Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(121,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 391.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.391 |
Dual form | 570.2.i.c.121.1 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0.500000 | + | 0.866025i | 0.204124 | + | 0.353553i | ||||
\(7\) | 3.00000 | 1.13389 | 0.566947 | − | 0.823754i | \(-0.308125\pi\) | ||||
0.566947 | + | 0.823754i | \(0.308125\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | 1.00000 | 0.301511 | 0.150756 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150756 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | − | 1.73205i | −0.277350 | − | 0.480384i | 0.693375 | − | 0.720577i | \(-0.256123\pi\) |
−0.970725 | + | 0.240192i | \(0.922790\pi\) | |||||||
\(14\) | −1.50000 | + | 2.59808i | −0.400892 | + | 0.694365i | ||||
\(15\) | −0.500000 | − | 0.866025i | −0.129099 | − | 0.223607i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.00000 | + | 1.73205i | −0.242536 | + | 0.420084i | −0.961436 | − | 0.275029i | \(-0.911312\pi\) |
0.718900 | + | 0.695113i | \(0.244646\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 0.500000 | − | 4.33013i | 0.114708 | − | 0.993399i | ||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 1.50000 | − | 2.59808i | 0.327327 | − | 0.566947i | ||||
\(22\) | −0.500000 | + | 0.866025i | −0.106600 | + | 0.184637i | ||||
\(23\) | −0.500000 | − | 0.866025i | −0.104257 | − | 0.180579i | 0.809177 | − | 0.587565i | \(-0.199913\pi\) |
−0.913434 | + | 0.406986i | \(0.866580\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.50000 | − | 2.59808i | −0.283473 | − | 0.490990i | ||||
\(29\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0.500000 | − | 0.866025i | 0.0870388 | − | 0.150756i | ||||
\(34\) | −1.00000 | − | 1.73205i | −0.171499 | − | 0.297044i | ||||
\(35\) | 1.50000 | − | 2.59808i | 0.253546 | − | 0.439155i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | 9.00000 | 1.47959 | 0.739795 | − | 0.672832i | \(-0.234922\pi\) | ||||
0.739795 | + | 0.672832i | \(0.234922\pi\) | |||||||
\(38\) | 3.50000 | + | 2.59808i | 0.567775 | + | 0.421464i | ||||
\(39\) | −2.00000 | −0.320256 | ||||||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | −0.500000 | + | 0.866025i | −0.0780869 | + | 0.135250i | −0.902424 | − | 0.430848i | \(-0.858214\pi\) |
0.824338 | + | 0.566099i | \(0.191548\pi\) | |||||||
\(42\) | 1.50000 | + | 2.59808i | 0.231455 | + | 0.400892i | ||||
\(43\) | 5.00000 | − | 8.66025i | 0.762493 | − | 1.32068i | −0.179069 | − | 0.983836i | \(-0.557309\pi\) |
0.941562 | − | 0.336840i | \(-0.109358\pi\) | |||||||
\(44\) | −0.500000 | − | 0.866025i | −0.0753778 | − | 0.130558i | ||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0.500000 | + | 0.866025i | 0.0721688 | + | 0.125000i | ||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 1.00000 | + | 1.73205i | 0.140028 | + | 0.242536i | ||||
\(52\) | −1.00000 | + | 1.73205i | −0.138675 | + | 0.240192i | ||||
\(53\) | −1.50000 | − | 2.59808i | −0.206041 | − | 0.356873i | 0.744423 | − | 0.667708i | \(-0.232725\pi\) |
−0.950464 | + | 0.310835i | \(0.899391\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 0.500000 | − | 0.866025i | 0.0674200 | − | 0.116775i | ||||
\(56\) | 3.00000 | 0.400892 | ||||||||
\(57\) | −3.50000 | − | 2.59808i | −0.463586 | − | 0.344124i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.00000 | + | 10.3923i | −0.781133 | + | 1.35296i | 0.150148 | + | 0.988663i | \(0.452025\pi\) |
−0.931282 | + | 0.364299i | \(0.881308\pi\) | |||||||
\(60\) | −0.500000 | + | 0.866025i | −0.0645497 | + | 0.111803i | ||||
\(61\) | 1.00000 | + | 1.73205i | 0.128037 | + | 0.221766i | 0.922916 | − | 0.385002i | \(-0.125799\pi\) |
−0.794879 | + | 0.606768i | \(0.792466\pi\) | |||||||
\(62\) | −2.00000 | + | 3.46410i | −0.254000 | + | 0.439941i | ||||
\(63\) | −1.50000 | − | 2.59808i | −0.188982 | − | 0.327327i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.00000 | −0.248069 | ||||||||
\(66\) | 0.500000 | + | 0.866025i | 0.0615457 | + | 0.106600i | ||||
\(67\) | 1.00000 | + | 1.73205i | 0.122169 | + | 0.211604i | 0.920623 | − | 0.390453i | \(-0.127682\pi\) |
−0.798454 | + | 0.602056i | \(0.794348\pi\) | |||||||
\(68\) | 2.00000 | 0.242536 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 1.50000 | + | 2.59808i | 0.179284 | + | 0.310530i | ||||
\(71\) | −4.00000 | + | 6.92820i | −0.474713 | + | 0.822226i | −0.999581 | − | 0.0289572i | \(-0.990781\pi\) |
0.524868 | + | 0.851184i | \(0.324115\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | 6.00000 | − | 10.3923i | 0.702247 | − | 1.21633i | −0.265429 | − | 0.964130i | \(-0.585514\pi\) |
0.967676 | − | 0.252197i | \(-0.0811531\pi\) | |||||||
\(74\) | −4.50000 | + | 7.79423i | −0.523114 | + | 0.906061i | ||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −4.00000 | + | 1.73205i | −0.458831 | + | 0.198680i | ||||
\(77\) | 3.00000 | 0.341882 | ||||||||
\(78\) | 1.00000 | − | 1.73205i | 0.113228 | − | 0.196116i | ||||
\(79\) | −7.00000 | + | 12.1244i | −0.787562 | + | 1.36410i | 0.139895 | + | 0.990166i | \(0.455323\pi\) |
−0.927457 | + | 0.373930i | \(0.878010\pi\) | |||||||
\(80\) | 0.500000 | + | 0.866025i | 0.0559017 | + | 0.0968246i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −0.500000 | − | 0.866025i | −0.0552158 | − | 0.0956365i | ||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | −3.00000 | −0.327327 | ||||||||
\(85\) | 1.00000 | + | 1.73205i | 0.108465 | + | 0.187867i | ||||
\(86\) | 5.00000 | + | 8.66025i | 0.539164 | + | 0.933859i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 2.50000 | + | 4.33013i | 0.264999 | + | 0.458993i | 0.967563 | − | 0.252628i | \(-0.0812949\pi\) |
−0.702564 | + | 0.711621i | \(0.747962\pi\) | |||||||
\(90\) | 0.500000 | − | 0.866025i | 0.0527046 | − | 0.0912871i | ||||
\(91\) | −3.00000 | − | 5.19615i | −0.314485 | − | 0.544705i | ||||
\(92\) | −0.500000 | + | 0.866025i | −0.0521286 | + | 0.0902894i | ||||
\(93\) | 2.00000 | − | 3.46410i | 0.207390 | − | 0.359211i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.50000 | − | 2.59808i | −0.359092 | − | 0.266557i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −4.00000 | + | 6.92820i | −0.406138 | + | 0.703452i | −0.994453 | − | 0.105180i | \(-0.966458\pi\) |
0.588315 | + | 0.808632i | \(0.299792\pi\) | |||||||
\(98\) | −1.00000 | + | 1.73205i | −0.101015 | + | 0.174964i | ||||
\(99\) | −0.500000 | − | 0.866025i | −0.0502519 | − | 0.0870388i | ||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | 1.00000 | + | 1.73205i | 0.0995037 | + | 0.172345i | 0.911479 | − | 0.411346i | \(-0.134941\pi\) |
−0.811976 | + | 0.583691i | \(0.801608\pi\) | |||||||
\(102\) | −2.00000 | −0.198030 | ||||||||
\(103\) | −13.0000 | −1.28093 | −0.640464 | − | 0.767988i | \(-0.721258\pi\) | ||||
−0.640464 | + | 0.767988i | \(0.721258\pi\) | |||||||
\(104\) | −1.00000 | − | 1.73205i | −0.0980581 | − | 0.169842i | ||||
\(105\) | −1.50000 | − | 2.59808i | −0.146385 | − | 0.253546i | ||||
\(106\) | 3.00000 | 0.291386 | ||||||||
\(107\) | −10.0000 | −0.966736 | −0.483368 | − | 0.875417i | \(-0.660587\pi\) | ||||
−0.483368 | + | 0.875417i | \(0.660587\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | 3.00000 | − | 5.19615i | 0.287348 | − | 0.497701i | −0.685828 | − | 0.727764i | \(-0.740560\pi\) |
0.973176 | + | 0.230063i | \(0.0738931\pi\) | |||||||
\(110\) | 0.500000 | + | 0.866025i | 0.0476731 | + | 0.0825723i | ||||
\(111\) | 4.50000 | − | 7.79423i | 0.427121 | − | 0.739795i | ||||
\(112\) | −1.50000 | + | 2.59808i | −0.141737 | + | 0.245495i | ||||
\(113\) | 10.0000 | 0.940721 | 0.470360 | − | 0.882474i | \(-0.344124\pi\) | ||||
0.470360 | + | 0.882474i | \(0.344124\pi\) | |||||||
\(114\) | 4.00000 | − | 1.73205i | 0.374634 | − | 0.162221i | ||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | + | 1.73205i | −0.0924500 | + | 0.160128i | ||||
\(118\) | −6.00000 | − | 10.3923i | −0.552345 | − | 0.956689i | ||||
\(119\) | −3.00000 | + | 5.19615i | −0.275010 | + | 0.476331i | ||||
\(120\) | −0.500000 | − | 0.866025i | −0.0456435 | − | 0.0790569i | ||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | −2.00000 | −0.181071 | ||||||||
\(123\) | 0.500000 | + | 0.866025i | 0.0450835 | + | 0.0780869i | ||||
\(124\) | −2.00000 | − | 3.46410i | −0.179605 | − | 0.311086i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 3.00000 | 0.267261 | ||||||||
\(127\) | 0.500000 | + | 0.866025i | 0.0443678 | + | 0.0768473i | 0.887357 | − | 0.461084i | \(-0.152539\pi\) |
−0.842989 | + | 0.537931i | \(0.819206\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −5.00000 | − | 8.66025i | −0.440225 | − | 0.762493i | ||||
\(130\) | 1.00000 | − | 1.73205i | 0.0877058 | − | 0.151911i | ||||
\(131\) | −10.5000 | + | 18.1865i | −0.917389 | + | 1.58896i | −0.114024 | + | 0.993478i | \(0.536374\pi\) |
−0.803365 | + | 0.595487i | \(0.796959\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | 1.50000 | − | 12.9904i | 0.130066 | − | 1.12641i | ||||
