Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(43,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.s (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 127.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.127 |
Dual form | 546.2.s.b.43.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 2.73205i | 1.22181i | 0.791704 | + | 0.610905i | \(0.209194\pi\) | ||||
−0.791704 | + | 0.610905i | \(0.790806\pi\) | |||||||
\(6\) | 0.866025 | + | 0.500000i | 0.353553 | + | 0.204124i | ||||
\(7\) | −0.866025 | − | 0.500000i | −0.327327 | − | 0.188982i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −1.36603 | − | 2.36603i | −0.431975 | − | 0.748203i | ||||
\(11\) | 4.50000 | − | 2.59808i | 1.35680 | − | 0.783349i | 0.367610 | − | 0.929980i | \(-0.380176\pi\) |
0.989191 | + | 0.146631i | \(0.0468429\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −0.866025 | + | 3.50000i | −0.240192 | + | 0.970725i | ||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 2.36603 | − | 1.36603i | 0.610905 | − | 0.352706i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.86603 | + | 4.96410i | −0.695113 | + | 1.20397i | 0.275029 | + | 0.961436i | \(0.411312\pi\) |
−0.970143 | + | 0.242536i | \(0.922021\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −5.59808 | − | 3.23205i | −1.28429 | − | 0.741483i | −0.306658 | − | 0.951820i | \(-0.599211\pi\) |
−0.977629 | + | 0.210337i | \(0.932544\pi\) | |||||||
\(20\) | 2.36603 | + | 1.36603i | 0.529059 | + | 0.305453i | ||||
\(21\) | 1.00000i | 0.218218i | ||||||||
\(22\) | −2.59808 | + | 4.50000i | −0.553912 | + | 0.959403i | ||||
\(23\) | −0.267949 | − | 0.464102i | −0.0558713 | − | 0.0967719i | 0.836737 | − | 0.547605i | \(-0.184460\pi\) |
−0.892608 | + | 0.450833i | \(0.851127\pi\) | |||||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | −2.46410 | −0.492820 | ||||||||
\(26\) | −1.00000 | − | 3.46410i | −0.196116 | − | 0.679366i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.866025 | + | 0.500000i | −0.163663 | + | 0.0944911i | ||||
\(29\) | 5.23205 | + | 9.06218i | 0.971567 | + | 1.68280i | 0.690826 | + | 0.723021i | \(0.257247\pi\) |
0.280741 | + | 0.959784i | \(0.409420\pi\) | |||||||
\(30\) | −1.36603 | + | 2.36603i | −0.249401 | + | 0.431975i | ||||
\(31\) | 6.73205i | 1.20911i | 0.796563 | + | 0.604556i | \(0.206649\pi\) | ||||
−0.796563 | + | 0.604556i | \(0.793351\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | −4.50000 | − | 2.59808i | −0.783349 | − | 0.452267i | ||||
\(34\) | − | 5.73205i | − | 0.983039i | ||||||
\(35\) | 1.36603 | − | 2.36603i | 0.230900 | − | 0.399931i | ||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | −2.83013 | + | 1.63397i | −0.465270 | + | 0.268624i | −0.714258 | − | 0.699883i | \(-0.753235\pi\) |
0.248988 | + | 0.968507i | \(0.419902\pi\) | |||||||
\(38\) | 6.46410 | 1.04862 | ||||||||
\(39\) | 3.46410 | − | 1.00000i | 0.554700 | − | 0.160128i | ||||
\(40\) | −2.73205 | −0.431975 | ||||||||
\(41\) | 1.33013 | − | 0.767949i | 0.207731 | − | 0.119934i | −0.392525 | − | 0.919741i | \(-0.628399\pi\) |
0.600256 | + | 0.799808i | \(0.295065\pi\) | |||||||
\(42\) | −0.500000 | − | 0.866025i | −0.0771517 | − | 0.133631i | ||||
\(43\) | −2.63397 | + | 4.56218i | −0.401677 | + | 0.695726i | −0.993929 | − | 0.110028i | \(-0.964906\pi\) |
0.592251 | + | 0.805753i | \(0.298239\pi\) | |||||||
\(44\) | − | 5.19615i | − | 0.783349i | ||||||
\(45\) | −2.36603 | − | 1.36603i | −0.352706 | − | 0.203635i | ||||
\(46\) | 0.464102 | + | 0.267949i | 0.0684280 | + | 0.0395070i | ||||
\(47\) | 9.92820i | 1.44818i | 0.689707 | + | 0.724089i | \(0.257739\pi\) | ||||
−0.689707 | + | 0.724089i | \(0.742261\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | 0.500000 | + | 0.866025i | 0.0714286 | + | 0.123718i | ||||
\(50\) | 2.13397 | − | 1.23205i | 0.301790 | − | 0.174238i | ||||
\(51\) | 5.73205 | 0.802648 | ||||||||
\(52\) | 2.59808 | + | 2.50000i | 0.360288 | + | 0.346688i | ||||
\(53\) | 3.92820 | 0.539580 | 0.269790 | − | 0.962919i | \(-0.413046\pi\) | ||||
0.269790 | + | 0.962919i | \(0.413046\pi\) | |||||||
\(54\) | −0.866025 | + | 0.500000i | −0.117851 | + | 0.0680414i | ||||
\(55\) | 7.09808 | + | 12.2942i | 0.957104 | + | 1.65775i | ||||
\(56\) | 0.500000 | − | 0.866025i | 0.0668153 | − | 0.115728i | ||||
\(57\) | 6.46410i | 0.856191i | ||||||||
\(58\) | −9.06218 | − | 5.23205i | −1.18992 | − | 0.687002i | ||||
\(59\) | 4.26795 | + | 2.46410i | 0.555640 | + | 0.320799i | 0.751394 | − | 0.659854i | \(-0.229382\pi\) |
−0.195754 | + | 0.980653i | \(0.562715\pi\) | |||||||
\(60\) | − | 2.73205i | − | 0.352706i | ||||||
\(61\) | −0.133975 | + | 0.232051i | −0.0171537 | + | 0.0297111i | −0.874475 | − | 0.485071i | \(-0.838794\pi\) |
0.857321 | + | 0.514782i | \(0.172127\pi\) | |||||||
\(62\) | −3.36603 | − | 5.83013i | −0.427486 | − | 0.740427i | ||||
\(63\) | 0.866025 | − | 0.500000i | 0.109109 | − | 0.0629941i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −9.56218 | − | 2.36603i | −1.18604 | − | 0.293469i | ||||
\(66\) | 5.19615 | 0.639602 | ||||||||
\(67\) | −8.66025 | + | 5.00000i | −1.05802 | + | 0.610847i | −0.924883 | − | 0.380251i | \(-0.875838\pi\) |
−0.133135 | + | 0.991098i | \(0.542504\pi\) | |||||||
\(68\) | 2.86603 | + | 4.96410i | 0.347557 | + | 0.601986i | ||||
\(69\) | −0.267949 | + | 0.464102i | −0.0322573 | + | 0.0558713i | ||||
\(70\) | 2.73205i | 0.326543i | ||||||||
\(71\) | −9.29423 | − | 5.36603i | −1.10302 | − | 0.636830i | −0.166009 | − | 0.986124i | \(-0.553088\pi\) |
−0.937013 | + | 0.349294i | \(0.886421\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | − | 5.46410i | − | 0.639525i | −0.947498 | − | 0.319762i | \(-0.896397\pi\) | ||
0.947498 | − | 0.319762i | \(-0.103603\pi\) | |||||||
\(74\) | 1.63397 | − | 2.83013i | 0.189946 | − | 0.328996i | ||||
\(75\) | 1.23205 | + | 2.13397i | 0.142265 | + | 0.246410i | ||||
\(76\) | −5.59808 | + | 3.23205i | −0.642143 | + | 0.370742i | ||||
\(77\) | −5.19615 | −0.592157 | ||||||||
\(78\) | −2.50000 | + | 2.59808i | −0.283069 | + | 0.294174i | ||||
\(79\) | 9.00000 | 1.01258 | 0.506290 | − | 0.862364i | \(-0.331017\pi\) | ||||
0.506290 | + | 0.862364i | \(0.331017\pi\) | |||||||
\(80\) | 2.36603 | − | 1.36603i | 0.264530 | − | 0.152726i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −0.767949 | + | 1.33013i | −0.0848058 | + | 0.146888i | ||||
\(83\) | − | 12.7321i | − | 1.39752i | −0.715354 | − | 0.698762i | \(-0.753735\pi\) | ||
0.715354 | − | 0.698762i | \(-0.246265\pi\) | |||||||
\(84\) | 0.866025 | + | 0.500000i | 0.0944911 | + | 0.0545545i | ||||
\(85\) | −13.5622 | − | 7.83013i | −1.47102 | − | 0.849297i | ||||
\(86\) | − | 5.26795i | − | 0.568058i | ||||||
\(87\) | 5.23205 | − | 9.06218i | 0.560935 | − | 0.971567i | ||||
\(88\) | 2.59808 | + | 4.50000i | 0.276956 | + | 0.479702i | ||||
\(89\) | −9.40192 | + | 5.42820i | −0.996602 | + | 0.575388i | −0.907241 | − | 0.420611i | \(-0.861816\pi\) |
−0.0893608 | + | 0.995999i | \(0.528482\pi\) | |||||||
\(90\) | 2.73205 | 0.287983 | ||||||||
\(91\) | 2.50000 | − | 2.59808i | 0.262071 | − | 0.272352i | ||||
\(92\) | −0.535898 | −0.0558713 | ||||||||
\(93\) | 5.83013 | − | 3.36603i | 0.604556 | − | 0.349041i | ||||
\(94\) | −4.96410 | − | 8.59808i | −0.512008 | − | 0.886824i | ||||
\(95\) | 8.83013 | − | 15.2942i | 0.905952 | − | 1.56915i | ||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | 3.29423 | + | 1.90192i | 0.334478 | + | 0.193111i | 0.657828 | − | 0.753169i | \(-0.271476\pi\) |
−0.323349 | + | 0.946280i | \(0.604809\pi\) | |||||||
\(98\) | −0.866025 | − | 0.500000i | −0.0874818 | − | 0.0505076i | ||||
\(99\) | 5.19615i | 0.522233i | ||||||||
\(100\) | −1.23205 | + | 2.13397i | −0.123205 | + | 0.213397i | ||||
\(101\) | −4.46410 | − | 7.73205i | −0.444195 | − | 0.769368i | 0.553801 | − | 0.832649i | \(-0.313177\pi\) |
−0.997996 | + | 0.0632812i | \(0.979843\pi\) | |||||||
\(102\) | −4.96410 | + | 2.86603i | −0.491519 | + | 0.283779i | ||||
\(103\) | 5.80385 | 0.571870 | 0.285935 | − | 0.958249i | \(-0.407696\pi\) | ||||
0.285935 | + | 0.958249i | \(0.407696\pi\) | |||||||
\(104\) | −3.50000 | − | 0.866025i | −0.343203 | − | 0.0849208i | ||||
\(105\) | −2.73205 | −0.266621 | ||||||||
\(106\) | −3.40192 | + | 1.96410i | −0.330424 | + | 0.190770i | ||||
\(107\) | 9.96410 | + | 17.2583i | 0.963266 | + | 1.66843i | 0.714203 | + | 0.699938i | \(0.246789\pi\) |
0.249063 | + | 0.968487i | \(0.419877\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | − | 14.7321i | − | 1.41107i | −0.708673 | − | 0.705537i | \(-0.750706\pi\) | ||
0.708673 | − | 0.705537i | \(-0.249294\pi\) | |||||||
\(110\) | −12.2942 | − | 7.09808i | −1.17221 | − | 0.676775i | ||||
\(111\) | 2.83013 | + | 1.63397i | 0.268624 | + | 0.155090i | ||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | 4.83013 | − | 8.36603i | 0.454380 | − | 0.787009i | −0.544272 | − | 0.838909i | \(-0.683194\pi\) |
0.998652 | + | 0.0518992i | \(0.0165275\pi\) | |||||||
\(114\) | −3.23205 | − | 5.59808i | −0.302709 | − | 0.524308i | ||||
\(115\) | 1.26795 | − | 0.732051i | 0.118237 | − | 0.0682641i | ||||
\(116\) | 10.4641 | 0.971567 | ||||||||
\(117\) | −2.59808 | − | 2.50000i | −0.240192 | − | 0.231125i | ||||
\(118\) | −4.92820 | −0.453678 | ||||||||
\(119\) | 4.96410 | − | 2.86603i | 0.455058 | − | 0.262728i | ||||
\(120\) | 1.36603 | + | 2.36603i | 0.124700 | + | 0.215988i | ||||
\(121\) | 8.00000 | − | 13.8564i | 0.727273 | − | 1.25967i | ||||
\(122\) | − | 0.267949i | − | 0.0242590i | ||||||
\(123\) | −1.33013 | − | 0.767949i | −0.119934 | − | 0.0692436i | ||||
