Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [195,2,Mod(16,195)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(195, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("195.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 195 = 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 195.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.55708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.1714608.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 30x^{2} - 21x + 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 16.2 | ||
Root | \(0.500000 + 1.75780i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 195.16 |
Dual form | 195.2.i.d.61.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/195\mathbb{Z}\right)^\times\).
\(n\) | \(106\) | \(131\) | \(157\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.169938 | + | 0.294342i | 0.120165 | + | 0.208131i | 0.919832 | − | 0.392311i | \(-0.128324\pi\) |
−0.799668 | + | 0.600443i | \(0.794991\pi\) | |||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0.942242 | − | 1.63201i | 0.471121 | − | 0.816005i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.169938 | + | 0.294342i | −0.0693771 | + | 0.120165i | ||||
\(7\) | −0.330062 | + | 0.571683i | −0.124752 | + | 0.216076i | −0.921636 | − | 0.388056i | \(-0.873147\pi\) |
0.796884 | + | 0.604132i | \(0.206480\pi\) | |||||||
\(8\) | 1.32025 | 0.466778 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0.169938 | + | 0.294342i | 0.0537393 | + | 0.0930791i | ||||
\(11\) | −0.339877 | − | 0.588684i | −0.102477 | − | 0.177495i | 0.810228 | − | 0.586115i | \(-0.199343\pi\) |
−0.912704 | + | 0.408620i | \(0.866010\pi\) | |||||||
\(12\) | 1.88448 | 0.544004 | ||||||||
\(13\) | 1.93243 | − | 3.04397i | 0.535959 | − | 0.844244i | ||||
\(14\) | −0.224361 | −0.0599629 | ||||||||
\(15\) | 0.500000 | + | 0.866025i | 0.129099 | + | 0.223607i | ||||
\(16\) | −1.66012 | − | 2.87542i | −0.415031 | − | 0.718854i | ||||
\(17\) | −3.71455 | + | 6.43378i | −0.900910 | + | 1.56042i | −0.0745938 | + | 0.997214i | \(0.523766\pi\) |
−0.826316 | + | 0.563207i | \(0.809567\pi\) | |||||||
\(18\) | −0.339877 | −0.0801098 | ||||||||
\(19\) | −0.0577581 | + | 0.100040i | −0.0132506 | + | 0.0229508i | −0.872575 | − | 0.488481i | \(-0.837551\pi\) |
0.859324 | + | 0.511431i | \(0.170885\pi\) | |||||||
\(20\) | 0.942242 | − | 1.63201i | 0.210692 | − | 0.364929i | ||||
\(21\) | −0.660123 | −0.144051 | ||||||||
\(22\) | 0.115516 | − | 0.200080i | 0.0246282 | − | 0.0426572i | ||||
\(23\) | 3.88448 | + | 6.72812i | 0.809971 | + | 1.40291i | 0.912883 | + | 0.408220i | \(0.133850\pi\) |
−0.102913 | + | 0.994690i | \(0.532816\pi\) | |||||||
\(24\) | 0.660123 | + | 1.14337i | 0.134747 | + | 0.233389i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.22436 | + | 0.0515075i | 0.240117 | + | 0.0101015i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.621996 | + | 1.07733i | 0.117546 | + | 0.203596i | ||||
\(29\) | −2.77230 | − | 4.80177i | −0.514804 | − | 0.891666i | −0.999852 | − | 0.0171792i | \(-0.994531\pi\) |
0.485049 | − | 0.874487i | \(-0.338802\pi\) | |||||||
\(30\) | −0.169938 | + | 0.294342i | −0.0310264 | + | 0.0537393i | ||||
\(31\) | −9.97370 | −1.79133 | −0.895664 | − | 0.444730i | \(-0.853299\pi\) | ||||
−0.895664 | + | 0.444730i | \(0.853299\pi\) | |||||||
\(32\) | 1.88448 | − | 3.26402i | 0.333133 | − | 0.577003i | ||||
\(33\) | 0.339877 | − | 0.588684i | 0.0591650 | − | 0.102477i | ||||
\(34\) | −2.52498 | −0.433030 | ||||||||
\(35\) | −0.330062 | + | 0.571683i | −0.0557906 | + | 0.0966321i | ||||
\(36\) | 0.942242 | + | 1.63201i | 0.157040 | + | 0.272002i | ||||
\(37\) | −4.88448 | − | 8.46017i | −0.803004 | − | 1.39084i | −0.917630 | − | 0.397435i | \(-0.869900\pi\) |
0.114626 | − | 0.993409i | \(-0.463433\pi\) | |||||||
\(38\) | −0.0392613 | −0.00636903 | ||||||||
\(39\) | 3.60236 | + | 0.151548i | 0.576840 | + | 0.0242670i | ||||
\(40\) | 1.32025 | 0.208749 | ||||||||
\(41\) | −2.11218 | − | 3.65840i | −0.329867 | − | 0.571347i | 0.652618 | − | 0.757687i | \(-0.273671\pi\) |
−0.982485 | + | 0.186340i | \(0.940337\pi\) | |||||||
\(42\) | −0.112180 | − | 0.194302i | −0.0173098 | − | 0.0299814i | ||||
\(43\) | 0.272303 | − | 0.471643i | 0.0415259 | − | 0.0719249i | −0.844515 | − | 0.535531i | \(-0.820111\pi\) |
0.886041 | + | 0.463606i | \(0.153445\pi\) | |||||||
\(44\) | −1.28098 | −0.193116 | ||||||||
\(45\) | −0.500000 | + | 0.866025i | −0.0745356 | + | 0.129099i | ||||
\(46\) | −1.32025 | + | 2.28673i | −0.194660 | + | 0.337160i | ||||
\(47\) | −5.01963 | −0.732188 | −0.366094 | − | 0.930578i | \(-0.619305\pi\) | ||||
−0.366094 | + | 0.930578i | \(0.619305\pi\) | |||||||
\(48\) | 1.66012 | − | 2.87542i | 0.239618 | − | 0.415031i | ||||
\(49\) | 3.28212 | + | 5.68480i | 0.468874 | + | 0.812114i | ||||
\(50\) | 0.169938 | + | 0.294342i | 0.0240329 | + | 0.0416262i | ||||
\(51\) | −7.42909 | −1.04028 | ||||||||
\(52\) | −3.14697 | − | 6.02189i | −0.436406 | − | 0.835086i | ||||
\(53\) | 0.679754 | 0.0933714 | 0.0466857 | − | 0.998910i | \(-0.485134\pi\) | ||||
0.0466857 | + | 0.998910i | \(0.485134\pi\) | |||||||
\(54\) | −0.169938 | − | 0.294342i | −0.0231257 | − | 0.0400549i | ||||
\(55\) | −0.339877 | − | 0.588684i | −0.0458290 | − | 0.0793781i | ||||
\(56\) | −0.435763 | + | 0.754763i | −0.0582312 | + | 0.100859i | ||||
\(57\) | −0.115516 | −0.0153005 | ||||||||
\(58\) | 0.942242 | − | 1.63201i | 0.123722 | − | 0.214294i | ||||
\(59\) | −1.11218 | + | 1.92635i | −0.144794 | + | 0.250790i | −0.929296 | − | 0.369336i | \(-0.879585\pi\) |
0.784502 | + | 0.620126i | \(0.212918\pi\) | |||||||
\(60\) | 1.88448 | 0.243286 | ||||||||
\(61\) | 2.10236 | − | 3.64140i | 0.269180 | − | 0.466234i | −0.699470 | − | 0.714662i | \(-0.746581\pi\) |
0.968650 | + | 0.248428i | \(0.0799139\pi\) | |||||||
\(62\) | −1.69491 | − | 2.93568i | −0.215254 | − | 0.372832i | ||||
\(63\) | −0.330062 | − | 0.571683i | −0.0415838 | − | 0.0720253i | ||||
\(64\) | −5.35951 | −0.669938 | ||||||||
\(65\) | 1.93243 | − | 3.04397i | 0.239688 | − | 0.377557i | ||||
\(66\) | 0.231033 | 0.0284381 | ||||||||
\(67\) | 3.81691 | + | 6.61108i | 0.466310 | + | 0.807672i | 0.999260 | − | 0.0384746i | \(-0.0122499\pi\) |
−0.532950 | + | 0.846147i | \(0.678917\pi\) | |||||||
\(68\) | 7.00000 | + | 12.1244i | 0.848875 | + | 1.47029i | ||||
\(69\) | −3.88448 | + | 6.72812i | −0.467637 | + | 0.809971i | ||||
\(70\) | −0.224361 | −0.0268162 | ||||||||
\(71\) | −3.65679 | + | 6.33374i | −0.433981 | + | 0.751677i | −0.997212 | − | 0.0746227i | \(-0.976225\pi\) |
0.563231 | + | 0.826299i | \(0.309558\pi\) | |||||||
\(72\) | −0.660123 | + | 1.14337i | −0.0777963 | + | 0.134747i | ||||
\(73\) | 8.01963 | 0.938627 | 0.469313 | − | 0.883032i | \(-0.344501\pi\) | ||||
0.469313 | + | 0.883032i | \(0.344501\pi\) | |||||||
\(74\) | 1.66012 | − | 2.87542i | 0.192985 | − | 0.334261i | ||||
\(75\) | 0.500000 | + | 0.866025i | 0.0577350 | + | 0.100000i | ||||
\(76\) | 0.108844 | + | 0.188524i | 0.0124853 | + | 0.0216252i | ||||
\(77\) | 0.448721 | 0.0511365 | ||||||||
\(78\) | 0.567573 | + | 1.08608i | 0.0642650 | + | 0.122974i | ||||
\(79\) | 9.97370 | 1.12213 | 0.561064 | − | 0.827772i | \(-0.310392\pi\) | ||||
0.561064 | + | 0.827772i | \(0.310392\pi\) | |||||||
\(80\) | −1.66012 | − | 2.87542i | −0.185607 | − | 0.321481i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0.717881 | − | 1.24341i | 0.0792767 | − | 0.137311i | ||||
\(83\) | 1.76897 | 0.194169 | 0.0970847 | − | 0.995276i | \(-0.469048\pi\) | ||||
0.0970847 | + | 0.995276i | \(0.469048\pi\) | |||||||
\(84\) | −0.621996 | + | 1.07733i | −0.0678653 | + | 0.117546i | ||||
\(85\) | −3.71455 | + | 6.43378i | −0.402899 | + | 0.697842i | ||||
\(86\) | 0.185099 | 0.0199598 | ||||||||
\(87\) | 2.77230 | − | 4.80177i | 0.297222 | − | 0.514804i | ||||
\(88\) | −0.448721 | − | 0.777208i | −0.0478338 | − | 0.0828506i | ||||
\(89\) | −6.77230 | − | 11.7300i | −0.717863 | − | 1.24337i | −0.961845 | − | 0.273595i | \(-0.911787\pi\) |
0.243982 | − | 0.969780i | \(-0.421546\pi\) | |||||||
\(90\) | −0.339877 | −0.0358262 | ||||||||
\(91\) | 1.10236 | + | 2.10943i | 0.115559 | + | 0.221129i | ||||
\(92\) | 14.6405 | 1.52638 | ||||||||
\(93\) | −4.98685 | − | 8.63748i | −0.517112 | − | 0.895664i | ||||
\(94\) | −0.853028 | − | 1.47749i | −0.0879831 | − | 0.152391i | ||||
\(95\) | −0.0577581 | + | 0.100040i | −0.00592586 | + | 0.0102639i | ||||
\(96\) | 3.76897 | 0.384669 | ||||||||
\(97\) | −4.95206 | + | 8.57721i | −0.502805 | + | 0.870884i | 0.497190 | + | 0.867642i | \(0.334365\pi\) |
−0.999995 | + | 0.00324223i | \(0.998968\pi\) | |||||||
\(98\) | −1.11552 | + | 1.93213i | −0.112684 | + | 0.195175i | ||||
\(99\) | 0.679754 | 0.0683178 | ||||||||
\(100\) | 0.942242 | − | 1.63201i | 0.0942242 | − | 0.163201i | ||||
\(101\) | 4.67975 | + | 8.10557i | 0.465653 | + | 0.806534i | 0.999231 | − | 0.0392165i | \(-0.0124862\pi\) |
−0.533578 | + | 0.845751i | \(0.679153\pi\) | |||||||
\(102\) | −1.26249 | − | 2.18669i | −0.125005 | − | 0.216515i | ||||
\(103\) | 4.50535 | 0.443925 | 0.221962 | − | 0.975055i | \(-0.428754\pi\) | ||||
0.221962 | + | 0.975055i | \(0.428754\pi\) | |||||||
\(104\) | 2.55128 | − | 4.01878i | 0.250173 | − | 0.394074i | ||||
\(105\) | −0.660123 | −0.0644214 | ||||||||
\(106\) | 0.115516 | + | 0.200080i | 0.0112199 | + | 0.0194335i | ||||
\(107\) | −0.285455 | − | 0.494422i | −0.0275960 | − | 0.0477976i | 0.851898 | − | 0.523708i | \(-0.175452\pi\) |
−0.879494 | + | 0.475911i | \(0.842119\pi\) | |||||||
\(108\) | −0.942242 | + | 1.63201i | −0.0906673 | + | 0.157040i | ||||
\(109\) | 15.4095 | 1.47596 | 0.737979 | − | 0.674823i | \(-0.235780\pi\) | ||||
0.737979 | + | 0.674823i | \(0.235780\pi\) | |||||||
\(110\) | 0.115516 | − | 0.200080i | 0.0110140 | − | 0.0190769i | ||||
