Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [114,2,Mod(65,114)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(114, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("114.65");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 114 = 2 \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 114.h (of order \(6\), 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: | \(0.910294583043\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 107.1 | ||
Root | \(1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 114.107 |
Dual form | 114.2.h.f.65.1 |
$q$-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 \(\left(\mathbb{Z}/114\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(97\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | −0.724745 | − | 1.57313i | −0.418432 | − | 0.908248i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 1.22474 | − | 0.707107i | 0.547723 | − | 0.316228i | −0.200480 | − | 0.979698i | \(-0.564250\pi\) |
0.748203 | + | 0.663470i | \(0.230917\pi\) | |||||||
\(6\) | 1.00000 | − | 1.41421i | 0.408248 | − | 0.577350i | ||||
\(7\) | 4.44949 | 1.68175 | 0.840875 | − | 0.541230i | \(-0.182041\pi\) | ||||
0.840875 | + | 0.541230i | \(0.182041\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.94949 | + | 2.28024i | −0.649830 | + | 0.760080i | ||||
\(10\) | 1.22474 | + | 0.707107i | 0.387298 | + | 0.223607i | ||||
\(11\) | − | 0.317837i | − | 0.0958315i | −0.998851 | − | 0.0479158i | \(-0.984742\pi\) | ||
0.998851 | − | 0.0479158i | \(-0.0152579\pi\) | |||||||
\(12\) | 1.72474 | + | 0.158919i | 0.497891 | + | 0.0458759i | ||||
\(13\) | −3.00000 | − | 1.73205i | −0.832050 | − | 0.480384i | 0.0225039 | − | 0.999747i | \(-0.492836\pi\) |
−0.854554 | + | 0.519362i | \(0.826170\pi\) | |||||||
\(14\) | 2.22474 | + | 3.85337i | 0.594588 | + | 1.02986i | ||||
\(15\) | −2.00000 | − | 1.41421i | −0.516398 | − | 0.365148i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −5.44949 | + | 3.14626i | −1.32170 | + | 0.763081i | −0.983999 | − | 0.178174i | \(-0.942981\pi\) |
−0.337696 | + | 0.941255i | \(0.609648\pi\) | |||||||
\(18\) | −2.94949 | − | 0.548188i | −0.695201 | − | 0.129209i | ||||
\(19\) | −4.17423 | − | 1.25529i | −0.957635 | − | 0.287984i | ||||
\(20\) | 1.41421i | 0.316228i | ||||||||
\(21\) | −3.22474 | − | 6.99964i | −0.703697 | − | 1.52745i | ||||
\(22\) | 0.275255 | − | 0.158919i | 0.0586846 | − | 0.0338816i | ||||
\(23\) | 6.12372 | + | 3.53553i | 1.27688 | + | 0.737210i | 0.976274 | − | 0.216537i | \(-0.0694763\pi\) |
0.300610 | + | 0.953747i | \(0.402810\pi\) | |||||||
\(24\) | 0.724745 | + | 1.57313i | 0.147938 | + | 0.321114i | ||||
\(25\) | −1.50000 | + | 2.59808i | −0.300000 | + | 0.519615i | ||||
\(26\) | − | 3.46410i | − | 0.679366i | ||||||
\(27\) | 5.00000 | + | 1.41421i | 0.962250 | + | 0.272166i | ||||
\(28\) | −2.22474 | + | 3.85337i | −0.420437 | + | 0.728219i | ||||
\(29\) | −1.22474 | + | 2.12132i | −0.227429 | + | 0.393919i | −0.957046 | − | 0.289938i | \(-0.906365\pi\) |
0.729616 | + | 0.683857i | \(0.239699\pi\) | |||||||
\(30\) | 0.224745 | − | 2.43916i | 0.0410326 | − | 0.445327i | ||||
\(31\) | − | 4.24264i | − | 0.762001i | −0.924575 | − | 0.381000i | \(-0.875580\pi\) | ||
0.924575 | − | 0.381000i | \(-0.124420\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −0.500000 | + | 0.230351i | −0.0870388 | + | 0.0400989i | ||||
\(34\) | −5.44949 | − | 3.14626i | −0.934580 | − | 0.539580i | ||||
\(35\) | 5.44949 | − | 3.14626i | 0.921132 | − | 0.531816i | ||||
\(36\) | −1.00000 | − | 2.82843i | −0.166667 | − | 0.471405i | ||||
\(37\) | 0.778539i | 0.127991i | 0.997950 | + | 0.0639955i | \(0.0203843\pi\) | ||||
−0.997950 | + | 0.0639955i | \(0.979616\pi\) | |||||||
\(38\) | −1.00000 | − | 4.24264i | −0.162221 | − | 0.688247i | ||||
\(39\) | −0.550510 | + | 5.97469i | −0.0881522 | + | 0.956716i | ||||
\(40\) | −1.22474 | + | 0.707107i | −0.193649 | + | 0.111803i | ||||
\(41\) | −1.50000 | − | 2.59808i | −0.234261 | − | 0.405751i | 0.724797 | − | 0.688963i | \(-0.241934\pi\) |
−0.959058 | + | 0.283211i | \(0.908600\pi\) | |||||||
\(42\) | 4.44949 | − | 6.29253i | 0.686571 | − | 0.970958i | ||||
\(43\) | −0.449490 | − | 0.778539i | −0.0685465 | − | 0.118726i | 0.829715 | − | 0.558187i | \(-0.188503\pi\) |
−0.898262 | + | 0.439461i | \(0.855169\pi\) | |||||||
\(44\) | 0.275255 | + | 0.158919i | 0.0414963 | + | 0.0239579i | ||||
\(45\) | −0.775255 | + | 4.17121i | −0.115568 | + | 0.621807i | ||||
\(46\) | 7.07107i | 1.04257i | ||||||||
\(47\) | −5.57321 | − | 3.21770i | −0.812937 | − | 0.469349i | 0.0350379 | − | 0.999386i | \(-0.488845\pi\) |
−0.847975 | + | 0.530037i | \(0.822178\pi\) | |||||||
\(48\) | −1.00000 | + | 1.41421i | −0.144338 | + | 0.204124i | ||||
\(49\) | 12.7980 | 1.82828 | ||||||||
\(50\) | −3.00000 | −0.424264 | ||||||||
\(51\) | 8.89898 | + | 6.29253i | 1.24611 | + | 0.881130i | ||||
\(52\) | 3.00000 | − | 1.73205i | 0.416025 | − | 0.240192i | ||||
\(53\) | −0.550510 | + | 0.953512i | −0.0756184 | + | 0.130975i | −0.901355 | − | 0.433081i | \(-0.857426\pi\) |
0.825737 | + | 0.564056i | \(0.190760\pi\) | |||||||
\(54\) | 1.27526 | + | 5.03723i | 0.173540 | + | 0.685481i | ||||
\(55\) | −0.224745 | − | 0.389270i | −0.0303046 | − | 0.0524891i | ||||
\(56\) | −4.44949 | −0.594588 | ||||||||
\(57\) | 1.05051 | + | 7.47639i | 0.139143 | + | 0.990272i | ||||
\(58\) | −2.44949 | −0.321634 | ||||||||
\(59\) | 3.27526 | + | 5.67291i | 0.426402 | + | 0.738550i | 0.996550 | − | 0.0829920i | \(-0.0264476\pi\) |
−0.570148 | + | 0.821542i | \(0.693114\pi\) | |||||||
\(60\) | 2.22474 | − | 1.02494i | 0.287213 | − | 0.132320i | ||||
\(61\) | 3.22474 | − | 5.58542i | 0.412886 | − | 0.715140i | −0.582318 | − | 0.812961i | \(-0.697854\pi\) |
0.995204 | + | 0.0978213i | \(0.0311874\pi\) | |||||||
\(62\) | 3.67423 | − | 2.12132i | 0.466628 | − | 0.269408i | ||||
\(63\) | −8.67423 | + | 10.1459i | −1.09285 | + | 1.27826i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.89898 | −0.607644 | ||||||||
\(66\) | −0.449490 | − | 0.317837i | −0.0553284 | − | 0.0391231i | ||||
\(67\) | −5.17423 | − | 2.98735i | −0.632133 | − | 0.364962i | 0.149444 | − | 0.988770i | \(-0.452251\pi\) |
−0.781578 | + | 0.623808i | \(0.785585\pi\) | |||||||
\(68\) | − | 6.29253i | − | 0.763081i | ||||||
\(69\) | 1.12372 | − | 12.1958i | 0.135281 | − | 1.46820i | ||||
\(70\) | 5.44949 | + | 3.14626i | 0.651339 | + | 0.376051i | ||||
\(71\) | 3.00000 | + | 5.19615i | 0.356034 | + | 0.616670i | 0.987294 | − | 0.158901i | \(-0.0507952\pi\) |
−0.631260 | + | 0.775571i | \(0.717462\pi\) | |||||||
\(72\) | 1.94949 | − | 2.28024i | 0.229750 | − | 0.268729i | ||||
\(73\) | 5.39898 | + | 9.35131i | 0.631903 | + | 1.09449i | 0.987162 | + | 0.159720i | \(0.0510591\pi\) |
−0.355260 | + | 0.934768i | \(0.615608\pi\) | |||||||
\(74\) | −0.674235 | + | 0.389270i | −0.0783782 | + | 0.0452517i | ||||
\(75\) | 5.17423 | + | 0.476756i | 0.597469 | + | 0.0550510i | ||||
\(76\) | 3.17423 | − | 2.98735i | 0.364110 | − | 0.342672i | ||||
\(77\) | − | 1.41421i | − | 0.161165i | ||||||
\(78\) | −5.44949 | + | 2.51059i | −0.617033 | + | 0.284268i | ||||
\(79\) | 7.34847 | − | 4.24264i | 0.826767 | − | 0.477334i | −0.0259772 | − | 0.999663i | \(-0.508270\pi\) |
0.852745 | + | 0.522328i | \(0.174936\pi\) | |||||||
\(80\) | −1.22474 | − | 0.707107i | −0.136931 | − | 0.0790569i | ||||
\(81\) | −1.39898 | − | 8.89060i | −0.155442 | − | 0.987845i | ||||
\(82\) | 1.50000 | − | 2.59808i | 0.165647 | − | 0.286910i | ||||
\(83\) | − | 14.1742i | − | 1.55583i | −0.628372 | − | 0.777913i | \(-0.716279\pi\) | ||
0.628372 | − | 0.777913i | \(-0.283721\pi\) | |||||||
\(84\) | 7.67423 | + | 0.707107i | 0.837328 | + | 0.0771517i | ||||
\(85\) | −4.44949 | + | 7.70674i | −0.482615 | + | 0.835914i | ||||
\(86\) | 0.449490 | − | 0.778539i | 0.0484697 | − | 0.0839520i | ||||
\(87\) | 4.22474 | + | 0.389270i | 0.452940 | + | 0.0417341i | ||||
\(88\) | 0.317837i | 0.0338816i | ||||||||
\(89\) | 8.44949 | − | 14.6349i | 0.895644 | − | 1.55130i | 0.0626387 | − | 0.998036i | \(-0.480048\pi\) |
0.833005 | − | 0.553265i | \(-0.186618\pi\) | |||||||
\(90\) | −4.00000 | + | 1.41421i | −0.421637 | + | 0.149071i | ||||
\(91\) | −13.3485 | − | 7.70674i | −1.39930 | − | 0.807886i | ||||
\(92\) | −6.12372 | + | 3.53553i | −0.638442 | + | 0.368605i | ||||
\(93\) | −6.67423 | + | 3.07483i | −0.692086 | + | 0.318845i | ||||
\(94\) | − | 6.43539i | − | 0.663760i | ||||||
\(95\) | −6.00000 | + | 1.41421i | −0.615587 | + | 0.145095i | ||||
\(96\) | −1.72474 | − | 0.158919i | −0.176031 | − | 0.0162196i | ||||
\(97\) | −11.8485 | + | 6.84072i | −1.20303 | + | 0.694570i | −0.961228 | − | 0.275756i | \(-0.911072\pi\) |
−0.241802 | + | 0.970326i | \(0.577738\pi\) | |||||||
\(98\) | 6.39898 | + | 11.0834i | 0.646395 | + | 1.11959i | ||||
\(99\) | 0.724745 | + | 0.619620i | 0.0728396 | + | 0.0622742i | ||||
\(100\) | −1.50000 | − | 2.59808i | −0.150000 | − | 0.259808i | ||||
\(101\) | −8.57321 | − | 4.94975i | −0.853067 | − | 0.492518i | 0.00861771 | − | 0.999963i | \(-0.497257\pi\) |
−0.861684 | + | 0.507445i | \(0.830590\pi\) | |||||||
\(102\) | −1.00000 | + | 10.8530i | −0.0990148 | + | 1.07461i | ||||
\(103\) | 11.9494i | 1.17741i | 0.808349 | + | 0.588704i | \(0.200362\pi\) | ||||
−0.808349 | + | 0.588704i | \(0.799638\pi\) | |||||||
\(104\) | 3.00000 | + | 1.73205i | 0.294174 | + | 0.169842i | ||||
\(105\) | −8.89898 | − | 6.29253i | −0.868451 | − | 0.614088i | ||||
\(106\) | −1.10102 | −0.106941 | ||||||||
\(107\) | 4.89898 | 0.473602 | 0.236801 | − | 0.971558i | \(-0.423901\pi\) | ||||
0.236801 | + | 0.971558i | \(0.423901\pi\) | |||||||
\(108\) | −3.72474 | + | 3.62302i | −0.358414 | + | 0.348625i | ||||
\(109\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(110\) | 0.224745 | − | 0.389270i | 0.0214286 | − | 0.0371154i | ||||
\(111\) | 1.22474 | − | 0.564242i | 0.116248 | − | 0.0535555i | ||||
\(112\) | −2.22474 | − | 3.85337i | −0.210219 | − | 0.364109i | ||||
