Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(211,546)]
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, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.l (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: | \(4.35983195036\) |
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 | 211.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.211 |
Dual form | 546.2.l.h.295.1 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 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 | ||||
\(5\) | 4.00000 | 1.78885 | 0.894427 | − | 0.447214i | \(-0.147584\pi\) | ||||
0.894427 | + | 0.447214i | \(0.147584\pi\) | |||||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 2.00000 | + | 3.46410i | 0.632456 | + | 1.09545i | ||||
\(11\) | 1.50000 | + | 2.59808i | 0.452267 | + | 0.783349i | 0.998526 | − | 0.0542666i | \(-0.0172821\pi\) |
−0.546259 | + | 0.837616i | \(0.683949\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −2.50000 | − | 2.59808i | −0.693375 | − | 0.720577i | ||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 2.00000 | + | 3.46410i | 0.516398 | + | 0.894427i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.50000 | − | 4.33013i | 0.606339 | − | 1.05021i | −0.385499 | − | 0.922708i | \(-0.625971\pi\) |
0.991838 | − | 0.127502i | \(-0.0406959\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.50000 | + | 2.59808i | −0.344124 | + | 0.596040i | −0.985194 | − | 0.171442i | \(-0.945157\pi\) |
0.641071 | + | 0.767482i | \(0.278491\pi\) | |||||||
\(20\) | −2.00000 | + | 3.46410i | −0.447214 | + | 0.774597i | ||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −1.50000 | + | 2.59808i | −0.319801 | + | 0.553912i | ||||
\(23\) | −3.00000 | − | 5.19615i | −0.625543 | − | 1.08347i | −0.988436 | − | 0.151642i | \(-0.951544\pi\) |
0.362892 | − | 0.931831i | \(-0.381789\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 11.0000 | 2.20000 | ||||||||
\(26\) | 1.00000 | − | 3.46410i | 0.196116 | − | 0.679366i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.500000 | − | 0.866025i | −0.0944911 | − | 0.163663i | ||||
\(29\) | 4.50000 | + | 7.79423i | 0.835629 | + | 1.44735i | 0.893517 | + | 0.449029i | \(0.148230\pi\) |
−0.0578882 | + | 0.998323i | \(0.518437\pi\) | |||||||
\(30\) | −2.00000 | + | 3.46410i | −0.365148 | + | 0.632456i | ||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −1.50000 | + | 2.59808i | −0.261116 | + | 0.452267i | ||||
\(34\) | 5.00000 | 0.857493 | ||||||||
\(35\) | −2.00000 | + | 3.46410i | −0.338062 | + | 0.585540i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | −2.00000 | − | 3.46410i | −0.328798 | − | 0.569495i | 0.653476 | − | 0.756948i | \(-0.273310\pi\) |
−0.982274 | + | 0.187453i | \(0.939977\pi\) | |||||||
\(38\) | −3.00000 | −0.486664 | ||||||||
\(39\) | 1.00000 | − | 3.46410i | 0.160128 | − | 0.554700i | ||||
\(40\) | −4.00000 | −0.632456 | ||||||||
\(41\) | −2.50000 | − | 4.33013i | −0.390434 | − | 0.676252i | 0.602072 | − | 0.798441i | \(-0.294342\pi\) |
−0.992507 | + | 0.122189i | \(0.961009\pi\) | |||||||
\(42\) | −0.500000 | − | 0.866025i | −0.0771517 | − | 0.133631i | ||||
\(43\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(44\) | −3.00000 | −0.452267 | ||||||||
\(45\) | −2.00000 | + | 3.46410i | −0.298142 | + | 0.516398i | ||||
\(46\) | 3.00000 | − | 5.19615i | 0.442326 | − | 0.766131i | ||||
\(47\) | −3.00000 | −0.437595 | −0.218797 | − | 0.975770i | \(-0.570213\pi\) | ||||
−0.218797 | + | 0.975770i | \(0.570213\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 5.50000 | + | 9.52628i | 0.777817 | + | 1.34722i | ||||
\(51\) | 5.00000 | 0.700140 | ||||||||
\(52\) | 3.50000 | − | 0.866025i | 0.485363 | − | 0.120096i | ||||
\(53\) | −11.0000 | −1.51097 | −0.755483 | − | 0.655168i | \(-0.772598\pi\) | ||||
−0.755483 | + | 0.655168i | \(0.772598\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | 6.00000 | + | 10.3923i | 0.809040 | + | 1.40130i | ||||
\(56\) | 0.500000 | − | 0.866025i | 0.0668153 | − | 0.115728i | ||||
\(57\) | −3.00000 | −0.397360 | ||||||||
\(58\) | −4.50000 | + | 7.79423i | −0.590879 | + | 1.02343i | ||||
\(59\) | −1.00000 | + | 1.73205i | −0.130189 | + | 0.225494i | −0.923749 | − | 0.382998i | \(-0.874892\pi\) |
0.793560 | + | 0.608492i | \(0.208225\pi\) | |||||||
\(60\) | −4.00000 | −0.516398 | ||||||||
\(61\) | 0.500000 | − | 0.866025i | 0.0640184 | − | 0.110883i | −0.832240 | − | 0.554416i | \(-0.812942\pi\) |
0.896258 | + | 0.443533i | \(0.146275\pi\) | |||||||
\(62\) | −2.00000 | − | 3.46410i | −0.254000 | − | 0.439941i | ||||
\(63\) | −0.500000 | − | 0.866025i | −0.0629941 | − | 0.109109i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −10.0000 | − | 10.3923i | −1.24035 | − | 1.28901i | ||||
\(66\) | −3.00000 | −0.369274 | ||||||||
\(67\) | −1.00000 | − | 1.73205i | −0.122169 | − | 0.211604i | 0.798454 | − | 0.602056i | \(-0.205652\pi\) |
−0.920623 | + | 0.390453i | \(0.872318\pi\) | |||||||
\(68\) | 2.50000 | + | 4.33013i | 0.303170 | + | 0.525105i | ||||
\(69\) | 3.00000 | − | 5.19615i | 0.361158 | − | 0.625543i | ||||
\(70\) | −4.00000 | −0.478091 | ||||||||
\(71\) | −3.00000 | + | 5.19615i | −0.356034 | + | 0.616670i | −0.987294 | − | 0.158901i | \(-0.949205\pi\) |
0.631260 | + | 0.775571i | \(0.282538\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 12.0000 | 1.40449 | 0.702247 | − | 0.711934i | \(-0.252180\pi\) | ||||
0.702247 | + | 0.711934i | \(0.252180\pi\) | |||||||
\(74\) | 2.00000 | − | 3.46410i | 0.232495 | − | 0.402694i | ||||
\(75\) | 5.50000 | + | 9.52628i | 0.635085 | + | 1.10000i | ||||
\(76\) | −1.50000 | − | 2.59808i | −0.172062 | − | 0.298020i | ||||
\(77\) | −3.00000 | −0.341882 | ||||||||
\(78\) | 3.50000 | − | 0.866025i | 0.396297 | − | 0.0980581i | ||||
\(79\) | 11.0000 | 1.23760 | 0.618798 | − | 0.785550i | \(-0.287620\pi\) | ||||
0.618798 | + | 0.785550i | \(0.287620\pi\) | |||||||
\(80\) | −2.00000 | − | 3.46410i | −0.223607 | − | 0.387298i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 2.50000 | − | 4.33013i | 0.276079 | − | 0.478183i | ||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | 0.500000 | − | 0.866025i | 0.0545545 | − | 0.0944911i | ||||
\(85\) | 10.0000 | − | 17.3205i | 1.08465 | − | 1.87867i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.50000 | + | 7.79423i | −0.482451 | + | 0.835629i | ||||
\(88\) | −1.50000 | − | 2.59808i | −0.159901 | − | 0.276956i | ||||
\(89\) | −3.50000 | − | 6.06218i | −0.370999 | − | 0.642590i | 0.618720 | − | 0.785611i | \(-0.287651\pi\) |
−0.989720 | + | 0.143022i | \(0.954318\pi\) | |||||||
\(90\) | −4.00000 | −0.421637 | ||||||||
\(91\) | 3.50000 | − | 0.866025i | 0.366900 | − | 0.0907841i | ||||
\(92\) | 6.00000 | 0.625543 | ||||||||
\(93\) | −2.00000 | − | 3.46410i | −0.207390 | − | 0.359211i | ||||
\(94\) | −1.50000 | − | 2.59808i | −0.154713 | − | 0.267971i | ||||
\(95\) | −6.00000 | + | 10.3923i | −0.615587 | + | 1.06623i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 6.00000 | − | 10.3923i | 0.609208 | − | 1.05518i | −0.382164 | − | 0.924095i | \(-0.624821\pi\) |
0.991371 | − | 0.131084i | \(-0.0418458\pi\) | |||||||
\(98\) | 0.500000 | − | 0.866025i | 0.0505076 | − | 0.0874818i | ||||
\(99\) | −3.00000 | −0.301511 | ||||||||
\(100\) | −5.50000 | + | 9.52628i | −0.550000 | + | 0.952628i | ||||
\(101\) | −5.00000 | − | 8.66025i | −0.497519 | − | 0.861727i | 0.502477 | − | 0.864590i | \(-0.332422\pi\) |
−0.999996 | + | 0.00286291i | \(0.999089\pi\) | |||||||
\(102\) | 2.50000 | + | 4.33013i | 0.247537 | + | 0.428746i | ||||
\(103\) | 20.0000 | 1.97066 | 0.985329 | − | 0.170664i | \(-0.0545913\pi\) | ||||
0.985329 | + | 0.170664i | \(0.0545913\pi\) | |||||||
\(104\) | 2.50000 | + | 2.59808i | 0.245145 | + | 0.254762i | ||||
\(105\) | −4.00000 | −0.390360 | ||||||||
\(106\) | −5.50000 | − | 9.52628i | −0.534207 | − | 0.925274i | ||||
\(107\) | −8.50000 | − | 14.7224i | −0.821726 | − | 1.42327i | −0.904396 | − | 0.426694i | \(-0.859678\pi\) |
0.0826699 | − | 0.996577i | \(-0.473655\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | −6.00000 | + | 10.3923i | −0.572078 | + | 0.990867i | ||||
\(111\) | 2.00000 | − | 3.46410i | 0.189832 | − | 0.328798i | ||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −6.00000 | + | 10.3923i | −0.564433 | + | 0.977626i | 0.432670 | + | 0.901553i | \(0.357572\pi\) |
−0.997102 | + | 0.0760733i | \(0.975762\pi\) | |||||||
\(114\) | −1.50000 | − | 2.59808i | −0.140488 | − | 0.243332i | ||||
\(115\) | −12.0000 | − | 20.7846i | −1.11901 | − | 1.93817i | ||||
\(116\) | −9.00000 | −0.835629 | ||||||||
\(117\) | 3.50000 | − | 0.866025i | 0.323575 | − | 0.0800641i | ||||
\(118\) | −2.00000 | −0.184115 | ||||||||
\(119\) | 2.50000 | + | 4.33013i | 0.229175 | + | 0.396942i | ||||
\(120\) | −2.00000 | − | 3.46410i | −0.182574 | − | 0.316228i | ||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 1.00000 | 0.0905357 | ||||||||
\(123\) | 2.50000 | − | 4.33013i | 0.225417 | − | 0.390434i | ||||
\(124\) | 2.00000 | − | 3.46410i | 0.179605 | − | 0.311086i | ||||
\(125\) | 24.0000 | 2.14663 | ||||||||
\(126\) | 0.500000 | − | 0.866025i | 0.0445435 | − | 0.0771517i | ||||
\(127\) | −4.00000 | − | 6.92820i | −0.354943 | − | 0.614779i | 0.632166 | − | 0.774833i | \(-0.282166\pi\) |