\(134\) | −2.00000 | −0.172774 | ||||||||
\(135\) | −0.500000 | + | 0.866025i | −0.0430331 | + | 0.0745356i | ||||
\(136\) | −1.00000 | + | 1.73205i | −0.0857493 | + | 0.148522i | ||||
\(137\) | −2.00000 | − | 3.46410i | −0.170872 | − | 0.295958i | 0.767853 | − | 0.640626i | \(-0.221325\pi\) |
−0.938725 | + | 0.344668i | \(0.887992\pi\) | |||||||
\(138\) | 0.500000 | − | 0.866025i | 0.0425628 | − | 0.0737210i | ||||
\(139\) | 10.0000 | + | 17.3205i | 0.848189 | + | 1.46911i | 0.882823 | + | 0.469706i | \(0.155640\pi\) |
−0.0346338 | + | 0.999400i | \(0.511026\pi\) | |||||||
\(140\) | −3.00000 | −0.253546 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.00000 | − | 6.92820i | −0.335673 | − | 0.581402i | ||||
\(143\) | −1.00000 | − | 1.73205i | −0.0836242 | − | 0.144841i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.00000 | + | 10.3923i | 0.496564 | + | 0.860073i | ||||
\(147\) | 1.00000 | − | 1.73205i | 0.0824786 | − | 0.142857i | ||||
\(148\) | −4.50000 | − | 7.79423i | −0.369898 | − | 0.640682i | ||||
\(149\) | 3.00000 | − | 5.19615i | 0.245770 | − | 0.425685i | −0.716578 | − | 0.697507i | \(-0.754293\pi\) |
0.962348 | + | 0.271821i | \(0.0876260\pi\) | |||||||
\(150\) | 0.500000 | − | 0.866025i | 0.0408248 | − | 0.0707107i | ||||
\(151\) | −18.0000 | −1.46482 | −0.732410 | − | 0.680864i | \(-0.761604\pi\) | ||||
−0.732410 | + | 0.680864i | \(0.761604\pi\) | |||||||
\(152\) | 0.500000 | − | 4.33013i | 0.0405554 | − | 0.351220i | ||||
\(153\) | 2.00000 | 0.161690 | ||||||||
\(154\) | −1.50000 | + | 2.59808i | −0.120873 | + | 0.209359i | ||||
\(155\) | 2.00000 | − | 3.46410i | 0.160644 | − | 0.278243i | ||||
\(156\) | 1.00000 | + | 1.73205i | 0.0800641 | + | 0.138675i | ||||
\(157\) | −3.50000 | + | 6.06218i | −0.279330 | + | 0.483814i | −0.971219 | − | 0.238190i | \(-0.923446\pi\) |
0.691888 | + | 0.722005i | \(0.256779\pi\) | |||||||
\(158\) | −7.00000 | − | 12.1244i | −0.556890 | − | 0.964562i | ||||
\(159\) | −3.00000 | −0.237915 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −1.50000 | − | 2.59808i | −0.118217 | − | 0.204757i | ||||
\(162\) | −0.500000 | − | 0.866025i | −0.0392837 | − | 0.0680414i | ||||
\(163\) | 2.00000 | 0.156652 | 0.0783260 | − | 0.996928i | \(-0.475042\pi\) | ||||
0.0783260 | + | 0.996928i | \(0.475042\pi\) | |||||||
\(164\) | 1.00000 | 0.0780869 | ||||||||
\(165\) | −0.500000 | − | 0.866025i | −0.0389249 | − | 0.0674200i | ||||
\(166\) | −3.00000 | + | 5.19615i | −0.232845 | + | 0.403300i | ||||
\(167\) | −1.50000 | − | 2.59808i | −0.116073 | − | 0.201045i | 0.802135 | − | 0.597143i | \(-0.203697\pi\) |
−0.918208 | + | 0.396098i | \(0.870364\pi\) | |||||||
\(168\) | 1.50000 | − | 2.59808i | 0.115728 | − | 0.200446i | ||||
\(169\) | 4.50000 | − | 7.79423i | 0.346154 | − | 0.599556i | ||||
\(170\) | −2.00000 | −0.153393 | ||||||||
\(171\) | −4.00000 | + | 1.73205i | −0.305888 | + | 0.132453i | ||||
\(172\) | −10.0000 | −0.762493 | ||||||||
\(173\) | −5.50000 | + | 9.52628i | −0.418157 | + | 0.724270i | −0.995754 | − | 0.0920525i | \(-0.970657\pi\) |
0.577597 | + | 0.816322i | \(0.303991\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.50000 | − | 2.59808i | −0.113389 | − | 0.196396i | ||||
\(176\) | −0.500000 | + | 0.866025i | −0.0376889 | + | 0.0652791i | ||||
\(177\) | 6.00000 | + | 10.3923i | 0.450988 | + | 0.781133i | ||||
\(178\) | −5.00000 | −0.374766 | ||||||||
\(179\) | −13.0000 | −0.971666 | −0.485833 | − | 0.874052i | \(-0.661484\pi\) | ||||
−0.485833 | + | 0.874052i | \(0.661484\pi\) | |||||||
\(180\) | 0.500000 | + | 0.866025i | 0.0372678 | + | 0.0645497i | ||||
\(181\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(182\) | 6.00000 | 0.444750 | ||||||||
\(183\) | 2.00000 | 0.147844 | ||||||||
\(184\) | −0.500000 | − | 0.866025i | −0.0368605 | − | 0.0638442i | ||||
\(185\) | 4.50000 | − | 7.79423i | 0.330847 | − | 0.573043i | ||||
\(186\) | 2.00000 | + | 3.46410i | 0.146647 | + | 0.254000i | ||||
\(187\) | −1.00000 | + | 1.73205i | −0.0731272 | + | 0.126660i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.00000 | −0.218218 | ||||||||
\(190\) | 4.00000 | − | 1.73205i | 0.290191 | − | 0.125656i | ||||
\(191\) | −10.0000 | −0.723575 | −0.361787 | − | 0.932261i | \(-0.617833\pi\) | ||||
−0.361787 | + | 0.932261i | \(0.617833\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −7.00000 | + | 12.1244i | −0.503871 | + | 0.872730i | 0.496119 | + | 0.868255i | \(0.334758\pi\) |
−0.999990 | + | 0.00447566i | \(0.998575\pi\) | |||||||
\(194\) | −4.00000 | − | 6.92820i | −0.287183 | − | 0.497416i | ||||
\(195\) | −1.00000 | + | 1.73205i | −0.0716115 | + | 0.124035i | ||||
\(196\) | −1.00000 | − | 1.73205i | −0.0714286 | − | 0.123718i | ||||
\(197\) | 5.00000 | 0.356235 | 0.178118 | − | 0.984009i | \(-0.442999\pi\) | ||||
0.178118 | + | 0.984009i | \(0.442999\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | 9.00000 | + | 15.5885i | 0.637993 | + | 1.10504i | 0.985873 | + | 0.167497i | \(0.0535685\pi\) |
−0.347879 | + | 0.937539i | \(0.613098\pi\) | |||||||
\(200\) | −0.500000 | − | 0.866025i | −0.0353553 | − | 0.0612372i | ||||
\(201\) | 2.00000 | 0.141069 | ||||||||
\(202\) | −2.00000 | −0.140720 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.00000 | − | 1.73205i | 0.0700140 | − | 0.121268i | ||||
\(205\) | 0.500000 | + | 0.866025i | 0.0349215 | + | 0.0604858i | ||||
\(206\) | 6.50000 | − | 11.2583i | 0.452876 | − | 0.784405i | ||||
\(207\) | −0.500000 | + | 0.866025i | −0.0347524 | + | 0.0601929i | ||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | 0.500000 | − | 4.33013i | 0.0345857 | − | 0.299521i | ||||
\(210\) | 3.00000 | 0.207020 | ||||||||
\(211\) | −11.5000 | + | 19.9186i | −0.791693 | + | 1.37125i | 0.133226 | + | 0.991086i | \(0.457467\pi\) |
−0.924918 | + | 0.380166i | \(0.875867\pi\) | |||||||
\(212\) | −1.50000 | + | 2.59808i | −0.103020 | + | 0.178437i | ||||
\(213\) | 4.00000 | + | 6.92820i | 0.274075 | + | 0.474713i | ||||
\(214\) | 5.00000 | − | 8.66025i | 0.341793 | − | 0.592003i | ||||
\(215\) | −5.00000 | − | 8.66025i | −0.340997 | − | 0.590624i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 12.0000 | 0.814613 | ||||||||
\(218\) | 3.00000 | + | 5.19615i | 0.203186 | + | 0.351928i | ||||
\(219\) | −6.00000 | − | 10.3923i | −0.405442 | − | 0.702247i | ||||
\(220\) | −1.00000 | −0.0674200 | ||||||||
\(221\) | 4.00000 | 0.269069 | ||||||||
\(222\) | 4.50000 | + | 7.79423i | 0.302020 | + | 0.523114i | ||||
\(223\) | −1.50000 | + | 2.59808i | −0.100447 | + | 0.173980i | −0.911869 | − | 0.410481i | \(-0.865361\pi\) |
0.811422 | + | 0.584461i | \(0.198694\pi\) | |||||||
\(224\) | −1.50000 | − | 2.59808i | −0.100223 | − | 0.173591i | ||||
\(225\) | −0.500000 | + | 0.866025i | −0.0333333 | + | 0.0577350i | ||||
\(226\) | −5.00000 | + | 8.66025i | −0.332595 | + | 0.576072i | ||||
\(227\) | 28.0000 | 1.85843 | 0.929213 | − | 0.369546i | \(-0.120487\pi\) | ||||
0.929213 | + | 0.369546i | \(0.120487\pi\) | |||||||
\(228\) | −0.500000 | + | 4.33013i | −0.0331133 | + | 0.286770i | ||||
\(229\) | 14.0000 | 0.925146 | 0.462573 | − | 0.886581i | \(-0.346926\pi\) | ||||
0.462573 | + | 0.886581i | \(0.346926\pi\) | |||||||
\(230\) | 0.500000 | − | 0.866025i | 0.0329690 | − | 0.0571040i | ||||
\(231\) | 1.50000 | − | 2.59808i | 0.0986928 | − | 0.170941i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.00000 | + | 5.19615i | −0.196537 | + | 0.340411i | −0.947403 | − | 0.320043i | \(-0.896303\pi\) |
0.750867 | + | 0.660454i | \(0.229636\pi\) | |||||||
\(234\) | −1.00000 | − | 1.73205i | −0.0653720 | − | 0.113228i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.0000 | 0.781133 | ||||||||
\(237\) | 7.00000 | + | 12.1244i | 0.454699 | + | 0.787562i | ||||
\(238\) | −3.00000 | − | 5.19615i | −0.194461 | − | 0.336817i | ||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | 5.00000 | + | 8.66025i | 0.322078 | + | 0.557856i | 0.980917 | − | 0.194429i | \(-0.0622852\pi\) |
−0.658838 | + | 0.752285i | \(0.728952\pi\) | |||||||
\(242\) | 5.00000 | − | 8.66025i | 0.321412 | − | 0.556702i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 1.00000 | − | 1.73205i | 0.0640184 | − | 0.110883i | ||||
\(245\) | 1.00000 | − | 1.73205i | 0.0638877 | − | 0.110657i | ||||
\(246\) | −1.00000 | −0.0637577 | ||||||||
\(247\) | −8.00000 | + | 3.46410i | −0.509028 | + | 0.220416i | ||||
\(248\) | 4.00000 | 0.254000 | ||||||||
\(249\) | 3.00000 | − | 5.19615i | 0.190117 | − | 0.329293i | ||||
\(250\) | 0.500000 | − | 0.866025i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | −14.0000 | − | 24.2487i | −0.883672 | − | 1.53057i | −0.847228 | − | 0.531229i | \(-0.821730\pi\) |
−0.0364441 | − | 0.999336i | \(-0.511603\pi\) | |||||||
\(252\) | −1.50000 | + | 2.59808i | −0.0944911 | + | 0.163663i | ||||
\(253\) | −0.500000 | − | 0.866025i | −0.0314347 | − | 0.0544466i | ||||
\(254\) | −1.00000 | −0.0627456 | ||||||||
\(255\) | 2.00000 | 0.125245 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −1.00000 | − | 1.73205i | −0.0623783 | − | 0.108042i | 0.833150 | − | 0.553047i | \(-0.186535\pi\) |