\(113\) | 0.797959 | 0.0750657 | 0.0375328 | − | 0.999295i | \(-0.488050\pi\) | ||||
0.0375328 | + | 0.999295i | \(0.488050\pi\) | |||||||
\(114\) | −5.94949 | + | 4.64796i | −0.557221 | + | 0.435322i | ||||
\(115\) | 10.0000 | 0.932505 | ||||||||
\(116\) | −1.22474 | − | 2.12132i | −0.113715 | − | 0.196960i | ||||
\(117\) | 9.79796 | − | 3.46410i | 0.905822 | − | 0.320256i | ||||
\(118\) | −3.27526 | + | 5.67291i | −0.301512 | + | 0.522234i | ||||
\(119\) | −24.2474 | + | 13.9993i | −2.22276 | + | 1.28331i | ||||
\(120\) | 2.00000 | + | 1.41421i | 0.182574 | + | 0.129099i | ||||
\(121\) | 10.8990 | 0.990816 | ||||||||
\(122\) | 6.44949 | 0.583909 | ||||||||
\(123\) | −3.00000 | + | 4.24264i | −0.270501 | + | 0.382546i | ||||
\(124\) | 3.67423 | + | 2.12132i | 0.329956 | + | 0.190500i | ||||
\(125\) | 11.3137i | 1.01193i | ||||||||
\(126\) | −13.1237 | − | 2.43916i | −1.16915 | − | 0.217297i | ||||
\(127\) | −9.00000 | − | 5.19615i | −0.798621 | − | 0.461084i | 0.0443678 | − | 0.999015i | \(-0.485873\pi\) |
−0.842989 | + | 0.537931i | \(0.819206\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −0.898979 | + | 1.27135i | −0.0791507 | + | 0.111936i | ||||
\(130\) | −2.44949 | − | 4.24264i | −0.214834 | − | 0.372104i | ||||
\(131\) | 19.0732 | − | 11.0119i | 1.66643 | − | 0.962116i | 0.696898 | − | 0.717171i | \(-0.254563\pi\) |
0.969537 | − | 0.244946i | \(-0.0787702\pi\) | |||||||
\(132\) | 0.0505103 | − | 0.548188i | 0.00439635 | − | 0.0477137i | ||||
\(133\) | −18.5732 | − | 5.58542i | −1.61050 | − | 0.484318i | ||||
\(134\) | − | 5.97469i | − | 0.516135i | ||||||
\(135\) | 7.12372 | − | 1.80348i | 0.613113 | − | 0.155219i | ||||
\(136\) | 5.44949 | − | 3.14626i | 0.467290 | − | 0.269790i | ||||
\(137\) | −6.39898 | − | 3.69445i | −0.546702 | − | 0.315638i | 0.201089 | − | 0.979573i | \(-0.435552\pi\) |
−0.747791 | + | 0.663935i | \(0.768885\pi\) | |||||||
\(138\) | 11.1237 | − | 5.12472i | 0.946914 | − | 0.436245i | ||||
\(139\) | −0.174235 | + | 0.301783i | −0.0147784 | + | 0.0255969i | −0.873320 | − | 0.487147i | \(-0.838038\pi\) |
0.858542 | + | 0.512744i | \(0.171371\pi\) | |||||||
\(140\) | 6.29253i | 0.531816i | ||||||||
\(141\) | −1.02270 | + | 11.0994i | −0.0861272 | + | 0.934739i | ||||
\(142\) | −3.00000 | + | 5.19615i | −0.251754 | + | 0.436051i | ||||
\(143\) | −0.550510 | + | 0.953512i | −0.0460360 | + | 0.0797367i | ||||
\(144\) | 2.94949 | + | 0.548188i | 0.245791 | + | 0.0456823i | ||||
\(145\) | 3.46410i | 0.287678i | ||||||||
\(146\) | −5.39898 | + | 9.35131i | −0.446823 | + | 0.773920i | ||||
\(147\) | −9.27526 | − | 20.1329i | −0.765010 | − | 1.66053i | ||||
\(148\) | −0.674235 | − | 0.389270i | −0.0554217 | − | 0.0319978i | ||||
\(149\) | 4.22474 | − | 2.43916i | 0.346105 | − | 0.199824i | −0.316864 | − | 0.948471i | \(-0.602630\pi\) |
0.662968 | + | 0.748648i | \(0.269296\pi\) | |||||||
\(150\) | 2.17423 | + | 4.71940i | 0.177526 | + | 0.385337i | ||||
\(151\) | − | 18.0990i | − | 1.47288i | −0.676503 | − | 0.736440i | \(-0.736505\pi\) | ||
0.676503 | − | 0.736440i | \(-0.263495\pi\) | |||||||
\(152\) | 4.17423 | + | 1.25529i | 0.338575 | + | 0.101818i | ||||
\(153\) | 3.44949 | − | 18.5597i | 0.278875 | − | 1.50047i | ||||
\(154\) | 1.22474 | − | 0.707107i | 0.0986928 | − | 0.0569803i | ||||
\(155\) | −3.00000 | − | 5.19615i | −0.240966 | − | 0.417365i | ||||
\(156\) | −4.89898 | − | 3.46410i | −0.392232 | − | 0.277350i | ||||
\(157\) | 9.34847 | + | 16.1920i | 0.746089 | + | 1.29226i | 0.949684 | + | 0.313209i | \(0.101404\pi\) |
−0.203595 | + | 0.979055i | \(0.565263\pi\) | |||||||
\(158\) | 7.34847 | + | 4.24264i | 0.584613 | + | 0.337526i | ||||
\(159\) | 1.89898 | + | 0.174973i | 0.150599 | + | 0.0138762i | ||||
\(160\) | − | 1.41421i | − | 0.111803i | ||||||
\(161\) | 27.2474 | + | 15.7313i | 2.14740 | + | 1.23980i | ||||
\(162\) | 7.00000 | − | 5.65685i | 0.549972 | − | 0.444444i | ||||
\(163\) | 3.65153 | 0.286010 | 0.143005 | − | 0.989722i | \(-0.454324\pi\) | ||||
0.143005 | + | 0.989722i | \(0.454324\pi\) | |||||||
\(164\) | 3.00000 | 0.234261 | ||||||||
\(165\) | −0.449490 | + | 0.635674i | −0.0349927 | + | 0.0494872i | ||||
\(166\) | 12.2753 | − | 7.08712i | 0.952745 | − | 0.550067i | ||||
\(167\) | 2.44949 | − | 4.24264i | 0.189547 | − | 0.328305i | −0.755552 | − | 0.655089i | \(-0.772631\pi\) |
0.945099 | + | 0.326783i | \(0.105965\pi\) | |||||||
\(168\) | 3.22474 | + | 6.99964i | 0.248794 | + | 0.540034i | ||||
\(169\) | −0.500000 | − | 0.866025i | −0.0384615 | − | 0.0666173i | ||||
\(170\) | −8.89898 | −0.682521 | ||||||||
\(171\) | 11.0000 | − | 7.07107i | 0.841191 | − | 0.540738i | ||||
\(172\) | 0.898979 | 0.0685465 | ||||||||
\(173\) | 5.44949 | + | 9.43879i | 0.414317 | + | 0.717618i | 0.995356 | − | 0.0962572i | \(-0.0306871\pi\) |
−0.581039 | + | 0.813875i | \(0.697354\pi\) | |||||||
\(174\) | 1.77526 | + | 3.85337i | 0.134582 | + | 0.292123i | ||||
\(175\) | −6.67423 | + | 11.5601i | −0.504525 | + | 0.873862i | ||||
\(176\) | −0.275255 | + | 0.158919i | −0.0207481 | + | 0.0119789i | ||||
\(177\) | 6.55051 | − | 9.26382i | 0.492367 | − | 0.696311i | ||||
\(178\) | 16.8990 | 1.26663 | ||||||||
\(179\) | −22.3485 | −1.67040 | −0.835202 | − | 0.549944i | \(-0.814649\pi\) | ||||
−0.835202 | + | 0.549944i | \(0.814649\pi\) | |||||||
\(180\) | −3.22474 | − | 2.75699i | −0.240358 | − | 0.205494i | ||||
\(181\) | 11.3258 | + | 6.53893i | 0.841838 | + | 0.486035i | 0.857888 | − | 0.513836i | \(-0.171776\pi\) |
−0.0160509 | + | 0.999871i | \(0.505109\pi\) | |||||||
\(182\) | − | 15.4135i | − | 1.14252i | ||||||
\(183\) | −11.1237 | − | 1.02494i | −0.822289 | − | 0.0757660i | ||||
\(184\) | −6.12372 | − | 3.53553i | −0.451447 | − | 0.260643i | ||||
\(185\) | 0.550510 | + | 0.953512i | 0.0404743 | + | 0.0701036i | ||||
\(186\) | −6.00000 | − | 4.24264i | −0.439941 | − | 0.311086i | ||||
\(187\) | 1.00000 | + | 1.73205i | 0.0731272 | + | 0.126660i | ||||
\(188\) | 5.57321 | − | 3.21770i | 0.406468 | − | 0.234675i | ||||
\(189\) | 22.2474 | + | 6.29253i | 1.61826 | + | 0.457714i | ||||
\(190\) | −4.22474 | − | 4.48905i | −0.306495 | − | 0.325670i | ||||
\(191\) | 19.5133i | 1.41193i | 0.708247 | + | 0.705965i | \(0.249486\pi\) | ||||
−0.708247 | + | 0.705965i | \(0.750514\pi\) | |||||||
\(192\) | −0.724745 | − | 1.57313i | −0.0523040 | − | 0.113531i | ||||
\(193\) | −7.65153 | + | 4.41761i | −0.550769 | + | 0.317987i | −0.749432 | − | 0.662081i | \(-0.769673\pi\) |
0.198663 | + | 0.980068i | \(0.436340\pi\) | |||||||
\(194\) | −11.8485 | − | 6.84072i | −0.850671 | − | 0.491135i | ||||
\(195\) | 3.55051 | + | 7.70674i | 0.254257 | + | 0.551891i | ||||
\(196\) | −6.39898 | + | 11.0834i | −0.457070 | + | 0.791668i | ||||
\(197\) | − | 0.492810i | − | 0.0351113i | −0.999846 | − | 0.0175556i | \(-0.994412\pi\) | ||
0.999846 | − | 0.0175556i | \(-0.00558842\pi\) | |||||||
\(198\) | −0.174235 | + | 0.937458i | −0.0123823 | + | 0.0666222i | ||||
\(199\) | −3.44949 | + | 5.97469i | −0.244528 | + | 0.423535i | −0.961999 | − | 0.273054i | \(-0.911966\pi\) |
0.717471 | + | 0.696588i | \(0.245300\pi\) | |||||||
\(200\) | 1.50000 | − | 2.59808i | 0.106066 | − | 0.183712i | ||||
\(201\) | −0.949490 | + | 10.3048i | −0.0669718 | + | 0.726846i | ||||
\(202\) | − | 9.89949i | − | 0.696526i | ||||||
\(203\) | −5.44949 | + | 9.43879i | −0.382479 | + | 0.662473i | ||||
\(204\) | −9.89898 | + | 4.56048i | −0.693067 | + | 0.319297i | ||||
\(205\) | −3.67423 | − | 2.12132i | −0.256620 | − | 0.148159i | ||||
\(206\) | −10.3485 | + | 5.97469i | −0.721012 | + | 0.416276i | ||||
\(207\) | −20.0000 | + | 7.07107i | −1.39010 | + | 0.491473i | ||||
\(208\) | 3.46410i | 0.240192i | ||||||||
\(209\) | −0.398979 | + | 1.32673i | −0.0275980 | + | 0.0917716i | ||||
\(210\) | 1.00000 | − | 10.8530i | 0.0690066 | − | 0.748929i | ||||
\(211\) | 13.3485 | − | 7.70674i | 0.918947 | − | 0.530554i | 0.0356477 | − | 0.999364i | \(-0.488651\pi\) |
0.883299 | + | 0.468810i | \(0.155317\pi\) | |||||||
\(212\) | −0.550510 | − | 0.953512i | −0.0378092 | − | 0.0654875i | ||||
\(213\) | 6.00000 | − | 8.48528i | 0.411113 | − | 0.581402i | ||||
\(214\) | 2.44949 | + | 4.24264i | 0.167444 | + | 0.290021i | ||||
\(215\) | −1.10102 | − | 0.635674i | −0.0750890 | − | 0.0433526i | ||||
\(216\) | −5.00000 | − | 1.41421i | −0.340207 | − | 0.0962250i | ||||
\(217\) | − | 18.8776i | − | 1.28149i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.7980 | − | 15.2706i | 0.729658 | − | 1.03189i | ||||
\(220\) | 0.449490 | 0.0303046 | ||||||||
\(221\) | 21.7980 | 1.46629 | ||||||||
\(222\) | 1.10102 | + | 0.778539i | 0.0738957 | + | 0.0522521i | ||||
\(223\) | −8.32577 | + | 4.80688i | −0.557534 | + | 0.321893i | −0.752155 | − | 0.658986i | \(-0.770986\pi\) |
0.194621 | + | 0.980879i | \(0.437652\pi\) | |||||||
\(224\) | 2.22474 | − | 3.85337i | 0.148647 | − | 0.257464i | ||||
\(225\) | −3.00000 | − | 8.48528i | −0.200000 | − | 0.565685i | ||||
\(226\) | 0.398979 | + | 0.691053i | 0.0265397 | + | 0.0459681i | ||||
\(227\) | 5.44949 | 0.361695 | 0.180848 | − | 0.983511i | \(-0.442116\pi\) | ||||
0.180848 | + | 0.983511i | \(0.442116\pi\) | |||||||
\(228\) | −7.00000 | − | 2.82843i | −0.463586 | − | 0.187317i | ||||
\(229\) | −8.89898 | −0.588061 | −0.294031 | − | 0.955796i | \(-0.594997\pi\) | ||||
−0.294031 | + | 0.955796i | \(0.594997\pi\) | |||||||
\(230\) | 5.00000 | + | 8.66025i | 0.329690 | + | 0.571040i | ||||
\(231\) | −2.22474 | + | 1.02494i | −0.146377 | + | 0.0674364i | ||||
\(232\) | 1.22474 | − | 2.12132i | 0.0804084 | − | 0.139272i | ||||
\(233\) | −5.60102 | + | 3.23375i | −0.366935 | + | 0.211850i | −0.672119 | − | 0.740443i | \(-0.734616\pi\) |
0.305184 | + | 0.952294i | \(0.401282\pi\) | |||||||
\(234\) | 7.89898 | + | 6.75323i | 0.516372 | + | 0.441472i | ||||
\(235\) | −9.10102 | −0.593685 | ||||||||
\(236\) | −6.55051 | −0.426402 | ||||||||
\(237\) | −12.0000 | − | 8.48528i | −0.779484 | − | 0.551178i | ||||
\(238\) | −24.2474 | − | 13.9993i | −1.57173 | − | 0.907438i | ||||
\(239\) | 7.21393i | 0.466630i | 0.972401 | + | 0.233315i | \(0.0749574\pi\) | ||||