−0.987108 | + | 0.160055i | \(0.948833\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.00000 | − | 13.8564i | 0.350823 | − | 1.21529i | ||||
\(131\) | 12.0000 | 1.04844 | 0.524222 | − | 0.851581i | \(-0.324356\pi\) | ||||
0.524222 | + | 0.851581i | \(0.324356\pi\) | |||||||
\(132\) | −1.50000 | − | 2.59808i | −0.130558 | − | 0.226134i | ||||
\(133\) | −1.50000 | − | 2.59808i | −0.130066 | − | 0.225282i | ||||
\(134\) | 1.00000 | − | 1.73205i | 0.0863868 | − | 0.149626i | ||||
\(135\) | −4.00000 | −0.344265 | ||||||||
\(136\) | −2.50000 | + | 4.33013i | −0.214373 | + | 0.371305i | ||||
\(137\) | 9.00000 | − | 15.5885i | 0.768922 | − | 1.33181i | −0.169226 | − | 0.985577i | \(-0.554127\pi\) |
0.938148 | − | 0.346235i | \(-0.112540\pi\) | |||||||
\(138\) | 6.00000 | 0.510754 | ||||||||
\(139\) | −6.50000 | + | 11.2583i | −0.551323 | + | 0.954919i | 0.446857 | + | 0.894606i | \(0.352543\pi\) |
−0.998179 | + | 0.0603135i | \(0.980790\pi\) | |||||||
\(140\) | −2.00000 | − | 3.46410i | −0.169031 | − | 0.292770i | ||||
\(141\) | −1.50000 | − | 2.59808i | −0.126323 | − | 0.218797i | ||||
\(142\) | −6.00000 | −0.503509 | ||||||||
\(143\) | 3.00000 | − | 10.3923i | 0.250873 | − | 0.869048i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 18.0000 | + | 31.1769i | 1.49482 | + | 2.58910i | ||||
\(146\) | 6.00000 | + | 10.3923i | 0.496564 | + | 0.860073i | ||||
\(147\) | 0.500000 | − | 0.866025i | 0.0412393 | − | 0.0714286i | ||||
\(148\) | 4.00000 | 0.328798 | ||||||||
\(149\) | −9.00000 | + | 15.5885i | −0.737309 | + | 1.27706i | 0.216394 | + | 0.976306i | \(0.430570\pi\) |
−0.953703 | + | 0.300750i | \(0.902763\pi\) | |||||||
\(150\) | −5.50000 | + | 9.52628i | −0.449073 | + | 0.777817i | ||||
\(151\) | −11.0000 | −0.895167 | −0.447584 | − | 0.894242i | \(-0.647715\pi\) | ||||
−0.447584 | + | 0.894242i | \(0.647715\pi\) | |||||||
\(152\) | 1.50000 | − | 2.59808i | 0.121666 | − | 0.210732i | ||||
\(153\) | 2.50000 | + | 4.33013i | 0.202113 | + | 0.350070i | ||||
\(154\) | −1.50000 | − | 2.59808i | −0.120873 | − | 0.209359i | ||||
\(155\) | −16.0000 | −1.28515 | ||||||||
\(156\) | 2.50000 | + | 2.59808i | 0.200160 | + | 0.208013i | ||||
\(157\) | −2.00000 | −0.159617 | −0.0798087 | − | 0.996810i | \(-0.525431\pi\) | ||||
−0.0798087 | + | 0.996810i | \(0.525431\pi\) | |||||||
\(158\) | 5.50000 | + | 9.52628i | 0.437557 | + | 0.757870i | ||||
\(159\) | −5.50000 | − | 9.52628i | −0.436178 | − | 0.755483i | ||||
\(160\) | 2.00000 | − | 3.46410i | 0.158114 | − | 0.273861i | ||||
\(161\) | 6.00000 | 0.472866 | ||||||||
\(162\) | 0.500000 | − | 0.866025i | 0.0392837 | − | 0.0680414i | ||||
\(163\) | −10.0000 | + | 17.3205i | −0.783260 | + | 1.35665i | 0.146772 | + | 0.989170i | \(0.453112\pi\) |
−0.930033 | + | 0.367477i | \(0.880222\pi\) | |||||||
\(164\) | 5.00000 | 0.390434 | ||||||||
\(165\) | −6.00000 | + | 10.3923i | −0.467099 | + | 0.809040i | ||||
\(166\) | 3.00000 | + | 5.19615i | 0.232845 | + | 0.403300i | ||||
\(167\) | 8.00000 | + | 13.8564i | 0.619059 | + | 1.07224i | 0.989658 | + | 0.143448i | \(0.0458190\pi\) |
−0.370599 | + | 0.928793i | \(0.620848\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | −0.500000 | + | 12.9904i | −0.0384615 | + | 0.999260i | ||||
\(170\) | 20.0000 | 1.53393 | ||||||||
\(171\) | −1.50000 | − | 2.59808i | −0.114708 | − | 0.198680i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.00000 | − | 1.73205i | 0.0760286 | − | 0.131685i | −0.825505 | − | 0.564396i | \(-0.809109\pi\) |
0.901533 | + | 0.432710i | \(0.142443\pi\) | |||||||
\(174\) | −9.00000 | −0.682288 | ||||||||
\(175\) | −5.50000 | + | 9.52628i | −0.415761 | + | 0.720119i | ||||
\(176\) | 1.50000 | − | 2.59808i | 0.113067 | − | 0.195837i | ||||
\(177\) | −2.00000 | −0.150329 | ||||||||
\(178\) | 3.50000 | − | 6.06218i | 0.262336 | − | 0.454379i | ||||
\(179\) | −12.0000 | − | 20.7846i | −0.896922 | − | 1.55351i | −0.831408 | − | 0.555663i | \(-0.812464\pi\) |
−0.0655145 | − | 0.997852i | \(-0.520869\pi\) | |||||||
\(180\) | −2.00000 | − | 3.46410i | −0.149071 | − | 0.258199i | ||||
\(181\) | −5.00000 | −0.371647 | −0.185824 | − | 0.982583i | \(-0.559495\pi\) | ||||
−0.185824 | + | 0.982583i | \(0.559495\pi\) | |||||||
\(182\) | 2.50000 | + | 2.59808i | 0.185312 | + | 0.192582i | ||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | 3.00000 | + | 5.19615i | 0.221163 | + | 0.383065i | ||||
\(185\) | −8.00000 | − | 13.8564i | −0.588172 | − | 1.01874i | ||||
\(186\) | 2.00000 | − | 3.46410i | 0.146647 | − | 0.254000i | ||||
\(187\) | 15.0000 | 1.09691 | ||||||||
\(188\) | 1.50000 | − | 2.59808i | 0.109399 | − | 0.189484i | ||||
\(189\) | 0.500000 | − | 0.866025i | 0.0363696 | − | 0.0629941i | ||||
\(190\) | −12.0000 | −0.870572 | ||||||||
\(191\) | 3.00000 | − | 5.19615i | 0.217072 | − | 0.375980i | −0.736839 | − | 0.676068i | \(-0.763683\pi\) |
0.953912 | + | 0.300088i | \(0.0970159\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | −6.50000 | − | 11.2583i | −0.467880 | − | 0.810392i | 0.531446 | − | 0.847092i | \(-0.321649\pi\) |
−0.999326 | + | 0.0366998i | \(0.988315\pi\) | |||||||
\(194\) | 12.0000 | 0.861550 | ||||||||
\(195\) | 4.00000 | − | 13.8564i | 0.286446 | − | 0.992278i | ||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 9.50000 | + | 16.4545i | 0.676847 | + | 1.17233i | 0.975925 | + | 0.218105i | \(0.0699875\pi\) |
−0.299078 | + | 0.954229i | \(0.596679\pi\) | |||||||
\(198\) | −1.50000 | − | 2.59808i | −0.106600 | − | 0.184637i | ||||
\(199\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(200\) | −11.0000 | −0.777817 | ||||||||
\(201\) | 1.00000 | − | 1.73205i | 0.0705346 | − | 0.122169i | ||||
\(202\) | 5.00000 | − | 8.66025i | 0.351799 | − | 0.609333i | ||||
\(203\) | −9.00000 | −0.631676 | ||||||||
\(204\) | −2.50000 | + | 4.33013i | −0.175035 | + | 0.303170i | ||||
\(205\) | −10.0000 | − | 17.3205i | −0.698430 | − | 1.20972i | ||||
\(206\) | 10.0000 | + | 17.3205i | 0.696733 | + | 1.20678i | ||||
\(207\) | 6.00000 | 0.417029 | ||||||||
\(208\) | −1.00000 | + | 3.46410i | −0.0693375 | + | 0.240192i | ||||
\(209\) | −9.00000 | −0.622543 | ||||||||
\(210\) | −2.00000 | − | 3.46410i | −0.138013 | − | 0.239046i | ||||
\(211\) | −7.00000 | − | 12.1244i | −0.481900 | − | 0.834675i | 0.517884 | − | 0.855451i | \(-0.326720\pi\) |
−0.999784 | + | 0.0207756i | \(0.993386\pi\) | |||||||
\(212\) | 5.50000 | − | 9.52628i | 0.377742 | − | 0.654268i | ||||
\(213\) | −6.00000 | −0.411113 | ||||||||
\(214\) | 8.50000 | − | 14.7224i | 0.581048 | − | 1.00640i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 2.00000 | − | 3.46410i | 0.135769 | − | 0.235159i | ||||
\(218\) | −1.00000 | − | 1.73205i | −0.0677285 | − | 0.117309i | ||||
\(219\) | 6.00000 | + | 10.3923i | 0.405442 | + | 0.702247i | ||||
\(220\) | −12.0000 | −0.809040 | ||||||||
\(221\) | −17.5000 | + | 4.33013i | −1.17718 | + | 0.291276i | ||||
\(222\) | 4.00000 | 0.268462 | ||||||||
\(223\) | 8.00000 | + | 13.8564i | 0.535720 | + | 0.927894i | 0.999128 | + | 0.0417488i | \(0.0132929\pi\) |
−0.463409 | + | 0.886145i | \(0.653374\pi\) | |||||||
\(224\) | 0.500000 | + | 0.866025i | 0.0334077 | + | 0.0578638i | ||||
\(225\) | −5.50000 | + | 9.52628i | −0.366667 | + | 0.635085i | ||||
\(226\) | −12.0000 | −0.798228 | ||||||||
\(227\) | −7.00000 | + | 12.1244i | −0.464606 | + | 0.804722i | −0.999184 | − | 0.0403978i | \(-0.987137\pi\) |
0.534577 | + | 0.845120i | \(0.320471\pi\) | |||||||
\(228\) | 1.50000 | − | 2.59808i | 0.0993399 | − | 0.172062i | ||||
\(229\) | −5.00000 | −0.330409 | −0.165205 | − | 0.986259i | \(-0.552828\pi\) | ||||
−0.165205 | + | 0.986259i | \(0.552828\pi\) | |||||||
\(230\) | 12.0000 | − | 20.7846i | 0.791257 | − | 1.37050i | ||||
\(231\) | −1.50000 | − | 2.59808i | −0.0986928 | − | 0.170941i | ||||
\(232\) | −4.50000 | − | 7.79423i | −0.295439 | − | 0.511716i | ||||
\(233\) | 4.00000 | 0.262049 | 0.131024 | − | 0.991379i | \(-0.458173\pi\) | ||||
0.131024 | + | 0.991379i | \(0.458173\pi\) | |||||||
\(234\) | 2.50000 | + | 2.59808i | 0.163430 | + | 0.169842i | ||||
\(235\) | −12.0000 | −0.782794 | ||||||||
\(236\) | −1.00000 | − | 1.73205i | −0.0650945 | − | 0.112747i | ||||
\(237\) | 5.50000 | + | 9.52628i | 0.357263 | + | 0.618798i | ||||
\(238\) | −2.50000 | + | 4.33013i | −0.162051 | + | 0.280680i | ||||
\(239\) | −26.0000 | −1.68180 | −0.840900 | − | 0.541190i | \(-0.817974\pi\) | ||||
−0.840900 | + | 0.541190i | \(0.817974\pi\) | |||||||
\(240\) | 2.00000 | − | 3.46410i | 0.129099 | − | 0.223607i | ||||
\(241\) | −6.00000 | + | 10.3923i | −0.386494 | + | 0.669427i | −0.991975 | − | 0.126432i | \(-0.959647\pi\) |
0.605481 | + | 0.795860i | \(0.292981\pi\) | |||||||
\(242\) | 2.00000 | 0.128565 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0.500000 | + | 0.866025i | 0.0320092 | + | 0.0554416i | ||||
\(245\) | −2.00000 | − | 3.46410i | −0.127775 | − | 0.221313i | ||||
\(246\) | 5.00000 | 0.318788 | ||||||||
\(247\) | 10.5000 | − | 2.59808i | 0.668099 | − | 0.165312i | ||||
\(248\) | 4.00000 | 0.254000 | ||||||||
\(249\) | 3.00000 | + | 5.19615i | 0.190117 | + | 0.329293i | ||||
\(250\) | 12.0000 | + | 20.7846i | 0.758947 | + | 1.31453i | ||||
