Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(165,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.h (of order \(3\), degree \(2\), not 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 8x^{14} + 45x^{12} + 124x^{10} + 248x^{8} + 250x^{6} + 177x^{4} + 14x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 471.7 | ||
Root | \(-0.756863 + 1.31093i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.471 |
Dual form | 637.2.h.m.165.7 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.43210 | 1.71975 | 0.859877 | − | 0.510502i | \(-0.170540\pi\) | ||||
0.859877 | + | 0.510502i | \(0.170540\pi\) | |||||||
\(3\) | −0.376796 | + | 0.652630i | −0.217543 | + | 0.376796i | −0.954056 | − | 0.299627i | \(-0.903138\pi\) |
0.736513 | + | 0.676423i | \(0.236471\pi\) | |||||||
\(4\) | 3.91511 | 1.95755 | ||||||||
\(5\) | −0.170769 | + | 0.295780i | −0.0763700 | + | 0.132277i | −0.901681 | − | 0.432401i | \(-0.857666\pi\) |
0.825311 | + | 0.564678i | \(0.191000\pi\) | |||||||
\(6\) | −0.916405 | + | 1.58726i | −0.374121 | + | 0.647996i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 4.65773 | 1.64675 | ||||||||
\(9\) | 1.21605 | + | 2.10626i | 0.405350 | + | 0.702086i | ||||
\(10\) | −0.415326 | + | 0.719366i | −0.131338 | + | 0.227483i | ||||
\(11\) | 1.21605 | − | 2.10626i | 0.366653 | − | 0.635061i | −0.622387 | − | 0.782710i | \(-0.713837\pi\) |
0.989040 | + | 0.147648i | \(0.0471704\pi\) | |||||||
\(12\) | −1.47520 | + | 2.55511i | −0.425852 | + | 0.737598i | ||||
\(13\) | 2.50139 | − | 2.59674i | 0.693760 | − | 0.720206i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.128690 | − | 0.222897i | −0.0332276 | − | 0.0575518i | ||||
\(16\) | 3.49784 | 0.874460 | ||||||||
\(17\) | −1.94823 | −0.472516 | −0.236258 | − | 0.971690i | \(-0.575921\pi\) | ||||
−0.236258 | + | 0.971690i | \(0.575921\pi\) | |||||||
\(18\) | 2.95755 | + | 5.12263i | 0.697102 | + | 1.20742i | ||||
\(19\) | 3.14519 | + | 5.44764i | 0.721557 | + | 1.24977i | 0.960376 | + | 0.278709i | \(0.0899065\pi\) |
−0.238819 | + | 0.971064i | \(0.576760\pi\) | |||||||
\(20\) | −0.668577 | + | 1.15801i | −0.149498 | + | 0.258939i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.95755 | − | 5.12263i | 0.630552 | − | 1.09215i | ||||
\(23\) | −3.68948 | −0.769309 | −0.384655 | − | 0.923061i | \(-0.625679\pi\) | ||||
−0.384655 | + | 0.923061i | \(0.625679\pi\) | |||||||
\(24\) | −1.75501 | + | 3.03977i | −0.358240 | + | 0.620491i | ||||
\(25\) | 2.44168 | + | 4.22911i | 0.488335 | + | 0.845821i | ||||
\(26\) | 6.08362 | − | 6.31553i | 1.19310 | − | 1.23858i | ||||
\(27\) | −4.09359 | −0.787811 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.22068 | − | 3.84632i | −0.412369 | − | 0.714244i | 0.582779 | − | 0.812631i | \(-0.301965\pi\) |
−0.995148 | + | 0.0983864i | \(0.968632\pi\) | |||||||
\(30\) | −0.312986 | − | 0.542108i | −0.0571432 | − | 0.0989750i | ||||
\(31\) | 0.987661 | + | 1.71068i | 0.177389 | + | 0.307247i | 0.940986 | − | 0.338447i | \(-0.109902\pi\) |
−0.763596 | + | 0.645694i | \(0.776568\pi\) | |||||||
\(32\) | −0.808361 | −0.142899 | ||||||||
\(33\) | 0.916405 | + | 1.58726i | 0.159526 | + | 0.276307i | ||||
\(34\) | −4.73830 | −0.812611 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.76096 | + | 8.24623i | 0.793494 | + | 1.37437i | ||||
\(37\) | −9.62867 | −1.58294 | −0.791472 | − | 0.611206i | \(-0.790685\pi\) | ||||
−0.791472 | + | 0.611206i | \(0.790685\pi\) | |||||||
\(38\) | 7.64942 | + | 13.2492i | 1.24090 | + | 2.14930i | ||||
\(39\) | 0.752198 | + | 2.61092i | 0.120448 | + | 0.418082i | ||||
\(40\) | −0.795393 | + | 1.37766i | −0.125763 | + | 0.217827i | ||||
\(41\) | −6.26793 | − | 10.8564i | −0.978887 | − | 1.69548i | −0.666461 | − | 0.745540i | \(-0.732192\pi\) |
−0.312426 | − | 0.949942i | \(-0.601141\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.20368 | − | 7.28099i | 0.641055 | − | 1.11034i | −0.344142 | − | 0.938918i | \(-0.611830\pi\) |
0.985198 | − | 0.171423i | \(-0.0548365\pi\) | |||||||
\(44\) | 4.76096 | − | 8.24623i | 0.717742 | − | 1.24317i | ||||
\(45\) | −0.830652 | −0.123826 | ||||||||
\(46\) | −8.97318 | −1.32302 | ||||||||
\(47\) | 4.50265 | − | 7.79882i | 0.656779 | − | 1.13757i | −0.324666 | − | 0.945829i | \(-0.605252\pi\) |
0.981445 | − | 0.191745i | \(-0.0614148\pi\) | |||||||
\(48\) | −1.31797 | + | 2.28279i | −0.190233 | + | 0.329493i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.93840 | + | 10.2856i | 0.839816 | + | 1.45460i | ||||
\(51\) | 0.734087 | − | 1.27148i | 0.102793 | − | 0.178042i | ||||
\(52\) | 9.79320 | − | 10.1665i | 1.35807 | − | 1.40984i | ||||
\(53\) | −0.746129 | − | 1.29233i | −0.102489 | − | 0.177516i | 0.810221 | − | 0.586125i | \(-0.199347\pi\) |
−0.912709 | + | 0.408609i | \(0.866014\pi\) | |||||||
\(54\) | −9.95601 | −1.35484 | ||||||||
\(55\) | 0.415326 | + | 0.719366i | 0.0560025 | + | 0.0969993i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.74039 | −0.627879 | ||||||||
\(58\) | −5.40090 | − | 9.35464i | −0.709173 | − | 1.22832i | ||||
\(59\) | 0.626991 | 0.0816273 | 0.0408136 | − | 0.999167i | \(-0.487005\pi\) | ||||
0.0408136 | + | 0.999167i | \(0.487005\pi\) | |||||||
\(60\) | −0.503834 | − | 0.872666i | −0.0650447 | − | 0.112661i | ||||
\(61\) | 0.571597 | + | 0.990035i | 0.0731855 | + | 0.126761i | 0.900296 | − | 0.435279i | \(-0.143350\pi\) |
−0.827110 | + | 0.562040i | \(0.810017\pi\) | |||||||
\(62\) | 2.40209 | + | 4.16054i | 0.305066 | + | 0.528389i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.96169 | −1.12021 | ||||||||
\(65\) | 0.340905 | + | 1.18330i | 0.0422841 | + | 0.146770i | ||||
\(66\) | 2.22879 | + | 3.86037i | 0.274345 | + | 0.475179i | ||||
\(67\) | 2.79599 | − | 4.84280i | 0.341585 | − | 0.591642i | −0.643142 | − | 0.765747i | \(-0.722370\pi\) |
0.984727 | + | 0.174104i | \(0.0557030\pi\) | |||||||
\(68\) | −7.62754 | −0.924975 | ||||||||
\(69\) | 1.39018 | − | 2.40786i | 0.167358 | − | 0.289873i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.74859 | + | 8.22481i | −0.563554 | + | 0.976105i | 0.433628 | + | 0.901092i | \(0.357233\pi\) |
−0.997183 | + | 0.0750130i | \(0.976100\pi\) | |||||||
\(72\) | 5.66402 | + | 9.81038i | 0.667512 | + | 1.15616i | ||||
\(73\) | −5.95934 | − | 10.3219i | −0.697488 | − | 1.20808i | −0.969335 | − | 0.245744i | \(-0.920968\pi\) |
0.271847 | − | 0.962340i | \(-0.412366\pi\) | |||||||
\(74\) | −23.4179 | −2.72227 | ||||||||
\(75\) | −3.68006 | −0.424936 | ||||||||
\(76\) | 12.3138 | + | 21.3281i | 1.41249 | + | 2.44650i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.82942 | + | 6.35002i | 0.207141 | + | 0.718998i | ||||
\(79\) | −2.23583 | + | 3.87258i | −0.251551 | + | 0.435699i | −0.963953 | − | 0.266073i | \(-0.914274\pi\) |
0.712402 | + | 0.701772i | \(0.247607\pi\) | |||||||
\(80\) | −0.597321 | + | 1.03459i | −0.0667825 | + | 0.115671i | ||||
\(81\) | −2.10570 | + | 3.64718i | −0.233967 | + | 0.405242i | ||||
\(82\) | −15.2442 | − | 26.4038i | −1.68344 | − | 2.91581i | ||||
\(83\) | 1.41231 | 0.155021 | 0.0775104 | − | 0.996992i | \(-0.475303\pi\) | ||||
0.0775104 | + | 0.996992i | \(0.475303\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.332697 | − | 0.576248i | 0.0360861 | − | 0.0625029i | ||||
\(86\) | 10.2238 | − | 17.7081i | 1.10246 | − | 1.90951i | ||||
\(87\) | 3.34697 | 0.358833 | ||||||||
\(88\) | 5.66402 | − | 9.81038i | 0.603787 | − | 1.04579i | ||||
\(89\) | 12.4444 | 1.31910 | 0.659551 | − | 0.751660i | \(-0.270747\pi\) | ||||
0.659551 | + | 0.751660i | \(0.270747\pi\) | |||||||
\(90\) | −2.02023 | −0.212951 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −14.4447 | −1.50596 | ||||||||
\(93\) | −1.48859 | −0.154359 | ||||||||
\(94\) | 10.9509 | − | 18.9675i | 1.12950 | − | 1.95635i | ||||
\(95\) | −2.14840 | −0.220421 | ||||||||
\(96\) | 0.304587 | − | 0.527560i | 0.0310868 | − | 0.0538439i | ||||
\(97\) | −5.13850 | + | 8.90014i | −0.521736 | + | 0.903673i | 0.477945 | + | 0.878390i | \(0.341382\pi\) |
−0.999680 | + | 0.0252826i | \(0.991951\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.91511 | 0.594490 | ||||||||
\(100\) | 9.55942 | + | 16.5574i | 0.955942 | + | 1.65574i | ||||
\(101\) | −7.52683 | + | 13.0369i | −0.748948 | + | 1.29722i | 0.199380 | + | 0.979922i | \(0.436107\pi\) |
−0.948328 | + | 0.317293i | \(0.897226\pi\) | |||||||
\(102\) | 1.78537 | − | 3.09235i | 0.176778 | − | 0.306189i | ||||
\(103\) | −8.80880 | + | 15.2573i | −0.867957 | + | 1.50335i | −0.00387687 | + | 0.999992i | \(0.501234\pi\) |
−0.864080 | + | 0.503354i | \(0.832099\pi\) | |||||||
\(104\) | 11.6508 | − | 12.0949i | 1.14245 | − | 1.18600i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.81466 | − | 3.14308i | −0.176255 | − | 0.305283i | ||||
\(107\) | 6.38454 | 0.617217 | 0.308608 | − | 0.951189i | \(-0.400137\pi\) | ||||
0.308608 | + | 0.951189i | \(0.400137\pi\) | |||||||
\(108\) | −16.0268 | −1.54218 | ||||||||
\(109\) | 4.08736 | + | 7.07951i | 0.391498 | + | 0.678095i | 0.992647 | − | 0.121042i | \(-0.0386236\pi\) |
−0.601149 | + | 0.799137i | \(0.705290\pi\) | |||||||
\(110\) | 1.01011 | + | 1.74957i | 0.0963106 | + | 0.166815i | ||||
