Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,3,Mod(13,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([0, 19]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.13");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.k (of order \(20\), degree \(8\), 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: | \(2.04360198270\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{20})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 13.9 | ||
Character | \(\chi\) | \(=\) | 75.13 |
Dual form | 75.3.k.a.52.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{19}{20}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.92729 | − | 0.463638i | 1.46365 | − | 0.231819i | 0.626767 | − | 0.779207i | \(-0.284378\pi\) |
0.836879 | + | 0.547388i | \(0.184378\pi\) | |||||||
\(3\) | 0.786335 | − | 1.54327i | 0.262112 | − | 0.514423i | ||||
\(4\) | 4.54985 | − | 1.47834i | 1.13746 | − | 0.369584i | ||||
\(5\) | −2.61452 | + | 4.26196i | −0.522904 | + | 0.852391i | ||||
\(6\) | 1.58631 | − | 4.88217i | 0.264386 | − | 0.813695i | ||||
\(7\) | 2.66748 | − | 2.66748i | 0.381068 | − | 0.381068i | −0.490419 | − | 0.871487i | \(-0.663156\pi\) |
0.871487 | + | 0.490419i | \(0.163156\pi\) | |||||||
\(8\) | 2.07035 | − | 1.05489i | 0.258793 | − | 0.131862i | ||||
\(9\) | −1.76336 | − | 2.42705i | −0.195928 | − | 0.269672i | ||||
\(10\) | −5.67746 | + | 13.6882i | −0.567746 | + | 1.36882i | ||||
\(11\) | −2.59311 | − | 1.88400i | −0.235737 | − | 0.171273i | 0.463645 | − | 0.886021i | \(-0.346541\pi\) |
−0.699382 | + | 0.714748i | \(0.746541\pi\) | |||||||
\(12\) | 1.29624 | − | 8.18412i | 0.108020 | − | 0.682010i | ||||
\(13\) | −14.9551 | − | 2.36865i | −1.15039 | − | 0.182204i | −0.448026 | − | 0.894020i | \(-0.647873\pi\) |
−0.702366 | + | 0.711816i | \(0.747873\pi\) | |||||||
\(14\) | 6.57174 | − | 9.04523i | 0.469410 | − | 0.646088i | ||||
\(15\) | 4.52146 | + | 7.38623i | 0.301430 | + | 0.492415i | ||||
\(16\) | −9.90993 | + | 7.19998i | −0.619370 | + | 0.449999i | ||||
\(17\) | 5.47793 | + | 10.7510i | 0.322231 | + | 0.632414i | 0.994126 | − | 0.108233i | \(-0.0345192\pi\) |
−0.671894 | + | 0.740647i | \(0.734519\pi\) | |||||||
\(18\) | −6.28713 | − | 6.28713i | −0.349285 | − | 0.349285i | ||||
\(19\) | 22.7308 | + | 7.38568i | 1.19636 | + | 0.388720i | 0.838420 | − | 0.545025i | \(-0.183480\pi\) |
0.357938 | + | 0.933745i | \(0.383480\pi\) | |||||||
\(20\) | −5.59508 | + | 23.2564i | −0.279754 | + | 1.16282i | ||||
\(21\) | −2.01910 | − | 6.21416i | −0.0961478 | − | 0.295913i | ||||
\(22\) | −8.46427 | − | 4.31276i | −0.384740 | − | 0.196035i | ||||
\(23\) | 1.40503 | + | 8.87104i | 0.0610884 | + | 0.385697i | 0.999223 | + | 0.0394251i | \(0.0125526\pi\) |
−0.938134 | + | 0.346272i | \(0.887447\pi\) | |||||||
\(24\) | − | 4.02460i | − | 0.167692i | ||||||
\(25\) | −11.3286 | − | 22.2860i | −0.453143 | − | 0.891438i | ||||
\(26\) | −44.8761 | −1.72600 | ||||||||
\(27\) | −5.13218 | + | 0.812857i | −0.190081 | + | 0.0301058i | ||||
\(28\) | 8.19320 | − | 16.0801i | 0.292614 | − | 0.574288i | ||||
\(29\) | 30.5703 | − | 9.93290i | 1.05415 | − | 0.342514i | 0.269854 | − | 0.962901i | \(-0.413025\pi\) |
0.784295 | + | 0.620388i | \(0.213025\pi\) | |||||||
\(30\) | 16.6602 | + | 19.5253i | 0.555339 | + | 0.650845i | ||||
\(31\) | 11.6600 | − | 35.8856i | 0.376128 | − | 1.15760i | −0.566587 | − | 0.824002i | \(-0.691737\pi\) |
0.942715 | − | 0.333600i | \(-0.108263\pi\) | |||||||
\(32\) | −32.2432 | + | 32.2432i | −1.00760 | + | 1.00760i | ||||
\(33\) | −4.94657 | + | 2.52040i | −0.149896 | + | 0.0763758i | ||||
\(34\) | 21.0201 | + | 28.9317i | 0.618238 | + | 0.850931i | ||||
\(35\) | 4.39450 | + | 18.3429i | 0.125557 | + | 0.524082i | ||||
\(36\) | −11.6110 | − | 8.43589i | −0.322528 | − | 0.234330i | ||||
\(37\) | 10.4793 | − | 66.1635i | 0.283224 | − | 1.78820i | −0.278043 | − | 0.960569i | \(-0.589686\pi\) |
0.561267 | − | 0.827635i | \(-0.310314\pi\) | |||||||
\(38\) | 69.9639 | + | 11.0812i | 1.84116 | + | 0.291611i | ||||
\(39\) | −15.4152 | + | 21.2172i | −0.395261 | + | 0.544030i | ||||
\(40\) | −0.917050 | + | 11.5818i | −0.0229262 | + | 0.289544i | ||||
\(41\) | −55.8597 | + | 40.5844i | −1.36243 | + | 0.989864i | −0.364144 | + | 0.931343i | \(0.618639\pi\) |
−0.998286 | + | 0.0585212i | \(0.981361\pi\) | |||||||
\(42\) | −8.79163 | − | 17.2545i | −0.209325 | − | 0.410822i | ||||
\(43\) | −34.9751 | − | 34.9751i | −0.813374 | − | 0.813374i | 0.171764 | − | 0.985138i | \(-0.445053\pi\) |
−0.985138 | + | 0.171764i | \(0.945053\pi\) | |||||||
\(44\) | −14.5834 | − | 4.73845i | −0.331442 | − | 0.107692i | ||||
\(45\) | 14.9543 | − | 1.16977i | 0.332318 | − | 0.0259949i | ||||
\(46\) | 8.22589 | + | 25.3167i | 0.178824 | + | 0.550363i | ||||
\(47\) | 35.6128 | + | 18.1456i | 0.757718 | + | 0.386077i | 0.789765 | − | 0.613410i | \(-0.210202\pi\) |
−0.0320466 | + | 0.999486i | \(0.510202\pi\) | |||||||
\(48\) | 3.31899 | + | 20.9553i | 0.0691456 | + | 0.436568i | ||||
\(49\) | 34.7691i | 0.709574i | ||||||||
\(50\) | −43.4946 | − | 59.9851i | −0.869892 | − | 1.19970i | ||||
\(51\) | 20.8992 | 0.409789 | ||||||||
\(52\) | −71.5452 | + | 11.3316i | −1.37587 | + | 0.217916i | ||||
\(53\) | 33.9753 | − | 66.6802i | 0.641043 | − | 1.25812i | −0.310491 | − | 0.950576i | \(-0.600494\pi\) |
0.951535 | − | 0.307542i | \(-0.0995064\pi\) | |||||||
\(54\) | −14.6465 | + | 4.75894i | −0.271232 | + | 0.0881286i | ||||
\(55\) | 14.8093 | − | 6.12594i | 0.269259 | − | 0.111381i | ||||
\(56\) | 2.70870 | − | 8.33651i | 0.0483696 | − | 0.148866i | ||||
\(57\) | 29.2721 | − | 29.2721i | 0.513546 | − | 0.513546i | ||||
\(58\) | 84.8830 | − | 43.2501i | 1.46350 | − | 0.745691i | ||||
\(59\) | 6.33807 | + | 8.72361i | 0.107425 | + | 0.147858i | 0.859345 | − | 0.511397i | \(-0.170872\pi\) |
−0.751920 | + | 0.659255i | \(0.770872\pi\) | |||||||
\(60\) | 31.4913 | + | 26.9220i | 0.524855 | + | 0.448701i | ||||
\(61\) | 65.9802 | + | 47.9374i | 1.08164 | + | 0.785860i | 0.977969 | − | 0.208752i | \(-0.0669400\pi\) |
0.103674 | + | 0.994611i | \(0.466940\pi\) | |||||||
\(62\) | 17.4942 | − | 110.454i | 0.282164 | − | 1.78151i | ||||
\(63\) | −11.1778 | − | 1.77039i | −0.177426 | − | 0.0281015i | ||||
\(64\) | −50.6362 | + | 69.6948i | −0.791191 | + | 1.08898i | ||||
\(65\) | 49.1955 | − | 57.5451i | 0.756854 | − | 0.885309i | ||||
\(66\) | −13.3115 | + | 9.67137i | −0.201689 | + | 0.146536i | ||||
\(67\) | 3.44626 | + | 6.76367i | 0.0514368 | + | 0.100950i | 0.915294 | − | 0.402786i | \(-0.131958\pi\) |
−0.863857 | + | 0.503737i | \(0.831958\pi\) | |||||||
\(68\) | 40.8174 | + | 40.8174i | 0.600256 | + | 0.600256i | ||||
\(69\) | 14.7952 | + | 4.80726i | 0.214423 | + | 0.0696704i | ||||
\(70\) | 21.3684 | + | 51.6574i | 0.305263 | + | 0.737963i | ||||
\(71\) | 30.8556 | + | 94.9637i | 0.434586 | + | 1.33752i | 0.893511 | + | 0.449042i | \(0.148235\pi\) |
−0.458925 | + | 0.888475i | \(0.651765\pi\) | |||||||
\(72\) | −6.21104 | − | 3.16468i | −0.0862645 | − | 0.0439539i | ||||
\(73\) | −3.29433 | − | 20.7996i | −0.0451278 | − | 0.284926i | 0.954796 | − | 0.297262i | \(-0.0960733\pi\) |
−0.999924 | + | 0.0123357i | \(0.996073\pi\) | |||||||
\(74\) | − | 198.539i | − | 2.68295i | ||||||
\(75\) | −43.3013 | − | 0.0411995i | −0.577350 | − | 0.000549326i | ||||
\(76\) | 114.340 | 1.50448 | ||||||||
\(77\) | −11.9426 | + | 1.89152i | −0.155098 | + | 0.0245652i | ||||
\(78\) | −35.2877 | + | 69.2559i | −0.452406 | + | 0.887896i | ||||
\(79\) | −116.946 | + | 37.9981i | −1.48033 | + | 0.480988i | −0.934211 | − | 0.356720i | \(-0.883895\pi\) |
−0.546118 | + | 0.837708i | \(0.683895\pi\) | |||||||
\(80\) | −4.77631 | − | 61.0602i | −0.0597039 | − | 0.763252i | ||||
\(81\) | −2.78115 | + | 8.55951i | −0.0343352 | + | 0.105673i | ||||
\(82\) | −144.701 | + | 144.701i | −1.76465 | + | 1.76465i | ||||
\(83\) | −69.6419 | + | 35.4843i | −0.839059 | + | 0.427522i | −0.820046 | − | 0.572298i | \(-0.806052\pi\) |
−0.0190125 | + | 0.999819i | \(0.506052\pi\) | |||||||
\(84\) | −18.3733 | − | 25.2886i | −0.218729 | − | 0.301055i | ||||
\(85\) | −60.1426 | − | 4.76212i | −0.707560 | − | 0.0560249i | ||||
\(86\) | −118.598 | − | 86.1665i | −1.37905 | − | 1.00194i | ||||
\(87\) | 8.70937 | − | 54.9888i | 0.100108 | − | 0.632055i | ||||
\(88\) | −7.35605 | − | 1.16508i | −0.0835915 | − | 0.0132396i | ||||
\(89\) | −29.4736 | + | 40.5670i | −0.331165 | + | 0.455809i | −0.941835 | − | 0.336076i | \(-0.890900\pi\) |
0.610670 | + | 0.791885i | \(0.290900\pi\) | |||||||
\(90\) | 43.2333 | − | 10.3576i | 0.480370 | − | 0.115085i | ||||
\(91\) | −46.2107 | + | 33.5740i | −0.507810 | + | 0.368946i | ||||
\(92\) | 19.5071 | + | 38.2848i | 0.212034 | + | 0.416139i | ||||
\(93\) | −46.2126 | − | 46.2126i | −0.496909 | − | 0.496909i | ||||
\(94\) | 112.662 | + | 36.6061i | 1.19853 | + | 0.389426i | ||||
\(95\) | −90.9076 | + | 77.5676i | −0.956922 | + | 0.816501i | ||||
\(96\) | 24.4060 | + | 75.1139i | 0.254229 | + | 0.782436i | ||||
\(97\) | 53.7184 | + | 27.3709i | 0.553798 | + | 0.282174i | 0.708410 | − | 0.705801i | \(-0.249413\pi\) |
−0.154612 | + | 0.987975i | \(0.549413\pi\) | |||||||
\(98\) | 16.1203 | + | 101.779i | 0.164493 | + | 1.03857i | ||||
\(99\) | 9.61576i | 0.0971289i | ||||||||
\(100\) | −84.4895 | − | 84.6504i | −0.844895 | − | 0.846504i | ||||
\(101\) | 51.5051 | 0.509952 | 0.254976 | − | 0.966947i | \(-0.417932\pi\) | ||||
0.254976 | + | 0.966947i | \(0.417932\pi\) | |||||||
\(102\) | 61.1781 | − | 9.68967i | 0.599786 | − | 0.0949967i | ||||
\(103\) | −36.4251 | + | 71.4882i | −0.353641 | + | 0.694061i | −0.997468 | − | 0.0711106i | \(-0.977346\pi\) |
0.643827 | + | 0.765171i | \(0.277346\pi\) | |||||||
\(104\) | −33.4609 | + | 10.8721i | −0.321740 | + | 0.104540i | ||||
\(105\) | 31.7635 | + | 7.64172i | 0.302509 | + | 0.0727783i | ||||
\(106\) | 68.5401 | − | 210.945i | 0.646605 | − | 1.99005i | ||||
\(107\) | −30.1998 | + | 30.1998i | −0.282241 | + | 0.282241i | −0.834002 | − | 0.551761i | \(-0.813956\pi\) |
0.551761 | + | 0.834002i | \(0.313956\pi\) | |||||||
\(108\) | −22.1490 | + | 11.2855i | −0.205083 | + | 0.104495i | ||||
\(109\) | 15.3903 | + | 21.1830i | 0.141196 | + | 0.194339i | 0.873758 | − | 0.486361i | \(-0.161676\pi\) |
−0.732563 | + | 0.680700i | \(0.761676\pi\) | |||||||
\(110\) | 40.5108 | − | 24.7986i | 0.368280 | − | 0.225441i | ||||
\(111\) | −93.8679 | − | 68.1990i | −0.845657 | − | 0.614406i | ||||
