12737 | + | 8.12737i | 0.327196 | + | 0.327196i | 0.851519 | − | 0.524323i | \(-0.175682\pi\) |
−0.524323 | + | 0.851519i | \(0.675682\pi\) | |||||||
\(618\) | 0.521624 | + | 3.23190i | 0.0209828 | + | 0.130006i | ||||
\(619\) | −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 | ||||
\(621\) | 27.9487 | + | 30.4952i | 1.12154 | + | 1.22373i | ||||
\(622\) | −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 | ||||
\(627\) | 4.23027 | − | 11.1178i | 0.168941 | − | 0.444001i | ||||
\(628\) | −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 | ||||
\(633\) | 7.38195 | − | 19.4009i | 0.293406 | − | 0.771115i | ||||
\(634\) | −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 | ||||
\(639\) | −18.0751 | + | 20.3133i | −0.715039 | + | 0.803580i | ||||
\(640\) | 4.19180 | − | 0.346809i | 0.165696 | − | 0.0137088i | ||||
\(641\) | 16.7716 | − | 9.68307i | 0.662437 | − | 0.382458i | −0.130768 | − | 0.991413i | \(-0.541744\pi\) |
0.793205 | + | 0.608955i | \(0.208411\pi\) | |||||||
\(642\) | 0.609823 | + | 3.77837i | 0.0240678 | + | 0.149120i | ||||
\(643\) | −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 | ||||||||
\(645\) | 0.370697 | + | 1.49814i | 0.0145962 | + | 0.0589893i | ||||
\(646\) | 0.892292 | − | 1.54550i | 0.0351068 | − | 0.0608067i | ||||
\(647\) | 3.89878 | − | 14.5504i | 0.153277 | − | 0.572037i | −0.845970 | − | 0.533231i | \(-0.820978\pi\) |
0.999247 | − | 0.0388063i | \(-0.0123555\pi\) | |||||||
\(648\) | 21.7281 | + | 17.1761i | 0.853560 | + | 0.674740i | ||||
\(649\) | 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 | 0.934618 | − | 0.355654i | \(-0.115742\pi\) |
−0.987230 | + | 0.159304i | \(0.949075\pi\) | |||||||
\(654\) | 4.76496 | + | 10.6182i | 0.186325 | + | 0.415204i | ||||
\(655\) | 19.7705 | − | 23.3370i | 0.772499 | − | 0.911854i | ||||
\(656\) | 3.23062 | + | 1.86520i | 0.126134 | + | 0.0728237i | ||||
\(657\) | −4.74456 | + | 3.12095i | −0.185103 | + | 0.121760i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −45.6844 | −1.77961 | −0.889807 | − | 0.456338i | \(-0.849161\pi\) | ||||
−0.889807 | + | 0.456338i | \(0.849161\pi\) | |||||||
\(660\) | 12.6683 | − | 6.99269i | 0.493113 | − | 0.272190i | ||||
\(661\) | −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 | ||||
\(663\) | 1.51301 | + | 9.37435i | 0.0587603 | + | 0.364070i | ||||
\(664\) | − | 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 | ||||
\(669\) | 27.2271 | − | 12.2183i | 1.05266 | − | 0.472387i | ||||
\(670\) | 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 | ||||
\(675\) | 25.7891 | − | 3.15021i | 0.992622 | − | 0.121252i | ||||
\(676\) | −2.90349 | − | 5.02899i | −0.111673 | − | 0.193423i | ||||
\(677\) | 41.0980 | − | 11.0122i | 1.57952 | − | 0.423232i | 0.640746 | − | 0.767753i | \(-0.278625\pi\) |
0.938779 | + | 0.344521i | \(0.111959\pi\) | |||||||
\(678\) | 0.421536 | + | 0.517437i | 0.0161890 | + | 0.0198721i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 7.73356 | − | 2.77352i | 0.296568 | − | 0.106360i | ||||
\(681\) | 8.28786 | + | 5.98435i | 0.317591 | + | 0.229321i | ||||
