Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [240,2,Mod(61,240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(240, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("240.61");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 240 = 2^{4} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 240.s (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.91640964851\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{18} - 4 x^{17} + 7 x^{16} + 16 x^{15} + 6 x^{14} - 36 x^{13} - 42 x^{12} + 40 x^{11} + \cdots + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 61.6 | ||
Root | \(-0.0861743 + 1.41159i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 240.61 |
Dual form | 240.2.s.c.181.6 |
$q$-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 \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(161\) | \(181\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0861743 | + | 1.41159i | −0.0609344 | + | 0.998142i | ||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | −1.98515 | − | 0.243285i | −0.992574 | − | 0.121642i | ||||
\(5\) | −0.707107 | + | 0.707107i | −0.316228 | + | 0.316228i | ||||
\(6\) | 1.05908 | − | 0.937207i | 0.432366 | − | 0.382613i | ||||
\(7\) | 2.76462i | 1.04493i | 0.852661 | + | 0.522464i | \(0.174987\pi\) | ||||
−0.852661 | + | 0.522464i | \(0.825013\pi\) | |||||||
\(8\) | 0.514486 | − | 2.78124i | 0.181898 | − | 0.983317i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | −0.937207 | − | 1.05908i | −0.296371 | − | 0.334909i | ||||
\(11\) | −3.51009 | + | 3.51009i | −1.05833 | + | 1.05833i | −0.0601437 | + | 0.998190i | \(0.519156\pi\) |
−0.998190 | + | 0.0601437i | \(0.980844\pi\) | |||||||
\(12\) | 1.23168 | + | 1.57574i | 0.355556 | + | 0.454877i | ||||
\(13\) | −4.55960 | − | 4.55960i | −1.26461 | − | 1.26461i | −0.948835 | − | 0.315771i | \(-0.897737\pi\) |
−0.315771 | − | 0.948835i | \(-0.602263\pi\) | |||||||
\(14\) | −3.90250 | − | 0.238239i | −1.04299 | − | 0.0636721i | ||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 3.88162 | + | 0.965913i | 0.970406 | + | 0.241478i | ||||
\(17\) | −5.00550 | −1.21401 | −0.607006 | − | 0.794697i | \(-0.707630\pi\) | ||||
−0.607006 | + | 0.794697i | \(0.707630\pi\) | |||||||
\(18\) | −1.41159 | − | 0.0861743i | −0.332714 | − | 0.0203115i | ||||
\(19\) | −0.812949 | − | 0.812949i | −0.186503 | − | 0.186503i | 0.607679 | − | 0.794183i | \(-0.292101\pi\) |
−0.794183 | + | 0.607679i | \(0.792101\pi\) | |||||||
\(20\) | 1.57574 | − | 1.23168i | 0.352346 | − | 0.275413i | ||||
\(21\) | 1.95488 | − | 1.95488i | 0.426590 | − | 0.426590i | ||||
\(22\) | −4.65232 | − | 5.25728i | −0.991878 | − | 1.12086i | ||||
\(23\) | 7.48205i | 1.56011i | 0.625708 | + | 0.780057i | \(0.284810\pi\) | ||||
−0.625708 | + | 0.780057i | \(0.715190\pi\) | |||||||
\(24\) | −2.33043 | + | 1.60284i | −0.475697 | + | 0.327178i | ||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | 6.82919 | − | 6.04335i | 1.33931 | − | 1.18520i | ||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0.672590 | − | 5.48818i | 0.127108 | − | 1.03717i | ||||
\(29\) | 6.03354 | + | 6.03354i | 1.12040 | + | 1.12040i | 0.991681 | + | 0.128719i | \(0.0410866\pi\) |
0.128719 | + | 0.991681i | \(0.458913\pi\) | |||||||
\(30\) | −0.0861743 | + | 1.41159i | −0.0157332 | + | 0.257719i | ||||
\(31\) | 7.58233 | 1.36183 | 0.680913 | − | 0.732364i | \(-0.261583\pi\) | ||||
0.680913 | + | 0.732364i | \(0.261583\pi\) | |||||||
\(32\) | −1.69796 | + | 5.39601i | −0.300161 | + | 0.953889i | ||||
\(33\) | 4.96402 | 0.864126 | ||||||||
\(34\) | 0.431345 | − | 7.06569i | 0.0739751 | − | 1.21176i | ||||
\(35\) | −1.95488 | − | 1.95488i | −0.330435 | − | 0.330435i | ||||
\(36\) | 0.243285 | − | 1.98515i | 0.0405475 | − | 0.330858i | ||||
\(37\) | 1.08674 | − | 1.08674i | 0.178659 | − | 0.178659i | −0.612112 | − | 0.790771i | \(-0.709680\pi\) |
0.790771 | + | 0.612112i | \(0.209680\pi\) | |||||||
\(38\) | 1.21760 | − | 1.07749i | 0.197521 | − | 0.174792i | ||||
\(39\) | 6.44825i | 1.03255i | ||||||||
\(40\) | 1.60284 | + | 2.33043i | 0.253431 | + | 0.368474i | ||||
\(41\) | − | 3.15671i | − | 0.492995i | −0.969143 | − | 0.246497i | \(-0.920720\pi\) | ||
0.969143 | − | 0.246497i | \(-0.0792797\pi\) | |||||||
\(42\) | 2.59102 | + | 2.92794i | 0.399803 | + | 0.451791i | ||||
\(43\) | −3.10932 | + | 3.10932i | −0.474166 | + | 0.474166i | −0.903260 | − | 0.429094i | \(-0.858833\pi\) |
0.429094 | + | 0.903260i | \(0.358833\pi\) | |||||||
\(44\) | 7.82201 | − | 6.11410i | 1.17921 | − | 0.921736i | ||||
\(45\) | −0.707107 | − | 0.707107i | −0.105409 | − | 0.105409i | ||||
\(46\) | −10.5616 | − | 0.644760i | −1.55722 | − | 0.0950647i | ||||
\(47\) | −2.76008 | −0.402599 | −0.201299 | − | 0.979530i | \(-0.564516\pi\) | ||||
−0.201299 | + | 0.979530i | \(0.564516\pi\) | |||||||
\(48\) | −2.06172 | − | 3.42773i | −0.297584 | − | 0.494750i | ||||
\(49\) | −0.643123 | −0.0918747 | ||||||||
\(50\) | 1.41159 | + | 0.0861743i | 0.199628 | + | 0.0121869i | ||||
\(51\) | 3.53942 | + | 3.53942i | 0.495618 | + | 0.495618i | ||||
\(52\) | 7.94221 | + | 10.1608i | 1.10139 | + | 1.40905i | ||||
\(53\) | 6.41096 | − | 6.41096i | 0.880613 | − | 0.880613i | −0.112983 | − | 0.993597i | \(-0.536041\pi\) |
0.993597 | + | 0.112983i | \(0.0360407\pi\) | |||||||
\(54\) | 0.937207 | + | 1.05908i | 0.127538 | + | 0.144122i | ||||
\(55\) | − | 4.96402i | − | 0.669349i | ||||||
\(56\) | 7.68908 | + | 1.42236i | 1.02750 | + | 0.190071i | ||||
\(57\) | 1.14968i | 0.152279i | ||||||||
\(58\) | −9.03679 | + | 7.99692i | −1.18659 | + | 1.05005i | ||||
\(59\) | −5.13756 | + | 5.13756i | −0.668854 | + | 0.668854i | −0.957451 | − | 0.288597i | \(-0.906811\pi\) |
0.288597 | + | 0.957451i | \(0.406811\pi\) | |||||||
\(60\) | −1.98515 | − | 0.243285i | −0.256282 | − | 0.0314079i | ||||
\(61\) | −2.49234 | − | 2.49234i | −0.319111 | − | 0.319111i | 0.529314 | − | 0.848426i | \(-0.322449\pi\) |
−0.848426 | + | 0.529314i | \(0.822449\pi\) | |||||||
\(62\) | −0.653402 | + | 10.7031i | −0.0829821 | + | 1.35930i | ||||
\(63\) | −2.76462 | −0.348309 | ||||||||
\(64\) | −7.47061 | − | 2.86182i | −0.933826 | − | 0.357728i | ||||
\(65\) | 6.44825 | 0.799807 | ||||||||
\(66\) | −0.427771 | + | 7.00714i | −0.0526550 | + | 0.862520i | ||||
\(67\) | −3.14625 | − | 3.14625i | −0.384376 | − | 0.384376i | 0.488300 | − | 0.872676i | \(-0.337617\pi\) |
−0.872676 | + | 0.488300i | \(0.837617\pi\) | |||||||
\(68\) | 9.93666 | + | 1.21776i | 1.20500 | + | 0.147675i | ||||
\(69\) | 5.29061 | − | 5.29061i | 0.636914 | − | 0.636914i | ||||
\(70\) | 2.92794 | − | 2.59102i | 0.349956 | − | 0.309686i | ||||
\(71\) | 3.50237i | 0.415655i | 0.978166 | + | 0.207827i | \(0.0666392\pi\) | ||||
−0.978166 | + | 0.207827i | \(0.933361\pi\) | |||||||
\(72\) | 2.78124 | + | 0.514486i | 0.327772 | + | 0.0606328i | ||||
\(73\) | 14.6145i | 1.71050i | 0.518217 | + | 0.855249i | \(0.326596\pi\) | ||||
−0.518217 | + | 0.855249i | \(0.673404\pi\) | |||||||
\(74\) | 1.44038 | + | 1.62767i | 0.167440 | + | 0.189213i | ||||
\(75\) | −0.707107 | + | 0.707107i | −0.0816497 | + | 0.0816497i | ||||
\(76\) | 1.41605 | + | 1.81160i | 0.162432 | + | 0.207805i | ||||
\(77\) | −9.70408 | − | 9.70408i | −1.10588 | − | 1.10588i | ||||
\(78\) | −9.10226 | − | 0.555674i | −1.03063 | − | 0.0629177i | ||||
\(79\) | 8.95325 | 1.00732 | 0.503660 | − | 0.863902i | \(-0.331987\pi\) | ||||
0.503660 | + | 0.863902i | \(0.331987\pi\) | |||||||
\(80\) | −3.42773 | + | 2.06172i | −0.383232 | + | 0.230507i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 4.45596 | + | 0.272027i | 0.492079 | + | 0.0300404i | ||||
\(83\) | −2.86293 | − | 2.86293i | −0.314247 | − | 0.314247i | 0.532305 | − | 0.846553i | \(-0.321326\pi\) |
−0.846553 | + | 0.532305i | \(0.821326\pi\) | |||||||
\(84\) | −4.35632 | + | 3.40514i | −0.475314 | + | 0.371531i | ||||
\(85\) | 3.53942 | − | 3.53942i | 0.383904 | − | 0.383904i | ||||
\(86\) | −4.12112 | − | 4.65701i | −0.444392 | − | 0.502178i | ||||
\(87\) | − | 8.53271i | − | 0.914803i | ||||||
\(88\) | 7.95653 | + | 11.5683i | 0.848169 | + | 1.23319i | ||||
\(89\) | 7.23560i | 0.766972i | 0.923547 | + | 0.383486i | \(0.125277\pi\) | ||||
−0.923547 | + | 0.383486i | \(0.874723\pi\) | |||||||
\(90\) | 1.05908 | − | 0.937207i | 0.111636 | − | 0.0987903i | ||||
\(91\) | 12.6056 | − | 12.6056i | 1.32142 | − | 1.32142i | ||||
\(92\) | 1.82027 | − | 14.8530i | 0.189776 | − | 1.54853i | ||||
\(93\) | −5.36151 | − | 5.36151i | −0.555963 | − | 0.555963i | ||||
\(94\) | 0.237848 | − | 3.89609i | 0.0245321 | − | 0.401851i | ||||
\(95\) | 1.14968 | 0.117955 | ||||||||
\(96\) | 5.01620 | − | 2.61491i | 0.511963 | − | 0.266883i | ||||
\(97\) | −8.24056 | −0.836702 | −0.418351 | − | 0.908285i | \(-0.637392\pi\) | ||||
−0.418351 | + | 0.908285i | \(0.637392\pi\) | |||||||
\(98\) | 0.0554207 | − | 0.907823i | 0.00559833 | − | 0.0917040i | ||||
\(99\) | −3.51009 | − | 3.51009i | −0.352778 | − | 0.352778i | ||||
\(100\) | −0.243285 | + | 1.98515i | −0.0243285 | + | 0.198515i | ||||
\(101\) | 1.07326 | − | 1.07326i | 0.106794 | − | 0.106794i | −0.651691 | − | 0.758485i | \(-0.725940\pi\) |
0.758485 | + | 0.651691i | \(0.225940\pi\) | |||||||
\(102\) | −5.30121 | + | 4.69119i | −0.524898 | + | 0.464497i | ||||
\(103\) | − | 1.66763i | − | 0.164316i | −0.996619 | − | 0.0821582i | \(-0.973819\pi\) | ||
0.996619 | − | 0.0821582i | \(-0.0261813\pi\) | |||||||
\(104\) | −15.0272 | + | 10.3355i | −1.47354 | + | 1.01348i | ||||
\(105\) | 2.76462i | 0.269799i | ||||||||
\(106\) | 8.49716 | + | 9.60208i | 0.825317 | + | 0.932637i | ||||
\(107\) | −6.08860 | + | 6.08860i | −0.588607 | + | 0.588607i | −0.937254 | − | 0.348647i | \(-0.886641\pi\) |
0.348647 | + | 0.937254i | \(0.386641\pi\) | |||||||
\(108\) | −1.57574 | + | 1.23168i | −0.151626 | + | 0.118519i | ||||
\(109\) | 2.92136 | + | 2.92136i | 0.279816 | + | 0.279816i | 0.833035 | − | 0.553220i | \(-0.186601\pi\) |
−0.553220 | + | 0.833035i | \(0.686601\pi\) | |||||||
