Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(199,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.c (of order \(2\), degree \(1\), 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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.5 | ||
Root | \(1.45161 - 1.45161i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.199 |
Dual form | 825.2.c.g.199.2 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.90321i | 1.34577i | 0.739745 | + | 0.672887i | \(0.234946\pi\) | ||||
−0.739745 | + | 0.672887i | \(0.765054\pi\) | |||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | −1.62222 | −0.811108 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.90321 | 0.776983 | ||||||||
\(7\) | − 4.42864i | − 1.67387i | −0.547304 | − | 0.836934i | \(-0.684346\pi\) | ||||
0.547304 | − | 0.836934i | \(-0.315654\pi\) | |||||||
\(8\) | 0.719004i | 0.254206i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.62222i | 0.468293i | ||||||||
\(13\) | 0.622216i | 0.172572i | 0.996270 | + | 0.0862858i | \(0.0274998\pi\) | ||||
−0.996270 | + | 0.0862858i | \(0.972500\pi\) | |||||||
\(14\) | 8.42864 | 2.25265 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.61285 | −1.15321 | ||||||||
\(17\) | − 5.18421i | − 1.25736i | −0.777666 | − | 0.628678i | \(-0.783597\pi\) | ||||
0.777666 | − | 0.628678i | \(-0.216403\pi\) | |||||||
\(18\) | − 1.90321i | − 0.448591i | ||||||||
\(19\) | −7.05086 | −1.61758 | −0.808789 | − | 0.588100i | \(-0.799876\pi\) | ||||
−0.808789 | + | 0.588100i | \(0.799876\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.42864 | −0.966408 | ||||||||
\(22\) | 1.90321i | 0.405766i | ||||||||
\(23\) | − 8.85728i | − 1.84687i | −0.383754 | − | 0.923435i | \(-0.625369\pi\) | ||||
0.383754 | − | 0.923435i | \(-0.374631\pi\) | |||||||
\(24\) | 0.719004 | 0.146766 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.18421 | −0.232242 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 7.18421i | 1.35769i | ||||||||
\(29\) | 7.80642 | 1.44962 | 0.724808 | − | 0.688951i | \(-0.241928\pi\) | ||||
0.724808 | + | 0.688951i | \(0.241928\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.75557 | 0.494915 | 0.247457 | − | 0.968899i | \(-0.420405\pi\) | ||||
0.247457 | + | 0.968899i | \(0.420405\pi\) | |||||||
\(32\) | − 7.34122i | − 1.29776i | ||||||||
\(33\) | − 1.00000i | − 0.174078i | ||||||||
\(34\) | 9.86665 | 1.69212 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.62222 | 0.270369 | ||||||||
\(37\) | − 2.00000i | − 0.328798i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) | ||||
0.986394 | − | 0.164399i | \(-0.0525685\pi\) | |||||||
\(38\) | − 13.4193i | − 2.17689i | ||||||||
\(39\) | 0.622216 | 0.0996342 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.193576 | −0.0302315 | −0.0151158 | − | 0.999886i | \(-0.504812\pi\) | ||||
−0.0151158 | + | 0.999886i | \(0.504812\pi\) | |||||||
\(42\) | − 8.42864i | − 1.30057i | ||||||||
\(43\) | − 5.67307i | − 0.865135i | −0.901602 | − | 0.432568i | \(-0.857608\pi\) | ||||
0.901602 | − | 0.432568i | \(-0.142392\pi\) | |||||||
\(44\) | −1.62222 | −0.244558 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 16.8573 | 2.48547 | ||||||||
\(47\) | − 2.75557i | − 0.401941i | −0.979597 | − | 0.200971i | \(-0.935590\pi\) | ||||
0.979597 | − | 0.200971i | \(-0.0644095\pi\) | |||||||
\(48\) | 4.61285i | 0.665807i | ||||||||
\(49\) | −12.6128 | −1.80184 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.18421 | −0.725934 | ||||||||
\(52\) | − 1.00937i | − 0.139974i | ||||||||
\(53\) | 10.8573i | 1.49136i | 0.666303 | + | 0.745681i | \(0.267876\pi\) | ||||
−0.666303 | + | 0.745681i | \(0.732124\pi\) | |||||||
\(54\) | −1.90321 | −0.258994 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.18421 | 0.425508 | ||||||||
\(57\) | 7.05086i | 0.933909i | ||||||||
\(58\) | 14.8573i | 1.95086i | ||||||||
\(59\) | 4.85728 | 0.632364 | 0.316182 | − | 0.948699i | \(-0.397599\pi\) | ||||
0.316182 | + | 0.948699i | \(0.397599\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.85728 | 0.877985 | 0.438992 | − | 0.898491i | \(-0.355336\pi\) | ||||
0.438992 | + | 0.898491i | \(0.355336\pi\) | |||||||
\(62\) | 5.24443i | 0.666043i | ||||||||
\(63\) | 4.42864i | 0.557956i | ||||||||
\(64\) | 4.74620 | 0.593275 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.90321 | 0.234269 | ||||||||
\(67\) | − 1.24443i | − 0.152031i | −0.997107 | − | 0.0760157i | \(-0.975780\pi\) | ||||
0.997107 | − | 0.0760157i | \(-0.0242199\pi\) | |||||||
\(68\) | 8.40990i | 1.01985i | ||||||||
\(69\) | −8.85728 | −1.06629 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.75557 | 0.327026 | 0.163513 | − | 0.986541i | \(-0.447717\pi\) | ||||
0.163513 | + | 0.986541i | \(0.447717\pi\) | |||||||
\(72\) | − 0.719004i | − 0.0847354i | ||||||||
\(73\) | − 4.23506i | − 0.495677i | −0.968801 | − | 0.247838i | \(-0.920280\pi\) | ||||
0.968801 | − | 0.247838i | \(-0.0797202\pi\) | |||||||
\(74\) | 3.80642 | 0.442488 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.4380 | 1.31203 | ||||||||
\(77\) | − 4.42864i | − 0.504690i | ||||||||
\(78\) | 1.18421i | 0.134085i | ||||||||
\(79\) | −8.56199 | −0.963299 | −0.481650 | − | 0.876364i | \(-0.659962\pi\) | ||||
−0.481650 | + | 0.876364i | \(0.659962\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 0.368416i | − 0.0406848i | ||||||||
\(83\) | − 0.133353i | − 0.0146374i | −0.999973 | − | 0.00731870i | \(-0.997670\pi\) | ||||
0.999973 | − | 0.00731870i | \(-0.00232964\pi\) | |||||||
\(84\) | 7.18421 | 0.783861 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 10.7971 | 1.16428 | ||||||||
\(87\) | − 7.80642i | − 0.836936i | ||||||||
\(88\) | 0.719004i | 0.0766461i | ||||||||
\(89\) | −5.61285 | −0.594961 | −0.297480 | − | 0.954728i | \(-0.596146\pi\) | ||||
−0.297480 | + | 0.954728i | \(0.596146\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.75557 | 0.288862 | ||||||||
\(92\) | 14.3684i | 1.49801i | ||||||||
\(93\) | − 2.75557i | − 0.285739i | ||||||||
\(94\) | 5.24443 | 0.540922 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −7.34122 | −0.749260 | ||||||||
\(97\) | 7.24443i | 0.735561i | 0.929913 | + | 0.367780i | \(0.119882\pi\) | ||||
−0.929913 | + | 0.367780i | \(0.880118\pi\) | |||||||
\(98\) | − 24.0049i | − 2.42486i | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.66370 | 0.464056 | 0.232028 | − | 0.972709i | \(-0.425464\pi\) | ||||
0.232028 | + | 0.972709i | \(0.425464\pi\) | |||||||
\(102\) | − 9.86665i | − 0.976944i | ||||||||
\(103\) | 11.6128i | 1.14425i | 0.820167 | + | 0.572124i | \(0.193880\pi\) | ||||
−0.820167 | + | 0.572124i | \(0.806120\pi\) | |||||||
\(104\) | −0.447375 | −0.0438688 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −20.6637 | −2.00704 | ||||||||
\(107\) | 2.62222i | 0.253499i | 0.991935 | + | 0.126750i | \(0.0404545\pi\) | ||||
−0.991935 | + | 0.126750i | \(0.959546\pi\) | |||||||
\(108\) | − 1.62222i | − 0.156098i | ||||||||
\(109\) | 19.7146 | 1.88831 | 0.944156 | − | 0.329499i | \(-0.106880\pi\) | ||||
0.944156 | + | 0.329499i | \(0.106880\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.00000 | −0.189832 | ||||||||