−0.972401 | + | 0.233315i | \(0.925043\pi\) | |||||||
\(240\) | −0.224745 | + | 2.43916i | −0.0145072 | + | 0.157447i | ||||
\(241\) | 8.84847 | + | 5.10867i | 0.569980 | + | 0.329078i | 0.757141 | − | 0.653251i | \(-0.226595\pi\) |
−0.187161 | + | 0.982329i | \(0.559929\pi\) | |||||||
\(242\) | 5.44949 | + | 9.43879i | 0.350306 | + | 0.606749i | ||||
\(243\) | −12.9722 | + | 8.64420i | −0.832167 | + | 0.554526i | ||||
\(244\) | 3.22474 | + | 5.58542i | 0.206443 | + | 0.357570i | ||||
\(245\) | 15.6742 | − | 9.04952i | 1.00139 | − | 0.578153i | ||||
\(246\) | −5.17423 | − | 0.476756i | −0.329897 | − | 0.0303968i | ||||
\(247\) | 10.3485 | + | 10.9959i | 0.658457 | + | 0.699651i | ||||
\(248\) | 4.24264i | 0.269408i | ||||||||
\(249\) | −22.2980 | + | 10.2727i | −1.41308 | + | 0.651007i | ||||
\(250\) | −9.79796 | + | 5.65685i | −0.619677 | + | 0.357771i | ||||
\(251\) | −5.72474 | − | 3.30518i | −0.361343 | − | 0.208621i | 0.308327 | − | 0.951280i | \(-0.400231\pi\) |
−0.669670 | + | 0.742659i | \(0.733564\pi\) | |||||||
\(252\) | −4.44949 | − | 12.5851i | −0.280292 | − | 0.792784i | ||||
\(253\) | 1.12372 | − | 1.94635i | 0.0706479 | − | 0.122366i | ||||
\(254\) | − | 10.3923i | − | 0.652071i | ||||||
\(255\) | 15.3485 | + | 1.41421i | 0.961158 | + | 0.0885615i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −7.50000 | + | 12.9904i | −0.467837 | + | 0.810318i | −0.999325 | − | 0.0367485i | \(-0.988300\pi\) |
0.531487 | + | 0.847066i | \(0.321633\pi\) | |||||||
\(258\) | −1.55051 | − | 0.142865i | −0.0965306 | − | 0.00889436i | ||||
\(259\) | 3.46410i | 0.215249i | ||||||||
\(260\) | 2.44949 | − | 4.24264i | 0.151911 | − | 0.263117i | ||||
\(261\) | −2.44949 | − | 6.92820i | −0.151620 | − | 0.428845i | ||||
\(262\) | 19.0732 | + | 11.0119i | 1.17835 | + | 0.680319i | ||||
\(263\) | 10.2247 | − | 5.90326i | 0.630485 | − | 0.364011i | −0.150455 | − | 0.988617i | \(-0.548074\pi\) |
0.780940 | + | 0.624606i | \(0.214741\pi\) | |||||||
\(264\) | 0.500000 | − | 0.230351i | 0.0307729 | − | 0.0141771i | ||||
\(265\) | 1.55708i | 0.0956506i | ||||||||
\(266\) | −4.44949 | − | 18.8776i | −0.272816 | − | 1.15746i | ||||
\(267\) | −29.1464 | − | 2.68556i | −1.78373 | − | 0.164354i | ||||
\(268\) | 5.17423 | − | 2.98735i | 0.316067 | − | 0.182481i | ||||
\(269\) | −12.2474 | − | 21.2132i | −0.746740 | − | 1.29339i | −0.949377 | − | 0.314138i | \(-0.898285\pi\) |
0.202637 | − | 0.979254i | \(-0.435049\pi\) | |||||||
\(270\) | 5.12372 | + | 5.26758i | 0.311820 | + | 0.320575i | ||||
\(271\) | −12.0227 | − | 20.8239i | −0.730327 | − | 1.26496i | −0.956743 | − | 0.290933i | \(-0.906034\pi\) |
0.226416 | − | 0.974031i | \(-0.427299\pi\) | |||||||
\(272\) | 5.44949 | + | 3.14626i | 0.330424 | + | 0.190770i | ||||
\(273\) | −2.44949 | + | 26.5843i | −0.148250 | + | 1.60896i | ||||
\(274\) | − | 7.38891i | − | 0.446380i | ||||||
\(275\) | 0.825765 | + | 0.476756i | 0.0497955 | + | 0.0287495i | ||||
\(276\) | 10.0000 | + | 7.07107i | 0.601929 | + | 0.425628i | ||||
\(277\) | −4.24745 | −0.255204 | −0.127602 | − | 0.991825i | \(-0.540728\pi\) | ||||
−0.127602 | + | 0.991825i | \(0.540728\pi\) | |||||||
\(278\) | −0.348469 | −0.0208998 | ||||||||
\(279\) | 9.67423 | + | 8.27098i | 0.579181 | + | 0.495171i | ||||
\(280\) | −5.44949 | + | 3.14626i | −0.325669 | + | 0.188025i | ||||
\(281\) | −8.29796 | + | 14.3725i | −0.495015 | + | 0.857391i | −0.999983 | − | 0.00574696i | \(-0.998171\pi\) |
0.504969 | + | 0.863138i | \(0.331504\pi\) | |||||||
\(282\) | −10.1237 | + | 4.66402i | −0.602859 | + | 0.277738i | ||||
\(283\) | 2.27526 | + | 3.94086i | 0.135250 | + | 0.234260i | 0.925693 | − | 0.378276i | \(-0.123483\pi\) |
−0.790443 | + | 0.612536i | \(0.790150\pi\) | |||||||
\(284\) | −6.00000 | −0.356034 | ||||||||
\(285\) | 6.57321 | + | 8.41385i | 0.389364 | + | 0.498393i | ||||
\(286\) | −1.10102 | −0.0651047 | ||||||||
\(287\) | −6.67423 | − | 11.5601i | −0.393968 | − | 0.682372i | ||||
\(288\) | 1.00000 | + | 2.82843i | 0.0589256 | + | 0.166667i | ||||
\(289\) | 11.2980 | − | 19.5686i | 0.664586 | − | 1.15110i | ||||
\(290\) | −3.00000 | + | 1.73205i | −0.176166 | + | 0.101710i | ||||
\(291\) | 19.3485 | + | 13.6814i | 1.13423 | + | 0.802020i | ||||
\(292\) | −10.7980 | −0.631903 | ||||||||
\(293\) | −4.65153 | −0.271745 | −0.135873 | − | 0.990726i | \(-0.543384\pi\) | ||||
−0.135873 | + | 0.990726i | \(0.543384\pi\) | |||||||
\(294\) | 12.7980 | − | 18.0990i | 0.746392 | − | 1.05556i | ||||
\(295\) | 8.02270 | + | 4.63191i | 0.467100 | + | 0.269680i | ||||
\(296\) | − | 0.778539i | − | 0.0452517i | ||||||
\(297\) | 0.449490 | − | 1.58919i | 0.0260820 | − | 0.0922139i | ||||
\(298\) | 4.22474 | + | 2.43916i | 0.244733 | + | 0.141297i | ||||
\(299\) | −12.2474 | − | 21.2132i | −0.708288 | − | 1.22679i | ||||
\(300\) | −3.00000 | + | 4.24264i | −0.173205 | + | 0.244949i | ||||
\(301\) | −2.00000 | − | 3.46410i | −0.115278 | − | 0.199667i | ||||
\(302\) | 15.6742 | − | 9.04952i | 0.901951 | − | 0.520742i | ||||
\(303\) | −1.57321 | + | 17.0741i | −0.0903788 | + | 0.980882i | ||||
\(304\) | 1.00000 | + | 4.24264i | 0.0573539 | + | 0.243332i | ||||
\(305\) | − | 9.12096i | − | 0.522264i | ||||||
\(306\) | 17.7980 | − | 6.29253i | 1.01744 | − | 0.359720i | ||||
\(307\) | −3.52270 | + | 2.03383i | −0.201051 | + | 0.116077i | −0.597146 | − | 0.802133i | \(-0.703699\pi\) |
0.396094 | + | 0.918210i | \(0.370365\pi\) | |||||||
\(308\) | 1.22474 | + | 0.707107i | 0.0697863 | + | 0.0402911i | ||||
\(309\) | 18.7980 | − | 8.66025i | 1.06938 | − | 0.492665i | ||||
\(310\) | 3.00000 | − | 5.19615i | 0.170389 | − | 0.295122i | ||||
\(311\) | − | 15.5563i | − | 0.882120i | −0.897478 | − | 0.441060i | \(-0.854603\pi\) | ||
0.897478 | − | 0.441060i | \(-0.145397\pi\) | |||||||
\(312\) | 0.550510 | − | 5.97469i | 0.0311665 | − | 0.338250i | ||||
\(313\) | 9.50000 | − | 16.4545i | 0.536972 | − | 0.930062i | −0.462093 | − | 0.886831i | \(-0.652902\pi\) |
0.999065 | − | 0.0432311i | \(-0.0137652\pi\) | |||||||
\(314\) | −9.34847 | + | 16.1920i | −0.527565 | + | 0.913769i | ||||
\(315\) | −3.44949 | + | 18.5597i | −0.194357 | + | 1.04572i | ||||
\(316\) | 8.48528i | 0.477334i | ||||||||
\(317\) | −3.00000 | + | 5.19615i | −0.168497 | + | 0.291845i | −0.937892 | − | 0.346929i | \(-0.887225\pi\) |
0.769395 | + | 0.638774i | \(0.220558\pi\) | |||||||
\(318\) | 0.797959 | + | 1.73205i | 0.0447473 | + | 0.0971286i | ||||
\(319\) | 0.674235 | + | 0.389270i | 0.0377499 | + | 0.0217949i | ||||
\(320\) | 1.22474 | − | 0.707107i | 0.0684653 | − | 0.0395285i | ||||
\(321\) | −3.55051 | − | 7.70674i | −0.198170 | − | 0.430148i | ||||
\(322\) | 31.4626i | 1.75334i | ||||||||
\(323\) | 26.6969 | − | 6.29253i | 1.48546 | − | 0.350126i | ||||
\(324\) | 8.39898 | + | 3.23375i | 0.466610 | + | 0.179653i | ||||
\(325\) | 9.00000 | − | 5.19615i | 0.499230 | − | 0.288231i | ||||
\(326\) | 1.82577 | + | 3.16232i | 0.101120 | + | 0.175145i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.50000 | + | 2.59808i | 0.0828236 | + | 0.143455i | ||||
\(329\) | −24.7980 | − | 14.3171i | −1.36716 | − | 0.789328i | ||||
\(330\) | −0.775255 | − | 0.0714323i | −0.0426764 | − | 0.00393222i | ||||
\(331\) | 14.8099i | 0.814027i | 0.913422 | + | 0.407013i | \(0.133430\pi\) | ||||
−0.913422 | + | 0.407013i | \(0.866570\pi\) | |||||||
\(332\) | 12.2753 | + | 7.08712i | 0.673692 | + | 0.388956i | ||||
\(333\) | −1.77526 | − | 1.51775i | −0.0972834 | − | 0.0831724i | ||||
\(334\) | 4.89898 | 0.268060 | ||||||||
\(335\) | −8.44949 | −0.461645 | ||||||||
\(336\) | −4.44949 | + | 6.29253i | −0.242740 | + | 0.343286i | ||||
\(337\) | −3.15153 | + | 1.81954i | −0.171675 | + | 0.0991165i | −0.583375 | − | 0.812203i | \(-0.698268\pi\) |
0.411701 | + | 0.911319i | \(0.364935\pi\) | |||||||
\(338\) | 0.500000 | − | 0.866025i | 0.0271964 | − | 0.0471056i | ||||
\(339\) | −0.578317 | − | 1.25529i | −0.0314099 | − | 0.0681783i | ||||
\(340\) | −4.44949 | − | 7.70674i | −0.241307 | − | 0.417957i | ||||
\(341\) | −1.34847 | −0.0730237 | ||||||||
\(342\) | 11.6237 | + | 5.99075i | 0.628539 | + | 0.323942i | ||||
\(343\) | 25.7980 | 1.39296 | ||||||||
\(344\) | 0.449490 | + | 0.778539i | 0.0242349 | + | 0.0419760i | ||||
\(345\) | −7.24745 | − | 15.7313i | −0.390190 | − | 0.846946i | ||||
\(346\) | −5.44949 | + | 9.43879i | −0.292966 | + | 0.507433i | ||||
\(347\) | 5.72474 | − | 3.30518i | 0.307320 | − | 0.177432i | −0.338406 | − | 0.941000i | \(-0.609888\pi\) |
0.645727 | + | 0.763569i | \(0.276555\pi\) | |||||||
\(348\) | −2.44949 | + | 3.46410i | −0.131306 | + | 0.185695i | ||||
\(349\) | −16.4949 | −0.882952 | −0.441476 | − | 0.897273i | \(-0.645545\pi\) | ||||
−0.441476 | + | 0.897273i | \(0.645545\pi\) | |||||||
\(350\) | −13.3485 | −0.713506 | ||||||||
\(351\) | −12.5505 | − | 12.9029i | −0.669897 | − | 0.688706i | ||||
\(352\) | −0.275255 | − | 0.158919i | −0.0146711 | − | 0.00847039i | ||||
\(353\) | − | 14.6028i | − | 0.777231i | −0.921400 | − | 0.388615i | \(-0.872954\pi\) | ||
0.921400 | − | 0.388615i | \(-0.127046\pi\) | |||||||
\(354\) | 11.2980 | + | 1.04100i | 0.600480 | + | 0.0553284i | ||||
\(355\) | 7.34847 | + | 4.24264i | 0.390016 | + | 0.225176i | ||||
\(356\) | 8.44949 | + | 14.6349i | 0.447822 | + | 0.775651i | ||||
\(357\) | 39.5959 | + | 27.9985i | 2.09564 | + | 1.48184i | ||||
\(358\) | −11.1742 | − | 19.3543i | −0.590577 | − | 1.02291i | ||||
\(359\) | −20.8207 | + | 12.0208i | −1.09887 | + | 0.634434i | −0.935925 | − | 0.352200i | \(-0.885434\pi\) |
−0.162948 | + | 0.986635i | \(0.552100\pi\) | |||||||
\(360\) | 0.775255 | − | 4.17121i | 0.0408595 | − | 0.219842i | ||||
\(361\) | 15.8485 | + | 10.4798i | 0.834130 | + | 0.551568i | ||||
\(362\) | 13.0779i | 0.687357i | ||||||||
\(363\) | −7.89898 | − | 17.1455i | −0.414589 | − | 0.899907i | ||||
\(364\) | 13.3485 | − | 7.70674i | 0.699650 | − | 0.403943i | ||||
\(365\) | 13.2247 | + | 7.63531i | 0.692215 | + | 0.399650i | ||||
\(366\) | −4.67423 | − | 10.1459i | −0.244326 | − | 0.530335i | ||||