\(682\) | 9.69914 | + | 2.59888i | 0.371399 | + | 0.0995162i | ||||
\(683\) | 2.02836 | + | 0.543497i | 0.0776129 | + | 0.0207963i | 0.297417 | − | 0.954748i | \(-0.403875\pi\) |
−0.219804 | + | 0.975544i | \(0.570542\pi\) | |||||||
\(684\) | 2.12519 | + | 1.89103i | 0.0812587 | + | 0.0723053i | ||||
\(685\) | −28.6628 | − | 13.5308i | −1.09515 | − | 0.516984i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 36.6201 | − | 29.8330i | 1.39714 | − | 1.13820i | ||||
\(688\) | 0.788169 | − | 0.211189i | 0.0300487 | − | 0.00805152i | ||||
\(689\) | −11.3986 | − | 19.7430i | −0.434253 | − | 0.752149i | ||||
\(690\) | 0.671343 | − | 34.8999i | 0.0255576 | − | 1.32862i | ||||
\(691\) | 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 | ||||
\(696\) | −9.56477 | − | 21.3140i | −0.362552 | − | 0.807906i | ||||
\(697\) | 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 | \(-0.699998\pi\) | ||
0.587781 | − | 0.809020i | \(-0.300002\pi\) | |||||||
\(702\) | 26.9876 | + | 1.17586i | 1.01858 | + | 0.0443800i | ||||
\(703\) | 0.827175 | − | 3.08706i | 0.0311975 | − | 0.116431i | ||||
\(704\) | −21.9495 | − | 38.0176i | −0.827251 | − | 1.43284i | ||||
\(705\) | 17.8703 | + | 5.15869i | 0.673035 | + | 0.194287i | ||||
\(706\) | 38.9746 | 1.46683 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.75314 | + | 1.42821i | −0.0658869 | + | 0.0536756i | ||||
\(709\) | 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 | ||||
\(711\) | −10.8552 | − | 32.7525i | −0.407102 | − | 1.22832i | ||||
\(712\) | 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 | ||||
\(717\) | −0.880459 | + | 2.31398i | −0.0328813 | + | 0.0864171i | ||||
\(718\) | −4.16574 | + | 15.5467i | −0.155464 | + | 0.580199i | ||||
\(719\) | −22.9808 | + | 39.8040i | −0.857041 | + | 1.48444i | 0.0176984 | + | 0.999843i | \(0.494366\pi\) |
−0.874739 | + | 0.484594i | \(0.838967\pi\) | |||||||
\(720\) | −1.92748 | − | 13.6004i | −0.0718330 | − | 0.506858i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13.8151 | + | 13.8151i | 0.514145 | + | 0.514145i | ||||
\(723\) | 49.8132 | − | 8.03978i | 1.85257 | − | 0.299003i | ||||
\(724\) | 8.82459 | − | 5.09488i | 0.327963 | − | 0.189350i | ||||
\(725\) | −20.5209 | − | 7.68911i | −0.762126 | − | 0.285566i | ||||
\(726\) | 25.5322 | + | 18.4359i | 0.947590 | + | 0.684219i | ||||
\(727\) | 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 | ||||
\(732\) | −2.87782 | − | 1.09500i | −0.106367 | − | 0.0404723i | ||||
\(733\) | −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 | ||||
\(738\) | 2.77662 | − | 5.52954i | 0.102209 | − | 0.203545i | ||||
\(739\) | −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 | −0.923135 | − | 0.384475i | \(-0.874382\pi\) |
0.384475 | + | 0.923135i | \(0.374382\pi\) | |||||||
\(744\) | −5.32023 | + | 7.36811i | −0.195049 | + | 0.270128i | ||||
\(745\) | 15.8771 | + | 13.4507i | 0.581692 | + | 0.492795i | ||||
\(746\) | 6.34892 | − | 3.66555i | 0.232450 | − | 0.134205i | ||||
\(747\) | −23.1339 | + | 1.34879i | −0.846424 | + | 0.0493497i | ||||