\(110\) | 7.00714 | + | 0.427771i | 0.668105 | + | 0.0407864i | ||||
\(111\) | −1.53688 | −0.145874 | ||||||||
\(112\) | −2.67038 | + | 10.7312i | −0.252327 | + | 1.01400i | ||||
\(113\) | −2.84395 | −0.267536 | −0.133768 | − | 0.991013i | \(-0.542708\pi\) | ||||
−0.133768 | + | 0.991013i | \(0.542708\pi\) | |||||||
\(114\) | −1.62288 | − | 0.0990732i | −0.151996 | − | 0.00927905i | ||||
\(115\) | −5.29061 | − | 5.29061i | −0.493352 | − | 0.493352i | ||||
\(116\) | −10.5096 | − | 13.4453i | −0.975792 | − | 1.24837i | ||||
\(117\) | 4.55960 | − | 4.55960i | 0.421535 | − | 0.421535i | ||||
\(118\) | −6.80938 | − | 7.69483i | −0.626855 | − | 0.708367i | ||||
\(119\) | − | 13.8383i | − | 1.26856i | ||||||
\(120\) | 0.514486 | − | 2.78124i | 0.0469659 | − | 0.253891i | ||||
\(121\) | − | 13.6415i | − | 1.24014i | ||||||
\(122\) | 3.73293 | − | 3.30337i | 0.337963 | − | 0.299073i | ||||
\(123\) | −2.23213 | + | 2.23213i | −0.201264 | + | 0.201264i | ||||
\(124\) | −15.0520 | − | 1.84466i | −1.35171 | − | 0.165656i | ||||
\(125\) | 0.707107 | + | 0.707107i | 0.0632456 | + | 0.0632456i | ||||
\(126\) | 0.238239 | − | 3.90250i | 0.0212240 | − | 0.347662i | ||||
\(127\) | −6.61073 | −0.586607 | −0.293304 | − | 0.956019i | \(-0.594755\pi\) | ||||
−0.293304 | + | 0.956019i | \(0.594755\pi\) | |||||||
\(128\) | 4.68348 | − | 10.2988i | 0.413965 | − | 0.910293i | ||||
\(129\) | 4.39724 | 0.387155 | ||||||||
\(130\) | −0.555674 | + | 9.10226i | −0.0487358 | + | 0.798321i | ||||
\(131\) | −6.70125 | − | 6.70125i | −0.585491 | − | 0.585491i | 0.350916 | − | 0.936407i | \(-0.385870\pi\) |
−0.936407 | + | 0.350916i | \(0.885870\pi\) | |||||||
\(132\) | −9.85432 | − | 1.20767i | −0.857709 | − | 0.105114i | ||||
\(133\) | 2.24749 | − | 2.24749i | 0.194883 | − | 0.194883i | ||||
\(134\) | 4.71233 | − | 4.17008i | 0.407083 | − | 0.360240i | ||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | −2.57526 | + | 13.9215i | −0.220827 | + | 1.19376i | ||||
\(137\) | − | 14.3908i | − | 1.22949i | −0.788725 | − | 0.614746i | \(-0.789258\pi\) | ||
0.788725 | − | 0.614746i | \(-0.210742\pi\) | |||||||
\(138\) | 7.01223 | + | 7.92406i | 0.596921 | + | 0.674541i | ||||
\(139\) | 0.292743 | − | 0.292743i | 0.0248302 | − | 0.0248302i | −0.694583 | − | 0.719413i | \(-0.744411\pi\) |
0.719413 | + | 0.694583i | \(0.244411\pi\) | |||||||
\(140\) | 3.40514 | + | 4.35632i | 0.287787 | + | 0.368176i | ||||
\(141\) | 1.95167 | + | 1.95167i | 0.164360 | + | 0.164360i | ||||
\(142\) | −4.94389 | − | 0.301814i | −0.414882 | − | 0.0253277i | ||||
\(143\) | 32.0093 | 2.67675 | ||||||||
\(144\) | −0.965913 | + | 3.88162i | −0.0804927 | + | 0.323469i | ||||
\(145\) | −8.53271 | −0.708603 | ||||||||
\(146\) | −20.6296 | − | 1.25940i | −1.70732 | − | 0.104228i | ||||
\(147\) | 0.454757 | + | 0.454757i | 0.0375077 | + | 0.0375077i | ||||
\(148\) | −2.42172 | + | 1.89295i | −0.199065 | + | 0.155600i | ||||
\(149\) | −10.9363 | + | 10.9363i | −0.895934 | + | 0.895934i | −0.995074 | − | 0.0991393i | \(-0.968391\pi\) |
0.0991393 | + | 0.995074i | \(0.468391\pi\) | |||||||
\(150\) | −0.937207 | − | 1.05908i | −0.0765227 | − | 0.0864732i | ||||
\(151\) | 13.5225i | 1.10045i | 0.835017 | + | 0.550223i | \(0.185457\pi\) | ||||
−0.835017 | + | 0.550223i | \(0.814543\pi\) | |||||||
\(152\) | −2.67926 | + | 1.84276i | −0.217317 | + | 0.149467i | ||||
\(153\) | − | 5.00550i | − | 0.404671i | ||||||
\(154\) | 14.5344 | − | 12.8619i | 1.17121 | − | 1.03644i | ||||
\(155\) | −5.36151 | + | 5.36151i | −0.430647 | + | 0.430647i | ||||
\(156\) | 1.56876 | − | 12.8007i | 0.125601 | − | 1.02488i | ||||
\(157\) | 2.76487 | + | 2.76487i | 0.220661 | + | 0.220661i | 0.808777 | − | 0.588116i | \(-0.200130\pi\) |
−0.588116 | + | 0.808777i | \(0.700130\pi\) | |||||||
\(158\) | −0.771540 | + | 12.6383i | −0.0613804 | + | 1.00545i | ||||
\(159\) | −9.06647 | −0.719018 | ||||||||
\(160\) | −2.61491 | − | 5.01620i | −0.206727 | − | 0.396565i | ||||
\(161\) | −20.6850 | −1.63021 | ||||||||
\(162\) | 0.0861743 | − | 1.41159i | 0.00677049 | − | 0.110905i | ||||
\(163\) | 15.4942 | + | 15.4942i | 1.21360 | + | 1.21360i | 0.969834 | + | 0.243767i | \(0.0783834\pi\) |
0.243767 | + | 0.969834i | \(0.421617\pi\) | |||||||
\(164\) | −0.767979 | + | 6.26653i | −0.0599691 | + | 0.489334i | ||||
\(165\) | −3.51009 | + | 3.51009i | −0.273261 | + | 0.273261i | ||||
\(166\) | 4.28798 | − | 3.79456i | 0.332812 | − | 0.294515i | ||||
\(167\) | − | 1.76898i | − | 0.136888i | −0.997655 | − | 0.0684439i | \(-0.978197\pi\) | ||
0.997655 | − | 0.0684439i | \(-0.0218034\pi\) | |||||||
\(168\) | −4.43124 | − | 6.44276i | −0.341877 | − | 0.497069i | ||||
\(169\) | 28.5800i | 2.19846i | ||||||||
\(170\) | 4.69119 | + | 5.30121i | 0.359798 | + | 0.406584i | ||||
\(171\) | 0.812949 | − | 0.812949i | 0.0621678 | − | 0.0621678i | ||||
\(172\) | 6.92890 | − | 5.41600i | 0.528324 | − | 0.412966i | ||||
\(173\) | 4.01351 | + | 4.01351i | 0.305142 | + | 0.305142i | 0.843022 | − | 0.537880i | \(-0.180775\pi\) |
−0.537880 | + | 0.843022i | \(0.680775\pi\) | |||||||
\(174\) | 12.0447 | + | 0.735301i | 0.913103 | + | 0.0557430i | ||||
\(175\) | 2.76462 | 0.208986 | ||||||||
\(176\) | −17.0153 | + | 10.2344i | −1.28258 | + | 0.771449i | ||||
\(177\) | 7.26561 | 0.546117 | ||||||||
\(178\) | −10.2137 | − | 0.623523i | −0.765547 | − | 0.0467350i | ||||
\(179\) | −5.31340 | − | 5.31340i | −0.397142 | − | 0.397142i | 0.480082 | − | 0.877224i | \(-0.340607\pi\) |
−0.877224 | + | 0.480082i | \(0.840607\pi\) | |||||||
\(180\) | 1.23168 | + | 1.57574i | 0.0918042 | + | 0.117449i | ||||
\(181\) | −8.74918 | + | 8.74918i | −0.650321 | + | 0.650321i | −0.953070 | − | 0.302749i | \(-0.902096\pi\) |
0.302749 | + | 0.953070i | \(0.402096\pi\) | |||||||
\(182\) | 16.7076 | + | 18.8801i | 1.23845 | + | 1.39949i | ||||
\(183\) | 3.52470i | 0.260553i | ||||||||
\(184\) | 20.8094 | + | 3.84941i | 1.53409 | + | 0.283782i | ||||
\(185\) | 1.53688i | 0.112994i | ||||||||
\(186\) | 8.03026 | − | 7.10621i | 0.588807 | − | 0.521053i | ||||
\(187\) | 17.5698 | − | 17.5698i | 1.28483 | − | 1.28483i | ||||
\(188\) | 5.47917 | + | 0.671485i | 0.399609 | + | 0.0489731i | ||||
\(189\) | 1.95488 | + | 1.95488i | 0.142197 | + | 0.142197i | ||||
\(190\) | −0.0990732 | + | 1.62288i | −0.00718752 | + | 0.117736i | ||||
\(191\) | −4.03787 | −0.292170 | −0.146085 | − | 0.989272i | \(-0.546667\pi\) | ||||
−0.146085 | + | 0.989272i | \(0.546667\pi\) | |||||||
\(192\) | 3.25891 | + | 7.30613i | 0.235191 | + | 0.527275i | ||||
\(193\) | 0.437111 | 0.0314639 | 0.0157320 | − | 0.999876i | \(-0.494992\pi\) | ||||
0.0157320 | + | 0.999876i | \(0.494992\pi\) | |||||||
\(194\) | 0.710124 | − | 11.6323i | 0.0509840 | − | 0.835147i | ||||
\(195\) | −4.55960 | − | 4.55960i | −0.326520 | − | 0.326520i | ||||
\(196\) | 1.27669 | + | 0.156462i | 0.0911924 | + | 0.0111759i | ||||
\(197\) | 11.6836 | − | 11.6836i | 0.832424 | − | 0.832424i | −0.155424 | − | 0.987848i | \(-0.549674\pi\) |
0.987848 | + | 0.155424i | \(0.0496743\pi\) | |||||||
\(198\) | 5.25728 | − | 4.65232i | 0.373619 | − | 0.330626i | ||||
\(199\) | − | 15.7412i | − | 1.11587i | −0.829886 | − | 0.557933i | \(-0.811595\pi\) | ||
0.829886 | − | 0.557933i | \(-0.188405\pi\) | |||||||
\(200\) | −2.78124 | − | 0.514486i | −0.196663 | − | 0.0363797i | ||||
\(201\) | 4.44947i | 0.313842i | ||||||||
\(202\) | 1.42251 | + | 1.60749i | 0.100088 | + | 0.113103i | ||||
\(203\) | −16.6804 | + | 16.6804i | −1.17074 | + | 1.17074i | ||||
\(204\) | −6.16519 | − | 7.88737i | −0.431650 | − | 0.552226i | ||||
\(205\) | 2.23213 | + | 2.23213i | 0.155899 | + | 0.155899i | ||||
\(206\) | 2.35400 | + | 0.143707i | 0.164011 | + | 0.0100125i | ||||
\(207\) | −7.48205 | −0.520038 | ||||||||
\(208\) | −13.2945 | − | 22.1029i | −0.921807 | − | 1.53256i | ||||
\(209\) | 5.70706 | 0.394765 | ||||||||
\(210\) | −3.90250 | − | 0.238239i | −0.269298 | − | 0.0164401i | ||||
\(211\) | −2.13765 | − | 2.13765i | −0.147162 | − | 0.147162i | 0.629687 | − | 0.776849i | \(-0.283183\pi\) |
−0.776849 | + | 0.629687i | \(0.783183\pi\) | |||||||
\(212\) | −14.2864 | + | 11.1670i | −0.981194 | + | 0.766954i | ||||
\(213\) | 2.47655 | − | 2.47655i | 0.169690 | − | 0.169690i | ||||
\(214\) | −8.06989 | − | 9.11926i | −0.551647 | − | 0.623379i | ||||
\(215\) | − | 4.39724i | − | 0.299889i | ||||||
\(216\) | −1.60284 | − | 2.33043i | −0.109059 | − | 0.158566i | ||||
\(217\) | 20.9622i | 1.42301i | ||||||||
\(218\) | −4.37550 | + | 3.87201i | −0.296346 | + | 0.262245i | ||||
\(219\) | 10.3340 | − | 10.3340i | 0.698308 | − | 0.698308i | ||||
\(220\) | −1.20767 | + | 9.85432i | −0.0814212 | + | 0.664378i | ||||
\(221\) | 22.8231 | + | 22.8231i | 1.53525 | + | 1.53525i | ||||
\(222\) | 0.132440 | − | 2.16944i | 0.00888877 | − | 0.145603i | ||||
\(223\) | 13.4768 | 0.902476 | 0.451238 | − | 0.892404i | \(-0.350983\pi\) | ||||
0.451238 | + | 0.892404i | \(0.350983\pi\) | |||||||
\(224\) | −14.9179 | − | 4.69423i | −0.996745 | − | 0.313646i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0.245075 | − | 4.01447i | 0.0163021 | − | 0.267039i | ||||
\(227\) | −2.70567 | − | 2.70567i | −0.179582 | − | 0.179582i | 0.611592 | − | 0.791174i | \(-0.290530\pi\) |
−0.791174 | + | 0.611592i | \(0.790530\pi\) | |||||||
\(228\) | 0.279701 | − | 2.28229i | 0.0185236 | − | 0.151148i | ||||
\(229\) | 0.507051 | − | 0.507051i | 0.0335069 | − | 0.0335069i | −0.690155 | − | 0.723662i | \(-0.742458\pi\) |
0.723662 | + | 0.690155i | \(0.242458\pi\) | |||||||
\(230\) | 7.92406 | − | 7.01223i | 0.522497 | − | 0.462373i | ||||
\(231\) | 13.7236i | 0.902949i | ||||||||
\(232\) | 19.8849 | − | 13.6766i | 1.30551 | − | 0.897910i | ||||
\(233\) | 8.16109i | 0.534651i | 0.963606 | + | 0.267325i | \(0.0861399\pi\) | ||||
−0.963606 | + | 0.267325i | \(0.913860\pi\) | |||||||
\(234\) | 6.04335 | + | 6.82919i | 0.395066 | + | 0.446438i | ||||
\(235\) | 1.95167 | − | 1.95167i | 0.127313 | − | 0.127313i | ||||
\(236\) | 11.4487 | − | 8.94893i | 0.745248 | − | 0.582526i | ||||