\(124\) | 5.83013 | + | 3.36603i | 0.523561 | + | 0.302278i | ||||
\(125\) | 6.92820i | 0.619677i | ||||||||
\(126\) | −0.500000 | + | 0.866025i | −0.0445435 | + | 0.0771517i | ||||
\(127\) | −3.19615 | − | 5.53590i | −0.283613 | − | 0.491232i | 0.688659 | − | 0.725085i | \(-0.258200\pi\) |
−0.972272 | + | 0.233854i | \(0.924866\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 5.26795 | 0.463817 | ||||||||
\(130\) | 9.46410 | − | 2.73205i | 0.830057 | − | 0.239617i | ||||
\(131\) | −1.07180 | −0.0936433 | −0.0468217 | − | 0.998903i | \(-0.514909\pi\) | ||||
−0.0468217 | + | 0.998903i | \(0.514909\pi\) | |||||||
\(132\) | −4.50000 | + | 2.59808i | −0.391675 | + | 0.226134i | ||||
\(133\) | 3.23205 | + | 5.59808i | 0.280254 | + | 0.485415i | ||||
\(134\) | 5.00000 | − | 8.66025i | 0.431934 | − | 0.748132i | ||||
\(135\) | 2.73205i | 0.235137i | ||||||||
\(136\) | −4.96410 | − | 2.86603i | −0.425668 | − | 0.245760i | ||||
\(137\) | 10.8564 | + | 6.26795i | 0.927525 | + | 0.535507i | 0.886028 | − | 0.463632i | \(-0.153454\pi\) |
0.0414973 | + | 0.999139i | \(0.486787\pi\) | |||||||
\(138\) | − | 0.535898i | − | 0.0456187i | ||||||
\(139\) | 10.5263 | − | 18.2321i | 0.892827 | − | 1.54642i | 0.0563567 | − | 0.998411i | \(-0.482052\pi\) |
0.836471 | − | 0.548012i | \(-0.184615\pi\) | |||||||
\(140\) | −1.36603 | − | 2.36603i | −0.115450 | − | 0.199966i | ||||
\(141\) | 8.59808 | − | 4.96410i | 0.724089 | − | 0.418053i | ||||
\(142\) | 10.7321 | 0.900614 | ||||||||
\(143\) | 5.19615 | + | 18.0000i | 0.434524 | + | 1.50524i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −24.7583 | + | 14.2942i | −2.05607 | + | 1.18707i | ||||
\(146\) | 2.73205 | + | 4.73205i | 0.226106 | + | 0.391627i | ||||
\(147\) | 0.500000 | − | 0.866025i | 0.0412393 | − | 0.0714286i | ||||
\(148\) | 3.26795i | 0.268624i | ||||||||
\(149\) | 6.92820 | + | 4.00000i | 0.567581 | + | 0.327693i | 0.756182 | − | 0.654361i | \(-0.227062\pi\) |
−0.188602 | + | 0.982054i | \(0.560396\pi\) | |||||||
\(150\) | −2.13397 | − | 1.23205i | −0.174238 | − | 0.100597i | ||||
\(151\) | − | 9.19615i | − | 0.748372i | −0.927354 | − | 0.374186i | \(-0.877922\pi\) | ||
0.927354 | − | 0.374186i | \(-0.122078\pi\) | |||||||
\(152\) | 3.23205 | − | 5.59808i | 0.262154 | − | 0.454064i | ||||
\(153\) | −2.86603 | − | 4.96410i | −0.231704 | − | 0.401324i | ||||
\(154\) | 4.50000 | − | 2.59808i | 0.362620 | − | 0.209359i | ||||
\(155\) | −18.3923 | −1.47731 | ||||||||
\(156\) | 0.866025 | − | 3.50000i | 0.0693375 | − | 0.280224i | ||||
\(157\) | −4.53590 | −0.362004 | −0.181002 | − | 0.983483i | \(-0.557934\pi\) | ||||
−0.181002 | + | 0.983483i | \(0.557934\pi\) | |||||||
\(158\) | −7.79423 | + | 4.50000i | −0.620076 | + | 0.358001i | ||||
\(159\) | −1.96410 | − | 3.40192i | −0.155763 | − | 0.269790i | ||||
\(160\) | −1.36603 | + | 2.36603i | −0.107994 | + | 0.187051i | ||||
\(161\) | 0.535898i | 0.0422347i | ||||||||
\(162\) | 0.866025 | + | 0.500000i | 0.0680414 | + | 0.0392837i | ||||
\(163\) | −14.8301 | − | 8.56218i | −1.16159 | − | 0.670642i | −0.209902 | − | 0.977722i | \(-0.567314\pi\) |
−0.951683 | + | 0.307081i | \(0.900648\pi\) | |||||||
\(164\) | − | 1.53590i | − | 0.119934i | ||||||
\(165\) | 7.09808 | − | 12.2942i | 0.552584 | − | 0.957104i | ||||
\(166\) | 6.36603 | + | 11.0263i | 0.494099 | + | 0.855805i | ||||
\(167\) | 16.3923 | − | 9.46410i | 1.26847 | − | 0.732354i | 0.293775 | − | 0.955874i | \(-0.405088\pi\) |
0.974699 | + | 0.223520i | \(0.0717549\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | −11.5000 | − | 6.06218i | −0.884615 | − | 0.466321i | ||||
\(170\) | 15.6603 | 1.20109 | ||||||||
\(171\) | 5.59808 | − | 3.23205i | 0.428096 | − | 0.247161i | ||||
\(172\) | 2.63397 | + | 4.56218i | 0.200839 | + | 0.347863i | ||||
\(173\) | −4.09808 | + | 7.09808i | −0.311571 | + | 0.539657i | −0.978703 | − | 0.205283i | \(-0.934188\pi\) |
0.667132 | + | 0.744940i | \(0.267522\pi\) | |||||||
\(174\) | 10.4641i | 0.793281i | ||||||||
\(175\) | 2.13397 | + | 1.23205i | 0.161313 | + | 0.0931343i | ||||
\(176\) | −4.50000 | − | 2.59808i | −0.339200 | − | 0.195837i | ||||
\(177\) | − | 4.92820i | − | 0.370426i | ||||||
\(178\) | 5.42820 | − | 9.40192i | 0.406861 | − | 0.704704i | ||||
\(179\) | 1.73205 | + | 3.00000i | 0.129460 | + | 0.224231i | 0.923467 | − | 0.383677i | \(-0.125342\pi\) |
−0.794008 | + | 0.607908i | \(0.792009\pi\) | |||||||
\(180\) | −2.36603 | + | 1.36603i | −0.176353 | + | 0.101818i | ||||
\(181\) | 17.7321 | 1.31801 | 0.659006 | − | 0.752137i | \(-0.270977\pi\) | ||||
0.659006 | + | 0.752137i | \(0.270977\pi\) | |||||||
\(182\) | −0.866025 | + | 3.50000i | −0.0641941 | + | 0.259437i | ||||
\(183\) | 0.267949 | 0.0198074 | ||||||||
\(184\) | 0.464102 | − | 0.267949i | 0.0342140 | − | 0.0197535i | ||||
\(185\) | −4.46410 | − | 7.73205i | −0.328207 | − | 0.568472i | ||||
\(186\) | −3.36603 | + | 5.83013i | −0.246809 | + | 0.427486i | ||||
\(187\) | 29.7846i | 2.17807i | ||||||||
\(188\) | 8.59808 | + | 4.96410i | 0.627079 | + | 0.362044i | ||||
\(189\) | −0.866025 | − | 0.500000i | −0.0629941 | − | 0.0363696i | ||||
\(190\) | 17.6603i | 1.28121i | ||||||||
\(191\) | −1.09808 | + | 1.90192i | −0.0794540 | + | 0.137618i | −0.903014 | − | 0.429610i | \(-0.858651\pi\) |
0.823560 | + | 0.567228i | \(0.191984\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 20.4282 | − | 11.7942i | 1.47045 | − | 0.848967i | 0.471004 | − | 0.882131i | \(-0.343892\pi\) |
0.999450 | + | 0.0331638i | \(0.0105583\pi\) | |||||||
\(194\) | −3.80385 | −0.273100 | ||||||||
\(195\) | 2.73205 | + | 9.46410i | 0.195646 | + | 0.677738i | ||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −3.23205 | + | 1.86603i | −0.230274 | + | 0.132949i | −0.610698 | − | 0.791863i | \(-0.709111\pi\) |
0.380424 | + | 0.924812i | \(0.375778\pi\) | |||||||
\(198\) | −2.59808 | − | 4.50000i | −0.184637 | − | 0.319801i | ||||
\(199\) | −3.29423 | + | 5.70577i | −0.233522 | + | 0.404471i | −0.958842 | − | 0.283940i | \(-0.908358\pi\) |
0.725320 | + | 0.688412i | \(0.241692\pi\) | |||||||
\(200\) | − | 2.46410i | − | 0.174238i | ||||||
\(201\) | 8.66025 | + | 5.00000i | 0.610847 | + | 0.352673i | ||||
\(202\) | 7.73205 | + | 4.46410i | 0.544025 | + | 0.314093i | ||||
\(203\) | − | 10.4641i | − | 0.734436i | ||||||
\(204\) | 2.86603 | − | 4.96410i | 0.200662 | − | 0.347557i | ||||
\(205\) | 2.09808 | + | 3.63397i | 0.146536 | + | 0.253808i | ||||
\(206\) | −5.02628 | + | 2.90192i | −0.350197 | + | 0.202187i | ||||
\(207\) | 0.535898 | 0.0372475 | ||||||||
\(208\) | 3.46410 | − | 1.00000i | 0.240192 | − | 0.0693375i | ||||
\(209\) | −33.5885 | −2.32336 | ||||||||
\(210\) | 2.36603 | − | 1.36603i | 0.163271 | − | 0.0942647i | ||||
\(211\) | −5.53590 | − | 9.58846i | −0.381107 | − | 0.660097i | 0.610114 | − | 0.792314i | \(-0.291124\pi\) |
−0.991221 | + | 0.132217i | \(0.957790\pi\) | |||||||
\(212\) | 1.96410 | − | 3.40192i | 0.134895 | − | 0.233645i | ||||
\(213\) | 10.7321i | 0.735348i | ||||||||
\(214\) | −17.2583 | − | 9.96410i | −1.17976 | − | 0.681132i | ||||
\(215\) | −12.4641 | − | 7.19615i | −0.850045 | − | 0.490774i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 3.36603 | − | 5.83013i | 0.228501 | − | 0.395775i | ||||
\(218\) | 7.36603 | + | 12.7583i | 0.498890 | + | 0.864103i | ||||
\(219\) | −4.73205 | + | 2.73205i | −0.319762 | + | 0.184615i | ||||
\(220\) | 14.1962 | 0.957104 | ||||||||
\(221\) | −14.8923 | − | 14.3301i | −1.00176 | − | 0.963949i | ||||
\(222\) | −3.26795 | −0.219330 | ||||||||
\(223\) | −1.26795 | + | 0.732051i | −0.0849082 | + | 0.0490217i | −0.541853 | − | 0.840473i | \(-0.682277\pi\) |
0.456945 | + | 0.889495i | \(0.348944\pi\) | |||||||
\(224\) | −0.500000 | − | 0.866025i | −0.0334077 | − | 0.0578638i | ||||
\(225\) | 1.23205 | − | 2.13397i | 0.0821367 | − | 0.142265i | ||||
\(226\) | 9.66025i | 0.642591i | ||||||||
\(227\) | −18.4641 | − | 10.6603i | −1.22551 | − | 0.707546i | −0.259419 | − | 0.965765i | \(-0.583531\pi\) |
−0.966086 | + | 0.258219i | \(0.916864\pi\) | |||||||
\(228\) | 5.59808 | + | 3.23205i | 0.370742 | + | 0.214048i | ||||
\(229\) | 3.39230i | 0.224170i | 0.993699 | + | 0.112085i | \(0.0357529\pi\) | ||||
−0.993699 | + | 0.112085i | \(0.964247\pi\) | |||||||
\(230\) | −0.732051 | + | 1.26795i | −0.0482700 | + | 0.0836061i | ||||
\(231\) | 2.59808 | + | 4.50000i | 0.170941 | + | 0.296078i | ||||
\(232\) | −9.06218 | + | 5.23205i | −0.594961 | + | 0.343501i | ||||
\(233\) | −12.5885 | −0.824697 | −0.412349 | − | 0.911026i | \(-0.635291\pi\) | ||||
−0.412349 | + | 0.911026i | \(0.635291\pi\) | |||||||
\(234\) | 3.50000 | + | 0.866025i | 0.228802 | + | 0.0566139i | ||||
\(235\) | −27.1244 | −1.76940 | ||||||||
\(236\) | 4.26795 | − | 2.46410i | 0.277820 | − | 0.160399i | ||||
\(237\) | −4.50000 | − | 7.79423i | −0.292306 | − | 0.506290i | ||||
\(238\) | −2.86603 | + | 4.96410i | −0.185777 | + | 0.321775i | ||||
\(239\) | 4.58846i | 0.296803i | 0.988927 | + | 0.148401i | \(0.0474127\pi\) | ||||
−0.988927 | + | 0.148401i | \(0.952587\pi\) | |||||||
\(240\) | −2.36603 | − | 1.36603i | −0.152726 | − | 0.0881766i | ||||
\(241\) | 2.53590 | + | 1.46410i | 0.163352 | + | 0.0943111i | 0.579447 | − | 0.815010i | \(-0.303269\pi\) |
−0.416096 | + | 0.909321i | \(0.636602\pi\) | |||||||
\(242\) | 16.0000i | 1.02852i | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0.133975 | + | 0.232051i | 0.00857684 | + | 0.0148555i | ||||
\(245\) | −2.36603 | + | 1.36603i | −0.151160 | + | 0.0872722i | ||||
\(246\) | 1.53590 | 0.0979253 | ||||||||
