Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [700,2,Mod(401,700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(700, 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("700.401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.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: | \(5.58952814149\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.1783323.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 501.3 | ||
Root | \(-0.956115 - 1.65604i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 700.501 |
Dual form | 700.2.i.d.401.3 |
$q$-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 \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(477\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.28442 | − | 2.22469i | 0.741563 | − | 1.28442i | −0.210220 | − | 0.977654i | \(-0.567418\pi\) |
0.951783 | − | 0.306771i | \(-0.0992485\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.58392 | − | 0.568650i | 0.976630 | − | 0.214929i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.79949 | − | 3.11682i | −0.599831 | − | 1.03894i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.784425 | − | 1.35866i | 0.236513 | − | 0.409652i | −0.723198 | − | 0.690640i | \(-0.757329\pi\) |
0.959711 | + | 0.280988i | \(0.0906621\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.56885 | 1.54452 | 0.772260 | − | 0.635306i | \(-0.219126\pi\) | ||||
0.772260 | + | 0.635306i | \(0.219126\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.58392 | + | 6.20753i | −0.869228 | + | 1.50555i | −0.00644117 | + | 0.999979i | \(0.502050\pi\) |
−0.862787 | + | 0.505568i | \(0.831283\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.58392 | − | 2.74343i | −0.363376 | − | 0.629386i | 0.625138 | − | 0.780514i | \(-0.285043\pi\) |
−0.988514 | + | 0.151129i | \(0.951709\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.05378 | − | 6.47880i | 0.448172 | − | 1.41379i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.86834 | − | 4.96812i | −0.598091 | − | 1.03592i | −0.993103 | − | 0.117248i | \(-0.962593\pi\) |
0.395012 | − | 0.918676i | \(-0.370741\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.53871 | −0.296125 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.96986 | 0.365794 | 0.182897 | − | 0.983132i | \(-0.441453\pi\) | ||||
0.182897 | + | 0.983132i | \(0.441453\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.484931 | + | 0.839925i | −0.0870961 | + | 0.150855i | −0.906282 | − | 0.422673i | \(-0.861092\pi\) |
0.819186 | + | 0.573527i | \(0.194425\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.01507 | − | 3.49020i | −0.350779 | − | 0.607566i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.35327 | + | 5.80804i | 0.551275 | + | 0.954836i | 0.998183 | + | 0.0602563i | \(0.0191918\pi\) |
−0.446908 | + | 0.894580i | \(0.647475\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.15277 | − | 12.3890i | 1.14536 | − | 1.98382i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.87439 | −1.38595 | −0.692973 | − | 0.720963i | \(-0.743700\pi\) | ||||
−0.692973 | + | 0.720963i | \(0.743700\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.59899 | −0.701339 | −0.350670 | − | 0.936499i | \(-0.614046\pi\) | ||||
−0.350670 | + | 0.936499i | \(0.614046\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.200506 | − | 0.347286i | −0.0292468 | − | 0.0506569i | 0.851032 | − | 0.525115i | \(-0.175978\pi\) |
−0.880278 | + | 0.474458i | \(0.842644\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.35327 | − | 2.93869i | 0.907611 | − | 0.419813i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.20655 | + | 15.9462i | 1.28917 | + | 2.23292i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.76936 | + | 8.26077i | −0.655121 | + | 1.13470i | 0.326742 | + | 0.945114i | \(0.394049\pi\) |
−0.981863 | + | 0.189590i | \(0.939284\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.13770 | −1.07786 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.28442 | − | 3.95674i | 0.297407 | − | 0.515124i | −0.678135 | − | 0.734937i | \(-0.737212\pi\) |
0.975542 | + | 0.219814i | \(0.0705449\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.65277 | − | 13.2550i | −0.979837 | − | 1.69713i | −0.662951 | − | 0.748663i | \(-0.730696\pi\) |
−0.316886 | − | 0.948464i | \(-0.602637\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.42212 | − | 7.03032i | −0.809112 | − | 0.885737i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.431150 | + | 0.746774i | −0.0526734 | + | 0.0912330i | −0.891160 | − | 0.453689i | \(-0.850108\pi\) |
0.838486 | + | 0.544922i | \(0.183441\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −14.7367 | −1.77409 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.1377 | −1.44048 | −0.720240 | − | 0.693725i | \(-0.755968\pi\) | ||||
−0.720240 | + | 0.693725i | \(0.755968\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.00000 | + | 3.46410i | −0.234082 | + | 0.405442i | −0.959006 | − | 0.283387i | \(-0.908542\pi\) |
0.724923 | + | 0.688830i | \(0.241875\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.25429 | − | 3.95674i | 0.142939 | − | 0.450912i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.43719 | + | 11.1495i | 0.724241 | + | 1.25442i | 0.959286 | + | 0.282437i | \(0.0911430\pi\) |
−0.235045 | + | 0.971985i | \(0.575524\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.42212 | − | 5.92729i | 0.380236 | − | 0.658588i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.1076 | 1.87780 | 0.938899 | − | 0.344192i | \(-0.111847\pi\) | ||||
0.938899 | + | 0.344192i | \(0.111847\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.53014 | − | 4.38233i | 0.271259 | − | 0.469835i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.79949 | + | 4.84887i | 0.296746 | + | 0.513979i | 0.975389 | − | 0.220489i | \(-0.0707653\pi\) |
−0.678644 | + | 0.734468i | \(0.737432\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.3895 | − | 3.16673i | 1.50842 | − | 0.331963i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.24571 | + | 2.15764i | 0.129175 | + | 0.223737i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.233174 | 0.0236752 | 0.0118376 | − | 0.999930i | \(-0.496232\pi\) | ||||
0.0118376 | + | 0.999930i | \(0.496232\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.64627 | −0.567472 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.25176 | + | 10.8284i | −0.622073 | + | 1.07746i | 0.367026 | + | 0.930211i | \(0.380376\pi\) |
−0.989099 | + | 0.147251i | \(0.952957\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.68544 | − | 2.91926i | −0.166071 | − | 0.287643i | 0.770964 | − | 0.636879i | \(-0.219775\pi\) |
−0.937035 | + | 0.349235i | \(0.886441\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.86834 | + | 15.3604i | 0.857335 | + | 1.48495i | 0.874462 | + | 0.485095i | \(0.161215\pi\) |
