Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(118,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("403.118");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.h (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Relative dimension: | \(17\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 118.2 | ||
Character | \(\chi\) | \(=\) | 403.118 |
Dual form | 403.2.h.b.222.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00723 | −1.41933 | −0.709664 | − | 0.704540i | \(-0.751153\pi\) | ||||
−0.709664 | + | 0.704540i | \(0.751153\pi\) | |||||||
\(3\) | 0.235463 | + | 0.407833i | 0.135944 | + | 0.235463i | 0.925958 | − | 0.377627i | \(-0.123260\pi\) |
−0.790013 | + | 0.613090i | \(0.789926\pi\) | |||||||
\(4\) | 2.02898 | 1.01449 | ||||||||
\(5\) | −0.859670 | + | 1.48899i | −0.384456 | + | 0.665897i | −0.991694 | − | 0.128623i | \(-0.958944\pi\) |
0.607238 | + | 0.794520i | \(0.292278\pi\) | |||||||
\(6\) | −0.472628 | − | 0.818616i | −0.192950 | − | 0.334199i | ||||
\(7\) | 1.82223 | + | 3.15619i | 0.688737 | + | 1.19293i | 0.972247 | + | 0.233958i | \(0.0751678\pi\) |
−0.283510 | + | 0.958969i | \(0.591499\pi\) | |||||||
\(8\) | −0.0581753 | −0.0205681 | ||||||||
\(9\) | 1.38911 | − | 2.40602i | 0.463038 | − | 0.802006i | ||||
\(10\) | 1.72556 | − | 2.98875i | 0.545669 | − | 0.945127i | ||||
\(11\) | 0.222871 | − | 0.386024i | 0.0671981 | − | 0.116390i | −0.830469 | − | 0.557065i | \(-0.811927\pi\) |
0.897667 | + | 0.440675i | \(0.145261\pi\) | |||||||
\(12\) | 0.477750 | + | 0.827487i | 0.137914 | + | 0.238875i | ||||
\(13\) | −0.500000 | + | 0.866025i | −0.138675 | + | 0.240192i | ||||
\(14\) | −3.65763 | − | 6.33520i | −0.977543 | − | 1.69315i | ||||
\(15\) | −0.809681 | −0.209059 | ||||||||
\(16\) | −3.94119 | −0.985299 | ||||||||
\(17\) | 0.176467 | + | 0.305651i | 0.0427996 | + | 0.0741311i | 0.886632 | − | 0.462476i | \(-0.153039\pi\) |
−0.843832 | + | 0.536607i | \(0.819706\pi\) | |||||||
\(18\) | −2.78828 | + | 4.82944i | −0.657203 | + | 1.13831i | ||||
\(19\) | 0.901237 | + | 1.56099i | 0.206758 | + | 0.358115i | 0.950691 | − | 0.310138i | \(-0.100375\pi\) |
−0.743933 | + | 0.668254i | \(0.767042\pi\) | |||||||
\(20\) | −1.74426 | + | 3.02114i | −0.390027 | + | 0.675547i | ||||
\(21\) | −0.858132 | + | 1.48633i | −0.187260 | + | 0.324344i | ||||
\(22\) | −0.447353 | + | 0.774839i | −0.0953761 | + | 0.165196i | ||||
\(23\) | 0.216337 | 0.0451094 | 0.0225547 | − | 0.999746i | \(-0.492820\pi\) | ||||
0.0225547 | + | 0.999746i | \(0.492820\pi\) | |||||||
\(24\) | −0.0136981 | − | 0.0237258i | −0.00279611 | − | 0.00484301i | ||||
\(25\) | 1.02194 | + | 1.77004i | 0.204387 | + | 0.354009i | ||||
\(26\) | 1.00362 | − | 1.73831i | 0.196825 | − | 0.340912i | ||||
\(27\) | 2.72111 | 0.523679 | ||||||||
\(28\) | 3.69727 | + | 6.40385i | 0.698718 | + | 1.21021i | ||||
\(29\) | −8.89550 | −1.65185 | −0.825926 | − | 0.563778i | \(-0.809347\pi\) | ||||
−0.825926 | + | 0.563778i | \(0.809347\pi\) | |||||||
\(30\) | 1.62522 | 0.296723 | ||||||||
\(31\) | 3.84206 | + | 4.02971i | 0.690055 | + | 0.723757i | ||||
\(32\) | 8.02724 | 1.41903 | ||||||||
\(33\) | 0.209911 | 0.0365408 | ||||||||
\(34\) | −0.354211 | − | 0.613512i | −0.0607467 | − | 0.105216i | ||||
\(35\) | −6.26605 | −1.05916 | ||||||||
\(36\) | 2.81849 | − | 4.88177i | 0.469748 | − | 0.813628i | ||||
\(37\) | 2.74617 | + | 4.75651i | 0.451468 | + | 0.781966i | 0.998477 | − | 0.0551606i | \(-0.0175671\pi\) |
−0.547009 | + | 0.837127i | \(0.684234\pi\) | |||||||
\(38\) | −1.80899 | − | 3.13327i | −0.293457 | − | 0.508283i | ||||
\(39\) | −0.470925 | −0.0754084 | ||||||||
\(40\) | 0.0500115 | − | 0.0866225i | 0.00790752 | − | 0.0136962i | ||||
\(41\) | 0.304476 | − | 0.527368i | 0.0475512 | − | 0.0823611i | −0.841270 | − | 0.540615i | \(-0.818192\pi\) |
0.888821 | + | 0.458254i | \(0.151525\pi\) | |||||||
\(42\) | 1.72247 | − | 2.98341i | 0.265783 | − | 0.460350i | ||||
\(43\) | 4.29525 | + | 7.43960i | 0.655020 | + | 1.13453i | 0.981889 | + | 0.189458i | \(0.0606732\pi\) |
−0.326869 | + | 0.945070i | \(0.605993\pi\) | |||||||
\(44\) | 0.452201 | − | 0.783235i | 0.0681719 | − | 0.118077i | ||||
\(45\) | 2.38836 | + | 4.13676i | 0.356036 | + | 0.616672i | ||||
\(46\) | −0.434239 | −0.0640251 | ||||||||
\(47\) | −10.5394 | −1.53733 | −0.768665 | − | 0.639651i | \(-0.779079\pi\) | ||||
−0.768665 | + | 0.639651i | \(0.779079\pi\) | |||||||
\(48\) | −0.928004 | − | 1.60735i | −0.133946 | − | 0.232001i | ||||
\(49\) | −3.14102 | + | 5.44040i | −0.448717 | + | 0.777200i | ||||
\(50\) | −2.05126 | − | 3.55289i | −0.290092 | − | 0.502454i | ||||
\(51\) | −0.0831030 | + | 0.143939i | −0.0116367 | + | 0.0201554i | ||||
\(52\) | −1.01449 | + | 1.75715i | −0.140685 | + | 0.243673i | ||||
\(53\) | −3.42032 | + | 5.92417i | −0.469817 | + | 0.813748i | −0.999404 | − | 0.0345079i | \(-0.989014\pi\) |
0.529587 | + | 0.848256i | \(0.322347\pi\) | |||||||
\(54\) | −5.46191 | −0.743272 | ||||||||
\(55\) | 0.383191 | + | 0.663706i | 0.0516694 | + | 0.0894940i | ||||
\(56\) | −0.106008 | − | 0.183612i | −0.0141660 | − | 0.0245362i | ||||
\(57\) | −0.424415 | + | 0.735109i | −0.0562152 | + | 0.0973675i | ||||
\(58\) | 17.8553 | 2.34452 | ||||||||
\(59\) | 3.69865 | + | 6.40624i | 0.481523 | + | 0.834022i | 0.999775 | − | 0.0212059i | \(-0.00675056\pi\) |
−0.518252 | + | 0.855228i | \(0.673417\pi\) | |||||||
\(60\) | −1.64283 | −0.212088 | ||||||||
\(61\) | −4.81243 | −0.616169 | −0.308084 | − | 0.951359i | \(-0.599688\pi\) | ||||
−0.308084 | + | 0.951359i | \(0.599688\pi\) | |||||||
\(62\) | −7.71191 | − | 8.08857i | −0.979414 | − | 1.02725i | ||||
\(63\) | 10.1251 | 1.27565 | ||||||||
\(64\) | −8.23016 | −1.02877 | ||||||||
\(65\) | −0.859670 | − | 1.48899i | −0.106629 | − | 0.184687i | ||||
\(66\) | −0.421340 | −0.0518634 | ||||||||
\(67\) | 0.121090 | − | 0.209735i | 0.0147935 | − | 0.0256232i | −0.858534 | − | 0.512757i | \(-0.828624\pi\) |
0.873327 | + | 0.487134i | \(0.161958\pi\) | |||||||
\(68\) | 0.358049 | + | 0.620160i | 0.0434199 | + | 0.0752054i | ||||
\(69\) | 0.0509394 | + | 0.0882295i | 0.00613238 | + | 0.0106216i | ||||
\(70\) | 12.5774 | 1.50329 | ||||||||
\(71\) | −3.15749 | + | 5.46893i | −0.374725 | + | 0.649043i | −0.990286 | − | 0.139046i | \(-0.955596\pi\) |
0.615561 | + | 0.788089i | \(0.288930\pi\) | |||||||
\(72\) | −0.0808121 | + | 0.139971i | −0.00952380 | + | 0.0164957i | ||||
\(73\) | 0.0149946 | − | 0.0259715i | 0.00175499 | − | 0.00303973i | −0.865147 | − | 0.501519i | \(-0.832775\pi\) |
0.866902 | + | 0.498479i | \(0.166108\pi\) | |||||||
\(74\) | −5.51221 | − | 9.54743i | −0.640781 | − | 1.10987i | ||||
\(75\) | −0.481255 | + | 0.833558i | −0.0555706 | + | 0.0962510i | ||||
\(76\) | 1.82859 | + | 3.16722i | 0.209754 | + | 0.363305i | ||||
\(77\) | 1.62448 | 0.185127 | ||||||||
\(78\) | 0.945257 | 0.107029 | ||||||||
\(79\) | −7.18003 | − | 12.4362i | −0.807817 | − | 1.39918i | −0.914373 | − | 0.404873i | \(-0.867316\pi\) |
0.106556 | − | 0.994307i | \(-0.466018\pi\) | |||||||
\(80\) | 3.38813 | − | 5.86841i | 0.378804 | − | 0.656108i | ||||
\(81\) | −3.52662 | − | 6.10829i | −0.391847 | − | 0.678699i | ||||
\(82\) | −0.611155 | + | 1.05855i | −0.0674907 | + | 0.116897i | ||||
\(83\) | 7.97508 | − | 13.8132i | 0.875379 | − | 1.51620i | 0.0190207 | − | 0.999819i | \(-0.493945\pi\) |
0.856358 | − | 0.516382i | \(-0.172721\pi\) | |||||||
\(84\) | −1.74114 | + | 3.01574i | −0.189973 | + | 0.329044i | ||||
\(85\) | −0.606815 | −0.0658183 | ||||||||
\(86\) | −8.62158 | − | 14.9330i | −0.929688 | − | 1.61027i | ||||
\(87\) | −2.09456 | − | 3.62788i | −0.224560 | − | 0.388949i | ||||
\(88\) | −0.0129656 | + | 0.0224570i | −0.00138213 | + | 0.00239393i | ||||
\(89\) | 8.87410 | 0.940653 | 0.470326 | − | 0.882492i | \(-0.344136\pi\) | ||||
0.470326 | + | 0.882492i | \(0.344136\pi\) | |||||||
\(90\) | −4.79399 | − | 8.30344i | −0.505331 | − | 0.875260i | ||||
\(91\) | −3.64445 | −0.382042 | ||||||||
\(92\) | 0.438945 | 0.0457631 | ||||||||
\(93\) | −0.738788 | + | 2.51577i | −0.0766087 | + | 0.260873i | ||||
\(94\) | 21.1550 | 2.18198 | ||||||||
\(95\) | −3.09907 | −0.317957 | ||||||||
\(96\) | 1.89012 | + | 3.27378i | 0.192909 | + | 0.334128i | ||||
\(97\) | 3.84994 | 0.390902 | 0.195451 | − | 0.980713i | \(-0.437383\pi\) | ||||
0.195451 | + | 0.980713i | \(0.437383\pi\) | |||||||
\(98\) | 6.30475 | − | 10.9202i | 0.636876 | − | 1.10310i | ||||
\(99\) | −0.619186 | − | 1.07246i | −0.0622305 | − | 0.107786i | ||||
\(100\) | 2.07349 | + | 3.59139i | 0.207349 | + | 0.359139i | ||||
\(101\) | 2.77472 | 0.276095 | 0.138048 | − | 0.990426i | \(-0.455917\pi\) | ||||
0.138048 | + | 0.990426i | \(0.455917\pi\) | |||||||
\(102\) | 0.166807 | − | 0.288918i | 0.0165164 | − | 0.0286072i | ||||
\(103\) | 4.76129 | − | 8.24680i | 0.469144 | − | 0.812581i | −0.530234 | − | 0.847852i | \(-0.677896\pi\) |
0.999378 | + | 0.0352701i | \(0.0112292\pi\) | |||||||
\(104\) | 0.0290876 | − | 0.0503813i | 0.00285228 | − | 0.00494029i | ||||
\(105\) | −1.47542 | − | 2.55550i | −0.143986 | − | 0.249392i | ||||
\(106\) | 6.86538 | − | 11.8912i | 0.666825 | − | 1.15497i | ||||
\(107\) | 2.57420 | + | 4.45865i | 0.248858 | + | 0.431034i | 0.963209 | − | 0.268753i | \(-0.0866116\pi\) |
−0.714352 | + | 0.699787i | \(0.753278\pi\) | |||||||
\(108\) | 5.52109 | 0.531267 | ||||||||
\(109\) | −10.2902 | −0.985622 | −0.492811 | − | 0.870136i | \(-0.664031\pi\) | ||||
−0.492811 | + | 0.870136i | \(0.664031\pi\) | |||||||
\(110\) | −0.769153 | − | 1.33221i | −0.0733358 | − | 0.127021i | ||||
\(111\) | −1.29324 | + | 2.23996i | −0.122749 | + | 0.212608i | ||||
