Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [435,2,Mod(1,435)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(435, 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("435.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 435 = 3 \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 435.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: | \(3.47349248793\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{21}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 5 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.79129\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 435.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.79129 | 1.26663 | 0.633316 | − | 0.773893i | \(-0.281693\pi\) | ||||
0.633316 | + | 0.773893i | \(0.281693\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.20871 | 0.604356 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.79129 | 0.731290 | ||||||||
\(7\) | 1.00000 | 0.377964 | 0.188982 | − | 0.981981i | \(-0.439481\pi\) | ||||
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | −1.41742 | −0.501135 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.79129 | 0.566455 | ||||||||
\(11\) | 5.00000 | 1.50756 | 0.753778 | − | 0.657129i | \(-0.228229\pi\) | ||||
0.753778 | + | 0.657129i | \(0.228229\pi\) | |||||||
\(12\) | 1.20871 | 0.348925 | ||||||||
\(13\) | −4.58258 | −1.27098 | −0.635489 | − | 0.772110i | \(-0.719201\pi\) | ||||
−0.635489 | + | 0.772110i | \(0.719201\pi\) | |||||||
\(14\) | 1.79129 | 0.478742 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −4.95644 | −1.23911 | ||||||||
\(17\) | −3.00000 | −0.727607 | −0.363803 | − | 0.931476i | \(-0.618522\pi\) | ||||
−0.363803 | + | 0.931476i | \(0.618522\pi\) | |||||||
\(18\) | 1.79129 | 0.422211 | ||||||||
\(19\) | 3.58258 | 0.821899 | 0.410950 | − | 0.911658i | \(-0.365197\pi\) | ||||
0.410950 | + | 0.911658i | \(0.365197\pi\) | |||||||
\(20\) | 1.20871 | 0.270276 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 8.95644 | 1.90952 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | −1.41742 | −0.289331 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −8.20871 | −1.60986 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.20871 | 0.228425 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 1.79129 | 0.327043 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | −6.04356 | −1.06836 | ||||||||
\(33\) | 5.00000 | 0.870388 | ||||||||
\(34\) | −5.37386 | −0.921610 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 1.20871 | 0.201452 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 6.41742 | 1.04104 | ||||||||
\(39\) | −4.58258 | −0.733799 | ||||||||
\(40\) | −1.41742 | −0.224114 | ||||||||
\(41\) | −9.16515 | −1.43136 | −0.715678 | − | 0.698430i | \(-0.753882\pi\) | ||||
−0.715678 | + | 0.698430i | \(0.753882\pi\) | |||||||
\(42\) | 1.79129 | 0.276402 | ||||||||
\(43\) | −9.58258 | −1.46133 | −0.730665 | − | 0.682737i | \(-0.760790\pi\) | ||||
−0.730665 | + | 0.682737i | \(0.760790\pi\) | |||||||
\(44\) | 6.04356 | 0.911101 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −7.16515 | −1.05644 | ||||||||
\(47\) | 10.5826 | 1.54363 | 0.771814 | − | 0.635849i | \(-0.219350\pi\) | ||||
0.771814 | + | 0.635849i | \(0.219350\pi\) | |||||||
\(48\) | −4.95644 | −0.715400 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | 1.79129 | 0.253326 | ||||||||
\(51\) | −3.00000 | −0.420084 | ||||||||
\(52\) | −5.53901 | −0.768123 | ||||||||
\(53\) | 0.417424 | 0.0573376 | 0.0286688 | − | 0.999589i | \(-0.490873\pi\) | ||||
0.0286688 | + | 0.999589i | \(0.490873\pi\) | |||||||
\(54\) | 1.79129 | 0.243763 | ||||||||
\(55\) | 5.00000 | 0.674200 | ||||||||
\(56\) | −1.41742 | −0.189411 | ||||||||
\(57\) | 3.58258 | 0.474524 | ||||||||
\(58\) | 1.79129 | 0.235208 | ||||||||
\(59\) | −7.58258 | −0.987167 | −0.493584 | − | 0.869698i | \(-0.664313\pi\) | ||||
−0.493584 | + | 0.869698i | \(0.664313\pi\) | |||||||
\(60\) | 1.20871 | 0.156044 | ||||||||
\(61\) | 12.7477 | 1.63218 | 0.816090 | − | 0.577925i | \(-0.196138\pi\) | ||||
0.816090 | + | 0.577925i | \(0.196138\pi\) | |||||||
\(62\) | 7.16515 | 0.909975 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −0.912878 | −0.114110 | ||||||||
\(65\) | −4.58258 | −0.568399 | ||||||||
\(66\) | 8.95644 | 1.10246 | ||||||||
\(67\) | −4.16515 | −0.508854 | −0.254427 | − | 0.967092i | \(-0.581887\pi\) | ||||
−0.254427 | + | 0.967092i | \(0.581887\pi\) | |||||||
\(68\) | −3.62614 | −0.439734 | ||||||||
\(69\) | −4.00000 | −0.481543 | ||||||||
\(70\) | 1.79129 | 0.214100 | ||||||||
\(71\) | −9.58258 | −1.13724 | −0.568621 | − | 0.822599i | \(-0.692523\pi\) | ||||
−0.568621 | + | 0.822599i | \(0.692523\pi\) | |||||||
\(72\) | −1.41742 | −0.167045 | ||||||||
\(73\) | 4.00000 | 0.468165 | 0.234082 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234082 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(74\) | −7.16515 | −0.832932 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 4.33030 | 0.496720 | ||||||||
\(77\) | 5.00000 | 0.569803 | ||||||||
\(78\) | −8.20871 | −0.929454 | ||||||||
\(79\) | 7.58258 | 0.853106 | 0.426553 | − | 0.904462i | \(-0.359728\pi\) | ||||
0.426553 | + | 0.904462i | \(0.359728\pi\) | |||||||
\(80\) | −4.95644 | −0.554147 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −16.4174 | −1.81300 | ||||||||
\(83\) | −11.5826 | −1.27135 | −0.635676 | − | 0.771956i | \(-0.719279\pi\) | ||||
−0.635676 | + | 0.771956i | \(0.719279\pi\) | |||||||
\(84\) | 1.20871 | 0.131881 | ||||||||
\(85\) | −3.00000 | −0.325396 | ||||||||
\(86\) | −17.1652 | −1.85097 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | −7.08712 | −0.755490 | ||||||||
\(89\) | 1.41742 | 0.150247 | 0.0751233 | − | 0.997174i | \(-0.476065\pi\) | ||||
0.0751233 | + | 0.997174i | \(0.476065\pi\) | |||||||
\(90\) | 1.79129 | 0.188818 | ||||||||
\(91\) | −4.58258 | −0.480384 | ||||||||
\(92\) | −4.83485 | −0.504068 | ||||||||
\(93\) | 4.00000 | 0.414781 | ||||||||
\(94\) | 18.9564 | 1.95521 | ||||||||
\(95\) | 3.58258 | 0.367565 | ||||||||
\(96\) | −6.04356 | −0.616818 | ||||||||
\(97\) | 11.5826 | 1.17603 | 0.588016 | − | 0.808849i | \(-0.299909\pi\) | ||||
0.588016 | + | 0.808849i | \(0.299909\pi\) | |||||||
\(98\) | −10.7477 | −1.08568 | ||||||||
\(99\) | 5.00000 | 0.502519 | ||||||||
\(100\) | 1.20871 | 0.120871 | ||||||||
\(101\) | −0.582576 | −0.0579684 | −0.0289842 | − | 0.999580i | \(-0.509227\pi\) | ||||
−0.0289842 | + | 0.999580i | \(0.509227\pi\) | |||||||
\(102\) | −5.37386 | −0.532092 | ||||||||
\(103\) | 15.1652 | 1.49427 | 0.747133 | − | 0.664674i | \(-0.231430\pi\) | ||||
0.747133 | + | 0.664674i | \(0.231430\pi\) | |||||||
\(104\) | 6.49545 | 0.636932 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | 0.747727 | 0.0726257 | ||||||||
\(107\) | 5.16515 | 0.499334 | 0.249667 | − | 0.968332i | \(-0.419679\pi\) | ||||
0.249667 | + | 0.968332i | \(0.419679\pi\) | |||||||
\(108\) | 1.20871 | 0.116308 | ||||||||
\(109\) | 14.1652 | 1.35678 | 0.678388 | − | 0.734704i | \(-0.262679\pi\) | ||||
0.678388 | + | 0.734704i | \(0.262679\pi\) | |||||||
\(110\) | 8.95644 | 0.853963 | ||||||||
\(111\) | −4.00000 | −0.379663 | ||||||||