\(111\) | 3.62804 | − | 6.28396i | 0.344359 | − | 0.596447i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.81083 | − | 8.33259i | 0.452564 | − | 0.783865i | −0.545980 | − | 0.837798i | \(-0.683843\pi\) |
0.998545 | + | 0.0539336i | \(0.0171759\pi\) | |||||||
\(114\) | −11.5291 | −1.07980 | ||||||||
\(115\) | 0.630047 | − | 1.09127i | 0.0587522 | − | 0.101762i | ||||
\(116\) | −8.69418 | − | 15.0588i | −0.807234 | − | 1.39817i | ||||
\(117\) | 8.51122 | + | 2.11081i | 0.786863 | + | 0.195144i | ||||
\(118\) | 1.52490 | 0.140379 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.599402 | − | 1.03819i | −0.0547177 | − | 0.0947738i | ||||
\(121\) | 2.54245 | + | 4.40365i | 0.231132 | + | 0.400332i | ||||
\(122\) | 1.39018 | + | 2.40786i | 0.125861 | + | 0.217998i | ||||
\(123\) | 9.44693 | 0.851801 | ||||||||
\(124\) | 3.86680 | + | 6.69749i | 0.347249 | + | 0.601452i | ||||
\(125\) | −3.37553 | −0.301917 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.50988 | − | 7.81134i | −0.400187 | − | 0.693145i | 0.593561 | − | 0.804789i | \(-0.297722\pi\) |
−0.993748 | + | 0.111644i | \(0.964388\pi\) | |||||||
\(128\) | −20.1790 | −1.78359 | ||||||||
\(129\) | 3.16786 | + | 5.48690i | 0.278915 | + | 0.483094i | ||||
\(130\) | 0.829115 | + | 2.87791i | 0.0727182 | + | 0.252409i | ||||
\(131\) | 0.0962416 | − | 0.166695i | 0.00840867 | − | 0.0145642i | −0.861790 | − | 0.507264i | \(-0.830657\pi\) |
0.870199 | + | 0.492700i | \(0.163990\pi\) | |||||||
\(132\) | 3.58782 | + | 6.21429i | 0.312280 | + | 0.540885i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.80013 | − | 11.7782i | 0.587442 | − | 1.01748i | ||||
\(135\) | 0.699056 | − | 1.21080i | 0.0601651 | − | 0.104209i | ||||
\(136\) | −9.07434 | −0.778118 | ||||||||
\(137\) | 4.87680 | 0.416653 | 0.208326 | − | 0.978059i | \(-0.433198\pi\) | ||||
0.208326 | + | 0.978059i | \(0.433198\pi\) | |||||||
\(138\) | 3.38106 | − | 5.85616i | 0.287815 | − | 0.498510i | ||||
\(139\) | 5.53701 | − | 9.59038i | 0.469643 | − | 0.813446i | −0.529755 | − | 0.848151i | \(-0.677716\pi\) |
0.999398 | + | 0.0347054i | \(0.0110493\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.39316 | + | 5.87713i | 0.285756 | + | 0.494943i | ||||
\(142\) | −11.5491 | + | 20.0035i | −0.969175 | + | 1.67866i | ||||
\(143\) | −2.42760 | − | 8.42634i | −0.203006 | − | 0.704646i | ||||
\(144\) | 4.25355 | + | 7.36736i | 0.354462 | + | 0.613946i | ||||
\(145\) | 1.51689 | 0.125971 | ||||||||
\(146\) | −14.4937 | − | 25.1038i | −1.19951 | − | 2.07761i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −37.6973 | −3.09869 | ||||||||
\(149\) | −7.95435 | − | 13.7773i | −0.651646 | − | 1.12868i | −0.982723 | − | 0.185080i | \(-0.940746\pi\) |
0.331078 | − | 0.943603i | \(-0.392588\pi\) | |||||||
\(150\) | −8.95026 | −0.730786 | ||||||||
\(151\) | 5.29518 | + | 9.17152i | 0.430916 | + | 0.746368i | 0.996952 | − | 0.0780122i | \(-0.0248573\pi\) |
−0.566037 | + | 0.824380i | \(0.691524\pi\) | |||||||
\(152\) | 14.6494 | + | 25.3736i | 1.18823 | + | 2.05807i | ||||
\(153\) | −2.36915 | − | 4.10349i | −0.191534 | − | 0.331747i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.674646 | −0.0541889 | ||||||||
\(156\) | 2.94493 | + | 10.2220i | 0.235783 | + | 0.818418i | ||||
\(157\) | −4.56194 | − | 7.90151i | −0.364082 | − | 0.630609i | 0.624546 | − | 0.780988i | \(-0.285284\pi\) |
−0.988628 | + | 0.150379i | \(0.951951\pi\) | |||||||
\(158\) | −5.43777 | + | 9.41849i | −0.432606 | + | 0.749295i | ||||
\(159\) | 1.12455 | 0.0891829 | ||||||||
\(160\) | 0.138043 | − | 0.239097i | 0.0109132 | − | 0.0189023i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −5.12127 | + | 8.87031i | −0.402365 | + | 0.696917i | ||||
\(163\) | 5.48196 | + | 9.49504i | 0.429380 | + | 0.743709i | 0.996818 | − | 0.0797075i | \(-0.0253986\pi\) |
−0.567438 | + | 0.823416i | \(0.692065\pi\) | |||||||
\(164\) | −24.5396 | − | 42.5039i | −1.91622 | − | 3.31900i | ||||
\(165\) | −0.625973 | −0.0487319 | ||||||||
\(166\) | 3.43487 | 0.266598 | ||||||||
\(167\) | 9.13884 | + | 15.8289i | 0.707185 | + | 1.22488i | 0.965897 | + | 0.258925i | \(0.0833683\pi\) |
−0.258713 | + | 0.965954i | \(0.583298\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.486122 | − | 12.9909i | −0.0373940 | − | 0.999301i | ||||
\(170\) | 0.809152 | − | 1.40149i | 0.0620591 | − | 0.107490i | ||||
\(171\) | −7.64942 | + | 13.2492i | −0.584966 | + | 1.01319i | ||||
\(172\) | 16.4579 | − | 28.5058i | 1.25490 | − | 2.17355i | ||||
\(173\) | 4.09918 | + | 7.09998i | 0.311655 | + | 0.539802i | 0.978721 | − | 0.205197i | \(-0.0657835\pi\) |
−0.667066 | + | 0.744999i | \(0.732450\pi\) | |||||||
\(174\) | 8.14015 | 0.617104 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.25355 | − | 7.36736i | 0.320623 | − | 0.555335i | ||||
\(177\) | −0.236248 | + | 0.409193i | −0.0177575 | + | 0.0307568i | ||||
\(178\) | 30.2659 | 2.26853 | ||||||||
\(179\) | 7.77684 | − | 13.4699i | 0.581268 | − | 1.00679i | −0.414061 | − | 0.910249i | \(-0.635890\pi\) |
0.995329 | − | 0.0965370i | \(-0.0307766\pi\) | |||||||
\(180\) | −3.25209 | −0.242396 | ||||||||
\(181\) | −6.67302 | −0.496001 | −0.248001 | − | 0.968760i | \(-0.579774\pi\) | ||||
−0.248001 | + | 0.968760i | \(0.579774\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.861502 | −0.0636841 | ||||||||
\(184\) | −17.1846 | −1.26686 | ||||||||
\(185\) | 1.64427 | − | 2.84797i | 0.120889 | − | 0.209387i | ||||
\(186\) | −3.62039 | −0.265460 | ||||||||
\(187\) | −2.36915 | + | 4.10349i | −0.173249 | + | 0.300077i | ||||
\(188\) | 17.6283 | − | 30.5332i | 1.28568 | − | 2.22686i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.22512 | −0.379070 | ||||||||
\(191\) | 9.37296 | + | 16.2344i | 0.678204 | + | 1.17468i | 0.975521 | + | 0.219905i | \(0.0705746\pi\) |
−0.297318 | + | 0.954779i | \(0.596092\pi\) | |||||||
\(192\) | 3.37673 | − | 5.84867i | 0.243694 | − | 0.422091i | ||||
\(193\) | 4.08655 | − | 7.07811i | 0.294156 | − | 0.509493i | −0.680632 | − | 0.732625i | \(-0.738295\pi\) |
0.974788 | + | 0.223132i | \(0.0716281\pi\) | |||||||
\(194\) | −12.4973 | + | 21.6460i | −0.897257 | + | 1.55409i | ||||
\(195\) | −0.900710 | − | 0.223378i | −0.0645012 | − | 0.0159965i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.36006 | − | 7.55184i | −0.310641 | − | 0.538047i | 0.667860 | − | 0.744287i | \(-0.267210\pi\) |
−0.978501 | + | 0.206240i | \(0.933877\pi\) | |||||||
\(198\) | 14.3861 | 1.02238 | ||||||||
\(199\) | −17.4666 | −1.23818 | −0.619089 | − | 0.785321i | \(-0.712498\pi\) | ||||
−0.619089 | + | 0.785321i | \(0.712498\pi\) | |||||||
\(200\) | 11.3727 | + | 19.6980i | 0.804168 | + | 1.39286i | ||||
\(201\) | 2.10704 | + | 3.64950i | 0.148619 | + | 0.257416i | ||||
\(202\) | −18.3060 | + | 31.7069i | −1.28801 | + | 2.23089i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.87403 | − | 4.97796i | 0.201222 | − | 0.348527i | ||||
\(205\) | 4.28146 | 0.299030 | ||||||||
\(206\) | −21.4239 | + | 37.1073i | −1.49267 | + | 2.58539i | ||||
\(207\) | −4.48659 | − | 7.77100i | −0.311839 | − | 0.540122i | ||||
\(208\) | 8.74945 | − | 9.08298i | 0.606665 | − | 0.629791i | ||||
\(209\) | 15.2988 | 1.05824 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.6284 | + | 20.1410i | 0.800535 | + | 1.38657i | 0.919265 | + | 0.393640i | \(0.128784\pi\) |
−0.118730 | + | 0.992927i | \(0.537882\pi\) | |||||||
\(212\) | −2.92117 | − | 5.05962i | −0.200627 | − | 0.347496i | ||||
\(213\) | −3.57850 | − | 6.19815i | −0.245195 | − | 0.424690i | ||||
\(214\) | 15.5278 | 1.06146 | ||||||||
\(215\) | 1.43571 | + | 2.48673i | 0.0979148 | + | 0.169593i | ||||
\(216\) | −19.0668 | −1.29733 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 9.94086 | + | 17.2181i | 0.673280 | + | 1.16616i | ||||
\(219\) | 8.98182 | 0.606935 | ||||||||
\(220\) | 1.62605 | + | 2.81639i | 0.109628 | + | 0.189881i | ||||
\(221\) | −4.87329 | + | 5.05906i | −0.327813 | + | 0.340309i | ||||
\(222\) | 8.82376 | − | 15.2832i | 0.592212 | − | 1.02574i | ||||
\(223\) | 14.6364 | + | 25.3510i | 0.980128 | + | 1.69763i | 0.661855 | + | 0.749632i | \(0.269769\pi\) |
0.318272 | + | 0.947999i | \(0.396897\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.93840 | + | 10.2856i | −0.395893 | + | 0.685707i | ||||
\(226\) | 11.7004 | − | 20.2657i | 0.778299 | − | 1.34805i | ||||
\(227\) | 19.8110 | 1.31490 | 0.657452 | − | 0.753496i | \(-0.271634\pi\) | ||||
0.657452 | + | 0.753496i | \(0.271634\pi\) | |||||||
\(228\) | −18.5591 | −1.22911 | ||||||||
\(229\) | 0.664107 | − | 1.15027i | 0.0438855 | − | 0.0760118i | −0.843248 | − | 0.537524i | \(-0.819360\pi\) |
0.887134 | + | 0.461512i | \(0.152693\pi\) | |||||||
\(230\) | 1.53234 | − | 2.65408i | 0.101039 | − | 0.175005i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.3433 | − | 17.9151i | −0.679071 | − | 1.17618i | ||||
\(233\) | −0.758171 | + | 1.31319i | −0.0496695 | + | 0.0860300i | −0.889791 | − | 0.456368i | \(-0.849150\pi\) |
0.840122 | + | 0.542398i | \(0.182483\pi\) | |||||||
\(234\) | 20.7001 | + | 5.13369i | 1.35321 | + | 0.335600i | ||||
\(235\) | 1.53782 | + | 2.66358i | 0.100316 | + | 0.173753i | ||||
\(236\) | 2.45474 | 0.159790 | ||||||||
\(237\) | −1.68491 | − | 2.91834i | −0.109446 | − | 0.189567i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.4793 | 1.45406 | 0.727032 | − | 0.686603i | \(-0.240899\pi\) | ||||