\(112\) | 20.4286i | 1.93032i | ||||||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | −13.4193 | −1.25683 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −12.6637 | −1.17580 | ||||||||
\(117\) | − 0.622216i | − 0.0575239i | ||||||||
\(118\) | 9.24443i | 0.851019i | ||||||||
\(119\) | −22.9590 | −2.10465 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 13.0509i | 1.18157i | ||||||||
\(123\) | 0.193576i | 0.0174542i | ||||||||
\(124\) | −4.47013 | −0.401429 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −8.42864 | −0.750883 | ||||||||
\(127\) | − 15.1842i | − 1.34738i | −0.739014 | − | 0.673690i | \(-0.764708\pi\) | ||||
0.739014 | − | 0.673690i | \(-0.235292\pi\) | |||||||
\(128\) | − 5.64941i | − 0.499342i | ||||||||
\(129\) | −5.67307 | −0.499486 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.24443 | 0.108726 | 0.0543632 | − | 0.998521i | \(-0.482687\pi\) | ||||
0.0543632 | + | 0.998521i | \(0.482687\pi\) | |||||||
\(132\) | 1.62222i | 0.141196i | ||||||||
\(133\) | 31.2257i | 2.70761i | ||||||||
\(134\) | 2.36842 | 0.204600 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.72746 | 0.319627 | ||||||||
\(137\) | − 0.488863i | − 0.0417663i | −0.999782 | − | 0.0208832i | \(-0.993352\pi\) | ||||
0.999782 | − | 0.0208832i | \(-0.00664780\pi\) | |||||||
\(138\) | − 16.8573i | − 1.43499i | ||||||||
\(139\) | −17.8064 | −1.51032 | −0.755161 | − | 0.655540i | \(-0.772441\pi\) | ||||
−0.755161 | + | 0.655540i | \(0.772441\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.75557 | −0.232061 | ||||||||
\(142\) | 5.24443i | 0.440103i | ||||||||
\(143\) | 0.622216i | 0.0520323i | ||||||||
\(144\) | 4.61285 | 0.384404 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.06022 | 0.667069 | ||||||||
\(147\) | 12.6128i | 1.04029i | ||||||||
\(148\) | 3.24443i | 0.266691i | ||||||||
\(149\) | 1.43801 | 0.117806 | 0.0589031 | − | 0.998264i | \(-0.481240\pi\) | ||||
0.0589031 | + | 0.998264i | \(0.481240\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.1748 | −0.990774 | −0.495387 | − | 0.868672i | \(-0.664974\pi\) | ||||
−0.495387 | + | 0.868672i | \(0.664974\pi\) | |||||||
\(152\) | − 5.06959i | − 0.411198i | ||||||||
\(153\) | 5.18421i | 0.419118i | ||||||||
\(154\) | 8.42864 | 0.679199 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.00937 | −0.0808141 | ||||||||
\(157\) | 18.4701i | 1.47408i | 0.675851 | + | 0.737038i | \(0.263776\pi\) | ||||
−0.675851 | + | 0.737038i | \(0.736224\pi\) | |||||||
\(158\) | − 16.2953i | − 1.29638i | ||||||||
\(159\) | 10.8573 | 0.861038 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −39.2257 | −3.09142 | ||||||||
\(162\) | 1.90321i | 0.149530i | ||||||||
\(163\) | 10.1017i | 0.791227i | 0.918417 | + | 0.395614i | \(0.129468\pi\) | ||||
−0.918417 | + | 0.395614i | \(0.870532\pi\) | |||||||
\(164\) | 0.314022 | 0.0245210 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.253799 | 0.0196986 | ||||||||
\(167\) | − 16.3368i | − 1.26418i | −0.774896 | − | 0.632089i | \(-0.782198\pi\) | ||||
0.774896 | − | 0.632089i | \(-0.217802\pi\) | |||||||
\(168\) | − 3.18421i | − 0.245667i | ||||||||
\(169\) | 12.6128 | 0.970219 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.05086 | 0.539192 | ||||||||
\(172\) | 9.20294i | 0.701718i | ||||||||
\(173\) | 9.18421i | 0.698262i | 0.937074 | + | 0.349131i | \(0.113523\pi\) | ||||
−0.937074 | + | 0.349131i | \(0.886477\pi\) | |||||||
\(174\) | 14.8573 | 1.12633 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.61285 | −0.347706 | ||||||||
\(177\) | − 4.85728i | − 0.365095i | ||||||||
\(178\) | − 10.6824i | − 0.800683i | ||||||||
\(179\) | 25.3274 | 1.89306 | 0.946530 | − | 0.322617i | \(-0.104563\pi\) | ||||
0.946530 | + | 0.322617i | \(0.104563\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.6128 | −1.01184 | −0.505918 | − | 0.862582i | \(-0.668846\pi\) | ||||
−0.505918 | + | 0.862582i | \(0.668846\pi\) | |||||||
\(182\) | 5.24443i | 0.388743i | ||||||||
\(183\) | − 6.85728i | − 0.506905i | ||||||||
\(184\) | 6.36842 | 0.469486 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.24443 | 0.384540 | ||||||||
\(187\) | − 5.18421i | − 0.379107i | ||||||||
\(188\) | 4.47013i | 0.326017i | ||||||||
\(189\) | 4.42864 | 0.322136 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.10171 | 0.441504 | 0.220752 | − | 0.975330i | \(-0.429149\pi\) | ||||
0.220752 | + | 0.975330i | \(0.429149\pi\) | |||||||
\(192\) | − 4.74620i | − 0.342528i | ||||||||
\(193\) | − 18.3368i | − 1.31991i | −0.751305 | − | 0.659955i | \(-0.770575\pi\) | ||||
0.751305 | − | 0.659955i | \(-0.229425\pi\) | |||||||
\(194\) | −13.7877 | −0.989898 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 20.4608 | 1.46148 | ||||||||
\(197\) | − 6.69535i | − 0.477024i | −0.971140 | − | 0.238512i | \(-0.923340\pi\) | ||||
0.971140 | − | 0.238512i | \(-0.0766596\pi\) | |||||||
\(198\) | − 1.90321i | − 0.135255i | ||||||||
\(199\) | −14.1017 | −0.999644 | −0.499822 | − | 0.866128i | \(-0.666601\pi\) | ||||
−0.499822 | + | 0.866128i | \(0.666601\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.24443 | −0.0877754 | ||||||||
\(202\) | 8.87601i | 0.624514i | ||||||||
\(203\) | − 34.5718i | − 2.42647i | ||||||||
\(204\) | 8.40990 | 0.588811 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −22.1017 | −1.53990 | ||||||||
\(207\) | 8.85728i | 0.615623i | ||||||||
\(208\) | − 2.87019i | − 0.199012i | ||||||||
\(209\) | −7.05086 | −0.487718 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.6637 | −0.734120 | −0.367060 | − | 0.930197i | \(-0.619636\pi\) | ||||
−0.367060 | + | 0.930197i | \(0.619636\pi\) | |||||||
\(212\) | − 17.6128i | − 1.20966i | ||||||||
\(213\) | − 2.75557i | − 0.188808i | ||||||||
\(214\) | −4.99063 | −0.341153 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.719004 | −0.0489220 | ||||||||
\(217\) | − 12.2034i | − 0.828422i | ||||||||
\(218\) | 37.5210i | 2.54124i | ||||||||
\(219\) | −4.23506 | −0.286179 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.22570 | 0.216984 | ||||||||
\(222\) | − 3.80642i | − 0.255470i | ||||||||
\(223\) | − 8.85728i | − 0.593127i | −0.955013 | − | 0.296564i | \(-0.904159\pi\) | ||||
0.955013 | − | 0.296564i | \(-0.0958407\pi\) | |||||||
\(224\) | −32.5116 | −2.17227 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.4193 | −0.759599 | ||||||||
\(227\) | 13.3778i | 0.887915i | 0.896048 | + | 0.443957i | \(0.146426\pi\) | ||||
−0.896048 | + | 0.443957i | \(0.853574\pi\) | |||||||
\(228\) | − 11.4380i | − 0.757501i | ||||||||
\(229\) | −11.5111 | −0.760677 | −0.380339 | − | 0.924847i | \(-0.624193\pi\) | ||||
−0.380339 | + | 0.924847i | \(0.624193\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.42864 | −0.291383 | ||||||||
\(232\) | 5.61285i | 0.368502i | ||||||||
\(233\) | 4.32693i | 0.283467i | 0.989905 | + | 0.141733i | \(0.0452675\pi\) | ||||
−0.989905 | + | 0.141733i | \(0.954732\pi\) | |||||||
\(234\) | 1.18421 | 0.0774141 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.87955 | −0.512915 | ||||||||
\(237\) | 8.56199i | 0.556161i | ||||||||
\(238\) | − 43.6958i | − 2.83238i | ||||||||
\(239\) | 3.34614 | 0.216444 | 0.108222 | − | 0.994127i | \(-0.465484\pi\) | ||||