\(112\) | −7.18175 | − | 12.4392i | −0.678611 | − | 1.17539i | ||||
\(113\) | 8.82568 | − | 15.2865i | 0.830250 | − | 1.43803i | −0.0675902 | − | 0.997713i | \(-0.521531\pi\) |
0.897840 | − | 0.440322i | \(-0.145136\pi\) | |||||||
\(114\) | 0.851900 | − | 1.47553i | 0.0797878 | − | 0.138196i | ||||
\(115\) | −0.185979 | + | 0.322125i | −0.0173426 | + | 0.0300383i | ||||
\(116\) | −18.0488 | −1.67579 | ||||||||
\(117\) | 1.38911 | + | 2.40602i | 0.128424 | + | 0.222436i | ||||
\(118\) | −7.42404 | − | 12.8588i | −0.683439 | − | 1.18375i | ||||
\(119\) | −0.643127 | + | 1.11393i | −0.0589554 | + | 0.102114i | ||||
\(120\) | 0.0471034 | 0.00429993 | ||||||||
\(121\) | 5.40066 | + | 9.35421i | 0.490969 | + | 0.850383i | ||||
\(122\) | 9.65967 | 0.874545 | ||||||||
\(123\) | 0.286771 | 0.0258573 | ||||||||
\(124\) | 7.79548 | + | 8.17621i | 0.700054 | + | 0.734246i | ||||
\(125\) | −12.1108 | −1.08322 | ||||||||
\(126\) | −20.3235 | −1.81056 | ||||||||
\(127\) | −3.58746 | − | 6.21366i | −0.318336 | − | 0.551374i | 0.661805 | − | 0.749676i | \(-0.269791\pi\) |
−0.980141 | + | 0.198302i | \(0.936457\pi\) | |||||||
\(128\) | 0.465353 | 0.0411318 | ||||||||
\(129\) | −2.02274 | + | 3.50350i | −0.178093 | + | 0.308466i | ||||
\(130\) | 1.72556 | + | 2.98875i | 0.151341 | + | 0.262131i | ||||
\(131\) | −0.804645 | − | 1.39369i | −0.0703022 | − | 0.121767i | 0.828732 | − | 0.559646i | \(-0.189063\pi\) |
−0.899034 | + | 0.437879i | \(0.855730\pi\) | |||||||
\(132\) | 0.425906 | 0.0370703 | ||||||||
\(133\) | −3.28452 | + | 5.68895i | −0.284804 | + | 0.493294i | ||||
\(134\) | −0.243057 | + | 0.420986i | −0.0209969 | + | 0.0363677i | ||||
\(135\) | −2.33926 | + | 4.05172i | −0.201331 | + | 0.348716i | ||||
\(136\) | −0.0102660 | − | 0.0177813i | −0.000880305 | − | 0.00152473i | ||||
\(137\) | 1.56184 | − | 2.70519i | 0.133437 | − | 0.231120i | −0.791562 | − | 0.611089i | \(-0.790732\pi\) |
0.924999 | + | 0.379969i | \(0.124065\pi\) | |||||||
\(138\) | −0.102247 | − | 0.177097i | −0.00870385 | − | 0.0150755i | ||||
\(139\) | −1.45923 | −0.123770 | −0.0618849 | − | 0.998083i | \(-0.519711\pi\) | ||||
−0.0618849 | + | 0.998083i | \(0.519711\pi\) | |||||||
\(140\) | −12.7137 | −1.07450 | ||||||||
\(141\) | −2.48164 | − | 4.29832i | −0.208991 | − | 0.361984i | ||||
\(142\) | 6.33782 | − | 10.9774i | 0.531858 | − | 0.921205i | ||||
\(143\) | 0.222871 | + | 0.386024i | 0.0186374 | + | 0.0322809i | ||||
\(144\) | −5.47477 | + | 9.48258i | −0.456231 | + | 0.790215i | ||||
\(145\) | 7.64719 | − | 13.2453i | 0.635065 | − | 1.09996i | ||||
\(146\) | −0.0300977 | + | 0.0521308i | −0.00249091 | + | 0.00431438i | ||||
\(147\) | −2.95837 | −0.244002 | ||||||||
\(148\) | 5.57194 | + | 9.65088i | 0.458011 | + | 0.793298i | ||||
\(149\) | 10.3200 | + | 17.8748i | 0.845448 | + | 1.46436i | 0.885232 | + | 0.465150i | \(0.154000\pi\) |
−0.0397839 | + | 0.999208i | \(0.512667\pi\) | |||||||
\(150\) | 0.965991 | − | 1.67315i | 0.0788728 | − | 0.136612i | ||||
\(151\) | 1.97063 | 0.160368 | 0.0801839 | − | 0.996780i | \(-0.474449\pi\) | ||||
0.0801839 | + | 0.996780i | \(0.474449\pi\) | |||||||
\(152\) | −0.0524297 | − | 0.0908109i | −0.00425261 | − | 0.00736574i | ||||
\(153\) | 0.980534 | 0.0792715 | ||||||||
\(154\) | −3.26072 | −0.262756 | ||||||||
\(155\) | −9.30311 | + | 2.25658i | −0.747244 | + | 0.181253i | ||||
\(156\) | −0.955499 | −0.0765012 | ||||||||
\(157\) | 10.4868 | 0.836941 | 0.418471 | − | 0.908230i | \(-0.362566\pi\) | ||||
0.418471 | + | 0.908230i | \(0.362566\pi\) | |||||||
\(158\) | 14.4120 | + | 24.9623i | 1.14656 | + | 1.98589i | ||||
\(159\) | −3.22143 | −0.255476 | ||||||||
\(160\) | −6.90078 | + | 11.9525i | −0.545555 | + | 0.944928i | ||||
\(161\) | 0.394216 | + | 0.682801i | 0.0310685 | + | 0.0538123i | ||||
\(162\) | 7.07875 | + | 12.2608i | 0.556159 | + | 0.963296i | ||||
\(163\) | 22.4603 | 1.75922 | 0.879612 | − | 0.475692i | \(-0.157802\pi\) | ||||
0.879612 | + | 0.475692i | \(0.157802\pi\) | |||||||
\(164\) | 0.617777 | − | 1.07002i | 0.0482403 | − | 0.0835546i | ||||
\(165\) | −0.180454 | + | 0.312556i | −0.0140483 | + | 0.0243324i | ||||
\(166\) | −16.0078 | + | 27.7264i | −1.24245 | + | 2.15199i | ||||
\(167\) | −1.04495 | − | 1.80991i | −0.0808610 | − | 0.140055i | 0.822759 | − | 0.568390i | \(-0.192434\pi\) |
−0.903620 | + | 0.428335i | \(0.859100\pi\) | |||||||
\(168\) | 0.0499221 | − | 0.0864676i | 0.00385157 | − | 0.00667112i | ||||
\(169\) | −0.500000 | − | 0.866025i | −0.0384615 | − | 0.0666173i | ||||
\(170\) | 1.21802 | 0.0934178 | ||||||||
\(171\) | 5.00769 | 0.382947 | ||||||||
\(172\) | 8.71500 | + | 15.0948i | 0.664512 | + | 1.15097i | ||||
\(173\) | 6.41005 | − | 11.1025i | 0.487347 | − | 0.844110i | −0.512547 | − | 0.858659i | \(-0.671298\pi\) |
0.999894 | + | 0.0145489i | \(0.00463124\pi\) | |||||||
\(174\) | 4.20426 | + | 7.28200i | 0.318724 | + | 0.552047i | ||||
\(175\) | −3.72439 | + | 6.45084i | −0.281538 | + | 0.487638i | ||||
\(176\) | −0.878377 | + | 1.52139i | −0.0662102 | + | 0.114679i | ||||
\(177\) | −1.74179 | + | 3.01686i | −0.130921 | + | 0.226761i | ||||
\(178\) | −17.8124 | −1.33509 | ||||||||
\(179\) | 5.02894 | + | 8.71038i | 0.375881 | + | 0.651044i | 0.990458 | − | 0.137812i | \(-0.0440069\pi\) |
−0.614578 | + | 0.788856i | \(0.710674\pi\) | |||||||
\(180\) | 4.84594 | + | 8.39342i | 0.361195 | + | 0.625608i | ||||
\(181\) | −1.78299 | + | 3.08822i | −0.132528 | + | 0.229546i | −0.924651 | − | 0.380817i | \(-0.875643\pi\) |
0.792122 | + | 0.610362i | \(0.208976\pi\) | |||||||
\(182\) | 7.31526 | 0.542243 | ||||||||
\(183\) | −1.13315 | − | 1.96267i | −0.0837647 | − | 0.145085i | ||||
\(184\) | −0.0125855 | −0.000927814 | ||||||||
\(185\) | −9.44321 | −0.694279 | ||||||||
\(186\) | 1.48292 | − | 5.04973i | 0.108733 | − | 0.370264i | ||||
\(187\) | 0.157318 | 0.0115042 | ||||||||
\(188\) | −21.3843 | −1.55961 | ||||||||
\(189\) | 4.95849 | + | 8.58835i | 0.360677 | + | 0.624710i | ||||
\(190\) | 6.22054 | 0.451286 | ||||||||
\(191\) | −1.43122 | + | 2.47894i | −0.103559 | + | 0.179370i | −0.913149 | − | 0.407627i | \(-0.866356\pi\) |
0.809589 | + | 0.586997i | \(0.199690\pi\) | |||||||
\(192\) | −1.93789 | − | 3.35653i | −0.139855 | − | 0.242237i | ||||
\(193\) | 9.75227 | + | 16.8914i | 0.701984 | + | 1.21587i | 0.967769 | + | 0.251839i | \(0.0810353\pi\) |
−0.265786 | + | 0.964032i | \(0.585631\pi\) | |||||||
\(194\) | −7.72773 | −0.554819 | ||||||||
\(195\) | 0.404840 | − | 0.701204i | 0.0289912 | − | 0.0502143i | ||||
\(196\) | −6.37307 | + | 11.0385i | −0.455219 | + | 0.788463i | ||||
\(197\) | −7.09060 | + | 12.2813i | −0.505184 | + | 0.875005i | 0.494798 | + | 0.869008i | \(0.335242\pi\) |
−0.999982 | + | 0.00599659i | \(0.998091\pi\) | |||||||
\(198\) | 1.24285 | + | 2.15268i | 0.0883255 | + | 0.152984i | ||||
\(199\) | 11.8956 | − | 20.6038i | 0.843258 | − | 1.46057i | −0.0438666 | − | 0.999037i | \(-0.513968\pi\) |
0.887125 | − | 0.461529i | \(-0.152699\pi\) | |||||||
\(200\) | −0.0594514 | − | 0.102973i | −0.00420385 | − | 0.00728127i | ||||
\(201\) | 0.114049 | 0.00804440 | ||||||||
\(202\) | −5.56951 | −0.391869 | ||||||||
\(203\) | −16.2096 | − | 28.0759i | −1.13769 | − | 1.97054i | ||||
\(204\) | −0.168614 | + | 0.292049i | −0.0118054 | + | 0.0204475i | ||||
\(205\) | 0.523498 | + | 0.906725i | 0.0365627 | + | 0.0633285i | ||||
\(206\) | −9.55702 | + | 16.5532i | −0.665869 | + | 1.15332i | ||||
\(207\) | 0.300517 | − | 0.520511i | 0.0208874 | − | 0.0361780i | ||||
\(208\) | 1.97060 | − | 3.41317i | 0.136636 | − | 0.236661i | ||||
\(209\) | 0.803438 | 0.0555749 | ||||||||
\(210\) | 2.96151 | + | 5.12949i | 0.204364 | + | 0.353969i | ||||
\(211\) | −8.64303 | − | 14.9702i | −0.595011 | − | 1.03059i | −0.993545 | − | 0.113436i | \(-0.963814\pi\) |
0.398535 | − | 0.917153i | \(-0.369519\pi\) | |||||||
\(212\) | −6.93978 | + | 12.0200i | −0.476626 | + | 0.825540i | ||||
\(213\) | −2.97388 | −0.203767 | ||||||||
\(214\) | −5.16702 | − | 8.94955i | −0.353210 | − | 0.611778i | ||||
\(215\) | −14.7700 | −1.00731 | ||||||||
\(216\) | −0.158302 | −0.0107711 | ||||||||
\(217\) | −5.71742 | + | 19.4693i | −0.388124 | + | 1.32166i | ||||
\(218\) | 20.6548 | 1.39892 | ||||||||
\(219\) | 0.0141227 | 0.000954324 | ||||||||
\(220\) | 0.777487 | + | 1.34665i | 0.0524182 | + | 0.0907909i | ||||
\(221\) | −0.352935 | −0.0237410 | ||||||||
\(222\) | 2.59584 | − | 4.49613i | 0.174221 | − | 0.301760i | ||||
\(223\) | −11.4542 | − | 19.8393i | −0.767031 | − | 1.32854i | −0.939166 | − | 0.343463i | \(-0.888400\pi\) |
0.172135 | − | 0.985073i | \(-0.444933\pi\) | |||||||
\(224\) | 14.6275 | + | 25.3355i | 0.977338 | + | 1.69280i | ||||
\(225\) | 5.67834 | 0.378556 | ||||||||
\(226\) | −17.7152 | + | 30.6836i | −1.17840 | + | 2.04104i | ||||
\(227\) | −1.44440 | + | 2.50177i | −0.0958680 | + | 0.166048i | −0.909971 | − | 0.414673i | \(-0.863896\pi\) |
0.814103 | + | 0.580721i | \(0.197229\pi\) | |||||||
\(228\) | −0.861131 | + | 1.49152i | −0.0570298 | + | 0.0987785i | ||||
\(229\) | −4.19496 | − | 7.26588i | −0.277211 | − | 0.480143i | 0.693480 | − | 0.720476i | \(-0.256077\pi\) |
−0.970690 | + | 0.240333i | \(0.922743\pi\) | |||||||
\(230\) | 0.373302 | − | 0.646579i | 0.0246148 | − | 0.0426341i | ||||
\(231\) | 0.382505 | + | 0.662519i | 0.0251670 | + | 0.0435905i | ||||
\(232\) | 0.517498 | 0.0339754 | ||||||||
\(233\) | 10.3316 | 0.676843 | 0.338422 | − | 0.940995i | \(-0.390107\pi\) | ||||
0.338422 | + | 0.940995i | \(0.390107\pi\) | |||||||
\(234\) | −2.78828 | − | 4.82944i | −0.182275 | − | 0.315710i | ||||
\(235\) | 9.06041 | − | 15.6931i | 0.591036 | − | 1.02370i | ||||