\(247\) | 16.1603 | − | 16.7942i | 1.02825 | − | 1.06859i | ||||
\(248\) | −6.73205 | −0.427486 | ||||||||
\(249\) | −11.0263 | + | 6.36603i | −0.698762 | + | 0.403430i | ||||
\(250\) | −3.46410 | − | 6.00000i | −0.219089 | − | 0.379473i | ||||
\(251\) | −13.7583 | + | 23.8301i | −0.868418 | + | 1.50414i | −0.00480540 | + | 0.999988i | \(0.501530\pi\) |
−0.863613 | + | 0.504156i | \(0.831804\pi\) | |||||||
\(252\) | − | 1.00000i | − | 0.0629941i | ||||||
\(253\) | −2.41154 | − | 1.39230i | −0.151612 | − | 0.0875335i | ||||
\(254\) | 5.53590 | + | 3.19615i | 0.347353 | + | 0.200544i | ||||
\(255\) | 15.6603i | 0.980683i | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 6.52628 | + | 11.3038i | 0.407098 | + | 0.705115i | 0.994563 | − | 0.104135i | \(-0.0332074\pi\) |
−0.587465 | + | 0.809250i | \(0.699874\pi\) | |||||||
\(258\) | −4.56218 | + | 2.63397i | −0.284029 | + | 0.163984i | ||||
\(259\) | 3.26795 | 0.203060 | ||||||||
\(260\) | −6.83013 | + | 7.09808i | −0.423586 | + | 0.440204i | ||||
\(261\) | −10.4641 | −0.647712 | ||||||||
\(262\) | 0.928203 | − | 0.535898i | 0.0573446 | − | 0.0331079i | ||||
\(263\) | 10.5622 | + | 18.2942i | 0.651292 | + | 1.12807i | 0.982810 | + | 0.184622i | \(0.0591059\pi\) |
−0.331518 | + | 0.943449i | \(0.607561\pi\) | |||||||
\(264\) | 2.59808 | − | 4.50000i | 0.159901 | − | 0.276956i | ||||
\(265\) | 10.7321i | 0.659265i | ||||||||
\(266\) | −5.59808 | − | 3.23205i | −0.343240 | − | 0.198170i | ||||
\(267\) | 9.40192 | + | 5.42820i | 0.575388 | + | 0.332201i | ||||
\(268\) | 10.0000i | 0.610847i | ||||||||
\(269\) | 2.00000 | − | 3.46410i | 0.121942 | − | 0.211210i | −0.798591 | − | 0.601874i | \(-0.794421\pi\) |
0.920534 | + | 0.390664i | \(0.127754\pi\) | |||||||
\(270\) | −1.36603 | − | 2.36603i | −0.0831337 | − | 0.143992i | ||||
\(271\) | 8.36603 | − | 4.83013i | 0.508200 | − | 0.293409i | −0.223894 | − | 0.974614i | \(-0.571877\pi\) |
0.732093 | + | 0.681204i | \(0.238543\pi\) | |||||||
\(272\) | 5.73205 | 0.347557 | ||||||||
\(273\) | −3.50000 | − | 0.866025i | −0.211830 | − | 0.0524142i | ||||
\(274\) | −12.5359 | −0.757321 | ||||||||
\(275\) | −11.0885 | + | 6.40192i | −0.668659 | + | 0.386051i | ||||
\(276\) | 0.267949 | + | 0.464102i | 0.0161286 | + | 0.0279356i | ||||
\(277\) | 3.19615 | − | 5.53590i | 0.192038 | − | 0.332620i | −0.753887 | − | 0.657004i | \(-0.771824\pi\) |
0.945926 | + | 0.324384i | \(0.105157\pi\) | |||||||
\(278\) | 21.0526i | 1.26265i | ||||||||
\(279\) | −5.83013 | − | 3.36603i | −0.349041 | − | 0.201519i | ||||
\(280\) | 2.36603 | + | 1.36603i | 0.141397 | + | 0.0816356i | ||||
\(281\) | − | 9.26795i | − | 0.552879i | −0.961031 | − | 0.276440i | \(-0.910845\pi\) | ||
0.961031 | − | 0.276440i | \(-0.0891546\pi\) | |||||||
\(282\) | −4.96410 | + | 8.59808i | −0.295608 | + | 0.512008i | ||||
\(283\) | 4.92820 | + | 8.53590i | 0.292951 | + | 0.507406i | 0.974506 | − | 0.224360i | \(-0.0720293\pi\) |
−0.681555 | + | 0.731767i | \(0.738696\pi\) | |||||||
\(284\) | −9.29423 | + | 5.36603i | −0.551511 | + | 0.318415i | ||||
\(285\) | −17.6603 | −1.04610 | ||||||||
\(286\) | −13.5000 | − | 12.9904i | −0.798272 | − | 0.768137i | ||||
\(287\) | −1.53590 | −0.0906612 | ||||||||
\(288\) | −0.866025 | + | 0.500000i | −0.0510310 | + | 0.0294628i | ||||
\(289\) | −7.92820 | − | 13.7321i | −0.466365 | − | 0.807768i | ||||
\(290\) | 14.2942 | − | 24.7583i | 0.839386 | − | 1.45386i | ||||
\(291\) | − | 3.80385i | − | 0.222985i | ||||||
\(292\) | −4.73205 | − | 2.73205i | −0.276922 | − | 0.159881i | ||||
\(293\) | −12.9282 | − | 7.46410i | −0.755274 | − | 0.436057i | 0.0723226 | − | 0.997381i | \(-0.476959\pi\) |
−0.827596 | + | 0.561324i | \(0.810292\pi\) | |||||||
\(294\) | 1.00000i | 0.0583212i | ||||||||
\(295\) | −6.73205 | + | 11.6603i | −0.391955 | + | 0.678886i | ||||
\(296\) | −1.63397 | − | 2.83013i | −0.0949728 | − | 0.164498i | ||||
\(297\) | 4.50000 | − | 2.59808i | 0.261116 | − | 0.150756i | ||||
\(298\) | −8.00000 | −0.463428 | ||||||||
\(299\) | 1.85641 | − | 0.535898i | 0.107359 | − | 0.0309918i | ||||
\(300\) | 2.46410 | 0.142265 | ||||||||
\(301\) | 4.56218 | − | 2.63397i | 0.262960 | − | 0.151820i | ||||
\(302\) | 4.59808 | + | 7.96410i | 0.264590 | + | 0.458283i | ||||
\(303\) | −4.46410 | + | 7.73205i | −0.256456 | + | 0.444195i | ||||
\(304\) | 6.46410i | 0.370742i | ||||||||
\(305\) | −0.633975 | − | 0.366025i | −0.0363013 | − | 0.0209586i | ||||
\(306\) | 4.96410 | + | 2.86603i | 0.283779 | + | 0.163840i | ||||
\(307\) | 5.00000i | 0.285365i | 0.989769 | + | 0.142683i | \(0.0455728\pi\) | ||||
−0.989769 | + | 0.142683i | \(0.954427\pi\) | |||||||
\(308\) | −2.59808 | + | 4.50000i | −0.148039 | + | 0.256411i | ||||
\(309\) | −2.90192 | − | 5.02628i | −0.165085 | − | 0.285935i | ||||
\(310\) | 15.9282 | − | 9.19615i | 0.904661 | − | 0.522306i | ||||
\(311\) | 25.1962 | 1.42874 | 0.714371 | − | 0.699767i | \(-0.246713\pi\) | ||||
0.714371 | + | 0.699767i | \(0.246713\pi\) | |||||||
\(312\) | 1.00000 | + | 3.46410i | 0.0566139 | + | 0.196116i | ||||
\(313\) | 31.1244 | 1.75925 | 0.879626 | − | 0.475665i | \(-0.157793\pi\) | ||||
0.879626 | + | 0.475665i | \(0.157793\pi\) | |||||||
\(314\) | 3.92820 | − | 2.26795i | 0.221681 | − | 0.127988i | ||||
\(315\) | 1.36603 | + | 2.36603i | 0.0769668 | + | 0.133310i | ||||
\(316\) | 4.50000 | − | 7.79423i | 0.253145 | − | 0.438460i | ||||
\(317\) | 26.7846i | 1.50437i | 0.658950 | + | 0.752187i | \(0.271001\pi\) | ||||
−0.658950 | + | 0.752187i | \(0.728999\pi\) | |||||||
\(318\) | 3.40192 | + | 1.96410i | 0.190770 | + | 0.110141i | ||||
\(319\) | 47.0885 | + | 27.1865i | 2.63645 | + | 1.52215i | ||||
\(320\) | − | 2.73205i | − | 0.152726i | ||||||
\(321\) | 9.96410 | − | 17.2583i | 0.556142 | − | 0.963266i | ||||
\(322\) | −0.267949 | − | 0.464102i | −0.0149322 | − | 0.0258634i | ||||
\(323\) | 32.0885 | − | 18.5263i | 1.78545 | − | 1.03083i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 2.13397 | − | 8.62436i | 0.118372 | − | 0.478393i | ||||
\(326\) | 17.1244 | 0.948430 | ||||||||
\(327\) | −12.7583 | + | 7.36603i | −0.705537 | + | 0.407342i | ||||
\(328\) | 0.767949 | + | 1.33013i | 0.0424029 | + | 0.0734440i | ||||
\(329\) | 4.96410 | − | 8.59808i | 0.273680 | − | 0.474027i | ||||
\(330\) | 14.1962i | 0.781472i | ||||||||
\(331\) | 30.1244 | + | 17.3923i | 1.65578 | + | 0.955968i | 0.974628 | + | 0.223829i | \(0.0718558\pi\) |
0.681156 | + | 0.732138i | \(0.261478\pi\) | |||||||
\(332\) | −11.0263 | − | 6.36603i | −0.605146 | − | 0.349381i | ||||
\(333\) | − | 3.26795i | − | 0.179083i | ||||||
\(334\) | −9.46410 | + | 16.3923i | −0.517853 | + | 0.896947i | ||||
\(335\) | −13.6603 | − | 23.6603i | −0.746339 | − | 1.29270i | ||||
\(336\) | 0.866025 | − | 0.500000i | 0.0472456 | − | 0.0272772i | ||||
\(337\) | −11.0000 | −0.599208 | −0.299604 | − | 0.954064i | \(-0.596855\pi\) | ||||
−0.299604 | + | 0.954064i | \(0.596855\pi\) | |||||||
\(338\) | 12.9904 | − | 0.500000i | 0.706584 | − | 0.0271964i | ||||
\(339\) | −9.66025 | −0.524673 | ||||||||
\(340\) | −13.5622 | + | 7.83013i | −0.735512 | + | 0.424648i | ||||
\(341\) | 17.4904 | + | 30.2942i | 0.947157 | + | 1.64052i | ||||
\(342\) | −3.23205 | + | 5.59808i | −0.174769 | + | 0.302709i | ||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | −4.56218 | − | 2.63397i | −0.245976 | − | 0.142014i | ||||
\(345\) | −1.26795 | − | 0.732051i | −0.0682641 | − | 0.0394123i | ||||
\(346\) | − | 8.19615i | − | 0.440628i | ||||||
\(347\) | −0.232051 | + | 0.401924i | −0.0124571 | + | 0.0215764i | −0.872187 | − | 0.489173i | \(-0.837299\pi\) |
0.859730 | + | 0.510749i | \(0.170632\pi\) | |||||||
\(348\) | −5.23205 | − | 9.06218i | −0.280467 | − | 0.485784i | ||||
\(349\) | −29.3205 | + | 16.9282i | −1.56949 | + | 0.906146i | −0.573263 | + | 0.819372i | \(0.694323\pi\) |
−0.996228 | + | 0.0867744i | \(0.972344\pi\) | |||||||
\(350\) | −2.46410 | −0.131712 | ||||||||
\(351\) | −0.866025 | + | 3.50000i | −0.0462250 | + | 0.186816i | ||||
\(352\) | 5.19615 | 0.276956 | ||||||||
\(353\) | 2.87564 | − | 1.66025i | 0.153055 | − | 0.0883664i | −0.421516 | − | 0.906821i | \(-0.638502\pi\) |
0.574572 | + | 0.818454i | \(0.305169\pi\) | |||||||
\(354\) | 2.46410 | + | 4.26795i | 0.130966 | + | 0.226839i | ||||
\(355\) | 14.6603 | − | 25.3923i | 0.778085 | − | 1.34768i | ||||
\(356\) | 10.8564i | 0.575388i | ||||||||
\(357\) | −4.96410 | − | 2.86603i | −0.262728 | − | 0.151686i | ||||
\(358\) | −3.00000 | − | 1.73205i | −0.158555 | − | 0.0915417i | ||||
\(359\) | − | 24.4449i | − | 1.29015i | −0.764119 | − | 0.645075i | \(-0.776826\pi\) | ||
0.764119 | − | 0.645075i | \(-0.223174\pi\) | |||||||
\(360\) | 1.36603 | − | 2.36603i | 0.0719959 | − | 0.124700i | ||||
\(361\) | 11.3923 | + | 19.7321i | 0.599595 | + | 1.03853i | ||||
\(362\) | −15.3564 | + | 8.86603i | −0.807115 | + | 0.465988i | ||||
\(363\) | −16.0000 | −0.839782 | ||||||||
\(364\) | −1.00000 | − | 3.46410i | −0.0524142 | − | 0.181568i | ||||
\(365\) | 14.9282 | 0.781378 | ||||||||
\(366\) | −0.232051 | + | 0.133975i | −0.0121295 | + | 0.00700296i | ||||
\(367\) | 10.6603 | + | 18.4641i | 0.556461 | + | 0.963818i | 0.997788 | + | 0.0664722i | \(0.0211744\pi\) |
−0.441328 | + | 0.897346i | \(0.645492\pi\) | |||||||
\(368\) | −0.267949 | + | 0.464102i | −0.0139678 | + | 0.0241930i | ||||
\(369\) | 1.53590i | 0.0799557i | ||||||||
\(370\) | 7.73205 | + | 4.46410i | 0.401970 | + | 0.232078i | ||||
\(371\) | −3.40192 | − | 1.96410i | −0.176619 | − | 0.101971i | ||||
\(372\) | − | 6.73205i | − | 0.349041i | ||||||