−0.895528 | + | 0.445005i | \(0.853202\pi\) | |||||||
\(258\) | 10.0000 | 0.622573 | ||||||||
\(259\) | 27.0000 | 1.67770 | ||||||||
\(260\) | 1.00000 | + | 1.73205i | 0.0620174 | + | 0.107417i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.5000 | − | 18.1865i | −0.648692 | − | 1.12357i | ||||
\(263\) | 12.5000 | − | 21.6506i | 0.770783 | − | 1.33504i | −0.166351 | − | 0.986067i | \(-0.553199\pi\) |
0.937134 | − | 0.348969i | \(-0.113468\pi\) | |||||||
\(264\) | 0.500000 | − | 0.866025i | 0.0307729 | − | 0.0533002i | ||||
\(265\) | −3.00000 | −0.184289 | ||||||||
\(266\) | 10.5000 | + | 7.79423i | 0.643796 | + | 0.477895i | ||||
\(267\) | 5.00000 | 0.305995 | ||||||||
\(268\) | 1.00000 | − | 1.73205i | 0.0610847 | − | 0.105802i | ||||
\(269\) | 7.00000 | − | 12.1244i | 0.426798 | − | 0.739235i | −0.569789 | − | 0.821791i | \(-0.692975\pi\) |
0.996586 | + | 0.0825561i | \(0.0263084\pi\) | |||||||
\(270\) | −0.500000 | − | 0.866025i | −0.0304290 | − | 0.0527046i | ||||
\(271\) | −1.00000 | + | 1.73205i | −0.0607457 | + | 0.105215i | −0.894799 | − | 0.446469i | \(-0.852681\pi\) |
0.834053 | + | 0.551684i | \(0.186015\pi\) | |||||||
\(272\) | −1.00000 | − | 1.73205i | −0.0606339 | − | 0.105021i | ||||
\(273\) | −6.00000 | −0.363137 | ||||||||
\(274\) | 4.00000 | 0.241649 | ||||||||
\(275\) | −0.500000 | − | 0.866025i | −0.0301511 | − | 0.0522233i | ||||
\(276\) | 0.500000 | + | 0.866025i | 0.0300965 | + | 0.0521286i | ||||
\(277\) | 22.0000 | 1.32185 | 0.660926 | − | 0.750451i | \(-0.270164\pi\) | ||||
0.660926 | + | 0.750451i | \(0.270164\pi\) | |||||||
\(278\) | −20.0000 | −1.19952 | ||||||||
\(279\) | −2.00000 | − | 3.46410i | −0.119737 | − | 0.207390i | ||||
\(280\) | 1.50000 | − | 2.59808i | 0.0896421 | − | 0.155265i | ||||
\(281\) | 10.5000 | + | 18.1865i | 0.626377 | + | 1.08492i | 0.988273 | + | 0.152699i | \(0.0487965\pi\) |
−0.361895 | + | 0.932219i | \(0.617870\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.00000 | + | 1.73205i | −0.0594438 | + | 0.102960i | −0.894216 | − | 0.447636i | \(-0.852266\pi\) |
0.834772 | + | 0.550596i | \(0.185599\pi\) | |||||||
\(284\) | 8.00000 | 0.474713 | ||||||||
\(285\) | −4.00000 | + | 1.73205i | −0.236940 | + | 0.102598i | ||||
\(286\) | 2.00000 | 0.118262 | ||||||||
\(287\) | −1.50000 | + | 2.59808i | −0.0885422 | + | 0.153360i | ||||
\(288\) | −0.500000 | + | 0.866025i | −0.0294628 | + | 0.0510310i | ||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.00000 | + | 6.92820i | 0.234484 | + | 0.406138i | ||||
\(292\) | −12.0000 | −0.702247 | ||||||||
\(293\) | 1.00000 | 0.0584206 | 0.0292103 | − | 0.999573i | \(-0.490701\pi\) | ||||
0.0292103 | + | 0.999573i | \(0.490701\pi\) | |||||||
\(294\) | 1.00000 | + | 1.73205i | 0.0583212 | + | 0.101015i | ||||
\(295\) | 6.00000 | + | 10.3923i | 0.349334 | + | 0.605063i | ||||
\(296\) | 9.00000 | 0.523114 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 3.00000 | + | 5.19615i | 0.173785 | + | 0.301005i | ||||
\(299\) | −1.00000 | + | 1.73205i | −0.0578315 | + | 0.100167i | ||||
\(300\) | 0.500000 | + | 0.866025i | 0.0288675 | + | 0.0500000i | ||||
\(301\) | 15.0000 | − | 25.9808i | 0.864586 | − | 1.49751i | ||||
\(302\) | 9.00000 | − | 15.5885i | 0.517892 | − | 0.897015i | ||||
\(303\) | 2.00000 | 0.114897 | ||||||||
\(304\) | 3.50000 | + | 2.59808i | 0.200739 | + | 0.149010i | ||||
\(305\) | 2.00000 | 0.114520 | ||||||||
\(306\) | −1.00000 | + | 1.73205i | −0.0571662 | + | 0.0990148i | ||||
\(307\) | −8.00000 | + | 13.8564i | −0.456584 | + | 0.790827i | −0.998778 | − | 0.0494267i | \(-0.984261\pi\) |
0.542194 | + | 0.840254i | \(0.317594\pi\) | |||||||
\(308\) | −1.50000 | − | 2.59808i | −0.0854704 | − | 0.148039i | ||||
\(309\) | −6.50000 | + | 11.2583i | −0.369772 | + | 0.640464i | ||||
\(310\) | 2.00000 | + | 3.46410i | 0.113592 | + | 0.196748i | ||||
\(311\) | −16.0000 | −0.907277 | −0.453638 | − | 0.891186i | \(-0.649874\pi\) | ||||
−0.453638 | + | 0.891186i | \(0.649874\pi\) | |||||||
\(312\) | −2.00000 | −0.113228 | ||||||||
\(313\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(314\) | −3.50000 | − | 6.06218i | −0.197516 | − | 0.342108i | ||||
\(315\) | −3.00000 | −0.169031 | ||||||||
\(316\) | 14.0000 | 0.787562 | ||||||||
\(317\) | −3.50000 | − | 6.06218i | −0.196580 | − | 0.340486i | 0.750838 | − | 0.660487i | \(-0.229650\pi\) |
−0.947417 | + | 0.320001i | \(0.896317\pi\) | |||||||
\(318\) | 1.50000 | − | 2.59808i | 0.0841158 | − | 0.145693i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.500000 | − | 0.866025i | 0.0279508 | − | 0.0484123i | ||||
\(321\) | −5.00000 | + | 8.66025i | −0.279073 | + | 0.483368i | ||||
\(322\) | 3.00000 | 0.167183 | ||||||||
\(323\) | 7.00000 | + | 5.19615i | 0.389490 | + | 0.289122i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −1.00000 | + | 1.73205i | −0.0554700 | + | 0.0960769i | ||||
\(326\) | −1.00000 | + | 1.73205i | −0.0553849 | + | 0.0959294i | ||||
\(327\) | −3.00000 | − | 5.19615i | −0.165900 | − | 0.287348i | ||||
\(328\) | −0.500000 | + | 0.866025i | −0.0276079 | + | 0.0478183i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.00000 | 0.0550482 | ||||||||
\(331\) | 13.0000 | 0.714545 | 0.357272 | − | 0.934000i | \(-0.383707\pi\) | ||||
0.357272 | + | 0.934000i | \(0.383707\pi\) | |||||||
\(332\) | −3.00000 | − | 5.19615i | −0.164646 | − | 0.285176i | ||||
\(333\) | −4.50000 | − | 7.79423i | −0.246598 | − | 0.427121i | ||||
\(334\) | 3.00000 | 0.164153 | ||||||||
\(335\) | 2.00000 | 0.109272 | ||||||||
\(336\) | 1.50000 | + | 2.59808i | 0.0818317 | + | 0.141737i | ||||
\(337\) | −1.00000 | + | 1.73205i | −0.0544735 | + | 0.0943508i | −0.891976 | − | 0.452082i | \(-0.850681\pi\) |
0.837503 | + | 0.546433i | \(0.184015\pi\) | |||||||
\(338\) | 4.50000 | + | 7.79423i | 0.244768 | + | 0.423950i | ||||
\(339\) | 5.00000 | − | 8.66025i | 0.271563 | − | 0.470360i | ||||
\(340\) | 1.00000 | − | 1.73205i | 0.0542326 | − | 0.0939336i | ||||
\(341\) | 4.00000 | 0.216612 | ||||||||
\(342\) | 0.500000 | − | 4.33013i | 0.0270369 | − | 0.234146i | ||||
\(343\) | −15.0000 | −0.809924 | ||||||||
\(344\) | 5.00000 | − | 8.66025i | 0.269582 | − | 0.466930i | ||||
\(345\) | −0.500000 | + | 0.866025i | −0.0269191 | + | 0.0466252i | ||||
\(346\) | −5.50000 | − | 9.52628i | −0.295682 | − | 0.512136i | ||||
\(347\) | −9.00000 | + | 15.5885i | −0.483145 | + | 0.836832i | −0.999813 | − | 0.0193540i | \(-0.993839\pi\) |
0.516667 | + | 0.856186i | \(0.327172\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.0000 | 1.39175 | 0.695874 | − | 0.718164i | \(-0.255017\pi\) | ||||
0.695874 | + | 0.718164i | \(0.255017\pi\) | |||||||
\(350\) | 3.00000 | 0.160357 | ||||||||
\(351\) | 1.00000 | + | 1.73205i | 0.0533761 | + | 0.0924500i | ||||
\(352\) | −0.500000 | − | 0.866025i | −0.0266501 | − | 0.0461593i | ||||
\(353\) | 26.0000 | 1.38384 | 0.691920 | − | 0.721974i | \(-0.256765\pi\) | ||||
0.691920 | + | 0.721974i | \(0.256765\pi\) | |||||||
\(354\) | −12.0000 | −0.637793 | ||||||||
\(355\) | 4.00000 | + | 6.92820i | 0.212298 | + | 0.367711i | ||||
\(356\) | 2.50000 | − | 4.33013i | 0.132500 | − | 0.229496i | ||||
\(357\) | 3.00000 | + | 5.19615i | 0.158777 | + | 0.275010i | ||||
\(358\) | 6.50000 | − | 11.2583i | 0.343536 | − | 0.595021i | ||||
\(359\) | −6.00000 | + | 10.3923i | −0.316668 | + | 0.548485i | −0.979791 | − | 0.200026i | \(-0.935897\pi\) |
0.663123 | + | 0.748511i | \(0.269231\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | −18.5000 | − | 4.33013i | −0.973684 | − | 0.227901i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.00000 | + | 8.66025i | −0.262432 | + | 0.454545i | ||||
\(364\) | −3.00000 | + | 5.19615i | −0.157243 | + | 0.272352i | ||||
\(365\) | −6.00000 | − | 10.3923i | −0.314054 | − | 0.543958i | ||||
\(366\) | −1.00000 | + | 1.73205i | −0.0522708 | + | 0.0905357i | ||||
\(367\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | 4.50000 | + | 7.79423i | 0.233944 | + | 0.405203i | ||||
\(371\) | −4.50000 | − | 7.79423i | −0.233628 | − | 0.404656i | ||||
\(372\) | −4.00000 | −0.207390 | ||||||||
\(373\) | −37.0000 | −1.91579 | −0.957894 | − | 0.287123i | \(-0.907301\pi\) | ||||
−0.957894 | + | 0.287123i | \(0.907301\pi\) | |||||||
\(374\) | −1.00000 | − | 1.73205i | −0.0517088 | − | 0.0895622i | ||||
\(375\) | −0.500000 | + | 0.866025i | −0.0258199 | + | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.50000 | − | 2.59808i | 0.0771517 | − | 0.133631i | ||||
\(379\) | 16.0000 | 0.821865 | 0.410932 | − | 0.911666i | \(-0.365203\pi\) | ||||
0.410932 | + | 0.911666i | \(0.365203\pi\) | |||||||
\(380\) | −0.500000 | + | 4.33013i | −0.0256495 | + | 0.222131i | ||||
\(381\) | 1.00000 | 0.0512316 | ||||||||
\(382\) | 5.00000 | − | 8.66025i | 0.255822 | − | 0.443097i | ||||
\(383\) | 12.0000 | − | 20.7846i | 0.613171 | − | 1.06204i | −0.377531 | − | 0.925997i | \(-0.623227\pi\) |
0.990702 | − | 0.136047i | \(-0.0434398\pi\) | |||||||