\(111\) | 4.88448 | − | 8.46017i | 0.463615 | − | 0.803004i | ||||
\(112\) | 2.19177 | 0.207103 | ||||||||
\(113\) | 2.66012 | − | 4.60747i | 0.250243 | − | 0.433434i | −0.713349 | − | 0.700809i | \(-0.752823\pi\) |
0.963593 | + | 0.267374i | \(0.0861560\pi\) | |||||||
\(114\) | −0.0196307 | − | 0.0340013i | −0.00183858 | − | 0.00318451i | ||||
\(115\) | 3.88448 | + | 6.72812i | 0.362230 | + | 0.627401i | ||||
\(116\) | −10.4487 | −0.970139 | ||||||||
\(117\) | 1.66994 | + | 3.19551i | 0.154386 | + | 0.295425i | ||||
\(118\) | −0.756009 | −0.0695962 | ||||||||
\(119\) | −2.45206 | − | 4.24709i | −0.224780 | − | 0.389330i | ||||
\(120\) | 0.660123 | + | 1.14337i | 0.0602607 | + | 0.104375i | ||||
\(121\) | 5.26897 | − | 9.12612i | 0.478997 | − | 0.829647i | ||||
\(122\) | 1.42909 | 0.129384 | ||||||||
\(123\) | 2.11218 | − | 3.65840i | 0.190449 | − | 0.329867i | ||||
\(124\) | −9.39764 | + | 16.2772i | −0.843933 | + | 1.46173i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0.112180 | − | 0.194302i | 0.00999381 | − | 0.0173098i | ||||
\(127\) | 6.00982 | + | 10.4093i | 0.533285 | + | 0.923676i | 0.999244 | + | 0.0388704i | \(0.0123759\pi\) |
−0.465959 | + | 0.884806i | \(0.654291\pi\) | |||||||
\(128\) | −4.67975 | − | 8.10557i | −0.413636 | − | 0.716438i | ||||
\(129\) | 0.544607 | 0.0479500 | ||||||||
\(130\) | 1.22436 | + | 0.0515075i | 0.107384 | + | 0.00451751i | ||||
\(131\) | 10.9041 | 0.952697 | 0.476348 | − | 0.879257i | \(-0.341960\pi\) | ||||
0.476348 | + | 0.879257i | \(0.341960\pi\) | |||||||
\(132\) | −0.640492 | − | 1.10937i | −0.0557477 | − | 0.0965579i | ||||
\(133\) | −0.0381275 | − | 0.0660387i | −0.00330607 | − | 0.00572629i | ||||
\(134\) | −1.29728 | + | 2.24695i | −0.112068 | + | 0.194107i | ||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −4.90411 | + | 8.49418i | −0.420524 | + | 0.728370i | ||||
\(137\) | −1.69491 | + | 2.93568i | −0.144806 | + | 0.250812i | −0.929301 | − | 0.369324i | \(-0.879589\pi\) |
0.784494 | + | 0.620136i | \(0.212923\pi\) | |||||||
\(138\) | −2.64049 | −0.224774 | ||||||||
\(139\) | −7.40411 | + | 12.8243i | −0.628009 | + | 1.08774i | 0.359942 | + | 0.932975i | \(0.382796\pi\) |
−0.987951 | + | 0.154768i | \(0.950537\pi\) | |||||||
\(140\) | 0.621996 | + | 1.07733i | 0.0525682 | + | 0.0910508i | ||||
\(141\) | −2.50982 | − | 4.34713i | −0.211365 | − | 0.366094i | ||||
\(142\) | −2.48571 | −0.208597 | ||||||||
\(143\) | −2.44872 | − | 0.103015i | −0.204772 | − | 0.00861455i | ||||
\(144\) | 3.32025 | 0.276687 | ||||||||
\(145\) | −2.77230 | − | 4.80177i | −0.230227 | − | 0.398765i | ||||
\(146\) | 1.36284 | + | 2.36051i | 0.112790 | + | 0.195358i | ||||
\(147\) | −3.28212 | + | 5.68480i | −0.270705 | + | 0.468874i | ||||
\(148\) | −18.4095 | −1.51325 | ||||||||
\(149\) | 8.54461 | − | 14.7997i | 0.700001 | − | 1.21244i | −0.268464 | − | 0.963290i | \(-0.586516\pi\) |
0.968465 | − | 0.249148i | \(-0.0801507\pi\) | |||||||
\(150\) | −0.169938 | + | 0.294342i | −0.0138754 | + | 0.0240329i | ||||
\(151\) | 13.0130 | 1.05898 | 0.529490 | − | 0.848316i | \(-0.322383\pi\) | ||||
0.529490 | + | 0.848316i | \(0.322383\pi\) | |||||||
\(152\) | −0.0762550 | + | 0.132077i | −0.00618510 | + | 0.0107129i | ||||
\(153\) | −3.71455 | − | 6.43378i | −0.300303 | − | 0.520140i | ||||
\(154\) | 0.0762550 | + | 0.132077i | 0.00614480 | + | 0.0106431i | ||||
\(155\) | −9.97370 | −0.801107 | ||||||||
\(156\) | 3.64163 | − | 5.73630i | 0.291563 | − | 0.459272i | ||||
\(157\) | −0.775639 | −0.0619028 | −0.0309514 | − | 0.999521i | \(-0.509854\pi\) | ||||
−0.0309514 | + | 0.999521i | \(0.509854\pi\) | |||||||
\(158\) | 1.69491 | + | 2.93568i | 0.134840 | + | 0.233550i | ||||
\(159\) | 0.339877 | + | 0.588684i | 0.0269540 | + | 0.0466857i | ||||
\(160\) | 1.88448 | − | 3.26402i | 0.148982 | − | 0.258044i | ||||
\(161\) | −5.12847 | −0.404180 | ||||||||
\(162\) | 0.169938 | − | 0.294342i | 0.0133516 | − | 0.0231257i | ||||
\(163\) | −6.09903 | + | 10.5638i | −0.477713 | + | 0.827423i | −0.999674 | − | 0.0255466i | \(-0.991867\pi\) |
0.521961 | + | 0.852969i | \(0.325201\pi\) | |||||||
\(164\) | −7.96074 | −0.621629 | ||||||||
\(165\) | 0.339877 | − | 0.588684i | 0.0264594 | − | 0.0458290i | ||||
\(166\) | 0.300616 | + | 0.520681i | 0.0233323 | + | 0.0404127i | ||||
\(167\) | 0.795270 | + | 1.37745i | 0.0615398 | + | 0.106590i | 0.895154 | − | 0.445757i | \(-0.147066\pi\) |
−0.833614 | + | 0.552347i | \(0.813732\pi\) | |||||||
\(168\) | −0.871525 | −0.0672396 | ||||||||
\(169\) | −5.53146 | − | 11.7645i | −0.425497 | − | 0.904960i | ||||
\(170\) | −2.52498 | −0.193657 | ||||||||
\(171\) | −0.0577581 | − | 0.100040i | −0.00441688 | − | 0.00765025i | ||||
\(172\) | −0.513151 | − | 0.888804i | −0.0391274 | − | 0.0677707i | ||||
\(173\) | −6.37467 | + | 11.0412i | −0.484657 | + | 0.839451i | −0.999845 | − | 0.0176268i | \(-0.994389\pi\) |
0.515188 | + | 0.857077i | \(0.327722\pi\) | |||||||
\(174\) | 1.88448 | 0.142862 | ||||||||
\(175\) | −0.330062 | + | 0.571683i | −0.0249503 | + | 0.0432152i | ||||
\(176\) | −1.12847 | + | 1.95458i | −0.0850620 | + | 0.147332i | ||||
\(177\) | −2.22436 | −0.167193 | ||||||||
\(178\) | 2.30175 | − | 3.98675i | 0.172523 | − | 0.298819i | ||||
\(179\) | −8.88115 | − | 15.3826i | −0.663808 | − | 1.14975i | −0.979607 | − | 0.200923i | \(-0.935606\pi\) |
0.315799 | − | 0.948826i | \(-0.397728\pi\) | |||||||
\(180\) | 0.942242 | + | 1.63201i | 0.0702306 | + | 0.121643i | ||||
\(181\) | 7.02630 | 0.522261 | 0.261130 | − | 0.965304i | \(-0.415905\pi\) | ||||
0.261130 | + | 0.965304i | \(0.415905\pi\) | |||||||
\(182\) | −0.433560 | + | 0.682946i | −0.0321376 | + | 0.0506233i | ||||
\(183\) | 4.20473 | 0.310823 | ||||||||
\(184\) | 5.12847 | + | 8.88278i | 0.378076 | + | 0.654847i | ||||
\(185\) | −4.88448 | − | 8.46017i | −0.359114 | − | 0.622004i | ||||
\(186\) | 1.69491 | − | 2.93568i | 0.124277 | − | 0.215254i | ||||
\(187\) | 5.04995 | 0.369289 | ||||||||
\(188\) | −4.72971 | + | 8.19209i | −0.344949 | + | 0.597470i | ||||
\(189\) | 0.330062 | − | 0.571683i | 0.0240084 | − | 0.0415838i | ||||
\(190\) | −0.0392613 | −0.00284832 | ||||||||
\(191\) | 6.97703 | − | 12.0846i | 0.504840 | − | 0.874409i | −0.495144 | − | 0.868811i | \(-0.664885\pi\) |
0.999984 | − | 0.00559828i | \(-0.00178200\pi\) | |||||||
\(192\) | −2.67975 | − | 4.64147i | −0.193395 | − | 0.334969i | ||||
\(193\) | −11.8747 | − | 20.5675i | −0.854757 | − | 1.48048i | −0.876870 | − | 0.480728i | \(-0.840373\pi\) |
0.0221126 | − | 0.999755i | \(-0.492961\pi\) | |||||||
\(194\) | −3.36618 | −0.241678 | ||||||||
\(195\) | 3.60236 | + | 0.151548i | 0.257971 | + | 0.0108525i | ||||
\(196\) | 12.3702 | 0.883586 | ||||||||
\(197\) | −7.90411 | − | 13.6903i | −0.563145 | − | 0.975395i | −0.997220 | − | 0.0745186i | \(-0.976258\pi\) |
0.434075 | − | 0.900877i | \(-0.357075\pi\) | |||||||
\(198\) | 0.115516 | + | 0.200080i | 0.00820939 | + | 0.0142191i | ||||
\(199\) | −4.38448 | + | 7.59415i | −0.310808 | + | 0.538335i | −0.978537 | − | 0.206069i | \(-0.933933\pi\) |
0.667730 | + | 0.744404i | \(0.267266\pi\) | |||||||
\(200\) | 1.32025 | 0.0933555 | ||||||||
\(201\) | −3.81691 | + | 6.61108i | −0.269224 | + | 0.466310i | ||||
\(202\) | −1.59054 | + | 2.75490i | −0.111910 | + | 0.193834i | ||||
\(203\) | 3.66012 | 0.256890 | ||||||||
\(204\) | −7.00000 | + | 12.1244i | −0.490098 | + | 0.848875i | ||||
\(205\) | −2.11218 | − | 3.65840i | −0.147521 | − | 0.255514i | ||||
\(206\) | 0.765631 | + | 1.32611i | 0.0533441 | + | 0.0923946i | ||||
\(207\) | −7.76897 | −0.539981 | ||||||||
\(208\) | −11.9607 | − | 0.503175i | −0.829328 | − | 0.0348889i | ||||
\(209\) | 0.0785226 | 0.00543152 | ||||||||
\(210\) | −0.112180 | − | 0.194302i | −0.00774118 | − | 0.0134081i | ||||
\(211\) | −4.40411 | − | 7.62815i | −0.303192 | − | 0.525143i | 0.673665 | − | 0.739037i | \(-0.264719\pi\) |
−0.976857 | + | 0.213893i | \(0.931386\pi\) | |||||||
\(212\) | 0.640492 | − | 1.10937i | 0.0439892 | − | 0.0761915i | ||||
\(213\) | −7.31357 | −0.501118 | ||||||||
\(214\) | 0.0970195 | − | 0.168043i | 0.00663211 | − | 0.0114872i | ||||
\(215\) | 0.272303 | − | 0.471643i | 0.0185709 | − | 0.0321658i | ||||
\(216\) | −1.32025 | −0.0898314 | ||||||||
\(217\) | 3.29193 | − | 5.70180i | 0.223471 | − | 0.387063i | ||||
\(218\) | 2.61866 | + | 4.53565i | 0.177358 | + | 0.307193i | ||||
\(219\) | 4.00982 | + | 6.94520i | 0.270958 | + | 0.469313i | ||||
\(220\) | −1.28098 | −0.0863640 | ||||||||
\(221\) | 12.4061 | + | 23.7398i | 0.834526 | + | 1.59691i | ||||
\(222\) | 3.32025 | 0.222840 | ||||||||
\(223\) | −5.01963 | − | 8.69426i | −0.336139 | − | 0.582210i | 0.647564 | − | 0.762011i | \(-0.275788\pi\) |
−0.983703 | + | 0.179801i | \(0.942455\pi\) | |||||||
\(224\) | 1.24399 | + | 2.15466i | 0.0831177 | + | 0.143964i | ||||
\(225\) | −0.500000 | + | 0.866025i | −0.0333333 | + | 0.0577350i | ||||
\(226\) | 1.80823 | 0.120282 | ||||||||
\(227\) | −0.605701 | + | 1.04910i | −0.0402018 | + | 0.0696315i | −0.885426 | − | 0.464780i | \(-0.846133\pi\) |
0.845224 | + | 0.534412i | \(0.179467\pi\) | |||||||
\(228\) | −0.108844 | + | 0.188524i | −0.00720839 | + | 0.0124853i | ||||
\(229\) | 19.2440 | 1.27168 | 0.635839 | − | 0.771821i | \(-0.280654\pi\) | ||||
0.635839 | + | 0.771821i | \(0.280654\pi\) | |||||||
\(230\) | −1.32025 | + | 2.28673i | −0.0870545 | + | 0.150783i | ||||
\(231\) | 0.224361 | + | 0.388604i | 0.0147618 | + | 0.0255683i | ||||
\(232\) | −3.66012 | − | 6.33952i | −0.240299 | − | 0.416210i | ||||
\(233\) | −23.9081 | −1.56627 | −0.783137 | − | 0.621849i | \(-0.786382\pi\) | ||||
−0.783137 | + | 0.621849i | \(0.786382\pi\) | |||||||
\(234\) | −0.656787 | + | 1.03457i | −0.0429355 | + | 0.0676322i | ||||
\(235\) | −5.01963 | −0.327445 | ||||||||
\(236\) | 2.09589 | + | 3.63018i | 0.136431 | + | 0.236305i | ||||
\(237\) | 4.98685 | + | 8.63748i | 0.323931 | + | 0.561064i | ||||