\(251\) | −7.00000 | + | 12.1244i | −0.441836 | + | 0.765283i | −0.997826 | − | 0.0659066i | \(-0.979006\pi\) |
0.555990 | + | 0.831189i | \(0.312339\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | 9.00000 | − | 15.5885i | 0.565825 | − | 0.980038i | ||||
\(254\) | 4.00000 | − | 6.92820i | 0.250982 | − | 0.434714i | ||||
\(255\) | 20.0000 | 1.25245 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −3.50000 | − | 6.06218i | −0.218324 | − | 0.378148i | 0.735972 | − | 0.677012i | \(-0.236726\pi\) |
−0.954296 | + | 0.298864i | \(0.903392\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000 | 0.248548 | ||||||||
\(260\) | 14.0000 | − | 3.46410i | 0.868243 | − | 0.214834i | ||||
\(261\) | −9.00000 | −0.557086 | ||||||||
\(262\) | 6.00000 | + | 10.3923i | 0.370681 | + | 0.642039i | ||||
\(263\) | 13.0000 | + | 22.5167i | 0.801614 | + | 1.38844i | 0.918553 | + | 0.395298i | \(0.129359\pi\) |
−0.116939 | + | 0.993139i | \(0.537308\pi\) | |||||||
\(264\) | 1.50000 | − | 2.59808i | 0.0923186 | − | 0.159901i | ||||
\(265\) | −44.0000 | −2.70290 | ||||||||
\(266\) | 1.50000 | − | 2.59808i | 0.0919709 | − | 0.159298i | ||||
\(267\) | 3.50000 | − | 6.06218i | 0.214197 | − | 0.370999i | ||||
\(268\) | 2.00000 | 0.122169 | ||||||||
\(269\) | 12.0000 | − | 20.7846i | 0.731653 | − | 1.26726i | −0.224523 | − | 0.974469i | \(-0.572083\pi\) |
0.956176 | − | 0.292791i | \(-0.0945841\pi\) | |||||||
\(270\) | −2.00000 | − | 3.46410i | −0.121716 | − | 0.210819i | ||||
\(271\) | 6.00000 | + | 10.3923i | 0.364474 | + | 0.631288i | 0.988692 | − | 0.149963i | \(-0.0479155\pi\) |
−0.624218 | + | 0.781251i | \(0.714582\pi\) | |||||||
\(272\) | −5.00000 | −0.303170 | ||||||||
\(273\) | 2.50000 | + | 2.59808i | 0.151307 | + | 0.157243i | ||||
\(274\) | 18.0000 | 1.08742 | ||||||||
\(275\) | 16.5000 | + | 28.5788i | 0.994987 | + | 1.72337i | ||||
\(276\) | 3.00000 | + | 5.19615i | 0.180579 | + | 0.312772i | ||||
\(277\) | −7.00000 | + | 12.1244i | −0.420589 | + | 0.728482i | −0.995997 | − | 0.0893846i | \(-0.971510\pi\) |
0.575408 | + | 0.817867i | \(0.304843\pi\) | |||||||
\(278\) | −13.0000 | −0.779688 | ||||||||
\(279\) | 2.00000 | − | 3.46410i | 0.119737 | − | 0.207390i | ||||
\(280\) | 2.00000 | − | 3.46410i | 0.119523 | − | 0.207020i | ||||
\(281\) | 30.0000 | 1.78965 | 0.894825 | − | 0.446417i | \(-0.147300\pi\) | ||||
0.894825 | + | 0.446417i | \(0.147300\pi\) | |||||||
\(282\) | 1.50000 | − | 2.59808i | 0.0893237 | − | 0.154713i | ||||
\(283\) | 2.00000 | + | 3.46410i | 0.118888 | + | 0.205919i | 0.919327 | − | 0.393494i | \(-0.128734\pi\) |
−0.800439 | + | 0.599414i | \(0.795400\pi\) | |||||||
\(284\) | −3.00000 | − | 5.19615i | −0.178017 | − | 0.308335i | ||||
\(285\) | −12.0000 | −0.710819 | ||||||||
\(286\) | 10.5000 | − | 2.59808i | 0.620878 | − | 0.153627i | ||||
\(287\) | 5.00000 | 0.295141 | ||||||||
\(288\) | 0.500000 | + | 0.866025i | 0.0294628 | + | 0.0510310i | ||||
\(289\) | −4.00000 | − | 6.92820i | −0.235294 | − | 0.407541i | ||||
\(290\) | −18.0000 | + | 31.1769i | −1.05700 | + | 1.83077i | ||||
\(291\) | 12.0000 | 0.703452 | ||||||||
\(292\) | −6.00000 | + | 10.3923i | −0.351123 | + | 0.608164i | ||||
\(293\) | −12.0000 | + | 20.7846i | −0.701047 | + | 1.21425i | 0.267052 | + | 0.963682i | \(0.413951\pi\) |
−0.968099 | + | 0.250568i | \(0.919383\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | −4.00000 | + | 6.92820i | −0.232889 | + | 0.403376i | ||||
\(296\) | 2.00000 | + | 3.46410i | 0.116248 | + | 0.201347i | ||||
\(297\) | −1.50000 | − | 2.59808i | −0.0870388 | − | 0.150756i | ||||
\(298\) | −18.0000 | −1.04271 | ||||||||
\(299\) | −6.00000 | + | 20.7846i | −0.346989 | + | 1.20201i | ||||
\(300\) | −11.0000 | −0.635085 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5.50000 | − | 9.52628i | −0.316489 | − | 0.548176i | ||||
\(303\) | 5.00000 | − | 8.66025i | 0.287242 | − | 0.497519i | ||||
\(304\) | 3.00000 | 0.172062 | ||||||||
\(305\) | 2.00000 | − | 3.46410i | 0.114520 | − | 0.198354i | ||||
\(306\) | −2.50000 | + | 4.33013i | −0.142915 | + | 0.247537i | ||||
\(307\) | 21.0000 | 1.19853 | 0.599267 | − | 0.800549i | \(-0.295459\pi\) | ||||
0.599267 | + | 0.800549i | \(0.295459\pi\) | |||||||
\(308\) | 1.50000 | − | 2.59808i | 0.0854704 | − | 0.148039i | ||||
\(309\) | 10.0000 | + | 17.3205i | 0.568880 | + | 0.985329i | ||||
\(310\) | −8.00000 | − | 13.8564i | −0.454369 | − | 0.786991i | ||||
\(311\) | −19.0000 | −1.07739 | −0.538696 | − | 0.842500i | \(-0.681083\pi\) | ||||
−0.538696 | + | 0.842500i | \(0.681083\pi\) | |||||||
\(312\) | −1.00000 | + | 3.46410i | −0.0566139 | + | 0.196116i | ||||
\(313\) | −14.0000 | −0.791327 | −0.395663 | − | 0.918396i | \(-0.629485\pi\) | ||||
−0.395663 | + | 0.918396i | \(0.629485\pi\) | |||||||
\(314\) | −1.00000 | − | 1.73205i | −0.0564333 | − | 0.0977453i | ||||
\(315\) | −2.00000 | − | 3.46410i | −0.112687 | − | 0.195180i | ||||
\(316\) | −5.50000 | + | 9.52628i | −0.309399 | + | 0.535895i | ||||
\(317\) | −18.0000 | −1.01098 | −0.505490 | − | 0.862832i | \(-0.668688\pi\) | ||||
−0.505490 | + | 0.862832i | \(0.668688\pi\) | |||||||
\(318\) | 5.50000 | − | 9.52628i | 0.308425 | − | 0.534207i | ||||
\(319\) | −13.5000 | + | 23.3827i | −0.755855 | + | 1.30918i | ||||
\(320\) | 4.00000 | 0.223607 | ||||||||
\(321\) | 8.50000 | − | 14.7224i | 0.474424 | − | 0.821726i | ||||
\(322\) | 3.00000 | + | 5.19615i | 0.167183 | + | 0.289570i | ||||
\(323\) | 7.50000 | + | 12.9904i | 0.417311 | + | 0.722804i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −27.5000 | − | 28.5788i | −1.52543 | − | 1.58527i | ||||
\(326\) | −20.0000 | −1.10770 | ||||||||
\(327\) | −1.00000 | − | 1.73205i | −0.0553001 | − | 0.0957826i | ||||
\(328\) | 2.50000 | + | 4.33013i | 0.138039 | + | 0.239091i | ||||
\(329\) | 1.50000 | − | 2.59808i | 0.0826977 | − | 0.143237i | ||||
\(330\) | −12.0000 | −0.660578 | ||||||||
\(331\) | −1.00000 | + | 1.73205i | −0.0549650 | + | 0.0952021i | −0.892199 | − | 0.451643i | \(-0.850838\pi\) |
0.837234 | + | 0.546845i | \(0.184171\pi\) | |||||||
\(332\) | −3.00000 | + | 5.19615i | −0.164646 | + | 0.285176i | ||||
\(333\) | 4.00000 | 0.219199 | ||||||||
\(334\) | −8.00000 | + | 13.8564i | −0.437741 | + | 0.758189i | ||||
\(335\) | −4.00000 | − | 6.92820i | −0.218543 | − | 0.378528i | ||||
\(336\) | 0.500000 | + | 0.866025i | 0.0272772 | + | 0.0472456i | ||||
\(337\) | 31.0000 | 1.68868 | 0.844339 | − | 0.535810i | \(-0.179994\pi\) | ||||
0.844339 | + | 0.535810i | \(0.179994\pi\) | |||||||
\(338\) | −11.5000 | + | 6.06218i | −0.625518 | + | 0.329739i | ||||
\(339\) | −12.0000 | −0.651751 | ||||||||
\(340\) | 10.0000 | + | 17.3205i | 0.542326 | + | 0.939336i | ||||
\(341\) | −6.00000 | − | 10.3923i | −0.324918 | − | 0.562775i | ||||
\(342\) | 1.50000 | − | 2.59808i | 0.0811107 | − | 0.140488i | ||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.0000 | − | 20.7846i | 0.646058 | − | 1.11901i | ||||
\(346\) | 2.00000 | 0.107521 | ||||||||
\(347\) | −5.50000 | + | 9.52628i | −0.295255 | + | 0.511397i | −0.975044 | − | 0.222010i | \(-0.928738\pi\) |
0.679789 | + | 0.733408i | \(0.262071\pi\) | |||||||
\(348\) | −4.50000 | − | 7.79423i | −0.241225 | − | 0.417815i | ||||
\(349\) | 17.0000 | + | 29.4449i | 0.909989 | + | 1.57615i | 0.814076 | + | 0.580758i | \(0.197244\pi\) |
0.0959126 | + | 0.995390i | \(0.469423\pi\) | |||||||
\(350\) | −11.0000 | −0.587975 | ||||||||
\(351\) | 2.50000 | + | 2.59808i | 0.133440 | + | 0.138675i | ||||
\(352\) | 3.00000 | 0.159901 | ||||||||
\(353\) | 9.00000 | + | 15.5885i | 0.479022 | + | 0.829690i | 0.999711 | − | 0.0240566i | \(-0.00765819\pi\) |
−0.520689 | + | 0.853746i | \(0.674325\pi\) | |||||||
\(354\) | −1.00000 | − | 1.73205i | −0.0531494 | − | 0.0920575i | ||||
\(355\) | −12.0000 | + | 20.7846i | −0.636894 | + | 1.10313i | ||||
\(356\) | 7.00000 | 0.370999 | ||||||||
\(357\) | −2.50000 | + | 4.33013i | −0.132314 | + | 0.229175i | ||||
\(358\) | 12.0000 | − | 20.7846i | 0.634220 | − | 1.09850i | ||||
\(359\) | −20.0000 | −1.05556 | −0.527780 | − | 0.849381i | \(-0.676975\pi\) | ||||
−0.527780 | + | 0.849381i | \(0.676975\pi\) | |||||||
\(360\) | 2.00000 | − | 3.46410i | 0.105409 | − | 0.182574i | ||||
\(361\) | 5.00000 | + | 8.66025i | 0.263158 | + | 0.455803i | ||||
\(362\) | −2.50000 | − | 4.33013i | −0.131397 | − | 0.227586i | ||||
\(363\) | 2.00000 | 0.104973 | ||||||||
\(364\) | −1.00000 | + | 3.46410i | −0.0524142 | + | 0.181568i | ||||
\(365\) | 48.0000 | 2.51243 | ||||||||
\(366\) | 0.500000 | + | 0.866025i | 0.0261354 | + | 0.0452679i | ||||
\(367\) | −9.00000 | − | 15.5885i | −0.469796 | − | 0.813711i | 0.529607 | − | 0.848243i | \(-0.322339\pi\) |
−0.999404 | + | 0.0345320i | \(0.989006\pi\) | |||||||
\(368\) | −3.00000 | + | 5.19615i | −0.156386 | + | 0.270868i | ||||
\(369\) | 5.00000 | 0.260290 | ||||||||
\(370\) | 8.00000 | − | 13.8564i | 0.415900 | − | 0.720360i | ||||
\(371\) | 5.50000 | − | 9.52628i | 0.285546 | − | 0.494580i | ||||
\(372\) | 4.00000 | 0.207390 | ||||||||
\(373\) | −17.0000 | + | 29.4449i | −0.880227 | + | 1.52460i | −0.0291379 | + | 0.999575i | \(0.509276\pi\) |
−0.851089 | + | 0.525022i | \(0.824057\pi\) | |||||||
\(374\) | 7.50000 | + | 12.9904i | 0.387816 | + | 0.671717i | ||||