0.108222 | + | 0.994127i | \(0.465484\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.34614 | −0.0867126 | −0.0433563 | − | 0.999060i | \(-0.513805\pi\) | ||||
−0.0433563 | + | 0.999060i | \(0.513805\pi\) | |||||||
\(242\) | 1.90321i | 0.122343i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | −11.1240 | −0.712140 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.368416 | −0.0234894 | ||||||||
\(247\) | − 4.38715i | − 0.279148i | ||||||||
\(248\) | 1.98126i | 0.125810i | ||||||||
\(249\) | −0.133353 | −0.00845091 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.7556 | 1.43632 | 0.718159 | − | 0.695879i | \(-0.244985\pi\) | ||||
0.718159 | + | 0.695879i | \(0.244985\pi\) | |||||||
\(252\) | − 7.18421i | − 0.452563i | ||||||||
\(253\) | − 8.85728i | − 0.556852i | ||||||||
\(254\) | 28.8988 | 1.81327 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.2444 | 1.26528 | ||||||||
\(257\) | − 6.85728i | − 0.427745i | −0.976862 | − | 0.213873i | \(-0.931392\pi\) | ||||
0.976862 | − | 0.213873i | \(-0.0686078\pi\) | |||||||
\(258\) | − 10.7971i | − 0.672195i | ||||||||
\(259\) | −8.85728 | −0.550365 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.80642 | −0.483206 | ||||||||
\(262\) | 2.36842i | 0.146321i | ||||||||
\(263\) | 29.5812i | 1.82406i | 0.410129 | + | 0.912028i | \(0.365484\pi\) | ||||
−0.410129 | + | 0.912028i | \(0.634516\pi\) | |||||||
\(264\) | 0.719004 | 0.0442516 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −59.4291 | −3.64383 | ||||||||
\(267\) | 5.61285i | 0.343501i | ||||||||
\(268\) | 2.01874i | 0.123314i | ||||||||
\(269\) | −8.48886 | −0.517575 | −0.258788 | − | 0.965934i | \(-0.583323\pi\) | ||||
−0.258788 | + | 0.965934i | \(0.583323\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.6637 | 0.890757 | 0.445378 | − | 0.895343i | \(-0.353069\pi\) | ||||
0.445378 | + | 0.895343i | \(0.353069\pi\) | |||||||
\(272\) | 23.9140i | 1.45000i | ||||||||
\(273\) | − 2.75557i | − 0.166775i | ||||||||
\(274\) | 0.930409 | 0.0562081 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 14.3684 | 0.864877 | ||||||||
\(277\) | 14.6035i | 0.877438i | 0.898624 | + | 0.438719i | \(0.144568\pi\) | ||||
−0.898624 | + | 0.438719i | \(0.855432\pi\) | |||||||
\(278\) | − 33.8894i | − 2.03255i | ||||||||
\(279\) | −2.75557 | −0.164972 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.193576 | −0.0115478 | −0.00577389 | − | 0.999983i | \(-0.501838\pi\) | ||||
−0.00577389 | + | 0.999983i | \(0.501838\pi\) | |||||||
\(282\) | − 5.24443i | − 0.312301i | ||||||||
\(283\) | − 27.1842i | − 1.61593i | −0.589228 | − | 0.807967i | \(-0.700568\pi\) | ||||
0.589228 | − | 0.807967i | \(-0.299432\pi\) | |||||||
\(284\) | −4.47013 | −0.265253 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.18421 | −0.0700237 | ||||||||
\(287\) | 0.857279i | 0.0506036i | ||||||||
\(288\) | 7.34122i | 0.432585i | ||||||||
\(289\) | −9.87601 | −0.580942 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.24443 | 0.424676 | ||||||||
\(292\) | 6.87019i | 0.402047i | ||||||||
\(293\) | 2.81579i | 0.164500i | 0.996612 | + | 0.0822502i | \(0.0262106\pi\) | ||||
−0.996612 | + | 0.0822502i | \(0.973789\pi\) | |||||||
\(294\) | −24.0049 | −1.40000 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.43801 | 0.0835825 | ||||||||
\(297\) | 1.00000i | 0.0580259i | ||||||||
\(298\) | 2.73683i | 0.158540i | ||||||||
\(299\) | 5.51114 | 0.318717 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.1240 | −1.44812 | ||||||||
\(302\) | − 23.1713i | − 1.33336i | ||||||||
\(303\) | − 4.66370i | − 0.267923i | ||||||||
\(304\) | 32.5245 | 1.86541 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −9.86665 | −0.564039 | ||||||||
\(307\) | − 24.4286i | − 1.39422i | −0.716966 | − | 0.697108i | \(-0.754470\pi\) | ||||
0.716966 | − | 0.697108i | \(-0.245530\pi\) | |||||||
\(308\) | 7.18421i | 0.409358i | ||||||||
\(309\) | 11.6128 | 0.660632 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.8796 | 1.12727 | 0.563633 | − | 0.826025i | \(-0.309403\pi\) | ||||
0.563633 | + | 0.826025i | \(0.309403\pi\) | |||||||
\(312\) | 0.447375i | 0.0253276i | ||||||||
\(313\) | 15.7146i | 0.888239i | 0.895967 | + | 0.444120i | \(0.146483\pi\) | ||||
−0.895967 | + | 0.444120i | \(0.853517\pi\) | |||||||
\(314\) | −35.1526 | −1.98377 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.8894 | 0.781340 | ||||||||
\(317\) | 16.4889i | 0.926107i | 0.886330 | + | 0.463053i | \(0.153246\pi\) | ||||
−0.886330 | + | 0.463053i | \(0.846754\pi\) | |||||||
\(318\) | 20.6637i | 1.15876i | ||||||||
\(319\) | 7.80642 | 0.437076 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.62222 | 0.146358 | ||||||||
\(322\) | − 74.6548i | − 4.16035i | ||||||||
\(323\) | 36.5531i | 2.03387i | ||||||||
\(324\) | −1.62222 | −0.0901231 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −19.2257 | −1.06481 | ||||||||
\(327\) | − 19.7146i | − 1.09022i | ||||||||
\(328\) | − 0.139182i | − 0.00768504i | ||||||||
\(329\) | −12.2034 | −0.672796 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.3461 | 0.843500 | 0.421750 | − | 0.906712i | \(-0.361416\pi\) | ||||
0.421750 | + | 0.906712i | \(0.361416\pi\) | |||||||
\(332\) | 0.216327i | 0.0118725i | ||||||||
\(333\) | 2.00000i | 0.109599i | ||||||||
\(334\) | 31.0923 | 1.70130 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 20.4286 | 1.11447 | ||||||||
\(337\) | 28.2351i | 1.53806i | 0.639212 | + | 0.769031i | \(0.279261\pi\) | ||||
−0.639212 | + | 0.769031i | \(0.720739\pi\) | |||||||
\(338\) | 24.0049i | 1.30570i | ||||||||
\(339\) | 6.00000 | 0.325875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.75557 | 0.149222 | ||||||||
\(342\) | 13.4193i | 0.725631i | ||||||||
\(343\) | 24.8573i | 1.34217i | ||||||||
\(344\) | 4.07896 | 0.219923 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.4795 | −0.939703 | ||||||||
\(347\) | 2.62222i | 0.140768i | 0.997520 | + | 0.0703840i | \(0.0224224\pi\) | ||||
−0.997520 | + | 0.0703840i | \(0.977578\pi\) | |||||||
\(348\) | 12.6637i | 0.678846i | ||||||||
\(349\) | −5.14272 | −0.275284 | −0.137642 | − | 0.990482i | \(-0.543952\pi\) | ||||
−0.137642 | + | 0.990482i | \(0.543952\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.622216 | −0.0332114 | ||||||||
\(352\) | − 7.34122i | − 0.391288i | ||||||||
\(353\) | 9.34614i | 0.497445i | 0.968575 | + | 0.248722i | \(0.0800107\pi\) | ||||
−0.968575 | + | 0.248722i | \(0.919989\pi\) | |||||||
\(354\) | 9.24443 | 0.491336 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 9.10525 | 0.482577 | ||||||||
\(357\) | 22.9590i | 1.21512i | ||||||||
\(358\) | 48.2034i | 2.54763i | ||||||||
\(359\) | −10.7556 | −0.567657 | −0.283829 | − | 0.958875i | \(-0.591605\pi\) | ||||
−0.283829 | + | 0.958875i | \(0.591605\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 30.7146 | 1.61656 | ||||||||
\(362\) | − 25.9081i | − 1.36170i | ||||||||
\(363\) | − 1.00000i | − 0.0524864i | ||||||||
\(364\) | −4.47013 | −0.234298 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 13.0509 | 0.682179 | ||||||||
\(367\) | 33.7975i | 1.76422i | 0.471046 | + | 0.882108i | \(0.343876\pi\) | ||||