0.727032 | + | 0.686603i | \(0.240899\pi\) | |||||||
\(240\) | −0.450136 | − | 0.779659i | −0.0290562 | − | 0.0503268i | ||||
\(241\) | 13.3106 | 0.857409 | 0.428704 | − | 0.903445i | \(-0.358970\pi\) | ||||
0.428704 | + | 0.903445i | \(0.358970\pi\) | |||||||
\(242\) | 6.18348 | + | 10.7101i | 0.397489 | + | 0.688472i | ||||
\(243\) | −7.72722 | − | 13.3839i | −0.495701 | − | 0.858580i | ||||
\(244\) | 2.23786 | + | 3.87609i | 0.143265 | + | 0.248141i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 22.9759 | 1.46489 | ||||||||
\(247\) | 22.0134 | + | 5.45939i | 1.40068 | + | 0.347373i | ||||
\(248\) | 4.60026 | + | 7.96788i | 0.292116 | + | 0.505961i | ||||
\(249\) | −0.532152 | + | 0.921714i | −0.0337238 | + | 0.0584113i | ||||
\(250\) | −8.20963 | −0.519222 | ||||||||
\(251\) | −7.95169 | + | 13.7727i | −0.501906 | + | 0.869327i | 0.498091 | + | 0.867125i | \(0.334034\pi\) |
−0.999998 | + | 0.00220260i | \(0.999299\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.48659 | + | 7.77100i | −0.282069 | + | 0.488559i | ||||
\(254\) | −10.9685 | − | 18.9980i | −0.688224 | − | 1.19204i | ||||
\(255\) | 0.250718 | + | 0.434256i | 0.0157006 | + | 0.0271942i | ||||
\(256\) | −31.1539 | −1.94712 | ||||||||
\(257\) | −29.2397 | −1.82392 | −0.911960 | − | 0.410280i | \(-0.865431\pi\) | ||||
−0.911960 | + | 0.410280i | \(0.865431\pi\) | |||||||
\(258\) | 7.70455 | + | 13.3447i | 0.479664 | + | 0.830803i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.33468 | + | 4.63275i | 0.0827733 | + | 0.287311i | ||||
\(261\) | 5.40090 | − | 9.35464i | 0.334307 | − | 0.579037i | ||||
\(262\) | 0.234069 | − | 0.405420i | 0.0144608 | − | 0.0250469i | ||||
\(263\) | 0.852177 | − | 1.47601i | 0.0525475 | − | 0.0910149i | −0.838555 | − | 0.544817i | \(-0.816599\pi\) |
0.891103 | + | 0.453802i | \(0.149933\pi\) | |||||||
\(264\) | 4.26836 | + | 7.39302i | 0.262700 | + | 0.455009i | ||||
\(265\) | 0.509661 | 0.0313083 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.68899 | + | 8.12157i | −0.286962 | + | 0.497032i | ||||
\(268\) | 10.9466 | − | 18.9601i | 0.668670 | − | 1.15817i | ||||
\(269\) | 8.37874 | 0.510861 | 0.255430 | − | 0.966827i | \(-0.417783\pi\) | ||||
0.255430 | + | 0.966827i | \(0.417783\pi\) | |||||||
\(270\) | 1.70017 | − | 2.94479i | 0.103469 | − | 0.179214i | ||||
\(271\) | −12.1575 | −0.738518 | −0.369259 | − | 0.929327i | \(-0.620388\pi\) | ||||
−0.369259 | + | 0.929327i | \(0.620388\pi\) | |||||||
\(272\) | −6.81461 | −0.413196 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.8609 | 0.716540 | ||||||||
\(275\) | 11.8768 | 0.716198 | ||||||||
\(276\) | 5.44270 | − | 9.42704i | 0.327612 | − | 0.567441i | ||||
\(277\) | 10.3181 | 0.619957 | 0.309979 | − | 0.950744i | \(-0.399678\pi\) | ||||
0.309979 | + | 0.950744i | \(0.399678\pi\) | |||||||
\(278\) | 13.4666 | − | 23.3248i | 0.807670 | − | 1.39893i | ||||
\(279\) | −2.40209 | + | 4.16054i | −0.143809 | + | 0.249085i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.59677 | −0.154910 | −0.0774551 | − | 0.996996i | \(-0.524679\pi\) | ||||
−0.0774551 | + | 0.996996i | \(0.524679\pi\) | |||||||
\(282\) | 8.25250 | + | 14.2938i | 0.491429 | + | 0.851181i | ||||
\(283\) | −2.30184 | + | 3.98690i | −0.136830 | + | 0.236997i | −0.926295 | − | 0.376799i | \(-0.877025\pi\) |
0.789465 | + | 0.613796i | \(0.210358\pi\) | |||||||
\(284\) | −18.5912 | + | 32.2010i | −1.10319 | + | 1.91078i | ||||
\(285\) | 0.809509 | − | 1.40211i | 0.0479512 | − | 0.0830539i | ||||
\(286\) | −5.90416 | − | 20.4937i | −0.349120 | − | 1.21182i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.983006 | − | 1.70262i | −0.0579242 | − | 0.100328i | ||||
\(289\) | −13.2044 | −0.776729 | ||||||||
\(290\) | 3.68922 | 0.216638 | ||||||||
\(291\) | −3.87233 | − | 6.70708i | −0.227000 | − | 0.393176i | ||||
\(292\) | −23.3314 | − | 40.4112i | −1.36537 | − | 2.36489i | ||||
\(293\) | 0.980596 | − | 1.69844i | 0.0572870 | − | 0.0992241i | −0.835960 | − | 0.548791i | \(-0.815088\pi\) |
0.893247 | + | 0.449567i | \(0.148422\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.107070 | + | 0.185451i | −0.00623388 | + | 0.0107974i | ||||
\(296\) | −44.8477 | −2.60672 | ||||||||
\(297\) | −4.97800 | + | 8.62216i | −0.288853 | + | 0.500308i | ||||
\(298\) | −19.3458 | − | 33.5078i | −1.12067 | − | 1.94106i | ||||
\(299\) | −9.22882 | + | 9.58062i | −0.533716 | + | 0.554061i | ||||
\(300\) | −14.4078 | −0.831835 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 12.8784 | + | 22.3060i | 0.741069 | + | 1.28357i | ||||
\(303\) | −5.67216 | − | 9.82447i | −0.325857 | − | 0.564401i | ||||
\(304\) | 11.0014 | + | 19.0550i | 0.630972 | + | 1.09288i | ||||
\(305\) | −0.390443 | −0.0223567 | ||||||||
\(306\) | −5.76200 | − | 9.98008i | −0.329392 | − | 0.570523i | ||||
\(307\) | 7.37658 | 0.421004 | 0.210502 | − | 0.977593i | \(-0.432490\pi\) | ||||
0.210502 | + | 0.977593i | \(0.432490\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.63825 | − | 11.4978i | −0.377637 | − | 0.654086i | ||||
\(310\) | −1.64081 | −0.0931915 | ||||||||
\(311\) | −7.08088 | − | 12.2644i | −0.401520 | − | 0.695453i | 0.592390 | − | 0.805652i | \(-0.298185\pi\) |
−0.993910 | + | 0.110199i | \(0.964851\pi\) | |||||||
\(312\) | 3.50353 | + | 12.1610i | 0.198348 | + | 0.688479i | ||||
\(313\) | 13.3576 | − | 23.1361i | 0.755017 | − | 1.30773i | −0.190349 | − | 0.981716i | \(-0.560962\pi\) |
0.945366 | − | 0.326011i | \(-0.105705\pi\) | |||||||
\(314\) | −11.0951 | − | 19.2173i | −0.626132 | − | 1.08449i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.75352 | + | 15.1615i | −0.492424 | + | 0.852904i | ||||
\(317\) | −10.7181 | + | 18.5643i | −0.601989 | + | 1.04268i | 0.390530 | + | 0.920590i | \(0.372292\pi\) |
−0.992520 | + | 0.122086i | \(0.961042\pi\) | |||||||
\(318\) | 2.73503 | 0.153373 | ||||||||
\(319\) | −10.8018 | −0.604785 | ||||||||
\(320\) | 1.53037 | − | 2.65069i | 0.0855506 | − | 0.148178i | ||||
\(321\) | −2.40567 | + | 4.16674i | −0.134271 | + | 0.232565i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.12757 | − | 10.6133i | −0.340947 | − | 0.590538i | ||||
\(324\) | −8.24404 | + | 14.2791i | −0.458002 | + | 0.793283i | ||||
\(325\) | 17.0895 | + | 4.23824i | 0.947953 | + | 0.235095i | ||||
\(326\) | 13.3327 | + | 23.0929i | 0.738429 | + | 1.27900i | ||||
\(327\) | −6.16040 | −0.340671 | ||||||||
\(328\) | −29.1943 | − | 50.5660i | −1.61199 | − | 2.79204i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.52243 | −0.0838069 | ||||||||
\(331\) | −5.30692 | − | 9.19185i | −0.291695 | − | 0.505230i | 0.682516 | − | 0.730871i | \(-0.260886\pi\) |
−0.974211 | + | 0.225641i | \(0.927552\pi\) | |||||||
\(332\) | 5.52933 | 0.303462 | ||||||||
\(333\) | −11.7089 | − | 20.2805i | −0.641646 | − | 1.11136i | ||||
\(334\) | 22.2266 | + | 38.4975i | 1.21618 | + | 2.10649i | ||||
\(335\) | 0.954935 | + | 1.65400i | 0.0521737 | + | 0.0903675i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.75587 | 0.368016 | 0.184008 | − | 0.982925i | \(-0.441093\pi\) | ||||
0.184008 | + | 0.982925i | \(0.441093\pi\) | |||||||
\(338\) | −1.18230 | − | 31.5952i | −0.0643085 | − | 1.71855i | ||||
\(339\) | 3.62540 | + | 6.27938i | 0.196905 | + | 0.341049i | ||||
\(340\) | 1.30254 | − | 2.25607i | 0.0706404 | − | 0.122353i | ||||
\(341\) | 4.80418 | 0.260161 | ||||||||
\(342\) | −18.6042 | + | 32.2233i | −1.00600 | + | 1.74244i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 19.5796 | − | 33.9129i | 1.05566 | − | 1.82846i | ||||
\(345\) | 0.474798 | + | 0.822375i | 0.0255623 | + | 0.0442752i | ||||
\(346\) | 9.96960 | + | 17.2679i | 0.535969 | + | 0.928326i | ||||
\(347\) | −16.0204 | −0.860021 | −0.430010 | − | 0.902824i | \(-0.641490\pi\) | ||||
−0.430010 | + | 0.902824i | \(0.641490\pi\) | |||||||
\(348\) | 13.1037 | 0.702434 | ||||||||
\(349\) | −8.01922 | − | 13.8897i | −0.429259 | − | 0.743498i | 0.567549 | − | 0.823340i | \(-0.307892\pi\) |
−0.996808 | + | 0.0798418i | \(0.974558\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.2396 | + | 10.6300i | −0.546552 | + | 0.567386i | ||||
\(352\) | −0.983006 | + | 1.70262i | −0.0523944 | + | 0.0907498i | ||||
\(353\) | −1.92156 | + | 3.32823i | −0.102274 | + | 0.177144i | −0.912621 | − | 0.408806i | \(-0.865945\pi\) |
0.810347 | + | 0.585950i | \(0.199279\pi\) | |||||||
\(354\) | −0.574578 | + | 0.995198i | −0.0305385 | + | 0.0528942i | ||||
\(355\) | −1.62182 | − | 2.80908i | −0.0860773 | − | 0.149090i | ||||
\(356\) | 48.7210 | 2.58221 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 18.9140 | − | 32.7601i | 0.999638 | − | 1.73142i | ||||
\(359\) | 10.5668 | − | 18.3022i | 0.557692 | − | 0.965952i | −0.439996 | − | 0.898000i | \(-0.645020\pi\) |
0.997689 | − | 0.0679519i | \(-0.0216465\pi\) | |||||||
\(360\) | −3.86895 | −0.203912 | ||||||||
\(361\) | −10.2845 | + | 17.8133i | −0.541289 | + | 0.937540i | ||||
\(362\) | −16.2294 | −0.853000 | ||||||||
\(363\) | −3.83194 | −0.201125 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.07067 | 0.213069 | ||||||||
\(366\) | −2.09526 | −0.109521 | ||||||||
\(367\) | 7.36961 | − | 12.7645i | 0.384690 | − | 0.666303i | −0.607036 | − | 0.794674i | \(-0.707642\pi\) |
0.991726 | + | 0.128371i | \(0.0409749\pi\) | |||||||