\(375\) | 12.0000 | + | 20.7846i | 0.619677 | + | 1.07331i | ||||
\(376\) | 3.00000 | 0.154713 | ||||||||
\(377\) | 9.00000 | − | 31.1769i | 0.463524 | − | 1.60569i | ||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | 9.00000 | + | 15.5885i | 0.462299 | + | 0.800725i | 0.999075 | − | 0.0429994i | \(-0.0136914\pi\) |
−0.536776 | + | 0.843725i | \(0.680358\pi\) | |||||||
\(380\) | −6.00000 | − | 10.3923i | −0.307794 | − | 0.533114i | ||||
\(381\) | 4.00000 | − | 6.92820i | 0.204926 | − | 0.354943i | ||||
\(382\) | 6.00000 | 0.306987 | ||||||||
\(383\) | 5.50000 | − | 9.52628i | 0.281037 | − | 0.486770i | −0.690604 | − | 0.723234i | \(-0.742655\pi\) |
0.971640 | + | 0.236463i | \(0.0759883\pi\) | |||||||
\(384\) | −0.500000 | + | 0.866025i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | −12.0000 | −0.611577 | ||||||||
\(386\) | 6.50000 | − | 11.2583i | 0.330841 | − | 0.573034i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.00000 | + | 10.3923i | 0.304604 | + | 0.527589i | ||||
\(389\) | −26.0000 | −1.31825 | −0.659126 | − | 0.752032i | \(-0.729074\pi\) | ||||
−0.659126 | + | 0.752032i | \(0.729074\pi\) | |||||||
\(390\) | 14.0000 | − | 3.46410i | 0.708918 | − | 0.175412i | ||||
\(391\) | −30.0000 | −1.51717 | ||||||||
\(392\) | 0.500000 | + | 0.866025i | 0.0252538 | + | 0.0437409i | ||||
\(393\) | 6.00000 | + | 10.3923i | 0.302660 | + | 0.524222i | ||||
\(394\) | −9.50000 | + | 16.4545i | −0.478603 | + | 0.828965i | ||||
\(395\) | 44.0000 | 2.21388 | ||||||||
\(396\) | 1.50000 | − | 2.59808i | 0.0753778 | − | 0.130558i | ||||
\(397\) | 11.5000 | − | 19.9186i | 0.577168 | − | 0.999685i | −0.418634 | − | 0.908155i | \(-0.637491\pi\) |
0.995802 | − | 0.0915300i | \(-0.0291757\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.50000 | − | 2.59808i | 0.0750939 | − | 0.130066i | ||||
\(400\) | −5.50000 | − | 9.52628i | −0.275000 | − | 0.476314i | ||||
\(401\) | −9.00000 | − | 15.5885i | −0.449439 | − | 0.778450i | 0.548911 | − | 0.835881i | \(-0.315043\pi\) |
−0.998350 | + | 0.0574304i | \(0.981709\pi\) | |||||||
\(402\) | 2.00000 | 0.0997509 | ||||||||
\(403\) | 10.0000 | + | 10.3923i | 0.498135 | + | 0.517678i | ||||
\(404\) | 10.0000 | 0.497519 | ||||||||
\(405\) | −2.00000 | − | 3.46410i | −0.0993808 | − | 0.172133i | ||||
\(406\) | −4.50000 | − | 7.79423i | −0.223331 | − | 0.386821i | ||||
\(407\) | 6.00000 | − | 10.3923i | 0.297409 | − | 0.515127i | ||||
\(408\) | −5.00000 | −0.247537 | ||||||||
\(409\) | 1.00000 | − | 1.73205i | 0.0494468 | − | 0.0856444i | −0.840243 | − | 0.542211i | \(-0.817588\pi\) |
0.889689 | + | 0.456566i | \(0.150921\pi\) | |||||||
\(410\) | 10.0000 | − | 17.3205i | 0.493865 | − | 0.855399i | ||||
\(411\) | 18.0000 | 0.887875 | ||||||||
\(412\) | −10.0000 | + | 17.3205i | −0.492665 | + | 0.853320i | ||||
\(413\) | −1.00000 | − | 1.73205i | −0.0492068 | − | 0.0852286i | ||||
\(414\) | 3.00000 | + | 5.19615i | 0.147442 | + | 0.255377i | ||||
\(415\) | 24.0000 | 1.17811 | ||||||||
\(416\) | −3.50000 | + | 0.866025i | −0.171602 | + | 0.0424604i | ||||
\(417\) | −13.0000 | −0.636613 | ||||||||
\(418\) | −4.50000 | − | 7.79423i | −0.220102 | − | 0.381228i | ||||
\(419\) | −9.00000 | − | 15.5885i | −0.439679 | − | 0.761546i | 0.557986 | − | 0.829851i | \(-0.311574\pi\) |
−0.997665 | + | 0.0683046i | \(0.978241\pi\) | |||||||
\(420\) | 2.00000 | − | 3.46410i | 0.0975900 | − | 0.169031i | ||||
\(421\) | −18.0000 | −0.877266 | −0.438633 | − | 0.898666i | \(-0.644537\pi\) | ||||
−0.438633 | + | 0.898666i | \(0.644537\pi\) | |||||||
\(422\) | 7.00000 | − | 12.1244i | 0.340755 | − | 0.590204i | ||||
\(423\) | 1.50000 | − | 2.59808i | 0.0729325 | − | 0.126323i | ||||
\(424\) | 11.0000 | 0.534207 | ||||||||
\(425\) | 27.5000 | − | 47.6314i | 1.33395 | − | 2.31046i | ||||
\(426\) | −3.00000 | − | 5.19615i | −0.145350 | − | 0.251754i | ||||
\(427\) | 0.500000 | + | 0.866025i | 0.0241967 | + | 0.0419099i | ||||
\(428\) | 17.0000 | 0.821726 | ||||||||
\(429\) | 10.5000 | − | 2.59808i | 0.506945 | − | 0.125436i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −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 | ||||
\(433\) | −17.0000 | + | 29.4449i | −0.816968 | + | 1.41503i | 0.0909384 | + | 0.995857i | \(0.471013\pi\) |
−0.907906 | + | 0.419173i | \(0.862320\pi\) | |||||||
\(434\) | 4.00000 | 0.192006 | ||||||||
\(435\) | −18.0000 | + | 31.1769i | −0.863034 | + | 1.49482i | ||||
\(436\) | 1.00000 | − | 1.73205i | 0.0478913 | − | 0.0829502i | ||||
\(437\) | 18.0000 | 0.861057 | ||||||||
\(438\) | −6.00000 | + | 10.3923i | −0.286691 | + | 0.496564i | ||||
\(439\) | −20.0000 | − | 34.6410i | −0.954548 | − | 1.65333i | −0.735399 | − | 0.677634i | \(-0.763005\pi\) |
−0.219149 | − | 0.975691i | \(-0.570328\pi\) | |||||||
\(440\) | −6.00000 | − | 10.3923i | −0.286039 | − | 0.495434i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −12.5000 | − | 12.9904i | −0.594564 | − | 0.617889i | ||||
\(443\) | −15.0000 | −0.712672 | −0.356336 | − | 0.934358i | \(-0.615974\pi\) | ||||
−0.356336 | + | 0.934358i | \(0.615974\pi\) | |||||||
\(444\) | 2.00000 | + | 3.46410i | 0.0949158 | + | 0.164399i | ||||
\(445\) | −14.0000 | − | 24.2487i | −0.663664 | − | 1.14950i | ||||
\(446\) | −8.00000 | + | 13.8564i | −0.378811 | + | 0.656120i | ||||
\(447\) | −18.0000 | −0.851371 | ||||||||
\(448\) | −0.500000 | + | 0.866025i | −0.0236228 | + | 0.0409159i | ||||
\(449\) | −10.0000 | + | 17.3205i | −0.471929 | + | 0.817405i | −0.999484 | − | 0.0321156i | \(-0.989776\pi\) |
0.527555 | + | 0.849521i | \(0.323109\pi\) | |||||||
\(450\) | −11.0000 | −0.518545 | ||||||||
\(451\) | 7.50000 | − | 12.9904i | 0.353161 | − | 0.611693i | ||||
\(452\) | −6.00000 | − | 10.3923i | −0.282216 | − | 0.488813i | ||||
\(453\) | −5.50000 | − | 9.52628i | −0.258413 | − | 0.447584i | ||||
\(454\) | −14.0000 | −0.657053 | ||||||||
\(455\) | 14.0000 | − | 3.46410i | 0.656330 | − | 0.162400i | ||||
\(456\) | 3.00000 | 0.140488 | ||||||||
\(457\) | 1.00000 | + | 1.73205i | 0.0467780 | + | 0.0810219i | 0.888466 | − | 0.458942i | \(-0.151771\pi\) |
−0.841688 | + | 0.539964i | \(0.818438\pi\) | |||||||
\(458\) | −2.50000 | − | 4.33013i | −0.116817 | − | 0.202334i | ||||
\(459\) | −2.50000 | + | 4.33013i | −0.116690 | + | 0.202113i | ||||
\(460\) | 24.0000 | 1.11901 | ||||||||
\(461\) | 16.0000 | − | 27.7128i | 0.745194 | − | 1.29071i | −0.204910 | − | 0.978781i | \(-0.565690\pi\) |
0.950104 | − | 0.311933i | \(-0.100977\pi\) | |||||||
\(462\) | 1.50000 | − | 2.59808i | 0.0697863 | − | 0.120873i | ||||
\(463\) | 1.00000 | 0.0464739 | 0.0232370 | − | 0.999730i | \(-0.492603\pi\) | ||||
0.0232370 | + | 0.999730i | \(0.492603\pi\) | |||||||
\(464\) | 4.50000 | − | 7.79423i | 0.208907 | − | 0.361838i | ||||
\(465\) | −8.00000 | − | 13.8564i | −0.370991 | − | 0.642575i | ||||
\(466\) | 2.00000 | + | 3.46410i | 0.0926482 | + | 0.160471i | ||||
\(467\) | −12.0000 | −0.555294 | −0.277647 | − | 0.960683i | \(-0.589555\pi\) | ||||
−0.277647 | + | 0.960683i | \(0.589555\pi\) | |||||||
\(468\) | −1.00000 | + | 3.46410i | −0.0462250 | + | 0.160128i | ||||
\(469\) | 2.00000 | 0.0923514 | ||||||||
\(470\) | −6.00000 | − | 10.3923i | −0.276759 | − | 0.479361i | ||||
\(471\) | −1.00000 | − | 1.73205i | −0.0460776 | − | 0.0798087i | ||||
\(472\) | 1.00000 | − | 1.73205i | 0.0460287 | − | 0.0797241i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −5.50000 | + | 9.52628i | −0.252623 | + | 0.437557i | ||||
\(475\) | −16.5000 | + | 28.5788i | −0.757072 | + | 1.31129i | ||||
\(476\) | −5.00000 | −0.229175 | ||||||||
\(477\) | 5.50000 | − | 9.52628i | 0.251828 | − | 0.436178i | ||||
\(478\) | −13.0000 | − | 22.5167i | −0.594606 | − | 1.02989i | ||||
\(479\) | 16.5000 | + | 28.5788i | 0.753904 | + | 1.30580i | 0.945917 | + | 0.324408i | \(0.105165\pi\) |
−0.192013 | + | 0.981392i | \(0.561502\pi\) | |||||||
\(480\) | 4.00000 | 0.182574 | ||||||||
\(481\) | −4.00000 | + | 13.8564i | −0.182384 | + | 0.631798i | ||||
\(482\) | −12.0000 | −0.546585 | ||||||||
\(483\) | 3.00000 | + | 5.19615i | 0.136505 | + | 0.236433i | ||||
\(484\) | 1.00000 | + | 1.73205i | 0.0454545 | + | 0.0787296i | ||||
\(485\) | 24.0000 | − | 41.5692i | 1.08978 | − | 1.88756i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 10.5000 | − | 18.1865i | 0.475800 | − | 0.824110i | −0.523815 | − | 0.851832i | \(-0.675492\pi\) |
0.999616 | + | 0.0277214i | \(0.00882512\pi\) | |||||||
\(488\) | −0.500000 | + | 0.866025i | −0.0226339 | + | 0.0392031i | ||||
\(489\) | −20.0000 | −0.904431 | ||||||||
\(490\) | 2.00000 | − | 3.46410i | 0.0903508 | − | 0.156492i | ||||
\(491\) | 10.0000 | + | 17.3205i | 0.451294 | + | 0.781664i | 0.998467 | − | 0.0553560i | \(-0.0176294\pi\) |
−0.547173 | + | 0.837020i | \(0.684296\pi\) | |||||||
\(492\) | 2.50000 | + | 4.33013i | 0.112709 | + | 0.195217i | ||||
\(493\) | 45.0000 | 2.02670 | ||||||||
\(494\) | 7.50000 | + | 7.79423i | 0.337441 | + | 0.350679i | ||||
\(495\) | −12.0000 | −0.539360 | ||||||||
\(496\) | 2.00000 | + | 3.46410i | 0.0898027 | + | 0.155543i | ||||
\(497\) | −3.00000 | − | 5.19615i | −0.134568 | − | 0.233079i | ||||
\(498\) | −3.00000 | + | 5.19615i | −0.134433 | + | 0.232845i | ||||
\(499\) | 40.0000 | 1.79065 | 0.895323 | − | 0.445418i | \(-0.146945\pi\) | ||||