−0.471046 | + | 0.882108i | \(0.656124\pi\) | |||||||
\(368\) | 40.8573i | 2.12983i | ||||||||
\(369\) | 0.193576 | 0.0100772 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 48.0830 | 2.49634 | ||||||||
\(372\) | 4.47013i | 0.231765i | ||||||||
\(373\) | − 33.9496i | − 1.75784i | −0.476965 | − | 0.878922i | \(-0.658263\pi\) | ||||
0.476965 | − | 0.878922i | \(-0.341737\pi\) | |||||||
\(374\) | 9.86665 | 0.510192 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.98126 | 0.102176 | ||||||||
\(377\) | 4.85728i | 0.250163i | ||||||||
\(378\) | 8.42864i | 0.433522i | ||||||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.1842 | −0.777911 | ||||||||
\(382\) | 11.6128i | 0.594165i | ||||||||
\(383\) | 14.6351i | 0.747820i | 0.927465 | + | 0.373910i | \(0.121983\pi\) | ||||
−0.927465 | + | 0.373910i | \(0.878017\pi\) | |||||||
\(384\) | −5.64941 | −0.288295 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 34.8988 | 1.77630 | ||||||||
\(387\) | 5.67307i | 0.288378i | ||||||||
\(388\) | − 11.7520i | − 0.596619i | ||||||||
\(389\) | 5.61285 | 0.284583 | 0.142291 | − | 0.989825i | \(-0.454553\pi\) | ||||
0.142291 | + | 0.989825i | \(0.454553\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −45.9180 | −2.32217 | ||||||||
\(392\) | − 9.06868i | − 0.458038i | ||||||||
\(393\) | − 1.24443i | − 0.0627733i | ||||||||
\(394\) | 12.7427 | 0.641966 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.62222 | 0.0815194 | ||||||||
\(397\) | − 12.7556i | − 0.640184i | −0.947387 | − | 0.320092i | \(-0.896286\pi\) | ||||
0.947387 | − | 0.320092i | \(-0.103714\pi\) | |||||||
\(398\) | − 26.8385i | − 1.34529i | ||||||||
\(399\) | 31.2257 | 1.56324 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.00000 | 0.0998752 | 0.0499376 | − | 0.998752i | \(-0.484098\pi\) | ||||
0.0499376 | + | 0.998752i | \(0.484098\pi\) | |||||||
\(402\) | − 2.36842i | − 0.118126i | ||||||||
\(403\) | 1.71456i | 0.0854082i | ||||||||
\(404\) | −7.56553 | −0.376399 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 65.7975 | 3.26548 | ||||||||
\(407\) | − 2.00000i | − 0.0991363i | ||||||||
\(408\) | − 3.72746i | − 0.184537i | ||||||||
\(409\) | 7.12399 | 0.352258 | 0.176129 | − | 0.984367i | \(-0.443642\pi\) | ||||
0.176129 | + | 0.984367i | \(0.443642\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.488863 | −0.0241138 | ||||||||
\(412\) | − 18.8385i | − 0.928108i | ||||||||
\(413\) | − 21.5111i | − 1.05849i | ||||||||
\(414\) | −16.8573 | −0.828490 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.56782 | 0.223956 | ||||||||
\(417\) | 17.8064i | 0.871984i | ||||||||
\(418\) | − 13.4193i | − 0.656358i | ||||||||
\(419\) | −15.6128 | −0.762738 | −0.381369 | − | 0.924423i | \(-0.624547\pi\) | ||||
−0.381369 | + | 0.924423i | \(0.624547\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.89829 | 0.384939 | 0.192470 | − | 0.981303i | \(-0.438350\pi\) | ||||
0.192470 | + | 0.981303i | \(0.438350\pi\) | |||||||
\(422\) | − 20.2953i | − 0.987959i | ||||||||
\(423\) | 2.75557i | 0.133980i | ||||||||
\(424\) | −7.80642 | −0.379113 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.24443 | 0.254094 | ||||||||
\(427\) | − 30.3684i | − 1.46963i | ||||||||
\(428\) | − 4.25380i | − 0.205615i | ||||||||
\(429\) | 0.622216 | 0.0300409 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.3051 | 1.65242 | 0.826210 | − | 0.563362i | \(-0.190492\pi\) | ||||
0.826210 | + | 0.563362i | \(0.190492\pi\) | |||||||
\(432\) | − 4.61285i | − 0.221936i | ||||||||
\(433\) | − 14.4701i | − 0.695390i | −0.937608 | − | 0.347695i | \(-0.886964\pi\) | ||||
0.937608 | − | 0.347695i | \(-0.113036\pi\) | |||||||
\(434\) | 23.2257 | 1.11487 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −31.9813 | −1.53162 | ||||||||
\(437\) | 62.4514i | 2.98746i | ||||||||
\(438\) | − 8.06022i | − 0.385132i | ||||||||
\(439\) | 19.3176 | 0.921977 | 0.460988 | − | 0.887406i | \(-0.347495\pi\) | ||||
0.460988 | + | 0.887406i | \(0.347495\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.6128 | 0.600612 | ||||||||
\(442\) | 6.13918i | 0.292011i | ||||||||
\(443\) | 13.1240i | 0.623539i | 0.950158 | + | 0.311770i | \(0.100922\pi\) | ||||
−0.950158 | + | 0.311770i | \(0.899078\pi\) | |||||||
\(444\) | 3.24443 | 0.153974 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 16.8573 | 0.798215 | ||||||||
\(447\) | − 1.43801i | − 0.0680154i | ||||||||
\(448\) | − 21.0192i | − 0.993064i | ||||||||
\(449\) | 32.3051 | 1.52457 | 0.762287 | − | 0.647240i | \(-0.224077\pi\) | ||||
0.762287 | + | 0.647240i | \(0.224077\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.193576 | −0.00911514 | ||||||||
\(452\) | − 9.73329i | − 0.457816i | ||||||||
\(453\) | 12.1748i | 0.572024i | ||||||||
\(454\) | −25.4608 | −1.19493 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.06959 | −0.237405 | ||||||||
\(457\) | − 23.4608i | − 1.09745i | −0.836004 | − | 0.548724i | \(-0.815114\pi\) | ||||
0.836004 | − | 0.548724i | \(-0.184886\pi\) | |||||||
\(458\) | − 21.9081i | − 1.02370i | ||||||||
\(459\) | 5.18421 | 0.241978 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.8671 | −1.34448 | −0.672238 | − | 0.740335i | \(-0.734667\pi\) | ||||
−0.672238 | + | 0.740335i | \(0.734667\pi\) | |||||||
\(462\) | − 8.42864i | − 0.392136i | ||||||||
\(463\) | 19.3461i | 0.899091i | 0.893257 | + | 0.449546i | \(0.148414\pi\) | ||||
−0.893257 | + | 0.449546i | \(0.851586\pi\) | |||||||
\(464\) | −36.0098 | −1.67172 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.23506 | −0.381482 | ||||||||
\(467\) | 3.14272i | 0.145428i | 0.997353 | + | 0.0727139i | \(0.0231660\pi\) | ||||
−0.997353 | + | 0.0727139i | \(0.976834\pi\) | |||||||
\(468\) | 1.00937i | 0.0466580i | ||||||||
\(469\) | −5.51114 | −0.254481 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.4701 | 0.851059 | ||||||||
\(472\) | 3.49240i | 0.160751i | ||||||||
\(473\) | − 5.67307i | − 0.260848i | ||||||||
\(474\) | −16.2953 | −0.748467 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 37.2444 | 1.70710 | ||||||||
\(477\) | − 10.8573i | − 0.497121i | ||||||||
\(478\) | 6.36842i | 0.291285i | ||||||||
\(479\) | 24.8573 | 1.13576 | 0.567879 | − | 0.823112i | \(-0.307764\pi\) | ||||
0.567879 | + | 0.823112i | \(0.307764\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.24443 | 0.0567412 | ||||||||
\(482\) | − 2.56199i | − 0.116696i | ||||||||
\(483\) | 39.2257i | 1.78483i | ||||||||
\(484\) | −1.62222 | −0.0737371 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.90321 | 0.0863314 | ||||||||
\(487\) | − 11.5299i | − 0.522468i | −0.965275 | − | 0.261234i | \(-0.915871\pi\) | ||||
0.965275 | − | 0.261234i | \(-0.0841295\pi\) | |||||||
\(488\) | 4.93041i | 0.223189i | ||||||||
\(489\) | 10.1017 | 0.456815 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.3872 | 0.739542 | 0.369771 | − | 0.929123i | \(-0.379436\pi\) | ||||
0.369771 | + | 0.929123i | \(0.379436\pi\) | |||||||
\(492\) | − 0.314022i | − 0.0141572i | ||||||||
\(493\) | − 40.4701i | − 1.82268i | ||||||||
\(494\) | 8.34968 | 0.375670 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12.7110 | −0.570742 | ||||||||