−0.0171265 | + | 0.999853i | \(0.505452\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.95226 | + | 5.11347i | −0.282775 | + | 0.489782i | −0.972067 | − | 0.234702i | \(-0.924588\pi\) |
0.689292 | + | 0.724484i | \(0.257922\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17.2281 | 1.63522 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.6412 | 1.47140 | 0.735701 | − | 0.677307i | \(-0.236853\pi\) | ||||
0.735701 | + | 0.677307i | \(0.236853\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.0211 | − | 17.3571i | −0.926452 | − | 1.60466i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.73064 | + | 18.0777i | −0.525327 | + | 1.65718i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.26936 | + | 7.39474i | 0.388123 | + | 0.672249i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.3985 | + | 19.7428i | −1.02777 | + | 1.78014i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.8744 | 1.14242 | 0.571209 | − | 0.820805i | \(-0.306475\pi\) | ||||
0.571209 | + | 0.820805i | \(0.306475\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.90705 | + | 10.2313i | −0.520087 | + | 0.900817i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.114058 | + | 0.197554i | 0.00996526 | + | 0.0172603i | 0.870965 | − | 0.491345i | \(-0.163495\pi\) |
−0.861000 | + | 0.508605i | \(0.830161\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.65277 | − | 6.18810i | −0.490157 | − | 0.536576i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.83821 | − | 8.38002i | 0.413356 | − | 0.715953i | −0.581899 | − | 0.813261i | \(-0.697690\pi\) |
0.995254 | + | 0.0973082i | \(0.0310233\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.3709 | −1.04928 | −0.524642 | − | 0.851323i | \(-0.675801\pi\) | ||||
−0.524642 | + | 0.851323i | \(0.675801\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.03014 | −0.0867533 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.36834 | − | 7.56619i | 0.365299 | − | 0.632717i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.62263 | − | 17.9086i | 0.133832 | − | 1.47708i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.95479 | − | 10.3140i | −0.487836 | − | 0.844956i | 0.512067 | − | 0.858946i | \(-0.328880\pi\) |
−0.999902 | + | 0.0139898i | \(0.995547\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.98493 | + | 8.63415i | −0.405668 | + | 0.702637i | −0.994399 | − | 0.105692i | \(-0.966294\pi\) |
0.588731 | + | 0.808329i | \(0.299628\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 25.7970 | 2.08556 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.02111 | − | 10.4289i | 0.480537 | − | 0.832315i | −0.519214 | − | 0.854645i | \(-0.673775\pi\) |
0.999751 | + | 0.0223299i | \(0.00710841\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.2518 | + | 21.2207i | 0.971628 | + | 1.68291i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.2367 | − | 11.2061i | −0.806764 | − | 0.883167i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.36834 | + | 14.4944i | 0.655459 | + | 1.13529i | 0.981778 | + | 0.190029i | \(0.0608582\pi\) |
−0.326319 | + | 0.945260i | \(0.605808\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.76683 | −0.523633 | −0.261816 | − | 0.965118i | \(-0.584321\pi\) | ||||
−0.261816 | + | 0.965118i | \(0.584321\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.0121 | 1.38555 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.70051 | + | 9.87357i | −0.435929 | + | 0.755050i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.34723 | − | 4.06552i | −0.178457 | − | 0.309096i | 0.762895 | − | 0.646522i | \(-0.223777\pi\) |
−0.941352 | + | 0.337426i | \(0.890444\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.86834 | − | 10.1643i | −0.441092 | − | 0.763993i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.73669 | + | 9.93623i | −0.428780 | + | 0.742669i | −0.996765 | − | 0.0803699i | \(-0.974390\pi\) |
0.567985 | + | 0.823039i | \(0.307723\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.832162 | 0.0618541 | 0.0309271 | − | 0.999522i | \(-0.490154\pi\) | ||||
0.0309271 | + | 0.999522i | \(0.490154\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −39.3176 | −2.90644 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.62263 | + | 9.73868i | 0.411167 | + | 0.712163i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.97590 | + | 0.874988i | −0.289204 | + | 0.0636460i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.46986 | − | 6.00998i | −0.251070 | − | 0.434867i | 0.712750 | − | 0.701418i | \(-0.247449\pi\) |
−0.963821 | + | 0.266551i | \(0.914116\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.83821 | + | 17.0403i | −0.708169 | + | 1.22659i | 0.257366 | + | 0.966314i | \(0.417145\pi\) |
−0.965535 | + | 0.260272i | \(0.916188\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.0422 | −1.14296 | −0.571481 | − | 0.820616i | \(-0.693631\pi\) | ||||
−0.571481 | + | 0.820616i | \(0.693631\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.33821 | − | 9.24604i | 0.378415 | − | 0.655435i | −0.612417 | − | 0.790535i | \(-0.709802\pi\) |
0.990832 | + | 0.135101i | \(0.0431358\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.10756 | + | 1.91835i | 0.0781213 | + | 0.135310i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.08996 | − | 1.12016i | 0.357245 | − | 0.0786199i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.3231 | + | 17.8802i | −0.717508 | + | 1.24276i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.96986 | −0.343772 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.3658 | 0.782455 | 0.391227 | − | 0.920294i | \(-0.372051\pi\) | ||||
0.391227 | + | 0.920294i | \(0.372051\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15.5900 | + | 27.0026i | −1.06821 | + | 1.85019i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.775398 | + | 2.44605i | −0.0526375 | + | 0.166049i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.13770 | + | 8.89876i | 0.347174 | + | 0.601322i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.9583 | + | 34.5688i | −1.34254 | + | 2.32535i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.04222 | −0.404617 | −0.202309 | − | 0.979322i | \(-0.564844\pi\) | ||||
−0.202309 | + | 0.979322i | \(0.564844\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.8206 | + | 18.7418i | −0.718189 | + | 1.24394i | 0.243528 | + | 0.969894i | \(0.421695\pi\) |
−0.961717 | + | 0.274046i | \(0.911638\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.71558 | + | 4.70351i | 0.179450 | + | 0.310817i | 0.941692 | − | 0.336475i | \(-0.109235\pi\) |
−0.762242 | + | 0.647292i | \(0.775901\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.19148 | − | 7.87253i | −0.473165 | − | 0.517975i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.46986 | + | 6.00998i | 0.227318 | + | 0.393727i | 0.957012 | − | 0.290047i | \(-0.0936709\pi\) |