\(384\) | 0.500000 | + | 0.866025i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | 1.50000 | − | 2.59808i | 0.0764471 | − | 0.132410i | ||||
\(386\) | −7.00000 | − | 12.1244i | −0.356291 | − | 0.617113i | ||||
\(387\) | −10.0000 | −0.508329 | ||||||||
\(388\) | 8.00000 | 0.406138 | ||||||||
\(389\) | −4.00000 | − | 6.92820i | −0.202808 | − | 0.351274i | 0.746624 | − | 0.665246i | \(-0.231673\pi\) |
−0.949432 | + | 0.313972i | \(0.898340\pi\) | |||||||
\(390\) | −1.00000 | − | 1.73205i | −0.0506370 | − | 0.0877058i | ||||
\(391\) | 2.00000 | 0.101144 | ||||||||
\(392\) | 2.00000 | 0.101015 | ||||||||
\(393\) | 10.5000 | + | 18.1865i | 0.529655 | + | 0.917389i | ||||
\(394\) | −2.50000 | + | 4.33013i | −0.125948 | + | 0.218149i | ||||
\(395\) | 7.00000 | + | 12.1244i | 0.352208 | + | 0.610043i | ||||
\(396\) | −0.500000 | + | 0.866025i | −0.0251259 | + | 0.0435194i | ||||
\(397\) | 7.50000 | − | 12.9904i | 0.376414 | − | 0.651969i | −0.614123 | − | 0.789210i | \(-0.710490\pi\) |
0.990538 | + | 0.137241i | \(0.0438236\pi\) | |||||||
\(398\) | −18.0000 | −0.902258 | ||||||||
\(399\) | −10.5000 | − | 7.79423i | −0.525657 | − | 0.390199i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 1.00000 | − | 1.73205i | 0.0499376 | − | 0.0864945i | −0.839976 | − | 0.542623i | \(-0.817431\pi\) |
0.889914 | + | 0.456129i | \(0.150764\pi\) | |||||||
\(402\) | −1.00000 | + | 1.73205i | −0.0498755 | + | 0.0863868i | ||||
\(403\) | −4.00000 | − | 6.92820i | −0.199254 | − | 0.345118i | ||||
\(404\) | 1.00000 | − | 1.73205i | 0.0497519 | − | 0.0861727i | ||||
\(405\) | 0.500000 | + | 0.866025i | 0.0248452 | + | 0.0430331i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.00000 | 0.446113 | ||||||||
\(408\) | 1.00000 | + | 1.73205i | 0.0495074 | + | 0.0857493i | ||||
\(409\) | −10.5000 | − | 18.1865i | −0.519192 | − | 0.899266i | −0.999751 | − | 0.0223042i | \(-0.992900\pi\) |
0.480560 | − | 0.876962i | \(-0.340434\pi\) | |||||||
\(410\) | −1.00000 | −0.0493865 | ||||||||
\(411\) | −4.00000 | −0.197305 | ||||||||
\(412\) | 6.50000 | + | 11.2583i | 0.320232 | + | 0.554658i | ||||
\(413\) | −18.0000 | + | 31.1769i | −0.885722 | + | 1.53412i | ||||
\(414\) | −0.500000 | − | 0.866025i | −0.0245737 | − | 0.0425628i | ||||
\(415\) | 3.00000 | − | 5.19615i | 0.147264 | − | 0.255069i | ||||
\(416\) | −1.00000 | + | 1.73205i | −0.0490290 | + | 0.0849208i | ||||
\(417\) | 20.0000 | 0.979404 | ||||||||
\(418\) | 3.50000 | + | 2.59808i | 0.171191 | + | 0.127076i | ||||
\(419\) | −15.0000 | −0.732798 | −0.366399 | − | 0.930458i | \(-0.619409\pi\) | ||||
−0.366399 | + | 0.930458i | \(0.619409\pi\) | |||||||
\(420\) | −1.50000 | + | 2.59808i | −0.0731925 | + | 0.126773i | ||||
\(421\) | 11.0000 | − | 19.0526i | 0.536107 | − | 0.928565i | −0.463002 | − | 0.886357i | \(-0.653228\pi\) |
0.999109 | − | 0.0422075i | \(-0.0134391\pi\) | |||||||
\(422\) | −11.5000 | − | 19.9186i | −0.559811 | − | 0.969622i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.50000 | − | 2.59808i | −0.0728464 | − | 0.126174i | ||||
\(425\) | 2.00000 | 0.0970143 | ||||||||
\(426\) | −8.00000 | −0.387601 | ||||||||
\(427\) | 3.00000 | + | 5.19615i | 0.145180 | + | 0.251459i | ||||
\(428\) | 5.00000 | + | 8.66025i | 0.241684 | + | 0.418609i | ||||
\(429\) | −2.00000 | −0.0965609 | ||||||||
\(430\) | 10.0000 | 0.482243 | ||||||||
\(431\) | −19.0000 | − | 32.9090i | −0.915198 | − | 1.58517i | −0.806611 | − | 0.591082i | \(-0.798701\pi\) |
−0.108586 | − | 0.994087i | \(-0.534632\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | −8.00000 | − | 13.8564i | −0.384455 | − | 0.665896i | 0.607238 | − | 0.794520i | \(-0.292277\pi\) |
−0.991693 | + | 0.128624i | \(0.958944\pi\) | |||||||
\(434\) | −6.00000 | + | 10.3923i | −0.288009 | + | 0.498847i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.00000 | −0.287348 | ||||||||
\(437\) | −4.00000 | + | 1.73205i | −0.191346 | + | 0.0828552i | ||||
\(438\) | 12.0000 | 0.573382 | ||||||||
\(439\) | −15.0000 | + | 25.9808i | −0.715911 | + | 1.23999i | 0.246696 | + | 0.969093i | \(0.420655\pi\) |
−0.962607 | + | 0.270901i | \(0.912678\pi\) | |||||||
\(440\) | 0.500000 | − | 0.866025i | 0.0238366 | − | 0.0412861i | ||||
\(441\) | −1.00000 | − | 1.73205i | −0.0476190 | − | 0.0824786i | ||||
\(442\) | −2.00000 | + | 3.46410i | −0.0951303 | + | 0.164771i | ||||
\(443\) | −11.0000 | − | 19.0526i | −0.522626 | − | 0.905214i | −0.999653 | − | 0.0263261i | \(-0.991619\pi\) |
0.477028 | − | 0.878888i | \(-0.341714\pi\) | |||||||
\(444\) | −9.00000 | −0.427121 | ||||||||
\(445\) | 5.00000 | 0.237023 | ||||||||
\(446\) | −1.50000 | − | 2.59808i | −0.0710271 | − | 0.123022i | ||||
\(447\) | −3.00000 | − | 5.19615i | −0.141895 | − | 0.245770i | ||||
\(448\) | 3.00000 | 0.141737 | ||||||||
\(449\) | −9.00000 | −0.424736 | −0.212368 | − | 0.977190i | \(-0.568118\pi\) | ||||
−0.212368 | + | 0.977190i | \(0.568118\pi\) | |||||||
\(450\) | −0.500000 | − | 0.866025i | −0.0235702 | − | 0.0408248i | ||||
\(451\) | −0.500000 | + | 0.866025i | −0.0235441 | + | 0.0407795i | ||||
\(452\) | −5.00000 | − | 8.66025i | −0.235180 | − | 0.407344i | ||||
\(453\) | −9.00000 | + | 15.5885i | −0.422857 | + | 0.732410i | ||||
\(454\) | −14.0000 | + | 24.2487i | −0.657053 | + | 1.13805i | ||||
\(455\) | −6.00000 | −0.281284 | ||||||||
\(456\) | −3.50000 | − | 2.59808i | −0.163903 | − | 0.121666i | ||||
\(457\) | −18.0000 | −0.842004 | −0.421002 | − | 0.907060i | \(-0.638322\pi\) | ||||
−0.421002 | + | 0.907060i | \(0.638322\pi\) | |||||||
\(458\) | −7.00000 | + | 12.1244i | −0.327089 | + | 0.566534i | ||||
\(459\) | 1.00000 | − | 1.73205i | 0.0466760 | − | 0.0808452i | ||||
\(460\) | 0.500000 | + | 0.866025i | 0.0233126 | + | 0.0403786i | ||||
\(461\) | −11.0000 | + | 19.0526i | −0.512321 | + | 0.887366i | 0.487577 | + | 0.873080i | \(0.337881\pi\) |
−0.999898 | + | 0.0142861i | \(0.995452\pi\) | |||||||
\(462\) | 1.50000 | + | 2.59808i | 0.0697863 | + | 0.120873i | ||||
\(463\) | −25.0000 | −1.16185 | −0.580924 | − | 0.813958i | \(-0.697309\pi\) | ||||
−0.580924 | + | 0.813958i | \(0.697309\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.00000 | − | 3.46410i | −0.0927478 | − | 0.160644i | ||||
\(466\) | −3.00000 | − | 5.19615i | −0.138972 | − | 0.240707i | ||||
\(467\) | 32.0000 | 1.48078 | 0.740392 | − | 0.672176i | \(-0.234640\pi\) | ||||
0.740392 | + | 0.672176i | \(0.234640\pi\) | |||||||
\(468\) | 2.00000 | 0.0924500 | ||||||||
\(469\) | 3.00000 | + | 5.19615i | 0.138527 | + | 0.239936i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.50000 | + | 6.06218i | 0.161271 | + | 0.279330i | ||||
\(472\) | −6.00000 | + | 10.3923i | −0.276172 | + | 0.478345i | ||||
\(473\) | 5.00000 | − | 8.66025i | 0.229900 | − | 0.398199i | ||||
\(474\) | −14.0000 | −0.643041 | ||||||||
\(475\) | −4.00000 | + | 1.73205i | −0.183533 | + | 0.0794719i | ||||
\(476\) | 6.00000 | 0.275010 | ||||||||
\(477\) | −1.50000 | + | 2.59808i | −0.0686803 | + | 0.118958i | ||||
\(478\) | −6.00000 | + | 10.3923i | −0.274434 | + | 0.475333i | ||||
\(479\) | −10.0000 | − | 17.3205i | −0.456912 | − | 0.791394i | 0.541884 | − | 0.840453i | \(-0.317711\pi\) |
−0.998796 | + | 0.0490589i | \(0.984378\pi\) | |||||||
\(480\) | −0.500000 | + | 0.866025i | −0.0228218 | + | 0.0395285i | ||||
\(481\) | −9.00000 | − | 15.5885i | −0.410365 | − | 0.710772i | ||||
\(482\) | −10.0000 | −0.455488 | ||||||||
\(483\) | −3.00000 | −0.136505 | ||||||||
\(484\) | 5.00000 | + | 8.66025i | 0.227273 | + | 0.393648i | ||||
\(485\) | 4.00000 | + | 6.92820i | 0.181631 | + | 0.314594i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −41.0000 | −1.85789 | −0.928944 | − | 0.370221i | \(-0.879282\pi\) | ||||
−0.928944 | + | 0.370221i | \(0.879282\pi\) | |||||||
\(488\) | 1.00000 | + | 1.73205i | 0.0452679 | + | 0.0784063i | ||||
\(489\) | 1.00000 | − | 1.73205i | 0.0452216 | − | 0.0783260i | ||||
\(490\) | 1.00000 | + | 1.73205i | 0.0451754 | + | 0.0782461i | ||||
\(491\) | 16.5000 | − | 28.5788i | 0.744635 | − | 1.28974i | −0.205731 | − | 0.978609i | \(-0.565957\pi\) |
0.950365 | − | 0.311136i | \(-0.100710\pi\) | |||||||
\(492\) | 0.500000 | − | 0.866025i | 0.0225417 | − | 0.0390434i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 1.00000 | − | 8.66025i | 0.0449921 | − | 0.389643i | ||||
\(495\) | −1.00000 | −0.0449467 | ||||||||
\(496\) | −2.00000 | + | 3.46410i | −0.0898027 | + | 0.155543i | ||||
\(497\) | −12.0000 | + | 20.7846i | −0.538274 | + | 0.932317i | ||||
\(498\) | 3.00000 | + | 5.19615i | 0.134433 | + | 0.232845i | ||||
\(499\) | −7.50000 | + | 12.9904i | −0.335746 | + | 0.581529i | −0.983628 | − | 0.180212i | \(-0.942322\pi\) |
0.647882 | + | 0.761741i | \(0.275655\pi\) | |||||||
\(500\) | 0.500000 | + | 0.866025i | 0.0223607 | + | 0.0387298i | ||||
\(501\) | −3.00000 | −0.134030 | ||||||||
\(502\) | 28.0000 | 1.24970 | ||||||||
\(503\) | 4.50000 | + | 7.79423i | 0.200645 | + | 0.347527i | 0.948736 | − | 0.316068i | \(-0.102363\pi\) |