\(497\) | − 12.2034i | − 0.547398i | ||||||||
\(498\) | − 0.253799i | − 0.0113730i | ||||||||
\(499\) | 25.3274 | 1.13381 | 0.566905 | − | 0.823783i | \(-0.308141\pi\) | ||||
0.566905 | + | 0.823783i | \(0.308141\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.3368 | −0.729873 | ||||||||
\(502\) | 43.3087i | 1.93296i | ||||||||
\(503\) | − 19.0923i | − 0.851285i | −0.904891 | − | 0.425643i | \(-0.860048\pi\) | ||||
0.904891 | − | 0.425643i | \(-0.139952\pi\) | |||||||
\(504\) | −3.18421 | −0.141836 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 16.8573 | 0.749397 | ||||||||
\(507\) | − 12.6128i | − 0.560156i | ||||||||
\(508\) | 24.6321i | 1.09287i | ||||||||
\(509\) | 32.4514 | 1.43838 | 0.719191 | − | 0.694812i | \(-0.244512\pi\) | ||||
0.719191 | + | 0.694812i | \(0.244512\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.7556 | −0.829698 | ||||||||
\(512\) | 27.2306i | 1.20343i | ||||||||
\(513\) | − 7.05086i | − 0.311303i | ||||||||
\(514\) | 13.0509 | 0.575649 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 9.20294 | 0.405137 | ||||||||
\(517\) | − 2.75557i | − 0.121190i | ||||||||
\(518\) | − 16.8573i | − 0.740666i | ||||||||
\(519\) | 9.18421 | 0.403142 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.2257 | −1.28040 | −0.640200 | − | 0.768208i | \(-0.721149\pi\) | ||||
−0.640200 | + | 0.768208i | \(0.721149\pi\) | |||||||
\(522\) | − 14.8573i | − 0.650285i | ||||||||
\(523\) | − 6.71408i | − 0.293586i | −0.989167 | − | 0.146793i | \(-0.953105\pi\) | ||||
0.989167 | − | 0.146793i | \(-0.0468952\pi\) | |||||||
\(524\) | −2.01874 | −0.0881889 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −56.2993 | −2.45477 | ||||||||
\(527\) | − 14.2854i | − 0.622284i | ||||||||
\(528\) | 4.61285i | 0.200748i | ||||||||
\(529\) | −55.4514 | −2.41093 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.85728 | −0.210788 | ||||||||
\(532\) | − 50.6548i | − 2.19616i | ||||||||
\(533\) | − 0.120446i | − 0.00521710i | ||||||||
\(534\) | −10.6824 | −0.462274 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.894751 | 0.0386473 | ||||||||
\(537\) | − 25.3274i | − 1.09296i | ||||||||
\(538\) | − 16.1561i | − 0.696539i | ||||||||
\(539\) | −12.6128 | −0.543274 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.0000 | −0.773880 | −0.386940 | − | 0.922105i | \(-0.626468\pi\) | ||||
−0.386940 | + | 0.922105i | \(0.626468\pi\) | |||||||
\(542\) | 27.9081i | 1.19876i | ||||||||
\(543\) | 13.6128i | 0.584183i | ||||||||
\(544\) | −38.0584 | −1.63174 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 5.24443 | 0.224441 | ||||||||
\(547\) | 41.3689i | 1.76881i | 0.466724 | + | 0.884403i | \(0.345434\pi\) | ||||
−0.466724 | + | 0.884403i | \(0.654566\pi\) | |||||||
\(548\) | 0.793040i | 0.0338770i | ||||||||
\(549\) | −6.85728 | −0.292662 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −55.0420 | −2.34487 | ||||||||
\(552\) | − 6.36842i | − 0.271058i | ||||||||
\(553\) | 37.9180i | 1.61244i | ||||||||
\(554\) | −27.7935 | −1.18083 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 28.8859 | 1.22503 | ||||||||
\(557\) | − 20.7971i | − 0.881200i | −0.897704 | − | 0.440600i | \(-0.854766\pi\) | ||||
0.897704 | − | 0.440600i | \(-0.145234\pi\) | |||||||
\(558\) | − 5.24443i | − 0.222014i | ||||||||
\(559\) | 3.52987 | 0.149298 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.18421 | −0.218877 | ||||||||
\(562\) | − 0.368416i | − 0.0155407i | ||||||||
\(563\) | − 37.7275i | − 1.59002i | −0.606594 | − | 0.795012i | \(-0.707465\pi\) | ||||
0.606594 | − | 0.795012i | \(-0.292535\pi\) | |||||||
\(564\) | 4.47013 | 0.188226 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 51.7373 | 2.17468 | ||||||||
\(567\) | − 4.42864i | − 0.185985i | ||||||||
\(568\) | 1.98126i | 0.0831320i | ||||||||
\(569\) | 7.33630 | 0.307554 | 0.153777 | − | 0.988106i | \(-0.450856\pi\) | ||||
0.153777 | + | 0.988106i | \(0.450856\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.6450 | 1.53354 | 0.766772 | − | 0.641919i | \(-0.221862\pi\) | ||||
0.766772 | + | 0.641919i | \(0.221862\pi\) | |||||||
\(572\) | − 1.00937i | − 0.0422038i | ||||||||
\(573\) | − 6.10171i | − 0.254903i | ||||||||
\(574\) | −1.63158 | −0.0681010 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.74620 | −0.197758 | ||||||||
\(577\) | 4.22216i | 0.175771i | 0.996131 | + | 0.0878853i | \(0.0280109\pi\) | ||||
−0.996131 | + | 0.0878853i | \(0.971989\pi\) | |||||||
\(578\) | − 18.7961i | − 0.781817i | ||||||||
\(579\) | −18.3368 | −0.762050 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.590573 | −0.0245011 | ||||||||
\(582\) | 13.7877i | 0.571518i | ||||||||
\(583\) | 10.8573i | 0.449663i | ||||||||
\(584\) | 3.04503 | 0.126004 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.35905 | −0.221380 | ||||||||
\(587\) | 34.3684i | 1.41854i | 0.704939 | + | 0.709268i | \(0.250974\pi\) | ||||
−0.704939 | + | 0.709268i | \(0.749026\pi\) | |||||||
\(588\) | − 20.4608i | − 0.843787i | ||||||||
\(589\) | −19.4291 | −0.800563 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.69535 | −0.275410 | ||||||||
\(592\) | 9.22570i | 0.379174i | ||||||||
\(593\) | − 27.9398i | − 1.14735i | −0.819083 | − | 0.573675i | \(-0.805517\pi\) | ||||
0.819083 | − | 0.573675i | \(-0.194483\pi\) | |||||||
\(594\) | −1.90321 | −0.0780897 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.33276 | −0.0955535 | ||||||||
\(597\) | 14.1017i | 0.577145i | ||||||||
\(598\) | 10.4889i | 0.428921i | ||||||||
\(599\) | 31.2257 | 1.27585 | 0.637924 | − | 0.770100i | \(-0.279794\pi\) | ||||
0.637924 | + | 0.770100i | \(0.279794\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.75557 | −0.357147 | −0.178574 | − | 0.983927i | \(-0.557148\pi\) | ||||
−0.178574 | + | 0.983927i | \(0.557148\pi\) | |||||||
\(602\) | − 47.8163i | − 1.94885i | ||||||||
\(603\) | 1.24443i | 0.0506772i | ||||||||
\(604\) | 19.7502 | 0.803625 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 8.87601 | 0.360563 | ||||||||
\(607\) | − 15.1842i | − 0.616308i | −0.951336 | − | 0.308154i | \(-0.900289\pi\) | ||||
0.951336 | − | 0.308154i | \(-0.0997112\pi\) | |||||||
\(608\) | 51.7619i | 2.09922i | ||||||||
\(609\) | −34.5718 | −1.40092 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.71456 | 0.0693636 | ||||||||
\(612\) | − 8.40990i | − 0.339950i | ||||||||
\(613\) | − 42.7239i | − 1.72560i | −0.505543 | − | 0.862802i | \(-0.668708\pi\) | ||||
0.505543 | − | 0.862802i | \(-0.331292\pi\) | |||||||
\(614\) | 46.4929 | 1.87630 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.18421 | 0.128295 | ||||||||
\(617\) | − 3.51114i | − 0.141353i | −0.997499 | − | 0.0706765i | \(-0.977484\pi\) | ||||
0.997499 | − | 0.0706765i | \(-0.0225158\pi\) | |||||||
\(618\) | 22.1017i | 0.889061i | ||||||||
\(619\) | −17.5941 | −0.707167 | −0.353584 | − | 0.935403i | \(-0.615037\pi\) | ||||
−0.353584 | + | 0.935403i | \(0.615037\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.85728 | 0.355430 | ||||||||
\(622\) | 37.8350i | 1.51705i | ||||||||
\(623\) | 24.8573i | 0.995886i | ||||||||
\(624\) | −2.87019 | −0.114899 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −29.9081 | −1.19537 | ||||||||