\(236\) | 7.50449 | + | 12.9982i | 0.488501 | + | 0.846108i | ||||
\(237\) | 3.38126 | − | 5.85651i | 0.219636 | − | 0.380421i | ||||
\(238\) | 1.29091 | − | 2.23591i | 0.0836770 | − | 0.144933i | ||||
\(239\) | 8.47112 | − | 14.6724i | 0.547951 | − | 0.949079i | −0.450464 | − | 0.892795i | \(-0.648741\pi\) |
0.998415 | − | 0.0562842i | \(-0.0179253\pi\) | |||||||
\(240\) | 3.19111 | 0.205985 | ||||||||
\(241\) | 8.32522 | + | 14.4197i | 0.536275 | + | 0.928855i | 0.999100 | + | 0.0424056i | \(0.0135022\pi\) |
−0.462826 | + | 0.886449i | \(0.653164\pi\) | |||||||
\(242\) | −10.8404 | − | 18.7761i | −0.696846 | − | 1.20697i | ||||
\(243\) | 5.74245 | − | 9.94621i | 0.368378 | − | 0.638050i | ||||
\(244\) | −9.76434 | −0.625098 | ||||||||
\(245\) | −5.40048 | − | 9.35390i | −0.345024 | − | 0.597599i | ||||
\(246\) | −0.575616 | −0.0367000 | ||||||||
\(247\) | −1.80247 | −0.114689 | ||||||||
\(248\) | −0.223513 | − | 0.234429i | −0.0141931 | − | 0.0148863i | ||||
\(249\) | 7.51134 | 0.476012 | ||||||||
\(250\) | 24.3092 | 1.53745 | ||||||||
\(251\) | −8.63178 | − | 14.9507i | −0.544833 | − | 0.943678i | −0.998617 | − | 0.0525667i | \(-0.983260\pi\) |
0.453785 | − | 0.891111i | \(-0.350074\pi\) | |||||||
\(252\) | 20.5437 | 1.29413 | ||||||||
\(253\) | 0.0482153 | − | 0.0835113i | 0.00303127 | − | 0.00525031i | ||||
\(254\) | 7.20087 | + | 12.4723i | 0.451823 | + | 0.782580i | ||||
\(255\) | −0.142882 | − | 0.247479i | −0.00894763 | − | 0.0154978i | ||||
\(256\) | 15.5262 | 0.970390 | ||||||||
\(257\) | −2.13247 | + | 3.69355i | −0.133020 | + | 0.230397i | −0.924839 | − | 0.380358i | \(-0.875801\pi\) |
0.791819 | + | 0.610755i | \(0.209134\pi\) | |||||||
\(258\) | 4.06012 | − | 7.03233i | 0.252772 | − | 0.437814i | ||||
\(259\) | −10.0083 | + | 17.3349i | −0.621886 | + | 1.07714i | ||||
\(260\) | −1.74426 | − | 3.02114i | −0.108174 | − | 0.187363i | ||||
\(261\) | −12.3569 | + | 21.4027i | −0.764871 | + | 1.32479i | ||||
\(262\) | 1.61511 | + | 2.79745i | 0.0997819 | + | 0.172827i | ||||
\(263\) | 20.8920 | 1.28825 | 0.644127 | − | 0.764919i | \(-0.277221\pi\) | ||||
0.644127 | + | 0.764919i | \(0.277221\pi\) | |||||||
\(264\) | −0.0122116 | −0.000751573 | ||||||||
\(265\) | −5.88070 | − | 10.1857i | −0.361248 | − | 0.625701i | ||||
\(266\) | 6.59279 | − | 11.4190i | 0.404230 | − | 0.700146i | ||||
\(267\) | 2.08952 | + | 3.61915i | 0.127877 | + | 0.221489i | ||||
\(268\) | 0.245690 | − | 0.425548i | 0.0150079 | − | 0.0259945i | ||||
\(269\) | 2.48179 | − | 4.29858i | 0.151317 | − | 0.262089i | −0.780395 | − | 0.625287i | \(-0.784982\pi\) |
0.931712 | + | 0.363198i | \(0.118315\pi\) | |||||||
\(270\) | 4.69544 | − | 8.13274i | 0.285755 | − | 0.494943i | ||||
\(271\) | −21.3745 | −1.29841 | −0.649205 | − | 0.760614i | \(-0.724898\pi\) | ||||
−0.649205 | + | 0.760614i | \(0.724898\pi\) | |||||||
\(272\) | −0.695492 | − | 1.20463i | −0.0421704 | − | 0.0730413i | ||||
\(273\) | −0.858132 | − | 1.48633i | −0.0519365 | − | 0.0899567i | ||||
\(274\) | −3.13498 | + | 5.42995i | −0.189391 | + | 0.328035i | ||||
\(275\) | 0.911038 | 0.0549377 | ||||||||
\(276\) | 0.103355 | + | 0.179016i | 0.00622124 | + | 0.0107755i | ||||
\(277\) | −22.5893 | −1.35726 | −0.678630 | − | 0.734480i | \(-0.737426\pi\) | ||||
−0.678630 | + | 0.734480i | \(0.737426\pi\) | |||||||
\(278\) | 2.92900 | 0.175670 | ||||||||
\(279\) | 15.0326 | − | 3.64634i | 0.899979 | − | 0.218300i | ||||
\(280\) | 0.364529 | 0.0217848 | ||||||||
\(281\) | −19.1394 | −1.14176 | −0.570880 | − | 0.821033i | \(-0.693398\pi\) | ||||
−0.570880 | + | 0.821033i | \(0.693398\pi\) | |||||||
\(282\) | 4.98122 | + | 8.62773i | 0.296627 | + | 0.513774i | ||||
\(283\) | 24.4535 | 1.45361 | 0.726804 | − | 0.686845i | \(-0.241005\pi\) | ||||
0.726804 | + | 0.686845i | \(0.241005\pi\) | |||||||
\(284\) | −6.40649 | + | 11.0964i | −0.380155 | + | 0.658449i | ||||
\(285\) | −0.729714 | − | 1.26390i | −0.0432245 | − | 0.0748671i | ||||
\(286\) | −0.447353 | − | 0.774839i | −0.0264526 | − | 0.0458172i | ||||
\(287\) | 2.21930 | 0.131001 | ||||||||
\(288\) | 11.1508 | − | 19.3137i | 0.657065 | − | 1.13807i | ||||
\(289\) | 8.43772 | − | 14.6146i | 0.496336 | − | 0.859680i | ||||
\(290\) | −15.3497 | + | 26.5864i | −0.901365 | + | 1.56121i | ||||
\(291\) | 0.906518 | + | 1.57013i | 0.0531410 | + | 0.0920429i | ||||
\(292\) | 0.0304239 | − | 0.0526957i | 0.00178042 | − | 0.00308378i | ||||
\(293\) | −5.70491 | − | 9.88119i | −0.333284 | − | 0.577265i | 0.649870 | − | 0.760046i | \(-0.274823\pi\) |
−0.983154 | + | 0.182781i | \(0.941490\pi\) | |||||||
\(294\) | 5.93813 | 0.346319 | ||||||||
\(295\) | −12.7185 | −0.740497 | ||||||||
\(296\) | −0.159759 | − | 0.276711i | −0.00928583 | − | 0.0160835i | ||||
\(297\) | 0.606457 | − | 1.05041i | 0.0351902 | − | 0.0609512i | ||||
\(298\) | −20.7147 | − | 35.8788i | −1.19997 | − | 2.07840i | ||||
\(299\) | −0.108169 | + | 0.187354i | −0.00625556 | + | 0.0108349i | ||||
\(300\) | −0.976458 | + | 1.69128i | −0.0563759 | + | 0.0976458i | ||||
\(301\) | −15.6539 | + | 27.1133i | −0.902273 | + | 1.56278i | ||||
\(302\) | −3.95552 | −0.227614 | ||||||||
\(303\) | 0.653343 | + | 1.13162i | 0.0375336 | + | 0.0650101i | ||||
\(304\) | −3.55195 | − | 6.15216i | −0.203718 | − | 0.352850i | ||||
\(305\) | 4.13710 | − | 7.16567i | 0.236890 | − | 0.410305i | ||||
\(306\) | −1.96816 | −0.112512 | ||||||||
\(307\) | −7.01132 | − | 12.1440i | −0.400157 | − | 0.693093i | 0.593587 | − | 0.804770i | \(-0.297711\pi\) |
−0.993745 | + | 0.111677i | \(0.964378\pi\) | |||||||
\(308\) | 3.29605 | 0.187810 | ||||||||
\(309\) | 4.48443 | 0.255110 | ||||||||
\(310\) | 18.6735 | − | 4.52948i | 1.06058 | − | 0.257257i | ||||
\(311\) | 23.9609 | 1.35870 | 0.679349 | − | 0.733815i | \(-0.262262\pi\) | ||||
0.679349 | + | 0.733815i | \(0.262262\pi\) | |||||||
\(312\) | 0.0273962 | 0.00155100 | ||||||||
\(313\) | 0.187183 | + | 0.324210i | 0.0105802 | + | 0.0183254i | 0.871267 | − | 0.490809i | \(-0.163299\pi\) |
−0.860687 | + | 0.509135i | \(0.829965\pi\) | |||||||
\(314\) | −21.0495 | −1.18789 | ||||||||
\(315\) | −8.70427 | + | 15.0762i | −0.490430 | + | 0.849449i | ||||
\(316\) | −14.5682 | − | 25.2328i | −0.819523 | − | 1.41946i | ||||
\(317\) | 13.3143 | + | 23.0611i | 0.747807 | + | 1.29524i | 0.948872 | + | 0.315661i | \(0.102226\pi\) |
−0.201065 | + | 0.979578i | \(0.564440\pi\) | |||||||
\(318\) | 6.46617 | 0.362605 | ||||||||
\(319\) | −1.98255 | + | 3.43387i | −0.111001 | + | 0.192260i | ||||
\(320\) | 7.07522 | − | 12.2546i | 0.395517 | − | 0.685055i | ||||
\(321\) | −1.21226 | + | 2.09969i | −0.0676616 | + | 0.117193i | ||||
\(322\) | −0.791282 | − | 1.37054i | −0.0440964 | − | 0.0763773i | ||||
\(323\) | −0.318078 | + | 0.550927i | −0.0176983 | + | 0.0306544i | ||||
\(324\) | −7.15546 | − | 12.3936i | −0.397525 | − | 0.688534i | ||||
\(325\) | −2.04387 | −0.113374 | ||||||||
\(326\) | −45.0830 | −2.49692 | ||||||||
\(327\) | −2.42296 | − | 4.19669i | −0.133990 | − | 0.232077i | ||||
\(328\) | −0.0177130 | + | 0.0306798i | −0.000978036 | + | 0.00169401i | ||||
\(329\) | −19.2052 | − | 33.2644i | −1.05882 | − | 1.83392i | ||||
\(330\) | 0.362213 | − | 0.627372i | 0.0199392 | − | 0.0345357i | ||||
\(331\) | 4.48442 | − | 7.76725i | 0.246486 | − | 0.426926i | −0.716062 | − | 0.698036i | \(-0.754057\pi\) |
0.962548 | + | 0.271110i | \(0.0873907\pi\) | |||||||
\(332\) | 16.1813 | − | 28.0268i | 0.888065 | − | 1.53817i | ||||
\(333\) | 15.2590 | 0.836188 | ||||||||
\(334\) | 2.09747 | + | 3.63292i | 0.114768 | + | 0.198784i | ||||
\(335\) | 0.208196 | + | 0.360605i | 0.0113749 | + | 0.0197020i | ||||
\(336\) | 3.38207 | − | 5.85791i | 0.184507 | − | 0.319575i | ||||
\(337\) | 0.362985 | 0.0197730 | 0.00988651 | − | 0.999951i | \(-0.496853\pi\) | ||||
0.00988651 | + | 0.999951i | \(0.496853\pi\) | |||||||
\(338\) | 1.00362 | + | 1.73831i | 0.0545895 | + | 0.0945518i | ||||
\(339\) | 8.31247 | 0.451471 | ||||||||
\(340\) | −1.23122 | −0.0667721 | ||||||||
\(341\) | 2.41185 | − | 0.585021i | 0.130609 | − | 0.0316807i | ||||
\(342\) | −10.0516 | −0.543528 | ||||||||
\(343\) | 2.61659 | 0.141283 | ||||||||
\(344\) | −0.249878 | − | 0.432801i | −0.0134725 | − | 0.0233350i | ||||
\(345\) | −0.175164 | −0.00943052 | ||||||||
\(346\) | −12.8665 | + | 22.2854i | −0.691706 | + | 1.19807i | ||||
\(347\) | 13.2075 | + | 22.8760i | 0.709014 | + | 1.22805i | 0.965223 | + | 0.261427i | \(0.0841932\pi\) |
−0.256209 | + | 0.966621i | \(0.582473\pi\) | |||||||
\(348\) | −4.24982 | − | 7.36090i | −0.227814 | − | 0.394586i | ||||
\(349\) | −5.68665 | −0.304399 | −0.152200 | − | 0.988350i | \(-0.548636\pi\) | ||||
−0.152200 | + | 0.988350i | \(0.548636\pi\) | |||||||
\(350\) | 7.47573 | − | 12.9483i | 0.399594 | − | 0.692118i | ||||
\(351\) | −1.36056 | + | 2.35655i | −0.0726212 | + | 0.125784i | ||||
\(352\) | 1.78904 | − | 3.09871i | 0.0953561 | − | 0.165162i | ||||
\(353\) | 13.3736 | + | 23.1637i | 0.711804 | + | 1.23288i | 0.964179 | + | 0.265251i | \(0.0854550\pi\) |
−0.252375 | + | 0.967629i | \(0.581212\pi\) | |||||||
\(354\) | 3.49617 | − | 6.05554i | 0.185819 | − | 0.321848i | ||||
\(355\) | −5.42880 | − | 9.40295i | −0.288131 | − | 0.499057i | ||||
\(356\) | 18.0054 | 0.954284 | ||||||||
\(357\) | −0.605730 | −0.0320586 | ||||||||
\(358\) | −10.0943 | − | 17.4838i | −0.533498 | − | 0.924045i | ||||
\(359\) | −2.69195 | + | 4.66260i | −0.142076 | + | 0.246082i | −0.928278 | − | 0.371887i | \(-0.878711\pi\) |
0.786202 | + | 0.617969i | \(0.212044\pi\) | |||||||
\(360\) | −0.138943 | − | 0.240657i | −0.00732296 | − | 0.0126837i | ||||
\(361\) | 7.87554 | − | 13.6408i | 0.414502 | − | 0.717939i | ||||