\(367\) | 11.6742 | − | 20.2204i | 0.609390 | − | 1.05549i | −0.381951 | − | 0.924183i | \(-0.624748\pi\) |
0.991341 | − | 0.131312i | \(-0.0419190\pi\) | |||||||
\(368\) | − | 7.07107i | − | 0.368605i | ||||||
\(369\) | 8.84847 | + | 1.64456i | 0.460633 | + | 0.0856126i | ||||
\(370\) | −0.550510 | + | 0.953512i | −0.0286197 | + | 0.0495707i | ||||
\(371\) | −2.44949 | + | 4.24264i | −0.127171 | + | 0.220267i | ||||
\(372\) | 0.674235 | − | 7.31747i | 0.0349574 | − | 0.379393i | ||||
\(373\) | 25.4558i | 1.31805i | 0.752119 | + | 0.659027i | \(0.229032\pi\) | ||||
−0.752119 | + | 0.659027i | \(0.770968\pi\) | |||||||
\(374\) | −1.00000 | + | 1.73205i | −0.0517088 | + | 0.0895622i | ||||
\(375\) | 17.7980 | − | 8.19955i | 0.919083 | − | 0.423423i | ||||
\(376\) | 5.57321 | + | 3.21770i | 0.287417 | + | 0.165940i | ||||
\(377\) | 7.34847 | − | 4.24264i | 0.378465 | − | 0.218507i | ||||
\(378\) | 5.67423 | + | 22.4131i | 0.291851 | + | 1.15281i | ||||
\(379\) | − | 15.4135i | − | 0.791738i | −0.918307 | − | 0.395869i | \(-0.870444\pi\) | ||
0.918307 | − | 0.395869i | \(-0.129556\pi\) | |||||||
\(380\) | 1.77526 | − | 5.90326i | 0.0910687 | − | 0.302831i | ||||
\(381\) | −1.65153 | + | 17.9241i | −0.0846105 | + | 0.918278i | ||||
\(382\) | −16.8990 | + | 9.75663i | −0.864627 | + | 0.499193i | ||||
\(383\) | 7.77526 | + | 13.4671i | 0.397297 | + | 0.688139i | 0.993391 | − | 0.114776i | \(-0.0366150\pi\) |
−0.596094 | + | 0.802914i | \(0.703282\pi\) | |||||||
\(384\) | 1.00000 | − | 1.41421i | 0.0510310 | − | 0.0721688i | ||||
\(385\) | −1.00000 | − | 1.73205i | −0.0509647 | − | 0.0882735i | ||||
\(386\) | −7.65153 | − | 4.41761i | −0.389453 | − | 0.224851i | ||||
\(387\) | 2.65153 | + | 0.492810i | 0.134785 | + | 0.0250509i | ||||
\(388\) | − | 13.6814i | − | 0.694570i | ||||||
\(389\) | −22.8990 | − | 13.2207i | −1.16102 | − | 0.670318i | −0.209475 | − | 0.977814i | \(-0.567176\pi\) |
−0.951549 | + | 0.307496i | \(0.900509\pi\) | |||||||
\(390\) | −4.89898 | + | 6.92820i | −0.248069 | + | 0.350823i | ||||
\(391\) | −44.4949 | −2.25020 | ||||||||
\(392\) | −12.7980 | −0.646395 | ||||||||
\(393\) | −31.1464 | − | 22.0239i | −1.57113 | − | 1.11096i | ||||
\(394\) | 0.426786 | − | 0.246405i | 0.0215012 | − | 0.0124137i | ||||
\(395\) | 6.00000 | − | 10.3923i | 0.301893 | − | 0.522894i | ||||
\(396\) | −0.898979 | + | 0.317837i | −0.0451754 | + | 0.0159719i | ||||
\(397\) | −4.67423 | − | 8.09601i | −0.234593 | − | 0.406327i | 0.724561 | − | 0.689210i | \(-0.242042\pi\) |
−0.959154 | + | 0.282883i | \(0.908709\pi\) | |||||||
\(398\) | −6.89898 | −0.345815 | ||||||||
\(399\) | 4.67423 | + | 33.2661i | 0.234004 | + | 1.66539i | ||||
\(400\) | 3.00000 | 0.150000 | ||||||||
\(401\) | 6.39898 | + | 11.0834i | 0.319550 | + | 0.553476i | 0.980394 | − | 0.197047i | \(-0.0631350\pi\) |
−0.660844 | + | 0.750523i | \(0.729802\pi\) | |||||||
\(402\) | −9.39898 | + | 4.33013i | −0.468778 | + | 0.215967i | ||||
\(403\) | −7.34847 | + | 12.7279i | −0.366053 | + | 0.634023i | ||||
\(404\) | 8.57321 | − | 4.94975i | 0.426533 | − | 0.246259i | ||||
\(405\) | −8.00000 | − | 9.89949i | −0.397523 | − | 0.491910i | ||||
\(406\) | −10.8990 | −0.540907 | ||||||||
\(407\) | 0.247449 | 0.0122656 | ||||||||
\(408\) | −8.89898 | − | 6.29253i | −0.440565 | − | 0.311527i | ||||
\(409\) | 17.8485 | + | 10.3048i | 0.882550 | + | 0.509540i | 0.871498 | − | 0.490398i | \(-0.163149\pi\) |
0.0110517 | + | 0.999939i | \(0.496482\pi\) | |||||||
\(410\) | − | 4.24264i | − | 0.209529i | ||||||
\(411\) | −1.17423 | + | 12.7440i | −0.0579207 | + | 0.628614i | ||||
\(412\) | −10.3485 | − | 5.97469i | −0.509832 | − | 0.294352i | ||||
\(413\) | 14.5732 | + | 25.2415i | 0.717101 | + | 1.24206i | ||||
\(414\) | −16.1237 | − | 13.7850i | −0.792438 | − | 0.677495i | ||||
\(415\) | −10.0227 | − | 17.3598i | −0.491995 | − | 0.852161i | ||||
\(416\) | −3.00000 | + | 1.73205i | −0.147087 | + | 0.0849208i | ||||
\(417\) | 0.601021 | + | 0.0553782i | 0.0294321 | + | 0.00271188i | ||||
\(418\) | −1.34847 | + | 0.317837i | −0.0659558 | + | 0.0155459i | ||||
\(419\) | 3.74983i | 0.183191i | 0.995796 | + | 0.0915956i | \(0.0291967\pi\) | ||||
−0.995796 | + | 0.0915956i | \(0.970803\pi\) | |||||||
\(420\) | 9.89898 | − | 4.56048i | 0.483021 | − | 0.222529i | ||||
\(421\) | −26.0227 | + | 15.0242i | −1.26827 | + | 0.732235i | −0.974660 | − | 0.223690i | \(-0.928190\pi\) |
−0.293609 | + | 0.955926i | \(0.594856\pi\) | |||||||
\(422\) | 13.3485 | + | 7.70674i | 0.649793 | + | 0.375158i | ||||
\(423\) | 18.2020 | − | 6.43539i | 0.885014 | − | 0.312900i | ||||
\(424\) | 0.550510 | − | 0.953512i | 0.0267351 | − | 0.0463066i | ||||
\(425\) | − | 18.8776i | − | 0.915697i | ||||||
\(426\) | 10.3485 | + | 0.953512i | 0.501385 | + | 0.0461978i | ||||
\(427\) | 14.3485 | − | 24.8523i | 0.694371 | − | 1.20269i | ||||
\(428\) | −2.44949 | + | 4.24264i | −0.118401 | + | 0.205076i | ||||
\(429\) | 1.89898 | + | 0.174973i | 0.0916836 | + | 0.00844776i | ||||
\(430\) | − | 1.27135i | − | 0.0613099i | ||||||
\(431\) | 16.3485 | − | 28.3164i | 0.787478 | − | 1.36395i | −0.140029 | − | 0.990147i | \(-0.544720\pi\) |
0.927507 | − | 0.373805i | \(-0.121947\pi\) | |||||||
\(432\) | −1.27526 | − | 5.03723i | −0.0613557 | − | 0.242354i | ||||
\(433\) | 11.6969 | + | 6.75323i | 0.562119 | + | 0.324540i | 0.753996 | − | 0.656880i | \(-0.228124\pi\) |
−0.191877 | + | 0.981419i | \(0.561457\pi\) | |||||||
\(434\) | 16.3485 | − | 9.43879i | 0.784752 | − | 0.453077i | ||||
\(435\) | 5.44949 | − | 2.51059i | 0.261283 | − | 0.120374i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −21.1237 | − | 22.4452i | −1.01048 | − | 1.07370i | ||||
\(438\) | 18.6237 | + | 1.71600i | 0.889876 | + | 0.0819935i | ||||
\(439\) | −2.32577 | + | 1.34278i | −0.111003 | + | 0.0640875i | −0.554474 | − | 0.832201i | \(-0.687080\pi\) |
0.443471 | + | 0.896289i | \(0.353747\pi\) | |||||||
\(440\) | 0.224745 | + | 0.389270i | 0.0107143 | + | 0.0185577i | ||||
\(441\) | −24.9495 | + | 29.1824i | −1.18807 | + | 1.38964i | ||||
\(442\) | 10.8990 | + | 18.8776i | 0.518412 | + | 0.897915i | ||||
\(443\) | 25.3207 | + | 14.6189i | 1.20302 | + | 0.694564i | 0.961226 | − | 0.275763i | \(-0.0889304\pi\) |
0.241795 | + | 0.970327i | \(0.422264\pi\) | |||||||
\(444\) | −0.123724 | + | 1.34278i | −0.00587170 | + | 0.0637256i | ||||
\(445\) | − | 23.8988i | − | 1.13291i | ||||||
\(446\) | −8.32577 | − | 4.80688i | −0.394236 | − | 0.227613i | ||||
\(447\) | −6.89898 | − | 4.87832i | −0.326311 | − | 0.230736i | ||||
\(448\) | 4.44949 | 0.210219 | ||||||||
\(449\) | 11.2020 | 0.528657 | 0.264329 | − | 0.964433i | \(-0.414850\pi\) | ||||
0.264329 | + | 0.964433i | \(0.414850\pi\) | |||||||
\(450\) | 5.84847 | − | 6.84072i | 0.275699 | − | 0.322474i | ||||
\(451\) | −0.825765 | + | 0.476756i | −0.0388838 | + | 0.0224496i | ||||
\(452\) | −0.398979 | + | 0.691053i | −0.0187664 | + | 0.0325044i | ||||
\(453\) | −28.4722 | + | 13.1172i | −1.33774 | + | 0.616299i | ||||
\(454\) | 2.72474 | + | 4.71940i | 0.127879 | + | 0.221492i | ||||
\(455\) | −21.7980 | −1.02190 | ||||||||
\(456\) | −1.05051 | − | 7.47639i | −0.0491947 | − | 0.350114i | ||||
\(457\) | −13.0000 | −0.608114 | −0.304057 | − | 0.952654i | \(-0.598341\pi\) | ||||
−0.304057 | + | 0.952654i | \(0.598341\pi\) | |||||||
\(458\) | −4.44949 | − | 7.70674i | −0.207911 | − | 0.360112i | ||||
\(459\) | −31.6969 | + | 8.02458i | −1.47949 | + | 0.374555i | ||||
\(460\) | −5.00000 | + | 8.66025i | −0.233126 | + | 0.403786i | ||||
\(461\) | −8.75255 | + | 5.05329i | −0.407647 | + | 0.235355i | −0.689778 | − | 0.724021i | \(-0.742292\pi\) |
0.282131 | + | 0.959376i | \(0.408959\pi\) | |||||||
\(462\) | −2.00000 | − | 1.41421i | −0.0930484 | − | 0.0657952i | ||||
\(463\) | −0.202041 | −0.00938964 | −0.00469482 | − | 0.999989i | \(-0.501494\pi\) | ||||
−0.00469482 | + | 0.999989i | \(0.501494\pi\) | |||||||
\(464\) | 2.44949 | 0.113715 | ||||||||
\(465\) | −6.00000 | + | 8.48528i | −0.278243 | + | 0.393496i | ||||
\(466\) | −5.60102 | − | 3.23375i | −0.259462 | − | 0.149801i | ||||
\(467\) | 32.4162i | 1.50004i | 0.661415 | + | 0.750020i | \(0.269956\pi\) | ||||
−0.661415 | + | 0.750020i | \(0.730044\pi\) | |||||||
\(468\) | −1.89898 | + | 10.2173i | −0.0877804 | + | 0.472296i | ||||
\(469\) | −23.0227 | − | 13.2922i | −1.06309 | − | 0.613775i | ||||
\(470\) | −4.55051 | − | 7.88171i | −0.209899 | − | 0.363556i | ||||
\(471\) | 18.6969 | − | 26.4415i | 0.861509 | − | 1.21836i | ||||
\(472\) | −3.27526 | − | 5.67291i | −0.150756 | − | 0.261117i | ||||
\(473\) | −0.247449 | + | 0.142865i | −0.0113777 | + | 0.00656892i | ||||
\(474\) | 1.34847 | − | 14.6349i | 0.0619372 | − | 0.672205i | ||||
\(475\) | 9.52270 | − | 8.96204i | 0.436932 | − | 0.411206i | ||||
\(476\) | − | 27.9985i | − | 1.28331i | ||||||
\(477\) | −1.10102 | − | 3.11416i | −0.0504123 | − | 0.142587i | ||||
\(478\) | −6.24745 | + | 3.60697i | −0.285752 | + | 0.164979i | ||||
\(479\) | 35.1464 | + | 20.2918i | 1.60588 | + | 0.927156i | 0.990278 | + | 0.139099i | \(0.0444208\pi\) |
0.615603 | + | 0.788057i | \(0.288913\pi\) | |||||||
\(480\) | −2.22474 | + | 1.02494i | −0.101545 | + | 0.0467821i | ||||
\(481\) | 1.34847 | − | 2.33562i | 0.0614849 | − | 0.106495i | ||||
\(482\) | 10.2173i | 0.465387i | ||||||||
\(483\) | 5.00000 | − | 54.2650i | 0.227508 | − | 2.46914i | ||||
\(484\) | −5.44949 | + | 9.43879i | −0.247704 | + | 0.429036i | ||||
\(485\) | −9.67423 | + | 16.7563i | −0.439284 | + | 0.760863i | ||||
\(486\) | −13.9722 | − | 6.91215i | −0.633792 | − | 0.313541i | ||||
\(487\) | 16.5420i | 0.749588i | 0.927108 | + | 0.374794i | \(0.122287\pi\) | ||||
−0.927108 | + | 0.374794i | \(0.877713\pi\) | |||||||
\(488\) | −3.22474 | + | 5.58542i | −0.145977 | + | 0.252840i | ||||
\(489\) | −2.64643 | − | 5.74434i | −0.119676 | − | 0.259768i | ||||
\(490\) | 15.6742 | + | 9.04952i | 0.708090 | + | 0.408816i | ||||
\(491\) | −4.10102 | + | 2.36773i | −0.185076 | + | 0.106854i | −0.589676 | − | 0.807640i | \(-0.700744\pi\) |