\(748\) | −3.15418 | − | 3.15418i | −0.115328 | − | 0.115328i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −17.5912 | − | 13.0848i | −0.642341 | − | 0.477790i | ||||
\(751\) | 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 | ||||
\(753\) | −20.0698 | − | 7.63646i | −0.731383 | − | 0.278288i | ||||
\(754\) | −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 | ||||
\(759\) | −65.4390 | + | 29.3661i | −2.37529 | + | 1.06592i | ||||
\(760\) | −0.749099 | − | 9.05420i | −0.0271727 | − | 0.328430i | ||||
\(761\) | 19.3001 | + | 11.1429i | 0.699629 | + | 0.403931i | 0.807209 | − | 0.590265i | \(-0.200977\pi\) |
−0.107580 | + | 0.994196i | \(0.534310\pi\) | |||||||
\(762\) | −7.98603 | − | 9.80288i | −0.289303 | − | 0.355121i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −11.2367 | −0.406530 | ||||||||
\(765\) | −3.13794 | − | 7.36877i | −0.113452 | − | 0.266418i | ||||
\(766\) | 14.4232 | + | 24.9817i | 0.521131 | + | 0.902625i | ||||
\(767\) | −2.16028 | + | 8.06229i | −0.0780033 | + | 0.291112i | ||||
\(768\) | 25.2186 | − | 4.07025i | 0.909998 | − | 0.146872i | ||||
\(769\) | − | 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 | 0.725624 | − | 0.688091i | \(-0.241551\pi\) |
0.284363 | + | 0.958717i | \(0.408218\pi\) | |||||||
\(774\) | −0.425794 | − | 1.28471i | −0.0153048 | − | 0.0461781i | ||||
\(775\) | 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 | ||||
\(780\) | 8.85657 | + | 9.20399i | 0.317116 | + | 0.329556i | ||||
\(781\) | −23.5739 | − | 40.8313i | −0.843542 | − | 1.46106i | ||||
\(782\) | −10.3939 | + | 2.78505i | −0.371686 | + | 0.0995930i | ||||
\(783\) | −20.1997 | + | 10.5176i | −0.721877 | + | 0.375868i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.18838 | − | 19.4642i | 0.327947 | − | 0.694706i | ||||
\(786\) | −15.7021 | + | 21.7462i | −0.560075 | + | 0.775661i | ||||
\(787\) | 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 | ||||
\(789\) | 17.6249 | − | 24.4092i | 0.627464 | − | 0.868989i | ||||
\(790\) | −12.4297 | + | 26.3305i | −0.442230 | + | 0.936797i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −40.1234 | + | 26.3930i | −1.42572 | + | 0.937836i | ||||
\(793\) | −10.9782 | + | 2.94161i | −0.389848 | + | 0.104459i | ||||
\(794\) | 3.54673 | + | 6.14312i | 0.125869 | + | 0.218011i | ||||
\(795\) | 13.3324 | + | 13.8554i | 0.472853 | + | 0.491401i | ||||
\(796\) | −5.18273 | + | 8.97676i | −0.183697 | + | 0.318173i | ||||
\(797\) | −5.16008 | − | 5.16008i | −0.182779 | − | 0.182779i | 0.609786 | − | 0.792566i | \(-0.291255\pi\) |
−0.792566 | + | 0.609786i | \(0.791255\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 5.73382i | − | 0.202848i | ||||||
\(800\) | 11.1508 | − | 15.6093i | 0.394239 | − | 0.551871i | ||||
\(801\) | 26.8568 | − | 8.90118i | 0.948940 | − | 0.314508i | ||||
\(802\) | 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 | ||||||||
\(807\) | −32.7511 | + | 5.28597i | −1.15289 | + | 0.186075i | ||||
\(808\) | −2.96012 | + | 11.0473i | −0.104137 | + | 0.388644i | ||||
\(809\) | −6.43076 | − | 11.1384i | −0.226093 | − | 0.391605i | 0.730554 | − | 0.682855i | \(-0.239262\pi\) |