\(238\) | 0.833398 | − | 1.44349i | 0.0540211 | − | 0.0935674i | ||||
\(239\) | 18.6798 | 1.20829 | 0.604146 | − | 0.796873i | \(-0.293514\pi\) | ||||
0.604146 | + | 0.796873i | \(0.293514\pi\) | |||||||
\(240\) | 1.66012 | − | 2.87542i | 0.107160 | − | 0.185607i | ||||
\(241\) | −3.05776 | + | 5.29619i | −0.196968 | + | 0.341158i | −0.947544 | − | 0.319626i | \(-0.896443\pi\) |
0.750576 | + | 0.660784i | \(0.229776\pi\) | |||||||
\(242\) | 3.58160 | 0.230234 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −3.96187 | − | 6.86216i | −0.253633 | − | 0.439305i | ||||
\(245\) | 3.28212 | + | 5.68480i | 0.209687 | + | 0.363188i | ||||
\(246\) | 1.43576 | 0.0915409 | ||||||||
\(247\) | 0.192905 | + | 0.369134i | 0.0122743 | + | 0.0234874i | ||||
\(248\) | −13.1677 | −0.836152 | ||||||||
\(249\) | 0.884484 | + | 1.53197i | 0.0560519 | + | 0.0970847i | ||||
\(250\) | 0.169938 | + | 0.294342i | 0.0107479 | + | 0.0186158i | ||||
\(251\) | −1.67975 | + | 2.90942i | −0.106025 | + | 0.183641i | −0.914157 | − | 0.405361i | \(-0.867146\pi\) |
0.808131 | + | 0.589002i | \(0.200479\pi\) | |||||||
\(252\) | −1.24399 | −0.0783641 | ||||||||
\(253\) | 2.64049 | − | 4.57347i | 0.166006 | − | 0.287531i | ||||
\(254\) | −2.04260 | + | 3.53788i | −0.128164 | + | 0.221986i | ||||
\(255\) | −7.42909 | −0.465228 | ||||||||
\(256\) | −3.76897 | + | 6.52804i | −0.235560 | + | 0.408003i | ||||
\(257\) | 5.05442 | + | 8.75452i | 0.315286 | + | 0.546092i | 0.979498 | − | 0.201452i | \(-0.0645662\pi\) |
−0.664212 | + | 0.747544i | \(0.731233\pi\) | |||||||
\(258\) | 0.0925496 | + | 0.160301i | 0.00576189 | + | 0.00997988i | ||||
\(259\) | 6.44872 | 0.400704 | ||||||||
\(260\) | −3.14697 | − | 6.02189i | −0.195167 | − | 0.373462i | ||||
\(261\) | 5.54461 | 0.343203 | ||||||||
\(262\) | 1.85303 | + | 3.20954i | 0.114480 | + | 0.198286i | ||||
\(263\) | 11.2592 | + | 19.5014i | 0.694269 | + | 1.20251i | 0.970426 | + | 0.241397i | \(0.0776056\pi\) |
−0.276157 | + | 0.961112i | \(0.589061\pi\) | |||||||
\(264\) | 0.448721 | − | 0.777208i | 0.0276169 | − | 0.0478338i | ||||
\(265\) | 0.679754 | 0.0417569 | ||||||||
\(266\) | 0.0129587 | − | 0.0224450i | 0.000794546 | − | 0.00137619i | ||||
\(267\) | 6.77230 | − | 11.7300i | 0.414458 | − | 0.717863i | ||||
\(268\) | 14.3858 | 0.878753 | ||||||||
\(269\) | −4.24733 | + | 7.35659i | −0.258964 | + | 0.448539i | −0.965965 | − | 0.258674i | \(-0.916714\pi\) |
0.707001 | + | 0.707213i | \(0.250048\pi\) | |||||||
\(270\) | −0.169938 | − | 0.294342i | −0.0103421 | − | 0.0179131i | ||||
\(271\) | −4.68510 | − | 8.11483i | −0.284600 | − | 0.492941i | 0.687912 | − | 0.725794i | \(-0.258527\pi\) |
−0.972512 | + | 0.232853i | \(0.925194\pi\) | |||||||
\(272\) | 24.6664 | 1.49562 | ||||||||
\(273\) | −1.27564 | + | 2.00939i | −0.0772052 | + | 0.121614i | ||||
\(274\) | −1.15212 | −0.0696024 | ||||||||
\(275\) | −0.339877 | − | 0.588684i | −0.0204953 | − | 0.0354990i | ||||
\(276\) | 7.32025 | + | 12.6790i | 0.440627 | + | 0.763188i | ||||
\(277\) | −0.359508 | + | 0.622685i | −0.0216007 | + | 0.0374135i | −0.876624 | − | 0.481177i | \(-0.840210\pi\) |
0.855023 | + | 0.518590i | \(0.173543\pi\) | |||||||
\(278\) | −5.03297 | −0.301858 | ||||||||
\(279\) | 4.98685 | − | 8.63748i | 0.298555 | − | 0.517112i | ||||
\(280\) | −0.435763 | + | 0.754763i | −0.0260418 | + | 0.0451057i | ||||
\(281\) | 1.54461 | 0.0921435 | 0.0460718 | − | 0.998938i | \(-0.485330\pi\) | ||||
0.0460718 | + | 0.998938i | \(0.485330\pi\) | |||||||
\(282\) | 0.853028 | − | 1.47749i | 0.0507971 | − | 0.0879831i | ||||
\(283\) | 9.05977 | + | 15.6920i | 0.538547 | + | 0.932791i | 0.998983 | + | 0.0450980i | \(0.0143600\pi\) |
−0.460435 | + | 0.887693i | \(0.652307\pi\) | |||||||
\(284\) | 6.89116 | + | 11.9358i | 0.408915 | + | 0.708261i | ||||
\(285\) | −0.115516 | −0.00684259 | ||||||||
\(286\) | −0.385810 | − | 0.738268i | −0.0228134 | − | 0.0436547i | ||||
\(287\) | 2.78860 | 0.164606 | ||||||||
\(288\) | 1.88448 | + | 3.26402i | 0.111044 | + | 0.192334i | ||||
\(289\) | −19.0957 | − | 33.0747i | −1.12328 | − | 1.94557i | ||||
\(290\) | 0.942242 | − | 1.63201i | 0.0553303 | − | 0.0958350i | ||||
\(291\) | −9.90411 | −0.580589 | ||||||||
\(292\) | 7.55643 | − | 13.0881i | 0.442207 | − | 0.765924i | ||||
\(293\) | 15.2525 | − | 26.4181i | 0.891059 | − | 1.54336i | 0.0524523 | − | 0.998623i | \(-0.483296\pi\) |
0.838607 | − | 0.544737i | \(-0.183370\pi\) | |||||||
\(294\) | −2.23103 | −0.130116 | ||||||||
\(295\) | −1.11218 | + | 1.92635i | −0.0647536 | + | 0.112157i | ||||
\(296\) | −6.44872 | − | 11.1695i | −0.374824 | − | 0.649215i | ||||
\(297\) | 0.339877 | + | 0.588684i | 0.0197217 | + | 0.0341589i | ||||
\(298\) | 5.80823 | 0.336462 | ||||||||
\(299\) | 27.9867 | + | 1.17737i | 1.61851 | + | 0.0680890i | ||||
\(300\) | 1.88448 | 0.108801 | ||||||||
\(301\) | 0.179754 | + | 0.311343i | 0.0103608 | + | 0.0179455i | ||||
\(302\) | 2.21140 | + | 3.83026i | 0.127252 | + | 0.220407i | ||||
\(303\) | −4.67975 | + | 8.10557i | −0.268845 | + | 0.465653i | ||||
\(304\) | 0.383543 | 0.0219977 | ||||||||
\(305\) | 2.10236 | − | 3.64140i | 0.120381 | − | 0.208506i | ||||
\(306\) | 1.26249 | − | 2.18669i | 0.0721716 | − | 0.125005i | ||||
\(307\) | −4.77564 | −0.272560 | −0.136280 | − | 0.990670i | \(-0.543515\pi\) | ||||
−0.136280 | + | 0.990670i | \(0.543515\pi\) | |||||||
\(308\) | 0.422804 | − | 0.732318i | 0.0240915 | − | 0.0417277i | ||||
\(309\) | 2.25267 | + | 3.90174i | 0.128150 | + | 0.221962i | ||||
\(310\) | −1.69491 | − | 2.93568i | −0.0962647 | − | 0.166735i | ||||
\(311\) | 30.5812 | 1.73410 | 0.867051 | − | 0.498220i | \(-0.166013\pi\) | ||||
0.867051 | + | 0.498220i | \(0.166013\pi\) | |||||||
\(312\) | 4.75601 | + | 0.200080i | 0.269256 | + | 0.0113273i | ||||
\(313\) | −26.7230 | −1.51048 | −0.755238 | − | 0.655451i | \(-0.772479\pi\) | ||||
−0.755238 | + | 0.655451i | \(0.772479\pi\) | |||||||
\(314\) | −0.131811 | − | 0.228303i | −0.00743852 | − | 0.0128839i | ||||
\(315\) | −0.330062 | − | 0.571683i | −0.0185969 | − | 0.0322107i | ||||
\(316\) | 9.39764 | − | 16.2772i | 0.528658 | − | 0.915663i | ||||
\(317\) | −20.6271 | −1.15854 | −0.579268 | − | 0.815137i | \(-0.696662\pi\) | ||||
−0.579268 | + | 0.815137i | \(0.696662\pi\) | |||||||
\(318\) | −0.115516 | + | 0.200080i | −0.00647783 | + | 0.0112199i | ||||
\(319\) | −1.88448 | + | 3.26402i | −0.105511 | + | 0.182750i | ||||
\(320\) | −5.35951 | −0.299606 | ||||||||
\(321\) | 0.285455 | − | 0.494422i | 0.0159325 | − | 0.0275960i | ||||
\(322\) | −0.871525 | − | 1.50953i | −0.0485682 | − | 0.0841226i | ||||
\(323\) | −0.429091 | − | 0.743207i | −0.0238752 | − | 0.0413531i | ||||
\(324\) | −1.88448 | −0.104694 | ||||||||
\(325\) | 1.93243 | − | 3.04397i | 0.107192 | − | 0.168849i | ||||
\(326\) | −4.14584 | −0.229617 | ||||||||
\(327\) | 7.70473 | + | 13.3450i | 0.426073 | + | 0.737979i | ||||
\(328\) | −2.78860 | − | 4.82999i | −0.153975 | − | 0.266692i | ||||
\(329\) | 1.65679 | − | 2.86964i | 0.0913416 | − | 0.158208i | ||||
\(330\) | 0.231033 | 0.0127179 | ||||||||
\(331\) | −2.68510 | + | 4.65073i | −0.147586 | + | 0.255627i | −0.930335 | − | 0.366711i | \(-0.880484\pi\) |
0.782749 | + | 0.622338i | \(0.213817\pi\) | |||||||
\(332\) | 1.66680 | − | 2.88697i | 0.0914773 | − | 0.158443i | ||||
\(333\) | 9.76897 | 0.535336 | ||||||||
\(334\) | −0.270294 | + | 0.468163i | −0.0147898 | + | 0.0256167i | ||||
\(335\) | 3.81691 | + | 6.61108i | 0.208540 | + | 0.361202i | ||||
\(336\) | 1.09589 | + | 1.89813i | 0.0597855 | + | 0.103551i | ||||
\(337\) | 28.7623 | 1.56678 | 0.783391 | − | 0.621529i | \(-0.213488\pi\) | ||||
0.783391 | + | 0.621529i | \(0.213488\pi\) | |||||||
\(338\) | 2.52277 | − | 3.62738i | 0.137221 | − | 0.197303i | ||||
\(339\) | 5.32025 | 0.288956 | ||||||||
\(340\) | 7.00000 | + | 12.1244i | 0.379628 | + | 0.657536i | ||||
\(341\) | 3.38983 | + | 5.87136i | 0.183570 | + | 0.317952i | ||||
\(342\) | 0.0196307 | − | 0.0340013i | 0.00106150 | − | 0.00183858i | ||||
\(343\) | −8.95407 | −0.483474 | ||||||||
\(344\) | 0.359508 | − | 0.622685i | 0.0193833 | − | 0.0335729i | ||||
\(345\) | −3.88448 | + | 6.72812i | −0.209134 | + | 0.362230i | ||||
\(346\) | −4.33320 | −0.232955 | ||||||||
\(347\) | −11.1981 | + | 19.3956i | −0.601143 | + | 1.04121i | 0.391505 | + | 0.920176i | \(0.371955\pi\) |
−0.992648 | + | 0.121035i | \(0.961379\pi\) | |||||||
\(348\) | −5.22436 | − | 9.04886i | −0.280055 | − | 0.485070i | ||||
\(349\) | 5.98685 | + | 10.3695i | 0.320469 | + | 0.555068i | 0.980585 | − | 0.196096i | \(-0.0628263\pi\) |
−0.660116 | + | 0.751164i | \(0.729493\pi\) | |||||||
\(350\) | −0.224361 | −0.0119926 | ||||||||
\(351\) | −1.93243 | + | 3.04397i | −0.103145 | + | 0.162475i | ||||
\(352\) | −2.56197 | −0.136553 | ||||||||
\(353\) | 8.51830 | + | 14.7541i | 0.453384 | + | 0.785283i | 0.998594 | − | 0.0530161i | \(-0.0168834\pi\) |
−0.545210 | + | 0.838299i | \(0.683550\pi\) | |||||||
\(354\) | −0.378004 | − | 0.654723i | −0.0200907 | − | 0.0347981i | ||||
\(355\) | −3.65679 | + | 6.33374i | −0.194082 | + | 0.336160i | ||||
\(356\) | −25.5246 | −1.35280 | ||||||||
\(357\) | 2.45206 | − | 4.24709i | 0.129777 | − | 0.224780i | ||||
\(358\) | 3.01850 | − | 5.22819i | 0.159533 | − | 0.276318i | ||||
\(359\) | −35.0825 | −1.85159 | −0.925793 | − | 0.378031i | \(-0.876601\pi\) | ||||
−0.925793 | + | 0.378031i | \(0.876601\pi\) | |||||||
\(360\) | −0.660123 | + | 1.14337i | −0.0347915 | + | 0.0602607i | ||||
\(361\) | 9.49333 | + | 16.4429i | 0.499649 | + | 0.865417i | ||||
\(362\) | 1.19404 | + | 2.06814i | 0.0627573 | + | 0.108699i | ||||
\(363\) | 10.5379 | 0.553098 | ||||||||
\(364\) | 4.48131 | + | 0.188524i | 0.234884 | + | 0.00988133i | ||||
\(365\) | 8.01963 | 0.419767 | ||||||||
\(366\) | 0.714545 | + | 1.23763i | 0.0373499 | + | 0.0646919i | ||||