\(362\) | 3.57887 | − | 6.19878i | 0.188101 | − | 0.325801i | ||||
\(363\) | −2.54331 | + | 4.40513i | −0.133489 | + | 0.231210i | ||||
\(364\) | −7.39453 | −0.387579 | ||||||||
\(365\) | 0.0257809 | + | 0.0446538i | 0.00134943 | + | 0.00233729i | ||||
\(366\) | 2.27449 | + | 3.93953i | 0.118890 | + | 0.205923i | ||||
\(367\) | 11.9921 | − | 20.7709i | 0.625981 | − | 1.08423i | −0.362370 | − | 0.932034i | \(-0.618032\pi\) |
0.988350 | − | 0.152196i | \(-0.0486345\pi\) | |||||||
\(368\) | −0.852627 | −0.0444463 | ||||||||
\(369\) | −0.845905 | − | 1.46515i | −0.0440361 | − | 0.0762727i | ||||
\(370\) | 18.9547 | 0.985409 | ||||||||
\(371\) | −24.9304 | −1.29432 | ||||||||
\(372\) | −1.49899 | + | 5.10445i | −0.0777189 | + | 0.264653i | ||||
\(373\) | 16.3367 | 0.845881 | 0.422941 | − | 0.906157i | \(-0.360998\pi\) | ||||
0.422941 | + | 0.906157i | \(0.360998\pi\) | |||||||
\(374\) | −0.315773 | −0.0163282 | ||||||||
\(375\) | −2.85164 | − | 4.93919i | −0.147258 | − | 0.255059i | ||||
\(376\) | 0.613133 | 0.0316199 | ||||||||
\(377\) | 4.44775 | − | 7.70373i | 0.229071 | − | 0.396762i | ||||
\(378\) | −9.95283 | − | 17.2388i | −0.511919 | − | 0.886669i | ||||
\(379\) | −7.44173 | − | 12.8895i | −0.382256 | − | 0.662087i | 0.609128 | − | 0.793072i | \(-0.291519\pi\) |
−0.991384 | + | 0.130985i | \(0.958186\pi\) | |||||||
\(380\) | −6.28795 | −0.322565 | ||||||||
\(381\) | 1.68943 | − | 2.92617i | 0.0865519 | − | 0.149912i | ||||
\(382\) | 2.87279 | − | 4.97581i | 0.146985 | − | 0.254585i | ||||
\(383\) | 9.59419 | − | 16.6176i | 0.490240 | − | 0.849121i | −0.509697 | − | 0.860354i | \(-0.670242\pi\) |
0.999937 | + | 0.0112331i | \(0.00357567\pi\) | |||||||
\(384\) | 0.109573 | + | 0.189786i | 0.00559164 | + | 0.00968500i | ||||
\(385\) | −1.39652 | + | 2.41884i | −0.0711732 | + | 0.123276i | ||||
\(386\) | −19.5751 | − | 33.9050i | −0.996345 | − | 1.72572i | ||||
\(387\) | 23.8664 | 1.21320 | ||||||||
\(388\) | 7.81147 | 0.396567 | ||||||||
\(389\) | 1.02000 | + | 1.76669i | 0.0517159 | + | 0.0895745i | 0.890724 | − | 0.454544i | \(-0.150198\pi\) |
−0.839009 | + | 0.544118i | \(0.816864\pi\) | |||||||
\(390\) | −0.812609 | + | 1.40748i | −0.0411480 | + | 0.0712705i | ||||
\(391\) | 0.0381765 | + | 0.0661236i | 0.00193067 | + | 0.00334401i | ||||
\(392\) | 0.182729 | − | 0.316497i | 0.00922923 | − | 0.0159855i | ||||
\(393\) | 0.378928 | − | 0.656322i | 0.0191144 | − | 0.0331071i | ||||
\(394\) | 14.2325 | − | 24.6514i | 0.717022 | − | 1.24192i | ||||
\(395\) | 24.6898 | 1.24228 | ||||||||
\(396\) | −1.25632 | − | 2.17601i | −0.0631324 | − | 0.109348i | ||||
\(397\) | −9.21047 | − | 15.9530i | −0.462260 | − | 0.800658i | 0.536813 | − | 0.843701i | \(-0.319628\pi\) |
−0.999073 | + | 0.0430431i | \(0.986295\pi\) | |||||||
\(398\) | −23.8773 | + | 41.3567i | −1.19686 | + | 2.07302i | ||||
\(399\) | −3.09352 | −0.154870 | ||||||||
\(400\) | −4.02765 | − | 6.97609i | −0.201382 | − | 0.348804i | ||||
\(401\) | −6.42109 | −0.320654 | −0.160327 | − | 0.987064i | \(-0.551255\pi\) | ||||
−0.160327 | + | 0.987064i | \(0.551255\pi\) | |||||||
\(402\) | −0.228923 | −0.0114176 | ||||||||
\(403\) | −5.41086 | + | 1.31247i | −0.269534 | + | 0.0653787i | ||||
\(404\) | 5.62986 | 0.280096 | ||||||||
\(405\) | 12.1269 | 0.602592 | ||||||||
\(406\) | 32.5365 | + | 56.3548i | 1.61476 | + | 2.79684i | ||||
\(407\) | 2.44817 | 0.121351 | ||||||||
\(408\) | 0.00483454 | − | 0.00837366i | 0.000239345 | − | 0.000414558i | ||||
\(409\) | 1.42257 | + | 2.46396i | 0.0703416 | + | 0.121835i | 0.899051 | − | 0.437844i | \(-0.144258\pi\) |
−0.828709 | + | 0.559679i | \(0.810924\pi\) | |||||||
\(410\) | −1.05078 | − | 1.82001i | −0.0518945 | − | 0.0898838i | ||||
\(411\) | 1.47102 | 0.0725602 | ||||||||
\(412\) | 9.66058 | − | 16.7326i | 0.475943 | − | 0.824357i | ||||
\(413\) | −13.4795 | + | 23.3472i | −0.663285 | + | 1.14884i | ||||
\(414\) | −0.603208 | + | 1.04479i | −0.0296461 | + | 0.0513485i | ||||
\(415\) | 13.7119 | + | 23.7497i | 0.673090 | + | 1.16583i | ||||
\(416\) | −4.01362 | + | 6.95180i | −0.196784 | + | 0.340840i | ||||
\(417\) | −0.343593 | − | 0.595121i | −0.0168258 | − | 0.0291432i | ||||
\(418\) | −1.61269 | −0.0788791 | ||||||||
\(419\) | 0.515869 | 0.0252019 | 0.0126009 | − | 0.999921i | \(-0.495989\pi\) | ||||
0.0126009 | + | 0.999921i | \(0.495989\pi\) | |||||||
\(420\) | −2.99360 | − | 5.18507i | −0.146073 | − | 0.253006i | ||||
\(421\) | −14.7094 | + | 25.4774i | −0.716892 | + | 1.24169i | 0.245334 | + | 0.969439i | \(0.421102\pi\) |
−0.962225 | + | 0.272254i | \(0.912231\pi\) | |||||||
\(422\) | 17.3486 | + | 30.0486i | 0.844515 | + | 1.46274i | ||||
\(423\) | −14.6404 | + | 25.3580i | −0.711843 | + | 1.23295i | ||||
\(424\) | 0.198978 | − | 0.344640i | 0.00966323 | − | 0.0167372i | ||||
\(425\) | −0.360677 | + | 0.624710i | −0.0174954 | + | 0.0303029i | ||||
\(426\) | 5.96928 | 0.289212 | ||||||||
\(427\) | −8.76934 | − | 15.1889i | −0.424378 | − | 0.735044i | ||||
\(428\) | 5.22301 | + | 9.04652i | 0.252464 | + | 0.437280i | ||||
\(429\) | −0.104955 | + | 0.181788i | −0.00506730 | + | 0.00877682i | ||||
\(430\) | 29.6468 | 1.42970 | ||||||||
\(431\) | −15.8951 | − | 27.5311i | −0.765638 | − | 1.32612i | −0.939908 | − | 0.341427i | \(-0.889090\pi\) |
0.174270 | − | 0.984698i | \(-0.444243\pi\) | |||||||
\(432\) | −10.7244 | −0.515980 | ||||||||
\(433\) | −18.8132 | −0.904103 | −0.452052 | − | 0.891992i | \(-0.649308\pi\) | ||||
−0.452052 | + | 0.891992i | \(0.649308\pi\) | |||||||
\(434\) | 11.4762 | − | 39.0794i | 0.550875 | − | 1.87587i | ||||
\(435\) | 7.20251 | 0.345334 | ||||||||
\(436\) | −20.8786 | −0.999905 | ||||||||
\(437\) | 0.194971 | + | 0.337700i | 0.00932674 | + | 0.0161544i | ||||
\(438\) | −0.0283476 | −0.00135450 | ||||||||
\(439\) | 8.84877 | − | 15.3265i | 0.422329 | − | 0.731495i | −0.573838 | − | 0.818969i | \(-0.694546\pi\) |
0.996167 | + | 0.0874741i | \(0.0278795\pi\) | |||||||
\(440\) | −0.0222922 | − | 0.0386112i | −0.00106274 | − | 0.00184072i | ||||
\(441\) | 8.72647 | + | 15.1147i | 0.415546 | + | 0.719747i | ||||
\(442\) | 0.708422 | 0.0336962 | ||||||||
\(443\) | −5.65530 | + | 9.79526i | −0.268691 | + | 0.465387i | −0.968524 | − | 0.248920i | \(-0.919924\pi\) |
0.699833 | + | 0.714307i | \(0.253258\pi\) | |||||||
\(444\) | −2.62397 | + | 4.54485i | −0.124528 | + | 0.215689i | ||||
\(445\) | −7.62880 | + | 13.2135i | −0.361640 | + | 0.626378i | ||||
\(446\) | 22.9913 | + | 39.8220i | 1.08867 | + | 1.88563i | ||||
\(447\) | −4.85995 | + | 8.41768i | −0.229868 | + | 0.398143i | ||||
\(448\) | −14.9972 | − | 25.9759i | −0.708552 | − | 1.22725i | ||||
\(449\) | 37.3937 | 1.76472 | 0.882358 | − | 0.470578i | \(-0.155955\pi\) | ||||
0.882358 | + | 0.470578i | \(0.155955\pi\) | |||||||
\(450\) | −11.3978 | −0.537295 | ||||||||
\(451\) | −0.135718 | − | 0.235070i | −0.00639070 | − | 0.0110690i | ||||
\(452\) | 17.9071 | − | 31.0161i | 0.842281 | − | 1.45887i | ||||
\(453\) | 0.464010 | + | 0.803689i | 0.0218011 | + | 0.0377606i | ||||
\(454\) | 2.89924 | − | 5.02163i | 0.136068 | − | 0.235677i | ||||
\(455\) | 3.13303 | − | 5.42656i | 0.146879 | − | 0.254401i | ||||
\(456\) | 0.0246905 | − | 0.0427651i | 0.00115624 | − | 0.00200266i | ||||
\(457\) | −39.5060 | −1.84801 | −0.924007 | − | 0.382376i | \(-0.875106\pi\) | ||||
−0.924007 | + | 0.382376i | \(0.875106\pi\) | |||||||
\(458\) | 8.42026 | + | 14.5843i | 0.393453 | + | 0.681480i | ||||
\(459\) | 0.480188 | + | 0.831710i | 0.0224133 | + | 0.0388209i | ||||
\(460\) | −0.377348 | + | 0.653585i | −0.0175939 | + | 0.0304736i | ||||
\(461\) | −18.7601 | −0.873744 | −0.436872 | − | 0.899524i | \(-0.643914\pi\) | ||||
−0.436872 | + | 0.899524i | \(0.643914\pi\) | |||||||
\(462\) | −0.767777 | − | 1.32983i | −0.0357202 | − | 0.0618692i | ||||
\(463\) | 18.5138 | 0.860410 | 0.430205 | − | 0.902731i | \(-0.358441\pi\) | ||||
0.430205 | + | 0.902731i | \(0.358441\pi\) | |||||||
\(464\) | 35.0589 | 1.62757 | ||||||||
\(465\) | −3.11084 | − | 3.26278i | −0.144262 | − | 0.151308i | ||||
\(466\) | −20.7379 | −0.960662 | ||||||||
\(467\) | 10.2725 | 0.475354 | 0.237677 | − | 0.971344i | \(-0.423614\pi\) | ||||
0.237677 | + | 0.971344i | \(0.423614\pi\) | |||||||
\(468\) | 2.81849 | + | 4.88177i | 0.130285 | + | 0.225660i | ||||
\(469\) | 0.882616 | 0.0407554 | ||||||||
\(470\) | −18.1864 | + | 31.4997i | −0.838874 | + | 1.45297i | ||||
\(471\) | 2.46926 | + | 4.27688i | 0.113778 | + | 0.197068i | ||||
\(472\) | −0.215170 | − | 0.372685i | −0.00990399 | − | 0.0171542i | ||||
\(473\) | 3.82915 | 0.176064 | ||||||||
\(474\) | −6.78697 | + | 11.7554i | −0.311736 | + | 0.539942i | ||||
\(475\) | −1.84201 | + | 3.19046i | −0.0845173 | + | 0.146388i | ||||
\(476\) | −1.30489 | + | 2.26014i | −0.0598097 | + | 0.103593i | ||||
\(477\) | 9.50244 | + | 16.4587i | 0.435087 | + | 0.753593i | ||||
\(478\) | −17.0035 | + | 29.4509i | −0.777722 | + | 1.34705i | ||||
\(479\) | −1.18279 | − | 2.04865i | −0.0540429 | − | 0.0936050i | 0.837738 | − | 0.546072i | \(-0.183877\pi\) |
−0.891781 | + | 0.452467i | \(0.850544\pi\) | |||||||
\(480\) | −6.49950 | −0.296660 | ||||||||
\(481\) | −5.49235 | −0.250430 | ||||||||
\(482\) | −16.7107 | − | 28.9437i | −0.761149 | − | 1.31835i | ||||
\(483\) | −0.185646 | + | 0.321548i | −0.00844719 | + | 0.0146310i | ||||
\(484\) | 10.9578 | + | 18.9795i | 0.498084 | + | 0.862706i | ||||
\(485\) | −3.30968 | + | 5.73253i | −0.150285 | + | 0.260301i | ||||
\(486\) | −11.5264 | + | 19.9644i | −0.522849 | + | 0.905602i | ||||
\(487\) | −7.28324 | + | 12.6149i | −0.330035 | + | 0.571637i | −0.982518 | − | 0.186166i | \(-0.940394\pi\) |