−0.748091 | + | 0.663596i | \(0.769030\pi\) | |||||||
\(504\) | −1.50000 | − | 2.59808i | −0.0668153 | − | 0.115728i | ||||
\(505\) | 2.00000 | 0.0889988 | ||||||||
\(506\) | 1.00000 | 0.0444554 | ||||||||
\(507\) | −4.50000 | − | 7.79423i | −0.199852 | − | 0.346154i | ||||
\(508\) | 0.500000 | − | 0.866025i | 0.0221839 | − | 0.0384237i | ||||
\(509\) | −15.0000 | − | 25.9808i | −0.664863 | − | 1.15158i | −0.979322 | − | 0.202306i | \(-0.935156\pi\) |
0.314459 | − | 0.949271i | \(-0.398177\pi\) | |||||||
\(510\) | −1.00000 | + | 1.73205i | −0.0442807 | + | 0.0766965i | ||||
\(511\) | 18.0000 | − | 31.1769i | 0.796273 | − | 1.37919i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.500000 | + | 4.33013i | −0.0220755 | + | 0.191180i | ||||
\(514\) | 2.00000 | 0.0882162 | ||||||||
\(515\) | −6.50000 | + | 11.2583i | −0.286424 | + | 0.496101i | ||||
\(516\) | −5.00000 | + | 8.66025i | −0.220113 | + | 0.381246i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −13.5000 | + | 23.3827i | −0.593156 | + | 1.02738i | ||||
\(519\) | 5.50000 | + | 9.52628i | 0.241423 | + | 0.418157i | ||||
\(520\) | −2.00000 | −0.0877058 | ||||||||
\(521\) | 6.00000 | 0.262865 | 0.131432 | − | 0.991325i | \(-0.458042\pi\) | ||||
0.131432 | + | 0.991325i | \(0.458042\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.0000 | + | 27.7128i | 0.699631 | + | 1.21180i | 0.968594 | + | 0.248646i | \(0.0799857\pi\) |
−0.268963 | + | 0.963150i | \(0.586681\pi\) | |||||||
\(524\) | 21.0000 | 0.917389 | ||||||||
\(525\) | −3.00000 | −0.130931 | ||||||||
\(526\) | 12.5000 | + | 21.6506i | 0.545026 | + | 0.944013i | ||||
\(527\) | −4.00000 | + | 6.92820i | −0.174243 | + | 0.301797i | ||||
\(528\) | 0.500000 | + | 0.866025i | 0.0217597 | + | 0.0376889i | ||||
\(529\) | 11.0000 | − | 19.0526i | 0.478261 | − | 0.828372i | ||||
\(530\) | 1.50000 | − | 2.59808i | 0.0651558 | − | 0.112853i | ||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | −12.0000 | + | 5.19615i | −0.520266 | + | 0.225282i | ||||
\(533\) | 2.00000 | 0.0866296 | ||||||||
\(534\) | −2.50000 | + | 4.33013i | −0.108186 | + | 0.187383i | ||||
\(535\) | −5.00000 | + | 8.66025i | −0.216169 | + | 0.374415i | ||||
\(536\) | 1.00000 | + | 1.73205i | 0.0431934 | + | 0.0748132i | ||||
\(537\) | −6.50000 | + | 11.2583i | −0.280496 | + | 0.485833i | ||||
\(538\) | 7.00000 | + | 12.1244i | 0.301791 | + | 0.522718i | ||||
\(539\) | 2.00000 | 0.0861461 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | −10.0000 | − | 17.3205i | −0.429934 | − | 0.744667i | 0.566933 | − | 0.823764i | \(-0.308130\pi\) |
−0.996867 | + | 0.0790969i | \(0.974796\pi\) | |||||||
\(542\) | −1.00000 | − | 1.73205i | −0.0429537 | − | 0.0743980i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.00000 | 0.0857493 | ||||||||
\(545\) | −3.00000 | − | 5.19615i | −0.128506 | − | 0.222579i | ||||
\(546\) | 3.00000 | − | 5.19615i | 0.128388 | − | 0.222375i | ||||
\(547\) | −1.00000 | − | 1.73205i | −0.0427569 | − | 0.0740571i | 0.843855 | − | 0.536571i | \(-0.180281\pi\) |
−0.886612 | + | 0.462514i | \(0.846947\pi\) | |||||||
\(548\) | −2.00000 | + | 3.46410i | −0.0854358 | + | 0.147979i | ||||
\(549\) | 1.00000 | − | 1.73205i | 0.0426790 | − | 0.0739221i | ||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | −21.0000 | + | 36.3731i | −0.893011 | + | 1.54674i | ||||
\(554\) | −11.0000 | + | 19.0526i | −0.467345 | + | 0.809466i | ||||
\(555\) | −4.50000 | − | 7.79423i | −0.191014 | − | 0.330847i | ||||
\(556\) | 10.0000 | − | 17.3205i | 0.424094 | − | 0.734553i | ||||
\(557\) | −16.5000 | − | 28.5788i | −0.699127 | − | 1.21092i | −0.968769 | − | 0.247964i | \(-0.920239\pi\) |
0.269642 | − | 0.962961i | \(-0.413095\pi\) | |||||||
\(558\) | 4.00000 | 0.169334 | ||||||||
\(559\) | −20.0000 | −0.845910 | ||||||||
\(560\) | 1.50000 | + | 2.59808i | 0.0633866 | + | 0.109789i | ||||
\(561\) | 1.00000 | + | 1.73205i | 0.0422200 | + | 0.0731272i | ||||
\(562\) | −21.0000 | −0.885832 | ||||||||
\(563\) | 28.0000 | 1.18006 | 0.590030 | − | 0.807382i | \(-0.299116\pi\) | ||||
0.590030 | + | 0.807382i | \(0.299116\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.00000 | − | 8.66025i | 0.210352 | − | 0.364340i | ||||
\(566\) | −1.00000 | − | 1.73205i | −0.0420331 | − | 0.0728035i | ||||
\(567\) | −1.50000 | + | 2.59808i | −0.0629941 | + | 0.109109i | ||||
\(568\) | −4.00000 | + | 6.92820i | −0.167836 | + | 0.290701i | ||||
\(569\) | 31.0000 | 1.29959 | 0.649794 | − | 0.760111i | \(-0.274855\pi\) | ||||
0.649794 | + | 0.760111i | \(0.274855\pi\) | |||||||
\(570\) | 0.500000 | − | 4.33013i | 0.0209427 | − | 0.181369i | ||||
\(571\) | −20.0000 | −0.836974 | −0.418487 | − | 0.908223i | \(-0.637439\pi\) | ||||
−0.418487 | + | 0.908223i | \(0.637439\pi\) | |||||||
\(572\) | −1.00000 | + | 1.73205i | −0.0418121 | + | 0.0724207i | ||||
\(573\) | −5.00000 | + | 8.66025i | −0.208878 | + | 0.361787i | ||||
\(574\) | −1.50000 | − | 2.59808i | −0.0626088 | − | 0.108442i | ||||
\(575\) | −0.500000 | + | 0.866025i | −0.0208514 | + | 0.0361158i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 42.0000 | 1.74848 | 0.874241 | − | 0.485491i | \(-0.161359\pi\) | ||||
0.874241 | + | 0.485491i | \(0.161359\pi\) | |||||||
\(578\) | −13.0000 | −0.540729 | ||||||||
\(579\) | 7.00000 | + | 12.1244i | 0.290910 | + | 0.503871i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.0000 | 0.746766 | ||||||||
\(582\) | −8.00000 | −0.331611 | ||||||||
\(583\) | −1.50000 | − | 2.59808i | −0.0621237 | − | 0.107601i | ||||
\(584\) | 6.00000 | − | 10.3923i | 0.248282 | − | 0.430037i | ||||
\(585\) | 1.00000 | + | 1.73205i | 0.0413449 | + | 0.0716115i | ||||
\(586\) | −0.500000 | + | 0.866025i | −0.0206548 | + | 0.0357752i | ||||
\(587\) | 14.0000 | − | 24.2487i | 0.577842 | − | 1.00085i | −0.417885 | − | 0.908500i | \(-0.637228\pi\) |
0.995726 | − | 0.0923513i | \(-0.0294383\pi\) | |||||||
\(588\) | −2.00000 | −0.0824786 | ||||||||
\(589\) | 2.00000 | − | 17.3205i | 0.0824086 | − | 0.713679i | ||||
\(590\) | −12.0000 | −0.494032 | ||||||||
\(591\) | 2.50000 | − | 4.33013i | 0.102836 | − | 0.178118i | ||||
\(592\) | −4.50000 | + | 7.79423i | −0.184949 | + | 0.320341i | ||||
\(593\) | 22.0000 | + | 38.1051i | 0.903432 | + | 1.56479i | 0.823009 | + | 0.568029i | \(0.192294\pi\) |
0.0804231 | + | 0.996761i | \(0.474373\pi\) | |||||||
\(594\) | 0.500000 | − | 0.866025i | 0.0205152 | − | 0.0355335i | ||||
\(595\) | 3.00000 | + | 5.19615i | 0.122988 | + | 0.213021i | ||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | 18.0000 | 0.736691 | ||||||||
\(598\) | −1.00000 | − | 1.73205i | −0.0408930 | − | 0.0708288i | ||||
\(599\) | −17.0000 | − | 29.4449i | −0.694601 | − | 1.20308i | −0.970315 | − | 0.241845i | \(-0.922248\pi\) |
0.275714 | − | 0.961240i | \(-0.411086\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | 25.0000 | 1.01977 | 0.509886 | − | 0.860242i | \(-0.329688\pi\) | ||||
0.509886 | + | 0.860242i | \(0.329688\pi\) | |||||||
\(602\) | 15.0000 | + | 25.9808i | 0.611354 | + | 1.05890i | ||||
\(603\) | 1.00000 | − | 1.73205i | 0.0407231 | − | 0.0705346i | ||||
\(604\) | 9.00000 | + | 15.5885i | 0.366205 | + | 0.634285i | ||||
\(605\) | −5.00000 | + | 8.66025i | −0.203279 | + | 0.352089i | ||||
\(606\) | −1.00000 | + | 1.73205i | −0.0406222 | + | 0.0703598i | ||||
\(607\) | −5.00000 | −0.202944 | −0.101472 | − | 0.994838i | \(-0.532355\pi\) | ||||
−0.101472 | + | 0.994838i | \(0.532355\pi\) | |||||||
\(608\) | −4.00000 | + | 1.73205i | −0.162221 | + | 0.0702439i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.00000 | + | 1.73205i | −0.0404888 | + | 0.0701287i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1.00000 | − | 1.73205i | −0.0404226 | − | 0.0700140i | ||||
\(613\) | 5.50000 | − | 9.52628i | 0.222143 | − | 0.384763i | −0.733316 | − | 0.679888i | \(-0.762028\pi\) |
0.955458 | + | 0.295126i | \(0.0953615\pi\) | |||||||
\(614\) | −8.00000 | − | 13.8564i | −0.322854 | − | 0.559199i | ||||
\(615\) | 1.00000 | 0.0403239 | ||||||||
\(616\) | 3.00000 | 0.120873 | ||||||||
\(617\) | −8.00000 | − | 13.8564i | −0.322068 | − | 0.557838i | 0.658847 | − | 0.752277i | \(-0.271045\pi\) |
−0.980915 | + | 0.194439i | \(0.937711\pi\) | |||||||
\(618\) | −6.50000 | − | 11.2583i | −0.261468 | − | 0.452876i | ||||
\(619\) | 13.0000 | 0.522514 | 0.261257 | − | 0.965269i | \(-0.415863\pi\) | ||||
0.261257 | + | 0.965269i | \(0.415863\pi\) | |||||||
\(620\) | −4.00000 | −0.160644 | ||||||||
\(621\) | 0.500000 | + | 0.866025i | 0.0200643 | + | 0.0347524i | ||||
\(622\) | 8.00000 | − | 13.8564i | 0.320771 | − | 0.555591i | ||||
\(623\) | 7.50000 | + | 12.9904i | 0.300481 | + | 0.520449i | ||||
\(624\) | 1.00000 | − | 1.73205i | 0.0400320 | − | 0.0693375i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.50000 | − | 2.59808i | −0.139777 | − | 0.103757i | ||||
\(628\) | 7.00000 | 0.279330 | ||||||||
\(629\) | −9.00000 | + | 15.5885i | −0.358854 | + | 0.621552i | ||||
\(630\) | 1.50000 | − | 2.59808i | 0.0597614 | − | 0.103510i | ||||