\(367\) | −10.0413 | − | 17.3920i | −0.524150 | − | 0.907855i | −0.999605 | − | 0.0281143i | \(-0.991050\pi\) |
0.475455 | − | 0.879740i | \(-0.342284\pi\) | |||||||
\(368\) | 12.8974 | − | 22.3390i | 0.672326 | − | 1.16450i | ||||
\(369\) | 4.22436 | 0.219911 | ||||||||
\(370\) | 1.66012 | − | 2.87542i | 0.0863057 | − | 0.149486i | ||||
\(371\) | −0.224361 | + | 0.388604i | −0.0116482 | + | 0.0201753i | ||||
\(372\) | −18.7953 | −0.974489 | ||||||||
\(373\) | 11.7395 | − | 20.3334i | 0.607849 | − | 1.05283i | −0.383745 | − | 0.923439i | \(-0.625366\pi\) |
0.991594 | − | 0.129387i | \(-0.0413009\pi\) | |||||||
\(374\) | 0.858181 | + | 1.48641i | 0.0443755 | + | 0.0768606i | ||||
\(375\) | 0.500000 | + | 0.866025i | 0.0258199 | + | 0.0447214i | ||||
\(376\) | −6.62715 | −0.341769 | ||||||||
\(377\) | −19.9737 | − | 0.840272i | −1.02870 | − | 0.0432762i | ||||
\(378\) | 0.224361 | 0.0115399 | ||||||||
\(379\) | −10.5707 | − | 18.3090i | −0.542981 | − | 0.940471i | −0.998731 | − | 0.0503631i | \(-0.983962\pi\) |
0.455750 | − | 0.890108i | \(-0.349371\pi\) | |||||||
\(380\) | 0.108844 | + | 0.188524i | 0.00558359 | + | 0.00967107i | ||||
\(381\) | −6.00982 | + | 10.4093i | −0.307892 | + | 0.533285i | ||||
\(382\) | 4.74266 | 0.242656 | ||||||||
\(383\) | −0.869323 | + | 1.50571i | −0.0444203 | + | 0.0769383i | −0.887381 | − | 0.461037i | \(-0.847477\pi\) |
0.842960 | + | 0.537976i | \(0.180811\pi\) | |||||||
\(384\) | 4.67975 | − | 8.10557i | 0.238813 | − | 0.413636i | ||||
\(385\) | 0.448721 | 0.0228689 | ||||||||
\(386\) | 4.03593 | − | 6.99043i | 0.205423 | − | 0.355803i | ||||
\(387\) | 0.272303 | + | 0.471643i | 0.0138420 | + | 0.0239750i | ||||
\(388\) | 9.33207 | + | 16.1636i | 0.473764 | + | 0.820584i | ||||
\(389\) | −26.6664 | −1.35204 | −0.676020 | − | 0.736883i | \(-0.736297\pi\) | ||||
−0.676020 | + | 0.736883i | \(0.736297\pi\) | |||||||
\(390\) | 0.567573 | + | 1.08608i | 0.0287402 | + | 0.0549959i | ||||
\(391\) | −57.7164 | −2.91884 | ||||||||
\(392\) | 4.33320 | + | 7.50533i | 0.218860 | + | 0.379076i | ||||
\(393\) | 5.45206 | + | 9.44324i | 0.275020 | + | 0.476348i | ||||
\(394\) | 2.68643 | − | 4.65303i | 0.135340 | − | 0.234416i | ||||
\(395\) | 9.97370 | 0.501831 | ||||||||
\(396\) | 0.640492 | − | 1.10937i | 0.0321860 | − | 0.0557477i | ||||
\(397\) | −7.27230 | + | 12.5960i | −0.364986 | + | 0.632175i | −0.988774 | − | 0.149419i | \(-0.952260\pi\) |
0.623788 | + | 0.781594i | \(0.285593\pi\) | |||||||
\(398\) | −2.98037 | −0.149392 | ||||||||
\(399\) | 0.0381275 | − | 0.0660387i | 0.00190876 | − | 0.00330607i | ||||
\(400\) | −1.66012 | − | 2.87542i | −0.0830062 | − | 0.143771i | ||||
\(401\) | 4.18510 | + | 7.24880i | 0.208994 | + | 0.361988i | 0.951398 | − | 0.307964i | \(-0.0996478\pi\) |
−0.742404 | + | 0.669952i | \(0.766314\pi\) | |||||||
\(402\) | −2.59456 | −0.129405 | ||||||||
\(403\) | −19.2734 | + | 30.3596i | −0.960078 | + | 1.51232i | ||||
\(404\) | 17.6378 | 0.877515 | ||||||||
\(405\) | −0.500000 | − | 0.866025i | −0.0248452 | − | 0.0430331i | ||||
\(406\) | 0.621996 | + | 1.07733i | 0.0308691 | + | 0.0534669i | ||||
\(407\) | −3.32025 | + | 5.75084i | −0.164578 | + | 0.285058i | ||||
\(408\) | −9.80823 | −0.485580 | ||||||||
\(409\) | −8.62734 | + | 14.9430i | −0.426595 | + | 0.738883i | −0.996568 | − | 0.0827798i | \(-0.973620\pi\) |
0.569973 | + | 0.821663i | \(0.306954\pi\) | |||||||
\(410\) | 0.717881 | − | 1.24341i | 0.0354536 | − | 0.0614075i | ||||
\(411\) | −3.38983 | −0.167208 | ||||||||
\(412\) | 4.24513 | − | 7.35277i | 0.209142 | − | 0.362245i | ||||
\(413\) | −0.734176 | − | 1.27163i | −0.0361264 | − | 0.0625728i | ||||
\(414\) | −1.32025 | − | 2.28673i | −0.0648866 | − | 0.112387i | ||||
\(415\) | 1.76897 | 0.0868352 | ||||||||
\(416\) | −6.29394 | − | 12.0438i | −0.308586 | − | 0.590495i | ||||
\(417\) | −14.8082 | −0.725162 | ||||||||
\(418\) | 0.0133440 | + | 0.0231125i | 0.000652677 | + | 0.00113047i | ||||
\(419\) | −6.43243 | − | 11.1413i | −0.314245 | − | 0.544288i | 0.665032 | − | 0.746815i | \(-0.268418\pi\) |
−0.979277 | + | 0.202527i | \(0.935085\pi\) | |||||||
\(420\) | −0.621996 | + | 1.07733i | −0.0303503 | + | 0.0525682i | ||||
\(421\) | 24.5616 | 1.19706 | 0.598529 | − | 0.801101i | \(-0.295752\pi\) | ||||
0.598529 | + | 0.801101i | \(0.295752\pi\) | |||||||
\(422\) | 1.49686 | − | 2.59263i | 0.0728658 | − | 0.126207i | ||||
\(423\) | 2.50982 | − | 4.34713i | 0.122031 | − | 0.211365i | ||||
\(424\) | 0.897442 | 0.0435837 | ||||||||
\(425\) | −3.71455 | + | 6.43378i | −0.180182 | + | 0.312084i | ||||
\(426\) | −1.24286 | − | 2.15269i | −0.0602166 | − | 0.104298i | ||||
\(427\) | 1.38782 | + | 2.40377i | 0.0671613 | + | 0.116327i | ||||
\(428\) | −1.07587 | −0.0520041 | ||||||||
\(429\) | −1.13515 | − | 2.17216i | −0.0548054 | − | 0.104873i | ||||
\(430\) | 0.185099 | 0.00892628 | ||||||||
\(431\) | −12.3898 | − | 21.4598i | −0.596797 | − | 1.03368i | −0.993291 | − | 0.115645i | \(-0.963106\pi\) |
0.396493 | − | 0.918038i | \(-0.370227\pi\) | |||||||
\(432\) | 1.66012 | + | 2.87542i | 0.0798727 | + | 0.138344i | ||||
\(433\) | 7.02945 | − | 12.1754i | 0.337814 | − | 0.585110i | −0.646208 | − | 0.763162i | \(-0.723646\pi\) |
0.984021 | + | 0.178051i | \(0.0569793\pi\) | |||||||
\(434\) | 2.23770 | 0.107413 | ||||||||
\(435\) | 2.77230 | − | 4.80177i | 0.132922 | − | 0.230227i | ||||
\(436\) | 14.5194 | − | 25.1484i | 0.695355 | − | 1.20439i | ||||
\(437\) | −0.897442 | −0.0429305 | ||||||||
\(438\) | −1.36284 | + | 2.36051i | −0.0651192 | + | 0.112790i | ||||
\(439\) | −10.4226 | − | 18.0525i | −0.497444 | − | 0.861598i | 0.502552 | − | 0.864547i | \(-0.332395\pi\) |
−0.999996 | + | 0.00294880i | \(0.999061\pi\) | |||||||
\(440\) | −0.448721 | − | 0.777208i | −0.0213919 | − | 0.0370519i | ||||
\(441\) | −6.56424 | −0.312583 | ||||||||
\(442\) | −4.87933 | + | 7.68594i | −0.232086 | + | 0.365583i | ||||
\(443\) | −11.4291 | −0.543012 | −0.271506 | − | 0.962437i | \(-0.587522\pi\) | ||||
−0.271506 | + | 0.962437i | \(0.587522\pi\) | |||||||
\(444\) | −9.20473 | − | 15.9431i | −0.436837 | − | 0.756624i | ||||
\(445\) | −6.77230 | − | 11.7300i | −0.321038 | − | 0.556054i | ||||
\(446\) | 1.70606 | − | 2.95498i | 0.0807841 | − | 0.139922i | ||||
\(447\) | 17.0892 | 0.808292 | ||||||||
\(448\) | 1.76897 | − | 3.06394i | 0.0835759 | − | 0.144758i | ||||
\(449\) | −12.9541 | + | 22.4371i | −0.611340 | + | 1.05887i | 0.379675 | + | 0.925120i | \(0.376036\pi\) |
−0.991015 | + | 0.133752i | \(0.957297\pi\) | |||||||
\(450\) | −0.339877 | −0.0160220 | ||||||||
\(451\) | −1.43576 | + | 2.48681i | −0.0676074 | + | 0.117099i | ||||
\(452\) | −5.01296 | − | 8.68270i | −0.235790 | − | 0.408400i | ||||
\(453\) | 6.50648 | + | 11.2696i | 0.305701 | + | 0.529490i | ||||
\(454\) | −0.411728 | −0.0193233 | ||||||||
\(455\) | 1.10236 | + | 2.10943i | 0.0516797 | + | 0.0988917i | ||||
\(456\) | −0.152510 | −0.00714193 | ||||||||
\(457\) | −2.95206 | − | 5.11311i | −0.138091 | − | 0.239181i | 0.788683 | − | 0.614800i | \(-0.210763\pi\) |
−0.926774 | + | 0.375619i | \(0.877430\pi\) | |||||||
\(458\) | 3.27029 | + | 5.66432i | 0.152811 | + | 0.264676i | ||||
\(459\) | 3.71455 | − | 6.43378i | 0.173380 | − | 0.300303i | ||||
\(460\) | 14.6405 | 0.682616 | ||||||||
\(461\) | 7.74600 | − | 13.4165i | 0.360767 | − | 0.624867i | −0.627320 | − | 0.778762i | \(-0.715848\pi\) |
0.988087 | + | 0.153894i | \(0.0491815\pi\) | |||||||
\(462\) | −0.0762550 | + | 0.132077i | −0.00354770 | + | 0.00614480i | ||||
\(463\) | 17.4420 | 0.810601 | 0.405300 | − | 0.914184i | \(-0.367167\pi\) | ||||
0.405300 | + | 0.914184i | \(0.367167\pi\) | |||||||
\(464\) | −9.20473 | + | 15.9431i | −0.427319 | + | 0.740138i | ||||
\(465\) | −4.98685 | − | 8.63748i | −0.231260 | − | 0.400553i | ||||
\(466\) | −4.06291 | − | 7.03717i | −0.188211 | − | 0.325991i | ||||
\(467\) | −20.4790 | −0.947657 | −0.473829 | − | 0.880617i | \(-0.657128\pi\) | ||||
−0.473829 | + | 0.880617i | \(0.657128\pi\) | |||||||
\(468\) | 6.78860 | + | 0.285589i | 0.313803 | + | 0.0132014i | ||||
\(469\) | −5.03926 | −0.232691 | ||||||||
\(470\) | −0.853028 | − | 1.47749i | −0.0393473 | − | 0.0681514i | ||||
\(471\) | −0.387820 | − | 0.671723i | −0.0178698 | − | 0.0309514i | ||||
\(472\) | −1.46835 | + | 2.54326i | −0.0675864 | + | 0.117063i | ||||
\(473\) | −0.370199 | −0.0170217 | ||||||||
\(474\) | −1.69491 | + | 2.93568i | −0.0778500 | + | 0.134840i | ||||
\(475\) | −0.0577581 | + | 0.100040i | −0.00265013 | + | 0.00459015i | ||||
\(476\) | −9.24172 | −0.423594 | ||||||||
\(477\) | −0.339877 | + | 0.588684i | −0.0155619 | + | 0.0269540i | ||||
\(478\) | 3.17441 | + | 5.49824i | 0.145194 | + | 0.251483i | ||||
\(479\) | 20.4953 | + | 35.4990i | 0.936456 | + | 1.62199i | 0.772017 | + | 0.635602i | \(0.219248\pi\) |
0.164439 | + | 0.986387i | \(0.447419\pi\) | |||||||
\(480\) | 3.76897 | 0.172029 | ||||||||
\(481\) | −35.1914 | − | 1.48046i | −1.60459 | − | 0.0675033i | ||||
\(482\) | −2.07852 | −0.0946741 | ||||||||
\(483\) | −2.56424 | − | 4.44139i | −0.116677 | − | 0.202090i | ||||
\(484\) | −9.92928 | − | 17.1980i | −0.451331 | − | 0.781728i | ||||
\(485\) | −4.95206 | + | 8.57721i | −0.224861 | + | 0.389471i | ||||
\(486\) | 0.339877 | 0.0154171 | ||||||||
\(487\) | −12.0315 | + | 20.8391i | −0.545197 | + | 0.944309i | 0.453397 | + | 0.891309i | \(0.350212\pi\) |
−0.998594 | + | 0.0530008i | \(0.983121\pi\) | |||||||
\(488\) | 2.77564 | − | 4.80755i | 0.125647 | − | 0.217627i | ||||
\(489\) | −12.1981 | −0.551615 | ||||||||
\(490\) | −1.11552 | + | 1.93213i | −0.0503939 | + | 0.0872848i | ||||
\(491\) | −18.3865 | − | 31.8463i | −0.829771 | − | 1.43721i | −0.898218 | − | 0.439550i | \(-0.855138\pi\) |
0.0684471 | − | 0.997655i | \(-0.478196\pi\) | |||||||
\(492\) | −3.98037 | − | 6.89420i | −0.179449 | − | 0.310815i | ||||