−0.956647 | + | 0.291250i | \(0.905929\pi\) | |||||||
\(810\) | −22.3344 | + | 4.50468i | −0.784751 | + | 0.158278i | ||||
\(811\) | −0.485057 | −0.0170327 | −0.00851633 | − | 0.999964i | \(-0.502711\pi\) | ||||
−0.00851633 | + | 0.999964i | \(0.502711\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.1978 | − | 24.7929i | −0.708368 | − | 0.869524i | ||||
\(814\) | 12.3465 | + | 7.12827i | 0.432745 | + | 0.249846i | ||||
\(815\) | 2.28921 | + | 27.6692i | 0.0801875 | + | 0.969209i | ||||
\(816\) | −3.86332 | + | 1.73369i | −0.135243 | + | 0.0606911i | ||||
\(817\) | −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 | 0.861110 | − | 0.508419i | \(-0.169770\pi\) |
−0.00974941 | + | 0.999952i | \(0.503103\pi\) | |||||||
\(822\) | 25.9792 | + | 9.88497i | 0.906128 | + | 0.344778i | ||||
\(823\) | 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 | ||||
\(825\) | −8.88318 | + | 44.1653i | −0.309273 | + | 1.53764i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.0314 | + | 24.0314i | 0.835652 | + | 0.835652i | 0.988283 | − | 0.152631i | \(-0.0487746\pi\) |
−0.152631 | + | 0.988283i | \(0.548775\pi\) | |||||||
\(828\) | −0.998385 | − | 17.1238i | −0.0346963 | − | 0.595095i | ||||
\(829\) | −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 | ||||
\(831\) | 10.9851 | − | 15.2135i | 0.381069 | − | 0.527751i | ||||
\(832\) | 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 | ||||
\(837\) | 7.47236 | + | 4.75947i | 0.258283 | + | 0.164511i | ||||
\(838\) | −18.6136 | + | 4.98750i | −0.642996 | + | 0.172290i | ||||
\(839\) | 1.64172 | 0.0566785 | 0.0283392 | − | 0.999598i | \(-0.490978\pi\) | ||||
0.0283392 | + | 0.999598i | \(0.490978\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.79087 | −0.337616 | ||||||||
\(842\) | −23.7824 | + | 6.37248i | −0.819596 | + | 0.219610i | ||||
\(843\) | −33.1287 | − | 12.6053i | −1.14101 | − | 0.434150i | ||||
\(844\) | −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 | ||||
\(849\) | 16.3743 | + | 11.8233i | 0.561965 | + | 0.405773i | ||||
\(850\) | −2.37139 | + | 6.32883i | −0.0813382 | + | 0.217077i | ||||
\(851\) | −16.6890 | + | 9.63541i | −0.572092 | + | 0.330298i | ||||
\(852\) | 11.1311 | − | 1.79655i | 0.381346 | − | 0.0615487i | ||||
\(853\) | −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 | ||||||||
\(855\) | −8.76886 | + | 1.24274i | −0.299889 | + | 0.0425009i | ||||
\(856\) | 3.00320 | − | 5.20169i | 0.102647 | − | 0.177790i | ||||
\(857\) | 3.07062 | − | 11.4597i | 0.104890 | − | 0.391456i | −0.893442 | − | 0.449178i | \(-0.851717\pi\) |
0.998333 | + | 0.0577219i | \(0.0183837\pi\) | |||||||
\(858\) | −16.6574 | + | 43.7780i | −0.568673 | + | 1.49456i | ||||
\(859\) | 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 | 0.893308 | − | 0.449445i | \(-0.148378\pi\) |
−0.998350 | + | 0.0574232i | \(0.981712\pi\) | |||||||
\(864\) | −4.31661 | − | 19.4626i | −0.146854 | − | 0.662133i | ||||
\(865\) | 43.4802 | − | 3.59733i | 1.47837 | − | 0.122313i | ||||
\(866\) | 0.647440 | + | 0.373800i | 0.0220009 | + | 0.0127022i | ||||