\(112\) | −7.22871 | + | 45.6403i | −0.0645421 | + | 0.407503i | ||||
\(113\) | −186.893 | − | 29.6010i | −1.65392 | − | 0.261956i | −0.741424 | − | 0.671037i | \(-0.765849\pi\) |
−0.912498 | + | 0.409081i | \(0.865849\pi\) | |||||||
\(114\) | 72.1163 | − | 99.2596i | 0.632599 | − | 0.870698i | ||||
\(115\) | −41.4815 | − | 17.2053i | −0.360708 | − | 0.149611i | ||||
\(116\) | 124.406 | − | 90.3865i | 1.07247 | − | 0.779194i | ||||
\(117\) | 20.6223 | + | 40.4736i | 0.176259 | + | 0.345928i | ||||
\(118\) | 22.5980 | + | 22.5980i | 0.191508 | + | 0.191508i | ||||
\(119\) | 43.2904 | + | 14.0659i | 0.363785 | + | 0.118201i | ||||
\(120\) | 17.1527 | + | 10.5224i | 0.142939 | + | 0.0876867i | ||||
\(121\) | −34.2163 | − | 105.307i | −0.282780 | − | 0.870306i | ||||
\(122\) | 215.369 | + | 109.736i | 1.76532 | + | 0.899475i | ||||
\(123\) | 18.7083 | + | 118.119i | 0.152100 | + | 0.960320i | ||||
\(124\) | − | 180.512i | − | 1.45574i | ||||||
\(125\) | 124.601 | + | 9.98523i | 0.996804 | + | 0.0798818i | ||||
\(126\) | −33.5416 | −0.266203 | ||||||||
\(127\) | 26.9140 | − | 4.26276i | 0.211921 | − | 0.0335650i | −0.0495711 | − | 0.998771i | \(-0.515785\pi\) |
0.261492 | + | 0.965206i | \(0.415785\pi\) | |||||||
\(128\) | −33.1082 | + | 64.9786i | −0.258658 | + | 0.507645i | ||||
\(129\) | −81.4780 | + | 26.4738i | −0.631613 | + | 0.205223i | ||||
\(130\) | 117.330 | − | 191.260i | 0.902535 | − | 1.47123i | ||||
\(131\) | −18.0898 | + | 55.6746i | −0.138090 | + | 0.424997i | −0.996058 | − | 0.0887064i | \(-0.971727\pi\) |
0.857968 | + | 0.513703i | \(0.171727\pi\) | |||||||
\(132\) | −18.7802 | + | 18.7802i | −0.142274 | + | 0.142274i | ||||
\(133\) | 80.3350 | − | 40.9327i | 0.604023 | − | 0.307765i | ||||
\(134\) | 13.2241 | + | 18.2014i | 0.0986874 | + | 0.135832i | ||||
\(135\) | 9.95383 | − | 23.9984i | 0.0737320 | − | 0.177766i | ||||
\(136\) | 22.6824 | + | 16.4797i | 0.166783 | + | 0.121175i | ||||
\(137\) | 18.9766 | − | 119.813i | 0.138515 | − | 0.874549i | −0.816360 | − | 0.577543i | \(-0.804012\pi\) |
0.954875 | − | 0.297007i | \(-0.0959883\pi\) | |||||||
\(138\) | 45.5388 | + | 7.21263i | 0.329991 | + | 0.0522654i | ||||
\(139\) | 44.1543 | − | 60.7732i | 0.317657 | − | 0.437217i | −0.620093 | − | 0.784528i | \(-0.712905\pi\) |
0.937750 | + | 0.347311i | \(0.112905\pi\) | |||||||
\(140\) | 47.1113 | + | 76.9608i | 0.336509 | + | 0.549720i | ||||
\(141\) | 56.0071 | − | 40.6915i | 0.397213 | − | 0.288592i | ||||
\(142\) | 134.352 | + | 263.681i | 0.946141 | + | 1.85691i | ||||
\(143\) | 34.3176 | + | 34.3176i | 0.239983 | + | 0.239983i | ||||
\(144\) | 34.9495 | + | 11.3558i | 0.242705 | + | 0.0788595i | ||||
\(145\) | −37.5931 | + | 156.259i | −0.259263 | + | 1.07765i | ||||
\(146\) | −19.2869 | − | 59.3591i | −0.132102 | − | 0.406569i | ||||
\(147\) | 53.6581 | + | 27.3402i | 0.365021 | + | 0.185988i | ||||
\(148\) | −50.1329 | − | 316.526i | −0.338735 | − | 2.13869i | ||||
\(149\) | − | 106.919i | − | 0.717579i | −0.933418 | − | 0.358790i | \(-0.883190\pi\) | ||
0.933418 | − | 0.358790i | \(-0.116810\pi\) | |||||||
\(150\) | −126.775 | + | 19.9555i | −0.845163 | + | 0.133037i | ||||
\(151\) | 234.915 | 1.55573 | 0.777864 | − | 0.628432i | \(-0.216303\pi\) | ||||
0.777864 | + | 0.628432i | \(0.216303\pi\) | |||||||
\(152\) | 54.8517 | − | 8.68766i | 0.360867 | − | 0.0571557i | ||||
\(153\) | 16.4338 | − | 32.2531i | 0.107410 | − | 0.210805i | ||||
\(154\) | −34.0825 | + | 11.0741i | −0.221315 | + | 0.0719095i | ||||
\(155\) | 122.458 | + | 143.518i | 0.790051 | + | 0.925922i | ||||
\(156\) | −38.7707 | + | 119.324i | −0.248530 | + | 0.764897i | ||||
\(157\) | 45.9560 | − | 45.9560i | 0.292713 | − | 0.292713i | −0.545438 | − | 0.838151i | \(-0.683637\pi\) |
0.838151 | + | 0.545438i | \(0.183637\pi\) | |||||||
\(158\) | −324.718 | + | 165.452i | −2.05518 | + | 1.04716i | ||||
\(159\) | −76.1896 | − | 104.866i | −0.479180 | − | 0.659534i | ||||
\(160\) | −53.1187 | − | 221.720i | −0.331992 | − | 1.38575i | ||||
\(161\) | 27.4112 | + | 19.9154i | 0.170256 | + | 0.123698i | ||||
\(162\) | −4.17274 | + | 26.3456i | −0.0257576 | + | 0.162627i | ||||
\(163\) | −165.714 | − | 26.2466i | −1.01665 | − | 0.161022i | −0.374200 | − | 0.927348i | \(-0.622083\pi\) |
−0.642452 | + | 0.766326i | \(0.722083\pi\) | |||||||
\(164\) | −194.156 | + | 267.233i | −1.18388 | + | 1.62947i | ||||
\(165\) | 2.19106 | − | 27.6717i | 0.0132791 | − | 0.167707i | ||||
\(166\) | −187.410 | + | 136.162i | −1.12898 | + | 0.820250i | ||||
\(167\) | −10.2158 | − | 20.0497i | −0.0611726 | − | 0.120058i | 0.858396 | − | 0.512988i | \(-0.171461\pi\) |
−0.919568 | + | 0.392930i | \(0.871461\pi\) | |||||||
\(168\) | −10.7355 | − | 10.7355i | −0.0639020 | − | 0.0639020i | ||||
\(169\) | 57.3158 | + | 18.6230i | 0.339147 | + | 0.110195i | ||||
\(170\) | −178.263 | + | 13.9443i | −1.04861 | + | 0.0820251i | ||||
\(171\) | −22.1570 | − | 68.1924i | −0.129573 | − | 0.398786i | ||||
\(172\) | −210.836 | − | 107.427i | −1.22579 | − | 0.624573i | ||||
\(173\) | −33.2739 | − | 210.083i | −0.192335 | − | 1.21435i | −0.875182 | − | 0.483793i | \(-0.839259\pi\) |
0.682847 | − | 0.730561i | \(-0.260741\pi\) | |||||||
\(174\) | − | 165.006i | − | 0.948312i | ||||||
\(175\) | −89.6660 | − | 29.2286i | −0.512377 | − | 0.167021i | ||||
\(176\) | 39.2623 | 0.223081 | ||||||||
\(177\) | 18.4467 | − | 2.92167i | 0.104219 | − | 0.0165066i | ||||
\(178\) | −67.4696 | + | 132.417i | −0.379043 | + | 0.743913i | ||||
\(179\) | −243.955 | + | 79.2659i | −1.36288 | + | 0.442826i | −0.897003 | − | 0.442024i | \(-0.854261\pi\) |
−0.465876 | + | 0.884850i | \(0.654261\pi\) | |||||||
\(180\) | 66.3107 | − | 27.4298i | 0.368393 | − | 0.152388i | ||||
\(181\) | −37.1986 | + | 114.486i | −0.205517 | + | 0.632517i | 0.794174 | + | 0.607690i | \(0.207904\pi\) |
−0.999692 | + | 0.0248275i | \(0.992096\pi\) | |||||||
\(182\) | −119.706 | + | 119.706i | −0.657726 | + | 0.657726i | ||||
\(183\) | 125.863 | − | 64.1303i | 0.687775 | − | 0.350439i | ||||
\(184\) | 12.2669 | + | 16.8840i | 0.0666680 | + | 0.0917607i | ||||
\(185\) | 254.588 | + | 217.648i | 1.37615 | + | 1.17648i | ||||
\(186\) | −156.704 | − | 113.852i | −0.842492 | − | 0.612106i | ||||
\(187\) | 6.05013 | − | 38.1990i | 0.0323536 | − | 0.204273i | ||||
\(188\) | 188.858 | + | 29.9122i | 1.00456 | + | 0.159107i | ||||
\(189\) | −11.5217 | + | 15.8583i | −0.0609614 | + | 0.0839061i | ||||
\(190\) | −230.150 | + | 269.211i | −1.21131 | + | 1.41690i | ||||
\(191\) | 229.742 | − | 166.917i | 1.20284 | − | 0.873912i | 0.208276 | − | 0.978070i | \(-0.433215\pi\) |
0.994561 | + | 0.104158i | \(0.0332149\pi\) | |||||||
\(192\) | 67.7408 | + | 132.949i | 0.352816 | + | 0.692441i | ||||
\(193\) | 158.631 | + | 158.631i | 0.821924 | + | 0.821924i | 0.986384 | − | 0.164460i | \(-0.0525882\pi\) |
−0.164460 | + | 0.986384i | \(0.552588\pi\) | |||||||
\(194\) | 169.940 | + | 55.2167i | 0.875977 | + | 0.284622i | ||||
\(195\) | −50.1234 | − | 121.172i | −0.257043 | − | 0.621393i | ||||
\(196\) | 51.4005 | + | 158.194i | 0.262247 | + | 0.807115i | ||||
\(197\) | −299.748 | − | 152.729i | −1.52156 | − | 0.775274i | −0.524466 | − | 0.851431i | \(-0.675735\pi\) |
−0.997096 | + | 0.0761570i | \(0.975735\pi\) | |||||||
\(198\) | 4.45823 | + | 28.1482i | 0.0225163 | + | 0.142162i | ||||
\(199\) | 174.588i | 0.877327i | 0.898651 | + | 0.438663i | \(0.144548\pi\) | ||||
−0.898651 | + | 0.438663i | \(0.855452\pi\) | |||||||
\(200\) | −46.9634 | − | 34.1892i | −0.234817 | − | 0.170946i | ||||
\(201\) | 13.1481 | 0.0654134 | ||||||||
\(202\) | 150.771 | − | 23.8797i | 0.746389 | − | 0.118216i | ||||
\(203\) | 55.0499 | − | 108.041i | 0.271182 | − | 0.532224i | ||||
\(204\) | 95.0884 | − | 30.8961i | 0.466120 | − | 0.151452i | ||||
\(205\) | −26.9228 | − | 344.180i | −0.131331 | − | 1.67893i | ||||
\(206\) | −73.4822 | + | 226.155i | −0.356710 | + | 1.09784i | ||||
\(207\) | 19.0529 | − | 19.0529i | 0.0920429 | − | 0.0920429i | ||||
\(208\) | 165.258 | − | 84.2032i | 0.794510 | − | 0.404823i | ||||
\(209\) | −45.0287 | − | 61.9767i | −0.215448 | − | 0.296539i | ||||
\(210\) | 96.5240 | + | 7.64281i | 0.459638 | + | 0.0363943i | ||||
\(211\) | 257.285 | + | 186.929i | 1.21936 | + | 0.885917i | 0.996047 | − | 0.0888292i | \(-0.0283125\pi\) |
0.223314 | + | 0.974747i | \(0.428313\pi\) | |||||||
\(212\) | 56.0067 | − | 353.612i | 0.264183 | − | 1.66798i | ||||
\(213\) | 170.817 | + | 27.0548i | 0.801959 | + | 0.127018i | ||||
\(214\) | −74.4020 | + | 102.406i | −0.347673 | + | 0.478530i | ||||
\(215\) | 240.505 | − | 57.6192i | 1.11863 | − | 0.267996i | ||||
\(216\) | −9.76791 | + | 7.09680i | −0.0452218 | + | 0.0328556i | ||||
\(217\) | −64.6215 | − | 126.827i | −0.297795 | − | 0.584455i | ||||
\(218\) | 54.8732 | + | 54.8732i | 0.251712 | + | 0.251712i | ||||
\(219\) | −34.6898 | − | 11.2714i | −0.158401 | − | 0.0514676i | ||||
\(220\) | 58.3238 | − | 49.7652i | 0.265108 | − | 0.226206i | ||||
\(221\) | −56.4574 | − | 173.758i | −0.255464 | − | 0.786236i | ||||
\(222\) | −306.398 | − | 156.118i | −1.38017 | − | 0.703233i | ||||
\(223\) | 38.5866 | + | 243.626i | 0.173034 | + | 1.09249i | 0.909404 | + | 0.415915i | \(0.136539\pi\) |
−0.736369 | + | 0.676580i | \(0.763461\pi\) | |||||||
\(224\) | 172.016i | 0.767929i | ||||||||
\(225\) | −34.1129 | + | 66.7931i | −0.151613 | + | 0.296858i | ||||
\(226\) | −560.815 | −2.48148 | ||||||||
\(227\) | −27.5940 | + | 4.37046i | −0.121559 | + | 0.0192531i | −0.216918 | − | 0.976190i | \(-0.569600\pi\) |
0.0953583 | + | 0.995443i | \(0.469600\pi\) | |||||||
\(228\) | 89.9097 | − | 176.458i | 0.394341 | − | 0.773938i | ||||
\(229\) | 94.0683 | − | 30.5646i | 0.410779 | − | 0.133470i | −0.0963357 | − | 0.995349i | \(-0.530712\pi\) |
0.507114 | + | 0.861879i | \(0.330712\pi\) | |||||||
\(230\) | −129.405 | − | 31.1326i | −0.562632 | − | 0.135359i | ||||
\(231\) | −6.47174 | + | 19.9180i | −0.0280162 | + | 0.0862250i | ||||
\(232\) | 52.8130 | − | 52.8130i | 0.227642 | − | 0.227642i | ||||
\(233\) | 173.156 | − | 88.2272i | 0.743158 | − | 0.378658i | −0.0410493 | − | 0.999157i | \(-0.513070\pi\) |
0.784207 | + | 0.620499i | \(0.213070\pi\) | |||||||
\(234\) | 79.1326 | + | 108.917i | 0.338173 | + | 0.465456i | ||||
\(235\) | −170.446 | + | 104.338i | −0.725303 | + | 0.443992i | ||||
\(236\) | 41.7337 | + | 30.3213i | 0.176838 | + | 0.128480i | ||||
\(237\) | −33.3175 | + | 210.358i | −0.140580 | + | 0.887588i | ||||
