Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(1,825)]
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, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.a (trivial) |
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: | yes |
Analytic conductor: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 3x + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.90321 | −1.34577 | −0.672887 | − | 0.739745i | \(-0.734946\pi\) | ||||
−0.672887 | + | 0.739745i | \(0.734946\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.62222 | 0.811108 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.90321 | 0.776983 | ||||||||
\(7\) | 4.42864 | 1.67387 | 0.836934 | − | 0.547304i | \(-0.184346\pi\) | ||||
0.836934 | + | 0.547304i | \(0.184346\pi\) | |||||||
\(8\) | 0.719004 | 0.254206 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.62222 | −0.468293 | ||||||||
\(13\) | 0.622216 | 0.172572 | 0.0862858 | − | 0.996270i | \(-0.472500\pi\) | ||||
0.0862858 | + | 0.996270i | \(0.472500\pi\) | |||||||
\(14\) | −8.42864 | −2.25265 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.61285 | −1.15321 | ||||||||
\(17\) | 5.18421 | 1.25736 | 0.628678 | − | 0.777666i | \(-0.283597\pi\) | ||||
0.628678 | + | 0.777666i | \(0.283597\pi\) | |||||||
\(18\) | −1.90321 | −0.448591 | ||||||||
\(19\) | 7.05086 | 1.61758 | 0.808789 | − | 0.588100i | \(-0.200124\pi\) | ||||
0.808789 | + | 0.588100i | \(0.200124\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.42864 | −0.966408 | ||||||||
\(22\) | −1.90321 | −0.405766 | ||||||||
\(23\) | −8.85728 | −1.84687 | −0.923435 | − | 0.383754i | \(-0.874631\pi\) | ||||
−0.923435 | + | 0.383754i | \(0.874631\pi\) | |||||||
\(24\) | −0.719004 | −0.146766 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.18421 | −0.232242 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 7.18421 | 1.35769 | ||||||||
\(29\) | −7.80642 | −1.44962 | −0.724808 | − | 0.688951i | \(-0.758072\pi\) | ||||
−0.724808 | + | 0.688951i | \(0.758072\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.75557 | 0.494915 | 0.247457 | − | 0.968899i | \(-0.420405\pi\) | ||||
0.247457 | + | 0.968899i | \(0.420405\pi\) | |||||||
\(32\) | 7.34122 | 1.29776 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −9.86665 | −1.69212 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.62222 | 0.270369 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | −13.4193 | −2.17689 | ||||||||
\(39\) | −0.622216 | −0.0996342 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.193576 | −0.0302315 | −0.0151158 | − | 0.999886i | \(-0.504812\pi\) | ||||
−0.0151158 | + | 0.999886i | \(0.504812\pi\) | |||||||
\(42\) | 8.42864 | 1.30057 | ||||||||
\(43\) | −5.67307 | −0.865135 | −0.432568 | − | 0.901602i | \(-0.642392\pi\) | ||||
−0.432568 | + | 0.901602i | \(0.642392\pi\) | |||||||
\(44\) | 1.62222 | 0.244558 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 16.8573 | 2.48547 | ||||||||
\(47\) | 2.75557 | 0.401941 | 0.200971 | − | 0.979597i | \(-0.435590\pi\) | ||||
0.200971 | + | 0.979597i | \(0.435590\pi\) | |||||||
\(48\) | 4.61285 | 0.665807 | ||||||||
\(49\) | 12.6128 | 1.80184 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.18421 | −0.725934 | ||||||||
\(52\) | 1.00937 | 0.139974 | ||||||||
\(53\) | 10.8573 | 1.49136 | 0.745681 | − | 0.666303i | \(-0.232124\pi\) | ||||
0.745681 | + | 0.666303i | \(0.232124\pi\) | |||||||
\(54\) | 1.90321 | 0.258994 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.18421 | 0.425508 | ||||||||
\(57\) | −7.05086 | −0.933909 | ||||||||
\(58\) | 14.8573 | 1.95086 | ||||||||
\(59\) | −4.85728 | −0.632364 | −0.316182 | − | 0.948699i | \(-0.602401\pi\) | ||||
−0.316182 | + | 0.948699i | \(0.602401\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.85728 | 0.877985 | 0.438992 | − | 0.898491i | \(-0.355336\pi\) | ||||
0.438992 | + | 0.898491i | \(0.355336\pi\) | |||||||
\(62\) | −5.24443 | −0.666043 | ||||||||
\(63\) | 4.42864 | 0.557956 | ||||||||
\(64\) | −4.74620 | −0.593275 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.90321 | 0.234269 | ||||||||
\(67\) | 1.24443 | 0.152031 | 0.0760157 | − | 0.997107i | \(-0.475780\pi\) | ||||
0.0760157 | + | 0.997107i | \(0.475780\pi\) | |||||||
\(68\) | 8.40990 | 1.01985 | ||||||||
\(69\) | 8.85728 | 1.06629 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.75557 | 0.327026 | 0.163513 | − | 0.986541i | \(-0.447717\pi\) | ||||
0.163513 | + | 0.986541i | \(0.447717\pi\) | |||||||
\(72\) | 0.719004 | 0.0847354 | ||||||||
\(73\) | −4.23506 | −0.495677 | −0.247838 | − | 0.968801i | \(-0.579720\pi\) | ||||
−0.247838 | + | 0.968801i | \(0.579720\pi\) | |||||||
\(74\) | −3.80642 | −0.442488 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.4380 | 1.31203 | ||||||||
\(77\) | 4.42864 | 0.504690 | ||||||||
\(78\) | 1.18421 | 0.134085 | ||||||||
\(79\) | 8.56199 | 0.963299 | 0.481650 | − | 0.876364i | \(-0.340038\pi\) | ||||
0.481650 | + | 0.876364i | \(0.340038\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.368416 | 0.0406848 | ||||||||
\(83\) | −0.133353 | −0.0146374 | −0.00731870 | − | 0.999973i | \(-0.502330\pi\) | ||||
−0.00731870 | + | 0.999973i | \(0.502330\pi\) | |||||||
\(84\) | −7.18421 | −0.783861 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 10.7971 | 1.16428 | ||||||||
\(87\) | 7.80642 | 0.836936 | ||||||||
\(88\) | 0.719004 | 0.0766461 | ||||||||
\(89\) | 5.61285 | 0.594961 | 0.297480 | − | 0.954728i | \(-0.403854\pi\) | ||||
0.297480 | + | 0.954728i | \(0.403854\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.75557 | 0.288862 | ||||||||
\(92\) | −14.3684 | −1.49801 | ||||||||
\(93\) | −2.75557 | −0.285739 | ||||||||
\(94\) | −5.24443 | −0.540922 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −7.34122 | −0.749260 | ||||||||
\(97\) | −7.24443 | −0.735561 | −0.367780 | − | 0.929913i | \(-0.619882\pi\) | ||||
−0.367780 | + | 0.929913i | \(0.619882\pi\) | |||||||
\(98\) | −24.0049 | −2.42486 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.66370 | 0.464056 | 0.232028 | − | 0.972709i | \(-0.425464\pi\) | ||||
0.232028 | + | 0.972709i | \(0.425464\pi\) | |||||||
\(102\) | 9.86665 | 0.976944 | ||||||||
\(103\) | 11.6128 | 1.14425 | 0.572124 | − | 0.820167i | \(-0.306120\pi\) | ||||
0.572124 | + | 0.820167i | \(0.306120\pi\) | |||||||
\(104\) | 0.447375 | 0.0438688 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −20.6637 | −2.00704 | ||||||||
\(107\) | −2.62222 | −0.253499 | −0.126750 | − | 0.991935i | \(-0.540454\pi\) | ||||
−0.126750 | + | 0.991935i | \(0.540454\pi\) | |||||||
\(108\) | −1.62222 | −0.156098 | ||||||||
\(109\) | −19.7146 | −1.88831 | −0.944156 | − | 0.329499i | \(-0.893120\pi\) | ||||
−0.944156 | + | 0.329499i | \(0.893120\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.00000 | −0.189832 | ||||||||
\(112\) | −20.4286 | −1.93032 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 13.4193 | 1.25683 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −12.6637 | −1.17580 | ||||||||