−0.729694 | + | 0.683774i | \(0.760338\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 33.0724 | 2.14828 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.69446 | 0.109606 | 0.0548028 | − | 0.998497i | \(-0.482547\pi\) | ||||
0.0548028 | + | 0.998497i | \(0.482547\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.46733 | − | 12.9338i | 0.481013 | − | 0.833139i | −0.518749 | − | 0.854926i | \(-0.673602\pi\) |
0.999763 | + | 0.0217871i | \(0.00693559\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.0990 | − | 19.2240i | −0.712000 | − | 1.23322i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.82061 | − | 15.2777i | −0.561242 | − | 0.972099i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 21.9734 | − | 38.0590i | 1.39251 | − | 2.41189i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.90958 | 0.562368 | 0.281184 | − | 0.959654i | \(-0.409273\pi\) | ||||
0.281184 | + | 0.959654i | \(0.409273\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.00000 | −0.565825 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.83216 | − | 8.36955i | −0.301422 | − | 0.522078i | 0.675036 | − | 0.737785i | \(-0.264128\pi\) |
−0.976458 | + | 0.215706i | \(0.930795\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.9673 | + | 13.1007i | 0.743614 | + | 0.814036i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.54475 | − | 6.13969i | −0.219415 | − | 0.380038i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.05125 | − | 5.28492i | 0.188148 | − | 0.325882i | −0.756485 | − | 0.654011i | \(-0.773085\pi\) |
0.944633 | + | 0.328129i | \(0.106418\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.3830 | 0.880223 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.2668 | + | 19.5147i | −0.686951 | + | 1.18983i | 0.285869 | + | 0.958269i | \(0.407718\pi\) |
−0.972820 | + | 0.231565i | \(0.925616\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.23064 | − | 3.86359i | −0.135502 | − | 0.234696i | 0.790287 | − | 0.612737i | \(-0.209931\pi\) |
−0.925789 | + | 0.378040i | \(0.876598\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.4372 | − | 36.0795i | 0.692210 | − | 2.18363i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.25429 | + | 5.63659i | −0.195531 | + | 0.338670i | −0.947074 | − | 0.321014i | \(-0.895976\pi\) |
0.751543 | + | 0.659684i | \(0.229310\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.49052 | 0.208972 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.1980 | −0.668015 | −0.334008 | − | 0.942570i | \(-0.608401\pi\) | ||||
−0.334008 | + | 0.942570i | \(0.608401\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.82314 | − | 6.62187i | 0.227262 | − | 0.393629i | −0.729734 | − | 0.683731i | \(-0.760356\pi\) |
0.956996 | + | 0.290102i | \(0.0936893\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −22.9307 | + | 5.04642i | −1.35356 | + | 0.297881i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.1890 | − | 29.7721i | −1.01111 | − | 1.75130i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.299494 | − | 0.518739i | 0.0175567 | − | 0.0304090i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.12561 | 0.357862 | 0.178931 | − | 0.983862i | \(-0.442736\pi\) | ||||
0.178931 | + | 0.983862i | \(0.442736\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.20700 | + | 2.09059i | −0.0700374 | + | 0.121308i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.9734 | − | 27.6667i | −0.923764 | − | 1.60001i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.8834 | + | 2.61521i | −0.684949 | + | 0.150738i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.0598 | + | 27.8164i | 0.922613 | + | 1.59801i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.4080 | 1.50719 | 0.753593 | − | 0.657341i | \(-0.228319\pi\) | ||||
0.753593 | + | 0.657341i | \(0.228319\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.65927 | −0.492608 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.67641 | − | 16.7600i | 0.548699 | − | 0.950374i | −0.449665 | − | 0.893197i | \(-0.648457\pi\) |
0.998364 | − | 0.0571771i | \(-0.0182100\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.35327 | − | 7.54009i | −0.246062 | − | 0.426191i | 0.716368 | − | 0.697723i | \(-0.245803\pi\) |
−0.962430 | + | 0.271531i | \(0.912470\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.63770 | − | 13.2289i | −0.428976 | − | 0.743008i | 0.567807 | − | 0.823162i | \(-0.307792\pi\) |
−0.996782 | + | 0.0801539i | \(0.974459\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.54521 | − | 2.67638i | 0.0865150 | − | 0.149848i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 45.5629 | 2.54307 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 22.7065 | 1.26343 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.58392 | + | 13.1357i | 0.419392 | + | 0.726408i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.715575 | − | 0.783342i | −0.0394509 | − | 0.0431870i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.37439 | − | 14.5049i | −0.460298 | − | 0.797259i | 0.538678 | − | 0.842512i | \(-0.318924\pi\) |
−0.998976 | + | 0.0452526i | \(0.985591\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.0684 | − | 20.9031i | 0.661344 | − | 1.14548i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.2453 | −1.70204 | −0.851019 | − | 0.525135i | \(-0.824015\pi\) | ||||
−0.851019 | + | 0.525135i | \(0.824015\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 20.0900 | − | 34.7968i | 1.09114 | − | 1.88990i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.760783 | + | 1.31772i | 0.0411987 | + | 0.0713583i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.7453 | − | 11.2061i | 0.796169 | − | 0.605074i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.05125 | + | 10.4811i | −0.324848 | + | 0.562654i | −0.981482 | − | 0.191556i | \(-0.938647\pi\) |
0.656633 | + | 0.754210i | \(0.271980\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.87439 | −0.207391 | −0.103696 | − | 0.994609i | \(-0.533067\pi\) | ||||
−0.103696 | + | 0.994609i | \(0.533067\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.56885 | −0.457371 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.28190 | − | 2.22031i | 0.0682284 | − | 0.118175i | −0.829893 | − | 0.557922i | \(-0.811599\pi\) |
0.898122 | + | 0.439747i | \(0.144932\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 32.8568 | + | 35.9684i | 1.73897 | + | 1.90365i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.4196 | − | 18.0473i | −0.549925 | − | 0.952498i | −0.998279 | − | 0.0586422i | \(-0.981323\pi\) |