\(373\) | −4.56218 | + | 7.90192i | −0.236221 | + | 0.409146i | −0.959627 | − | 0.281277i | \(-0.909242\pi\) |
0.723406 | + | 0.690423i | \(0.242575\pi\) | |||||||
\(374\) | −14.8923 | − | 25.7942i | −0.770063 | − | 1.33379i | ||||
\(375\) | 6.00000 | − | 3.46410i | 0.309839 | − | 0.178885i | ||||
\(376\) | −9.92820 | −0.512008 | ||||||||
\(377\) | −36.2487 | + | 10.4641i | −1.86690 | + | 0.538929i | ||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | −1.77757 | + | 1.02628i | −0.0913075 | + | 0.0527164i | −0.544959 | − | 0.838463i | \(-0.683455\pi\) |
0.453651 | + | 0.891179i | \(0.350121\pi\) | |||||||
\(380\) | −8.83013 | − | 15.2942i | −0.452976 | − | 0.784577i | ||||
\(381\) | −3.19615 | + | 5.53590i | −0.163744 | + | 0.283613i | ||||
\(382\) | − | 2.19615i | − | 0.112365i | ||||||
\(383\) | −26.8468 | − | 15.5000i | −1.37181 | − | 0.792013i | −0.380651 | − | 0.924719i | \(-0.624300\pi\) |
−0.991155 | + | 0.132706i | \(0.957633\pi\) | |||||||
\(384\) | −0.866025 | − | 0.500000i | −0.0441942 | − | 0.0255155i | ||||
\(385\) | − | 14.1962i | − | 0.723503i | ||||||
\(386\) | −11.7942 | + | 20.4282i | −0.600310 | + | 1.03977i | ||||
\(387\) | −2.63397 | − | 4.56218i | −0.133892 | − | 0.231909i | ||||
\(388\) | 3.29423 | − | 1.90192i | 0.167239 | − | 0.0965556i | ||||
\(389\) | 14.5359 | 0.736999 | 0.368500 | − | 0.929628i | \(-0.379872\pi\) | ||||
0.368500 | + | 0.929628i | \(0.379872\pi\) | |||||||
\(390\) | −7.09808 | − | 6.83013i | −0.359425 | − | 0.345857i | ||||
\(391\) | 3.07180 | 0.155347 | ||||||||
\(392\) | −0.866025 | + | 0.500000i | −0.0437409 | + | 0.0252538i | ||||
\(393\) | 0.535898 | + | 0.928203i | 0.0270325 | + | 0.0468217i | ||||
\(394\) | 1.86603 | − | 3.23205i | 0.0940090 | − | 0.162828i | ||||
\(395\) | 24.5885i | 1.23718i | ||||||||
\(396\) | 4.50000 | + | 2.59808i | 0.226134 | + | 0.130558i | ||||
\(397\) | 0.526279 | + | 0.303848i | 0.0264132 | + | 0.0152497i | 0.513148 | − | 0.858300i | \(-0.328479\pi\) |
−0.486735 | + | 0.873550i | \(0.661812\pi\) | |||||||
\(398\) | − | 6.58846i | − | 0.330250i | ||||||
\(399\) | 3.23205 | − | 5.59808i | 0.161805 | − | 0.280254i | ||||
\(400\) | 1.23205 | + | 2.13397i | 0.0616025 | + | 0.106699i | ||||
\(401\) | 21.5885 | − | 12.4641i | 1.07808 | − | 0.622428i | 0.147699 | − | 0.989032i | \(-0.452813\pi\) |
0.930377 | + | 0.366605i | \(0.119480\pi\) | |||||||
\(402\) | −10.0000 | −0.498755 | ||||||||
\(403\) | −23.5622 | − | 5.83013i | −1.17372 | − | 0.290419i | ||||
\(404\) | −8.92820 | −0.444195 | ||||||||
\(405\) | 2.36603 | − | 1.36603i | 0.117569 | − | 0.0678783i | ||||
\(406\) | 5.23205 | + | 9.06218i | 0.259662 | + | 0.449748i | ||||
\(407\) | −8.49038 | + | 14.7058i | −0.420853 | + | 0.728938i | ||||
\(408\) | 5.73205i | 0.283779i | ||||||||
\(409\) | −12.6340 | − | 7.29423i | −0.624710 | − | 0.360676i | 0.153991 | − | 0.988072i | \(-0.450787\pi\) |
−0.778700 | + | 0.627396i | \(0.784121\pi\) | |||||||
\(410\) | −3.63397 | − | 2.09808i | −0.179469 | − | 0.103617i | ||||
\(411\) | − | 12.5359i | − | 0.618350i | ||||||
\(412\) | 2.90192 | − | 5.02628i | 0.142968 | − | 0.247627i | ||||
\(413\) | −2.46410 | − | 4.26795i | −0.121251 | − | 0.210012i | ||||
\(414\) | −0.464102 | + | 0.267949i | −0.0228093 | + | 0.0131690i | ||||
\(415\) | 34.7846 | 1.70751 | ||||||||
\(416\) | −2.50000 | + | 2.59808i | −0.122573 | + | 0.127381i | ||||
\(417\) | −21.0526 | −1.03095 | ||||||||
\(418\) | 29.0885 | − | 16.7942i | 1.42276 | − | 0.821433i | ||||
\(419\) | −8.29423 | − | 14.3660i | −0.405200 | − | 0.701826i | 0.589145 | − | 0.808027i | \(-0.299465\pi\) |
−0.994345 | + | 0.106201i | \(0.966131\pi\) | |||||||
\(420\) | −1.36603 | + | 2.36603i | −0.0666552 | + | 0.115450i | ||||
\(421\) | 9.32051i | 0.454254i | 0.973865 | + | 0.227127i | \(0.0729332\pi\) | ||||
−0.973865 | + | 0.227127i | \(0.927067\pi\) | |||||||
\(422\) | 9.58846 | + | 5.53590i | 0.466759 | + | 0.269483i | ||||
\(423\) | −8.59808 | − | 4.96410i | −0.418053 | − | 0.241363i | ||||
\(424\) | 3.92820i | 0.190770i | ||||||||
\(425\) | 7.06218 | − | 12.2321i | 0.342566 | − | 0.593342i | ||||
\(426\) | −5.36603 | − | 9.29423i | −0.259985 | − | 0.450307i | ||||
\(427\) | 0.232051 | − | 0.133975i | 0.0112297 | − | 0.00648349i | ||||
\(428\) | 19.9282 | 0.963266 | ||||||||
\(429\) | 12.9904 | − | 13.5000i | 0.627182 | − | 0.651786i | ||||
\(430\) | 14.3923 | 0.694059 | ||||||||
\(431\) | 9.63397 | − | 5.56218i | 0.464052 | − | 0.267921i | −0.249694 | − | 0.968325i | \(-0.580330\pi\) |
0.713747 | + | 0.700404i | \(0.246997\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | 19.9282 | − | 34.5167i | 0.957688 | − | 1.65876i | 0.229596 | − | 0.973286i | \(-0.426260\pi\) |
0.728093 | − | 0.685479i | \(-0.240407\pi\) | |||||||
\(434\) | 6.73205i | 0.323149i | ||||||||
\(435\) | 24.7583 | + | 14.2942i | 1.18707 | + | 0.685356i | ||||
\(436\) | −12.7583 | − | 7.36603i | −0.611013 | − | 0.352769i | ||||
\(437\) | 3.46410i | 0.165710i | ||||||||
\(438\) | 2.73205 | − | 4.73205i | 0.130542 | − | 0.226106i | ||||
\(439\) | −5.66025 | − | 9.80385i | −0.270149 | − | 0.467912i | 0.698751 | − | 0.715365i | \(-0.253740\pi\) |
−0.968900 | + | 0.247453i | \(0.920406\pi\) | |||||||
\(440\) | −12.2942 | + | 7.09808i | −0.586104 | + | 0.338388i | ||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | 20.0622 | + | 4.96410i | 0.954260 | + | 0.236118i | ||||
\(443\) | −25.0000 | −1.18779 | −0.593893 | − | 0.804544i | \(-0.702410\pi\) | ||||
−0.593893 | + | 0.804544i | \(0.702410\pi\) | |||||||
\(444\) | 2.83013 | − | 1.63397i | 0.134312 | − | 0.0775450i | ||||
\(445\) | −14.8301 | − | 25.6865i | −0.703015 | − | 1.21766i | ||||
\(446\) | 0.732051 | − | 1.26795i | 0.0346636 | − | 0.0600391i | ||||
\(447\) | − | 8.00000i | − | 0.378387i | ||||||
\(448\) | 0.866025 | + | 0.500000i | 0.0409159 | + | 0.0236228i | ||||
\(449\) | 19.9019 | + | 11.4904i | 0.939230 | + | 0.542265i | 0.889719 | − | 0.456509i | \(-0.150900\pi\) |
0.0495110 | + | 0.998774i | \(0.484234\pi\) | |||||||
\(450\) | 2.46410i | 0.116159i | ||||||||
\(451\) | 3.99038 | − | 6.91154i | 0.187900 | − | 0.325452i | ||||
\(452\) | −4.83013 | − | 8.36603i | −0.227190 | − | 0.393505i | ||||
\(453\) | −7.96410 | + | 4.59808i | −0.374186 | + | 0.216036i | ||||
\(454\) | 21.3205 | 1.00062 | ||||||||
\(455\) | 7.09808 | + | 6.83013i | 0.332763 | + | 0.320201i | ||||
\(456\) | −6.46410 | −0.302709 | ||||||||
\(457\) | −22.2679 | + | 12.8564i | −1.04165 | + | 0.601397i | −0.920300 | − | 0.391212i | \(-0.872056\pi\) |
−0.121350 | + | 0.992610i | \(0.538722\pi\) | |||||||
\(458\) | −1.69615 | − | 2.93782i | −0.0792560 | − | 0.137275i | ||||
\(459\) | −2.86603 | + | 4.96410i | −0.133775 | + | 0.231704i | ||||
\(460\) | − | 1.46410i | − | 0.0682641i | ||||||
\(461\) | 6.00000 | + | 3.46410i | 0.279448 | + | 0.161339i | 0.633173 | − | 0.774010i | \(-0.281752\pi\) |
−0.353726 | + | 0.935349i | \(0.615085\pi\) | |||||||
\(462\) | −4.50000 | − | 2.59808i | −0.209359 | − | 0.120873i | ||||
\(463\) | − | 32.6603i | − | 1.51785i | −0.651178 | − | 0.758925i | \(-0.725725\pi\) | ||
0.651178 | − | 0.758925i | \(-0.274275\pi\) | |||||||
\(464\) | 5.23205 | − | 9.06218i | 0.242892 | − | 0.420701i | ||||
\(465\) | 9.19615 | + | 15.9282i | 0.426461 | + | 0.738653i | ||||
\(466\) | 10.9019 | − | 6.29423i | 0.505022 | − | 0.291575i | ||||
\(467\) | 5.07180 | 0.234695 | 0.117347 | − | 0.993091i | \(-0.462561\pi\) | ||||
0.117347 | + | 0.993091i | \(0.462561\pi\) | |||||||
\(468\) | −3.46410 | + | 1.00000i | −0.160128 | + | 0.0462250i | ||||
\(469\) | 10.0000 | 0.461757 | ||||||||
\(470\) | 23.4904 | − | 13.5622i | 1.08353 | − | 0.625577i | ||||
\(471\) | 2.26795 | + | 3.92820i | 0.104502 | + | 0.181002i | ||||
\(472\) | −2.46410 | + | 4.26795i | −0.113419 | + | 0.196448i | ||||
\(473\) | 27.3731i | 1.25861i | ||||||||
\(474\) | 7.79423 | + | 4.50000i | 0.358001 | + | 0.206692i | ||||
\(475\) | 13.7942 | + | 7.96410i | 0.632923 | + | 0.365418i | ||||
\(476\) | − | 5.73205i | − | 0.262728i | ||||||
\(477\) | −1.96410 | + | 3.40192i | −0.0899300 | + | 0.155763i | ||||
\(478\) | −2.29423 | − | 3.97372i | −0.104936 | − | 0.181754i | ||||
\(479\) | 19.7942 | − | 11.4282i | 0.904421 | − | 0.522168i | 0.0257894 | − | 0.999667i | \(-0.491790\pi\) |
0.878632 | + | 0.477499i | \(0.158457\pi\) | |||||||
\(480\) | 2.73205 | 0.124700 | ||||||||
\(481\) | −3.26795 | − | 11.3205i | −0.149006 | − | 0.516171i | ||||
\(482\) | −2.92820 | −0.133376 | ||||||||
\(483\) | 0.464102 | − | 0.267949i | 0.0211174 | − | 0.0121921i | ||||
\(484\) | −8.00000 | − | 13.8564i | −0.363636 | − | 0.629837i | ||||
\(485\) | −5.19615 | + | 9.00000i | −0.235945 | + | 0.408669i | ||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | −25.5000 | − | 14.7224i | −1.15552 | − | 0.667137i | −0.205290 | − | 0.978701i | \(-0.565814\pi\) |
−0.950225 | + | 0.311564i | \(0.899147\pi\) | |||||||
\(488\) | −0.232051 | − | 0.133975i | −0.0105044 | − | 0.00606475i | ||||
\(489\) | 17.1244i | 0.774390i | ||||||||
\(490\) | 1.36603 | − | 2.36603i | 0.0617107 | − | 0.106886i | ||||
\(491\) | 7.19615 | + | 12.4641i | 0.324758 | + | 0.562497i | 0.981463 | − | 0.191650i | \(-0.0613839\pi\) |
−0.656706 | + | 0.754147i | \(0.728051\pi\) | |||||||
\(492\) | −1.33013 | + | 0.767949i | −0.0599668 | + | 0.0346218i | ||||
\(493\) | −59.9808 | −2.70140 | ||||||||
\(494\) | −5.59808 | + | 22.6244i | −0.251869 | + | 1.01792i | ||||
\(495\) | −14.1962 | −0.638070 | ||||||||
\(496\) | 5.83013 | − | 3.36603i | 0.261780 | − | 0.151139i | ||||
\(497\) | 5.36603 | + | 9.29423i | 0.240699 | + | 0.416903i | ||||