\(631\) | 4.00000 | + | 6.92820i | 0.159237 | + | 0.275807i | 0.934594 | − | 0.355716i | \(-0.115763\pi\) |
−0.775356 | + | 0.631524i | \(0.782430\pi\) | |||||||
\(632\) | −7.00000 | + | 12.1244i | −0.278445 | + | 0.482281i | ||||
\(633\) | 11.5000 | + | 19.9186i | 0.457084 | + | 0.791693i | ||||
\(634\) | 7.00000 | 0.278006 | ||||||||
\(635\) | 1.00000 | 0.0396838 | ||||||||
\(636\) | 1.50000 | + | 2.59808i | 0.0594789 | + | 0.103020i | ||||
\(637\) | −2.00000 | − | 3.46410i | −0.0792429 | − | 0.137253i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.00000 | 0.316475 | ||||||||
\(640\) | 0.500000 | + | 0.866025i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | −21.0000 | + | 36.3731i | −0.829450 | + | 1.43665i | 0.0690201 | + | 0.997615i | \(0.478013\pi\) |
−0.898470 | + | 0.439034i | \(0.855321\pi\) | |||||||
\(642\) | −5.00000 | − | 8.66025i | −0.197334 | − | 0.341793i | ||||
\(643\) | −7.00000 | + | 12.1244i | −0.276053 | + | 0.478138i | −0.970400 | − | 0.241502i | \(-0.922360\pi\) |
0.694347 | + | 0.719640i | \(0.255693\pi\) | |||||||
\(644\) | −1.50000 | + | 2.59808i | −0.0591083 | + | 0.102379i | ||||
\(645\) | −10.0000 | −0.393750 | ||||||||
\(646\) | −8.00000 | + | 3.46410i | −0.314756 | + | 0.136293i | ||||
\(647\) | −39.0000 | −1.53325 | −0.766624 | − | 0.642096i | \(-0.778065\pi\) | ||||
−0.766624 | + | 0.642096i | \(0.778065\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | −6.00000 | + | 10.3923i | −0.235521 | + | 0.407934i | ||||
\(650\) | −1.00000 | − | 1.73205i | −0.0392232 | − | 0.0679366i | ||||
\(651\) | 6.00000 | − | 10.3923i | 0.235159 | − | 0.407307i | ||||
\(652\) | −1.00000 | − | 1.73205i | −0.0391630 | − | 0.0678323i | ||||
\(653\) | 9.00000 | 0.352197 | 0.176099 | − | 0.984373i | \(-0.443652\pi\) | ||||
0.176099 | + | 0.984373i | \(0.443652\pi\) | |||||||
\(654\) | 6.00000 | 0.234619 | ||||||||
\(655\) | 10.5000 | + | 18.1865i | 0.410269 | + | 0.710607i | ||||
\(656\) | −0.500000 | − | 0.866025i | −0.0195217 | − | 0.0338126i | ||||
\(657\) | −12.0000 | −0.468165 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.50000 | + | 12.9904i | 0.292159 | + | 0.506033i | 0.974320 | − | 0.225168i | \(-0.0722932\pi\) |
−0.682161 | + | 0.731202i | \(0.738960\pi\) | |||||||
\(660\) | −0.500000 | + | 0.866025i | −0.0194625 | + | 0.0337100i | ||||
\(661\) | −2.00000 | − | 3.46410i | −0.0777910 | − | 0.134738i | 0.824506 | − | 0.565854i | \(-0.191453\pi\) |
−0.902297 | + | 0.431116i | \(0.858120\pi\) | |||||||
\(662\) | −6.50000 | + | 11.2583i | −0.252630 | + | 0.437567i | ||||
\(663\) | 2.00000 | − | 3.46410i | 0.0776736 | − | 0.134535i | ||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | −10.5000 | − | 7.79423i | −0.407173 | − | 0.302247i | ||||
\(666\) | 9.00000 | 0.348743 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −1.50000 | + | 2.59808i | −0.0580367 | + | 0.100523i | ||||
\(669\) | 1.50000 | + | 2.59808i | 0.0579934 | + | 0.100447i | ||||
\(670\) | −1.00000 | + | 1.73205i | −0.0386334 | + | 0.0669150i | ||||
\(671\) | 1.00000 | + | 1.73205i | 0.0386046 | + | 0.0668651i | ||||
\(672\) | −3.00000 | −0.115728 | ||||||||
\(673\) | 16.0000 | 0.616755 | 0.308377 | − | 0.951264i | \(-0.400214\pi\) | ||||
0.308377 | + | 0.951264i | \(0.400214\pi\) | |||||||
\(674\) | −1.00000 | − | 1.73205i | −0.0385186 | − | 0.0667161i | ||||
\(675\) | 0.500000 | + | 0.866025i | 0.0192450 | + | 0.0333333i | ||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | −39.0000 | −1.49889 | −0.749446 | − | 0.662066i | \(-0.769680\pi\) | ||||
−0.749446 | + | 0.662066i | \(0.769680\pi\) | |||||||
\(678\) | 5.00000 | + | 8.66025i | 0.192024 | + | 0.332595i | ||||
\(679\) | −12.0000 | + | 20.7846i | −0.460518 | + | 0.797640i | ||||
\(680\) | 1.00000 | + | 1.73205i | 0.0383482 | + | 0.0664211i | ||||
\(681\) | 14.0000 | − | 24.2487i | 0.536481 | − | 0.929213i | ||||
\(682\) | −2.00000 | + | 3.46410i | −0.0765840 | + | 0.132647i | ||||
\(683\) | 6.00000 | 0.229584 | 0.114792 | − | 0.993390i | \(-0.463380\pi\) | ||||
0.114792 | + | 0.993390i | \(0.463380\pi\) | |||||||
\(684\) | 3.50000 | + | 2.59808i | 0.133826 | + | 0.0993399i | ||||
\(685\) | −4.00000 | −0.152832 | ||||||||
\(686\) | 7.50000 | − | 12.9904i | 0.286351 | − | 0.495975i | ||||
\(687\) | 7.00000 | − | 12.1244i | 0.267067 | − | 0.462573i | ||||
\(688\) | 5.00000 | + | 8.66025i | 0.190623 | + | 0.330169i | ||||
\(689\) | −3.00000 | + | 5.19615i | −0.114291 | + | 0.197958i | ||||
\(690\) | −0.500000 | − | 0.866025i | −0.0190347 | − | 0.0329690i | ||||
\(691\) | 23.0000 | 0.874961 | 0.437481 | − | 0.899228i | \(-0.355871\pi\) | ||||
0.437481 | + | 0.899228i | \(0.355871\pi\) | |||||||
\(692\) | 11.0000 | 0.418157 | ||||||||
\(693\) | −1.50000 | − | 2.59808i | −0.0569803 | − | 0.0986928i | ||||
\(694\) | −9.00000 | − | 15.5885i | −0.341635 | − | 0.591730i | ||||
\(695\) | 20.0000 | 0.758643 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.00000 | − | 1.73205i | −0.0378777 | − | 0.0656061i | ||||
\(698\) | −13.0000 | + | 22.5167i | −0.492057 | + | 0.852268i | ||||
\(699\) | 3.00000 | + | 5.19615i | 0.113470 | + | 0.196537i | ||||
\(700\) | −1.50000 | + | 2.59808i | −0.0566947 | + | 0.0981981i | ||||
\(701\) | 21.0000 | − | 36.3731i | 0.793159 | − | 1.37379i | −0.130843 | − | 0.991403i | \(-0.541768\pi\) |
0.924002 | − | 0.382389i | \(-0.124898\pi\) | |||||||
\(702\) | −2.00000 | −0.0754851 | ||||||||
\(703\) | 4.50000 | − | 38.9711i | 0.169721 | − | 1.46982i | ||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.0000 | + | 22.5167i | −0.489261 | + | 0.847426i | ||||
\(707\) | 3.00000 | + | 5.19615i | 0.112827 | + | 0.195421i | ||||
\(708\) | 6.00000 | − | 10.3923i | 0.225494 | − | 0.390567i | ||||
\(709\) | −19.0000 | − | 32.9090i | −0.713560 | − | 1.23592i | −0.963512 | − | 0.267664i | \(-0.913748\pi\) |
0.249952 | − | 0.968258i | \(-0.419585\pi\) | |||||||
\(710\) | −8.00000 | −0.300235 | ||||||||
\(711\) | 14.0000 | 0.525041 | ||||||||
\(712\) | 2.50000 | + | 4.33013i | 0.0936915 | + | 0.162278i | ||||
\(713\) | −2.00000 | − | 3.46410i | −0.0749006 | − | 0.129732i | ||||
\(714\) | −6.00000 | −0.224544 | ||||||||
\(715\) | −2.00000 | −0.0747958 | ||||||||
\(716\) | 6.50000 | + | 11.2583i | 0.242916 | + | 0.420744i | ||||
\(717\) | 6.00000 | − | 10.3923i | 0.224074 | − | 0.388108i | ||||
\(718\) | −6.00000 | − | 10.3923i | −0.223918 | − | 0.387837i | ||||
\(719\) | −14.0000 | + | 24.2487i | −0.522112 | + | 0.904324i | 0.477557 | + | 0.878601i | \(0.341522\pi\) |
−0.999669 | + | 0.0257237i | \(0.991811\pi\) | |||||||
\(720\) | 0.500000 | − | 0.866025i | 0.0186339 | − | 0.0322749i | ||||
\(721\) | −39.0000 | −1.45244 | ||||||||
\(722\) | 13.0000 | − | 13.8564i | 0.483810 | − | 0.515682i | ||||
\(723\) | 10.0000 | 0.371904 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.00000 | − | 8.66025i | −0.185567 | − | 0.321412i | ||||
\(727\) | 16.0000 | − | 27.7128i | 0.593407 | − | 1.02781i | −0.400362 | − | 0.916357i | \(-0.631116\pi\) |
0.993770 | − | 0.111454i | \(-0.0355509\pi\) | |||||||
\(728\) | −3.00000 | − | 5.19615i | −0.111187 | − | 0.192582i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 12.0000 | 0.444140 | ||||||||
\(731\) | 10.0000 | + | 17.3205i | 0.369863 | + | 0.640622i | ||||
\(732\) | −1.00000 | − | 1.73205i | −0.0369611 | − | 0.0640184i | ||||
\(733\) | −35.0000 | −1.29275 | −0.646377 | − | 0.763018i | \(-0.723717\pi\) | ||||
−0.646377 | + | 0.763018i | \(0.723717\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.00000 | − | 1.73205i | −0.0368856 | − | 0.0638877i | ||||
\(736\) | −0.500000 | + | 0.866025i | −0.0184302 | + | 0.0319221i | ||||
\(737\) | 1.00000 | + | 1.73205i | 0.0368355 | + | 0.0638009i | ||||
\(738\) | −0.500000 | + | 0.866025i | −0.0184053 | + | 0.0318788i | ||||
\(739\) | −3.50000 | + | 6.06218i | −0.128750 | + | 0.223001i | −0.923192 | − | 0.384338i | \(-0.874430\pi\) |
0.794443 | + | 0.607339i | \(0.207763\pi\) | |||||||
\(740\) | −9.00000 | −0.330847 | ||||||||
\(741\) | −1.00000 | + | 8.66025i | −0.0367359 | + | 0.318142i | ||||
\(742\) | 9.00000 | 0.330400 | ||||||||
\(743\) | 11.5000 | − | 19.9186i | 0.421894 | − | 0.730742i | −0.574231 | − | 0.818694i | \(-0.694699\pi\) |
0.996125 | + | 0.0879516i | \(0.0280321\pi\) | |||||||
\(744\) | 2.00000 | − | 3.46410i | 0.0733236 | − | 0.127000i | ||||
\(745\) | −3.00000 | − | 5.19615i | −0.109911 | − | 0.190372i | ||||
\(746\) | 18.5000 | − | 32.0429i | 0.677333 | − | 1.17318i | ||||
\(747\) | −3.00000 | − | 5.19615i | −0.109764 | − | 0.190117i | ||||
\(748\) | 2.00000 | 0.0731272 | ||||||||
\(749\) | −30.0000 | −1.09618 | ||||||||
\(750\) | −0.500000 | − | 0.866025i | −0.0182574 | − | 0.0316228i | ||||
\(751\) | −16.0000 | − | 27.7128i | −0.583848 | − | 1.01125i | −0.995018 | − | 0.0996961i | \(-0.968213\pi\) |
0.411170 | − | 0.911559i | \(-0.365120\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −28.0000 | −1.02038 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.00000 | + | 15.5885i | −0.327544 | + | 0.567322i | ||||