\(117\) | 0.622216 | 0.0575239 | ||||||||
\(118\) | 9.24443 | 0.851019 | ||||||||
\(119\) | 22.9590 | 2.10465 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −13.0509 | −1.18157 | ||||||||
\(123\) | 0.193576 | 0.0174542 | ||||||||
\(124\) | 4.47013 | 0.401429 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −8.42864 | −0.750883 | ||||||||
\(127\) | 15.1842 | 1.34738 | 0.673690 | − | 0.739014i | \(-0.264708\pi\) | ||||
0.673690 | + | 0.739014i | \(0.264708\pi\) | |||||||
\(128\) | −5.64941 | −0.499342 | ||||||||
\(129\) | 5.67307 | 0.499486 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.24443 | 0.108726 | 0.0543632 | − | 0.998521i | \(-0.482687\pi\) | ||||
0.0543632 | + | 0.998521i | \(0.482687\pi\) | |||||||
\(132\) | −1.62222 | −0.141196 | ||||||||
\(133\) | 31.2257 | 2.70761 | ||||||||
\(134\) | −2.36842 | −0.204600 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.72746 | 0.319627 | ||||||||
\(137\) | 0.488863 | 0.0417663 | 0.0208832 | − | 0.999782i | \(-0.493352\pi\) | ||||
0.0208832 | + | 0.999782i | \(0.493352\pi\) | |||||||
\(138\) | −16.8573 | −1.43499 | ||||||||
\(139\) | 17.8064 | 1.51032 | 0.755161 | − | 0.655540i | \(-0.227559\pi\) | ||||
0.755161 | + | 0.655540i | \(0.227559\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.75557 | −0.232061 | ||||||||
\(142\) | −5.24443 | −0.440103 | ||||||||
\(143\) | 0.622216 | 0.0520323 | ||||||||
\(144\) | −4.61285 | −0.384404 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.06022 | 0.667069 | ||||||||
\(147\) | −12.6128 | −1.04029 | ||||||||
\(148\) | 3.24443 | 0.266691 | ||||||||
\(149\) | −1.43801 | −0.117806 | −0.0589031 | − | 0.998264i | \(-0.518760\pi\) | ||||
−0.0589031 | + | 0.998264i | \(0.518760\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.1748 | −0.990774 | −0.495387 | − | 0.868672i | \(-0.664974\pi\) | ||||
−0.495387 | + | 0.868672i | \(0.664974\pi\) | |||||||
\(152\) | 5.06959 | 0.411198 | ||||||||
\(153\) | 5.18421 | 0.419118 | ||||||||
\(154\) | −8.42864 | −0.679199 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.00937 | −0.0808141 | ||||||||
\(157\) | −18.4701 | −1.47408 | −0.737038 | − | 0.675851i | \(-0.763776\pi\) | ||||
−0.737038 | + | 0.675851i | \(0.763776\pi\) | |||||||
\(158\) | −16.2953 | −1.29638 | ||||||||
\(159\) | −10.8573 | −0.861038 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −39.2257 | −3.09142 | ||||||||
\(162\) | −1.90321 | −0.149530 | ||||||||
\(163\) | 10.1017 | 0.791227 | 0.395614 | − | 0.918417i | \(-0.370532\pi\) | ||||
0.395614 | + | 0.918417i | \(0.370532\pi\) | |||||||
\(164\) | −0.314022 | −0.0245210 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.253799 | 0.0196986 | ||||||||
\(167\) | 16.3368 | 1.26418 | 0.632089 | − | 0.774896i | \(-0.282198\pi\) | ||||
0.632089 | + | 0.774896i | \(0.282198\pi\) | |||||||
\(168\) | −3.18421 | −0.245667 | ||||||||
\(169\) | −12.6128 | −0.970219 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.05086 | 0.539192 | ||||||||
\(172\) | −9.20294 | −0.701718 | ||||||||
\(173\) | 9.18421 | 0.698262 | 0.349131 | − | 0.937074i | \(-0.386477\pi\) | ||||
0.349131 | + | 0.937074i | \(0.386477\pi\) | |||||||
\(174\) | −14.8573 | −1.12633 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.61285 | −0.347706 | ||||||||
\(177\) | 4.85728 | 0.365095 | ||||||||
\(178\) | −10.6824 | −0.800683 | ||||||||
\(179\) | −25.3274 | −1.89306 | −0.946530 | − | 0.322617i | \(-0.895437\pi\) | ||||
−0.946530 | + | 0.322617i | \(0.895437\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.6128 | −1.01184 | −0.505918 | − | 0.862582i | \(-0.668846\pi\) | ||||
−0.505918 | + | 0.862582i | \(0.668846\pi\) | |||||||
\(182\) | −5.24443 | −0.388743 | ||||||||
\(183\) | −6.85728 | −0.506905 | ||||||||
\(184\) | −6.36842 | −0.469486 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.24443 | 0.384540 | ||||||||
\(187\) | 5.18421 | 0.379107 | ||||||||
\(188\) | 4.47013 | 0.326017 | ||||||||
\(189\) | −4.42864 | −0.322136 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.10171 | 0.441504 | 0.220752 | − | 0.975330i | \(-0.429149\pi\) | ||||
0.220752 | + | 0.975330i | \(0.429149\pi\) | |||||||
\(192\) | 4.74620 | 0.342528 | ||||||||
\(193\) | −18.3368 | −1.31991 | −0.659955 | − | 0.751305i | \(-0.729425\pi\) | ||||
−0.659955 | + | 0.751305i | \(0.729425\pi\) | |||||||
\(194\) | 13.7877 | 0.989898 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 20.4608 | 1.46148 | ||||||||
\(197\) | 6.69535 | 0.477024 | 0.238512 | − | 0.971140i | \(-0.423340\pi\) | ||||
0.238512 | + | 0.971140i | \(0.423340\pi\) | |||||||
\(198\) | −1.90321 | −0.135255 | ||||||||
\(199\) | 14.1017 | 0.999644 | 0.499822 | − | 0.866128i | \(-0.333399\pi\) | ||||
0.499822 | + | 0.866128i | \(0.333399\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.24443 | −0.0877754 | ||||||||
\(202\) | −8.87601 | −0.624514 | ||||||||
\(203\) | −34.5718 | −2.42647 | ||||||||
\(204\) | −8.40990 | −0.588811 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −22.1017 | −1.53990 | ||||||||
\(207\) | −8.85728 | −0.615623 | ||||||||
\(208\) | −2.87019 | −0.199012 | ||||||||
\(209\) | 7.05086 | 0.487718 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.6637 | −0.734120 | −0.367060 | − | 0.930197i | \(-0.619636\pi\) | ||||
−0.367060 | + | 0.930197i | \(0.619636\pi\) | |||||||
\(212\) | 17.6128 | 1.20966 | ||||||||
\(213\) | −2.75557 | −0.188808 | ||||||||
\(214\) | 4.99063 | 0.341153 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.719004 | −0.0489220 | ||||||||
\(217\) | 12.2034 | 0.828422 | ||||||||
\(218\) | 37.5210 | 2.54124 | ||||||||
\(219\) | 4.23506 | 0.286179 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.22570 | 0.216984 | ||||||||
\(222\) | 3.80642 | 0.255470 | ||||||||
\(223\) | −8.85728 | −0.593127 | −0.296564 | − | 0.955013i | \(-0.595841\pi\) | ||||
−0.296564 | + | 0.955013i | \(0.595841\pi\) | |||||||
\(224\) | 32.5116 | 2.17227 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.4193 | −0.759599 | ||||||||
\(227\) | −13.3778 | −0.887915 | −0.443957 | − | 0.896048i | \(-0.646426\pi\) | ||||
−0.443957 | + | 0.896048i | \(0.646426\pi\) | |||||||
\(228\) | −11.4380 | −0.757501 | ||||||||
\(229\) | 11.5111 | 0.760677 | 0.380339 | − | 0.924847i | \(-0.375807\pi\) | ||||
0.380339 | + | 0.924847i | \(0.375807\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.42864 | −0.291383 | ||||||||
\(232\) | −5.61285 | −0.368502 | ||||||||
\(233\) | 4.32693 | 0.283467 | 0.141733 | − | 0.989905i | \(-0.454732\pi\) | ||||
0.141733 | + | 0.989905i | \(0.454732\pi\) | |||||||
\(234\) | −1.18421 | −0.0774141 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.87955 | −0.512915 | ||||||||
\(237\) | −8.56199 | −0.556161 | ||||||||
\(238\) | −43.6958 | −2.83238 | ||||||||
\(239\) | −3.34614 | −0.216444 | −0.108222 | − | 0.994127i | \(-0.534516\pi\) | ||||
−0.108222 | + | 0.994127i | \(0.534516\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.34614 | −0.0867126 | −0.0433563 | − | 0.999060i | \(-0.513805\pi\) | ||||
