Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2940,2,Mod(949,2940)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2940, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2940.949");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2940.bb (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(23.4760181943\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 949.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2940.949 |
Dual form | 2940.2.bb.c.1549.1 |
$q$-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 \(\left(\mathbb{Z}/2940\mathbb{Z}\right)^\times\).
\(n\) | \(1081\) | \(1177\) | \(1471\) | \(1961\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.86603 | − | 1.23205i | −0.834512 | − | 0.550990i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | − | 3.46410i | 0.603023 | − | 1.04447i | −0.389338 | − | 0.921095i | \(-0.627296\pi\) |
0.992361 | − | 0.123371i | \(-0.0393705\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.00000i | 1.66410i | 0.554700 | + | 0.832050i | \(0.312833\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | + | 2.00000i | 0.258199 | + | 0.516398i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.73205 | − | 1.00000i | −0.420084 | − | 0.242536i | 0.275029 | − | 0.961436i | \(-0.411312\pi\) |
−0.695113 | + | 0.718900i | \(0.744646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.00000 | − | 5.19615i | −0.688247 | − | 1.19208i | −0.972404 | − | 0.233301i | \(-0.925047\pi\) |
0.284157 | − | 0.958778i | \(-0.408286\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.73205 | − | 1.00000i | 0.361158 | − | 0.208514i | −0.308431 | − | 0.951247i | \(-0.599804\pi\) |
0.669588 | + | 0.742732i | \(0.266471\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.96410 | + | 4.59808i | 0.392820 | + | 0.919615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | + | 1.73205i | −0.179605 | + | 0.311086i | −0.941745 | − | 0.336327i | \(-0.890815\pi\) |
0.762140 | + | 0.647412i | \(0.224149\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.46410 | + | 2.00000i | −0.603023 | + | 0.348155i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.46410 | − | 2.00000i | 0.569495 | − | 0.328798i | −0.187453 | − | 0.982274i | \(-0.560023\pi\) |
0.756948 | + | 0.653476i | \(0.226690\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.00000 | − | 5.19615i | 0.480384 | − | 0.832050i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.00000 | −1.24939 | −0.624695 | − | 0.780869i | \(-0.714777\pi\) | ||||
−0.624695 | + | 0.780869i | \(0.714777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.00000i | − | 0.609994i | −0.952353 | − | 0.304997i | \(-0.901344\pi\) | ||
0.952353 | − | 0.304997i | \(-0.0986555\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.133975 | − | 2.23205i | 0.0199718 | − | 0.332734i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.46410 | − | 2.00000i | 0.505291 | − | 0.291730i | −0.225605 | − | 0.974219i | \(-0.572436\pi\) |
0.730896 | + | 0.682489i | \(0.239102\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.00000 | + | 1.73205i | 0.140028 | + | 0.242536i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.19615 | − | 3.00000i | −0.713746 | − | 0.412082i | 0.0987002 | − | 0.995117i | \(-0.468532\pi\) |
−0.812447 | + | 0.583036i | \(0.801865\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.00000 | + | 4.00000i | −1.07872 | + | 0.539360i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.00000i | 0.794719i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.00000 | + | 3.46410i | −0.260378 | + | 0.450988i | −0.966342 | − | 0.257260i | \(-0.917180\pi\) |
0.705965 | + | 0.708247i | \(0.250514\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.00000 | + | 12.1244i | 0.896258 | + | 1.55236i | 0.832240 | + | 0.554416i | \(0.187058\pi\) |
0.0640184 | + | 0.997949i | \(0.479608\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.39230 | − | 11.1962i | 0.916903 | − | 1.38871i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.46410 | + | 2.00000i | 0.423207 | + | 0.244339i | 0.696449 | − | 0.717607i | \(-0.254762\pi\) |
−0.273241 | + | 0.961946i | \(0.588096\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.00000 | −0.240772 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.66025 | − | 5.00000i | −1.01361 | − | 0.585206i | −0.101361 | − | 0.994850i | \(-0.532320\pi\) |
−0.912245 | + | 0.409644i | \(0.865653\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.598076 | − | 4.96410i | 0.0690599 | − | 0.573205i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.0000i | 1.75623i | 0.478451 | + | 0.878114i | \(0.341198\pi\) | ||||
−0.478451 | + | 0.878114i | \(0.658802\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000 | + | 4.00000i | 0.216930 | + | 0.433861i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.19615 | + | 3.00000i | 0.557086 | + | 0.321634i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.00000 | − | 6.92820i | −0.423999 | − | 0.734388i | 0.572327 | − | 0.820025i | \(-0.306041\pi\) |
−0.996326 | + | 0.0856373i | \(0.972707\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.73205 | − | 1.00000i | 0.179605 | − | 0.103695i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.803848 | + | 13.3923i | −0.0824730 | + | 1.37402i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0000i | 1.01535i | 0.861550 | + | 0.507673i | \(0.169494\pi\) | ||||
−0.861550 | + | 0.507673i | \(0.830506\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.00000 | 0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.00000 | − | 13.8564i | 0.796030 | − | 1.37876i | −0.126153 | − | 0.992011i | \(-0.540263\pi\) |
0.922183 | − | 0.386753i | \(-0.126403\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.8564 | + | 8.00000i | −1.36531 | + | 0.788263i | −0.990325 | − | 0.138767i | \(-0.955686\pi\) |
−0.374987 | + | 0.927030i | \(0.622353\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.19615 | − | 3.00000i | 0.502331 | − | 0.290021i | −0.227345 | − | 0.973814i | \(-0.573004\pi\) |
0.729676 | + | 0.683793i | \(0.239671\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.00000 | + | 12.1244i | −0.670478 | + | 1.16130i | 0.307290 | + | 0.951616i | \(0.400578\pi\) |
−0.977769 | + | 0.209687i | \(0.932756\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.00000 | −0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.0000i | 1.69330i | 0.532152 | + | 0.846649i | \(0.321383\pi\) | ||||