\(498\) | 6.36603 | − | 11.0263i | 0.285268 | − | 0.494099i | ||||
\(499\) | 10.5885i | 0.474004i | 0.971509 | + | 0.237002i | \(0.0761649\pi\) | ||||
−0.971509 | + | 0.237002i | \(0.923835\pi\) | |||||||
\(500\) | 6.00000 | + | 3.46410i | 0.268328 | + | 0.154919i | ||||
\(501\) | −16.3923 | − | 9.46410i | −0.732354 | − | 0.422825i | ||||
\(502\) | − | 27.5167i | − | 1.22813i | ||||||
\(503\) | 8.53590 | − | 14.7846i | 0.380597 | − | 0.659213i | −0.610551 | − | 0.791977i | \(-0.709052\pi\) |
0.991148 | + | 0.132764i | \(0.0423852\pi\) | |||||||
\(504\) | 0.500000 | + | 0.866025i | 0.0222718 | + | 0.0385758i | ||||
\(505\) | 21.1244 | − | 12.1962i | 0.940021 | − | 0.542722i | ||||
\(506\) | 2.78461 | 0.123791 | ||||||||
\(507\) | 0.500000 | + | 12.9904i | 0.0222058 | + | 0.576923i | ||||
\(508\) | −6.39230 | −0.283613 | ||||||||
\(509\) | 10.6865 | − | 6.16987i | 0.473672 | − | 0.273475i | −0.244103 | − | 0.969749i | \(-0.578494\pi\) |
0.717776 | + | 0.696274i | \(0.245160\pi\) | |||||||
\(510\) | −7.83013 | − | 13.5622i | −0.346724 | − | 0.600543i | ||||
\(511\) | −2.73205 | + | 4.73205i | −0.120859 | + | 0.209334i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −5.59808 | − | 3.23205i | −0.247161 | − | 0.142699i | ||||
\(514\) | −11.3038 | − | 6.52628i | −0.498591 | − | 0.287862i | ||||
\(515\) | 15.8564i | 0.698717i | ||||||||
\(516\) | 2.63397 | − | 4.56218i | 0.115954 | − | 0.200839i | ||||
\(517\) | 25.7942 | + | 44.6769i | 1.13443 | + | 1.96489i | ||||
\(518\) | −2.83013 | + | 1.63397i | −0.124349 | + | 0.0717927i | ||||
\(519\) | 8.19615 | 0.359771 | ||||||||
\(520\) | 2.36603 | − | 9.56218i | 0.103757 | − | 0.419329i | ||||
\(521\) | 9.58846 | 0.420078 | 0.210039 | − | 0.977693i | \(-0.432641\pi\) | ||||
0.210039 | + | 0.977693i | \(0.432641\pi\) | |||||||
\(522\) | 9.06218 | − | 5.23205i | 0.396641 | − | 0.229001i | ||||
\(523\) | 7.40192 | + | 12.8205i | 0.323664 | + | 0.560602i | 0.981241 | − | 0.192785i | \(-0.0617521\pi\) |
−0.657577 | + | 0.753387i | \(0.728419\pi\) | |||||||
\(524\) | −0.535898 | + | 0.928203i | −0.0234108 | + | 0.0405487i | ||||
\(525\) | − | 2.46410i | − | 0.107542i | ||||||
\(526\) | −18.2942 | − | 10.5622i | −0.797666 | − | 0.460533i | ||||
\(527\) | −33.4186 | − | 19.2942i | −1.45574 | − | 0.840470i | ||||
\(528\) | 5.19615i | 0.226134i | ||||||||
\(529\) | 11.3564 | − | 19.6699i | 0.493757 | − | 0.855212i | ||||
\(530\) | −5.36603 | − | 9.29423i | −0.233085 | − | 0.403715i | ||||
\(531\) | −4.26795 | + | 2.46410i | −0.185213 | + | 0.106933i | ||||
\(532\) | 6.46410 | 0.280254 | ||||||||
\(533\) | 1.53590 | + | 5.32051i | 0.0665271 | + | 0.230457i | ||||
\(534\) | −10.8564 | −0.469803 | ||||||||
\(535\) | −47.1506 | + | 27.2224i | −2.03850 | + | 1.17693i | ||||
\(536\) | −5.00000 | − | 8.66025i | −0.215967 | − | 0.374066i | ||||
\(537\) | 1.73205 | − | 3.00000i | 0.0747435 | − | 0.129460i | ||||
\(538\) | 4.00000i | 0.172452i | ||||||||
\(539\) | 4.50000 | + | 2.59808i | 0.193829 | + | 0.111907i | ||||
\(540\) | 2.36603 | + | 1.36603i | 0.101818 | + | 0.0587844i | ||||
\(541\) | 30.0526i | 1.29206i | 0.763312 | + | 0.646030i | \(0.223572\pi\) | ||||
−0.763312 | + | 0.646030i | \(0.776428\pi\) | |||||||
\(542\) | −4.83013 | + | 8.36603i | −0.207472 | + | 0.359352i | ||||
\(543\) | −8.86603 | − | 15.3564i | −0.380478 | − | 0.659006i | ||||
\(544\) | −4.96410 | + | 2.86603i | −0.212834 | + | 0.122880i | ||||
\(545\) | 40.2487 | 1.72407 | ||||||||
\(546\) | 3.46410 | − | 1.00000i | 0.148250 | − | 0.0427960i | ||||
\(547\) | 6.19615 | 0.264928 | 0.132464 | − | 0.991188i | \(-0.457711\pi\) | ||||
0.132464 | + | 0.991188i | \(0.457711\pi\) | |||||||
\(548\) | 10.8564 | − | 6.26795i | 0.463763 | − | 0.267754i | ||||
\(549\) | −0.133975 | − | 0.232051i | −0.00571790 | − | 0.00990369i | ||||
\(550\) | 6.40192 | − | 11.0885i | 0.272979 | − | 0.472813i | ||||
\(551\) | − | 67.6410i | − | 2.88160i | ||||||
\(552\) | −0.464102 | − | 0.267949i | −0.0197535 | − | 0.0114047i | ||||
\(553\) | −7.79423 | − | 4.50000i | −0.331444 | − | 0.191359i | ||||
\(554\) | 6.39230i | 0.271583i | ||||||||
\(555\) | −4.46410 | + | 7.73205i | −0.189491 | + | 0.328207i | ||||
\(556\) | −10.5263 | − | 18.2321i | −0.446414 | − | 0.773211i | ||||
\(557\) | −14.0885 | + | 8.13397i | −0.596947 | + | 0.344648i | −0.767840 | − | 0.640642i | \(-0.778668\pi\) |
0.170893 | + | 0.985290i | \(0.445335\pi\) | |||||||
\(558\) | 6.73205 | 0.284990 | ||||||||
\(559\) | −13.6865 | − | 13.1699i | −0.578879 | − | 0.557026i | ||||
\(560\) | −2.73205 | −0.115450 | ||||||||
\(561\) | 25.7942 | − | 14.8923i | 1.08903 | − | 0.628754i | ||||
\(562\) | 4.63397 | + | 8.02628i | 0.195472 | + | 0.338568i | ||||
\(563\) | 1.83013 | − | 3.16987i | 0.0771307 | − | 0.133594i | −0.824880 | − | 0.565308i | \(-0.808757\pi\) |
0.902011 | + | 0.431713i | \(0.142091\pi\) | |||||||
\(564\) | − | 9.92820i | − | 0.418053i | ||||||
\(565\) | 22.8564 | + | 13.1962i | 0.961576 | + | 0.555166i | ||||
\(566\) | −8.53590 | − | 4.92820i | −0.358791 | − | 0.207148i | ||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | 5.36603 | − | 9.29423i | 0.225153 | − | 0.389977i | ||||
\(569\) | −7.83013 | − | 13.5622i | −0.328256 | − | 0.568556i | 0.653910 | − | 0.756572i | \(-0.273128\pi\) |
−0.982166 | + | 0.188016i | \(0.939794\pi\) | |||||||
\(570\) | 15.2942 | − | 8.83013i | 0.640605 | − | 0.369853i | ||||
\(571\) | −5.51666 | −0.230865 | −0.115433 | − | 0.993315i | \(-0.536825\pi\) | ||||
−0.115433 | + | 0.993315i | \(0.536825\pi\) | |||||||
\(572\) | 18.1865 | + | 4.50000i | 0.760417 | + | 0.188154i | ||||
\(573\) | 2.19615 | 0.0917456 | ||||||||
\(574\) | 1.33013 | − | 0.767949i | 0.0555184 | − | 0.0320536i | ||||
\(575\) | 0.660254 | + | 1.14359i | 0.0275345 | + | 0.0476911i | ||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | − | 2.58846i | − | 0.107759i | −0.998547 | − | 0.0538794i | \(-0.982841\pi\) | ||
0.998547 | − | 0.0538794i | \(-0.0171587\pi\) | |||||||
\(578\) | 13.7321 | + | 7.92820i | 0.571178 | + | 0.329770i | ||||
\(579\) | −20.4282 | − | 11.7942i | −0.848967 | − | 0.490151i | ||||
\(580\) | 28.5885i | 1.18707i | ||||||||
\(581\) | −6.36603 | + | 11.0263i | −0.264107 | + | 0.457447i | ||||
\(582\) | 1.90192 | + | 3.29423i | 0.0788373 | + | 0.136550i | ||||
\(583\) | 17.6769 | − | 10.2058i | 0.732103 | − | 0.422680i | ||||
\(584\) | 5.46410 | 0.226106 | ||||||||
\(585\) | 6.83013 | − | 7.09808i | 0.282391 | − | 0.293469i | ||||
\(586\) | 14.9282 | 0.616678 | ||||||||
\(587\) | −16.5622 | + | 9.56218i | −0.683594 | + | 0.394673i | −0.801208 | − | 0.598386i | \(-0.795809\pi\) |
0.117614 | + | 0.993059i | \(0.462476\pi\) | |||||||
\(588\) | −0.500000 | − | 0.866025i | −0.0206197 | − | 0.0357143i | ||||
\(589\) | 21.7583 | − | 37.6865i | 0.896536 | − | 1.55285i | ||||
\(590\) | − | 13.4641i | − | 0.554308i | ||||||
\(591\) | 3.23205 | + | 1.86603i | 0.132949 | + | 0.0767580i | ||||
\(592\) | 2.83013 | + | 1.63397i | 0.116318 | + | 0.0671559i | ||||
\(593\) | 37.0000i | 1.51941i | 0.650269 | + | 0.759704i | \(0.274656\pi\) | ||||
−0.650269 | + | 0.759704i | \(0.725344\pi\) | |||||||
\(594\) | −2.59808 | + | 4.50000i | −0.106600 | + | 0.184637i | ||||
\(595\) | 7.83013 | + | 13.5622i | 0.321004 | + | 0.555995i | ||||
\(596\) | 6.92820 | − | 4.00000i | 0.283790 | − | 0.163846i | ||||
\(597\) | 6.58846 | 0.269648 | ||||||||
\(598\) | −1.33975 | + | 1.39230i | −0.0547863 | + | 0.0569356i | ||||
\(599\) | 35.5692 | 1.45332 | 0.726659 | − | 0.686998i | \(-0.241072\pi\) | ||||
0.726659 | + | 0.686998i | \(0.241072\pi\) | |||||||
\(600\) | −2.13397 | + | 1.23205i | −0.0871191 | + | 0.0502983i | ||||
\(601\) | −19.1506 | − | 33.1699i | −0.781171 | − | 1.35303i | −0.931260 | − | 0.364355i | \(-0.881290\pi\) |
0.150089 | − | 0.988672i | \(-0.452044\pi\) | |||||||
\(602\) | −2.63397 | + | 4.56218i | −0.107353 | + | 0.185940i | ||||
\(603\) | − | 10.0000i | − | 0.407231i | ||||||
\(604\) | −7.96410 | − | 4.59808i | −0.324055 | − | 0.187093i | ||||
\(605\) | 37.8564 | + | 21.8564i | 1.53908 | + | 0.888589i | ||||
\(606\) | − | 8.92820i | − | 0.362683i | ||||||
\(607\) | 4.16987 | − | 7.22243i | 0.169250 | − | 0.293149i | −0.768906 | − | 0.639361i | \(-0.779199\pi\) |
0.938156 | + | 0.346212i | \(0.112532\pi\) | |||||||
\(608\) | −3.23205 | − | 5.59808i | −0.131077 | − | 0.227032i | ||||
\(609\) | −9.06218 | + | 5.23205i | −0.367218 | + | 0.212013i | ||||
\(610\) | 0.732051 | 0.0296399 | ||||||||
\(611\) | −34.7487 | − | 8.59808i | −1.40578 | − | 0.347841i | ||||
\(612\) | −5.73205 | −0.231704 | ||||||||
\(613\) | −6.67949 | + | 3.85641i | −0.269782 | + | 0.155759i | −0.628789 | − | 0.777576i | \(-0.716449\pi\) |
0.359006 | + | 0.933335i | \(0.383116\pi\) | |||||||
\(614\) | −2.50000 | − | 4.33013i | −0.100892 | − | 0.174750i | ||||
\(615\) | 2.09808 | − | 3.63397i | 0.0846026 | − | 0.146536i | ||||
\(616\) | − | 5.19615i | − | 0.209359i | ||||||
\(617\) | −20.9545 | − | 12.0981i | −0.843596 | − | 0.487050i | 0.0148891 | − | 0.999889i | \(-0.495260\pi\) |
−0.858485 | + | 0.512839i | \(0.828594\pi\) | |||||||
\(618\) | 5.02628 | + | 2.90192i | 0.202187 | + | 0.116732i | ||||
\(619\) | 9.39230i | 0.377509i | 0.982024 | + | 0.188754i | \(0.0604450\pi\) | ||||
−0.982024 | + | 0.188754i | \(0.939555\pi\) | |||||||
\(620\) | −9.19615 | + | 15.9282i | −0.369326 | + | 0.639692i | ||||
\(621\) | −0.267949 | − | 0.464102i | −0.0107524 | − | 0.0186238i | ||||
\(622\) | −21.8205 | + | 12.5981i | −0.874923 | + | 0.505137i | ||||
\(623\) | 10.8564 | 0.434953 | ||||||||