\(237\) | −6.33090 | − | 6.33090i | −0.411236 | − | 0.411236i | ||||
\(238\) | 19.5340 | + | 1.19251i | 1.26620 | + | 0.0772987i | ||||
\(239\) | −2.46397 | −0.159381 | −0.0796905 | − | 0.996820i | \(-0.525393\pi\) | ||||
−0.0796905 | + | 0.996820i | \(0.525393\pi\) | |||||||
\(240\) | 3.88162 | + | 0.965913i | 0.250558 | + | 0.0623494i | ||||
\(241\) | 7.38073 | 0.475434 | 0.237717 | − | 0.971334i | \(-0.423601\pi\) | ||||
0.237717 | + | 0.971334i | \(0.423601\pi\) | |||||||
\(242\) | 19.2562 | + | 1.17555i | 1.23783 | + | 0.0755672i | ||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 4.34131 | + | 5.55401i | 0.277924 | + | 0.355559i | ||||
\(245\) | 0.454757 | − | 0.454757i | 0.0290533 | − | 0.0290533i | ||||
\(246\) | −2.95849 | − | 3.34319i | −0.188626 | − | 0.213154i | ||||
\(247\) | 7.41345i | 0.471707i | ||||||||
\(248\) | 3.90100 | − | 21.0883i | 0.247714 | − | 1.33911i | ||||
\(249\) | 4.04880i | 0.256582i | ||||||||
\(250\) | −1.05908 | + | 0.937207i | −0.0669819 | + | 0.0592742i | ||||
\(251\) | −5.15322 | + | 5.15322i | −0.325268 | + | 0.325268i | −0.850784 | − | 0.525516i | \(-0.823872\pi\) |
0.525516 | + | 0.850784i | \(0.323872\pi\) | |||||||
\(252\) | 5.48818 | + | 0.672590i | 0.345723 | + | 0.0423692i | ||||
\(253\) | −26.2627 | − | 26.2627i | −1.65112 | − | 1.65112i | ||||
\(254\) | 0.569675 | − | 9.33161i | 0.0357446 | − | 0.585517i | ||||
\(255\) | −5.00550 | −0.313457 | ||||||||
\(256\) | 14.1340 | + | 7.49862i | 0.883377 | + | 0.468664i | ||||
\(257\) | 9.84129 | 0.613883 | 0.306942 | − | 0.951728i | \(-0.400694\pi\) | ||||
0.306942 | + | 0.951728i | \(0.400694\pi\) | |||||||
\(258\) | −0.378929 | + | 6.20708i | −0.0235911 | + | 0.386436i | ||||
\(259\) | 3.00442 | + | 3.00442i | 0.186686 | + | 0.186686i | ||||
\(260\) | −12.8007 | − | 1.56876i | −0.793868 | − | 0.0972905i | ||||
\(261\) | −6.03354 | + | 6.03354i | −0.373467 | + | 0.373467i | ||||
\(262\) | 10.0369 | − | 8.88192i | 0.620080 | − | 0.548727i | ||||
\(263\) | − | 27.5027i | − | 1.69589i | −0.530086 | − | 0.847944i | \(-0.677840\pi\) | ||
0.530086 | − | 0.847944i | \(-0.322160\pi\) | |||||||
\(264\) | 2.55392 | − | 13.8061i | 0.157183 | − | 0.849710i | ||||
\(265\) | 9.06647i | 0.556949i | ||||||||
\(266\) | 2.97886 | + | 3.36621i | 0.182645 | + | 0.206395i | ||||
\(267\) | 5.11634 | − | 5.11634i | 0.313115 | − | 0.313115i | ||||
\(268\) | 5.48034 | + | 7.01121i | 0.334765 | + | 0.428278i | ||||
\(269\) | 7.35280 | + | 7.35280i | 0.448308 | + | 0.448308i | 0.894792 | − | 0.446484i | \(-0.147324\pi\) |
−0.446484 | + | 0.894792i | \(0.647324\pi\) | |||||||
\(270\) | −1.41159 | − | 0.0861743i | −0.0859064 | − | 0.00524440i | ||||
\(271\) | −16.1826 | −0.983023 | −0.491511 | − | 0.870871i | \(-0.663555\pi\) | ||||
−0.491511 | + | 0.870871i | \(0.663555\pi\) | |||||||
\(272\) | −19.4295 | − | 4.83488i | −1.17808 | − | 0.293157i | ||||
\(273\) | −17.8270 | −1.07894 | ||||||||
\(274\) | 20.3139 | + | 1.24012i | 1.22721 | + | 0.0749185i | ||||
\(275\) | 3.51009 | + | 3.51009i | 0.211667 | + | 0.211667i | ||||
\(276\) | −11.7898 | + | 9.21551i | −0.709660 | + | 0.554709i | ||||
\(277\) | −19.3725 | + | 19.3725i | −1.16398 | + | 1.16398i | −0.180381 | + | 0.983597i | \(0.557733\pi\) |
−0.983597 | + | 0.180381i | \(0.942267\pi\) | |||||||
\(278\) | 0.388005 | + | 0.438459i | 0.0232710 | + | 0.0262970i | ||||
\(279\) | 7.58233i | 0.453942i | ||||||||
\(280\) | −6.44276 | + | 4.43124i | −0.385028 | + | 0.264817i | ||||
\(281\) | − | 18.1786i | − | 1.08445i | −0.840235 | − | 0.542223i | \(-0.817583\pi\) | ||
0.840235 | − | 0.542223i | \(-0.182417\pi\) | |||||||
\(282\) | −2.92313 | + | 2.58677i | −0.174070 | + | 0.154040i | ||||
\(283\) | −7.74925 | + | 7.74925i | −0.460645 | + | 0.460645i | −0.898867 | − | 0.438222i | \(-0.855609\pi\) |
0.438222 | + | 0.898867i | \(0.355609\pi\) | |||||||
\(284\) | 0.852073 | − | 6.95272i | 0.0505612 | − | 0.412568i | ||||
\(285\) | −0.812949 | − | 0.812949i | −0.0481549 | − | 0.0481549i | ||||
\(286\) | −2.75838 | + | 45.1838i | −0.163106 | + | 2.67178i | ||||
\(287\) | 8.72709 | 0.515144 | ||||||||
\(288\) | −5.39601 | − | 1.69796i | −0.317963 | − | 0.100054i | ||||
\(289\) | 8.05503 | 0.473825 | ||||||||
\(290\) | 0.735301 | − | 12.0447i | 0.0431783 | − | 0.707287i | ||||
\(291\) | 5.82695 | + | 5.82695i | 0.341582 | + | 0.341582i | ||||
\(292\) | 3.55549 | − | 29.0120i | 0.208069 | − | 1.69780i | ||||
\(293\) | −1.24572 | + | 1.24572i | −0.0727760 | + | 0.0727760i | −0.742558 | − | 0.669782i | \(-0.766388\pi\) |
0.669782 | + | 0.742558i | \(0.266388\pi\) | |||||||
\(294\) | −0.681116 | + | 0.602739i | −0.0397235 | + | 0.0351525i | ||||
\(295\) | − | 7.26561i | − | 0.423020i | ||||||
\(296\) | −2.46337 | − | 3.58160i | −0.143181 | − | 0.208176i | ||||
\(297\) | 4.96402i | 0.288042i | ||||||||
\(298\) | −14.4951 | − | 16.3799i | −0.839676 | − | 0.948863i | ||||
\(299\) | 34.1152 | − | 34.1152i | 1.97293 | − | 1.97293i | ||||
\(300\) | 1.57574 | − | 1.23168i | 0.0909754 | − | 0.0711113i | ||||
\(301\) | −8.59608 | − | 8.59608i | −0.495470 | − | 0.495470i | ||||
\(302\) | −19.0882 | − | 1.16529i | −1.09840 | − | 0.0670551i | ||||
\(303\) | −1.51782 | −0.0871966 | ||||||||
\(304\) | −2.37033 | − | 3.94080i | −0.135947 | − | 0.226020i | ||||
\(305\) | 3.52470 | 0.201824 | ||||||||
\(306\) | 7.06569 | + | 0.431345i | 0.403919 | + | 0.0246584i | ||||
\(307\) | 13.5042 | + | 13.5042i | 0.770727 | + | 0.770727i | 0.978234 | − | 0.207506i | \(-0.0665348\pi\) |
−0.207506 | + | 0.978234i | \(0.566535\pi\) | |||||||
\(308\) | 16.9032 | + | 21.6249i | 0.963148 | + | 1.23219i | ||||
\(309\) | −1.17919 | + | 1.17919i | −0.0670819 | + | 0.0670819i | ||||
\(310\) | −7.10621 | − | 8.03026i | −0.403606 | − | 0.456088i | ||||
\(311\) | 11.9549i | 0.677901i | 0.940804 | + | 0.338951i | \(0.110072\pi\) | ||||
−0.940804 | + | 0.338951i | \(0.889928\pi\) | |||||||
\(312\) | 17.9341 | + | 3.31754i | 1.01532 | + | 0.187819i | ||||
\(313\) | − | 15.2385i | − | 0.861333i | −0.902511 | − | 0.430667i | \(-0.858279\pi\) | ||
0.902511 | − | 0.430667i | \(-0.141721\pi\) | |||||||
\(314\) | −4.14111 | + | 3.66459i | −0.233697 | + | 0.206805i | ||||
\(315\) | 1.95488 | − | 1.95488i | 0.110145 | − | 0.110145i | ||||
\(316\) | −17.7735 | − | 2.17819i | −0.999839 | − | 0.122533i | ||||
\(317\) | 22.4062 | + | 22.4062i | 1.25846 | + | 1.25846i | 0.951830 | + | 0.306625i | \(0.0991998\pi\) |
0.306625 | + | 0.951830i | \(0.400800\pi\) | |||||||
\(318\) | 0.781297 | − | 12.7981i | 0.0438129 | − | 0.717682i | ||||
\(319\) | −42.3566 | −2.37151 | ||||||||
\(320\) | 7.30613 | − | 3.25891i | 0.408425 | − | 0.182178i | ||||
\(321\) | 8.61058 | 0.480595 | ||||||||
\(322\) | 1.78252 | − | 29.1987i | 0.0993358 | − | 1.62718i | ||||
\(323\) | 4.06922 | + | 4.06922i | 0.226417 | + | 0.226417i | ||||
\(324\) | 1.98515 | + | 0.243285i | 0.110286 | + | 0.0135158i | ||||
\(325\) | −4.55960 | + | 4.55960i | −0.252921 | + | 0.252921i | ||||
\(326\) | −23.2066 | + | 20.5362i | −1.28530 | + | 1.13740i | ||||
\(327\) | − | 4.13143i | − | 0.228469i | ||||||
\(328\) | −8.77956 | − | 1.62408i | −0.484770 | − | 0.0896749i | ||||
\(329\) | − | 7.63057i | − | 0.420687i | ||||||
\(330\) | −4.65232 | − | 5.25728i | −0.256102 | − | 0.289404i | ||||
\(331\) | 8.11650 | − | 8.11650i | 0.446123 | − | 0.446123i | −0.447940 | − | 0.894063i | \(-0.647842\pi\) |
0.894063 | + | 0.447940i | \(0.147842\pi\) | |||||||
\(332\) | 4.98683 | + | 6.37985i | 0.273688 | + | 0.350140i | ||||
\(333\) | 1.08674 | + | 1.08674i | 0.0595529 | + | 0.0595529i | ||||
\(334\) | 2.49707 | + | 0.152441i | 0.136633 | + | 0.00834118i | ||||
\(335\) | 4.44947 | 0.243101 | ||||||||
\(336\) | 9.47636 | − | 5.69987i | 0.516978 | − | 0.310953i | ||||
\(337\) | −19.1995 | −1.04587 | −0.522933 | − | 0.852374i | \(-0.675162\pi\) | ||||
−0.522933 | + | 0.852374i | \(0.675162\pi\) | |||||||
\(338\) | −40.3431 | − | 2.46286i | −2.19437 | − | 0.133962i | ||||
\(339\) | 2.01097 | + | 2.01097i | 0.109221 | + | 0.109221i | ||||
\(340\) | −7.88737 | + | 6.16519i | −0.427752 | + | 0.334354i | ||||
\(341\) | −26.6147 | + | 26.6147i | −1.44127 | + | 1.44127i | ||||
\(342\) | 1.07749 | + | 1.21760i | 0.0582641 | + | 0.0658404i | ||||
\(343\) | 17.5743i | 0.948926i | ||||||||
\(344\) | 7.04806 | + | 10.2475i | 0.380006 | + | 0.552506i | ||||
\(345\) | 7.48205i | 0.402820i | ||||||||
\(346\) | −6.01128 | + | 5.31956i | −0.323169 | + | 0.285981i | ||||
\(347\) | −3.64968 | + | 3.64968i | −0.195925 | + | 0.195925i | −0.798251 | − | 0.602325i | \(-0.794241\pi\) |
0.602325 | + | 0.798251i | \(0.294241\pi\) | |||||||
\(348\) | −2.07588 | + | 16.9387i | −0.111279 | + | 0.908010i | ||||
\(349\) | 16.7180 | + | 16.7180i | 0.894896 | + | 0.894896i | 0.994979 | − | 0.100083i | \(-0.0319107\pi\) |
−0.100083 | + | 0.994979i | \(0.531911\pi\) | |||||||
\(350\) | −0.238239 | + | 3.90250i | −0.0127344 | + | 0.208597i | ||||
\(351\) | −6.44825 | −0.344182 | ||||||||
\(352\) | −12.9805 | − | 24.9005i | −0.691862 | − | 1.32720i | ||||
\(353\) | 9.42887 | 0.501848 | 0.250924 | − | 0.968007i | \(-0.419266\pi\) | ||||
0.250924 | + | 0.968007i | \(0.419266\pi\) | |||||||
\(354\) | −0.626109 | + | 10.2560i | −0.0332773 | + | 0.545102i | ||||
\(355\) | −2.47655 | − | 2.47655i | −0.131442 | − | 0.131442i | ||||
\(356\) | 1.76031 | − | 14.3637i | 0.0932963 | − | 0.761276i | ||||
\(357\) | −9.78516 | + | 9.78516i | −0.517886 | + | 0.517886i | ||||
\(358\) | 7.95820 | − | 7.04244i | 0.420604 | − | 0.372204i | ||||
\(359\) | − | 1.12135i | − | 0.0591826i | −0.999562 | − | 0.0295913i | \(-0.990579\pi\) | ||
0.999562 | − | 0.0295913i | \(-0.00942059\pi\) | |||||||
\(360\) | −2.33043 | + | 1.60284i | −0.122825 | + | 0.0844770i | ||||
\(361\) | − | 17.6782i | − | 0.930433i | ||||||
\(362\) | −11.5963 | − | 13.1042i | −0.609486 | − | 0.688740i | ||||
\(363\) | −9.64602 | + | 9.64602i | −0.506285 | + | 0.506285i | ||||
\(364\) | −28.0907 | + | 21.9572i | −1.47235 | + | 1.15087i | ||||
\(365\) | −10.3340 | − | 10.3340i | −0.540907 | − | 0.540907i | ||||