−0.532152 | + | 0.846649i | \(0.678617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.46410 | − | 0.267949i | −0.416280 | − | 0.0249864i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.19615 | + | 3.00000i | −0.480384 | + | 0.277350i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.50000 | − | 4.33013i | −0.227273 | − | 0.393648i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.92820 | + | 4.00000i | 0.624695 | + | 0.360668i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.00000 | − | 11.0000i | 0.178885 | − | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0000i | 1.41977i | 0.704317 | + | 0.709885i | \(0.251253\pi\) | ||||
−0.704317 | + | 0.709885i | \(0.748747\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.00000 | + | 3.46410i | −0.176090 | + | 0.304997i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00000 | − | 10.3923i | −0.524222 | − | 0.907980i | −0.999602 | − | 0.0281993i | \(-0.991023\pi\) |
0.475380 | − | 0.879781i | \(-0.342311\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.23205 | + | 1.86603i | −0.106038 | + | 0.160602i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.5885 | + | 9.00000i | 1.33181 | + | 0.768922i | 0.985577 | − | 0.169226i | \(-0.0541268\pi\) |
0.346235 | + | 0.938148i | \(0.387460\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0000 | 0.848189 | 0.424094 | − | 0.905618i | \(-0.360592\pi\) | ||||
0.424094 | + | 0.905618i | \(0.360592\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.00000 | −0.336861 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 20.7846 | + | 12.0000i | 1.73810 | + | 1.00349i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.1962 | + | 7.39230i | 0.929790 | + | 0.613898i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.0000 | + | 19.0526i | 0.901155 | + | 1.56085i | 0.825997 | + | 0.563675i | \(0.190613\pi\) |
0.0751583 | + | 0.997172i | \(0.476054\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | + | 13.8564i | −0.651031 | + | 1.12762i | 0.331842 | + | 0.943335i | \(0.392330\pi\) |
−0.982873 | + | 0.184284i | \(0.941004\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.00000i | − | 0.161690i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | − | 2.00000i | 0.321288 | − | 0.160644i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.66025 | − | 5.00000i | −0.691164 | − | 0.399043i | 0.112884 | − | 0.993608i | \(-0.463991\pi\) |
−0.804048 | + | 0.594565i | \(0.797324\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.00000 | + | 5.19615i | 0.237915 | + | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.92820 | + | 4.00000i | −0.542659 | + | 0.313304i | −0.746156 | − | 0.665771i | \(-0.768103\pi\) |
0.203497 | + | 0.979076i | \(0.434769\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.92820 | + | 0.535898i | 0.695060 | + | 0.0417196i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 24.0000i | 1.85718i | 0.371113 | + | 0.928588i | \(0.378976\pi\) | ||||
−0.371113 | + | 0.928588i | \(0.621024\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.0000 | −1.76923 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.00000 | − | 5.19615i | 0.229416 | − | 0.397360i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.73205 | − | 1.00000i | 0.131685 | − | 0.0760286i | −0.432710 | − | 0.901533i | \(-0.642443\pi\) |
0.564396 | + | 0.825505i | \(0.309109\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.46410 | − | 2.00000i | 0.260378 | − | 0.150329i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.00000 | − | 3.46410i | 0.149487 | − | 0.258919i | −0.781551 | − | 0.623841i | \(-0.785571\pi\) |
0.931038 | + | 0.364922i | \(0.118904\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 14.0000i | − | 1.03491i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.92820 | − | 0.535898i | −0.656415 | − | 0.0394000i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.92820 | + | 4.00000i | −0.506640 | + | 0.292509i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.92820 | − | 4.00000i | −0.498703 | − | 0.287926i | 0.229475 | − | 0.973315i | \(-0.426299\pi\) |
−0.728178 | + | 0.685388i | \(0.759632\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −12.0000 | + | 6.00000i | −0.859338 | + | 0.429669i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 10.0000i | − | 0.712470i | −0.934396 | − | 0.356235i | \(-0.884060\pi\) | ||
0.934396 | − | 0.356235i | \(-0.115940\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.00000 | + | 15.5885i | −0.637993 | + | 1.10504i | 0.347879 | + | 0.937539i | \(0.386902\pi\) |
−0.985873 | + | 0.167497i | \(0.946431\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.00000 | − | 3.46410i | −0.141069 | − | 0.244339i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.9282 | + | 9.85641i | 1.04263 | + | 0.688401i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.73205 | + | 1.00000i | 0.120386 | + | 0.0695048i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −24.0000 | −1.66011 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.0000 | −1.65223 | −0.826114 | − | 0.563503i | \(-0.809453\pi\) | ||||
−0.826114 | + | 0.563503i | \(0.809453\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.92820 | + | 7.46410i | −0.336101 | + | 0.509048i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.00000 | + | 8.66025i | 0.337869 | + | 0.585206i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.00000 | − | 10.3923i | 0.403604 | − | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.0000i | 1.07144i | 0.844396 | + | 0.535720i | \(0.179960\pi\) | ||||
−0.844396 | + | 0.535720i | \(0.820040\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | + | 4.00000i | −0.200000 | + | 0.266667i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.3205 | − | 10.0000i | −1.14960 | − | 0.663723i | −0.200812 | − | 0.979630i | \(-0.564358\pi\) |
−0.948790 | + | 0.315906i | \(0.897691\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.00000 | − | 1.73205i | −0.0660819 | − | 0.114457i | 0.831092 | − | 0.556136i | \(-0.187717\pi\) |
−0.897173 | + | 0.441679i | \(0.854383\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.5167 | + | 13.0000i | −1.47512 | + | 0.851658i | −0.999606 | − | 0.0280525i | \(-0.991069\pi\) |
−0.475509 | + | 0.879711i | \(0.657736\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.92820 | − | 0.535898i | −0.582412 | − | 0.0349582i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.0000 | 1.03495 | 0.517477 | − | 0.855697i | \(-0.326871\pi\) | ||||
0.517477 | + | 0.855697i | \(0.326871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.00000 | − | 8.66025i | 0.322078 | − | 0.557856i | −0.658838 | − | 0.752285i | \(-0.728952\pi\) |