0.404599 | + | 0.914494i | \(0.367411\pi\) | |||||||
\(492\) | −2.17423 | − | 4.71940i | −0.0980221 | − | 0.212767i | ||||
\(493\) | − | 15.4135i | − | 0.694188i | ||||||
\(494\) | −4.34847 | + | 14.4600i | −0.195647 | + | 0.650585i | ||||
\(495\) | 1.32577 | + | 0.246405i | 0.0595887 | + | 0.0110751i | ||||
\(496\) | −3.67423 | + | 2.12132i | −0.164978 | + | 0.0952501i | ||||
\(497\) | 13.3485 | + | 23.1202i | 0.598761 | + | 1.03708i | ||||
\(498\) | −20.0454 | − | 14.1742i | −0.898256 | − | 0.635163i | ||||
\(499\) | −1.27526 | − | 2.20881i | −0.0570883 | − | 0.0988798i | 0.836069 | − | 0.548624i | \(-0.184848\pi\) |
−0.893157 | + | 0.449745i | \(0.851515\pi\) | |||||||
\(500\) | −9.79796 | − | 5.65685i | −0.438178 | − | 0.252982i | ||||
\(501\) | −8.44949 | − | 0.778539i | −0.377495 | − | 0.0347826i | ||||
\(502\) | − | 6.61037i | − | 0.295035i | ||||||
\(503\) | 13.4722 | + | 7.77817i | 0.600695 | + | 0.346812i | 0.769315 | − | 0.638870i | \(-0.220598\pi\) |
−0.168620 | + | 0.985681i | \(0.553931\pi\) | |||||||
\(504\) | 8.67423 | − | 10.1459i | 0.386381 | − | 0.451934i | ||||
\(505\) | −14.0000 | −0.622992 | ||||||||
\(506\) | 2.24745 | 0.0999113 | ||||||||
\(507\) | −1.00000 | + | 1.41421i | −0.0444116 | + | 0.0628074i | ||||
\(508\) | 9.00000 | − | 5.19615i | 0.399310 | − | 0.230542i | ||||
\(509\) | −20.6969 | + | 35.8481i | −0.917376 | + | 1.58894i | −0.113990 | + | 0.993482i | \(0.536363\pi\) |
−0.803385 | + | 0.595459i | \(0.796970\pi\) | |||||||
\(510\) | 6.44949 | + | 13.9993i | 0.285588 | + | 0.619898i | ||||
\(511\) | 24.0227 | + | 41.6085i | 1.06270 | + | 1.84065i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −19.0959 | − | 12.1797i | −0.843105 | − | 0.537748i | ||||
\(514\) | −15.0000 | −0.661622 | ||||||||
\(515\) | 8.44949 | + | 14.6349i | 0.372329 | + | 0.644893i | ||||
\(516\) | −0.651531 | − | 1.41421i | −0.0286820 | − | 0.0622573i | ||||
\(517\) | −1.02270 | + | 1.77138i | −0.0449785 | + | 0.0779050i | ||||
\(518\) | −3.00000 | + | 1.73205i | −0.131812 | + | 0.0761019i | ||||
\(519\) | 10.8990 | − | 15.4135i | 0.478412 | − | 0.676577i | ||||
\(520\) | 4.89898 | 0.214834 | ||||||||
\(521\) | −16.1010 | −0.705399 | −0.352699 | − | 0.935737i | \(-0.614736\pi\) | ||||
−0.352699 | + | 0.935737i | \(0.614736\pi\) | |||||||
\(522\) | 4.77526 | − | 5.58542i | 0.209007 | − | 0.244467i | ||||
\(523\) | 23.6969 | + | 13.6814i | 1.03619 | + | 0.598247i | 0.918753 | − | 0.394832i | \(-0.129197\pi\) |
0.117442 | + | 0.993080i | \(0.462531\pi\) | |||||||
\(524\) | 22.0239i | 0.962116i | ||||||||
\(525\) | 23.0227 | + | 2.12132i | 1.00479 | + | 0.0925820i | ||||
\(526\) | 10.2247 | + | 5.90326i | 0.445820 | + | 0.257394i | ||||
\(527\) | 13.3485 | + | 23.1202i | 0.581468 | + | 1.00713i | ||||
\(528\) | 0.449490 | + | 0.317837i | 0.0195615 | + | 0.0138321i | ||||
\(529\) | 13.5000 | + | 23.3827i | 0.586957 | + | 1.01664i | ||||
\(530\) | −1.34847 | + | 0.778539i | −0.0585738 | + | 0.0338176i | ||||
\(531\) | −19.3207 | − | 3.59091i | −0.838445 | − | 0.155832i | ||||
\(532\) | 14.1237 | − | 13.2922i | 0.612341 | − | 0.576288i | ||||
\(533\) | 10.3923i | 0.450141i | ||||||||
\(534\) | −12.2474 | − | 26.5843i | −0.529999 | − | 1.15042i | ||||
\(535\) | 6.00000 | − | 3.46410i | 0.259403 | − | 0.149766i | ||||
\(536\) | 5.17423 | + | 2.98735i | 0.223493 | + | 0.129034i | ||||
\(537\) | 16.1969 | + | 35.1571i | 0.698949 | + | 1.51714i | ||||
\(538\) | 12.2474 | − | 21.2132i | 0.528025 | − | 0.914566i | ||||
\(539\) | − | 4.06767i | − | 0.175207i | ||||||
\(540\) | −2.00000 | + | 7.07107i | −0.0860663 | + | 0.304290i | ||||
\(541\) | 9.34847 | − | 16.1920i | 0.401922 | − | 0.696149i | −0.592036 | − | 0.805912i | \(-0.701676\pi\) |
0.993958 | + | 0.109762i | \(0.0350089\pi\) | |||||||
\(542\) | 12.0227 | − | 20.8239i | 0.516419 | − | 0.894465i | ||||
\(543\) | 2.07832 | − | 22.5560i | 0.0891891 | − | 0.967970i | ||||
\(544\) | 6.29253i | 0.269790i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −24.2474 | + | 11.1708i | −1.03770 | + | 0.478068i | ||||
\(547\) | 26.3939 | + | 15.2385i | 1.12852 | + | 0.651552i | 0.943562 | − | 0.331195i | \(-0.107452\pi\) |
0.184958 | + | 0.982746i | \(0.440785\pi\) | |||||||
\(548\) | 6.39898 | − | 3.69445i | 0.273351 | − | 0.157819i | ||||
\(549\) | 6.44949 | + | 18.2419i | 0.275258 | + | 0.778546i | ||||
\(550\) | 0.953512i | 0.0406579i | ||||||||
\(551\) | 7.77526 | − | 7.31747i | 0.331237 | − | 0.311735i | ||||
\(552\) | −1.12372 | + | 12.1958i | −0.0478289 | + | 0.519087i | ||||
\(553\) | 32.6969 | − | 18.8776i | 1.39042 | − | 0.802757i | ||||
\(554\) | −2.12372 | − | 3.67840i | −0.0902284 | − | 0.156280i | ||||
\(555\) | 1.10102 | − | 1.55708i | 0.0467357 | − | 0.0660943i | ||||
\(556\) | −0.174235 | − | 0.301783i | −0.00738919 | − | 0.0127985i | ||||
\(557\) | −24.2474 | − | 13.9993i | −1.02740 | − | 0.593168i | −0.111159 | − | 0.993803i | \(-0.535456\pi\) |
−0.916238 | + | 0.400634i | \(0.868790\pi\) | |||||||
\(558\) | −2.32577 | + | 12.5136i | −0.0984575 | + | 0.529744i | ||||
\(559\) | 3.11416i | 0.131715i | ||||||||
\(560\) | −5.44949 | − | 3.14626i | −0.230283 | − | 0.132954i | ||||
\(561\) | 2.00000 | − | 2.82843i | 0.0844401 | − | 0.119416i | ||||
\(562\) | −16.5959 | −0.700057 | ||||||||
\(563\) | −22.8434 | −0.962733 | −0.481367 | − | 0.876519i | \(-0.659859\pi\) | ||||
−0.481367 | + | 0.876519i | \(0.659859\pi\) | |||||||
\(564\) | −9.10102 | − | 6.43539i | −0.383222 | − | 0.270979i | ||||
\(565\) | 0.977296 | − | 0.564242i | 0.0411152 | − | 0.0237378i | ||||
\(566\) | −2.27526 | + | 3.94086i | −0.0956361 | + | 0.165647i | ||||
\(567\) | −6.22474 | − | 39.5587i | −0.261415 | − | 1.66131i | ||||
\(568\) | −3.00000 | − | 5.19615i | −0.125877 | − | 0.218026i | ||||
\(569\) | 34.2929 | 1.43763 | 0.718816 | − | 0.695201i | \(-0.244685\pi\) | ||||
0.718816 | + | 0.695201i | \(0.244685\pi\) | |||||||
\(570\) | −4.00000 | + | 9.89949i | −0.167542 | + | 0.414644i | ||||
\(571\) | −11.0454 | −0.462236 | −0.231118 | − | 0.972926i | \(-0.574238\pi\) | ||||
−0.231118 | + | 0.972926i | \(0.574238\pi\) | |||||||
\(572\) | −0.550510 | − | 0.953512i | −0.0230180 | − | 0.0398683i | ||||
\(573\) | 30.6969 | − | 14.1421i | 1.28238 | − | 0.590796i | ||||
\(574\) | 6.67423 | − | 11.5601i | 0.278577 | − | 0.482510i | ||||
\(575\) | −18.3712 | + | 10.6066i | −0.766131 | + | 0.442326i | ||||
\(576\) | −1.94949 | + | 2.28024i | −0.0812287 | + | 0.0950100i | ||||
\(577\) | −20.5959 | −0.857419 | −0.428710 | − | 0.903442i | \(-0.641032\pi\) | ||||
−0.428710 | + | 0.903442i | \(0.641032\pi\) | |||||||
\(578\) | 22.5959 | 0.939866 | ||||||||
\(579\) | 12.4949 | + | 8.83523i | 0.519270 | + | 0.367179i | ||||
\(580\) | −3.00000 | − | 1.73205i | −0.124568 | − | 0.0719195i | ||||
\(581\) | − | 63.0682i | − | 2.61651i | ||||||
\(582\) | −2.17423 | + | 23.5970i | −0.0901249 | + | 0.978126i | ||||
\(583\) | 0.303062 | + | 0.174973i | 0.0125515 | + | 0.00724663i | ||||
\(584\) | −5.39898 | − | 9.35131i | −0.223411 | − | 0.386960i | ||||
\(585\) | 9.55051 | − | 11.1708i | 0.394865 | − | 0.461858i | ||||
\(586\) | −2.32577 | − | 4.02834i | −0.0960765 | − | 0.166409i | ||||
\(587\) | −4.10102 | + | 2.36773i | −0.169267 | + | 0.0977265i | −0.582240 | − | 0.813017i | \(-0.697824\pi\) |
0.412973 | + | 0.910743i | \(0.364490\pi\) | |||||||
\(588\) | 22.0732 | + | 2.03383i | 0.910284 | + | 0.0838739i | ||||
\(589\) | −5.32577 | + | 17.7098i | −0.219444 | + | 0.729719i | ||||
\(590\) | 9.26382i | 0.381385i | ||||||||
\(591\) | −0.775255 | + | 0.357161i | −0.0318897 | + | 0.0146917i | ||||
\(592\) | 0.674235 | − | 0.389270i | 0.0277109 | − | 0.0159989i | ||||
\(593\) | −24.0959 | − | 13.9118i | −0.989501 | − | 0.571289i | −0.0843757 | − | 0.996434i | \(-0.526890\pi\) |
−0.905125 | + | 0.425145i | \(0.860223\pi\) | |||||||
\(594\) | 1.60102 | − | 0.405324i | 0.0656907 | − | 0.0166306i | ||||
\(595\) | −19.7980 | + | 34.2911i | −0.811637 | + | 1.40580i | ||||
\(596\) | 4.87832i | 0.199824i | ||||||||
\(597\) | 11.8990 | + | 1.09638i | 0.486993 | + | 0.0448717i | ||||
\(598\) | 12.2474 | − | 21.2132i | 0.500835 | − | 0.867472i | ||||
\(599\) | 14.5732 | − | 25.2415i | 0.595445 | − | 1.03134i | −0.398038 | − | 0.917369i | \(-0.630309\pi\) |
0.993484 | − | 0.113973i | \(-0.0363577\pi\) | |||||||
\(600\) | −5.17423 | − | 0.476756i | −0.211237 | − | 0.0194635i | ||||
\(601\) | − | 31.0019i | − | 1.26460i | −0.774725 | − | 0.632298i | \(-0.782112\pi\) | ||
0.774725 | − | 0.632298i | \(-0.217888\pi\) | |||||||
\(602\) | 2.00000 | − | 3.46410i | 0.0815139 | − | 0.141186i | ||||
\(603\) | 16.8990 | − | 5.97469i | 0.688180 | − | 0.243308i | ||||
\(604\) | 15.6742 | + | 9.04952i | 0.637776 | + | 0.368220i | ||||
\(605\) | 13.3485 | − | 7.70674i | 0.542692 | − | 0.313324i | ||||
\(606\) | −15.5732 | + | 7.17461i | −0.632619 | + | 0.291449i | ||||
\(607\) | 36.9766i | 1.50084i | 0.660964 | + | 0.750418i | \(0.270148\pi\) | ||||
−0.660964 | + | 0.750418i | \(0.729852\pi\) | |||||||
\(608\) | −3.17423 | + | 2.98735i | −0.128732 | + | 0.121153i | ||||
\(609\) | 18.7980 | + | 1.73205i | 0.761732 | + | 0.0701862i | ||||
\(610\) | 7.89898 | − | 4.56048i | 0.319820 | − | 0.184648i | ||||
\(611\) | 11.1464 | + | 19.3062i | 0.450936 | + | 0.781044i | ||||
\(612\) | 14.3485 | + | 12.2672i | 0.580002 | + | 0.495873i | ||||
\(613\) | −14.1010 | − | 24.4237i | −0.569535 | − | 0.986463i | −0.996612 | − | 0.0822481i | \(-0.973790\pi\) |
0.427077 | − | 0.904215i | \(-0.359543\pi\) | |||||||
\(614\) | −3.52270 | − | 2.03383i | −0.142165 | − | 0.0820789i | ||||
\(615\) | −0.674235 | + | 7.31747i | −0.0271878 | + | 0.295069i | ||||
\(616\) | 1.41421i | 0.0569803i | ||||||||
\(617\) | 12.9495 | + | 7.47639i | 0.521327 | + | 0.300988i | 0.737477 | − | 0.675372i | \(-0.236017\pi\) |
−0.216151 | + | 0.976360i | \(0.569350\pi\) | |||||||
\(618\) | 16.8990 | + | 11.9494i | 0.679777 | + | 0.480675i | ||||
\(619\) | −1.30306 | −0.0523745 | −0.0261872 | − | 0.999657i | \(-0.508337\pi\) | ||||