\(366\) | −4.97541 | − | 0.303739i | −0.260069 | − | 0.0158767i | ||||
\(367\) | −7.22666 | −0.377228 | −0.188614 | − | 0.982051i | \(-0.560400\pi\) | ||||
−0.188614 | + | 0.982051i | \(0.560400\pi\) | |||||||
\(368\) | −7.22701 | + | 29.0425i | −0.376734 | + | 1.51395i | ||||
\(369\) | 3.15671 | 0.164332 | ||||||||
\(370\) | −2.16944 | − | 0.132440i | −0.112784 | − | 0.00688521i | ||||
\(371\) | 17.7239 | + | 17.7239i | 0.920178 | + | 0.920178i | ||||
\(372\) | 9.33902 | + | 11.9478i | 0.484206 | + | 0.619463i | ||||
\(373\) | −8.83590 | + | 8.83590i | −0.457506 | + | 0.457506i | −0.897836 | − | 0.440330i | \(-0.854861\pi\) |
0.440330 | + | 0.897836i | \(0.354861\pi\) | |||||||
\(374\) | 23.2872 | + | 26.3153i | 1.20415 | + | 1.36073i | ||||
\(375\) | − | 1.00000i | − | 0.0516398i | ||||||
\(376\) | −1.42002 | + | 7.67645i | −0.0732321 | + | 0.395883i | ||||
\(377\) | − | 55.0211i | − | 2.83373i | ||||||
\(378\) | −2.92794 | + | 2.59102i | −0.150597 | + | 0.133268i | ||||
\(379\) | −26.2339 | + | 26.2339i | −1.34754 | + | 1.34754i | −0.459223 | + | 0.888321i | \(0.651872\pi\) |
−0.888321 | + | 0.459223i | \(0.848128\pi\) | |||||||
\(380\) | −2.28229 | − | 0.279701i | −0.117079 | − | 0.0143483i | ||||
\(381\) | 4.67449 | + | 4.67449i | 0.239481 | + | 0.239481i | ||||
\(382\) | 0.347961 | − | 5.69980i | 0.0178032 | − | 0.291627i | ||||
\(383\) | 14.3557 | 0.733544 | 0.366772 | − | 0.930311i | \(-0.380463\pi\) | ||||
0.366772 | + | 0.930311i | \(0.380463\pi\) | |||||||
\(384\) | −10.5941 | + | 3.97062i | −0.540626 | + | 0.202625i | ||||
\(385\) | 13.7236 | 0.699421 | ||||||||
\(386\) | −0.0376677 | + | 0.617019i | −0.00191724 | + | 0.0314054i | ||||
\(387\) | −3.10932 | − | 3.10932i | −0.158055 | − | 0.158055i | ||||
\(388\) | 16.3587 | + | 2.00480i | 0.830489 | + | 0.101778i | ||||
\(389\) | −1.07721 | + | 1.07721i | −0.0546168 | + | 0.0546168i | −0.733888 | − | 0.679271i | \(-0.762296\pi\) |
0.679271 | + | 0.733888i | \(0.262296\pi\) | |||||||
\(390\) | 6.82919 | − | 6.04335i | 0.345810 | − | 0.306017i | ||||
\(391\) | − | 37.4514i | − | 1.89400i | ||||||
\(392\) | −0.330878 | + | 1.78868i | −0.0167119 | + | 0.0903420i | ||||
\(393\) | 9.47700i | 0.478052i | ||||||||
\(394\) | 15.4856 | + | 17.4993i | 0.780154 | + | 0.881601i | ||||
\(395\) | −6.33090 | + | 6.33090i | −0.318542 | + | 0.318542i | ||||
\(396\) | 6.11410 | + | 7.82201i | 0.307245 | + | 0.393071i | ||||
\(397\) | 16.8838 | + | 16.8838i | 0.847376 | + | 0.847376i | 0.989805 | − | 0.142429i | \(-0.0454913\pi\) |
−0.142429 | + | 0.989805i | \(0.545491\pi\) | |||||||
\(398\) | 22.2201 | + | 1.35649i | 1.11379 | + | 0.0679947i | ||||
\(399\) | −3.17844 | −0.159121 | ||||||||
\(400\) | 0.965913 | − | 3.88162i | 0.0482956 | − | 0.194081i | ||||
\(401\) | −0.406306 | −0.0202900 | −0.0101450 | − | 0.999949i | \(-0.503229\pi\) | ||||
−0.0101450 | + | 0.999949i | \(0.503229\pi\) | |||||||
\(402\) | −6.28081 | − | 0.383430i | −0.313258 | − | 0.0191238i | ||||
\(403\) | −34.5724 | − | 34.5724i | −1.72217 | − | 1.72217i | ||||
\(404\) | −2.39169 | + | 1.86948i | −0.118991 | + | 0.0930099i | ||||
\(405\) | 0.707107 | − | 0.707107i | 0.0351364 | − | 0.0351364i | ||||
\(406\) | −22.1085 | − | 24.9833i | −1.09722 | − | 1.23990i | ||||
\(407\) | 7.62911i | 0.378161i | ||||||||
\(408\) | 11.6650 | − | 8.02301i | 0.577502 | − | 0.397198i | ||||
\(409\) | − | 38.0171i | − | 1.87983i | −0.341413 | − | 0.939913i | \(-0.610906\pi\) | ||
0.341413 | − | 0.939913i | \(-0.389094\pi\) | |||||||
\(410\) | −3.34319 | + | 2.95849i | −0.165109 | + | 0.146109i | ||||
\(411\) | −10.1759 | + | 10.1759i | −0.501938 | + | 0.501938i | ||||
\(412\) | −0.405709 | + | 3.31049i | −0.0199878 | + | 0.163096i | ||||
\(413\) | −14.2034 | − | 14.2034i | −0.698904 | − | 0.698904i | ||||
\(414\) | 0.644760 | − | 10.5616i | 0.0316882 | − | 0.519072i | ||||
\(415\) | 4.04880 | 0.198748 | ||||||||
\(416\) | 32.3457 | − | 16.8616i | 1.58588 | − | 0.826709i | ||||
\(417\) | −0.414002 | −0.0202737 | ||||||||
\(418\) | −0.491802 | + | 8.05600i | −0.0240548 | + | 0.394032i | ||||
\(419\) | −23.2302 | − | 23.2302i | −1.13487 | − | 1.13487i | −0.989357 | − | 0.145512i | \(-0.953517\pi\) |
−0.145512 | − | 0.989357i | \(-0.546483\pi\) | |||||||
\(420\) | 0.672590 | − | 5.48818i | 0.0328190 | − | 0.267796i | ||||
\(421\) | 26.7883 | − | 26.7883i | 1.30558 | − | 1.30558i | 0.381009 | − | 0.924572i | \(-0.375577\pi\) |
0.924572 | − | 0.381009i | \(-0.124423\pi\) | |||||||
\(422\) | 3.20168 | − | 2.83326i | 0.155855 | − | 0.137921i | ||||
\(423\) | − | 2.76008i | − | 0.134200i | ||||||
\(424\) | −14.5321 | − | 21.1288i | −0.705740 | − | 1.02610i | ||||
\(425\) | 5.00550i | 0.242802i | ||||||||
\(426\) | 3.28245 | + | 3.70927i | 0.159035 | + | 0.179715i | ||||
\(427\) | 6.89037 | − | 6.89037i | 0.333448 | − | 0.333448i | ||||
\(428\) | 13.5680 | − | 10.6055i | 0.655835 | − | 0.512636i | ||||
\(429\) | −22.6340 | − | 22.6340i | −1.09278 | − | 1.09278i | ||||
\(430\) | 6.20708 | + | 0.378929i | 0.299332 | + | 0.0182736i | ||||
\(431\) | −9.17509 | −0.441949 | −0.220974 | − | 0.975280i | \(-0.570924\pi\) | ||||
−0.220974 | + | 0.975280i | \(0.570924\pi\) | |||||||
\(432\) | 3.42773 | − | 2.06172i | 0.164917 | − | 0.0991945i | ||||
\(433\) | 36.5762 | 1.75774 | 0.878869 | − | 0.477063i | \(-0.158299\pi\) | ||||
0.878869 | + | 0.477063i | \(0.158299\pi\) | |||||||
\(434\) | −29.5900 | − | 1.80641i | −1.42037 | − | 0.0867103i | ||||
\(435\) | 6.03354 | + | 6.03354i | 0.289286 | + | 0.289286i | ||||
\(436\) | −5.08861 | − | 6.51006i | −0.243700 | − | 0.311775i | ||||
\(437\) | 6.08252 | − | 6.08252i | 0.290967 | − | 0.290967i | ||||
\(438\) | 13.6968 | + | 15.4779i | 0.654460 | + | 0.739562i | ||||
\(439\) | 6.96346i | 0.332348i | 0.986096 | + | 0.166174i | \(0.0531413\pi\) | ||||
−0.986096 | + | 0.166174i | \(0.946859\pi\) | |||||||
\(440\) | −13.8061 | − | 2.55392i | −0.658182 | − | 0.121753i | ||||
\(441\) | − | 0.643123i | − | 0.0306249i | ||||||
\(442\) | −34.1835 | + | 30.2500i | −1.62594 | + | 1.43885i | ||||
\(443\) | 2.15777 | − | 2.15777i | 0.102519 | − | 0.102519i | −0.653987 | − | 0.756506i | \(-0.726905\pi\) |
0.756506 | + | 0.653987i | \(0.226905\pi\) | |||||||
\(444\) | 3.05094 | + | 0.373900i | 0.144791 | + | 0.0177445i | ||||
\(445\) | −5.11634 | − | 5.11634i | −0.242538 | − | 0.242538i | ||||
\(446\) | −1.16136 | + | 19.0237i | −0.0549919 | + | 0.900799i | ||||
\(447\) | 15.4662 | 0.731527 | ||||||||
\(448\) | 7.91185 | − | 20.6534i | 0.373800 | − | 0.975781i | ||||
\(449\) | 13.1720 | 0.621627 | 0.310814 | − | 0.950471i | \(-0.399398\pi\) | ||||
0.310814 | + | 0.950471i | \(0.399398\pi\) | |||||||
\(450\) | −0.0861743 | + | 1.41159i | −0.00406230 | + | 0.0665428i | ||||
\(451\) | 11.0803 | + | 11.0803i | 0.521753 | + | 0.521753i | ||||
\(452\) | 5.64565 | + | 0.691889i | 0.265549 | + | 0.0325437i | ||||
\(453\) | 9.56186 | − | 9.56186i | 0.449256 | − | 0.449256i | ||||
\(454\) | 4.05245 | − | 3.58613i | 0.190191 | − | 0.168305i | ||||
\(455\) | 17.8270i | 0.835741i | ||||||||
\(456\) | 3.19755 | + | 0.591496i | 0.149739 | + | 0.0276993i | ||||
\(457\) | − | 10.0012i | − | 0.467834i | −0.972257 | − | 0.233917i | \(-0.924846\pi\) | ||
0.972257 | − | 0.233917i | \(-0.0751545\pi\) | |||||||
\(458\) | 0.672051 | + | 0.759441i | 0.0314029 | + | 0.0354863i | ||||
\(459\) | −3.53942 | + | 3.53942i | −0.165206 | + | 0.165206i | ||||
\(460\) | 9.21551 | + | 11.7898i | 0.429676 | + | 0.549700i | ||||
\(461\) | −1.79443 | − | 1.79443i | −0.0835750 | − | 0.0835750i | 0.664083 | − | 0.747658i | \(-0.268822\pi\) |
−0.747658 | + | 0.664083i | \(0.768822\pi\) | |||||||
\(462\) | −19.3721 | − | 1.18263i | −0.901271 | − | 0.0550207i | ||||
\(463\) | −2.58325 | −0.120054 | −0.0600269 | − | 0.998197i | \(-0.519119\pi\) | ||||
−0.0600269 | + | 0.998197i | \(0.519119\pi\) | |||||||
\(464\) | 17.5921 | + | 29.2478i | 0.816691 | + | 1.35780i | ||||
\(465\) | 7.58233 | 0.351622 | ||||||||
\(466\) | −11.5201 | − | 0.703277i | −0.533657 | − | 0.0325787i | ||||
\(467\) | 24.6809 | + | 24.6809i | 1.14210 | + | 1.14210i | 0.988066 | + | 0.154029i | \(0.0492250\pi\) |
0.154029 | + | 0.988066i | \(0.450775\pi\) | |||||||
\(468\) | −10.1608 | + | 7.94221i | −0.469682 | + | 0.367129i | ||||
\(469\) | 8.69819 | − | 8.69819i | 0.401645 | − | 0.401645i | ||||
\(470\) | 2.58677 | + | 2.92313i | 0.119319 | + | 0.134834i | ||||
\(471\) | − | 3.91012i | − | 0.180169i | ||||||
\(472\) | 11.6456 | + | 16.9320i | 0.536032 | + | 0.779359i | ||||
\(473\) | − | 21.8280i | − | 1.00365i | ||||||
\(474\) | 9.48217 | − | 8.39105i | 0.435531 | − | 0.385414i | ||||
\(475\) | −0.812949 | + | 0.812949i | −0.0373007 | + | 0.0373007i | ||||
\(476\) | −3.36665 | + | 27.4711i | −0.154310 | + | 1.25913i | ||||
\(477\) | 6.41096 | + | 6.41096i | 0.293538 | + | 0.293538i | ||||
\(478\) | 0.212331 | − | 3.47810i | 0.00971179 | − | 0.159085i | ||||
\(479\) | 1.39344 | 0.0636679 | 0.0318339 | − | 0.999493i | \(-0.489865\pi\) | ||||
0.0318339 | + | 0.999493i | \(0.489865\pi\) | |||||||
\(480\) | −1.69796 | + | 5.39601i | −0.0775011 | + | 0.246293i | ||||
\(481\) | −9.91020 | −0.451866 | ||||||||
\(482\) | −0.636029 | + | 10.4185i | −0.0289703 | + | 0.474551i | ||||
\(483\) | 14.6265 | + | 14.6265i | 0.665530 | + | 0.665530i | ||||
\(484\) | −3.31878 | + | 27.0805i | −0.150854 | + | 1.23093i | ||||
\(485\) | 5.82695 | − | 5.82695i | 0.264588 | − | 0.264588i | ||||
\(486\) | −1.05908 | + | 0.937207i | −0.0480407 | + | 0.0425126i | ||||
\(487\) | 26.7044i | 1.21009i | 0.796191 | + | 0.605045i | \(0.206845\pi\) | ||||
−0.796191 | + | 0.605045i | \(0.793155\pi\) | |||||||
\(488\) | −8.21407 | + | 5.64952i | −0.371833 | + | 0.255742i | ||||
\(489\) | − | 21.9121i | − | 0.990901i | ||||||
\(490\) | 0.602739 | + | 0.681116i | 0.0272290 | + | 0.0307697i | ||||
\(491\) | 16.3259 | − | 16.3259i | 0.736775 | − | 0.736775i | −0.235177 | − | 0.971953i | \(-0.575567\pi\) |
0.971953 | + | 0.235177i | \(0.0755670\pi\) | |||||||
