Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(373,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.373");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.i (of order \(3\), 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: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1537.1 | ||
Root | \(0.500000 + 2.05195i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1537 |
Dual form | 1764.2.i.d.373.1 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.73025 | + | 0.0789082i | −0.998962 | + | 0.0455577i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.23025 | − | 2.13086i | 0.550186 | − | 0.952949i | −0.448075 | − | 0.893996i | \(-0.647890\pi\) |
0.998261 | − | 0.0589535i | \(-0.0187764\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.98755 | − | 0.273062i | 0.995849 | − | 0.0910208i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.32383 | − | 4.02499i | −0.700662 | − | 1.21358i | −0.968234 | − | 0.250044i | \(-0.919555\pi\) |
0.267573 | − | 0.963538i | \(-0.413778\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.55408 | + | 6.15585i | 0.985726 | + | 1.70733i | 0.638667 | + | 0.769484i | \(0.279486\pi\) |
0.347059 | + | 0.937843i | \(0.387180\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.96050 | + | 3.78400i | −0.506200 | + | 0.977025i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.25729 | + | 3.90975i | −0.547474 | + | 0.948253i | 0.450972 | + | 0.892538i | \(0.351077\pi\) |
−0.998447 | + | 0.0557155i | \(0.982256\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.16372 | + | 3.74766i | 0.496390 | + | 0.859773i | 0.999991 | − | 0.00416311i | \(-0.00132516\pi\) |
−0.503601 | + | 0.863936i | \(0.667992\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.93346 | + | 5.08091i | −0.611669 | + | 1.05944i | 0.379290 | + | 0.925278i | \(0.376168\pi\) |
−0.990959 | + | 0.134164i | \(0.957165\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.527042 | − | 0.912864i | −0.105408 | − | 0.182573i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.14766 | + | 0.708209i | −0.990668 | + | 0.136295i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.48755 | − | 6.04061i | 0.647621 | − | 1.12171i | −0.336068 | − | 0.941838i | \(-0.609097\pi\) |
0.983689 | − | 0.179875i | \(-0.0575694\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.38151 | 1.32576 | 0.662880 | − | 0.748726i | \(-0.269334\pi\) | ||||
0.662880 | + | 0.748726i | \(0.269334\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.33842 | + | 6.78089i | 0.755222 | + | 1.18040i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.363327 | + | 0.629301i | 0.0597306 | + | 0.103456i | 0.894344 | − | 0.447379i | \(-0.147643\pi\) |
−0.834614 | + | 0.550835i | \(0.814309\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.63521 | − | 10.3707i | −1.06248 | − | 1.66065i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.136673 | + | 0.236725i | 0.0213448 | + | 0.0369702i | 0.876500 | − | 0.481401i | \(-0.159872\pi\) |
−0.855156 | + | 0.518371i | \(0.826539\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.41741 | − | 4.18708i | 0.368652 | − | 0.638524i | −0.620703 | − | 0.784046i | \(-0.713153\pi\) |
0.989355 | + | 0.145522i | \(0.0464862\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.09358 | − | 6.70198i | 0.461164 | − | 0.999072i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.67257 | −0.535699 | −0.267850 | − | 0.963461i | \(-0.586313\pi\) | ||||
−0.267850 | + | 0.963461i | \(0.586313\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.59718 | − | 6.94297i | 0.503706 | − | 0.972210i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.52704 | + | 4.37697i | −0.347116 | + | 0.601222i | −0.985736 | − | 0.168300i | \(-0.946172\pi\) |
0.638620 | + | 0.769522i | \(0.279506\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.4356 | −1.54198 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.03950 | − | 6.31367i | −0.535044 | − | 0.836266i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.13307 | −1.18903 | −0.594513 | − | 0.804086i | \(-0.702655\pi\) | ||||
−0.594513 | + | 0.804086i | \(0.702655\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.8171 | 1.76910 | 0.884550 | − | 0.466445i | \(-0.154466\pi\) | ||||
0.884550 | + | 0.466445i | \(0.154466\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 17.4897 | 2.16933 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.32743 | −0.162171 | −0.0810857 | − | 0.996707i | \(-0.525839\pi\) | ||||
−0.0810857 | + | 0.996707i | \(0.525839\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.67471 | − | 9.02273i | 0.562768 | − | 1.08621i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.5218 | 1.60474 | 0.802370 | − | 0.596826i | \(-0.203572\pi\) | ||||
0.802370 | + | 0.596826i | \(0.203572\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.16372 | + | 3.74766i | −0.253244 | + | 0.438631i | −0.964417 | − | 0.264386i | \(-0.914831\pi\) |
0.711173 | + | 0.703017i | \(0.248164\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.983948 | + | 1.53790i | 0.113617 | + | 0.177581i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.43560 | 0.724061 | 0.362031 | − | 0.932166i | \(-0.382084\pi\) | ||||
0.362031 | + | 0.932166i | \(0.382084\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.85087 | − | 1.63157i | 0.983430 | − | 0.181286i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.742705 | − | 1.28640i | 0.0815225 | − | 0.141201i | −0.822382 | − | 0.568936i | \(-0.807355\pi\) |
0.903904 | + | 0.427735i | \(0.140688\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.55408 | + | 9.61996i | 0.602425 | + | 1.04343i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.55768 | + | 10.7270i | −0.595846 | + | 1.15005i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.91741 | + | 8.51721i | 0.521245 | + | 0.902822i | 0.999695 | + | 0.0247073i | \(0.00786539\pi\) |
−0.478450 | + | 0.878115i | \(0.658801\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.7719 | + | 0.582462i | −1.32438 | + | 0.0603985i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.6477 | 1.09243 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.246304 | + | 0.426611i | −0.0250084 | + | 0.0433158i | −0.878259 | − | 0.478186i | \(-0.841295\pi\) |
0.853250 | + | 0.521502i | \(0.174628\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.04163 | − | 11.3903i | −0.808214 | − | 1.14477i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.70321 | + | 2.95005i | 0.169476 | + | 0.293541i | 0.938236 | − | 0.345997i | \(-0.112459\pi\) |
−0.768760 | + | 0.639537i | \(0.779126\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.58113 | − | 4.47064i | 0.254326 | − | 0.440505i | −0.710386 | − | 0.703812i | \(-0.751480\pi\) |
0.964712 | + | 0.263307i | \(0.0848131\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.88151 | + | 4.99093i | 0.278567 | + | 0.482491i | 0.971029 | − | 0.238963i | \(-0.0768074\pi\) |
−0.692462 | + | 0.721454i | \(0.743474\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.49115 | − | 7.77889i | 0.430174 | − | 0.745083i | −0.566714 | − | 0.823914i | \(-0.691786\pi\) |