\(368\) | −12.9052 | −0.672730 | ||||||||
\(369\) | 15.2442 | − | 26.4038i | 0.793583 | − | 1.37453i | ||||
\(370\) | 3.99904 | − | 6.92653i | 0.207900 | − | 0.360093i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −5.82798 | −0.302166 | ||||||||
\(373\) | −6.46330 | − | 11.1948i | −0.334657 | − | 0.579643i | 0.648762 | − | 0.760991i | \(-0.275287\pi\) |
−0.983419 | + | 0.181349i | \(0.941954\pi\) | |||||||
\(374\) | −5.76200 | + | 9.98008i | −0.297946 | + | 0.516058i | ||||
\(375\) | 1.27189 | − | 2.20297i | 0.0656800 | − | 0.113761i | ||||
\(376\) | 20.9721 | − | 36.3247i | 1.08155 | − | 1.87331i | ||||
\(377\) | −15.5427 | − | 3.85463i | −0.800488 | − | 0.198523i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.4179 | + | 23.2405i | 0.689231 | + | 1.19378i | 0.972087 | + | 0.234621i | \(0.0753848\pi\) |
−0.282856 | + | 0.959162i | \(0.591282\pi\) | |||||||
\(380\) | −8.41121 | −0.431486 | ||||||||
\(381\) | 6.79722 | 0.348232 | ||||||||
\(382\) | 22.7960 | + | 39.4838i | 1.16634 | + | 2.02017i | ||||
\(383\) | 1.45391 | + | 2.51825i | 0.0742914 | + | 0.128677i | 0.900778 | − | 0.434280i | \(-0.142997\pi\) |
−0.826487 | + | 0.562957i | \(0.809664\pi\) | |||||||
\(384\) | 7.60337 | − | 13.1694i | 0.388008 | − | 0.672049i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.93889 | − | 17.2147i | 0.505876 | − | 0.876203i | ||||
\(387\) | 20.4475 | 1.03941 | ||||||||
\(388\) | −20.1178 | + | 34.8450i | −1.02132 | + | 1.76899i | ||||
\(389\) | 8.35048 | + | 14.4635i | 0.423386 | + | 0.733327i | 0.996268 | − | 0.0863114i | \(-0.0275080\pi\) |
−0.572882 | + | 0.819638i | \(0.694175\pi\) | |||||||
\(390\) | −2.19061 | − | 0.543278i | −0.110926 | − | 0.0275100i | ||||
\(391\) | 7.18797 | 0.363511 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.0725269 | + | 0.125620i | 0.00365850 | + | 0.00633671i | ||||
\(394\) | −10.6041 | − | 18.3668i | −0.534227 | − | 0.925308i | ||||
\(395\) | −0.763620 | − | 1.32263i | −0.0384219 | − | 0.0665487i | ||||
\(396\) | 23.1583 | 1.16375 | ||||||||
\(397\) | 12.0492 | + | 20.8699i | 0.604733 | + | 1.04743i | 0.992094 | + | 0.125500i | \(0.0400536\pi\) |
−0.387360 | + | 0.921928i | \(0.626613\pi\) | |||||||
\(398\) | −42.4806 | −2.12936 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.54059 | + | 14.7927i | 0.427030 | + | 0.739637i | ||||
\(401\) | 1.84490 | 0.0921297 | 0.0460649 | − | 0.998938i | \(-0.485332\pi\) | ||||
0.0460649 | + | 0.998938i | \(0.485332\pi\) | |||||||
\(402\) | 5.12453 | + | 8.87594i | 0.255588 | + | 0.442692i | ||||
\(403\) | 6.91271 | + | 1.71437i | 0.344347 | + | 0.0853990i | ||||
\(404\) | −29.4683 | + | 51.0406i | −1.46610 | + | 2.53937i | ||||
\(405\) | −0.719175 | − | 1.24565i | −0.0357361 | − | 0.0618967i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.7089 | + | 20.2805i | −0.580390 | + | 1.00527i | ||||
\(408\) | 3.41918 | − | 5.92218i | 0.169274 | − | 0.293192i | ||||
\(409\) | −25.6703 | −1.26931 | −0.634657 | − | 0.772794i | \(-0.718859\pi\) | ||||
−0.634657 | + | 0.772794i | \(0.718859\pi\) | |||||||
\(410\) | 10.4129 | 0.514259 | ||||||||
\(411\) | −1.83756 | + | 3.18274i | −0.0906400 | + | 0.156993i | ||||
\(412\) | −34.4874 | + | 59.7339i | −1.69907 | + | 2.94288i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −10.9118 | − | 18.8998i | −0.536287 | − | 0.928876i | ||||
\(415\) | −0.241178 | + | 0.417732i | −0.0118389 | + | 0.0205057i | ||||
\(416\) | −2.02202 | + | 2.09910i | −0.0991378 | + | 0.102917i | ||||
\(417\) | 4.17265 | + | 7.22724i | 0.204335 | + | 0.353919i | ||||
\(418\) | 37.2083 | 1.81992 | ||||||||
\(419\) | 13.1199 | + | 22.7244i | 0.640950 | + | 1.11016i | 0.985221 | + | 0.171288i | \(0.0547928\pi\) |
−0.344271 | + | 0.938870i | \(0.611874\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.6637 | 1.15330 | 0.576650 | − | 0.816992i | \(-0.304360\pi\) | ||||
0.576650 | + | 0.816992i | \(0.304360\pi\) | |||||||
\(422\) | 28.2815 | + | 48.9850i | 1.37672 | + | 2.38455i | ||||
\(423\) | 21.9018 | 1.06490 | ||||||||
\(424\) | −3.47526 | − | 6.01933i | −0.168774 | − | 0.292325i | ||||
\(425\) | −4.75696 | − | 8.23929i | −0.230746 | − | 0.399664i | ||||
\(426\) | −8.70327 | − | 15.0745i | −0.421675 | − | 0.730362i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 24.9961 | 1.20823 | ||||||||
\(429\) | 6.41399 | + | 1.59069i | 0.309670 | + | 0.0767991i | ||||
\(430\) | 3.49180 | + | 6.04797i | 0.168389 | + | 0.291659i | ||||
\(431\) | 11.5088 | − | 19.9339i | 0.554361 | − | 0.960182i | −0.443592 | − | 0.896229i | \(-0.646296\pi\) |
0.997953 | − | 0.0639528i | \(-0.0203707\pi\) | |||||||
\(432\) | −14.3187 | −0.688909 | ||||||||
\(433\) | 12.9304 | − | 22.3961i | 0.621394 | − | 1.07629i | −0.367832 | − | 0.929892i | \(-0.619900\pi\) |
0.989226 | − | 0.146394i | \(-0.0467667\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.571557 | + | 0.989965i | −0.0274040 | + | 0.0474652i | ||||
\(436\) | 16.0024 | + | 27.7170i | 0.766378 | + | 1.32741i | ||||
\(437\) | −11.6041 | − | 20.0989i | −0.555101 | − | 0.961462i | ||||
\(438\) | 21.8447 | 1.04378 | ||||||||
\(439\) | −35.6771 | −1.70277 | −0.851387 | − | 0.524537i | \(-0.824238\pi\) | ||||
−0.851387 | + | 0.524537i | \(0.824238\pi\) | |||||||
\(440\) | 1.93447 | + | 3.35061i | 0.0922225 | + | 0.159734i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.8523 | + | 12.3041i | −0.563757 | + | 0.585248i | ||||
\(443\) | 3.42940 | − | 5.93990i | 0.162936 | − | 0.282213i | −0.772984 | − | 0.634425i | \(-0.781237\pi\) |
0.935920 | + | 0.352212i | \(0.114570\pi\) | |||||||
\(444\) | 14.2042 | − | 24.6024i | 0.674100 | − | 1.16758i | ||||
\(445\) | −2.12511 | + | 3.68079i | −0.100740 | + | 0.174486i | ||||
\(446\) | 35.5972 | + | 61.6562i | 1.68558 | + | 2.91951i | ||||
\(447\) | 11.9887 | 0.567045 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.99075 | − | 8.64423i | 0.235528 | − | 0.407946i | −0.723898 | − | 0.689907i | \(-0.757651\pi\) |
0.959426 | + | 0.281961i | \(0.0909847\pi\) | |||||||
\(450\) | −14.4428 | + | 25.0156i | −0.680839 | + | 1.17925i | ||||
\(451\) | −30.4885 | −1.43565 | ||||||||
\(452\) | 18.8349 | − | 32.6230i | 0.885919 | − | 1.53446i | ||||
\(453\) | −7.98081 | −0.374971 | ||||||||
\(454\) | 48.1824 | 2.26131 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −22.0794 | −1.03396 | ||||||||
\(457\) | −8.77311 | −0.410389 | −0.205194 | − | 0.978721i | \(-0.565783\pi\) | ||||
−0.205194 | + | 0.978721i | \(0.565783\pi\) | |||||||
\(458\) | 1.61518 | − | 2.79757i | 0.0754722 | − | 0.130722i | ||||
\(459\) | 7.97526 | 0.372253 | ||||||||
\(460\) | 2.46670 | − | 4.27245i | 0.115010 | − | 0.199204i | ||||
\(461\) | −3.44272 | + | 5.96296i | −0.160343 | + | 0.277723i | −0.934992 | − | 0.354669i | \(-0.884593\pi\) |
0.774649 | + | 0.632392i | \(0.217927\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.9526 | −0.648432 | −0.324216 | − | 0.945983i | \(-0.605100\pi\) | ||||
−0.324216 | + | 0.945983i | \(0.605100\pi\) | |||||||
\(464\) | −7.76757 | − | 13.4538i | −0.360600 | − | 0.624578i | ||||
\(465\) | 0.254204 | − | 0.440294i | 0.0117884 | − | 0.0204181i | ||||
\(466\) | −1.84395 | + | 3.19381i | −0.0854192 | + | 0.147950i | ||||
\(467\) | 14.4056 | − | 24.9513i | 0.666613 | − | 1.15461i | −0.312232 | − | 0.950006i | \(-0.601077\pi\) |
0.978845 | − | 0.204602i | \(-0.0655900\pi\) | |||||||
\(468\) | 33.3223 | + | 8.26403i | 1.54032 | + | 0.382005i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.74013 | + | 6.47810i | 0.172520 | + | 0.298813i | ||||
\(471\) | 6.87568 | 0.316815 | ||||||||
\(472\) | 2.92035 | 0.134420 | ||||||||
\(473\) | −10.2238 | − | 17.7081i | −0.470089 | − | 0.814219i | ||||
\(474\) | −4.09786 | − | 7.09770i | −0.188221 | − | 0.326008i | ||||
\(475\) | −15.3591 | + | 26.6027i | −0.704723 | + | 1.22062i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.81466 | − | 3.14308i | 0.0830876 | − | 0.143912i | ||||
\(478\) | 54.6719 | 2.50063 | ||||||||
\(479\) | 12.2936 | − | 21.2931i | 0.561707 | − | 0.972906i | −0.435640 | − | 0.900121i | \(-0.643478\pi\) |
0.997348 | − | 0.0727849i | \(-0.0231887\pi\) | |||||||
\(480\) | 0.104028 | + | 0.180181i | 0.00474820 | + | 0.00822412i | ||||
\(481\) | −24.0850 | + | 25.0032i | −1.09818 | + | 1.14005i | ||||
\(482\) | 32.3726 | 1.47453 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.95395 | + | 17.2407i | 0.452452 | + | 0.783670i | ||||
\(485\) | −1.75499 | − | 3.03973i | −0.0796899 | − | 0.138027i | ||||
\(486\) | −18.7934 | − | 32.5511i | −0.852484 | − | 1.47655i | ||||
\(487\) | −2.57316 | −0.116601 | −0.0583004 | − | 0.998299i | \(-0.518568\pi\) | ||||
−0.0583004 | + | 0.998299i | \(0.518568\pi\) | |||||||
\(488\) | 2.66234 | + | 4.61131i | 0.120519 | + | 0.208744i | ||||
\(489\) | −8.26233 | −0.373635 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.01897 | − | 12.1572i | −0.316762 | − | 0.548647i | 0.663049 | − | 0.748576i | \(-0.269262\pi\) |
−0.979810 | + | 0.199929i | \(0.935929\pi\) | |||||||
\(492\) | 36.9857 | 1.66745 | ||||||||
\(493\) | 4.32639 | + | 7.49354i | 0.194851 | + | 0.337492i | ||||
\(494\) | 53.5389 | + | 13.2778i | 2.40883 | + | 0.597396i | ||||
\(495\) | −1.01011 | + | 1.74957i | −0.0454012 | + | 0.0786373i | ||||