0.652483 | + | 0.757803i | \(0.273727\pi\) | |||||||
\(488\) | 0.279964 | 0.0126734 | ||||||||
\(489\) | 5.28855 | + | 9.16004i | 0.239157 | + | 0.414231i | ||||
\(490\) | 10.8400 | + | 18.7755i | 0.489702 | + | 0.848188i | ||||
\(491\) | 5.40094 | − | 9.35470i | 0.243741 | − | 0.422172i | −0.718036 | − | 0.696006i | \(-0.754959\pi\) |
0.961777 | + | 0.273834i | \(0.0882920\pi\) | |||||||
\(492\) | 0.581854 | 0.0262320 | ||||||||
\(493\) | −1.56977 | − | 2.71891i | −0.0706987 | − | 0.122454i | ||||
\(494\) | 3.61798 | 0.162781 | ||||||||
\(495\) | 2.12918 | 0.0956996 | ||||||||
\(496\) | −15.1423 | − | 15.8819i | −0.679910 | − | 0.713117i | ||||
\(497\) | −23.0146 | −1.03235 | ||||||||
\(498\) | −15.0770 | −0.675616 | ||||||||
\(499\) | −11.0495 | − | 19.1383i | −0.494645 | − | 0.856749i | 0.505336 | − | 0.862922i | \(-0.331368\pi\) |
−0.999981 | + | 0.00617295i | \(0.998035\pi\) | |||||||
\(500\) | −24.5726 | −1.09892 | ||||||||
\(501\) | 0.492095 | − | 0.852334i | 0.0219852 | − | 0.0380795i | ||||
\(502\) | 17.3260 | + | 30.0095i | 0.773296 | + | 1.33939i | ||||
\(503\) | 3.87267 | + | 6.70767i | 0.172674 | + | 0.299080i | 0.939354 | − | 0.342950i | \(-0.111426\pi\) |
−0.766680 | + | 0.642030i | \(0.778093\pi\) | |||||||
\(504\) | −0.589032 | −0.0262376 | ||||||||
\(505\) | −2.38534 | + | 4.13154i | −0.106146 | + | 0.183851i | ||||
\(506\) | −0.0967793 | + | 0.167627i | −0.00430236 | + | 0.00745191i | ||||
\(507\) | 0.235463 | − | 0.407833i | 0.0104573 | − | 0.0181125i | ||||
\(508\) | −7.27890 | − | 12.6074i | −0.322949 | − | 0.559364i | ||||
\(509\) | 11.5266 | − | 19.9647i | 0.510907 | − | 0.884918i | −0.489013 | − | 0.872277i | \(-0.662643\pi\) |
0.999920 | − | 0.0126410i | \(-0.00402385\pi\) | |||||||
\(510\) | 0.286798 | + | 0.496748i | 0.0126996 | + | 0.0219964i | ||||
\(511\) | 0.109295 | 0.00483490 | ||||||||
\(512\) | −32.0955 | −1.41843 | ||||||||
\(513\) | 2.45237 | + | 4.24763i | 0.108275 | + | 0.187537i | ||||
\(514\) | 4.28036 | − | 7.41381i | 0.188799 | − | 0.327009i | ||||
\(515\) | 8.18628 | + | 14.1791i | 0.360731 | + | 0.624804i | ||||
\(516\) | −4.10411 | + | 7.10853i | −0.180673 | + | 0.312936i | ||||
\(517\) | −2.34893 | + | 4.06846i | −0.103306 | + | 0.178931i | ||||
\(518\) | 20.0890 | − | 34.7952i | 0.882660 | − | 1.52881i | ||||
\(519\) | 6.03731 | 0.265009 | ||||||||
\(520\) | 0.0500115 | + | 0.0866225i | 0.00219315 | + | 0.00379865i | ||||
\(521\) | −21.6428 | − | 37.4865i | −0.948190 | − | 1.64231i | −0.749235 | − | 0.662305i | \(-0.769578\pi\) |
−0.198955 | − | 0.980009i | \(-0.563755\pi\) | |||||||
\(522\) | 24.8031 | − | 42.9602i | 1.08560 | − | 1.88032i | ||||
\(523\) | −26.4266 | −1.15555 | −0.577777 | − | 0.816195i | \(-0.696080\pi\) | ||||
−0.577777 | + | 0.816195i | \(0.696080\pi\) | |||||||
\(524\) | −1.63261 | − | 2.82777i | −0.0713210 | − | 0.123532i | ||||
\(525\) | −3.50782 | −0.153094 | ||||||||
\(526\) | −41.9350 | −1.82845 | ||||||||
\(527\) | −0.553685 | + | 1.88544i | −0.0241189 | + | 0.0821311i | ||||
\(528\) | −0.827300 | −0.0360036 | ||||||||
\(529\) | −22.9532 | −0.997965 | ||||||||
\(530\) | 11.8039 | + | 20.4450i | 0.512730 | + | 0.888074i | ||||
\(531\) | 20.5514 | 0.891854 | ||||||||
\(532\) | −6.66423 | + | 11.5428i | −0.288931 | + | 0.500443i | ||||
\(533\) | 0.304476 | + | 0.527368i | 0.0131883 | + | 0.0228429i | ||||
\(534\) | −4.19415 | − | 7.26448i | −0.181499 | − | 0.314365i | ||||
\(535\) | −8.85186 | −0.382699 | ||||||||
\(536\) | −0.00704447 | + | 0.0122014i | −0.000304275 | + | 0.000527019i | ||||
\(537\) | −2.36826 | + | 4.10194i | −0.102198 | + | 0.177012i | ||||
\(538\) | −4.98152 | + | 8.62825i | −0.214769 | + | 0.371990i | ||||
\(539\) | 1.40008 | + | 2.42501i | 0.0603058 | + | 0.104453i | ||||
\(540\) | −4.74632 | + | 8.22086i | −0.204249 | + | 0.353770i | ||||
\(541\) | 3.34753 | + | 5.79809i | 0.143922 | + | 0.249279i | 0.928970 | − | 0.370155i | \(-0.120695\pi\) |
−0.785049 | + | 0.619434i | \(0.787362\pi\) | |||||||
\(542\) | 42.9036 | 1.84287 | ||||||||
\(543\) | −1.67931 | −0.0720659 | ||||||||
\(544\) | 1.41655 | + | 2.45353i | 0.0607340 | + | 0.105194i | ||||
\(545\) | 8.84618 | − | 15.3220i | 0.378929 | − | 0.656323i | ||||
\(546\) | 1.72247 | + | 2.98341i | 0.0737150 | + | 0.127678i | ||||
\(547\) | −13.1634 | + | 22.7997i | −0.562827 | + | 0.974845i | 0.434421 | + | 0.900710i | \(0.356953\pi\) |
−0.997248 | + | 0.0741349i | \(0.976380\pi\) | |||||||
\(548\) | 3.16895 | − | 5.48879i | 0.135371 | − | 0.234469i | ||||
\(549\) | −6.68502 | + | 11.5788i | −0.285310 | + | 0.494171i | ||||
\(550\) | −1.82867 | −0.0779746 | ||||||||
\(551\) | −8.01695 | − | 13.8858i | −0.341534 | − | 0.591553i | ||||
\(552\) | −0.00296341 | − | 0.00513278i | −0.000126131 | − | 0.000218465i | ||||
\(553\) | 26.1673 | − | 45.3231i | 1.11275 | − | 1.92733i | ||||
\(554\) | 45.3420 | 1.92640 | ||||||||
\(555\) | −2.22352 | − | 3.85126i | −0.0943833 | − | 0.163477i | ||||
\(556\) | −2.96074 | −0.125563 | ||||||||
\(557\) | 7.64301 | 0.323845 | 0.161922 | − | 0.986804i | \(-0.448231\pi\) | ||||
0.161922 | + | 0.986804i | \(0.448231\pi\) | |||||||
\(558\) | −30.1740 | + | 7.31904i | −1.27737 | + | 0.309840i | ||||
\(559\) | −8.59051 | −0.363340 | ||||||||
\(560\) | 24.6957 | 1.04359 | ||||||||
\(561\) | 0.0370424 | + | 0.0641594i | 0.00156393 | + | 0.00270881i | ||||
\(562\) | 38.4172 | 1.62053 | ||||||||
\(563\) | −6.17330 | + | 10.6925i | −0.260174 | + | 0.450634i | −0.966288 | − | 0.257464i | \(-0.917113\pi\) |
0.706114 | + | 0.708098i | \(0.250447\pi\) | |||||||
\(564\) | −5.03520 | − | 8.72122i | −0.212020 | − | 0.367230i | ||||
\(565\) | 15.1743 | + | 26.2827i | 0.638389 | + | 1.10572i | ||||
\(566\) | −49.0838 | −2.06315 | ||||||||
\(567\) | 12.8526 | − | 22.2614i | 0.539759 | − | 0.934890i | ||||
\(568\) | 0.183688 | − | 0.318157i | 0.00770737 | − | 0.0133496i | ||||
\(569\) | −11.0423 | + | 19.1259i | −0.462919 | + | 0.801800i | −0.999105 | − | 0.0423003i | \(-0.986531\pi\) |
0.536186 | + | 0.844100i | \(0.319865\pi\) | |||||||
\(570\) | 1.46471 | + | 2.53694i | 0.0613498 | + | 0.106261i | ||||
\(571\) | 14.2827 | − | 24.7383i | 0.597711 | − | 1.03527i | −0.395447 | − | 0.918489i | \(-0.629410\pi\) |
0.993158 | − | 0.116777i | \(-0.0372562\pi\) | |||||||
\(572\) | 0.452201 | + | 0.783235i | 0.0189075 | + | 0.0327487i | ||||
\(573\) | −1.34799 | −0.0563132 | ||||||||
\(574\) | −4.45465 | −0.185933 | ||||||||
\(575\) | 0.221083 | + | 0.382927i | 0.00921979 | + | 0.0159691i | ||||
\(576\) | −11.4326 | + | 19.8019i | −0.476360 | + | 0.825079i | ||||
\(577\) | 19.8553 | + | 34.3904i | 0.826587 | + | 1.43169i | 0.900701 | + | 0.434440i | \(0.143054\pi\) |
−0.0741139 | + | 0.997250i | \(0.523613\pi\) | |||||||
\(578\) | −16.9365 | + | 29.3348i | −0.704464 | + | 1.22017i | ||||
\(579\) | −4.59259 | + | 7.95460i | −0.190861 | + | 0.330582i | ||||
\(580\) | 15.5160 | − | 26.8745i | 0.644268 | − | 1.11590i | ||||
\(581\) | 58.1296 | 2.41162 | ||||||||
\(582\) | −1.81959 | − | 3.15163i | −0.0754245 | − | 0.130639i | ||||
\(583\) | 1.52458 | + | 2.64065i | 0.0631417 | + | 0.109365i | ||||
\(584\) | −0.000872317 | 0.00151090i | −3.60967e−5 | 6.25214e-5i | ||||||
\(585\) | −4.77672 | −0.197493 | ||||||||
\(586\) | 11.4511 | + | 19.8338i | 0.473039 | + | 0.819328i | ||||
\(587\) | −29.3827 | −1.21276 | −0.606378 | − | 0.795177i | \(-0.707378\pi\) | ||||
−0.606378 | + | 0.795177i | \(0.707378\pi\) | |||||||
\(588\) | −6.00248 | −0.247538 | ||||||||
\(589\) | −2.82772 | + | 9.62914i | −0.116514 | + | 0.396762i | ||||
\(590\) | 25.5289 | 1.05101 | ||||||||
\(591\) | −6.67828 | −0.274708 | ||||||||
\(592\) | −10.8232 | − | 18.7463i | −0.444831 | − | 0.770470i | ||||
\(593\) | 23.5849 | 0.968518 | 0.484259 | − | 0.874925i | \(-0.339089\pi\) | ||||
0.484259 | + | 0.874925i | \(0.339089\pi\) | |||||||
\(594\) | −1.21730 | + | 2.10843i | −0.0499464 | + | 0.0865097i | ||||
\(595\) | −1.10575 | − | 1.91522i | −0.0453315 | − | 0.0785165i | ||||
\(596\) | 20.9391 | + | 36.2676i | 0.857700 | + | 1.48558i | ||||
\(597\) | 11.2039 | 0.458545 | ||||||||
\(598\) | 0.217120 | − | 0.376062i | 0.00887868 | − | 0.0153783i | ||||
\(599\) | −2.76860 | + | 4.79536i | −0.113122 | + | 0.195933i | −0.917027 | − | 0.398824i | \(-0.869418\pi\) |
0.803905 | + | 0.594757i | \(0.202752\pi\) | |||||||
\(600\) | 0.0279971 | − | 0.0484925i | 0.00114298 | − | 0.00197970i | ||||
\(601\) | −19.7320 | − | 34.1768i | −0.804885 | − | 1.39410i | −0.916369 | − | 0.400336i | \(-0.868894\pi\) |
0.111484 | − | 0.993766i | \(-0.464440\pi\) | |||||||
\(602\) | 31.4209 | − | 54.4226i | 1.28062 | − | 2.21810i | ||||
\(603\) | −0.336417 | − | 0.582691i | −0.0137000 | − | 0.0237290i | ||||
\(604\) | 3.99838 | 0.162692 | ||||||||
\(605\) | −18.5711 | −0.755024 | ||||||||
\(606\) | −1.31141 | − | 2.27143i | −0.0532725 | − | 0.0922706i | ||||
\(607\) | −0.712082 | + | 1.23336i | −0.0289025 | + | 0.0500607i | −0.880115 | − | 0.474761i | \(-0.842535\pi\) |
0.851212 | + | 0.524821i | \(0.175868\pi\) | |||||||
\(608\) | 7.23445 | + | 12.5304i | 0.293396 | + | 0.508176i | ||||
\(609\) | 7.63351 | − | 13.2216i | 0.309326 | − | 0.535768i | ||||
\(610\) | −8.30413 | + | 14.3832i | −0.336224 | + | 0.582357i | ||||
\(611\) | 5.26970 | − | 9.12739i | 0.213189 | − | 0.369255i | ||||
\(612\) | 1.98949 | 0.0804202 | ||||||||
\(613\) | −9.82573 | − | 17.0187i | −0.396858 | − | 0.687377i | 0.596479 | − | 0.802629i | \(-0.296566\pi\) |
−0.993336 | + | 0.115251i | \(0.963233\pi\) | |||||||
\(614\) | 14.0734 | + | 24.3758i | 0.567954 | + | 0.983726i | ||||