\(867\) | 20.9142 | − | 17.0380i | 0.710285 | − | 0.578642i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 59.8298 | 2.02959 | ||||||||
\(870\) | 18.4639 | + | 5.33004i | 0.625985 | + | 0.180705i | ||||
\(871\) | −25.7200 | − | 44.5483i | −0.871488 | − | 1.50946i | ||||
\(872\) | 4.72729 | − | 17.6425i | 0.160086 | − | 0.597450i | ||||
\(873\) | −12.9738 | + | 0.756423i | −0.439097 | + | 0.0256010i | ||||
\(874\) | 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 | ||||
\(879\) | 19.7791 | + | 44.0754i | 0.667131 | + | 1.48663i | ||||
\(880\) | 23.4367 | + | 4.24667i | 0.790051 | + | 0.143155i | ||||
\(881\) | 16.9744i | 0.571882i | 0.958247 | + | 0.285941i | \(0.0923061\pi\) | ||||
−0.958247 | + | 0.285941i | \(0.907694\pi\) | |||||||
\(882\) | 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 | ||||
\(885\) | 0.135398 | − | 7.03869i | 0.00455135 | − | 0.236603i | ||||
\(886\) | −13.5258 | − | 23.4274i | −0.454409 | − | 0.787060i | ||||
\(887\) | −17.1474 | + | 4.59462i | −0.575752 | + | 0.154272i | −0.534933 | − | 0.844894i | \(-0.679663\pi\) |
−0.0408187 | + | 0.999167i | \(0.512997\pi\) | |||||||
\(888\) | −10.0038 | + | 8.14969i | −0.335705 | + | 0.273486i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −21.5908 | − | 10.1923i | −0.723726 | − | 0.341647i | ||||
\(891\) | 27.9618 | + | 37.5498i | 0.936755 | + | 1.25796i | ||||
\(892\) | −11.9533 | − | 3.20288i | −0.400227 | − | 0.107240i | ||||
\(893\) | −6.12444 | − | 1.64104i | −0.204947 | − | 0.0549153i | ||||
\(894\) | −14.7948 | − | 10.6827i | −0.494811 | − | 0.357284i | ||||
\(895\) | −14.8001 | + | 5.30784i | −0.494714 | + | 0.177422i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −39.9895 | − | 49.0873i | −1.33521 | − | 1.63898i | ||||
\(898\) | 12.6464 | − | 3.38860i | 0.422017 | − | 0.113079i | ||||
\(899\) | −3.73633 | − | 6.47152i | −0.124614 | − | 0.215837i | ||||
\(900\) | −9.11600 | − | 5.74155i | −0.303867 | − | 0.191385i | ||||
\(901\) | 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 | ||||
\(906\) | −30.1053 | + | 13.5099i | −1.00018 | + | 0.448836i | ||||
\(907\) | 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 | \(0.124511\pi\) | ||||
−0.924467 | + | 0.381263i | \(0.875489\pi\) | |||||||
\(912\) | 0.746097 | + | 4.62270i | 0.0247057 | + | 0.153073i | ||||
\(913\) | 10.3997 | − | 38.8124i | 0.344181 | − | 1.28450i | ||||
\(914\) | 14.2829 | + | 24.7387i | 0.472436 | + | 0.818283i | ||||
\(915\) | 8.39253 | − | 4.63254i | 0.277448 | − | 0.153147i | ||||
\(916\) | −19.5865 | −0.647155 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3.24373 | + | 6.22977i | 0.107059 | + | 0.205613i | ||||
\(919\) | 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 | ||||
\(921\) | −13.3379 | − | 29.7220i | −0.439499 | − | 0.979375i | ||||
\(922\) | −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 | ||||
\(927\) | −4.47579 | − | 2.24749i | −0.147004 | − | 0.0738172i | ||||
\(928\) | −4.35208 | + | 16.2422i | −0.142864 | + | 0.533176i | ||||
\(929\) | −25.8842 | + | 44.8327i | −0.849232 | + | 1.47091i | 0.0326620 | + | 0.999466i | \(0.489602\pi\) |
−0.881894 | + | 0.471447i | \(0.843732\pi\) | |||||||