0.980917 | + | 0.194429i | \(0.0622852\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 31.1769 | − | 18.0000i | 1.98374 | − | 1.14531i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.00000 | − | 13.8564i | 0.506979 | − | 0.878114i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 8.00000i | − | 0.502956i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.267949 | − | 4.46410i | 0.0167796 | − | 0.279553i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.19615 | − | 3.00000i | 0.324127 | − | 0.187135i | −0.329104 | − | 0.944294i | \(-0.606747\pi\) |
0.653231 | + | 0.757159i | \(0.273413\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.00000 | − | 5.19615i | −0.185695 | − | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.66025 | + | 5.00000i | 0.534014 | + | 0.308313i | 0.742650 | − | 0.669680i | \(-0.233569\pi\) |
−0.208635 | + | 0.977993i | \(0.566902\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.00000 | + | 12.0000i | 0.368577 | + | 0.737154i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.00000i | 0.489592i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.00000 | − | 10.3923i | 0.365826 | − | 0.633630i | −0.623082 | − | 0.782157i | \(-0.714120\pi\) |
0.988908 | + | 0.148527i | \(0.0474530\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.00000 | − | 12.1244i | −0.425220 | − | 0.736502i | 0.571221 | − | 0.820796i | \(-0.306470\pi\) |
−0.996441 | + | 0.0842940i | \(0.973137\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 19.8564 | + | 2.39230i | 1.19739 | + | 0.144261i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.2487 | − | 14.0000i | −1.45696 | − | 0.841178i | −0.458103 | − | 0.888899i | \(-0.651471\pi\) |
−0.998861 | + | 0.0477206i | \(0.984804\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.00000 | −0.119737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.2487 | + | 14.0000i | 1.44144 | + | 0.832214i | 0.997946 | − | 0.0640654i | \(-0.0204066\pi\) |
0.443491 | + | 0.896279i | \(0.353740\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.39230 | − | 11.1962i | 0.437882 | − | 0.663203i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.50000 | − | 11.2583i | −0.382353 | − | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.00000 | − | 8.66025i | 0.293105 | − | 0.507673i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.00000i | 0.350524i | 0.984522 | + | 0.175262i | \(0.0560772\pi\) | ||||
−0.984522 | + | 0.175262i | \(0.943923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000 | − | 4.00000i | 0.465778 | − | 0.232889i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.46410 | − | 2.00000i | −0.201008 | − | 0.116052i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.00000 | + | 10.3923i | 0.346989 | + | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.8564 | + | 8.00000i | −0.796030 | + | 0.459588i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.87564 | − | 31.2487i | 0.107399 | − | 1.78930i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 12.0000i | − | 0.684876i | −0.939540 | − | 0.342438i | \(-0.888747\pi\) | ||
0.939540 | − | 0.342438i | \(-0.111253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.0000 | 0.910208 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.00000 | − | 10.3923i | 0.340229 | − | 0.589294i | −0.644246 | − | 0.764818i | \(-0.722829\pi\) |
0.984475 | + | 0.175525i | \(0.0561621\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.1244 | + | 7.00000i | −0.685309 | + | 0.395663i | −0.801852 | − | 0.597522i | \(-0.796152\pi\) |
0.116543 | + | 0.993186i | \(0.462819\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.1244 | + | 7.00000i | −0.680972 | + | 0.393159i | −0.800221 | − | 0.599705i | \(-0.795285\pi\) |
0.119249 | + | 0.992864i | \(0.461951\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.0000 | + | 20.7846i | −0.671871 | + | 1.16371i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.00000 | −0.334887 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.0000i | 0.667698i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −27.5885 | + | 11.7846i | −1.53033 | + | 0.653693i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.1244 | − | 7.00000i | 0.670478 | − | 0.387101i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.00000 | + | 6.92820i | 0.219860 | + | 0.380808i | 0.954765 | − | 0.297361i | \(-0.0961066\pi\) |
−0.734905 | + | 0.678170i | \(0.762773\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.46410 | + | 2.00000i | 0.189832 | + | 0.109599i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.00000 | − | 8.00000i | −0.218543 | − | 0.437087i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 8.00000i | − | 0.435788i | −0.975972 | − | 0.217894i | \(-0.930081\pi\) | ||
0.975972 | − | 0.217894i | \(-0.0699187\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.00000 | − | 15.5885i | 0.488813 | − | 0.846649i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.00000 | + | 6.92820i | 0.216612 | + | 0.375183i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.73205 | + | 2.46410i | 0.200927 | + | 0.132663i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.5885 | + | 9.00000i | 0.836832 | + | 0.483145i | 0.856186 | − | 0.516667i | \(-0.172828\pi\) |
−0.0193540 | + | 0.999813i | \(0.506161\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.0000 | 1.17763 | 0.588817 | − | 0.808267i | \(-0.299594\pi\) | ||||
0.588817 | + | 0.808267i | \(0.299594\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.00000 | 0.320256 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.73205 | − | 1.00000i | −0.0921878 | − | 0.0532246i | 0.453197 | − | 0.891410i | \(-0.350283\pi\) |
−0.545385 | + | 0.838186i | \(0.683617\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.50000 | + | 14.7224i | −0.447368 | + | 0.774865i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.00000i | 0.262432i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.0000 | + | 20.0000i | 0.523424 | + | 1.04685i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.8564 | + | 8.00000i | 0.723299 | + | 0.417597i | 0.815966 | − | 0.578101i | \(-0.196206\pi\) |
−0.0926670 | + | 0.995697i | \(0.529539\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.00000 | − | 6.92820i | −0.208232 | − | 0.360668i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.7846 | + | 12.0000i | −1.07619 | + | 0.621336i | −0.929865 | − | 0.367901i | \(-0.880077\pi\) |
−0.146321 | + | 0.989237i | \(0.546743\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.23205 | + | 8.52628i | −0.373461 | + | 0.440295i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 36.0000i | − | 1.85409i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.0000 | 1.43826 | 0.719132 | − | 0.694874i | \(-0.244540\pi\) | ||||
0.719132 | + | 0.694874i | \(0.244540\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.00000 | − | 13.8564i | 0.409852 | − | 0.709885i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.2487 | + | 14.0000i | −1.23905 | + | 0.715367i | −0.968900 | − | 0.247451i | \(-0.920407\pi\) |