\(615\) | −0.246529 | + | 0.427000i | −0.00994099 | + | 0.0172183i | ||||
\(616\) | −0.0945048 | −0.00380771 | ||||||||
\(617\) | −14.9320 | − | 25.8630i | −0.601140 | − | 1.04121i | −0.992649 | − | 0.121031i | \(-0.961380\pi\) |
0.391509 | − | 0.920174i | \(-0.371953\pi\) | |||||||
\(618\) | −9.00129 | −0.362085 | ||||||||
\(619\) | 28.9314 | 1.16285 | 0.581426 | − | 0.813599i | \(-0.302495\pi\) | ||||
0.581426 | + | 0.813599i | \(0.302495\pi\) | |||||||
\(620\) | −18.8759 | + | 4.57856i | −0.758072 | + | 0.183879i | ||||
\(621\) | 0.588679 | 0.0236229 | ||||||||
\(622\) | −48.0951 | −1.92844 | ||||||||
\(623\) | 16.1706 | + | 28.0083i | 0.647862 | + | 1.12213i | ||||
\(624\) | 1.85601 | 0.0742998 | ||||||||
\(625\) | 5.30162 | − | 9.18267i | 0.212065 | − | 0.367307i | ||||
\(626\) | −0.375719 | − | 0.650765i | −0.0150168 | − | 0.0260098i | ||||
\(627\) | 0.189180 | + | 0.327669i | 0.00755510 | + | 0.0130858i | ||||
\(628\) | 21.2776 | 0.849070 | ||||||||
\(629\) | −0.969221 | + | 1.67874i | −0.0386454 | + | 0.0669357i | ||||
\(630\) | 17.4715 | − | 30.2615i | 0.696081 | − | 1.20565i | ||||
\(631\) | 12.0906 | − | 20.9416i | 0.481320 | − | 0.833670i | −0.518450 | − | 0.855108i | \(-0.673491\pi\) |
0.999770 | + | 0.0214374i | \(0.00682425\pi\) | |||||||
\(632\) | 0.417700 | + | 0.723478i | 0.0166152 | + | 0.0287784i | ||||
\(633\) | 4.07022 | − | 7.04983i | 0.161777 | − | 0.280206i | ||||
\(634\) | −26.7249 | − | 46.2889i | −1.06138 | − | 1.83837i | ||||
\(635\) | 12.3361 | 0.489544 | ||||||||
\(636\) | −6.53623 | −0.259178 | ||||||||
\(637\) | −3.14102 | − | 5.44040i | −0.124452 | − | 0.215557i | ||||
\(638\) | 3.97943 | − | 6.89258i | 0.157547 | − | 0.272880i | ||||
\(639\) | 8.77223 | + | 15.1940i | 0.347024 | + | 0.601063i | ||||
\(640\) | −0.400050 | + | 0.692907i | −0.0158134 | + | 0.0273896i | ||||
\(641\) | 0.899094 | − | 1.55728i | 0.0355121 | − | 0.0615087i | −0.847723 | − | 0.530439i | \(-0.822027\pi\) |
0.883235 | + | 0.468930i | \(0.155360\pi\) | |||||||
\(642\) | 2.43328 | − | 4.21457i | 0.0960340 | − | 0.166336i | ||||
\(643\) | −21.2900 | −0.839594 | −0.419797 | − | 0.907618i | \(-0.637899\pi\) | ||||
−0.419797 | + | 0.907618i | \(0.637899\pi\) | |||||||
\(644\) | 0.799857 | + | 1.38539i | 0.0315188 | + | 0.0545921i | ||||
\(645\) | −3.47778 | − | 6.02370i | −0.136938 | − | 0.237183i | ||||
\(646\) | 0.638456 | − | 1.10584i | 0.0251197 | − | 0.0435086i | ||||
\(647\) | −16.7900 | −0.660084 | −0.330042 | − | 0.943966i | \(-0.607063\pi\) | ||||
−0.330042 | + | 0.943966i | \(0.607063\pi\) | |||||||
\(648\) | 0.205162 | + | 0.355351i | 0.00805953 | + | 0.0139595i | ||||
\(649\) | 3.29728 | 0.129430 | ||||||||
\(650\) | 4.10252 | 0.160914 | ||||||||
\(651\) | −9.28647 | + | 2.25254i | −0.363966 | + | 0.0882841i | ||||
\(652\) | 45.5715 | 1.78472 | ||||||||
\(653\) | 2.77823 | 0.108721 | 0.0543604 | − | 0.998521i | \(-0.482688\pi\) | ||||
0.0543604 | + | 0.998521i | \(0.482688\pi\) | |||||||
\(654\) | 4.86344 | + | 8.42372i | 0.190176 | + | 0.329394i | ||||
\(655\) | 2.76692 | 0.108112 | ||||||||
\(656\) | −1.20000 | + | 2.07846i | −0.0468521 | + | 0.0811503i | ||||
\(657\) | −0.0416586 | − | 0.0721547i | −0.00162525 | − | 0.00281502i | ||||
\(658\) | 38.5493 | + | 66.7693i | 1.50281 | + | 2.60294i | ||||
\(659\) | −40.3945 | −1.57354 | −0.786772 | − | 0.617243i | \(-0.788249\pi\) | ||||
−0.786772 | + | 0.617243i | \(0.788249\pi\) | |||||||
\(660\) | −0.366138 | + | 0.634170i | −0.0142519 | + | 0.0246850i | ||||
\(661\) | −10.8765 | + | 18.8386i | −0.423045 | + | 0.732735i | −0.996236 | − | 0.0866866i | \(-0.972372\pi\) |
0.573191 | + | 0.819422i | \(0.305705\pi\) | |||||||
\(662\) | −9.00128 | + | 15.5907i | −0.349845 | + | 0.605949i | ||||
\(663\) | −0.0831030 | − | 0.143939i | −0.00322745 | − | 0.00559011i | ||||
\(664\) | −0.463953 | + | 0.803589i | −0.0180048 | + | 0.0311853i | ||||
\(665\) | −5.64720 | − | 9.78123i | −0.218989 | − | 0.379300i | ||||
\(666\) | −30.6284 | −1.18683 | ||||||||
\(667\) | −1.92443 | −0.0745141 | ||||||||
\(668\) | −2.12019 | − | 3.67228i | −0.0820328 | − | 0.142085i | ||||
\(669\) | 5.39408 | − | 9.34282i | 0.208547 | − | 0.361214i | ||||
\(670\) | −0.417897 | − | 0.723819i | −0.0161448 | − | 0.0279636i | ||||
\(671\) | −1.07255 | + | 1.85771i | −0.0414053 | + | 0.0717162i | ||||
\(672\) | −6.88844 | + | 11.9311i | −0.265727 | + | 0.460253i | ||||
\(673\) | −10.2675 | + | 17.7839i | −0.395784 | + | 0.685518i | −0.993201 | − | 0.116413i | \(-0.962860\pi\) |
0.597417 | + | 0.801931i | \(0.296194\pi\) | |||||||
\(674\) | −0.728594 | −0.0280644 | ||||||||
\(675\) | 2.78080 | + | 4.81649i | 0.107033 | + | 0.185387i | ||||
\(676\) | −1.01449 | − | 1.75715i | −0.0390189 | − | 0.0675827i | ||||
\(677\) | −8.55005 | + | 14.8091i | −0.328605 | + | 0.569161i | −0.982235 | − | 0.187653i | \(-0.939912\pi\) |
0.653630 | + | 0.756814i | \(0.273245\pi\) | |||||||
\(678\) | −16.6851 | −0.640786 | ||||||||
\(679\) | 7.01547 | + | 12.1511i | 0.269229 | + | 0.466318i | ||||
\(680\) | 0.0353016 | 0.00135376 | ||||||||
\(681\) | −1.36041 | −0.0521309 | ||||||||
\(682\) | −4.84114 | + | 1.17427i | −0.185377 | + | 0.0449653i | ||||
\(683\) | −48.9591 | −1.87337 | −0.936683 | − | 0.350178i | \(-0.886121\pi\) | ||||
−0.936683 | + | 0.350178i | \(0.886121\pi\) | |||||||
\(684\) | 10.1605 | 0.388497 | ||||||||
\(685\) | 2.68534 | + | 4.65114i | 0.102602 | + | 0.177711i | ||||
\(686\) | −5.25211 | −0.200526 | ||||||||
\(687\) | 1.97551 | − | 3.42169i | 0.0753705 | − | 0.130546i | ||||
\(688\) | −16.9284 | − | 29.3209i | −0.645390 | − | 1.11785i | ||||
\(689\) | −3.42032 | − | 5.92417i | −0.130304 | − | 0.225693i | ||||
\(690\) | 0.351595 | 0.0133850 | ||||||||
\(691\) | 11.9291 | − | 20.6619i | 0.453806 | − | 0.786015i | −0.544813 | − | 0.838558i | \(-0.683399\pi\) |
0.998619 | + | 0.0525428i | \(0.0167326\pi\) | |||||||
\(692\) | 13.0059 | − | 22.5269i | 0.494410 | − | 0.856343i | ||||
\(693\) | 2.25659 | − | 3.90854i | 0.0857209 | − | 0.148473i | ||||
\(694\) | −26.5105 | − | 45.9175i | −1.00632 | − | 1.74300i | ||||
\(695\) | 1.25445 | − | 2.17277i | 0.0475841 | − | 0.0824180i | ||||
\(696\) | 0.121851 | + | 0.211053i | 0.00461876 | + | 0.00799994i | ||||
\(697\) | 0.214921 | 0.00814070 | ||||||||
\(698\) | 11.4144 | 0.432042 | ||||||||
\(699\) | 2.43270 | + | 4.21356i | 0.0920131 | + | 0.159371i | ||||
\(700\) | −7.55673 | + | 13.0886i | −0.285618 | + | 0.494704i | ||||
\(701\) | 18.9854 | + | 32.8836i | 0.717067 | + | 1.24200i | 0.962157 | + | 0.272497i | \(0.0878493\pi\) |
−0.245089 | + | 0.969500i | \(0.578817\pi\) | |||||||
\(702\) | 2.73095 | − | 4.73015i | 0.103073 | − | 0.178528i | ||||
\(703\) | −4.94991 | + | 8.57349i | −0.186689 | + | 0.323355i | ||||
\(704\) | −1.83426 | + | 3.17703i | −0.0691313 | + | 0.119739i | ||||
\(705\) | 8.53355 | 0.321392 | ||||||||
\(706\) | −26.8439 | − | 46.4950i | −1.01028 | − | 1.74986i | ||||
\(707\) | 5.05617 | + | 8.75754i | 0.190157 | + | 0.329361i | ||||
\(708\) | −3.53405 | + | 6.12116i | −0.132818 | + | 0.230047i | ||||
\(709\) | 44.6884 | 1.67831 | 0.839153 | − | 0.543895i | \(-0.183051\pi\) | ||||
0.839153 | + | 0.543895i | \(0.183051\pi\) | |||||||
\(710\) | 10.8969 | + | 18.8739i | 0.408952 | + | 0.708326i | ||||
\(711\) | −39.8955 | −1.49620 | ||||||||
\(712\) | −0.516253 | −0.0193474 | ||||||||
\(713\) | 0.831181 | + | 0.871777i | 0.0311280 | + | 0.0326483i | ||||
\(714\) | 1.21584 | 0.0455017 | ||||||||
\(715\) | −0.766381 | −0.0286610 | ||||||||
\(716\) | 10.2036 | + | 17.6732i | 0.381328 | + | 0.660479i | ||||
\(717\) | 7.97852 | 0.297963 | ||||||||
\(718\) | 5.40337 | − | 9.35892i | 0.201652 | − | 0.349272i | ||||
\(719\) | 23.0223 | + | 39.8757i | 0.858585 | + | 1.48711i | 0.873279 | + | 0.487221i | \(0.161989\pi\) |
−0.0146936 | + | 0.999892i | \(0.504677\pi\) | |||||||
\(720\) | −9.41299 | − | 16.3038i | −0.350801 | − | 0.607606i | ||||
\(721\) | 34.7046 | 1.29247 | ||||||||
\(722\) | −15.8080 | + | 27.3803i | −0.588315 | + | 1.01899i | ||||
\(723\) | −3.92056 | + | 6.79060i | −0.145807 | + | 0.252545i | ||||
\(724\) | −3.61765 | + | 6.26595i | −0.134449 | + | 0.232872i | ||||
\(725\) | −9.09062 | − | 15.7454i | −0.337617 | − | 0.584770i | ||||
\(726\) | 5.10501 | − | 8.84213i | 0.189465 | − | 0.328162i | ||||
\(727\) | 18.2093 | + | 31.5395i | 0.675346 | + | 1.16973i | 0.976368 | + | 0.216116i | \(0.0693391\pi\) |
−0.301021 | + | 0.953617i | \(0.597328\pi\) | |||||||
\(728\) | 0.212017 | 0.00785787 | ||||||||
\(729\) | −15.7512 | −0.583378 | ||||||||
\(730\) | −0.0517482 | − | 0.0896306i | −0.00191529 | − | 0.00331738i | ||||
\(731\) | −1.51595 | + | 2.62569i | −0.0560693 | + | 0.0971148i | ||||
\(732\) | −2.29914 | − | 3.98222i | −0.0849786 | − | 0.147187i | ||||
\(733\) | −7.00023 | + | 12.1248i | −0.258560 | + | 0.447838i | −0.965856 | − | 0.259079i | \(-0.916581\pi\) |
0.707297 | + | 0.706917i | \(0.249914\pi\) | |||||||
\(734\) | −24.0709 | + | 41.6920i | −0.888472 | + | 1.53888i | ||||
\(735\) | 2.54322 | − | 4.40499i | 0.0938081 | − | 0.162480i | ||||
\(736\) | 1.73659 | 0.0640116 | ||||||||
\(737\) | −0.0539750 | − | 0.0934875i | −0.00198820 | − | 0.00344366i | ||||
\(738\) | 1.69793 | + | 2.94090i | 0.0625016 | + | 0.108256i | ||||
\(739\) | −15.5995 | + | 27.0191i | −0.573837 | + | 0.993914i | 0.422330 | + | 0.906442i | \(0.361212\pi\) |
−0.996167 | + | 0.0874722i | \(0.972121\pi\) | |||||||
\(740\) | −19.1601 | −0.704340 | ||||||||
\(741\) | −0.424415 | − | 0.735109i | −0.0155913 | − | 0.0270049i | ||||
\(742\) | 50.0411 | 1.83707 | ||||||||
\(743\) | 12.3296 | 0.452330 | 0.226165 | − | 0.974089i | \(-0.427381\pi\) | ||||