\(624\) | −2.59808 | − | 2.50000i | −0.104006 | − | 0.100080i | ||||
\(625\) | −31.2487 | −1.24995 | ||||||||
\(626\) | −26.9545 | + | 15.5622i | −1.07732 | + | 0.621990i | ||||
\(627\) | 16.7942 | + | 29.0885i | 0.670697 | + | 1.16168i | ||||
\(628\) | −2.26795 | + | 3.92820i | −0.0905010 | + | 0.156752i | ||||
\(629\) | − | 18.7321i | − | 0.746896i | ||||||
\(630\) | −2.36603 | − | 1.36603i | −0.0942647 | − | 0.0544238i | ||||
\(631\) | −22.6244 | − | 13.0622i | −0.900661 | − | 0.519997i | −0.0232467 | − | 0.999730i | \(-0.507400\pi\) |
−0.877415 | + | 0.479733i | \(0.840734\pi\) | |||||||
\(632\) | 9.00000i | 0.358001i | ||||||||
\(633\) | −5.53590 | + | 9.58846i | −0.220032 | + | 0.381107i | ||||
\(634\) | −13.3923 | − | 23.1962i | −0.531876 | − | 0.921237i | ||||
\(635\) | 15.1244 | − | 8.73205i | 0.600192 | − | 0.346521i | ||||
\(636\) | −3.92820 | −0.155763 | ||||||||
\(637\) | −3.46410 | + | 1.00000i | −0.137253 | + | 0.0396214i | ||||
\(638\) | −54.3731 | −2.15265 | ||||||||
\(639\) | 9.29423 | − | 5.36603i | 0.367674 | − | 0.212277i | ||||
\(640\) | 1.36603 | + | 2.36603i | 0.0539969 | + | 0.0935254i | ||||
\(641\) | 8.66025 | − | 15.0000i | 0.342059 | − | 0.592464i | −0.642756 | − | 0.766071i | \(-0.722209\pi\) |
0.984815 | + | 0.173607i | \(0.0555422\pi\) | |||||||
\(642\) | 19.9282i | 0.786503i | ||||||||
\(643\) | 27.9904 | + | 16.1603i | 1.10383 | + | 0.637298i | 0.937225 | − | 0.348725i | \(-0.113385\pi\) |
0.166608 | + | 0.986023i | \(0.446719\pi\) | |||||||
\(644\) | 0.464102 | + | 0.267949i | 0.0182882 | + | 0.0105587i | ||||
\(645\) | 14.3923i | 0.566696i | ||||||||
\(646\) | −18.5263 | + | 32.0885i | −0.728907 | + | 1.26250i | ||||
\(647\) | −10.1340 | − | 17.5526i | −0.398408 | − | 0.690062i | 0.595122 | − | 0.803635i | \(-0.297104\pi\) |
−0.993530 | + | 0.113573i | \(0.963770\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | 25.6077 | 1.00519 | ||||||||
\(650\) | 2.46410 | + | 8.53590i | 0.0966500 | + | 0.334805i | ||||
\(651\) | −6.73205 | −0.263850 | ||||||||
\(652\) | −14.8301 | + | 8.56218i | −0.580793 | + | 0.335321i | ||||
\(653\) | −20.3564 | − | 35.2583i | −0.796608 | − | 1.37977i | −0.921813 | − | 0.387634i | \(-0.873292\pi\) |
0.125206 | − | 0.992131i | \(-0.460041\pi\) | |||||||
\(654\) | 7.36603 | − | 12.7583i | 0.288034 | − | 0.498890i | ||||
\(655\) | − | 2.92820i | − | 0.114414i | ||||||
\(656\) | −1.33013 | − | 0.767949i | −0.0519327 | − | 0.0299834i | ||||
\(657\) | 4.73205 | + | 2.73205i | 0.184615 | + | 0.106587i | ||||
\(658\) | 9.92820i | 0.387042i | ||||||||
\(659\) | −17.6244 | + | 30.5263i | −0.686547 | + | 1.18914i | 0.286400 | + | 0.958110i | \(0.407541\pi\) |
−0.972948 | + | 0.231025i | \(0.925792\pi\) | |||||||
\(660\) | −7.09808 | − | 12.2942i | −0.276292 | − | 0.478552i | ||||
\(661\) | −25.5167 | + | 14.7321i | −0.992483 | + | 0.573010i | −0.906016 | − | 0.423244i | \(-0.860891\pi\) |
−0.0864675 | + | 0.996255i | \(0.527558\pi\) | |||||||
\(662\) | −34.7846 | −1.35194 | ||||||||
\(663\) | −4.96410 | + | 20.0622i | −0.192790 | + | 0.779150i | ||||
\(664\) | 12.7321 | 0.494099 | ||||||||
\(665\) | −15.2942 | + | 8.83013i | −0.593085 | + | 0.342418i | ||||
\(666\) | 1.63397 | + | 2.83013i | 0.0633152 | + | 0.109665i | ||||
\(667\) | 2.80385 | − | 4.85641i | 0.108565 | − | 0.188041i | ||||
\(668\) | − | 18.9282i | − | 0.732354i | ||||||
\(669\) | 1.26795 | + | 0.732051i | 0.0490217 | + | 0.0283027i | ||||
\(670\) | 23.6603 | + | 13.6603i | 0.914075 | + | 0.527742i | ||||
\(671\) | 1.39230i | 0.0537493i | ||||||||
\(672\) | −0.500000 | + | 0.866025i | −0.0192879 | + | 0.0334077i | ||||
\(673\) | 12.8205 | + | 22.2058i | 0.494194 | + | 0.855970i | 0.999978 | − | 0.00669096i | \(-0.00212981\pi\) |
−0.505783 | + | 0.862661i | \(0.668796\pi\) | |||||||
\(674\) | 9.52628 | − | 5.50000i | 0.366939 | − | 0.211852i | ||||
\(675\) | −2.46410 | −0.0948433 | ||||||||
\(676\) | −11.0000 | + | 6.92820i | −0.423077 | + | 0.266469i | ||||
\(677\) | 46.7321 | 1.79606 | 0.898029 | − | 0.439936i | \(-0.144999\pi\) | ||||
0.898029 | + | 0.439936i | \(0.144999\pi\) | |||||||
\(678\) | 8.36603 | − | 4.83013i | 0.321295 | − | 0.185500i | ||||
\(679\) | −1.90192 | − | 3.29423i | −0.0729891 | − | 0.126421i | ||||
\(680\) | 7.83013 | − | 13.5622i | 0.300272 | − | 0.520086i | ||||
\(681\) | 21.3205i | 0.817004i | ||||||||
\(682\) | −30.2942 | − | 17.4904i | −1.16003 | − | 0.669741i | ||||
\(683\) | −15.0000 | − | 8.66025i | −0.573959 | − | 0.331375i | 0.184770 | − | 0.982782i | \(-0.440846\pi\) |
−0.758729 | + | 0.651406i | \(0.774179\pi\) | |||||||
\(684\) | − | 6.46410i | − | 0.247161i | ||||||
\(685\) | −17.1244 | + | 29.6603i | −0.654288 | + | 1.13326i | ||||
\(686\) | 0.500000 | + | 0.866025i | 0.0190901 | + | 0.0330650i | ||||
\(687\) | 2.93782 | − | 1.69615i | 0.112085 | − | 0.0647123i | ||||
\(688\) | 5.26795 | 0.200839 | ||||||||
\(689\) | −3.40192 | + | 13.7487i | −0.129603 | + | 0.523784i | ||||
\(690\) | 1.46410 | 0.0557374 | ||||||||
\(691\) | −44.1051 | + | 25.4641i | −1.67784 | + | 0.968700i | −0.714802 | + | 0.699327i | \(0.753483\pi\) |
−0.963036 | + | 0.269373i | \(0.913184\pi\) | |||||||
\(692\) | 4.09808 | + | 7.09808i | 0.155785 | + | 0.269828i | ||||
\(693\) | 2.59808 | − | 4.50000i | 0.0986928 | − | 0.170941i | ||||
\(694\) | − | 0.464102i | − | 0.0176171i | ||||||
\(695\) | 49.8109 | + | 28.7583i | 1.88943 | + | 1.09087i | ||||
\(696\) | 9.06218 | + | 5.23205i | 0.343501 | + | 0.198320i | ||||
\(697\) | 8.80385i | 0.333470i | ||||||||
\(698\) | 16.9282 | − | 29.3205i | 0.640742 | − | 1.10980i | ||||
\(699\) | 6.29423 | + | 10.9019i | 0.238070 | + | 0.412349i | ||||
\(700\) | 2.13397 | − | 1.23205i | 0.0806567 | − | 0.0465671i | ||||
\(701\) | 15.7846 | 0.596176 | 0.298088 | − | 0.954538i | \(-0.403651\pi\) | ||||
0.298088 | + | 0.954538i | \(0.403651\pi\) | |||||||
\(702\) | −1.00000 | − | 3.46410i | −0.0377426 | − | 0.130744i | ||||
\(703\) | 21.1244 | 0.796720 | ||||||||
\(704\) | −4.50000 | + | 2.59808i | −0.169600 | + | 0.0979187i | ||||
\(705\) | 13.5622 | + | 23.4904i | 0.510781 | + | 0.884699i | ||||
\(706\) | −1.66025 | + | 2.87564i | −0.0624845 | + | 0.108226i | ||||
\(707\) | 8.92820i | 0.335780i | ||||||||
\(708\) | −4.26795 | − | 2.46410i | −0.160399 | − | 0.0926066i | ||||
\(709\) | 18.5096 | + | 10.6865i | 0.695143 | + | 0.401341i | 0.805536 | − | 0.592547i | \(-0.201878\pi\) |
−0.110393 | + | 0.993888i | \(0.535211\pi\) | |||||||
\(710\) | 29.3205i | 1.10038i | ||||||||
\(711\) | −4.50000 | + | 7.79423i | −0.168763 | + | 0.292306i | ||||
\(712\) | −5.42820 | − | 9.40192i | −0.203431 | − | 0.352352i | ||||
\(713\) | 3.12436 | − | 1.80385i | 0.117008 | − | 0.0675546i | ||||
\(714\) | 5.73205 | 0.214517 | ||||||||
\(715\) | −49.1769 | + | 14.1962i | −1.83911 | + | 0.530906i | ||||
\(716\) | 3.46410 | 0.129460 | ||||||||
\(717\) | 3.97372 | − | 2.29423i | 0.148401 | − | 0.0856795i | ||||
\(718\) | 12.2224 | + | 21.1699i | 0.456137 | + | 0.790053i | ||||
\(719\) | −9.72243 | + | 16.8397i | −0.362586 | + | 0.628017i | −0.988386 | − | 0.151967i | \(-0.951439\pi\) |
0.625800 | + | 0.779984i | \(0.284773\pi\) | |||||||
\(720\) | 2.73205i | 0.101818i | ||||||||
\(721\) | −5.02628 | − | 2.90192i | −0.187188 | − | 0.108073i | ||||
\(722\) | −19.7321 | − | 11.3923i | −0.734351 | − | 0.423978i | ||||
\(723\) | − | 2.92820i | − | 0.108901i | ||||||
\(724\) | 8.86603 | − | 15.3564i | 0.329503 | − | 0.570716i | ||||
\(725\) | −12.8923 | − | 22.3301i | −0.478808 | − | 0.829320i | ||||
\(726\) | 13.8564 | − | 8.00000i | 0.514259 | − | 0.296908i | ||||
\(727\) | 24.3923 | 0.904661 | 0.452330 | − | 0.891851i | \(-0.350593\pi\) | ||||
0.452330 | + | 0.891851i | \(0.350593\pi\) | |||||||
\(728\) | 2.59808 | + | 2.50000i | 0.0962911 | + | 0.0926562i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −12.9282 | + | 7.46410i | −0.478494 | + | 0.276259i | ||||
\(731\) | −15.0981 | − | 26.1506i | −0.558423 | − | 0.967216i | ||||
\(732\) | 0.133975 | − | 0.232051i | 0.00495184 | − | 0.00857684i | ||||
\(733\) | − | 15.7846i | − | 0.583018i | −0.956568 | − | 0.291509i | \(-0.905843\pi\) | ||
0.956568 | − | 0.291509i | \(-0.0941573\pi\) | |||||||
\(734\) | −18.4641 | − | 10.6603i | −0.681522 | − | 0.393477i | ||||
\(735\) | 2.36603 | + | 1.36603i | 0.0872722 | + | 0.0503866i | ||||
\(736\) | − | 0.535898i | − | 0.0197535i | ||||||
\(737\) | −25.9808 | + | 45.0000i | −0.957014 | + | 1.65760i | ||||
\(738\) | −0.767949 | − | 1.33013i | −0.0282686 | − | 0.0489627i | ||||
\(739\) | −20.0718 | + | 11.5885i | −0.738353 | + | 0.426288i | −0.821470 | − | 0.570251i | \(-0.806846\pi\) |
0.0831172 | + | 0.996540i | \(0.473512\pi\) | |||||||
\(740\) | −8.92820 | −0.328207 | ||||||||
\(741\) | −22.6244 | − | 5.59808i | −0.831126 | − | 0.205650i | ||||
\(742\) | 3.92820 | 0.144209 | ||||||||
\(743\) | 20.8301 | − | 12.0263i | 0.764183 | − | 0.441201i | −0.0666124 | − | 0.997779i | \(-0.521219\pi\) |
0.830796 | + | 0.556578i | \(0.187886\pi\) | |||||||
\(744\) | 3.36603 | + | 5.83013i | 0.123404 | + | 0.213743i | ||||
\(745\) | −10.9282 | + | 18.9282i | −0.400378 | + | 0.693476i | ||||
\(746\) | − | 9.12436i | − | 0.334066i | ||||||
\(747\) | 11.0263 | + | 6.36603i | 0.403430 | + | 0.232921i | ||||
\(748\) | 25.7942 | + | 14.8923i | 0.943130 | + | 0.544517i | ||||
\(749\) | − | 19.9282i | − | 0.728161i | ||||||
\(750\) | −3.46410 | + | 6.00000i | −0.126491 | + | 0.219089i | ||||
\(751\) | 16.4282 | + | 28.4545i | 0.599474 | + | 1.03832i | 0.992899 | + | 0.118962i | \(0.0379567\pi\) |
−0.393425 | + | 0.919357i | \(0.628710\pi\) | |||||||