\(496\) | 3.45468 | + | 5.98368i | 0.155120 | + | 0.268675i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.29425 | + | 2.24170i | −0.0579965 | + | 0.100453i | ||||
\(499\) | −6.76726 | + | 11.7212i | −0.302944 | + | 0.524715i | −0.976801 | − | 0.214147i | \(-0.931303\pi\) |
0.673857 | + | 0.738862i | \(0.264636\pi\) | |||||||
\(500\) | −13.2156 | −0.591018 | ||||||||
\(501\) | −13.7739 | −0.615373 | ||||||||
\(502\) | −19.3393 | + | 33.4966i | −0.863155 | + | 1.49503i | ||||
\(503\) | 4.13877 | − | 7.16856i | 0.184539 | − | 0.319630i | −0.758882 | − | 0.651228i | \(-0.774254\pi\) |
0.943421 | + | 0.331597i | \(0.107588\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.57069 | − | 4.45257i | −0.114394 | − | 0.198137i | ||||
\(506\) | −10.9118 | + | 18.8998i | −0.485090 | + | 0.840200i | ||||
\(507\) | 8.66142 | + | 4.57766i | 0.384667 | + | 0.203301i | ||||
\(508\) | −17.6567 | − | 30.5822i | −0.783388 | − | 1.35687i | ||||
\(509\) | −0.166218 | −0.00736750 | −0.00368375 | − | 0.999993i | \(-0.501173\pi\) | ||||
−0.00368375 | + | 0.999993i | \(0.501173\pi\) | |||||||
\(510\) | 0.609771 | + | 1.05615i | 0.0270011 | + | 0.0467673i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −35.4115 | −1.56498 | ||||||||
\(513\) | −12.8751 | − | 22.3004i | −0.568451 | − | 0.984585i | ||||
\(514\) | −71.1137 | −3.13669 | ||||||||
\(515\) | −3.00853 | − | 5.21093i | −0.132572 | − | 0.229621i | ||||
\(516\) | 12.4025 | + | 21.4818i | 0.545990 | + | 0.945683i | ||||
\(517\) | −10.9509 | − | 18.9675i | −0.481619 | − | 0.834189i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.17821 | −0.271193 | ||||||||
\(520\) | 1.58784 | + | 5.51149i | 0.0696315 | + | 0.241695i | ||||
\(521\) | 3.53090 | + | 6.11569i | 0.154691 | + | 0.267933i | 0.932947 | − | 0.360015i | \(-0.117228\pi\) |
−0.778255 | + | 0.627948i | \(0.783895\pi\) | |||||||
\(522\) | 13.1355 | − | 22.7514i | 0.574926 | − | 0.995802i | ||||
\(523\) | 23.3912 | 1.02283 | 0.511414 | − | 0.859335i | \(-0.329122\pi\) | ||||
0.511414 | + | 0.859335i | \(0.329122\pi\) | |||||||
\(524\) | 0.376796 | − | 0.652630i | 0.0164604 | − | 0.0285103i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.07258 | − | 3.58981i | 0.0903687 | − | 0.156523i | ||||
\(527\) | −1.92420 | − | 3.33280i | −0.0838193 | − | 0.145179i | ||||
\(528\) | 3.20544 | + | 5.55198i | 0.139499 | + | 0.241619i | ||||
\(529\) | −9.38775 | −0.408163 | ||||||||
\(530\) | 1.23955 | 0.0538425 | ||||||||
\(531\) | 0.762452 | + | 1.32061i | 0.0330876 | + | 0.0573094i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −43.8697 | − | 10.8798i | −1.90021 | − | 0.471257i | ||||
\(534\) | −11.4041 | + | 19.7525i | −0.493503 | + | 0.854773i | ||||
\(535\) | −1.09028 | + | 1.88842i | −0.0471368 | + | 0.0816434i | ||||
\(536\) | 13.0230 | − | 22.5564i | 0.562507 | − | 0.974290i | ||||
\(537\) | 5.86056 | + | 10.1508i | 0.252902 | + | 0.438039i | ||||
\(538\) | 20.3779 | 0.878554 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.73688 | − | 4.74041i | 0.117776 | − | 0.203995i | ||||
\(541\) | −13.1540 | + | 22.7833i | −0.565533 | + | 0.979532i | 0.431467 | + | 0.902129i | \(0.357996\pi\) |
−0.997000 | + | 0.0774030i | \(0.975337\pi\) | |||||||
\(542\) | −29.5683 | −1.27007 | ||||||||
\(543\) | 2.51437 | − | 4.35501i | 0.107902 | − | 0.186891i | ||||
\(544\) | 1.57488 | 0.0675222 | ||||||||
\(545\) | −2.79197 | −0.119595 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 41.7636 | 1.78568 | 0.892841 | − | 0.450371i | \(-0.148708\pi\) | ||||
0.892841 | + | 0.450371i | \(0.148708\pi\) | |||||||
\(548\) | 19.0932 | 0.815620 | ||||||||
\(549\) | −1.39018 | + | 2.40786i | −0.0593315 | + | 0.102765i | ||||
\(550\) | 28.8855 | 1.23168 | ||||||||
\(551\) | 13.9689 | − | 24.1949i | 0.595095 | − | 1.03074i | ||||
\(552\) | 6.47508 | − | 11.2152i | 0.275598 | − | 0.477349i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 25.0948 | 1.06617 | ||||||||
\(555\) | 1.23911 | + | 2.14620i | 0.0525974 | + | 0.0911013i | ||||
\(556\) | 21.6780 | − | 37.5474i | 0.919351 | − | 1.59236i | ||||
\(557\) | −3.65494 | + | 6.33053i | −0.154865 | + | 0.268233i | −0.933010 | − | 0.359851i | \(-0.882827\pi\) |
0.778145 | + | 0.628085i | \(0.216161\pi\) | |||||||
\(558\) | −5.84212 | + | 10.1188i | −0.247317 | + | 0.428365i | ||||
\(559\) | −8.39181 | − | 29.1284i | −0.354936 | − | 1.23200i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.78537 | − | 3.09235i | −0.0753785 | − | 0.130559i | ||||
\(562\) | −6.31560 | −0.266407 | ||||||||
\(563\) | 44.7737 | 1.88699 | 0.943493 | − | 0.331393i | \(-0.107519\pi\) | ||||
0.943493 | + | 0.331393i | \(0.107519\pi\) | |||||||
\(564\) | 13.2846 | + | 23.0096i | 0.559382 | + | 0.968878i | ||||
\(565\) | 1.64308 | + | 2.84589i | 0.0691247 | + | 0.119727i | ||||
\(566\) | −5.59830 | + | 9.69654i | −0.235314 | + | 0.407576i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −22.1176 | + | 38.3089i | −0.928036 | + | 1.60741i | ||||
\(569\) | −42.5127 | −1.78222 | −0.891112 | − | 0.453784i | \(-0.850074\pi\) | ||||
−0.891112 | + | 0.453784i | \(0.850074\pi\) | |||||||
\(570\) | 1.96881 | − | 3.41007i | 0.0824642 | − | 0.142832i | ||||
\(571\) | 20.4324 | + | 35.3899i | 0.855069 | + | 1.48102i | 0.876581 | + | 0.481254i | \(0.159818\pi\) |
−0.0215128 | + | 0.999769i | \(0.506848\pi\) | |||||||
\(572\) | −9.50430 | − | 32.9900i | −0.397395 | − | 1.37938i | ||||
\(573\) | −14.1268 | −0.590155 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.00851 | − | 15.6032i | −0.375681 | − | 0.650698i | ||||
\(576\) | −10.8979 | − | 18.8756i | −0.454077 | − | 0.786485i | ||||
\(577\) | 10.8640 | + | 18.8170i | 0.452275 | + | 0.783363i | 0.998527 | − | 0.0542578i | \(-0.0172793\pi\) |
−0.546252 | + | 0.837621i | \(0.683946\pi\) | |||||||
\(578\) | −32.1144 | −1.33578 | ||||||||
\(579\) | 3.07959 | + | 5.33400i | 0.127983 | + | 0.221674i | ||||
\(580\) | 5.93877 | 0.246594 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −9.41790 | − | 16.3123i | −0.390384 | − | 0.676166i | ||||
\(583\) | −3.62932 | −0.150311 | ||||||||
\(584\) | −27.7570 | − | 48.0765i | −1.14859 | − | 1.98942i | ||||
\(585\) | −2.07778 | + | 2.15699i | −0.0859057 | + | 0.0891805i | ||||
\(586\) | 2.38491 | − | 4.13078i | 0.0985196 | − | 0.170641i | ||||
\(587\) | −10.2408 | − | 17.7376i | −0.422683 | − | 0.732108i | 0.573518 | − | 0.819193i | \(-0.305578\pi\) |
−0.996201 | + | 0.0870851i | \(0.972245\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.21277 | + | 10.7608i | −0.255993 | + | 0.443393i | ||||
\(590\) | −0.260406 | + | 0.451036i | −0.0107207 | + | 0.0185688i | ||||
\(591\) | 6.57141 | 0.270312 | ||||||||
\(592\) | −33.6795 | −1.38422 | ||||||||
\(593\) | 2.81930 | − | 4.88318i | 0.115775 | − | 0.200528i | −0.802314 | − | 0.596902i | \(-0.796398\pi\) |
0.918089 | + | 0.396374i | \(0.129732\pi\) | |||||||
\(594\) | −12.1070 | + | 20.9699i | −0.496756 | + | 0.860407i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −31.1421 | − | 53.9397i | −1.27563 | − | 2.20946i | ||||
\(597\) | 6.58136 | − | 11.3993i | 0.269357 | − | 0.466541i | ||||
\(598\) | −22.4454 | + | 23.3010i | −0.917860 | + | 0.952849i | ||||
\(599\) | −19.8359 | − | 34.3568i | −0.810474 | − | 1.40378i | −0.912533 | − | 0.409004i | \(-0.865876\pi\) |
0.102058 | − | 0.994778i | \(-0.467457\pi\) | |||||||
\(600\) | −17.1407 | −0.699766 | ||||||||
\(601\) | −8.41334 | − | 14.5723i | −0.343187 | − | 0.594418i | 0.641836 | − | 0.766842i | \(-0.278173\pi\) |
−0.985023 | + | 0.172425i | \(0.944840\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.6003 | 0.553845 | ||||||||
\(604\) | 20.7312 | + | 35.9075i | 0.843540 | + | 1.46105i | ||||
\(605\) | −1.73668 | −0.0706061 | ||||||||
\(606\) | −13.7953 | − | 23.8941i | −0.560394 | − | 0.970631i | ||||
\(607\) | −11.2490 | − | 19.4838i | −0.456582 | − | 0.790823i | 0.542196 | − | 0.840252i | \(-0.317593\pi\) |
−0.998778 | + | 0.0494290i | \(0.984260\pi\) | |||||||
\(608\) | −2.54245 | − | 4.40365i | −0.103110 | − | 0.178592i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.949597 | −0.0384480 | ||||||||
\(611\) | −8.98863 | − | 31.2001i | −0.363641 | − | 1.26222i | ||||
\(612\) | −9.27547 | − | 16.0656i | −0.374939 | − | 0.649413i | ||||
\(613\) | −13.7135 | + | 23.7524i | −0.553882 | + | 0.959351i | 0.444108 | + | 0.895973i | \(0.353521\pi\) |
−0.997990 | + | 0.0633780i | \(0.979813\pi\) | |||||||
\(614\) | 17.9406 | 0.724022 | ||||||||
\(615\) | −1.61324 | + | 2.79421i | −0.0650521 | + | 0.112673i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.31896 | + | 9.21271i | −0.214133 | + | 0.370890i | −0.953004 | − | 0.302957i | \(-0.902026\pi\) |
0.738871 | + | 0.673847i | \(0.235359\pi\) | |||||||
\(618\) | −16.1449 | − | 27.9637i | −0.649442 | − | 1.12487i | ||||
\(619\) | 22.7339 | + | 39.3762i | 0.913751 | + | 1.58266i | 0.808719 | + | 0.588195i | \(0.200161\pi\) |
0.105032 | + | 0.994469i | \(0.466505\pi\) | |||||||
\(620\) | −2.64131 | −0.106078 | ||||||||
\(621\) | 15.1032 | 0.606071 | ||||||||
\(622\) | −17.2214 | − | 29.8283i | −0.690515 | − | 1.19601i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.63107 | + | 9.13258i | 0.105327 | + | 0.365596i | ||||
\(625\) | −11.6319 | + | 20.1471i | −0.465278 | + | 0.805885i | ||||