0.895323 | + | 0.445418i | \(0.146945\pi\) | |||||||
\(500\) | −12.0000 | + | 20.7846i | −0.536656 | + | 0.929516i | ||||
\(501\) | −8.00000 | + | 13.8564i | −0.357414 | + | 0.619059i | ||||
\(502\) | −14.0000 | −0.624851 | ||||||||
\(503\) | −8.00000 | + | 13.8564i | −0.356702 | + | 0.617827i | −0.987408 | − | 0.158196i | \(-0.949432\pi\) |
0.630705 | + | 0.776022i | \(0.282766\pi\) | |||||||
\(504\) | 0.500000 | + | 0.866025i | 0.0222718 | + | 0.0385758i | ||||
\(505\) | −20.0000 | − | 34.6410i | −0.889988 | − | 1.54150i | ||||
\(506\) | 18.0000 | 0.800198 | ||||||||
\(507\) | −11.5000 | + | 6.06218i | −0.510733 | + | 0.269231i | ||||
\(508\) | 8.00000 | 0.354943 | ||||||||
\(509\) | 15.0000 | + | 25.9808i | 0.664863 | + | 1.15158i | 0.979322 | + | 0.202306i | \(0.0648436\pi\) |
−0.314459 | + | 0.949271i | \(0.601823\pi\) | |||||||
\(510\) | 10.0000 | + | 17.3205i | 0.442807 | + | 0.766965i | ||||
\(511\) | −6.00000 | + | 10.3923i | −0.265424 | + | 0.459728i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.50000 | − | 2.59808i | 0.0662266 | − | 0.114708i | ||||
\(514\) | 3.50000 | − | 6.06218i | 0.154378 | − | 0.267391i | ||||
\(515\) | 80.0000 | 3.52522 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.50000 | − | 7.79423i | −0.197910 | − | 0.342790i | ||||
\(518\) | 2.00000 | + | 3.46410i | 0.0878750 | + | 0.152204i | ||||
\(519\) | 2.00000 | 0.0877903 | ||||||||
\(520\) | 10.0000 | + | 10.3923i | 0.438529 | + | 0.455733i | ||||
\(521\) | −5.00000 | −0.219054 | −0.109527 | − | 0.993984i | \(-0.534934\pi\) | ||||
−0.109527 | + | 0.993984i | \(0.534934\pi\) | |||||||
\(522\) | −4.50000 | − | 7.79423i | −0.196960 | − | 0.341144i | ||||
\(523\) | −13.5000 | − | 23.3827i | −0.590314 | − | 1.02245i | −0.994190 | − | 0.107640i | \(-0.965671\pi\) |
0.403876 | − | 0.914814i | \(-0.367663\pi\) | |||||||
\(524\) | −6.00000 | + | 10.3923i | −0.262111 | + | 0.453990i | ||||
\(525\) | −11.0000 | −0.480079 | ||||||||
\(526\) | −13.0000 | + | 22.5167i | −0.566827 | + | 0.981773i | ||||
\(527\) | −10.0000 | + | 17.3205i | −0.435607 | + | 0.754493i | ||||
\(528\) | 3.00000 | 0.130558 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | −22.0000 | − | 38.1051i | −0.955619 | − | 1.65518i | ||||
\(531\) | −1.00000 | − | 1.73205i | −0.0433963 | − | 0.0751646i | ||||
\(532\) | 3.00000 | 0.130066 | ||||||||
\(533\) | −5.00000 | + | 17.3205i | −0.216574 | + | 0.750234i | ||||
\(534\) | 7.00000 | 0.302920 | ||||||||
\(535\) | −34.0000 | − | 58.8897i | −1.46995 | − | 2.54602i | ||||
\(536\) | 1.00000 | + | 1.73205i | 0.0431934 | + | 0.0748132i | ||||
\(537\) | 12.0000 | − | 20.7846i | 0.517838 | − | 0.896922i | ||||
\(538\) | 24.0000 | 1.03471 | ||||||||
\(539\) | 1.50000 | − | 2.59808i | 0.0646096 | − | 0.111907i | ||||
\(540\) | 2.00000 | − | 3.46410i | 0.0860663 | − | 0.149071i | ||||
\(541\) | −2.00000 | −0.0859867 | −0.0429934 | − | 0.999075i | \(-0.513689\pi\) | ||||
−0.0429934 | + | 0.999075i | \(0.513689\pi\) | |||||||
\(542\) | −6.00000 | + | 10.3923i | −0.257722 | + | 0.446388i | ||||
\(543\) | −2.50000 | − | 4.33013i | −0.107285 | − | 0.185824i | ||||
\(544\) | −2.50000 | − | 4.33013i | −0.107187 | − | 0.185653i | ||||
\(545\) | −8.00000 | −0.342682 | ||||||||
\(546\) | −1.00000 | + | 3.46410i | −0.0427960 | + | 0.148250i | ||||
\(547\) | 2.00000 | 0.0855138 | 0.0427569 | − | 0.999086i | \(-0.486386\pi\) | ||||
0.0427569 | + | 0.999086i | \(0.486386\pi\) | |||||||
\(548\) | 9.00000 | + | 15.5885i | 0.384461 | + | 0.665906i | ||||
\(549\) | 0.500000 | + | 0.866025i | 0.0213395 | + | 0.0369611i | ||||
\(550\) | −16.5000 | + | 28.5788i | −0.703562 | + | 1.21861i | ||||
\(551\) | −27.0000 | −1.15024 | ||||||||
\(552\) | −3.00000 | + | 5.19615i | −0.127688 | + | 0.221163i | ||||
\(553\) | −5.50000 | + | 9.52628i | −0.233884 | + | 0.405099i | ||||
\(554\) | −14.0000 | −0.594803 | ||||||||
\(555\) | 8.00000 | − | 13.8564i | 0.339581 | − | 0.588172i | ||||
\(556\) | −6.50000 | − | 11.2583i | −0.275661 | − | 0.477460i | ||||
\(557\) | −5.50000 | − | 9.52628i | −0.233042 | − | 0.403641i | 0.725660 | − | 0.688054i | \(-0.241535\pi\) |
−0.958702 | + | 0.284413i | \(0.908201\pi\) | |||||||
\(558\) | 4.00000 | 0.169334 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 4.00000 | 0.169031 | ||||||||
\(561\) | 7.50000 | + | 12.9904i | 0.316650 | + | 0.548454i | ||||
\(562\) | 15.0000 | + | 25.9808i | 0.632737 | + | 1.09593i | ||||
\(563\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(564\) | 3.00000 | 0.126323 | ||||||||
\(565\) | −24.0000 | + | 41.5692i | −1.00969 | + | 1.74883i | ||||
\(566\) | −2.00000 | + | 3.46410i | −0.0840663 | + | 0.145607i | ||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 3.00000 | − | 5.19615i | 0.125877 | − | 0.218026i | ||||
\(569\) | −3.00000 | − | 5.19615i | −0.125767 | − | 0.217834i | 0.796266 | − | 0.604947i | \(-0.206806\pi\) |
−0.922032 | + | 0.387113i | \(0.873472\pi\) | |||||||
\(570\) | −6.00000 | − | 10.3923i | −0.251312 | − | 0.435286i | ||||
\(571\) | 38.0000 | 1.59025 | 0.795125 | − | 0.606445i | \(-0.207405\pi\) | ||||
0.795125 | + | 0.606445i | \(0.207405\pi\) | |||||||
\(572\) | 7.50000 | + | 7.79423i | 0.313591 | + | 0.325893i | ||||
\(573\) | 6.00000 | 0.250654 | ||||||||
\(574\) | 2.50000 | + | 4.33013i | 0.104348 | + | 0.180736i | ||||
\(575\) | −33.0000 | − | 57.1577i | −1.37620 | − | 2.38364i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −18.0000 | −0.749350 | −0.374675 | − | 0.927156i | \(-0.622246\pi\) | ||||
−0.374675 | + | 0.927156i | \(0.622246\pi\) | |||||||
\(578\) | 4.00000 | − | 6.92820i | 0.166378 | − | 0.288175i | ||||
\(579\) | 6.50000 | − | 11.2583i | 0.270131 | − | 0.467880i | ||||
\(580\) | −36.0000 | −1.49482 | ||||||||
\(581\) | −3.00000 | + | 5.19615i | −0.124461 | + | 0.215573i | ||||
\(582\) | 6.00000 | + | 10.3923i | 0.248708 | + | 0.430775i | ||||
\(583\) | −16.5000 | − | 28.5788i | −0.683360 | − | 1.18361i | ||||
\(584\) | −12.0000 | −0.496564 | ||||||||
\(585\) | 14.0000 | − | 3.46410i | 0.578829 | − | 0.143223i | ||||
\(586\) | −24.0000 | −0.991431 | ||||||||
\(587\) | 6.00000 | + | 10.3923i | 0.247647 | + | 0.428936i | 0.962872 | − | 0.269957i | \(-0.0870095\pi\) |
−0.715226 | + | 0.698893i | \(0.753676\pi\) | |||||||
\(588\) | 0.500000 | + | 0.866025i | 0.0206197 | + | 0.0357143i | ||||
\(589\) | 6.00000 | − | 10.3923i | 0.247226 | − | 0.428207i | ||||
\(590\) | −8.00000 | −0.329355 | ||||||||
\(591\) | −9.50000 | + | 16.4545i | −0.390778 | + | 0.676847i | ||||
\(592\) | −2.00000 | + | 3.46410i | −0.0821995 | + | 0.142374i | ||||
\(593\) | 41.0000 | 1.68367 | 0.841834 | − | 0.539736i | \(-0.181476\pi\) | ||||
0.841834 | + | 0.539736i | \(0.181476\pi\) | |||||||
\(594\) | 1.50000 | − | 2.59808i | 0.0615457 | − | 0.106600i | ||||
\(595\) | 10.0000 | + | 17.3205i | 0.409960 | + | 0.710072i | ||||
\(596\) | −9.00000 | − | 15.5885i | −0.368654 | − | 0.638528i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −21.0000 | + | 5.19615i | −0.858754 | + | 0.212486i | ||||
\(599\) | −30.0000 | −1.22577 | −0.612883 | − | 0.790173i | \(-0.709990\pi\) | ||||
−0.612883 | + | 0.790173i | \(0.709990\pi\) | |||||||
\(600\) | −5.50000 | − | 9.52628i | −0.224537 | − | 0.388909i | ||||
\(601\) | 22.0000 | + | 38.1051i | 0.897399 | + | 1.55434i | 0.830808 | + | 0.556560i | \(0.187879\pi\) |
0.0665912 | + | 0.997780i | \(0.478788\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.00000 | 0.0814463 | ||||||||
\(604\) | 5.50000 | − | 9.52628i | 0.223792 | − | 0.387619i | ||||
\(605\) | 4.00000 | − | 6.92820i | 0.162623 | − | 0.281672i | ||||
\(606\) | 10.0000 | 0.406222 | ||||||||
\(607\) | 4.00000 | − | 6.92820i | 0.162355 | − | 0.281207i | −0.773358 | − | 0.633970i | \(-0.781424\pi\) |
0.935713 | + | 0.352763i | \(0.114758\pi\) | |||||||
\(608\) | 1.50000 | + | 2.59808i | 0.0608330 | + | 0.105366i | ||||
\(609\) | −4.50000 | − | 7.79423i | −0.182349 | − | 0.315838i | ||||
\(610\) | 4.00000 | 0.161955 | ||||||||
\(611\) | 7.50000 | + | 7.79423i | 0.303418 | + | 0.315321i | ||||
\(612\) | −5.00000 | −0.202113 | ||||||||
\(613\) | −4.00000 | − | 6.92820i | −0.161558 | − | 0.279827i | 0.773869 | − | 0.633345i | \(-0.218319\pi\) |
−0.935428 | + | 0.353518i | \(0.884985\pi\) | |||||||
\(614\) | 10.5000 | + | 18.1865i | 0.423746 | + | 0.733949i | ||||
\(615\) | 10.0000 | − | 17.3205i | 0.403239 | − | 0.698430i | ||||
\(616\) | 3.00000 | 0.120873 | ||||||||
\(617\) | −5.00000 | + | 8.66025i | −0.201292 | + | 0.348649i | −0.948945 | − | 0.315441i | \(-0.897847\pi\) |
0.747653 | + | 0.664090i | \(0.231181\pi\) | |||||||
\(618\) | −10.0000 | + | 17.3205i | −0.402259 | + | 0.696733i | ||||
\(619\) | 17.0000 | 0.683288 | 0.341644 | − | 0.939829i | \(-0.389016\pi\) | ||||
0.341644 | + | 0.939829i | \(0.389016\pi\) | |||||||
\(620\) | 8.00000 | − | 13.8564i | 0.321288 | − | 0.556487i | ||||
\(621\) | 3.00000 | + | 5.19615i | 0.120386 | + | 0.208514i | ||||
\(622\) | −9.50000 | − | 16.4545i | −0.380915 | − | 0.659765i | ||||
\(623\) | 7.00000 | 0.280449 | ||||||||
\(624\) | −3.50000 | + | 0.866025i | −0.140112 | + | 0.0346688i | ||||
\(625\) | 41.0000 | 1.64000 | ||||||||
\(626\) | −7.00000 | − | 12.1244i | −0.279776 | − | 0.484587i | ||||