\(752\) | 8.59808 | − | 4.96410i | 0.313540 | − | 0.181022i | ||||
\(753\) | 27.5167 | 1.00276 | ||||||||
\(754\) | 26.1603 | − | 27.1865i | 0.952700 | − | 0.990075i | ||||
\(755\) | 25.1244 | 0.914369 | ||||||||
\(756\) | −0.866025 | + | 0.500000i | −0.0314970 | + | 0.0181848i | ||||
\(757\) | −2.90192 | − | 5.02628i | −0.105472 | − | 0.182683i | 0.808459 | − | 0.588553i | \(-0.200302\pi\) |
−0.913931 | + | 0.405870i | \(0.866969\pi\) | |||||||
\(758\) | 1.02628 | − | 1.77757i | 0.0372761 | − | 0.0645642i | ||||
\(759\) | 2.78461i | 0.101075i | ||||||||
\(760\) | 15.2942 | + | 8.83013i | 0.554780 | + | 0.320302i | ||||
\(761\) | −26.1962 | − | 15.1244i | −0.949610 | − | 0.548257i | −0.0566501 | − | 0.998394i | \(-0.518042\pi\) |
−0.892960 | + | 0.450137i | \(0.851375\pi\) | |||||||
\(762\) | − | 6.39230i | − | 0.231569i | ||||||
\(763\) | −7.36603 | + | 12.7583i | −0.266668 | + | 0.461883i | ||||
\(764\) | 1.09808 | + | 1.90192i | 0.0397270 | + | 0.0688092i | ||||
\(765\) | 13.5622 | − | 7.83013i | 0.490342 | − | 0.283099i | ||||
\(766\) | 31.0000 | 1.12008 | ||||||||
\(767\) | −12.3205 | + | 12.8038i | −0.444868 | + | 0.462320i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 40.4711 | − | 23.3660i | 1.45943 | − | 0.842600i | 0.460444 | − | 0.887689i | \(-0.347690\pi\) |
0.998983 | + | 0.0450885i | \(0.0143570\pi\) | |||||||
\(770\) | 7.09808 | + | 12.2942i | 0.255797 | + | 0.443053i | ||||
\(771\) | 6.52628 | − | 11.3038i | 0.235038 | − | 0.407098i | ||||
\(772\) | − | 23.5885i | − | 0.848967i | ||||||
\(773\) | 37.3923 | + | 21.5885i | 1.34491 | + | 0.776483i | 0.987523 | − | 0.157474i | \(-0.0503352\pi\) |
0.357385 | + | 0.933957i | \(0.383669\pi\) | |||||||
\(774\) | 4.56218 | + | 2.63397i | 0.163984 | + | 0.0946763i | ||||
\(775\) | − | 16.5885i | − | 0.595875i | ||||||
\(776\) | −1.90192 | + | 3.29423i | −0.0682751 | + | 0.118256i | ||||
\(777\) | −1.63397 | − | 2.83013i | −0.0586185 | − | 0.101530i | ||||
\(778\) | −12.5885 | + | 7.26795i | −0.451318 | + | 0.260569i | ||||
\(779\) | −9.92820 | −0.355715 | ||||||||
\(780\) | 9.56218 | + | 2.36603i | 0.342381 | + | 0.0847173i | ||||
\(781\) | −55.7654 | −1.99544 | ||||||||
\(782\) | −2.66025 | + | 1.53590i | −0.0951305 | + | 0.0549236i | ||||
\(783\) | 5.23205 | + | 9.06218i | 0.186978 | + | 0.323856i | ||||
\(784\) | 0.500000 | − | 0.866025i | 0.0178571 | − | 0.0309295i | ||||
\(785\) | − | 12.3923i | − | 0.442300i | ||||||
\(786\) | −0.928203 | − | 0.535898i | −0.0331079 | − | 0.0191149i | ||||
\(787\) | 16.3301 | + | 9.42820i | 0.582106 | + | 0.336079i | 0.761970 | − | 0.647612i | \(-0.224232\pi\) |
−0.179864 | + | 0.983692i | \(0.557566\pi\) | |||||||
\(788\) | 3.73205i | 0.132949i | ||||||||
\(789\) | 10.5622 | − | 18.2942i | 0.376023 | − | 0.651292i | ||||
\(790\) | −12.2942 | − | 21.2942i | −0.437409 | − | 0.757615i | ||||
\(791\) | −8.36603 | + | 4.83013i | −0.297462 | + | 0.171740i | ||||
\(792\) | −5.19615 | −0.184637 | ||||||||
\(793\) | −0.696152 | − | 0.669873i | −0.0247211 | − | 0.0237879i | ||||
\(794\) | −0.607695 | −0.0215663 | ||||||||
\(795\) | 9.29423 | − | 5.36603i | 0.329632 | − | 0.190313i | ||||
\(796\) | 3.29423 | + | 5.70577i | 0.116761 | + | 0.202236i | ||||
\(797\) | −18.6865 | + | 32.3660i | −0.661911 | + | 1.14646i | 0.318202 | + | 0.948023i | \(0.396921\pi\) |
−0.980113 | + | 0.198440i | \(0.936412\pi\) | |||||||
\(798\) | 6.46410i | 0.228827i | ||||||||
\(799\) | −49.2846 | − | 28.4545i | −1.74356 | − | 1.00665i | ||||
\(800\) | −2.13397 | − | 1.23205i | −0.0754474 | − | 0.0435596i | ||||
\(801\) | − | 10.8564i | − | 0.383592i | ||||||
\(802\) | −12.4641 | + | 21.5885i | −0.440123 | + | 0.762315i | ||||
\(803\) | −14.1962 | − | 24.5885i | −0.500971 | − | 0.867708i | ||||
\(804\) | 8.66025 | − | 5.00000i | 0.305424 | − | 0.176336i | ||||
\(805\) | −1.46410 | −0.0516028 | ||||||||
\(806\) | 23.3205 | − | 6.73205i | 0.821430 | − | 0.237126i | ||||
\(807\) | −4.00000 | −0.140807 | ||||||||
\(808\) | 7.73205 | − | 4.46410i | 0.272013 | − | 0.157047i | ||||
\(809\) | 6.36603 | + | 11.0263i | 0.223818 | + | 0.387663i | 0.955964 | − | 0.293484i | \(-0.0948147\pi\) |
−0.732146 | + | 0.681147i | \(0.761481\pi\) | |||||||
\(810\) | −1.36603 | + | 2.36603i | −0.0479972 | + | 0.0831337i | ||||
\(811\) | − | 54.1051i | − | 1.89989i | −0.312421 | − | 0.949944i | \(-0.601140\pi\) | ||
0.312421 | − | 0.949944i | \(-0.398860\pi\) | |||||||
\(812\) | −9.06218 | − | 5.23205i | −0.318020 | − | 0.183609i | ||||
\(813\) | −8.36603 | − | 4.83013i | −0.293409 | − | 0.169400i | ||||
\(814\) | − | 16.9808i | − | 0.595175i | ||||||
\(815\) | 23.3923 | − | 40.5167i | 0.819397 | − | 1.41924i | ||||
\(816\) | −2.86603 | − | 4.96410i | −0.100331 | − | 0.173778i | ||||
\(817\) | 29.4904 | − | 17.0263i | 1.03174 | − | 0.595674i | ||||
\(818\) | 14.5885 | 0.510073 | ||||||||
\(819\) | 1.00000 | + | 3.46410i | 0.0349428 | + | 0.121046i | ||||
\(820\) | 4.19615 | 0.146536 | ||||||||
\(821\) | 25.2846 | − | 14.5981i | 0.882439 | − | 0.509476i | 0.0109772 | − | 0.999940i | \(-0.496506\pi\) |
0.871462 | + | 0.490463i | \(0.163172\pi\) | |||||||
\(822\) | 6.26795 | + | 10.8564i | 0.218620 | + | 0.378661i | ||||
\(823\) | −16.8564 | + | 29.1962i | −0.587577 | + | 1.01771i | 0.406971 | + | 0.913441i | \(0.366585\pi\) |
−0.994549 | + | 0.104273i | \(0.966748\pi\) | |||||||
\(824\) | 5.80385i | 0.202187i | ||||||||
\(825\) | 11.0885 | + | 6.40192i | 0.386051 | + | 0.222886i | ||||
\(826\) | 4.26795 | + | 2.46410i | 0.148501 | + | 0.0857371i | ||||
\(827\) | − | 16.3923i | − | 0.570016i | −0.958525 | − | 0.285008i | \(-0.908004\pi\) | ||
0.958525 | − | 0.285008i | \(-0.0919963\pi\) | |||||||
\(828\) | 0.267949 | − | 0.464102i | 0.00931188 | − | 0.0161286i | ||||
\(829\) | 23.2583 | + | 40.2846i | 0.807795 | + | 1.39914i | 0.914388 | + | 0.404840i | \(0.132673\pi\) |
−0.106593 | + | 0.994303i | \(0.533994\pi\) | |||||||
\(830\) | −30.1244 | + | 17.3923i | −1.04563 | + | 0.603696i | ||||
\(831\) | −6.39230 | −0.221747 | ||||||||
\(832\) | 0.866025 | − | 3.50000i | 0.0300240 | − | 0.121341i | ||||
\(833\) | −5.73205 | −0.198604 | ||||||||
\(834\) | 18.2321 | − | 10.5263i | 0.631324 | − | 0.364495i | ||||
\(835\) | 25.8564 | + | 44.7846i | 0.894798 | + | 1.54984i | ||||
\(836\) | −16.7942 | + | 29.0885i | −0.580841 | + | 1.00605i | ||||
\(837\) | 6.73205i | 0.232694i | ||||||||
\(838\) | 14.3660 | + | 8.29423i | 0.496266 | + | 0.286519i | ||||
\(839\) | 2.32051 | + | 1.33975i | 0.0801128 | + | 0.0462532i | 0.539521 | − | 0.841972i | \(-0.318605\pi\) |
−0.459408 | + | 0.888225i | \(0.651939\pi\) | |||||||
\(840\) | − | 2.73205i | − | 0.0942647i | ||||||
\(841\) | −40.2487 | + | 69.7128i | −1.38789 | + | 2.40389i | ||||
\(842\) | −4.66025 | − | 8.07180i | −0.160603 | − | 0.278172i | ||||
\(843\) | −8.02628 | + | 4.63397i | −0.276440 | + | 0.159603i | ||||
\(844\) | −11.0718 | −0.381107 | ||||||||
\(845\) | 16.5622 | − | 31.4186i | 0.569756 | − | 1.08083i | ||||
\(846\) | 9.92820 | 0.341339 | ||||||||
\(847\) | −13.8564 | + | 8.00000i | −0.476112 | + | 0.274883i | ||||
\(848\) | −1.96410 | − | 3.40192i | −0.0674475 | − | 0.116823i | ||||
\(849\) | 4.92820 | − | 8.53590i | 0.169135 | − | 0.292951i | ||||
\(850\) | 14.1244i | 0.484461i | ||||||||
\(851\) | 1.51666 | + | 0.875644i | 0.0519905 | + | 0.0300167i | ||||
\(852\) | 9.29423 | + | 5.36603i | 0.318415 | + | 0.183837i | ||||
\(853\) | − | 23.2487i | − | 0.796021i | −0.917381 | − | 0.398010i | \(-0.869701\pi\) | ||
0.917381 | − | 0.398010i | \(-0.130299\pi\) | |||||||
\(854\) | −0.133975 | + | 0.232051i | −0.00458452 | + | 0.00794062i | ||||
\(855\) | 8.83013 | + | 15.2942i | 0.301984 | + | 0.523052i | ||||
\(856\) | −17.2583 | + | 9.96410i | −0.589878 | + | 0.340566i | ||||
\(857\) | −12.5359 | −0.428218 | −0.214109 | − | 0.976810i | \(-0.568685\pi\) | ||||
−0.214109 | + | 0.976810i | \(0.568685\pi\) | |||||||
\(858\) | −4.50000 | + | 18.1865i | −0.153627 | + | 0.620878i | ||||
\(859\) | 27.1962 | 0.927921 | 0.463960 | − | 0.885856i | \(-0.346428\pi\) | ||||
0.463960 | + | 0.885856i | \(0.346428\pi\) | |||||||
\(860\) | −12.4641 | + | 7.19615i | −0.425022 | + | 0.245387i | ||||
\(861\) | 0.767949 | + | 1.33013i | 0.0261716 | + | 0.0453306i | ||||
\(862\) | −5.56218 | + | 9.63397i | −0.189449 | + | 0.328134i | ||||
\(863\) | − | 11.8564i | − | 0.403597i | −0.979427 | − | 0.201798i | \(-0.935321\pi\) | ||
0.979427 | − | 0.201798i | \(-0.0646786\pi\) | |||||||
\(864\) | 0.866025 | + | 0.500000i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | −19.3923 | − | 11.1962i | −0.659358 | − | 0.380681i | ||||
\(866\) | 39.8564i | 1.35438i | ||||||||
\(867\) | −7.92820 | + | 13.7321i | −0.269256 | + | 0.466365i | ||||
\(868\) | −3.36603 | − | 5.83013i | −0.114250 | − | 0.197887i | ||||
\(869\) | 40.5000 | − | 23.3827i | 1.37387 | − | 0.793203i | ||||
\(870\) | −28.5885 | −0.969239 | ||||||||
\(871\) | −10.0000 | − | 34.6410i | −0.338837 | − | 1.17377i | ||||
\(872\) | 14.7321 | 0.498890 | ||||||||
\(873\) | −3.29423 | + | 1.90192i | −0.111493 | + | 0.0643704i | ||||
\(874\) | −1.73205 | − | 3.00000i | −0.0585875 | − | 0.101477i | ||||
\(875\) | 3.46410 | − | 6.00000i | 0.117108 | − | 0.202837i | ||||
\(876\) | 5.46410i | 0.184615i | ||||||||
\(877\) | 16.8109 | + | 9.70577i | 0.567663 | + | 0.327741i | 0.756216 | − | 0.654323i | \(-0.227046\pi\) |
−0.188552 | + | 0.982063i | \(0.560379\pi\) | |||||||
\(878\) | 9.80385 | + | 5.66025i | 0.330864 | + | 0.191024i | ||||
\(879\) | 14.9282i | 0.503516i | ||||||||