\(930\) | −1.79570 | − | 7.25720i | −0.0588834 | − | 0.237973i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.41341 | − | 1.41341i | −0.0462979 | − | 0.0462979i | ||||
\(933\) | −6.56965 | − | 40.7045i | −0.215081 | − | 1.33261i | ||||
\(934\) | −13.0424 | + | 7.53004i | −0.426761 | + | 0.246391i | ||||
\(935\) | 13.8402 | − | 1.14507i | 0.452623 | − | 0.0374478i | ||||
\(936\) | −31.6708 | − | 28.1812i | −1.03519 | − | 0.921132i | ||||
\(937\) | −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 | −0.697684 | − | 0.716406i | \(-0.745786\pi\) |
0.271584 | + | 0.962415i | \(0.412453\pi\) | |||||||
\(942\) | −6.71262 | + | 17.6418i | −0.218709 | + | 0.574800i | ||||
\(943\) | −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 | 0.421341 | − | 0.906902i | \(-0.361559\pi\) |
0.818343 | + | 0.574730i | \(0.194893\pi\) | |||||||
\(948\) | −5.08824 | + | 13.3727i | −0.165258 | + | 0.434324i | ||||
\(949\) | 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 | −0.500906 | − | 0.865501i | \(-0.667000\pi\) |
0.865501 | + | 0.500906i | \(0.167000\pi\) | |||||||
\(954\) | −12.5974 | − | 11.2093i | −0.407855 | − | 0.362916i | ||||
\(955\) | 22.6131 | − | 26.6923i | 0.731742 | − | 0.863744i | ||||
\(956\) | 0.889104 | − | 0.513324i | 0.0287557 | − | 0.0166021i | ||||
\(957\) | −6.29205 | − | 38.9846i | −0.203393 | − | 1.26019i | ||||
\(958\) | −31.1166 | − | 31.1166i | −1.00533 | − | 1.00533i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −16.8834 | + | 27.9857i | −0.544910 | + | 0.903236i | ||||
\(961\) | 14.0465 | − | 24.3293i | 0.453113 | − | 0.784815i | ||||
\(962\) | −3.25714 | + | 12.1558i | −0.105014 | + | 0.391919i | ||||
\(963\) | −5.23258 | − | 2.62751i | −0.168618 | − | 0.0846702i | ||||
\(964\) | −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 | ||||
\(969\) | 1.11779 | + | 2.49088i | 0.0359087 | + | 0.0800185i | ||||
\(970\) | 8.36758 | + | 7.08879i | 0.268667 | + | 0.227607i | ||||
\(971\) | −49.8746 | − | 28.7951i | −1.60055 | − | 0.924079i | −0.991377 | − | 0.131043i | \(-0.958167\pi\) |
−0.609175 | − | 0.793036i | \(-0.708499\pi\) | |||||||
\(972\) | −10.7708 | + | 3.05636i | −0.345475 | + | 0.0980328i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 38.3544 | 1.22895 | ||||||||
\(975\) | −39.6870 | + | 2.51607i | −1.27100 | + | 0.0805786i | ||||
\(976\) | −2.53416 | − | 4.38930i | −0.0811165 | − | 0.140498i | ||||
\(977\) | −2.74417 | + | 10.2414i | −0.0877939 | + | 0.327651i | −0.995829 | − | 0.0912438i | \(-0.970916\pi\) |
0.908035 | + | 0.418895i | \(0.137582\pi\) | |||||||
\(978\) | −3.87948 | − | 24.0367i | −0.124052 | − | 0.768608i | ||||
\(979\) | 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 | 0.216697 | − | 0.976239i | \(-0.430472\pi\) |
−0.300454 | + | 0.953796i | \(0.597138\pi\) | |||||||
\(984\) | −8.85935 | + | 3.97568i | −0.282426 | + | 0.126740i | ||||
\(985\) | 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 | ||||
\(990\) | 4.76926 | − | 39.2181i | 0.151577 | − | 1.24643i | ||||
\(991\) | 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 | ||||