−0.0433563 | + | 0.999060i | \(0.513805\pi\) | |||||||
\(242\) | −1.90321 | −0.122343 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 11.1240 | 0.712140 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.368416 | −0.0234894 | ||||||||
\(247\) | 4.38715 | 0.279148 | ||||||||
\(248\) | 1.98126 | 0.125810 | ||||||||
\(249\) | 0.133353 | 0.00845091 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.7556 | 1.43632 | 0.718159 | − | 0.695879i | \(-0.244985\pi\) | ||||
0.718159 | + | 0.695879i | \(0.244985\pi\) | |||||||
\(252\) | 7.18421 | 0.452563 | ||||||||
\(253\) | −8.85728 | −0.556852 | ||||||||
\(254\) | −28.8988 | −1.81327 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.2444 | 1.26528 | ||||||||
\(257\) | 6.85728 | 0.427745 | 0.213873 | − | 0.976862i | \(-0.431392\pi\) | ||||
0.213873 | + | 0.976862i | \(0.431392\pi\) | |||||||
\(258\) | −10.7971 | −0.672195 | ||||||||
\(259\) | 8.85728 | 0.550365 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.80642 | −0.483206 | ||||||||
\(262\) | −2.36842 | −0.146321 | ||||||||
\(263\) | 29.5812 | 1.82406 | 0.912028 | − | 0.410129i | \(-0.134516\pi\) | ||||
0.912028 | + | 0.410129i | \(0.134516\pi\) | |||||||
\(264\) | −0.719004 | −0.0442516 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −59.4291 | −3.64383 | ||||||||
\(267\) | −5.61285 | −0.343501 | ||||||||
\(268\) | 2.01874 | 0.123314 | ||||||||
\(269\) | 8.48886 | 0.517575 | 0.258788 | − | 0.965934i | \(-0.416677\pi\) | ||||
0.258788 | + | 0.965934i | \(0.416677\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.6637 | 0.890757 | 0.445378 | − | 0.895343i | \(-0.353069\pi\) | ||||
0.445378 | + | 0.895343i | \(0.353069\pi\) | |||||||
\(272\) | −23.9140 | −1.45000 | ||||||||
\(273\) | −2.75557 | −0.166775 | ||||||||
\(274\) | −0.930409 | −0.0562081 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 14.3684 | 0.864877 | ||||||||
\(277\) | −14.6035 | −0.877438 | −0.438719 | − | 0.898624i | \(-0.644568\pi\) | ||||
−0.438719 | + | 0.898624i | \(0.644568\pi\) | |||||||
\(278\) | −33.8894 | −2.03255 | ||||||||
\(279\) | 2.75557 | 0.164972 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.193576 | −0.0115478 | −0.00577389 | − | 0.999983i | \(-0.501838\pi\) | ||||
−0.00577389 | + | 0.999983i | \(0.501838\pi\) | |||||||
\(282\) | 5.24443 | 0.312301 | ||||||||
\(283\) | −27.1842 | −1.61593 | −0.807967 | − | 0.589228i | \(-0.799432\pi\) | ||||
−0.807967 | + | 0.589228i | \(0.799432\pi\) | |||||||
\(284\) | 4.47013 | 0.265253 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.18421 | −0.0700237 | ||||||||
\(287\) | −0.857279 | −0.0506036 | ||||||||
\(288\) | 7.34122 | 0.432585 | ||||||||
\(289\) | 9.87601 | 0.580942 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.24443 | 0.424676 | ||||||||
\(292\) | −6.87019 | −0.402047 | ||||||||
\(293\) | 2.81579 | 0.164500 | 0.0822502 | − | 0.996612i | \(-0.473789\pi\) | ||||
0.0822502 | + | 0.996612i | \(0.473789\pi\) | |||||||
\(294\) | 24.0049 | 1.40000 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.43801 | 0.0835825 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 2.73683 | 0.158540 | ||||||||
\(299\) | −5.51114 | −0.318717 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.1240 | −1.44812 | ||||||||
\(302\) | 23.1713 | 1.33336 | ||||||||
\(303\) | −4.66370 | −0.267923 | ||||||||
\(304\) | −32.5245 | −1.86541 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −9.86665 | −0.564039 | ||||||||
\(307\) | 24.4286 | 1.39422 | 0.697108 | − | 0.716966i | \(-0.254470\pi\) | ||||
0.697108 | + | 0.716966i | \(0.254470\pi\) | |||||||
\(308\) | 7.18421 | 0.409358 | ||||||||
\(309\) | −11.6128 | −0.660632 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.8796 | 1.12727 | 0.563633 | − | 0.826025i | \(-0.309403\pi\) | ||||
0.563633 | + | 0.826025i | \(0.309403\pi\) | |||||||
\(312\) | −0.447375 | −0.0253276 | ||||||||
\(313\) | 15.7146 | 0.888239 | 0.444120 | − | 0.895967i | \(-0.353517\pi\) | ||||
0.444120 | + | 0.895967i | \(0.353517\pi\) | |||||||
\(314\) | 35.1526 | 1.98377 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.8894 | 0.781340 | ||||||||
\(317\) | −16.4889 | −0.926107 | −0.463053 | − | 0.886330i | \(-0.653246\pi\) | ||||
−0.463053 | + | 0.886330i | \(0.653246\pi\) | |||||||
\(318\) | 20.6637 | 1.15876 | ||||||||
\(319\) | −7.80642 | −0.437076 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.62222 | 0.146358 | ||||||||
\(322\) | 74.6548 | 4.16035 | ||||||||
\(323\) | 36.5531 | 2.03387 | ||||||||
\(324\) | 1.62222 | 0.0901231 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −19.2257 | −1.06481 | ||||||||
\(327\) | 19.7146 | 1.09022 | ||||||||
\(328\) | −0.139182 | −0.00768504 | ||||||||
\(329\) | 12.2034 | 0.672796 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.3461 | 0.843500 | 0.421750 | − | 0.906712i | \(-0.361416\pi\) | ||||
0.421750 | + | 0.906712i | \(0.361416\pi\) | |||||||
\(332\) | −0.216327 | −0.0118725 | ||||||||
\(333\) | 2.00000 | 0.109599 | ||||||||
\(334\) | −31.0923 | −1.70130 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 20.4286 | 1.11447 | ||||||||
\(337\) | −28.2351 | −1.53806 | −0.769031 | − | 0.639212i | \(-0.779261\pi\) | ||||
−0.769031 | + | 0.639212i | \(0.779261\pi\) | |||||||
\(338\) | 24.0049 | 1.30570 | ||||||||
\(339\) | −6.00000 | −0.325875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.75557 | 0.149222 | ||||||||
\(342\) | −13.4193 | −0.725631 | ||||||||
\(343\) | 24.8573 | 1.34217 | ||||||||
\(344\) | −4.07896 | −0.219923 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.4795 | −0.939703 | ||||||||
\(347\) | −2.62222 | −0.140768 | −0.0703840 | − | 0.997520i | \(-0.522422\pi\) | ||||
−0.0703840 | + | 0.997520i | \(0.522422\pi\) | |||||||
\(348\) | 12.6637 | 0.678846 | ||||||||
\(349\) | 5.14272 | 0.275284 | 0.137642 | − | 0.990482i | \(-0.456048\pi\) | ||||
0.137642 | + | 0.990482i | \(0.456048\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.622216 | −0.0332114 | ||||||||
\(352\) | 7.34122 | 0.391288 | ||||||||
\(353\) | 9.34614 | 0.497445 | 0.248722 | − | 0.968575i | \(-0.419989\pi\) | ||||
0.248722 | + | 0.968575i | \(0.419989\pi\) | |||||||
\(354\) | −9.24443 | −0.491336 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 9.10525 | 0.482577 | ||||||||
\(357\) | −22.9590 | −1.21512 | ||||||||
\(358\) | 48.2034 | 2.54763 | ||||||||
\(359\) | 10.7556 | 0.567657 | 0.283829 | − | 0.958875i | \(-0.408395\pi\) | ||||
0.283829 | + | 0.958875i | \(0.408395\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 30.7146 | 1.61656 | ||||||||
\(362\) | 25.9081 | 1.36170 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 4.47013 | 0.234298 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 13.0509 | 0.682179 | ||||||||
\(367\) | −33.7975 | −1.76422 | −0.882108 | − | 0.471046i | \(-0.843876\pi\) | ||||
−0.882108 | + | 0.471046i | \(0.843876\pi\) | |||||||
\(368\) | 40.8573 | 2.12983 | ||||||||