\(238\) | 133.245 | + | 21.1040i | 0.559854 | + | 0.0886721i | ||||
\(239\) | 72.7549 | − | 100.138i | 0.304414 | − | 0.418989i | −0.629215 | − | 0.777231i | \(-0.716624\pi\) |
0.933629 | + | 0.358242i | \(0.116624\pi\) | |||||||
\(240\) | −97.9881 | − | 40.6426i | −0.408284 | − | 0.169344i | ||||
\(241\) | −136.086 | + | 98.8722i | −0.564672 | + | 0.410258i | −0.833166 | − | 0.553023i | \(-0.813474\pi\) |
0.268494 | + | 0.963281i | \(0.413474\pi\) | |||||||
\(242\) | −148.985 | − | 292.400i | −0.615642 | − | 1.20827i | ||||
\(243\) | 11.0227 | + | 11.0227i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 371.068 | + | 120.567i | 1.52077 | + | 0.494129i | ||||
\(245\) | −148.185 | − | 90.9046i | −0.604835 | − | 0.371039i | ||||
\(246\) | 109.529 | + | 337.096i | 0.445240 | + | 1.37031i | ||||
\(247\) | −322.447 | − | 164.295i | −1.30545 | − | 0.665162i | ||||
\(248\) | −13.7154 | − | 86.5958i | −0.0553041 | − | 0.349176i | ||||
\(249\) | 135.379i | 0.543689i | ||||||||
\(250\) | 369.372 | − | 28.5398i | 1.47749 | − | 0.114159i | ||||
\(251\) | −107.500 | −0.428287 | −0.214144 | − | 0.976802i | \(-0.568696\pi\) | ||||
−0.214144 | + | 0.976802i | \(0.568696\pi\) | |||||||
\(252\) | −53.4747 | + | 8.46956i | −0.212201 | + | 0.0336094i | ||||
\(253\) | 13.0696 | − | 25.6506i | 0.0516587 | − | 0.101386i | ||||
\(254\) | 76.8087 | − | 24.9567i | 0.302397 | − | 0.0982546i | ||||
\(255\) | −54.6415 | + | 89.0716i | −0.214280 | + | 0.349300i | ||||
\(256\) | 39.6932 | − | 122.163i | 0.155052 | − | 0.477200i | ||||
\(257\) | −87.6024 | + | 87.6024i | −0.340865 | + | 0.340865i | −0.856693 | − | 0.515827i | \(-0.827485\pi\) |
0.515827 | + | 0.856693i | \(0.327485\pi\) | |||||||
\(258\) | −226.236 | + | 115.273i | −0.876883 | + | 0.446794i | ||||
\(259\) | −148.537 | − | 204.443i | −0.573500 | − | 0.789355i | ||||
\(260\) | 138.761 | − | 334.549i | 0.533698 | − | 1.28673i | ||||
\(261\) | −78.0140 | − | 56.6805i | −0.298904 | − | 0.217167i | ||||
\(262\) | −27.1412 | + | 171.363i | −0.103592 | + | 0.654057i | ||||
\(263\) | 54.9321 | + | 8.70039i | 0.208867 | + | 0.0330813i | 0.259991 | − | 0.965611i | \(-0.416280\pi\) |
−0.0511239 | + | 0.998692i | \(0.516280\pi\) | |||||||
\(264\) | −7.58235 | + | 10.4362i | −0.0287210 | + | 0.0395311i | ||||
\(265\) | 195.359 | + | 319.138i | 0.737205 | + | 1.20429i | ||||
\(266\) | 216.186 | − | 157.068i | 0.812730 | − | 0.590483i | ||||
\(267\) | 39.4296 | + | 77.3850i | 0.147676 | + | 0.289831i | ||||
\(268\) | 25.6790 | + | 25.6790i | 0.0958171 | + | 0.0958171i | ||||
\(269\) | 27.6442 | + | 8.98216i | 0.102767 | + | 0.0333909i | 0.359949 | − | 0.932972i | \(-0.382794\pi\) |
−0.257182 | + | 0.966363i | \(0.582794\pi\) | |||||||
\(270\) | 18.0112 | − | 74.8652i | 0.0667082 | − | 0.277278i | ||||
\(271\) | −95.3779 | − | 293.543i | −0.351948 | − | 1.08318i | −0.957758 | − | 0.287575i | \(-0.907151\pi\) |
0.605810 | − | 0.795609i | \(-0.292849\pi\) | |||||||
\(272\) | −131.693 | − | 67.1010i | −0.484166 | − | 0.246695i | ||||
\(273\) | 15.4767 | + | 97.7160i | 0.0566912 | + | 0.357934i | ||||
\(274\) | − | 359.527i | − | 1.31214i | ||||||
\(275\) | −12.6106 | + | 79.1329i | −0.0458567 | + | 0.287756i | ||||
\(276\) | 74.4228 | 0.269648 | ||||||||
\(277\) | 194.312 | − | 30.7760i | 0.701488 | − | 0.111105i | 0.204506 | − | 0.978865i | \(-0.434441\pi\) |
0.496982 | + | 0.867761i | \(0.334441\pi\) | |||||||
\(278\) | 101.076 | − | 198.372i | 0.363582 | − | 0.713570i | ||||
\(279\) | −107.657 | + | 34.9799i | −0.385867 | + | 0.125376i | ||||
\(280\) | 28.4479 | + | 33.3403i | 0.101600 | + | 0.119073i | ||||
\(281\) | −83.9149 | + | 258.264i | −0.298630 | + | 0.919088i | 0.683348 | + | 0.730092i | \(0.260523\pi\) |
−0.981978 | + | 0.188995i | \(0.939477\pi\) | |||||||
\(282\) | 145.083 | − | 145.083i | 0.514479 | − | 0.514479i | ||||
\(283\) | 222.387 | − | 113.312i | 0.785818 | − | 0.400394i | −0.0145569 | − | 0.999894i | \(-0.504634\pi\) |
0.800375 | + | 0.599500i | \(0.204634\pi\) | |||||||
\(284\) | 280.777 | + | 386.456i | 0.988651 | + | 1.36076i | ||||
\(285\) | 48.2239 | + | 201.289i | 0.169207 | + | 0.706277i | ||||
\(286\) | 116.369 | + | 84.5467i | 0.406883 | + | 0.295618i | ||||
\(287\) | −40.7464 | + | 257.262i | −0.141973 | + | 0.896385i | ||||
\(288\) | 135.112 | + | 21.3997i | 0.469140 | + | 0.0743044i | ||||
\(289\) | 84.2928 | − | 116.019i | 0.291671 | − | 0.401450i | ||||
\(290\) | −37.5985 | + | 474.846i | −0.129650 | + | 1.63740i | ||||
\(291\) | 84.4813 | − | 61.3792i | 0.290314 | − | 0.210925i | ||||
\(292\) | −45.7375 | − | 89.7650i | −0.156635 | − | 0.307414i | ||||
\(293\) | −355.357 | − | 355.357i | −1.21282 | − | 1.21282i | −0.970094 | − | 0.242728i | \(-0.921958\pi\) |
−0.242728 | − | 0.970094i | \(-0.578042\pi\) | |||||||
\(294\) | 169.749 | + | 55.1547i | 0.577377 | + | 0.187601i | ||||
\(295\) | −53.7507 | + | 4.20454i | −0.182206 | + | 0.0142527i | ||||
\(296\) | −48.0998 | − | 148.036i | −0.162499 | − | 0.500122i | ||||
\(297\) | 14.8397 | + | 7.56121i | 0.0499653 | + | 0.0254586i | ||||
\(298\) | −49.5718 | − | 312.984i | −0.166348 | − | 1.05028i | ||||
\(299\) | − | 135.995i | − | 0.454834i | ||||||
\(300\) | −197.075 | + | 63.8264i | −0.656918 | + | 0.212755i | ||||
\(301\) | −186.590 | −0.619902 | ||||||||
\(302\) | 687.665 | − | 108.915i | 2.27704 | − | 0.360647i | ||||
\(303\) | 40.5003 | − | 79.4862i | 0.133664 | − | 0.262331i | ||||
\(304\) | −278.437 | + | 90.4697i | −0.915912 | + | 0.297598i | ||||
\(305\) | −376.814 | + | 155.872i | −1.23546 | + | 0.511054i | ||||
\(306\) | 33.1527 | − | 102.034i | 0.108342 | − | 0.333443i | ||||
\(307\) | 227.454 | − | 227.454i | 0.740893 | − | 0.740893i | −0.231857 | − | 0.972750i | \(-0.574480\pi\) |
0.972750 | + | 0.231857i | \(0.0744800\pi\) | |||||||
\(308\) | −51.5407 | + | 26.2613i | −0.167340 | + | 0.0852640i | ||||
\(309\) | 81.6832 | + | 112.427i | 0.264347 | + | 0.363843i | ||||
\(310\) | 425.010 | + | 363.343i | 1.37100 | + | 1.17207i | ||||
\(311\) | 67.6661 | + | 49.1623i | 0.217576 | + | 0.158078i | 0.691235 | − | 0.722630i | \(-0.257067\pi\) |
−0.473659 | + | 0.880708i | \(0.657067\pi\) | |||||||
\(312\) | −9.53289 | + | 60.1883i | −0.0305541 | + | 0.192911i | ||||
\(313\) | −443.561 | − | 70.2532i | −1.41713 | − | 0.224451i | −0.599582 | − | 0.800313i | \(-0.704667\pi\) |
−0.817547 | + | 0.575862i | \(0.804667\pi\) | |||||||
\(314\) | 113.220 | − | 155.834i | 0.360572 | − | 0.496285i | ||||
\(315\) | 36.7700 | − | 43.0107i | 0.116730 | − | 0.136542i | ||||
\(316\) | −475.913 | + | 345.771i | −1.50605 | + | 1.09421i | ||||
\(317\) | 51.5638 | + | 101.200i | 0.162662 | + | 0.319242i | 0.957923 | − | 0.287025i | \(-0.0926664\pi\) |
−0.795261 | + | 0.606267i | \(0.792666\pi\) | |||||||
\(318\) | −271.649 | − | 271.649i | −0.854242 | − | 0.854242i | ||||
\(319\) | −97.9857 | − | 31.8375i | −0.307165 | − | 0.0998040i | ||||
\(320\) | −164.647 | − | 398.028i | −0.514521 | − | 1.24384i | ||||
\(321\) | 22.8593 | + | 70.3536i | 0.0712127 | + | 0.219170i | ||||
\(322\) | 89.4741 | + | 45.5893i | 0.277870 | + | 0.141582i | ||||
\(323\) | 45.1139 | + | 284.838i | 0.139671 | + | 0.881851i | ||||
\(324\) | 43.0560i | 0.132889i | ||||||||
\(325\) | 116.632 | + | 360.122i | 0.358868 | + | 1.10807i | ||||
\(326\) | −497.263 | −1.52535 | ||||||||
\(327\) | 44.7930 | − | 7.09451i | 0.136982 | − | 0.0216957i | ||||
\(328\) | −72.8366 | + | 142.950i | −0.222063 | + | 0.435823i | ||||
\(329\) | 143.399 | − | 46.5932i | 0.435864 | − | 0.141621i | ||||
\(330\) | −6.41578 | − | 82.0190i | −0.0194418 | − | 0.248543i | ||||
\(331\) | 177.857 | − | 547.387i | 0.537332 | − | 1.65374i | −0.201224 | − | 0.979545i | \(-0.564492\pi\) |
0.738556 | − | 0.674193i | \(-0.235508\pi\) | |||||||
\(332\) | −264.403 | + | 264.403i | −0.796393 | + | 0.796393i | ||||
\(333\) | −179.061 | + | 91.2361i | −0.537721 | + | 0.273982i | ||||
\(334\) | −39.2005 | − | 53.9548i | −0.117367 | − | 0.161541i | ||||
\(335\) | −37.8368 | − | 2.99593i | −0.112946 | − | 0.00894309i | ||||
\(336\) | 64.7511 | + | 47.0444i | 0.192712 | + | 0.140013i | ||||
\(337\) | −29.5779 | + | 186.748i | −0.0877683 | + | 0.554147i | 0.904145 | + | 0.427227i | \(0.140509\pi\) |
−0.991913 | + | 0.126921i | \(0.959491\pi\) | |||||||
\(338\) | 176.414 | + | 27.9413i | 0.521936 | + | 0.0826665i | ||||
\(339\) | −192.643 | + | 265.150i | −0.568268 | + | 0.782154i | ||||
\(340\) | −280.680 | + | 67.2442i | −0.825530 | + | 0.197777i | ||||
\(341\) | −97.8441 | + | 71.0879i | −0.286933 | + | 0.208469i | ||||
\(342\) | −96.4767 | − | 189.346i | −0.282096 | − | 0.553644i | ||||
\(343\) | 223.452 | + | 223.452i | 0.651464 | + | 0.651464i | ||||
\(344\) | −109.306 | − | 35.5155i | −0.317749 | − | 0.103243i | ||||
\(345\) | −59.1707 | + | 50.4879i | −0.171509 | + | 0.146342i | ||||
\(346\) | −194.805 | − | 599.548i | −0.563020 | − | 1.73280i | ||||
\(347\) | 333.286 | + | 169.818i | 0.960480 | + | 0.489389i | 0.862643 | − | 0.505814i | \(-0.168808\pi\) |
0.0978368 | + | 0.995202i | \(0.468808\pi\) | |||||||
\(348\) | −41.6656 | − | 263.066i | −0.119729 | − | 0.755938i | ||||
\(349\) | − | 156.078i | − | 0.447215i | −0.974679 | − | 0.223607i | \(-0.928217\pi\) | ||
0.974679 | − | 0.223607i | \(-0.0717833\pi\) | |||||||
\(350\) | −276.030 | − | 43.9881i | −0.788657 | − | 0.125680i | ||||
\(351\) | 78.6776 | 0.224153 | ||||||||
\(352\) | 144.356 | − | 22.8638i | 0.410103 | − | 0.0649540i | ||||
\(353\) | 43.4608 | − | 85.2966i | 0.123118 | − | 0.241633i | −0.821218 | − | 0.570614i | \(-0.806705\pi\) |
0.944337 | + | 0.328981i | \(0.106705\pi\) | |||||||
\(354\) | 52.6443 | − | 17.1052i | 0.148713 | − | 0.0483197i | ||||
\(355\) | −485.404 | − | 116.779i | −1.36733 | − | 0.328956i | ||||
\(356\) | −74.1291 | + | 228.146i | −0.208228 | + | 0.640859i | ||||
\(357\) | 55.7482 | − | 55.7482i | 0.156157 | − | 0.156157i | ||||
\(358\) | −677.378 | + | 345.141i | −1.89212 | + | 0.964082i | ||||
\(359\) | −129.426 | − | 178.139i | −0.360517 | − | 0.496209i | 0.589776 | − | 0.807567i | \(-0.299216\pi\) |
−0.950293 | + | 0.311358i | \(0.899216\pi\) | |||||||
\(360\) | 29.7266 | − | 18.1971i | 0.0825740 | − | 0.0505474i | ||||
\(361\) | 170.085 | + | 123.574i | 0.471151 | + | 0.342311i | ||||
\(362\) | −55.8115 | + | 352.380i | −0.154175 | + | 0.973424i | ||||
\(363\) | −189.422 | − | 30.0016i | −0.521825 | − | 0.0826490i | ||||
\(364\) | −160.618 | + | 221.072i | −0.441259 | + | 0.607341i | ||||