\(493\) | 41.1914 | 1.85517 | ||||||||
\(494\) | −0.0758696 | + | 0.119510i | −0.00341354 | + | 0.00537701i | ||||
\(495\) | 0.679754 | 0.0305527 | ||||||||
\(496\) | 16.5576 | + | 28.6785i | 0.743457 | + | 1.28770i | ||||
\(497\) | −2.41393 | − | 4.18105i | −0.108280 | − | 0.187546i | ||||
\(498\) | −0.300616 | + | 0.520681i | −0.0134709 | + | 0.0233323i | ||||
\(499\) | 34.8212 | 1.55881 | 0.779405 | − | 0.626520i | \(-0.215521\pi\) | ||||
0.779405 | + | 0.626520i | \(0.215521\pi\) | |||||||
\(500\) | 0.942242 | − | 1.63201i | 0.0421383 | − | 0.0729857i | ||||
\(501\) | −0.795270 | + | 1.37745i | −0.0355300 | + | 0.0615398i | ||||
\(502\) | −1.14182 | −0.0509619 | ||||||||
\(503\) | 16.0130 | − | 27.7353i | 0.713983 | − | 1.23665i | −0.249368 | − | 0.968409i | \(-0.580223\pi\) |
0.963351 | − | 0.268245i | \(-0.0864438\pi\) | |||||||
\(504\) | −0.435763 | − | 0.754763i | −0.0194104 | − | 0.0336198i | ||||
\(505\) | 4.67975 | + | 8.10557i | 0.208246 | + | 0.360693i | ||||
\(506\) | 1.79488 | 0.0797924 | ||||||||
\(507\) | 7.42261 | − | 10.6726i | 0.329650 | − | 0.473988i | ||||
\(508\) | 22.6508 | 1.00497 | ||||||||
\(509\) | 20.6731 | + | 35.8068i | 0.916318 | + | 1.58711i | 0.804960 | + | 0.593329i | \(0.202187\pi\) |
0.111359 | + | 0.993780i | \(0.464480\pi\) | |||||||
\(510\) | −1.26249 | − | 2.18669i | −0.0559039 | − | 0.0968284i | ||||
\(511\) | −2.64697 | + | 4.58469i | −0.117095 | + | 0.202815i | ||||
\(512\) | −21.2810 | −0.940496 | ||||||||
\(513\) | 0.0577581 | − | 0.100040i | 0.00255008 | − | 0.00441688i | ||||
\(514\) | −1.71788 | + | 2.97546i | −0.0757725 | + | 0.131242i | ||||
\(515\) | 4.50535 | 0.198529 | ||||||||
\(516\) | 0.513151 | − | 0.888804i | 0.0225902 | − | 0.0391274i | ||||
\(517\) | 1.70606 | + | 2.95498i | 0.0750323 | + | 0.129960i | ||||
\(518\) | 1.09589 | + | 1.89813i | 0.0481505 | + | 0.0833990i | ||||
\(519\) | −12.7493 | −0.559634 | ||||||||
\(520\) | 2.55128 | − | 4.01878i | 0.111881 | − | 0.176235i | ||||
\(521\) | 4.40279 | 0.192890 | 0.0964448 | − | 0.995338i | \(-0.469253\pi\) | ||||
0.0964448 | + | 0.995338i | \(0.469253\pi\) | |||||||
\(522\) | 0.942242 | + | 1.63201i | 0.0412408 | + | 0.0714312i | ||||
\(523\) | 16.2244 | + | 28.1014i | 0.709442 | + | 1.22879i | 0.965064 | + | 0.262013i | \(0.0843862\pi\) |
−0.255623 | + | 0.966777i | \(0.582280\pi\) | |||||||
\(524\) | 10.2743 | − | 17.7956i | 0.448835 | − | 0.777406i | ||||
\(525\) | −0.660123 | −0.0288101 | ||||||||
\(526\) | −3.82673 | + | 6.62808i | −0.166853 | + | 0.288998i | ||||
\(527\) | 37.0478 | − | 64.1686i | 1.61383 | − | 2.79523i | ||||
\(528\) | −2.25695 | −0.0982211 | ||||||||
\(529\) | −18.6784 | + | 32.3520i | −0.812106 | + | 1.40661i | ||||
\(530\) | 0.115516 | + | 0.200080i | 0.00501771 | + | 0.00869092i | ||||
\(531\) | −1.11218 | − | 1.92635i | −0.0482645 | − | 0.0835966i | ||||
\(532\) | −0.143701 | −0.00623024 | ||||||||
\(533\) | −15.2177 | − | 0.640192i | −0.659151 | − | 0.0277298i | ||||
\(534\) | 4.60350 | 0.199213 | ||||||||
\(535\) | −0.285455 | − | 0.494422i | −0.0123413 | − | 0.0213757i | ||||
\(536\) | 5.03926 | + | 8.72826i | 0.217663 | + | 0.377003i | ||||
\(537\) | 8.88115 | − | 15.3826i | 0.383250 | − | 0.663808i | ||||
\(538\) | −2.88714 | −0.124473 | ||||||||
\(539\) | 2.23103 | − | 3.86426i | 0.0960974 | − | 0.166446i | ||||
\(540\) | −0.942242 | + | 1.63201i | −0.0405476 | + | 0.0702306i | ||||
\(541\) | −8.57720 | −0.368762 | −0.184381 | − | 0.982855i | \(-0.559028\pi\) | ||||
−0.184381 | + | 0.982855i | \(0.559028\pi\) | |||||||
\(542\) | 1.59236 | − | 2.75804i | 0.0683976 | − | 0.118468i | ||||
\(543\) | 3.51315 | + | 6.08496i | 0.150764 | + | 0.261130i | ||||
\(544\) | 14.0000 | + | 24.2487i | 0.600245 | + | 1.03965i | ||||
\(545\) | 15.4095 | 0.660069 | ||||||||
\(546\) | −0.808229 | − | 0.0340013i | −0.0345890 | − | 0.00145512i | ||||
\(547\) | −32.4920 | −1.38926 | −0.694629 | − | 0.719368i | \(-0.744431\pi\) | ||||
−0.694629 | + | 0.719368i | \(0.744431\pi\) | |||||||
\(548\) | 3.19404 | + | 5.53224i | 0.136443 | + | 0.236325i | ||||
\(549\) | 2.10236 | + | 3.64140i | 0.0897268 | + | 0.155411i | ||||
\(550\) | 0.115516 | − | 0.200080i | 0.00492563 | − | 0.00853144i | ||||
\(551\) | 0.640492 | 0.0272859 | ||||||||
\(552\) | −5.12847 | + | 8.88278i | −0.218282 | + | 0.378076i | ||||
\(553\) | −3.29193 | + | 5.70180i | −0.139987 | + | 0.242465i | ||||
\(554\) | −0.244377 | −0.0103826 | ||||||||
\(555\) | 4.88448 | − | 8.46017i | 0.207335 | − | 0.359114i | ||||
\(556\) | 13.9529 | + | 24.1672i | 0.591736 | + | 1.02492i | ||||
\(557\) | 20.6075 | + | 35.6933i | 0.873169 | + | 1.51237i | 0.858701 | + | 0.512477i | \(0.171272\pi\) |
0.0144676 | + | 0.999895i | \(0.495395\pi\) | |||||||
\(558\) | 3.38983 | 0.143503 | ||||||||
\(559\) | −0.909460 | − | 1.74030i | −0.0384661 | − | 0.0736068i | ||||
\(560\) | 2.19177 | 0.0926192 | ||||||||
\(561\) | 2.52498 | + | 4.37339i | 0.106605 | + | 0.184645i | ||||
\(562\) | 0.262488 | + | 0.454643i | 0.0110724 | + | 0.0191779i | ||||
\(563\) | 6.08921 | − | 10.5468i | 0.256630 | − | 0.444496i | −0.708707 | − | 0.705503i | \(-0.750721\pi\) |
0.965337 | + | 0.261007i | \(0.0840546\pi\) | |||||||
\(564\) | −9.45941 | −0.398313 | ||||||||
\(565\) | 2.66012 | − | 4.60747i | 0.111912 | − | 0.193838i | ||||
\(566\) | −3.07921 | + | 5.33334i | −0.129429 | + | 0.224177i | ||||
\(567\) | 0.660123 | 0.0277226 | ||||||||
\(568\) | −4.82786 | + | 8.36210i | −0.202572 | + | 0.350866i | ||||
\(569\) | −3.47169 | − | 6.01314i | −0.145541 | − | 0.252084i | 0.784034 | − | 0.620718i | \(-0.213159\pi\) |
−0.929575 | + | 0.368634i | \(0.879826\pi\) | |||||||
\(570\) | −0.0196307 | − | 0.0340013i | −0.000822238 | − | 0.00142416i | ||||
\(571\) | 3.51429 | 0.147068 | 0.0735341 | − | 0.997293i | \(-0.476572\pi\) | ||||
0.0735341 | + | 0.997293i | \(0.476572\pi\) | |||||||
\(572\) | −2.47541 | + | 3.89927i | −0.103502 | + | 0.163037i | ||||
\(573\) | 13.9541 | 0.582939 | ||||||||
\(574\) | 0.473890 | + | 0.820802i | 0.0197798 | + | 0.0342596i | ||||
\(575\) | 3.88448 | + | 6.72812i | 0.161994 | + | 0.280582i | ||||
\(576\) | 2.67975 | − | 4.64147i | 0.111656 | − | 0.193395i | ||||
\(577\) | 3.14182 | 0.130796 | 0.0653978 | − | 0.997859i | \(-0.479168\pi\) | ||||
0.0653978 | + | 0.997859i | \(0.479168\pi\) | |||||||
\(578\) | 6.49018 | − | 11.2413i | 0.269956 | − | 0.467578i | ||||
\(579\) | 11.8747 | − | 20.5675i | 0.493494 | − | 0.854757i | ||||
\(580\) | −10.4487 | −0.433860 | ||||||||
\(581\) | −0.583868 | + | 1.01129i | −0.0242229 | + | 0.0419553i | ||||
\(582\) | −1.68309 | − | 2.91520i | −0.0697663 | − | 0.120839i | ||||
\(583\) | −0.231033 | − | 0.400160i | −0.00956839 | − | 0.0165729i | ||||
\(584\) | 10.5879 | 0.438130 | ||||||||
\(585\) | 1.66994 | + | 3.19551i | 0.0690435 | + | 0.132118i | ||||
\(586\) | 10.3679 | 0.428295 | ||||||||
\(587\) | −18.9889 | − | 32.8897i | −0.783754 | − | 1.35750i | −0.929741 | − | 0.368215i | \(-0.879969\pi\) |
0.145987 | − | 0.989287i | \(-0.453364\pi\) | |||||||
\(588\) | 6.18510 | + | 10.7129i | 0.255069 | + | 0.441793i | ||||
\(589\) | 0.576062 | − | 0.997769i | 0.0237362 | − | 0.0411124i | ||||
\(590\) | −0.756009 | −0.0311244 | ||||||||
\(591\) | 7.90411 | − | 13.6903i | 0.325132 | − | 0.563145i | ||||
\(592\) | −16.2177 | + | 28.0899i | −0.666543 | + | 1.15449i | ||||
\(593\) | 10.4487 | 0.429078 | 0.214539 | − | 0.976715i | \(-0.431175\pi\) | ||||
0.214539 | + | 0.976715i | \(0.431175\pi\) | |||||||
\(594\) | −0.115516 | + | 0.200080i | −0.00473969 | + | 0.00820939i | ||||
\(595\) | −2.45206 | − | 4.24709i | −0.100525 | − | 0.174114i | ||||
\(596\) | −16.1022 | − | 27.8898i | −0.659571 | − | 1.14241i | ||||
\(597\) | −8.76897 | −0.358890 | ||||||||
\(598\) | 4.40946 | + | 8.43773i | 0.180316 | + | 0.345044i | ||||
\(599\) | −45.5705 | −1.86196 | −0.930981 | − | 0.365069i | \(-0.881045\pi\) | ||||
−0.930981 | + | 0.365069i | \(0.881045\pi\) | |||||||
\(600\) | 0.660123 | + | 1.14337i | 0.0269494 | + | 0.0466778i | ||||
\(601\) | 7.39096 | + | 12.8015i | 0.301484 | + | 0.522185i | 0.976472 | − | 0.215643i | \(-0.0691848\pi\) |
−0.674989 | + | 0.737828i | \(0.735851\pi\) | |||||||
\(602\) | −0.0610942 | + | 0.105818i | −0.00249001 | + | 0.00431283i | ||||
\(603\) | −7.63382 | −0.310873 | ||||||||
\(604\) | 12.2614 | − | 21.2373i | 0.498907 | − | 0.864133i | ||||
\(605\) | 5.26897 | − | 9.12612i | 0.214214 | − | 0.371030i | ||||
\(606\) | −3.18108 | −0.129223 | ||||||||
\(607\) | 9.46722 | − | 16.3977i | 0.384263 | − | 0.665562i | −0.607404 | − | 0.794393i | \(-0.707789\pi\) |
0.991667 | + | 0.128831i | \(0.0411224\pi\) | |||||||
\(608\) | 0.217689 | + | 0.377048i | 0.00882844 | + | 0.0152913i | ||||
\(609\) | 1.83006 | + | 3.16976i | 0.0741578 | + | 0.128445i | ||||
\(610\) | 1.42909 | 0.0578622 | ||||||||
\(611\) | −9.70007 | + | 15.2796i | −0.392423 | + | 0.618146i | ||||
\(612\) | −14.0000 | −0.565916 | ||||||||
\(613\) | 1.29193 | + | 2.23770i | 0.0521807 | + | 0.0903797i | 0.890936 | − | 0.454129i | \(-0.150049\pi\) |
−0.838755 | + | 0.544509i | \(0.816716\pi\) | |||||||
\(614\) | −0.811565 | − | 1.40567i | −0.0327521 | − | 0.0567283i | ||||
\(615\) | 2.11218 | − | 3.65840i | 0.0851713 | − | 0.147521i | ||||
\(616\) | 0.592422 | 0.0238694 | ||||||||
\(617\) | −7.01963 | + | 12.1584i | −0.282600 | + | 0.489477i | −0.972024 | − | 0.234880i | \(-0.924530\pi\) |
0.689425 | + | 0.724357i | \(0.257863\pi\) | |||||||
\(618\) | −0.765631 | + | 1.32611i | −0.0307982 | + | 0.0533441i | ||||
\(619\) | −17.8582 | −0.717781 | −0.358890 | − | 0.933380i | \(-0.616845\pi\) | ||||
−0.358890 | + | 0.933380i | \(0.616845\pi\) | |||||||
\(620\) | −9.39764 | + | 16.2772i | −0.377418 | + | 0.653707i | ||||
\(621\) | −3.88448 | − | 6.72812i | −0.155879 | − | 0.269990i | ||||
\(622\) | 5.19692 | + | 9.00134i | 0.208378 | + | 0.360921i | ||||