\(369\) | −0.193576 | −0.0100772 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 48.0830 | 2.49634 | ||||||||
\(372\) | −4.47013 | −0.231765 | ||||||||
\(373\) | −33.9496 | −1.75784 | −0.878922 | − | 0.476965i | \(-0.841737\pi\) | ||||
−0.878922 | + | 0.476965i | \(0.841737\pi\) | |||||||
\(374\) | −9.86665 | −0.510192 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.98126 | 0.102176 | ||||||||
\(377\) | −4.85728 | −0.250163 | ||||||||
\(378\) | 8.42864 | 0.433522 | ||||||||
\(379\) | −20.0000 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.1842 | −0.777911 | ||||||||
\(382\) | −11.6128 | −0.594165 | ||||||||
\(383\) | 14.6351 | 0.747820 | 0.373910 | − | 0.927465i | \(-0.378017\pi\) | ||||
0.373910 | + | 0.927465i | \(0.378017\pi\) | |||||||
\(384\) | 5.64941 | 0.288295 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 34.8988 | 1.77630 | ||||||||
\(387\) | −5.67307 | −0.288378 | ||||||||
\(388\) | −11.7520 | −0.596619 | ||||||||
\(389\) | −5.61285 | −0.284583 | −0.142291 | − | 0.989825i | \(-0.545447\pi\) | ||||
−0.142291 | + | 0.989825i | \(0.545447\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −45.9180 | −2.32217 | ||||||||
\(392\) | 9.06868 | 0.458038 | ||||||||
\(393\) | −1.24443 | −0.0627733 | ||||||||
\(394\) | −12.7427 | −0.641966 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.62222 | 0.0815194 | ||||||||
\(397\) | 12.7556 | 0.640184 | 0.320092 | − | 0.947387i | \(-0.396286\pi\) | ||||
0.320092 | + | 0.947387i | \(0.396286\pi\) | |||||||
\(398\) | −26.8385 | −1.34529 | ||||||||
\(399\) | −31.2257 | −1.56324 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.00000 | 0.0998752 | 0.0499376 | − | 0.998752i | \(-0.484098\pi\) | ||||
0.0499376 | + | 0.998752i | \(0.484098\pi\) | |||||||
\(402\) | 2.36842 | 0.118126 | ||||||||
\(403\) | 1.71456 | 0.0854082 | ||||||||
\(404\) | 7.56553 | 0.376399 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 65.7975 | 3.26548 | ||||||||
\(407\) | 2.00000 | 0.0991363 | ||||||||
\(408\) | −3.72746 | −0.184537 | ||||||||
\(409\) | −7.12399 | −0.352258 | −0.176129 | − | 0.984367i | \(-0.556358\pi\) | ||||
−0.176129 | + | 0.984367i | \(0.556358\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.488863 | −0.0241138 | ||||||||
\(412\) | 18.8385 | 0.928108 | ||||||||
\(413\) | −21.5111 | −1.05849 | ||||||||
\(414\) | 16.8573 | 0.828490 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.56782 | 0.223956 | ||||||||
\(417\) | −17.8064 | −0.871984 | ||||||||
\(418\) | −13.4193 | −0.656358 | ||||||||
\(419\) | 15.6128 | 0.762738 | 0.381369 | − | 0.924423i | \(-0.375453\pi\) | ||||
0.381369 | + | 0.924423i | \(0.375453\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.89829 | 0.384939 | 0.192470 | − | 0.981303i | \(-0.438350\pi\) | ||||
0.192470 | + | 0.981303i | \(0.438350\pi\) | |||||||
\(422\) | 20.2953 | 0.987959 | ||||||||
\(423\) | 2.75557 | 0.133980 | ||||||||
\(424\) | 7.80642 | 0.379113 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.24443 | 0.254094 | ||||||||
\(427\) | 30.3684 | 1.46963 | ||||||||
\(428\) | −4.25380 | −0.205615 | ||||||||
\(429\) | −0.622216 | −0.0300409 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.3051 | 1.65242 | 0.826210 | − | 0.563362i | \(-0.190492\pi\) | ||||
0.826210 | + | 0.563362i | \(0.190492\pi\) | |||||||
\(432\) | 4.61285 | 0.221936 | ||||||||
\(433\) | −14.4701 | −0.695390 | −0.347695 | − | 0.937608i | \(-0.613036\pi\) | ||||
−0.347695 | + | 0.937608i | \(0.613036\pi\) | |||||||
\(434\) | −23.2257 | −1.11487 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −31.9813 | −1.53162 | ||||||||
\(437\) | −62.4514 | −2.98746 | ||||||||
\(438\) | −8.06022 | −0.385132 | ||||||||
\(439\) | −19.3176 | −0.921977 | −0.460988 | − | 0.887406i | \(-0.652505\pi\) | ||||
−0.460988 | + | 0.887406i | \(0.652505\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.6128 | 0.600612 | ||||||||
\(442\) | −6.13918 | −0.292011 | ||||||||
\(443\) | 13.1240 | 0.623539 | 0.311770 | − | 0.950158i | \(-0.399078\pi\) | ||||
0.311770 | + | 0.950158i | \(0.399078\pi\) | |||||||
\(444\) | −3.24443 | −0.153974 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 16.8573 | 0.798215 | ||||||||
\(447\) | 1.43801 | 0.0680154 | ||||||||
\(448\) | −21.0192 | −0.993064 | ||||||||
\(449\) | −32.3051 | −1.52457 | −0.762287 | − | 0.647240i | \(-0.775923\pi\) | ||||
−0.762287 | + | 0.647240i | \(0.775923\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.193576 | −0.00911514 | ||||||||
\(452\) | 9.73329 | 0.457816 | ||||||||
\(453\) | 12.1748 | 0.572024 | ||||||||
\(454\) | 25.4608 | 1.19493 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.06959 | −0.237405 | ||||||||
\(457\) | 23.4608 | 1.09745 | 0.548724 | − | 0.836004i | \(-0.315114\pi\) | ||||
0.548724 | + | 0.836004i | \(0.315114\pi\) | |||||||
\(458\) | −21.9081 | −1.02370 | ||||||||
\(459\) | −5.18421 | −0.241978 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.8671 | −1.34448 | −0.672238 | − | 0.740335i | \(-0.734667\pi\) | ||||
−0.672238 | + | 0.740335i | \(0.734667\pi\) | |||||||
\(462\) | 8.42864 | 0.392136 | ||||||||
\(463\) | 19.3461 | 0.899091 | 0.449546 | − | 0.893257i | \(-0.351586\pi\) | ||||
0.449546 | + | 0.893257i | \(0.351586\pi\) | |||||||
\(464\) | 36.0098 | 1.67172 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.23506 | −0.381482 | ||||||||
\(467\) | −3.14272 | −0.145428 | −0.0727139 | − | 0.997353i | \(-0.523166\pi\) | ||||
−0.0727139 | + | 0.997353i | \(0.523166\pi\) | |||||||
\(468\) | 1.00937 | 0.0466580 | ||||||||
\(469\) | 5.51114 | 0.254481 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.4701 | 0.851059 | ||||||||
\(472\) | −3.49240 | −0.160751 | ||||||||
\(473\) | −5.67307 | −0.260848 | ||||||||
\(474\) | 16.2953 | 0.748467 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 37.2444 | 1.70710 | ||||||||
\(477\) | 10.8573 | 0.497121 | ||||||||
\(478\) | 6.36842 | 0.291285 | ||||||||
\(479\) | −24.8573 | −1.13576 | −0.567879 | − | 0.823112i | \(-0.692236\pi\) | ||||
−0.567879 | + | 0.823112i | \(0.692236\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.24443 | 0.0567412 | ||||||||
\(482\) | 2.56199 | 0.116696 | ||||||||
\(483\) | 39.2257 | 1.78483 | ||||||||
\(484\) | 1.62222 | 0.0737371 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.90321 | 0.0863314 | ||||||||
\(487\) | 11.5299 | 0.522468 | 0.261234 | − | 0.965275i | \(-0.415871\pi\) | ||||
0.261234 | + | 0.965275i | \(0.415871\pi\) | |||||||
\(488\) | 4.93041 | 0.223189 | ||||||||
\(489\) | −10.1017 | −0.456815 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.3872 | 0.739542 | 0.369771 | − | 0.929123i | \(-0.379436\pi\) | ||||
0.369771 | + | 0.929123i | \(0.379436\pi\) | |||||||
\(492\) | 0.314022 | 0.0141572 | ||||||||
\(493\) | −40.4701 | −1.82268 | ||||||||
\(494\) | −8.34968 | −0.375670 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12.7110 | −0.570742 | ||||||||
\(497\) | 12.2034 | 0.547398 | ||||||||
\(498\) | −0.253799 | −0.0113730 | ||||||||