\(627\) | 7.05086i | 0.281584i | ||||||||
\(628\) | − 29.9625i | − 1.19564i | ||||||||
\(629\) | −10.3684 | −0.413416 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.8163 | 0.629636 | 0.314818 | − | 0.949152i | \(-0.398057\pi\) | ||||
0.314818 | + | 0.949152i | \(0.398057\pi\) | |||||||
\(632\) | − 6.15610i | − 0.244877i | ||||||||
\(633\) | 10.6637i | 0.423844i | ||||||||
\(634\) | −31.3818 | −1.24633 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −17.6128 | −0.698395 | ||||||||
\(637\) | − 7.84791i | − 0.310946i | ||||||||
\(638\) | 14.8573i | 0.588205i | ||||||||
\(639\) | −2.75557 | −0.109009 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.8163 | 1.01968 | 0.509841 | − | 0.860269i | \(-0.329704\pi\) | ||||
0.509841 | + | 0.860269i | \(0.329704\pi\) | |||||||
\(642\) | 4.99063i | 0.196965i | ||||||||
\(643\) | − 18.1017i | − 0.713862i | −0.934131 | − | 0.356931i | \(-0.883823\pi\) | ||||
0.934131 | − | 0.356931i | \(-0.116177\pi\) | |||||||
\(644\) | 63.6325 | 2.50747 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −69.5683 | −2.73713 | ||||||||
\(647\) | − 47.0420i | − 1.84941i | −0.380684 | − | 0.924705i | \(-0.624311\pi\) | ||||
0.380684 | − | 0.924705i | \(-0.375689\pi\) | |||||||
\(648\) | 0.719004i | 0.0282451i | ||||||||
\(649\) | 4.85728 | 0.190665 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.2034 | −0.478290 | ||||||||
\(652\) | − 16.3872i | − 0.641770i | ||||||||
\(653\) | − 30.0830i | − 1.17724i | −0.808411 | − | 0.588619i | \(-0.799672\pi\) | ||||
0.808411 | − | 0.588619i | \(-0.200328\pi\) | |||||||
\(654\) | 37.5210 | 1.46719 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.892937 | 0.0348633 | ||||||||
\(657\) | 4.23506i | 0.165226i | ||||||||
\(658\) | − 23.2257i | − 0.905432i | ||||||||
\(659\) | 10.2854 | 0.400664 | 0.200332 | − | 0.979728i | \(-0.435798\pi\) | ||||
0.200332 | + | 0.979728i | \(0.435798\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.7146 | −1.07797 | −0.538986 | − | 0.842315i | \(-0.681192\pi\) | ||||
−0.538986 | + | 0.842315i | \(0.681192\pi\) | |||||||
\(662\) | 29.2070i | 1.13516i | ||||||||
\(663\) | − 3.22570i | − 0.125276i | ||||||||
\(664\) | 0.0958814 | 0.00372092 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.80642 | −0.147496 | ||||||||
\(667\) | − 69.1437i | − 2.67725i | ||||||||
\(668\) | 26.5018i | 1.02538i | ||||||||
\(669\) | −8.85728 | −0.342442 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.85728 | 0.264722 | ||||||||
\(672\) | 32.5116i | 1.25416i | ||||||||
\(673\) | 9.86665i | 0.380331i | 0.981752 | + | 0.190166i | \(0.0609025\pi\) | ||||
−0.981752 | + | 0.190166i | \(0.939097\pi\) | |||||||
\(674\) | −53.7373 | −2.06988 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −20.4608 | −0.786952 | ||||||||
\(677\) | − 5.65433i | − 0.217314i | −0.994079 | − | 0.108657i | \(-0.965345\pi\) | ||||
0.994079 | − | 0.108657i | \(-0.0346550\pi\) | |||||||
\(678\) | 11.4193i | 0.438554i | ||||||||
\(679\) | 32.0830 | 1.23123 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.3778 | 0.512638 | ||||||||
\(682\) | 5.24443i | 0.200820i | ||||||||
\(683\) | − 34.1847i | − 1.30804i | −0.756477 | − | 0.654020i | \(-0.773081\pi\) | ||||
0.756477 | − | 0.654020i | \(-0.226919\pi\) | |||||||
\(684\) | −11.4380 | −0.437343 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −47.3087 | −1.80625 | ||||||||
\(687\) | 11.5111i | 0.439177i | ||||||||
\(688\) | 26.1690i | 0.997684i | ||||||||
\(689\) | −6.75557 | −0.257367 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.2257 | −0.731380 | −0.365690 | − | 0.930737i | \(-0.619167\pi\) | ||||
−0.365690 | + | 0.930737i | \(0.619167\pi\) | |||||||
\(692\) | − 14.8988i | − 0.566366i | ||||||||
\(693\) | 4.42864i | 0.168230i | ||||||||
\(694\) | −4.99063 | −0.189442 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.61285 | 0.212754 | ||||||||
\(697\) | 1.00354i | 0.0380118i | ||||||||
\(698\) | − 9.78769i | − 0.370469i | ||||||||
\(699\) | 4.32693 | 0.163659 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.9081 | −1.12961 | −0.564807 | − | 0.825223i | \(-0.691050\pi\) | ||||
−0.564807 | + | 0.825223i | \(0.691050\pi\) | |||||||
\(702\) | − 1.18421i | − 0.0446951i | ||||||||
\(703\) | 14.1017i | 0.531856i | ||||||||
\(704\) | 4.74620 | 0.178879 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.7877 | −0.669448 | ||||||||
\(707\) | − 20.6539i | − 0.776768i | ||||||||
\(708\) | 7.87955i | 0.296132i | ||||||||
\(709\) | 15.3274 | 0.575633 | 0.287816 | − | 0.957686i | \(-0.407071\pi\) | ||||
0.287816 | + | 0.957686i | \(0.407071\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.56199 | 0.321100 | ||||||||
\(712\) | − 4.03566i | − 0.151243i | ||||||||
\(713\) | − 24.4068i | − 0.914043i | ||||||||
\(714\) | −43.6958 | −1.63528 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −41.0865 | −1.53548 | ||||||||
\(717\) | − 3.34614i | − 0.124964i | ||||||||
\(718\) | − 20.4701i | − 0.763938i | ||||||||
\(719\) | −23.8163 | −0.888197 | −0.444098 | − | 0.895978i | \(-0.646476\pi\) | ||||
−0.444098 | + | 0.895978i | \(0.646476\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 51.4291 | 1.91532 | ||||||||
\(722\) | 58.4563i | 2.17552i | ||||||||
\(723\) | 1.34614i | 0.0500635i | ||||||||
\(724\) | 22.0830 | 0.820707 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.90321 | 0.0706348 | ||||||||
\(727\) | − 32.9403i | − 1.22169i | −0.791752 | − | 0.610843i | \(-0.790831\pi\) | ||||
0.791752 | − | 0.610843i | \(-0.209169\pi\) | |||||||
\(728\) | 1.98126i | 0.0734305i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −29.4104 | −1.08778 | ||||||||
\(732\) | 11.1240i | 0.411154i | ||||||||
\(733\) | 29.8666i | 1.10315i | 0.834125 | + | 0.551575i | \(0.185973\pi\) | ||||
−0.834125 | + | 0.551575i | \(0.814027\pi\) | |||||||
\(734\) | −64.3239 | −2.37424 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −65.0232 | −2.39679 | ||||||||
\(737\) | − 1.24443i | − 0.0458392i | ||||||||
\(738\) | 0.368416i | 0.0135616i | ||||||||
\(739\) | 5.06959 | 0.186488 | 0.0932440 | − | 0.995643i | \(-0.470276\pi\) | ||||
0.0932440 | + | 0.995643i | \(0.470276\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.38715 | −0.161166 | ||||||||
\(742\) | 91.5121i | 3.35951i | ||||||||
\(743\) | − 22.4385i | − 0.823188i | −0.911367 | − | 0.411594i | \(-0.864972\pi\) | ||||
0.911367 | − | 0.411594i | \(-0.135028\pi\) | |||||||
\(744\) | 1.98126 | 0.0726367 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 64.6133 | 2.36566 | ||||||||
\(747\) | 0.133353i | 0.00487913i | ||||||||
\(748\) | 8.40990i | 0.307497i | ||||||||
\(749\) | 11.6128 | 0.424324 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.63512 | −0.242119 | −0.121060 | − | 0.992645i | \(-0.538629\pi\) | ||||
−0.121060 | + | 0.992645i | \(0.538629\pi\) | |||||||
\(752\) | 12.7110i | 0.463523i | ||||||||
\(753\) | − 22.7556i | − 0.829259i | ||||||||
\(754\) | −9.24443 | −0.336662 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −7.18421 | −0.261287 | ||||||||
\(757\) | 8.75557i | 0.318227i | 0.987260 | + | 0.159113i | \(0.0508635\pi\) | ||||
−0.987260 | + | 0.159113i | \(0.949136\pi\) | |||||||