0.996888 | + | 0.0788317i | \(0.0251190\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.678304 | − | 1.06018i | −0.0643818 | − | 0.100628i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.679767 | + | 1.17739i | 0.0639471 | + | 0.110760i | 0.896226 | − | 0.443597i | \(-0.146298\pi\) |
−0.832279 | + | 0.554356i | \(0.812964\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.21780 | + | 12.5016i | 0.673063 | + | 1.16578i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.2989 | + | 17.4204i | 1.13704 | + | 1.61052i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.30039 | + | 9.18054i | −0.481853 | + | 0.834595i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.255158 | − | 0.398809i | −0.0230069 | − | 0.0359594i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.70895 | 0.868394 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.820039 | −0.0727667 | −0.0363833 | − | 0.999338i | \(-0.511584\pi\) | ||||
−0.0363833 | + | 0.999338i | \(0.511584\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.85234 | + | 7.43546i | −0.339179 | + | 0.654655i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.89397 | − | 6.74455i | 0.340218 | − | 0.589274i | −0.644255 | − | 0.764810i | \(-0.722833\pi\) |
0.984473 | + | 0.175536i | \(0.0561660\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.82383 | + | 11.8402i | −0.415169 | + | 1.01904i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.49640 | + | 2.59184i | 0.127846 | + | 0.221436i | 0.922842 | − | 0.385179i | \(-0.125860\pi\) |
−0.794996 | + | 0.606615i | \(0.792527\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.16372 | + | 5.47972i | 0.268343 | + | 0.464783i | 0.968434 | − | 0.249270i | \(-0.0801907\pi\) |
−0.700091 | + | 0.714053i | \(0.746857\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.35447 | − | 0.289796i | 0.535143 | − | 0.0244052i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.5182 | − | 28.6103i | 1.38132 | − | 2.39252i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.58113 | − | 14.8629i | −0.712624 | − | 1.23430i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.19076 | − | 3.79450i | 0.179474 | − | 0.310858i | −0.762227 | − | 0.647310i | \(-0.775894\pi\) |
0.941700 | + | 0.336452i | \(0.109227\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.30039 | − | 5.71644i | −0.268582 | − | 0.465197i | 0.699914 | − | 0.714227i | \(-0.253222\pi\) |
−0.968496 | + | 0.249030i | \(0.919888\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.67617 | + | 12.2969i | −0.458891 | + | 0.994149i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.08113 | − | 15.7290i | 0.729414 | − | 1.26338i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.78074 | 0.461353 | 0.230677 | − | 0.973030i | \(-0.425906\pi\) | ||||
0.230677 | + | 0.973030i | \(0.425906\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.02704 | − | 7.77266i | 0.319365 | − | 0.616412i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.66372 | − | 6.34574i | −0.286964 | − | 0.497037i | 0.686119 | − | 0.727489i | \(-0.259313\pi\) |
−0.973084 | + | 0.230452i | \(0.925979\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 19.7865 | − | 0.902363i | 1.54037 | − | 0.0702489i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.01459 | − | 10.4176i | −0.465423 | − | 0.806136i | 0.533798 | − | 0.845612i | \(-0.320764\pi\) |
−0.999221 | + | 0.0394762i | \(0.987431\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18.7630 | + | 32.4985i | −1.44331 | + | 2.49989i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.48755 | + | 10.6055i | 0.572587 | + | 0.811022i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.89903 | −0.372466 | −0.186233 | − | 0.982506i | \(-0.559628\pi\) | ||||
−0.186233 | + | 0.982506i | \(0.559628\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.8025 | − | 0.720675i | 1.18779 | − | 0.0541692i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.890369 | − | 1.54216i | 0.0665493 | − | 0.115267i | −0.830831 | − | 0.556525i | \(-0.812134\pi\) |
0.897380 | + | 0.441258i | \(0.145468\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.9430 | 1.25936 | 0.629681 | − | 0.776854i | \(-0.283185\pi\) | ||||
0.629681 | + | 0.776854i | \(0.283185\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −23.9071 | + | 1.09028i | −1.76726 | + | 0.0805961i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.78794 | 0.131452 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.9823 | 1.53438 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.48968 | −0.397220 | −0.198610 | − | 0.980079i | \(-0.563643\pi\) | ||||
−0.198610 | + | 0.980079i | \(0.563643\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.50739 | −0.396431 | −0.198215 | − | 0.980158i | \(-0.563515\pi\) | ||||
−0.198215 | + | 0.980158i | \(0.563515\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −30.2616 | + | 1.38008i | −2.16708 | + | 0.0988296i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.6300 | 0.828600 | 0.414300 | − | 0.910140i | \(-0.364026\pi\) | ||||
0.414300 | + | 0.910140i | \(0.364026\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.07373 | + | 3.59181i | −0.147003 | + | 0.254617i | −0.930118 | − | 0.367260i | \(-0.880296\pi\) |
0.783115 | + | 0.621876i | \(0.213629\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.29679 | − | 0.104745i | 0.162003 | − | 0.00738816i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.672570 | 0.0469743 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.37645 | + | 15.9805i | −0.512699 | + | 1.11072i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.0562 | − | 17.4179i | 0.695603 | − | 1.20482i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.6082 | + | 23.5700i | 0.936825 | + | 1.62263i | 0.771347 | + | 0.636415i | \(0.219583\pi\) |
0.165478 | + | 0.986213i | \(0.447083\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −23.3961 | + | 1.06698i | −1.60307 | + | 0.0731083i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.94805 | − | 10.3023i | −0.405654 | − | 0.702613i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.44805 | − | 6.65514i | 0.232998 | − | 0.449713i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −32.0905 | −2.15864 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.60817 | + | 2.78543i | −0.107691 | + | 0.186526i | −0.914834 | − | 0.403829i | \(-0.867679\pi\) |
0.807144 | + | 0.590355i | \(0.201012\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.82383 | − | 2.58331i | −0.121589 | − | 0.172221i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.97296 | + | 13.8096i | 0.529184 | + | 0.916573i | 0.999421 | + | 0.0340330i | \(0.0108351\pi\) |
−0.470237 | + | 0.882540i | \(0.655832\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.608168 | + | 1.05338i | −0.0401889 | + | 0.0696092i | −0.885420 | − | 0.464791i | \(-0.846129\pi\) |