\(365\) | 97.2600 | + | 40.3407i | 0.266466 | + | 0.110522i | ||||
\(366\) | 338.704 | − | 246.083i | 0.925421 | − | 0.672358i | ||||
\(367\) | 198.031 | + | 388.657i | 0.539593 | + | 1.05901i | 0.986397 | + | 0.164379i | \(0.0525621\pi\) |
−0.446804 | + | 0.894632i | \(0.647438\pi\) | |||||||
\(368\) | −77.7951 | − | 77.7951i | −0.211400 | − | 0.211400i | ||||
\(369\) | 197.001 | + | 64.0095i | 0.533878 | + | 0.173467i | ||||
\(370\) | 846.163 | + | 519.083i | 2.28693 | + | 1.40293i | ||||
\(371\) | −87.2398 | − | 268.496i | −0.235148 | − | 0.723710i | ||||
\(372\) | −278.578 | − | 141.943i | −0.748866 | − | 0.381566i | ||||
\(373\) | 33.7994 | + | 213.401i | 0.0906150 | + | 0.572120i | 0.990663 | + | 0.136330i | \(0.0435309\pi\) |
−0.900048 | + | 0.435790i | \(0.856469\pi\) | |||||||
\(374\) | − | 114.625i | − | 0.306483i | ||||||
\(375\) | 113.388 | − | 184.440i | 0.302367 | − | 0.491841i | ||||
\(376\) | 92.8725 | 0.247001 | ||||||||
\(377\) | −480.710 | + | 76.1369i | −1.27509 | + | 0.201955i | ||||
\(378\) | −26.3749 | + | 51.7636i | −0.0697748 | + | 0.136941i | ||||
\(379\) | 181.518 | − | 58.9787i | 0.478938 | − | 0.155617i | −0.0595916 | − | 0.998223i | \(-0.518980\pi\) |
0.538530 | + | 0.842606i | \(0.318980\pi\) | |||||||
\(380\) | −298.945 | + | 487.314i | −0.786698 | + | 1.28240i | ||||
\(381\) | 14.5848 | − | 44.8875i | 0.0382804 | − | 0.117815i | ||||
\(382\) | 595.132 | − | 595.132i | 1.55794 | − | 1.55794i | ||||
\(383\) | 372.337 | − | 189.715i | 0.972159 | − | 0.495340i | 0.105597 | − | 0.994409i | \(-0.466325\pi\) |
0.866562 | + | 0.499069i | \(0.166325\pi\) | |||||||
\(384\) | 74.2452 | + | 102.190i | 0.193347 | + | 0.266119i | ||||
\(385\) | 23.1626 | − | 55.8442i | 0.0601625 | − | 0.145050i | ||||
\(386\) | 537.907 | + | 390.813i | 1.39354 | + | 1.01247i | ||||
\(387\) | −23.2128 | + | 146.560i | −0.0599814 | + | 0.378707i | ||||
\(388\) | 284.874 | + | 45.1197i | 0.734212 | + | 0.116288i | ||||
\(389\) | 238.891 | − | 328.805i | 0.614116 | − | 0.845258i | −0.382792 | − | 0.923834i | \(-0.625038\pi\) |
0.996908 | + | 0.0785766i | \(0.0250375\pi\) | |||||||
\(390\) | −202.905 | − | 331.466i | −0.520270 | − | 0.849912i | ||||
\(391\) | −87.6762 | + | 63.7005i | −0.224236 | + | 0.162917i | ||||
\(392\) | 36.6778 | + | 71.9841i | 0.0935657 | + | 0.183633i | ||||
\(393\) | 71.6962 | + | 71.6962i | 0.182433 | + | 0.182433i | ||||
\(394\) | −948.260 | − | 308.108i | −2.40675 | − | 0.782001i | ||||
\(395\) | 143.812 | − | 597.766i | 0.364080 | − | 1.51333i | ||||
\(396\) | 14.2153 | + | 43.7503i | 0.0358973 | + | 0.110481i | ||||
\(397\) | −476.549 | − | 242.814i | −1.20038 | − | 0.611622i | −0.264648 | − | 0.964345i | \(-0.585256\pi\) |
−0.935728 | + | 0.352723i | \(0.885256\pi\) | |||||||
\(398\) | 80.9456 | + | 511.070i | 0.203381 | + | 1.28410i | ||||
\(399\) | − | 156.165i | − | 0.391392i | ||||||
\(400\) | 272.724 | + | 139.287i | 0.681809 | + | 0.348217i | ||||
\(401\) | −283.049 | −0.705859 | −0.352929 | − | 0.935650i | \(-0.614814\pi\) | ||||
−0.352929 | + | 0.935650i | \(0.614814\pi\) | |||||||
\(402\) | 38.4883 | − | 6.09595i | 0.0957420 | − | 0.0151640i | ||||
\(403\) | −259.376 | + | 509.055i | −0.643614 | + | 1.26316i | ||||
\(404\) | 234.341 | − | 76.1419i | 0.580051 | − | 0.188470i | ||||
\(405\) | −29.2089 | − | 34.2322i | −0.0721207 | − | 0.0845239i | ||||
\(406\) | 111.055 | − | 341.792i | 0.273534 | − | 0.841853i | ||||
\(407\) | −151.826 | + | 151.826i | −0.373037 | + | 0.373037i | ||||
\(408\) | 43.2687 | − | 22.0465i | 0.106051 | − | 0.0540355i | ||||
\(409\) | 187.227 | + | 257.695i | 0.457767 | + | 0.630062i | 0.974044 | − | 0.226360i | \(-0.0726825\pi\) |
−0.516277 | + | 0.856422i | \(0.672682\pi\) | |||||||
\(410\) | −238.386 | − | 995.034i | −0.581429 | − | 2.42691i | ||||
\(411\) | −169.982 | − | 123.499i | −0.413582 | − | 0.300485i | ||||
\(412\) | −60.0451 | + | 379.110i | −0.145740 | + | 0.920169i | ||||
\(413\) | 40.1767 | + | 6.36336i | 0.0972801 | + | 0.0154077i | ||||
\(414\) | 46.9397 | − | 64.6070i | 0.113381 | − | 0.156056i | ||||
\(415\) | 30.8475 | − | 389.585i | 0.0743313 | − | 0.938759i | ||||
\(416\) | 558.573 | − | 405.827i | 1.34272 | − | 0.975546i | ||||
\(417\) | −59.0693 | − | 115.930i | −0.141653 | − | 0.278010i | ||||
\(418\) | −160.547 | − | 160.547i | −0.384083 | − | 0.384083i | ||||
\(419\) | 585.104 | + | 190.112i | 1.39643 | + | 0.453728i | 0.908035 | − | 0.418895i | \(-0.137582\pi\) |
0.488395 | + | 0.872622i | \(0.337582\pi\) | |||||||
\(420\) | 155.816 | − | 12.1884i | 0.370991 | − | 0.0290201i | ||||
\(421\) | 109.343 | + | 336.522i | 0.259721 | + | 0.799341i | 0.992863 | + | 0.119264i | \(0.0380535\pi\) |
−0.733141 | + | 0.680077i | \(0.761947\pi\) | |||||||
\(422\) | 839.816 | + | 427.908i | 1.99008 | + | 1.01400i | ||||
\(423\) | −18.7577 | − | 118.431i | −0.0443443 | − | 0.279979i | ||||
\(424\) | − | 173.892i | − | 0.410122i | ||||||
\(425\) | 177.540 | − | 243.875i | 0.417741 | − | 0.573823i | ||||
\(426\) | 512.576 | 1.20323 | ||||||||
\(427\) | 303.873 | − | 48.1287i | 0.711646 | − | 0.112714i | ||||
\(428\) | −92.7593 | + | 182.050i | −0.216727 | + | 0.425351i | ||||
\(429\) | 79.9464 | − | 25.9761i | 0.186355 | − | 0.0605505i | ||||
\(430\) | 677.315 | − | 280.176i | 1.57515 | − | 0.651571i | ||||
\(431\) | −98.1469 | + | 302.065i | −0.227719 | + | 0.700847i | 0.770285 | + | 0.637700i | \(0.220114\pi\) |
−0.998004 | + | 0.0631474i | \(0.979886\pi\) | |||||||
\(432\) | 45.0070 | − | 45.0070i | 0.104183 | − | 0.104183i | ||||
\(433\) | 50.0527 | − | 25.5031i | 0.115595 | − | 0.0588986i | −0.395237 | − | 0.918579i | \(-0.629337\pi\) |
0.510832 | + | 0.859681i | \(0.329337\pi\) | |||||||
\(434\) | −247.968 | − | 341.298i | −0.571354 | − | 0.786401i | ||||
\(435\) | 211.589 | + | 180.888i | 0.486412 | + | 0.415835i | ||||
\(436\) | 101.339 | + | 73.6274i | 0.232430 | + | 0.168870i | ||||
\(437\) | −33.5811 | + | 212.023i | −0.0768447 | + | 0.485178i | ||||
\(438\) | −106.773 | − | 16.9112i | −0.243774 | − | 0.0386100i | ||||
\(439\) | 206.646 | − | 284.423i | 0.470719 | − | 0.647889i | −0.505969 | − | 0.862551i | \(-0.668865\pi\) |
0.976688 | + | 0.214662i | \(0.0688651\pi\) | |||||||
\(440\) | 24.1981 | − | 28.3050i | 0.0549956 | − | 0.0643296i | ||||
\(441\) | 84.3864 | − | 61.3103i | 0.191352 | − | 0.139026i | ||||
\(442\) | −245.828 | − | 482.465i | −0.556172 | − | 1.09155i | ||||
\(443\) | 236.089 | + | 236.089i | 0.532932 | + | 0.532932i | 0.921444 | − | 0.388512i | \(-0.127011\pi\) |
−0.388512 | + | 0.921444i | \(0.627011\pi\) | |||||||
\(444\) | −527.906 | − | 171.527i | −1.18898 | − | 0.386322i | ||||
\(445\) | −95.8354 | − | 231.679i | −0.215360 | − | 0.520626i | ||||
\(446\) | 225.909 | + | 695.275i | 0.506521 | + | 1.55891i | ||||
\(447\) | −165.005 | − | 84.0743i | −0.369139 | − | 0.188086i | ||||
\(448\) | 50.8383 | + | 320.980i | 0.113478 | + | 0.716474i | ||||
\(449\) | 548.645i | 1.22193i | 0.791659 | + | 0.610963i | \(0.209218\pi\) | ||||
−0.791659 | + | 0.610963i | \(0.790782\pi\) | |||||||
\(450\) | −68.8905 | + | 211.339i | −0.153090 | + | 0.469642i | ||||
\(451\) | 221.311 | 0.490712 | ||||||||
\(452\) | −894.097 | + | 141.611i | −1.97809 | + | 0.313299i | ||||
\(453\) | 184.722 | − | 362.537i | 0.407774 | − | 0.800302i | ||||
\(454\) | −78.7493 | + | 25.5872i | −0.173457 | + | 0.0563595i | ||||
\(455\) | −22.2723 | − | 284.728i | −0.0489501 | − | 0.625776i | ||||
\(456\) | 29.7244 | − | 91.4824i | 0.0651851 | − | 0.200619i | ||||
\(457\) | −51.8314 | + | 51.8314i | −0.113417 | + | 0.113417i | −0.761537 | − | 0.648121i | \(-0.775555\pi\) |
0.648121 | + | 0.761537i | \(0.275555\pi\) | |||||||
\(458\) | 261.194 | − | 133.085i | 0.570294 | − | 0.290579i | ||||
\(459\) | −36.8528 | − | 50.7235i | −0.0802893 | − | 0.110509i | ||||
\(460\) | −214.170 | − | 16.9581i | −0.465587 | − | 0.0368654i | ||||
\(461\) | −282.819 | − | 205.480i | −0.613491 | − | 0.445727i | 0.237151 | − | 0.971473i | \(-0.423786\pi\) |
−0.850642 | + | 0.525746i | \(0.823786\pi\) | |||||||
\(462\) | −9.70996 | + | 61.3063i | −0.0210172 | + | 0.132698i | ||||
\(463\) | −711.727 | − | 112.726i | −1.53721 | − | 0.243470i | −0.670357 | − | 0.742039i | \(-0.733859\pi\) |
−0.866850 | + | 0.498569i | \(0.833859\pi\) | |||||||
\(464\) | −231.433 | + | 318.540i | −0.498778 | + | 0.686509i | ||||
\(465\) | 317.780 | − | 76.1323i | 0.683397 | − | 0.163725i | ||||
\(466\) | 465.972 | − | 338.548i | 0.999940 | − | 0.726499i | ||||
\(467\) | 53.2132 | + | 104.437i | 0.113947 | + | 0.223633i | 0.940936 | − | 0.338585i | \(-0.109948\pi\) |
−0.826989 | + | 0.562218i | \(0.809948\pi\) | |||||||
\(468\) | 153.662 | + | 153.662i | 0.328338 | + | 0.328338i | ||||
\(469\) | 27.2348 | + | 8.84912i | 0.0580699 | + | 0.0188681i | ||||
\(470\) | −450.571 | + | 384.453i | −0.958661 | + | 0.817985i | ||||
\(471\) | −34.7857 | − | 107.059i | −0.0738549 | − | 0.227302i | ||||
\(472\) | 22.3245 | + | 11.3749i | 0.0472977 | + | 0.0240994i | ||||
\(473\) | 24.8010 | + | 156.587i | 0.0524333 | + | 0.331051i | ||||
\(474\) | 631.227i | 1.33170i | ||||||||
\(475\) | −92.9103 | − | 590.246i | −0.195601 | − | 1.24262i | ||||
\(476\) | 217.759 | 0.457477 | ||||||||
\(477\) | −221.747 | + | 35.1213i | −0.464878 | + | 0.0736295i | ||||
\(478\) | 166.547 | − | 326.866i | 0.348424 | − | 0.683821i | ||||
\(479\) | −846.762 | + | 275.130i | −1.76777 | + | 0.574383i | −0.997957 | − | 0.0638859i | \(-0.979651\pi\) |
−0.769813 | + | 0.638269i | \(0.779651\pi\) | |||||||
\(480\) | −383.942 | − | 92.3696i | −0.799880 | − | 0.192437i | ||||
\(481\) | −313.437 | + | 964.660i | −0.651636 | + | 2.00553i | ||||
\(482\) | −352.522 | + | 352.522i | −0.731374 | + | 0.731374i | ||||
\(483\) | 52.2892 | − | 26.6427i | 0.108259 | − | 0.0551608i | ||||
\(484\) | −311.359 | − | 428.548i | −0.643303 | − | 0.885430i | ||||
\(485\) | −257.101 | + | 157.384i | −0.530106 | + | 0.324503i | ||||
\(486\) | 37.3772 | + | 27.1561i | 0.0769079 | + | 0.0558768i | ||||
\(487\) | 124.029 | − | 783.086i | 0.254679 | − | 1.60798i | −0.446359 | − | 0.894854i | \(-0.647279\pi\) |
0.701037 | − | 0.713125i | \(-0.252721\pi\) | |||||||
\(488\) | 187.171 | + | 29.6450i | 0.383547 | + | 0.0607479i | ||||
\(489\) | −170.812 | + | 235.103i | −0.349309 | + | 0.480783i | ||||
\(490\) | −475.926 | − | 197.400i | −0.971278 | − | 0.402858i | ||||
\(491\) | −159.270 | + | 115.717i | −0.324380 | + | 0.235676i | −0.738042 | − | 0.674755i | \(-0.764249\pi\) |