\(756\) | 1.50000 | + | 2.59808i | 0.0545545 | + | 0.0944911i | ||||
\(757\) | 9.50000 | − | 16.4545i | 0.345283 | − | 0.598048i | −0.640122 | − | 0.768273i | \(-0.721116\pi\) |
0.985405 | + | 0.170225i | \(0.0544495\pi\) | |||||||
\(758\) | −8.00000 | + | 13.8564i | −0.290573 | + | 0.503287i | ||||
\(759\) | −1.00000 | −0.0362977 | ||||||||
\(760\) | −3.50000 | − | 2.59808i | −0.126958 | − | 0.0942421i | ||||
\(761\) | −45.0000 | −1.63125 | −0.815624 | − | 0.578582i | \(-0.803606\pi\) | ||||
−0.815624 | + | 0.578582i | \(0.803606\pi\) | |||||||
\(762\) | −0.500000 | + | 0.866025i | −0.0181131 | + | 0.0313728i | ||||
\(763\) | 9.00000 | − | 15.5885i | 0.325822 | − | 0.564340i | ||||
\(764\) | 5.00000 | + | 8.66025i | 0.180894 | + | 0.313317i | ||||
\(765\) | 1.00000 | − | 1.73205i | 0.0361551 | − | 0.0626224i | ||||
\(766\) | 12.0000 | + | 20.7846i | 0.433578 | + | 0.750978i | ||||
\(767\) | 24.0000 | 0.866590 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −1.00000 | − | 1.73205i | −0.0360609 | − | 0.0624593i | 0.847432 | − | 0.530904i | \(-0.178148\pi\) |
−0.883493 | + | 0.468445i | \(0.844814\pi\) | |||||||
\(770\) | 1.50000 | + | 2.59808i | 0.0540562 | + | 0.0936282i | ||||
\(771\) | −2.00000 | −0.0720282 | ||||||||
\(772\) | 14.0000 | 0.503871 | ||||||||
\(773\) | 22.5000 | + | 38.9711i | 0.809269 | + | 1.40169i | 0.913371 | + | 0.407128i | \(0.133470\pi\) |
−0.104102 | + | 0.994567i | \(0.533197\pi\) | |||||||
\(774\) | 5.00000 | − | 8.66025i | 0.179721 | − | 0.311286i | ||||
\(775\) | −2.00000 | − | 3.46410i | −0.0718421 | − | 0.124434i | ||||
\(776\) | −4.00000 | + | 6.92820i | −0.143592 | + | 0.248708i | ||||
\(777\) | 13.5000 | − | 23.3827i | 0.484310 | − | 0.838849i | ||||
\(778\) | 8.00000 | 0.286814 | ||||||||
\(779\) | 3.50000 | + | 2.59808i | 0.125401 | + | 0.0930857i | ||||
\(780\) | 2.00000 | 0.0716115 | ||||||||
\(781\) | −4.00000 | + | 6.92820i | −0.143131 | + | 0.247911i | ||||
\(782\) | −1.00000 | + | 1.73205i | −0.0357599 | + | 0.0619380i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.00000 | + | 1.73205i | −0.0357143 | + | 0.0618590i | ||||
\(785\) | 3.50000 | + | 6.06218i | 0.124920 | + | 0.216368i | ||||
\(786\) | −21.0000 | −0.749045 | ||||||||
\(787\) | 32.0000 | 1.14068 | 0.570338 | − | 0.821410i | \(-0.306812\pi\) | ||||
0.570338 | + | 0.821410i | \(0.306812\pi\) | |||||||
\(788\) | −2.50000 | − | 4.33013i | −0.0890588 | − | 0.154254i | ||||
\(789\) | −12.5000 | − | 21.6506i | −0.445012 | − | 0.770783i | ||||
\(790\) | −14.0000 | −0.498098 | ||||||||
\(791\) | 30.0000 | 1.06668 | ||||||||
\(792\) | −0.500000 | − | 0.866025i | −0.0177667 | − | 0.0307729i | ||||
\(793\) | 2.00000 | − | 3.46410i | 0.0710221 | − | 0.123014i | ||||
\(794\) | 7.50000 | + | 12.9904i | 0.266165 | + | 0.461011i | ||||
\(795\) | −1.50000 | + | 2.59808i | −0.0531995 | + | 0.0921443i | ||||
\(796\) | 9.00000 | − | 15.5885i | 0.318997 | − | 0.552518i | ||||
\(797\) | 15.0000 | 0.531327 | 0.265664 | − | 0.964066i | \(-0.414409\pi\) | ||||
0.265664 | + | 0.964066i | \(0.414409\pi\) | |||||||
\(798\) | 12.0000 | − | 5.19615i | 0.424795 | − | 0.183942i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.500000 | + | 0.866025i | −0.0176777 | + | 0.0306186i | ||||
\(801\) | 2.50000 | − | 4.33013i | 0.0883332 | − | 0.152998i | ||||
\(802\) | 1.00000 | + | 1.73205i | 0.0353112 | + | 0.0611608i | ||||
\(803\) | 6.00000 | − | 10.3923i | 0.211735 | − | 0.366736i | ||||
\(804\) | −1.00000 | − | 1.73205i | −0.0352673 | − | 0.0610847i | ||||
\(805\) | −3.00000 | −0.105736 | ||||||||
\(806\) | 8.00000 | 0.281788 | ||||||||
\(807\) | −7.00000 | − | 12.1244i | −0.246412 | − | 0.426798i | ||||
\(808\) | 1.00000 | + | 1.73205i | 0.0351799 | + | 0.0609333i | ||||
\(809\) | 34.0000 | 1.19538 | 0.597688 | − | 0.801729i | \(-0.296086\pi\) | ||||
0.597688 | + | 0.801729i | \(0.296086\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 5.50000 | + | 9.52628i | 0.193131 | + | 0.334513i | 0.946286 | − | 0.323330i | \(-0.104802\pi\) |
−0.753155 | + | 0.657843i | \(0.771469\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.00000 | + | 1.73205i | 0.0350715 | + | 0.0607457i | ||||
\(814\) | −4.50000 | + | 7.79423i | −0.157725 | + | 0.273188i | ||||
\(815\) | 1.00000 | − | 1.73205i | 0.0350285 | − | 0.0606711i | ||||
\(816\) | −2.00000 | −0.0700140 | ||||||||
\(817\) | −35.0000 | − | 25.9808i | −1.22449 | − | 0.908952i | ||||
\(818\) | 21.0000 | 0.734248 | ||||||||
\(819\) | −3.00000 | + | 5.19615i | −0.104828 | + | 0.181568i | ||||
\(820\) | 0.500000 | − | 0.866025i | 0.0174608 | − | 0.0302429i | ||||
\(821\) | 5.00000 | + | 8.66025i | 0.174501 | + | 0.302245i | 0.939989 | − | 0.341206i | \(-0.110835\pi\) |
−0.765487 | + | 0.643451i | \(0.777502\pi\) | |||||||
\(822\) | 2.00000 | − | 3.46410i | 0.0697580 | − | 0.120824i | ||||
\(823\) | −2.50000 | − | 4.33013i | −0.0871445 | − | 0.150939i | 0.819159 | − | 0.573567i | \(-0.194441\pi\) |
−0.906303 | + | 0.422628i | \(0.861108\pi\) | |||||||
\(824\) | −13.0000 | −0.452876 | ||||||||
\(825\) | −1.00000 | −0.0348155 | ||||||||
\(826\) | −18.0000 | − | 31.1769i | −0.626300 | − | 1.08478i | ||||
\(827\) | 24.0000 | + | 41.5692i | 0.834562 | + | 1.44550i | 0.894387 | + | 0.447295i | \(0.147612\pi\) |
−0.0598250 | + | 0.998209i | \(0.519054\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | −8.00000 | −0.277851 | −0.138926 | − | 0.990303i | \(-0.544365\pi\) | ||||
−0.138926 | + | 0.990303i | \(0.544365\pi\) | |||||||
\(830\) | 3.00000 | + | 5.19615i | 0.104132 | + | 0.180361i | ||||
\(831\) | 11.0000 | − | 19.0526i | 0.381586 | − | 0.660926i | ||||
\(832\) | −1.00000 | − | 1.73205i | −0.0346688 | − | 0.0600481i | ||||
\(833\) | −2.00000 | + | 3.46410i | −0.0692959 | + | 0.120024i | ||||
\(834\) | −10.0000 | + | 17.3205i | −0.346272 | + | 0.599760i | ||||
\(835\) | −3.00000 | −0.103819 | ||||||||
\(836\) | −4.00000 | + | 1.73205i | −0.138343 | + | 0.0599042i | ||||
\(837\) | −4.00000 | −0.138260 | ||||||||
\(838\) | 7.50000 | − | 12.9904i | 0.259083 | − | 0.448745i | ||||
\(839\) | 15.0000 | − | 25.9808i | 0.517858 | − | 0.896956i | −0.481927 | − | 0.876211i | \(-0.660063\pi\) |
0.999785 | − | 0.0207443i | \(-0.00660359\pi\) | |||||||
\(840\) | −1.50000 | − | 2.59808i | −0.0517549 | − | 0.0896421i | ||||
\(841\) | 14.5000 | − | 25.1147i | 0.500000 | − | 0.866025i | ||||
\(842\) | 11.0000 | + | 19.0526i | 0.379085 | + | 0.656595i | ||||
\(843\) | 21.0000 | 0.723278 | ||||||||
\(844\) | 23.0000 | 0.791693 | ||||||||
\(845\) | −4.50000 | − | 7.79423i | −0.154805 | − | 0.268130i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −30.0000 | −1.03081 | ||||||||
\(848\) | 3.00000 | 0.103020 | ||||||||
\(849\) | 1.00000 | + | 1.73205i | 0.0343199 | + | 0.0594438i | ||||
\(850\) | −1.00000 | + | 1.73205i | −0.0342997 | + | 0.0594089i | ||||
\(851\) | −4.50000 | − | 7.79423i | −0.154258 | − | 0.267183i | ||||
\(852\) | 4.00000 | − | 6.92820i | 0.137038 | − | 0.237356i | ||||
\(853\) | −19.0000 | + | 32.9090i | −0.650548 | + | 1.12678i | 0.332443 | + | 0.943123i | \(0.392127\pi\) |
−0.982990 | + | 0.183658i | \(0.941206\pi\) | |||||||
\(854\) | −6.00000 | −0.205316 | ||||||||
\(855\) | −0.500000 | + | 4.33013i | −0.0170996 | + | 0.148087i | ||||
\(856\) | −10.0000 | −0.341793 | ||||||||
\(857\) | 20.0000 | − | 34.6410i | 0.683187 | − | 1.18331i | −0.290816 | − | 0.956779i | \(-0.593927\pi\) |
0.974003 | − | 0.226536i | \(-0.0727399\pi\) | |||||||
\(858\) | 1.00000 | − | 1.73205i | 0.0341394 | − | 0.0591312i | ||||
\(859\) | 7.50000 | + | 12.9904i | 0.255897 | + | 0.443226i | 0.965139 | − | 0.261739i | \(-0.0842960\pi\) |
−0.709242 | + | 0.704965i | \(0.750963\pi\) | |||||||
\(860\) | −5.00000 | + | 8.66025i | −0.170499 | + | 0.295312i | ||||
\(861\) | 1.50000 | + | 2.59808i | 0.0511199 | + | 0.0885422i | ||||
\(862\) | 38.0000 | 1.29429 | ||||||||
\(863\) | 17.0000 | 0.578687 | 0.289343 | − | 0.957225i | \(-0.406563\pi\) | ||||
0.289343 | + | 0.957225i | \(0.406563\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 5.50000 | + | 9.52628i | 0.187006 | + | 0.323903i | ||||
\(866\) | 16.0000 | 0.543702 | ||||||||
\(867\) | 13.0000 | 0.441503 | ||||||||
\(868\) | −6.00000 | − | 10.3923i | −0.203653 | − | 0.352738i | ||||
\(869\) | −7.00000 | + | 12.1244i | −0.237459 | + | 0.411291i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.00000 | − | 3.46410i | 0.0677674 | − | 0.117377i | ||||
\(872\) | 3.00000 | − | 5.19615i | 0.101593 | − | 0.175964i | ||||
\(873\) | 8.00000 | 0.270759 | ||||||||
\(874\) | 0.500000 | − | 4.33013i | 0.0169128 | − | 0.146469i | ||||
\(875\) | −3.00000 | −0.101419 | ||||||||
\(876\) | −6.00000 | + | 10.3923i | −0.202721 | + | 0.351123i | ||||
\(877\) | 0.500000 | − | 0.866025i | 0.0168838 | − | 0.0292436i | −0.857460 | − | 0.514551i | \(-0.827959\pi\) |
0.874344 | + | 0.485307i | \(0.161292\pi\) | |||||||
\(878\) | −15.0000 | − | 25.9808i | −0.506225 | − | 0.876808i | ||||
\(879\) | 0.500000 | − | 0.866025i | 0.0168646 | − | 0.0292103i | ||||