0.845231 | + | 0.534401i | \(0.179463\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.98608 | − | 17.2964i | −0.654210 | − | 1.13313i | −0.982091 | − | 0.188406i | \(-0.939668\pi\) |
0.327881 | − | 0.944719i | \(-0.393665\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.51819 | + | 7.82573i | −0.294734 | + | 0.510494i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.1352 | + | 0.507822i | −0.723310 | + | 0.0329866i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.00739 | − | 5.20896i | −0.194532 | − | 0.336939i | 0.752215 | − | 0.658918i | \(-0.228985\pi\) |
−0.946747 | + | 0.321978i | \(0.895652\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.30778 | − | 16.1215i | −0.599567 | − | 1.03848i | −0.992885 | − | 0.119078i | \(-0.962006\pi\) |
0.393318 | − | 0.919402i | \(-0.371327\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.1855 | + | 3.52144i | −0.974150 | + | 0.225901i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.3801 | + | 26.6390i | −0.978609 | + | 1.69500i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.18356 | + | 2.28441i | −0.0750051 | + | 0.144769i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.99707 | −0.441651 | −0.220826 | − | 0.975313i | \(-0.570875\pi\) | ||||
−0.220826 | + | 0.975313i | \(0.570875\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.2675 | 1.71429 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.3691 | − | 16.2067i | −0.649336 | − | 1.01490i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.88891 | + | 15.3960i | −0.554475 | + | 0.960378i | 0.443469 | + | 0.896289i | \(0.353747\pi\) |
−0.997944 | + | 0.0640889i | \(0.979586\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.76975 | − | 18.9989i | 0.542834 | − | 1.17600i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.5993 | + | 23.5547i | 0.838570 | + | 1.45245i | 0.891091 | + | 0.453825i | \(0.149941\pi\) |
−0.0525210 | + | 0.998620i | \(0.516726\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.21780 | + | 10.7695i | 0.381956 | + | 0.661568i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.18044 | − | 14.3489i | −0.561834 | − | 0.878138i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.9481 | − | 20.6946i | 0.728486 | − | 1.26177i | −0.229038 | − | 0.973418i | \(-0.573558\pi\) |
0.957523 | − | 0.288356i | \(-0.0931088\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.13667 | + | 10.6290i | 0.372776 | + | 0.645668i | 0.989992 | − | 0.141127i | \(-0.0450725\pi\) |
−0.617215 | + | 0.786794i | \(0.711739\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.44951 | + | 4.24268i | −0.147711 | + | 0.255843i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.39037 | − | 11.0684i | −0.383960 | − | 0.665038i | 0.607664 | − | 0.794194i | \(-0.292107\pi\) |
−0.991624 | + | 0.129156i | \(0.958773\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 22.0526 | − | 2.01561i | 1.32026 | − | 0.120672i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.2573 | − | 24.6944i | 0.850519 | − | 1.47314i | −0.0302219 | − | 0.999543i | \(-0.509621\pi\) |
0.880741 | − | 0.473599i | \(-0.157045\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.726654 | −0.0431951 | −0.0215975 | − | 0.999767i | \(-0.506875\pi\) | ||||
−0.0215975 | + | 0.999767i | \(0.506875\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −18.4231 | + | 0.840188i | −1.09129 | + | 0.0497685i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.69076 | − | 2.92848i | −0.0994563 | − | 0.172263i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.392505 | − | 0.757580i | 0.0230091 | − | 0.0444102i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.7901 | + | 22.1531i | 0.747204 | + | 1.29420i | 0.949158 | + | 0.314800i | \(0.101938\pi\) |
−0.201954 | + | 0.979395i | \(0.564729\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.2360 | + | 19.4613i | −0.654184 | + | 1.13308i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 14.8128 | + | 19.0736i | 0.859528 | + | 1.10676i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −41.7031 | −2.41175 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.17977 | − | 4.96993i | −0.182673 | − | 0.285515i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.9985 | − | 29.4423i | 0.973333 | − | 1.68586i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.23405 | 0.355796 | 0.177898 | − | 0.984049i | \(-0.443070\pi\) | ||||
0.177898 | + | 0.984049i | \(0.443070\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.11323 | + | 7.93901i | −0.233993 | + | 0.451635i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.2383 | −1.65795 | −0.828976 | − | 0.559284i | \(-0.811076\pi\) | ||||
−0.828976 | + | 0.559284i | \(0.811076\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.4868 | −1.61017 | −0.805083 | − | 0.593162i | \(-0.797879\pi\) | ||||
−0.805083 | + | 0.593162i | \(0.797879\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.61849 | 0.0909032 | 0.0454516 | − | 0.998967i | \(-0.485527\pi\) | ||||
0.0454516 | + | 0.998967i | \(0.485527\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −32.4179 | −1.81505 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.37957 | − | 8.40819i | −0.300258 | − | 0.469300i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.5366 | −1.08704 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.74630 | − | 6.48879i | 0.207808 | − | 0.359933i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.15700 | + | 13.8138i | −0.395783 | + | 0.763907i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.9823 | −0.768536 | −0.384268 | − | 0.923222i | \(-0.625546\pi\) | ||||
−0.384268 | + | 0.923222i | \(0.625546\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.25729 | + | 1.78085i | 0.0688993 | + | 0.0975902i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.63307 | + | 2.82857i | −0.0892244 | + | 0.154541i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.8619 | − | 24.0095i | −0.755104 | − | 1.30788i | −0.945323 | − | 0.326137i | \(-0.894253\pi\) |
0.190219 | − | 0.981742i | \(-0.439080\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.26907 | − | 1.98354i | −0.0689266 | − | 0.107731i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.1534 | − | 29.7106i | −0.928909 | − | 1.60892i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −13.4751 | − | 21.0614i | −0.725475 | − | 1.13391i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.52898 | 0.404177 | 0.202089 | − | 0.979367i | \(-0.435227\pi\) | ||||
0.202089 | + | 0.979367i | \(0.435227\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.0541 | + | 26.0744i | −0.805827 | + | 1.39573i | 0.109905 | + | 0.993942i | \(0.464945\pi\) |
−0.915732 | + | 0.401791i | \(0.868388\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −22.6549 | − | 29.1712i | −1.20923 | − | 1.55705i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.1819 | − | 17.6356i | −0.541928 | − | 0.938647i | −0.998793 | − | 0.0491110i | \(-0.984361\pi\) |
0.456865 | − | 0.889536i | \(-0.348972\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.6352 | − | 28.8130i | 0.882905 | − | 1.52924i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.01313 | + | 13.8791i | 0.422917 | + | 0.732513i | 0.996223 | − | 0.0868277i | \(-0.0276730\pi\) |