\(880\) | 7.09808 | − | 12.2942i | 0.239276 | − | 0.414438i | ||||
\(881\) | 7.85641 | + | 13.6077i | 0.264689 | + | 0.458455i | 0.967482 | − | 0.252939i | \(-0.0813973\pi\) |
−0.702793 | + | 0.711394i | \(0.748064\pi\) | |||||||
\(882\) | 0.866025 | − | 0.500000i | 0.0291606 | − | 0.0168359i | ||||
\(883\) | 19.5167 | 0.656788 | 0.328394 | − | 0.944541i | \(-0.393493\pi\) | ||||
0.328394 | + | 0.944541i | \(0.393493\pi\) | |||||||
\(884\) | −19.8564 | + | 5.73205i | −0.667843 | + | 0.192790i | ||||
\(885\) | 13.4641 | 0.452591 | ||||||||
\(886\) | 21.6506 | − | 12.5000i | 0.727367 | − | 0.419946i | ||||
\(887\) | 1.66987 | + | 2.89230i | 0.0560688 | + | 0.0971141i | 0.892697 | − | 0.450656i | \(-0.148810\pi\) |
−0.836629 | + | 0.547770i | \(0.815477\pi\) | |||||||
\(888\) | −1.63397 | + | 2.83013i | −0.0548326 | + | 0.0949728i | ||||
\(889\) | 6.39230i | 0.214391i | ||||||||
\(890\) | 25.6865 | + | 14.8301i | 0.861015 | + | 0.497107i | ||||
\(891\) | −4.50000 | − | 2.59808i | −0.150756 | − | 0.0870388i | ||||
\(892\) | 1.46410i | 0.0490217i | ||||||||
\(893\) | 32.0885 | − | 55.5788i | 1.07380 | − | 1.85987i | ||||
\(894\) | 4.00000 | + | 6.92820i | 0.133780 | + | 0.231714i | ||||
\(895\) | −8.19615 | + | 4.73205i | −0.273967 | + | 0.158175i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −1.39230 | − | 1.33975i | −0.0464877 | − | 0.0447328i | ||||
\(898\) | −22.9808 | −0.766878 | ||||||||
\(899\) | −61.0070 | + | 35.2224i | −2.03470 | + | 1.17473i | ||||
\(900\) | −1.23205 | − | 2.13397i | −0.0410684 | − | 0.0711325i | ||||
\(901\) | −11.2583 | + | 19.5000i | −0.375069 | + | 0.649639i | ||||
\(902\) | 7.98076i | 0.265730i | ||||||||
\(903\) | −4.56218 | − | 2.63397i | −0.151820 | − | 0.0876532i | ||||
\(904\) | 8.36603 | + | 4.83013i | 0.278250 | + | 0.160648i | ||||
\(905\) | 48.4449i | 1.61036i | ||||||||
\(906\) | 4.59808 | − | 7.96410i | 0.152761 | − | 0.264590i | ||||
\(907\) | 4.80385 | + | 8.32051i | 0.159509 | + | 0.276278i | 0.934692 | − | 0.355459i | \(-0.115676\pi\) |
−0.775183 | + | 0.631737i | \(0.782342\pi\) | |||||||
\(908\) | −18.4641 | + | 10.6603i | −0.612753 | + | 0.353773i | ||||
\(909\) | 8.92820 | 0.296130 | ||||||||
\(910\) | −9.56218 | − | 2.36603i | −0.316983 | − | 0.0784330i | ||||
\(911\) | 14.8756 | 0.492852 | 0.246426 | − | 0.969162i | \(-0.420744\pi\) | ||||
0.246426 | + | 0.969162i | \(0.420744\pi\) | |||||||
\(912\) | 5.59808 | − | 3.23205i | 0.185371 | − | 0.107024i | ||||
\(913\) | −33.0788 | − | 57.2942i | −1.09475 | − | 1.89616i | ||||
\(914\) | 12.8564 | − | 22.2679i | 0.425252 | − | 0.736558i | ||||
\(915\) | 0.732051i | 0.0242009i | ||||||||
\(916\) | 2.93782 | + | 1.69615i | 0.0970684 | + | 0.0560425i | ||||
\(917\) | 0.928203 | + | 0.535898i | 0.0306520 | + | 0.0176969i | ||||
\(918\) | − | 5.73205i | − | 0.189186i | ||||||
\(919\) | −21.3564 | + | 36.9904i | −0.704483 | + | 1.22020i | 0.262395 | + | 0.964961i | \(0.415488\pi\) |
−0.966878 | + | 0.255240i | \(0.917846\pi\) | |||||||
\(920\) | 0.732051 | + | 1.26795i | 0.0241350 | + | 0.0418030i | ||||
\(921\) | 4.33013 | − | 2.50000i | 0.142683 | − | 0.0823778i | ||||
\(922\) | −6.92820 | −0.228168 | ||||||||
\(923\) | 26.8301 | − | 27.8827i | 0.883124 | − | 0.917770i | ||||
\(924\) | 5.19615 | 0.170941 | ||||||||
\(925\) | 6.97372 | − | 4.02628i | 0.229295 | − | 0.132383i | ||||
\(926\) | 16.3301 | + | 28.2846i | 0.536641 | + | 0.929490i | ||||
\(927\) | −2.90192 | + | 5.02628i | −0.0953117 | + | 0.165085i | ||||
\(928\) | 10.4641i | 0.343501i | ||||||||
\(929\) | 8.59808 | + | 4.96410i | 0.282094 | + | 0.162867i | 0.634371 | − | 0.773029i | \(-0.281259\pi\) |
−0.352277 | + | 0.935896i | \(0.614593\pi\) | |||||||
\(930\) | −15.9282 | − | 9.19615i | −0.522306 | − | 0.301554i | ||||
\(931\) | − | 6.46410i | − | 0.211852i | ||||||
\(932\) | −6.29423 | + | 10.9019i | −0.206174 | + | 0.357104i | ||||
\(933\) | −12.5981 | − | 21.8205i | −0.412442 | − | 0.714371i | ||||
\(934\) | −4.39230 | + | 2.53590i | −0.143721 | + | 0.0829771i | ||||
\(935\) | −81.3731 | −2.66118 | ||||||||
\(936\) | 2.50000 | − | 2.59808i | 0.0817151 | − | 0.0849208i | ||||
\(937\) | −11.7128 | −0.382641 | −0.191320 | − | 0.981528i | \(-0.561277\pi\) | ||||
−0.191320 | + | 0.981528i | \(0.561277\pi\) | |||||||
\(938\) | −8.66025 | + | 5.00000i | −0.282767 | + | 0.163256i | ||||
\(939\) | −15.5622 | − | 26.9545i | −0.507852 | − | 0.879626i | ||||
\(940\) | −13.5622 | + | 23.4904i | −0.442349 | + | 0.766172i | ||||
\(941\) | − | 7.32051i | − | 0.238642i | −0.992856 | − | 0.119321i | \(-0.961928\pi\) | ||
0.992856 | − | 0.119321i | \(-0.0380717\pi\) | |||||||
\(942\) | −3.92820 | − | 2.26795i | −0.127988 | − | 0.0738938i | ||||
\(943\) | −0.712813 | − | 0.411543i | −0.0232124 | − | 0.0134017i | ||||
\(944\) | − | 4.92820i | − | 0.160399i | ||||||
\(945\) | 1.36603 | − | 2.36603i | 0.0444368 | − | 0.0769668i | ||||
\(946\) | −13.6865 | − | 23.7058i | −0.444988 | − | 0.770741i | ||||
\(947\) | −19.8397 | + | 11.4545i | −0.644705 | + | 0.372221i | −0.786425 | − | 0.617686i | \(-0.788070\pi\) |
0.141720 | + | 0.989907i | \(0.454737\pi\) | |||||||
\(948\) | −9.00000 | −0.292306 | ||||||||
\(949\) | 19.1244 | + | 4.73205i | 0.620803 | + | 0.153609i | ||||
\(950\) | −15.9282 | −0.516779 | ||||||||
\(951\) | 23.1962 | − | 13.3923i | 0.752187 | − | 0.434275i | ||||
\(952\) | 2.86603 | + | 4.96410i | 0.0928884 | + | 0.160887i | ||||
\(953\) | −8.83013 | + | 15.2942i | −0.286036 | + | 0.495429i | −0.972860 | − | 0.231395i | \(-0.925671\pi\) |
0.686824 | + | 0.726824i | \(0.259004\pi\) | |||||||
\(954\) | − | 3.92820i | − | 0.127180i | ||||||
\(955\) | −5.19615 | − | 3.00000i | −0.168144 | − | 0.0970777i | ||||
\(956\) | 3.97372 | + | 2.29423i | 0.128519 | + | 0.0742007i | ||||
\(957\) | − | 54.3731i | − | 1.75763i | ||||||
\(958\) | −11.4282 | + | 19.7942i | −0.369228 | + | 0.639522i | ||||
\(959\) | −6.26795 | − | 10.8564i | −0.202403 | − | 0.350572i | ||||
\(960\) | −2.36603 | + | 1.36603i | −0.0763631 | + | 0.0440883i | ||||
\(961\) | −14.3205 | −0.461952 | ||||||||
\(962\) | 8.49038 | + | 8.16987i | 0.273741 | + | 0.263407i | ||||
\(963\) | −19.9282 | −0.642177 | ||||||||
\(964\) | 2.53590 | − | 1.46410i | 0.0816758 | − | 0.0471555i | ||||
\(965\) | 32.2224 | + | 55.8109i | 1.03728 | + | 1.79662i | ||||
\(966\) | −0.267949 | + | 0.464102i | −0.00862112 | + | 0.0149322i | ||||
\(967\) | − | 28.7846i | − | 0.925651i | −0.886450 | − | 0.462825i | \(-0.846836\pi\) | ||
0.886450 | − | 0.462825i | \(-0.153164\pi\) | |||||||
\(968\) | 13.8564 | + | 8.00000i | 0.445362 | + | 0.257130i | ||||
\(969\) | −32.0885 | − | 18.5263i | −1.03083 | − | 0.595150i | ||||
\(970\) | − | 10.3923i | − | 0.333677i | ||||||
\(971\) | 19.0526 | − | 33.0000i | 0.611426 | − | 1.05902i | −0.379575 | − | 0.925161i | \(-0.623930\pi\) |
0.991000 | − | 0.133859i | \(-0.0427370\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | −18.2321 | + | 10.5263i | −0.584493 | + | 0.337457i | ||||
\(974\) | 29.4449 | 0.943474 | ||||||||
\(975\) | −8.53590 | + | 2.46410i | −0.273368 | + | 0.0789144i | ||||
\(976\) | 0.267949 | 0.00857684 | ||||||||
\(977\) | 16.9808 | − | 9.80385i | 0.543263 | − | 0.313653i | −0.203138 | − | 0.979150i | \(-0.565114\pi\) |
0.746400 | + | 0.665497i | \(0.231781\pi\) | |||||||
\(978\) | −8.56218 | − | 14.8301i | −0.273788 | − | 0.474215i | ||||
\(979\) | −28.2058 | + | 48.8538i | −0.901460 | + | 1.56138i | ||||
\(980\) | 2.73205i | 0.0872722i | ||||||||
\(981\) | 12.7583 | + | 7.36603i | 0.407342 | + | 0.235179i | ||||
\(982\) | −12.4641 | − | 7.19615i | −0.397745 | − | 0.229638i | ||||
\(983\) | − | 18.0000i | − | 0.574111i | −0.957914 | − | 0.287055i | \(-0.907324\pi\) | ||
0.957914 | − | 0.287055i | \(-0.0926764\pi\) | |||||||
\(984\) | 0.767949 | − | 1.33013i | 0.0244813 | − | 0.0424029i | ||||
\(985\) | −5.09808 | − | 8.83013i | −0.162438 | − | 0.281351i | ||||
\(986\) | 51.9449 | − | 29.9904i | 1.65426 | − | 0.955088i | ||||
\(987\) | −9.92820 | −0.316018 | ||||||||
\(988\) | −6.46410 | − | 22.3923i | −0.205650 | − | 0.712394i | ||||
\(989\) | 2.82309 | 0.0897689 | ||||||||
\(990\) | 12.2942 | − | 7.09808i | 0.390736 | − | 0.225592i | ||||
\(991\) | 5.62436 | + | 9.74167i | 0.178664 | + | 0.309454i | 0.941423 | − | 0.337228i | \(-0.109489\pi\) |
−0.762759 | + | 0.646682i | \(0.776156\pi\) | |||||||
\(992\) | −3.36603 | + | 5.83013i | −0.106871 | + | 0.185107i | ||||
\(993\) | − | 34.7846i | − | 1.10386i | ||||||
\(994\) | −9.29423 | − | 5.36603i | −0.294795 | − | 0.170200i | ||||
\(995\) | −15.5885 | − | 9.00000i | −0.494187 | − | 0.285319i | ||||
\(996\) | 12.7321i | 0.403430i | ||||||||
\(997\) | 4.45448 | − | 7.71539i | 0.141075 | − | 0.244349i | −0.786827 | − | 0.617174i | \(-0.788278\pi\) |
0.927902 | + | 0.372825i | \(0.121611\pi\) | |||||||
\(998\) | −5.29423 | − | 9.16987i | −0.167586 | − | 0.290267i | ||||
\(999\) | −2.83013 | + | 1.63397i | −0.0895413 | + | 0.0516967i |
(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 | 546.2.s.b.127.1 | yes | 4 | |
3.2 | odd | 2 | 1638.2.bj.a.127.2 | 4 | |||
13.2 | odd | 12 | 7098.2.a.bo.1.2 | 2 | |||
13.4 | even | 6 | inner | 546.2.s.b.43.1 | ✓ | 4 | |
13.11 | odd | 12 | 7098.2.a.by.1.1 | 2 | |||
39.17 | odd | 6 | 1638.2.bj.a.1135.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.s.b.43.1 | ✓ | 4 | 13.4 | even | 6 | inner | |
546.2.s.b.127.1 | yes | 4 | 1.1 | even | 1 | trivial | |
1638.2.bj.a.127.2 | 4 | 3.2 | odd | 2 | |||
1638.2.bj.a.1135.2 | 4 | 39.17 | odd | 6 | |||
7098.2.a.bo.1.2 | 2 | 13.2 | odd | 12 | |||
7098.2.a.by.1.1 | 2 | 13.11 | odd | 12 |