\(626\) | 32.4870 | − | 56.2692i | 1.29844 | − | 2.24897i | ||||
\(627\) | −5.76454 | + | 9.98448i | −0.230214 | + | 0.398742i | ||||
\(628\) | −17.8605 | − | 30.9353i | −0.712711 | − | 1.23445i | ||||
\(629\) | 18.7589 | 0.747966 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.7992 | + | 25.6329i | −0.589146 | + | 1.02043i | 0.405199 | + | 0.914229i | \(0.367202\pi\) |
−0.994345 | + | 0.106202i | \(0.966131\pi\) | |||||||
\(632\) | −10.4139 | + | 18.0374i | −0.414243 | + | 0.717489i | ||||
\(633\) | −17.5262 | −0.696604 | ||||||||
\(634\) | −26.0675 | + | 45.1503i | −1.03527 | + | 1.79315i | ||||
\(635\) | 3.08058 | 0.122249 | ||||||||
\(636\) | 4.40275 | 0.174580 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −26.2711 | −1.04008 | ||||||||
\(639\) | −23.0981 | −0.913747 | ||||||||
\(640\) | 3.44594 | − | 5.96854i | 0.136213 | − | 0.235927i | ||||
\(641\) | −42.5646 | −1.68120 | −0.840601 | − | 0.541654i | \(-0.817798\pi\) | ||||
−0.840601 | + | 0.541654i | \(0.817798\pi\) | |||||||
\(642\) | −5.85082 | + | 10.1339i | −0.230914 | + | 0.399954i | ||||
\(643\) | −10.9980 | + | 19.0492i | −0.433721 | + | 0.751226i | −0.997190 | − | 0.0749106i | \(-0.976133\pi\) |
0.563470 | + | 0.826137i | \(0.309466\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.16388 | −0.0852029 | ||||||||
\(646\) | −14.9029 | − | 25.8125i | −0.586345 | − | 1.01558i | ||||
\(647\) | −17.4026 | + | 30.1421i | −0.684166 | + | 1.18501i | 0.289533 | + | 0.957168i | \(0.406500\pi\) |
−0.973698 | + | 0.227841i | \(0.926833\pi\) | |||||||
\(648\) | −9.80778 | + | 16.9876i | −0.385286 | + | 0.667335i | ||||
\(649\) | 0.762452 | − | 1.32061i | 0.0299289 | − | 0.0518383i | ||||
\(650\) | 41.5633 | + | 10.3078i | 1.63025 | + | 0.404306i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 21.4625 | + | 37.1741i | 0.840535 | + | 1.45585i | ||||
\(653\) | −50.8167 | −1.98861 | −0.994306 | − | 0.106559i | \(-0.966017\pi\) | ||||
−0.994306 | + | 0.106559i | \(0.966017\pi\) | |||||||
\(654\) | −14.9827 | −0.585870 | ||||||||
\(655\) | 0.0328701 | + | 0.0569326i | 0.00128434 | + | 0.00222454i | ||||
\(656\) | −21.9242 | − | 37.9739i | −0.855997 | − | 1.48263i | ||||
\(657\) | 14.4937 | − | 25.1038i | 0.565453 | − | 0.979394i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.37203 | − | 12.7687i | 0.287173 | − | 0.497399i | −0.685960 | − | 0.727639i | \(-0.740618\pi\) |
0.973134 | + | 0.230240i | \(0.0739511\pi\) | |||||||
\(660\) | −2.45075 | −0.0953953 | ||||||||
\(661\) | 9.06227 | − | 15.6963i | 0.352481 | − | 0.610516i | −0.634202 | − | 0.773167i | \(-0.718671\pi\) |
0.986684 | + | 0.162651i | \(0.0520046\pi\) | |||||||
\(662\) | −12.9069 | − | 22.3555i | −0.501643 | − | 0.868871i | ||||
\(663\) | −1.46546 | − | 5.08669i | −0.0569136 | − | 0.197551i | ||||
\(664\) | 6.57814 | 0.255281 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −28.4773 | − | 49.3241i | −1.10347 | − | 1.91127i | ||||
\(667\) | 8.19313 | + | 14.1909i | 0.317239 | + | 0.549475i | ||||
\(668\) | 35.7795 | + | 61.9719i | 1.38435 | + | 2.39777i | ||||
\(669\) | −22.0598 | −0.852881 | ||||||||
\(670\) | 2.32250 | + | 4.02268i | 0.0897259 | + | 0.155410i | ||||
\(671\) | 2.78036 | 0.107335 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.4574 | − | 18.1127i | −0.403102 | − | 0.698193i | 0.590997 | − | 0.806674i | \(-0.298735\pi\) |
−0.994099 | + | 0.108481i | \(0.965401\pi\) | |||||||
\(674\) | 16.4309 | 0.632896 | ||||||||
\(675\) | −9.99521 | − | 17.3122i | −0.384716 | − | 0.666348i | ||||
\(676\) | −1.90322 | − | 50.8608i | −0.0732008 | − | 1.95618i | ||||
\(677\) | 19.1089 | − | 33.0976i | 0.734416 | − | 1.27205i | −0.220563 | − | 0.975373i | \(-0.570790\pi\) |
0.954979 | − | 0.296673i | \(-0.0958771\pi\) | |||||||
\(678\) | 8.81733 | + | 15.2721i | 0.338628 | + | 0.586520i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.54961 | − | 2.68401i | 0.0594249 | − | 0.102927i | ||||
\(681\) | −7.46472 | + | 12.9293i | −0.286049 | + | 0.495451i | ||||
\(682\) | 11.6842 | 0.447413 | ||||||||
\(683\) | −23.8253 | −0.911649 | −0.455825 | − | 0.890070i | \(-0.650656\pi\) | ||||
−0.455825 | + | 0.890070i | \(0.650656\pi\) | |||||||
\(684\) | −29.9483 | + | 51.8720i | −1.14510 | + | 1.98337i | ||||
\(685\) | −0.832803 | + | 1.44246i | −0.0318198 | + | 0.0551135i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.500466 | + | 0.866833i | 0.0190940 | + | 0.0330717i | ||||
\(688\) | 14.7038 | − | 25.4677i | 0.560577 | − | 0.970948i | ||||
\(689\) | −5.22221 | − | 1.29512i | −0.198950 | − | 0.0493403i | ||||
\(690\) | 1.15476 | + | 2.00010i | 0.0439608 | + | 0.0761424i | ||||
\(691\) | −19.1413 | −0.728168 | −0.364084 | − | 0.931366i | \(-0.618618\pi\) | ||||
−0.364084 | + | 0.931366i | \(0.618618\pi\) | |||||||
\(692\) | 16.0487 | + | 27.7972i | 0.610080 | + | 1.05669i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −38.9632 | −1.47902 | ||||||||
\(695\) | 1.89109 | + | 3.27547i | 0.0717333 | + | 0.124246i | ||||
\(696\) | 15.5893 | 0.590909 | ||||||||
\(697\) | 12.2114 | + | 21.1508i | 0.462540 | + | 0.801143i | ||||
\(698\) | −19.5035 | − | 33.7811i | −0.738219 | − | 1.27863i | ||||
\(699\) | −0.571352 | − | 0.989611i | −0.0216105 | − | 0.0374305i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.2956 | −1.03094 | −0.515471 | − | 0.856907i | \(-0.672383\pi\) | ||||
−0.515471 | + | 0.856907i | \(0.672383\pi\) | |||||||
\(702\) | −24.9038 | + | 25.8532i | −0.939935 | + | 0.975765i | ||||
\(703\) | −30.2840 | − | 52.4535i | −1.14218 | − | 1.97832i | ||||
\(704\) | −10.8979 | + | 18.8756i | −0.410729 | + | 0.711403i | ||||
\(705\) | −2.31778 | −0.0872927 | ||||||||
\(706\) | −4.67342 | + | 8.09460i | −0.175886 | + | 0.304644i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.924935 | + | 1.60203i | −0.0347612 | + | 0.0602081i | ||||
\(709\) | −3.08583 | − | 5.34481i | −0.115891 | − | 0.200729i | 0.802245 | − | 0.596995i | \(-0.203639\pi\) |
−0.918135 | + | 0.396267i | \(0.870306\pi\) | |||||||
\(710\) | −3.94443 | − | 6.83195i | −0.148032 | − | 0.256399i | ||||
\(711\) | −10.8755 | −0.407865 | ||||||||
\(712\) | 57.9625 | 2.17224 | ||||||||
\(713\) | −3.64395 | − | 6.31152i | −0.136467 | − | 0.236368i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.90690 | + | 0.720919i | 0.108712 | + | 0.0269608i | ||||
\(716\) | 30.4471 | − | 52.7360i | 1.13786 | − | 1.97084i | ||||
\(717\) | −8.47011 | + | 14.6707i | −0.316322 | + | 0.547886i | ||||
\(718\) | 25.6994 | − | 44.5127i | 0.959094 | − | 1.66120i | ||||
\(719\) | −1.36066 | − | 2.35674i | −0.0507442 | − | 0.0878915i | 0.839538 | − | 0.543302i | \(-0.182826\pi\) |
−0.890282 | + | 0.455410i | \(0.849493\pi\) | |||||||
\(720\) | −2.90549 | −0.108281 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −25.0129 | + | 43.3236i | −0.930883 | + | 1.61234i | ||||
\(723\) | −5.01537 | + | 8.68687i | −0.186524 | + | 0.323068i | ||||
\(724\) | −26.1256 | −0.970949 | ||||||||
\(725\) | 10.8443 | − | 18.7829i | 0.402749 | − | 0.697581i | ||||
\(726\) | −9.31965 | −0.345885 | ||||||||
\(727\) | −9.47153 | −0.351280 | −0.175640 | − | 0.984455i | \(-0.556199\pi\) | ||||
−0.175640 | + | 0.984455i | \(0.556199\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.987863 | −0.0365875 | ||||||||
\(730\) | 9.90027 | 0.366426 | ||||||||
\(731\) | −8.18976 | + | 14.1851i | −0.302909 | + | 0.524654i | ||||
\(732\) | −3.37287 | −0.124665 | ||||||||
\(733\) | −1.74853 | + | 3.02855i | −0.0645836 | + | 0.111862i | −0.896509 | − | 0.443025i | \(-0.853905\pi\) |
0.831926 | + | 0.554887i | \(0.187239\pi\) | |||||||
\(734\) | 17.9236 | − | 31.0446i | 0.661573 | − | 1.14588i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.98243 | 0.109934 | ||||||||
\(737\) | −6.80013 | − | 11.7782i | −0.250486 | − | 0.433855i | ||||
\(738\) | 37.0755 | − | 64.2166i | 1.36477 | − | 2.36385i | ||||
\(739\) | −16.0151 | + | 27.7390i | −0.589126 | + | 1.02040i | 0.405221 | + | 0.914219i | \(0.367195\pi\) |
−0.994347 | + | 0.106178i | \(0.966139\pi\) | |||||||
\(740\) | 6.43750 | − | 11.1501i | 0.236647 | − | 0.409885i | ||||
\(741\) | −11.8575 | + | 12.3096i | −0.435598 | + | 0.452203i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.4593 | − | 30.2404i | −0.640519 | − | 1.10941i | −0.985317 | − | 0.170734i | \(-0.945386\pi\) |
0.344798 | − | 0.938677i | \(-0.387947\pi\) | |||||||
\(744\) | −6.93343 | −0.254192 | ||||||||
\(745\) | 5.43341 | 0.199065 | ||||||||
\(746\) | −15.7194 | − | 27.2268i | −0.575527 | − | 0.996842i | ||||
\(747\) | 1.71744 | + | 2.97469i | 0.0628377 | + | 0.108838i | ||||
\(748\) | −9.27547 | + | 16.0656i | −0.339145 | + | 0.587416i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 3.09335 | − | 5.35785i | 0.112953 | − | 0.195641i | ||||
\(751\) | 26.9972 | 0.985143 | 0.492571 | − | 0.870272i | \(-0.336057\pi\) | ||||
0.492571 | + | 0.870272i | \(0.336057\pi\) | |||||||
\(752\) | 15.7495 | − | 27.2790i | 0.574327 | − | 0.994763i | ||||
\(753\) | −5.99233 | − | 10.3790i | −0.218373 | − | 0.378233i | ||||
\(754\) | −37.8013 | − | 9.37483i | −1.37664 | − | 0.341411i | ||||
\(755\) | −3.61700 | −0.131636 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.2950 | + | 45.5442i | 0.955707 | + | 1.65533i | 0.732742 | + | 0.680507i | \(0.238240\pi\) |