−0.573307 | + | 0.819341i | \(0.694340\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.136673 | − | 0.236725i | 0.00719332 | − | 0.0124592i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.44659 | − | 16.3029i | 0.443331 | − | 0.855680i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.32383 | + | 9.22115i | 0.278662 | + | 0.482657i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.79893 | − | 11.7761i | −0.354901 | − | 0.614707i | 0.632200 | − | 0.774805i | \(-0.282152\pi\) |
−0.987101 | + | 0.160099i | \(0.948819\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.472958 | + | 0.669906i | 0.0246212 | + | 0.0348739i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.9641 | − | 18.9904i | 0.567700 | − | 0.983285i | −0.429093 | − | 0.903260i | \(-0.641167\pi\) |
0.996793 | − | 0.0800246i | \(-0.0254999\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −16.7989 | + | 0.766116i | −0.867493 | + | 0.0395621i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 49.5801 | 2.55351 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.7965 | −1.53054 | −0.765271 | − | 0.643708i | \(-0.777395\pi\) | ||||
−0.765271 | + | 0.643708i | \(0.777395\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.41887 | − | 0.0647078i | 0.0726911 | − | 0.00331508i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.0109905 | + | 0.0190361i | −0.000561587 | + | 0.000972697i | −0.866306 | − | 0.499514i | \(-0.833512\pi\) |
0.865744 | + | 0.500486i | \(0.166845\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.07880 | − | 13.1692i | 0.309003 | − | 0.669428i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.6783 | + | 30.6197i | 0.896326 | + | 1.55248i | 0.832155 | + | 0.554543i | \(0.187107\pi\) |
0.0641702 | + | 0.997939i | \(0.479560\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.2434 | − | 22.9382i | −0.669746 | − | 1.16003i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.20535 | + | 11.9770i | −0.313018 | + | 0.604162i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.91741 | − | 13.7134i | 0.398368 | − | 0.689994i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.47150 | − | 14.6731i | −0.425172 | − | 0.736420i | 0.571264 | − | 0.820766i | \(-0.306453\pi\) |
−0.996436 | + | 0.0843464i | \(0.973120\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.48181 | − | 2.56657i | 0.0739982 | − | 0.128169i | −0.826652 | − | 0.562713i | \(-0.809757\pi\) |
0.900650 | + | 0.434545i | \(0.143091\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.2345 | + | 45.4395i | 1.30683 | + | 2.26350i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.41216 | − | 20.8672i | 0.368313 | − | 1.03690i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.68862 | − | 2.92478i | 0.0837018 | − | 0.144976i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.6549 | 0.724636 | 0.362318 | − | 0.932054i | \(-0.381985\pi\) | ||||
0.362318 | + | 0.932054i | \(0.381985\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.79367 | − | 4.36646i | −0.137802 | − | 0.215382i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.82743 | − | 3.16520i | −0.0897050 | − | 0.155374i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.90642 | − | 9.23165i | −0.289239 | − | 0.452076i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.6352 | − | 21.8848i | −0.617270 | − | 1.06914i | −0.989982 | − | 0.141196i | \(-0.954905\pi\) |
0.372711 | − | 0.927947i | \(-0.378428\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.99854 | − | 13.8539i | 0.389825 | − | 0.675196i | −0.602601 | − | 0.798043i | \(-0.705869\pi\) |
0.992426 | + | 0.122846i | \(0.0392022\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.9720 | + | 1.00284i | −0.533476 | + | 0.0487598i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.75876 | 0.230834 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −26.3230 | + | 50.8065i | −1.27089 | + | 2.45296i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.51673 | + | 11.2873i | −0.313900 | + | 0.543690i | −0.979203 | − | 0.202883i | \(-0.934969\pi\) |
0.665303 | + | 0.746573i | \(0.268302\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.5467 | −1.13158 | −0.565791 | − | 0.824549i | \(-0.691429\pi\) | ||||
−0.565791 | + | 0.824549i | \(0.691429\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.0203 | + | 25.0395i | 0.768116 | + | 1.20055i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −25.3887 | −1.21451 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.70895 | −0.320200 | −0.160100 | − | 0.987101i | \(-0.551182\pi\) | ||||
−0.160100 | + | 0.987101i | \(0.551182\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 35.2455 | 1.67456 | 0.837282 | − | 0.546771i | \(-0.184143\pi\) | ||||
0.837282 | + | 0.546771i | \(0.184143\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.1986 | 1.14712 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.49115 | + | 6.73832i | −0.165126 | + | 0.318711i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.9387 | −0.610616 | −0.305308 | − | 0.952254i | \(-0.598759\pi\) | ||||
−0.305308 | + | 0.952254i | \(0.598759\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.635211 | − | 1.10022i | 0.0299109 | − | 0.0518072i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.16158 | + | 9.63046i | 0.289496 | + | 0.452478i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.1986 | −1.36585 | −0.682927 | − | 0.730487i | \(-0.739293\pi\) | ||||
−0.682927 | + | 0.730487i | \(0.739293\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.85087 | − | 21.7247i | 0.413123 | − | 1.01402i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.34348 | + | 16.1834i | −0.435169 | + | 0.753735i | −0.997309 | − | 0.0733066i | \(-0.976645\pi\) |
0.562140 | + | 0.827042i | \(0.309978\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.1249 | + | 33.1253i | 0.888809 | + | 1.53946i | 0.841285 | + | 0.540593i | \(0.181800\pi\) |
0.0475247 | + | 0.998870i | \(0.484867\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.4715 | + | 27.9317i | −0.671100 | + | 1.29530i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.64387 | − | 13.2396i | −0.353716 | − | 0.612654i | 0.633181 | − | 0.774004i | \(-0.281749\pi\) |
−0.986897 | + | 0.161349i | \(0.948415\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.0021 | + | 0.456148i | −0.460874 | + | 0.0210182i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22.4706 | −1.03320 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.28074 | − | 3.95035i | 0.104647 | − | 0.181255i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.35447 | + | 13.7664i | −0.290951 | + | 0.630322i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.51605 | + | 9.55408i | 0.252035 | + | 0.436537i | 0.964086 | − | 0.265591i | \(-0.0855669\pi\) |