0.448354 | − | 0.893856i | \(-0.352010\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.48240 | − | 7.76375i | 0.235916 | − | 0.408618i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 21.9347 | 1.15127 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.91608 | − | 13.7111i | 0.413216 | − | 0.715711i | −0.582023 | − | 0.813172i | \(-0.697739\pi\) |
0.995239 | + | 0.0974609i | \(0.0310721\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 15.9694 | + | 27.6598i | 0.831334 | + | 1.43991i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.62614 | + | 24.0572i | −0.395930 | + | 1.24899i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.2518 | − | 19.4886i | −0.582594 | − | 1.00908i | −0.995171 | − | 0.0981594i | \(-0.968704\pi\) |
0.412577 | − | 0.910923i | \(-0.364629\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.9699 | 0.564977 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.36581 | −0.378356 | −0.189178 | − | 0.981943i | \(-0.560582\pi\) | ||||
−0.189178 | + | 0.981943i | \(0.560582\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.5362 | − | 28.6415i | 0.847174 | − | 1.46735i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.8266 | − | 29.1446i | −0.859802 | − | 1.48922i | −0.872118 | − | 0.489296i | \(-0.837254\pi\) |
0.0123162 | − | 0.999924i | \(-0.496080\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.27585 | + | 14.3342i | 0.420685 | + | 0.728648i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.74273 | + | 15.1429i | −0.443274 | + | 0.767773i | −0.997930 | − | 0.0643065i | \(-0.979516\pi\) |
0.554656 | + | 0.832080i | \(0.312850\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 41.1196 | 2.07951 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.585994 | 0.0295595 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.79949 | + | 6.58092i | 0.190691 | + | 0.330287i | 0.945479 | − | 0.325682i | \(-0.105594\pi\) |
−0.754788 | + | 0.655968i | \(0.772260\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −21.0272 | + | 4.62750i | −1.05267 | + | 0.231665i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.42212 | − | 9.39139i | −0.270768 | − | 0.468984i | 0.698291 | − | 0.715814i | \(-0.253944\pi\) |
−0.969059 | + | 0.246830i | \(0.920611\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.70051 | + | 4.67741i | −0.134522 | + | 0.232999i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.5216 | 0.521535 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.43466 | − | 14.6093i | 0.417067 | − | 0.722382i | −0.578576 | − | 0.815629i | \(-0.696391\pi\) |
0.995643 | + | 0.0932469i | \(0.0297246\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.4286 | − | 21.5270i | −0.613059 | − | 1.06185i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.65277 | − | 11.5229i | 0.179741 | − | 0.567006i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.8895 | + | 27.5213i | −0.778110 | + | 1.34773i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.03014 | −0.196885 | −0.0984426 | − | 0.995143i | \(-0.531386\pi\) | ||||
−0.0984426 | + | 0.995143i | \(0.531386\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.1196 | 1.22426 | 0.612128 | − | 0.790758i | \(-0.290314\pi\) | ||||
0.612128 | + | 0.790758i | \(0.290314\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.721618 | + | 1.24988i | −0.0350863 | + | 0.0607712i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −27.3116 | − | 29.8981i | −1.32170 | − | 1.44687i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.2216 | − | 19.4364i | −0.541785 | − | 0.938399i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.1201 | + | 26.1888i | −0.728310 | + | 1.26147i | 0.229288 | + | 0.973359i | \(0.426360\pi\) |
−0.957597 | + | 0.288111i | \(0.906973\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.9769 | −1.10420 | −0.552099 | − | 0.833778i | \(-0.686173\pi\) | ||||
−0.552099 | + | 0.833778i | \(0.686173\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.08645 | + | 15.7382i | −0.434664 | + | 0.752860i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.97590 | − | 10.3506i | −0.285214 | − | 0.494006i | 0.687447 | − | 0.726235i | \(-0.258731\pi\) |
−0.972661 | + | 0.232229i | \(0.925398\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.5920 | − | 14.5138i | −0.980573 | − | 0.691135i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.05378 | + | 12.2175i | 0.335135 | + | 0.580471i | 0.983511 | − | 0.180849i | \(-0.0578847\pi\) |
−0.648376 | + | 0.761321i | \(0.724551\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −30.5939 | −1.44704 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.9468 | 1.79082 | 0.895409 | − | 0.445245i | \(-0.146883\pi\) | ||||
0.895409 | + | 0.445245i | \(0.146883\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.96129 | + | 12.0573i | −0.327794 | + | 0.567756i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.8055 | + | 22.1798i | 0.601657 | + | 1.04210i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.27287 | + | 16.0611i | 0.433767 | + | 0.751306i | 0.997194 | − | 0.0748598i | \(-0.0238509\pi\) |
−0.563428 | + | 0.826165i | \(0.690518\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.51462 | − | 9.55159i | 0.257400 | − | 0.445830i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.2453 | −1.08264 | −0.541320 | − | 0.840817i | \(-0.682075\pi\) | ||||
−0.541320 | + | 0.840817i | \(0.682075\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.59393 | 0.352920 | 0.176460 | − | 0.984308i | \(-0.443535\pi\) | ||||
0.176460 | + | 0.984308i | \(0.443535\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.0839 | − | 24.3941i | −0.651726 | − | 1.12882i | −0.982704 | − | 0.185184i | \(-0.940712\pi\) |
0.330978 | − | 0.943639i | \(-0.392621\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.689404 | + | 2.17478i | −0.0318337 | + | 0.100422i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.4673 | − | 26.7902i | −0.712697 | − | 1.23443i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.60756 | + | 6.24848i | −0.165876 | + | 0.287305i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 34.3297 | 1.57185 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.0900 | − | 29.6007i | 0.780860 | − | 1.35249i | −0.150581 | − | 0.988598i | \(-0.548114\pi\) |
0.931441 | − | 0.363892i | \(-0.118552\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.6739 | + | 32.3441i | 0.851456 | + | 1.47476i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −38.0784 | + | 8.38002i | −1.73263 | + | 0.381304i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.75176 | − | 9.96234i | 0.260637 | − | 0.451436i | −0.705774 | − | 0.708437i | \(-0.749401\pi\) |
0.966411 | + | 0.257000i | \(0.0827341\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 42.9940 | 1.94426 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.5337 | −1.15232 | −0.576159 | − | 0.817338i | \(-0.695449\pi\) | ||||