\(492\) | 4.97415 | − | 3.88806i | 0.224252 | − | 0.175287i | ||||
\(493\) | −30.2009 | − | 30.2009i | −1.36018 | − | 1.36018i | ||||
\(494\) | −10.4647 | − | 0.638849i | −0.470830 | − | 0.0287432i | ||||
\(495\) | 4.96402 | 0.223116 | ||||||||
\(496\) | 29.4317 | + | 7.32387i | 1.32152 | + | 0.328851i | ||||
\(497\) | −9.68272 | −0.434329 | ||||||||
\(498\) | −5.71522 | − | 0.348902i | −0.256105 | − | 0.0156347i | ||||
\(499\) | 26.4923 | + | 26.4923i | 1.18596 | + | 1.18596i | 0.978175 | + | 0.207783i | \(0.0666247\pi\) |
0.207783 | + | 0.978175i | \(0.433375\pi\) | |||||||
\(500\) | −1.23168 | − | 1.57574i | −0.0550825 | − | 0.0704692i | ||||
\(501\) | −1.25086 | + | 1.25086i | −0.0558842 | + | 0.0558842i | ||||
\(502\) | −6.83013 | − | 7.71828i | −0.304844 | − | 0.344484i | ||||
\(503\) | − | 14.2132i | − | 0.633737i | −0.948470 | − | 0.316868i | \(-0.897369\pi\) | ||
0.948470 | − | 0.316868i | \(-0.102631\pi\) | |||||||
\(504\) | −1.42236 | + | 7.68908i | −0.0633569 | + | 0.342499i | ||||
\(505\) | 1.51782i | 0.0675422i | ||||||||
\(506\) | 39.3352 | − | 34.8089i | 1.74866 | − | 1.54744i | ||||
\(507\) | 20.2091 | − | 20.2091i | 0.897517 | − | 0.897517i | ||||
\(508\) | 13.1233 | + | 1.60829i | 0.582251 | + | 0.0713563i | ||||
\(509\) | 4.26128 | + | 4.26128i | 0.188878 | + | 0.188878i | 0.795211 | − | 0.606333i | \(-0.207360\pi\) |
−0.606333 | + | 0.795211i | \(0.707360\pi\) | |||||||
\(510\) | 0.431345 | − | 7.06569i | 0.0191003 | − | 0.312874i | ||||
\(511\) | −40.4036 | −1.78735 | ||||||||
\(512\) | −11.8029 | + | 19.3052i | −0.521621 | + | 0.853177i | ||||
\(513\) | −1.14968 | −0.0507598 | ||||||||
\(514\) | −0.848067 | + | 13.8918i | −0.0374066 | + | 0.612742i | ||||
\(515\) | 1.17919 | + | 1.17919i | 0.0519614 | + | 0.0519614i | ||||
\(516\) | −8.72917 | − | 1.06978i | −0.384280 | − | 0.0470945i | ||||
\(517\) | 9.68814 | − | 9.68814i | 0.426084 | − | 0.426084i | ||||
\(518\) | −4.49990 | + | 3.98209i | −0.197714 | + | 0.174963i | ||||
\(519\) | − | 5.67597i | − | 0.249147i | ||||||
\(520\) | 3.31754 | − | 17.9341i | 0.145484 | − | 0.786464i | ||||
\(521\) | − | 31.9522i | − | 1.39985i | −0.714215 | − | 0.699926i | \(-0.753216\pi\) | ||
0.714215 | − | 0.699926i | \(-0.246784\pi\) | |||||||
\(522\) | −7.99692 | − | 9.03679i | −0.350016 | − | 0.395530i | ||||
\(523\) | 12.3608 | − | 12.3608i | 0.540498 | − | 0.540498i | −0.383177 | − | 0.923675i | \(-0.625170\pi\) |
0.923675 | + | 0.383177i | \(0.125170\pi\) | |||||||
\(524\) | 11.6727 | + | 14.9333i | 0.509923 | + | 0.652364i | ||||
\(525\) | −1.95488 | − | 1.95488i | −0.0853180 | − | 0.0853180i | ||||
\(526\) | 38.8224 | + | 2.37002i | 1.69274 | + | 0.103338i | ||||
\(527\) | −37.9533 | −1.65327 | ||||||||
\(528\) | 19.2685 | + | 4.79481i | 0.838553 | + | 0.208667i | ||||
\(529\) | −32.9810 | −1.43396 | ||||||||
\(530\) | −12.7981 | − | 0.781297i | −0.555914 | − | 0.0339374i | ||||
\(531\) | −5.13756 | − | 5.13756i | −0.222951 | − | 0.222951i | ||||
\(532\) | −5.00839 | + | 3.91483i | −0.217141 | + | 0.169729i | ||||
\(533\) | −14.3933 | + | 14.3933i | −0.623444 | + | 0.623444i | ||||
\(534\) | 6.78126 | + | 7.66305i | 0.293454 | + | 0.331613i | ||||
\(535\) | − | 8.61058i | − | 0.372268i | ||||||
\(536\) | −10.3692 | + | 7.13179i | −0.447881 | + | 0.308046i | ||||
\(537\) | 7.51428i | 0.324265i | ||||||||
\(538\) | −11.0127 | + | 9.74549i | −0.474793 | + | 0.420158i | ||||
\(539\) | 2.25742 | − | 2.25742i | 0.0972341 | − | 0.0972341i | ||||
\(540\) | 0.243285 | − | 1.98515i | 0.0104693 | − | 0.0854272i | ||||
\(541\) | 25.6126 | + | 25.6126i | 1.10117 | + | 1.10117i | 0.994270 | + | 0.106902i | \(0.0340932\pi\) |
0.106902 | + | 0.994270i | \(0.465907\pi\) | |||||||
\(542\) | 1.39452 | − | 22.8431i | 0.0598999 | − | 0.981196i | ||||
\(543\) | 12.3732 | 0.530985 | ||||||||
\(544\) | 8.49916 | − | 27.0097i | 0.364399 | − | 1.15803i | ||||
\(545\) | −4.13143 | −0.176971 | ||||||||
\(546\) | 1.53623 | − | 25.1643i | 0.0657444 | − | 1.07693i | ||||
\(547\) | 1.56643 | + | 1.56643i | 0.0669759 | + | 0.0669759i | 0.739801 | − | 0.672825i | \(-0.234919\pi\) |
−0.672825 | + | 0.739801i | \(0.734919\pi\) | |||||||
\(548\) | −3.50107 | + | 28.5680i | −0.149558 | + | 1.22036i | ||||
\(549\) | 2.49234 | − | 2.49234i | 0.106370 | − | 0.106370i | ||||
\(550\) | −5.25728 | + | 4.65232i | −0.224171 | + | 0.198376i | ||||
\(551\) | − | 9.80992i | − | 0.417917i | ||||||
\(552\) | −11.9925 | − | 17.4364i | −0.510435 | − | 0.742142i | ||||
\(553\) | 24.7523i | 1.05258i | ||||||||
\(554\) | −25.6765 | − | 29.0153i | −1.09089 | − | 1.23274i | ||||
\(555\) | 1.08674 | − | 1.08674i | 0.0461295 | − | 0.0461295i | ||||
\(556\) | −0.652359 | + | 0.509919i | −0.0276662 | + | 0.0216254i | ||||
\(557\) | 3.96707 | + | 3.96707i | 0.168090 | + | 0.168090i | 0.786139 | − | 0.618049i | \(-0.212077\pi\) |
−0.618049 | + | 0.786139i | \(0.712077\pi\) | |||||||
\(558\) | −10.7031 | − | 0.653402i | −0.453098 | − | 0.0276607i | ||||
\(559\) | 28.3545 | 1.19927 | ||||||||
\(560\) | −5.69987 | − | 9.47636i | −0.240864 | − | 0.400449i | ||||
\(561\) | −24.8474 | −1.04906 | ||||||||
\(562\) | 25.6607 | + | 1.56653i | 1.08243 | + | 0.0660801i | ||||
\(563\) | 23.0565 | + | 23.0565i | 0.971715 | + | 0.971715i | 0.999611 | − | 0.0278956i | \(-0.00888059\pi\) |
−0.0278956 | + | 0.999611i | \(0.508881\pi\) | |||||||
\(564\) | −3.39954 | − | 4.34917i | −0.143147 | − | 0.183133i | ||||
\(565\) | 2.01097 | − | 2.01097i | 0.0846023 | − | 0.0846023i | ||||
\(566\) | −10.2709 | − | 11.6065i | −0.431720 | − | 0.487859i | ||||
\(567\) | − | 2.76462i | − | 0.116103i | ||||||
\(568\) | 9.74093 | + | 1.80192i | 0.408720 | + | 0.0756069i | ||||
\(569\) | 32.6228i | 1.36762i | 0.729660 | + | 0.683810i | \(0.239678\pi\) | ||||
−0.729660 | + | 0.683810i | \(0.760322\pi\) | |||||||
\(570\) | 1.21760 | − | 1.07749i | 0.0509998 | − | 0.0451312i | ||||
\(571\) | 13.3559 | − | 13.3559i | 0.558926 | − | 0.558926i | −0.370076 | − | 0.929002i | \(-0.620668\pi\) |
0.929002 | + | 0.370076i | \(0.120668\pi\) | |||||||
\(572\) | −63.5432 | − | 7.78737i | −2.65687 | − | 0.325606i | ||||
\(573\) | 2.85521 | + | 2.85521i | 0.119278 | + | 0.119278i | ||||
\(574\) | −0.752051 | + | 12.3190i | −0.0313900 | + | 0.514187i | ||||
\(575\) | 7.48205 | 0.312023 | ||||||||
\(576\) | 2.86182 | − | 7.47061i | 0.119243 | − | 0.311275i | ||||
\(577\) | 46.5999 | 1.93998 | 0.969989 | − | 0.243147i | \(-0.0781798\pi\) | ||||
0.969989 | + | 0.243147i | \(0.0781798\pi\) | |||||||
\(578\) | −0.694137 | + | 11.3704i | −0.0288723 | + | 0.472945i | ||||
\(579\) | −0.309084 | − | 0.309084i | −0.0128451 | − | 0.0128451i | ||||
\(580\) | 16.9387 | + | 2.07588i | 0.703341 | + | 0.0861962i | ||||
\(581\) | 7.91492 | − | 7.91492i | 0.328366 | − | 0.328366i | ||||
\(582\) | −8.72738 | + | 7.72311i | −0.361762 | + | 0.320133i | ||||
\(583\) | 45.0062i | 1.86397i | ||||||||
\(584\) | 40.6465 | + | 7.51896i | 1.68196 | + | 0.311137i | ||||
\(585\) | 6.44825i | 0.266602i | ||||||||
\(586\) | −1.65110 | − | 1.86580i | −0.0682062 | − | 0.0770753i | ||||
\(587\) | −29.5590 | + | 29.5590i | −1.22003 | + | 1.22003i | −0.252408 | + | 0.967621i | \(0.581222\pi\) |
−0.967621 | + | 0.252408i | \(0.918778\pi\) | |||||||
\(588\) | −0.792124 | − | 1.01339i | −0.0326666 | − | 0.0417917i | ||||
\(589\) | −6.16404 | − | 6.16404i | −0.253985 | − | 0.253985i | ||||
\(590\) | 10.2560 | + | 0.626109i | 0.422234 | + | 0.0257765i | ||||
\(591\) | −16.5231 | −0.679671 | ||||||||
\(592\) | 5.26801 | − | 3.16862i | 0.216514 | − | 0.130229i | ||||
\(593\) | −35.4555 | −1.45598 | −0.727991 | − | 0.685587i | \(-0.759546\pi\) | ||||
−0.727991 | + | 0.685587i | \(0.759546\pi\) | |||||||
\(594\) | −7.00714 | − | 0.427771i | −0.287507 | − | 0.0175517i | ||||
\(595\) | 9.78516 | + | 9.78516i | 0.401152 | + | 0.401152i | ||||
\(596\) | 24.3707 | − | 19.0495i | 0.998265 | − | 0.780297i | ||||
\(597\) | −11.1307 | + | 11.1307i | −0.455551 | + | 0.455551i | ||||
\(598\) | 45.2166 | + | 51.0963i | 1.84905 | + | 2.08948i | ||||
\(599\) | − | 22.8571i | − | 0.933915i | −0.884280 | − | 0.466958i | \(-0.845350\pi\) | ||
0.884280 | − | 0.466958i | \(-0.154650\pi\) | |||||||
\(600\) | 1.60284 | + | 2.33043i | 0.0654356 | + | 0.0951395i | ||||
\(601\) | − | 19.4253i | − | 0.792374i | −0.918170 | − | 0.396187i | \(-0.870333\pi\) | ||
0.918170 | − | 0.396187i | \(-0.129667\pi\) | |||||||
\(602\) | 12.8749 | − | 11.3933i | 0.524740 | − | 0.464358i | ||||
\(603\) | 3.14625 | − | 3.14625i | 0.128125 | − | 0.128125i | ||||
\(604\) | 3.28982 | − | 26.8442i | 0.133861 | − | 1.09227i | ||||
\(605\) | 9.64602 | + | 9.64602i | 0.392166 | + | 0.392166i | ||||
\(606\) | 0.130797 | − | 2.14254i | 0.00531327 | − | 0.0870345i | ||||
\(607\) | −19.2455 | −0.781149 | −0.390574 | − | 0.920571i | \(-0.627724\pi\) | ||||
−0.390574 | + | 0.920571i | \(0.627724\pi\) | |||||||
\(608\) | 5.76704 | − | 3.00632i | 0.233884 | − | 0.121922i | ||||
\(609\) | 23.5897 | 0.955903 | ||||||||
\(610\) | −0.303739 | + | 4.97541i | −0.0122980 | + | 0.201449i | ||||
\(611\) | 12.5849 | + | 12.5849i | 0.509129 | + | 0.509129i | ||||
\(612\) | −1.21776 | + | 9.93666i | −0.0492251 | + | 0.401666i | ||||
\(613\) | 17.3922 | − | 17.3922i | 0.702465 | − | 0.702465i | −0.262474 | − | 0.964939i | \(-0.584538\pi\) |
0.964939 | + | 0.262474i | \(0.0845383\pi\) | |||||||
\(614\) | −20.2261 | + | 17.8987i | −0.816259 | + | 0.722331i | ||||
\(615\) | − | 3.15671i | − | 0.127291i | ||||||
\(616\) | −31.9820 | + | 21.9968i | −1.28859 | + | 0.886275i | ||||
\(617\) | 29.7863i | 1.19915i | 0.800318 | + | 0.599576i | \(0.204664\pi\) | ||||
−0.800318 | + | 0.599576i | \(0.795336\pi\) | |||||||
\(618\) | −1.56291 | − | 1.76615i | −0.0628696 | − | 0.0710448i | ||||
\(619\) | −10.6404 | + | 10.6404i | −0.427673 | + | 0.427673i | −0.887835 | − | 0.460162i | \(-0.847791\pi\) |
0.460162 | + | 0.887835i | \(0.347791\pi\) | |||||||
\(620\) | 11.9478 | − | 9.33902i | 0.479834 | − | 0.375064i | ||||