−0.712051 | + | 0.702128i | \(0.752234\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.58259 | + | 4.47318i | −0.117756 | + | 0.203959i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.606032 | + | 1.04968i | 0.0275185 | + | 0.0476635i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.30039 | + | 14.3767i | −0.376126 | + | 0.651470i | −0.990495 | − | 0.137549i | \(-0.956078\pi\) |
0.614368 | + | 0.789019i | \(0.289411\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.83988 | + | 10.6906i | 0.309310 | + | 0.483447i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.3633 | + | 23.1460i | 0.603079 | + | 1.04456i | 0.992352 | + | 0.123440i | \(0.0393928\pi\) |
−0.389273 | + | 0.921122i | \(0.627274\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.7448 | + | 27.2709i | 0.709112 | + | 1.22822i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −34.1644 | + | 3.12263i | −1.53558 | + | 0.140352i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.618485 | + | 1.07125i | −0.0276872 | + | 0.0479557i | −0.879537 | − | 0.475830i | \(-0.842148\pi\) |
0.851850 | + | 0.523786i | \(0.175481\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.2288 | + | 17.5504i | 0.501665 | + | 0.784095i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.07179 | 0.0477889 | 0.0238944 | − | 0.999714i | \(-0.492393\pi\) | ||||
0.0238944 | + | 0.999714i | \(0.492393\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.38151 | 0.372973 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 29.9004 | − | 57.7112i | 1.32792 | − | 2.56304i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.0344 | − | 17.3801i | 0.444768 | − | 0.770362i | −0.553268 | − | 0.833004i | \(-0.686619\pi\) |
0.998036 | + | 0.0626420i | \(0.0199526\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −13.7922 | − | 17.7594i | −0.608941 | − | 0.784095i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.35087 | − | 11.0000i | −0.279853 | − | 0.484720i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.53443 | + | 14.7821i | 0.375344 | + | 0.650115i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.47656 | − | 0.386574i | 0.372080 | − | 0.0169687i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.4430 | + | 26.7480i | −0.676570 | + | 1.17185i | 0.299438 | + | 0.954116i | \(0.403201\pi\) |
−0.976007 | + | 0.217737i | \(0.930132\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.69961 | − | 6.40792i | −0.161773 | − | 0.280199i | 0.773732 | − | 0.633513i | \(-0.218388\pi\) |
−0.935505 | + | 0.353315i | \(0.885054\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.6623 | + | 28.8599i | −0.725819 | + | 1.25716i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.71041 | − | 9.89072i | −0.248279 | − | 0.430031i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −27.2855 | + | 2.49390i | −1.18409 | + | 0.108226i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.971495 | + | 1.68268i | −0.0420801 | + | 0.0728849i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.1800 | 0.613053 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.41887 | + | 2.73859i | −0.0612289 | + | 0.118179i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.3348 | − | 19.6325i | −0.487322 | − | 0.844067i | 0.512572 | − | 0.858644i | \(-0.328693\pi\) |
−0.999894 | + | 0.0145779i | \(0.995360\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −29.3157 | + | 1.33694i | −1.25805 | + | 0.0573737i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.0505 | − | 19.1400i | −0.473351 | − | 0.819868i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.07373 | − | 5.32386i | 0.131423 | − | 0.227632i | −0.792802 | − | 0.609479i | \(-0.791379\pi\) |
0.924225 | + | 0.381847i | \(0.124712\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 41.2793 | − | 3.77293i | 1.76176 | − | 0.161025i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30.1842 | 1.28589 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.09358 | + | 0.141083i | −0.131315 | + | 0.00598863i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.8370 | + | 25.6984i | −0.628662 | + | 1.08887i | 0.359158 | + | 0.933277i | \(0.383064\pi\) |
−0.987820 | + | 0.155598i | \(0.950270\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.3667 | 1.45356 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −36.3047 | + | 1.65568i | −1.53278 | + | 0.0699027i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.3111 | 1.23531 | 0.617657 | − | 0.786447i | \(-0.288082\pi\) | ||||
0.617657 | + | 0.786447i | \(0.288082\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.34514 | 0.140731 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −36.8860 | −1.54634 | −0.773170 | − | 0.634198i | \(-0.781330\pi\) | ||||
−0.773170 | + | 0.634198i | \(0.781330\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.3786 | 1.35500 | 0.677501 | − | 0.735522i | \(-0.263063\pi\) | ||||
0.677501 | + | 0.735522i | \(0.263063\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.49854 | − | 0.433181i | 0.396807 | − | 0.0180964i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.18423 | 0.257900 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.5093 | − | 19.9348i | 0.479140 | − | 0.829895i | −0.520574 | − | 0.853817i | \(-0.674282\pi\) |
0.999714 | + | 0.0239220i | \(0.00761535\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.52918 | − | 0.434579i | 0.396019 | − | 0.0180605i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.4897 | 0.972843 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 52.2512 | − | 4.77577i | 2.16032 | − | 0.197454i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.87052 | − | 4.97189i | 0.118479 | − | 0.205212i | −0.800686 | − | 0.599084i | \(-0.795531\pi\) |
0.919165 | + | 0.393872i | \(0.128865\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.9715 | + | 27.6634i | 0.658094 | + | 1.13985i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.1228 | + | 0.917699i | −0.827740 | + | 0.0377491i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.8727 | + | 24.0282i | 0.569682 | + | 0.986718i | 0.996597 | + | 0.0824263i | \(0.0262669\pi\) |
−0.426915 | + | 0.904292i | \(0.640400\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.30466 | − | 6.37838i | 0.135251 | − | 0.261050i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.10817 | 0.167855 | 0.0839276 | − | 0.996472i | \(-0.473254\pi\) | ||||
0.0839276 | + | 0.996472i | \(0.473254\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.80924 | − | 13.5260i | 0.318546 | − | 0.551737i | −0.661639 | − | 0.749822i | \(-0.730139\pi\) |
0.980185 | + | 0.198085i | \(0.0634723\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.96576 | + | 0.362471i | −0.161498 | + | 0.0147610i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.0416 | + | 22.5888i | 0.530218 | + | 0.918364i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.280738 | + | 0.486253i | −0.0113948 | + | 0.0197364i | −0.871667 | − | 0.490099i | \(-0.836960\pi\) |
0.860272 | + | 0.509836i | \(0.170294\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.0526 | − | 22.6078i | −0.528053 | − | 0.914614i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.1008 | − | 17.4951i | 0.407967 | − | 0.706619i | −0.586695 | − | 0.809808i | \(-0.699571\pi\) |