\(627\) | −4.50000 | − | 7.79423i | −0.179713 | − | 0.311272i | ||||
\(628\) | 1.00000 | − | 1.73205i | 0.0399043 | − | 0.0691164i | ||||
\(629\) | −20.0000 | −0.797452 | ||||||||
\(630\) | 2.00000 | − | 3.46410i | 0.0796819 | − | 0.138013i | ||||
\(631\) | 6.50000 | − | 11.2583i | 0.258761 | − | 0.448187i | −0.707149 | − | 0.707064i | \(-0.750019\pi\) |
0.965910 | + | 0.258877i | \(0.0833525\pi\) | |||||||
\(632\) | −11.0000 | −0.437557 | ||||||||
\(633\) | 7.00000 | − | 12.1244i | 0.278225 | − | 0.481900i | ||||
\(634\) | −9.00000 | − | 15.5885i | −0.357436 | − | 0.619097i | ||||
\(635\) | −16.0000 | − | 27.7128i | −0.634941 | − | 1.09975i | ||||
\(636\) | 11.0000 | 0.436178 | ||||||||
\(637\) | −1.00000 | + | 3.46410i | −0.0396214 | + | 0.137253i | ||||
\(638\) | −27.0000 | −1.06894 | ||||||||
\(639\) | −3.00000 | − | 5.19615i | −0.118678 | − | 0.205557i | ||||
\(640\) | 2.00000 | + | 3.46410i | 0.0790569 | + | 0.136931i | ||||
\(641\) | 15.0000 | − | 25.9808i | 0.592464 | − | 1.02618i | −0.401435 | − | 0.915888i | \(-0.631488\pi\) |
0.993899 | − | 0.110291i | \(-0.0351782\pi\) | |||||||
\(642\) | 17.0000 | 0.670936 | ||||||||
\(643\) | 8.50000 | − | 14.7224i | 0.335207 | − | 0.580596i | −0.648317 | − | 0.761370i | \(-0.724527\pi\) |
0.983525 | + | 0.180774i | \(0.0578603\pi\) | |||||||
\(644\) | −3.00000 | + | 5.19615i | −0.118217 | + | 0.204757i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.50000 | + | 12.9904i | −0.295084 | + | 0.511100i | ||||
\(647\) | −7.50000 | − | 12.9904i | −0.294855 | − | 0.510705i | 0.680096 | − | 0.733123i | \(-0.261938\pi\) |
−0.974951 | + | 0.222419i | \(0.928605\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | −6.00000 | −0.235521 | ||||||||
\(650\) | 11.0000 | − | 38.1051i | 0.431455 | − | 1.49461i | ||||
\(651\) | 4.00000 | 0.156772 | ||||||||
\(652\) | −10.0000 | − | 17.3205i | −0.391630 | − | 0.678323i | ||||
\(653\) | 13.5000 | + | 23.3827i | 0.528296 | + | 0.915035i | 0.999456 | + | 0.0329874i | \(0.0105021\pi\) |
−0.471160 | + | 0.882048i | \(0.656165\pi\) | |||||||
\(654\) | 1.00000 | − | 1.73205i | 0.0391031 | − | 0.0677285i | ||||
\(655\) | 48.0000 | 1.87552 | ||||||||
\(656\) | −2.50000 | + | 4.33013i | −0.0976086 | + | 0.169063i | ||||
\(657\) | −6.00000 | + | 10.3923i | −0.234082 | + | 0.405442i | ||||
\(658\) | 3.00000 | 0.116952 | ||||||||
\(659\) | −19.5000 | + | 33.7750i | −0.759612 | + | 1.31569i | 0.183436 | + | 0.983032i | \(0.441278\pi\) |
−0.943049 | + | 0.332655i | \(0.892055\pi\) | |||||||
\(660\) | −6.00000 | − | 10.3923i | −0.233550 | − | 0.404520i | ||||
\(661\) | 5.00000 | + | 8.66025i | 0.194477 | + | 0.336845i | 0.946729 | − | 0.322031i | \(-0.104366\pi\) |
−0.752252 | + | 0.658876i | \(0.771032\pi\) | |||||||
\(662\) | −2.00000 | −0.0777322 | ||||||||
\(663\) | −12.5000 | − | 12.9904i | −0.485460 | − | 0.504505i | ||||
\(664\) | −6.00000 | −0.232845 | ||||||||
\(665\) | −6.00000 | − | 10.3923i | −0.232670 | − | 0.402996i | ||||
\(666\) | 2.00000 | + | 3.46410i | 0.0774984 | + | 0.134231i | ||||
\(667\) | 27.0000 | − | 46.7654i | 1.04544 | − | 1.81076i | ||||
\(668\) | −16.0000 | −0.619059 | ||||||||
\(669\) | −8.00000 | + | 13.8564i | −0.309298 | + | 0.535720i | ||||
\(670\) | 4.00000 | − | 6.92820i | 0.154533 | − | 0.267660i | ||||
\(671\) | 3.00000 | 0.115814 | ||||||||
\(672\) | −0.500000 | + | 0.866025i | −0.0192879 | + | 0.0334077i | ||||
\(673\) | −11.5000 | − | 19.9186i | −0.443292 | − | 0.767805i | 0.554639 | − | 0.832091i | \(-0.312856\pi\) |
−0.997932 | + | 0.0642860i | \(0.979523\pi\) | |||||||
\(674\) | 15.5000 | + | 26.8468i | 0.597038 | + | 1.03410i | ||||
\(675\) | −11.0000 | −0.423390 | ||||||||
\(676\) | −11.0000 | − | 6.92820i | −0.423077 | − | 0.266469i | ||||
\(677\) | −26.0000 | −0.999261 | −0.499631 | − | 0.866239i | \(-0.666531\pi\) | ||||
−0.499631 | + | 0.866239i | \(0.666531\pi\) | |||||||
\(678\) | −6.00000 | − | 10.3923i | −0.230429 | − | 0.399114i | ||||
\(679\) | 6.00000 | + | 10.3923i | 0.230259 | + | 0.398820i | ||||
\(680\) | −10.0000 | + | 17.3205i | −0.383482 | + | 0.664211i | ||||
\(681\) | −14.0000 | −0.536481 | ||||||||
\(682\) | 6.00000 | − | 10.3923i | 0.229752 | − | 0.397942i | ||||
\(683\) | 10.0000 | − | 17.3205i | 0.382639 | − | 0.662751i | −0.608799 | − | 0.793324i | \(-0.708349\pi\) |
0.991439 | + | 0.130573i | \(0.0416818\pi\) | |||||||
\(684\) | 3.00000 | 0.114708 | ||||||||
\(685\) | 36.0000 | − | 62.3538i | 1.37549 | − | 2.38242i | ||||
\(686\) | 0.500000 | + | 0.866025i | 0.0190901 | + | 0.0330650i | ||||
\(687\) | −2.50000 | − | 4.33013i | −0.0953809 | − | 0.165205i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 27.5000 | + | 28.5788i | 1.04767 | + | 1.08877i | ||||
\(690\) | 24.0000 | 0.913664 | ||||||||
\(691\) | −4.00000 | − | 6.92820i | −0.152167 | − | 0.263561i | 0.779857 | − | 0.625958i | \(-0.215292\pi\) |
−0.932024 | + | 0.362397i | \(0.881959\pi\) | |||||||
\(692\) | 1.00000 | + | 1.73205i | 0.0380143 | + | 0.0658427i | ||||
\(693\) | 1.50000 | − | 2.59808i | 0.0569803 | − | 0.0986928i | ||||
\(694\) | −11.0000 | −0.417554 | ||||||||
\(695\) | −26.0000 | + | 45.0333i | −0.986236 | + | 1.70821i | ||||
\(696\) | 4.50000 | − | 7.79423i | 0.170572 | − | 0.295439i | ||||
\(697\) | −25.0000 | −0.946943 | ||||||||
\(698\) | −17.0000 | + | 29.4449i | −0.643459 | + | 1.11450i | ||||
\(699\) | 2.00000 | + | 3.46410i | 0.0756469 | + | 0.131024i | ||||
\(700\) | −5.50000 | − | 9.52628i | −0.207880 | − | 0.360060i | ||||
\(701\) | −21.0000 | −0.793159 | −0.396580 | − | 0.918000i | \(-0.629803\pi\) | ||||
−0.396580 | + | 0.918000i | \(0.629803\pi\) | |||||||
\(702\) | −1.00000 | + | 3.46410i | −0.0377426 | + | 0.130744i | ||||
\(703\) | 12.0000 | 0.452589 | ||||||||
\(704\) | 1.50000 | + | 2.59808i | 0.0565334 | + | 0.0979187i | ||||
\(705\) | −6.00000 | − | 10.3923i | −0.225973 | − | 0.391397i | ||||
\(706\) | −9.00000 | + | 15.5885i | −0.338719 | + | 0.586679i | ||||
\(707\) | 10.0000 | 0.376089 | ||||||||
\(708\) | 1.00000 | − | 1.73205i | 0.0375823 | − | 0.0650945i | ||||
\(709\) | −5.00000 | + | 8.66025i | −0.187779 | + | 0.325243i | −0.944509 | − | 0.328484i | \(-0.893462\pi\) |
0.756730 | + | 0.653727i | \(0.226796\pi\) | |||||||
\(710\) | −24.0000 | −0.900704 | ||||||||
\(711\) | −5.50000 | + | 9.52628i | −0.206266 | + | 0.357263i | ||||
\(712\) | 3.50000 | + | 6.06218i | 0.131168 | + | 0.227190i | ||||
\(713\) | 12.0000 | + | 20.7846i | 0.449404 | + | 0.778390i | ||||
\(714\) | −5.00000 | −0.187120 | ||||||||
\(715\) | 12.0000 | − | 41.5692i | 0.448775 | − | 1.55460i | ||||
\(716\) | 24.0000 | 0.896922 | ||||||||
\(717\) | −13.0000 | − | 22.5167i | −0.485494 | − | 0.840900i | ||||
\(718\) | −10.0000 | − | 17.3205i | −0.373197 | − | 0.646396i | ||||
\(719\) | 0.500000 | − | 0.866025i | 0.0186469 | − | 0.0322973i | −0.856551 | − | 0.516062i | \(-0.827398\pi\) |
0.875198 | + | 0.483764i | \(0.160731\pi\) | |||||||
\(720\) | 4.00000 | 0.149071 | ||||||||
\(721\) | −10.0000 | + | 17.3205i | −0.372419 | + | 0.645049i | ||||
\(722\) | −5.00000 | + | 8.66025i | −0.186081 | + | 0.322301i | ||||
\(723\) | −12.0000 | −0.446285 | ||||||||
\(724\) | 2.50000 | − | 4.33013i | 0.0929118 | − | 0.160928i | ||||
\(725\) | 49.5000 | + | 85.7365i | 1.83838 | + | 3.18417i | ||||
\(726\) | 1.00000 | + | 1.73205i | 0.0371135 | + | 0.0642824i | ||||
\(727\) | 12.0000 | 0.445055 | 0.222528 | − | 0.974926i | \(-0.428569\pi\) | ||||
0.222528 | + | 0.974926i | \(0.428569\pi\) | |||||||
\(728\) | −3.50000 | + | 0.866025i | −0.129719 | + | 0.0320970i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 24.0000 | + | 41.5692i | 0.888280 | + | 1.53855i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −0.500000 | + | 0.866025i | −0.0184805 | + | 0.0320092i | ||||
\(733\) | 13.0000 | 0.480166 | 0.240083 | − | 0.970752i | \(-0.422825\pi\) | ||||
0.240083 | + | 0.970752i | \(0.422825\pi\) | |||||||
\(734\) | 9.00000 | − | 15.5885i | 0.332196 | − | 0.575380i | ||||
\(735\) | 2.00000 | − | 3.46410i | 0.0737711 | − | 0.127775i | ||||
\(736\) | −6.00000 | −0.221163 | ||||||||
\(737\) | 3.00000 | − | 5.19615i | 0.110506 | − | 0.191403i | ||||
\(738\) | 2.50000 | + | 4.33013i | 0.0920263 | + | 0.159394i | ||||
\(739\) | 27.0000 | + | 46.7654i | 0.993211 | + | 1.72029i | 0.597347 | + | 0.801983i | \(0.296222\pi\) |
0.395864 | + | 0.918309i | \(0.370445\pi\) | |||||||
\(740\) | 16.0000 | 0.588172 | ||||||||
\(741\) | 7.50000 | + | 7.79423i | 0.275519 | + | 0.286328i | ||||
\(742\) | 11.0000 | 0.403823 | ||||||||
\(743\) | −14.0000 | − | 24.2487i | −0.513610 | − | 0.889599i | −0.999875 | − | 0.0157876i | \(-0.994974\pi\) |
0.486265 | − | 0.873811i | \(-0.338359\pi\) | |||||||
\(744\) | 2.00000 | + | 3.46410i | 0.0733236 | + | 0.127000i | ||||
\(745\) | −36.0000 | + | 62.3538i | −1.31894 | + | 2.28447i | ||||
\(746\) | −34.0000 | −1.24483 | ||||||||
\(747\) | −3.00000 | + | 5.19615i | −0.109764 | + | 0.190117i | ||||
\(748\) | −7.50000 | + | 12.9904i | −0.274227 | + | 0.474975i | ||||
\(749\) | 17.0000 | 0.621166 | ||||||||
\(750\) | −12.0000 | + | 20.7846i | −0.438178 | + | 0.758947i | ||||
\(751\) | −15.5000 | − | 26.8468i | −0.565603 | − | 0.979653i | −0.996993 | − | 0.0774878i | \(-0.975310\pi\) |