−0.0261872 | + | 0.999657i | \(0.508337\pi\) | |||||||
\(620\) | 6.00000 | 0.240966 | ||||||||
\(621\) | 25.6186 | + | 26.3379i | 1.02804 | + | 1.05690i | ||||
\(622\) | 13.4722 | − | 7.77817i | 0.540186 | − | 0.311876i | ||||
\(623\) | 37.5959 | − | 65.1180i | 1.50625 | − | 2.60890i | ||||
\(624\) | 5.44949 | − | 2.51059i | 0.218154 | − | 0.100504i | ||||
\(625\) | 0.500000 | + | 0.866025i | 0.0200000 | + | 0.0346410i | ||||
\(626\) | 19.0000 | 0.759393 | ||||||||
\(627\) | 2.37628 | − | 0.333891i | 0.0948993 | − | 0.0133343i | ||||
\(628\) | −18.6969 | −0.746089 | ||||||||
\(629\) | −2.44949 | − | 4.24264i | −0.0976676 | − | 0.169165i | ||||
\(630\) | −17.7980 | + | 6.29253i | −0.709088 | + | 0.250700i | ||||
\(631\) | 4.87628 | − | 8.44596i | 0.194121 | − | 0.336228i | −0.752491 | − | 0.658603i | \(-0.771148\pi\) |
0.946612 | + | 0.322375i | \(0.104481\pi\) | |||||||
\(632\) | −7.34847 | + | 4.24264i | −0.292306 | + | 0.168763i | ||||
\(633\) | −21.7980 | − | 15.4135i | −0.866391 | − | 0.612631i | ||||
\(634\) | −6.00000 | −0.238290 | ||||||||
\(635\) | −14.6969 | −0.583230 | ||||||||
\(636\) | −1.10102 | + | 1.55708i | −0.0436583 | + | 0.0617422i | ||||
\(637\) | −38.3939 | − | 22.1667i | −1.52122 | − | 0.878277i | ||||
\(638\) | 0.778539i | 0.0308227i | ||||||||
\(639\) | −17.6969 | − | 3.28913i | −0.700080 | − | 0.130116i | ||||
\(640\) | 1.22474 | + | 0.707107i | 0.0484123 | + | 0.0279508i | ||||
\(641\) | 16.1969 | + | 28.0539i | 0.639741 | + | 1.10806i | 0.985490 | + | 0.169736i | \(0.0542916\pi\) |
−0.345749 | + | 0.938327i | \(0.612375\pi\) | |||||||
\(642\) | 4.89898 | − | 6.92820i | 0.193347 | − | 0.273434i | ||||
\(643\) | 12.0732 | + | 20.9114i | 0.476121 | + | 0.824666i | 0.999626 | − | 0.0273569i | \(-0.00870906\pi\) |
−0.523505 | + | 0.852023i | \(0.675376\pi\) | |||||||
\(644\) | −27.2474 | + | 15.7313i | −1.07370 | + | 0.619901i | ||||
\(645\) | −0.202041 | + | 2.19275i | −0.00795536 | + | 0.0863396i | ||||
\(646\) | 18.7980 | + | 19.9740i | 0.739596 | + | 0.785865i | ||||
\(647\) | − | 7.84961i | − | 0.308600i | −0.988024 | − | 0.154300i | \(-0.950688\pi\) | ||
0.988024 | − | 0.154300i | \(-0.0493122\pi\) | |||||||
\(648\) | 1.39898 | + | 8.89060i | 0.0549571 | + | 0.349256i | ||||
\(649\) | 1.80306 | − | 1.04100i | 0.0707764 | − | 0.0408627i | ||||
\(650\) | 9.00000 | + | 5.19615i | 0.353009 | + | 0.203810i | ||||
\(651\) | −29.6969 | + | 13.6814i | −1.16391 | + | 0.536218i | ||||
\(652\) | −1.82577 | + | 3.16232i | −0.0715025 | + | 0.123846i | ||||
\(653\) | 19.5133i | 0.763613i | 0.924242 | + | 0.381806i | \(0.124698\pi\) | ||||
−0.924242 | + | 0.381806i | \(0.875302\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.5732 | − | 26.9736i | 0.608496 | − | 1.05395i | ||||
\(656\) | −1.50000 | + | 2.59808i | −0.0585652 | + | 0.101438i | ||||
\(657\) | −31.8485 | − | 5.91931i | −1.24253 | − | 0.230934i | ||||
\(658\) | − | 28.6342i | − | 1.11628i | ||||||
\(659\) | −12.0000 | + | 20.7846i | −0.467454 | + | 0.809653i | −0.999309 | − | 0.0371821i | \(-0.988162\pi\) |
0.531855 | + | 0.846836i | \(0.321495\pi\) | |||||||
\(660\) | −0.325765 | − | 0.707107i | −0.0126804 | − | 0.0275241i | ||||
\(661\) | −25.7196 | − | 14.8492i | −1.00038 | − | 0.577569i | −0.0920180 | − | 0.995757i | \(-0.529332\pi\) |
−0.908360 | + | 0.418189i | \(0.862665\pi\) | |||||||
\(662\) | −12.8258 | + | 7.40496i | −0.498488 | + | 0.287802i | ||||
\(663\) | −15.7980 | − | 34.2911i | −0.613542 | − | 1.33175i | ||||
\(664\) | 14.1742i | 0.550067i | ||||||||
\(665\) | −26.6969 | + | 6.29253i | −1.03526 | + | 0.244014i | ||||
\(666\) | 0.426786 | − | 2.29629i | 0.0165376 | − | 0.0889795i | ||||
\(667\) | −15.0000 | + | 8.66025i | −0.580802 | + | 0.335326i | ||||
\(668\) | 2.44949 | + | 4.24264i | 0.0947736 | + | 0.164153i | ||||
\(669\) | 13.5959 | + | 9.61377i | 0.525649 | + | 0.371690i | ||||
\(670\) | −4.22474 | − | 7.31747i | −0.163216 | − | 0.282699i | ||||
\(671\) | −1.77526 | − | 1.02494i | −0.0685330 | − | 0.0395675i | ||||
\(672\) | −7.67423 | − | 0.707107i | −0.296040 | − | 0.0272772i | ||||
\(673\) | 3.46410i | 0.133531i | 0.997769 | + | 0.0667657i | \(0.0212680\pi\) | ||||
−0.997769 | + | 0.0667657i | \(0.978732\pi\) | |||||||
\(674\) | −3.15153 | − | 1.81954i | −0.121392 | − | 0.0700860i | ||||
\(675\) | −11.1742 | + | 10.8691i | −0.430096 | + | 0.418350i | ||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −3.30306 | −0.126947 | −0.0634735 | − | 0.997984i | \(-0.520218\pi\) | ||||
−0.0634735 | + | 0.997984i | \(0.520218\pi\) | |||||||
\(678\) | 0.797959 | − | 1.12848i | 0.0306454 | − | 0.0433392i | ||||
\(679\) | −52.7196 | + | 30.4377i | −2.02319 | + | 1.16809i | ||||
\(680\) | 4.44949 | − | 7.70674i | 0.170630 | − | 0.295540i | ||||
\(681\) | −3.94949 | − | 8.57277i | −0.151345 | − | 0.328509i | ||||
\(682\) | −0.674235 | − | 1.16781i | −0.0258178 | − | 0.0447177i | ||||
\(683\) | −41.3939 | −1.58389 | −0.791946 | − | 0.610591i | \(-0.790932\pi\) | ||||
−0.791946 | + | 0.610591i | \(0.790932\pi\) | |||||||
\(684\) | 0.623724 | + | 13.0618i | 0.0238487 | + | 0.499431i | ||||
\(685\) | −10.4495 | −0.399254 | ||||||||
\(686\) | 12.8990 | + | 22.3417i | 0.492485 | + | 0.853010i | ||||
\(687\) | 6.44949 | + | 13.9993i | 0.246063 | + | 0.534106i | ||||
\(688\) | −0.449490 | + | 0.778539i | −0.0171366 | + | 0.0296815i | ||||
\(689\) | 3.30306 | − | 1.90702i | 0.125837 | − | 0.0726518i | ||||
\(690\) | 10.0000 | − | 14.1421i | 0.380693 | − | 0.538382i | ||||
\(691\) | −40.0000 | −1.52167 | −0.760836 | − | 0.648944i | \(-0.775211\pi\) | ||||
−0.760836 | + | 0.648944i | \(0.775211\pi\) | |||||||
\(692\) | −10.8990 | −0.414317 | ||||||||
\(693\) | 3.22474 | + | 2.75699i | 0.122498 | + | 0.104730i | ||||
\(694\) | 5.72474 | + | 3.30518i | 0.217308 | + | 0.125463i | ||||
\(695\) | 0.492810i | 0.0186933i | ||||||||
\(696\) | −4.22474 | − | 0.389270i | −0.160139 | − | 0.0147552i | ||||
\(697\) | 16.3485 | + | 9.43879i | 0.619242 | + | 0.357520i | ||||
\(698\) | −8.24745 | − | 14.2850i | −0.312171 | − | 0.540695i | ||||
\(699\) | 9.14643 | + | 6.46750i | 0.345950 | + | 0.244623i | ||||
\(700\) | −6.67423 | − | 11.5601i | −0.252262 | − | 0.436931i | ||||
\(701\) | 8.57321 | − | 4.94975i | 0.323806 | − | 0.186949i | −0.329282 | − | 0.944232i | \(-0.606807\pi\) |
0.653088 | + | 0.757282i | \(0.273473\pi\) | |||||||
\(702\) | 4.89898 | − | 17.3205i | 0.184900 | − | 0.653720i | ||||
\(703\) | 0.977296 | − | 3.24980i | 0.0368594 | − | 0.122569i | ||||
\(704\) | − | 0.317837i | − | 0.0119789i | ||||||
\(705\) | 6.59592 | + | 14.3171i | 0.248417 | + | 0.539213i | ||||
\(706\) | 12.6464 | − | 7.30142i | 0.475955 | − | 0.274793i | ||||
\(707\) | −38.1464 | − | 22.0239i | −1.43464 | − | 0.828292i | ||||
\(708\) | 4.74745 | + | 10.3048i | 0.178420 | + | 0.387279i | ||||
\(709\) | 1.32577 | − | 2.29629i | 0.0497902 | − | 0.0862391i | −0.840056 | − | 0.542499i | \(-0.817478\pi\) |
0.889846 | + | 0.456260i | \(0.150811\pi\) | |||||||
\(710\) | 8.48528i | 0.318447i | ||||||||
\(711\) | −4.65153 | + | 25.0273i | −0.174446 | + | 0.938595i | ||||
\(712\) | −8.44949 | + | 14.6349i | −0.316658 | + | 0.548468i | ||||
\(713\) | 15.0000 | − | 25.9808i | 0.561754 | − | 0.972987i | ||||
\(714\) | −4.44949 | + | 48.2903i | −0.166518 | + | 1.80722i | ||||
\(715\) | 1.55708i | 0.0582314i | ||||||||
\(716\) | 11.1742 | − | 19.3543i | 0.417601 | − | 0.723306i | ||||
\(717\) | 11.3485 | − | 5.22826i | 0.423816 | − | 0.195253i | ||||
\(718\) | −20.8207 | − | 12.0208i | −0.777020 | − | 0.448613i | ||||
\(719\) | −8.14643 | + | 4.70334i | −0.303811 | + | 0.175405i | −0.644153 | − | 0.764896i | \(-0.722790\pi\) |
0.340343 | + | 0.940301i | \(0.389457\pi\) | |||||||
\(720\) | 4.00000 | − | 1.41421i | 0.149071 | − | 0.0527046i | ||||
\(721\) | 53.1687i | 1.98010i | ||||||||
\(722\) | −1.15153 | + | 18.9651i | −0.0428555 | + | 0.705807i | ||||
\(723\) | 1.62372 | − | 17.6223i | 0.0603870 | − | 0.655380i | ||||
\(724\) | −11.3258 | + | 6.53893i | −0.420919 | + | 0.243018i | ||||
\(725\) | −3.67423 | − | 6.36396i | −0.136458 | − | 0.236352i | ||||
\(726\) | 10.8990 | − | 15.4135i | 0.404499 | − | 0.572048i | ||||
\(727\) | −4.00000 | − | 6.92820i | −0.148352 | − | 0.256953i | 0.782267 | − | 0.622944i | \(-0.214063\pi\) |
−0.930618 | + | 0.365991i | \(0.880730\pi\) | |||||||
\(728\) | 13.3485 | + | 7.70674i | 0.494727 | + | 0.285631i | ||||
\(729\) | 23.0000 | + | 14.1421i | 0.851852 | + | 0.523783i | ||||
\(730\) | 15.2706i | 0.565191i | ||||||||
\(731\) | 4.89898 | + | 2.82843i | 0.181195 | + | 0.104613i | ||||
\(732\) | 6.44949 | − | 9.12096i | 0.238380 | − | 0.337120i | ||||
\(733\) | 24.0454 | 0.888137 | 0.444069 | − | 0.895993i | \(-0.353535\pi\) | ||||
0.444069 | + | 0.895993i | \(0.353535\pi\) | |||||||
\(734\) | 23.3485 | 0.861808 | ||||||||
\(735\) | −25.5959 | − | 18.0990i | −0.944120 | − | 0.667593i | ||||
\(736\) | 6.12372 | − | 3.53553i | 0.225723 | − | 0.130322i | ||||
\(737\) | −0.949490 | + | 1.64456i | −0.0349749 | + | 0.0605783i | ||||
\(738\) | 3.00000 | + | 8.48528i | 0.110432 | + | 0.312348i | ||||
\(739\) | −4.82577 | − | 8.35847i | −0.177519 | − | 0.307471i | 0.763511 | − | 0.645794i | \(-0.223474\pi\) |
−0.941030 | + | 0.338323i | \(0.890140\pi\) | |||||||
\(740\) | −1.10102 | −0.0404743 | ||||||||
\(741\) | 9.79796 | − | 24.2487i | 0.359937 | − | 0.890799i | ||||
\(742\) | −4.89898 | −0.179847 | ||||||||
\(743\) | −9.67423 | − | 16.7563i | −0.354913 | − | 0.614728i | 0.632190 | − | 0.774814i | \(-0.282156\pi\) |
−0.987103 | + | 0.160086i | \(0.948823\pi\) | |||||||
\(744\) | 6.67423 | − | 3.07483i | 0.244689 | − | 0.112729i | ||||
\(745\) | 3.44949 | − | 5.97469i | 0.126380 | − | 0.218896i | ||||
\(746\) | −22.0454 | + | 12.7279i | −0.807140 | + | 0.466002i | ||||
\(747\) | 32.3207 | + | 27.6325i | 1.18255 | + | 1.01102i | ||||
\(748\) | −2.00000 | −0.0731272 | ||||||||
\(749\) | 21.7980 | 0.796480 | ||||||||
\(750\) | 16.0000 | + | 11.3137i | 0.584237 | + | 0.413118i | ||||