0.994662 | + | 0.103189i | \(0.0329047\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.16372 | + | 0.0530713i | −0.0469255 | + | 0.00214004i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.4569 | + | 19.8439i | 0.461238 | + | 0.798887i | 0.999023 | − | 0.0441948i | \(-0.0140722\pi\) |
−0.537785 | + | 0.843082i | \(0.680739\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.8515 | + | 34.3839i | 0.797901 | + | 1.38201i | 0.920981 | + | 0.389608i | \(0.127390\pi\) |
−0.123080 | + | 0.992397i | \(0.539277\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.5021 | − | 28.2323i | 0.461565 | − | 1.13292i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5797 | − | 25.2527i | 0.583187 | − | 1.01011i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.0254 | + | 30.9309i | −0.639992 | + | 1.23526i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.28054 | −0.130804 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.0364 | −1.23554 | −0.617769 | − | 0.786359i | \(-0.711963\pi\) | ||||
−0.617769 | + | 0.786359i | \(0.711963\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −25.4054 | − | 39.7083i | −1.00978 | − | 1.57826i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.00885 | + | 1.74739i | −0.0400352 | + | 0.0693429i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 40.3970 | − | 3.69229i | 1.59808 | − | 0.146065i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.7932 | + | 25.6226i | 0.584296 | + | 1.01203i | 0.994963 | + | 0.100245i | \(0.0319626\pi\) |
−0.410667 | + | 0.911785i | \(0.634704\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.8442 | + | 22.2467i | 0.506524 | + | 0.877325i | 0.999972 | + | 0.00754978i | \(0.00240319\pi\) |
−0.493447 | + | 0.869776i | \(0.664263\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.1046 | + | 17.3563i | 0.437242 | + | 0.683403i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.50885 | − | 14.7378i | 0.334518 | − | 0.579401i | −0.648874 | − | 0.760895i | \(-0.724760\pi\) |
0.983392 | + | 0.181494i | \(0.0580933\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21.2237 | + | 36.7606i | 0.833104 | + | 1.44298i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.735508 | + | 1.27394i | −0.0287827 | + | 0.0498530i | −0.880058 | − | 0.474866i | \(-0.842496\pi\) |
0.851275 | + | 0.524719i | \(0.175830\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.58113 | − | 16.5950i | −0.374366 | − | 0.648420i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.44085 | + | 11.7872i | −0.212268 | + | 0.459861i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.7003 | − | 35.8539i | 0.806369 | − | 1.39667i | −0.108995 | − | 0.994042i | \(-0.534763\pi\) |
0.915363 | − | 0.402629i | \(-0.131904\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.2704 | −1.48855 | −0.744273 | − | 0.667875i | \(-0.767204\pi\) | ||||
−0.744273 | + | 0.667875i | \(0.767204\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 55.5246 | − | 2.53220i | 2.15640 | − | 0.0983426i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.4612 | + | 35.4398i | 0.792260 | + | 1.37223i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.56274 | − | 4.94639i | 0.0990814 | − | 0.191239i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −32.1086 | − | 55.6138i | −1.23954 | − | 2.14695i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.2448 | − | 26.4048i | 0.587645 | − | 1.01783i | −0.406894 | − | 0.913475i | \(-0.633388\pi\) |
0.994540 | − | 0.104357i | \(-0.0332783\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.35953 | + | 4.32586i | 0.129309 | + | 0.166502i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −44.9253 | −1.72662 | −0.863309 | − | 0.504675i | \(-0.831612\pi\) | ||||
−0.863309 | + | 0.504675i | \(0.831612\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.8849 | − | 23.2649i | −0.570391 | − | 0.891513i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.1986 | − | 41.9133i | 0.925935 | − | 1.60377i | 0.135884 | − | 0.990725i | \(-0.456613\pi\) |
0.790051 | − | 0.613041i | \(-0.210054\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.36381 | 0.281357 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.969165 | − | 1.87060i | 0.0369759 | − | 0.0713679i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −35.9253 | −1.36864 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.3815 | −0.699266 | −0.349633 | − | 0.936887i | \(-0.613694\pi\) | ||||
−0.349633 | + | 0.936887i | \(0.613694\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.5687 | 0.590553 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.23405 | −0.0467428 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.6433 | + | 29.1392i | 0.705153 | + | 1.10214i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.0292 | −1.02088 | −0.510439 | − | 0.859914i | \(-0.670517\pi\) | ||||
−0.510439 | + | 0.859914i | \(0.670517\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.57227 | + | 2.72325i | −0.0592994 | + | 0.102710i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.20009 | − | 13.8970i | 0.271171 | − | 0.523392i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.98522 | 0.187224 | 0.0936119 | − | 0.995609i | \(-0.470159\pi\) | ||||
0.0936119 | + | 0.995609i | \(0.470159\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 19.2267 | − | 1.75732i | 0.721056 | − | 0.0659046i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21.6534 | + | 37.5048i | −0.810926 | + | 1.40457i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −40.6431 | − | 70.3959i | −1.51997 | − | 2.63266i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.61458 | + | 8.77550i | 0.209680 | + | 0.327727i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.84708 | + | 13.5915i | 0.292647 | + | 0.506879i | 0.974435 | − | 0.224671i | \(-0.0721307\pi\) |
−0.681788 | + | 0.731550i | \(0.738797\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.3769 | + | 27.1599i | 0.646255 | + | 1.01009i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.35234 | −0.273059 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.9071 | − | 18.8916i | 0.404522 | − | 0.700652i | −0.589744 | − | 0.807590i | \(-0.700771\pi\) |
0.994266 | + | 0.106938i | \(0.0341047\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.9969 | − | 7.29124i | 0.962847 | − | 0.270046i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.9136 | + | 18.9029i | 0.403655 | + | 0.699151i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.0074 | + | 20.7974i | −0.443503 | + | 0.768170i | −0.997947 | − | 0.0640514i | \(-0.979598\pi\) |
0.554443 | + | 0.832221i | \(0.312931\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.08472 | + | 5.34290i | 0.113627 | + | 0.196808i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.35447 | + | 16.2024i | −0.344110 | + | 0.596016i | −0.985192 | − | 0.171457i | \(-0.945153\pi\) |