−0.270151 | + | 0.962818i | \(0.587074\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.46410 | − | 2.00000i | 0.176090 | − | 0.101666i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.00000 | − | 1.73205i | 0.0507020 | − | 0.0878185i | −0.839561 | − | 0.543266i | \(-0.817187\pi\) |
0.890263 | + | 0.455448i | \(0.150521\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.00000 | −0.202289 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.0000i | 0.605320i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.66025 | + | 5.00000i | −0.434646 | + | 0.250943i | −0.701324 | − | 0.712843i | \(-0.747407\pi\) |
0.266678 | + | 0.963786i | \(0.414074\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.0000 | − | 19.0526i | −0.549314 | − | 0.951439i | −0.998322 | − | 0.0579116i | \(-0.981556\pi\) |
0.449008 | − | 0.893528i | \(-0.351777\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.3923 | − | 6.00000i | −0.517678 | − | 0.298881i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.00000 | − | 1.00000i | 0.0993808 | − | 0.0496904i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 16.0000i | − | 0.793091i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.00000 | − | 8.66025i | 0.247234 | − | 0.428222i | −0.715523 | − | 0.698589i | \(-0.753812\pi\) |
0.962757 | + | 0.270367i | \(0.0871450\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.00000 | − | 15.5885i | −0.443937 | − | 0.768922i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.7128 | − | 29.8564i | 0.967664 | − | 1.46559i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.66025 | − | 5.00000i | −0.424094 | − | 0.244851i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −40.0000 | −1.95413 | −0.977064 | − | 0.212946i | \(-0.931694\pi\) | ||||
−0.977064 | + | 0.212946i | \(0.931694\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.46410 | + | 2.00000i | 0.168430 | + | 0.0972433i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.19615 | − | 9.92820i | 0.0580219 | − | 0.481589i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.0000 | − | 20.7846i | −0.579365 | − | 1.00349i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.00000 | − | 13.8564i | 0.385346 | − | 0.667440i | −0.606471 | − | 0.795106i | \(-0.707415\pi\) |
0.991817 | + | 0.127666i | \(0.0407486\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.0000i | 0.480569i | 0.970702 | + | 0.240285i | \(0.0772408\pi\) | ||||
−0.970702 | + | 0.240285i | \(0.922759\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.00000 | − | 12.0000i | −0.287678 | − | 0.575356i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.3923 | − | 6.00000i | −0.497131 | − | 0.287019i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.0000 | + | 25.9808i | 0.715911 | + | 1.23999i | 0.962607 | + | 0.270901i | \(0.0873217\pi\) |
−0.246696 | + | 0.969093i | \(0.579345\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.9808 | + | 15.0000i | −1.23438 | + | 0.712672i | −0.967941 | − | 0.251179i | \(-0.919182\pi\) |
−0.266443 | + | 0.963851i | \(0.585848\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.07180 | + | 17.8564i | −0.0508080 | + | 0.846475i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 22.0000i | − | 1.04056i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.0000 | + | 27.7128i | −0.753411 | + | 1.30495i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.8564 | − | 8.00000i | 0.651031 | − | 0.375873i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.3205 | + | 10.0000i | −0.810219 | + | 0.467780i | −0.847032 | − | 0.531542i | \(-0.821613\pi\) |
0.0368128 | + | 0.999322i | \(0.488279\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.00000 | + | 1.73205i | −0.0466760 | + | 0.0808452i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 24.0000i | − | 1.11537i | −0.830051 | − | 0.557687i | \(-0.811689\pi\) | ||
0.830051 | − | 0.557687i | \(-0.188311\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.46410 | − | 0.267949i | −0.207018 | − | 0.0124258i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.3923 | − | 6.00000i | 0.480899 | − | 0.277647i | −0.239892 | − | 0.970799i | \(-0.577112\pi\) |
0.720791 | + | 0.693153i | \(0.243779\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.00000 | + | 8.66025i | 0.230388 | + | 0.399043i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.8564 | − | 8.00000i | −0.637118 | − | 0.367840i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.0000 | − | 24.0000i | 0.825897 | − | 1.10120i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 6.00000i | − | 0.274721i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.00000 | − | 3.46410i | 0.0913823 | − | 0.158279i | −0.816711 | − | 0.577047i | \(-0.804205\pi\) |
0.908093 | + | 0.418769i | \(0.137538\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.0000 | + | 20.7846i | 0.547153 | + | 0.947697i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.3205 | − | 18.6603i | 0.559445 | − | 0.847318i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.3923 | − | 6.00000i | −0.470920 | − | 0.271886i | 0.245705 | − | 0.969345i | \(-0.420981\pi\) |
−0.716625 | + | 0.697459i | \(0.754314\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.00000 | 0.361773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0000 | 0.541552 | 0.270776 | − | 0.962642i | \(-0.412720\pi\) | ||||
0.270776 | + | 0.962642i | \(0.412720\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.3923 | + | 6.00000i | 0.468046 | + | 0.270226i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.46410 | − | 4.92820i | −0.335486 | − | 0.221506i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.0000 | − | 31.1769i | −0.805791 | − | 1.39567i | −0.915756 | − | 0.401735i | \(-0.868407\pi\) |
0.109965 | − | 0.993935i | \(-0.464926\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.0000 | − | 20.7846i | 0.536120 | − | 0.928588i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 36.0000i | − | 1.60516i | −0.596544 | − | 0.802580i | \(-0.703460\pi\) | ||
0.596544 | − | 0.802580i | \(-0.296540\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −32.0000 | + | 16.0000i | −1.42398 | + | 0.711991i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.9186 | + | 11.5000i | 0.884615 | + | 0.510733i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.00000 | − | 10.3923i | −0.265945 | − | 0.460631i | 0.701866 | − | 0.712309i | \(-0.252351\pi\) |