0.413662 | + | 0.910430i | \(0.364249\pi\) | |||||||
\(492\) | 259.740 | + | 509.769i | 0.527927 | + | 1.03612i | ||||
\(493\) | 274.251 | + | 274.251i | 0.556290 | + | 0.556290i | ||||
\(494\) | −1020.07 | − | 331.441i | −2.06492 | − | 0.670933i | ||||
\(495\) | −40.9820 | − | 25.1406i | −0.0827919 | − | 0.0507891i | ||||
\(496\) | 142.827 | + | 439.576i | 0.287957 | + | 0.886241i | ||||
\(497\) | 335.620 | + | 171.007i | 0.675292 | + | 0.344078i | ||||
\(498\) | 62.7666 | + | 396.293i | 0.126037 | + | 0.795769i | ||||
\(499\) | 384.731i | 0.771004i | 0.922707 | + | 0.385502i | \(0.125972\pi\) | ||||
−0.922707 | + | 0.385502i | \(0.874028\pi\) | |||||||
\(500\) | 581.676 | − | 138.770i | 1.16335 | − | 0.277541i | ||||
\(501\) | −38.9751 | −0.0777946 | ||||||||
\(502\) | −314.684 | + | 49.8411i | −0.626861 | + | 0.0992850i | ||||
\(503\) | −273.130 | + | 536.048i | −0.543002 | + | 1.06570i | 0.442616 | + | 0.896711i | \(0.354051\pi\) |
−0.985618 | + | 0.168990i | \(0.945949\pi\) | |||||||
\(504\) | −25.0095 | + | 8.12609i | −0.0496221 | + | 0.0161232i | ||||
\(505\) | −134.661 | + | 219.513i | −0.266656 | + | 0.434678i | ||||
\(506\) | 26.3661 | − | 81.1464i | 0.0521069 | − | 0.160368i | ||||
\(507\) | 73.8097 | − | 73.8097i | 0.145581 | − | 0.145581i | ||||
\(508\) | 116.153 | − | 59.1829i | 0.228647 | − | 0.116502i | ||||
\(509\) | −229.621 | − | 316.046i | −0.451122 | − | 0.620916i | 0.521516 | − | 0.853241i | \(-0.325367\pi\) |
−0.972638 | + | 0.232325i | \(0.925367\pi\) | |||||||
\(510\) | −118.655 | + | 286.072i | −0.232656 | + | 0.560926i | ||||
\(511\) | −64.2700 | − | 46.6949i | −0.125773 | − | 0.0913794i | ||||
\(512\) | 105.187 | − | 664.127i | 0.205444 | − | 1.29712i | ||||
\(513\) | −122.662 | − | 19.4278i | −0.239107 | − | 0.0378709i | ||||
\(514\) | −215.822 | + | 297.053i | −0.419887 | + | 0.577925i | ||||
\(515\) | −209.446 | − | 342.150i | −0.406691 | − | 0.664368i | ||||
\(516\) | −331.576 | + | 240.904i | −0.642589 | + | 0.466868i | ||||
\(517\) | −58.1613 | − | 114.148i | −0.112498 | − | 0.220789i | ||||
\(518\) | −529.597 | − | 529.597i | −1.02239 | − | 1.02239i | ||||
\(519\) | −350.379 | − | 113.845i | −0.675105 | − | 0.219355i | ||||
\(520\) | 41.1478 | − | 171.034i | 0.0791303 | − | 0.328912i | ||||
\(521\) | −155.041 | − | 477.166i | −0.297583 | − | 0.915865i | −0.982342 | − | 0.187096i | \(-0.940093\pi\) |
0.684759 | − | 0.728769i | \(-0.259907\pi\) | |||||||
\(522\) | −254.649 | − | 129.750i | −0.487833 | − | 0.248564i | ||||
\(523\) | −52.7905 | − | 333.306i | −0.100938 | − | 0.637297i | −0.985344 | − | 0.170579i | \(-0.945436\pi\) |
0.884406 | − | 0.466718i | \(-0.154564\pi\) | |||||||
\(524\) | 280.054i | 0.534454i | ||||||||
\(525\) | −115.615 | + | 115.395i | −0.220219 | + | 0.219800i | ||||
\(526\) | 164.836 | 0.313377 | ||||||||
\(527\) | 449.680 | − | 71.2224i | 0.853283 | − | 0.135147i | ||||
\(528\) | 30.8733 | − | 60.5922i | 0.0584721 | − | 0.114758i | ||||
\(529\) | 426.388 | − | 138.542i | 0.806026 | − | 0.261894i | ||||
\(530\) | 719.838 | + | 843.635i | 1.35819 | + | 1.59176i | ||||
\(531\) | 9.99637 | − | 30.7656i | 0.0188255 | − | 0.0579391i | ||||
\(532\) | 305.000 | − | 305.000i | 0.573309 | − | 0.573309i | ||||
\(533\) | 931.517 | − | 474.632i | 1.74769 | − | 0.890491i | ||||
\(534\) | 151.301 | + | 208.247i | 0.283334 | + | 0.389976i | ||||
\(535\) | −49.7523 | − | 207.668i | −0.0929950 | − | 0.388165i | ||||
\(536\) | 14.2699 | + | 10.3677i | 0.0266230 | + | 0.0193427i | ||||
\(537\) | −69.5020 | + | 438.818i | −0.129426 | + | 0.817166i | ||||
\(538\) | 85.0872 | + | 13.4765i | 0.158155 | + | 0.0250492i | ||||
\(539\) | 65.5051 | − | 90.1600i | 0.121531 | − | 0.167273i | ||||
\(540\) | 9.81078 | − | 123.904i | 0.0181681 | − | 0.229452i | ||||
\(541\) | −700.747 | + | 509.123i | −1.29528 | + | 0.941077i | −0.999898 | − | 0.0143018i | \(-0.995447\pi\) |
−0.295384 | + | 0.955379i | \(0.595447\pi\) | |||||||
\(542\) | −415.296 | − | 815.065i | −0.766230 | − | 1.50381i | ||||
\(543\) | 147.432 | + | 147.432i | 0.271513 | + | 0.271513i | ||||
\(544\) | −523.274 | − | 170.022i | −0.961901 | − | 0.312541i | ||||
\(545\) | −130.519 | + | 10.2096i | −0.239485 | + | 0.0187332i | ||||
\(546\) | 90.6096 | + | 278.868i | 0.165952 | + | 0.510747i | ||||
\(547\) | 780.975 | + | 397.927i | 1.42774 | + | 0.727471i | 0.985540 | − | 0.169444i | \(-0.0541971\pi\) |
0.442203 | + | 0.896915i | \(0.354197\pi\) | |||||||
\(548\) | −90.7838 | − | 573.187i | −0.165664 | − | 1.04596i | ||||
\(549\) | − | 244.668i | − | 0.445661i | ||||||
\(550\) | −0.225964 | + | 237.492i | −0.000410844 | + | 0.431803i | ||||
\(551\) | 768.249 | 1.39428 | ||||||||
\(552\) | 35.7024 | − | 5.65470i | 0.0646782 | − | 0.0102440i | ||||
\(553\) | −210.592 | + | 413.310i | −0.380817 | + | 0.747396i | ||||
\(554\) | 554.540 | − | 180.181i | 1.00097 | − | 0.325236i | ||||
\(555\) | 536.081 | − | 221.753i | 0.965911 | − | 0.399555i | ||||
\(556\) | 111.052 | − | 341.784i | 0.199734 | − | 0.614719i | ||||
\(557\) | 107.969 | − | 107.969i | 0.193841 | − | 0.193841i | −0.603513 | − | 0.797353i | \(-0.706233\pi\) |
0.797353 | + | 0.603513i | \(0.206233\pi\) | |||||||
\(558\) | −298.925 | + | 152.310i | −0.535708 | + | 0.272957i | ||||
\(559\) | 440.212 | + | 605.899i | 0.787498 | + | 1.08390i | ||||
\(560\) | −175.617 | − | 150.136i | −0.313603 | − | 0.268100i | ||||
\(561\) | −54.1939 | − | 39.3742i | −0.0966023 | − | 0.0701857i | ||||
\(562\) | −125.903 | + | 794.919i | −0.224026 | + | 1.41445i | ||||
\(563\) | −347.620 | − | 55.0577i | −0.617443 | − | 0.0977934i | −0.160125 | − | 0.987097i | \(-0.551190\pi\) |
−0.457318 | + | 0.889303i | \(0.651190\pi\) | |||||||
\(564\) | 194.668 | − | 267.938i | 0.345157 | − | 0.475067i | ||||
\(565\) | 614.794 | − | 719.138i | 1.08813 | − | 1.27281i | ||||
\(566\) | 598.455 | − | 434.803i | 1.05734 | − | 0.768203i | ||||
\(567\) | 15.4136 | + | 30.2510i | 0.0271845 | + | 0.0533527i | ||||
\(568\) | 164.058 | + | 164.058i | 0.288835 | + | 0.288835i | ||||
\(569\) | 263.942 | + | 85.7600i | 0.463870 | + | 0.150721i | 0.531622 | − | 0.846982i | \(-0.321583\pi\) |
−0.0677518 | + | 0.997702i | \(0.521583\pi\) | |||||||
\(570\) | 234.491 | + | 566.873i | 0.411387 | + | 0.994514i | ||||
\(571\) | −15.1133 | − | 46.5140i | −0.0264682 | − | 0.0814607i | 0.936950 | − | 0.349464i | \(-0.113636\pi\) |
−0.963418 | + | 0.268003i | \(0.913636\pi\) | |||||||
\(572\) | 206.873 | + | 105.407i | 0.361666 | + | 0.184278i | ||||
\(573\) | −76.9441 | − | 485.806i | −0.134283 | − | 0.847829i | ||||
\(574\) | 771.974i | 1.34490i | ||||||||
\(575\) | 181.782 | − | 131.809i | 0.316143 | − | 0.229232i | ||||
\(576\) | 258.442 | 0.448685 | ||||||||
\(577\) | −334.695 | + | 53.0106i | −0.580061 | + | 0.0918727i | −0.439569 | − | 0.898209i | \(-0.644869\pi\) |
−0.140493 | + | 0.990082i | \(0.544869\pi\) | |||||||
\(578\) | 192.959 | − | 378.703i | 0.333839 | − | 0.655195i | ||||
\(579\) | 369.548 | − | 120.073i | 0.638252 | − | 0.207381i | ||||
\(580\) | 59.9605 | + | 766.532i | 0.103380 | + | 1.32161i | ||||
\(581\) | −91.1145 | + | 280.422i | −0.156824 | + | 0.482654i | ||||
\(582\) | 218.844 | − | 218.844i | 0.376020 | − | 0.376020i | ||||
\(583\) | −213.727 | + | 108.899i | −0.366599 | + | 0.186791i | ||||
\(584\) | −28.7618 | − | 39.5872i | −0.0492496 | − | 0.0677863i | ||||
\(585\) | −226.414 | − | 17.9276i | −0.387033 | − | 0.0306454i | ||||
\(586\) | −1204.99 | − | 875.477i | −2.05630 | − | 1.49399i | ||||
\(587\) | 58.1663 | − | 367.247i | 0.0990907 | − | 0.625634i | −0.887297 | − | 0.461198i | \(-0.847420\pi\) |
0.986388 | − | 0.164436i | \(-0.0525804\pi\) | |||||||
\(588\) | 284.555 | + | 45.0690i | 0.483936 | + | 0.0766480i | ||||
\(589\) | 530.080 | − | 729.592i | 0.899966 | − | 1.23870i | ||||
\(590\) | −155.395 | + | 37.2287i | −0.263381 | + | 0.0630996i | ||||
\(591\) | −471.404 | + | 342.495i | −0.797638 | + | 0.579518i | ||||
\(592\) | 372.528 | + | 731.126i | 0.629270 | + | 1.23501i | ||||
\(593\) | −357.080 | − | 357.080i | −0.602158 | − | 0.602158i | 0.338727 | − | 0.940885i | \(-0.390004\pi\) |
−0.940885 | + | 0.338727i | \(0.890004\pi\) | |||||||
\(594\) | 46.9458 | + | 15.2536i | 0.0790334 | + | 0.0256795i | ||||
\(595\) | −173.132 | + | 147.726i | −0.290978 | + | 0.248279i | ||||
\(596\) | −158.063 | − | 486.467i | −0.265206 | − | 0.816220i | ||||
\(597\) | 269.436 | + | 137.285i | 0.451317 | + | 0.229958i | ||||
\(598\) | −63.0525 | − | 398.098i | −0.105439 | − | 0.665715i | ||||
\(599\) | 618.437i | 1.03245i | 0.856453 | + | 0.516225i | \(0.172663\pi\) | ||||
−0.856453 | + | 0.516225i | \(0.827337\pi\) | |||||||
\(600\) | −89.6921 | + | 45.5930i | −0.149487 | + | 0.0759883i | ||||
\(601\) | 801.428 | 1.33349 | 0.666745 | − | 0.745286i | \(-0.267687\pi\) | ||||
0.666745 | + | 0.745286i | \(0.267687\pi\) | |||||||
\(602\) | −546.205 | + | 86.5103i | −0.907317 | + | 0.143705i | ||||
\(603\) | 10.3388 | − | 20.2910i | 0.0171456 | − | 0.0336501i | ||||
\(604\) | 1068.83 | − | 347.284i | 1.76958 | − | 0.574973i | ||||
\(605\) | 538.273 | + | 129.499i | 0.889708 | + | 0.214048i | ||||
\(606\) | 81.7033 | − | 251.457i | 0.134824 | − | 0.414945i | ||||
\(607\) | −541.619 | + | 541.619i | −0.892288 | + | 0.892288i | −0.994738 | − | 0.102450i | \(-0.967332\pi\) |
0.102450 | + | 0.994738i | \(0.467332\pi\) | |||||||
\(608\) | −971.052 | + | 494.776i | −1.59712 | + | 0.813776i | ||||
\(609\) | −123.449 | − | 169.913i | −0.202708 | − | 0.279004i | ||||
\(610\) | −1030.78 | + | 630.987i | −1.68980 | + | 1.03440i | ||||
\(611\) | −489.612 | − | 355.724i | −0.801328 | − | 0.582199i | ||||
\(612\) | 27.0903 | − | 171.042i | 0.0442653 | − | 0.279480i | ||||
\(613\) | 409.251 | + | 64.8189i | 0.667619 | + | 0.105740i | 0.481039 | − | 0.876699i | \(-0.340260\pi\) |
0.186580 | + | 0.982440i | \(0.440260\pi\) | |||||||
\(614\) | 560.369 | − | 771.281i | 0.912653 | − | 1.25616i | ||||
\(615\) | −552.333 | − | 229.092i | −0.898102 | − | 0.372507i | ||||
\(616\) | −22.7299 | + | 16.5143i | −0.0368992 | + | 0.0268089i | ||||
\(617\) | −334.883 | − | 657.246i | −0.542761 | − | 1.06523i | −0.985674 | − | 0.168664i | \(-0.946055\pi\) |
0.442913 | − | 0.896565i | \(-0.353945\pi\) | |||||||
\(618\) | 291.236 | + | 291.236i | 0.471256 | + | 0.471256i | ||||
\(619\) | −282.209 | − | 91.6951i | −0.455910 | − | 0.148134i | 0.0720540 | − | 0.997401i | \(-0.477045\pi\) |
−0.527965 | + | 0.849266i | \(0.677045\pi\) | |||||||