\(623\) | 8.94111 | 0.358218 | ||||||||
\(624\) | −5.54461 | − | 10.6099i | −0.221962 | − | 0.424736i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −4.54127 | − | 7.86571i | −0.181506 | − | 0.314377i | ||||
\(627\) | 0.0392613 | + | 0.0680026i | 0.00156795 | + | 0.00271576i | ||||
\(628\) | −0.730840 | + | 1.26585i | −0.0291637 | + | 0.0505130i | ||||
\(629\) | 72.5745 | 2.89374 | ||||||||
\(630\) | 0.112180 | − | 0.194302i | 0.00446937 | − | 0.00774118i | ||||
\(631\) | 12.4815 | − | 21.6186i | 0.496881 | − | 0.860623i | −0.503113 | − | 0.864221i | \(-0.667812\pi\) |
0.999994 | + | 0.00359801i | \(0.00114528\pi\) | |||||||
\(632\) | 13.1677 | 0.523784 | ||||||||
\(633\) | 4.40411 | − | 7.62815i | 0.175048 | − | 0.303192i | ||||
\(634\) | −3.50535 | − | 6.07144i | −0.139215 | − | 0.241128i | ||||
\(635\) | 6.00982 | + | 10.4093i | 0.238492 | + | 0.413081i | ||||
\(636\) | 1.28098 | 0.0507944 | ||||||||
\(637\) | 23.6468 | + | 0.994794i | 0.936920 | + | 0.0394152i | ||||
\(638\) | −1.28098 | −0.0507147 | ||||||||
\(639\) | −3.65679 | − | 6.33374i | −0.144660 | − | 0.250559i | ||||
\(640\) | −4.67975 | − | 8.10557i | −0.184984 | − | 0.320401i | ||||
\(641\) | −11.6535 | + | 20.1844i | −0.460284 | + | 0.797235i | −0.998975 | − | 0.0452686i | \(-0.985586\pi\) |
0.538691 | + | 0.842503i | \(0.318919\pi\) | |||||||
\(642\) | 0.194039 | 0.00765811 | ||||||||
\(643\) | −22.7395 | + | 39.3860i | −0.896759 | + | 1.55323i | −0.0651470 | + | 0.997876i | \(0.520752\pi\) |
−0.831612 | + | 0.555357i | \(0.812582\pi\) | |||||||
\(644\) | −4.83226 | + | 8.36973i | −0.190418 | + | 0.329813i | ||||
\(645\) | 0.544607 | 0.0214439 | ||||||||
\(646\) | 0.145838 | − | 0.252599i | 0.00573792 | − | 0.00993836i | ||||
\(647\) | −3.20473 | − | 5.55076i | −0.125991 | − | 0.218223i | 0.796129 | − | 0.605127i | \(-0.206878\pi\) |
−0.922120 | + | 0.386904i | \(0.873544\pi\) | |||||||
\(648\) | −0.660123 | − | 1.14337i | −0.0259321 | − | 0.0449157i | ||||
\(649\) | 1.51202 | 0.0593519 | ||||||||
\(650\) | 1.22436 | + | 0.0515075i | 0.0480234 | + | 0.00202029i | ||||
\(651\) | 6.58387 | 0.258042 | ||||||||
\(652\) | 11.4935 | + | 19.9074i | 0.450121 | + | 0.779632i | ||||
\(653\) | −0.740848 | − | 1.28319i | −0.0289916 | − | 0.0502150i | 0.851166 | − | 0.524897i | \(-0.175896\pi\) |
−0.880157 | + | 0.474682i | \(0.842563\pi\) | |||||||
\(654\) | −2.61866 | + | 4.53565i | −0.102398 | + | 0.177358i | ||||
\(655\) | 10.9041 | 0.426059 | ||||||||
\(656\) | −7.01296 | + | 12.1468i | −0.273810 | + | 0.474253i | ||||
\(657\) | −4.00982 | + | 6.94520i | −0.156438 | + | 0.270958i | ||||
\(658\) | 1.12621 | 0.0439041 | ||||||||
\(659\) | 3.54461 | − | 6.13944i | 0.138078 | − | 0.239159i | −0.788691 | − | 0.614790i | \(-0.789241\pi\) |
0.926769 | + | 0.375631i | \(0.122574\pi\) | |||||||
\(660\) | −0.640492 | − | 1.10937i | −0.0249311 | − | 0.0431820i | ||||
\(661\) | −0.589214 | − | 1.02055i | −0.0229178 | − | 0.0396947i | 0.854339 | − | 0.519716i | \(-0.173962\pi\) |
−0.877257 | + | 0.480021i | \(0.840629\pi\) | |||||||
\(662\) | −1.82521 | −0.0709387 | ||||||||
\(663\) | −14.3562 | + | 22.6139i | −0.557548 | + | 0.878251i | ||||
\(664\) | 2.33547 | 0.0906339 | ||||||||
\(665\) | −0.0381275 | − | 0.0660387i | −0.00147852 | − | 0.00256087i | ||||
\(666\) | 1.66012 | + | 2.87542i | 0.0643285 | + | 0.111420i | ||||
\(667\) | 21.5379 | − | 37.3048i | 0.833952 | − | 1.44445i | ||||
\(668\) | 2.99735 | 0.115971 | ||||||||
\(669\) | 5.01963 | − | 8.69426i | 0.194070 | − | 0.336139i | ||||
\(670\) | −1.29728 | + | 2.24695i | −0.0501183 | + | 0.0868074i | ||||
\(671\) | −2.85818 | −0.110339 | ||||||||
\(672\) | −1.24399 | + | 2.15466i | −0.0479880 | + | 0.0831177i | ||||
\(673\) | −6.77878 | − | 11.7412i | −0.261303 | − | 0.452590i | 0.705286 | − | 0.708923i | \(-0.250819\pi\) |
−0.966588 | + | 0.256334i | \(0.917485\pi\) | |||||||
\(674\) | 4.88782 | + | 8.46595i | 0.188272 | + | 0.326096i | ||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −24.4117 | − | 2.05759i | −0.938913 | − | 0.0791381i | ||||
\(677\) | 9.53793 | 0.366573 | 0.183286 | − | 0.983060i | \(-0.441326\pi\) | ||||
0.183286 | + | 0.983060i | \(0.441326\pi\) | |||||||
\(678\) | 0.904114 | + | 1.56597i | 0.0347223 | + | 0.0601408i | ||||
\(679\) | −3.26897 | − | 5.66202i | −0.125451 | − | 0.217288i | ||||
\(680\) | −4.90411 | + | 8.49418i | −0.188064 | + | 0.325737i | ||||
\(681\) | −1.21140 | −0.0464210 | ||||||||
\(682\) | −1.15212 | + | 1.99554i | −0.0441171 | + | 0.0764131i | ||||
\(683\) | 22.2592 | − | 38.5540i | 0.851723 | − | 1.47523i | −0.0279296 | − | 0.999610i | \(-0.508891\pi\) |
0.879652 | − | 0.475617i | \(-0.157775\pi\) | |||||||
\(684\) | −0.217689 | −0.00832353 | ||||||||
\(685\) | −1.69491 | + | 2.93568i | −0.0647594 | + | 0.112166i | ||||
\(686\) | −1.52164 | − | 2.63556i | −0.0580965 | − | 0.100626i | ||||
\(687\) | 9.62200 | + | 16.6658i | 0.367102 | + | 0.635839i | ||||
\(688\) | −1.80823 | −0.0689381 | ||||||||
\(689\) | 1.31357 | − | 2.06915i | 0.0500432 | − | 0.0788282i | ||||
\(690\) | −2.64049 | −0.100522 | ||||||||
\(691\) | 2.64030 | + | 4.57313i | 0.100442 | + | 0.173970i | 0.911867 | − | 0.410486i | \(-0.134641\pi\) |
−0.811425 | + | 0.584457i | \(0.801308\pi\) | |||||||
\(692\) | 12.0130 | + | 20.8071i | 0.456664 | + | 0.790966i | ||||
\(693\) | −0.224361 | + | 0.388604i | −0.00852275 | + | 0.0147618i | ||||
\(694\) | −7.61192 | −0.288945 | ||||||||
\(695\) | −7.40411 | + | 12.8243i | −0.280854 | + | 0.486454i | ||||
\(696\) | 3.66012 | − | 6.33952i | 0.138737 | − | 0.240299i | ||||
\(697\) | 31.3832 | 1.18872 | ||||||||
\(698\) | −2.03479 | + | 3.52436i | −0.0770180 | + | 0.133399i | ||||
\(699\) | −11.9541 | − | 20.7051i | −0.452144 | − | 0.783137i | ||||
\(700\) | 0.621996 | + | 1.07733i | 0.0235092 | + | 0.0407192i | ||||
\(701\) | 20.1392 | 0.760646 | 0.380323 | − | 0.924854i | \(-0.375813\pi\) | ||||
0.380323 | + | 0.924854i | \(0.375813\pi\) | |||||||
\(702\) | −1.22436 | − | 0.0515075i | −0.0462105 | − | 0.00194403i | ||||
\(703\) | 1.12847 | 0.0425612 | ||||||||
\(704\) | 1.82157 | + | 3.15506i | 0.0686531 | + | 0.118911i | ||||
\(705\) | −2.50982 | − | 4.34713i | −0.0945251 | − | 0.163722i | ||||
\(706\) | −2.89517 | + | 5.01459i | −0.108961 | + | 0.188727i | ||||
\(707\) | −6.17843 | −0.232364 | ||||||||
\(708\) | −2.09589 | + | 3.63018i | −0.0787682 | + | 0.136431i | ||||
\(709\) | −0.770294 | + | 1.33419i | −0.0289290 | + | 0.0501065i | −0.880127 | − | 0.474737i | \(-0.842543\pi\) |
0.851198 | + | 0.524844i | \(0.175876\pi\) | |||||||
\(710\) | −2.48571 | −0.0932872 | ||||||||
\(711\) | −4.98685 | + | 8.63748i | −0.187021 | + | 0.323931i | ||||
\(712\) | −8.94111 | − | 15.4865i | −0.335082 | − | 0.580379i | ||||
\(713\) | −38.7427 | − | 67.1043i | −1.45092 | − | 2.51307i | ||||
\(714\) | 1.66680 | 0.0623782 | ||||||||
\(715\) | −2.44872 | − | 0.103015i | −0.0915770 | − | 0.00385254i | ||||
\(716\) | −33.4728 | −1.25094 | ||||||||
\(717\) | 9.33988 | + | 16.1771i | 0.348804 | + | 0.604146i | ||||
\(718\) | −5.96187 | − | 10.3263i | −0.222495 | − | 0.385373i | ||||
\(719\) | −18.5020 | + | 32.0464i | −0.690009 | + | 1.19513i | 0.281826 | + | 0.959466i | \(0.409060\pi\) |
−0.971835 | + | 0.235664i | \(0.924273\pi\) | |||||||
\(720\) | 3.32025 | 0.123738 | ||||||||
\(721\) | −1.48704 | + | 2.57563i | −0.0553803 | + | 0.0959215i | ||||
\(722\) | −3.22656 | + | 5.58857i | −0.120080 | + | 0.207985i | ||||
\(723\) | −6.11552 | −0.227438 | ||||||||
\(724\) | 6.62048 | − | 11.4670i | 0.246048 | − | 0.426168i | ||||
\(725\) | −2.77230 | − | 4.80177i | −0.102961 | − | 0.178333i | ||||
\(726\) | 1.79080 | + | 3.10176i | 0.0664628 | + | 0.115117i | ||||
\(727\) | −44.9015 | −1.66530 | −0.832652 | − | 0.553797i | \(-0.813178\pi\) | ||||
−0.832652 | + | 0.553797i | \(0.813178\pi\) | |||||||
\(728\) | 1.45539 | + | 2.78497i | 0.0539405 | + | 0.103218i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.36284 | + | 2.36051i | 0.0504411 | + | 0.0873666i | ||||
\(731\) | 2.02297 | + | 3.50388i | 0.0748221 | + | 0.129596i | ||||
\(732\) | 3.96187 | − | 6.86216i | 0.146435 | − | 0.253633i | ||||
\(733\) | −4.94072 | −0.182490 | −0.0912449 | − | 0.995828i | \(-0.529085\pi\) | ||||
−0.0912449 | + | 0.995828i | \(0.529085\pi\) | |||||||
\(734\) | 3.41280 | − | 5.91114i | 0.125969 | − | 0.218184i | ||||
\(735\) | −3.28212 | + | 5.68480i | −0.121063 | + | 0.209687i | ||||
\(736\) | 29.2810 | 1.07931 | ||||||||
\(737\) | 2.59456 | − | 4.49391i | 0.0955718 | − | 0.165535i | ||||
\(738\) | 0.717881 | + | 1.24341i | 0.0264256 | + | 0.0457704i | ||||
\(739\) | −3.01963 | − | 5.23015i | −0.111079 | − | 0.192394i | 0.805127 | − | 0.593103i | \(-0.202097\pi\) |
−0.916206 | + | 0.400709i | \(0.868764\pi\) | |||||||
\(740\) | −18.4095 | −0.676745 | ||||||||
\(741\) | −0.223227 | + | 0.351628i | −0.00820044 | + | 0.0129174i | ||||
\(742\) | −0.152510 | −0.00559882 | ||||||||
\(743\) | 6.52945 | + | 11.3093i | 0.239542 | + | 0.414899i | 0.960583 | − | 0.277993i | \(-0.0896693\pi\) |
−0.721041 | + | 0.692893i | \(0.756336\pi\) | |||||||
\(744\) | −6.58387 | − | 11.4036i | −0.241376 | − | 0.418076i | ||||
\(745\) | 8.54461 | − | 14.7997i | 0.313050 | − | 0.542219i | ||||
\(746\) | 7.97998 | 0.292168 | ||||||||
\(747\) | −0.884484 | + | 1.53197i | −0.0323616 | + | 0.0560519i | ||||
\(748\) | 4.75828 | − | 8.24158i | 0.173980 | − | 0.301342i | ||||
\(749\) | 0.376871 | 0.0137706 | ||||||||
\(750\) | −0.169938 | + | 0.294342i | −0.00620527 | + | 0.0107479i | ||||
\(751\) | −24.0118 | − | 41.5897i | −0.876204 | − | 1.51763i | −0.855475 | − | 0.517845i | \(-0.826735\pi\) |
−0.0207292 | − | 0.999785i | \(-0.506599\pi\) | |||||||
\(752\) | 8.33320 | + | 14.4335i | 0.303881 | + | 0.526337i | ||||
\(753\) | −3.35951 | −0.122427 | ||||||||
\(754\) | −3.14697 | − | 6.02189i | −0.114606 | − | 0.219304i | ||||