\(499\) | −25.3274 | −1.13381 | −0.566905 | − | 0.823783i | \(-0.691859\pi\) | ||||
−0.566905 | + | 0.823783i | \(0.691859\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.3368 | −0.729873 | ||||||||
\(502\) | −43.3087 | −1.93296 | ||||||||
\(503\) | −19.0923 | −0.851285 | −0.425643 | − | 0.904891i | \(-0.639952\pi\) | ||||
−0.425643 | + | 0.904891i | \(0.639952\pi\) | |||||||
\(504\) | 3.18421 | 0.141836 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 16.8573 | 0.749397 | ||||||||
\(507\) | 12.6128 | 0.560156 | ||||||||
\(508\) | 24.6321 | 1.09287 | ||||||||
\(509\) | −32.4514 | −1.43838 | −0.719191 | − | 0.694812i | \(-0.755488\pi\) | ||||
−0.719191 | + | 0.694812i | \(0.755488\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.7556 | −0.829698 | ||||||||
\(512\) | −27.2306 | −1.20343 | ||||||||
\(513\) | −7.05086 | −0.311303 | ||||||||
\(514\) | −13.0509 | −0.575649 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 9.20294 | 0.405137 | ||||||||
\(517\) | 2.75557 | 0.121190 | ||||||||
\(518\) | −16.8573 | −0.740666 | ||||||||
\(519\) | −9.18421 | −0.403142 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.2257 | −1.28040 | −0.640200 | − | 0.768208i | \(-0.721149\pi\) | ||||
−0.640200 | + | 0.768208i | \(0.721149\pi\) | |||||||
\(522\) | 14.8573 | 0.650285 | ||||||||
\(523\) | −6.71408 | −0.293586 | −0.146793 | − | 0.989167i | \(-0.546895\pi\) | ||||
−0.146793 | + | 0.989167i | \(0.546895\pi\) | |||||||
\(524\) | 2.01874 | 0.0881889 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −56.2993 | −2.45477 | ||||||||
\(527\) | 14.2854 | 0.622284 | ||||||||
\(528\) | 4.61285 | 0.200748 | ||||||||
\(529\) | 55.4514 | 2.41093 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.85728 | −0.210788 | ||||||||
\(532\) | 50.6548 | 2.19616 | ||||||||
\(533\) | −0.120446 | −0.00521710 | ||||||||
\(534\) | 10.6824 | 0.462274 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.894751 | 0.0386473 | ||||||||
\(537\) | 25.3274 | 1.09296 | ||||||||
\(538\) | −16.1561 | −0.696539 | ||||||||
\(539\) | 12.6128 | 0.543274 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.0000 | −0.773880 | −0.386940 | − | 0.922105i | \(-0.626468\pi\) | ||||
−0.386940 | + | 0.922105i | \(0.626468\pi\) | |||||||
\(542\) | −27.9081 | −1.19876 | ||||||||
\(543\) | 13.6128 | 0.584183 | ||||||||
\(544\) | 38.0584 | 1.63174 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 5.24443 | 0.224441 | ||||||||
\(547\) | −41.3689 | −1.76881 | −0.884403 | − | 0.466724i | \(-0.845434\pi\) | ||||
−0.884403 | + | 0.466724i | \(0.845434\pi\) | |||||||
\(548\) | 0.793040 | 0.0338770 | ||||||||
\(549\) | 6.85728 | 0.292662 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −55.0420 | −2.34487 | ||||||||
\(552\) | 6.36842 | 0.271058 | ||||||||
\(553\) | 37.9180 | 1.61244 | ||||||||
\(554\) | 27.7935 | 1.18083 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 28.8859 | 1.22503 | ||||||||
\(557\) | 20.7971 | 0.881200 | 0.440600 | − | 0.897704i | \(-0.354766\pi\) | ||||
0.440600 | + | 0.897704i | \(0.354766\pi\) | |||||||
\(558\) | −5.24443 | −0.222014 | ||||||||
\(559\) | −3.52987 | −0.149298 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.18421 | −0.218877 | ||||||||
\(562\) | 0.368416 | 0.0155407 | ||||||||
\(563\) | −37.7275 | −1.59002 | −0.795012 | − | 0.606594i | \(-0.792535\pi\) | ||||
−0.795012 | + | 0.606594i | \(0.792535\pi\) | |||||||
\(564\) | −4.47013 | −0.188226 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 51.7373 | 2.17468 | ||||||||
\(567\) | 4.42864 | 0.185985 | ||||||||
\(568\) | 1.98126 | 0.0831320 | ||||||||
\(569\) | −7.33630 | −0.307554 | −0.153777 | − | 0.988106i | \(-0.549144\pi\) | ||||
−0.153777 | + | 0.988106i | \(0.549144\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.6450 | 1.53354 | 0.766772 | − | 0.641919i | \(-0.221862\pi\) | ||||
0.766772 | + | 0.641919i | \(0.221862\pi\) | |||||||
\(572\) | 1.00937 | 0.0422038 | ||||||||
\(573\) | −6.10171 | −0.254903 | ||||||||
\(574\) | 1.63158 | 0.0681010 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.74620 | −0.197758 | ||||||||
\(577\) | −4.22216 | −0.175771 | −0.0878853 | − | 0.996131i | \(-0.528011\pi\) | ||||
−0.0878853 | + | 0.996131i | \(0.528011\pi\) | |||||||
\(578\) | −18.7961 | −0.781817 | ||||||||
\(579\) | 18.3368 | 0.762050 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.590573 | −0.0245011 | ||||||||
\(582\) | −13.7877 | −0.571518 | ||||||||
\(583\) | 10.8573 | 0.449663 | ||||||||
\(584\) | −3.04503 | −0.126004 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.35905 | −0.221380 | ||||||||
\(587\) | −34.3684 | −1.41854 | −0.709268 | − | 0.704939i | \(-0.750974\pi\) | ||||
−0.709268 | + | 0.704939i | \(0.750974\pi\) | |||||||
\(588\) | −20.4608 | −0.843787 | ||||||||
\(589\) | 19.4291 | 0.800563 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.69535 | −0.275410 | ||||||||
\(592\) | −9.22570 | −0.379174 | ||||||||
\(593\) | −27.9398 | −1.14735 | −0.573675 | − | 0.819083i | \(-0.694483\pi\) | ||||
−0.573675 | + | 0.819083i | \(0.694483\pi\) | |||||||
\(594\) | 1.90321 | 0.0780897 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.33276 | −0.0955535 | ||||||||
\(597\) | −14.1017 | −0.577145 | ||||||||
\(598\) | 10.4889 | 0.428921 | ||||||||
\(599\) | −31.2257 | −1.27585 | −0.637924 | − | 0.770100i | \(-0.720206\pi\) | ||||
−0.637924 | + | 0.770100i | \(0.720206\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.75557 | −0.357147 | −0.178574 | − | 0.983927i | \(-0.557148\pi\) | ||||
−0.178574 | + | 0.983927i | \(0.557148\pi\) | |||||||
\(602\) | 47.8163 | 1.94885 | ||||||||
\(603\) | 1.24443 | 0.0506772 | ||||||||
\(604\) | −19.7502 | −0.803625 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 8.87601 | 0.360563 | ||||||||
\(607\) | 15.1842 | 0.616308 | 0.308154 | − | 0.951336i | \(-0.400289\pi\) | ||||
0.308154 | + | 0.951336i | \(0.400289\pi\) | |||||||
\(608\) | 51.7619 | 2.09922 | ||||||||
\(609\) | 34.5718 | 1.40092 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.71456 | 0.0693636 | ||||||||
\(612\) | 8.40990 | 0.339950 | ||||||||
\(613\) | −42.7239 | −1.72560 | −0.862802 | − | 0.505543i | \(-0.831292\pi\) | ||||
−0.862802 | + | 0.505543i | \(0.831292\pi\) | |||||||
\(614\) | −46.4929 | −1.87630 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.18421 | 0.128295 | ||||||||
\(617\) | 3.51114 | 0.141353 | 0.0706765 | − | 0.997499i | \(-0.477484\pi\) | ||||
0.0706765 | + | 0.997499i | \(0.477484\pi\) | |||||||
\(618\) | 22.1017 | 0.889061 | ||||||||
\(619\) | 17.5941 | 0.707167 | 0.353584 | − | 0.935403i | \(-0.384963\pi\) | ||||
0.353584 | + | 0.935403i | \(0.384963\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.85728 | 0.355430 | ||||||||
\(622\) | −37.8350 | −1.51705 | ||||||||
\(623\) | 24.8573 | 0.995886 | ||||||||
\(624\) | 2.87019 | 0.114899 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −29.9081 | −1.19537 | ||||||||
\(627\) | −7.05086 | −0.281584 | ||||||||