−0.576159 | + | 0.817338i | \(0.695449\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.05982 | + | 12.2280i | −0.317958 | + | 0.550720i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −31.3628 | + | 6.90210i | −1.40682 | + | 0.309602i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.69798 | + | 9.86919i | 0.255076 | + | 0.441805i | 0.964916 | − | 0.262558i | \(-0.0845660\pi\) |
−0.709840 | + | 0.704363i | \(0.751233\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.69148 | + | 15.0541i | −0.388307 | + | 0.672567i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.49649 | −0.111313 | −0.0556564 | − | 0.998450i | \(-0.517725\pi\) | ||||
−0.0556564 | + | 0.998450i | \(0.517725\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 23.1352 | − | 40.0713i | 1.02747 | − | 1.77963i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.77188 | − | 9.99720i | −0.255834 | − | 0.443118i | 0.709287 | − | 0.704919i | \(-0.249017\pi\) |
−0.965122 | + | 0.261801i | \(0.915683\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.19798 | + | 10.0883i | −0.141470 | + | 0.446278i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.43719 | + | 4.22134i | 0.107605 | + | 0.186377i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.629127 | −0.0276690 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.0594 | −0.529348 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.8744 | + | 20.5670i | −0.520226 | + | 0.901058i | 0.479497 | + | 0.877543i | \(0.340819\pi\) |
−0.999723 | + | 0.0235150i | \(0.992514\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.06885 | − | 13.9757i | −0.352826 | − | 0.611113i | 0.633917 | − | 0.773401i | \(-0.281446\pi\) |
−0.986743 | + | 0.162288i | \(0.948113\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.47590 | − | 6.02044i | −0.151413 | − | 0.262255i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.95479 | + | 8.58195i | −0.215426 | + | 0.373128i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −16.4432 | −0.713576 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −49.4201 | −2.14062 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.7367 | + | 25.5247i | 0.635935 | + | 1.10147i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.990974 | − | 10.9371i | 0.0426843 | − | 0.471096i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.769355 | + | 1.33256i | 0.0330772 | + | 0.0572913i | 0.882090 | − | 0.471081i | \(-0.156136\pi\) |
−0.849013 | + | 0.528372i | \(0.822803\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.06885 | − | 1.85130i | 0.0458687 | − | 0.0794470i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.3779 | −0.614755 | −0.307377 | − | 0.951588i | \(-0.599451\pi\) | ||||
−0.307377 | + | 0.951588i | \(0.599451\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −27.5422 | + | 47.7045i | −1.17547 | + | 2.03598i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.12010 | − | 5.40417i | −0.132921 | − | 0.230226i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.9734 | + | 25.1490i | 0.976927 | + | 1.06944i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.46733 | − | 14.6658i | 0.358772 | − | 0.621412i | −0.628984 | − | 0.777419i | \(-0.716529\pi\) |
0.987756 | + | 0.156007i | \(0.0498621\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.6111 | −1.08323 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 28.8874 | 1.21963 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.332162 | + | 0.575322i | −0.0139990 | + | 0.0242469i | −0.872940 | − | 0.487828i | \(-0.837789\pi\) |
0.858941 | + | 0.512074i | \(0.171123\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.47194 | − | 17.2616i | 0.229800 | − | 0.724921i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.5186 | + | 35.5392i | 0.860184 | + | 1.48988i | 0.871751 | + | 0.489949i | \(0.162985\pi\) |
−0.0115674 | + | 0.999933i | \(0.503682\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.3146 | − | 24.7936i | 0.599046 | − | 1.03758i | −0.393916 | − | 0.919146i | \(-0.628880\pi\) |
0.992962 | − | 0.118432i | \(-0.0377866\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.8271 | −0.744738 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.7302 | + | 27.2455i | −0.654856 | + | 1.13424i | 0.327073 | + | 0.944999i | \(0.393938\pi\) |
−0.981930 | + | 0.189246i | \(0.939396\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25.2729 | + | 43.7739i | 1.05030 | + | 1.81918i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 44.2046 | − | 9.72821i | 1.83391 | − | 0.403594i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.48240 | + | 12.9599i | 0.309889 | + | 0.536744i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.53871 | −0.393705 | −0.196852 | − | 0.980433i | \(-0.563072\pi\) | ||||
−0.196852 | + | 0.980433i | \(0.563072\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.07236 | 0.126595 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.6050 | + | 35.6890i | −0.847578 | + | 1.46805i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.96986 | − | 8.60805i | −0.204088 | − | 0.353490i | 0.745754 | − | 0.666221i | \(-0.232089\pi\) |
−0.949842 | + | 0.312731i | \(0.898756\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.7130 | − | 23.7517i | −0.561238 | − | 0.972092i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.70655 | + | 8.15198i | −0.192304 | + | 0.333081i | −0.946014 | − | 0.324127i | \(-0.894929\pi\) |
0.753709 | + | 0.657208i | \(0.228263\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.00506 | −0.122579 | −0.0612894 | − | 0.998120i | \(-0.519521\pi\) | ||||
−0.0612894 | + | 0.998120i | \(0.519521\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.10341 | 0.126381 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.41608 | + | 16.3091i | 0.382187 | + | 0.661967i | 0.991375 | − | 0.131059i | \(-0.0418377\pi\) |
−0.609188 | + | 0.793026i | \(0.708504\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.04566 | − | 12.7623i | 0.163939 | − | 0.517156i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.11659 | − | 1.93399i | −0.0451723 | − | 0.0782407i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.91959 | + | 13.7171i | −0.319869 | + | 0.554030i | −0.980461 | − | 0.196716i | \(-0.936972\pi\) |
0.660591 | + | 0.750746i | \(0.270306\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.778912 | −0.0313578 | −0.0156789 | − | 0.999877i | \(-0.504991\pi\) | ||||
−0.0156789 | + | 0.999877i | \(0.504991\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.97338 | + | 8.61414i | −0.199897 | + | 0.346231i | −0.948495 | − | 0.316793i | \(-0.897394\pi\) |
0.748598 | + | 0.663024i | \(0.230727\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.41355 | + | 7.64450i | 0.177110 | + | 0.306763i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.99097 | + | 10.9371i | 0.400280 | + | 0.438187i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.38341 | + | 11.0564i | −0.254929 | + | 0.441550i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −48.0715 | −1.91673 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.5638 | −0.500157 | −0.250078 | − | 0.968226i | \(-0.580456\pi\) | ||||