\(620\) | 769.334 | + | 471.952i | 1.24086 | + | 0.761213i | ||||
\(621\) | −14.4218 | − | 44.3857i | −0.0232235 | − | 0.0714745i | ||||
\(622\) | 220.872 | + | 112.540i | 0.355100 | + | 0.180932i | ||||
\(623\) | 29.5913 | + | 186.832i | 0.0474980 | + | 0.299891i | ||||
\(624\) | − | 321.250i | − | 0.514823i | ||||||
\(625\) | −368.327 | + | 504.936i | −0.589324 | + | 0.807897i | ||||
\(626\) | −1331.01 | −2.12621 | ||||||||
\(627\) | −131.054 | + | 20.7570i | −0.209018 | + | 0.0331052i | ||||
\(628\) | 141.155 | − | 277.032i | 0.224769 | − | 0.441133i | ||||
\(629\) | 768.732 | − | 249.776i | 1.22215 | − | 0.397100i | ||||
\(630\) | 87.6951 | − | 142.953i | 0.139199 | − | 0.226909i | ||||
\(631\) | −5.38412 | + | 16.5706i | −0.00853267 | + | 0.0262609i | −0.955232 | − | 0.295857i | \(-0.904395\pi\) |
0.946700 | + | 0.322118i | \(0.104395\pi\) | |||||||
\(632\) | −202.035 | + | 202.035i | −0.319675 | + | 0.319675i | ||||
\(633\) | 490.793 | − | 250.072i | 0.775345 | − | 0.395058i | ||||
\(634\) | 197.862 | + | 272.334i | 0.312085 | + | 0.429549i | ||||
\(635\) | −52.1995 | + | 125.851i | −0.0822039 | + | 0.198191i | ||||
\(636\) | −501.679 | − | 364.491i | −0.788803 | − | 0.573099i | ||||
\(637\) | 82.3560 | − | 519.976i | 0.129287 | − | 0.816288i | ||||
\(638\) | −301.594 | − | 47.7678i | −0.472718 | − | 0.0748711i | ||||
\(639\) | 176.072 | − | 242.343i | 0.275544 | − | 0.379253i | ||||
\(640\) | −190.374 | − | 310.994i | −0.297459 | − | 0.485928i | ||||
\(641\) | 52.2009 | − | 37.9262i | 0.0814367 | − | 0.0591672i | −0.546322 | − | 0.837575i | \(-0.683972\pi\) |
0.627759 | + | 0.778408i | \(0.283972\pi\) | |||||||
\(642\) | 99.5344 | + | 195.347i | 0.155038 | + | 0.304279i | ||||
\(643\) | 133.819 | + | 133.819i | 0.208117 | + | 0.208117i | 0.803467 | − | 0.595350i | \(-0.202987\pi\) |
−0.595350 | + | 0.803467i | \(0.702987\pi\) | |||||||
\(644\) | 154.159 | + | 50.0892i | 0.239377 | + | 0.0777782i | ||||
\(645\) | 100.196 | − | 416.472i | 0.155342 | − | 0.645693i | ||||
\(646\) | 264.123 | + | 812.887i | 0.408859 | + | 1.25834i | ||||
\(647\) | 1116.71 | + | 568.992i | 1.72598 | + | 0.879431i | 0.975940 | + | 0.218041i | \(0.0699666\pi\) |
0.750042 | + | 0.661391i | \(0.230033\pi\) | |||||||
\(648\) | 3.27143 | + | 20.6550i | 0.00504850 | + | 0.0318750i | ||||
\(649\) | − | 34.5622i | − | 0.0532545i | ||||||
\(650\) | 508.382 | + | 1000.11i | 0.782126 | + | 1.53863i | ||||
\(651\) | −246.542 | −0.378713 | ||||||||
\(652\) | −792.777 | + | 125.564i | −1.21592 | + | 0.192582i | ||||
\(653\) | −240.812 | + | 472.620i | −0.368778 | + | 0.723768i | −0.998596 | − | 0.0529751i | \(-0.983130\pi\) |
0.629818 | + | 0.776743i | \(0.283130\pi\) | |||||||
\(654\) | 127.833 | − | 41.5354i | 0.195463 | − | 0.0635098i | ||||
\(655\) | −189.987 | − | 222.660i | −0.290056 | − | 0.339939i | ||||
\(656\) | 261.358 | − | 804.377i | 0.398412 | − | 1.22618i | ||||
\(657\) | −44.6726 | + | 44.6726i | −0.0679948 | + | 0.0679948i | ||||
\(658\) | 398.169 | − | 202.877i | 0.605120 | − | 0.308324i | ||||
\(659\) | 22.4848 | + | 30.9477i | 0.0341196 | + | 0.0469615i | 0.825736 | − | 0.564057i | \(-0.190760\pi\) |
−0.791616 | + | 0.611018i | \(0.790760\pi\) | |||||||
\(660\) | −30.9391 | − | 129.141i | −0.0468775 | − | 0.195669i | ||||
\(661\) | −756.059 | − | 549.309i | −1.14381 | − | 0.831027i | −0.156165 | − | 0.987731i | \(-0.549913\pi\) |
−0.987646 | + | 0.156704i | \(0.949913\pi\) | |||||||
\(662\) | 266.850 | − | 1684.82i | 0.403096 | − | 2.54505i | ||||
\(663\) | −312.550 | − | 49.5030i | −0.471418 | − | 0.0746652i | ||||
\(664\) | −106.751 | + | 146.930i | −0.160769 | + | 0.221280i | ||||
\(665\) | −35.5840 | + | 449.404i | −0.0535097 | + | 0.675795i | ||||
\(666\) | −481.863 | + | 350.094i | −0.723518 | + | 0.525667i | ||||
\(667\) | 131.067 | + | 257.234i | 0.196503 | + | 0.385659i | ||||
\(668\) | −76.1207 | − | 76.1207i | −0.113953 | − | 0.113953i | ||||
\(669\) | 406.323 | + | 132.022i | 0.607358 | + | 0.197343i | ||||
\(670\) | −112.148 | + | 8.77260i | −0.167386 | + | 0.0130934i | ||||
\(671\) | −80.7795 | − | 248.614i | −0.120387 | − | 0.370512i | ||||
\(672\) | 265.467 | + | 135.262i | 0.395040 | + | 0.201283i | ||||
\(673\) | −8.22955 | − | 51.9593i | −0.0122282 | − | 0.0772055i | 0.980820 | − | 0.194918i | \(-0.0624440\pi\) |
−0.993048 | + | 0.117712i | \(0.962444\pi\) | |||||||
\(674\) | 560.378i | 0.831422i | ||||||||
\(675\) | 76.2555 | + | 105.167i | 0.112971 | + | 0.155803i | ||||
\(676\) | 288.309 | 0.426493 | ||||||||
\(677\) | −180.544 | + | 28.5953i | −0.266682 | + | 0.0422383i | −0.288343 | − | 0.957527i | \(-0.593104\pi\) |
0.0216614 | + | 0.999765i | \(0.493104\pi\) | |||||||
\(678\) | −440.988 | + | 865.488i | −0.650425 | + | 1.27653i | ||||
\(679\) | 216.304 | − | 70.2814i | 0.318562 | − | 0.103507i | ||||
\(680\) | −129.540 | + | 53.5849i | −0.190499 | + | 0.0788013i | ||||
\(681\) | −14.9533 | + | 46.0216i | −0.0219579 | + | 0.0675794i | ||||
\(682\) | −253.459 | + | 253.459i | −0.371641 | + | 0.371641i | ||||
\(683\) | −907.556 | + | 462.423i | −1.32878 | + | 0.677047i | −0.966895 | − | 0.255176i | \(-0.917866\pi\) |
−0.361884 | + | 0.932223i | \(0.617866\pi\) | |||||||
\(684\) | −201.623 | − | 277.510i | −0.294770 | − | 0.405716i | ||||
\(685\) | 461.024 | + | 394.132i | 0.673028 | + | 0.575375i | ||||
\(686\) | 757.711 | + | 550.509i | 1.10454 | + | 0.802492i | ||||
\(687\) | 26.7997 | − | 169.207i | 0.0390098 | − | 0.246298i | ||||
\(688\) | 598.420 | + | 94.7805i | 0.869797 | + | 0.137762i | ||||
\(689\) | −666.046 | + | 916.734i | −0.966685 | + | 1.33053i | ||||
\(690\) | −149.802 | + | 175.227i | −0.217104 | + | 0.253952i | ||||
\(691\) | 154.293 | − | 112.101i | 0.223290 | − | 0.162230i | −0.470516 | − | 0.882391i | \(-0.655932\pi\) |
0.693806 | + | 0.720162i | \(0.255932\pi\) | |||||||
\(692\) | −461.966 | − | 906.659i | −0.667580 | − | 1.31020i | ||||
\(693\) | 25.6498 | + | 25.6498i | 0.0370128 | + | 0.0370128i | ||||
\(694\) | 1054.36 | + | 342.583i | 1.51925 | + | 0.493635i | ||||
\(695\) | 143.570 | + | 347.076i | 0.206576 | + | 0.499390i | ||||
\(696\) | −39.9760 | − | 123.033i | −0.0574367 | − | 0.176772i | ||||
\(697\) | −742.320 | − | 378.231i | −1.06502 | − | 0.542655i | ||||
\(698\) | −72.3636 | − | 456.886i | −0.103673 | − | 0.654564i | ||||
\(699\) | − | 336.602i | − | 0.481548i | ||||||
\(700\) | −451.177 | − | 0.429277i | −0.644538 | − | 0.000613253i | ||||
\(701\) | 171.400 | 0.244508 | 0.122254 | − | 0.992499i | \(-0.460988\pi\) | ||||
0.122254 | + | 0.992499i | \(0.460988\pi\) | |||||||
\(702\) | 230.312 | − | 36.4779i | 0.328080 | − | 0.0519628i | ||||
\(703\) | 726.865 | − | 1426.55i | 1.03395 | − | 2.02924i | ||||
\(704\) | 262.610 | − | 85.3272i | 0.373026 | − | 0.121203i | ||||
\(705\) | 26.9939 | + | 345.089i | 0.0382892 | + | 0.489488i | ||||
\(706\) | 87.6757 | − | 269.838i | 0.124187 | − | 0.382207i | ||||
\(707\) | 137.389 | − | 137.389i | 0.194326 | − | 0.194326i | ||||
\(708\) | 79.6107 | − | 40.5637i | 0.112444 | − | 0.0572933i | ||||
\(709\) | −451.404 | − | 621.304i | −0.636677 | − | 0.876311i | 0.361756 | − | 0.932273i | \(-0.382177\pi\) |
−0.998433 | + | 0.0559622i | \(0.982177\pi\) | |||||||
\(710\) | −1475.06 | − | 116.796i | −2.07755 | − | 0.164501i | ||||
\(711\) | 298.441 | + | 216.830i | 0.419748 | + | 0.304965i | ||||
\(712\) | −18.2268 | + | 115.079i | −0.0255994 | + | 0.161628i | ||||
\(713\) | 334.726 | + | 53.0153i | 0.469461 | + | 0.0743553i | ||||
\(714\) | 137.344 | − | 189.038i | 0.192359 | − | 0.264760i | ||||
\(715\) | −235.984 | + | 56.5361i | −0.330048 | + | 0.0790714i | ||||
\(716\) | −992.780 | + | 721.297i | −1.38656 | + | 1.00740i | ||||
\(717\) | −97.3309 | − | 191.023i | −0.135747 | − | 0.266419i | ||||
\(718\) | −461.459 | − | 461.459i | −0.642700 | − | 0.642700i | ||||
\(719\) | −417.040 | − | 135.505i | −0.580028 | − | 0.188463i | 0.00428501 | − | 0.999991i | \(-0.498636\pi\) |
−0.584313 | + | 0.811528i | \(0.698636\pi\) | |||||||
\(720\) | −139.774 | + | 119.263i | −0.194130 | + | 0.165643i | ||||
\(721\) | 93.5302 | + | 287.856i | 0.129723 | + | 0.399246i | ||||
\(722\) | 555.183 | + | 282.880i | 0.768952 | + | 0.391801i | ||||
\(723\) | 45.5773 | + | 287.764i | 0.0630391 | + | 0.398013i | ||||
\(724\) | 575.885i | 0.795422i | ||||||||
\(725\) | −567.682 | − | 568.763i | −0.783010 | − | 0.784501i | ||||
\(726\) | −568.405 | −0.782927 | ||||||||
\(727\) | −633.104 | + | 100.274i | −0.870845 | + | 0.137928i | −0.575835 | − | 0.817566i | \(-0.695323\pi\) |
−0.295010 | + | 0.955494i | \(0.595323\pi\) | |||||||
\(728\) | −60.2551 | + | 118.257i | −0.0827680 | + | 0.162441i | ||||
\(729\) | 25.6785 | − | 8.34346i | 0.0352243 | − | 0.0114451i | ||||
\(730\) | 303.412 | + | 72.9955i | 0.415633 | + | 0.0999938i | ||||
\(731\) | 184.427 | − | 567.609i | 0.252295 | − | 0.776483i | ||||
\(732\) | 477.852 | − | 477.852i | 0.652803 | − | 0.652803i | ||||
\(733\) | 312.714 | − | 159.336i | 0.426621 | − | 0.217374i | −0.227478 | − | 0.973783i | \(-0.573048\pi\) |
0.654099 | + | 0.756409i | \(0.273048\pi\) | |||||||
\(734\) | 759.890 | + | 1045.90i | 1.03527 | + | 1.42493i | ||||
\(735\) | −256.813 | + | 157.207i | −0.349405 | + | 0.213887i | ||||
\(736\) | −331.334 | − | 240.728i | −0.450182 | − | 0.327076i | ||||
\(737\) | 3.80625 | − | 24.0317i | 0.00516451 | − | 0.0326074i | ||||
\(738\) | 606.356 | + | 96.0374i | 0.821621 | + | 0.130132i | ||||
\(739\) | 280.598 | − | 386.210i | 0.379699 | − | 0.522611i | −0.575806 | − | 0.817587i | \(-0.695311\pi\) |
0.955505 | + | 0.294975i | \(0.0953115\pi\) | |||||||
\(740\) | 1480.10 | + | 613.901i | 2.00013 | + | 0.829595i | ||||
\(741\) | −507.102 | + | 368.431i | −0.684349 | + | 0.497208i | ||||
\(742\) | −379.861 | − | 745.520i | −0.511942 | − | 1.00474i | ||||
\(743\) | 955.391 | + | 955.391i | 1.28586 | + | 1.28586i | 0.937281 | + | 0.348574i | \(0.113334\pi\) |
0.348574 | + | 0.937281i | \(0.386666\pi\) | |||||||
\(744\) | −144.425 | − | 46.9267i | −0.194120 | − | 0.0630735i | ||||
\(745\) | 455.685 | + | 279.543i | 0.611658 | + | 0.375225i | ||||
\(746\) | 197.881 | + | 609.016i | 0.265256 | + | 0.816375i | ||||
\(747\) | 208.926 | + | 106.453i | 0.279686 | + | 0.142507i | ||||
\(748\) | −28.9438 | − | 182.744i | −0.0386949 | − | 0.244310i | ||||
\(749\) | 161.115i | 0.215106i | ||||||||
\(750\) | 246.405 | − | 592.482i | 0.328540 | − | 0.789976i | ||||