\(112\) | −4.95644 | −0.468339 | ||||||||
\(113\) | −14.1652 | −1.33255 | −0.666273 | − | 0.745708i | \(-0.732111\pi\) | ||||
−0.666273 | + | 0.745708i | \(0.732111\pi\) | |||||||
\(114\) | 6.41742 | 0.601047 | ||||||||
\(115\) | −4.00000 | −0.373002 | ||||||||
\(116\) | 1.20871 | 0.112226 | ||||||||
\(117\) | −4.58258 | −0.423659 | ||||||||
\(118\) | −13.5826 | −1.25038 | ||||||||
\(119\) | −3.00000 | −0.275010 | ||||||||
\(120\) | −1.41742 | −0.129393 | ||||||||
\(121\) | 14.0000 | 1.27273 | ||||||||
\(122\) | 22.8348 | 2.06737 | ||||||||
\(123\) | −9.16515 | −0.826394 | ||||||||
\(124\) | 4.83485 | 0.434182 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 1.79129 | 0.159581 | ||||||||
\(127\) | 2.00000 | 0.177471 | 0.0887357 | − | 0.996055i | \(-0.471717\pi\) | ||||
0.0887357 | + | 0.996055i | \(0.471717\pi\) | |||||||
\(128\) | 10.4519 | 0.923826 | ||||||||
\(129\) | −9.58258 | −0.843699 | ||||||||
\(130\) | −8.20871 | −0.719952 | ||||||||
\(131\) | −15.0000 | −1.31056 | −0.655278 | − | 0.755388i | \(-0.727449\pi\) | ||||
−0.655278 | + | 0.755388i | \(0.727449\pi\) | |||||||
\(132\) | 6.04356 | 0.526024 | ||||||||
\(133\) | 3.58258 | 0.310649 | ||||||||
\(134\) | −7.46099 | −0.644531 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 4.25227 | 0.364629 | ||||||||
\(137\) | 16.3303 | 1.39519 | 0.697596 | − | 0.716491i | \(-0.254253\pi\) | ||||
0.697596 | + | 0.716491i | \(0.254253\pi\) | |||||||
\(138\) | −7.16515 | −0.609938 | ||||||||
\(139\) | −9.41742 | −0.798776 | −0.399388 | − | 0.916782i | \(-0.630777\pi\) | ||||
−0.399388 | + | 0.916782i | \(0.630777\pi\) | |||||||
\(140\) | 1.20871 | 0.102155 | ||||||||
\(141\) | 10.5826 | 0.891214 | ||||||||
\(142\) | −17.1652 | −1.44047 | ||||||||
\(143\) | −22.9129 | −1.91607 | ||||||||
\(144\) | −4.95644 | −0.413037 | ||||||||
\(145\) | 1.00000 | 0.0830455 | ||||||||
\(146\) | 7.16515 | 0.592992 | ||||||||
\(147\) | −6.00000 | −0.494872 | ||||||||
\(148\) | −4.83485 | −0.397422 | ||||||||
\(149\) | 16.7477 | 1.37203 | 0.686014 | − | 0.727589i | \(-0.259359\pi\) | ||||
0.686014 | + | 0.727589i | \(0.259359\pi\) | |||||||
\(150\) | 1.79129 | 0.146258 | ||||||||
\(151\) | 7.16515 | 0.583092 | 0.291546 | − | 0.956557i | \(-0.405830\pi\) | ||||
0.291546 | + | 0.956557i | \(0.405830\pi\) | |||||||
\(152\) | −5.07803 | −0.411883 | ||||||||
\(153\) | −3.00000 | −0.242536 | ||||||||
\(154\) | 8.95644 | 0.721730 | ||||||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | −5.53901 | −0.443476 | ||||||||
\(157\) | 10.7477 | 0.857762 | 0.428881 | − | 0.903361i | \(-0.358908\pi\) | ||||
0.428881 | + | 0.903361i | \(0.358908\pi\) | |||||||
\(158\) | 13.5826 | 1.08057 | ||||||||
\(159\) | 0.417424 | 0.0331039 | ||||||||
\(160\) | −6.04356 | −0.477785 | ||||||||
\(161\) | −4.00000 | −0.315244 | ||||||||
\(162\) | 1.79129 | 0.140737 | ||||||||
\(163\) | 7.58258 | 0.593913 | 0.296957 | − | 0.954891i | \(-0.404028\pi\) | ||||
0.296957 | + | 0.954891i | \(0.404028\pi\) | |||||||
\(164\) | −11.0780 | −0.865049 | ||||||||
\(165\) | 5.00000 | 0.389249 | ||||||||
\(166\) | −20.7477 | −1.61034 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | −1.41742 | −0.109357 | ||||||||
\(169\) | 8.00000 | 0.615385 | ||||||||
\(170\) | −5.37386 | −0.412157 | ||||||||
\(171\) | 3.58258 | 0.273966 | ||||||||
\(172\) | −11.5826 | −0.883163 | ||||||||
\(173\) | −3.16515 | −0.240642 | −0.120321 | − | 0.992735i | \(-0.538392\pi\) | ||||
−0.120321 | + | 0.992735i | \(0.538392\pi\) | |||||||
\(174\) | 1.79129 | 0.135797 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −24.7822 | −1.86803 | ||||||||
\(177\) | −7.58258 | −0.569941 | ||||||||
\(178\) | 2.53901 | 0.190307 | ||||||||
\(179\) | 4.74773 | 0.354862 | 0.177431 | − | 0.984133i | \(-0.443221\pi\) | ||||
0.177431 | + | 0.984133i | \(0.443221\pi\) | |||||||
\(180\) | 1.20871 | 0.0900921 | ||||||||
\(181\) | 16.1652 | 1.20155 | 0.600773 | − | 0.799420i | \(-0.294860\pi\) | ||||
0.600773 | + | 0.799420i | \(0.294860\pi\) | |||||||
\(182\) | −8.20871 | −0.608470 | ||||||||
\(183\) | 12.7477 | 0.942339 | ||||||||
\(184\) | 5.66970 | 0.417976 | ||||||||
\(185\) | −4.00000 | −0.294086 | ||||||||
\(186\) | 7.16515 | 0.525374 | ||||||||
\(187\) | −15.0000 | −1.09691 | ||||||||
\(188\) | 12.7913 | 0.932901 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 6.41742 | 0.465569 | ||||||||
\(191\) | −4.00000 | −0.289430 | −0.144715 | − | 0.989473i | \(-0.546227\pi\) | ||||
−0.144715 | + | 0.989473i | \(0.546227\pi\) | |||||||
\(192\) | −0.912878 | −0.0658813 | ||||||||
\(193\) | −20.3303 | −1.46341 | −0.731704 | − | 0.681623i | \(-0.761274\pi\) | ||||
−0.731704 | + | 0.681623i | \(0.761274\pi\) | |||||||
\(194\) | 20.7477 | 1.48960 | ||||||||
\(195\) | −4.58258 | −0.328165 | ||||||||
\(196\) | −7.25227 | −0.518019 | ||||||||
\(197\) | −16.3303 | −1.16349 | −0.581743 | − | 0.813373i | \(-0.697629\pi\) | ||||
−0.581743 | + | 0.813373i | \(0.697629\pi\) | |||||||
\(198\) | 8.95644 | 0.636506 | ||||||||
\(199\) | 13.4174 | 0.951136 | 0.475568 | − | 0.879679i | \(-0.342243\pi\) | ||||
0.475568 | + | 0.879679i | \(0.342243\pi\) | |||||||
\(200\) | −1.41742 | −0.100227 | ||||||||
\(201\) | −4.16515 | −0.293787 | ||||||||
\(202\) | −1.04356 | −0.0734247 | ||||||||
\(203\) | 1.00000 | 0.0701862 | ||||||||
\(204\) | −3.62614 | −0.253880 | ||||||||
\(205\) | −9.16515 | −0.640122 | ||||||||
\(206\) | 27.1652 | 1.89269 | ||||||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | 22.7133 | 1.57488 | ||||||||
\(209\) | 17.9129 | 1.23906 | ||||||||
\(210\) | 1.79129 | 0.123611 | ||||||||
\(211\) | 20.3303 | 1.39960 | 0.699798 | − | 0.714341i | \(-0.253273\pi\) | ||||
0.699798 | + | 0.714341i | \(0.253273\pi\) | |||||||
\(212\) | 0.504546 | 0.0346523 | ||||||||
\(213\) | −9.58258 | −0.656587 | ||||||||
\(214\) | 9.25227 | 0.632472 | ||||||||
\(215\) | −9.58258 | −0.653526 | ||||||||
\(216\) | −1.41742 | −0.0964435 | ||||||||
\(217\) | 4.00000 | 0.271538 | ||||||||
\(218\) | 25.3739 | 1.71853 | ||||||||
\(219\) | 4.00000 | 0.270295 | ||||||||
\(220\) | 6.04356 | 0.407457 | ||||||||
\(221\) | 13.7477 | 0.924772 | ||||||||
\(222\) | −7.16515 | −0.480893 | ||||||||
\(223\) | 7.00000 | 0.468755 | 0.234377 | − | 0.972146i | \(-0.424695\pi\) | ||||
0.234377 | + | 0.972146i | \(0.424695\pi\) | |||||||
\(224\) | −6.04356 | −0.403802 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −25.3739 | −1.68784 | ||||||||
\(227\) | −7.58258 | −0.503273 | −0.251637 | − | 0.967822i | \(-0.580969\pi\) | ||||
−0.251637 | + | 0.967822i | \(0.580969\pi\) | |||||||
\(228\) | 4.33030 | 0.286781 | ||||||||
\(229\) | −17.1652 | −1.13431 | −0.567153 | − | 0.823613i | \(-0.691955\pi\) | ||||
−0.567153 | + | 0.823613i | \(0.691955\pi\) | |||||||
\(230\) | −7.16515 | −0.472456 | ||||||||
\(231\) | 5.00000 | 0.328976 | ||||||||
\(232\) | −1.41742 | −0.0930585 | ||||||||
\(233\) | −13.1652 | −0.862478 | −0.431239 | − | 0.902238i | \(-0.641923\pi\) | ||||
−0.431239 | + | 0.902238i | \(0.641923\pi\) | |||||||
\(234\) | −8.20871 | −0.536620 | ||||||||
\(235\) | 10.5826 | 0.690331 | ||||||||
\(236\) | −9.16515 | −0.596601 | ||||||||
\(237\) | 7.58258 | 0.492541 | ||||||||
\(238\) | −5.37386 | −0.348336 | ||||||||