−0.250078 | + | 0.968226i | \(0.580456\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.5985 | − | 25.2854i | 0.580240 | − | 1.00500i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 35.3804 | − | 16.3651i | 1.40182 | − | 0.648410i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 21.8417 | + | 37.8310i | 0.864045 | + | 1.49657i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.76033 | − | 9.97718i | 0.227519 | − | 0.394075i | −0.729553 | − | 0.683924i | \(-0.760272\pi\) |
0.957072 | + | 0.289849i | \(0.0936052\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.74175 | −0.384177 | −0.192088 | − | 0.981378i | \(-0.561526\pi\) | ||||
−0.192088 | + | 0.981378i | \(0.561526\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.8769 | − | 22.3035i | 0.506244 | − | 0.876840i | −0.493730 | − | 0.869615i | \(-0.664367\pi\) |
0.999974 | − | 0.00722479i | \(-0.00229974\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.58392 | − | 6.20753i | −0.140681 | − | 0.243667i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.44577 | + | 4.86679i | 0.174243 | + | 0.190745i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.59646 | + | 13.1575i | 0.297272 | + | 0.514891i | 0.975511 | − | 0.219951i | \(-0.0705897\pi\) |
−0.678239 | + | 0.734842i | \(0.737256\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.3960 | 0.561640 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.6894 | −0.572218 | −0.286109 | − | 0.958197i | \(-0.592362\pi\) | ||||
−0.286109 | + | 0.958197i | \(0.592362\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.16784 | + | 3.75481i | −0.0843191 | + | 0.146045i | −0.905101 | − | 0.425197i | \(-0.860205\pi\) |
0.820782 | + | 0.571242i | \(0.193538\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 51.2699 | + | 88.8020i | 1.99116 | + | 3.44879i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.65024 | − | 9.78650i | −0.218778 | − | 0.378935i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.76078 | + | 13.4421i | −0.300049 | + | 0.519700i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.0121 | −0.926976 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.1971 | 1.31820 | 0.659100 | − | 0.752055i | \(-0.270937\pi\) | ||||
0.659100 | + | 0.752055i | \(0.270937\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.04521 | − | 15.6668i | −0.347636 | − | 0.602122i | 0.638193 | − | 0.769876i | \(-0.279682\pi\) |
−0.985829 | + | 0.167754i | \(0.946349\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.602502 | − | 0.132594i | 0.0231219 | − | 0.00508850i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.7965 | + | 48.1450i | 1.06516 | + | 1.84492i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.0628 | − | 20.8934i | 0.461570 | − | 0.799464i | −0.537469 | − | 0.843284i | \(-0.680619\pi\) |
0.999039 | + | 0.0438200i | \(0.0139528\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.9518 | 0.532295 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −26.5598 | + | 46.0030i | −1.01185 | + | 1.75257i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.72415 | − | 15.1107i | −0.331882 | − | 0.574837i | 0.650999 | − | 0.759079i | \(-0.274350\pi\) |
−0.982881 | + | 0.184242i | \(0.941017\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14.5895 | + | 3.21075i | −0.554210 | + | 0.121966i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31.8051 | − | 55.0880i | 1.20470 | − | 2.08661i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17.8271 | 0.674283 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.7015 | 0.781885 | 0.390942 | − | 0.920415i | \(-0.372149\pi\) | ||||
0.390942 | + | 0.920415i | \(0.372149\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.6226 | − | 18.3989i | 0.400640 | − | 0.693929i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.99649 | + | 31.5347i | −0.375957 | + | 1.18598i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.54774 | − | 6.14486i | −0.133238 | − | 0.230775i | 0.791685 | − | 0.610930i | \(-0.209204\pi\) |
−0.924923 | + | 0.380154i | \(0.875871\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.1674 | − | 40.1271i | 0.868845 | − | 1.50488i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.56379 | 0.208366 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.17641 | − | 3.76965i | 0.0812795 | − | 0.140780i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.2216 | − | 45.4172i | −0.977901 | − | 1.69377i | −0.670008 | − | 0.742354i | \(-0.733709\pi\) |
−0.307893 | − | 0.951421i | \(-0.599624\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.01507 | − | 6.58471i | −0.224013 | − | 0.245227i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19.1825 | − | 33.2250i | −0.713403 | − | 1.23565i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.9045 | −1.10910 | −0.554549 | − | 0.832151i | \(-0.687109\pi\) | ||||
−0.554549 | + | 0.832151i | \(0.687109\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −36.4905 | −1.35150 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.4824 | − | 28.5484i | 0.609624 | − | 1.05590i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.79047 | − | 4.83323i | −0.103068 | − | 0.178519i | 0.809879 | − | 0.586597i | \(-0.199533\pi\) |
−0.912947 | + | 0.408077i | \(0.866199\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.676410 | + | 1.17158i | 0.0249159 | + | 0.0431556i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.3744 | + | 35.2895i | −0.749484 | + | 1.29814i | 0.198586 | + | 0.980083i | \(0.436365\pi\) |
−0.948070 | + | 0.318061i | \(0.896968\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −45.3176 | −1.66478 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 50.5327 | 1.85387 | 0.926933 | − | 0.375226i | \(-0.122435\pi\) | ||||
0.926933 | + | 0.375226i | \(0.122435\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −30.7850 | − | 53.3211i | −1.12636 | − | 1.95092i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 31.6498 | + | 34.6471i | 1.15646 | + | 1.26598i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.3568 | + | 26.5987i | 0.560377 | + | 0.970602i | 0.997463 | + | 0.0711821i | \(0.0226771\pi\) |
−0.437086 | + | 0.899420i | \(0.643990\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.4437 | − | 19.8211i | 0.417031 | − | 0.722319i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.7116 | −0.752776 | −0.376388 | − | 0.926462i | \(-0.622834\pi\) | ||||