\(758\) | 38.0642i | 1.38256i | ||||||||
\(759\) | −8.85728 | −0.321499 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.15257 | 0.114280 | 0.0571402 | − | 0.998366i | \(-0.481802\pi\) | ||||
0.0571402 | + | 0.998366i | \(0.481802\pi\) | |||||||
\(762\) | − 28.8988i | − 1.04689i | ||||||||
\(763\) | − 87.3087i | − 3.16079i | ||||||||
\(764\) | −9.89829 | −0.358108 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −27.8537 | −1.00640 | ||||||||
\(767\) | 3.02227i | 0.109128i | ||||||||
\(768\) | − 20.2444i | − 0.730508i | ||||||||
\(769\) | 28.9590 | 1.04429 | 0.522144 | − | 0.852857i | \(-0.325132\pi\) | ||||
0.522144 | + | 0.852857i | \(0.325132\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.85728 | −0.246959 | ||||||||
\(772\) | 29.7462i | 1.07059i | ||||||||
\(773\) | − 29.1427i | − 1.04819i | −0.851660 | − | 0.524095i | \(-0.824404\pi\) | ||||
0.851660 | − | 0.524095i | \(-0.175596\pi\) | |||||||
\(774\) | −10.7971 | −0.388092 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.20877 | −0.186984 | ||||||||
\(777\) | 8.85728i | 0.317753i | ||||||||
\(778\) | 10.6824i | 0.382984i | ||||||||
\(779\) | 1.36488 | 0.0489018 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.75557 | 0.0986020 | ||||||||
\(782\) | − 87.3916i | − 3.12512i | ||||||||
\(783\) | 7.80642i | 0.278979i | ||||||||
\(784\) | 58.1811 | 2.07790 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.36842 | 0.0844786 | ||||||||
\(787\) | − 11.2672i | − 0.401632i | −0.979629 | − | 0.200816i | \(-0.935641\pi\) | ||||
0.979629 | − | 0.200816i | \(-0.0643593\pi\) | |||||||
\(788\) | 10.8613i | 0.386918i | ||||||||
\(789\) | 29.5812 | 1.05312 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26.5718 | 0.944786 | ||||||||
\(792\) | − 0.719004i | − 0.0255487i | ||||||||
\(793\) | 4.26671i | 0.151515i | ||||||||
\(794\) | 24.2766 | 0.861543 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22.8760 | 0.810819 | ||||||||
\(797\) | 41.9625i | 1.48639i | 0.669075 | + | 0.743195i | \(0.266690\pi\) | ||||
−0.669075 | + | 0.743195i | \(0.733310\pi\) | |||||||
\(798\) | 59.4291i | 2.10377i | ||||||||
\(799\) | −14.2854 | −0.505383 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.61285 | 0.198320 | ||||||||
\(802\) | 3.80642i | 0.134409i | ||||||||
\(803\) | − 4.23506i | − 0.149452i | ||||||||
\(804\) | 2.01874 | 0.0711953 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.26317 | −0.114940 | ||||||||
\(807\) | 8.48886i | 0.298822i | ||||||||
\(808\) | 3.35322i | 0.117966i | ||||||||
\(809\) | 27.8064 | 0.977622 | 0.488811 | − | 0.872390i | \(-0.337431\pi\) | ||||
0.488811 | + | 0.872390i | \(0.337431\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.78415 | 0.238224 | 0.119112 | − | 0.992881i | \(-0.461995\pi\) | ||||
0.119112 | + | 0.992881i | \(0.461995\pi\) | |||||||
\(812\) | 56.0830i | 1.96813i | ||||||||
\(813\) | − 14.6637i | − 0.514279i | ||||||||
\(814\) | 3.80642 | 0.133415 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 23.9140 | 0.837156 | ||||||||
\(817\) | 40.0000i | 1.39942i | ||||||||
\(818\) | 13.5585i | 0.474060i | ||||||||
\(819\) | −2.75557 | −0.0962874 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.62269 | 0.126433 | 0.0632164 | − | 0.998000i | \(-0.479864\pi\) | ||||
0.0632164 | + | 0.998000i | \(0.479864\pi\) | |||||||
\(822\) | − 0.930409i | − 0.0324517i | ||||||||
\(823\) | − 42.0642i | − 1.46627i | −0.680085 | − | 0.733134i | \(-0.738057\pi\) | ||||
0.680085 | − | 0.733134i | \(-0.261943\pi\) | |||||||
\(824\) | −8.34968 | −0.290875 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 40.9403 | 1.42449 | ||||||||
\(827\) | 30.8256i | 1.07191i | 0.844246 | + | 0.535956i | \(0.180049\pi\) | ||||
−0.844246 | + | 0.535956i | \(0.819951\pi\) | |||||||
\(828\) | − 14.3684i | − 0.499337i | ||||||||
\(829\) | −7.12399 | −0.247426 | −0.123713 | − | 0.992318i | \(-0.539480\pi\) | ||||
−0.123713 | + | 0.992318i | \(0.539480\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.6035 | 0.506589 | ||||||||
\(832\) | 2.95316i | 0.102382i | ||||||||
\(833\) | 65.3876i | 2.26555i | ||||||||
\(834\) | −33.8894 | −1.17349 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 11.4380 | 0.395592 | ||||||||
\(837\) | 2.75557i | 0.0952464i | ||||||||
\(838\) | − 29.7146i | − 1.02647i | ||||||||
\(839\) | −3.34614 | −0.115522 | −0.0577608 | − | 0.998330i | \(-0.518396\pi\) | ||||
−0.0577608 | + | 0.998330i | \(0.518396\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31.9403 | 1.10139 | ||||||||
\(842\) | 15.0321i | 0.518041i | ||||||||
\(843\) | 0.193576i | 0.00666712i | ||||||||
\(844\) | 17.2988 | 0.595450 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.24443 | −0.180307 | ||||||||
\(847\) | − 4.42864i | − 0.152170i | ||||||||
\(848\) | − 50.0830i | − 1.71986i | ||||||||
\(849\) | −27.1842 | −0.932960 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.7146 | −0.607247 | ||||||||
\(852\) | 4.47013i | 0.153144i | ||||||||
\(853\) | 26.4197i | 0.904595i | 0.891867 | + | 0.452297i | \(0.149395\pi\) | ||||
−0.891867 | + | 0.452297i | \(0.850605\pi\) | |||||||
\(854\) | 57.7975 | 1.97779 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.88538 | −0.0644411 | ||||||||
\(857\) | 38.7783i | 1.32464i | 0.749220 | + | 0.662321i | \(0.230429\pi\) | ||||
−0.749220 | + | 0.662321i | \(0.769571\pi\) | |||||||
\(858\) | 1.18421i | 0.0404282i | ||||||||
\(859\) | 27.3087 | 0.931760 | 0.465880 | − | 0.884848i | \(-0.345738\pi\) | ||||
0.465880 | + | 0.884848i | \(0.345738\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.857279 | 0.0292160 | ||||||||
\(862\) | 65.2899i | 2.22378i | ||||||||
\(863\) | 49.5308i | 1.68605i | 0.537875 | + | 0.843024i | \(0.319227\pi\) | ||||
−0.537875 | + | 0.843024i | \(0.680773\pi\) | |||||||
\(864\) | 7.34122 | 0.249753 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 27.5397 | 0.935838 | ||||||||
\(867\) | 9.87601i | 0.335407i | ||||||||
\(868\) | 19.7966i | 0.671940i | ||||||||
\(869\) | −8.56199 | −0.290446 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.774305 | 0.0262363 | ||||||||
\(872\) | 14.1748i | 0.480021i | ||||||||
\(873\) | − 7.24443i | − 0.245187i | ||||||||
\(874\) | −118.858 | −4.02044 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.87019 | 0.232122 | ||||||||
\(877\) | − 4.50177i | − 0.152014i | −0.997107 | − | 0.0760070i | \(-0.975783\pi\) | ||||
0.997107 | − | 0.0760070i | \(-0.0242171\pi\) | |||||||
\(878\) | 36.7654i | 1.24077i | ||||||||
\(879\) | 2.81579 | 0.0949743 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.1240 | −0.509540 | −0.254770 | − | 0.967002i | \(-0.582000\pi\) | ||||
−0.254770 | + | 0.967002i | \(0.582000\pi\) | |||||||
\(882\) | 24.0049i | 0.808288i | ||||||||
\(883\) | 30.2480i | 1.01793i | 0.860789 | + | 0.508963i | \(0.169971\pi\) | ||||
−0.860789 | + | 0.508963i | \(0.830029\pi\) | |||||||
\(884\) | −5.23277 | −0.175997 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.9777 | −0.839143 | ||||||||
\(887\) | 57.1941i | 1.92039i | 0.279333 | + | 0.960194i | \(0.409887\pi\) | ||||
−0.279333 | + | 0.960194i | \(0.590113\pi\) | |||||||