\(751\) | −11.6969 | − | 6.75323i | −0.426827 | − | 0.246429i | 0.271167 | − | 0.962532i | \(-0.412591\pi\) |
−0.697994 | + | 0.716103i | \(0.745924\pi\) | |||||||
\(752\) | 6.43539i | 0.234675i | ||||||||
\(753\) | −1.05051 | + | 11.4012i | −0.0382827 | + | 0.415483i | ||||
\(754\) | 7.34847 | + | 4.24264i | 0.267615 | + | 0.154508i | ||||
\(755\) | −12.7980 | − | 22.1667i | −0.465765 | − | 0.806729i | ||||
\(756\) | −16.5732 | + | 16.1206i | −0.602762 | + | 0.586300i | ||||
\(757\) | −9.69694 | − | 16.7956i | −0.352441 | − | 0.610446i | 0.634235 | − | 0.773140i | \(-0.281315\pi\) |
−0.986677 | + | 0.162694i | \(0.947982\pi\) | |||||||
\(758\) | 13.3485 | − | 7.70674i | 0.484838 | − | 0.279921i | ||||
\(759\) | −3.87628 | − | 0.357161i | −0.140700 | − | 0.0129641i | ||||
\(760\) | 6.00000 | − | 1.41421i | 0.217643 | − | 0.0512989i | ||||
\(761\) | − | 41.9657i | − | 1.52126i | −0.649188 | − | 0.760628i | \(-0.724891\pi\) | ||
0.649188 | − | 0.760628i | \(-0.275109\pi\) | |||||||
\(762\) | −16.3485 | + | 7.53177i | −0.592243 | + | 0.272847i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −16.8990 | − | 9.75663i | −0.611384 | − | 0.352982i | ||||
\(765\) | −8.89898 | − | 25.1701i | −0.321743 | − | 0.910027i | ||||
\(766\) | −7.77526 | + | 13.4671i | −0.280931 | + | 0.486587i | ||||
\(767\) | − | 22.6916i | − | 0.819347i | ||||||
\(768\) | 1.72474 | + | 0.158919i | 0.0622364 | + | 0.00573448i | ||||
\(769\) | 17.7980 | − | 30.8270i | 0.641811 | − | 1.11165i | −0.343217 | − | 0.939256i | \(-0.611517\pi\) |
0.985028 | − | 0.172393i | \(-0.0551499\pi\) | |||||||
\(770\) | 1.00000 | − | 1.73205i | 0.0360375 | − | 0.0624188i | ||||
\(771\) | 25.8712 | + | 2.38378i | 0.931728 | + | 0.0858497i | ||||
\(772\) | − | 8.83523i | − | 0.317987i | ||||||
\(773\) | 1.22474 | − | 2.12132i | 0.0440510 | − | 0.0762986i | −0.843159 | − | 0.537664i | \(-0.819307\pi\) |
0.887210 | + | 0.461365i | \(0.152640\pi\) | |||||||
\(774\) | 0.898979 | + | 2.54270i | 0.0323132 | + | 0.0913954i | ||||
\(775\) | 11.0227 | + | 6.36396i | 0.395947 | + | 0.228600i | ||||
\(776\) | 11.8485 | − | 6.84072i | 0.425335 | − | 0.245567i | ||||
\(777\) | 5.44949 | − | 2.51059i | 0.195499 | − | 0.0900669i | ||||
\(778\) | − | 26.4415i | − | 0.947972i | ||||||
\(779\) | 3.00000 | + | 12.7279i | 0.107486 | + | 0.456025i | ||||
\(780\) | −8.44949 | − | 0.778539i | −0.302540 | − | 0.0278762i | ||||
\(781\) | 1.65153 | − | 0.953512i | 0.0590964 | − | 0.0341193i | ||||
\(782\) | −22.2474 | − | 38.5337i | −0.795567 | − | 1.37796i | ||||
\(783\) | −9.12372 | + | 8.87455i | −0.326055 | + | 0.317151i | ||||
\(784\) | −6.39898 | − | 11.0834i | −0.228535 | − | 0.395834i | ||||
\(785\) | 22.8990 | + | 13.2207i | 0.817300 | + | 0.471868i | ||||
\(786\) | 3.50000 | − | 37.9855i | 0.124841 | − | 1.35490i | ||||
\(787\) | − | 17.9241i | − | 0.638924i | −0.947599 | − | 0.319462i | \(-0.896498\pi\) | ||
0.947599 | − | 0.319462i | \(-0.103502\pi\) | |||||||
\(788\) | 0.426786 | + | 0.246405i | 0.0152036 | + | 0.00877781i | ||||
\(789\) | −16.6969 | − | 11.8065i | −0.594427 | − | 0.420323i | ||||
\(790\) | 12.0000 | 0.426941 | ||||||||
\(791\) | 3.55051 | 0.126242 | ||||||||
\(792\) | −0.724745 | − | 0.619620i | −0.0257527 | − | 0.0220173i | ||||
\(793\) | −19.3485 | + | 11.1708i | −0.687084 | + | 0.396688i | ||||
\(794\) | 4.67423 | − | 8.09601i | 0.165882 | − | 0.287317i | ||||
\(795\) | 2.44949 | − | 1.12848i | 0.0868744 | − | 0.0400232i | ||||
\(796\) | −3.44949 | − | 5.97469i | −0.122264 | − | 0.211767i | ||||
\(797\) | 22.6515 | 0.802358 | 0.401179 | − | 0.916000i | \(-0.368600\pi\) | ||||
0.401179 | + | 0.916000i | \(0.368600\pi\) | |||||||
\(798\) | −26.4722 | + | 20.6811i | −0.937105 | + | 0.732102i | ||||
\(799\) | 40.4949 | 1.43261 | ||||||||
\(800\) | 1.50000 | + | 2.59808i | 0.0530330 | + | 0.0918559i | ||||
\(801\) | 16.8990 | + | 47.7975i | 0.597096 | + | 1.68884i | ||||
\(802\) | −6.39898 | + | 11.0834i | −0.225956 | + | 0.391367i | ||||
\(803\) | 2.97219 | − | 1.71600i | 0.104886 | − | 0.0605562i | ||||
\(804\) | −8.44949 | − | 5.97469i | −0.297991 | − | 0.210711i | ||||
\(805\) | 44.4949 | 1.56824 | ||||||||
\(806\) | −14.6969 | −0.517678 | ||||||||
\(807\) | −24.4949 | + | 34.6410i | −0.862261 | + | 1.21942i | ||||
\(808\) | 8.57321 | + | 4.94975i | 0.301605 | + | 0.174132i | ||||
\(809\) | 2.36773i | 0.0832448i | 0.999133 | + | 0.0416224i | \(0.0132526\pi\) | ||||
−0.999133 | + | 0.0416224i | \(0.986747\pi\) | |||||||
\(810\) | 4.57321 | − | 11.8780i | 0.160686 | − | 0.417349i | ||||
\(811\) | 3.00000 | + | 1.73205i | 0.105344 | + | 0.0608205i | 0.551746 | − | 0.834012i | \(-0.313962\pi\) |
−0.446402 | + | 0.894832i | \(0.647295\pi\) | |||||||
\(812\) | −5.44949 | − | 9.43879i | −0.191240 | − | 0.331237i | ||||
\(813\) | −24.0454 | + | 34.0053i | −0.843309 | + | 1.19262i | ||||
\(814\) | 0.123724 | + | 0.214297i | 0.00433654 | + | 0.00751110i | ||||
\(815\) | 4.47219 | − | 2.58202i | 0.156654 | − | 0.0904443i | ||||
\(816\) | 1.00000 | − | 10.8530i | 0.0350070 | − | 0.379931i | ||||
\(817\) | 0.898979 | + | 3.81405i | 0.0314513 | + | 0.133437i | ||||
\(818\) | 20.6096i | 0.720599i | ||||||||
\(819\) | 43.5959 | − | 15.4135i | 1.52336 | − | 0.538591i | ||||
\(820\) | 3.67423 | − | 2.12132i | 0.128310 | − | 0.0740797i | ||||
\(821\) | −0.550510 | − | 0.317837i | −0.0192129 | − | 0.0110926i | 0.490363 | − | 0.871518i | \(-0.336864\pi\) |
−0.509576 | + | 0.860426i | \(0.670198\pi\) | |||||||
\(822\) | −11.6237 | + | 5.35507i | −0.405424 | + | 0.186780i | ||||
\(823\) | 9.65153 | − | 16.7169i | 0.336431 | − | 0.582716i | −0.647327 | − | 0.762212i | \(-0.724113\pi\) |
0.983759 | + | 0.179496i | \(0.0574467\pi\) | |||||||
\(824\) | − | 11.9494i | − | 0.416276i | ||||||
\(825\) | 0.151531 | − | 1.64456i | 0.00527562 | − | 0.0572564i | ||||
\(826\) | −14.5732 | + | 25.2415i | −0.507067 | + | 0.878266i | ||||
\(827\) | 1.62372 | − | 2.81237i | 0.0564624 | − | 0.0977958i | −0.836413 | − | 0.548100i | \(-0.815351\pi\) |
0.892875 | + | 0.450304i | \(0.148685\pi\) | |||||||
\(828\) | 3.87628 | − | 20.8560i | 0.134710 | − | 0.724798i | ||||
\(829\) | 36.1981i | 1.25721i | 0.777724 | + | 0.628606i | \(0.216374\pi\) | ||||
−0.777724 | + | 0.628606i | \(0.783626\pi\) | |||||||
\(830\) | 10.0227 | − | 17.3598i | 0.347893 | − | 0.602569i | ||||
\(831\) | 3.07832 | + | 6.68180i | 0.106786 | + | 0.231789i | ||||
\(832\) | −3.00000 | − | 1.73205i | −0.104006 | − | 0.0600481i | ||||
\(833\) | −69.7423 | + | 40.2658i | −2.41643 | + | 1.39513i | ||||
\(834\) | 0.252551 | + | 0.548188i | 0.00874514 | + | 0.0189822i | ||||
\(835\) | − | 6.92820i | − | 0.239760i | ||||||
\(836\) | −0.949490 | − | 1.00889i | −0.0328388 | − | 0.0348932i | ||||
\(837\) | 6.00000 | − | 21.2132i | 0.207390 | − | 0.733236i | ||||
\(838\) | −3.24745 | + | 1.87492i | −0.112181 | + | 0.0647679i | ||||
\(839\) | −0.674235 | − | 1.16781i | −0.0232772 | − | 0.0403172i | 0.854152 | − | 0.520023i | \(-0.174077\pi\) |
−0.877429 | + | 0.479706i | \(0.840743\pi\) | |||||||
\(840\) | 8.89898 | + | 6.29253i | 0.307044 | + | 0.217113i | ||||
\(841\) | 11.5000 | + | 19.9186i | 0.396552 | + | 0.686848i | ||||
\(842\) | −26.0227 | − | 15.0242i | −0.896802 | − | 0.517769i | ||||
\(843\) | 28.6237 | + | 2.63740i | 0.985853 | + | 0.0908369i | ||||
\(844\) | 15.4135i | 0.530554i | ||||||||
\(845\) | −1.22474 | − | 0.707107i | −0.0421325 | − | 0.0243252i | ||||
\(846\) | 14.6742 | + | 12.5457i | 0.504511 | + | 0.431331i | ||||
\(847\) | 48.4949 | 1.66630 | ||||||||
\(848\) | 1.10102 | 0.0378092 | ||||||||
\(849\) | 4.55051 | − | 6.43539i | 0.156173 | − | 0.220862i | ||||
\(850\) | 16.3485 | − | 9.43879i | 0.560748 | − | 0.323748i | ||||
\(851\) | −2.75255 | + | 4.76756i | −0.0943562 | + | 0.163430i | ||||
\(852\) | 4.34847 | + | 9.43879i | 0.148976 | + | 0.323368i | ||||
\(853\) | 5.00000 | + | 8.66025i | 0.171197 | + | 0.296521i | 0.938839 | − | 0.344358i | \(-0.111903\pi\) |
−0.767642 | + | 0.640879i | \(0.778570\pi\) | |||||||
\(854\) | 28.6969 | 0.981989 | ||||||||
\(855\) | 8.47219 | − | 16.4384i | 0.289743 | − | 0.562182i | ||||
\(856\) | −4.89898 | −0.167444 | ||||||||
\(857\) | −11.2980 | − | 19.5686i | −0.385931 | − | 0.668452i | 0.605967 | − | 0.795490i | \(-0.292786\pi\) |
−0.991898 | + | 0.127038i | \(0.959453\pi\) | |||||||
\(858\) | 0.797959 | + | 1.73205i | 0.0272419 | + | 0.0591312i | ||||
\(859\) | 22.4217 | − | 38.8355i | 0.765018 | − | 1.32505i | −0.175219 | − | 0.984529i | \(-0.556063\pi\) |
0.940237 | − | 0.340521i | \(-0.110603\pi\) | |||||||
\(860\) | 1.10102 | − | 0.635674i | 0.0375445 | − | 0.0216763i | ||||
\(861\) | −13.3485 | + | 18.8776i | −0.454915 | + | 0.643346i | ||||
\(862\) | 32.6969 | 1.11366 | ||||||||
\(863\) | 31.3485 | 1.06711 | 0.533557 | − | 0.845764i | \(-0.320855\pi\) | ||||
0.533557 | + | 0.845764i | \(0.320855\pi\) | |||||||
\(864\) | 3.72474 | − | 3.62302i | 0.126718 | − | 0.123258i | ||||
\(865\) | 13.3485 | + | 7.70674i | 0.453862 | + | 0.262037i | ||||
\(866\) | 13.5065i | 0.458968i | ||||||||
\(867\) | −38.9722 | − | 3.59091i | −1.32357 | − | 0.121954i | ||||
\(868\) | 16.3485 | + | 9.43879i | 0.554903 | + | 0.320374i | ||||
\(869\) | −1.34847 | − | 2.33562i | −0.0457437 | − | 0.0792304i | ||||
\(870\) | 4.89898 | + | 3.46410i | 0.166091 | + | 0.117444i | ||||
\(871\) | 10.3485 | + | 17.9241i | 0.350645 | + | 0.607334i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.50000 | − | 40.3532i | 0.253837 | − | 1.36575i | ||||
\(874\) | 8.87628 | − | 29.5163i | 0.300245 | − | 0.998404i | ||||
\(875\) | 50.3402i | 1.70181i | ||||||||
\(876\) | 7.82577 | + | 16.9866i | 0.264408 | + | 0.573925i | ||||
\(877\) | 0.371173 | − | 0.214297i | 0.0125336 | − | 0.00723629i | −0.493720 | − | 0.869621i | \(-0.664363\pi\) |
0.506254 | + | 0.862385i | \(0.331030\pi\) | |||||||
\(878\) | −2.32577 | − | 1.34278i | −0.0784908 | − | 0.0453167i | ||||
\(879\) | 3.37117 | + | 7.31747i | 0.113707 | + | 0.246812i | ||||
\(880\) | −0.224745 | + | 0.389270i | −0.00757615 | + | 0.0131223i | ||||