0.226165 | + | 0.974089i | \(0.427381\pi\) | |||||||
\(744\) | 0.0429792 | − | 0.146355i | 0.00157569 | − | 0.00536565i | ||||
\(745\) | −35.4872 | −1.30015 | ||||||||
\(746\) | −32.7915 | −1.20058 | ||||||||
\(747\) | −22.1566 | − | 38.3764i | −0.810668 | − | 1.40412i | ||||
\(748\) | 0.319195 | 0.0116709 | ||||||||
\(749\) | −9.38156 | + | 16.2493i | −0.342795 | + | 0.593738i | ||||
\(750\) | 5.72391 | + | 9.91410i | 0.209008 | + | 0.362012i | ||||
\(751\) | 3.59880 | + | 6.23331i | 0.131322 | + | 0.227457i | 0.924187 | − | 0.381941i | \(-0.124744\pi\) |
−0.792864 | + | 0.609398i | \(0.791411\pi\) | |||||||
\(752\) | 41.5379 | 1.51473 | ||||||||
\(753\) | 4.06492 | − | 7.04065i | 0.148134 | − | 0.256576i | ||||
\(754\) | −8.92766 | + | 15.4632i | −0.325126 | + | 0.563135i | ||||
\(755\) | −1.69409 | + | 2.93425i | −0.0616543 | + | 0.106788i | ||||
\(756\) | 10.0607 | + | 17.4256i | 0.365903 | + | 0.633763i | ||||
\(757\) | 26.8370 | − | 46.4831i | 0.975408 | − | 1.68946i | 0.296827 | − | 0.954931i | \(-0.404071\pi\) |
0.678581 | − | 0.734526i | \(-0.262595\pi\) | |||||||
\(758\) | 14.9373 | + | 25.8722i | 0.542547 | + | 0.939719i | ||||
\(759\) | 0.0454116 | 0.00164834 | ||||||||
\(760\) | 0.180289 | 0.00653977 | ||||||||
\(761\) | 10.3426 | + | 17.9139i | 0.374918 | + | 0.649377i | 0.990315 | − | 0.138841i | \(-0.0443376\pi\) |
−0.615397 | + | 0.788217i | \(0.711004\pi\) | |||||||
\(762\) | −3.39107 | + | 5.87351i | −0.122846 | + | 0.212775i | ||||
\(763\) | −18.7511 | − | 32.4778i | −0.678834 | − | 1.17578i | ||||
\(764\) | −2.90392 | + | 5.02973i | −0.105060 | + | 0.181969i | ||||
\(765\) | −0.842935 | + | 1.46001i | −0.0304764 | + | 0.0527867i | ||||
\(766\) | −19.2578 | + | 33.3554i | −0.695812 | + | 1.20518i | ||||
\(767\) | −7.39729 | −0.267101 | ||||||||
\(768\) | 3.65585 | + | 6.33212i | 0.131919 | + | 0.228491i | ||||
\(769\) | 0.347788 | + | 0.602387i | 0.0125416 | + | 0.0217226i | 0.872228 | − | 0.489099i | \(-0.162674\pi\) |
−0.859687 | + | 0.510822i | \(0.829341\pi\) | |||||||
\(770\) | 2.80314 | − | 4.85518i | 0.101018 | − | 0.174969i | ||||
\(771\) | −2.00847 | −0.0723332 | ||||||||
\(772\) | 19.7872 | + | 34.2724i | 0.712156 | + | 1.23349i | ||||
\(773\) | 27.9146 | 1.00402 | 0.502010 | − | 0.864862i | \(-0.332594\pi\) | ||||
0.502010 | + | 0.864862i | \(0.332594\pi\) | |||||||
\(774\) | −47.9054 | −1.72193 | ||||||||
\(775\) | −3.20643 | + | 10.9187i | −0.115178 | + | 0.392212i | ||||
\(776\) | −0.223971 | −0.00804011 | ||||||||
\(777\) | −9.42632 | −0.338168 | ||||||||
\(778\) | −2.04737 | − | 3.54615i | −0.0734018 | − | 0.127136i | ||||
\(779\) | 1.09762 | 0.0393264 | ||||||||
\(780\) | 0.821414 | − | 1.42273i | 0.0294113 | − | 0.0509419i | ||||
\(781\) | 1.40742 | + | 2.43773i | 0.0503616 | + | 0.0872289i | ||||
\(782\) | −0.0766291 | − | 0.132725i | −0.00274025 | − | 0.00474625i | ||||
\(783\) | −24.2057 | −0.865040 | ||||||||
\(784\) | 12.3794 | − | 21.4417i | 0.442120 | − | 0.765774i | ||||
\(785\) | −9.01523 | + | 15.6148i | −0.321767 | + | 0.557317i | ||||
\(786\) | −0.760596 | + | 1.31739i | −0.0271296 | + | 0.0469898i | ||||
\(787\) | −2.80944 | − | 4.86609i | −0.100146 | − | 0.173457i | 0.811599 | − | 0.584215i | \(-0.198598\pi\) |
−0.911745 | + | 0.410758i | \(0.865264\pi\) | |||||||
\(788\) | −14.3867 | + | 24.9185i | −0.512505 | + | 0.887685i | ||||
\(789\) | 4.91928 | + | 8.52044i | 0.175131 | + | 0.303336i | ||||
\(790\) | −49.5582 | −1.76320 | ||||||||
\(791\) | 64.3295 | 2.28729 | ||||||||
\(792\) | 0.0360213 | + | 0.0623907i | 0.00127996 | + | 0.00221696i | ||||
\(793\) | 2.40622 | − | 4.16769i | 0.0854472 | − | 0.147999i | ||||
\(794\) | 18.4876 | + | 32.0214i | 0.656099 | + | 1.13640i | ||||
\(795\) | 2.76937 | − | 4.79669i | 0.0982194 | − | 0.170121i | ||||
\(796\) | 24.1360 | − | 41.8048i | 0.855478 | − | 1.48173i | ||||
\(797\) | 0.692294 | − | 1.19909i | 0.0245223 | − | 0.0424739i | −0.853504 | − | 0.521087i | \(-0.825527\pi\) |
0.878026 | + | 0.478613i | \(0.158860\pi\) | |||||||
\(798\) | 6.20942 | 0.219811 | ||||||||
\(799\) | −1.85986 | − | 3.22138i | −0.0657972 | − | 0.113964i | ||||
\(800\) | 8.20332 | + | 14.2086i | 0.290031 | + | 0.502349i | ||||
\(801\) | 12.3271 | − | 21.3512i | 0.435558 | − | 0.754409i | ||||
\(802\) | 12.8886 | 0.455113 | ||||||||
\(803\) | −0.00668373 | − | 0.0115766i | −0.000235864 | − | 0.000408528i | ||||
\(804\) | 0.231404 | 0.00816097 | ||||||||
\(805\) | −1.35558 | −0.0477780 | ||||||||
\(806\) | 10.8609 | − | 2.63443i | 0.382557 | − | 0.0927937i | ||||
\(807\) | 2.33747 | 0.0822829 | ||||||||
\(808\) | −0.161420 | −0.00567874 | ||||||||
\(809\) | 8.39432 | + | 14.5394i | 0.295128 | + | 0.511177i | 0.975015 | − | 0.222140i | \(-0.0713042\pi\) |
−0.679886 | + | 0.733318i | \(0.737971\pi\) | |||||||
\(810\) | −24.3416 | −0.855275 | ||||||||
\(811\) | 19.3806 | − | 33.5681i | 0.680543 | − | 1.17874i | −0.294272 | − | 0.955722i | \(-0.595077\pi\) |
0.974815 | − | 0.223014i | \(-0.0715895\pi\) | |||||||
\(812\) | −32.8890 | − | 56.9654i | −1.15418 | − | 1.99910i | ||||
\(813\) | −5.03290 | − | 8.71724i | −0.176511 | − | 0.305727i | ||||
\(814\) | −4.91404 | −0.172237 | ||||||||
\(815\) | −19.3084 | + | 33.4432i | −0.676344 | + | 1.17146i | ||||
\(816\) | 0.327525 | − | 0.567290i | 0.0114657 | − | 0.0198591i | ||||
\(817\) | −7.74208 | + | 13.4097i | −0.270861 | + | 0.469145i | ||||
\(818\) | −2.85543 | − | 4.94575i | −0.0998377 | − | 0.172924i | ||||
\(819\) | −5.06256 | + | 8.76862i | −0.176900 | + | 0.306400i | ||||
\(820\) | 1.06217 | + | 1.83973i | 0.0370925 | + | 0.0642462i | ||||
\(821\) | −30.8873 | −1.07798 | −0.538988 | − | 0.842314i | \(-0.681193\pi\) | ||||
−0.538988 | + | 0.842314i | \(0.681193\pi\) | |||||||
\(822\) | −2.95268 | −0.102987 | ||||||||
\(823\) | 9.69244 | + | 16.7878i | 0.337857 | + | 0.585186i | 0.984029 | − | 0.178006i | \(-0.0569645\pi\) |
−0.646172 | + | 0.763192i | \(0.723631\pi\) | |||||||
\(824\) | −0.276989 | + | 0.479760i | −0.00964938 | + | 0.0167132i | ||||
\(825\) | 0.214515 | + | 0.371552i | 0.00746847 | + | 0.0129358i | ||||
\(826\) | 27.0566 | − | 46.8634i | 0.941419 | − | 1.63058i | ||||
\(827\) | −19.0949 | + | 33.0733i | −0.663995 | + | 1.15007i | 0.315562 | + | 0.948905i | \(0.397807\pi\) |
−0.979557 | + | 0.201167i | \(0.935526\pi\) | |||||||
\(828\) | 0.609745 | − | 1.05611i | 0.0211901 | − | 0.0367023i | ||||
\(829\) | −16.6606 | −0.578647 | −0.289324 | − | 0.957231i | \(-0.593430\pi\) | ||||
−0.289324 | + | 0.957231i | \(0.593430\pi\) | |||||||
\(830\) | −27.5229 | − | 47.6711i | −0.955335 | − | 1.65469i | ||||
\(831\) | −5.31894 | − | 9.21268i | −0.184512 | − | 0.319584i | ||||
\(832\) | 4.11508 | − | 7.12753i | 0.142665 | − | 0.247103i | ||||
\(833\) | −2.21715 | −0.0768196 | ||||||||
\(834\) | 0.689671 | + | 1.19455i | 0.0238814 | + | 0.0413637i | ||||
\(835\) | 3.59326 | 0.124350 | ||||||||
\(836\) | 1.63016 | 0.0563803 | ||||||||
\(837\) | 10.4547 | + | 10.9653i | 0.361367 | + | 0.379016i | ||||
\(838\) | −1.03547 | −0.0357697 | ||||||||
\(839\) | 41.6834 | 1.43907 | 0.719535 | − | 0.694456i | \(-0.244355\pi\) | ||||
0.719535 | + | 0.694456i | \(0.244355\pi\) | |||||||
\(840\) | 0.0858330 | + | 0.148667i | 0.00296152 | + | 0.00512950i | ||||
\(841\) | 50.1299 | 1.72862 | ||||||||
\(842\) | 29.5252 | − | 51.1391i | 1.01750 | − | 1.76237i | ||||
\(843\) | −4.50661 | − | 7.80568i | −0.155216 | − | 0.268842i | ||||
\(844\) | −17.5366 | − | 30.3742i | −0.603633 | − | 1.04552i | ||||
\(845\) | 1.71934 | 0.0591471 | ||||||||
\(846\) | 29.3868 | − | 50.8994i | 1.01034 | − | 1.74996i | ||||
\(847\) | −19.6824 | + | 34.0910i | −0.676297 | + | 1.17138i | ||||
\(848\) | 13.4802 | − | 23.3483i | 0.462910 | − | 0.801785i | ||||
\(849\) | 5.75788 | + | 9.97293i | 0.197610 | + | 0.342270i | ||||
\(850\) | 0.723962 | − | 1.25394i | 0.0248317 | − | 0.0430097i | ||||
\(851\) | 0.594100 | + | 1.02901i | 0.0203655 | + | 0.0352741i | ||||
\(852\) | −6.03396 | −0.206720 | ||||||||
\(853\) | 49.6400 | 1.69964 | 0.849821 | − | 0.527071i | \(-0.176710\pi\) | ||||
0.849821 | + | 0.527071i | \(0.176710\pi\) | |||||||
\(854\) | 17.6021 | + | 30.4877i | 0.602332 | + | 1.04327i | ||||
\(855\) | −4.30496 | + | 7.45640i | −0.147226 | + | 0.255004i | ||||
\(856\) | −0.149755 | − | 0.259383i | −0.00511852 | − | 0.00886553i | ||||
\(857\) | −1.09314 | + | 1.89338i | −0.0373410 | + | 0.0646765i | −0.884092 | − | 0.467313i | \(-0.845222\pi\) |
0.846751 | + | 0.531990i | \(0.178555\pi\) | |||||||
\(858\) | 0.210670 | − | 0.364891i | 0.00719216 | − | 0.0124572i | ||||
\(859\) | 3.68591 | − | 6.38418i | 0.125762 | − | 0.217826i | −0.796269 | − | 0.604943i | \(-0.793196\pi\) |
0.922030 | + | 0.387117i | \(0.126529\pi\) | |||||||
\(860\) | −29.9681 | −1.02190 | ||||||||
\(861\) | 0.522562 | + | 0.905104i | 0.0178089 | + | 0.0308459i | ||||
\(862\) | 31.9051 | + | 55.2612i | 1.08669 | + | 1.88221i | ||||
\(863\) | −3.55709 | + | 6.16106i | −0.121085 | + | 0.209725i | −0.920196 | − | 0.391459i | \(-0.871971\pi\) |
0.799111 | + | 0.601184i | \(0.205304\pi\) | |||||||
\(864\) | 21.8430 | 0.743116 | ||||||||
\(865\) | 11.0211 | + | 19.0890i | 0.374727 | + | 0.649047i | ||||
\(866\) | 37.7624 | 1.28322 | ||||||||
\(867\) | 7.94707 | 0.269897 | ||||||||
\(868\) | −11.6005 | + | 39.5029i | −0.393748 | + | 1.34082i | ||||
\(869\) | −6.40088 | −0.217135 | ||||||||
\(870\) | −14.4571 | −0.490142 | ||||||||
\(871\) | 0.121090 | + | 0.209735i | 0.00410299 | + | 0.00710659i | ||||
\(872\) | 0.598635 | 0.0202723 | ||||||||
\(873\) | 5.34801 | − | 9.26303i | 0.181003 | − | 0.313506i | ||||
\(874\) | −0.391353 | − | 0.677842i | −0.0132377 | − | 0.0229284i | ||||