\(628\) | −29.9625 | −1.19564 | ||||||||
\(629\) | 10.3684 | 0.413416 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.8163 | 0.629636 | 0.314818 | − | 0.949152i | \(-0.398057\pi\) | ||||
0.314818 | + | 0.949152i | \(0.398057\pi\) | |||||||
\(632\) | 6.15610 | 0.244877 | ||||||||
\(633\) | 10.6637 | 0.423844 | ||||||||
\(634\) | 31.3818 | 1.24633 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −17.6128 | −0.698395 | ||||||||
\(637\) | 7.84791 | 0.310946 | ||||||||
\(638\) | 14.8573 | 0.588205 | ||||||||
\(639\) | 2.75557 | 0.109009 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.8163 | 1.01968 | 0.509841 | − | 0.860269i | \(-0.329704\pi\) | ||||
0.509841 | + | 0.860269i | \(0.329704\pi\) | |||||||
\(642\) | −4.99063 | −0.196965 | ||||||||
\(643\) | −18.1017 | −0.713862 | −0.356931 | − | 0.934131i | \(-0.616177\pi\) | ||||
−0.356931 | + | 0.934131i | \(0.616177\pi\) | |||||||
\(644\) | −63.6325 | −2.50747 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −69.5683 | −2.73713 | ||||||||
\(647\) | 47.0420 | 1.84941 | 0.924705 | − | 0.380684i | \(-0.124311\pi\) | ||||
0.924705 | + | 0.380684i | \(0.124311\pi\) | |||||||
\(648\) | 0.719004 | 0.0282451 | ||||||||
\(649\) | −4.85728 | −0.190665 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.2034 | −0.478290 | ||||||||
\(652\) | 16.3872 | 0.641770 | ||||||||
\(653\) | −30.0830 | −1.17724 | −0.588619 | − | 0.808411i | \(-0.700328\pi\) | ||||
−0.588619 | + | 0.808411i | \(0.700328\pi\) | |||||||
\(654\) | −37.5210 | −1.46719 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.892937 | 0.0348633 | ||||||||
\(657\) | −4.23506 | −0.165226 | ||||||||
\(658\) | −23.2257 | −0.905432 | ||||||||
\(659\) | −10.2854 | −0.400664 | −0.200332 | − | 0.979728i | \(-0.564202\pi\) | ||||
−0.200332 | + | 0.979728i | \(0.564202\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.7146 | −1.07797 | −0.538986 | − | 0.842315i | \(-0.681192\pi\) | ||||
−0.538986 | + | 0.842315i | \(0.681192\pi\) | |||||||
\(662\) | −29.2070 | −1.13516 | ||||||||
\(663\) | −3.22570 | −0.125276 | ||||||||
\(664\) | −0.0958814 | −0.00372092 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.80642 | −0.147496 | ||||||||
\(667\) | 69.1437 | 2.67725 | ||||||||
\(668\) | 26.5018 | 1.02538 | ||||||||
\(669\) | 8.85728 | 0.342442 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.85728 | 0.264722 | ||||||||
\(672\) | −32.5116 | −1.25416 | ||||||||
\(673\) | 9.86665 | 0.380331 | 0.190166 | − | 0.981752i | \(-0.439097\pi\) | ||||
0.190166 | + | 0.981752i | \(0.439097\pi\) | |||||||
\(674\) | 53.7373 | 2.06988 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −20.4608 | −0.786952 | ||||||||
\(677\) | 5.65433 | 0.217314 | 0.108657 | − | 0.994079i | \(-0.465345\pi\) | ||||
0.108657 | + | 0.994079i | \(0.465345\pi\) | |||||||
\(678\) | 11.4193 | 0.438554 | ||||||||
\(679\) | −32.0830 | −1.23123 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.3778 | 0.512638 | ||||||||
\(682\) | −5.24443 | −0.200820 | ||||||||
\(683\) | −34.1847 | −1.30804 | −0.654020 | − | 0.756477i | \(-0.726919\pi\) | ||||
−0.654020 | + | 0.756477i | \(0.726919\pi\) | |||||||
\(684\) | 11.4380 | 0.437343 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −47.3087 | −1.80625 | ||||||||
\(687\) | −11.5111 | −0.439177 | ||||||||
\(688\) | 26.1690 | 0.997684 | ||||||||
\(689\) | 6.75557 | 0.257367 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.2257 | −0.731380 | −0.365690 | − | 0.930737i | \(-0.619167\pi\) | ||||
−0.365690 | + | 0.930737i | \(0.619167\pi\) | |||||||
\(692\) | 14.8988 | 0.566366 | ||||||||
\(693\) | 4.42864 | 0.168230 | ||||||||
\(694\) | 4.99063 | 0.189442 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.61285 | 0.212754 | ||||||||
\(697\) | −1.00354 | −0.0380118 | ||||||||
\(698\) | −9.78769 | −0.370469 | ||||||||
\(699\) | −4.32693 | −0.163659 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.9081 | −1.12961 | −0.564807 | − | 0.825223i | \(-0.691050\pi\) | ||||
−0.564807 | + | 0.825223i | \(0.691050\pi\) | |||||||
\(702\) | 1.18421 | 0.0446951 | ||||||||
\(703\) | 14.1017 | 0.531856 | ||||||||
\(704\) | −4.74620 | −0.178879 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.7877 | −0.669448 | ||||||||
\(707\) | 20.6539 | 0.776768 | ||||||||
\(708\) | 7.87955 | 0.296132 | ||||||||
\(709\) | −15.3274 | −0.575633 | −0.287816 | − | 0.957686i | \(-0.592929\pi\) | ||||
−0.287816 | + | 0.957686i | \(0.592929\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.56199 | 0.321100 | ||||||||
\(712\) | 4.03566 | 0.151243 | ||||||||
\(713\) | −24.4068 | −0.914043 | ||||||||
\(714\) | 43.6958 | 1.63528 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −41.0865 | −1.53548 | ||||||||
\(717\) | 3.34614 | 0.124964 | ||||||||
\(718\) | −20.4701 | −0.763938 | ||||||||
\(719\) | 23.8163 | 0.888197 | 0.444098 | − | 0.895978i | \(-0.353524\pi\) | ||||
0.444098 | + | 0.895978i | \(0.353524\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 51.4291 | 1.91532 | ||||||||
\(722\) | −58.4563 | −2.17552 | ||||||||
\(723\) | 1.34614 | 0.0500635 | ||||||||
\(724\) | −22.0830 | −0.820707 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.90321 | 0.0706348 | ||||||||
\(727\) | 32.9403 | 1.22169 | 0.610843 | − | 0.791752i | \(-0.290831\pi\) | ||||
0.610843 | + | 0.791752i | \(0.290831\pi\) | |||||||
\(728\) | 1.98126 | 0.0734305 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −29.4104 | −1.08778 | ||||||||
\(732\) | −11.1240 | −0.411154 | ||||||||
\(733\) | 29.8666 | 1.10315 | 0.551575 | − | 0.834125i | \(-0.314027\pi\) | ||||
0.551575 | + | 0.834125i | \(0.314027\pi\) | |||||||
\(734\) | 64.3239 | 2.37424 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −65.0232 | −2.39679 | ||||||||
\(737\) | 1.24443 | 0.0458392 | ||||||||
\(738\) | 0.368416 | 0.0135616 | ||||||||
\(739\) | −5.06959 | −0.186488 | −0.0932440 | − | 0.995643i | \(-0.529724\pi\) | ||||
−0.0932440 | + | 0.995643i | \(0.529724\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.38715 | −0.161166 | ||||||||
\(742\) | −91.5121 | −3.35951 | ||||||||
\(743\) | −22.4385 | −0.823188 | −0.411594 | − | 0.911367i | \(-0.635028\pi\) | ||||
−0.411594 | + | 0.911367i | \(0.635028\pi\) | |||||||
\(744\) | −1.98126 | −0.0726367 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 64.6133 | 2.36566 | ||||||||
\(747\) | −0.133353 | −0.00487913 | ||||||||
\(748\) | 8.40990 | 0.307497 | ||||||||
\(749\) | −11.6128 | −0.424324 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.63512 | −0.242119 | −0.121060 | − | 0.992645i | \(-0.538629\pi\) | ||||
−0.121060 | + | 0.992645i | \(0.538629\pi\) | |||||||
\(752\) | −12.7110 | −0.463523 | ||||||||
\(753\) | −22.7556 | −0.829259 | ||||||||
\(754\) | 9.24443 | 0.336662 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −7.18421 | −0.261287 | ||||||||
\(757\) | −8.75557 | −0.318227 | −0.159113 | − | 0.987260i | \(-0.550864\pi\) | ||||
−0.159113 | + | 0.987260i | \(0.550864\pi\) | |||||||
\(758\) | 38.0642 | 1.38256 | ||||||||