\(881\) | 55.5364i | 1.87107i | 0.353236 | + | 0.935534i | \(0.385081\pi\) | ||||
−0.353236 | + | 0.935534i | \(0.614919\pi\) | |||||||
\(882\) | −37.7474 | − | 7.01569i | −1.27102 | − | 0.236231i | ||||
\(883\) | −21.4217 | + | 37.1034i | −0.720897 | + | 1.24863i | 0.239744 | + | 0.970836i | \(0.422937\pi\) |
−0.960641 | + | 0.277794i | \(0.910397\pi\) | |||||||
\(884\) | −10.8990 | + | 18.8776i | −0.366572 | + | 0.634922i | ||||
\(885\) | 1.47219 | − | 15.9777i | 0.0494872 | − | 0.537085i | ||||
\(886\) | 29.2378i | 0.982263i | ||||||||
\(887\) | −16.0454 | + | 27.7915i | −0.538752 | + | 0.933146i | 0.460220 | + | 0.887805i | \(0.347771\pi\) |
−0.998972 | + | 0.0453408i | \(0.985563\pi\) | |||||||
\(888\) | −1.22474 | + | 0.564242i | −0.0410997 | + | 0.0189347i | ||||
\(889\) | −40.0454 | − | 23.1202i | −1.34308 | − | 0.775428i | ||||
\(890\) | 20.6969 | − | 11.9494i | 0.693763 | − | 0.400544i | ||||
\(891\) | −2.82577 | + | 0.444648i | −0.0946667 | + | 0.0148963i | ||||
\(892\) | − | 9.61377i | − | 0.321893i | ||||||
\(893\) | 19.2247 | + | 20.4274i | 0.643332 | + | 0.683578i | ||||
\(894\) | 0.775255 | − | 8.41385i | 0.0259284 | − | 0.281401i | ||||
\(895\) | −27.3712 | + | 15.8028i | −0.914917 | + | 0.528228i | ||||
\(896\) | 2.22474 | + | 3.85337i | 0.0743235 | + | 0.128732i | ||||
\(897\) | −24.4949 | + | 34.6410i | −0.817861 | + | 1.15663i | ||||
\(898\) | 5.60102 | + | 9.70125i | 0.186908 | + | 0.323735i | ||||
\(899\) | 9.00000 | + | 5.19615i | 0.300167 | + | 0.173301i | ||||
\(900\) | 8.84847 | + | 1.64456i | 0.294949 | + | 0.0548188i | ||||
\(901\) | − | 6.92820i | − | 0.230812i | ||||||
\(902\) | −0.825765 | − | 0.476756i | −0.0274950 | − | 0.0158742i | ||||
\(903\) | −4.00000 | + | 5.65685i | −0.133112 | + | 0.188248i | ||||
\(904\) | −0.797959 | −0.0265397 | ||||||||
\(905\) | 18.4949 | 0.614791 | ||||||||
\(906\) | −25.5959 | − | 18.0990i | −0.850367 | − | 0.601301i | ||||
\(907\) | 47.9166 | − | 27.6647i | 1.59104 | − | 0.918590i | 0.597916 | − | 0.801559i | \(-0.295996\pi\) |
0.993128 | − | 0.117031i | \(-0.0373376\pi\) | |||||||
\(908\) | −2.72474 | + | 4.71940i | −0.0904238 | + | 0.156619i | ||||
\(909\) | 28.0000 | − | 9.89949i | 0.928701 | − | 0.328346i | ||||
\(910\) | −10.8990 | − | 18.8776i | −0.361298 | − | 0.625786i | ||||
\(911\) | −43.3485 | −1.43620 | −0.718099 | − | 0.695941i | \(-0.754988\pi\) | ||||
−0.718099 | + | 0.695941i | \(0.754988\pi\) | |||||||
\(912\) | 5.94949 | − | 4.64796i | 0.197007 | − | 0.153909i | ||||
\(913\) | −4.50510 | −0.149097 | ||||||||
\(914\) | −6.50000 | − | 11.2583i | −0.215001 | − | 0.372392i | ||||
\(915\) | −14.3485 | + | 6.61037i | −0.474346 | + | 0.218532i | ||||
\(916\) | 4.44949 | − | 7.70674i | 0.147015 | − | 0.254638i | ||||
\(917\) | 84.8661 | − | 48.9974i | 2.80252 | − | 1.61804i | ||||
\(918\) | −22.7980 | − | 23.4381i | −0.752445 | − | 0.773571i | ||||
\(919\) | −7.30306 | −0.240906 | −0.120453 | − | 0.992719i | \(-0.538435\pi\) | ||||
−0.120453 | + | 0.992719i | \(0.538435\pi\) | |||||||
\(920\) | −10.0000 | −0.329690 | ||||||||
\(921\) | 5.75255 | + | 4.06767i | 0.189553 | + | 0.134034i | ||||
\(922\) | −8.75255 | − | 5.05329i | −0.288250 | − | 0.166421i | ||||
\(923\) | − | 20.7846i | − | 0.684134i | ||||||
\(924\) | 0.224745 | − | 2.43916i | 0.00739356 | − | 0.0802424i | ||||
\(925\) | −2.02270 | − | 1.16781i | −0.0665061 | − | 0.0383973i | ||||
\(926\) | −0.101021 | − | 0.174973i | −0.00331974 | − | 0.00574996i | ||||
\(927\) | −27.2474 | − | 23.2952i | −0.894924 | − | 0.765115i | ||||
\(928\) | 1.22474 | + | 2.12132i | 0.0402042 | + | 0.0696358i | ||||
\(929\) | 15.0959 | − | 8.71563i | 0.495281 | − | 0.285951i | −0.231482 | − | 0.972839i | \(-0.574357\pi\) |
0.726763 | + | 0.686889i | \(0.241024\pi\) | |||||||
\(930\) | −10.3485 | − | 0.953512i | −0.339340 | − | 0.0312669i | ||||
\(931\) | −53.4217 | − | 16.0652i | −1.75082 | − | 0.526516i | ||||
\(932\) | − | 6.46750i | − | 0.211850i | ||||||
\(933\) | −24.4722 | + | 11.2744i | −0.801184 | + | 0.369107i | ||||
\(934\) | −28.0732 | + | 16.2081i | −0.918584 | + | 0.530345i | ||||
\(935\) | 2.44949 | + | 1.41421i | 0.0801069 | + | 0.0462497i | ||||
\(936\) | −9.79796 | + | 3.46410i | −0.320256 | + | 0.113228i | ||||
\(937\) | −11.5000 | + | 19.9186i | −0.375689 | + | 0.650712i | −0.990430 | − | 0.138017i | \(-0.955927\pi\) |
0.614741 | + | 0.788729i | \(0.289260\pi\) | |||||||
\(938\) | − | 26.5843i | − | 0.868009i | ||||||
\(939\) | −32.7702 | − | 3.01945i | −1.06941 | − | 0.0985362i | ||||
\(940\) | 4.55051 | − | 7.88171i | 0.148421 | − | 0.257073i | ||||
\(941\) | −27.4949 | + | 47.6226i | −0.896308 | + | 1.55245i | −0.0641307 | + | 0.997942i | \(0.520427\pi\) |
−0.832177 | + | 0.554510i | \(0.812906\pi\) | |||||||
\(942\) | 32.2474 | + | 2.97129i | 1.05068 | + | 0.0968099i | ||||
\(943\) | − | 21.2132i | − | 0.690797i | ||||||
\(944\) | 3.27526 | − | 5.67291i | 0.106600 | − | 0.184637i | ||||
\(945\) | 31.6969 | − | 8.02458i | 1.03110 | − | 0.261040i | ||||
\(946\) | −0.247449 | − | 0.142865i | −0.00804525 | − | 0.00464493i | ||||
\(947\) | −11.4495 | + | 6.61037i | −0.372058 | + | 0.214808i | −0.674357 | − | 0.738405i | \(-0.735579\pi\) |
0.302299 | + | 0.953213i | \(0.402246\pi\) | |||||||
\(948\) | 13.3485 | − | 6.14966i | 0.433538 | − | 0.199732i | ||||
\(949\) | − | 37.4052i | − | 1.21423i | ||||||
\(950\) | 12.5227 | + | 3.76588i | 0.406290 | + | 0.122181i | ||||
\(951\) | 10.3485 | + | 0.953512i | 0.335572 | + | 0.0309197i | ||||
\(952\) | 24.2474 | − | 13.9993i | 0.785864 | − | 0.453719i | ||||
\(953\) | −2.60102 | − | 4.50510i | −0.0842553 | − | 0.145934i | 0.820818 | − | 0.571189i | \(-0.193518\pi\) |
−0.905074 | + | 0.425255i | \(0.860184\pi\) | |||||||
\(954\) | 2.14643 | − | 2.51059i | 0.0694932 | − | 0.0812833i | ||||
\(955\) | 13.7980 | + | 23.8988i | 0.446491 | + | 0.773346i | ||||
\(956\) | −6.24745 | − | 3.60697i | −0.202057 | − | 0.116658i | ||||
\(957\) | 0.123724 | − | 1.34278i | 0.00399944 | − | 0.0434060i | ||||
\(958\) | 40.5836i | 1.31120i | ||||||||
\(959\) | −28.4722 | − | 16.4384i | −0.919415 | − | 0.530825i | ||||
\(960\) | −2.00000 | − | 1.41421i | −0.0645497 | − | 0.0456435i | ||||
\(961\) | 13.0000 | 0.419355 | ||||||||
\(962\) | 2.69694 | 0.0869528 | ||||||||
\(963\) | −9.55051 | + | 11.1708i | −0.307761 | + | 0.359975i | ||||
\(964\) | −8.84847 | + | 5.10867i | −0.284990 | + | 0.164539i | ||||
\(965\) | −6.24745 | + | 10.8209i | −0.201112 | + | 0.348337i | ||||
\(966\) | 49.4949 | − | 22.8024i | 1.59247 | − | 0.733655i | ||||
\(967\) | −3.69694 | − | 6.40329i | −0.118886 | − | 0.205916i | 0.800441 | − | 0.599412i | \(-0.204599\pi\) |
−0.919326 | + | 0.393496i | \(0.871265\pi\) | |||||||
\(968\) | −10.8990 | −0.350306 | ||||||||
\(969\) | −29.2474 | − | 37.4373i | −0.939563 | − | 1.20266i | ||||
\(970\) | −19.3485 | −0.621242 | ||||||||
\(971\) | 13.0732 | + | 22.6435i | 0.419539 | + | 0.726664i | 0.995893 | − | 0.0905368i | \(-0.0288583\pi\) |
−0.576354 | + | 0.817200i | \(0.695525\pi\) | |||||||
\(972\) | −1.00000 | − | 15.5563i | −0.0320750 | − | 0.498970i | ||||
\(973\) | −0.775255 | + | 1.34278i | −0.0248535 | + | 0.0430476i | ||||
\(974\) | −14.3258 | + | 8.27098i | −0.459027 | + | 0.265019i | ||||
\(975\) | −14.6969 | − | 10.3923i | −0.470679 | − | 0.332820i | ||||
\(976\) | −6.44949 | −0.206443 | ||||||||
\(977\) | 49.8990 | 1.59641 | 0.798205 | − | 0.602386i | \(-0.205783\pi\) | ||||
0.798205 | + | 0.602386i | \(0.205783\pi\) | |||||||
\(978\) | 3.65153 | − | 5.16404i | 0.116763 | − | 0.165128i | ||||
\(979\) | −4.65153 | − | 2.68556i | −0.148664 | − | 0.0858310i | ||||
\(980\) | 18.0990i | 0.578153i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.10102 | − | 2.36773i | −0.130869 | − | 0.0755572i | ||||
\(983\) | −19.1010 | − | 33.0839i | −0.609228 | − | 1.05521i | −0.991368 | − | 0.131109i | \(-0.958146\pi\) |
0.382140 | − | 0.924104i | \(-0.375187\pi\) | |||||||
\(984\) | 3.00000 | − | 4.24264i | 0.0956365 | − | 0.135250i | ||||
\(985\) | −0.348469 | − | 0.603566i | −0.0111032 | − | 0.0192312i | ||||
\(986\) | 13.3485 | − | 7.70674i | 0.425102 | − | 0.245433i | ||||
\(987\) | −4.55051 | + | 49.3867i | −0.144844 | + | 1.57200i | ||||
\(988\) | −14.6969 | + | 3.46410i | −0.467572 | + | 0.110208i | ||||
\(989\) | − | 6.35674i | − | 0.202133i | ||||||
\(990\) | 0.449490 | + | 1.27135i | 0.0142857 | + | 0.0404061i | ||||
\(991\) | 44.6969 | − | 25.8058i | 1.41985 | − | 0.819748i | 0.423560 | − | 0.905868i | \(-0.360780\pi\) |
0.996285 | + | 0.0861200i | \(0.0274468\pi\) | |||||||
\(992\) | −3.67423 | − | 2.12132i | −0.116657 | − | 0.0673520i | ||||
\(993\) | 23.2980 | − | 10.7334i | 0.739338 | − | 0.340615i | ||||
\(994\) | −13.3485 | + | 23.1202i | −0.423388 | + | 0.733329i | ||||
\(995\) | 9.75663i | 0.309306i | ||||||||
\(996\) | 2.25255 | − | 24.4470i | 0.0713748 | − | 0.774631i | ||||
\(997\) | −29.7196 | + | 51.4759i | −0.941231 | + | 1.63026i | −0.178102 | + | 0.984012i | \(0.556996\pi\) |
−0.763128 | + | 0.646247i | \(0.776338\pi\) | |||||||
\(998\) | 1.27526 | − | 2.20881i | 0.0403675 | − | 0.0699186i | ||||
\(999\) | −1.10102 | + | 3.89270i | −0.0348347 | + | 0.123159i |
(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 | 114.2.h.f.107.1 | yes | 4 | |
3.2 | odd | 2 | 114.2.h.e.107.2 | yes | 4 | ||
4.3 | odd | 2 | 912.2.bn.h.449.2 | 4 | |||
12.11 | even | 2 | 912.2.bn.g.449.1 | 4 | |||
19.8 | odd | 6 | 114.2.h.e.65.1 | ✓ | 4 | ||
57.8 | even | 6 | inner | 114.2.h.f.65.1 | yes | 4 | |
76.27 | even | 6 | 912.2.bn.g.65.2 | 4 | |||
228.179 | odd | 6 | 912.2.bn.h.65.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.2.h.e.65.1 | ✓ | 4 | 19.8 | odd | 6 | ||
114.2.h.e.107.2 | yes | 4 | 3.2 | odd | 2 | ||
114.2.h.f.65.1 | yes | 4 | 57.8 | even | 6 | inner | |
114.2.h.f.107.1 | yes | 4 | 1.1 | even | 1 | trivial | |
912.2.bn.g.65.2 | 4 | 76.27 | even | 6 | |||
912.2.bn.g.449.1 | 4 | 12.11 | even | 2 | |||
912.2.bn.h.65.2 | 4 | 228.179 | odd | 6 | |||
912.2.bn.h.449.2 | 4 | 4.3 | odd | 2 |