0.641082 | + | 0.767473i | \(0.278486\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.5093 | − | 47.3059i | 0.900373 | − | 1.73782i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.1534 | + | 34.9067i | 0.739356 | + | 1.28060i | 0.952785 | + | 0.303644i | \(0.0982035\pi\) |
−0.213429 | + | 0.976959i | \(0.568463\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.39037 | − | 9.33639i | −0.197488 | − | 0.342059i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.86760 | − | 4.04600i | 0.0683319 | − | 0.148035i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.5629 | − | 18.2955i | 0.385447 | − | 0.667614i | −0.606384 | − | 0.795172i | \(-0.707381\pi\) |
0.991831 | + | 0.127558i | \(0.0407139\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.1067 | − | 0.552127i | 0.441193 | − | 0.0201206i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.2412 | −0.591079 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.85934 | 0.321998 | 0.160999 | − | 0.986955i | \(-0.448528\pi\) | ||||
0.160999 | + | 0.986955i | \(0.448528\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −47.1797 | + | 2.15163i | −1.71251 | + | 0.0780992i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.694551 | − | 1.20300i | 0.0251774 | − | 0.0436086i | −0.853162 | − | 0.521646i | \(-0.825318\pi\) |
0.878340 | + | 0.478037i | \(0.158652\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 19.2199 | + | 27.2235i | 0.694898 | + | 0.984266i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −32.4597 | − | 56.2219i | −1.17205 | − | 2.03005i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.9626 | − | 32.8443i | −0.683810 | − | 1.18439i | −0.973809 | − | 0.227367i | \(-0.926988\pi\) |
0.289999 | − | 0.957027i | \(-0.406345\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.1652 | − | 27.3404i | 0.510146 | − | 0.984642i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.657981 | − | 1.13966i | 0.0236659 | − | 0.0409906i | −0.853950 | − | 0.520355i | \(-0.825800\pi\) |
0.877616 | + | 0.479365i | \(0.159133\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.89037 | − | 6.73832i | −0.139746 | − | 0.242047i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.591443 | + | 1.02441i | −0.0211907 | + | 0.0367033i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.4224 | − | 54.4251i | −1.12438 | − | 1.94748i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −13.6747 | + | 33.5649i | −0.488694 | + | 1.19951i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.11177 | − | 12.3179i | 0.253830 | − | 0.439646i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.2586 | −0.436971 | −0.218485 | − | 0.975840i | \(-0.570112\pi\) | ||||
−0.218485 | + | 0.975840i | \(0.570112\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25.3889 | − | 39.6825i | −0.903869 | − | 1.41273i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 49.1072 | + | 85.0561i | 1.74385 | + | 3.02043i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.6082 | − | 18.1434i | −0.411699 | − | 0.643480i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.7178 | + | 18.5638i | 0.379644 | + | 0.657563i | 0.991010 | − | 0.133785i | \(-0.0427132\pi\) |
−0.611366 | + | 0.791348i | \(0.709380\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.29007 | − | 14.3588i | 0.293282 | − | 0.507979i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.0167 | + | 24.1028i | 0.601256 | + | 0.851630i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.1124 | 0.709753 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.0402 | + | 36.7497i | −0.670246 | + | 1.29365i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.3478 | + | 23.1190i | −0.469282 | + | 0.812820i | −0.999383 | − | 0.0351140i | \(-0.988821\pi\) |
0.530101 | + | 0.847934i | \(0.322154\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.2852 | −1.34438 | −0.672188 | − | 0.740381i | \(-0.734645\pi\) | ||||
−0.672188 | + | 0.740381i | \(0.734645\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.4567 | − | 17.9067i | −0.401804 | − | 0.628014i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.0292 | −0.631535 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.9224 | 0.731981 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.4998 | −0.366446 | −0.183223 | − | 0.983071i | \(-0.558653\pi\) | ||||
−0.183223 | + | 0.983071i | \(0.558653\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.0000 | 0.557725 | 0.278862 | − | 0.960331i | \(-0.410043\pi\) | ||||
0.278862 | + | 0.960331i | \(0.410043\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.90350 | − | 7.53420i | 0.135902 | − | 0.262307i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −48.7817 | −1.69631 | −0.848153 | − | 0.529752i | \(-0.822285\pi\) | ||||
−0.848153 | + | 0.529752i | \(0.822285\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.10963 | + | 5.38604i | −0.108002 | + | 0.187065i | −0.914961 | − | 0.403543i | \(-0.867779\pi\) |
0.806959 | + | 0.590608i | \(0.201112\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.9303 | + | 18.6469i | 0.413859 | + | 0.646855i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −29.5979 | −1.02428 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −37.9976 | + | 5.22765i | −1.31339 | + | 0.180694i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.0366 | + | 36.4364i | −0.726263 | + | 1.25792i | 0.232189 | + | 0.972671i | \(0.425411\pi\) |
−0.958452 | + | 0.285254i | \(0.907922\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.82597 | − | 17.0191i | −0.338826 | − | 0.586865i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −22.7201 | + | 43.8525i | −0.782523 | + | 1.51036i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 46.1665 | + | 79.9628i | 1.58818 | + | 2.75080i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.25729 | − | 0.0573390i | 0.0431502 | − | 0.00196787i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.26322 | −0.146141 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.72519 | + | 11.6484i | −0.230266 | + | 0.398833i | −0.957886 | − | 0.287147i | \(-0.907293\pi\) |
0.727620 | + | 0.685980i | \(0.240626\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 31.8104 | − | 2.90748i | 1.08789 | − | 0.0994336i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.6893 | + | 35.8349i | 0.706733 | + | 1.22410i | 0.966063 | + | 0.258308i | \(0.0831650\pi\) |
−0.259330 | + | 0.965789i | \(0.583502\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.8815 | + | 34.4358i | −0.678349 | + | 1.17493i | 0.297129 | + | 0.954837i | \(0.403971\pi\) |
−0.975478 | + | 0.220097i | \(0.929363\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.6929 | − | 46.2334i | −0.908637 | − | 1.57380i | −0.815960 | − | 0.578109i | \(-0.803791\pi\) |
−0.0926768 | − | 0.995696i | \(-0.529542\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.02704 | + | 10.4391i | −0.204926 | + | 0.354942i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.15652 | + | 4.93359i | 0.107201 | + | 0.167554i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.9552 | − | 25.9033i | −0.507322 | − | 0.878708i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.71780 | − | 8.17147i | −0.159857 | − | 0.276880i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.619354 | + | 1.34178i | −0.0209619 | + | 0.0454123i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.42674 | − | 5.93530i | 0.115713 | − | 0.200421i | −0.802352 | − | 0.596852i | \(-0.796418\pi\) |