\(759\) | 8.85728 | 0.321499 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.15257 | 0.114280 | 0.0571402 | − | 0.998366i | \(-0.481802\pi\) | ||||
0.0571402 | + | 0.998366i | \(0.481802\pi\) | |||||||
\(762\) | 28.8988 | 1.04689 | ||||||||
\(763\) | −87.3087 | −3.16079 | ||||||||
\(764\) | 9.89829 | 0.358108 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −27.8537 | −1.00640 | ||||||||
\(767\) | −3.02227 | −0.109128 | ||||||||
\(768\) | −20.2444 | −0.730508 | ||||||||
\(769\) | −28.9590 | −1.04429 | −0.522144 | − | 0.852857i | \(-0.674868\pi\) | ||||
−0.522144 | + | 0.852857i | \(0.674868\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.85728 | −0.246959 | ||||||||
\(772\) | −29.7462 | −1.07059 | ||||||||
\(773\) | −29.1427 | −1.04819 | −0.524095 | − | 0.851660i | \(-0.675596\pi\) | ||||
−0.524095 | + | 0.851660i | \(0.675596\pi\) | |||||||
\(774\) | 10.7971 | 0.388092 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.20877 | −0.186984 | ||||||||
\(777\) | −8.85728 | −0.317753 | ||||||||
\(778\) | 10.6824 | 0.382984 | ||||||||
\(779\) | −1.36488 | −0.0489018 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.75557 | 0.0986020 | ||||||||
\(782\) | 87.3916 | 3.12512 | ||||||||
\(783\) | 7.80642 | 0.278979 | ||||||||
\(784\) | −58.1811 | −2.07790 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.36842 | 0.0844786 | ||||||||
\(787\) | 11.2672 | 0.401632 | 0.200816 | − | 0.979629i | \(-0.435641\pi\) | ||||
0.200816 | + | 0.979629i | \(0.435641\pi\) | |||||||
\(788\) | 10.8613 | 0.386918 | ||||||||
\(789\) | −29.5812 | −1.05312 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26.5718 | 0.944786 | ||||||||
\(792\) | 0.719004 | 0.0255487 | ||||||||
\(793\) | 4.26671 | 0.151515 | ||||||||
\(794\) | −24.2766 | −0.861543 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22.8760 | 0.810819 | ||||||||
\(797\) | −41.9625 | −1.48639 | −0.743195 | − | 0.669075i | \(-0.766690\pi\) | ||||
−0.743195 | + | 0.669075i | \(0.766690\pi\) | |||||||
\(798\) | 59.4291 | 2.10377 | ||||||||
\(799\) | 14.2854 | 0.505383 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.61285 | 0.198320 | ||||||||
\(802\) | −3.80642 | −0.134409 | ||||||||
\(803\) | −4.23506 | −0.149452 | ||||||||
\(804\) | −2.01874 | −0.0711953 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.26317 | −0.114940 | ||||||||
\(807\) | −8.48886 | −0.298822 | ||||||||
\(808\) | 3.35322 | 0.117966 | ||||||||
\(809\) | −27.8064 | −0.977622 | −0.488811 | − | 0.872390i | \(-0.662569\pi\) | ||||
−0.488811 | + | 0.872390i | \(0.662569\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.78415 | 0.238224 | 0.119112 | − | 0.992881i | \(-0.461995\pi\) | ||||
0.119112 | + | 0.992881i | \(0.461995\pi\) | |||||||
\(812\) | −56.0830 | −1.96813 | ||||||||
\(813\) | −14.6637 | −0.514279 | ||||||||
\(814\) | −3.80642 | −0.133415 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 23.9140 | 0.837156 | ||||||||
\(817\) | −40.0000 | −1.39942 | ||||||||
\(818\) | 13.5585 | 0.474060 | ||||||||
\(819\) | 2.75557 | 0.0962874 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.62269 | 0.126433 | 0.0632164 | − | 0.998000i | \(-0.479864\pi\) | ||||
0.0632164 | + | 0.998000i | \(0.479864\pi\) | |||||||
\(822\) | 0.930409 | 0.0324517 | ||||||||
\(823\) | −42.0642 | −1.46627 | −0.733134 | − | 0.680085i | \(-0.761943\pi\) | ||||
−0.733134 | + | 0.680085i | \(0.761943\pi\) | |||||||
\(824\) | 8.34968 | 0.290875 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 40.9403 | 1.42449 | ||||||||
\(827\) | −30.8256 | −1.07191 | −0.535956 | − | 0.844246i | \(-0.680049\pi\) | ||||
−0.535956 | + | 0.844246i | \(0.680049\pi\) | |||||||
\(828\) | −14.3684 | −0.499337 | ||||||||
\(829\) | 7.12399 | 0.247426 | 0.123713 | − | 0.992318i | \(-0.460520\pi\) | ||||
0.123713 | + | 0.992318i | \(0.460520\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.6035 | 0.506589 | ||||||||
\(832\) | −2.95316 | −0.102382 | ||||||||
\(833\) | 65.3876 | 2.26555 | ||||||||
\(834\) | 33.8894 | 1.17349 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 11.4380 | 0.395592 | ||||||||
\(837\) | −2.75557 | −0.0952464 | ||||||||
\(838\) | −29.7146 | −1.02647 | ||||||||
\(839\) | 3.34614 | 0.115522 | 0.0577608 | − | 0.998330i | \(-0.481604\pi\) | ||||
0.0577608 | + | 0.998330i | \(0.481604\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31.9403 | 1.10139 | ||||||||
\(842\) | −15.0321 | −0.518041 | ||||||||
\(843\) | 0.193576 | 0.00666712 | ||||||||
\(844\) | −17.2988 | −0.595450 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.24443 | −0.180307 | ||||||||
\(847\) | 4.42864 | 0.152170 | ||||||||
\(848\) | −50.0830 | −1.71986 | ||||||||
\(849\) | 27.1842 | 0.932960 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.7146 | −0.607247 | ||||||||
\(852\) | −4.47013 | −0.153144 | ||||||||
\(853\) | 26.4197 | 0.904595 | 0.452297 | − | 0.891867i | \(-0.350605\pi\) | ||||
0.452297 | + | 0.891867i | \(0.350605\pi\) | |||||||
\(854\) | −57.7975 | −1.97779 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.88538 | −0.0644411 | ||||||||
\(857\) | −38.7783 | −1.32464 | −0.662321 | − | 0.749220i | \(-0.730429\pi\) | ||||
−0.662321 | + | 0.749220i | \(0.730429\pi\) | |||||||
\(858\) | 1.18421 | 0.0404282 | ||||||||
\(859\) | −27.3087 | −0.931760 | −0.465880 | − | 0.884848i | \(-0.654262\pi\) | ||||
−0.465880 | + | 0.884848i | \(0.654262\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.857279 | 0.0292160 | ||||||||
\(862\) | −65.2899 | −2.22378 | ||||||||
\(863\) | 49.5308 | 1.68605 | 0.843024 | − | 0.537875i | \(-0.180773\pi\) | ||||
0.843024 | + | 0.537875i | \(0.180773\pi\) | |||||||
\(864\) | −7.34122 | −0.249753 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 27.5397 | 0.935838 | ||||||||
\(867\) | −9.87601 | −0.335407 | ||||||||
\(868\) | 19.7966 | 0.671940 | ||||||||
\(869\) | 8.56199 | 0.290446 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.774305 | 0.0262363 | ||||||||
\(872\) | −14.1748 | −0.480021 | ||||||||
\(873\) | −7.24443 | −0.245187 | ||||||||
\(874\) | 118.858 | 4.02044 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.87019 | 0.232122 | ||||||||
\(877\) | 4.50177 | 0.152014 | 0.0760070 | − | 0.997107i | \(-0.475783\pi\) | ||||
0.0760070 | + | 0.997107i | \(0.475783\pi\) | |||||||
\(878\) | 36.7654 | 1.24077 | ||||||||
\(879\) | −2.81579 | −0.0949743 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.1240 | −0.509540 | −0.254770 | − | 0.967002i | \(-0.582000\pi\) | ||||
−0.254770 | + | 0.967002i | \(0.582000\pi\) | |||||||
\(882\) | −24.0049 | −0.808288 | ||||||||
\(883\) | 30.2480 | 1.01793 | 0.508963 | − | 0.860789i | \(-0.330029\pi\) | ||||
0.508963 | + | 0.860789i | \(0.330029\pi\) | |||||||
\(884\) | 5.23277 | 0.175997 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.9777 | −0.839143 | ||||||||
\(887\) | −57.1941 | −1.92039 | −0.960194 | − | 0.279333i | \(-0.909887\pi\) | ||||
−0.960194 | + | 0.279333i | \(0.909887\pi\) | |||||||