\(239\) | −26.0000 | −1.68180 | −0.840900 | − | 0.541190i | \(-0.817974\pi\) | ||||
−0.840900 | + | 0.541190i | \(0.817974\pi\) | |||||||
\(240\) | −4.95644 | −0.319937 | ||||||||
\(241\) | 29.3303 | 1.88933 | 0.944665 | − | 0.328035i | \(-0.106387\pi\) | ||||
0.944665 | + | 0.328035i | \(0.106387\pi\) | |||||||
\(242\) | 25.0780 | 1.61208 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 15.4083 | 0.986417 | ||||||||
\(245\) | −6.00000 | −0.383326 | ||||||||
\(246\) | −16.4174 | −1.04674 | ||||||||
\(247\) | −16.4174 | −1.04462 | ||||||||
\(248\) | −5.66970 | −0.360026 | ||||||||
\(249\) | −11.5826 | −0.734016 | ||||||||
\(250\) | 1.79129 | 0.113291 | ||||||||
\(251\) | 16.1652 | 1.02034 | 0.510168 | − | 0.860075i | \(-0.329583\pi\) | ||||
0.510168 | + | 0.860075i | \(0.329583\pi\) | |||||||
\(252\) | 1.20871 | 0.0761417 | ||||||||
\(253\) | −20.0000 | −1.25739 | ||||||||
\(254\) | 3.58258 | 0.224791 | ||||||||
\(255\) | −3.00000 | −0.187867 | ||||||||
\(256\) | 20.5481 | 1.28426 | ||||||||
\(257\) | 12.7477 | 0.795181 | 0.397591 | − | 0.917563i | \(-0.369846\pi\) | ||||
0.397591 | + | 0.917563i | \(0.369846\pi\) | |||||||
\(258\) | −17.1652 | −1.06866 | ||||||||
\(259\) | −4.00000 | −0.248548 | ||||||||
\(260\) | −5.53901 | −0.343515 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | −26.8693 | −1.65999 | ||||||||
\(263\) | 30.3303 | 1.87025 | 0.935123 | − | 0.354322i | \(-0.115288\pi\) | ||||
0.935123 | + | 0.354322i | \(0.115288\pi\) | |||||||
\(264\) | −7.08712 | −0.436182 | ||||||||
\(265\) | 0.417424 | 0.0256422 | ||||||||
\(266\) | 6.41742 | 0.393478 | ||||||||
\(267\) | 1.41742 | 0.0867450 | ||||||||
\(268\) | −5.03447 | −0.307529 | ||||||||
\(269\) | 22.5826 | 1.37688 | 0.688442 | − | 0.725291i | \(-0.258295\pi\) | ||||
0.688442 | + | 0.725291i | \(0.258295\pi\) | |||||||
\(270\) | 1.79129 | 0.109014 | ||||||||
\(271\) | 1.16515 | 0.0707779 | 0.0353890 | − | 0.999374i | \(-0.488733\pi\) | ||||
0.0353890 | + | 0.999374i | \(0.488733\pi\) | |||||||
\(272\) | 14.8693 | 0.901585 | ||||||||
\(273\) | −4.58258 | −0.277350 | ||||||||
\(274\) | 29.2523 | 1.76719 | ||||||||
\(275\) | 5.00000 | 0.301511 | ||||||||
\(276\) | −4.83485 | −0.291024 | ||||||||
\(277\) | −24.9129 | −1.49687 | −0.748435 | − | 0.663208i | \(-0.769194\pi\) | ||||
−0.748435 | + | 0.663208i | \(0.769194\pi\) | |||||||
\(278\) | −16.8693 | −1.01175 | ||||||||
\(279\) | 4.00000 | 0.239474 | ||||||||
\(280\) | −1.41742 | −0.0847073 | ||||||||
\(281\) | −0.417424 | −0.0249014 | −0.0124507 | − | 0.999922i | \(-0.503963\pi\) | ||||
−0.0124507 | + | 0.999922i | \(0.503963\pi\) | |||||||
\(282\) | 18.9564 | 1.12884 | ||||||||
\(283\) | −0.834849 | −0.0496266 | −0.0248133 | − | 0.999692i | \(-0.507899\pi\) | ||||
−0.0248133 | + | 0.999692i | \(0.507899\pi\) | |||||||
\(284\) | −11.5826 | −0.687299 | ||||||||
\(285\) | 3.58258 | 0.212213 | ||||||||
\(286\) | −41.0436 | −2.42696 | ||||||||
\(287\) | −9.16515 | −0.541002 | ||||||||
\(288\) | −6.04356 | −0.356120 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 1.79129 | 0.105188 | ||||||||
\(291\) | 11.5826 | 0.678983 | ||||||||
\(292\) | 4.83485 | 0.282938 | ||||||||
\(293\) | 30.1652 | 1.76227 | 0.881133 | − | 0.472868i | \(-0.156781\pi\) | ||||
0.881133 | + | 0.472868i | \(0.156781\pi\) | |||||||
\(294\) | −10.7477 | −0.626820 | ||||||||
\(295\) | −7.58258 | −0.441475 | ||||||||
\(296\) | 5.66970 | 0.329544 | ||||||||
\(297\) | 5.00000 | 0.290129 | ||||||||
\(298\) | 30.0000 | 1.73785 | ||||||||
\(299\) | 18.3303 | 1.06007 | ||||||||
\(300\) | 1.20871 | 0.0697850 | ||||||||
\(301\) | −9.58258 | −0.552330 | ||||||||
\(302\) | 12.8348 | 0.738563 | ||||||||
\(303\) | −0.582576 | −0.0334681 | ||||||||
\(304\) | −17.7568 | −1.01842 | ||||||||
\(305\) | 12.7477 | 0.729933 | ||||||||
\(306\) | −5.37386 | −0.307203 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | 6.04356 | 0.344364 | ||||||||
\(309\) | 15.1652 | 0.862715 | ||||||||
\(310\) | 7.16515 | 0.406953 | ||||||||
\(311\) | −3.00000 | −0.170114 | −0.0850572 | − | 0.996376i | \(-0.527107\pi\) | ||||
−0.0850572 | + | 0.996376i | \(0.527107\pi\) | |||||||
\(312\) | 6.49545 | 0.367733 | ||||||||
\(313\) | 10.5826 | 0.598163 | 0.299081 | − | 0.954228i | \(-0.403320\pi\) | ||||
0.299081 | + | 0.954228i | \(0.403320\pi\) | |||||||
\(314\) | 19.2523 | 1.08647 | ||||||||
\(315\) | 1.00000 | 0.0563436 | ||||||||
\(316\) | 9.16515 | 0.515580 | ||||||||
\(317\) | −25.0000 | −1.40414 | −0.702070 | − | 0.712108i | \(-0.747741\pi\) | ||||
−0.702070 | + | 0.712108i | \(0.747741\pi\) | |||||||
\(318\) | 0.747727 | 0.0419305 | ||||||||
\(319\) | 5.00000 | 0.279946 | ||||||||
\(320\) | −0.912878 | −0.0510315 | ||||||||
\(321\) | 5.16515 | 0.288291 | ||||||||
\(322\) | −7.16515 | −0.399298 | ||||||||
\(323\) | −10.7477 | −0.598020 | ||||||||
\(324\) | 1.20871 | 0.0671507 | ||||||||
\(325\) | −4.58258 | −0.254196 | ||||||||
\(326\) | 13.5826 | 0.752269 | ||||||||
\(327\) | 14.1652 | 0.783335 | ||||||||
\(328\) | 12.9909 | 0.717303 | ||||||||
\(329\) | 10.5826 | 0.583436 | ||||||||
\(330\) | 8.95644 | 0.493036 | ||||||||
\(331\) | −8.33030 | −0.457875 | −0.228937 | − | 0.973441i | \(-0.573525\pi\) | ||||
−0.228937 | + | 0.973441i | \(0.573525\pi\) | |||||||
\(332\) | −14.0000 | −0.768350 | ||||||||
\(333\) | −4.00000 | −0.219199 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.16515 | −0.227567 | ||||||||
\(336\) | −4.95644 | −0.270396 | ||||||||
\(337\) | −21.1652 | −1.15294 | −0.576470 | − | 0.817119i | \(-0.695570\pi\) | ||||
−0.576470 | + | 0.817119i | \(0.695570\pi\) | |||||||
\(338\) | 14.3303 | 0.779466 | ||||||||
\(339\) | −14.1652 | −0.769345 | ||||||||
\(340\) | −3.62614 | −0.196655 | ||||||||
\(341\) | 20.0000 | 1.08306 | ||||||||
\(342\) | 6.41742 | 0.347015 | ||||||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | 13.5826 | 0.732323 | ||||||||
\(345\) | −4.00000 | −0.215353 | ||||||||
\(346\) | −5.66970 | −0.304805 | ||||||||
\(347\) | 7.16515 | 0.384645 | 0.192323 | − | 0.981332i | \(-0.438398\pi\) | ||||
0.192323 | + | 0.981332i | \(0.438398\pi\) | |||||||
\(348\) | 1.20871 | 0.0647938 | ||||||||
\(349\) | −4.33030 | −0.231796 | −0.115898 | − | 0.993261i | \(-0.536975\pi\) | ||||
−0.115898 | + | 0.993261i | \(0.536975\pi\) | |||||||
\(350\) | 1.79129 | 0.0957484 | ||||||||
\(351\) | −4.58258 | −0.244600 | ||||||||
\(352\) | −30.2178 | −1.61061 | ||||||||
\(353\) | −14.8348 | −0.789579 | −0.394790 | − | 0.918772i | \(-0.629183\pi\) | ||||
−0.394790 | + | 0.918772i | \(0.629183\pi\) | |||||||
\(354\) | −13.5826 | −0.721906 | ||||||||
\(355\) | −9.58258 | −0.508590 | ||||||||
\(356\) | 1.71326 | 0.0908025 | ||||||||
\(357\) | −3.00000 | −0.158777 | ||||||||
\(358\) | 8.50455 | 0.449479 | ||||||||
\(359\) | −27.1652 | −1.43372 | −0.716861 | − | 0.697216i | \(-0.754422\pi\) | ||||
−0.716861 | + | 0.697216i | \(0.754422\pi\) | |||||||
\(360\) | −1.41742 | −0.0747048 | ||||||||
\(361\) | −6.16515 | −0.324482 | ||||||||
\(362\) | 28.9564 | 1.52192 | ||||||||
\(363\) | 14.0000 | 0.734809 | ||||||||
\(364\) | −5.53901 | −0.290323 | ||||||||
\(365\) | 4.00000 | 0.209370 | ||||||||
\(366\) | 22.8348 | 1.19360 | ||||||||