\(751\) | −170.736 | −0.227344 | −0.113672 | − | 0.993518i | \(-0.536261\pi\) | ||||
−0.113672 | + | 0.993518i | \(0.536261\pi\) | |||||||
\(752\) | −483.568 | + | 76.5896i | −0.643043 | + | 0.101848i | ||||
\(753\) | −84.5310 | + | 165.901i | −0.112259 | + | 0.220321i | ||||
\(754\) | −1371.88 | + | 445.750i | −1.81947 | + | 0.591181i | ||||
\(755\) | −614.190 | + | 1001.20i | −0.813497 | + | 1.32609i | ||||
\(756\) | −28.9782 | + | 89.1857i | −0.0383309 | + | 0.117970i | ||||
\(757\) | 188.024 | − | 188.024i | 0.248381 | − | 0.248381i | −0.571925 | − | 0.820306i | \(-0.693803\pi\) |
0.820306 | + | 0.571925i | \(0.193803\pi\) | |||||||
\(758\) | 504.010 | − | 256.806i | 0.664921 | − | 0.338794i | ||||
\(759\) | −29.3087 | − | 40.3399i | −0.0386149 | − | 0.0531488i | ||||
\(760\) | −106.385 | + | 256.490i | −0.139980 | + | 0.337487i | ||||
\(761\) | 839.386 | + | 609.850i | 1.10300 | + | 0.801379i | 0.981548 | − | 0.191217i | \(-0.0612436\pi\) |
0.121456 | + | 0.992597i | \(0.461244\pi\) | |||||||
\(762\) | 21.8825 | − | 138.161i | 0.0287172 | − | 0.181313i | ||||
\(763\) | 97.5585 | + | 15.4517i | 0.127862 | + | 0.0202513i | ||||
\(764\) | 798.532 | − | 1099.08i | 1.04520 | − | 1.43859i | ||||
\(765\) | 94.4950 | + | 154.367i | 0.123523 | + | 0.201786i | ||||
\(766\) | 1001.98 | − | 727.981i | 1.30807 | − | 0.950367i | ||||
\(767\) | −74.1233 | − | 145.475i | −0.0966405 | − | 0.189668i | ||||
\(768\) | −157.318 | − | 157.318i | −0.204842 | − | 0.204842i | ||||
\(769\) | −507.845 | − | 165.009i | −0.660397 | − | 0.214576i | −0.0404041 | − | 0.999183i | \(-0.512865\pi\) |
−0.619993 | + | 0.784607i | \(0.712865\pi\) | |||||||
\(770\) | 41.9121 | − | 174.211i | 0.0544313 | − | 0.226248i | ||||
\(771\) | 66.3092 | + | 204.079i | 0.0860041 | + | 0.264694i | ||||
\(772\) | 956.260 | + | 487.239i | 1.23868 | + | 0.631138i | ||||
\(773\) | −55.7537 | − | 352.015i | −0.0721264 | − | 0.455388i | −0.997148 | − | 0.0754733i | \(-0.975953\pi\) |
0.925021 | − | 0.379915i | \(-0.124047\pi\) | |||||||
\(774\) | 439.786i | 0.568198i | ||||||||
\(775\) | −931.836 | + | 146.680i | −1.20237 | + | 0.189264i | ||||
\(776\) | 140.089 | 0.180527 | ||||||||
\(777\) | −432.310 | + | 68.4712i | −0.556383 | + | 0.0881225i | ||||
\(778\) | 546.857 | − | 1073.27i | 0.702901 | − | 1.37952i | ||||
\(779\) | −1569.48 | + | 509.954i | −2.01473 | + | 0.654627i | ||||
\(780\) | −407.187 | − | 477.214i | −0.522034 | − | 0.611812i | ||||
\(781\) | 98.9000 | − | 304.383i | 0.126632 | − | 0.389735i | ||||
\(782\) | −227.120 | + | 227.120i | −0.290435 | + | 0.290435i | ||||
\(783\) | −148.818 | + | 75.8267i | −0.190062 | + | 0.0968413i | ||||
\(784\) | −250.337 | − | 344.559i | −0.319308 | − | 0.439489i | ||||
\(785\) | 75.7096 | + | 316.015i | 0.0964454 | + | 0.402567i | ||||
\(786\) | 243.117 | + | 176.635i | 0.309309 | + | 0.224726i | ||||
\(787\) | −225.398 | + | 1423.11i | −0.286402 | + | 1.80827i | 0.254379 | + | 0.967104i | \(0.418129\pi\) |
−0.540781 | + | 0.841163i | \(0.681871\pi\) | |||||||
\(788\) | −1589.59 | − | 251.767i | −2.01725 | − | 0.319501i | ||||
\(789\) | 56.6221 | − | 77.9336i | 0.0717643 | − | 0.0987751i | ||||
\(790\) | 143.832 | − | 1816.51i | 0.182066 | − | 2.29938i | ||||
\(791\) | −577.493 | + | 419.574i | −0.730080 | + | 0.530434i | ||||
\(792\) | 10.1436 | + | 19.9080i | 0.0128076 | + | 0.0251363i | ||||
\(793\) | −873.193 | − | 873.193i | −1.10113 | − | 1.10113i | ||||
\(794\) | −1507.58 | − | 489.841i | −1.89871 | − | 0.616928i | ||||
\(795\) | 646.134 | − | 50.5425i | 0.812747 | − | 0.0635755i | ||||
\(796\) | 258.100 | + | 794.350i | 0.324246 | + | 0.997927i | ||||
\(797\) | 92.9463 | + | 47.3585i | 0.116620 | + | 0.0594209i | 0.511327 | − | 0.859386i | \(-0.329154\pi\) |
−0.394707 | + | 0.918807i | \(0.629154\pi\) | |||||||
\(798\) | −72.4041 | − | 457.142i | −0.0907320 | − | 0.572859i | ||||
\(799\) | 482.275i | 0.603598i | ||||||||
\(800\) | 1083.84 | + | 353.301i | 1.35480 | + | 0.441627i | ||||
\(801\) | 150.431 | 0.187804 | ||||||||
\(802\) | −828.568 | + | 131.232i | −1.03313 | + | 0.163631i | ||||
\(803\) | −30.6439 | + | 60.1420i | −0.0381618 | + | 0.0748967i | ||||
\(804\) | 59.8219 | − | 19.4373i | 0.0744053 | − | 0.0241757i | ||||
\(805\) | −156.546 | + | 64.7561i | −0.194467 | + | 0.0804424i | ||||
\(806\) | −523.254 | + | 1610.41i | −0.649198 | + | 1.99803i | ||||
\(807\) | 35.5995 | − | 35.5995i | 0.0441134 | − | 0.0441134i | ||||
\(808\) | 106.633 | − | 54.3325i | 0.131972 | − | 0.0672431i | ||||
\(809\) | 37.0600 | + | 51.0088i | 0.0458097 | + | 0.0630516i | 0.831307 | − | 0.555813i | \(-0.187593\pi\) |
−0.785498 | + | 0.618865i | \(0.787593\pi\) | |||||||
\(810\) | −101.374 | − | 86.6652i | −0.125153 | − | 0.106994i | ||||
\(811\) | 432.662 | + | 314.348i | 0.533492 | + | 0.387605i | 0.821662 | − | 0.569974i | \(-0.193047\pi\) |
−0.288170 | + | 0.957579i | \(0.593047\pi\) | |||||||
\(812\) | 90.7472 | − | 572.955i | 0.111758 | − | 0.705610i | ||||
\(813\) | −528.014 | − | 83.6293i | −0.649464 | − | 0.102865i | ||||
\(814\) | −374.047 | + | 514.832i | −0.459517 | + | 0.632471i | ||||
\(815\) | 545.125 | − | 637.645i | 0.668865 | − | 0.782386i | ||||
\(816\) | −207.110 | + | 150.474i | −0.253811 | + | 0.184405i | ||||
\(817\) | −536.696 | − | 1053.33i | −0.656911 | − | 1.28926i | ||||
\(818\) | 667.544 | + | 667.544i | 0.816069 | + | 0.816069i | ||||
\(819\) | 162.972 | + | 52.9528i | 0.198989 | + | 0.0646554i | ||||
\(820\) | −631.309 | − | 1526.17i | −0.769890 | − | 1.86118i | ||||
\(821\) | −161.216 | − | 496.172i | −0.196365 | − | 0.604351i | −0.999958 | − | 0.00917082i | \(-0.997081\pi\) |
0.803592 | − | 0.595180i | \(-0.202919\pi\) | |||||||
\(822\) | −554.846 | − | 282.708i | −0.674995 | − | 0.343927i | ||||
\(823\) | 109.552 | + | 691.687i | 0.133114 | + | 0.840446i | 0.960392 | + | 0.278653i | \(0.0898880\pi\) |
−0.827278 | + | 0.561792i | \(0.810112\pi\) | |||||||
\(824\) | 186.430i | 0.226250i | ||||||||
\(825\) | 112.207 | + | 81.6864i | 0.136009 | + | 0.0990139i | ||||
\(826\) | 120.559 | 0.145955 | ||||||||
\(827\) | 103.550 | − | 16.4007i | 0.125212 | − | 0.0198316i | −0.0935141 | − | 0.995618i | \(-0.529810\pi\) |
0.218726 | + | 0.975786i | \(0.429810\pi\) | |||||||
\(828\) | 58.5213 | − | 114.854i | 0.0706779 | − | 0.138713i | ||||
\(829\) | 186.783 | − | 60.6896i | 0.225312 | − | 0.0732082i | −0.194186 | − | 0.980965i | \(-0.562206\pi\) |
0.419497 | + | 0.907757i | \(0.362206\pi\) | |||||||
\(830\) | −90.3266 | − | 1154.73i | −0.108827 | − | 1.39124i | ||||
\(831\) | 105.299 | − | 324.076i | 0.126713 | − | 0.389983i | ||||
\(832\) | 922.352 | − | 922.352i | 1.10860 | − | 1.10860i | ||||
\(833\) | −373.804 | + | 190.463i | −0.448745 | + | 0.228647i | ||||
\(834\) | −226.662 | − | 311.974i | −0.271778 | − | 0.374070i | ||||
\(835\) | 112.160 | + | 8.88090i | 0.134324 | + | 0.0106358i | ||||
\(836\) | −296.496 | − | 215.417i | −0.354661 | − | 0.257676i | ||||
\(837\) | −30.6711 | + | 193.649i | −0.0366440 | + | 0.231361i | ||||
\(838\) | 1800.91 | + | 285.237i | 2.14906 | + | 0.340378i | ||||
\(839\) | −479.806 | + | 660.396i | −0.571878 | + | 0.787122i | −0.992776 | − | 0.119986i | \(-0.961715\pi\) |
0.420898 | + | 0.907108i | \(0.361715\pi\) | |||||||
\(840\) | 73.8227 | − | 17.6861i | 0.0878841 | − | 0.0210549i | ||||
\(841\) | 155.499 | − | 112.977i | 0.184898 | − | 0.134336i | ||||
\(842\) | 476.103 | + | 934.404i | 0.565443 | + | 1.10974i | ||||
\(843\) | 332.585 | + | 332.585i | 0.394525 | + | 0.394525i | ||||
\(844\) | 1446.95 | + | 470.144i | 1.71440 | + | 0.557042i | ||||
\(845\) | −229.224 | + | 195.587i | −0.271271 | + | 0.231464i | ||||
\(846\) | −109.818 | − | 337.986i | −0.129809 | − | 0.399510i | ||||
\(847\) | −372.175 | − | 189.633i | −0.439404 | − | 0.223888i | ||||
\(848\) | 143.404 | + | 905.418i | 0.169109 | + | 1.06771i | ||||
\(849\) | − | 432.303i | − | 0.509191i | ||||||
\(850\) | 406.642 | − | 796.207i | 0.478403 | − | 0.936714i | ||||
\(851\) | 601.663 | 0.707007 | ||||||||
\(852\) | 817.190 | − | 129.430i | 0.959143 | − | 0.151913i | ||||
\(853\) | 130.878 | − | 256.862i | 0.153432 | − | 0.301128i | −0.801477 | − | 0.598026i | \(-0.795952\pi\) |
0.954909 | + | 0.296898i | \(0.0959521\pi\) | |||||||
\(854\) | 867.210 | − | 281.774i | 1.01547 | − | 0.329946i | ||||
\(855\) | 348.563 | + | 83.8580i | 0.407676 | + | 0.0980795i | ||||
\(856\) | −30.6665 | + | 94.3818i | −0.0358253 | + | 0.110259i | ||||
\(857\) | −697.530 | + | 697.530i | −0.813921 | + | 0.813921i | −0.985219 | − | 0.171298i | \(-0.945204\pi\) |
0.171298 | + | 0.985219i | \(0.445204\pi\) | |||||||
\(858\) | 221.983 | − | 113.106i | 0.258721 | − | 0.131825i | ||||
\(859\) | 441.134 | + | 607.170i | 0.513544 | + | 0.706833i | 0.984512 | − | 0.175317i | \(-0.0560952\pi\) |
−0.470968 | + | 0.882150i | \(0.656095\pi\) | |||||||
\(860\) | 1009.08 | − | 617.707i | 1.17335 | − | 0.718264i | ||||
\(861\) | 364.985 | + | 265.177i | 0.423908 | + | 0.307987i | ||||
\(862\) | −147.256 | + | 929.737i | −0.170831 | + | 1.07858i | ||||
\(863\) | 1105.28 | + | 175.059i | 1.28074 | + | 0.202849i | 0.759469 | − | 0.650544i | \(-0.225459\pi\) |
0.521268 | + | 0.853393i | \(0.325459\pi\) | |||||||
\(864\) | 139.269 | − | 191.687i | 0.161191 | − | 0.221860i | ||||
\(865\) | 982.362 | + | 407.455i | 1.13568 | + | 0.471046i | ||||
\(866\) | 134.695 | − | 97.8614i | 0.155537 | − | 0.113004i | ||||
\(867\) | −112.766 | − | 221.316i | −0.130065 | − | 0.255267i | ||||
\(868\) | −481.511 | − | 481.511i | −0.554736 | − | 0.554736i | ||||
\(869\) | 374.842 | + | 121.793i | 0.431348 | + | 0.140154i | ||||
\(870\) | 703.250 | + | 431.412i | 0.808333 | + | 0.495876i | ||||
\(871\) | −35.5184 | − | 109.314i | −0.0407789 | − | 0.125504i | ||||
\(872\) | 54.2091 | + | 27.6209i | 0.0621664 | + | 0.0316754i | ||||
\(873\) | −28.2941 | − | 178.642i | −0.0324102 | − | 0.204630i | ||||
\(874\) | 636.222i | 0.727943i | ||||||||
\(875\) | 359.005 | − | 305.734i | 0.410291 | − | 0.349410i | ||||
\(876\) | −174.496 | −0.199197 | ||||||||
\(877\) | 249.430 | − | 39.5058i | 0.284412 | − | 0.0450465i | −0.0125983 | − | 0.999921i | \(-0.504010\pi\) |
0.297011 | + | 0.954874i | \(0.404010\pi\) | |||||||
\(878\) | 473.043 | − | 928.399i | 0.538773 | − | 1.05740i | ||||
\(879\) | −827.841 | + | 268.982i | −0.941798 | + | 0.306009i | ||||
\(880\) | −102.652 | + | 167.334i | −0.116650 | + | 0.190152i | ||||
\(881\) | 477.436 | − | 1469.40i | 0.541925 | − | 1.66787i | −0.186265 | − | 0.982500i | \(-0.559638\pi\) |