\(621\) | 5.29061 | + | 5.29061i | 0.212305 | + | 0.212305i | ||||
\(622\) | −16.8754 | − | 1.03021i | −0.676642 | − | 0.0413075i | ||||
\(623\) | −20.0037 | −0.801430 | ||||||||
\(624\) | −6.22845 | + | 25.0297i | −0.249338 | + | 1.00199i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 21.5105 | + | 1.31317i | 0.859732 | + | 0.0524848i | ||||
\(627\) | −4.03550 | − | 4.03550i | −0.161162 | − | 0.161162i | ||||
\(628\) | −4.81603 | − | 6.16133i | −0.192180 | − | 0.245864i | ||||
\(629\) | −5.43967 | + | 5.43967i | −0.216894 | + | 0.216894i | ||||
\(630\) | 2.59102 | + | 2.92794i | 0.103229 | + | 0.116652i | ||||
\(631\) | 38.7660i | 1.54325i | 0.636078 | + | 0.771625i | \(0.280556\pi\) | ||||
−0.636078 | + | 0.771625i | \(0.719444\pi\) | |||||||
\(632\) | 4.60632 | − | 24.9011i | 0.183230 | − | 0.990515i | ||||
\(633\) | 3.02309i | 0.120157i | ||||||||
\(634\) | −33.5591 | + | 29.6974i | −1.33280 | + | 1.17943i | ||||
\(635\) | 4.67449 | − | 4.67449i | 0.185502 | − | 0.185502i | ||||
\(636\) | 17.9983 | + | 2.20573i | 0.713678 | + | 0.0874631i | ||||
\(637\) | 2.93239 | + | 2.93239i | 0.116185 | + | 0.116185i | ||||
\(638\) | 3.65005 | − | 59.7900i | 0.144507 | − | 2.36711i | ||||
\(639\) | −3.50237 | −0.138552 | ||||||||
\(640\) | 3.97062 | + | 10.5941i | 0.156953 | + | 0.418767i | ||||
\(641\) | 3.84117 | 0.151717 | 0.0758585 | − | 0.997119i | \(-0.475830\pi\) | ||||
0.0758585 | + | 0.997119i | \(0.475830\pi\) | |||||||
\(642\) | −0.742010 | + | 12.1546i | −0.0292848 | + | 0.479702i | ||||
\(643\) | −4.00729 | − | 4.00729i | −0.158032 | − | 0.158032i | 0.623662 | − | 0.781694i | \(-0.285644\pi\) |
−0.781694 | + | 0.623662i | \(0.785644\pi\) | |||||||
\(644\) | 41.0628 | + | 5.03235i | 1.61810 | + | 0.198302i | ||||
\(645\) | −3.10932 | + | 3.10932i | −0.122429 | + | 0.122429i | ||||
\(646\) | −6.09471 | + | 5.39338i | −0.239793 | + | 0.212200i | ||||
\(647\) | 25.3385i | 0.996158i | 0.867132 | + | 0.498079i | \(0.165961\pi\) | ||||
−0.867132 | + | 0.498079i | \(0.834039\pi\) | |||||||
\(648\) | −0.514486 | + | 2.78124i | −0.0202109 | + | 0.109257i | ||||
\(649\) | − | 36.0667i | − | 1.41574i | ||||||
\(650\) | −6.04335 | − | 6.82919i | −0.237040 | − | 0.267863i | ||||
\(651\) | 14.8225 | − | 14.8225i | 0.580941 | − | 0.580941i | ||||
\(652\) | −26.9888 | − | 34.5278i | −1.05696 | − | 1.35221i | ||||
\(653\) | 0.690132 | + | 0.690132i | 0.0270069 | + | 0.0270069i | 0.720481 | − | 0.693474i | \(-0.243921\pi\) |
−0.693474 | + | 0.720481i | \(0.743921\pi\) | |||||||
\(654\) | 5.83187 | + | 0.356023i | 0.228044 | + | 0.0139216i | ||||
\(655\) | 9.47700 | 0.370297 | ||||||||
\(656\) | 3.04910 | − | 12.2532i | 0.119048 | − | 0.478405i | ||||
\(657\) | −14.6145 | −0.570166 | ||||||||
\(658\) | 10.7712 | + | 0.657559i | 0.419905 | + | 0.0256343i | ||||
\(659\) | −27.4031 | − | 27.4031i | −1.06747 | − | 1.06747i | −0.997552 | − | 0.0699222i | \(-0.977725\pi\) |
−0.0699222 | − | 0.997552i | \(-0.522275\pi\) | |||||||
\(660\) | 7.82201 | − | 6.11410i | 0.304471 | − | 0.237991i | ||||
\(661\) | 14.4586 | − | 14.4586i | 0.562373 | − | 0.562373i | −0.367608 | − | 0.929981i | \(-0.619823\pi\) |
0.929981 | + | 0.367608i | \(0.119823\pi\) | |||||||
\(662\) | 10.7577 | + | 12.1566i | 0.418110 | + | 0.472479i | ||||
\(663\) | − | 32.2767i | − | 1.25352i | ||||||
\(664\) | −9.43544 | + | 6.48956i | −0.366166 | + | 0.251844i | ||||
\(665\) | 3.17844i | 0.123255i | ||||||||
\(666\) | −1.62767 | + | 1.44038i | −0.0630711 | + | 0.0558134i | ||||
\(667\) | −45.1432 | + | 45.1432i | −1.74795 | + | 1.74795i | ||||
\(668\) | −0.430366 | + | 3.51169i | −0.0166514 | + | 0.135871i | ||||
\(669\) | −9.52957 | − | 9.52957i | −0.368434 | − | 0.368434i | ||||
\(670\) | −0.383430 | + | 6.28081i | −0.0148132 | + | 0.242649i | ||||
\(671\) | 17.4967 | 0.675452 | ||||||||
\(672\) | 7.22924 | + | 13.8679i | 0.278874 | + | 0.534965i | ||||
\(673\) | 38.4496 | 1.48212 | 0.741061 | − | 0.671438i | \(-0.234323\pi\) | ||||
0.741061 | + | 0.671438i | \(0.234323\pi\) | |||||||
\(674\) | 1.65451 | − | 27.1018i | 0.0637292 | − | 1.04392i | ||||
\(675\) | −0.707107 | − | 0.707107i | −0.0272166 | − | 0.0272166i | ||||
\(676\) | 6.95307 | − | 56.7355i | 0.267426 | − | 2.18213i | ||||
\(677\) | −15.2625 | + | 15.2625i | −0.586586 | + | 0.586586i | −0.936705 | − | 0.350119i | \(-0.886141\pi\) |
0.350119 | + | 0.936705i | \(0.386141\pi\) | |||||||
\(678\) | −3.01195 | + | 2.66537i | −0.115673 | + | 0.102363i | ||||
\(679\) | − | 22.7820i | − | 0.874293i | ||||||
\(680\) | −8.02301 | − | 11.6650i | −0.307668 | − | 0.447331i | ||||
\(681\) | 3.82640i | 0.146628i | ||||||||
\(682\) | −35.2754 | − | 39.8624i | −1.35076 | − | 1.52641i | ||||
\(683\) | −31.6516 | + | 31.6516i | −1.21111 | + | 1.21111i | −0.240453 | + | 0.970661i | \(0.577296\pi\) |
−0.970661 | + | 0.240453i | \(0.922704\pi\) | |||||||
\(684\) | −1.81160 | + | 1.41605i | −0.0692683 | + | 0.0541439i | ||||
\(685\) | 10.1759 | + | 10.1759i | 0.388800 | + | 0.388800i | ||||
\(686\) | −24.8077 | − | 1.51446i | −0.947162 | − | 0.0578223i | ||||
\(687\) | −0.717078 | −0.0273582 | ||||||||
\(688\) | −15.0725 | + | 9.06587i | −0.574635 | + | 0.345633i | ||||
\(689\) | −58.4629 | −2.22726 | ||||||||
\(690\) | −10.5616 | − | 0.644760i | −0.402071 | − | 0.0245456i | ||||
\(691\) | −12.0010 | − | 12.0010i | −0.456539 | − | 0.456539i | 0.440979 | − | 0.897518i | \(-0.354631\pi\) |
−0.897518 | + | 0.440979i | \(0.854631\pi\) | |||||||
\(692\) | −6.99099 | − | 8.94385i | −0.265758 | − | 0.339994i | ||||
\(693\) | 9.70408 | − | 9.70408i | 0.368627 | − | 0.368627i | ||||
\(694\) | −4.83733 | − | 5.46635i | −0.183623 | − | 0.207500i | ||||
\(695\) | 0.414002i | 0.0157040i | ||||||||
\(696\) | −23.7315 | − | 4.38996i | −0.899542 | − | 0.166401i | ||||
\(697\) | 15.8009i | 0.598502i | ||||||||
\(698\) | −25.0396 | + | 22.1583i | −0.947763 | + | 0.838703i | ||||
\(699\) | 5.77076 | − | 5.77076i | 0.218270 | − | 0.218270i | ||||
\(700\) | −5.48818 | − | 0.672590i | −0.207434 | − | 0.0254215i | ||||
\(701\) | −0.298277 | − | 0.298277i | −0.0112658 | − | 0.0112658i | 0.701451 | − | 0.712717i | \(-0.252536\pi\) |
−0.712717 | + | 0.701451i | \(0.752536\pi\) | |||||||
\(702\) | 0.555674 | − | 9.10226i | 0.0209726 | − | 0.343543i | ||||
\(703\) | −1.76693 | −0.0666409 | ||||||||
\(704\) | 36.2678 | − | 16.1773i | 1.36689 | − | 0.609704i | ||||
\(705\) | −2.76008 | −0.103951 | ||||||||
\(706\) | −0.812526 | + | 13.3097i | −0.0305798 | + | 0.500915i | ||||
\(707\) | 2.96716 | + | 2.96716i | 0.111592 | + | 0.111592i | ||||
\(708\) | −14.4233 | − | 1.76761i | −0.542061 | − | 0.0664310i | ||||
\(709\) | −11.6489 | + | 11.6489i | −0.437485 | + | 0.437485i | −0.891165 | − | 0.453680i | \(-0.850111\pi\) |
0.453680 | + | 0.891165i | \(0.350111\pi\) | |||||||
\(710\) | 3.70927 | − | 3.28245i | 0.139207 | − | 0.123188i | ||||
\(711\) | 8.95325i | 0.335773i | ||||||||
\(712\) | 20.1239 | + | 3.72262i | 0.754177 | + | 0.139511i | ||||
\(713\) | 56.7313i | 2.12460i | ||||||||
\(714\) | −12.9694 | − | 14.6558i | −0.485366 | − | 0.548480i | ||||
\(715\) | −22.6340 | + | 22.6340i | −0.846463 | + | 0.846463i | ||||
\(716\) | 9.25521 | + | 11.8406i | 0.345884 | + | 0.442502i | ||||
\(717\) | 1.74229 | + | 1.74229i | 0.0650670 | + | 0.0650670i | ||||
\(718\) | 1.58288 | + | 0.0966317i | 0.0590727 | + | 0.00360626i | ||||
\(719\) | 1.69024 | 0.0630353 | 0.0315177 | − | 0.999503i | \(-0.489966\pi\) | ||||
0.0315177 | + | 0.999503i | \(0.489966\pi\) | |||||||
\(720\) | −2.06172 | − | 3.42773i | −0.0768358 | − | 0.127744i | ||||
\(721\) | 4.61036 | 0.171699 | ||||||||
\(722\) | 24.9543 | + | 1.52341i | 0.928704 | + | 0.0566954i | ||||
\(723\) | −5.21896 | − | 5.21896i | −0.194095 | − | 0.194095i | ||||
\(724\) | 19.4970 | − | 15.2399i | 0.724599 | − | 0.566385i | ||||
\(725\) | 6.03354 | − | 6.03354i | 0.224080 | − | 0.224080i | ||||
\(726\) | −12.7849 | − | 14.4474i | −0.474494 | − | 0.536194i | ||||
\(727\) | − | 27.2221i | − | 1.00961i | −0.863233 | − | 0.504805i | \(-0.831564\pi\) | ||
0.863233 | − | 0.504805i | \(-0.168436\pi\) | |||||||
\(728\) | −28.5737 | − | 41.5445i | −1.05901 | − | 1.53974i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 15.4779 | − | 13.6968i | 0.572862 | − | 0.506942i | ||||
\(731\) | 15.5637 | − | 15.5637i | 0.575644 | − | 0.575644i | ||||
\(732\) | 0.857506 | − | 6.99705i | 0.0316943 | − | 0.258618i | ||||
\(733\) | 20.9172 | + | 20.9172i | 0.772596 | + | 0.772596i | 0.978560 | − | 0.205963i | \(-0.0660328\pi\) |
−0.205963 | + | 0.978560i | \(0.566033\pi\) | |||||||
\(734\) | 0.622752 | − | 10.2010i | 0.0229862 | − | 0.376528i | ||||
\(735\) | −0.643123 | −0.0237219 | ||||||||
\(736\) | −40.3732 | − | 12.7043i | −1.48818 | − | 0.468285i | ||||
\(737\) | 22.0873 | 0.813596 | ||||||||
\(738\) | −0.272027 | + | 4.45596i | −0.0100135 | + | 0.164026i | ||||
\(739\) | −3.53634 | − | 3.53634i | −0.130086 | − | 0.130086i | 0.639066 | − | 0.769152i | \(-0.279321\pi\) |
−0.769152 | + | 0.639066i | \(0.779321\pi\) | |||||||
\(740\) | 0.373900 | − | 3.05094i | 0.0137448 | − | 0.112155i | ||||
\(741\) | 5.24210 | − | 5.24210i | 0.192573 | − | 0.192573i | ||||
\(742\) | −26.5461 | + | 23.4914i | −0.974538 | + | 0.862397i | ||||
\(743\) | − | 38.5438i | − | 1.41403i | −0.707196 | − | 0.707017i | \(-0.750040\pi\) | ||
0.707196 | − | 0.707017i | \(-0.249960\pi\) | |||||||
\(744\) | −17.6701 | + | 12.1532i | −0.647817 | + | 0.445559i | ||||
\(745\) | − | 15.4662i | − | 0.566639i | ||||||
\(746\) | −11.7112 | − | 13.2341i | −0.428778 | − | 0.484533i | ||||
\(747\) | 2.86293 | − | 2.86293i | 0.104749 | − | 0.104749i | ||||
\(748\) | −39.1531 | + | 30.6042i | −1.43158 | + | 1.11900i | ||||
\(749\) | −16.8327 | − | 16.8327i | −0.615052 | − | 0.615052i | ||||
\(750\) | 1.41159 | + | 0.0861743i | 0.0515438 | + | 0.00314664i | ||||
\(751\) | −7.07646 | −0.258224 | −0.129112 | − | 0.991630i | \(-0.541213\pi\) | ||||
−0.129112 | + | 0.991630i | \(0.541213\pi\) | |||||||
\(752\) | −10.7136 | − | 2.66600i | −0.390685 | − | 0.0972189i | ||||