\(367\) | −37.4955 | −1.95725 | −0.978623 | − | 0.205661i | \(-0.934066\pi\) | ||||
−0.978623 | + | 0.205661i | \(0.934066\pi\) | |||||||
\(368\) | 19.8258 | 1.03349 | ||||||||
\(369\) | −9.16515 | −0.477119 | ||||||||
\(370\) | −7.16515 | −0.372498 | ||||||||
\(371\) | 0.417424 | 0.0216716 | ||||||||
\(372\) | 4.83485 | 0.250675 | ||||||||
\(373\) | 28.3303 | 1.46689 | 0.733444 | − | 0.679750i | \(-0.237912\pi\) | ||||
0.733444 | + | 0.679750i | \(0.237912\pi\) | |||||||
\(374\) | −26.8693 | −1.38938 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −15.0000 | −0.773566 | ||||||||
\(377\) | −4.58258 | −0.236015 | ||||||||
\(378\) | 1.79129 | 0.0921339 | ||||||||
\(379\) | −26.0000 | −1.33553 | −0.667765 | − | 0.744372i | \(-0.732749\pi\) | ||||
−0.667765 | + | 0.744372i | \(0.732749\pi\) | |||||||
\(380\) | 4.33030 | 0.222140 | ||||||||
\(381\) | 2.00000 | 0.102463 | ||||||||
\(382\) | −7.16515 | −0.366601 | ||||||||
\(383\) | 3.58258 | 0.183061 | 0.0915305 | − | 0.995802i | \(-0.470824\pi\) | ||||
0.0915305 | + | 0.995802i | \(0.470824\pi\) | |||||||
\(384\) | 10.4519 | 0.533371 | ||||||||
\(385\) | 5.00000 | 0.254824 | ||||||||
\(386\) | −36.4174 | −1.85360 | ||||||||
\(387\) | −9.58258 | −0.487110 | ||||||||
\(388\) | 14.0000 | 0.710742 | ||||||||
\(389\) | −6.58258 | −0.333750 | −0.166875 | − | 0.985978i | \(-0.553368\pi\) | ||||
−0.166875 | + | 0.985978i | \(0.553368\pi\) | |||||||
\(390\) | −8.20871 | −0.415664 | ||||||||
\(391\) | 12.0000 | 0.606866 | ||||||||
\(392\) | 8.50455 | 0.429544 | ||||||||
\(393\) | −15.0000 | −0.756650 | ||||||||
\(394\) | −29.2523 | −1.47371 | ||||||||
\(395\) | 7.58258 | 0.381521 | ||||||||
\(396\) | 6.04356 | 0.303700 | ||||||||
\(397\) | 10.8348 | 0.543785 | 0.271893 | − | 0.962328i | \(-0.412350\pi\) | ||||
0.271893 | + | 0.962328i | \(0.412350\pi\) | |||||||
\(398\) | 24.0345 | 1.20474 | ||||||||
\(399\) | 3.58258 | 0.179353 | ||||||||
\(400\) | −4.95644 | −0.247822 | ||||||||
\(401\) | 12.4174 | 0.620097 | 0.310048 | − | 0.950721i | \(-0.399655\pi\) | ||||
0.310048 | + | 0.950721i | \(0.399655\pi\) | |||||||
\(402\) | −7.46099 | −0.372120 | ||||||||
\(403\) | −18.3303 | −0.913097 | ||||||||
\(404\) | −0.704166 | −0.0350336 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 1.79129 | 0.0889001 | ||||||||
\(407\) | −20.0000 | −0.991363 | ||||||||
\(408\) | 4.25227 | 0.210519 | ||||||||
\(409\) | −2.74773 | −0.135866 | −0.0679332 | − | 0.997690i | \(-0.521640\pi\) | ||||
−0.0679332 | + | 0.997690i | \(0.521640\pi\) | |||||||
\(410\) | −16.4174 | −0.810799 | ||||||||
\(411\) | 16.3303 | 0.805514 | ||||||||
\(412\) | 18.3303 | 0.903069 | ||||||||
\(413\) | −7.58258 | −0.373114 | ||||||||
\(414\) | −7.16515 | −0.352148 | ||||||||
\(415\) | −11.5826 | −0.568566 | ||||||||
\(416\) | 27.6951 | 1.35786 | ||||||||
\(417\) | −9.41742 | −0.461173 | ||||||||
\(418\) | 32.0871 | 1.56943 | ||||||||
\(419\) | −37.1652 | −1.81564 | −0.907818 | − | 0.419364i | \(-0.862253\pi\) | ||||
−0.907818 | + | 0.419364i | \(0.862253\pi\) | |||||||
\(420\) | 1.20871 | 0.0589791 | ||||||||
\(421\) | 4.41742 | 0.215292 | 0.107646 | − | 0.994189i | \(-0.465669\pi\) | ||||
0.107646 | + | 0.994189i | \(0.465669\pi\) | |||||||
\(422\) | 36.4174 | 1.77277 | ||||||||
\(423\) | 10.5826 | 0.514542 | ||||||||
\(424\) | −0.591667 | −0.0287339 | ||||||||
\(425\) | −3.00000 | −0.145521 | ||||||||
\(426\) | −17.1652 | −0.831654 | ||||||||
\(427\) | 12.7477 | 0.616906 | ||||||||
\(428\) | 6.24318 | 0.301776 | ||||||||
\(429\) | −22.9129 | −1.10624 | ||||||||
\(430\) | −17.1652 | −0.827777 | ||||||||
\(431\) | −39.1652 | −1.88652 | −0.943259 | − | 0.332057i | \(-0.892258\pi\) | ||||
−0.943259 | + | 0.332057i | \(0.892258\pi\) | |||||||
\(432\) | −4.95644 | −0.238467 | ||||||||
\(433\) | 25.0780 | 1.20517 | 0.602587 | − | 0.798053i | \(-0.294137\pi\) | ||||
0.602587 | + | 0.798053i | \(0.294137\pi\) | |||||||
\(434\) | 7.16515 | 0.343938 | ||||||||
\(435\) | 1.00000 | 0.0479463 | ||||||||
\(436\) | 17.1216 | 0.819975 | ||||||||
\(437\) | −14.3303 | −0.685511 | ||||||||
\(438\) | 7.16515 | 0.342364 | ||||||||
\(439\) | −16.9129 | −0.807208 | −0.403604 | − | 0.914934i | \(-0.632243\pi\) | ||||
−0.403604 | + | 0.914934i | \(0.632243\pi\) | |||||||
\(440\) | −7.08712 | −0.337865 | ||||||||
\(441\) | −6.00000 | −0.285714 | ||||||||
\(442\) | 24.6261 | 1.17135 | ||||||||
\(443\) | 0.582576 | 0.0276790 | 0.0138395 | − | 0.999904i | \(-0.495595\pi\) | ||||
0.0138395 | + | 0.999904i | \(0.495595\pi\) | |||||||
\(444\) | −4.83485 | −0.229452 | ||||||||
\(445\) | 1.41742 | 0.0671924 | ||||||||
\(446\) | 12.5390 | 0.593740 | ||||||||
\(447\) | 16.7477 | 0.792140 | ||||||||
\(448\) | −0.912878 | −0.0431295 | ||||||||
\(449\) | −30.0780 | −1.41947 | −0.709735 | − | 0.704469i | \(-0.751185\pi\) | ||||
−0.709735 | + | 0.704469i | \(0.751185\pi\) | |||||||
\(450\) | 1.79129 | 0.0844421 | ||||||||
\(451\) | −45.8258 | −2.15785 | ||||||||
\(452\) | −17.1216 | −0.805332 | ||||||||
\(453\) | 7.16515 | 0.336648 | ||||||||
\(454\) | −13.5826 | −0.637462 | ||||||||
\(455\) | −4.58258 | −0.214834 | ||||||||
\(456\) | −5.07803 | −0.237801 | ||||||||
\(457\) | −3.74773 | −0.175311 | −0.0876556 | − | 0.996151i | \(-0.527938\pi\) | ||||
−0.0876556 | + | 0.996151i | \(0.527938\pi\) | |||||||
\(458\) | −30.7477 | −1.43675 | ||||||||
\(459\) | −3.00000 | −0.140028 | ||||||||
\(460\) | −4.83485 | −0.225426 | ||||||||
\(461\) | −9.16515 | −0.426864 | −0.213432 | − | 0.976958i | \(-0.568464\pi\) | ||||
−0.213432 | + | 0.976958i | \(0.568464\pi\) | |||||||
\(462\) | 8.95644 | 0.416691 | ||||||||
\(463\) | −0.165151 | −0.00767524 | −0.00383762 | − | 0.999993i | \(-0.501222\pi\) | ||||
−0.00383762 | + | 0.999993i | \(0.501222\pi\) | |||||||
\(464\) | −4.95644 | −0.230097 | ||||||||
\(465\) | 4.00000 | 0.185496 | ||||||||
\(466\) | −23.5826 | −1.09244 | ||||||||
\(467\) | −8.00000 | −0.370196 | −0.185098 | − | 0.982720i | \(-0.559260\pi\) | ||||
−0.185098 | + | 0.982720i | \(0.559260\pi\) | |||||||
\(468\) | −5.53901 | −0.256041 | ||||||||
\(469\) | −4.16515 | −0.192329 | ||||||||
\(470\) | 18.9564 | 0.874395 | ||||||||
\(471\) | 10.7477 | 0.495229 | ||||||||
\(472\) | 10.7477 | 0.494704 | ||||||||
\(473\) | −47.9129 | −2.20304 | ||||||||
\(474\) | 13.5826 | 0.623868 | ||||||||
\(475\) | 3.58258 | 0.164380 | ||||||||
\(476\) | −3.62614 | −0.166204 | ||||||||
\(477\) | 0.417424 | 0.0191125 | ||||||||
\(478\) | −46.5735 | −2.13022 | ||||||||
\(479\) | −19.1652 | −0.875678 | −0.437839 | − | 0.899053i | \(-0.644256\pi\) | ||||
−0.437839 | + | 0.899053i | \(0.644256\pi\) | |||||||
\(480\) | −6.04356 | −0.275850 | ||||||||
\(481\) | 18.3303 | 0.835790 | ||||||||
\(482\) | 52.5390 | 2.39309 | ||||||||
\(483\) | −4.00000 | −0.182006 | ||||||||
\(484\) | 16.9220 | 0.769180 | ||||||||
\(485\) | 11.5826 | 0.525938 | ||||||||
\(486\) | 1.79129 | 0.0812545 | ||||||||
\(487\) | 2.33030 | 0.105596 | 0.0527980 | − | 0.998605i | \(-0.483186\pi\) | ||||
0.0527980 | + | 0.998605i | \(0.483186\pi\) | |||||||
\(488\) | −18.0689 | −0.817942 | ||||||||
\(489\) | 7.58258 | 0.342896 | ||||||||
\(490\) | −10.7477 | −0.485533 | ||||||||