−0.376388 | + | 0.926462i | \(0.622834\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.5598 | + | 20.0222i | −0.419595 | + | 0.726760i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.1764 | + | 29.7504i | 0.622644 | + | 1.07845i | 0.988991 | + | 0.147973i | \(0.0472750\pi\) |
−0.366347 | + | 0.930478i | \(0.619392\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.72063 | + | 14.8916i | −0.170898 | + | 0.539112i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.7216 | − | 22.0345i | 0.459351 | − | 0.795619i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 46.8392 | 1.68906 | 0.844532 | − | 0.535505i | \(-0.179879\pi\) | ||||
0.844532 | + | 0.535505i | \(0.179879\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.8262 | −0.894094 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.6653 | + | 28.8652i | −0.599409 | + | 1.03821i | 0.393499 | + | 0.919325i | \(0.371265\pi\) |
−0.992908 | + | 0.118883i | \(0.962069\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 44.5161 | − | 9.79677i | 1.59700 | − | 0.351457i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.0563 | + | 24.3462i | 0.503620 | + | 0.872295i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.52111 | + | 16.4911i | −0.340692 | + | 0.590096i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.03105 | −0.108321 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.20402 | + | 7.28158i | −0.149857 | + | 0.259560i | −0.931175 | − | 0.364574i | \(-0.881215\pi\) |
0.781317 | + | 0.624134i | \(0.214548\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.83821 | − | 13.5762i | −0.279047 | − | 0.483324i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 40.4156 | − | 8.89438i | 1.43701 | − | 0.316248i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −42.6171 | − | 73.8150i | −1.51338 | − | 2.62125i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.2935 | 0.577144 | 0.288572 | − | 0.957458i | \(-0.406820\pi\) | ||||
0.288572 | + | 0.957458i | \(0.406820\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.87439 | 0.101688 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.0753 | − | 17.4510i | 0.355995 | − | 0.616601i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.13770 | + | 5.43465i | 0.110727 | + | 0.191785i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 28.9428 | + | 50.1304i | 1.01883 | + | 1.76467i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.75176 | − | 13.4264i | 0.272537 | − | 0.472048i | −0.696974 | − | 0.717097i | \(-0.745471\pi\) |
0.969511 | + | 0.245048i | \(0.0788039\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.6232 | −1.28601 | −0.643007 | − | 0.765861i | \(-0.722313\pi\) | ||||
−0.643007 | + | 0.765861i | \(0.722313\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.4604 | −0.401933 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.28442 | + | 12.6170i | 0.254850 | + | 0.441413i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −35.7638 | − | 39.1508i | −1.24969 | − | 1.36804i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.6649 | + | 37.5246i | 0.756109 | + | 1.30962i | 0.944821 | + | 0.327586i | \(0.106235\pi\) |
−0.188713 | + | 0.982032i | \(0.560431\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.5272 | + | 35.5541i | −0.715532 | + | 1.23934i | 0.247222 | + | 0.968959i | \(0.420482\pi\) |
−0.962754 | + | 0.270378i | \(0.912851\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.0473 | 1.04485 | 0.522423 | − | 0.852686i | \(-0.325028\pi\) | ||||
0.522423 | + | 0.852686i | \(0.325028\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.0146 | − | 36.3984i | 0.729868 | − | 1.26417i | −0.227071 | − | 0.973878i | \(-0.572915\pi\) |
0.956939 | − | 0.290290i | \(-0.0937517\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.35977 | + | 14.4795i | 0.289997 | + | 0.502290i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.52761 | + | 49.9702i | −0.156872 | + | 1.73136i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.746168 | − | 1.29240i | 0.0257913 | − | 0.0446719i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.38893 | 0.116999 | 0.0584994 | − | 0.998287i | \(-0.481368\pi\) | ||||
0.0584994 | + | 0.998287i | \(0.481368\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.1196 | −0.866195 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.3830 | + | 24.9120i | −0.495375 | + | 0.858015i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.2367 | + | 16.6796i | 0.523539 | + | 0.573119i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.82106 | − | 17.0106i | −0.337058 | − | 0.583801i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.2367 | − | 33.3189i | 0.659425 | − | 1.14216i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.1267 | 0.860321 | 0.430160 | − | 0.902752i | \(-0.358457\pi\) | ||||
0.430160 | + | 0.902752i | \(0.358457\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.8683 | + | 41.3412i | −0.815327 | + | 1.41219i | 0.0937657 | + | 0.995594i | \(0.470110\pi\) |
−0.909093 | + | 0.416594i | \(0.863224\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.5211 | + | 35.5436i | 0.700171 | + | 1.21273i | 0.968406 | + | 0.249379i | \(0.0802264\pi\) |
−0.268235 | + | 0.963354i | \(0.586440\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18.2260 | + | 57.4954i | −0.621142 | + | 1.95944i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.5663 | − | 26.9617i | −0.529884 | − | 0.917786i | −0.999392 | − | 0.0348576i | \(-0.988902\pi\) |
0.469509 | − | 0.882928i | \(-0.344431\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −88.3117 | −2.99922 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.1980 | 0.685169 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.40101 | + | 4.15867i | −0.0813552 | + | 0.140911i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.419595 | − | 0.726760i | −0.0142011 | − | 0.0245971i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.96986 | − | 6.87600i | −0.134053 | − | 0.232186i | 0.791182 | − | 0.611580i | \(-0.209466\pi\) |
−0.925235 | + | 0.379394i | \(0.876132\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.86789 | − | 13.6276i | 0.265377 | − | 0.459647i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.3709 | −0.989530 | −0.494765 | − | 0.869027i | \(-0.664746\pi\) | ||||
−0.494765 | + | 0.869027i | \(0.664746\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.9718 | −0.907674 | −0.453837 | − | 0.891085i | \(-0.649945\pi\) | ||||
−0.453837 | + | 0.891085i | \(0.649945\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.7427 | + | 20.3390i | 0.394282 | + | 0.682917i | 0.993009 | − | 0.118036i | \(-0.0376599\pi\) |