\(875\) | −22.0686 | − | 38.2240i | −0.746056 | − | 1.29221i | ||||
\(876\) | 0.0286547 | 0.000968154 | ||||||||
\(877\) | 8.44811 | − | 14.6326i | 0.285272 | − | 0.494106i | −0.687403 | − | 0.726276i | \(-0.741249\pi\) |
0.972675 | + | 0.232170i | \(0.0745826\pi\) | |||||||
\(878\) | −17.7615 | + | 30.7639i | −0.599423 | + | 1.03823i | ||||
\(879\) | 2.68658 | − | 4.65330i | 0.0906162 | − | 0.156952i | ||||
\(880\) | −1.51023 | − | 2.61579i | −0.0509098 | − | 0.0881784i | ||||
\(881\) | 6.21669 | − | 10.7676i | 0.209446 | − | 0.362771i | −0.742094 | − | 0.670295i | \(-0.766167\pi\) |
0.951540 | + | 0.307525i | \(0.0995007\pi\) | |||||||
\(882\) | −17.5160 | − | 30.3387i | −0.589796 | − | 1.02156i | ||||
\(883\) | 19.7671 | 0.665217 | 0.332609 | − | 0.943065i | \(-0.392071\pi\) | ||||
0.332609 | + | 0.943065i | \(0.392071\pi\) | |||||||
\(884\) | −0.716099 | −0.0240850 | ||||||||
\(885\) | −2.99472 | − | 5.18701i | −0.100666 | − | 0.174359i | ||||
\(886\) | 11.3515 | − | 19.6614i | 0.381361 | − | 0.660537i | ||||
\(887\) | −13.0771 | − | 22.6501i | −0.439085 | − | 0.760517i | 0.558534 | − | 0.829482i | \(-0.311364\pi\) |
−0.997619 | + | 0.0689640i | \(0.978031\pi\) | |||||||
\(888\) | 0.0752347 | − | 0.130310i | 0.00252471 | − | 0.00437293i | ||||
\(889\) | 13.0743 | − | 22.6454i | 0.438499 | − | 0.759503i | ||||
\(890\) | 15.3128 | − | 26.5225i | 0.513285 | − | 0.889036i | ||||
\(891\) | −3.14393 | −0.105325 | ||||||||
\(892\) | −23.2404 | − | 40.2536i | −0.778146 | − | 1.34779i | ||||
\(893\) | −9.49850 | − | 16.4519i | −0.317855 | − | 0.550542i | ||||
\(894\) | 9.75505 | − | 16.8962i | 0.326258 | − | 0.565095i | ||||
\(895\) | −17.2929 | −0.578038 | ||||||||
\(896\) | 0.847979 | + | 1.46874i | 0.0283290 | + | 0.0490672i | ||||
\(897\) | −0.101879 | −0.00340163 | ||||||||
\(898\) | −75.0578 | −2.50471 | ||||||||
\(899\) | −34.1770 | − | 35.8463i | −1.13987 | − | 1.19554i | ||||
\(900\) | 11.5213 | 0.384042 | ||||||||
\(901\) | −2.41430 | −0.0804321 | ||||||||
\(902\) | 0.272417 | + | 0.471840i | 0.00907050 | + | 0.0157106i | ||||
\(903\) | −14.7436 | −0.490636 | ||||||||
\(904\) | −0.513436 | + | 0.889297i | −0.0170766 | + | 0.0295776i | ||||
\(905\) | −3.06556 | − | 5.30970i | −0.101903 | − | 0.176501i | ||||
\(906\) | −0.931376 | − | 1.61319i | −0.0309429 | − | 0.0535947i | ||||
\(907\) | −0.319670 | −0.0106145 | −0.00530724 | − | 0.999986i | \(-0.501689\pi\) | ||||
−0.00530724 | + | 0.999986i | \(0.501689\pi\) | |||||||
\(908\) | −2.93066 | + | 5.07605i | −0.0972573 | + | 0.168455i | ||||
\(909\) | 3.85441 | − | 6.67603i | 0.127843 | − | 0.221430i | ||||
\(910\) | −6.28871 | + | 10.8924i | −0.208469 | + | 0.361079i | ||||
\(911\) | −11.2173 | − | 19.4289i | −0.371644 | − | 0.643707i | 0.618174 | − | 0.786041i | \(-0.287873\pi\) |
−0.989819 | + | 0.142334i | \(0.954539\pi\) | |||||||
\(912\) | 1.67270 | − | 2.89721i | 0.0553887 | − | 0.0959361i | ||||
\(913\) | −3.55483 | − | 6.15714i | −0.117648 | − | 0.203772i | ||||
\(914\) | 79.2978 | 2.62294 | ||||||||
\(915\) | 3.89653 | 0.128815 | ||||||||
\(916\) | −8.51150 | − | 14.7424i | −0.281228 | − | 0.487101i | ||||
\(917\) | 2.93249 | − | 5.07923i | 0.0968394 | − | 0.167731i | ||||
\(918\) | −0.963849 | − | 1.66944i | −0.0318118 | − | 0.0550996i | ||||
\(919\) | 10.7727 | − | 18.6589i | 0.355359 | − | 0.615500i | −0.631820 | − | 0.775115i | \(-0.717692\pi\) |
0.987179 | + | 0.159615i | \(0.0510252\pi\) | |||||||
\(920\) | 0.0108194 | − | 0.0187397i | 0.000356704 | − | 0.000617829i | ||||
\(921\) | 3.30181 | − | 5.71890i | 0.108798 | − | 0.188444i | ||||
\(922\) | 37.6558 | 1.24013 | ||||||||
\(923\) | −3.15749 | − | 5.46893i | −0.103930 | − | 0.180012i | ||||
\(924\) | 0.776097 | + | 1.34424i | 0.0255317 | + | 0.0442222i | ||||
\(925\) | −5.61283 | + | 9.72170i | −0.184549 | + | 0.319647i | ||||
\(926\) | −37.1615 | −1.22120 | ||||||||
\(927\) | −13.2280 | − | 22.9115i | −0.434463 | − | 0.752513i | ||||
\(928\) | −71.4063 | −2.34403 | ||||||||
\(929\) | −42.4431 | −1.39251 | −0.696256 | − | 0.717793i | \(-0.745152\pi\) | ||||
−0.696256 | + | 0.717793i | \(0.745152\pi\) | |||||||
\(930\) | 6.24418 | + | 6.54915i | 0.204755 | + | 0.214755i | ||||
\(931\) | −11.3232 | −0.371103 | ||||||||
\(932\) | 20.9626 | 0.686652 | ||||||||
\(933\) | 5.64190 | + | 9.77206i | 0.184707 | + | 0.319923i | ||||
\(934\) | −20.6193 | −0.674684 | ||||||||
\(935\) | −0.135241 | + | 0.234245i | −0.00442286 | + | 0.00766062i | ||||
\(936\) | −0.0808121 | − | 0.139971i | −0.00264143 | − | 0.00457508i | ||||
\(937\) | 17.8194 | + | 30.8641i | 0.582135 | + | 1.00829i | 0.995226 | + | 0.0975974i | \(0.0311157\pi\) |
−0.413091 | + | 0.910690i | \(0.635551\pi\) | |||||||
\(938\) | −1.77162 | −0.0578453 | ||||||||
\(939\) | −0.0881491 | + | 0.152679i | −0.00287664 | + | 0.00498248i | ||||
\(940\) | 18.3834 | − | 31.8410i | 0.599601 | − | 1.03854i | ||||
\(941\) | −2.34229 | + | 4.05696i | −0.0763564 | + | 0.132253i | −0.901675 | − | 0.432414i | \(-0.857662\pi\) |
0.825319 | + | 0.564667i | \(0.190995\pi\) | |||||||
\(942\) | −4.95638 | − | 8.58470i | −0.161488 | − | 0.279705i | ||||
\(943\) | 0.0658696 | − | 0.114089i | 0.00214501 | − | 0.00371526i | ||||
\(944\) | −14.5771 | − | 25.2482i | −0.474444 | − | 0.821760i | ||||
\(945\) | −17.0506 | −0.554657 | ||||||||
\(946\) | −7.68599 | −0.249893 | ||||||||
\(947\) | −6.95589 | − | 12.0480i | −0.226036 | − | 0.391506i | 0.730594 | − | 0.682812i | \(-0.239243\pi\) |
−0.956630 | + | 0.291307i | \(0.905910\pi\) | |||||||
\(948\) | 6.86051 | − | 11.8828i | 0.222819 | − | 0.385934i | ||||
\(949\) | 0.0149946 | + | 0.0259715i | 0.000486747 | + | 0.000843070i | ||||
\(950\) | 3.69735 | − | 6.40399i | 0.119958 | − | 0.207773i | ||||
\(951\) | −6.27005 | + | 10.8600i | −0.203320 | + | 0.352161i | ||||
\(952\) | 0.0374141 | − | 0.0648031i | 0.00121260 | − | 0.00210028i | ||||
\(953\) | −38.8395 | −1.25813 | −0.629067 | − | 0.777351i | \(-0.716563\pi\) | ||||
−0.629067 | + | 0.777351i | \(0.716563\pi\) | |||||||
\(954\) | −19.0736 | − | 33.0365i | −0.617531 | − | 1.06959i | ||||
\(955\) | −2.46075 | − | 4.26215i | −0.0796280 | − | 0.137920i | ||||
\(956\) | 17.1877 | − | 29.7701i | 0.555892 | − | 0.962832i | ||||
\(957\) | −1.86726 | −0.0603600 | ||||||||
\(958\) | 2.37413 | + | 4.11211i | 0.0767046 | + | 0.132856i | ||||
\(959\) | 11.3841 | 0.367613 | ||||||||
\(960\) | 6.66380 | 0.215073 | ||||||||
\(961\) | −1.47713 | + | 30.9648i | −0.0476494 | + | 0.998864i | ||||
\(962\) | 11.0244 | 0.355442 | ||||||||
\(963\) | 14.3034 | 0.460922 | ||||||||
\(964\) | 16.8917 | + | 29.2573i | 0.544046 | + | 0.942315i | ||||
\(965\) | −33.5349 | −1.07953 | ||||||||
\(966\) | 0.372635 | − | 0.645422i | 0.0119893 | − | 0.0207661i | ||||
\(967\) | −7.80511 | − | 13.5189i | −0.250995 | − | 0.434737i | 0.712805 | − | 0.701363i | \(-0.247425\pi\) |
−0.963800 | + | 0.266626i | \(0.914091\pi\) | |||||||
\(968\) | −0.314185 | − | 0.544184i | −0.0100983 | − | 0.0174907i | ||||
\(969\) | −0.299582 | −0.00962396 | ||||||||
\(970\) | 6.64330 | − | 11.5065i | 0.213303 | − | 0.369452i | ||||
\(971\) | −1.15154 | + | 1.99452i | −0.0369546 | + | 0.0640073i | −0.883911 | − | 0.467655i | \(-0.845099\pi\) |
0.846957 | + | 0.531662i | \(0.178432\pi\) | |||||||
\(972\) | 11.6513 | − | 20.1807i | 0.373716 | − | 0.647296i | ||||
\(973\) | −2.65904 | − | 4.60559i | −0.0852449 | − | 0.147648i | ||||
\(974\) | 14.6191 | − | 25.3211i | 0.468428 | − | 0.811341i | ||||
\(975\) | −0.481255 | − | 0.833558i | −0.0154125 | − | 0.0266952i | ||||
\(976\) | 18.9667 | 0.607110 | ||||||||
\(977\) | 42.1845 | 1.34960 | 0.674801 | − | 0.738000i | \(-0.264230\pi\) | ||||
0.674801 | + | 0.738000i | \(0.264230\pi\) | |||||||
\(978\) | −10.6154 | − | 18.3863i | −0.339442 | − | 0.587930i | ||||
\(979\) | 1.97778 | − | 3.42561i | 0.0632101 | − | 0.109483i | ||||
\(980\) | −10.9575 | − | 18.9789i | −0.350024 | − | 0.606259i | ||||
\(981\) | −14.2943 | + | 24.7584i | −0.456381 | + | 0.790475i | ||||
\(982\) | −10.8409 | + | 18.7771i | −0.345948 | + | 0.599200i | ||||
\(983\) | −6.88194 | + | 11.9199i | −0.219500 | + | 0.380185i | −0.954655 | − | 0.297714i | \(-0.903776\pi\) |
0.735155 | + | 0.677899i | \(0.237109\pi\) | |||||||
\(984\) | −0.0166830 | −0.000531834 | ||||||||
\(985\) | −12.1911 | − | 21.1157i | −0.388442 | − | 0.672802i | ||||
\(986\) | 3.15088 | + | 5.45749i | 0.100345 | + | 0.173802i | ||||
\(987\) | 9.04421 | − | 15.6650i | 0.287880 | − | 0.498623i | ||||
\(988\) | −3.65719 | −0.116351 | ||||||||
\(989\) | 0.929224 | + | 1.60946i | 0.0295476 | + | 0.0511779i | ||||
\(990\) | −4.27377 | −0.135829 | ||||||||
\(991\) | 20.0612 | 0.637264 | 0.318632 | − | 0.947878i | \(-0.396777\pi\) | ||||
0.318632 | + | 0.947878i | \(0.396777\pi\) | |||||||
\(992\) | 30.8412 | + | 32.3475i | 0.979208 | + | 1.02703i | ||||
\(993\) | 4.22365 | 0.134034 | ||||||||
\(994\) | 46.1957 | 1.46524 | ||||||||
\(995\) | 20.4526 | + | 35.4250i | 0.648392 | + | 1.12305i | ||||
\(996\) | 15.2404 | 0.482910 | ||||||||
\(997\) | −13.7721 | + | 23.8540i | −0.436166 | + | 0.755462i | −0.997390 | − | 0.0722019i | \(-0.976997\pi\) |
0.561224 | + | 0.827664i | \(0.310331\pi\) | |||||||
\(998\) | 22.1790 | + | 38.4151i | 0.702063 | + | 1.21601i | ||||
\(999\) | 7.47265 | + | 12.9430i | 0.236424 | + | 0.409499i |
(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 | 403.2.h.b.118.2 | ✓ | 34 | |
31.5 | even | 3 | inner | 403.2.h.b.222.2 | yes | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.h.b.118.2 | ✓ | 34 | 1.1 | even | 1 | trivial | |
403.2.h.b.222.2 | yes | 34 | 31.5 | even | 3 | inner |