−0.967811 | + | 0.251679i | \(0.919017\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.19615 | + | 3.00000i | −0.229416 | + | 0.132453i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 35.7128 | + | 2.14359i | 1.57369 | + | 0.0944580i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 16.0000i | − | 0.703679i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.00000 | −0.0877903 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.0000 | + | 38.1051i | −0.963837 | + | 1.66942i | −0.251131 | + | 0.967953i | \(0.580803\pi\) |
−0.712706 | + | 0.701462i | \(0.752531\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.3205 | − | 10.0000i | 0.757373 | − | 0.437269i | −0.0709788 | − | 0.997478i | \(-0.522612\pi\) |
0.828352 | + | 0.560208i | \(0.189279\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.46410 | − | 2.00000i | 0.150899 | − | 0.0871214i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.50000 | + | 16.4545i | −0.413043 | + | 0.715412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.00000 | −0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 48.0000i | − | 2.07911i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.3923 | − | 0.803848i | −0.579000 | − | 0.0347534i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.46410 | + | 2.00000i | −0.149487 | + | 0.0863064i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.00000 | − | 8.66025i | −0.214967 | − | 0.372333i | 0.738296 | − | 0.674477i | \(-0.235631\pi\) |
−0.953262 | + | 0.302144i | \(0.902298\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.66025 | − | 5.00000i | −0.371647 | − | 0.214571i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 28.0000 | − | 14.0000i | 1.19939 | − | 0.599694i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 20.0000i | − | 0.855138i | −0.903983 | − | 0.427569i | \(-0.859370\pi\) | ||
0.903983 | − | 0.427569i | \(-0.140630\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.00000 | + | 12.1244i | −0.298753 | + | 0.517455i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.0000 | + | 31.1769i | 0.766826 | + | 1.32818i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.46410 | + | 4.92820i | 0.316833 | + | 0.209191i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.19615 | + | 3.00000i | 0.220168 | + | 0.127114i | 0.606028 | − | 0.795443i | \(-0.292762\pi\) |
−0.385860 | + | 0.922557i | \(0.626095\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.0000 | 1.01509 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | 0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 34.6410 | + | 20.0000i | 1.45994 | + | 0.842900i | 0.999008 | − | 0.0445334i | \(-0.0141801\pi\) |
0.460937 | + | 0.887433i | \(0.347513\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.1769 | − | 33.5885i | 0.932990 | − | 1.41308i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.00000 | − | 8.66025i | −0.209611 | − | 0.363057i | 0.741981 | − | 0.670421i | \(-0.233886\pi\) |
−0.951592 | + | 0.307364i | \(0.900553\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.00000 | − | 6.92820i | 0.167395 | − | 0.289936i | −0.770108 | − | 0.637913i | \(-0.779798\pi\) |
0.937503 | + | 0.347977i | \(0.113131\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.00000 | + | 6.00000i | 0.333623 | + | 0.250217i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.9090 | − | 19.0000i | −1.37002 | − | 0.790980i | −0.379088 | − | 0.925361i | \(-0.623762\pi\) |
−0.990930 | + | 0.134380i | \(0.957096\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.00000 | + | 6.92820i | 0.166234 | + | 0.287926i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.7846 | + | 12.0000i | −0.860811 | + | 0.496989i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13.3923 | + | 0.803848i | 0.553704 | + | 0.0332350i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.0000 | 0.494451 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.00000 | + | 8.66025i | −0.205673 | + | 0.356235i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.5885 | + | 9.00000i | −0.640141 | + | 0.369586i | −0.784669 | − | 0.619915i | \(-0.787167\pi\) |
0.144528 | + | 0.989501i | \(0.453834\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.5885 | − | 9.00000i | 0.637993 | − | 0.368345i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.0000 | 1.38689 | 0.693444 | − | 0.720510i | \(-0.256092\pi\) | ||||
0.693444 | + | 0.720510i | \(0.256092\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.00000i | 0.162893i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.669873 | + | 11.1603i | −0.0272342 | + | 0.453729i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.6410 | − | 20.0000i | 1.40604 | − | 0.811775i | 0.411033 | − | 0.911621i | \(-0.365168\pi\) |
0.995003 | + | 0.0998457i | \(0.0318349\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.0000 | + | 20.7846i | 0.485468 | + | 0.840855i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −38.1051 | − | 22.0000i | −1.53905 | − | 0.888572i | −0.998895 | − | 0.0470071i | \(-0.985032\pi\) |
−0.540157 | − | 0.841564i | \(-0.681635\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.00000 | − | 16.0000i | −0.322591 | − | 0.645182i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.0000i | 1.36879i | 0.729112 | + | 0.684394i | \(0.239933\pi\) | ||||
−0.729112 | + | 0.684394i | \(0.760067\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.0000 | + | 22.5167i | −0.522514 | + | 0.905021i | 0.477143 | + | 0.878826i | \(0.341672\pi\) |
−0.999657 | + | 0.0261952i | \(0.991661\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | − | 1.73205i | −0.0401286 | − | 0.0695048i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.2846 | + | 18.0622i | −0.691384 | + | 0.722487i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.7846 | + | 12.0000i | 0.830057 | + | 0.479234i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.00000 | −0.318981 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20.7846 | + | 12.0000i | 0.826114 | + | 0.476957i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.7128 | − | 29.8564i | 0.782279 | − | 1.18482i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.00000 | + | 1.73205i | −0.0394976 | + | 0.0684119i | −0.885098 | − | 0.465404i | \(-0.845909\pi\) |
0.845601 | + | 0.533816i | \(0.179242\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.0000i | 0.473234i | 0.971603 | + | 0.236617i | \(0.0760386\pi\) | ||||
−0.971603 | + | 0.236617i | \(0.923961\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.00000 | − | 4.00000i | 0.315000 | − | 0.157500i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.7846 | + | 12.0000i | 0.817127 | + | 0.471769i | 0.849425 | − | 0.527710i | \(-0.176949\pi\) |