\(755\) | 13.0130 | 0.473590 | ||||||||
\(756\) | −0.621996 | − | 1.07733i | −0.0226218 | − | 0.0391820i | ||||
\(757\) | 2.28212 | + | 3.95275i | 0.0829450 | + | 0.143665i | 0.904514 | − | 0.426445i | \(-0.140234\pi\) |
−0.821569 | + | 0.570110i | \(0.806901\pi\) | |||||||
\(758\) | 3.59274 | − | 6.22281i | 0.130494 | − | 0.226023i | ||||
\(759\) | 5.28098 | 0.191688 | ||||||||
\(760\) | −0.0762550 | + | 0.132077i | −0.00276606 | + | 0.00479095i | ||||
\(761\) | −10.5446 | + | 18.2638i | −0.382242 | + | 0.662062i | −0.991382 | − | 0.131000i | \(-0.958181\pi\) |
0.609141 | + | 0.793062i | \(0.291514\pi\) | |||||||
\(762\) | −4.08519 | −0.147991 | ||||||||
\(763\) | −5.08607 | + | 8.80933i | −0.184128 | + | 0.318919i | ||||
\(764\) | −13.1481 | − | 22.7732i | −0.475682 | − | 0.823905i | ||||
\(765\) | −3.71455 | − | 6.43378i | −0.134300 | − | 0.232614i | ||||
\(766\) | −0.590926 | −0.0213510 | ||||||||
\(767\) | 3.71455 | + | 7.10797i | 0.134124 | + | 0.256654i | ||||
\(768\) | −7.53793 | −0.272002 | ||||||||
\(769\) | −21.1666 | − | 36.6616i | −0.763287 | − | 1.32205i | −0.941147 | − | 0.337996i | \(-0.890251\pi\) |
0.177860 | − | 0.984056i | \(-0.443083\pi\) | |||||||
\(770\) | 0.0762550 | + | 0.132077i | 0.00274804 | + | 0.00475974i | ||||
\(771\) | −5.05442 | + | 8.75452i | −0.182031 | + | 0.315286i | ||||
\(772\) | −44.7552 | −1.61078 | ||||||||
\(773\) | −25.1218 | + | 43.5122i | −0.903568 | + | 1.56503i | −0.0807410 | + | 0.996735i | \(0.525729\pi\) |
−0.822827 | + | 0.568291i | \(0.807605\pi\) | |||||||
\(774\) | −0.0925496 | + | 0.160301i | −0.00332663 | + | 0.00576189i | ||||
\(775\) | −9.97370 | −0.358266 | ||||||||
\(776\) | −6.53793 | + | 11.3240i | −0.234698 | + | 0.406509i | ||||
\(777\) | 3.22436 | + | 5.58476i | 0.115673 | + | 0.200352i | ||||
\(778\) | −4.53165 | − | 7.84904i | −0.162467 | − | 0.281402i | ||||
\(779\) | 0.487982 | 0.0174838 | ||||||||
\(780\) | 3.64163 | − | 5.73630i | 0.130391 | − | 0.205393i | ||||
\(781\) | 4.97143 | 0.177892 | ||||||||
\(782\) | −9.80823 | − | 16.9884i | −0.350742 | − | 0.607502i | ||||
\(783\) | 2.77230 | + | 4.80177i | 0.0990740 | + | 0.171601i | ||||
\(784\) | 10.8974 | − | 18.8749i | 0.389194 | − | 0.674104i | ||||
\(785\) | −0.775639 | −0.0276838 | ||||||||
\(786\) | −1.85303 | + | 3.20954i | −0.0660953 | + | 0.114480i | ||||
\(787\) | 5.29080 | − | 9.16393i | 0.188597 | − | 0.326659i | −0.756186 | − | 0.654357i | \(-0.772939\pi\) |
0.944783 | + | 0.327698i | \(0.106273\pi\) | |||||||
\(788\) | −29.7903 | −1.06124 | ||||||||
\(789\) | −11.2592 | + | 19.5014i | −0.400836 | + | 0.694269i | ||||
\(790\) | 1.69491 | + | 2.93568i | 0.0603024 | + | 0.104447i | ||||
\(791\) | 1.75601 | + | 3.04150i | 0.0624365 | + | 0.108143i | ||||
\(792\) | 0.897442 | 0.0318892 | ||||||||
\(793\) | −7.02164 | − | 13.4363i | −0.249346 | − | 0.477136i | ||||
\(794\) | −4.94338 | −0.175434 | ||||||||
\(795\) | 0.339877 | + | 0.588684i | 0.0120542 | + | 0.0208785i | ||||
\(796\) | 8.26249 | + | 14.3110i | 0.292856 | + | 0.507242i | ||||
\(797\) | 10.0741 | − | 17.4488i | 0.356841 | − | 0.618067i | −0.630590 | − | 0.776116i | \(-0.717187\pi\) |
0.987431 | + | 0.158049i | \(0.0505204\pi\) | |||||||
\(798\) | 0.0259173 | 0.000917463 | ||||||||
\(799\) | 18.6456 | − | 32.2952i | 0.659636 | − | 1.14252i | ||||
\(800\) | 1.88448 | − | 3.26402i | 0.0666266 | − | 0.115401i | ||||
\(801\) | 13.5446 | 0.478575 | ||||||||
\(802\) | −1.42242 | + | 2.46370i | −0.0502273 | + | 0.0869963i | ||||
\(803\) | −2.72569 | − | 4.72103i | −0.0961874 | − | 0.166601i | ||||
\(804\) | 7.19291 | + | 12.4585i | 0.253674 | + | 0.439377i | ||||
\(805\) | −5.12847 | −0.180755 | ||||||||
\(806\) | −12.2114 | − | 0.513720i | −0.430128 | − | 0.0180950i | ||||
\(807\) | −8.49465 | −0.299026 | ||||||||
\(808\) | 6.17843 | + | 10.7013i | 0.217356 | + | 0.376472i | ||||
\(809\) | −6.45539 | − | 11.1811i | −0.226960 | − | 0.393105i | 0.729946 | − | 0.683505i | \(-0.239545\pi\) |
−0.956906 | + | 0.290399i | \(0.906212\pi\) | |||||||
\(810\) | 0.169938 | − | 0.294342i | 0.00597103 | − | 0.0103421i | ||||
\(811\) | −15.8974 | −0.558235 | −0.279117 | − | 0.960257i | \(-0.590042\pi\) | ||||
−0.279117 | + | 0.960257i | \(0.590042\pi\) | |||||||
\(812\) | 3.44872 | − | 5.97336i | 0.121026 | − | 0.209624i | ||||
\(813\) | 4.68510 | − | 8.11483i | 0.164314 | − | 0.284600i | ||||
\(814\) | −2.25695 | −0.0791061 | ||||||||
\(815\) | −6.09903 | + | 10.5638i | −0.213640 | + | 0.370035i | ||||
\(816\) | 12.3332 | + | 21.3617i | 0.431749 | + | 0.747810i | ||||
\(817\) | 0.0314555 | + | 0.0544825i | 0.00110049 | + | 0.00190610i | ||||
\(818\) | −5.86447 | −0.205046 | ||||||||
\(819\) | −2.37800 | − | 0.100040i | −0.0830942 | − | 0.00349568i | ||||
\(820\) | −7.96074 | −0.278001 | ||||||||
\(821\) | 18.6142 | + | 32.2407i | 0.649640 | + | 1.12521i | 0.983209 | + | 0.182483i | \(0.0584136\pi\) |
−0.333569 | + | 0.942726i | \(0.608253\pi\) | |||||||
\(822\) | −0.576062 | − | 0.997769i | −0.0200925 | − | 0.0348012i | ||||
\(823\) | 2.44872 | − | 4.24131i | 0.0853571 | − | 0.147843i | −0.820186 | − | 0.572097i | \(-0.806130\pi\) |
0.905543 | + | 0.424254i | \(0.139464\pi\) | |||||||
\(824\) | 5.94817 | 0.207214 | ||||||||
\(825\) | 0.339877 | − | 0.588684i | 0.0118330 | − | 0.0204953i | ||||
\(826\) | 0.249529 | − | 0.432198i | 0.00868224 | − | 0.0150381i | ||||
\(827\) | 37.6334 | 1.30864 | 0.654321 | − | 0.756217i | \(-0.272954\pi\) | ||||
0.654321 | + | 0.756217i | \(0.272954\pi\) | |||||||
\(828\) | −7.32025 | + | 12.6790i | −0.254396 | + | 0.440627i | ||||
\(829\) | 24.4552 | + | 42.3576i | 0.849364 | + | 1.47114i | 0.881777 | + | 0.471667i | \(0.156348\pi\) |
−0.0324123 | + | 0.999475i | \(0.510319\pi\) | |||||||
\(830\) | 0.300616 | + | 0.520681i | 0.0104345 | + | 0.0180731i | ||||
\(831\) | −0.719015 | −0.0249424 | ||||||||
\(832\) | −10.3569 | + | 16.3142i | −0.359059 | + | 0.565592i | ||||
\(833\) | −48.7663 | −1.68965 | ||||||||
\(834\) | −2.51649 | − | 4.35868i | −0.0871388 | − | 0.150929i | ||||
\(835\) | 0.795270 | + | 1.37745i | 0.0275215 | + | 0.0476686i | ||||
\(836\) | 0.0739873 | − | 0.128150i | 0.00255890 | − | 0.00443215i | ||||
\(837\) | 9.97370 | 0.344741 | ||||||||
\(838\) | 2.18623 | − | 3.78667i | 0.0755222 | − | 0.130808i | ||||
\(839\) | −24.1392 | + | 41.8103i | −0.833377 | + | 1.44345i | 0.0619688 | + | 0.998078i | \(0.480262\pi\) |
−0.895345 | + | 0.445372i | \(0.853071\pi\) | |||||||
\(840\) | −0.871525 | −0.0300705 | ||||||||
\(841\) | −0.871332 | + | 1.50919i | −0.0300459 | + | 0.0520411i | ||||
\(842\) | 4.17396 | + | 7.22951i | 0.143844 | + | 0.249145i | ||||
\(843\) | 0.772303 | + | 1.33767i | 0.0265995 | + | 0.0460718i | ||||
\(844\) | −16.5990 | −0.571360 | ||||||||
\(845\) | −5.53146 | − | 11.7645i | −0.190288 | − | 0.404710i | ||||
\(846\) | 1.70606 | 0.0586554 | ||||||||
\(847\) | 3.47817 | + | 6.02436i | 0.119511 | + | 0.207000i | ||||
\(848\) | −1.12847 | − | 1.95458i | −0.0387520 | − | 0.0671204i | ||||
\(849\) | −9.05977 | + | 15.6920i | −0.310930 | + | 0.538547i | ||||
\(850\) | −2.52498 | −0.0866060 | ||||||||
\(851\) | 37.9474 | − | 65.7268i | 1.30082 | − | 2.25309i | ||||
\(852\) | −6.89116 | + | 11.9358i | −0.236087 | + | 0.408915i | ||||
\(853\) | −14.4291 | −0.494043 | −0.247021 | − | 0.969010i | \(-0.579452\pi\) | ||||
−0.247021 | + | 0.969010i | \(0.579452\pi\) | |||||||
\(854\) | −0.471688 | + | 0.816987i | −0.0161408 | + | 0.0279567i | ||||
\(855\) | −0.0577581 | − | 0.100040i | −0.00197529 | − | 0.00342130i | ||||
\(856\) | −0.376871 | − | 0.652759i | −0.0128812 | − | 0.0223108i | ||||
\(857\) | 3.64678 | 0.124572 | 0.0622858 | − | 0.998058i | \(-0.480161\pi\) | ||||
0.0622858 | + | 0.998058i | \(0.480161\pi\) | |||||||
\(858\) | 0.446454 | − | 0.703255i | 0.0152417 | − | 0.0240087i | ||||
\(859\) | 21.7427 | 0.741850 | 0.370925 | − | 0.928663i | \(-0.379041\pi\) | ||||
0.370925 | + | 0.928663i | \(0.379041\pi\) | |||||||
\(860\) | −0.513151 | − | 0.888804i | −0.0174983 | − | 0.0303080i | ||||
\(861\) | 1.39430 | + | 2.41500i | 0.0475176 | + | 0.0823029i | ||||
\(862\) | 4.21102 | − | 7.29369i | 0.143428 | − | 0.248424i | ||||
\(863\) | −17.0892 | −0.581724 | −0.290862 | − | 0.956765i | \(-0.593942\pi\) | ||||
−0.290862 | + | 0.956765i | \(0.593942\pi\) | |||||||
\(864\) | −1.88448 | + | 3.26402i | −0.0641114 | + | 0.111044i | ||||
\(865\) | −6.37467 | + | 11.0412i | −0.216745 | + | 0.375414i | ||||
\(866\) | 4.77829 | 0.162373 | ||||||||
\(867\) | 19.0957 | − | 33.0747i | 0.648524 | − | 1.12328i | ||||
\(868\) | −6.20360 | − | 10.7449i | −0.210564 | − | 0.364707i | ||||
\(869\) | −3.38983 | − | 5.87136i | −0.114992 | − | 0.199172i | ||||
\(870\) | 1.88448 | 0.0638900 | ||||||||
\(871\) | 27.4998 | + | 1.15689i | 0.931795 | + | 0.0391996i | ||||
\(872\) | 20.3443 | 0.688944 | ||||||||
\(873\) | −4.95206 | − | 8.57721i | −0.167602 | − | 0.290295i | ||||
\(874\) | −0.152510 | − | 0.264155i | −0.00515873 | − | 0.00893518i | ||||
\(875\) | −0.330062 | + | 0.571683i | −0.0111581 | + | 0.0193264i | ||||
\(876\) | 15.1129 | 0.510616 | ||||||||
\(877\) | 2.42909 | − | 4.20731i | 0.0820246 | − | 0.142071i | −0.822095 | − | 0.569351i | \(-0.807195\pi\) |
0.904119 | + | 0.427280i | \(0.140528\pi\) | |||||||
\(878\) | 3.54240 | − | 6.13562i | 0.119550 | − | 0.207067i | ||||
\(879\) | 30.5050 | 1.02891 | ||||||||
\(880\) | −1.12847 | + | 1.95458i | −0.0380409 | + | 0.0658887i | ||||
\(881\) | 11.6601 | + | 20.1959i | 0.392840 | + | 0.680418i | 0.992823 | − | 0.119595i | \(-0.0381595\pi\) |
−0.599983 | + | 0.800013i | \(0.704826\pi\) | |||||||
\(882\) | −1.11552 | − | 1.93213i | −0.0375614 | − | 0.0650582i | ||||
\(883\) | −12.8934 | −0.433898 | −0.216949 | − | 0.976183i | \(-0.569611\pi\) | ||||
−0.216949 | + | 0.976183i | \(0.569611\pi\) | |||||||