0.431390 | − | 0.902165i | \(-0.358023\pi\) | |||||||
\(752\) | 1.50000 | + | 2.59808i | 0.0546994 | + | 0.0947421i | ||||
\(753\) | −14.0000 | −0.510188 | ||||||||
\(754\) | 31.5000 | − | 7.79423i | 1.14716 | − | 0.283849i | ||||
\(755\) | −44.0000 | −1.60132 | ||||||||
\(756\) | 0.500000 | + | 0.866025i | 0.0181848 | + | 0.0314970i | ||||
\(757\) | −11.0000 | − | 19.0526i | −0.399802 | − | 0.692477i | 0.593899 | − | 0.804539i | \(-0.297588\pi\) |
−0.993701 | + | 0.112062i | \(0.964254\pi\) | |||||||
\(758\) | −9.00000 | + | 15.5885i | −0.326895 | + | 0.566198i | ||||
\(759\) | 18.0000 | 0.653359 | ||||||||
\(760\) | 6.00000 | − | 10.3923i | 0.217643 | − | 0.376969i | ||||
\(761\) | 13.0000 | − | 22.5167i | 0.471250 | − | 0.816228i | −0.528209 | − | 0.849114i | \(-0.677136\pi\) |
0.999459 | + | 0.0328858i | \(0.0104698\pi\) | |||||||
\(762\) | 8.00000 | 0.289809 | ||||||||
\(763\) | 1.00000 | − | 1.73205i | 0.0362024 | − | 0.0627044i | ||||
\(764\) | 3.00000 | + | 5.19615i | 0.108536 | + | 0.187990i | ||||
\(765\) | 10.0000 | + | 17.3205i | 0.361551 | + | 0.626224i | ||||
\(766\) | 11.0000 | 0.397446 | ||||||||
\(767\) | 7.00000 | − | 1.73205i | 0.252755 | − | 0.0625407i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 2.00000 | + | 3.46410i | 0.0721218 | + | 0.124919i | 0.899831 | − | 0.436239i | \(-0.143690\pi\) |
−0.827709 | + | 0.561157i | \(0.810356\pi\) | |||||||
\(770\) | −6.00000 | − | 10.3923i | −0.216225 | − | 0.374513i | ||||
\(771\) | 3.50000 | − | 6.06218i | 0.126049 | − | 0.218324i | ||||
\(772\) | 13.0000 | 0.467880 | ||||||||
\(773\) | −9.00000 | + | 15.5885i | −0.323708 | + | 0.560678i | −0.981250 | − | 0.192740i | \(-0.938263\pi\) |
0.657542 | + | 0.753418i | \(0.271596\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −44.0000 | −1.58053 | ||||||||
\(776\) | −6.00000 | + | 10.3923i | −0.215387 | + | 0.373062i | ||||
\(777\) | 2.00000 | + | 3.46410i | 0.0717496 | + | 0.124274i | ||||
\(778\) | −13.0000 | − | 22.5167i | −0.466073 | − | 0.807261i | ||||
\(779\) | 15.0000 | 0.537431 | ||||||||
\(780\) | 10.0000 | + | 10.3923i | 0.358057 | + | 0.372104i | ||||
\(781\) | −18.0000 | −0.644091 | ||||||||
\(782\) | −15.0000 | − | 25.9808i | −0.536399 | − | 0.929070i | ||||
\(783\) | −4.50000 | − | 7.79423i | −0.160817 | − | 0.278543i | ||||
\(784\) | −0.500000 | + | 0.866025i | −0.0178571 | + | 0.0309295i | ||||
\(785\) | −8.00000 | −0.285532 | ||||||||
\(786\) | −6.00000 | + | 10.3923i | −0.214013 | + | 0.370681i | ||||
\(787\) | 5.50000 | − | 9.52628i | 0.196054 | − | 0.339575i | −0.751192 | − | 0.660084i | \(-0.770521\pi\) |
0.947245 | + | 0.320509i | \(0.103854\pi\) | |||||||
\(788\) | −19.0000 | −0.676847 | ||||||||
\(789\) | −13.0000 | + | 22.5167i | −0.462812 | + | 0.801614i | ||||
\(790\) | 22.0000 | + | 38.1051i | 0.782725 | + | 1.35572i | ||||
\(791\) | −6.00000 | − | 10.3923i | −0.213335 | − | 0.369508i | ||||
\(792\) | 3.00000 | 0.106600 | ||||||||
\(793\) | −3.50000 | + | 0.866025i | −0.124289 | + | 0.0307535i | ||||
\(794\) | 23.0000 | 0.816239 | ||||||||
\(795\) | −22.0000 | − | 38.1051i | −0.780260 | − | 1.35145i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.00000 | − | 1.73205i | 0.0354218 | − | 0.0613524i | −0.847771 | − | 0.530362i | \(-0.822056\pi\) |
0.883193 | + | 0.469010i | \(0.155389\pi\) | |||||||
\(798\) | 3.00000 | 0.106199 | ||||||||
\(799\) | −7.50000 | + | 12.9904i | −0.265331 | + | 0.459567i | ||||
\(800\) | 5.50000 | − | 9.52628i | 0.194454 | − | 0.336805i | ||||
\(801\) | 7.00000 | 0.247333 | ||||||||
\(802\) | 9.00000 | − | 15.5885i | 0.317801 | − | 0.550448i | ||||
\(803\) | 18.0000 | + | 31.1769i | 0.635206 | + | 1.10021i | ||||
\(804\) | 1.00000 | + | 1.73205i | 0.0352673 | + | 0.0610847i | ||||
\(805\) | 24.0000 | 0.845889 | ||||||||
\(806\) | −4.00000 | + | 13.8564i | −0.140894 | + | 0.488071i | ||||
\(807\) | 24.0000 | 0.844840 | ||||||||
\(808\) | 5.00000 | + | 8.66025i | 0.175899 | + | 0.304667i | ||||
\(809\) | 25.0000 | + | 43.3013i | 0.878953 | + | 1.52239i | 0.852491 | + | 0.522742i | \(0.175091\pi\) |
0.0264621 | + | 0.999650i | \(0.491576\pi\) | |||||||
\(810\) | 2.00000 | − | 3.46410i | 0.0702728 | − | 0.121716i | ||||
\(811\) | 24.0000 | 0.842754 | 0.421377 | − | 0.906886i | \(-0.361547\pi\) | ||||
0.421377 | + | 0.906886i | \(0.361547\pi\) | |||||||
\(812\) | 4.50000 | − | 7.79423i | 0.157919 | − | 0.273524i | ||||
\(813\) | −6.00000 | + | 10.3923i | −0.210429 | + | 0.364474i | ||||
\(814\) | 12.0000 | 0.420600 | ||||||||
\(815\) | −40.0000 | + | 69.2820i | −1.40114 | + | 2.42684i | ||||
\(816\) | −2.50000 | − | 4.33013i | −0.0875175 | − | 0.151585i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 2.00000 | 0.0699284 | ||||||||
\(819\) | −1.00000 | + | 3.46410i | −0.0349428 | + | 0.121046i | ||||
\(820\) | 20.0000 | 0.698430 | ||||||||
\(821\) | 7.50000 | + | 12.9904i | 0.261752 | + | 0.453367i | 0.966708 | − | 0.255884i | \(-0.0823665\pi\) |
−0.704956 | + | 0.709251i | \(0.749033\pi\) | |||||||
\(822\) | 9.00000 | + | 15.5885i | 0.313911 | + | 0.543710i | ||||
\(823\) | 8.00000 | − | 13.8564i | 0.278862 | − | 0.483004i | −0.692240 | − | 0.721668i | \(-0.743376\pi\) |
0.971102 | + | 0.238664i | \(0.0767093\pi\) | |||||||
\(824\) | −20.0000 | −0.696733 | ||||||||
\(825\) | −16.5000 | + | 28.5788i | −0.574456 | + | 0.994987i | ||||
\(826\) | 1.00000 | − | 1.73205i | 0.0347945 | − | 0.0602658i | ||||
\(827\) | 12.0000 | 0.417281 | 0.208640 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208640 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(828\) | −3.00000 | + | 5.19615i | −0.104257 | + | 0.180579i | ||||
\(829\) | −2.50000 | − | 4.33013i | −0.0868286 | − | 0.150392i | 0.819340 | − | 0.573307i | \(-0.194340\pi\) |
−0.906169 | + | 0.422916i | \(0.861007\pi\) | |||||||
\(830\) | 12.0000 | + | 20.7846i | 0.416526 | + | 0.721444i | ||||
\(831\) | −14.0000 | −0.485655 | ||||||||
\(832\) | −2.50000 | − | 2.59808i | −0.0866719 | − | 0.0900721i | ||||
\(833\) | −5.00000 | −0.173240 | ||||||||
\(834\) | −6.50000 | − | 11.2583i | −0.225077 | − | 0.389844i | ||||
\(835\) | 32.0000 | + | 55.4256i | 1.10741 | + | 1.91808i | ||||
\(836\) | 4.50000 | − | 7.79423i | 0.155636 | − | 0.269569i | ||||
\(837\) | 4.00000 | 0.138260 | ||||||||
\(838\) | 9.00000 | − | 15.5885i | 0.310900 | − | 0.538494i | ||||
\(839\) | −22.0000 | + | 38.1051i | −0.759524 | + | 1.31553i | 0.183569 | + | 0.983007i | \(0.441235\pi\) |
−0.943093 | + | 0.332528i | \(0.892098\pi\) | |||||||
\(840\) | 4.00000 | 0.138013 | ||||||||
\(841\) | −26.0000 | + | 45.0333i | −0.896552 | + | 1.55287i | ||||
\(842\) | −9.00000 | − | 15.5885i | −0.310160 | − | 0.537214i | ||||
\(843\) | 15.0000 | + | 25.9808i | 0.516627 | + | 0.894825i | ||||
\(844\) | 14.0000 | 0.481900 | ||||||||
\(845\) | −2.00000 | + | 51.9615i | −0.0688021 | + | 1.78753i | ||||
\(846\) | 3.00000 | 0.103142 | ||||||||
\(847\) | 1.00000 | + | 1.73205i | 0.0343604 | + | 0.0595140i | ||||
\(848\) | 5.50000 | + | 9.52628i | 0.188871 | + | 0.327134i | ||||
\(849\) | −2.00000 | + | 3.46410i | −0.0686398 | + | 0.118888i | ||||
\(850\) | 55.0000 | 1.88648 | ||||||||
\(851\) | −12.0000 | + | 20.7846i | −0.411355 | + | 0.712487i | ||||
\(852\) | 3.00000 | − | 5.19615i | 0.102778 | − | 0.178017i | ||||
\(853\) | 49.0000 | 1.67773 | 0.838864 | − | 0.544341i | \(-0.183220\pi\) | ||||
0.838864 | + | 0.544341i | \(0.183220\pi\) | |||||||
\(854\) | −0.500000 | + | 0.866025i | −0.0171096 | + | 0.0296348i | ||||
\(855\) | −6.00000 | − | 10.3923i | −0.205196 | − | 0.355409i | ||||
\(856\) | 8.50000 | + | 14.7224i | 0.290524 | + | 0.503202i | ||||
\(857\) | 10.0000 | 0.341593 | 0.170797 | − | 0.985306i | \(-0.445366\pi\) | ||||
0.170797 | + | 0.985306i | \(0.445366\pi\) | |||||||
\(858\) | 7.50000 | + | 7.79423i | 0.256046 | + | 0.266091i | ||||
\(859\) | −5.00000 | −0.170598 | −0.0852989 | − | 0.996355i | \(-0.527185\pi\) | ||||
−0.0852989 | + | 0.996355i | \(0.527185\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.50000 | + | 4.33013i | 0.0851998 | + | 0.147570i | ||||
\(862\) | 19.0000 | − | 32.9090i | 0.647143 | − | 1.12088i | ||||
\(863\) | −14.0000 | −0.476566 | −0.238283 | − | 0.971196i | \(-0.576585\pi\) | ||||
−0.238283 | + | 0.971196i | \(0.576585\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | 4.00000 | − | 6.92820i | 0.136004 | − | 0.235566i | ||||
\(866\) | −34.0000 | −1.15537 | ||||||||
\(867\) | 4.00000 | − | 6.92820i | 0.135847 | − | 0.235294i | ||||
\(868\) | 2.00000 | + | 3.46410i | 0.0678844 | + | 0.117579i | ||||
\(869\) | 16.5000 | + | 28.5788i | 0.559724 | + | 0.969471i | ||||
\(870\) | −36.0000 | −1.22051 | ||||||||
\(871\) | −2.00000 | + | 6.92820i | −0.0677674 | + | 0.234753i | ||||
\(872\) | 2.00000 | 0.0677285 | ||||||||
\(873\) | 6.00000 | + | 10.3923i | 0.203069 | + | 0.351726i | ||||
\(874\) | 9.00000 | + | 15.5885i | 0.304430 | + | 0.527287i | ||||
\(875\) | −12.0000 | + | 20.7846i | −0.405674 | + | 0.702648i | ||||
\(876\) | −12.0000 | −0.405442 | ||||||||
\(877\) | −21.0000 | + | 36.3731i | −0.709120 | + | 1.22823i | 0.256064 | + | 0.966660i | \(0.417574\pi\) |
−0.965184 | + | 0.261571i | \(0.915759\pi\) | |||||||
\(878\) | 20.0000 | − | 34.6410i | 0.674967 | − | 1.16908i | ||||