\(753\) | 7.28775 | 0.265580 | ||||||||
\(754\) | 77.6670 | + | 4.74141i | 2.82847 | + | 0.172672i | ||||
\(755\) | −9.56186 | − | 9.56186i | −0.347992 | − | 0.347992i | ||||
\(756\) | −3.40514 | − | 4.35632i | −0.123844 | − | 0.158438i | ||||
\(757\) | −32.5233 | + | 32.5233i | −1.18208 | + | 1.18208i | −0.202873 | + | 0.979205i | \(0.565028\pi\) |
−0.979205 | + | 0.202873i | \(0.934972\pi\) | |||||||
\(758\) | −34.7707 | − | 39.2921i | −1.26293 | − | 1.42715i | ||||
\(759\) | 37.1411i | 1.34814i | ||||||||
\(760\) | 0.591496 | − | 3.19755i | 0.0214558 | − | 0.115987i | ||||
\(761\) | 43.1903i | 1.56565i | 0.622243 | + | 0.782824i | \(0.286222\pi\) | ||||
−0.622243 | + | 0.782824i | \(0.713778\pi\) | |||||||
\(762\) | −7.00127 | + | 6.19562i | −0.253629 | + | 0.224444i | ||||
\(763\) | −8.07645 | + | 8.07645i | −0.292387 | + | 0.292387i | ||||
\(764\) | 8.01577 | + | 0.982353i | 0.290000 | + | 0.0355403i | ||||
\(765\) | 3.53942 | + | 3.53942i | 0.127968 | + | 0.127968i | ||||
\(766\) | −1.23710 | + | 20.2644i | −0.0446981 | + | 0.732181i | ||||
\(767\) | 46.8505 | 1.69167 | ||||||||
\(768\) | −4.69194 | − | 15.2966i | −0.169306 | − | 0.551968i | ||||
\(769\) | −31.1675 | −1.12393 | −0.561965 | − | 0.827161i | \(-0.689955\pi\) | ||||
−0.561965 | + | 0.827161i | \(0.689955\pi\) | |||||||
\(770\) | −1.18263 | + | 19.3721i | −0.0426188 | + | 0.698122i | ||||
\(771\) | −6.95885 | − | 6.95885i | −0.250617 | − | 0.250617i | ||||
\(772\) | −0.867729 | − | 0.106342i | −0.0312303 | − | 0.00382735i | ||||
\(773\) | 11.7904 | − | 11.7904i | 0.424072 | − | 0.424072i | −0.462531 | − | 0.886603i | \(-0.653059\pi\) |
0.886603 | + | 0.462531i | \(0.153059\pi\) | |||||||
\(774\) | 4.65701 | − | 4.12112i | 0.167393 | − | 0.148131i | ||||
\(775\) | − | 7.58233i | − | 0.272365i | ||||||
\(776\) | −4.23965 | + | 22.9190i | −0.152195 | + | 0.822743i | ||||
\(777\) | − | 4.24889i | − | 0.152428i | ||||||
\(778\) | −1.42775 | − | 1.61340i | −0.0511873 | − | 0.0578434i | ||||
\(779\) | −2.56624 | + | 2.56624i | −0.0919452 | + | 0.0919452i | ||||
\(780\) | 7.94221 | + | 10.1608i | 0.284377 | + | 0.363814i | ||||
\(781\) | −12.2936 | − | 12.2936i | −0.439901 | − | 0.439901i | ||||
\(782\) | 52.8658 | + | 3.22735i | 1.89048 | + | 0.115410i | ||||
\(783\) | 8.53271 | 0.304934 | ||||||||
\(784\) | −2.49636 | − | 0.621201i | −0.0891558 | − | 0.0221857i | ||||
\(785\) | −3.91012 | −0.139558 | ||||||||
\(786\) | −13.3776 | − | 0.816674i | −0.477163 | − | 0.0291298i | ||||
\(787\) | −3.50469 | − | 3.50469i | −0.124929 | − | 0.124929i | 0.641878 | − | 0.766807i | \(-0.278156\pi\) |
−0.766807 | + | 0.641878i | \(0.778156\pi\) | |||||||
\(788\) | −26.0362 | + | 20.3513i | −0.927501 | + | 0.724984i | ||||
\(789\) | −19.4473 | + | 19.4473i | −0.692343 | + | 0.692343i | ||||
\(790\) | −8.39105 | − | 9.48217i | −0.298540 | − | 0.337361i | ||||
\(791\) | − | 7.86243i | − | 0.279556i | ||||||
\(792\) | −11.5683 | + | 7.95653i | −0.411062 | + | 0.282723i | ||||
\(793\) | 22.7282i | 0.807100i | ||||||||
\(794\) | −25.2880 | + | 22.3780i | −0.897436 | + | 0.794167i | ||||
\(795\) | 6.41096 | − | 6.41096i | 0.227373 | − | 0.227373i | ||||
\(796\) | −3.82960 | + | 31.2487i | −0.135737 | + | 1.10758i | ||||
\(797\) | −34.1882 | − | 34.1882i | −1.21101 | − | 1.21101i | −0.970696 | − | 0.240312i | \(-0.922750\pi\) |
−0.240312 | − | 0.970696i | \(-0.577250\pi\) | |||||||
\(798\) | 0.273900 | − | 4.48664i | 0.00969594 | − | 0.158825i | ||||
\(799\) | 13.8156 | 0.488760 | ||||||||
\(800\) | 5.39601 | + | 1.69796i | 0.190778 | + | 0.0600321i | ||||
\(801\) | −7.23560 | −0.255657 | ||||||||
\(802\) | 0.0350132 | − | 0.573536i | 0.00123636 | − | 0.0202523i | ||||
\(803\) | −51.2983 | − | 51.2983i | −1.81028 | − | 1.81028i | ||||
\(804\) | 1.08249 | − | 8.83286i | 0.0381765 | − | 0.311511i | ||||
\(805\) | 14.6265 | − | 14.6265i | 0.515517 | − | 0.515517i | ||||
\(806\) | 51.7812 | − | 45.8227i | 1.82391 | − | 1.61403i | ||||
\(807\) | − | 10.3984i | − | 0.366042i | ||||||
\(808\) | −2.43282 | − | 3.53718i | −0.0855864 | − | 0.124438i | ||||
\(809\) | − | 0.637755i | − | 0.0224223i | −0.999937 | − | 0.0112111i | \(-0.996431\pi\) | ||
0.999937 | − | 0.0112111i | \(-0.00356869\pi\) | |||||||
\(810\) | 0.937207 | + | 1.05908i | 0.0329301 | + | 0.0372121i | ||||
\(811\) | 30.6724 | − | 30.6724i | 1.07705 | − | 1.07705i | 0.0802798 | − | 0.996772i | \(-0.474419\pi\) |
0.996772 | − | 0.0802798i | \(-0.0255814\pi\) | |||||||
\(812\) | 37.1713 | − | 29.0551i | 1.30446 | − | 1.01963i | ||||
\(813\) | 11.4428 | + | 11.4428i | 0.401317 | + | 0.401317i | ||||
\(814\) | −10.7691 | − | 0.657434i | −0.377458 | − | 0.0230430i | ||||
\(815\) | −21.9121 | −0.767549 | ||||||||
\(816\) | 10.3199 | + | 17.1575i | 0.361270 | + | 0.600632i | ||||
\(817\) | 5.05543 | 0.176867 | ||||||||
\(818\) | 53.6645 | + | 3.27610i | 1.87633 | + | 0.114546i | ||||
\(819\) | 12.6056 | + | 12.6056i | 0.440474 | + | 0.440474i | ||||
\(820\) | −3.88806 | − | 4.97415i | −0.135777 | − | 0.173705i | ||||
\(821\) | 2.40778 | − | 2.40778i | 0.0840320 | − | 0.0840320i | −0.663841 | − | 0.747873i | \(-0.731075\pi\) |
0.747873 | + | 0.663841i | \(0.231075\pi\) | |||||||
\(822\) | −13.4872 | − | 15.2410i | −0.470420 | − | 0.531591i | ||||
\(823\) | − | 32.4455i | − | 1.13098i | −0.824755 | − | 0.565490i | \(-0.808687\pi\) | ||
0.824755 | − | 0.565490i | \(-0.191313\pi\) | |||||||
\(824\) | −4.63808 | − | 0.857972i | −0.161575 | − | 0.0298889i | ||||
\(825\) | − | 4.96402i | − | 0.172825i | ||||||
\(826\) | 21.2733 | − | 18.8254i | 0.740193 | − | 0.655018i | ||||
\(827\) | 32.2278 | − | 32.2278i | 1.12067 | − | 1.12067i | 0.129028 | − | 0.991641i | \(-0.458814\pi\) |
0.991641 | − | 0.129028i | \(-0.0411857\pi\) | |||||||
\(828\) | 14.8530 | + | 1.82027i | 0.516176 | + | 0.0632587i | ||||
\(829\) | 29.6767 | + | 29.6767i | 1.03072 | + | 1.03072i | 0.999513 | + | 0.0312027i | \(0.00993375\pi\) |
0.0312027 | + | 0.999513i | \(0.490066\pi\) | |||||||
\(830\) | −0.348902 | + | 5.71522i | −0.0121106 | + | 0.198378i | ||||
\(831\) | 27.3968 | 0.950384 | ||||||||
\(832\) | 21.0142 | + | 47.1118i | 0.728538 | + | 1.63331i | ||||
\(833\) | 3.21915 | 0.111537 | ||||||||
\(834\) | 0.0356763 | − | 0.584399i | 0.00123537 | − | 0.0202361i | ||||
\(835\) | 1.25086 | + | 1.25086i | 0.0432877 | + | 0.0432877i | ||||
\(836\) | −11.3294 | − | 1.38844i | −0.391834 | − | 0.0480202i | ||||
\(837\) | 5.36151 | − | 5.36151i | 0.185321 | − | 0.185321i | ||||
\(838\) | 34.7932 | − | 30.7895i | 1.20191 | − | 1.06361i | ||||
\(839\) | 42.4417i | 1.46525i | 0.680632 | + | 0.732625i | \(0.261705\pi\) | ||||
−0.680632 | + | 0.732625i | \(0.738295\pi\) | |||||||
\(840\) | 7.68908 | + | 1.42236i | 0.265298 | + | 0.0490760i | ||||
\(841\) | 43.8072i | 1.51059i | ||||||||
\(842\) | 35.5055 | + | 40.1224i | 1.22360 | + | 1.38271i | ||||
\(843\) | −12.8542 | + | 12.8542i | −0.442723 | + | 0.442723i | ||||
\(844\) | 3.72349 | + | 4.76360i | 0.128168 | + | 0.163970i | ||||
\(845\) | −20.2091 | − | 20.2091i | −0.695214 | − | 0.695214i | ||||
\(846\) | 3.89609 | + | 0.237848i | 0.133950 | + | 0.00817738i | ||||
\(847\) | 37.7136 | 1.29586 | ||||||||
\(848\) | 31.0774 | − | 18.6925i | 1.06720 | − | 0.641904i | ||||
\(849\) | 10.9591 | 0.376115 | ||||||||
\(850\) | −7.06569 | − | 0.431345i | −0.242351 | − | 0.0147950i | ||||
\(851\) | 8.13103 | + | 8.13103i | 0.278728 | + | 0.278728i | ||||
\(852\) | −5.51882 | + | 4.31381i | −0.189072 | + | 0.147789i | ||||
\(853\) | −16.7844 | + | 16.7844i | −0.574686 | + | 0.574686i | −0.933434 | − | 0.358748i | \(-0.883204\pi\) |
0.358748 | + | 0.933434i | \(0.383204\pi\) | |||||||
\(854\) | 9.13257 | + | 10.3201i | 0.312510 | + | 0.353147i | ||||
\(855\) | 1.14968i | 0.0393183i | ||||||||
\(856\) | 13.8014 | + | 20.0664i | 0.471721 | + | 0.685854i | ||||
\(857\) | − | 31.0924i | − | 1.06210i | −0.847341 | − | 0.531049i | \(-0.821798\pi\) | ||
0.847341 | − | 0.531049i | \(-0.178202\pi\) | |||||||
\(858\) | 33.9003 | − | 29.9993i | 1.15734 | − | 1.02416i | ||||
\(859\) | −16.2508 | + | 16.2508i | −0.554469 | + | 0.554469i | −0.927727 | − | 0.373258i | \(-0.878241\pi\) |
0.373258 | + | 0.927727i | \(0.378241\pi\) | |||||||
\(860\) | −1.06978 | + | 8.72917i | −0.0364792 | + | 0.297662i | ||||
\(861\) | −6.17099 | − | 6.17099i | −0.210307 | − | 0.210307i | ||||
\(862\) | 0.790657 | − | 12.9514i | 0.0269299 | − | 0.441127i | ||||
\(863\) | −22.4656 | −0.764739 | −0.382369 | − | 0.924010i | \(-0.624892\pi\) | ||||
−0.382369 | + | 0.924010i | \(0.624892\pi\) | |||||||
\(864\) | 2.61491 | + | 5.01620i | 0.0889611 | + | 0.170654i | ||||
\(865\) | −5.67597 | −0.192989 | ||||||||
\(866\) | −3.15193 | + | 51.6304i | −0.107107 | + | 1.75447i | ||||
\(867\) | −5.69577 | − | 5.69577i | −0.193438 | − | 0.193438i | ||||
\(868\) | 5.09980 | − | 41.6132i | 0.173098 | − | 1.41244i | ||||
\(869\) | −31.4268 | + | 31.4268i | −1.06608 | + | 1.06608i | ||||
\(870\) | −9.03679 | + | 7.99692i | −0.306376 | + | 0.271121i | ||||
\(871\) | 28.6913i | 0.972169i | ||||||||
\(872\) | 9.62801 | − | 6.62201i | 0.326046 | − | 0.224250i | ||||
\(873\) | − | 8.24056i | − | 0.278901i | ||||||
\(874\) | 8.06185 | + | 9.11016i | 0.272696 | + | 0.308156i | ||||
\(875\) | −1.95488 | + | 1.95488i | −0.0660871 | + | 0.0660871i | ||||
\(876\) | −23.0287 | + | 18.0004i | −0.778066 | + | 0.608179i | ||||
\(877\) | 1.46527 | + | 1.46527i | 0.0494785 | + | 0.0494785i | 0.731413 | − | 0.681935i | \(-0.238861\pi\) |
−0.681935 | + | 0.731413i | \(0.738861\pi\) | |||||||
\(878\) | −9.82952 | − | 0.600071i | −0.331730 | − | 0.0202514i | ||||
\(879\) | 1.76172 | 0.0594213 | ||||||||
\(880\) | 4.79481 | − | 19.2685i | 0.161633 | − | 0.649540i | ||||
\(881\) | 0.578022 | 0.0194740 | 0.00973702 | − | 0.999953i | \(-0.496901\pi\) | ||||
0.00973702 | + | 0.999953i | \(0.496901\pi\) | |||||||
\(882\) | 0.907823 | + | 0.0554207i | 0.0305680 | + | 0.00186611i | ||||
\(883\) | −10.1372 | − | 10.1372i | −0.341144 | − | 0.341144i | 0.515653 | − | 0.856797i | \(-0.327549\pi\) |