\(884\) | 50.4331 | + | 2.12167i | 1.69625 | + | 0.0713593i | ||||
\(885\) | −2.22436 | −0.0747711 | ||||||||
\(886\) | −1.94224 | − | 3.36406i | −0.0652509 | − | 0.113018i | ||||
\(887\) | −15.4639 | − | 26.7842i | −0.519226 | − | 0.899326i | −0.999750 | − | 0.0223448i | \(-0.992887\pi\) |
0.480524 | − | 0.876982i | \(-0.340447\pi\) | |||||||
\(888\) | 6.44872 | − | 11.1695i | 0.216405 | − | 0.374824i | ||||
\(889\) | −7.93444 | −0.266112 | ||||||||
\(890\) | 2.30175 | − | 3.98675i | 0.0771548 | − | 0.133636i | ||||
\(891\) | −0.339877 | + | 0.588684i | −0.0113863 | + | 0.0197217i | ||||
\(892\) | −18.9188 | −0.633449 | ||||||||
\(893\) | 0.289925 | − | 0.502164i | 0.00970196 | − | 0.0168043i | ||||
\(894\) | 2.90411 | + | 5.03007i | 0.0971281 | + | 0.168231i | ||||
\(895\) | −8.88115 | − | 15.3826i | −0.296864 | − | 0.514184i | ||||
\(896\) | 6.17843 | 0.206407 | ||||||||
\(897\) | 12.9737 | + | 24.8258i | 0.433179 | + | 0.828911i | ||||
\(898\) | −8.80558 | −0.293846 | ||||||||
\(899\) | 27.6501 | + | 47.8914i | 0.922183 | + | 1.59727i | ||||
\(900\) | 0.942242 | + | 1.63201i | 0.0314081 | + | 0.0544004i | ||||
\(901\) | −2.52498 | + | 4.37339i | −0.0841192 | + | 0.145699i | ||||
\(902\) | −0.975965 | −0.0324961 | ||||||||
\(903\) | −0.179754 | + | 0.311343i | −0.00598183 | + | 0.0103608i | ||||
\(904\) | 3.51202 | − | 6.08299i | 0.116808 | − | 0.202317i | ||||
\(905\) | 7.02630 | 0.233562 | ||||||||
\(906\) | −2.21140 | + | 3.83026i | −0.0734689 | + | 0.127252i | ||||
\(907\) | 8.48018 | + | 14.6881i | 0.281580 | + | 0.487710i | 0.971774 | − | 0.235914i | \(-0.0758083\pi\) |
−0.690194 | + | 0.723624i | \(0.742475\pi\) | |||||||
\(908\) | 1.14143 | + | 1.97702i | 0.0378798 | + | 0.0656097i | ||||
\(909\) | −9.35951 | −0.310435 | ||||||||
\(910\) | −0.433560 | + | 0.682946i | −0.0143724 | + | 0.0226394i | ||||
\(911\) | 37.7297 | 1.25004 | 0.625020 | − | 0.780608i | \(-0.285091\pi\) | ||||
0.625020 | + | 0.780608i | \(0.285091\pi\) | |||||||
\(912\) | 0.191771 | + | 0.332158i | 0.00635018 | + | 0.0109988i | ||||
\(913\) | −0.601231 | − | 1.04136i | −0.0198978 | − | 0.0344641i | ||||
\(914\) | 1.00334 | − | 1.73783i | 0.0331874 | − | 0.0574823i | ||||
\(915\) | 4.20473 | 0.139004 | ||||||||
\(916\) | 18.1325 | − | 31.4064i | 0.599114 | − | 1.03770i | ||||
\(917\) | −3.59903 | + | 6.23370i | −0.118850 | + | 0.205855i | ||||
\(918\) | 2.52498 | 0.0833366 | ||||||||
\(919\) | −20.0814 | + | 34.7820i | −0.662425 | + | 1.14735i | 0.317552 | + | 0.948241i | \(0.397139\pi\) |
−0.979977 | + | 0.199112i | \(0.936194\pi\) | |||||||
\(920\) | 5.12847 | + | 8.88278i | 0.169081 | + | 0.292857i | ||||
\(921\) | −2.38782 | − | 4.13583i | −0.0786813 | − | 0.136280i | ||||
\(922\) | 5.26537 | 0.173406 | ||||||||
\(923\) | 12.2132 | + | 23.3706i | 0.402003 | + | 0.769253i | ||||
\(924\) | 0.845608 | 0.0278185 | ||||||||
\(925\) | −4.88448 | − | 8.46017i | −0.160601 | − | 0.278169i | ||||
\(926\) | 2.96407 | + | 5.13393i | 0.0974055 | + | 0.168711i | ||||
\(927\) | −2.25267 | + | 3.90174i | −0.0739875 | + | 0.128150i | ||||
\(928\) | −20.8974 | −0.685992 | ||||||||
\(929\) | −11.8845 | + | 20.5845i | −0.389917 | + | 0.675357i | −0.992438 | − | 0.122747i | \(-0.960830\pi\) |
0.602521 | + | 0.798103i | \(0.294163\pi\) | |||||||
\(930\) | 1.69491 | − | 2.93568i | 0.0555784 | − | 0.0962647i | ||||
\(931\) | −0.758276 | −0.0248515 | ||||||||
\(932\) | −22.5272 | + | 39.0183i | −0.737904 | + | 1.27809i | ||||
\(933\) | 15.2906 | + | 26.4841i | 0.500592 | + | 0.867051i | ||||
\(934\) | −3.48018 | − | 6.02784i | −0.113875 | − | 0.197237i | ||||
\(935\) | 5.04995 | 0.165151 | ||||||||
\(936\) | 2.20473 | + | 4.21886i | 0.0720639 | + | 0.137898i | ||||
\(937\) | −7.43803 | −0.242990 | −0.121495 | − | 0.992592i | \(-0.538769\pi\) | ||||
−0.121495 | + | 0.992592i | \(0.538769\pi\) | |||||||
\(938\) | −0.856364 | − | 1.48327i | −0.0279613 | − | 0.0484304i | ||||
\(939\) | −13.3615 | − | 23.1428i | −0.436037 | − | 0.755238i | ||||
\(940\) | −4.72971 | + | 8.19209i | −0.154266 | + | 0.267197i | ||||
\(941\) | −19.3528 | −0.630884 | −0.315442 | − | 0.948945i | \(-0.602153\pi\) | ||||
−0.315442 | + | 0.948945i | \(0.602153\pi\) | |||||||
\(942\) | 0.131811 | − | 0.228303i | 0.00429463 | − | 0.00743852i | ||||
\(943\) | 16.4095 | − | 28.4220i | 0.534366 | − | 0.925548i | ||||
\(944\) | 7.38542 | 0.240375 | ||||||||
\(945\) | 0.330062 | − | 0.571683i | 0.0107369 | − | 0.0185969i | ||||
\(946\) | −0.0629110 | − | 0.108965i | −0.00204541 | − | 0.00354276i | ||||
\(947\) | −6.95854 | − | 12.0525i | −0.226122 | − | 0.391655i | 0.730533 | − | 0.682877i | \(-0.239271\pi\) |
−0.956655 | + | 0.291222i | \(0.905938\pi\) | |||||||
\(948\) | 18.7953 | 0.610442 | ||||||||
\(949\) | 15.4973 | − | 24.4115i | 0.503065 | − | 0.792430i | ||||
\(950\) | −0.0392613 | −0.00127381 | ||||||||
\(951\) | −10.3136 | − | 17.8636i | −0.334441 | − | 0.579268i | ||||
\(952\) | −3.23732 | − | 5.60720i | −0.104922 | − | 0.181730i | ||||
\(953\) | 5.31357 | − | 9.20338i | 0.172124 | − | 0.298127i | −0.767039 | − | 0.641601i | \(-0.778271\pi\) |
0.939162 | + | 0.343474i | \(0.111604\pi\) | |||||||
\(954\) | −0.231033 | −0.00747996 | ||||||||
\(955\) | 6.97703 | − | 12.0846i | 0.225771 | − | 0.391048i | ||||
\(956\) | 17.6008 | − | 30.4856i | 0.569252 | − | 0.985973i | ||||
\(957\) | −3.76897 | −0.121833 | ||||||||
\(958\) | −6.96589 | + | 12.0653i | −0.225058 | + | 0.389811i | ||||
\(959\) | −1.11885 | − | 1.93791i | −0.0361296 | − | 0.0625783i | ||||
\(960\) | −2.67975 | − | 4.64147i | −0.0864887 | − | 0.149803i | ||||
\(961\) | 68.4746 | 2.20886 | ||||||||
\(962\) | −5.54461 | − | 10.6099i | −0.178765 | − | 0.342077i | ||||
\(963\) | 0.570909 | 0.0183973 | ||||||||
\(964\) | 5.76230 | + | 9.98059i | 0.185591 | + | 0.321453i | ||||
\(965\) | −11.8747 | − | 20.5675i | −0.382259 | − | 0.662092i | ||||
\(966\) | 0.871525 | − | 1.50953i | 0.0280409 | − | 0.0485682i | ||||
\(967\) | 51.6771 | 1.66182 | 0.830912 | − | 0.556404i | \(-0.187819\pi\) | ||||
0.830912 | + | 0.556404i | \(0.187819\pi\) | |||||||
\(968\) | 6.95633 | − | 12.0487i | 0.223585 | − | 0.387261i | ||||
\(969\) | 0.429091 | − | 0.743207i | 0.0137844 | − | 0.0238752i | ||||
\(970\) | −3.36618 | −0.108082 | ||||||||
\(971\) | 21.4487 | − | 37.1503i | 0.688322 | − | 1.19221i | −0.284058 | − | 0.958807i | \(-0.591681\pi\) |
0.972380 | − | 0.233402i | \(-0.0749858\pi\) | |||||||
\(972\) | −0.942242 | − | 1.63201i | −0.0302224 | − | 0.0523468i | ||||
\(973\) | −4.88763 | − | 8.46562i | −0.156690 | − | 0.271395i | ||||
\(974\) | −8.17843 | −0.262054 | ||||||||
\(975\) | 3.60236 | + | 0.151548i | 0.115368 | + | 0.00485341i | ||||
\(976\) | −13.9607 | −0.446872 | ||||||||
\(977\) | −9.08254 | − | 15.7314i | −0.290576 | − | 0.503293i | 0.683370 | − | 0.730072i | \(-0.260514\pi\) |
−0.973946 | + | 0.226780i | \(0.927180\pi\) | |||||||
\(978\) | −2.07292 | − | 3.59040i | −0.0662846 | − | 0.114808i | ||||
\(979\) | −4.60350 | + | 7.97349i | −0.147128 | + | 0.254834i | ||||
\(980\) | 12.3702 | 0.395151 | ||||||||
\(981\) | −7.70473 | + | 13.3450i | −0.245993 | + | 0.426073i | ||||
\(982\) | 6.24914 | − | 10.8238i | 0.199418 | − | 0.345402i | ||||
\(983\) | −10.8582 | −0.346322 | −0.173161 | − | 0.984894i | \(-0.555398\pi\) | ||||
−0.173161 | + | 0.984894i | \(0.555398\pi\) | |||||||
\(984\) | 2.78860 | − | 4.82999i | 0.0888973 | − | 0.153975i | ||||
\(985\) | −7.90411 | − | 13.6903i | −0.251846 | − | 0.436210i | ||||
\(986\) | 7.00000 | + | 12.1244i | 0.222925 | + | 0.386118i | ||||
\(987\) | 3.31357 | 0.105472 | ||||||||
\(988\) | 0.784194 | + | 0.0329902i | 0.0249485 | + | 0.00104956i | ||||
\(989\) | 4.23103 | 0.134539 | ||||||||
\(990\) | 0.115516 | + | 0.200080i | 0.00367135 | + | 0.00635896i | ||||
\(991\) | 11.1862 | + | 19.3751i | 0.355342 | + | 0.615471i | 0.987177 | − | 0.159633i | \(-0.0510309\pi\) |
−0.631834 | + | 0.775104i | \(0.717698\pi\) | |||||||
\(992\) | −18.7953 | + | 32.5544i | −0.596750 | + | 1.03360i | ||||
\(993\) | −5.37020 | −0.170418 | ||||||||
\(994\) | 0.820439 | − | 1.42104i | 0.0260227 | − | 0.0450727i | ||||
\(995\) | −4.38448 | + | 7.59415i | −0.138997 | + | 0.240751i | ||||
\(996\) | 3.33359 | 0.105629 | ||||||||
\(997\) | 12.1187 | − | 20.9901i | 0.383802 | − | 0.664764i | −0.607800 | − | 0.794090i | \(-0.707948\pi\) |
0.991602 | + | 0.129326i | \(0.0412813\pi\) | |||||||
\(998\) | 5.91746 | + | 10.2493i | 0.187314 | + | 0.324437i | ||||
\(999\) | 4.88448 | + | 8.46017i | 0.154538 | + | 0.267668i |
(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 | 195.2.i.d.16.2 | ✓ | 6 | |
3.2 | odd | 2 | 585.2.j.f.406.2 | 6 | |||
5.2 | odd | 4 | 975.2.bb.k.874.3 | 12 | |||
5.3 | odd | 4 | 975.2.bb.k.874.4 | 12 | |||
5.4 | even | 2 | 975.2.i.l.601.2 | 6 | |||
13.3 | even | 3 | 2535.2.a.bb.1.2 | 3 | |||
13.9 | even | 3 | inner | 195.2.i.d.61.2 | yes | 6 | |
13.10 | even | 6 | 2535.2.a.ba.1.2 | 3 | |||
39.23 | odd | 6 | 7605.2.a.bw.1.2 | 3 | |||
39.29 | odd | 6 | 7605.2.a.bv.1.2 | 3 | |||
39.35 | odd | 6 | 585.2.j.f.451.2 | 6 | |||
65.9 | even | 6 | 975.2.i.l.451.2 | 6 | |||
65.22 | odd | 12 | 975.2.bb.k.724.4 | 12 | |||
65.48 | odd | 12 | 975.2.bb.k.724.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.i.d.16.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
195.2.i.d.61.2 | yes | 6 | 13.9 | even | 3 | inner | |
585.2.j.f.406.2 | 6 | 3.2 | odd | 2 | |||
585.2.j.f.451.2 | 6 | 39.35 | odd | 6 | |||
975.2.i.l.451.2 | 6 | 65.9 | even | 6 | |||
975.2.i.l.601.2 | 6 | 5.4 | even | 2 | |||
975.2.bb.k.724.3 | 12 | 65.48 | odd | 12 | |||
975.2.bb.k.724.4 | 12 | 65.22 | odd | 12 | |||
975.2.bb.k.874.3 | 12 | 5.2 | odd | 4 | |||
975.2.bb.k.874.4 | 12 | 5.3 | odd | 4 | |||
2535.2.a.ba.1.2 | 3 | 13.10 | even | 6 | |||
2535.2.a.bb.1.2 | 3 | 13.3 | even | 3 | |||
7605.2.a.bv.1.2 | 3 | 39.29 | odd | 6 | |||
7605.2.a.bw.1.2 | 3 | 39.23 | odd | 6 |