\(491\) | 16.0000 | 0.722070 | 0.361035 | − | 0.932552i | \(-0.382424\pi\) | ||||
0.361035 | + | 0.932552i | \(0.382424\pi\) | |||||||
\(492\) | −11.0780 | −0.499436 | ||||||||
\(493\) | −3.00000 | −0.135113 | ||||||||
\(494\) | −29.4083 | −1.32314 | ||||||||
\(495\) | 5.00000 | 0.224733 | ||||||||
\(496\) | −19.8258 | −0.890203 | ||||||||
\(497\) | −9.58258 | −0.429837 | ||||||||
\(498\) | −20.7477 | −0.929728 | ||||||||
\(499\) | −13.4174 | −0.600646 | −0.300323 | − | 0.953837i | \(-0.597095\pi\) | ||||
−0.300323 | + | 0.953837i | \(0.597095\pi\) | |||||||
\(500\) | 1.20871 | 0.0540553 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 28.9564 | 1.29239 | ||||||||
\(503\) | −22.9129 | −1.02163 | −0.510817 | − | 0.859689i | \(-0.670657\pi\) | ||||
−0.510817 | + | 0.859689i | \(0.670657\pi\) | |||||||
\(504\) | −1.41742 | −0.0631371 | ||||||||
\(505\) | −0.582576 | −0.0259243 | ||||||||
\(506\) | −35.8258 | −1.59265 | ||||||||
\(507\) | 8.00000 | 0.355292 | ||||||||
\(508\) | 2.41742 | 0.107256 | ||||||||
\(509\) | 26.7477 | 1.18557 | 0.592786 | − | 0.805360i | \(-0.298028\pi\) | ||||
0.592786 | + | 0.805360i | \(0.298028\pi\) | |||||||
\(510\) | −5.37386 | −0.237959 | ||||||||
\(511\) | 4.00000 | 0.176950 | ||||||||
\(512\) | 15.9038 | 0.702855 | ||||||||
\(513\) | 3.58258 | 0.158175 | ||||||||
\(514\) | 22.8348 | 1.00720 | ||||||||
\(515\) | 15.1652 | 0.668256 | ||||||||
\(516\) | −11.5826 | −0.509894 | ||||||||
\(517\) | 52.9129 | 2.32711 | ||||||||
\(518\) | −7.16515 | −0.314819 | ||||||||
\(519\) | −3.16515 | −0.138935 | ||||||||
\(520\) | 6.49545 | 0.284845 | ||||||||
\(521\) | 43.0780 | 1.88728 | 0.943641 | − | 0.330970i | \(-0.107376\pi\) | ||||
0.943641 | + | 0.330970i | \(0.107376\pi\) | |||||||
\(522\) | 1.79129 | 0.0784025 | ||||||||
\(523\) | −33.3303 | −1.45743 | −0.728716 | − | 0.684816i | \(-0.759883\pi\) | ||||
−0.728716 | + | 0.684816i | \(0.759883\pi\) | |||||||
\(524\) | −18.1307 | −0.792043 | ||||||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | 54.3303 | 2.36891 | ||||||||
\(527\) | −12.0000 | −0.522728 | ||||||||
\(528\) | −24.7822 | −1.07851 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0.747727 | 0.0324792 | ||||||||
\(531\) | −7.58258 | −0.329056 | ||||||||
\(532\) | 4.33030 | 0.187742 | ||||||||
\(533\) | 42.0000 | 1.81922 | ||||||||
\(534\) | 2.53901 | 0.109874 | ||||||||
\(535\) | 5.16515 | 0.223309 | ||||||||
\(536\) | 5.90379 | 0.255005 | ||||||||
\(537\) | 4.74773 | 0.204880 | ||||||||
\(538\) | 40.4519 | 1.74400 | ||||||||
\(539\) | −30.0000 | −1.29219 | ||||||||
\(540\) | 1.20871 | 0.0520147 | ||||||||
\(541\) | −31.4955 | −1.35410 | −0.677048 | − | 0.735939i | \(-0.736741\pi\) | ||||
−0.677048 | + | 0.735939i | \(0.736741\pi\) | |||||||
\(542\) | 2.08712 | 0.0896495 | ||||||||
\(543\) | 16.1652 | 0.693713 | ||||||||
\(544\) | 18.1307 | 0.777347 | ||||||||
\(545\) | 14.1652 | 0.606768 | ||||||||
\(546\) | −8.20871 | −0.351300 | ||||||||
\(547\) | 4.16515 | 0.178089 | 0.0890445 | − | 0.996028i | \(-0.471619\pi\) | ||||
0.0890445 | + | 0.996028i | \(0.471619\pi\) | |||||||
\(548\) | 19.7386 | 0.843193 | ||||||||
\(549\) | 12.7477 | 0.544060 | ||||||||
\(550\) | 8.95644 | 0.381904 | ||||||||
\(551\) | 3.58258 | 0.152623 | ||||||||
\(552\) | 5.66970 | 0.241318 | ||||||||
\(553\) | 7.58258 | 0.322444 | ||||||||
\(554\) | −44.6261 | −1.89598 | ||||||||
\(555\) | −4.00000 | −0.169791 | ||||||||
\(556\) | −11.3830 | −0.482745 | ||||||||
\(557\) | −22.7477 | −0.963852 | −0.481926 | − | 0.876212i | \(-0.660063\pi\) | ||||
−0.481926 | + | 0.876212i | \(0.660063\pi\) | |||||||
\(558\) | 7.16515 | 0.303325 | ||||||||
\(559\) | 43.9129 | 1.85732 | ||||||||
\(560\) | −4.95644 | −0.209448 | ||||||||
\(561\) | −15.0000 | −0.633300 | ||||||||
\(562\) | −0.747727 | −0.0315410 | ||||||||
\(563\) | −14.5826 | −0.614582 | −0.307291 | − | 0.951616i | \(-0.599423\pi\) | ||||
−0.307291 | + | 0.951616i | \(0.599423\pi\) | |||||||
\(564\) | 12.7913 | 0.538610 | ||||||||
\(565\) | −14.1652 | −0.595932 | ||||||||
\(566\) | −1.49545 | −0.0628586 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 13.5826 | 0.569912 | ||||||||
\(569\) | 28.5826 | 1.19824 | 0.599122 | − | 0.800658i | \(-0.295516\pi\) | ||||
0.599122 | + | 0.800658i | \(0.295516\pi\) | |||||||
\(570\) | 6.41742 | 0.268796 | ||||||||
\(571\) | 12.0000 | 0.502184 | 0.251092 | − | 0.967963i | \(-0.419210\pi\) | ||||
0.251092 | + | 0.967963i | \(0.419210\pi\) | |||||||
\(572\) | −27.6951 | −1.15799 | ||||||||
\(573\) | −4.00000 | −0.167102 | ||||||||
\(574\) | −16.4174 | −0.685250 | ||||||||
\(575\) | −4.00000 | −0.166812 | ||||||||
\(576\) | −0.912878 | −0.0380366 | ||||||||
\(577\) | −19.1652 | −0.797856 | −0.398928 | − | 0.916982i | \(-0.630618\pi\) | ||||
−0.398928 | + | 0.916982i | \(0.630618\pi\) | |||||||
\(578\) | −14.3303 | −0.596062 | ||||||||
\(579\) | −20.3303 | −0.844899 | ||||||||
\(580\) | 1.20871 | 0.0501890 | ||||||||
\(581\) | −11.5826 | −0.480526 | ||||||||
\(582\) | 20.7477 | 0.860021 | ||||||||
\(583\) | 2.08712 | 0.0864397 | ||||||||
\(584\) | −5.66970 | −0.234614 | ||||||||
\(585\) | −4.58258 | −0.189466 | ||||||||
\(586\) | 54.0345 | 2.23214 | ||||||||
\(587\) | −11.5826 | −0.478064 | −0.239032 | − | 0.971012i | \(-0.576830\pi\) | ||||
−0.239032 | + | 0.971012i | \(0.576830\pi\) | |||||||
\(588\) | −7.25227 | −0.299079 | ||||||||
\(589\) | 14.3303 | 0.590470 | ||||||||
\(590\) | −13.5826 | −0.559186 | ||||||||
\(591\) | −16.3303 | −0.671739 | ||||||||
\(592\) | 19.8258 | 0.814834 | ||||||||
\(593\) | 8.41742 | 0.345662 | 0.172831 | − | 0.984951i | \(-0.444709\pi\) | ||||
0.172831 | + | 0.984951i | \(0.444709\pi\) | |||||||
\(594\) | 8.95644 | 0.367487 | ||||||||
\(595\) | −3.00000 | −0.122988 | ||||||||
\(596\) | 20.2432 | 0.829193 | ||||||||
\(597\) | 13.4174 | 0.549139 | ||||||||
\(598\) | 32.8348 | 1.34272 | ||||||||
\(599\) | 0.165151 | 0.00674790 | 0.00337395 | − | 0.999994i | \(-0.498926\pi\) | ||||
0.00337395 | + | 0.999994i | \(0.498926\pi\) | |||||||
\(600\) | −1.41742 | −0.0578661 | ||||||||
\(601\) | −32.3303 | −1.31878 | −0.659390 | − | 0.751801i | \(-0.729185\pi\) | ||||
−0.659390 | + | 0.751801i | \(0.729185\pi\) | |||||||
\(602\) | −17.1652 | −0.699599 | ||||||||
\(603\) | −4.16515 | −0.169618 | ||||||||
\(604\) | 8.66061 | 0.352395 | ||||||||
\(605\) | 14.0000 | 0.569181 | ||||||||
\(606\) | −1.04356 | −0.0423918 | ||||||||
\(607\) | 3.58258 | 0.145412 | 0.0727061 | − | 0.997353i | \(-0.476836\pi\) | ||||
0.0727061 | + | 0.997353i | \(0.476836\pi\) | |||||||
\(608\) | −21.6515 | −0.878085 | ||||||||
\(609\) | 1.00000 | 0.0405220 | ||||||||
\(610\) | 22.8348 | 0.924556 | ||||||||
\(611\) | −48.4955 | −1.96192 | ||||||||
\(612\) | −3.62614 | −0.146578 | ||||||||
\(613\) | −43.7477 | −1.76695 | −0.883477 | − | 0.468474i | \(-0.844804\pi\) | ||||
−0.883477 | + | 0.468474i | \(0.844804\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.16515 | −0.369575 | ||||||||
\(616\) | −7.08712 | −0.285548 | ||||||||
\(617\) | 15.4955 | 0.623823 | 0.311912 | − | 0.950111i | \(-0.399031\pi\) | ||||
0.311912 | + | 0.950111i | \(0.399031\pi\) | |||||||
\(618\) | 27.1652 | 1.09274 | ||||||||
\(619\) | 13.1652 | 0.529152 | 0.264576 | − | 0.964365i | \(-0.414768\pi\) | ||||