\(888\) | −1.43801 | −0.0482564 | ||||||||
\(889\) | 67.2454 | 2.25534 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | −14.3684 | −0.481090 | ||||||||
\(893\) | 19.4291 | 0.650171 | ||||||||
\(894\) | −2.73683 | −0.0915334 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −25.0192 | −0.835833 | ||||||||
\(897\) | 5.51114 | 0.184012 | ||||||||
\(898\) | 61.4835 | 2.05173 | ||||||||
\(899\) | −21.5111 | −0.717437 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 56.2864 | 1.87517 | ||||||||
\(902\) | 0.368416 | 0.0122669 | ||||||||
\(903\) | 25.1240 | 0.836074 | ||||||||
\(904\) | 4.31402 | 0.143482 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −23.1713 | −0.769815 | ||||||||
\(907\) | 53.2641 | 1.76861 | 0.884303 | − | 0.466913i | \(-0.154634\pi\) | ||||
0.884303 | + | 0.466913i | \(0.154634\pi\) | |||||||
\(908\) | −21.7017 | −0.720195 | ||||||||
\(909\) | 4.66370 | 0.154685 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.590573 | −0.0195665 | −0.00978327 | − | 0.999952i | \(-0.503114\pi\) | ||||
−0.00978327 | + | 0.999952i | \(0.503114\pi\) | |||||||
\(912\) | 32.5245 | 1.07699 | ||||||||
\(913\) | −0.133353 | −0.00441334 | ||||||||
\(914\) | −44.6508 | −1.47692 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.6735 | 0.616991 | ||||||||
\(917\) | 5.51114 | 0.181994 | ||||||||
\(918\) | 9.86665 | 0.325648 | ||||||||
\(919\) | 55.8707 | 1.84300 | 0.921502 | − | 0.388375i | \(-0.126963\pi\) | ||||
0.921502 | + | 0.388375i | \(0.126963\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.4286 | −0.804951 | ||||||||
\(922\) | 54.9403 | 1.80936 | ||||||||
\(923\) | 1.71456 | 0.0564354 | ||||||||
\(924\) | −7.18421 | −0.236343 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −36.8198 | −1.20997 | ||||||||
\(927\) | 11.6128 | 0.381416 | ||||||||
\(928\) | −57.3087 | −1.88125 | ||||||||
\(929\) | 15.3274 | 0.502876 | 0.251438 | − | 0.967873i | \(-0.419097\pi\) | ||||
0.251438 | + | 0.967873i | \(0.419097\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 88.9314 | 2.91461 | ||||||||
\(932\) | 7.01921 | 0.229922 | ||||||||
\(933\) | −19.8796 | −0.650827 | ||||||||
\(934\) | 5.98126 | 0.195713 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.447375 | 0.0146229 | ||||||||
\(937\) | 27.8479 | 0.909752 | 0.454876 | − | 0.890555i | \(-0.349684\pi\) | ||||
0.454876 | + | 0.890555i | \(0.349684\pi\) | |||||||
\(938\) | −10.4889 | −0.342474 | ||||||||
\(939\) | −15.7146 | −0.512825 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.4157 | 0.339543 | 0.169772 | − | 0.985483i | \(-0.445697\pi\) | ||||
0.169772 | + | 0.985483i | \(0.445697\pi\) | |||||||
\(942\) | −35.1526 | −1.14533 | ||||||||
\(943\) | 1.71456 | 0.0558337 | ||||||||
\(944\) | 22.4059 | 0.729250 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.7971 | 0.351043 | ||||||||
\(947\) | −8.47013 | −0.275242 | −0.137621 | − | 0.990485i | \(-0.543946\pi\) | ||||
−0.137621 | + | 0.990485i | \(0.543946\pi\) | |||||||
\(948\) | −13.8894 | −0.451107 | ||||||||
\(949\) | −2.63512 | −0.0855397 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.4889 | 0.534688 | ||||||||
\(952\) | 16.5076 | 0.535014 | ||||||||
\(953\) | 8.71408 | 0.282277 | 0.141138 | − | 0.989990i | \(-0.454924\pi\) | ||||
0.141138 | + | 0.989990i | \(0.454924\pi\) | |||||||
\(954\) | −20.6637 | −0.669012 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.42816 | −0.175559 | ||||||||
\(957\) | 7.80642 | 0.252346 | ||||||||
\(958\) | 47.3087 | 1.52847 | ||||||||
\(959\) | 2.16500 | 0.0699114 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.4068 | −0.755059 | ||||||||
\(962\) | −2.36842 | −0.0763608 | ||||||||
\(963\) | −2.62222 | −0.0844997 | ||||||||
\(964\) | −2.18373 | −0.0703333 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −74.6548 | −2.40198 | ||||||||
\(967\) | −44.2449 | −1.42282 | −0.711410 | − | 0.702777i | \(-0.751943\pi\) | ||||
−0.711410 | + | 0.702777i | \(0.751943\pi\) | |||||||
\(968\) | 0.719004 | 0.0231097 | ||||||||
\(969\) | −36.5531 | −1.17425 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −57.1437 | −1.83383 | −0.916914 | − | 0.399085i | \(-0.869328\pi\) | ||||
−0.916914 | + | 0.399085i | \(0.869328\pi\) | |||||||
\(972\) | −1.62222 | −0.0520326 | ||||||||
\(973\) | 78.8582 | 2.52808 | ||||||||
\(974\) | −21.9438 | −0.703124 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −31.6316 | −1.01250 | ||||||||
\(977\) | 16.2480 | 0.519819 | 0.259909 | − | 0.965633i | \(-0.416307\pi\) | ||||
0.259909 | + | 0.965633i | \(0.416307\pi\) | |||||||
\(978\) | 19.2257 | 0.614770 | ||||||||
\(979\) | 5.61285 | 0.179387 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.7146 | −0.629437 | ||||||||
\(982\) | −31.1882 | −0.995256 | ||||||||
\(983\) | −1.12399 | −0.0358496 | −0.0179248 | − | 0.999839i | \(-0.505706\pi\) | ||||
−0.0179248 | + | 0.999839i | \(0.505706\pi\) | |||||||
\(984\) | 0.139182 | 0.00443696 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 77.0232 | 2.45292 | ||||||||
\(987\) | −12.2034 | −0.388439 | ||||||||
\(988\) | 7.11691 | 0.226419 | ||||||||
\(989\) | 50.2480 | 1.59779 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −53.6513 | −1.70429 | −0.852144 | − | 0.523307i | \(-0.824698\pi\) | ||||
−0.852144 | + | 0.523307i | \(0.824698\pi\) | |||||||
\(992\) | 20.2292 | 0.642279 | ||||||||
\(993\) | −15.3461 | −0.486995 | ||||||||
\(994\) | −23.2257 | −0.736674 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.216327 | 0.00685460 | ||||||||
\(997\) | 35.7275 | 1.13150 | 0.565750 | − | 0.824577i | \(-0.308587\pi\) | ||||
0.565750 | + | 0.824577i | \(0.308587\pi\) | |||||||
\(998\) | 48.2034 | 1.52585 | ||||||||
\(999\) | −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.a.k.1.1 | 3 | ||
3.2 | odd | 2 | 2475.2.a.bb.1.3 | 3 | |||
5.2 | odd | 4 | 825.2.c.g.199.2 | 6 | |||
5.3 | odd | 4 | 825.2.c.g.199.5 | 6 | |||
5.4 | even | 2 | 165.2.a.c.1.3 | ✓ | 3 | ||
11.10 | odd | 2 | 9075.2.a.cf.1.3 | 3 | |||
15.2 | even | 4 | 2475.2.c.r.199.5 | 6 | |||
15.8 | even | 4 | 2475.2.c.r.199.2 | 6 | |||
15.14 | odd | 2 | 495.2.a.e.1.1 | 3 | |||
20.19 | odd | 2 | 2640.2.a.be.1.3 | 3 | |||
35.34 | odd | 2 | 8085.2.a.bk.1.3 | 3 | |||
55.54 | odd | 2 | 1815.2.a.m.1.1 | 3 | |||
60.59 | even | 2 | 7920.2.a.cj.1.3 | 3 | |||
165.164 | even | 2 | 5445.2.a.z.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.a.c.1.3 | ✓ | 3 | 5.4 | even | 2 | ||
495.2.a.e.1.1 | 3 | 15.14 | odd | 2 | |||
825.2.a.k.1.1 | 3 | 1.1 | even | 1 | trivial | ||
825.2.c.g.199.2 | 6 | 5.2 | odd | 4 | |||
825.2.c.g.199.5 | 6 | 5.3 | odd | 4 | |||
1815.2.a.m.1.1 | 3 | 55.54 | odd | 2 | |||
2475.2.a.bb.1.3 | 3 | 3.2 | odd | 2 | |||
2475.2.c.r.199.2 | 6 | 15.8 | even | 4 | |||
2475.2.c.r.199.5 | 6 | 15.2 | even | 4 | |||
2640.2.a.be.1.3 | 3 | 20.19 | odd | 2 | |||
5445.2.a.z.1.3 | 3 | 165.164 | even | 2 | |||
7920.2.a.cj.1.3 | 3 | 60.59 | even | 2 | |||
8085.2.a.bk.1.3 | 3 | 35.34 | odd | 2 | |||
9075.2.a.cf.1.3 | 3 | 11.10 | odd | 2 |