−0.598727 | + | 0.800953i | \(0.704327\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 33.2664 | − | 7.32102i | 1.11572 | − | 0.245539i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.36880 | − | 9.29903i | −0.179861 | − | 0.311529i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.635170 | + | 1.10015i | −0.0212552 | + | 0.0368150i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −82.0664 | −2.74012 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.955246 | + | 1.65453i | −0.0318592 | + | 0.0551818i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −34.1860 | − | 59.2118i | −1.13890 | − | 1.97263i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.44531 | + | 29.7959i | −0.314320 | + | 0.991547i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.79345 | + | 8.30250i | −0.159164 | + | 0.275680i | −0.934567 | − | 0.355786i | \(-0.884213\pi\) |
0.775403 | + | 0.631466i | \(0.217547\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 45.0000 | 1.49256 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.78994 | −0.125566 | −0.0627831 | − | 0.998027i | \(-0.519998\pi\) | ||||
−0.0627831 | + | 0.998027i | \(0.519998\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.4196 | − | 23.2434i | 0.444124 | − | 0.769245i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.407055 | + | 0.445604i | 0.0134421 | + | 0.0147151i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.6950 | − | 20.2563i | −0.385782 | − | 0.668194i | 0.606095 | − | 0.795392i | \(-0.292735\pi\) |
−0.991877 | + | 0.127198i | \(0.959402\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 33.9191 | − | 58.7497i | 1.11767 | − | 1.93587i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −67.5930 | −2.22485 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.06587 | + | 10.5064i | −0.199229 | + | 0.345075i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.1287 | − | 43.5241i | −0.824445 | − | 1.42798i | −0.902343 | − | 0.431019i | \(-0.858154\pi\) |
0.0778977 | − | 0.996961i | \(-0.475179\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.1252 | − | 12.7751i | −0.594028 | − | 0.418687i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.8572 | − | 43.0540i | −0.813790 | − | 1.40952i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.43621 | −0.0795875 | −0.0397937 | − | 0.999208i | \(-0.512670\pi\) | ||||
−0.0397937 | + | 0.999208i | \(0.512670\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.3658 | −0.729881 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.9824 | − | 20.7541i | 0.390615 | − | 0.676565i | −0.601916 | − | 0.798560i | \(-0.705596\pi\) |
0.992531 | + | 0.121994i | \(0.0389290\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.4548 | + | 44.0890i | 0.828922 | + | 1.43574i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.5809 | + | 44.3075i | 0.831269 | + | 1.43980i | 0.897033 | + | 0.441964i | \(0.145718\pi\) |
−0.0657639 | + | 0.997835i | \(0.520948\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.1377 | + | 19.2911i | −0.361545 | + | 0.626214i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −39.2402 | −1.27245 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.3306 | 1.07968 | 0.539842 | − | 0.841766i | \(-0.318484\pi\) | ||||
0.539842 | + | 0.841766i | \(0.318484\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.96941 | − | 6.87521i | −0.128313 | − | 0.222244i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.73623 | − | 24.4045i | 0.249816 | − | 0.788063i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0297 | + | 26.0322i | 0.484829 | + | 0.839748i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 31.9171 | − | 55.2820i | 1.02851 | − | 1.78144i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.8392 | −1.02388 | −0.511940 | − | 0.859021i | \(-0.671073\pi\) | ||||
−0.511940 | + | 0.859021i | \(0.671073\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 29.1649 | − | 50.5150i | 0.936910 | − | 1.62278i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.973375 | − | 1.68594i | −0.0312371 | − | 0.0541042i | 0.849984 | − | 0.526808i | \(-0.176611\pi\) |
−0.881221 | + | 0.472704i | \(0.843278\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −31.9653 | + | 7.03470i | −1.02476 | + | 0.225522i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.0598 | − | 43.4049i | 0.801735 | − | 1.38865i | −0.116739 | − | 0.993163i | \(-0.537244\pi\) |
0.918473 | − | 0.395483i | \(-0.129423\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.78397 | 0.280737 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21.2503 | 0.678470 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.9608 | − | 41.5014i | 0.764232 | − | 1.32369i | −0.176420 | − | 0.984315i | \(-0.556452\pi\) |
0.940652 | − | 0.339374i | \(-0.110215\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.66179 | + | 0.585788i | −0.0847259 | + | 0.0186458i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.1915 | + | 22.8483i | 0.419465 | + | 0.726534i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.43466 | + | 7.68106i | −0.140872 | + | 0.243997i | −0.927825 | − | 0.373015i | \(-0.878324\pi\) |
0.786953 | + | 0.617012i | \(0.211657\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −43.0251 | −1.36536 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.10503 | + | 10.5742i | −0.193348 | + | 0.334889i | −0.946358 | − | 0.323121i | \(-0.895268\pi\) |
0.753010 | + | 0.658010i | \(0.228601\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.15972 | − | 8.93690i | −0.163246 | − | 0.282751i |
(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 | 700.2.i.d.501.3 | yes | 6 | |
5.2 | odd | 4 | 700.2.r.d.249.2 | 12 | |||
5.3 | odd | 4 | 700.2.r.d.249.5 | 12 | |||
5.4 | even | 2 | 700.2.i.e.501.1 | yes | 6 | ||
7.2 | even | 3 | inner | 700.2.i.d.401.3 | ✓ | 6 | |
7.3 | odd | 6 | 4900.2.a.bb.1.3 | 3 | |||
7.4 | even | 3 | 4900.2.a.bc.1.1 | 3 | |||
35.2 | odd | 12 | 700.2.r.d.149.5 | 12 | |||
35.3 | even | 12 | 4900.2.e.s.2549.5 | 6 | |||
35.4 | even | 6 | 4900.2.a.ba.1.3 | 3 | |||
35.9 | even | 6 | 700.2.i.e.401.1 | yes | 6 | ||
35.17 | even | 12 | 4900.2.e.s.2549.2 | 6 | |||
35.18 | odd | 12 | 4900.2.e.t.2549.2 | 6 | |||
35.23 | odd | 12 | 700.2.r.d.149.2 | 12 | |||
35.24 | odd | 6 | 4900.2.a.bd.1.1 | 3 | |||
35.32 | odd | 12 | 4900.2.e.t.2549.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
700.2.i.d.401.3 | ✓ | 6 | 7.2 | even | 3 | inner | |
700.2.i.d.501.3 | yes | 6 | 1.1 | even | 1 | trivial | |
700.2.i.e.401.1 | yes | 6 | 35.9 | even | 6 | ||
700.2.i.e.501.1 | yes | 6 | 5.4 | even | 2 | ||
700.2.r.d.149.2 | 12 | 35.23 | odd | 12 | |||
700.2.r.d.149.5 | 12 | 35.2 | odd | 12 | |||
700.2.r.d.249.2 | 12 | 5.2 | odd | 4 | |||
700.2.r.d.249.5 | 12 | 5.3 | odd | 4 | |||
4900.2.a.ba.1.3 | 3 | 35.4 | even | 6 | |||
4900.2.a.bb.1.3 | 3 | 7.3 | odd | 6 | |||
4900.2.a.bc.1.1 | 3 | 7.4 | even | 3 | |||
4900.2.a.bd.1.1 | 3 | 35.24 | odd | 6 | |||
4900.2.e.s.2549.2 | 6 | 35.17 | even | 12 | |||
4900.2.e.s.2549.5 | 6 | 35.3 | even | 12 | |||
4900.2.e.t.2549.2 | 6 | 35.18 | odd | 12 | |||
4900.2.e.t.2549.5 | 6 | 35.32 | odd | 12 |