0.264576 | + | 0.964365i | \(0.414768\pi\) | |||||||
\(620\) | 4.83485 | 0.194172 | ||||||||
\(621\) | −4.00000 | −0.160514 | ||||||||
\(622\) | −5.37386 | −0.215472 | ||||||||
\(623\) | 1.41742 | 0.0567879 | ||||||||
\(624\) | 22.7133 | 0.909258 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 18.9564 | 0.757652 | ||||||||
\(627\) | 17.9129 | 0.715371 | ||||||||
\(628\) | 12.9909 | 0.518394 | ||||||||
\(629\) | 12.0000 | 0.478471 | ||||||||
\(630\) | 1.79129 | 0.0713666 | ||||||||
\(631\) | 10.9129 | 0.434435 | 0.217217 | − | 0.976123i | \(-0.430302\pi\) | ||||
0.217217 | + | 0.976123i | \(0.430302\pi\) | |||||||
\(632\) | −10.7477 | −0.427522 | ||||||||
\(633\) | 20.3303 | 0.808057 | ||||||||
\(634\) | −44.7822 | −1.77853 | ||||||||
\(635\) | 2.00000 | 0.0793676 | ||||||||
\(636\) | 0.504546 | 0.0200065 | ||||||||
\(637\) | 27.4955 | 1.08941 | ||||||||
\(638\) | 8.95644 | 0.354589 | ||||||||
\(639\) | −9.58258 | −0.379081 | ||||||||
\(640\) | 10.4519 | 0.413147 | ||||||||
\(641\) | −6.58258 | −0.259996 | −0.129998 | − | 0.991514i | \(-0.541497\pi\) | ||||
−0.129998 | + | 0.991514i | \(0.541497\pi\) | |||||||
\(642\) | 9.25227 | 0.365158 | ||||||||
\(643\) | 43.6606 | 1.72181 | 0.860903 | − | 0.508769i | \(-0.169899\pi\) | ||||
0.860903 | + | 0.508769i | \(0.169899\pi\) | |||||||
\(644\) | −4.83485 | −0.190520 | ||||||||
\(645\) | −9.58258 | −0.377314 | ||||||||
\(646\) | −19.2523 | −0.757471 | ||||||||
\(647\) | 24.7477 | 0.972934 | 0.486467 | − | 0.873699i | \(-0.338285\pi\) | ||||
0.486467 | + | 0.873699i | \(0.338285\pi\) | |||||||
\(648\) | −1.41742 | −0.0556817 | ||||||||
\(649\) | −37.9129 | −1.48821 | ||||||||
\(650\) | −8.20871 | −0.321972 | ||||||||
\(651\) | 4.00000 | 0.156772 | ||||||||
\(652\) | 9.16515 | 0.358935 | ||||||||
\(653\) | 26.1652 | 1.02392 | 0.511961 | − | 0.859009i | \(-0.328919\pi\) | ||||
0.511961 | + | 0.859009i | \(0.328919\pi\) | |||||||
\(654\) | 25.3739 | 0.992197 | ||||||||
\(655\) | −15.0000 | −0.586098 | ||||||||
\(656\) | 45.4265 | 1.77361 | ||||||||
\(657\) | 4.00000 | 0.156055 | ||||||||
\(658\) | 18.9564 | 0.738999 | ||||||||
\(659\) | 18.1652 | 0.707614 | 0.353807 | − | 0.935318i | \(-0.384887\pi\) | ||||
0.353807 | + | 0.935318i | \(0.384887\pi\) | |||||||
\(660\) | 6.04356 | 0.235245 | ||||||||
\(661\) | 25.0000 | 0.972387 | 0.486194 | − | 0.873851i | \(-0.338385\pi\) | ||||
0.486194 | + | 0.873851i | \(0.338385\pi\) | |||||||
\(662\) | −14.9220 | −0.579959 | ||||||||
\(663\) | 13.7477 | 0.533917 | ||||||||
\(664\) | 16.4174 | 0.637120 | ||||||||
\(665\) | 3.58258 | 0.138926 | ||||||||
\(666\) | −7.16515 | −0.277644 | ||||||||
\(667\) | −4.00000 | −0.154881 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.00000 | 0.270636 | ||||||||
\(670\) | −7.46099 | −0.288243 | ||||||||
\(671\) | 63.7386 | 2.46060 | ||||||||
\(672\) | −6.04356 | −0.233135 | ||||||||
\(673\) | 1.74773 | 0.0673699 | 0.0336850 | − | 0.999433i | \(-0.489276\pi\) | ||||
0.0336850 | + | 0.999433i | \(0.489276\pi\) | |||||||
\(674\) | −37.9129 | −1.46035 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 9.66970 | 0.371911 | ||||||||
\(677\) | 44.8258 | 1.72279 | 0.861397 | − | 0.507932i | \(-0.169590\pi\) | ||||
0.861397 | + | 0.507932i | \(0.169590\pi\) | |||||||
\(678\) | −25.3739 | −0.974477 | ||||||||
\(679\) | 11.5826 | 0.444498 | ||||||||
\(680\) | 4.25227 | 0.163067 | ||||||||
\(681\) | −7.58258 | −0.290565 | ||||||||
\(682\) | 35.8258 | 1.37184 | ||||||||
\(683\) | 7.16515 | 0.274167 | 0.137083 | − | 0.990560i | \(-0.456227\pi\) | ||||
0.137083 | + | 0.990560i | \(0.456227\pi\) | |||||||
\(684\) | 4.33030 | 0.165573 | ||||||||
\(685\) | 16.3303 | 0.623949 | ||||||||
\(686\) | −23.2867 | −0.889092 | ||||||||
\(687\) | −17.1652 | −0.654891 | ||||||||
\(688\) | 47.4955 | 1.81075 | ||||||||
\(689\) | −1.91288 | −0.0728749 | ||||||||
\(690\) | −7.16515 | −0.272773 | ||||||||
\(691\) | 42.9129 | 1.63248 | 0.816241 | − | 0.577711i | \(-0.196054\pi\) | ||||
0.816241 | + | 0.577711i | \(0.196054\pi\) | |||||||
\(692\) | −3.82576 | −0.145433 | ||||||||
\(693\) | 5.00000 | 0.189934 | ||||||||
\(694\) | 12.8348 | 0.487204 | ||||||||
\(695\) | −9.41742 | −0.357223 | ||||||||
\(696\) | −1.41742 | −0.0537273 | ||||||||
\(697\) | 27.4955 | 1.04146 | ||||||||
\(698\) | −7.75682 | −0.293600 | ||||||||
\(699\) | −13.1652 | −0.497952 | ||||||||
\(700\) | 1.20871 | 0.0456850 | ||||||||
\(701\) | −23.0780 | −0.871645 | −0.435823 | − | 0.900033i | \(-0.643542\pi\) | ||||
−0.435823 | + | 0.900033i | \(0.643542\pi\) | |||||||
\(702\) | −8.20871 | −0.309818 | ||||||||
\(703\) | −14.3303 | −0.540478 | ||||||||
\(704\) | −4.56439 | −0.172027 | ||||||||
\(705\) | 10.5826 | 0.398563 | ||||||||
\(706\) | −26.5735 | −1.00011 | ||||||||
\(707\) | −0.582576 | −0.0219100 | ||||||||
\(708\) | −9.16515 | −0.344447 | ||||||||
\(709\) | 10.0000 | 0.375558 | 0.187779 | − | 0.982211i | \(-0.439871\pi\) | ||||
0.187779 | + | 0.982211i | \(0.439871\pi\) | |||||||
\(710\) | −17.1652 | −0.644197 | ||||||||
\(711\) | 7.58258 | 0.284369 | ||||||||
\(712\) | −2.00909 | −0.0752939 | ||||||||
\(713\) | −16.0000 | −0.599205 | ||||||||
\(714\) | −5.37386 | −0.201112 | ||||||||
\(715\) | −22.9129 | −0.856893 | ||||||||
\(716\) | 5.73864 | 0.214463 | ||||||||
\(717\) | −26.0000 | −0.970988 | ||||||||
\(718\) | −48.6606 | −1.81600 | ||||||||
\(719\) | 7.91288 | 0.295101 | 0.147550 | − | 0.989055i | \(-0.452861\pi\) | ||||
0.147550 | + | 0.989055i | \(0.452861\pi\) | |||||||
\(720\) | −4.95644 | −0.184716 | ||||||||
\(721\) | 15.1652 | 0.564780 | ||||||||
\(722\) | −11.0436 | −0.410999 | ||||||||
\(723\) | 29.3303 | 1.09081 | ||||||||
\(724\) | 19.5390 | 0.726162 | ||||||||
\(725\) | 1.00000 | 0.0371391 | ||||||||
\(726\) | 25.0780 | 0.930733 | ||||||||
\(727\) | 9.66970 | 0.358629 | 0.179315 | − | 0.983792i | \(-0.442612\pi\) | ||||
0.179315 | + | 0.983792i | \(0.442612\pi\) | |||||||
\(728\) | 6.49545 | 0.240738 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 7.16515 | 0.265194 | ||||||||
\(731\) | 28.7477 | 1.06327 | ||||||||
\(732\) | 15.4083 | 0.569508 | ||||||||
\(733\) | −38.4174 | −1.41898 | −0.709490 | − | 0.704716i | \(-0.751075\pi\) | ||||
−0.709490 | + | 0.704716i | \(0.751075\pi\) | |||||||
\(734\) | −67.1652 | −2.47911 | ||||||||
\(735\) | −6.00000 | −0.221313 | ||||||||
\(736\) | 24.1742 | 0.891074 | ||||||||
\(737\) | −20.8258 | −0.767127 | ||||||||
\(738\) | −16.4174 | −0.604334 | ||||||||
\(739\) | 19.2523 | 0.708206 | 0.354103 | − | 0.935206i | \(-0.384786\pi\) | ||||
0.354103 | + | 0.935206i | \(0.384786\pi\) | |||||||
\(740\) | −4.83485 | −0.177733 | ||||||||
\(741\) | −16.4174 | −0.603109 | ||||||||
\(742\) | 0.747727 | 0.0274499 | ||||||||
\(743\) | 29.7477 | 1.09134 | 0.545669 | − | 0.838001i | \(-0.316276\pi\) | ||||
0.545669 | + | 0.838001i | \(0.316276\pi\) | |||||||
\(744\) | −5.66970 | −0.207861 | ||||||||
\(745\) | 16.7477 | 0.613589 | ||||||||
\(746\) | 50.7477 | 1.85801 | ||||||||
\(747\) | −11.5826 | −0.423784 | ||||||||
\(748\) | −18.1307 | −0.662923 | ||||||||
\(749\) | 5.16515 | 0.188731 | ||||||||
\(750\) | 1.79129 | 0.0654086 | ||||||||