−0.0322975 | + | 0.999478i | \(0.510282\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.00000 | + | 13.8564i | 0.314027 | + | 0.543912i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29.4449 | + | 17.0000i | −1.15227 | + | 0.665261i | −0.949439 | − | 0.313953i | \(-0.898347\pi\) |
−0.202828 | + | 0.979214i | \(0.565013\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.60770 | + | 26.7846i | −0.0628178 | + | 1.04656i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 10.0000i | − | 0.390137i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.00000 | −0.155818 | −0.0779089 | − | 0.996960i | \(-0.524824\pi\) | ||||
−0.0779089 | + | 0.996960i | \(0.524824\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.00000 | − | 12.1244i | 0.272268 | − | 0.471583i | −0.697174 | − | 0.716902i | \(-0.745559\pi\) |
0.969442 | + | 0.245319i | \(0.0788928\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.3923 | + | 6.00000i | −0.403604 | + | 0.233021i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.3923 | + | 6.00000i | −0.402392 | + | 0.232321i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.00000 | − | 13.8564i | 0.309298 | − | 0.535720i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 56.0000 | 2.16186 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.0000i | 0.462566i | 0.972887 | + | 0.231283i | \(0.0742923\pi\) | ||||
−0.972887 | + | 0.231283i | \(0.925708\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.59808 | − | 1.96410i | 0.176980 | − | 0.0755983i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.9090 | − | 19.0000i | 1.26479 | − | 0.730229i | 0.290796 | − | 0.956785i | \(-0.406080\pi\) |
0.973998 | + | 0.226556i | \(0.0727465\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.0000 | + | 17.3205i | 0.383201 | + | 0.663723i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.5167 | − | 13.0000i | −0.861576 | − | 0.497431i | 0.00296369 | − | 0.999996i | \(-0.499057\pi\) |
−0.864540 | + | 0.502564i | \(0.832390\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.0000 | − | 36.0000i | −0.687745 | − | 1.37549i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.00000i | 0.0763048i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.0000 | − | 31.1769i | 0.685745 | − | 1.18775i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.00000 | − | 1.73205i | −0.0380418 | − | 0.0658903i | 0.846378 | − | 0.532583i | \(-0.178779\pi\) |
−0.884419 | + | 0.466693i | \(0.845445\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.6603 | − | 12.3205i | −0.707824 | − | 0.467344i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.8564 | + | 8.00000i | 0.524849 | + | 0.303022i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 26.0000 | 0.983410 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.0000 | 1.43524 | 0.717620 | − | 0.696435i | \(-0.245231\pi\) | ||||
0.717620 | + | 0.696435i | \(0.245231\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.7846 | − | 12.0000i | −0.783906 | − | 0.452589i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.46410 | + | 4.92820i | 0.281114 | + | 0.185607i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.00000 | − | 5.19615i | −0.112667 | − | 0.195146i | 0.804178 | − | 0.594389i | \(-0.202606\pi\) |
−0.916845 | + | 0.399244i | \(0.869273\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.00000i | 0.149801i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.0000 | − | 48.0000i | −0.897549 | − | 1.79510i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.8564 | − | 8.00000i | −0.517477 | − | 0.298765i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.0000 | − | 38.1051i | −0.820462 | − | 1.42108i | −0.905339 | − | 0.424690i | \(-0.860383\pi\) |
0.0848774 | − | 0.996391i | \(-0.472950\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.66025 | + | 5.00000i | −0.322078 | + | 0.185952i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.7846 | − | 27.5885i | −0.437669 | − | 1.02461i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.00000 | + | 6.92820i | −0.147945 | + | 0.256249i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.4449 | + | 17.0000i | −1.08757 | + | 0.627909i | −0.932929 | − | 0.360061i | \(-0.882756\pi\) |
−0.154642 | + | 0.987971i | \(0.549422\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.8564 | − | 8.00000i | 0.510407 | − | 0.294684i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.00000 | − | 13.8564i | 0.294285 | − | 0.509716i | −0.680534 | − | 0.732717i | \(-0.738252\pi\) |
0.974818 | + | 0.223001i | \(0.0715853\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −36.0000 | −1.32249 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 54.0000i | − | 1.98107i | −0.137268 | − | 0.990534i | \(-0.543832\pi\) | ||
0.137268 | − | 0.990534i | \(-0.456168\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.94744 | − | 49.1051i | 0.107986 | − | 1.79907i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.8564 | + | 8.00000i | −0.506979 | + | 0.292705i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.0000 | − | 17.3205i | −0.364905 | − | 0.632034i | 0.623856 | − | 0.781540i | \(-0.285565\pi\) |
−0.988761 | + | 0.149505i | \(0.952232\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.3923 | − | 6.00000i | −0.378717 | − | 0.218652i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 32.0000 | − | 16.0000i | 1.16460 | − | 0.582300i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 8.00000i | − | 0.290765i | −0.989376 | − | 0.145382i | \(-0.953559\pi\) | ||
0.989376 | − | 0.145382i | \(-0.0464413\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.00000 | + | 6.92820i | −0.145191 | + | 0.251478i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.0000 | − | 20.7846i | −0.435000 | − | 0.753442i | 0.562296 | − | 0.826936i | \(-0.309918\pi\) |
−0.997296 | + | 0.0734946i | \(0.976585\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.46410 | + | 3.73205i | −0.0890898 | + | 0.134933i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.7846 | − | 12.0000i | −0.750489 | − | 0.433295i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.0000 | 1.08183 | 0.540914 | − | 0.841078i | \(-0.318079\pi\) | ||||
0.540914 | + | 0.841078i | \(0.318079\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.00000 | −0.216085 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.19615 | − | 3.00000i | −0.186893 | − | 0.107903i | 0.403634 | − | 0.914920i | \(-0.367747\pi\) |
−0.590527 | + | 0.807018i | \(0.701080\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.92820 | − | 1.19615i | −0.356632 | − | 0.0429671i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.0000 | + | 41.5692i | 0.859889 | + | 1.48937i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.00000i | 0.214423i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.0000 | + | 20.0000i | 0.356915 | + | 0.713831i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.46410 | + | 2.00000i | 0.123482 | + | 0.0712923i | 0.560469 | − | 0.828176i | \(-0.310621\pi\) |