\(879\) | −24.0000 | −0.809500 | ||||||||
\(880\) | 6.00000 | − | 10.3923i | 0.202260 | − | 0.350325i | ||||
\(881\) | −1.00000 | − | 1.73205i | −0.0336909 | − | 0.0583543i | 0.848688 | − | 0.528893i | \(-0.177393\pi\) |
−0.882379 | + | 0.470539i | \(0.844059\pi\) | |||||||
\(882\) | 0.500000 | + | 0.866025i | 0.0168359 | + | 0.0291606i | ||||
\(883\) | −8.00000 | −0.269221 | −0.134611 | − | 0.990899i | \(-0.542978\pi\) | ||||
−0.134611 | + | 0.990899i | \(0.542978\pi\) | |||||||
\(884\) | 5.00000 | − | 17.3205i | 0.168168 | − | 0.582552i | ||||
\(885\) | −8.00000 | −0.268917 | ||||||||
\(886\) | −7.50000 | − | 12.9904i | −0.251967 | − | 0.436420i | ||||
\(887\) | −19.5000 | − | 33.7750i | −0.654746 | − | 1.13405i | −0.981957 | − | 0.189102i | \(-0.939442\pi\) |
0.327212 | − | 0.944951i | \(-0.393891\pi\) | |||||||
\(888\) | −2.00000 | + | 3.46410i | −0.0671156 | + | 0.116248i | ||||
\(889\) | 8.00000 | 0.268311 | ||||||||
\(890\) | 14.0000 | − | 24.2487i | 0.469281 | − | 0.812819i | ||||
\(891\) | 1.50000 | − | 2.59808i | 0.0502519 | − | 0.0870388i | ||||
\(892\) | −16.0000 | −0.535720 | ||||||||
\(893\) | 4.50000 | − | 7.79423i | 0.150587 | − | 0.260824i | ||||
\(894\) | −9.00000 | − | 15.5885i | −0.301005 | − | 0.521356i | ||||
\(895\) | −48.0000 | − | 83.1384i | −1.60446 | − | 2.77901i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −21.0000 | + | 5.19615i | −0.701170 | + | 0.173494i | ||||
\(898\) | −20.0000 | −0.667409 | ||||||||
\(899\) | −18.0000 | − | 31.1769i | −0.600334 | − | 1.03981i | ||||
\(900\) | −5.50000 | − | 9.52628i | −0.183333 | − | 0.317543i | ||||
\(901\) | −27.5000 | + | 47.6314i | −0.916158 | + | 1.58683i | ||||
\(902\) | 15.0000 | 0.499445 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.00000 | − | 10.3923i | 0.199557 | − | 0.345643i | ||||
\(905\) | −20.0000 | −0.664822 | ||||||||
\(906\) | 5.50000 | − | 9.52628i | 0.182725 | − | 0.316489i | ||||
\(907\) | 7.00000 | + | 12.1244i | 0.232431 | + | 0.402583i | 0.958523 | − | 0.285015i | \(-0.0919986\pi\) |
−0.726092 | + | 0.687598i | \(0.758665\pi\) | |||||||
\(908\) | −7.00000 | − | 12.1244i | −0.232303 | − | 0.402361i | ||||
\(909\) | 10.0000 | 0.331679 | ||||||||
\(910\) | 10.0000 | + | 10.3923i | 0.331497 | + | 0.344502i | ||||
\(911\) | −2.00000 | −0.0662630 | −0.0331315 | − | 0.999451i | \(-0.510548\pi\) | ||||
−0.0331315 | + | 0.999451i | \(0.510548\pi\) | |||||||
\(912\) | 1.50000 | + | 2.59808i | 0.0496700 | + | 0.0860309i | ||||
\(913\) | 9.00000 | + | 15.5885i | 0.297857 | + | 0.515903i | ||||
\(914\) | −1.00000 | + | 1.73205i | −0.0330771 | + | 0.0572911i | ||||
\(915\) | 4.00000 | 0.132236 | ||||||||
\(916\) | 2.50000 | − | 4.33013i | 0.0826023 | − | 0.143071i | ||||
\(917\) | −6.00000 | + | 10.3923i | −0.198137 | + | 0.343184i | ||||
\(918\) | −5.00000 | −0.165025 | ||||||||
\(919\) | 5.50000 | − | 9.52628i | 0.181428 | − | 0.314243i | −0.760939 | − | 0.648824i | \(-0.775261\pi\) |
0.942367 | + | 0.334581i | \(0.108595\pi\) | |||||||
\(920\) | 12.0000 | + | 20.7846i | 0.395628 | + | 0.685248i | ||||
\(921\) | 10.5000 | + | 18.1865i | 0.345987 | + | 0.599267i | ||||
\(922\) | 32.0000 | 1.05386 | ||||||||
\(923\) | 21.0000 | − | 5.19615i | 0.691223 | − | 0.171033i | ||||
\(924\) | 3.00000 | 0.0986928 | ||||||||
\(925\) | −22.0000 | − | 38.1051i | −0.723356 | − | 1.25289i | ||||
\(926\) | 0.500000 | + | 0.866025i | 0.0164310 | + | 0.0284594i | ||||
\(927\) | −10.0000 | + | 17.3205i | −0.328443 | + | 0.568880i | ||||
\(928\) | 9.00000 | 0.295439 | ||||||||
\(929\) | 11.5000 | − | 19.9186i | 0.377303 | − | 0.653508i | −0.613366 | − | 0.789799i | \(-0.710185\pi\) |
0.990669 | + | 0.136291i | \(0.0435183\pi\) | |||||||
\(930\) | 8.00000 | − | 13.8564i | 0.262330 | − | 0.454369i | ||||
\(931\) | 3.00000 | 0.0983210 | ||||||||
\(932\) | −2.00000 | + | 3.46410i | −0.0655122 | + | 0.113470i | ||||
\(933\) | −9.50000 | − | 16.4545i | −0.311016 | − | 0.538696i | ||||
\(934\) | −6.00000 | − | 10.3923i | −0.196326 | − | 0.340047i | ||||
\(935\) | 60.0000 | 1.96221 | ||||||||
\(936\) | −3.50000 | + | 0.866025i | −0.114401 | + | 0.0283069i | ||||
\(937\) | 44.0000 | 1.43742 | 0.718709 | − | 0.695311i | \(-0.244734\pi\) | ||||
0.718709 | + | 0.695311i | \(0.244734\pi\) | |||||||
\(938\) | 1.00000 | + | 1.73205i | 0.0326512 | + | 0.0565535i | ||||
\(939\) | −7.00000 | − | 12.1244i | −0.228436 | − | 0.395663i | ||||
\(940\) | 6.00000 | − | 10.3923i | 0.195698 | − | 0.338960i | ||||
\(941\) | 48.0000 | 1.56476 | 0.782378 | − | 0.622804i | \(-0.214007\pi\) | ||||
0.782378 | + | 0.622804i | \(0.214007\pi\) | |||||||
\(942\) | 1.00000 | − | 1.73205i | 0.0325818 | − | 0.0564333i | ||||
\(943\) | −15.0000 | + | 25.9808i | −0.488467 | + | 0.846050i | ||||
\(944\) | 2.00000 | 0.0650945 | ||||||||
\(945\) | 2.00000 | − | 3.46410i | 0.0650600 | − | 0.112687i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.50000 | − | 2.59808i | −0.0487435 | − | 0.0844261i | 0.840624 | − | 0.541619i | \(-0.182188\pi\) |
−0.889368 | + | 0.457193i | \(0.848855\pi\) | |||||||
\(948\) | −11.0000 | −0.357263 | ||||||||
\(949\) | −30.0000 | − | 31.1769i | −0.973841 | − | 1.01205i | ||||
\(950\) | −33.0000 | −1.07066 | ||||||||
\(951\) | −9.00000 | − | 15.5885i | −0.291845 | − | 0.505490i | ||||
\(952\) | −2.50000 | − | 4.33013i | −0.0810255 | − | 0.140340i | ||||
\(953\) | −12.0000 | + | 20.7846i | −0.388718 | + | 0.673280i | −0.992277 | − | 0.124039i | \(-0.960415\pi\) |
0.603559 | + | 0.797318i | \(0.293749\pi\) | |||||||
\(954\) | 11.0000 | 0.356138 | ||||||||
\(955\) | 12.0000 | − | 20.7846i | 0.388311 | − | 0.672574i | ||||
\(956\) | 13.0000 | − | 22.5167i | 0.420450 | − | 0.728241i | ||||
\(957\) | −27.0000 | −0.872786 | ||||||||
\(958\) | −16.5000 | + | 28.5788i | −0.533091 | + | 0.923340i | ||||
\(959\) | 9.00000 | + | 15.5885i | 0.290625 | + | 0.503378i | ||||
\(960\) | 2.00000 | + | 3.46410i | 0.0645497 | + | 0.111803i | ||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | −14.0000 | + | 3.46410i | −0.451378 | + | 0.111687i | ||||
\(963\) | 17.0000 | 0.547817 | ||||||||
\(964\) | −6.00000 | − | 10.3923i | −0.193247 | − | 0.334714i | ||||
\(965\) | −26.0000 | − | 45.0333i | −0.836970 | − | 1.44967i | ||||
\(966\) | −3.00000 | + | 5.19615i | −0.0965234 | + | 0.167183i | ||||
\(967\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(968\) | −1.00000 | + | 1.73205i | −0.0321412 | + | 0.0556702i | ||||
\(969\) | −7.50000 | + | 12.9904i | −0.240935 | + | 0.417311i | ||||
\(970\) | 48.0000 | 1.54119 | ||||||||
\(971\) | 25.0000 | − | 43.3013i | 0.802288 | − | 1.38960i | −0.115818 | − | 0.993270i | \(-0.536949\pi\) |
0.918107 | − | 0.396333i | \(-0.129718\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | −6.50000 | − | 11.2583i | −0.208380 | − | 0.360925i | ||||
\(974\) | 21.0000 | 0.672883 | ||||||||
\(975\) | 11.0000 | − | 38.1051i | 0.352282 | − | 1.22034i | ||||
\(976\) | −1.00000 | −0.0320092 | ||||||||
\(977\) | 2.00000 | + | 3.46410i | 0.0639857 | + | 0.110826i | 0.896244 | − | 0.443562i | \(-0.146285\pi\) |
−0.832258 | + | 0.554389i | \(0.812952\pi\) | |||||||
\(978\) | −10.0000 | − | 17.3205i | −0.319765 | − | 0.553849i | ||||
\(979\) | 10.5000 | − | 18.1865i | 0.335581 | − | 0.581244i | ||||
\(980\) | 4.00000 | 0.127775 | ||||||||
\(981\) | 1.00000 | − | 1.73205i | 0.0319275 | − | 0.0553001i | ||||
\(982\) | −10.0000 | + | 17.3205i | −0.319113 | + | 0.552720i | ||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | −2.50000 | + | 4.33013i | −0.0796971 | + | 0.138039i | ||||
\(985\) | 38.0000 | + | 65.8179i | 1.21078 | + | 2.09713i | ||||
\(986\) | 22.5000 | + | 38.9711i | 0.716546 | + | 1.24109i | ||||
\(987\) | 3.00000 | 0.0954911 | ||||||||
\(988\) | −3.00000 | + | 10.3923i | −0.0954427 | + | 0.330623i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −6.00000 | − | 10.3923i | −0.190693 | − | 0.330289i | ||||
\(991\) | −16.5000 | − | 28.5788i | −0.524140 | − | 0.907837i | −0.999605 | − | 0.0281022i | \(-0.991054\pi\) |
0.475465 | − | 0.879734i | \(-0.342280\pi\) | |||||||
\(992\) | −2.00000 | + | 3.46410i | −0.0635001 | + | 0.109985i | ||||
\(993\) | −2.00000 | −0.0634681 | ||||||||
\(994\) | 3.00000 | − | 5.19615i | 0.0951542 | − | 0.164812i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.00000 | −0.190117 | ||||||||
\(997\) | 6.50000 | − | 11.2583i | 0.205857 | − | 0.356555i | −0.744548 | − | 0.667568i | \(-0.767335\pi\) |
0.950405 | + | 0.311014i | \(0.100668\pi\) | |||||||
\(998\) | 20.0000 | + | 34.6410i | 0.633089 | + | 1.09654i | ||||
\(999\) | 2.00000 | + | 3.46410i | 0.0632772 | + | 0.109599i |
(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.l.h.211.1 | ✓ | 2 | |
3.2 | odd | 2 | 1638.2.r.a.757.1 | 2 | |||
13.3 | even | 3 | 7098.2.a.g.1.1 | 1 | |||
13.9 | even | 3 | inner | 546.2.l.h.295.1 | yes | 2 | |
13.10 | even | 6 | 7098.2.a.q.1.1 | 1 | |||
39.35 | odd | 6 | 1638.2.r.a.1387.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.l.h.211.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
546.2.l.h.295.1 | yes | 2 | 13.9 | even | 3 | inner | |
1638.2.r.a.757.1 | 2 | 3.2 | odd | 2 | |||
1638.2.r.a.1387.1 | 2 | 39.35 | odd | 6 | |||
7098.2.a.g.1.1 | 1 | 13.3 | even | 3 | |||
7098.2.a.q.1.1 | 1 | 13.10 | even | 6 |