\(751\) | −17.4955 | −0.638418 | −0.319209 | − | 0.947684i | \(-0.603417\pi\) | ||||
−0.319209 | + | 0.947684i | \(0.603417\pi\) | |||||||
\(752\) | −52.4519 | −1.91272 | ||||||||
\(753\) | 16.1652 | 0.589091 | ||||||||
\(754\) | −8.20871 | −0.298944 | ||||||||
\(755\) | 7.16515 | 0.260767 | ||||||||
\(756\) | 1.20871 | 0.0439604 | ||||||||
\(757\) | −2.33030 | −0.0846963 | −0.0423481 | − | 0.999103i | \(-0.513484\pi\) | ||||
−0.0423481 | + | 0.999103i | \(0.513484\pi\) | |||||||
\(758\) | −46.5735 | −1.69163 | ||||||||
\(759\) | −20.0000 | −0.725954 | ||||||||
\(760\) | −5.07803 | −0.184200 | ||||||||
\(761\) | 36.4174 | 1.32013 | 0.660065 | − | 0.751208i | \(-0.270529\pi\) | ||||
0.660065 | + | 0.751208i | \(0.270529\pi\) | |||||||
\(762\) | 3.58258 | 0.129783 | ||||||||
\(763\) | 14.1652 | 0.512813 | ||||||||
\(764\) | −4.83485 | −0.174919 | ||||||||
\(765\) | −3.00000 | −0.108465 | ||||||||
\(766\) | 6.41742 | 0.231871 | ||||||||
\(767\) | 34.7477 | 1.25467 | ||||||||
\(768\) | 20.5481 | 0.741466 | ||||||||
\(769\) | 25.5826 | 0.922531 | 0.461266 | − | 0.887262i | \(-0.347396\pi\) | ||||
0.461266 | + | 0.887262i | \(0.347396\pi\) | |||||||
\(770\) | 8.95644 | 0.322768 | ||||||||
\(771\) | 12.7477 | 0.459098 | ||||||||
\(772\) | −24.5735 | −0.884419 | ||||||||
\(773\) | −5.16515 | −0.185778 | −0.0928888 | − | 0.995676i | \(-0.529610\pi\) | ||||
−0.0928888 | + | 0.995676i | \(0.529610\pi\) | |||||||
\(774\) | −17.1652 | −0.616989 | ||||||||
\(775\) | 4.00000 | 0.143684 | ||||||||
\(776\) | −16.4174 | −0.589351 | ||||||||
\(777\) | −4.00000 | −0.143499 | ||||||||
\(778\) | −11.7913 | −0.422738 | ||||||||
\(779\) | −32.8348 | −1.17643 | ||||||||
\(780\) | −5.53901 | −0.198329 | ||||||||
\(781\) | −47.9129 | −1.71446 | ||||||||
\(782\) | 21.4955 | 0.768676 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 29.7386 | 1.06209 | ||||||||
\(785\) | 10.7477 | 0.383603 | ||||||||
\(786\) | −26.8693 | −0.958397 | ||||||||
\(787\) | −24.0000 | −0.855508 | −0.427754 | − | 0.903895i | \(-0.640695\pi\) | ||||
−0.427754 | + | 0.903895i | \(0.640695\pi\) | |||||||
\(788\) | −19.7386 | −0.703160 | ||||||||
\(789\) | 30.3303 | 1.07979 | ||||||||
\(790\) | 13.5826 | 0.483246 | ||||||||
\(791\) | −14.1652 | −0.503655 | ||||||||
\(792\) | −7.08712 | −0.251830 | ||||||||
\(793\) | −58.4174 | −2.07446 | ||||||||
\(794\) | 19.4083 | 0.688776 | ||||||||
\(795\) | 0.417424 | 0.0148045 | ||||||||
\(796\) | 16.2178 | 0.574825 | ||||||||
\(797\) | 32.3303 | 1.14520 | 0.572599 | − | 0.819836i | \(-0.305935\pi\) | ||||
0.572599 | + | 0.819836i | \(0.305935\pi\) | |||||||
\(798\) | 6.41742 | 0.227174 | ||||||||
\(799\) | −31.7477 | −1.12315 | ||||||||
\(800\) | −6.04356 | −0.213672 | ||||||||
\(801\) | 1.41742 | 0.0500822 | ||||||||
\(802\) | 22.2432 | 0.785434 | ||||||||
\(803\) | 20.0000 | 0.705785 | ||||||||
\(804\) | −5.03447 | −0.177552 | ||||||||
\(805\) | −4.00000 | −0.140981 | ||||||||
\(806\) | −32.8348 | −1.15656 | ||||||||
\(807\) | 22.5826 | 0.794944 | ||||||||
\(808\) | 0.825757 | 0.0290500 | ||||||||
\(809\) | 44.0780 | 1.54970 | 0.774851 | − | 0.632145i | \(-0.217825\pi\) | ||||
0.774851 | + | 0.632145i | \(0.217825\pi\) | |||||||
\(810\) | 1.79129 | 0.0629394 | ||||||||
\(811\) | 32.5826 | 1.14413 | 0.572064 | − | 0.820209i | \(-0.306143\pi\) | ||||
0.572064 | + | 0.820209i | \(0.306143\pi\) | |||||||
\(812\) | 1.20871 | 0.0424175 | ||||||||
\(813\) | 1.16515 | 0.0408636 | ||||||||
\(814\) | −35.8258 | −1.25569 | ||||||||
\(815\) | 7.58258 | 0.265606 | ||||||||
\(816\) | 14.8693 | 0.520530 | ||||||||
\(817\) | −34.3303 | −1.20107 | ||||||||
\(818\) | −4.92197 | −0.172093 | ||||||||
\(819\) | −4.58258 | −0.160128 | ||||||||
\(820\) | −11.0780 | −0.386862 | ||||||||
\(821\) | −31.4955 | −1.09920 | −0.549599 | − | 0.835428i | \(-0.685220\pi\) | ||||
−0.549599 | + | 0.835428i | \(0.685220\pi\) | |||||||
\(822\) | 29.2523 | 1.02029 | ||||||||
\(823\) | 51.0780 | 1.78047 | 0.890234 | − | 0.455503i | \(-0.150541\pi\) | ||||
0.890234 | + | 0.455503i | \(0.150541\pi\) | |||||||
\(824\) | −21.4955 | −0.748830 | ||||||||
\(825\) | 5.00000 | 0.174078 | ||||||||
\(826\) | −13.5826 | −0.472598 | ||||||||
\(827\) | −43.8258 | −1.52397 | −0.761985 | − | 0.647594i | \(-0.775775\pi\) | ||||
−0.761985 | + | 0.647594i | \(0.775775\pi\) | |||||||
\(828\) | −4.83485 | −0.168023 | ||||||||
\(829\) | 4.00000 | 0.138926 | 0.0694629 | − | 0.997585i | \(-0.477871\pi\) | ||||
0.0694629 | + | 0.997585i | \(0.477871\pi\) | |||||||
\(830\) | −20.7477 | −0.720164 | ||||||||
\(831\) | −24.9129 | −0.864218 | ||||||||
\(832\) | 4.18333 | 0.145031 | ||||||||
\(833\) | 18.0000 | 0.623663 | ||||||||
\(834\) | −16.8693 | −0.584137 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 21.6515 | 0.748833 | ||||||||
\(837\) | 4.00000 | 0.138260 | ||||||||
\(838\) | −66.5735 | −2.29974 | ||||||||
\(839\) | −48.4955 | −1.67425 | −0.837125 | − | 0.547012i | \(-0.815765\pi\) | ||||
−0.837125 | + | 0.547012i | \(0.815765\pi\) | |||||||
\(840\) | −1.41742 | −0.0489058 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 7.91288 | 0.272696 | ||||||||
\(843\) | −0.417424 | −0.0143769 | ||||||||
\(844\) | 24.5735 | 0.845854 | ||||||||
\(845\) | 8.00000 | 0.275208 | ||||||||
\(846\) | 18.9564 | 0.651736 | ||||||||
\(847\) | 14.0000 | 0.481046 | ||||||||
\(848\) | −2.06894 | −0.0710476 | ||||||||
\(849\) | −0.834849 | −0.0286519 | ||||||||
\(850\) | −5.37386 | −0.184322 | ||||||||
\(851\) | 16.0000 | 0.548473 | ||||||||
\(852\) | −11.5826 | −0.396813 | ||||||||
\(853\) | 20.7477 | 0.710389 | 0.355194 | − | 0.934792i | \(-0.384415\pi\) | ||||
0.355194 | + | 0.934792i | \(0.384415\pi\) | |||||||
\(854\) | 22.8348 | 0.781392 | ||||||||
\(855\) | 3.58258 | 0.122522 | ||||||||
\(856\) | −7.32121 | −0.250234 | ||||||||
\(857\) | −46.6606 | −1.59390 | −0.796948 | − | 0.604048i | \(-0.793554\pi\) | ||||
−0.796948 | + | 0.604048i | \(0.793554\pi\) | |||||||
\(858\) | −41.0436 | −1.40120 | ||||||||
\(859\) | −47.5826 | −1.62350 | −0.811748 | − | 0.584007i | \(-0.801484\pi\) | ||||
−0.811748 | + | 0.584007i | \(0.801484\pi\) | |||||||
\(860\) | −11.5826 | −0.394963 | ||||||||
\(861\) | −9.16515 | −0.312348 | ||||||||
\(862\) | −70.1561 | −2.38952 | ||||||||
\(863\) | −6.41742 | −0.218452 | −0.109226 | − | 0.994017i | \(-0.534837\pi\) | ||||
−0.109226 | + | 0.994017i | \(0.534837\pi\) | |||||||
\(864\) | −6.04356 | −0.205606 | ||||||||
\(865\) | −3.16515 | −0.107618 | ||||||||
\(866\) | 44.9220 | 1.52651 | ||||||||
\(867\) | −8.00000 | −0.271694 | ||||||||
\(868\) | 4.83485 | 0.164105 | ||||||||
\(869\) | 37.9129 | 1.28611 | ||||||||
\(870\) | 1.79129 | 0.0607303 | ||||||||
\(871\) | 19.0871 | 0.646742 | ||||||||
\(872\) | −20.0780 | −0.679928 | ||||||||
\(873\) | 11.5826 | 0.392011 | ||||||||
\(874\) | −25.6697 | −0.868290 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 4.83485 | 0.163354 | ||||||||
\(877\) | 19.6697 | 0.664198 | 0.332099 | − | 0.943244i | \(-0.392243\pi\) | ||||
0.332099 | + | 0.943244i | \(0.392243\pi\) | |||||||
\(878\) | −30.2958 | −1.02243 | ||||||||
\(879\) | 30.1652 | 1.01745 | ||||||||
\(880\) | −24.7822 | −0.835408 | ||||||||
\(881\) | −32.0780 | −1.08074 | −0.540368 | − | 0.841429i | \(-0.681715\pi\) | ||||