−0.436987 | + | 0.899468i | \(0.643954\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.00000 | − | 8.66025i | −0.178005 | − | 0.308313i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −72.7461 | + | 42.0000i | −2.58329 | + | 1.49146i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.803848 | − | 13.3923i | 0.0285095 | − | 0.474976i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 34.0000i | − | 1.20434i | −0.798367 | − | 0.602171i | \(-0.794303\pi\) | ||
0.798367 | − | 0.602171i | \(-0.205697\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.00000 | −0.283020 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.00000 | − | 6.92820i | 0.141333 | − | 0.244796i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −34.6410 | + | 20.0000i | −1.22245 | + | 0.705785i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.3923 | + | 6.00000i | −0.365826 | + | 0.211210i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.00000 | + | 15.5885i | −0.316423 | + | 0.548061i | −0.979739 | − | 0.200279i | \(-0.935815\pi\) |
0.663316 | + | 0.748340i | \(0.269149\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.0000 | −1.19390 | −0.596951 | − | 0.802278i | \(-0.703621\pi\) | ||||
−0.596951 | + | 0.802278i | \(0.703621\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.0000i | 0.491001i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.8564 | + | 1.07180i | 0.625483 | + | 0.0375434i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.7846 | + | 12.0000i | −0.727161 | + | 0.419827i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.00000 | − | 8.66025i | −0.174501 | − | 0.302245i | 0.765487 | − | 0.643451i | \(-0.222498\pi\) |
−0.939989 | + | 0.341206i | \(0.889165\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.7846 | − | 12.0000i | −0.724506 | − | 0.418294i | 0.0919029 | − | 0.995768i | \(-0.470705\pi\) |
−0.816409 | + | 0.577474i | \(0.804038\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −16.0000 | − | 12.0000i | −0.557048 | − | 0.417786i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.0000i | 0.765015i | 0.923952 | + | 0.382507i | \(0.124939\pi\) | ||||
−0.923952 | + | 0.382507i | \(0.875061\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.00000 | + | 5.19615i | −0.104194 | + | 0.180470i | −0.913409 | − | 0.407044i | \(-0.866560\pi\) |
0.809214 | + | 0.587513i | \(0.199893\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.0000 | + | 24.2487i | 0.485655 | + | 0.841178i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29.5692 | − | 44.7846i | 1.02329 | − | 1.54984i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.73205 | + | 1.00000i | 0.0598684 | + | 0.0345651i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.0000 | −1.10476 | −0.552381 | − | 0.833592i | \(-0.686281\pi\) | ||||
−0.552381 | + | 0.833592i | \(0.686281\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.19615 | + | 3.00000i | 0.178965 | + | 0.103325i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 42.9186 | + | 28.3372i | 1.47644 | + | 0.974828i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.0000 | − | 24.2487i | −0.480479 | − | 0.832214i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.00000 | − | 6.92820i | 0.137118 | − | 0.237496i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.00000i | 0.0684787i | 0.999414 | + | 0.0342393i | \(0.0109009\pi\) | ||||
−0.999414 | + | 0.0342393i | \(0.989099\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.0000 | + | 6.00000i | −0.410391 | + | 0.205196i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.19615 | − | 3.00000i | −0.177497 | − | 0.102478i | 0.408619 | − | 0.912705i | \(-0.366010\pi\) |
−0.586116 | + | 0.810227i | \(0.699344\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.0000 | + | 39.8372i | 0.784750 | + | 1.35923i | 0.929148 | + | 0.369707i | \(0.120542\pi\) |
−0.144399 | + | 0.989520i | \(0.546125\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.5885 | − | 9.00000i | 0.530637 | − | 0.306364i | −0.210639 | − | 0.977564i | \(-0.567554\pi\) |
0.741276 | + | 0.671200i | \(0.234221\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.46410 | − | 0.267949i | −0.151784 | − | 0.00911055i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.0000i | 0.441503i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.0000 | + | 20.7846i | −0.406604 | + | 0.704260i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.66025 | + | 5.00000i | −0.293105 | + | 0.169224i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.1051 | − | 22.0000i | 1.28672 | − | 0.742887i | 0.308651 | − | 0.951175i | \(-0.400123\pi\) |
0.978068 | + | 0.208288i | \(0.0667892\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.00000 | − | 5.19615i | 0.101187 | − | 0.175262i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.0000 | −1.21287 | −0.606435 | − | 0.795133i | \(-0.707401\pi\) | ||||
−0.606435 | + | 0.795133i | \(0.707401\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 24.0000i | − | 0.807664i | −0.914833 | − | 0.403832i | \(-0.867678\pi\) | ||
0.914833 | − | 0.403832i | \(-0.132322\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.92820 | − | 0.535898i | −0.300118 | − | 0.0180140i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.3923 | − | 6.00000i | 0.348939 | − | 0.201460i | −0.315279 | − | 0.948999i | \(-0.602098\pi\) |
0.664218 | + | 0.747539i | \(0.268765\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.00000 | + | 3.46410i | 0.0670025 | + | 0.116052i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −20.7846 | − | 12.0000i | −0.695530 | − | 0.401565i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.00000 | + | 4.00000i | −0.267411 | + | 0.133705i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 12.0000i | − | 0.400668i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.00000 | − | 10.3923i | 0.200111 | − | 0.346603i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.00000 | + | 10.3923i | 0.199889 | + | 0.346218i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.6603 | − | 12.3205i | −0.620288 | − | 0.409548i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.7846 | + | 12.0000i | 0.690142 | + | 0.398453i | 0.803665 | − | 0.595082i | \(-0.202880\pi\) |
−0.113523 | + | 0.993535i | \(0.536214\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.0000 | 0.530687 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.0000 | −0.795155 | −0.397578 | − | 0.917568i | \(-0.630149\pi\) | ||||