0.222965 | + | 0.974826i | \(0.428426\pi\) | |||||||
\(758\) | 32.6337 | + | 56.5231i | 1.18531 | + | 2.05301i | ||||
\(759\) | −3.38106 | − | 5.85616i | −0.122725 | − | 0.212565i | ||||
\(760\) | −10.0067 | −0.362980 | ||||||||
\(761\) | −6.96431 | − | 12.0625i | −0.252456 | − | 0.437267i | 0.711745 | − | 0.702437i | \(-0.247905\pi\) |
−0.964201 | + | 0.265171i | \(0.914572\pi\) | |||||||
\(762\) | 16.5315 | 0.598874 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 36.6961 | + | 63.5596i | 1.32762 | + | 2.29950i | ||||
\(765\) | 1.61830 | 0.0585099 | ||||||||
\(766\) | 3.53606 | + | 6.12463i | 0.127763 | + | 0.221292i | ||||
\(767\) | 1.56835 | − | 1.62813i | 0.0566297 | − | 0.0587885i | ||||
\(768\) | 11.7387 | − | 20.3320i | 0.423583 | − | 0.733668i | ||||
\(769\) | −6.89545 | − | 11.9433i | −0.248656 | − | 0.430685i | 0.714497 | − | 0.699639i | \(-0.246656\pi\) |
−0.963153 | + | 0.268953i | \(0.913322\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.0174 | − | 19.0827i | 0.396781 | − | 0.687246i | ||||
\(772\) | 15.9993 | − | 27.7115i | 0.575826 | − | 0.997360i | ||||
\(773\) | 50.4870 | 1.81589 | 0.907946 | − | 0.419087i | \(-0.137650\pi\) | ||||
0.907946 | + | 0.419087i | \(0.137650\pi\) | |||||||
\(774\) | 49.7304 | 1.78752 | ||||||||
\(775\) | −4.82310 | + | 8.35385i | −0.173251 | + | 0.300079i | ||||
\(776\) | −23.9337 | + | 41.4544i | −0.859170 | + | 1.48813i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.3092 | + | 35.1766i | 0.728120 | + | 1.26114i | ||||
\(779\) | 39.4277 | − | 68.2908i | 1.41265 | − | 2.44677i | ||||
\(780\) | −3.52637 | − | 0.874550i | −0.126264 | − | 0.0313139i | ||||
\(781\) | 11.5491 | + | 20.0035i | 0.413258 | + | 0.715783i | ||||
\(782\) | 17.4818 | 0.625150 | ||||||||
\(783\) | 9.09053 | + | 15.7453i | 0.324869 | + | 0.562690i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.11614 | 0.111220 | ||||||||
\(786\) | 0.176393 | + | 0.305521i | 0.00629172 | + | 0.0108976i | ||||
\(787\) | 10.8638 | 0.387252 | 0.193626 | − | 0.981075i | \(-0.437975\pi\) | ||||
0.193626 | + | 0.981075i | \(0.437975\pi\) | |||||||
\(788\) | −17.0701 | − | 29.5663i | −0.608097 | − | 1.05325i | ||||
\(789\) | 0.642194 | + | 1.11231i | 0.0228627 | + | 0.0395994i | ||||
\(790\) | −1.85720 | − | 3.21676i | −0.0660762 | − | 0.114447i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 27.5509 | 0.978980 | ||||||||
\(793\) | 4.00065 | + | 0.992172i | 0.142067 | + | 0.0352331i | ||||
\(794\) | 29.3049 | + | 50.7576i | 1.03999 | + | 1.80132i | ||||
\(795\) | −0.192038 | + | 0.332620i | −0.00681090 | + | 0.0117968i | ||||
\(796\) | −68.3838 | −2.42380 | ||||||||
\(797\) | 3.95840 | − | 6.85616i | 0.140214 | − | 0.242858i | −0.787363 | − | 0.616489i | \(-0.788554\pi\) |
0.927577 | + | 0.373632i | \(0.121888\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.77221 | + | 15.1939i | −0.310339 | + | 0.537522i | ||||
\(800\) | −1.97375 | − | 3.41864i | −0.0697828 | − | 0.120867i | ||||
\(801\) | 15.1330 | + | 26.2111i | 0.534697 | + | 0.926123i | ||||
\(802\) | 4.48697 | 0.158440 | ||||||||
\(803\) | −28.9874 | −1.02294 | ||||||||
\(804\) | 8.24928 | + | 14.2882i | 0.290930 | + | 0.503905i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 16.8124 | + | 4.16952i | 0.592192 | + | 0.146865i | ||||
\(807\) | −3.15707 | + | 5.46821i | −0.111134 | + | 0.192490i | ||||
\(808\) | −35.0579 | + | 60.7221i | −1.23333 | + | 2.13620i | ||||
\(809\) | 14.8194 | − | 25.6680i | 0.521023 | − | 0.902439i | −0.478678 | − | 0.877991i | \(-0.658884\pi\) |
0.999701 | − | 0.0244482i | \(-0.00778287\pi\) | |||||||
\(810\) | −1.74910 | − | 3.02954i | −0.0614573 | − | 0.106447i | ||||
\(811\) | 15.8344 | 0.556022 | 0.278011 | − | 0.960578i | \(-0.410325\pi\) | ||||
0.278011 | + | 0.960578i | \(0.410325\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.58091 | − | 7.93438i | 0.160660 | − | 0.278271i | ||||
\(814\) | −28.4773 | + | 49.3241i | −0.998129 | + | 1.72881i | ||||
\(815\) | −3.74459 | −0.131167 | ||||||||
\(816\) | 2.56772 | − | 4.44742i | 0.0898881 | − | 0.155691i | ||||
\(817\) | 52.8856 | 1.85023 | ||||||||
\(818\) | −62.4327 | −2.18291 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 16.7624 | 0.585368 | ||||||||
\(821\) | 17.7394 | 0.619110 | 0.309555 | − | 0.950882i | \(-0.399820\pi\) | ||||
0.309555 | + | 0.950882i | \(0.399820\pi\) | |||||||
\(822\) | −4.46912 | + | 7.74075i | −0.155879 | + | 0.269990i | ||||
\(823\) | −8.68200 | −0.302635 | −0.151318 | − | 0.988485i | \(-0.548352\pi\) | ||||
−0.151318 | + | 0.988485i | \(0.548352\pi\) | |||||||
\(824\) | −41.0290 | + | 71.0643i | −1.42931 | + | 2.47564i | ||||
\(825\) | −4.47513 | + | 7.75115i | −0.155804 | + | 0.269860i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.3121 | 0.497681 | 0.248840 | − | 0.968545i | \(-0.419951\pi\) | ||||
0.248840 | + | 0.968545i | \(0.419951\pi\) | |||||||
\(828\) | −17.5655 | − | 30.4243i | −0.610442 | − | 1.05732i | ||||
\(829\) | −12.6533 | + | 21.9161i | −0.439467 | + | 0.761179i | −0.997648 | − | 0.0685401i | \(-0.978166\pi\) |
0.558182 | + | 0.829719i | \(0.311499\pi\) | |||||||
\(830\) | −0.586568 | + | 1.01597i | −0.0203601 | + | 0.0352647i | ||||
\(831\) | −3.88784 | + | 6.73393i | −0.134868 | + | 0.233597i | ||||
\(832\) | −22.4167 | + | 23.2712i | −0.777158 | + | 0.806783i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 10.1483 | + | 17.5774i | 0.351407 | + | 0.608654i | ||||
\(835\) | −6.24250 | −0.216031 | ||||||||
\(836\) | 59.8966 | 2.07157 | ||||||||
\(837\) | −4.04308 | − | 7.00281i | −0.139749 | − | 0.242053i | ||||
\(838\) | 31.9090 | + | 55.2679i | 1.10228 | + | 1.90920i | ||||
\(839\) | −6.52129 | + | 11.2952i | −0.225140 | + | 0.389954i | −0.956361 | − | 0.292186i | \(-0.905617\pi\) |
0.731222 | + | 0.682140i | \(0.238951\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.63720 | − | 8.03187i | 0.159904 | − | 0.276961i | ||||
\(842\) | 57.5525 | 1.98339 | ||||||||
\(843\) | 0.978452 | − | 1.69473i | 0.0336997 | − | 0.0583696i | ||||
\(844\) | 45.5266 | + | 78.8543i | 1.56709 | + | 2.71428i | ||||
\(845\) | 3.92546 | + | 2.07465i | 0.135040 | + | 0.0713702i | ||||
\(846\) | 53.2673 | 1.83137 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.60984 | − | 4.52037i | −0.0896223 | − | 0.155230i | ||||
\(849\) | −1.73465 | − | 3.00450i | −0.0595330 | − | 0.103114i | ||||
\(850\) | −11.5694 | − | 20.0388i | −0.396827 | − | 0.687324i | ||||
\(851\) | 35.5248 | 1.21777 | ||||||||
\(852\) | −14.0102 | − | 24.2664i | −0.479982 | − | 0.831353i | ||||
\(853\) | 18.8926 | 0.646869 | 0.323435 | − | 0.946251i | \(-0.395162\pi\) | ||||
0.323435 | + | 0.946251i | \(0.395162\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.61256 | − | 4.52509i | −0.0893477 | − | 0.154755i | ||||
\(856\) | 29.7374 | 1.01640 | ||||||||
\(857\) | −12.3219 | − | 21.3422i | −0.420909 | − | 0.729036i | 0.575119 | − | 0.818069i | \(-0.304956\pi\) |
−0.996029 | + | 0.0890333i | \(0.971622\pi\) | |||||||
\(858\) | 15.5995 | + | 3.86871i | 0.532557 | + | 0.132075i | ||||
\(859\) | −1.28571 | + | 2.22691i | −0.0438677 | + | 0.0759811i | −0.887126 | − | 0.461528i | \(-0.847301\pi\) |
0.843258 | + | 0.537509i | \(0.180635\pi\) | |||||||
\(860\) | 5.62097 | + | 9.73580i | 0.191673 | + | 0.331988i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.9906 | − | 48.4812i | 0.953365 | − | 1.65128i | ||||
\(863\) | −19.7704 | + | 34.2433i | −0.672991 | + | 1.16565i | 0.304061 | + | 0.952653i | \(0.401657\pi\) |
−0.977052 | + | 0.213002i | \(0.931676\pi\) | |||||||
\(864\) | 3.30909 | 0.112578 | ||||||||
\(865\) | −2.80004 | −0.0952043 | ||||||||
\(866\) | 31.4479 | − | 54.4694i | 1.06864 | − | 1.85095i | ||||
\(867\) | 4.97536 | − | 8.61758i | 0.168972 | − | 0.292668i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.43777 | + | 9.41849i | 0.184464 | + | 0.319500i | ||||
\(870\) | −1.39008 | + | 2.40769i | −0.0471282 | + | 0.0816284i | ||||
\(871\) | −5.58164 | − | 19.3742i | −0.189127 | − | 0.656469i | ||||
\(872\) | 19.0378 | + | 32.9744i | 0.644701 | + | 1.11666i | ||||
\(873\) | −24.9947 | −0.845942 | ||||||||
\(874\) | −28.2224 | − | 48.8826i | −0.954636 | − | 1.65348i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 35.1648 | 1.18811 | ||||||||
\(877\) | −10.5227 | − | 18.2259i | −0.355328 | − | 0.615445i | 0.631846 | − | 0.775094i | \(-0.282297\pi\) |
−0.987174 | + | 0.159648i | \(0.948964\pi\) | |||||||
\(878\) | −86.7702 | −2.92835 | ||||||||
\(879\) | 0.738970 | + | 1.27993i | 0.0249248 | + | 0.0431711i | ||||
\(880\) | 1.45274 | + | 2.51623i | 0.0489720 | + | 0.0848219i | ||||
\(881\) | 2.50592 | + | 4.34038i | 0.0844266 | + | 0.146231i | 0.905147 | − | 0.425099i | \(-0.139761\pi\) |
−0.820720 | + | 0.571330i | \(0.806427\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.13079 | −0.239970 | −0.119985 | − | 0.992776i | \(-0.538285\pi\) | ||||
−0.119985 | + | 0.992776i | \(0.538285\pi\) | |||||||
\(884\) | −19.0794 | + | 19.8067i | −0.641711 | + | 0.666173i | ||||
\(885\) | −0.0806874 | − | 0.139755i | −0.00271228 | − | 0.00469780i | ||||
\(886\) | 8.34065 | − | 14.4464i | 0.280210 | − | 0.485337i | ||||
\(887\) | 6.72602 | 0.225838 | 0.112919 | − | 0.993604i | \(-0.463980\pi\) | ||||
0.112919 | + | 0.993604i | \(0.463980\pi\) | |||||||