−0.540368 | + | 0.841429i | \(0.681715\pi\) | |||||||
\(882\) | −10.7477 | −0.361895 | ||||||||
\(883\) | 16.0000 | 0.538443 | 0.269221 | − | 0.963078i | \(-0.413234\pi\) | ||||
0.269221 | + | 0.963078i | \(0.413234\pi\) | |||||||
\(884\) | 16.6170 | 0.558892 | ||||||||
\(885\) | −7.58258 | −0.254885 | ||||||||
\(886\) | 1.04356 | 0.0350591 | ||||||||
\(887\) | −44.9129 | −1.50803 | −0.754013 | − | 0.656859i | \(-0.771885\pi\) | ||||
−0.754013 | + | 0.656859i | \(0.771885\pi\) | |||||||
\(888\) | 5.66970 | 0.190263 | ||||||||
\(889\) | 2.00000 | 0.0670778 | ||||||||
\(890\) | 2.53901 | 0.0851080 | ||||||||
\(891\) | 5.00000 | 0.167506 | ||||||||
\(892\) | 8.46099 | 0.283295 | ||||||||
\(893\) | 37.9129 | 1.26871 | ||||||||
\(894\) | 30.0000 | 1.00335 | ||||||||
\(895\) | 4.74773 | 0.158699 | ||||||||
\(896\) | 10.4519 | 0.349173 | ||||||||
\(897\) | 18.3303 | 0.612031 | ||||||||
\(898\) | −53.8784 | −1.79795 | ||||||||
\(899\) | 4.00000 | 0.133407 | ||||||||
\(900\) | 1.20871 | 0.0402904 | ||||||||
\(901\) | −1.25227 | −0.0417193 | ||||||||
\(902\) | −82.0871 | −2.73320 | ||||||||
\(903\) | −9.58258 | −0.318888 | ||||||||
\(904\) | 20.0780 | 0.667785 | ||||||||
\(905\) | 16.1652 | 0.537348 | ||||||||
\(906\) | 12.8348 | 0.426409 | ||||||||
\(907\) | 23.5826 | 0.783047 | 0.391523 | − | 0.920168i | \(-0.371948\pi\) | ||||
0.391523 | + | 0.920168i | \(0.371948\pi\) | |||||||
\(908\) | −9.16515 | −0.304156 | ||||||||
\(909\) | −0.582576 | −0.0193228 | ||||||||
\(910\) | −8.20871 | −0.272116 | ||||||||
\(911\) | −50.8258 | −1.68393 | −0.841966 | − | 0.539530i | \(-0.818602\pi\) | ||||
−0.841966 | + | 0.539530i | \(0.818602\pi\) | |||||||
\(912\) | −17.7568 | −0.587987 | ||||||||
\(913\) | −57.9129 | −1.91664 | ||||||||
\(914\) | −6.71326 | −0.222055 | ||||||||
\(915\) | 12.7477 | 0.421427 | ||||||||
\(916\) | −20.7477 | −0.685524 | ||||||||
\(917\) | −15.0000 | −0.495344 | ||||||||
\(918\) | −5.37386 | −0.177364 | ||||||||
\(919\) | 18.9129 | 0.623878 | 0.311939 | − | 0.950102i | \(-0.399021\pi\) | ||||
0.311939 | + | 0.950102i | \(0.399021\pi\) | |||||||
\(920\) | 5.66970 | 0.186924 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −16.4174 | −0.540679 | ||||||||
\(923\) | 43.9129 | 1.44541 | ||||||||
\(924\) | 6.04356 | 0.198819 | ||||||||
\(925\) | −4.00000 | −0.131519 | ||||||||
\(926\) | −0.295834 | −0.00972170 | ||||||||
\(927\) | 15.1652 | 0.498089 | ||||||||
\(928\) | −6.04356 | −0.198390 | ||||||||
\(929\) | 15.6697 | 0.514106 | 0.257053 | − | 0.966397i | \(-0.417248\pi\) | ||||
0.257053 | + | 0.966397i | \(0.417248\pi\) | |||||||
\(930\) | 7.16515 | 0.234955 | ||||||||
\(931\) | −21.4955 | −0.704485 | ||||||||
\(932\) | −15.9129 | −0.521244 | ||||||||
\(933\) | −3.00000 | −0.0982156 | ||||||||
\(934\) | −14.3303 | −0.468902 | ||||||||
\(935\) | −15.0000 | −0.490552 | ||||||||
\(936\) | 6.49545 | 0.212311 | ||||||||
\(937\) | −18.5826 | −0.607066 | −0.303533 | − | 0.952821i | \(-0.598166\pi\) | ||||
−0.303533 | + | 0.952821i | \(0.598166\pi\) | |||||||
\(938\) | −7.46099 | −0.243610 | ||||||||
\(939\) | 10.5826 | 0.345349 | ||||||||
\(940\) | 12.7913 | 0.417206 | ||||||||
\(941\) | 19.9129 | 0.649141 | 0.324571 | − | 0.945861i | \(-0.394780\pi\) | ||||
0.324571 | + | 0.945861i | \(0.394780\pi\) | |||||||
\(942\) | 19.2523 | 0.627273 | ||||||||
\(943\) | 36.6606 | 1.19383 | ||||||||
\(944\) | 37.5826 | 1.22321 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | −85.8258 | −2.79044 | ||||||||
\(947\) | −54.9129 | −1.78443 | −0.892214 | − | 0.451612i | \(-0.850849\pi\) | ||||
−0.892214 | + | 0.451612i | \(0.850849\pi\) | |||||||
\(948\) | 9.16515 | 0.297670 | ||||||||
\(949\) | −18.3303 | −0.595027 | ||||||||
\(950\) | 6.41742 | 0.208209 | ||||||||
\(951\) | −25.0000 | −0.810681 | ||||||||
\(952\) | 4.25227 | 0.137817 | ||||||||
\(953\) | −37.5826 | −1.21742 | −0.608710 | − | 0.793393i | \(-0.708313\pi\) | ||||
−0.608710 | + | 0.793393i | \(0.708313\pi\) | |||||||
\(954\) | 0.747727 | 0.0242086 | ||||||||
\(955\) | −4.00000 | −0.129437 | ||||||||
\(956\) | −31.4265 | −1.01641 | ||||||||
\(957\) | 5.00000 | 0.161627 | ||||||||
\(958\) | −34.3303 | −1.10916 | ||||||||
\(959\) | 16.3303 | 0.527333 | ||||||||
\(960\) | −0.912878 | −0.0294630 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 32.8348 | 1.05864 | ||||||||
\(963\) | 5.16515 | 0.166445 | ||||||||
\(964\) | 35.4519 | 1.14183 | ||||||||
\(965\) | −20.3303 | −0.654456 | ||||||||
\(966\) | −7.16515 | −0.230535 | ||||||||
\(967\) | 9.25227 | 0.297533 | 0.148767 | − | 0.988872i | \(-0.452470\pi\) | ||||
0.148767 | + | 0.988872i | \(0.452470\pi\) | |||||||
\(968\) | −19.8439 | −0.637808 | ||||||||
\(969\) | −10.7477 | −0.345267 | ||||||||
\(970\) | 20.7477 | 0.666169 | ||||||||
\(971\) | 20.0000 | 0.641831 | 0.320915 | − | 0.947108i | \(-0.396010\pi\) | ||||
0.320915 | + | 0.947108i | \(0.396010\pi\) | |||||||
\(972\) | 1.20871 | 0.0387695 | ||||||||
\(973\) | −9.41742 | −0.301909 | ||||||||
\(974\) | 4.17424 | 0.133751 | ||||||||
\(975\) | −4.58258 | −0.146760 | ||||||||
\(976\) | −63.1833 | −2.02245 | ||||||||
\(977\) | −2.50455 | −0.0801275 | −0.0400638 | − | 0.999197i | \(-0.512756\pi\) | ||||
−0.0400638 | + | 0.999197i | \(0.512756\pi\) | |||||||
\(978\) | 13.5826 | 0.434323 | ||||||||
\(979\) | 7.08712 | 0.226505 | ||||||||
\(980\) | −7.25227 | −0.231665 | ||||||||
\(981\) | 14.1652 | 0.452258 | ||||||||
\(982\) | 28.6606 | 0.914597 | ||||||||
\(983\) | 55.1652 | 1.75950 | 0.879748 | − | 0.475441i | \(-0.157712\pi\) | ||||
0.879748 | + | 0.475441i | \(0.157712\pi\) | |||||||
\(984\) | 12.9909 | 0.414135 | ||||||||
\(985\) | −16.3303 | −0.520327 | ||||||||
\(986\) | −5.37386 | −0.171139 | ||||||||
\(987\) | 10.5826 | 0.336847 | ||||||||
\(988\) | −19.8439 | −0.631320 | ||||||||
\(989\) | 38.3303 | 1.21883 | ||||||||
\(990\) | 8.95644 | 0.284654 | ||||||||
\(991\) | 16.0780 | 0.510735 | 0.255368 | − | 0.966844i | \(-0.417803\pi\) | ||||
0.255368 | + | 0.966844i | \(0.417803\pi\) | |||||||
\(992\) | −24.1742 | −0.767533 | ||||||||
\(993\) | −8.33030 | −0.264354 | ||||||||
\(994\) | −17.1652 | −0.544446 | ||||||||
\(995\) | 13.4174 | 0.425361 | ||||||||
\(996\) | −14.0000 | −0.443607 | ||||||||
\(997\) | −0.834849 | −0.0264399 | −0.0132200 | − | 0.999913i | \(-0.504208\pi\) | ||||
−0.0132200 | + | 0.999913i | \(0.504208\pi\) | |||||||
\(998\) | −24.0345 | −0.760798 | ||||||||
\(999\) | −4.00000 | −0.126554 |
(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 | 435.2.a.f.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 1305.2.a.m.1.1 | 2 | |||
4.3 | odd | 2 | 6960.2.a.bw.1.1 | 2 | |||
5.2 | odd | 4 | 2175.2.c.f.349.3 | 4 | |||
5.3 | odd | 4 | 2175.2.c.f.349.2 | 4 | |||
5.4 | even | 2 | 2175.2.a.r.1.1 | 2 | |||
15.14 | odd | 2 | 6525.2.a.t.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
435.2.a.f.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1305.2.a.m.1.1 | 2 | 3.2 | odd | 2 | |||
2175.2.a.r.1.1 | 2 | 5.4 | even | 2 | |||
2175.2.c.f.349.2 | 4 | 5.3 | odd | 4 | |||
2175.2.c.f.349.3 | 4 | 5.2 | odd | 4 | |||
6525.2.a.t.1.2 | 2 | 15.14 | odd | 2 | |||
6960.2.a.bw.1.1 | 2 | 4.3 | odd | 2 |