−0.856797 | + | 0.515653i | \(0.827549\pi\) | |||||||
\(884\) | −39.7547 | − | 50.8597i | −1.33710 | − | 1.71060i | ||||
\(885\) | −5.13756 | + | 5.13756i | −0.172697 | + | 0.172697i | ||||
\(886\) | 2.85993 | + | 3.23182i | 0.0960813 | + | 0.108575i | ||||
\(887\) | 56.0202i | 1.88097i | 0.339831 | + | 0.940487i | \(0.389630\pi\) | ||||
−0.339831 | + | 0.940487i | \(0.610370\pi\) | |||||||
\(888\) | −0.790704 | + | 4.27444i | −0.0265343 | + | 0.143441i | ||||
\(889\) | − | 18.2762i | − | 0.612962i | ||||||
\(890\) | 7.66305 | − | 6.78126i | 0.256866 | − | 0.227308i | ||||
\(891\) | 3.51009 | − | 3.51009i | 0.117593 | − | 0.117593i | ||||
\(892\) | −26.7535 | − | 3.27871i | −0.895774 | − | 0.109779i | ||||
\(893\) | 2.24380 | + | 2.24380i | 0.0750860 | + | 0.0750860i | ||||
\(894\) | −1.33279 | + | 21.8319i | −0.0445752 | + | 0.730168i | ||||
\(895\) | 7.51428 | 0.251175 | ||||||||
\(896\) | 28.4722 | + | 12.9480i | 0.951191 | + | 0.432564i | ||||
\(897\) | −48.2461 | −1.61089 | ||||||||
\(898\) | −1.13509 | + | 18.5935i | −0.0378785 | + | 0.620472i | ||||
\(899\) | 45.7483 | + | 45.7483i | 1.52579 | + | 1.52579i | ||||
\(900\) | −1.98515 | − | 0.243285i | −0.0661716 | − | 0.00810949i | ||||
\(901\) | −32.0901 | + | 32.0901i | −1.06908 | + | 1.06908i | ||||
\(902\) | −16.5957 | + | 14.6860i | −0.552576 | + | 0.488991i | ||||
\(903\) | 12.1567i | 0.404549i | ||||||||
\(904\) | −1.46317 | + | 7.90970i | −0.0486643 | + | 0.263073i | ||||
\(905\) | − | 12.3732i | − | 0.411299i | ||||||
\(906\) | 12.6734 | + | 14.3214i | 0.421046 | + | 0.475796i | ||||
\(907\) | 31.3292 | − | 31.3292i | 1.04027 | − | 1.04027i | 0.0411133 | − | 0.999154i | \(-0.486910\pi\) |
0.999154 | − | 0.0411133i | \(-0.0130905\pi\) | |||||||
\(908\) | 4.71291 | + | 6.02941i | 0.156404 | + | 0.200093i | ||||
\(909\) | 1.07326 | + | 1.07326i | 0.0355979 | + | 0.0355979i | ||||
\(910\) | −25.1643 | − | 1.53623i | −0.834188 | − | 0.0509254i | ||||
\(911\) | −24.7701 | −0.820670 | −0.410335 | − | 0.911935i | \(-0.634588\pi\) | ||||
−0.410335 | + | 0.911935i | \(0.634588\pi\) | |||||||
\(912\) | −1.11049 | + | 4.46264i | −0.0367721 | + | 0.147773i | ||||
\(913\) | 20.0983 | 0.665157 | ||||||||
\(914\) | 14.1175 | + | 0.861843i | 0.466965 | + | 0.0285072i | ||||
\(915\) | −2.49234 | − | 2.49234i | −0.0823942 | − | 0.0823942i | ||||
\(916\) | −1.12993 | + | 0.883214i | −0.0373339 | + | 0.0291822i | ||||
\(917\) | 18.5264 | − | 18.5264i | 0.611796 | − | 0.611796i | ||||
\(918\) | −4.69119 | − | 5.30121i | −0.154832 | − | 0.174966i | ||||
\(919\) | 7.82495i | 0.258121i | 0.991637 | + | 0.129061i | \(0.0411962\pi\) | ||||
−0.991637 | + | 0.129061i | \(0.958804\pi\) | |||||||
\(920\) | −17.4364 | + | 11.9925i | −0.574861 | + | 0.395381i | ||||
\(921\) | − | 19.0979i | − | 0.629296i | ||||||
\(922\) | 2.68763 | − | 2.37836i | 0.0885122 | − | 0.0783271i | ||||
\(923\) | 15.9694 | − | 15.9694i | 0.525640 | − | 0.525640i | ||||
\(924\) | 3.33875 | − | 27.2435i | 0.109837 | − | 0.896244i | ||||
\(925\) | −1.08674 | − | 1.08674i | −0.0357318 | − | 0.0357318i | ||||
\(926\) | 0.222610 | − | 3.64648i | 0.00731542 | − | 0.119831i | ||||
\(927\) | 1.66763 | 0.0547721 | ||||||||
\(928\) | −42.8018 | + | 22.3123i | −1.40504 | + | 0.732437i | ||||
\(929\) | 54.8650 | 1.80006 | 0.900031 | − | 0.435826i | \(-0.143544\pi\) | ||||
0.900031 | + | 0.435826i | \(0.143544\pi\) | |||||||
\(930\) | −0.653402 | + | 10.7031i | −0.0214259 | + | 0.350969i | ||||
\(931\) | 0.522826 | + | 0.522826i | 0.0171349 | + | 0.0171349i | ||||
\(932\) | 1.98547 | − | 16.2010i | 0.0650362 | − | 0.530681i | ||||
\(933\) | 8.45340 | − | 8.45340i | 0.276752 | − | 0.276752i | ||||
\(934\) | −36.9661 | + | 32.7123i | −1.20957 | + | 1.07038i | ||||
\(935\) | 24.8474i | 0.812598i | ||||||||
\(936\) | −10.3355 | − | 15.0272i | −0.337827 | − | 0.491180i | ||||
\(937\) | 19.3306i | 0.631504i | 0.948842 | + | 0.315752i | \(0.102257\pi\) | ||||
−0.948842 | + | 0.315752i | \(0.897743\pi\) | |||||||
\(938\) | 11.5287 | + | 13.0278i | 0.376425 | + | 0.425373i | ||||
\(939\) | −10.7753 | + | 10.7753i | −0.351638 | + | 0.351638i | ||||
\(940\) | −4.34917 | + | 3.39954i | −0.141854 | + | 0.110881i | ||||
\(941\) | 11.4226 | + | 11.4226i | 0.372365 | + | 0.372365i | 0.868338 | − | 0.495973i | \(-0.165188\pi\) |
−0.495973 | + | 0.868338i | \(0.665188\pi\) | |||||||
\(942\) | 5.51947 | + | 0.336952i | 0.179834 | + | 0.0109785i | ||||
\(943\) | 23.6186 | 0.769129 | ||||||||
\(944\) | −24.9045 | + | 14.9797i | −0.810573 | + | 0.487546i | ||||
\(945\) | −2.76462 | −0.0899331 | ||||||||
\(946\) | 30.8121 | + | 1.88101i | 1.00179 | + | 0.0611570i | ||||
\(947\) | −26.8761 | − | 26.8761i | −0.873357 | − | 0.873357i | 0.119480 | − | 0.992837i | \(-0.461877\pi\) |
−0.992837 | + | 0.119480i | \(0.961877\pi\) | |||||||
\(948\) | 11.0276 | + | 14.1080i | 0.358159 | + | 0.458206i | ||||
\(949\) | 66.6364 | − | 66.6364i | 2.16311 | − | 2.16311i | ||||
\(950\) | −1.07749 | − | 1.21760i | −0.0349584 | − | 0.0395042i | ||||
\(951\) | − | 31.6871i | − | 1.02752i | ||||||
\(952\) | −38.4877 | − | 7.11962i | −1.24739 | − | 0.230748i | ||||
\(953\) | 36.6661i | 1.18773i | 0.804564 | + | 0.593866i | \(0.202399\pi\) | ||||
−0.804564 | + | 0.593866i | \(0.797601\pi\) | |||||||
\(954\) | −9.60208 | + | 8.49716i | −0.310879 | + | 0.275106i | ||||
\(955\) | 2.85521 | − | 2.85521i | 0.0923923 | − | 0.0923923i | ||||
\(956\) | 4.89134 | + | 0.599446i | 0.158197 | + | 0.0193875i | ||||
\(957\) | 29.9506 | + | 29.9506i | 0.968167 | + | 0.968167i | ||||
\(958\) | −0.120079 | + | 1.96696i | −0.00387957 | + | 0.0635496i | ||||
\(959\) | 39.7852 | 1.28473 | ||||||||
\(960\) | −7.47061 | − | 2.86182i | −0.241113 | − | 0.0923649i | ||||
\(961\) | 26.4917 | 0.854570 | ||||||||
\(962\) | 0.854004 | − | 13.9891i | 0.0275342 | − | 0.451026i | ||||
\(963\) | −6.08860 | − | 6.08860i | −0.196202 | − | 0.196202i | ||||
\(964\) | −14.6518 | − | 1.79562i | −0.471904 | − | 0.0578330i | ||||
\(965\) | −0.309084 | + | 0.309084i | −0.00994976 | + | 0.00994976i | ||||
\(966\) | −21.9070 | + | 19.3862i | −0.704847 | + | 0.623739i | ||||
\(967\) | − | 43.0462i | − | 1.38427i | −0.721767 | − | 0.692136i | \(-0.756670\pi\) | ||
0.721767 | − | 0.692136i | \(-0.243330\pi\) | |||||||
\(968\) | −37.9404 | − | 7.01838i | −1.21945 | − | 0.225579i | ||||
\(969\) | − | 5.75474i | − | 0.184869i | ||||||
\(970\) | 7.72311 | + | 8.72738i | 0.247974 | + | 0.280219i | ||||
\(971\) | −3.26831 | + | 3.26831i | −0.104885 | + | 0.104885i | −0.757602 | − | 0.652717i | \(-0.773629\pi\) |
0.652717 | + | 0.757602i | \(0.273629\pi\) | |||||||
\(972\) | −1.23168 | − | 1.57574i | −0.0395063 | − | 0.0505419i | ||||
\(973\) | 0.809324 | + | 0.809324i | 0.0259457 | + | 0.0259457i | ||||
\(974\) | −37.6955 | − | 2.30123i | −1.20784 | − | 0.0737362i | ||||
\(975\) | 6.44825 | 0.206509 | ||||||||
\(976\) | −7.26694 | − | 12.0817i | −0.232609 | − | 0.386726i | ||||
\(977\) | 1.62437 | 0.0519681 | 0.0259840 | − | 0.999662i | \(-0.491728\pi\) | ||||
0.0259840 | + | 0.999662i | \(0.491728\pi\) | |||||||
\(978\) | 30.9309 | + | 1.88826i | 0.989060 | + | 0.0603800i | ||||
\(979\) | −25.3976 | − | 25.3976i | −0.811712 | − | 0.811712i | ||||
\(980\) | −1.01339 | + | 0.792124i | −0.0323717 | + | 0.0253035i | ||||
\(981\) | −2.92136 | + | 2.92136i | −0.0932719 | + | 0.0932719i | ||||
\(982\) | 21.6385 | + | 24.4522i | 0.690511 | + | 0.780301i | ||||
\(983\) | − | 45.7756i | − | 1.46001i | −0.683439 | − | 0.730007i | \(-0.739517\pi\) | ||
0.683439 | − | 0.730007i | \(-0.260483\pi\) | |||||||
\(984\) | 5.05969 | + | 7.35649i | 0.161297 | + | 0.234516i | ||||
\(985\) | 16.5231i | 0.526471i | ||||||||
\(986\) | 45.2337 | − | 40.0286i | 1.44053 | − | 1.27477i | ||||
\(987\) | −5.39563 | + | 5.39563i | −0.171745 | + | 0.171745i | ||||
\(988\) | 1.80358 | − | 14.7168i | 0.0573795 | − | 0.468204i | ||||
\(989\) | −23.2641 | − | 23.2641i | −0.739754 | − | 0.739754i | ||||
\(990\) | −0.427771 | + | 7.00714i | −0.0135955 | + | 0.222702i | ||||
\(991\) | 11.0608 | 0.351357 | 0.175679 | − | 0.984448i | \(-0.443788\pi\) | ||||
0.175679 | + | 0.984448i | \(0.443788\pi\) | |||||||
\(992\) | −12.8745 | + | 40.9143i | −0.408767 | + | 1.29903i | ||||
\(993\) | −11.4785 | −0.364258 | ||||||||
\(994\) | 0.834401 | − | 13.6680i | 0.0264656 | − | 0.433522i | ||||
\(995\) | 11.1307 | + | 11.1307i | 0.352868 | + | 0.352868i | ||||
\(996\) | 0.985011 | − | 8.03746i | 0.0312113 | − | 0.254677i | ||||
\(997\) | 21.9716 | − | 21.9716i | 0.695848 | − | 0.695848i | −0.267664 | − | 0.963512i | \(-0.586252\pi\) |
0.963512 | + | 0.267664i | \(0.0862518\pi\) | |||||||
\(998\) | −39.6791 | + | 35.1132i | −1.25602 | + | 1.11149i | ||||
\(999\) | − | 1.53688i | − | 0.0486248i |
(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 | 240.2.s.c.61.6 | ✓ | 20 | |
3.2 | odd | 2 | 720.2.t.d.541.5 | 20 | |||
4.3 | odd | 2 | 960.2.s.c.721.7 | 20 | |||
8.3 | odd | 2 | 1920.2.s.f.1441.2 | 20 | |||
8.5 | even | 2 | 1920.2.s.e.1441.9 | 20 | |||
12.11 | even | 2 | 2880.2.t.d.721.7 | 20 | |||
16.3 | odd | 4 | 1920.2.s.f.481.4 | 20 | |||
16.5 | even | 4 | inner | 240.2.s.c.181.6 | yes | 20 | |
16.11 | odd | 4 | 960.2.s.c.241.9 | 20 | |||
16.13 | even | 4 | 1920.2.s.e.481.7 | 20 | |||
48.5 | odd | 4 | 720.2.t.d.181.5 | 20 | |||
48.11 | even | 4 | 2880.2.t.d.2161.9 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
240.2.s.c.61.6 | ✓ | 20 | 1.1 | even | 1 | trivial | |
240.2.s.c.181.6 | yes | 20 | 16.5 | even | 4 | inner | |
720.2.t.d.181.5 | 20 | 48.5 | odd | 4 | |||
720.2.t.d.541.5 | 20 | 3.2 | odd | 2 | |||
960.2.s.c.241.9 | 20 | 16.11 | odd | 4 | |||
960.2.s.c.721.7 | 20 | 4.3 | odd | 2 | |||
1920.2.s.e.481.7 | 20 | 16.13 | even | 4 | |||
1920.2.s.e.1441.9 | 20 | 8.5 | even | 2 | |||
1920.2.s.f.481.4 | 20 | 16.3 | odd | 4 | |||
1920.2.s.f.1441.2 | 20 | 8.3 | odd | 2 | |||
2880.2.t.d.721.7 | 20 | 12.11 | even | 2 | |||
2880.2.t.d.2161.9 | 20 | 48.11 | even | 4 |