0.918065 | + | 0.396431i | \(0.129751\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23.8781 | − | 37.3211i | −0.805389 | − | 1.25881i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.5103 | 0.421483 | 0.210742 | − | 0.977542i | \(-0.432412\pi\) | ||||
0.210742 | + | 0.977542i | \(0.432412\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.69124 | 0.225178 | 0.112589 | − | 0.993642i | \(-0.464086\pi\) | ||||
0.112589 | + | 0.993642i | \(0.464086\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17.9054 | − | 34.5596i | 0.601885 | − | 1.16171i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.0708 | − | 27.8355i | 0.539605 | − | 0.934623i | −0.459320 | − | 0.888271i | \(-0.651907\pi\) |
0.998925 | − | 0.0463524i | \(-0.0147597\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −27.1350 | − | 31.8332i | −0.909057 | − | 1.06645i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.94639 | − | 13.7636i | −0.265916 | − | 0.460580i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.19076 | − | 3.79450i | −0.0732289 | − | 0.126836i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 72.1569 | − | 3.29072i | 2.40925 | − | 0.109874i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25.7434 | − | 44.5888i | 0.858590 | − | 1.48712i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.4086 | − | 19.7602i | −0.380074 | − | 0.658308i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.8442 | − | 36.1031i | 0.692883 | − | 1.20011i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.7016 | + | 27.1959i | 0.521362 | + | 0.903025i | 0.999691 | + | 0.0248444i | \(0.00790902\pi\) |
−0.478330 | + | 0.878180i | \(0.658758\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.89397 | + | 8.34832i | 0.195491 | + | 0.276896i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.8982 | + | 39.6609i | −0.758653 | + | 1.31402i | 0.184885 | + | 0.982760i | \(0.440809\pi\) |
−0.943538 | + | 0.331265i | \(0.892525\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.90369 | −0.228479 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −27.0885 | + | 52.2840i | −0.895519 | + | 1.72846i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.5900 | − | 23.5385i | −0.448292 | − | 0.776465i | 0.549983 | − | 0.835176i | \(-0.314634\pi\) |
−0.998275 | + | 0.0587112i | \(0.981301\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.7865 | + | 0.491918i | −0.355426 | + | 0.0162092i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 48.0576 | + | 83.2381i | 1.58183 | + | 2.73982i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.382977 | − | 0.663336i | 0.0125922 | − | 0.0218104i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.49047 | − | 14.0611i | 0.213175 | − | 0.461826i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 40.6677 | 1.33426 | 0.667132 | − | 0.744940i | \(-0.267522\pi\) | ||||
0.667132 | + | 0.744940i | \(0.267522\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 50.5897 | − | 2.30714i | 1.65623 | − | 0.0755325i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 25.8135 | − | 44.7103i | 0.844192 | − | 1.46218i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.4150 | −0.536254 | −0.268127 | − | 0.963384i | \(-0.586405\pi\) | ||||
−0.268127 | + | 0.963384i | \(0.586405\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 49.2893 | − | 2.24784i | 1.60849 | − | 0.0733555i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.33755 | −0.239197 | −0.119599 | − | 0.992822i | \(-0.538161\pi\) | ||||
−0.119599 | + | 0.992822i | \(0.538161\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.60370 | −0.0522237 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 59.1124 | 1.92090 | 0.960448 | − | 0.278459i | \(-0.0898236\pi\) | ||||
0.960448 | + | 0.278459i | \(0.0898236\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.7601 | −0.998515 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.80039 | + | 0.127712i | −0.0908088 | + | 0.00414134i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.9354 | −0.548592 | −0.274296 | − | 0.961645i | \(-0.588445\pi\) | ||||
−0.274296 | + | 0.961645i | \(0.588445\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.75370 | + | 11.6977i | −0.218544 | + | 0.378530i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 56.0911 | − | 2.55804i | 1.81317 | − | 0.0826897i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.4868 | 0.757637 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.97150 | + | 14.1238i | 0.321327 | + | 0.455133i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.77548 | + | 11.7355i | −0.218110 | + | 0.377778i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.55555 | + | 6.15839i | 0.114339 | + | 0.198040i | 0.917515 | − | 0.397701i | \(-0.130192\pi\) |
−0.803177 | + | 0.595741i | \(0.796858\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 33.8032 | − | 1.54160i | 1.08592 | − | 0.0495232i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.735508 | − | 1.27394i | −0.0236036 | − | 0.0408826i | 0.853982 | − | 0.520302i | \(-0.174181\pi\) |
−0.877586 | + | 0.479419i | \(0.840847\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.97003 | + | 11.5229i | −0.191194 | + | 0.369027i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.4327 | −0.621706 | −0.310853 | − | 0.950458i | \(-0.600615\pi\) | ||||
−0.310853 | + | 0.950458i | \(0.600615\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.8545 | − | 39.5851i | 0.730432 | − | 1.26515i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.2934 | − | 24.4662i | 0.360570 | − | 0.781145i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.87218 | + | 6.70681i | 0.123503 | + | 0.213914i | 0.921147 | − | 0.389215i | \(-0.127254\pi\) |
−0.797644 | + | 0.603129i | \(0.793920\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.3078 | − | 24.7818i | 0.455884 | − | 0.789614i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.1828 | + | 24.5653i | 0.450986 | + | 0.781130i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.23551 | − | 12.5323i | 0.229843 | − | 0.398101i | −0.727918 | − | 0.685664i | \(-0.759512\pi\) |
0.957762 | + | 0.287563i | \(0.0928452\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.1929 | − | 1.10332i | 0.767738 | − | 0.0350127i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.10243 | + | 8.83767i | 0.161758 | + | 0.280173i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.6549 | − | 47.8996i | −0.875838 | − | 1.51700i | −0.855867 | − | 0.517196i | \(-0.826976\pi\) |
−0.0199711 | − | 0.999801i | \(-0.506357\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.31596 | − | 2.98212i | −0.0732738 | − | 0.0943500i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))