−0.397578 | + | 0.917568i | \(0.630149\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 55.4256 | + | 32.0000i | 1.83432 | + | 1.05905i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −17.2487 | + | 26.1244i | −0.570225 | + | 0.863645i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.0000 | + | 31.1769i | 0.593765 | + | 1.02843i | 0.993720 | + | 0.111897i | \(0.0356925\pi\) |
−0.399955 | + | 0.916535i | \(0.630974\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.00000 | + | 10.3923i | −0.197707 | + | 0.342438i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.0000 | + | 12.0000i | 0.526077 | + | 0.394558i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13.8564 | − | 8.00000i | −0.455104 | − | 0.262754i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.0000 | − | 20.7846i | −0.393707 | − | 0.681921i | 0.599228 | − | 0.800578i | \(-0.295474\pi\) |
−0.992935 | + | 0.118657i | \(0.962141\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.3923 | + | 6.00000i | −0.340229 | + | 0.196431i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.8564 | + | 1.07180i | 0.583967 | + | 0.0350515i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 14.0000i | − | 0.457360i | −0.973502 | − | 0.228680i | \(-0.926559\pi\) | ||
0.973502 | − | 0.228680i | \(-0.0734410\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.0000 | 0.456873 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.0000 | − | 38.1051i | 0.717180 | − | 1.24219i | −0.244933 | − | 0.969540i | \(-0.578766\pi\) |
0.962113 | − | 0.272651i | \(-0.0879006\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.8564 | + | 8.00000i | −0.451227 | + | 0.260516i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.19615 | + | 3.00000i | −0.168852 | + | 0.0974869i | −0.582045 | − | 0.813157i | \(-0.697747\pi\) |
0.413192 | + | 0.910644i | \(0.364414\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30.0000 | − | 51.9615i | 0.973841 | − | 1.68674i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.0000 | 0.453981 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 14.0000i | − | 0.453504i | −0.973952 | − | 0.226752i | \(-0.927189\pi\) | ||
0.973952 | − | 0.226752i | \(-0.0728108\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.7846 | − | 12.0000i | 0.671871 | − | 0.387905i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.19615 | + | 3.00000i | 0.167444 | + | 0.0966736i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.00000 | + | 16.0000i | 0.257529 | + | 0.515058i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.0000i | 0.643157i | 0.946883 | + | 0.321578i | \(0.104213\pi\) | ||||
−0.946883 | + | 0.321578i | \(0.895787\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.00000 | − | 10.3923i | 0.192748 | − | 0.333849i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.0000 | − | 20.7846i | −0.385098 | − | 0.667010i | 0.606685 | − | 0.794943i | \(-0.292499\pi\) |
−0.991783 | + | 0.127933i | \(0.959166\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 29.7846 | + | 3.58846i | 0.953871 | + | 0.114923i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.5885 | − | 9.00000i | −0.498719 | − | 0.287936i | 0.229465 | − | 0.973317i | \(-0.426302\pi\) |
−0.728184 | + | 0.685381i | \(0.759636\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32.0000 | −1.02272 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.0000 | −0.446986 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.92820 | − | 4.00000i | −0.220975 | − | 0.127580i | 0.385426 | − | 0.922739i | \(-0.374054\pi\) |
−0.606402 | + | 0.795158i | \(0.707388\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.3205 | + | 18.6603i | −0.392564 | + | 0.594565i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.00000 | − | 6.92820i | −0.127193 | − | 0.220304i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.0000 | + | 45.0333i | −0.825917 | + | 1.43053i | 0.0752991 | + | 0.997161i | \(0.476009\pi\) |
−0.901216 | + | 0.433370i | \(0.857324\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 8.00000i | − | 0.253872i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 36.0000 | − | 18.0000i | 1.14128 | − | 0.570638i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.5885 | + | 9.00000i | 0.493691 | + | 0.285033i | 0.726105 | − | 0.687584i | \(-0.241329\pi\) |
−0.232413 | + | 0.972617i | \(0.574662\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −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 | 2940.2.bb.c.949.1 | 4 | ||
5.4 | even | 2 | inner | 2940.2.bb.c.949.2 | 4 | ||
7.2 | even | 3 | inner | 2940.2.bb.c.1549.2 | 4 | ||
7.3 | odd | 6 | 420.2.k.a.169.1 | ✓ | 2 | ||
7.4 | even | 3 | 2940.2.k.d.589.2 | 2 | |||
7.5 | odd | 6 | 2940.2.bb.h.1549.1 | 4 | |||
7.6 | odd | 2 | 2940.2.bb.h.949.2 | 4 | |||
21.17 | even | 6 | 1260.2.k.d.1009.1 | 2 | |||
28.3 | even | 6 | 1680.2.t.a.1009.2 | 2 | |||
35.3 | even | 12 | 2100.2.a.j.1.1 | 1 | |||
35.4 | even | 6 | 2940.2.k.d.589.1 | 2 | |||
35.9 | even | 6 | inner | 2940.2.bb.c.1549.1 | 4 | ||
35.17 | even | 12 | 2100.2.a.e.1.1 | 1 | |||
35.19 | odd | 6 | 2940.2.bb.h.1549.2 | 4 | |||
35.24 | odd | 6 | 420.2.k.a.169.2 | yes | 2 | ||
35.34 | odd | 2 | 2940.2.bb.h.949.1 | 4 | |||
84.59 | odd | 6 | 5040.2.t.o.1009.1 | 2 | |||
105.17 | odd | 12 | 6300.2.a.bc.1.1 | 1 | |||
105.38 | odd | 12 | 6300.2.a.n.1.1 | 1 | |||
105.59 | even | 6 | 1260.2.k.d.1009.2 | 2 | |||
140.3 | odd | 12 | 8400.2.a.bh.1.1 | 1 | |||
140.59 | even | 6 | 1680.2.t.a.1009.1 | 2 | |||
140.87 | odd | 12 | 8400.2.a.cd.1.1 | 1 | |||
420.59 | odd | 6 | 5040.2.t.o.1009.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.k.a.169.1 | ✓ | 2 | 7.3 | odd | 6 | ||
420.2.k.a.169.2 | yes | 2 | 35.24 | odd | 6 | ||
1260.2.k.d.1009.1 | 2 | 21.17 | even | 6 | |||
1260.2.k.d.1009.2 | 2 | 105.59 | even | 6 | |||
1680.2.t.a.1009.1 | 2 | 140.59 | even | 6 | |||
1680.2.t.a.1009.2 | 2 | 28.3 | even | 6 | |||
2100.2.a.e.1.1 | 1 | 35.17 | even | 12 | |||
2100.2.a.j.1.1 | 1 | 35.3 | even | 12 | |||
2940.2.k.d.589.1 | 2 | 35.4 | even | 6 | |||
2940.2.k.d.589.2 | 2 | 7.4 | even | 3 | |||
2940.2.bb.c.949.1 | 4 | 1.1 | even | 1 | trivial | ||
2940.2.bb.c.949.2 | 4 | 5.4 | even | 2 | inner | ||
2940.2.bb.c.1549.1 | 4 | 35.9 | even | 6 | inner | ||
2940.2.bb.c.1549.2 | 4 | 7.2 | even | 3 | inner | ||
2940.2.bb.h.949.1 | 4 | 35.34 | odd | 2 | |||
2940.2.bb.h.949.2 | 4 | 7.6 | odd | 2 | |||
2940.2.bb.h.1549.1 | 4 | 7.5 | odd | 6 | |||
2940.2.bb.h.1549.2 | 4 | 35.19 | odd | 6 | |||
5040.2.t.o.1009.1 | 2 | 84.59 | odd | 6 | |||
5040.2.t.o.1009.2 | 2 | 420.59 | odd | 6 | |||
6300.2.a.n.1.1 | 1 | 105.38 | odd | 12 | |||
6300.2.a.bc.1.1 | 1 | 105.17 | odd | 12 | |||
8400.2.a.bh.1.1 | 1 | 140.3 | odd | 12 | |||
8400.2.a.cd.1.1 | 1 | 140.87 | odd | 12 |