\(888\) | − 1.43801i | − 0.0482564i | ||||||||
\(889\) | −67.2454 | −2.25534 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 14.3684i | 0.481090i | ||||||||
\(893\) | 19.4291i | 0.650171i | ||||||||
\(894\) | 2.73683 | 0.0915334 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −25.0192 | −0.835833 | ||||||||
\(897\) | − 5.51114i | − 0.184012i | ||||||||
\(898\) | 61.4835i | 2.05173i | ||||||||
\(899\) | 21.5111 | 0.717437 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 56.2864 | 1.87517 | ||||||||
\(902\) | − 0.368416i | − 0.0122669i | ||||||||
\(903\) | 25.1240i | 0.836074i | ||||||||
\(904\) | −4.31402 | −0.143482 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −23.1713 | −0.769815 | ||||||||
\(907\) | − 53.2641i | − 1.76861i | −0.466913 | − | 0.884303i | \(-0.654634\pi\) | ||||
0.466913 | − | 0.884303i | \(-0.345366\pi\) | |||||||
\(908\) | − 21.7017i | − 0.720195i | ||||||||
\(909\) | −4.66370 | −0.154685 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.590573 | −0.0195665 | −0.00978327 | − | 0.999952i | \(-0.503114\pi\) | ||||
−0.00978327 | + | 0.999952i | \(0.503114\pi\) | |||||||
\(912\) | − 32.5245i | − 1.07699i | ||||||||
\(913\) | − 0.133353i | − 0.00441334i | ||||||||
\(914\) | 44.6508 | 1.47692 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.6735 | 0.616991 | ||||||||
\(917\) | − 5.51114i | − 0.181994i | ||||||||
\(918\) | 9.86665i | 0.325648i | ||||||||
\(919\) | −55.8707 | −1.84300 | −0.921502 | − | 0.388375i | \(-0.873037\pi\) | ||||
−0.921502 | + | 0.388375i | \(0.873037\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.4286 | −0.804951 | ||||||||
\(922\) | − 54.9403i | − 1.80936i | ||||||||
\(923\) | 1.71456i | 0.0564354i | ||||||||
\(924\) | 7.18421 | 0.236343 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −36.8198 | −1.20997 | ||||||||
\(927\) | − 11.6128i | − 0.381416i | ||||||||
\(928\) | − 57.3087i | − 1.88125i | ||||||||
\(929\) | −15.3274 | −0.502876 | −0.251438 | − | 0.967873i | \(-0.580903\pi\) | ||||
−0.251438 | + | 0.967873i | \(0.580903\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 88.9314 | 2.91461 | ||||||||
\(932\) | − 7.01921i | − 0.229922i | ||||||||
\(933\) | − 19.8796i | − 0.650827i | ||||||||
\(934\) | −5.98126 | −0.195713 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.447375 | 0.0146229 | ||||||||
\(937\) | − 27.8479i | − 0.909752i | −0.890555 | − | 0.454876i | \(-0.849684\pi\) | ||||
0.890555 | − | 0.454876i | \(-0.150316\pi\) | |||||||
\(938\) | − 10.4889i | − 0.342474i | ||||||||
\(939\) | 15.7146 | 0.512825 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.4157 | 0.339543 | 0.169772 | − | 0.985483i | \(-0.445697\pi\) | ||||
0.169772 | + | 0.985483i | \(0.445697\pi\) | |||||||
\(942\) | 35.1526i | 1.14533i | ||||||||
\(943\) | 1.71456i | 0.0558337i | ||||||||
\(944\) | −22.4059 | −0.729250 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.7971 | 0.351043 | ||||||||
\(947\) | 8.47013i | 0.275242i | 0.990485 | + | 0.137621i | \(0.0439456\pi\) | ||||
−0.990485 | + | 0.137621i | \(0.956054\pi\) | |||||||
\(948\) | − 13.8894i | − 0.451107i | ||||||||
\(949\) | 2.63512 | 0.0855397 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.4889 | 0.534688 | ||||||||
\(952\) | − 16.5076i | − 0.535014i | ||||||||
\(953\) | 8.71408i | 0.282277i | 0.989990 | + | 0.141138i | \(0.0450763\pi\) | ||||
−0.989990 | + | 0.141138i | \(0.954924\pi\) | |||||||
\(954\) | 20.6637 | 0.669012 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.42816 | −0.175559 | ||||||||
\(957\) | − 7.80642i | − 0.252346i | ||||||||
\(958\) | 47.3087i | 1.52847i | ||||||||
\(959\) | −2.16500 | −0.0699114 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.4068 | −0.755059 | ||||||||
\(962\) | 2.36842i | 0.0763608i | ||||||||
\(963\) | − 2.62222i | − 0.0844997i | ||||||||
\(964\) | 2.18373 | 0.0703333 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −74.6548 | −2.40198 | ||||||||
\(967\) | 44.2449i | 1.42282i | 0.702777 | + | 0.711410i | \(0.251943\pi\) | ||||
−0.702777 | + | 0.711410i | \(0.748057\pi\) | |||||||
\(968\) | 0.719004i | 0.0231097i | ||||||||
\(969\) | 36.5531 | 1.17425 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −57.1437 | −1.83383 | −0.916914 | − | 0.399085i | \(-0.869328\pi\) | ||||
−0.916914 | + | 0.399085i | \(0.869328\pi\) | |||||||
\(972\) | 1.62222i | 0.0520326i | ||||||||
\(973\) | 78.8582i | 2.52808i | ||||||||
\(974\) | 21.9438 | 0.703124 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −31.6316 | −1.01250 | ||||||||
\(977\) | − 16.2480i | − 0.519819i | −0.965633 | − | 0.259909i | \(-0.916307\pi\) | ||||
0.965633 | − | 0.259909i | \(-0.0836927\pi\) | |||||||
\(978\) | 19.2257i | 0.614770i | ||||||||
\(979\) | −5.61285 | −0.179387 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.7146 | −0.629437 | ||||||||
\(982\) | 31.1882i | 0.995256i | ||||||||
\(983\) | − 1.12399i | − 0.0358496i | −0.999839 | − | 0.0179248i | \(-0.994294\pi\) | ||||
0.999839 | − | 0.0179248i | \(-0.00570594\pi\) | |||||||
\(984\) | −0.139182 | −0.00443696 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 77.0232 | 2.45292 | ||||||||
\(987\) | 12.2034i | 0.388439i | ||||||||
\(988\) | 7.11691i | 0.226419i | ||||||||
\(989\) | −50.2480 | −1.59779 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −53.6513 | −1.70429 | −0.852144 | − | 0.523307i | \(-0.824698\pi\) | ||||
−0.852144 | + | 0.523307i | \(0.824698\pi\) | |||||||
\(992\) | − 20.2292i | − 0.642279i | ||||||||
\(993\) | − 15.3461i | − 0.486995i | ||||||||
\(994\) | 23.2257 | 0.736674 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.216327 | 0.00685460 | ||||||||
\(997\) | − 35.7275i | − 1.13150i | −0.824577 | − | 0.565750i | \(-0.808587\pi\) | ||||
0.824577 | − | 0.565750i | \(-0.191413\pi\) | |||||||
\(998\) | 48.2034i | 1.52585i | ||||||||
\(999\) | 2.00000 | 0.0632772 |
(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 | 825.2.c.g.199.5 | 6 | ||
3.2 | odd | 2 | 2475.2.c.r.199.2 | 6 | |||
5.2 | odd | 4 | 825.2.a.k.1.1 | 3 | |||
5.3 | odd | 4 | 165.2.a.c.1.3 | ✓ | 3 | ||
5.4 | even | 2 | inner | 825.2.c.g.199.2 | 6 | ||
15.2 | even | 4 | 2475.2.a.bb.1.3 | 3 | |||
15.8 | even | 4 | 495.2.a.e.1.1 | 3 | |||
15.14 | odd | 2 | 2475.2.c.r.199.5 | 6 | |||
20.3 | even | 4 | 2640.2.a.be.1.3 | 3 | |||
35.13 | even | 4 | 8085.2.a.bk.1.3 | 3 | |||
55.32 | even | 4 | 9075.2.a.cf.1.3 | 3 | |||
55.43 | even | 4 | 1815.2.a.m.1.1 | 3 | |||
60.23 | odd | 4 | 7920.2.a.cj.1.3 | 3 | |||
165.98 | odd | 4 | 5445.2.a.z.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.a.c.1.3 | ✓ | 3 | 5.3 | odd | 4 | ||
495.2.a.e.1.1 | 3 | 15.8 | even | 4 | |||
825.2.a.k.1.1 | 3 | 5.2 | odd | 4 | |||
825.2.c.g.199.2 | 6 | 5.4 | even | 2 | inner | ||
825.2.c.g.199.5 | 6 | 1.1 | even | 1 | trivial | ||
1815.2.a.m.1.1 | 3 | 55.43 | even | 4 | |||
2475.2.a.bb.1.3 | 3 | 15.2 | even | 4 | |||
2475.2.c.r.199.2 | 6 | 3.2 | odd | 2 | |||
2475.2.c.r.199.5 | 6 | 15.14 | odd | 2 | |||
2640.2.a.be.1.3 | 3 | 20.3 | even | 4 | |||
5445.2.a.z.1.3 | 3 | 165.98 | odd | 4 | |||
7920.2.a.cj.1.3 | 3 | 60.23 | odd | 4 | |||
8085.2.a.bk.1.3 | 3 | 35.13 | even | 4 | |||
9075.2.a.cf.1.3 | 3 | 55.32 | even | 4 |