\(993\) | −12.6788 | − | 15.5633i | −0.402350 | − | 0.493886i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.8941 | − | 30.3765i | −0.345365 | − | 0.962999i | ||||
\(996\) | 7.79057 | + | 5.62527i | 0.246854 | + | 0.178244i | ||||
\(997\) | 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 | ||||
\(999\) | 8.49873 | + | 9.27306i | 0.268888 | + | 0.293387i |
(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.128.4 | 48 | ||
3.2 | odd | 2 | inner | 735.2.y.g.128.9 | 48 | ||
5.2 | odd | 4 | inner | 735.2.y.g.422.4 | 48 | ||
7.2 | even | 3 | 735.2.j.h.638.9 | 24 | |||
7.3 | odd | 6 | 735.2.y.j.263.9 | 48 | |||
7.4 | even | 3 | inner | 735.2.y.g.263.9 | 48 | ||
7.5 | odd | 6 | 105.2.j.a.8.9 | yes | 24 | ||
7.6 | odd | 2 | 735.2.y.j.128.4 | 48 | |||
15.2 | even | 4 | inner | 735.2.y.g.422.9 | 48 | ||
21.2 | odd | 6 | 735.2.j.h.638.4 | 24 | |||
21.5 | even | 6 | 105.2.j.a.8.4 | ✓ | 24 | ||
21.11 | odd | 6 | inner | 735.2.y.g.263.4 | 48 | ||
21.17 | even | 6 | 735.2.y.j.263.4 | 48 | |||
21.20 | even | 2 | 735.2.y.j.128.9 | 48 | |||
35.2 | odd | 12 | 735.2.j.h.197.4 | 24 | |||
35.12 | even | 12 | 105.2.j.a.92.4 | yes | 24 | ||
35.17 | even | 12 | 735.2.y.j.557.9 | 48 | |||
35.19 | odd | 6 | 525.2.j.b.218.4 | 24 | |||
35.27 | even | 4 | 735.2.y.j.422.4 | 48 | |||
35.32 | odd | 12 | inner | 735.2.y.g.557.9 | 48 | ||
35.33 | even | 12 | 525.2.j.b.407.9 | 24 | |||
105.2 | even | 12 | 735.2.j.h.197.9 | 24 | |||
105.17 | odd | 12 | 735.2.y.j.557.4 | 48 | |||
105.32 | even | 12 | inner | 735.2.y.g.557.4 | 48 | ||
105.47 | odd | 12 | 105.2.j.a.92.9 | yes | 24 | ||
105.62 | odd | 4 | 735.2.y.j.422.9 | 48 | |||
105.68 | odd | 12 | 525.2.j.b.407.4 | 24 | |||
105.89 | even | 6 | 525.2.j.b.218.9 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.j.a.8.4 | ✓ | 24 | 21.5 | even | 6 | ||
105.2.j.a.8.9 | yes | 24 | 7.5 | odd | 6 | ||
105.2.j.a.92.4 | yes | 24 | 35.12 | even | 12 | ||
105.2.j.a.92.9 | yes | 24 | 105.47 | odd | 12 | ||
525.2.j.b.218.4 | 24 | 35.19 | odd | 6 | |||
525.2.j.b.218.9 | 24 | 105.89 | even | 6 | |||
525.2.j.b.407.4 | 24 | 105.68 | odd | 12 | |||
525.2.j.b.407.9 | 24 | 35.33 | even | 12 | |||
735.2.j.h.197.4 | 24 | 35.2 | odd | 12 | |||
735.2.j.h.197.9 | 24 | 105.2 | even | 12 | |||
735.2.j.h.638.4 | 24 | 21.2 | odd | 6 | |||
735.2.j.h.638.9 | 24 | 7.2 | even | 3 | |||
735.2.y.g.128.4 | 48 | 1.1 | even | 1 | trivial | ||
735.2.y.g.128.9 | 48 | 3.2 | odd | 2 | inner | ||
735.2.y.g.263.4 | 48 | 21.11 | odd | 6 | inner | ||
735.2.y.g.263.9 | 48 | 7.4 | even | 3 | inner | ||
735.2.y.g.422.4 | 48 | 5.2 | odd | 4 | inner | ||
735.2.y.g.422.9 | 48 | 15.2 | even | 4 | inner | ||
735.2.y.g.557.4 | 48 | 105.32 | even | 12 | inner | ||
735.2.y.g.557.9 | 48 | 35.32 | odd | 12 | inner | ||
735.2.y.j.128.4 | 48 | 7.6 | odd | 2 | |||
735.2.y.j.128.9 | 48 | 21.20 | even | 2 | |||
735.2.y.j.263.4 | 48 | 21.17 | even | 6 | |||
735.2.y.j.263.9 | 48 | 7.3 | odd | 6 | |||
735.2.y.j.422.4 | 48 | 35.27 | even | 4 | |||
735.2.y.j.422.9 | 48 | 105.62 | odd | 4 | |||
735.2.y.j.557.4 | 48 | 105.17 | odd | 12 | |||
735.2.y.j.557.9 | 48 | 35.17 | even | 12 |