\(880\) | 0.500000 | + | 0.866025i | 0.0168550 | + | 0.0291937i | ||||
\(881\) | −21.0000 | −0.707508 | −0.353754 | − | 0.935339i | \(-0.615095\pi\) | ||||
−0.353754 | + | 0.935339i | \(0.615095\pi\) | |||||||
\(882\) | 2.00000 | 0.0673435 | ||||||||
\(883\) | −1.00000 | − | 1.73205i | −0.0336527 | − | 0.0582882i | 0.848709 | − | 0.528861i | \(-0.177381\pi\) |
−0.882361 | + | 0.470573i | \(0.844047\pi\) | |||||||
\(884\) | −2.00000 | − | 3.46410i | −0.0672673 | − | 0.116510i | ||||
\(885\) | 12.0000 | 0.403376 | ||||||||
\(886\) | 22.0000 | 0.739104 | ||||||||
\(887\) | 6.00000 | + | 10.3923i | 0.201460 | + | 0.348939i | 0.948999 | − | 0.315279i | \(-0.102098\pi\) |
−0.747539 | + | 0.664218i | \(0.768765\pi\) | |||||||
\(888\) | 4.50000 | − | 7.79423i | 0.151010 | − | 0.261557i | ||||
\(889\) | 1.50000 | + | 2.59808i | 0.0503084 | + | 0.0871367i | ||||
\(890\) | −2.50000 | + | 4.33013i | −0.0838002 | + | 0.145146i | ||||
\(891\) | −0.500000 | + | 0.866025i | −0.0167506 | + | 0.0290129i | ||||
\(892\) | 3.00000 | 0.100447 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 6.00000 | 0.200670 | ||||||||
\(895\) | −6.50000 | + | 11.2583i | −0.217271 | + | 0.376324i | ||||
\(896\) | −1.50000 | + | 2.59808i | −0.0501115 | + | 0.0867956i | ||||
\(897\) | 1.00000 | + | 1.73205i | 0.0333890 | + | 0.0578315i | ||||
\(898\) | 4.50000 | − | 7.79423i | 0.150167 | − | 0.260097i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 6.00000 | 0.199889 | ||||||||
\(902\) | −0.500000 | − | 0.866025i | −0.0166482 | − | 0.0288355i | ||||
\(903\) | −15.0000 | − | 25.9808i | −0.499169 | − | 0.864586i | ||||
\(904\) | 10.0000 | 0.332595 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −9.00000 | − | 15.5885i | −0.299005 | − | 0.517892i | ||||
\(907\) | 13.0000 | − | 22.5167i | 0.431658 | − | 0.747653i | −0.565358 | − | 0.824845i | \(-0.691262\pi\) |
0.997016 | + | 0.0771920i | \(0.0245954\pi\) | |||||||
\(908\) | −14.0000 | − | 24.2487i | −0.464606 | − | 0.804722i | ||||
\(909\) | 1.00000 | − | 1.73205i | 0.0331679 | − | 0.0574485i | ||||
\(910\) | 3.00000 | − | 5.19615i | 0.0994490 | − | 0.172251i | ||||
\(911\) | 6.00000 | 0.198789 | 0.0993944 | − | 0.995048i | \(-0.468309\pi\) | ||||
0.0993944 | + | 0.995048i | \(0.468309\pi\) | |||||||
\(912\) | 4.00000 | − | 1.73205i | 0.132453 | − | 0.0573539i | ||||
\(913\) | 6.00000 | 0.198571 | ||||||||
\(914\) | 9.00000 | − | 15.5885i | 0.297694 | − | 0.515620i | ||||
\(915\) | 1.00000 | − | 1.73205i | 0.0330590 | − | 0.0572598i | ||||
\(916\) | −7.00000 | − | 12.1244i | −0.231287 | − | 0.400600i | ||||
\(917\) | −31.5000 | + | 54.5596i | −1.04022 | + | 1.80172i | ||||
\(918\) | 1.00000 | + | 1.73205i | 0.0330049 | + | 0.0571662i | ||||
\(919\) | 32.0000 | 1.05558 | 0.527791 | − | 0.849374i | \(-0.323020\pi\) | ||||
0.527791 | + | 0.849374i | \(0.323020\pi\) | |||||||
\(920\) | −1.00000 | −0.0329690 | ||||||||
\(921\) | 8.00000 | + | 13.8564i | 0.263609 | + | 0.456584i | ||||
\(922\) | −11.0000 | − | 19.0526i | −0.362266 | − | 0.627463i | ||||
\(923\) | 16.0000 | 0.526646 | ||||||||
\(924\) | −3.00000 | −0.0986928 | ||||||||
\(925\) | −4.50000 | − | 7.79423i | −0.147959 | − | 0.256273i | ||||
\(926\) | 12.5000 | − | 21.6506i | 0.410775 | − | 0.711484i | ||||
\(927\) | 6.50000 | + | 11.2583i | 0.213488 | + | 0.369772i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.5000 | + | 33.7750i | −0.639774 | + | 1.10812i | 0.345708 | + | 0.938342i | \(0.387639\pi\) |
−0.985482 | + | 0.169779i | \(0.945695\pi\) | |||||||
\(930\) | 4.00000 | 0.131165 | ||||||||
\(931\) | 1.00000 | − | 8.66025i | 0.0327737 | − | 0.283828i | ||||
\(932\) | 6.00000 | 0.196537 | ||||||||
\(933\) | −8.00000 | + | 13.8564i | −0.261908 | + | 0.453638i | ||||
\(934\) | −16.0000 | + | 27.7128i | −0.523536 | + | 0.906791i | ||||
\(935\) | 1.00000 | + | 1.73205i | 0.0327035 | + | 0.0566441i | ||||
\(936\) | −1.00000 | + | 1.73205i | −0.0326860 | + | 0.0566139i | ||||
\(937\) | −26.0000 | − | 45.0333i | −0.849383 | − | 1.47117i | −0.881760 | − | 0.471699i | \(-0.843641\pi\) |
0.0323768 | − | 0.999476i | \(-0.489692\pi\) | |||||||
\(938\) | −6.00000 | −0.195907 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.0000 | + | 20.7846i | 0.391189 | + | 0.677559i | 0.992607 | − | 0.121376i | \(-0.0387306\pi\) |
−0.601418 | + | 0.798935i | \(0.705397\pi\) | |||||||
\(942\) | −7.00000 | −0.228072 | ||||||||
\(943\) | 1.00000 | 0.0325645 | ||||||||
\(944\) | −6.00000 | − | 10.3923i | −0.195283 | − | 0.338241i | ||||
\(945\) | −1.50000 | + | 2.59808i | −0.0487950 | + | 0.0845154i | ||||
\(946\) | 5.00000 | + | 8.66025i | 0.162564 | + | 0.281569i | ||||
\(947\) | −5.00000 | + | 8.66025i | −0.162478 | + | 0.281420i | −0.935757 | − | 0.352646i | \(-0.885282\pi\) |
0.773279 | + | 0.634066i | \(0.218615\pi\) | |||||||
\(948\) | 7.00000 | − | 12.1244i | 0.227349 | − | 0.393781i | ||||
\(949\) | −24.0000 | −0.779073 | ||||||||
\(950\) | 0.500000 | − | 4.33013i | 0.0162221 | − | 0.140488i | ||||
\(951\) | −7.00000 | −0.226991 | ||||||||
\(952\) | −3.00000 | + | 5.19615i | −0.0972306 | + | 0.168408i | ||||
\(953\) | 24.0000 | − | 41.5692i | 0.777436 | − | 1.34656i | −0.155979 | − | 0.987760i | \(-0.549853\pi\) |
0.933415 | − | 0.358799i | \(-0.116814\pi\) | |||||||
\(954\) | −1.50000 | − | 2.59808i | −0.0485643 | − | 0.0841158i | ||||
\(955\) | −5.00000 | + | 8.66025i | −0.161796 | + | 0.280239i | ||||
\(956\) | −6.00000 | − | 10.3923i | −0.194054 | − | 0.336111i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 20.0000 | 0.646171 | ||||||||
\(959\) | −6.00000 | − | 10.3923i | −0.193750 | − | 0.335585i | ||||
\(960\) | −0.500000 | − | 0.866025i | −0.0161374 | − | 0.0279508i | ||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 18.0000 | 0.580343 | ||||||||
\(963\) | 5.00000 | + | 8.66025i | 0.161123 | + | 0.279073i | ||||
\(964\) | 5.00000 | − | 8.66025i | 0.161039 | − | 0.278928i | ||||
\(965\) | 7.00000 | + | 12.1244i | 0.225338 | + | 0.390297i | ||||
\(966\) | 1.50000 | − | 2.59808i | 0.0482617 | − | 0.0835917i | ||||
\(967\) | −2.00000 | + | 3.46410i | −0.0643157 | + | 0.111398i | −0.896390 | − | 0.443266i | \(-0.853820\pi\) |
0.832075 | + | 0.554664i | \(0.187153\pi\) | |||||||
\(968\) | −10.0000 | −0.321412 | ||||||||
\(969\) | 8.00000 | − | 3.46410i | 0.256997 | − | 0.111283i | ||||
\(970\) | −8.00000 | −0.256865 | ||||||||
\(971\) | −18.0000 | + | 31.1769i | −0.577647 | + | 1.00051i | 0.418101 | + | 0.908401i | \(0.362696\pi\) |
−0.995748 | + | 0.0921142i | \(0.970638\pi\) | |||||||
\(972\) | 0.500000 | − | 0.866025i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | 30.0000 | + | 51.9615i | 0.961756 | + | 1.66581i | ||||
\(974\) | 20.5000 | − | 35.5070i | 0.656862 | − | 1.13772i | ||||
\(975\) | 1.00000 | + | 1.73205i | 0.0320256 | + | 0.0554700i | ||||
\(976\) | −2.00000 | −0.0640184 | ||||||||
\(977\) | 8.00000 | 0.255943 | 0.127971 | − | 0.991778i | \(-0.459153\pi\) | ||||
0.127971 | + | 0.991778i | \(0.459153\pi\) | |||||||
\(978\) | 1.00000 | + | 1.73205i | 0.0319765 | + | 0.0553849i | ||||
\(979\) | 2.50000 | + | 4.33013i | 0.0799003 | + | 0.138391i | ||||
\(980\) | −2.00000 | −0.0638877 | ||||||||
\(981\) | −6.00000 | −0.191565 | ||||||||
\(982\) | 16.5000 | + | 28.5788i | 0.526536 | + | 0.911987i | ||||
\(983\) | −20.5000 | + | 35.5070i | −0.653848 | + | 1.13250i | 0.328333 | + | 0.944562i | \(0.393513\pi\) |
−0.982181 | + | 0.187937i | \(0.939820\pi\) | |||||||
\(984\) | 0.500000 | + | 0.866025i | 0.0159394 | + | 0.0276079i | ||||
\(985\) | 2.50000 | − | 4.33013i | 0.0796566 | − | 0.137969i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.00000 | + | 5.19615i | 0.222700 | + | 0.165312i | ||||
\(989\) | −10.0000 | −0.317982 | ||||||||
\(990\) | 0.500000 | − | 0.866025i | 0.0158910 | − | 0.0275241i | ||||
\(991\) | 10.0000 | − | 17.3205i | 0.317660 | − | 0.550204i | −0.662339 | − | 0.749204i | \(-0.730436\pi\) |
0.979999 | + | 0.199000i | \(0.0637695\pi\) | |||||||
\(992\) | −2.00000 | − | 3.46410i | −0.0635001 | − | 0.109985i | ||||
\(993\) | 6.50000 | − | 11.2583i | 0.206271 | − | 0.357272i | ||||
\(994\) | −12.0000 | − | 20.7846i | −0.380617 | − | 0.659248i | ||||
\(995\) | 18.0000 | 0.570638 | ||||||||
\(996\) | −6.00000 | −0.190117 | ||||||||
\(997\) | 6.50000 | + | 11.2583i | 0.205857 | + | 0.356555i | 0.950405 | − | 0.311014i | \(-0.100668\pi\) |
−0.744548 | + | 0.667568i | \(0.767335\pi\) | |||||||
\(998\) | −7.50000 | − | 12.9904i | −0.237408 | − | 0.411203i | ||||
\(999\) | −9.00000 | −0.284747 |
(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 | 570.2.i.c.391.1 | yes | 2 | |
3.2 | odd | 2 | 1710.2.l.i.1531.1 | 2 | |||
19.7 | even | 3 | inner | 570.2.i.c.121.1 | ✓ | 2 | |
57.26 | odd | 6 | 1710.2.l.i.1261.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.i.c.121.1 | ✓ | 2 | 19.7 | even | 3 | inner | |
570.2.i.c.391.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1710.2.l.i.1261.1 | 2 | 57.26 | odd | 6 | |||
1710.2.l.i.1531.1 | 2 | 3.2 | odd | 2 |