\(888\) | 16.8984 | − | 29.2689i | 0.567074 | − | 0.982202i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −5.16847 | + | 8.95206i | −0.173248 | + | 0.300074i | ||||
\(891\) | 5.12127 | + | 8.87031i | 0.171569 | + | 0.297166i | ||||
\(892\) | 57.3032 | + | 99.2520i | 1.91865 | + | 3.32320i | ||||
\(893\) | 56.6468 | 1.89561 | ||||||||
\(894\) | 29.1576 | 0.975177 | ||||||||
\(895\) | 2.65608 | + | 4.60046i | 0.0887829 | + | 0.153777i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.77522 | − | 9.63294i | −0.0926618 | − | 0.321635i | ||||
\(898\) | 12.1380 | − | 21.0236i | 0.405050 | − | 0.701567i | ||||
\(899\) | 4.38655 | − | 7.59773i | 0.146300 | − | 0.253398i | ||||
\(900\) | −23.2495 | + | 40.2692i | −0.774982 | + | 1.34231i | ||||
\(901\) | 1.45363 | + | 2.51777i | 0.0484276 | + | 0.0838790i | ||||
\(902\) | −74.1510 | −2.46896 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 22.4075 | − | 38.8109i | 0.745263 | − | 1.29083i | ||||
\(905\) | 1.13954 | − | 1.97374i | 0.0378796 | − | 0.0656095i | ||||
\(906\) | −19.4101 | −0.644858 | ||||||||
\(907\) | −14.7862 | + | 25.6105i | −0.490969 | + | 0.850383i | −0.999946 | − | 0.0103972i | \(-0.996690\pi\) |
0.508977 | + | 0.860780i | \(0.330024\pi\) | |||||||
\(908\) | 77.5623 | 2.57399 | ||||||||
\(909\) | −36.6120 | −1.21434 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.6132 | −0.682947 | −0.341473 | − | 0.939891i | \(-0.610926\pi\) | ||||
−0.341473 | + | 0.939891i | \(0.610926\pi\) | |||||||
\(912\) | −16.5811 | −0.549055 | ||||||||
\(913\) | 1.71744 | − | 2.97469i | 0.0568388 | − | 0.0984477i | ||||
\(914\) | −21.3371 | −0.705768 | ||||||||
\(915\) | 0.147117 | − | 0.254815i | 0.00486355 | − | 0.00842392i | ||||
\(916\) | 2.60005 | − | 4.50342i | 0.0859081 | − | 0.148797i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 19.3966 | 0.640184 | ||||||||
\(919\) | 2.08952 | + | 3.61916i | 0.0689269 | + | 0.119385i | 0.898429 | − | 0.439118i | \(-0.144709\pi\) |
−0.829502 | + | 0.558503i | \(0.811376\pi\) | |||||||
\(920\) | 2.93459 | − | 5.08285i | 0.0967504 | − | 0.167577i | ||||
\(921\) | −2.77947 | + | 4.81418i | −0.0915865 | + | 0.158632i | ||||
\(922\) | −8.37303 | + | 14.5025i | −0.275751 | + | 0.477615i | ||||
\(923\) | 9.47961 | + | 32.9043i | 0.312025 | + | 1.08306i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.5101 | − | 40.7207i | −0.773007 | − | 1.33889i | ||||
\(926\) | −33.9341 | −1.11514 | ||||||||
\(927\) | −42.8478 | −1.40731 | ||||||||
\(928\) | 1.79511 | + | 3.10922i | 0.0589273 | + | 0.102065i | ||||
\(929\) | 24.0456 | + | 41.6482i | 0.788910 | + | 1.36643i | 0.926635 | + | 0.375962i | \(0.122688\pi\) |
−0.137725 | + | 0.990470i | \(0.543979\pi\) | |||||||
\(930\) | 0.618249 | − | 1.07084i | 0.0202732 | − | 0.0351142i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.96832 | + | 5.14128i | −0.0972306 | + | 0.168408i | ||||
\(933\) | 10.6722 | 0.349392 | ||||||||
\(934\) | 35.0359 | − | 60.6840i | 1.14641 | − | 1.98564i | ||||
\(935\) | −0.809152 | − | 1.40149i | −0.0264621 | − | 0.0458337i | ||||
\(936\) | 39.6429 | + | 9.83156i | 1.29577 | + | 0.321354i | ||||
\(937\) | 12.5441 | 0.409798 | 0.204899 | − | 0.978783i | \(-0.434313\pi\) | ||||
0.204899 | + | 0.978783i | \(0.434313\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.0662 | + | 17.4352i | 0.328498 | + | 0.568975i | ||||
\(940\) | 6.02073 | + | 10.4282i | 0.196375 | + | 0.340131i | ||||
\(941\) | 15.2944 | + | 26.4907i | 0.498583 | + | 0.863572i | 0.999999 | − | 0.00163503i | \(-0.000520447\pi\) |
−0.501415 | + | 0.865207i | \(0.667187\pi\) | |||||||
\(942\) | 16.7223 | 0.544843 | ||||||||
\(943\) | 23.1254 | + | 40.0544i | 0.753067 | + | 1.30435i | ||||
\(944\) | 2.19311 | 0.0713798 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.8652 | − | 43.0678i | −0.808438 | − | 1.40026i | ||||
\(947\) | −7.78348 | −0.252929 | −0.126465 | − | 0.991971i | \(-0.540363\pi\) | ||||
−0.126465 | + | 0.991971i | \(0.540363\pi\) | |||||||
\(948\) | −6.59659 | − | 11.4256i | −0.214247 | − | 0.371087i | ||||
\(949\) | −41.7098 | − | 10.3442i | −1.35396 | − | 0.335786i | ||||
\(950\) | −37.3548 | + | 64.7005i | −1.21195 | + | 2.09916i | ||||
\(951\) | −8.07709 | − | 13.9899i | −0.261917 | − | 0.453654i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.2152 | − | 33.2817i | 0.622442 | − | 1.07810i | −0.366588 | − | 0.930383i | \(-0.619474\pi\) |
0.989030 | − | 0.147717i | \(-0.0471926\pi\) | |||||||
\(954\) | 4.41343 | − | 7.64429i | 0.142890 | − | 0.247493i | ||||
\(955\) | −6.40243 | −0.207178 | ||||||||
\(956\) | 88.0088 | 2.84641 | ||||||||
\(957\) | 4.07008 | − | 7.04958i | 0.131567 | − | 0.227881i | ||||
\(958\) | 29.8992 | − | 51.7869i | 0.965998 | − | 1.67316i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.15328 | + | 1.99754i | 0.0372219 | + | 0.0644702i | ||||
\(961\) | 13.5491 | − | 23.4676i | 0.437066 | − | 0.757021i | ||||
\(962\) | −58.5772 | + | 60.8101i | −1.88860 | + | 1.96060i | ||||
\(963\) | 7.76391 | + | 13.4475i | 0.250189 | + | 0.433339i | ||||
\(964\) | 52.1123 | 1.67842 | ||||||||
\(965\) | 1.39571 | + | 2.41744i | 0.0449294 | + | 0.0778200i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.80008 | 0.250834 | 0.125417 | − | 0.992104i | \(-0.459973\pi\) | ||||
0.125417 | + | 0.992104i | \(0.459973\pi\) | |||||||
\(968\) | 11.8420 | + | 20.5110i | 0.380617 | + | 0.659248i | ||||
\(969\) | 9.23538 | 0.296683 | ||||||||
\(970\) | −4.26830 | − | 7.39292i | −0.137047 | − | 0.237372i | ||||
\(971\) | −28.8957 | − | 50.0489i | −0.927308 | − | 1.60614i | −0.787807 | − | 0.615922i | \(-0.788784\pi\) |
−0.139501 | − | 0.990222i | \(-0.544550\pi\) | |||||||
\(972\) | −30.2529 | − | 52.3995i | −0.970362 | − | 1.68072i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −6.25817 | −0.200525 | ||||||||
\(975\) | −9.20525 | + | 9.55615i | −0.294804 | + | 0.306042i | ||||
\(976\) | 1.99936 | + | 3.46298i | 0.0639978 | + | 0.110847i | ||||
\(977\) | −4.33707 | + | 7.51203i | −0.138755 | + | 0.240331i | −0.927026 | − | 0.374998i | \(-0.877643\pi\) |
0.788270 | + | 0.615329i | \(0.210977\pi\) | |||||||
\(978\) | −20.0948 | −0.642561 | ||||||||
\(979\) | 15.1330 | − | 26.2111i | 0.483652 | − | 0.837710i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.94086 | + | 17.2181i | −0.317387 | + | 0.549731i | ||||
\(982\) | −17.0708 | − | 29.5675i | −0.544752 | − | 0.943538i | ||||
\(983\) | −18.5560 | − | 32.1400i | −0.591846 | − | 1.02511i | −0.993984 | − | 0.109528i | \(-0.965066\pi\) |
0.402138 | − | 0.915579i | \(-0.368267\pi\) | |||||||
\(984\) | 44.0012 | 1.40271 | ||||||||
\(985\) | 2.97824 | 0.0948947 | ||||||||
\(986\) | 10.5222 | + | 18.2250i | 0.335096 | + | 0.580403i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 86.1849 | + | 21.3741i | 2.74191 | + | 0.680001i | ||||
\(989\) | −15.5094 | + | 26.8631i | −0.493170 | + | 0.854196i | ||||
\(990\) | −2.45670 | + | 4.25512i | −0.0780790 | + | 0.135237i | ||||
\(991\) | 22.6318 | − | 39.1995i | 0.718924 | − | 1.24521i | −0.242502 | − | 0.970151i | \(-0.577968\pi\) |
0.961426 | − | 0.275062i | \(-0.0886984\pi\) | |||||||
\(992\) | −0.798386 | − | 1.38285i | −0.0253488 | − | 0.0439054i | ||||
\(993\) | 7.99850 | 0.253825 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.98275 | − | 5.16628i | 0.0945597 | − | 0.163782i | ||||
\(996\) | −2.08343 | + | 3.60861i | −0.0660160 | + | 0.114343i | ||||
\(997\) | −44.2554 | −1.40158 | −0.700791 | − | 0.713367i | \(-0.747169\pi\) | ||||
−0.700791 | + | 0.713367i | \(0.747169\pi\) | |||||||
\(998\) | −16.4586 | + | 28.5072i | −0.520989 | + | 0.902380i | ||||
\(999\) | 39.4158 | 1.24706 |
(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 | 637.2.h.m.471.7 | 16 | ||
7.2 | even | 3 | 637.2.f.l.393.1 | yes | 16 | ||
7.3 | odd | 6 | 637.2.g.m.263.1 | 16 | |||
7.4 | even | 3 | 637.2.g.m.263.2 | 16 | |||
7.5 | odd | 6 | 637.2.f.l.393.2 | yes | 16 | ||
7.6 | odd | 2 | inner | 637.2.h.m.471.8 | 16 | ||
13.9 | even | 3 | 637.2.g.m.373.2 | 16 | |||
91.9 | even | 3 | 637.2.f.l.295.1 | ✓ | 16 | ||
91.16 | even | 3 | 8281.2.a.ci.1.8 | 8 | |||
91.23 | even | 6 | 8281.2.a.cl.1.2 | 8 | |||
91.48 | odd | 6 | 637.2.g.m.373.1 | 16 | |||
91.61 | odd | 6 | 637.2.f.l.295.2 | yes | 16 | ||
91.68 | odd | 6 | 8281.2.a.ci.1.7 | 8 | |||
91.74 | even | 3 | inner | 637.2.h.m.165.7 | 16 | ||
91.75 | odd | 6 | 8281.2.a.cl.1.1 | 8 | |||
91.87 | odd | 6 | inner | 637.2.h.m.165.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.f.l.295.1 | ✓ | 16 | 91.9 | even | 3 | ||
637.2.f.l.295.2 | yes | 16 | 91.61 | odd | 6 | ||
637.2.f.l.393.1 | yes | 16 | 7.2 | even | 3 | ||
637.2.f.l.393.2 | yes | 16 | 7.5 | odd | 6 | ||
637.2.g.m.263.1 | 16 | 7.3 | odd | 6 | |||
637.2.g.m.263.2 | 16 | 7.4 | even | 3 | |||
637.2.g.m.373.1 | 16 | 91.48 | odd | 6 | |||
637.2.g.m.373.2 | 16 | 13.9 | even | 3 | |||
637.2.h.m.165.7 | 16 | 91.74 | even | 3 | inner | ||
637.2.h.m.165.8 | 16 | 91.87 | odd | 6 | inner | ||
637.2.h.m.471.7 | 16 | 1.1 | even | 1 | trivial | ||
637.2.h.m.471.8 | 16 | 7.6 | odd | 2 | inner | ||
8281.2.a.ci.1.7 | 8 | 91.68 | odd | 6 | |||
8281.2.a.ci.1.8 | 8 | 91.16 | even | 3 | |||
8281.2.a.cl.1.1 | 8 | 91.75 | odd | 6 | |||
8281.2.a.cl.1.2 | 8 | 91.23 | even | 6 |