0.728190 | − | 0.685375i | \(-0.240362\pi\) | |||||||
\(882\) | 218.598 | − | 218.598i | 0.247844 | − | 0.247844i | ||||
\(883\) | −745.643 | + | 379.924i | −0.844443 | + | 0.430265i | −0.822003 | − | 0.569483i | \(-0.807143\pi\) |
−0.0224398 | + | 0.999748i | \(0.507143\pi\) | |||||||
\(884\) | −513.746 | − | 707.111i | −0.581161 | − | 0.799899i | ||||
\(885\) | −35.7773 | + | 86.2579i | −0.0404263 | + | 0.0974665i | ||||
\(886\) | 800.560 | + | 581.641i | 0.903567 | + | 0.656480i | ||||
\(887\) | 23.9378 | − | 151.137i | 0.0269874 | − | 0.170392i | −0.970513 | − | 0.241047i | \(-0.922509\pi\) |
0.997501 | + | 0.0706556i | \(0.0225091\pi\) | |||||||
\(888\) | −266.282 | − | 42.1749i | −0.299867 | − | 0.0474943i | ||||
\(889\) | 60.4216 | − | 83.1633i | 0.0679659 | − | 0.0935470i | ||||
\(890\) | −387.953 | − | 633.758i | −0.435902 | − | 0.712088i | ||||
\(891\) | 23.3379 | − | 16.9560i | 0.0261930 | − | 0.0190303i | ||||
\(892\) | 535.725 | + | 1051.42i | 0.600589 | + | 1.17872i | ||||
\(893\) | 675.489 | + | 675.489i | 0.756426 | + | 0.756426i | ||||
\(894\) | −521.998 | − | 169.608i | −0.583891 | − | 0.189718i | ||||
\(895\) | 299.998 | − | 1246.97i | 0.335194 | − | 1.39326i | ||||
\(896\) | 85.0134 | + | 261.644i | 0.0948810 | + | 0.292014i | ||||
\(897\) | −209.877 | − | 106.938i | −0.233977 | − | 0.119217i | ||||
\(898\) | 254.372 | + | 1606.04i | 0.283266 | + | 1.78847i | ||||
\(899\) | − | 1212.85i | − | 1.34911i | ||||||
\(900\) | −56.4658 | + | 354.329i | −0.0627398 | + | 0.393699i | ||||
\(901\) | 902.996 | 1.00222 | ||||||||
\(902\) | 647.842 | − | 102.608i | 0.718229 | − | 0.113756i | ||||
\(903\) | −146.723 | + | 287.959i | −0.162483 | + | 0.318892i | ||||
\(904\) | −418.160 | + | 135.868i | −0.462566 | + | 0.150297i | ||||
\(905\) | −390.676 | − | 457.864i | −0.431687 | − | 0.505927i | ||||
\(906\) | 372.649 | − | 1146.90i | 0.411312 | − | 1.26589i | ||||
\(907\) | −858.411 | + | 858.411i | −0.946429 | + | 0.946429i | −0.998636 | − | 0.0522074i | \(-0.983374\pi\) |
0.0522074 | + | 0.998636i | \(0.483374\pi\) | |||||||
\(908\) | −119.088 | + | 60.6781i | −0.131154 | + | 0.0668262i | ||||
\(909\) | −90.8218 | − | 125.006i | −0.0999140 | − | 0.137520i | ||||
\(910\) | −197.208 | − | 823.156i | −0.216712 | − | 0.904567i | ||||
\(911\) | 124.673 | + | 90.5802i | 0.136853 | + | 0.0994295i | 0.654106 | − | 0.756403i | \(-0.273045\pi\) |
−0.517253 | + | 0.855833i | \(0.673045\pi\) | |||||||
\(912\) | −79.3257 | + | 500.843i | −0.0869800 | + | 0.549170i | ||||
\(913\) | 247.441 | + | 39.1908i | 0.271020 | + | 0.0429253i | ||||
\(914\) | −127.695 | + | 175.757i | −0.139710 | + | 0.192294i | ||||
\(915\) | −55.7503 | + | 704.092i | −0.0609293 | + | 0.769500i | ||||
\(916\) | 382.812 | − | 278.129i | 0.417917 | − | 0.303635i | ||||
\(917\) | 100.257 | + | 196.765i | 0.109331 | + | 0.214574i | ||||
\(918\) | −131.396 | − | 131.396i | −0.143133 | − | 0.143133i | ||||
\(919\) | −1262.85 | − | 410.326i | −1.37416 | − | 0.446492i | −0.473416 | − | 0.880839i | \(-0.656979\pi\) |
−0.900746 | + | 0.434347i | \(0.856979\pi\) | |||||||
\(920\) | −104.031 | + | 8.13761i | −0.113077 | + | 0.00884523i | ||||
\(921\) | −172.168 | − | 529.878i | −0.186936 | − | 0.575329i | ||||
\(922\) | −923.163 | − | 470.375i | −1.00126 | − | 0.510168i | ||||
\(923\) | −236.512 | − | 1493.28i | −0.256243 | − | 1.61785i | ||||
\(924\) | 100.191i | 0.108432i | ||||||||
\(925\) | −1593.23 | + | 515.997i | −1.72241 | + | 0.557835i | ||||
\(926\) | −2135.70 | −2.30637 | ||||||||
\(927\) | 237.736 | − | 37.6537i | 0.256457 | − | 0.0406189i | ||||
\(928\) | −665.417 | + | 1305.95i | −0.717044 | + | 1.40728i | ||||
\(929\) | 778.256 | − | 252.871i | 0.837736 | − | 0.272197i | 0.141435 | − | 0.989947i | \(-0.454828\pi\) |
0.696300 | + | 0.717751i | \(0.254828\pi\) | |||||||
\(930\) | 894.936 | − | 370.196i | 0.962297 | − | 0.398060i | ||||
\(931\) | −256.794 | + | 790.330i | −0.275826 | + | 0.848904i | ||||
\(932\) | 657.404 | − | 657.404i | 0.705369 | − | 0.705369i | ||||
\(933\) | 129.079 | − | 65.7690i | 0.138348 | − | 0.0704919i | ||||
\(934\) | 204.191 | + | 281.045i | 0.218620 | + | 0.300905i | ||||
\(935\) | 146.984 | + | 125.657i | 0.157203 | + | 0.134393i | ||||
\(936\) | 85.3907 | + | 62.0399i | 0.0912293 | + | 0.0662820i | ||||
\(937\) | 205.540 | − | 1297.73i | 0.219359 | − | 1.38498i | −0.594582 | − | 0.804035i | \(-0.702683\pi\) |
0.813942 | − | 0.580946i | \(-0.197317\pi\) | |||||||
\(938\) | 83.8270 | + | 13.2769i | 0.0893678 | + | 0.0141545i | ||||
\(939\) | −457.207 | + | 629.292i | −0.486909 | + | 0.670172i | ||||
\(940\) | −621.258 | + | 726.700i | −0.660913 | + | 0.773085i | ||||
\(941\) | −402.969 | + | 292.774i | −0.428235 | + | 0.311131i | −0.780943 | − | 0.624602i | \(-0.785261\pi\) |
0.352708 | + | 0.935734i | \(0.385261\pi\) | |||||||
\(942\) | −151.464 | − | 297.266i | −0.160790 | − | 0.315569i | ||||
\(943\) | −438.511 | − | 438.511i | −0.465016 | − | 0.465016i | ||||
\(944\) | −125.620 | − | 40.8163i | −0.133072 | − | 0.0432376i | ||||
\(945\) | −37.4635 | − | 90.5667i | −0.0396439 | − | 0.0958378i | ||||
\(946\) | 145.199 | + | 446.878i | 0.153488 | + | 0.472386i | ||||
\(947\) | −1170.22 | − | 596.258i | −1.23572 | − | 0.629629i | −0.290750 | − | 0.956799i | \(-0.593905\pi\) |
−0.944965 | + | 0.327170i | \(0.893905\pi\) | |||||||
\(948\) | 159.391 | + | 1006.35i | 0.168134 | + | 1.06155i | ||||
\(949\) | 318.863i | 0.335999i | ||||||||
\(950\) | −545.636 | − | 1684.75i | −0.574354 | − | 1.77342i | ||||
\(951\) | 196.725 | 0.206861 | ||||||||
\(952\) | 104.464 | − | 16.5455i | 0.109731 | − | 0.0173797i | ||||
\(953\) | −244.779 | + | 480.405i | −0.256851 | + | 0.504098i | −0.983039 | − | 0.183398i | \(-0.941290\pi\) |
0.726188 | + | 0.687496i | \(0.241290\pi\) | |||||||
\(954\) | −632.834 | + | 205.620i | −0.663348 | + | 0.215535i | ||||
\(955\) | 110.729 | + | 1415.56i | 0.115947 | + | 1.48226i | ||||
\(956\) | 182.986 | − | 563.172i | 0.191408 | − | 0.589092i | ||||
\(957\) | −126.183 | + | 126.183i | −0.131853 | + | 0.131853i | ||||
\(958\) | −2351.16 | + | 1197.98i | −2.45424 | + | 1.25050i | ||||
\(959\) | −268.980 | − | 370.219i | −0.280479 | − | 0.386047i | ||||
\(960\) | −743.731 | − | 58.8889i | −0.774720 | − | 0.0613427i | ||||
\(961\) | −374.360 | − | 271.988i | −0.389552 | − | 0.283026i | ||||
\(962\) | −470.269 | + | 2969.16i | −0.488845 | + | 3.08645i | ||||
\(963\) | 126.550 | + | 20.0435i | 0.131412 | + | 0.0208136i | ||||
\(964\) | −473.004 | + | 651.035i | −0.490668 | + | 0.675347i | ||||
\(965\) | −1090.82 | + | 261.335i | −1.13039 | + | 0.270813i | ||||
\(966\) | 140.713 | − | 102.234i | 0.145666 | − | 0.105832i | ||||
\(967\) | 751.595 | + | 1475.09i | 0.777244 | + | 1.52543i | 0.849231 | + | 0.528021i | \(0.177066\pi\) |
−0.0719874 | + | 0.997406i | \(0.522934\pi\) | |||||||
\(968\) | −181.927 | − | 181.927i | −0.187942 | − | 0.187942i | ||||
\(969\) | 475.056 | + | 154.355i | 0.490254 | + | 0.159293i | ||||
\(970\) | −679.642 | + | 579.910i | −0.700662 | + | 0.597846i | ||||
\(971\) | −496.664 | − | 1528.58i | −0.511498 | − | 1.57423i | −0.789565 | − | 0.613666i | \(-0.789694\pi\) |
0.278068 | − | 0.960561i | \(-0.410306\pi\) | |||||||
\(972\) | 66.4470 | + | 33.8564i | 0.0683611 | + | 0.0348317i | ||||
\(973\) | −44.3305 | − | 279.892i | −0.0455606 | − | 0.287658i | ||||
\(974\) | − | 2349.82i | − | 2.41255i | ||||||
\(975\) | 647.477 | + | 103.182i | 0.664079 | + | 0.105828i | ||||
\(976\) | −999.008 | −1.02357 | ||||||||
\(977\) | 914.524 | − | 144.846i | 0.936054 | − | 0.148256i | 0.330271 | − | 0.943886i | \(-0.392860\pi\) |
0.605783 | + | 0.795630i | \(0.292860\pi\) | |||||||
\(978\) | −391.015 | + | 767.410i | −0.399811 | + | 0.784673i | ||||
\(979\) | 152.857 | − | 49.6661i | 0.156135 | − | 0.0507315i | ||||
\(980\) | −808.606 | − | 194.536i | −0.825108 | − | 0.198506i | ||||
\(981\) | 24.2735 | − | 74.7062i | 0.0247437 | − | 0.0761532i | ||||
\(982\) | −412.580 | + | 412.580i | −0.420143 | + | 0.420143i | ||||
\(983\) | −375.845 | + | 191.503i | −0.382345 | + | 0.194814i | −0.634590 | − | 0.772849i | \(-0.718831\pi\) |
0.252245 | + | 0.967663i | \(0.418831\pi\) | |||||||
\(984\) | 163.336 | + | 224.813i | 0.165992 | + | 0.228468i | ||||
\(985\) | 1434.62 | − | 878.198i | 1.45647 | − | 0.891572i | ||||
\(986\) | 929.966 | + | 675.660i | 0.943171 | + | 0.685254i | ||||
\(987\) | 40.8539 | − | 257.941i | 0.0413920 | − | 0.261339i | ||||
\(988\) | −1709.97 | − | 270.833i | −1.73074 | − | 0.274122i | ||||
\(989\) | 261.124 | − | 359.406i | 0.264028 | − | 0.363404i | ||||
\(990\) | −131.622 | − | 54.5931i | −0.132952 | − | 0.0551446i | ||||
\(991\) | 1493.14 | − | 1084.83i | 1.50670 | − | 1.09468i | 0.539080 | − | 0.842255i | \(-0.318772\pi\) |
0.967617 | − | 0.252424i | \(-0.0812278\pi\) | |||||||
\(992\) | 781.114 | + | 1533.02i | 0.787414 | + | 1.54539i | ||||
\(993\) | −704.910 | − | 704.910i | −0.709880 | − | 0.709880i | ||||
\(994\) | 1061.74 | + | 344.981i | 1.06815 | + | 0.347064i | ||||
\(995\) | −744.087 | − | 456.464i | −0.747826 | − | 0.458758i | ||||
\(996\) | 200.135 | + | 615.953i | 0.200939 | + | 0.618427i | ||||
\(997\) | 451.791 | + | 230.199i | 0.453150 | + | 0.230892i | 0.665642 | − | 0.746271i | \(-0.268158\pi\) |
−0.212492 | + | 0.977163i | \(0.568158\pi\) | |||||||
\(998\) | 178.376 | + | 1126.22i | 0.178733 | + | 1.12848i | ||||
\(999\) | 348.081i | 0.348430i |
(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 | 75.3.k.a.13.9 | ✓ | 80 | |
3.2 | odd | 2 | 225.3.r.b.163.2 | 80 | |||
5.2 | odd | 4 | 375.3.k.c.82.9 | 80 | |||
5.3 | odd | 4 | 375.3.k.b.82.2 | 80 | |||
5.4 | even | 2 | 375.3.k.a.43.2 | 80 | |||
25.2 | odd | 20 | inner | 75.3.k.a.52.9 | yes | 80 | |
25.11 | even | 5 | 375.3.k.c.343.9 | 80 | |||
25.14 | even | 10 | 375.3.k.b.343.2 | 80 | |||
25.23 | odd | 20 | 375.3.k.a.157.2 | 80 | |||
75.2 | even | 20 | 225.3.r.b.127.2 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.3.k.a.13.9 | ✓ | 80 | 1.1 | even | 1 | trivial | |
75.3.k.a.52.9 | yes | 80 | 25.2 | odd | 20 | inner | |
225.3.r.b.127.2 | 80 | 75.2 | even | 20 | |||
225.3.r.b.163.2 | 80 | 3.2 | odd | 2 | |||
375.3.k.a.43.2 | 80 | 5.4 | even | 2 | |||
375.3.k.a.157.2 | 80 | 25.23 | odd | 20 | |||
375.3.k.b.82.2 | 80 | 5.3 | odd | 4 | |||
375.3.k.b.343.2 | 80 | 25.14 | even | 10 | |||
375.3.k.c.82.9 | 80 | 5.2 | odd | 4 | |||
375.3.k.c.343.9 | 80 | 25.11 | even | 5 |